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THE SHEAR STRENGTH OF ROCK MASSES by Kurt John Douglas BE(Hons) USyd A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy School of Civil and Environmental Engineering The University of New South Wales Sydney, Australia December 2002

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Page 1: Shear Strength of Rock

THE SHEAR STRENGTH OF ROCK MASSES

by

Kurt John Douglas BE(Hons) USyd

A thesis submitted in partial fulfilment of

the requirements for the degree of

Doctor of Philosophy

School of Civil and Environmental Engineering

The University of New South Wales

Sydney, Australia

December 2002

Page 2: Shear Strength of Rock

Thesis/Project Report Sheet Surname or Family Name: DOUGLAS

First Name: Kurt Other name/s: John

Abbreviation for degree as given in the University calendar: PhD

School: Civil and Environmental Engineering Faculty: Engineering

Title: The Shear Strength of Rock Masses

Declaration relating to disposition of project report/thesis

I am fully aware of the policy of the University relating to the retention and use of higher degree project reports and theses, namely that the University retains the copies submitted for examination and is free to allow them to be consulted or borrowed. Subject to the provisions of the Copyright Act 1968, the university may issue a project report or thesis in whole or in part, in photostate or microfilm or other copying medium.

I also authorise the publication by the University Microfilms of a 350 word abstract in Dissertations Abstracts International (applicable to doctorates only)

...................................................................... ...................................................................... ...................................................................... Signature Witness Date

The university recognise that there may be exceptional circumstances requiring restrictions on copying or conditions on use, Requests for restriction for a period of up to 2 years must made in writing to the Registrar. Requests for a longer period of restriction may be considered in exceptional circumstances if accompanied by a letter of support from the Supervisor or Head of School. Such requests must be submitted with the thesis/project report.

FOR OFFICE USE ONLY Date of completion of requirement for Award:

Registrar and Deputy Principal

THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS

Abstract 350 words maximum: The first section of this thesis (Chapter 2) describes the creation and analysis of a database on concrete and masonry dam incidents known as CONGDATA. The aim was to carry out as complete a study of concrete and masonry dam incidents as was practicable, with a greater emphasis than in other studies on the geology, mode of failure, and the warning signs that were observed. This analysis was used to develop a method of very approximately assessing probabilities of failure. This can be used in initial risk assessments of large concrete and masonry dams along with analysis of stability for various annual exceedance probability floods. The second and main section of this thesis (Chapters 3-6) had its origins in the results of Chapter 2. It was found that failure through the foundation was common in the list of dams analysed and that information on how to assess the strength of the foundations of dams on rock masses was limited. This section applies to all applications of rock mass strength. Methods used for assessing the shear strength of jointed rock masses are based on empirical criteria. As a general rule such criteria are based on laboratory scale specimens with very little, and often no, field validation. The Hoek-Brown empirical rock mass failure criterion was developed in 1980 for hard rock masses. Since its development it has become almost universally accepted and is now used for all types of rock masses and in all stress regimes. This thesis uses case studies and databases of intact rock and rockfill triaxial tests collated by the author to review the current Hoek-Brown criterion. The results highlight the inability of the criterion to fit all types of intact rock and poor quality rock masses. This arose predominately due to the exponent, a, being restrained to approximately 0.5 to 0.6 and using rock type as a predictor of mi. Modifications to the equations for determining the Hoek-Brown parameters are provided that overcome these problems. In the course of reviewing the Hoek-Brown criterion new equations were derived for estimating the shear strength of intact rock and rockfill. Empirical slope design curves have also been developed.

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Abstract Page i

ABSTRACT

The first section of this thesis (Chapter 2) describes the creation and analysis of a

database on concrete and masonry dam incidents known as CONGDATA. The aim was to

carry out as complete a study of concrete and masonry dam incidents as was practicable,

with a greater emphasis than in other studies on the geology, mode of failure, and the

warning signs that were observed. This analysis was used to develop a method of very

approximately assessing probabilities of failure. This can be used in initial risk

assessments of large concrete and masonry dams along with analysis of stability for

various annual exceedance probability floods.

The second and main section of this thesis (Chapters 3-6) had its origins in the results of

Chapter 2 and the general interests of the author. It was found that failure through the

foundation was common in the list of dams analysed and that information on how to

assess the strength of the foundations of dams on rock masses was limited. This section

applies to all applications of rock mass strength such as the stability of rock slopes.

Methods used for assessing the shear strength of jointed rock masses are based on

empirical criteria. As a general rule such criteria are based on laboratory scale

specimens with very little, and often no, field validation.

The Hoek-Brown empirical rock mass failure criterion was developed in 1980 for hard

rock masses. Since its development it has become virtually universally accepted and is

now used for all types of rock masses and in all stress regimes. This thesis uses case

studies and databases of intact rock and rockfill triaxial tests collated by the author to

review the current Hoek-Brown criterion. The results highlight the inability of the

criterion to fit all types of intact rock and poor quality rock masses. This arose

predominately due to the exponent a being restrained to approximately 0.5 to 0.62 and

using rock type as a predictor of mi. Modifications to the equations for determining the

Hoek-Brown parameters are provided that overcome these problems.

In the course of reviewing the Hoek-Brown criterion new equations were derived for

estimating the shear strength of intact rock and rockfill. Empirical slope design curves

have also been developed for use as a preliminary tool for slope design.

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Acknowledgements Page iii

ACKNOWLEDGEMENTS

The support of the sponsors of the research project - Dams Risk Project - Estimation of

the Probability of Failure, the Australian Research Council, and the Faculty of

Engineering at the University of New South Wales is acknowledged. The sponsors of

the Dams Risk Project were:

• ACT Electricity and Water;

• Australian Water Technologies, Sydney Water Corporation;

• Dams Safety Committee of NSW;

• Department of Land and Water Conservation;

• Department of Land and Water Conservation - Dams Safety;

• Electric Corporation of New Zealand (ECNZ);

• Goulburn Murray Water;

• Gutteridge Haskins and Davey (GHD);

• Hydro-Electric Commission, Tasmania;

• Melbourne Water;

• NSW Department of Public Works and Services;

• Pacific Power;

• Queensland Department of Natural Resources;

• Snowy Mountains Engineering Corporation (SMEC);

• Snowy Mountains Hydro-Electricity Authority.

• South Australia Water Corporation;

• Water Authority of Western Australia;

The access to, and assistance with collection of data provided by the United States

Bureau of Reclamation and BC Hydro is also acknowledged.

Thanks are made to Pells Sullivan Meynink Pty Ltd who provided the data for most of

the case studies for the rock mass component of this thesis. Thanks also to their staff

who were always available to provide assistance and encouragement. Particular thanks

to Alex Duran who worked with the author on the creation of the slope design curves.

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Acknowledgements Page iv

A general acknowledgement is made to the organisations that provided data on various

mine slopes and test results that have been used in the development of this thesis, yet for

the purposes of confidentiality their contributions cannot be properly referenced.

Marcus Helgstedt and Anna Tarua are acknowledged for their assistance with computer

analysis of some of the rock mass strength case studies.

To my fellow PhD comrades: Mark Foster, James Glastonbury and Gavan Hunter, a

major thankyou for your encouragement through example and your friendship.

To my friends, who have not only provided support but also nagging questions e.g. “Are

you finished yet?” … “Yes”.

To my parents, thanks for your values, your encouragement and your genes.

To my supervisor and co-supervisor Garry Mostyn and Robin Fell respectively,

thankyou not only for your invaluable assistance but also for the invaluable practical

experience you gave me in the areas of rock and dam engineering.

Finally, to my fiancée, Rebecca: thanks for hanging in all these years waiting for (and

putting up with) me.

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Table of contents Page v

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION

1.1 THESIS OBJECTIVES..........................................................................................1.1

1.2 THE BACKGROUND TO THIS THESIS ............................................................1.2

1.3 THE CHAPTERS IN THIS THESIS .....................................................................1.3

1.3.1 The analysis of concrete and masonry dam incidents ..........................................1.3

1.3.2 The shear strength of rock masses .......................................................................1.4

1.4 PUBLISHED PAPERS/REPORTS .......................................................................1.6

CHAPTER 2: THE ANALYSIS OF CONCRETE AND MASONRY DAM

INCIDENTS

2.1 OUTLINE OF THIS CHAPTER ...........................................................................2.1

2.2 STRUCTURE AND ASSEMBLY OF CONGDATA DATABASE.....................2.4

2.2.1 Sources of Data ....................................................................................................2.4

2.2.2 CONGDATA Layout ............................................................................................2.9

2.2.3 Data Entered into CONGDATA .........................................................................2.12

2.2.3.1 Definitions of Failures/Accidents............................................................... 2.12

2.2.3.2 Types of Dams............................................................................................ 2.14

2.2.3.3 Failure Types ............................................................................................. 2.14

2.2.3.4 Incident Time.............................................................................................. 2.15

2.2.3.5 Type of Foundation.................................................................................... 2.15

2.2.3.6 Dam Height ................................................................................................ 2.15

2.2.3.7 Detection Methods ..................................................................................... 2.16

2.2.3.8 Classification of Causes of Incidents of Dams And Reservoirs................. 2.17

2.2.3.9 Classification of Remedial Measures......................................................... 2.22

2.2.4 Selection of Additional Variables......................................................................2.24

2.2.4.1 Time of Incidents........................................................................................ 2.24

2.2.4.2 Foundation Incident Mode......................................................................... 2.25

2.2.4.3 Dam Incident Mode.................................................................................... 2.26

2.2.4.4 Comments on Incidents.............................................................................. 2.26

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2.2.4.5 Description of the Failure or Accident ...................................................... 2.26

2.2.4.6 Additional Geological Information............................................................ 2.26

2.2.4.7 Dam Dimensions........................................................................................ 2.28

2.2.4.8 Valley Shape............................................................................................... 2.29

2.2.4.9 Radius of Curvature................................................................................... 2.29

2.2.4.10 Monitoring and Surveillance Data ............................................................ 2.31

2.2.4.11 Warning Rating.......................................................................................... 2.32

2.2.4.12 Warning Time............................................................................................. 2.32

2.2.4.13 Other Design Factors................................................................................. 2.32

2.2.5 Assumptions Made in Assembling the Database...............................................2.33

2.2.6 Data on the Population of Dams ........................................................................2.36

2.3 RESULTS OF ANALYSIS OF THE DATABASE ............................................2.40

2.3.1 Summary of Incidents ........................................................................................2.40

2.3.2 Year Commissioned of Dams Experiencing Incidents ......................................2.45

2.3.3 Height.................................................................................................................2.54

2.3.4 Age at Failure.....................................................................................................2.60

2.3.5 Incident Causes..................................................................................................2.78

2.3.6 Monitoring and Surveillance Data .....................................................................2.85

2.3.6.1 Using ICOLD Terms .................................................................................. 2.85

2.3.6.2 Details of Warnings ................................................................................... 2.89

2.3.7 Remedial Measures............................................................................................2.98

2.3.8 Geology............................................................................................................2.101

2.3.8.1 Geology of Dam Foundations Experiencing Incidents............................ 2.101

2.3.8.2 Geology of the Population of Dams......................................................... 2.106

2.3.9.3 Geology - Comparison Between Incidents and Population..................... 2.112

2.3.9 Other Design Factors in Failed Dams ..............................................................2.123

2.4 METHOD OF FIRST ORDER PROBABILITY ASSESSMENT ....................2.132

2.4.1 Probability of Failure .......................................................................................2.132

2.4.1.1 Introduction.............................................................................................. 2.132

2.4.1.2 Population of Dams ................................................................................. 2.133

2.4.1.3 Dam Year ................................................................................................. 2.135

2.4.1.4 Probabilities of Failure............................................................................ 2.135

2.4.1.5 Gravity Dams - Separation of Concrete and Masonry Dams.................. 2.146

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2.4.2 General Approach for Estimating the Probability of Failure for Individual

Gravity Dams ...................................................................................................2.153

2.4.3 Details of the Method for Estimating the Probability of Failure for

Individual Gravity Dams .................................................................................2.154

2.4.4 Gravity Dam Probability Multiplication Factors .............................................2.158

2.4.4.1 Soil/Rock Foundation Factor, fSF and fPF ................................................ 2.158

2.4.4.2 Geology Types - Sliding on Rock, fSG....................................................... 2.161

2.4.4.3 Geology Type - Piping on Rock, fGE......................................................... 2.164

2.4.4.4 Height on Width Ratio, fH/W...................................................................... 2.164

2.4.4.5 Other Observations, fO............................................................................. 2.169

2.4.4.6 Surveillance, fS ......................................................................................... 2.169

2.4.5 Results..............................................................................................................2.170

2.5 DISCUSSION AND CONCLUSIONS..............................................................2.172

CHAPTER 3: THE SHEAR STRENGTH OF INTACT ROCK

3.1 INTRODUCTION..................................................................................................3.1

3.2 FAILURE CRITERIA FOR INTACT ROCK .......................................................3.2

3.3 LABORATORY TEST DATABASE FOR INTACT ROCK.............................3.12

3.4 AN ANALYSIS OF THE ANALYSIS OF DATA .............................................3.14

3.5 HOEK-BROWN CRITERION FOR INTACT ROCK........................................3.24

3.6 GENERALISED CRITERION FOR INTACT ROCK .......................................3.32

3.7 GLOBAL PREDICTION.....................................................................................3.49

3.8 COMPARISON OF CRITERIA..........................................................................3.60

3.9 SYSTEMATIC ERROR IN HOEK-BROWN CRITERION...............................3.64

3.10 APPLICATION TO SLOPE ENGINEERING ....................................................3.73

3.11 CONCLUSION....................................................................................................3.77

CHAPTER 4: THE SHEAR STRENGTH OF ROCKFILL

4.1 OUTLINE OF THIS CHAPTER ...........................................................................4.1

4.2 FACTORS AFFECTING THE SHEAR STRENGTH OF ROCKFILL ...............4.2

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4.2.1 Confining Pressure...............................................................................................4.2

4.2.2 Particle Strength...................................................................................................4.6

4.2.3 Uniformity Coefficient ........................................................................................4.8

4.2.4 Density...............................................................................................................4.10

4.2.5 Maximum Particle Size......................................................................................4.12

4.2.5.1 Increasing dmax with Constant D..................................................................4.13

4.2.5.2 Increasing dmax with Constant dmax/D ..........................................................4.13

4.2.6 Silt and Sand Fines versus Gravel and Larger Particle Content ........................4.14

4.2.7 Particle Angularity.............................................................................................4.16

4.2.8 Other Factors......................................................................................................4.17

4.2.9 Summary of Factors Affecting the Secant Friction Angle ................................4.18

4.3 SHEAR STRENGTH CRITERIA .......................................................................4.19

4.4 DATABASE OF TRIAXIAL SHEAR TESTS....................................................4.26

4.5 DATABASE ANALYSIS ....................................................................................4.29

4.5.1 Analysis Methodology.......................................................................................4.29

4.5.2 Secant Friction Angle, φsec, Versus Normal Stress, σn ......................................4.30

4.5.2.1 General Assessment of Database...............................................................4.30

4.5.2.2 Statistical Analysis of Database.................................................................4.40

4.5.3 Maximum Principal Stress, σ′1, versus Minimum Principal Stress, σ′3............4.41

4.5.3.1 Secant Friction Angle Versus Normal Stress.............................................4.58

4.5.4 Hoek-Brown Criterion.......................................................................................4.61

4.6 CONCLUSION....................................................................................................4.64

CHAPTER 5: EMPIRICAL ROCK SLOPE DESIGN

5.1 INTRODUCTION..................................................................................................5.1

5.2 REVIEW OF THE ROCK MASS RATING SYSTEMS ......................................5.2

5.2.1 Methods for Estimating the Basic Rock Mass Rating .........................................5.3

5.2.1.1 The Rock Mass Rating, RMR, and Geological Strength Index, GSI............ 5.3

5.2.1.2 Mining Rock Mass Rating, MRMR.............................................................. 5.6

5.2.1.3 Rock Mass Strength, RMS............................................................................ 5.9

5.2.1.4 Slope Rock Mass Rating, SRMR................................................................ 5.11

5.2.1.5 Modified Rock Mass Classification, M-RMR............................................. 5.14

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5.2.1.6 Basic Quality, BQ ...................................................................................... 5.17

5.2.2 Adjustment Factors to basic rock mass ratings..................................................5.19

5.3 A REVIEW OF SLOPE DESIGN METHODS WHICH ARE BASED ON

ROCK MASS RATINGS ....................................................................................5.25

5.3.1 Correlations with Shear Strength Parameters and Slope Angles .......................5.25

5.3.2 Available Slope Performance Curves................................................................5.30

5.3.3 Pells Sullivan Meynink Slope Performance Curves..........................................5.36

5.4 ANALYSIS OF CASE STUDY DATA ..............................................................5.39

5.4.1 Case Studies Used..............................................................................................5.39

5.4.2 Correlations of MRMR, SRMR and RMS with GSI.........................................5.40

5.4.3 General Assessment of the Parameters in GSI ..................................................5.51

5.4.4 Development of Generalised Slope Design Curves...........................................5.54

5.4.4.1 Use of MRMR in Haines and Terbrugge Method...................................... 5.54

5.4.4.2 Revised Method Using MRMR................................................................... 5.54

5.4.4.3 Method Based on the Use of the Geological Strength Index, GSI ............. 5.55

5.5 CONCLUSION....................................................................................................5.62

CHAPTER 6: THE SHEAR STRENGTH OF ROCK MASSES

6.1 INTRODUCTION..................................................................................................6.1

6.2 ESTIMATING THE SHEAR STRENGTH OF A ROCK MASS.........................6.3

6.2.1 Predicting Rock Mass Strength from Discontinuities..........................................6.3

6.2.2 Predicting Rock Mass Strength using Empirical Formulae.................................6.8

6.2.3 Predicting Rock Mass Strength using the Hoek-Brown Criterion.......................6.8

6.3 A DISCUSSION OF THE HOEK-BROWN CRITERION WITH

PARTICULAR REFERENCE TO SLOPES .......................................................6.16

6.3.1 Calculation of GSI.............................................................................................6.16

6.3.1.1 Intact Strength............................................................................................6.16

6.3.1.2 RQD ...........................................................................................................6.17

6.3.1.3 Defect spacing............................................................................................6.18

6.3.1.4 Joint condition............................................................................................6.18

6.3.1.7 GSI from published figures ........................................................................6.20

6.3.1.8 A Note on Schistose Rocks.........................................................................6.20

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6.3.2 Estimation of Parameters from GSI...................................................................6.26

6.3.2.1 The Rock Mass Disturbance Factor, D......................................................6.26

6.3.2.2 The Variation of the Hoek-Brown Parameters with GSI...........................6.27

6.4 VALIDATION OF THE HOEK-BROWN CRITERION ...................................6.30

6.4.1 Chichester Dam..................................................................................................6.30

6.4.2 Nattai North Escarpment Failure .......................................................................6.30

6.4.3 Katoomba Escarpment Failure...........................................................................6.35

6.4.4 Aviemore Dam Insitu Shear Tests .....................................................................6.39

6.4.5 Discussion of the Results of the Analysis..........................................................6.43

6.5 A NEW ESTIMATION OF ROCK MASS STRENGTH ...................................6.46

6.5.1 Development of a Modified Criterion ...............................................................6.46

6.5.1.1 Exponent ‘α’ ..............................................................................................6.47

6.5.1.2 Parameter ‘m’............................................................................................6.47

6.5.1.3 Parameter ‘s’ .............................................................................................6.48

6.5.2 Development of the Equations to Estimate the Parameters in the Hoek-

Brown Criterion.................................................................................................6.49

6.5.2.1 A New Equation for ‘mb’............................................................................6.50

6.5.2.2 A New Equation for ‘sb’ .............................................................................6.54

6.5.2.3 A New Equation for ‘αb’ ............................................................................6.56

6.5.2.4 The Overall Equation.................................................................................6.61

6.5.3 Summary of Method ..........................................................................................6.69

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS

7.1 CONCLUSIONS....................................................................................................7.1

7.1.1 The Analysis of Concrete and Masonry Dams ....................................................7.1

7.1.2 The Shear Strength of Intact Rock.......................................................................7.3

7.1.3 The Shear Strength of Rockfill ............................................................................7.4

7.1.4 Empirical Slope Design .......................................................................................7.4

7.1.5 The Shear Strength of Rock Masses....................................................................7.5

7.2 RECOMMENDATIONS FOR FURTHER RESEARCH .....................................7.7

7.2.1 The Analysis of Concrete and Masonry Dams ....................................................7.7

7.2.2 The Shear Strength of Rock Masses....................................................................7.7

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REFERENCES

APPENDICES

APPENDIX A – CONGDATA DATABASE ................................................... CD-ROM

APPENDIX B – DAM LIST - FAILURES .................................................................. A.1

APPENDIX C – POPULATION OF DAMS................................................................ A.3

APPENDIX D – CAUSES OF INCIDENTS.............................................................. A.11

APPENDIX E – SHEAR STRENGTH OF INTACT ROCK DATABASE ...... CD-ROM

APPENDIX F – SHEAR STRENGTH OF ROCKFILL DATABASE ............. CD-ROM

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TABLE OF FIGURES

Figure 1.1. Thesis structure..........................................................................................1.2

Figure 2.1. Definition of dimensions in CONGDATA...............................................2.30

Figure 2.2. Definition of dimensions in CONGDATA - section across river.............2.31

Figure 2.3. The distribution of reported dam incidents vs country............................2.43

Figure 2.4. Reported incidents as percentage of country’s dam population from

ICOLD (1984) .........................................................................................2.44

Figure 2.5. Year commissioned vs concrete gravity dam incidents ..........................2.47

Figure 2.6. Year commissioned vs masonry gravity dam incidents ..........................2.48

Figure 2.7. Year commissioned vs all dam incidents ................................................2.49

Figure 2.8. Year commissioned for world population data obtained from ICOLD

(1979) ......................................................................................................2.50

Figure 2.9. Year commissioned vs percentage of gravity dams constructed in the

USA .........................................................................................................2.51

Figure 2.10. Year commissioned - failures/population per period ..............................2.52

Figure 2.11. CONGDATA - height ranges for all dam significant incidents ...............2.55

Figure 2.12. CONGDATA - Height ranges for concrete gravity dam significant

incidents...................................................................................................2.56

Figure 2.13. CONGDATA - height ranges for masonry gravity dam significant

incidents...................................................................................................2.57

Figure 2.14. Height of failed dams - failures/population (%)......................................2.59

Figure 2.15. World dams - height ranges for all concrete & masonry dams ...............2.60

Figure 2.16. Age at incident - all dams ........................................................................2.64

Figure 2.17. Age at incident - concrete gravity dams ..................................................2.65

Figure 2.18. Age at incident - masonry gravity dams ..................................................2.66

Figure 2.19. Time to significant incident - gravity dam incidents/population (%)......2.67

Figure 2.20. Time to significant incident - all dam incidents/population (%).............2.67

Figure 2.21. Failure mode: age at failure versus year commissioned (all dams).........2.73

Figure 2.22. Over topping: age at failure versus year commissioned (all dams).........2.74

Figure 2.23. Dam type: age at failure versus year commissioned ...............................2.75

Figure 2.24. Age at significant incident versus year commissioned............................2.76

Figure 2.25. Age at significant incident versus year commissioned............................2.77

Figure 2.26. Causes of significant incidents (rock & unknown foundations) .............2.84

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Figure 2.27. Causes of significant incidents (soil foundations)...................................2.85

Figure 2.28. Warning types - gravity dams .................................................................2.86

Figure 2.29. Warning Types - All Dams .....................................................................2.87

Figure 2.30. Most common remedial measures - all dam incidents ............................2.99

Figure 2.31. Foundation incidents age, type and year commissioned - all dams ......2.104

Figure 2.32. Foundation incidents geology - all incidents .........................................2.105

Figure 2.33. Geology for incidents in the foundation and dam population – all

dams.......................................................................................................2.115

Figure 2.34. Geology for incidents in the foundation and dam population –

concrete gravity dams............................................................................2.116

Figure 2.35. Geology for incidents in the foundation and dam population –

masonry gravity dams ...........................................................................2.117

Figure 2.36. Foundation geology type as a percentage of the geology population –

all dams..................................................................................................2.118

Figure 2.37. Foundation geology type as a percentage of the geology population –

gravity dams ..........................................................................................2.119

Figure 2.38. Foundation geology type as a percentage of geology population –

arch dams ...............................................................................................2.120

Figure 2.39. Foundation geology type as a percentage of geology population –

buttress dams .........................................................................................2.121

Figure 2.40. Foundation incident geology and population – mode of

failure/accident ......................................................................................2.122

Figure 2.41. Average failure stresses for dams with failure through the foundation.2.131

Figure 2.42. Average failure stresses for Bhandardara Dam.....................................2.131

Figure 2.43. hd/W versus year commissioned............................................................2.166

Figure 2.44. hd/W versus hd .......................................................................................2.167

Figure 2.45. hd/W factors ...........................................................................................2.168

Figure 2.46. Range of annual probability of failure for concrete gravity dams .........2.170

Figure 2.47. Range of annual probability of failure for masonry gravity dams ........2.171

Figure 3.1. Generalised failure criterion......................................................................3.2

Figure 3.2. Comparison of test results with theoretically based failure criteria

(Johnston & Chiu, 1984) ...........................................................................3.3

Figure 3.3. Comparison of Hoek-Brown criterion (solid) and Johnston criterion

(dashed) for Melbourne mudstone (Johnston, 1985).................................3.4

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Figure 3.4. Fits to artificial data (a) full range (b) low stress range ..........................3.20

Figure 3.5. mi from literature against mi from test results and Hoek-Brown

Equation...................................................................................................3.26

Figure 3.6. Rock type against mi from test results and Hoek-Brown equation..........3.28

Figure 3.7. Unconfined compressive strength against that predicted by the Hoek-

Brown equation .......................................................................................3.30

Figure 3.8. Uniaxial tensile strength against that predicted by the Hoek-Brown

equation ...................................................................................................3.31

Figure 3.9. mi from literature against mi from test results and generalised

equation ...................................................................................................3.34

Figure 3.10. mi from literature against α mi from test results and generalised

equation ...................................................................................................3.36

Figure 3.11. Rock type against α mi from test results and generalised equation.........3.37

Figure 3.12. Unconfined compressive strength against that predicted by

generalised equation................................................................................3.39

Figure 3.13. Uniaxial tensile strength against that predicted by generalised

equation ...................................................................................................3.41

Figure 3.14. α against mi..............................................................................................3.43

Figure 3.15. α against mi categorised by σc.................................................................3.45

Figure 3.16. Family of failure envelopes.....................................................................3.46

Figure 3.17. Results showing failure envelopes crossing ............................................3.47

Figure 3.18. Residuals for global fit with α constant against σ′3/σc categorised by

-σc/σt........................................................................................................3.50

Figure 3.19. Residuals for global fit with variable α against σ′3/σc categorised by -

σc/σt .........................................................................................................3.52

Figure 3.20. Three dimensional plot of global fit ........................................................3.54

Figure 3.21. σ′1/σc with fits for variable α against σ′3/σc categorised by -σc/σt for

high stress ................................................................................................3.56

Figure 3.22. σ′1/σc with fits for variable α against σ′3/σc categorised by -σc/σt for

low stress .................................................................................................3.57

Figure 3.23. α against mi showing cases with measured or reported σ′3 and σt ......... .3.59

Figure 3.24. σ′1/σc with fits for published mI against σ′3/σc categorised by mI for

high stress ................................................................................................3.62

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Figure 3.25. σ′1/σc with fits for published mI against σ′3/σc categorised by mI for

low stress .................................................................................................3.63

Figure 3.26. Pattern of residuals for Hoek-Brown fits ................................................3.64

Figure 3.28. Hoek-Brown fits to artificial data............................................................3.67

Figure 3.29. Hoek-Brown fits to actual data ................................................................3.69

Figure 3.30. Residuals for Hoek-Brown fits for weak rock against σ′3/σ′3max

categorised by α ......................................................................................3.71

Figure 3.31. Residuals for generalised fits for weak rock against σ′3/σ′3max

categorised by α ......................................................................................3.72

Figure 3.32. Residuals against σ′3 for various fits .......................................................3.75

Figure 4.1. Methods for representing the shear strength envelope..............................4.4

Figure 4.2. Variation of secant friction angle, φsec, with respect to cell confining

stress, σ′3, for (a) dense and (b) medium dense crushed basalt from

triaxial tests (Al-Hussaini, 1983)...............................................................4.5

Figure 4.3. Average strength of rockfills from large-scale direct shear tests

(Anagnosti & Popovic, 1982)....................................................................4.5

Figure 4.4. Variation of secant friction angle, φsec, with normal stress σn

(Indraratna et al., 1993) .............................................................................4.6

Figure 4.5. Shear strength and grain size curves for crushed (a) limestone and (b)

marble (Anagnosti and Popovic, 1982) .....................................................4.7

Figure 4.6. Shear strength and grain size curves for crushed flysch sandstone-

marl rockfill (Anagnosti and Popovic, 1982) ............................................4.7

Figure 4.7. Shear strength and grain size curves for different gradings of

limestone gravel (Anagnosti and Popovic, 1982) .....................................4.9

Figure 4.8. Shear strength and grain size curves for (a) crystalline schist and (b)

sandstone gravels (Anagnosti and Popovic, 1982)....................................4.9

Figure 4.9. Scalped rockfill gradings (Marachi et al, 1969) ......................................4.11

Figure 4.10. Strength porosity relationships with σ3 = 88kPa (Marachi et al, 1969) ..4.11

Figure 4.12. Void ratio vs angle of friction (modified from Nakayama et al., 1982)..4.12

Figure 4.13. Friction angle vs ma ximum particle size (Thiers & Donovan, 1981) .....4.13

Figure 4.14. Effect of gravel content on φ for silty gravel based on USBR (1966) ....4.15

Figure 4.15. Effect of gravel content on φ for clayey gravel based on USBR

(1961) ......................................................................................................4.15

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Figure 4.16. –4.76mm content vs secant angle of friction (Nakayama et al., 1982) ...4.16

Figure 4.17. Gonzalez (1985) shear strength of rockfill equations..............................4.22

Figure 4.18. Friction angle, φ, vs normal stress, σn. ....................................................4.23

Figure 4.19. Frequency distributions for coefficients B versus porosity (Sarac &

Popovic, 1985).........................................................................................4.23

Figure 4.20. Dependence between coefficient A and gravel unit weight (Sarac &

Popovic, 1985).........................................................................................4.24

Figure 4.21. Dependence between coefficient A and mean grain diameter, d50

(Sarac & Popovic, 1985) .........................................................................4.24

Figure 4.22. Secant friction angle, φsec vs normal stress, σn........................................4.33

Figure 4.23. Secant friction angle, φsec vs normal stress, σn, sorted on angularity

rating........................................................................................................4.34

Figure 4.24. Secant friction angle, φsec vs normal stress, σn, sorted on rock type =

basalt........................................................................................................4.35

Figure 4.25. Secant friction angle, φsec vs normal stress, σn, sorted on coefficient

of uniformity, cu ......................................................................................4.36

Figure 4.26. Secant friction angle, φsec vs normal stress, σn, sorted on maximum

particle size, dmax .....................................................................................4.37

Figure 4.27. Secant friction angle, φsec vs normal stress, σn, sorted on percent fines

(passing 0.075mm) content .....................................................................4.38

Figure 4.28. Secant friction angle, φsec vs normal stress, σn, sorted on unconfined

compressive strength of the rock substance, UCS (MPa) .......................4.39

Figure 4.29. RFIe versus void ratio..............................................................................4.43

Figure 4.30. RFIUCS versus unconfined compressive strength.....................................4.43

Figure 4.31. RFIFINES versus percent fines...................................................................4.44

Figure 4.32 Residuals versus unconfined compressive strength of intact rock ...........4.46

Figure 4.33. Residuals versus dmax...............................................................................4.47

Figure 4.34. Residuals versus void ratio......................................................................4.48

Figure 4.35. Residuals versus angularity rating...........................................................4.49

Figure 4.36. Residuals versus fines content.................................................................4.50

Figure 4.37. Residuals versus sample diameter ...........................................................4.51

Figure 4.38. Effect of unconfined compressive strength on σ′1 ..................................4.52

Figure 4.39. Effect of angularity on σ′1 (7 = sub-angular to angular; 8 = angular).....4.52

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Table of contents Page xvii

Figure 4.40. Effect of fines content on σ′1...................................................................4.53

Figure 4.41. Effect of maximum particle size on σ′1...................................................4.53

Figure 4.42. Effect of initial void ratio on σ′1 ............................................................ .4.54

Figure 4.43. σ′1 vs σ′3 showing data used in analysis and RFI relationship................4.55

Figure 4.44. σ′1 vs σ′3 showing all data and RFI relationship.....................................4.56

Figure 4.45. σ′1 vs σ′3 showing all data and RFI relationship (σ′3 up to 1.5MPa)......4.57

Figure 4.46. Effect of unconfined compressive strength on φsec..................................4.59

Figure 4.47. Effect of angularity on φsec (7 = sub-angular to angular; 8 = angular) ....4.59

Figure 4.48. Effect of fines content on φsec..................................................................4.60

Figure 4.49. Effect of maximum particle size on φsec..................................................4.60

Figure 4.50. Effect of initial void ratio on φsec.............................................................4.61

Figure 4.51. Statistical analysis results using Hoek-Brown formula and for a = 0.6

and a = 0.95 .............................................................................................4.63

Figure 5.1. Estimate of GSI based on geological descriptions. (Hoek, 2000).............5.7

Figure 5.2. SRMR strength correlation (a) Island Copper Mine (b) Getchell Mine

(Robertson, 1988)....................................................................................5.14

Figure 5.3. Example of Planar Failure Case with High SMR....................................5.21

Figure 5.4. Slope height, H, vs slope height factor, ξ (after Chen, 1995) .................5.22

Figure 5.5. RMR versus slope angle (Orr, 1996).......................................................5.27

Figure 5.6. Observed cases (ESMR) vs (a) SMR, (b) CSMR (Chen, 1995) .............5.29

Figure 5.7. Upper bound slope height versus slope angle curve for rock masses

(Hoek & Bray, 1981)...............................................................................5.31

Figure 5.8. Slope angle versus slope height with regression curves (modified

after McMahon, 1976).............................................................................5.33

Figure 5.9. Slope height vs slope angle for MRMR (Haines & Terbrugge, 1991)....5.34

Figure 5.10. Haines & Terbrugge (1991) slope design replotted on basis of slope

angle versus slope height showing Haines & Terbrugge (1991) slope

data. .........................................................................................................5.35

Figure 5.11. Slope performance curves for case studies (Duran & Douglas, 1999)....5.37

Figure 5.12. Correlations of GSI with MRMR, SRMR, RMS rating (mod. Duran

and Douglas, 2002)..................................................................................5.42

Figure 5.13. GSI versus slope height for failed and stable slopes...............................5.51

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Figure 5.14. GSI defect spacing rating versus slope height for failed and stable

slopes.......................................................................................................5.52

Figure 5.15. GSI defect condition rating versus slope height for failed and stable

slopes.......................................................................................................5.52

Figure 5.16. GSI RQD rating versus slope height for failed and stable slopes ...........5.53

Figure 5.17. GSI UCS rating versus slope height for failed and stable slopes............5.53

Figure 5.18. Haines & Terbrugge (1991) slope design curves & slope data (Figure

5.10) with additional case studies (Duran & Douglas, 1999).................5.56

Figure 5.19. Suggested slope design curves for MRMR (Duran & Douglas, 1999)...5.57

Figure 5.20. Slope height vs slope angle case study data and the author’s proposed

design curves for a dry slope...................................................................5.58

Figure 5.21. Slope height vs slope angle case study data and a comparison of

design curves for a dry slope...................................................................5.59

Figure 5.22. Slope height vs slope angle case study data and the author’s proposed

design curves for moderate pressures......................................................5.60

Figure 5.23. Slope height vs slope angle case study data and a comparison of

design curves for moderate pressures......................................................5.61

Figure 6.1. Heavily jointed rock mass .........................................................................6.1

Figure 6.2. Example of shear failure through rock mass at the toe of a slope -

Nattai Escarpment Failure .........................................................................6.2

Figure 6.3. Assessment of Barton and Bandis (1982) JRC0 vs JRCn ..........................6.7

Figure 6.4. Values of the parameter mi for intact rock (Hoek, 1999) ........................6.11

Figure 6.5. Estimation of GSI (Hoek, 1997)..............................................................6.12

Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) ................................6.13

Figure 6.7. Scale effect of Intact Rock (Hoek and Brown, 1980) .............................6.17

Figure 6.8. Slope failure block size ...........................................................................6.19

Figure 6.9. Effect of scale on defect properties .........................................................6.19

Figure 6.10. GSI Table (Hoek et al, 1998) ..................................................................6.22

Figure 6.11. Ed versus GSI case study data and Hoek et al (1995) equation for σc

≥ 100MPa and σc = 10MPa .....................................................................6.24

Figure 6.12. Ed test from case studies versus Ed pred from Hoek et al (1995)

equation ...................................................................................................6.25

Figure 6.13. Variation of a, s and mb/mi with GSI.......................................................6.28

Figure 6.14. Typical section of the Nattai North failure (Pells et al, 1987).................6.31

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Figure 6.15. Illustration of the failure mechanism at Nattai North (Helgstedt,

1997)........................................................................................................6.32

Figure 6.16. Katoomba Escarpment Failure ................................................................6.36

Figure 6.17. Katoomba Escarpment Failure, column prior to collapse.......................6.37

Figure 6.18. Direct Shear Test Set up (Foster & Fairless, 1994).................................6.41

Figure 6.19. Example of mesh used (Helgstedt, 1997)................................................6.44

Figure 6.20. Close up of the simulated jack (Helgstedt, 1997) ...................................6.44

Figure 6.21. Back analysis results using Figure 6.5 for GSI.......................................6.45

Figure 6.22. Test results for tectonised quartzitic sandstone (Habimana et al,

2002)........................................................................................................6.52

Figure 6.23. The author’s statistical fits to Habimana et al (2002) data ......................6.53

Figure 6.24. mb versus GSI ..........................................................................................6.54

Figure 6.25. GSI for an intact or massive rock structure (Hoek, 1999).......................6.55

Figure 6.26. sb versus GSI ...........................................................................................6.56

Figure 6.27. αb versus GSI ..........................................................................................6.57

Figure 6.28. Graphical representation of the equations for α and m ...........................6.58

Figure 6.29. Transition of α and m from intact rock to rock mass ..............................6.59

Figure 6.30. Original and modified relationships for αi and mi...................................6.60

Figure 6.31. Shear strength curves for tectonised quartzitic sandstone (Habimana

et al, 2002)...............................................................................................6.61

Figure 6.32. Results of analysis of Habimana et al (2002) data using the new

equation and parameters from equations .................................................6.63

Figure 6.33. Results of global analysis of Habimana et al (2002) data using new

equations..................................................................................................6.64

Figure 6.34. Non-dimensionalised plot of new shear strength curves for mi = 40

and varying GSI.......................................................................................6.65

Figure 6.35. Non-dimensionalised plot of new shear strength curves for mi = 4

and varying GSI.......................................................................................6.66

Figure 6.1. Comparison of the author’s criterion and the Hoek-Brown criterion

(Hoek, 2002) for mi = 40 .........................................................................6.67

Figure 6.2. Comparison of the author’s criterion and the Hoek-Brown criterion

(Hoek, 2002) for mi = 4 ...........................................................................6.68

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Table of contents Page xx

TABLE OF TABLES

Table 2.1. Bibliography for failed dams in CONGDATA ..........................................2.6

Table 2.2. CONGDATA parameters ........................................................................2.10

Table 2.3. Causes of incidents of concrete dams ......................................................2.18

Table 2.4. Causes of incidents of masonry dams .....................................................2.19

Table 2.5. Causes of incidents to appurtenant works ...............................................2.20

Table 2.6. Causes of incidents of reservoirs.............................................................2.21

Table 2.7. Causes of incidents downstream of dam.................................................2.21

Table 2.8. Classification of remedial measures........................................................2.23

Table 2.9. Number of dam incidents in database by type ........................................2.40

Table 2.10. Number of significant dam incidents in database by type.......................2.40

Table 2.11. Number of dam incidents reported in each country................................2.42

Table 2.12. Year commissioned - failures vs population per period..........................2.53

Table 2.13. Year commissioned - accidents vs population per period.......................2.54

Table 2.14. Percent of concrete & masonry dam fails vs population for height ........2.58

Table 2.15. Percent of concrete & masonry accidents vs population for height ........2.58

Table 2.16. No. of dam foundation sliding & piping failures vs age at failure..........2.62

Table 2.17. No. of structural (shear or tensile) failures vs age at failure ...................2.63

Table 2.18. Time to significant incident - incident/population of dams surviving

period (%)................................................................................................2.68

Table 2.19. Time to significant incident.....................................................................2.69

Table 2.20. Details of dam failure water levels..........................................................2.70

Table 2.21. Failure types ............................................................................................2.78

Table 2.22. Main causes of incidents in all dams .......................................................2.79

Table 2.23. Main causes of incidents in concrete gravity dams .................................2.80

Table 2.24. Main causes of incidents in masonry gravity dams .................................2.80

Table 2.25. Main failure causes for dams with soil foundations ................................2.81

Table 2.26. Main significant incident causes for dams with rock or unknown

foundations ..............................................................................................2.82

Table 2.27. Warning types vs dam type - failures ......................................................2.88

Table 2.28. Warning types vs dam type - accidents ...................................................2.88

Table 2.29. Warning types vs dam type - major repairs.............................................2.89

Table 2.30. Warning ratings for failed dams ..............................................................2.90

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Table 2.31. Details of dam failures and descriptions of warnings .............................2.91

Table 2.32. Details of dam significant accidents and descriptions of warnings.........2.95

Table 2.33. Remedial measures - all dam incidents .................................................2.100

Table 2.34. Geology for dams with failure in the foundation..................................2.102

Table 2.35. Geology for dams with accidents in the foundation..............................2.103

Table 2.36. Foundation geology for Australia, New Zealand, Portugal and USBR

(percent and number for each group) ....................................................2.109

Table 2.37. Foundation geology for Australia, New Zealand, Portugal & USBR

dams - totalled Figures ..........................................................................2.111

Table 2.38. Failed dams with grouted foundation....................................................2.123

Table 2.39. Crest length/height for failed dams and population ..............................2.125

Table 2.40. Upstream and downstream slopes for failed dams ................................2.126

Table 2.41. Hd/W for failed dams .............................................................................2.128

Table 2.42. Back analysed shear strengths for failed dams (mod. from Rich,

1995)......................................................................................................2.129

Table 2.43. Calculated normal stresses along the failure plane of back analysed

gravity dams ..........................................................................................2.130

Table 2.44. Number of dams as at 1992 ...................................................................2.133

Table 2.45. Population of dams by dam type and year commissioned ....................2.134

Table 2.46. Number of dams (excluding China) in the population..........................2.134

Table 2.47. Annual probability of failure (1992, exc. China) - all failure types......2.136

Table 2.48. Probability of failure (as at 1992, exc. China, non-annualised) - all

failure types ...........................................................................................2.137

Table 2.49. Annual probability of failure (as at 1992, excluding China) - sliding

failures ...................................................................................................2.138

Table 2.50. Probability of failure (as at 1992, excluding China, non-annualised) -

sliding failures .......................................................................................2.139

Table 2.51. Annual probability of failure (as at 1992, excluding China) - piping

failures ...................................................................................................2.140

Table 2.52. Probability of failure (as at 1992, excluding China, non-annualised) -

piping failures........................................................................................2.141

Table 2.53. Annual probability of failure (as at 1992, excluding China) -

tension/shear failures through dam body...............................................2.142

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Table of contents Page xxii

Table 2.54. Probability of failure (as at 1992, excluding China, non-annualised) -

tension/shear failures through dam body...............................................2.143

Table 2.55. Number of failures during overtopping where the failure mode was

unknown................................................................................................2.144

Table 2.56. No. of failures where the failure mode was unknown (no

overtopping) ..........................................................................................2.145

Table 2.57. Distribution of concrete and masonry gravity dams in the USA...........2.146

Table 2.58. Distribution of concrete and masonry gravity dams chosen for

analysis ..................................................................................................2.148

Table 2.59. Summary of annualised probabilities of failure for gravity dams (exc.

China) ....................................................................................................2.148

Table 2.60. Suggested values for annualised probabilities of failure for gravity

dams (excluding China).........................................................................2.149

Table 2.61. Annualised probabilities of failure for gravity dams - all failures ........2.150

Table 2.62. Annualised probabilities of failure for gravity dams - sliding failures .2.150

Table 2.63. Annualised probabilities of failure for gravity dams - piping failures ..2.151

Table 2.64. Annualised probabilities of failure for gravity dams - dam body

tension/shear failures .............................................................................2.151

Table 2.65. Number of failures during overtopping where failure mode was

unknown................................................................................................2.152

Table 2.66. Number of failures where failure mode was unknown .........................2.152

Table 2.67. Foundation types - USBR......................................................................2.158

Table 2.68. Foundation types - Australia/New Zealand...........................................2.158

Table 2.69. Foundation types - Portugal ..................................................................2.159

Table 2.70. Gravity dam foundation types - combined ............................................2.159

Table 2.71. Foundations for gravity dam failures by sliding or piping ....................2.159

Table 2.72. Gravity dam factors for piping and sliding failure on soil and rock,

fSF and fPF...............................................................................................2.160

Table 2.73. Foundation types - accidents .................................................................2.160

Table 2.74. Weighting factors used for weighted average (ICOLD (1984) dam

population).............................................................................................2.161

Table 2.75. Adopted gravity dam factors for sliding on a rock foundation, fSG .......2.162

Table 2.76. Gravity dam factors for sliding on a rock foundation...........................2.163

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Table of contents Page xxiii

Table 2.77. Multiplication factors for structural height/width ratio of gravity

dams, fH/W...............................................................................................2.165

Table 2.78. Monitoring and surveillance multiplication factors, fS..........................2.169

Table 3.1. Various intact rock failure criteria.............................................................3.6

Table 3.2. Empirical estimates of exponents for the equations in Table 3.1............3.10

Table 3.3. Suggested values of constant k (Yudhbir et al, 1983 and Bieniawsi,

1974)........................................................................................................3.10

Table 3.4. Values of M and B for a range of materials (Johnston, 1991) ................3.10

Table 3.5. Intact rock database descriptors ..............................................................3.13

Table 3.6. Results of different regression methods on artificial data .......................3.19

Table 3.7. Error in approximating σut as -σc/(mi+1).................................................3.42

Table 3.8. Comparison of predictions ......................................................................3.60

Table 3.9. Errors in fitting Hoek-Brown criterion to materials with α ≠ 0.5 ...........3.65

Table 3.10. Variation of σc and mi with σ3max for exact simulated results .................3.66

Table 3.11. Variation of σc and mi with σ′3max for data set 434..................................3.68

Table 3.12. Triaxial component of strength ...............................................................3.73

Table 3.13. Comparison of predictions for weak rocks at low stress.........................3.74

Table 4.1. Increase in φ with dmax/D from Marsal (1973) data for different σn........4.13

Table 4.2. Reduction in φ with particle size, dmax, from Marsal (1973) data ...........4.13

Table 4.3. Summary of factors affecting the secant friction angle...........................4.18

Table 4.4. Parameters obtained using De Mello (1977) (Charles, 1991).................4.19

Table 4.5. Various shear strength criteria for rockfill ..............................................4.20

Table 4.6. List of parameters in triaxial shear strength database .............................4.27

Table 4.7. Summary of basic statistics from the rockfill database...........................4.28

Table 4.8. Changes in φsec on Figure 4.46 to Figure 4.50 for σn=1MPa and σn =

0.5MPa ....................................................................................................4.58

Table 4.9. Results from the statistical analysis of the rockfill database using the

Hoek-Brown equation .............................................................................4.62

Table 5.1. Comparison of weightings for various rock mass rating methods ............5.2

Table 5.2. Rock mass rating (Bieniawski, 1989)........................................................5.5

Table 5.3. Geological strength index, GSI (Hoek et al, 1995) ...................................5.6

Table 5.4. MRMR (Laubscher, 1977) ........................................................................5.8

Table 5.5. Defect condition rating for MRMR (Laubscher, 1977).............................5.8

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Table of contents Page xxiv

Table 5.6. RMS Classification and Ratings (mod. Selby, 1980)..............................5.10

Table 5.7. SRK Geomechanics Classification or Slope Rock Mass Rating

(SRMR) ...................................................................................................5.13

Table 5.8. SRMR strength correlation (Robertson, 1988)........................................5.14

Table 5.9. Joint condition index IJC (Ünal, 1996).....................................................5.16

Table 5.10. Ratings for joint condition parameters (Ünal, 1996)...............................5.17

Table 5.11. The basic quality, BQ, rock mass classes (Lin, 1998) ............................5.18

Table 5.12. Adjustment rating for joints (after Romana, 1985) .................................5.20

Table 5.13. Adjustment Rating for methods of excavation of slopes (after

Romana, 1985) ........................................................................................5.20

Table 5.14. Tentative description of SMR classes (after Romana, 1985) ..................5.21

Table 5.15. Discontinuity condition factor λ (Chen, 1995)........................................5.22

Table 5.16. Blasting adjustment, Ab (Ünal, 1996) ......................................................5.23

Table 5.17. Major plane of weakness adjustment, Aw (Ünal, 1996)...........................5.23

Table 5.18. Rock mass properties for RMR76 (Bieniawski, 1976).............................5.25

Table 5.19. Stable slope angle versus MRMR (Laubscher, 1977) .............................5.26

Table 5.20. Case records for SMR (after Romana, 1985) ..........................................5.28

Table 5.21. Parameters for McMahon’s (1976) slope relationship ............................5.32

Table 5.22. Summary of slope data from case studies ...............................................5.39

Table 5.23. Correlation between rating methods – author’s case studies...................5.41

Table 5.24. Summary of best estimate GSI data for mine cases ................................5.43

Table 5.25. Summary of defect condition for GSI .....................................................5.44

Table 5.26. Summary of best estimate of Laubscher’s MRMR data for mine

cases.........................................................................................................5.45

Table 5.27. Summary of best estimate of SRMR data for mine cases .......................5.47

Table 5.28. Summary of best estimate of RMS data for mine cases..........................5.49

Table 6.1. Estimation of Hoek-Brown co-efficients ..................................................6.9

Table 6.2. Rock mass deformability case studies.....................................................6.23

Table 6.3. Guidelines for estimating disturbance factor D (Hoek et al, 2002).........6.26

Table 6.4. Maximum and minimum values of Hoek-Brown parameters using

Figure 6.10...............................................................................................6.29

Table 6.5. Joint orientation, spacing and persistence for Nattai North .................... 6.34

Table 6.6. Summary of parameters used for the Nattai North Escarpment

Failure...................................................................................................... 6.34

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Table of contents Page xxv

Table 6.7. Summary of Hoek-Brown parameters for Nattai using RMR and the

Hoek-Brown chart ................................................................................... 6.35

Table 6.8. UDEC output: average shear and normal stresses along the predicted

failure plane ............................................................................................. 6.35

Table 6.9. Summary of parameters used for the Katoomba Escarpment Failure..... 6.38

Table 6.10. Summary of Hoek-Brown parameters for the Claystone in the

Katoomba Escarpment Failure using RMR and the Hoek-Brown

chart ......................................................................................................... 6.38

Table 6.11. Summary of the Joint Properties from the Joint Survey carried out by

Read et al (1996) .....................................................................................6.40

Table 6.12. Hoek Parameters for Aviemore Shear Tests using RMR, and the

Hoek-Brown Chart ..................................................................................6.40

Table 6.13. Intact material parameters .......................................................................6.43

Table 6.14. Defect and Interface Material Parameters ...............................................6.43

Table 6.15. Results of statistical analysis of Habimana et al (2002) test data............6.50

Page 27: Shear Strength of Rock

Introduction Page 1.1

1 INTRODUCTION

1.1 THESIS OBJECTIVES

The overall objective of this thesis was to improve design procedures for large-scale

structures constructed on or in rock.

The first objective of this thesis was the development of a comprehensive database and

analysis of concrete and masonry dam incidents world-wide, with a view to developing

methods of assessing the risk of failure of existing dam structures and as a consequence of

this, identifying possibilities for improvement in design. The results from this work

showed that a large proportion of dams had incidents associated with the strength of their

foundations, which indicated a need for a better understanding of the strength of rock

masses.

The second and major objective of this thesis was to provide a detailed assessment of the

applicability of the Hoek-Brown criterion to estimating the shear strength of jointed rock

masses and to improve upon any deficiencies found in the criterion. A particular focus

was placed on low stress situations (e.g. dams and slopes) in weak materials. This work

also included the development of methods for assessing the strength of intact rock and

rockfill and new methods for estimating the stability of rock slopes using rock mass rating

systems.

To achieve the first objective the author collated and analysed the largest and most

comprehensive database of world-wide concrete and masonry dam incidents using both

published literature and unpublished records personally obtained from the dam industry.

Results were presented on what factors have led to a higher chance of a dam incident

occurring. These results were then used to develop an approximate method of assessing

probabilities of failure.

The process for assessing the Hoek-Brown criterion had several components. Firstly,

large databases of triaxial tests on intact rock and rockfill were statistically analysed to

assess the applicability of the Hoek-Brown criterion at the limits of intact rock and very

poor rock mass. Secondly, analyses of the failures of large scale rock masses were

Page 28: Shear Strength of Rock

Introduction Page 1.2

carried out to assess how well the Hoek-Brown criterion predicted the insitu rock mass

strength. Finally, high quality triaxial tests on rock mass were obtained from the literature

and used together with the results of the previous steps and plausibility checks to create

new equations for estimating the parameters in the Hoek-Brown criterion.

1.2 THE BACKGROUND TO THIS THESIS

This thesis is divided into two sections: the risk assessment of concrete and masonry dam

failures and accidents and their causes, and the shear strength of rock masses as shown in

Figure 1.1.

The analysis of concrete and masonry dam incidentsChapter 2

The shear strength of intact rockChapter 3

The shear strength of rockfillChapter 4

Empirical rock slope designChapter 5

The shear strength of rock massesChapter 6

The shear strength of rock masses

Thesis

Figure 1.1. Thesis structure

The dams community as part of the Dams Risk Project (together with the ARC and The

Faculty of Engineering at the University of New South Wales) provided initial funding for

this research. Details of the specific contributors are provided in the acknowledgement

section. The first section of the thesis (Chapter 2) was carried out in response to the

specific needs of the research project and its sponsors. The aim of the project was to

provide a guide as to which types of dams were more likely to experience incidents

(failures and accidents) based on a statistical analysis of the historical performance of

dams. The author’s role on the project was to study concrete and masonry gravity dams.

The second section of this thesis (Chapters 3-6) had its origins in the results of Chapter 2

and the general interests of the author and the project sponsors. It was found that failure

through the foundation was common in the list of dams analysed. Furthermore, it was

Page 29: Shear Strength of Rock

Introduction Page 1.3

found that information on how to assess the strength of the foundations of dams on rock

masses was limited. For example, the ANCOLD (1991) guidelines on design criteria for

concrete gravity dams suggest using references such as McMahon (1985) and Hoek

(1983) to assess the strength of the foundation. The guidelines also state that “in the

absence of more reliable data, preliminary analysis of foundations on sound jointed hard

rock where sub-horizontal joints are not continuous, the following peak effective shear

strength parameters are suggested:”

cpeak = 0.14σc or 1.4MPa whichever is the lesser, where σc is the

unconfined compressive strength of the rock substance.

φpeak = 45°

This approach is very misleading and in many cases would over-estimate the strength.

The authors aim for this section was to assess how good the methods for estimating rock

mass strength were and to suggest possible changes to existing methods or new methods if

required

The work on rock mass strength was extended from looking at the foundations of dams to

looking at the strength of rock masses in slopes and other works. This was mainly in an

attempt to find better case studies to analyse, to cover a wider stress range and to provide

a work on rock mass strength that had applicability wherever an assessment of rock mass

strength was required.

The different sections of the thesis given in Figure 1.1 are described in more detail

below.

1.3 THE CHAPTERS IN THIS THESIS

1.3.1 The Analysis of Concrete and Masonry Dam Incidents

Many attempts have been made at compiling and assessing statistics of dam failures. The

main attempts at assessing dam incidents on a world-wide scale have been by ICOLD

(1974, 1983 and 1995). ICOLD (1974) analysed previous dam failures and accidents

based on questionnaires provided by the National Committees on Large Dams. ICOLD

Page 30: Shear Strength of Rock

Introduction Page 1.4

(1983) attempted to improve the completeness of the information with further

questionnaires. An existing dam population was also developed by ICOLD for

comparison with failures. The population comprised a sample of dams from the ICOLD

World Register of Dams (ICOLD 1973, 1976 and 1979). ICOLD (1995) was an attempt

to update the statistics on failures of dams with particular emphasis on comparisons with

dam types, heights and years commissioned of existing dams. Although an extensive

analysis, the ICOLD attempt lacks depth in some key areas. Most notably in information

on the foundation conditions and the geometry of the dams where failures have occurred.

The accuracy and consistency of the ICOLD data has also come into question during this

current research.

Various other attempts have been made to compile data on failures and accidents, all of

which either suffer from a lack of detail or from a limited data set. Most of the statistical

analyses of failures and accidents and attempts to determine probabilities of failure (Von

Thun (1985), da Silveira (1984, 1990), Fell (1996), Blind (1983), and Schnitter (1993))

tend not to go into much detail, generally assessing only height, year commissioned and

type of dam structure. Most of the emphasis in the analysis of dam incidents has been on

embankment dams.

This section of the thesis (Chapter 2) describes the creation and analysis of a database on

concrete and masonry dam incidents known as CONGDATA. The aim was to carry out as

complete a study of concrete and masonry dam incidents as was practicable, with a

greater emphasis than in other studies on the geology, mode of failure, and the warning

signs that were observed. The study assessed the characteristics of the population of

dams, and compared these with the characteristics of those dams that had experienced

incidents. This helped to provide a guide as to which dams were more likely to

experience incidents.

This analysis was used to develop an approximate method of assessing probabilities of

failure. This can be used in initial risk assessments of large concrete and masonry dams

along with analyses of stability for various annual exceedance probability floods.

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Introduction Page 1.5

1.3.2 The shear strength of rock masses

Methods used for assessing the shear strength of jointed rock masses are based on

empirical criteria (Hoek and Brown, 1980, Yudhbir et al, 1983, Ramamurthy et al, 1994

and Sheorey, 1997). As a general rule such criteria are based on laboratory scale

specimens with very little, and often no, field validation.

The most commonly used strength criterion, having received widespread interest and use

over the last two decades, is the Hoek-Brown empirical rock mass failure criterion, the

most general form of which is given in Equation 1.1. Hoek and Brown (1980) developed

this rock mass criterion as they “found that there were really no suitable criteria for the

purpose of underground excavation design” (Hoek, 2001). The equation, which has

subsequently been updated by Hoek and Brown (1988), Hoek et al. (1992), Hoek et al.

(1995) and Hoek et al (2002), was based on their criterion for intact rock. The only

‘rock mass’ tested and used in the original development of the Hoek-Brown criterion was

152mm core samples of Panguna Andesite from Bougainville in Papua New Guinea

(Hoek and Brown, 1980). Hoek and Brown (1988) later noted that it was likely this

material was in fact ‘disturbed’. The validation of the updates of the Hoek-Brown

criterion have been based on experience gained whilst using this criterion. To the

author’s knowledge the only data published supporting this experience has been two mine

slopes cited in Hoek et al (2002).

a

cbc sm

+

′+′=′

σσ

σσσ 331 (1.1)

This thesis assesses the Hoek-Brown criterion in detail and modifies it into a more

generalised form to account for various inconsistencies in the current version. The

assessment of the criterion is carried out by looking at several of its bounds including

intact rock (Chapter 3) and rockfill (Chapter 4). Case studies of various failures and

highly stressed rock masses are used, together with published laboratory test results on

rock mass samples, to assess the Hoek-Brown criterion and to develop new equations

that can be used to estimate the parameters of the Hoek-Brown equation (Chapter 6).

Page 32: Shear Strength of Rock

Introduction Page 1.6

The individual chapters in this section of the thesis not only provide a basis for modifying

the Hoek-Brown criterion (discussed in Chapter 6) but also have their own individual

results including:

• Chapter 3 - A statistical analysis of a database of over 4500 triaxial tests on intact

rock and the subsequent development of new shear strength criterion for intact rock.

• Chapter 4 - A review of current criteria for the shear strength of rockfill and the

development of a new shear strength criterion for compacted rockfill based on a

database of over 550 rockfill triaxial tests gathered from the literature and sponsors.

• Chapter 5 - An analysis of current empirical slope design methods and the

development of new slope design curves based on the author’s database of mine pit

slopes.

1.4 PUBLISHED PAPERS/REPORTS

The following papers and reports were published during the period of this thesis.

Douglas, K.J. (1998) Case studies in the assessment of rock mass criteria. 3rd Young

Geotechnical Professionals Conference, Melbourne.

Douglas, K.J. and Mostyn, G. (1999) Strength of large rock masses – field verification.

Rock Mechanics for Industry, Proceedings of the 37th U.S. Rock Mechanics Symposium,

Vail, Colorado, USA. 1:271-276. Balkema, Rotterdam, ISBN 90 5809 099 X0.

Douglas, K., Spannagle, M. and Fell, R. (1998a) Estimating the probability of failure of

concrete and masonry gravity dams. 1998 ANCOLD-NZSOLD Conference on Dams,

Sydney.

Douglas, K., Spannagle, M. and Fell, R. (1998b) Report on Analysis of Concrete and

Masonry Dam Incidents. UNICIV, The School of Civil and Environmental Engineering,

The University of New South Wales.

Page 33: Shear Strength of Rock

Introduction Page 1.7

Douglas, K., Spannagle, M. and Fell, R. (1999a) Analysis of Concrete and Masonry Dam

Incidents. The International Journal on Hydropower & Dams. 6(4):108-115.

Aqua~Media, Surrey, ISSN 1352-2523.

Douglas, K., Spannagle, M. and Fell, R. (1999b) Estimating the probability of failure of

concrete and masonry gravity dams. ANCOLD Bulletin. No. 112:53-63. Australian

National Committee on Large Dams, ISSN 0045-0731.

Duran, A. and Douglas, K. (1999) “Do slopes designed with empirical rock mass strength

criteria stand up?” Proceedings ISRM 9th International Congress on Rock Mechanics,

Paris, France, 1, pp. 87-90. Balkema, Rotterdam, ISBN 90 5809 070 1.

Duran, A. & Douglas, K.J. (2000) Experience with empirical rock slope design.

GeoEng2000: An International Conference on Geotechnical & Geological

Engineering, 19-24 November, Melbourne, Australia, 2, pp. 41 and CD-Rom paper no.

SNES1186, Technomic Publishing, Pennsylvania, ISBN 1-58716-068-4.

Glastonbury, J. & Douglas, K.J. (2000) Catastrophic rock slope failures. GeoEng2000:

An International Conference on Geotechnical & Geological Engineering, 19-24

November, Melbourne, Australia, Vol. 2 pp. 21 and CD-Rom paper no. SNES0507,

Technomic Publishing, Pennsylvania, ISBN 1-58716-068-4.

Helgstedt, M.D., Douglas, K.J. and Mostyn, G. (1997) A re-evaluation of in-situ direct

shear tests at Aviemore Dam, New Zealand. Australian Geomechanics, 37 (June), pp.

56-65.

Mostyn, G. & Douglas, K.J. (2000) Issues Lecture: The shear strength of intact rock and

rock masses. GeoEng2000: An International Conference on Geotechnical & Geological

Engineering, 19-24 November, Melbourne, Australia, Vol. 1, pp. 1389-1421, Technomic

Publishing, Pennsylvania, ISBN 1-58716-067-6.

Mostyn, G., M.D. Helgstedt and K.J. Douglas (1997) “Towards field bounds on rock

mass failure criteria”. International Journal of Rock Mechanics and Mining Sciences,

Vol. 34 (3-4): Paper No. 208.

Page 34: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.1

2 ANALYSIS OF CONCRETE AND MASONRY DAM INCIDENTS

2.1 OUTLINE OF THIS CHAPTER

This chapter comprises a component of the research project on the risk assessment of

dams. 17 sponsors comprising major dam owners and consultants from Australia and

New Zealand support the project. The United States Bureau of Reclamation (USBR)

and BC Hydro from Canada also assisted with the project.

The aim of this component of the research was to provide a guide as to which dams

were more likely to experience incidents based purely on a statistical analysis of

historical incidents. The chapter describes the analysis of historical concrete and

masonry dam incidents. For comparative purposes a compilation of data from a sample

of existing concrete and masonry dams from Australia, New Zealand, Portugal and the

USA is also presented for comparison with the incident database. A large portion (4168

dams from 22 countries) of the ICOLD (1973 and 1979) World Register was entered

into a computer for further comparative purposes. The source for the analysis was a

database developed by the author on failures and accidents in concrete and masonry

dams known as CONGDATA.

Many attempts have been made at compiling and assessing statistics of dam failures.

The main attempts at assessing dam incidents on a worldwide scale have been by

ICOLD (1974, 1983 and 1995). ICOLD (1974) analysed previous dam failures and

accidents based on questionnaires provided by the National Committees on Large

Dams. ICOLD (1983) attempted to improve the completeness of the information with

further questionnaires. The presentation of the data and analyses was improved with the

use of tables. An existing dam population was also developed for comparison with

failures. The population comprised a sample of dams from the ICOLD World Register

of Dams (ICOLD 1973, 1976 and 1979). ICOLD (1995) was an attempt to update the

statistics on failures of dams with particular emphasis on comparisons with dam types,

heights and years commissioned of existing dams. Although an extensive analysis, the

ICOLD attempt lacks depth in some key areas. Most notably in information on the

foundation conditions and the geometry of the dams where failures have occurred. The

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Analysis of Concrete and Masonry Dam Incidents Page 2.2

accuracy and consistency of the ICOLD data has also come into question during this

current research (see Section 2.2.5).

Vogel (1980, with updates to 1994) and Babb and Mermel (1968) have compiled lists of

dam incidents with some limited comments and dimensions. Their main value is in

providing a large source of references. USCOLD (1976 and 1988) collated a large

amount of information on incidents in the USA. Other attempts at collecting data on

historical incidents have been made by Jorgensen (1920), Jansen (1980), Varshney and

Raheem (1971), USCOLD (1996) and Rao (1960). All of these either suffer from a lack

of detail or from a limited data set.

Smaller country scale data collections have been made for:

• Spanish accidents and failures (Gomez Laa et al, 1979);

• the deterioration of Italian Dams (Paolina et al, 1991);

• South African dam incidents (Olwage & Oosthuizen, 1984);

• Swedish accidents (Graham & Bartsch, 1995);

• failures and accidents in the United Kingdom (Charles, 1985);

• incidents in Australia (Ingles, 1984); and

• failures and accidents in the USA (Hatem, 1985).

Von Thun (1985) made an assessment of USA dams and their probability of failure

based on a calculation of dam years. The parameters assessed were generally similar to

those of ICOLD. Others who have attempted to analyse probabilities of failure include:

da Silveira (1984, 1990); Fell (1996); Blind (1983); and Schnitter (1993) who generally

based their analysis on ICOLD data and experience. Serafim (1981a, 1981b); Tavares

and Serafim (1983); Smith (1972); Biswas and Chatterjee (1971); Gruner (1963, 1967);

Kaloustian (1984) analysed incidents using ICOLD data and their own selected

databases. These analyses tend not to go into much detail, generally assessing only

Page 36: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.3

height, year commissioned and type of dam structure. Most of the emphasis in the

analysis of dam incidents has been on embankment dams.

This study set out to carry out as complete a study of concrete and masonry dam failures

and accidents as was practicable, with a greater emphasis than in other studies on the

geology, mode of failure, and the warning signs that were observed. The study also sets

out to assess the characteristics of the population of dams, and compares the

characteristics of the failures and accidents with the population of dams, so a probability

of failure or accident can be assigned. This data provides the basis for initial risk

assessments of dams.

The basic definitions used in CONGDATA and the subsequent analyses have been taken

from ICOLD and are given in Section 2.2.3.1. The term incident has been used for both

accidents and failures.

Section 2.2 of this chapter describes the methods used in compiling and assessing the

incident statistics. The results have been presented in Section 2.3. A method of first

order probability assessment for gravity dams is provided in Section 2.4.

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Analysis of Concrete and Masonry Dam Incidents Page 2.4

2.2 STRUCTURE AND ASSEMBLY OF CONGDATA DATABASE

2.2.1 Sources of Data

CONGDATA began with the information from the three ICOLD compilations of failures

and accidents:

• ICOLD (1995) Dam Failures Statistical Analyses.

• ICOLD (1983) Deterioration of Dams and Reservoirs.

• ICOLD (1974) Lessons From Dam Incidents.

Where practicable ICOLD (1995) definitions were used. ICOLD (1995) was the main

reference for the failures whilst accidents were principally from ICOLD (1983). ICOLD

(1974) was used for further details when adding information into CONGDATA.

The information in CONGDATA was then checked and updated using other existing

databases including:

• USCOLD (1976) Lessons from dam incidents, USA.

• USCOLD (1988) Lessons from dam incidents. USA-II.

• Vogel (1980) Bibliography of the History of Dam Failures.

• Babb and Mermel (1968) Catalogue of Dam Disasters, Failures and Accidents.

A large literature review was then conducted to gather as much information on dam

failures and accidents as possible. References cited in the databases above were sought

and then further references were obtained from journals; conference proceedings;

reports; theses; and Internet pages. Published and unpublished reports were also

accessed through sponsors and dam organisations. All references were followed to their

origins as far as practically possible. The literature review was far more extensive than

those previously reported for the development of other databases. Table 2.1 shows the

bibliography for the failed dams contained in CONGDATA.

Data from several additional dams was added to the database during the data gathering

process. The additions are described in detail in Section 2.2.4.

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Analysis of Concrete and Masonry Dam Incidents Page 2.5

The sponsors of the research project, who are listed below, also provided access to

information on their dams.

• Australian Water Technologies, Sydney Water Corporation;

• Department of Land and Water Conservation;

• NSW Department of Public Works and Services;

• SA Water Corporation;

• ACT Electricity and Water;

• Hydro-Electric Commission;

• Dams Safety Committee of NSW;

• Department of Land and Water Conservation - Dams Safety;

• Snowy Mountains Engineering Corporation (SMEC);

• Queensland Department of Natural Resources;

• Goulburn-Murray Water;

• Gutteridge Haskins and Davey;

• Melbourne Water;

• Pacific Power;

• Sydney Water Corporation;

• Water Authority of Western Australia;

• Electric Corporation of New Zealand;

• Snowy Mountains Hydro-Electricity Authority.

The United States Bureau of Reclamation (USBR) in Denver allowed access to the

information on their dams. This information was collected over two, three-week periods

by the author together with Professor Robin Fell and Mark Foster. Other organisations

that allowed access to data included:

• BC Hydro; and the

• Alberta Dam Safety Association.

The data collected from the sponsors and other assisting organisations was used as a

source of information on failures and more notably to assist in a collation of information

on dam populations.

Page 39: Shear Strength of Rock

Page 2.6

Table 2.1. Bibliography for failed dams in CONGDATA

Dam References

Angels, USA Babb and Mermel (1968); ICOLD (1974, 1995); USCOLD (1975); Vogel (1994)

Ashley, USA Babb and Mermel (1968); Engineering News (1909); ICOLD (1974, 1984, 1995); Jorgensen (1920); Rao (1960); Scott and Von Thun (1993); Vogel (1994)

Austin (Texas), USA

Babb and Mermel (1968); Blanton (1915); Bowers (1928); Engineering News (1900a-e, 1901, 1902, 1908a-b, 1910b, 1915, 1916a-b); Engineering News Record (1911, 1918, 1911f); Engineering Record (1900a-b, 1911a-c, 1915a-b); Freeman and Alsop (1941); Hatton (1912); Hill (1902); Hornaday (1899); ICOLD (1974, 1995); Jorgensen (1920); King and Huber (1993); Leger et al (1997); McDonough (1940); Parker (1900); Patterson (1900); Rao (1960); Rosenberg (1900); Sawyer (1911); Schuyler (1908); Smith (1972); Taylor (1915); Taylor (1900); USCOLD (1975)

Bacino di Rutte, Italy Fry (1996); Vogel (1984, 1994)

Bayless, USA Babb and Mermel (1968); Bartholomew (1989); Bowers (1928); Engineering News (1910b, 1911); Engineering Record (1911d-e); ICOLD (1974, 1995); Jansen (1980); Leger et al (1997); Rao (1960); Scott and Von Thun (1993); Smith (1972)

Bouzey, France Babb and Mermel (1968); Baker (1897); Courtney (1897); Engineering News (1897?); Fry (1996); ICOLD (1969, 1974, 1995); Institute of Civil Engineering (1897?); Jansen (1980); Jorgensen (1920); Leger et al (1997); Mary (1968); Rao (1960); Schuyler (1908); Smith (1972, 1995); The Engineer (1896, 1942); Vogel (1984, 1994); Wegmann (1889)

Cheurfas, Algeria Babb and Mermel (1968); Benassini and Barona (1962); ICOLD (1969, 1974, 1995); Schuyler (1908); Smith (1972); Vogel (1994); Wegmann (1889)

Chickahole, India ICOLD (1995); Lempérière et al (1997); Lempérière (1993); Murthy et al (1979); Vogel (1994)

El Gasco, Spain Babb and Mermel (1968); Berga (1997); Gomez Laa et al (1979); ICOLD (1984); Jorgensen (1920); Schnitter (1994); Schuyler (1908); Smith (1972)

Elmali I, Turkey Babb and Mermel (1968); ICOLD (1974, 1995); Vogel (1994); Yildiz and Üzücek (1994)

Elwha River, USA Babb and Mermel (1968); Engineering Record (1912); ICOLD (1974, 1984, 1995); Reineking. (1914); USCOLD (1975); Vogel (1994)

Fergoug I & II, Algeria Babb and Mermel (1968); ICOLD (1969, 1974, 1995); Lempérière (1993)

Gallinas, USA Babb and Mermel (1968); Engineering News Record (1957); ICOLD (1974, 1984, 1995); Lempérière (1993); Sherman (1910); USCOLD (1975); Vogel (1994)

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Page 2.7

Dam References

Gleno, Italy Babb and Mermel (1968); Bowers (1928); Coutinho Rodrigues (1987); Engineering News Record (1924a-c); Gruner (1963); ICOLD (1974, 1984, 1995); ITCOLD (1967); Mary (1968); Smith (1972); Vogel (1984, 1994)

Granadillar, Spain Berga (1997); Gomez Laa et al (1979); ICOLD (1984)

Habra, Algeria Babb and Mermel (1968); Gruner (1963); Gurtu (1925); Jansen (1980); Jorgensen (1920); Leger et al (1997); Rao (1960); Schuyler (1908); Smith (1972); Vogel (1994); Wegmann (1889)

Hauser Lake II, USA Bowers (1928); ICOLD (1974, 1995); Jorgensen (1920); Rouve et al (1977); Sizer (1908); USCOLD (1975)

Idbar, Yugoslavia ICOLD (1974, 1984, 1995); Mary (1968); Milovanovitch (1958)

Khadakwasla, USA Babb and Mermel (1968); Biswas and Chatterjee (1971); Gruner (1967); Hunter (1964); ICOLD (1969, 1974, 1995); INCOLD (1967); Inglis (1962); Jansen (1980); Lempérière (1993); Murthy et al (1979); Murti (1967); Rao (1967); Vogel (1994)

Kohodiar, India ICOLD (1995)

Komoro, Japan Babb and Mermel (1968); ICOLD (1974, 1984, 1995); Vogel (1994)

Kundli, India Babb and Mermel (1968); ICOLD (1969, 1974, 1984, 1995); Rao (1960); Vogel (1994)

Lake Lanier, USA Babb and Mermel (1968); Bowers (1928); Coutinho Rodrigues (1987); Engineering News Record (1926a-b); Feld (1968); ICOLD (1974, 1984, 1995); Mary (1968); Rao (1960); Schnitter (1994); Scott and Von Thun (1993); USCOLD (1975); Veltrop, J.A. (1988); Vogel (1994)

Leguaseca, Spain Berga, L. (1997); Fry, J. (1996); Guerreiro et al (1991); ICOLD (1995); Lempérière et al (1997)

Lower Idaho Falls, USA ICOLD (1984, 1995); USCOLD (1988); Vogel (1994)

Lynx Creek, USA Babb and Mermel (1968); ICOLD (1974); Vogel (1994)

Malpasset, France

Babb and Mermel (1968); Bellier et al (1976); Biswas and Chatterjee (1971); Carlier (1974); Commission Administrative d'Enquête - France (1965a-b); Commission de Contre-Expertise - France (1966); Coutinho Rodrigues (1987); Engineering News Record (1959, 1960a-b, 1962, 1963, 1964a-b, 1967); Flagg; Gosselin (1960); Gruner (1963, 1967); ICOLD (1974, 1984, 1995); Jansen (1988); Londe (1977); Mary (1968); Rao (1960); Scott and Von Thun (1993); Smith (1972); Stapleton (1976); Steger and Unterberger (1990); Terzaghi (1962); Vogel (1984,1994)

Meihua, China Coutinho Rodrigues (1987); ICOLD (1995)

Mohamed V, Morocco ICOLD (1984)

Moyie River, USA Babb and Mermel (1968); Bowers (1928); Coutinho Rodrigues (1987); Engineering News Record (1926b); Feld (1968); ICOLD (1974, 1984,

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Page 2.8

Dam References

1995); Mary (1968); Rao (1960); Schnitter (1994); Scott and Von Thun (1993); USCOLD (1975); Veltrop (1988); Vogel (1994)

Overholser, USA ICOLD (1974, 1984, 1995)

Pagara, India Babb and Mermel (1968); ICOLD (1969, 1974, 1984, 1995); Rao (1960); Vogel (1994)

Puentes, Spain Anderson and Trigg (1976); Babb and Mermel (1968); Berga (1997); Gomez Laa et al (1979); Hinds (1953); ICOLD (1974, 1984, 1995); Jansen (1980); Jorgensen (1920); Mary (1968); Schnitter (1994); Schuyler (1908); Smith (1972); Vogel (1984, 1994); Wegmann (1889)

Santa Catalina, Mexico Babb and Mermel (1968); Lempérière (1993); Schuyler (1906); Vogel (1994)

Selsford, Sweden ICOLD (1974, 1984, 1995)

Sig, Algeria Babb and Mermel (1968); ICOLD (1969, 1974, 1995); Vogel (1994)

St Francis, USA

ASCE (1929); Babb and Mermel (1968); Bowers (1928); Clements (1969); David Rogers (1995); David Rogers and McMahon (1993); Engineering News Record (1928a-j, 1929a-b); Feld (1968); Gruner (1963); Grunsky and Grunsky (1928); ICOLD (1974, 1984, 1995); Jansen (1980, 1988); Jorgensen (1928); Leger et al (1997); Outland (1963); Ransome (1928); Rao (1960); Scott and Von Thun (1993); Smith (1972); Stapleton (1976); The Engineer (1928a-b); USCOLD (1975); Veesaert, C. (198?); Vogel (1994)

Stony River, USA Bowers (1928); Engineering News (1914a-c); Engineering Record (1914); Finch (1914); ICOLD (1974); Jorgensen (1920); Rao (1960)

Tigra, India Babb and Mermel (1968); Gurtu (1925); ICOLD (1969); ICOLD (1974); ICOLD (1984); ICOLD (1995); Jansen (1980); Lempérière (1993); Rao (1960); Vogel (1994)

Torrejon Tajo, Spain Gomez Laa et al (1979); ICOLD (1984)

Vega de Tera, Spain Babb and Mermel (1968); Berga (1997); Bollo (1965); Engineering News Record (1959b, 1960c); Gomez Laa et al (1979); Gruner (1963, 1967); ICOLD (1974, 1984, 1995); Rao (1960); Vogel (1984, 1994)

Xuriguera, Spain Berga (1997); Fry (1996); ICOLD (1995)

Zerbino, Italy Babb and Mermel (1968); Engineering News Record (1935); Fry, J. (1996); ICOLD (1974, 1984, 1995); ITCOLD (1967); Lempérière (1993); Vogel (1984, 1994)

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Analysis of Concrete and Masonry Dam Incidents Page 2.9

2.2.2 CONGDATA Layout

The database was created using Microsoft Access for Windows 95 Version 9.0 (Access).

The information was grouped under the following categories:

• General description;

• incident Details;

• dimensions;

• geology;

• hydrology; and

• references.

A list of the parameters entered into the database is given in Table 2.2.

Queries were developed in Access to analyse the data. Tables were then linked to

Microsoft Excel for Windows 95 (Excel) spreadsheets for further analysis and

interpretation. Excel was used to graph the various parameters.

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Analysis of Concrete and Masonry Dam Incidents Page 2.10

Table 2.2. CONGDATA parameters

Variable Description Codes

ID Identification number

Significant Incident? (Y/N) Whether incident is significant

Dam Name Name of dam

Country Country dam is in

Alternate Name 1 Other name

Dam Type Type of dam Section 2.2.3.2

Year Commissioned Year dam commissioned

Fail Acc Year of incident

Failure/Accident Incident Category Section 2.2.3.1

Fail-Time Time to incident Section 2.2.3.3

CDR Time Time to incident Section 2.2.4.1

Fail-Type Where incident occurred

Fail-Mode How incident occurred

Cause A-E Causes of incident Tables 2.2-2.6

Detection Method Method of detecting incident

Fail-Comments Comments about incident

Remedial Measures A-D Methods of remediation Table 2.7

Concrete/ Masonry Type of concrete/masonry

Foundation Whether foundation soil/rock Section 2.2.3.5

Geology A-C Types of foundation geology Section 2.2.4.4

Geology Comments Comments about foundation

Hlf(m) Height above lowest foundation Figure 2.1

Hd (m) Structural height Figure 2.1

hwu (m) Height of water upstream - FSL Figure 2.1

hwt (m) Height of water at toe Figure 2.1

Hf (m) Height to failure plane Figure 2.1

hwf (m) Height of water at failure Figure 2.1

W (m) Width of dam base Figure 2.1

Wf (m) Width at failure plane Figure 2.1

Width of Spillway (m) Length of spillway

Width of Non-Overflow Section (m) Crest length - spillway

Width of Failed Section Length of failed section

Where Failed Location of failure

Upstream (xH:1V) Upstream slope of dam Figure 2.1

Downstream (yH:1V) Downstream slope of dam Figure 2.1

Valley Shape, L1 (m) Crest length Figure 2.2

L2 Left abutment length Figure 2.2

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Analysis of Concrete and Masonry Dam Incidents Page 2.11

Table 2.2. CONGDATA parameters

Variable Description Codes

L3 Main valley width Figure 2.2

L4 Right abutment length Figure 2.2

Radius of Curvature (m) Radius of curvature of dam

Warning Type 1-3 Type of warning given Section 2.2.4.11

Warning Time (weeks) Time from warning to incident

Post-Tensioned? (Y/N) Whether post-tensioned

Gallery (Y/N) Whether there is a gallery

Gallery Elevation Height to gallery from dam base

Drain Depth (m) Depth of drains into foundation

Drain Spacing (m) Spacing of drains along dam

Shear Key (Y/N) Whether there is a shear key

Grouting Type Type of grouting

Grout Depth Depth of grouting into foundation

No. of victims Number of deaths due to incident

References: Main references

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2.2.3 Data Entered into CONGDATA

Details of dam incidents are given in CONGDATA. The following sections describe the

coding used for input into Access.

2.2.3.1 Definitions of Failures/Accidents

ICOLD(1995) define failure as ‘collapse or movement of part of a dam or part of its

foundation, so that the dam cannot retain water. In general, a failure results in the

release of large quantities of water, imposing risks on the people or property

downstream’. ICOLD(1974) give the following definitions for failures and accidents.

F1 - A major failure involving the complete abandonment of the dam

F2 - A failure which at the time may have been severe, but yet has permitted the

extent of damage to be successfully repaired and the dam again brought into use

A1 - An accident to a dam which has been in use for some time but which has been

prevented from becoming a failure by immediate remedial measures, including

possibly drawing down the water

A2 - An accident to a dam which has been observed during the initial filling of the

reservoir and which has been prevented from becoming a failure by immediate

remedial measures, including possibly drawing down the water

A3 - An accident to a dam during construction, i.e. by settlement of foundations,

slumping of side slopes etc., which have been noted before any water was

impounded and where the essential remedial measures have been carried out, and

the reservoir safely filled thereafter.

The term incident is used to describe failures, accidents and major repairs.

USCOLD(1988) give the following definitions for other accidents and deteriorations.

These have been adopted for the database.

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AR - Accidents or unusual problems encountered in the reservoir upstream of the

dam, which have occurred during operation of the project, but which have not

caused failure or major accident to the dam structure.

MR - Extensive or important repairs to a dam that were required because of

deterioration or to update certain features. Refacing of deteriorated concrete,

repair of deteriorated riprap, or replacement of gates are examples under this

definition.

DDC - Damage to partially constructed dam or to temporary structure required for

construction prior to the dam being essentially completed. Failure of cofferdam or

unplanned overtopping of partially completed dam are examples under this

definition.

Where the exact definition of the failure or accident is uncertain an ‘F’ or an ‘A’ has

been used respectively.

The term significant incident has been introduced to describe failures, accidents and

major repairs where the incident has directly affected the dam stability. Cases where the

dam has been repaired due to a ‘theoretical danger’, such as the updating of design

standards, or due to minor damage to the dam or spillways have not been included under

this term.

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2.2.3.2 Types of Dams

Coding for the types of dams in CONGDATA are:

PG

CB

VA

MV

PG(M)

CB(M)

VA(M)

MV(M)

- Concrete gravity

- Concrete buttress

- Concrete arch

- Concrete multi-arch

- Masonry gravity

- Masonry buttress

- Masonry arch

- Masonry multi-arch

2.2.3.3 Failure Types

Codes for the failure types were obtained from ICOLD(1983) and are:

Ff

Fm

Fb

Fa

Ffb

Ffa

Fba

Fbm

- Failure due to the dam foundation

- Failure due to the dam materials

- Failure due to the structural behaviour of the dam body

- Failure due to the appurtenant works

- Failure due to the foundation and to the structural behaviour of the dam body

- Failure due to the foundation of the dam and to the appurtenant works

- Failure due to the structural behaviour of the dam body and to the appurtenant

works

- Failure due to the structural behaviour of the dam body and to the dam materials

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2.2.3.4 Incident Time

The times at which the incident took place (or was detected) are indicated by the codes

below. These codes were obtained from ICOLD(1983). In Section 2.2.4.1 the incident

time is further discussed and T4 and T5 are redefined.

T1

T2

T3

T4

T5

- During construction

- During the first filling

- During the first five years

- After five years

- Not available

2.2.3.5 Type of Foundation

The foundation type was split into two categories as shown below.

R

S

- Rock mass

- Soil mass

This was further differentiated as discussed in Section 2.2.4.6.

2.2.3.6 Dam Height

Where the height of the dam (from lowest foundation) is uncertain the following

definitions from ICOLD(1983) have been used. In other cases the actual height has been

added.

H1 5m ≤ H1 < 15m

H2 15m ≤ H2 < 30m

H3 30m ≤ H3 < 50m

H4 50m ≤ H4 < 100m

H5 100m ≤ H5

H6 Not available

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2.2.3.7 Detection Methods

The methods for detecting incidents and the need for major repairs were obtained from

ICOLD(1983) and are:

D01

D02

D03

D04

D05

D06

D07

D08

D09

D10

D11

D12

D13

- Direct observation

- Sampling and laboratory test

- Water flow measurements

- Phreatic level measurements

- Uplift measurements

- Pore pressure measurements

- Turbidity measurements

- Chemical analysis of water

- Seepage path investigations

- Joint and crack measurements

- Horizontal displacement measurements

- Vertical displacement measurements

- Angular displacement measurements

D14

D15

D16

D17

D18

D19

D20

D21

D22

D23

D24

D25

- Strain measurements

- Stress measurements

- Water level measurements

- Temperature measurements

- Hydrometric measurements

- Rainfall measurements

- Seismicity control

- Sounding investigation

- Water pressure measurements

- Silting measurements

- Design revision (new criteria)

- Not available

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2.2.3.8 Classification of Causes of Incidents of Dams And Reservoirs

The following tables show the codes defining the types and causes of incidents and the

need for major repairs that occurred at the dams. The tables were obtained from

ICOLD(1983) with some additions from ICOLD(1995). The codes used are followed in

the database by a letter that determines their origin.

• x - ICOLD(1983)

• y - Not from ICOLD

• - ICOLD(1995)

It will be noted that the causes are an unfortunate mi xture of physical and human

factors. They have been adopted for consistency with ICOLD data.

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Table 2.3. Causes of incidents of concrete dams

1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.5.1 1.1.5.2 1.1.6 1.1.7 1.1.8 1.1.9 1.1.10 1.1.11 1.1.12 1.1.13 1.1.14 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.2.8 1.2.9 1.2.10 1.2.11 1.2.12 1.2.13 1.3 1.3.1

- Due to foundation - Inadequacy of site investigation - Deformation and land subsidence - Shear strength - Seepage - Internal erosion - in foundation - in abutment - Degradation (including swelling) - Initial state of stress - Tensile stresses at the upstream toe - Preparation of the foundation surface - Strengthening treatment - Grout curtains and other watertight systems - Drainage systems - Sealing of galleries, shafts and boreholes used for investigation - Leak of drainage system - Due to concrete - Reactions of concrete constituents (including alkali-aggregate reaction) - Reaction between concrete constituents and the environment (including dissolution of calcium hydroxide) - Resistance to freezing and thawing - Attack by bacteria - Compressive strength - Shear strength - Tensile strength - Permeability - Concreting (including order of casting of monoliths) - Cooling - Structural joints (including watertight systems) - Arrangement of reinforcements and anchorages - Ageing of concrete - Due to unforeseen actions or to actions of exceptional magnitude (as a principle, when the case does not fall under other headings) - Hydrostatic pressure and from accumulated silt (including pressure and impact of ice in the reservoir)

1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 1.3.7 1.3.7.2 1.3.7.3 1.3.8 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 1.4.7 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.5.6 1.6 1.6.1 1.7 1.7.1 1.7.2 1.7.3 1.7.4 1.7.5 2.3.9

- Uplift - Earthquakes (natural or man-made) - External temperature variation - Temperature variation due to the heat of hydration - Moisture variation - Overtopping - of abutment - of main section - Deterioration of concrete-rock interface - Due to structural behaviour of the arch and multiple arch dams (including the construction period) - Shape of the dam and its position in the valley - Tensile stresses - Stress concentration due to shape discontinuities in the foundation surface - Stress concentration at openings and shape discontinuities - Artificial abutments and foundation - Distribution and types of joints - Facings - Due to structural behaviour of gravity and buttress dams - shape of the dam and its position in the valley - Tensile stresses - Stress concentration due to shape discontinuities in the foundation surface - stress concentration at openings and shape discontinuities - Distribution and types of joints - Facings - Due to monitoring - Inadequacy of instrumentation - Due to maintenance - Periodic inspections - Cleaning of drains - Control of seepage - Pumping of seepage water - Deterioration of instrumentation - Failure due to an upstream dam collapse

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Table 2.4. Causes of incidents of masonry dams

3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.1.7 3.1.8 3.1.9 3.1.10 3.1.11 3.1.12 3.1.13 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 3.2.10 3.3 3.3.1 3.3.2

- Due to foundation - Inadequacy of site investigation - Deformation and land subsidence - Shear strength - Seepage - Internal erosion - Degradation (including swelling) - Initial state of stress - Tensile stresses at the upstream toe - Preparation of the foundation surface - Strengthening treatment - Grout curtains and other watertight systems - Drainage systems - Sealing of galleries, shafts and boreholes used for investigation - Due to mortar - Reactions of masonry constituents (including alkali-aggregate reaction) - Reaction between masonry constituents and the environment (including dissolution of calcium hydroxide) - Resistance to freezing and thawing - Attack by bacteria - Compressive strength - Shear strength - Tensile strength - Permeability - Masonry construction (including order of placement) - Structural joints (including watertight systems) - Due to stone - Weathering - Joints between stones

3.4 3.4.1 3.4.2 j3.4.3 3.4.4 3.4.5 3.4.6 3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.6 3.6.1 3.7 3.7.1 3.7.2 3.7.3 3.7.4 3.7.5

- Due to unforeseen actions or to actions of exceptional magnitude (as a principle, when the case does not fall under other headings) - Hydrostatic pressure and from accumulated silt (including pressure and impact of ice in the reservoir - Uplift - Earthquakes (natural or triggered) - External temperature variation - Variations due to changes of moisture content - Overtopping - Due to structural behaviour of masonry dams (including the construction period) - Shape of the dam and its position in the valley - Tensile stresses - Stress concentration due to shape discontinuities in the foundation surface - Distribution and types of joints - Facings - Due to monitoring - Inadequacy of instrumentation - Due to maintenance - Periodic inspections - Cleaning of drains - Control of seepage - Pumping of seepage water - Deterioration of instrumentation

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Table 2.5. Causes of incidents to appurtenant works

4.0 4.0.1 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 4.1.8 4.1.9 4.1.10 4.1.11 4.1.12 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8 4.2.9 4.2.10 4.2.11 4.2.12 4.2.13 4.3 4.3.1 4.3.2 4.4 4.4.1 4.4.2 4.4.3 4.4.4

- Inadequate design - Tunnels and canals - Due to foundations (when they don’t have good dam characteristics) - Inadequacy of site investigations - Deformation and land subsidence - Shear strength - Percolation - Internal erosion - Degradation (including swelling) - Initial state of stress - Preparation of foundation surface - Strengthening treatment - Grout curtains and other watertight systems - Drainage systems - Sealing of galleries, shafts and boreholes used for investigation - Due to concrete - Reactions of concrete constituents (including alkali-aggregate reaction) - Reactions between concrete constituents and the environment (including dissolution of calcium hydroxide) - Resistance to freezing and thawing - Attack by bacteria - Mechanical strength (including tensile strength) - Permeability - Concreting (cooling included) - Cracking - Surface finishing (facing included) - Structural joints (including watertight systems) - Arrangement of reinforcements and anchorages - Erosion by abrasion - Erosion by cavitation - Due to riprap - Disintegration of blocks - Removal of blocks - Due to steel and other materials - Chemical and biological agents - Erosion by abrasion - Erosion by cavitation - Mechanical strength

4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.4.2 4.7 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 4.7.6 4.7.7 4.7.8 4.7.9 4.7.10 4.8 4.9 4.9.1 4.9.2 4.10 4.10.1 4.11 4.11.1 4.11.2 4.11.3 4.11.4 4.11.5 4.11.6 4.11.7

- Due to unforeseen actions or actions of exceptional magnitude (when the case doesn’t fall under other headings) - Hydrostatic pressure and pressure due to silt accumulation - Pressure and impact of ice - Uplift - Earthquakes (natural or triggered) - Temperature and moisture variations - Delay in construction at the time of flood - Due to structural behaviour - Structural behaviour of spillways - Insufficient capacity of spillway - Erosion of spillway basement - Inadequate design of spillway - of canal or tunnel - Due to water flow, water level and water-borne debris (including construction periods) - Excessive rates of flow - Turbulence - Vortices - Waves - Abnormal pressures - Entrapped air - Inaccurate discharge curves - Solid materials carried by water flow - Discharge of floating materials - Piping outside inserted conduit - Due to local scour - Due to operation - Sudden opening of the discharge equipment - Inadequate instructions for operating the discharge equipment - Due to monitoring - Inadequacy of instrumentation - Due to maintenance - Periodic inspections - Cleaning of drains - Control of seepage - Pumping of seepage water - Deterioration of measurement instrumentation - Malfunction of discharge equipment - Debris in stilling basins

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Table 2.6. Causes of incidents of reservoirs

5.1 5.2 5.3 5.4 5.5

- Slope sliding - Overturning of rock blocks - Permeability - Silting - Ecological balance

Table 2.7. Causes of incidents downstream of dam

6.1 6.2 6.3

- Equilibrium of river bed - Slope stability - Ecological balance

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2.2.3.9 Classification of Remedial Measures

Table 2.8 shows the coding used for remedial measures. The codes used were obtained

from ICOLD(1983).The codes used are followed by a letter which determines their

origin.

• x - ICOLD(1983)

• y - Not from ICOLD

• - ICOLD(1995)

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Table 2.8. Classification of remedial measures

R101 R102 R103 R104 R105 R106 R107 R108 R109 R201 R202 R203 R204 R205 R301 R302 R303 R304 R305 R306 R307 R308 R309 R401 R402 R403 R404 R405 R406 R407 R408

- Of a general nature - Investigation - Monitoring - Lowering of reservoir level - Raising of dam crest - Overall reconstruction (same design - Reconstruction with new design - None - Not available - Scheme abandoned - In foundations - Water tightening treatment - Drain & filter construction or repair - Strengthening by grouting or other methods (excluding anchoring) - Filling in of fractures and cavities - Anchoring - In concrete and masonry dams - Water tightening treatment - Drain construction or repair - Thermal protection (excluding facing) - Facing - Reconstruction of deteriorated zones - Execution of joints - Strengthening by grouting - Strengthening by anchoring - Strengthening by shape correction - In earth and rockfill dams - Impervious core repair - Construction or repair of other watertight systems - Drain & filter construction or repair - Slope protection construction or repair - Filling in of cracks and cavities - Reconstruction of deteriorated zones - Upstream slope flattening, construction of upstream berm or other stabilisation methods - Downstream slope flattening, construction of downstream berm or other stabilisation methods

R501 R502 R503 R504 R505 R506 R507 R508 R509 R510 R511 R512 R513 R514 R515 R601 R602 R603 R604 R605 R606 R607 R701 R702

- In appurture works - Discharge increase - Construction of additional appurtenant work - Overall reconstruction of appurtenant works - Partial reconstruction with strengthening or structural changes - Shape correction of surfaces contacting flow - Aeration devices: construction or increase of capacity - Repair of surfaces contacting flow (including facings and special treatments) - Joint water tightening treatment - Construction & repair of drains - Slope protection & stabilisation - Sediment discharge removal from surfaces contacting flow - Construction, modification and repair of valves and gates - Establishment and updating of rules for gate and valve operations - Reconstruction of deteriorated zones and other correcting measures - Abandon of appurtenant work - In reservoir - Reforestation - Torrent training - Sediment discharge diversion - Slope regularisation, protection and strengthening - Draining - Water tightening - Dredging - Downstream of dam - Draining - Slope regularisation, protection and strengthening

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2.2.4 Selection of Additional Variables

As the ICOLD (1974, 1983 and 1996) databases were limited in their scope it was

decided to add additional variables to CONGDATA. The additional variables were

generally proposed by the author and reviewed by the sponsors. Further variables were

added where requested by the sponsors. Some potential variables were rejected due to

limited information in the literature, reports etc. Following is a description of the

additional data variables including a discussion of why each was chosen.

2.2.4.1 Time of Incidents

It is important to understand at what age dams are more likely to fail or experience

accidents. This can give dam owners a guide as to what intensity of monitoring they

need to have throughout the life of a dam. ICOLD (1983) have analysed the time to

failure and grouped their data into categories T1 to T5 as shown in Section 2.2.3.4. The

oldest group is T4, which indicates an incident occurred after five years. It is clear that

this is a large category that cannot adequately indicate potential deterioration effects in

dams. The following grouping was used to allow for a better distribution, and hence

understanding, of times to failure.

T1 - During construction

T2 - During first fill

T3 - 0-5 years

T4 - 5-10 years

T5 - 10-20 years

T6 - 20-30 years

T7 - 30-40 years

T8 - 40-50 years

T9 - >50 years

T10 - >5 years (else unknown)

T11 - Unknown

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2.2.4.2 Foundation Incident Mode

Where the foundation has played a part in the incident of the dam further codes have

been added. This allows for a better understanding of the foundation parameters

affecting different incident modes. The codes are:

S - Sliding - where failure has occurred by the dam sliding on the foundation. Sliding

can be along the dam-foundation interface or along a foundation discontinuity.

P - Piping - of materials within soil foundations or rock discontinuities (generally

joints).

SC - Scour - of the foundation or the abutment.

U - Uplift - in the foundation.

D - Deformation - settlement or other movements of the foundation not including

sliding.

L - Leakage - beneath the dam or through the abutments.

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2.2.4.3 Dam Incident Mode

Where the incident occurred in the dam the following codes have been used to define

the incident mode.

SH - Shear (sliding) within the dam.

T - Tensile (overturning) within the dam.

C - Compressive failure within the dam.

CR - Cracking (due to concrete hydration etc.)

ST - Structural damage to appurtenant structure such as spillway gates.

LD - Leakage - through dam.

EQ - Earthquake damage.

2.2.4.4 Comments on Incidents

The causes of incidents as given in Section 2.2.3.8 are often too general to explain the

type of incident. A brief description of the incident has been included in the database to

allow for a better understanding of the causes of the incident.

2.2.4.5 Description of the Failure or Accident

Brief descriptions of the failure or accident and warning are included in the database.

2.2.4.6 Additional Geological Information

Previous dam failure databases have only listed the foundation as soil, rock or both. The

dam geology has been included in the database in an attempt to determine whether

certain foundation geology types are more susceptible to incidents and vice-versa. The

geology of each dam was categorised into the following categories:

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Foundation Geology Categories - Rock

Sedimentary Metamorphic Igneous

Conglomerate Gneiss Granite

Sandstone Schist Gabbro

Mudstone Phyllite Rhyolite

Shale Slate Andesite

Siltstone Marble Basalt

Claystone Quartzite

Limestone Hornfels

Dolomite

Chalk

Agglomerate

Volcanic Breccia

Tuff

Saline Rocks

Coal

Lignite

Foundation Geology Categories - Soil

Alluvial Aeolian Marine

Lacustrine Colluvial Volcanic (ash)

Glacial Residual

Unfortunately this detail is often not available, so the database is incomplete.

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2.2.4.7 Dam Dimensions

The databases that have been developed previously included the height of the dam

(taken as above the lowest foundation for ICOLD) and crest length. These are

insufficient to fully describe the dam. To allow for the determination of gradients and

performing simple analyses of some of the dam incidents, further dimensions were

included in the database. The height to full supply level (FSL), tailwater height and the

water height at failure were included. These are shown in Figure 2.1 and listed below.

All heights, excluding Hlf, have the general foundation level of the dam as their

reference level.

Hlf - Height of dam above lowest foundation

hd - Structural height

hwu - Reservoir height at full supply level (FSL)

hwt - Height of the tail water

W - Base width of dam section

hf - Height to failure plane (=0 if in foundation)

hwf - Reservoir height at failure

Wf - Width of failure plane

xH:1V - Upstream slope

yH:1V - Downstream slope

The drain depth, gallery height and length of spillway were also included in the

database. The extent of each failure was also seen as important and so the length of the

failed section and where the dam failed (spillway section/non-overflow section/both)

were also included in the database.

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2.2.4.8 Valley Shape

Stress concentrations and differential movements can occur at changes of section. This

is particularly important with sharp section changes in the foundation. For this reason a

method was developed to assess the valley shape. The parameters given below are

shown in Figure 2.2.

L1 - Crest length

L2 - Left abutment length

L3 - Length of valley section

L4 - Right abutment length

2.2.4.9 Radius of Curvature

A dam will have increased stability where there is some curvature in the dam and load is

transferred to the dam abutments. The database includes the radius of curvature of the

dam. For dams with straight axes the radius is shown as straight.

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Figure 2.1. Definition of dimensions in CONGDATA

hf Hlf hwhd

Wf

hwt

Drain Depth

Gallery Height

W

1V

yH xH

1V

Full Supply Level

Dam Crest

Failure Surface (where applicable)

Gallery

Dam Foundation

Drain Holes

Grout Holes

Normal Tailwater

Level

Shear Key

Water Level at Failure

hwf

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Figure 2.2. Definition of dimensions in CONGDATA - section across river

2.2.4.10 Monitoring and Surveillance Data

In some cases there have been signs of displaceme nt, cracking, seepage and other

factors prior to the incident, giving some warning. These have been included in the

database as:

0 - None observed

1 - Foundation piping

2 - Foundation leakage

3 - Dam leakage

4 - Horizontal displacements

5 - Vertical displacements

6 - Cracking

7 - Expansion & cracking

8 - Concrete deterioration

9 - Scour of the foundation

11 - Overtopping

12 - Slide downstream of dam

13 - Abnormal uplift development

14 - Unknown

A brief description of the warning is also included. This allows some quantification of

the warning e.g. the amount of leakage, and time before failure.

L1

L2 L3 L4 Dam Crest

Slope Change Slope

Change

Dam Foundation

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2.2.4.11 Warning Rating

The following qualitative codes were used to show whether there was sufficient warning

prior to the failure to allow for preventative measures and/or warning of people

downstream.

Y - Yes

M - Maybe

N - No

F - Flood

DF - Dam failure upstream

? - No data

2.2.4.12 Warning Time

The time from when a warning was given to when the dam failed or when an accident

occurred and the dam was remediated was recorded as the warning time.

2.2.4.13 Other Design Factors

(a) Post-Tensioning

Whether the dam was post-tensioned was included to assess the effects of post-

tensioning dams.

(b) Gallery

The presence of a gallery allows for better maintenance and uplift pressure relief and the

provision or otherwise of a gallery is included in the database.

(c) Drain Depth and Spacing

Drain depths and spacing were included in the database to assess the effects of reducing

uplift pressure on dam stability.

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(d) Shear Key

A shear key may increase the resistance of a dam to sliding and the presence of the key

is included.

(e) Grouting Type and Depth

Consolidation and/or grout curtains can be used to improve the stability of dam

foundations and to reduce uplift pressures. The presence of, depth and spacing are

included in the database.

(f) Number of Victims of Dam Failures

This was included to crudely assess the hazard of the dam. It is possible that high hazard

dams may have a lower chance of failure as they have better maintenance and higher

factors of safety in design.

2.2.5 Assumptions Made in Assembling the Database

The majority of the information in CONGDATA has been derived from ICOLD

(1974,1983 and 1995). The ICOLD data was collated by sending questionnaires to the

various National Committees. This method of data collection caused several problems

(ICOLD, 1995).

• Some failures were not reported due to a lack of response from some National

Committees.

• Replies from National Committees were not consistent with each other - some

committees calling incidents failures where others would call them accidents.

• Gate failure was included by some committees whilst others did not include them. It

was ICOLD (1995) policy not to include gate failures.

• The data from China was inconsistent with the rest of the world. China has the same

amount of dams as the rest of the world put together yet has only reported 3 dam

failures as opposed to 180 for the world. When comparing similar construction

periods (post-1955) this becomes 3 failures as opposed to 50. It was ICOLD (1995)

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policy to ignore China when performing their statistical analyses. This policy has

also been adopted here.

When assessing the ICOLD data more specific inconsistencies were found in the

following:

• Dam type - Where failures occurred in composite structures (e.g.

embankment/concrete gravity) some National Committees listed the dam as a

composite structure (TE/PG) whereas others listed only the section of the dam that

failed (e.g. TE). It is important when analysing dam failures that the section that

failed be identified so that misleading conclusions are not made. Dams where failure

occurred only through the embankment section were discarded in the preparation of

CONGDATA.

• Height - When comparing ICOLD data to that of other reports/papers/drawings etc.

inconsistencies became apparent in the assigning of heights to each dam. Where

possible the data was changed to what was understood to be the accurate height.

Where corroborating information was not available the ICOLD heights were

assumed.

• Length - Similar inconsistencies to the height category were found here. Attempts

were also made to determine the crest length of the failed section.

• Year - generally the years of construction and incident were found to be accurate.

Some small inconsistencies (1-2 years) were found in old dams. There were some

errors found in the accidents.

• Foundation - In ICOLD some dams are noted as having soil/rock foundations. Where

possible it was determined where the failure occurred and which foundation type

played a part. Where there was no other information the ICOLD foundation was

assumed.

• Failure type and cause - It appears that most of the ICOLD causes were chosen by

the individual National Committees (and potentially smaller dam owners that the

questionnaires were passed on to). There appears to be a bias as to which failure

categories each country chooses. This has resulted in marked inconsistencies in the

ICOLD causes. It is also often difficult to assess how a dam failed by the failure

category alone. An attempt has been made to assess all the dams in CONGDATA

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independently. However, often the ICOLD data is the only available. Failure types

were found to be misleading in several dams and have been corrected.

• Remediation measures - Similar problems arise here as for failure type. However,

many of the failed dams have been abandoned and so the effects are minimal.

Many of the causes of incidents in CONGDATA are subjective but they have been

chosen with as much care as possible from the references available.

Where several sources have been found with conflicting information an attempt has

been made to select the most ‘credible’ source. Most of the dams with most uncertainty

are the older dams (prior-1950s).

It should be remembered that many of the failures occurred a long time ago and hence

information is scarce.

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2.2.6 Data on the Population of Dams

The assessment of dam incident statistics is of value to the dam engineering community.

With these statistics engineers can see which dams have had more dam incidents than

other types. This method of analysis however can lead to incorrect conclusions. For

example, from a cursory assessment of the failure statistics for concrete and masonry

and embankment dams it is shown that there is many more embankment failures

compared with concrete and masonry dams. This could lead to the assumption that an

embankment dam is much more likely to fail than a concrete dam. If the analysis is

continued by comparing the failure statistics to the total population of existing dams

then it is shown that the percentage of failures for each dam type is roughly the same

(ICOLD, 1995).

ICOLD (1995) was the first to attempt to produce statistics on failures taking into

account the number and type of existing dams. The population data was taken from the

ICOLD World Register of Dams (1984 edition and 1988 updating). ICOLD (1995)

compared statistics on existing and failed dams for their type, height and year

commissioned. The results of the analyses assisted in qualifying many assumptions that

were made on the basis of incident statistics alone.

The assessment of the incidents in CONGDATA needed to be qualified with dam

population data. ICOLD (1995) used a computerised version of the World Register of

Dams that was unavailable to the author. To overcome this, the populations of dams in

countries where either a failure had occurred or there was a large number of

concrete/masonry dams were entered into a database to use for basic comparisons with

the incident data. The table below shows the breakdown of the 4168 dams from 22

countries that were used.

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Population of Dams from World Register of Dams used for Analysis

Country Gravity Arch Buttress Multi-Arch

Total

Algeria 5 1 4 10 Australia 69 39 10 3 121 Austria 23 15 38 Brazil 86 3 9 4 102 Canada 190 6 19 2 217 France 130 85 11 12 238 Great Britain 95 11 14 1 121 India 146 146 Italy 208 65 24 8 305 Japan 536 44 17 3 600 Mexico 101 6 3 1 111 Morocco 11 4 15 Norway 26 38 42 3 109 New Zealand 13 19 2 34 Portugal 27 19 4 1 51 South Africa 95 59 7 15 176 Spain 546 30 23 4 603 Sweden 12 5 27 44 Switzerland 51 48 3 102 Turkey 12 1 1 14 USA 717 169 46 25 957 Yugoslavia 30 19 1 4 54

CONGDATA included many more variables for each dam incident than is included in

the World Register. A major component of this chapter is an assessment of the

foundation geology type that ICOLD does not assess. It was therefore assessed that the

population of dams needed to come from sources other than the World Register.

The ideal statistical analysis would be made on the total population of dams however

this would be impossible to collect. A compromise was made where large subsets of the

world population were chosen. The populations chosen and the reasons why are given

below.

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• Australia/New Zealand - This population was chosen for a number of reasons. The

dam population is large and covers numerous geology and topography types. The

sponsors of the project comprised the major dam owners in the two countries and

hence access to data was made easier. It was also important to make sure the project

produced results that could be used by the sponsors in Australia and New Zealand.

Appendix C provides a listing of the dams used.

• USBR - The USBR has been involved with a large number of dams that cover the

western half of the USA. This population covers a wide area and hence a wide range

of geology and topography. It was also seen as important to include a population

from the country with the highest number of reported incidents. Another major factor

was the free access to data that the USBR gave the author. Information on the dams

was also available from USBR(1996). The list of dams used for the population is

given in Appendix C.

• US National Inventory of Dams - This computerised database comprised 1049 large

concrete and masonry dams. Such statistics as foundation geology were not included.

The inventory instead allowed assessment of the basic variables of dam type, age and

height in the country with the greatest number of reported failures.

• Portugal - Due to the easy access to the LNEC(1992) report on the Internet this

population was also assessed. An attractive feature of this population was the

inclusion of foundation geology types in a country with a much different geological

environment (generally igneous and metamorphic). This population is shown in

Appendix C.

The populations of dams from the US National Inventory of Dams and Portugal were

collated directly from the CD-ROM and the Internet respectively. The author also

collected information from the USBR offices in Denver. Further information was taken

from the Internet, personal communication with USBR staff, journal papers and various

dam compilation reports published by the USBR and the United States Committee on

Large Dams (USCOLD). The information on the Australia/New Zealand population

was collected in person by the author and by using questionnaires sent to the sponsors

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and several other dam owners. Where required additional information was collected

from journal papers and conference proceedings.

The populations’ chosen above have several limitations including:

• Limited extent - Using subsets of the world population can limit the extent to which

the information is used. The information can be expected to be as accurate as

possible in the areas surveyed but may not be typical of other areas. Countries where

geological environments and dam design and construction methods are different to

those assessed are likely to have led to different results. It is believed that the use of

populations that cover a wide area of land and are located in the areas of most

failures has reduced potential inaccuracies.

• Errors/omissions - Where data has been collected second hand there is always a

chance of inconsistencies. Attempts to limit these were made by providing extensive

information with the questionnaires and checking data against other references. This

problem was also limited by personal collection of a large amount of the population

data.

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2.3 RESULTS OF ANALYSIS OF THE DATABASE

2.3.1 Summary of Incidents

This chapter describes the main results obtained from the analysis of the database

CONGDATA. A total of 485 dams comprising: 46 failures; 174 accidents; and 265

major repairs were entered into CONGDATA for 29 countries. Table 2.9 shows the

number of incidents by dam type in the database. Table 2.10 shows the number of

significant incidents as defined in Section 2.2.3.1. Figure 2.3 and Table 2.11 show the

distribution of reported incidents by country.

Table 2.9. Number of dam incidents in database by type

Type Failures Accidents Major Repairs

Total Population(1)

PG 10 44 165 219 3434 PG(M) 21 17 39 77 VA 3 85 22 110 808 VA(M) 3 0 0 3 CB 4 8 30 42 316 CB(M) 3 1 2 6 MV 2 17 6 25 105 MV(M) 0 2 1 3 Total 46 174 265 485 4663

Note (1) ICOLD (1984) world population excluding China.

Table 2.10. Number of significant dam incidents in database by type

Type Failures Accidents Major Repairs

Total Population(1)

PG 10 38 52 100 3434 PG(M) 21 15 19 55 VA 3 85 1 89 808 VA(M) 3 0 0 3 CB 4 8 11 23 316 CB(M) 3 1 0 4 MV 2 15 0 17 105 MV(M) 0 2 0 2 Total 46 164 83 293 4663

Note (1) ICOLD (1984) world population excluding China.

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Figure 2.4 shows the dam incidents as a percentage of the total population of dams in

each country. Algeria shows a large proportion of failures to their dams. The population

in Algeria was taken as 14 (those in existence in 1983 plus those that failed). Due to

their small populations Morocco and Turkey show high percentages of failures. India

(5%) is noticeable particularly for its larger population. The USA has a failure rate of

approximately 2%.

Unfortunately many of the variables for each dam remained unknown due to a lack of

published information. This was often due to insufficient reporting of old dam incidents.

To simplify the analysis, and improve the quality, the nature of the accidents and major

repairs to dams were initially assessed to see if the incident was likely to lead to failure

of the dam. These incidents were then denoted as ‘significant’, a term which is used in

some of the results in this chapter. It would appear likely that the few numbers of major

repairs in some countries might be due to inadequate data rather than the absence of

major repairs.

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Table 2.11. Number of dam incidents reported in each country

Country Failures Accidents Major Repairs Total Population(1) (No. of Cases) (No. of Cases) (No. of Cases) (No. of Cases) (No. of Dams)

Algeria 7 1 0 8 14 Australia 0 4 21 25 121 Austria 0 5 3 8 89 Brazil 0 2 2 4 121 Cameroon 0 1 0 1 2 Canada 0 1 9 10 219 Chin(2) 1 2 1 4 1290 Czechoslovakia 0 0 3 3 47 Finland 0 0 1 1 13 France 2 18 24 44 296 Germany 0 1 2 3 53 Great Britain 0 2 1 3 121 India 6 12 1 19 128 Ireland 0 0 1 1 8 Italy 3 21 57 81 327 Japan 1 4 11 16 703 Mexico 1 0 0 1 159 Morocco 1 0 0 1 18 New Zealand 0 0 1 1 38 Norway 0 1 0 1 108 Portugal 0 4 3 7 47 Rhodesia 0 6 3 9 19 South Africa 0 8 2 10 180 Spain 6 16 11 33 568 Sweden 1 0 0 1 45 Switzerland 0 10 4 14 106 Turkey 1 0 0 1 14 USA 16 56 102 174 754 Yugoslavia 0 1 2 3 58 TOTAL 46 176 265 487 5662

Note (1) Population from ICOLD (1984). (2) Chinese dams excluded in statistical analysis.

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0 5 10 15 20 25 30 35 40

Algeria

Australia

Austria

Brazil

Cameroon

Canada

China

Czechoslovakia

Finland

France

Germany

Great Britain

India

Italy

Japan

Mexico

Morocco

New Zealand

Norway

Portugal

Rhodesia

South Africa

Spain

Sweden

Switzerland

Turkey

USA

Yugoslavia

Percent of Total

Failure

Accident

MajorRepair

Figure 2.3. The distribution of reported dam incidents vs country

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0 10 20 30 40 50

Algeria

Austria

Cameroon

China

Finland

Germany

India

Japan

Morocco

Norway

Rhodesia

Spain

Switzerland

USA

Percentage of Total

Failure

Accident

Major Repair

Figure 2.4. Reported incidents as percentage of country’s dam population from

ICOLD (1984)

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2.3.2 Year Commissioned of Dams Experiencing Incidents

Figure 2.5 and Figure 2.6 show the year dams were commissioned (broken into

decades) for concrete gravity dam and masonry gravity dam incidents respectively.

There were a total of 10 failures, 44 accidents and 165 major repairs for concrete gravity

dams and 21 failures, 17 accidents and 39 major repairs for masonry gravity dams. Due

to their age, it is considered likely that masonry gravity dam accidents and major repairs

are less likely to have been reported to ICOLD.

Concrete gravity dam failures occurred in dams commissioned in the 1900’s through to

the 1920’s. No failures occurred in dams commissioned between 1926 and 1963. Three

concrete gravity dam failures occurred in the 1960’s. There was a similar lack of

failures in masonry gravity dams commissioned between 1930 and 1966. These periods

of no failures are likely to be a function of the number of dams built and improvement

in the understanding and construction of dams.

Figure 2.7 shows the year commissioned for all dam incidents. This shows failures and

accidents to dams commissioned in the 1930’s and 1940’s dropping off. This follows a

similar trend to the world population shown in Figure 2.8.

The ICOLD World Register data does not allow for the separation of concrete and

masonry gravity dams. The USA population of dams (FEMA, 1995) was used to give a

rough estimate of this separation. Figure 2.9 shows the year commissioned for concrete

and masonry gravity dams in the USA. It should be noted that the USA data has been

collated from dam owner responses and there is the chance that some dams have been

denoted as concrete where in fact they were masonry. The peak in construction of

masonry dams correlates reasonably with the peak in masonry gravity dam incidents

(Figure 2.6). Peaks in dam commissioning were noted in the 1880’s and 1910’s. Peaks

in failures of masonry gravity dams are noted in dams commissioned in the 1870’s to

1890’s and 1910’s to 1920’s.

The graphs show that there were more incidents to dams commissioned in the 1910’s,

1920’s, 1950’s and 1960’s. However this appears to follow the trend in construction of

dams. The incident numbers are likely to be partly a function of the number of dams

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built as well as design or construction deficiencies in these periods. The number of

accidents and major repairs drops off prior to 1920 but this is very likely to be due to the

way the data was collected. There is a much higher chance of having details of failures,

from the period prior to 1900, than accidents.

Figure 2.10, Table 2.12 and Table 2.13 compare the failure and accident statistics with

those of the population of dams as at 1983. The percentages refer to each subset (year

commissioned and dam type). Generally there was a reduction in the number of failures

per population with time. A small rise in the failure rate can be seen in the 1950’s and

1960’s. There are a number of various peaks in the percentage of failures for buttress

and multi-arch dams, but there are too few incidents to make definitive judgements on

this.

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To 1983 only

0 5 10 15 20 25 30 35 40

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

DecadeBeginning

Percentage of Total Incidents

Failure

Accident

Major Repair

Figure 2.5. Year commissioned vs concrete gravity dam incidents

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To 1983 only

0 5 10 15 20 25 30 35 40 45

<1800

1800-1859

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

DecadeBeginning

Percentage of Total Incidents

Failure

Accident

Major Repair

Figure 2.6. Year commissioned vs masonry gravity dam incidents

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To 1983 only

0 5 10 15 20 25 30

<1800

1800-1849

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

DecadeBeginning

Percentage of Total Incidents

Failure

Accident

Major Repair

Figure 2.7. Year commissioned vs all dam incidents

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Population to 1978

0 5 10 15 20 25 30 35

<1800

1800

1810

1820

1830

1840

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

DecadeBeginning

Percent of Total for Dam Type

Gravity

Arch

ButtressMulti-Arch

Figure 2.8. Year commissioned for world population data obtained from ICOLD

(1979)

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0

5

10

15

20

25

30

35

<1850 1850s 1860s 1870s 1880s 1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s >1990

Decade

%

Concrete Gravity

Masonry Gravity

All Gravity

Figure 2.9. Year commissioned vs percentage of gravity dams constructed in the

USA

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0 5 10 15 20 25

<1900

1900-1909

1910-1919

1920-1929

1930-1939

1940-1949

1950-1959

1960-1969

1970-1979

Failures/Population (%)

All

Gravity

Arch

Buttress

Multi-Arch

Figure 2.10. Year commissioned - failures/population per period

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Table 2.12. Year commissioned - failures vs population per period

Years Gravity Arch Buttress Multi-Arch All NUMBER OF FAILURES

<1900 14 0 0 0 14 1900-1909 4 0 1 0 5 1910-1919 4 1 2 0 7 1920-1929 4 2 2 1 9 1930-1939 1 0 0 0 1 1940-1949 0 0 1 0 1 1950-1959 0 2 1 1 4 1960-1969 4 0 0 0 4 1970-1979 0 0 0 0 0 1980-1983 0 1 0 0 1

FAILURES/POPULATION (%) <1900 11.2 - - - 10.3

1900-1909 3.5 - 22.4 - 3.6 1910-1919 1.9 3.1 8.9 - 2.5 1920-1929 1.1 2.0 7.2 5.3 1.7 1930-1939 0.3 - - - 0.2 1940-1949 - - 3.4 - 0.2 1950-1959 - 1.2 1.1 5.6 0.4 1960-1969 0.5 - - - 0.4 1970-1979 - - - - - 1980-1989 - 1.8 - - 0.2

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Table 2.13. Year commissioned - accidents vs population per period

Years Gravity Arch Buttress Multi-Arch All NUMBER OF SIGNIFICANT ACCIDENTS

<1900 2 1 1 0 4 1900-1909 3 2 0 0 5 1910-1919 8 6 2 4 20 1920-1929 6 11 1 3 21 1930-1939 4 6 0 2 12 1940-1949 2 6 0 3 11 1950-1959 7 28 3 4 42 1960-1969 15 21 2 0 38 1970-1979 5 4 0 1 10 1980-1983 1 0 0 0 1

ACCIDENTS/POPULATION (%) <1900 1.6 12.8 no pop - 2.9

1900-1909 2.6 11.2 - - 3.5 1910-1919 3.7 18.5 8.9 35.8 7.1 1920-1929 1.6 11.0 3.6 15.8 4.0 1930-1939 1.2 7.6 - 17.9 2.6 1940-1949 0.6 9.2 - 24.4 2.5 1950-1959 0.9 16.1 3.4 22.3 4.0 1960-1969 1.9 9.6 2.7 - 3.4 1970-1979 1.4 5.7 - 11.2 2.2

2.3.3 Height

Figure 2.11 shows the height range distribution for all the significant incidents in

CONGDATA. The last two ranges were chosen as ‘150-199m’ and ‘>200m’. The few

dams higher than 150m were spread over a large range of heights.

The failures appear to be more prevalent in the 15-50m height range (a total of 39).

There are seven reported failures for dams of height 50-70m. No reported failures have

occurred in dams higher than 70m. Most accidents occurred in the dams in the height

range 15-60m. The same numbers of major repairs have generally taken place per 10m

height range between 15m and 80m. There is a marked drop off from 80m onwards. The

number of major repairs per 10m peaks at a height range of 40-49m.

Figure 2.12 and Figure 2.13 show the height versus number of dams for significant

incidents in concrete gravity and masonry gravity dams respectively. Proportionally

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more failures, accidents and major repairs have occurred in higher dams for concrete

gravity dams than masonry gravity dams but this may simply reflect the fact that there

are fewer high masonry gravity dams.

There were no accidents reported in the range 120-199m for concrete gravity dams. No

incidents were reported for masonry gravity dams higher than 100m.

0 5 10 15 20 25

15-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

100-109

110-119

120-129

130-139

140-149

150-199

>200

Unknown

(m)

Number of Dams

FailuresAccidentsMajor Repairs

Figure 2.11. CONGDATA - height ranges for all dam significant incidents

(Insert: Figure 2.14 Failures/Population (%) for comparison)

Note: No failures for dams 70m or higher

0 1 2 3 4 5 6

15-19

20-29

30-39

40-49

50-59

60-69(m)

Failures/Population (%)

All

Gravity

Arch

Buttress

Multi-Arch

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0 2 4 6 8 10

15-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

100-109

110-119

120-129

130-139

140-149

150-199

>200

Unknown

(m)

Number of Dams

Failures

Accidents

Major Repairs

Figure 2.12. CONGDATA - Height ranges for concrete gravity dam significant

incidents (Insert: modified Figure 2.14 Failures/Population (%) for comparison)

Note: No failures for dams 70m or higher

0 1 2 3 4

15-19

20-29

30-39

40-49

50-59

60-69(m)

Failures/Population (%)

Gravity

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0 1 2 3 4 5 6 7 8

15-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

Unknown

(m)

Number of Dams

FailuresAccidentsMajor Repairs

Figure 2.13. CONGDATA - height ranges for masonry gravity dam significant

incidents

Table 2.14, Table 2.15 and Figure 2.14 show the percentage of failures and accidents of

concrete and masonry dams as a percentage of the population created from ICOLD

(1979 and 1984). The database was created from the ICOLD (1979) dam population and

extrapolated to the population in ICOLD (1984).

The data shows the ratio of failures to population does not exhibit any major trend.

There appears to be a higher percentage of failures to population in the 40-49m and 60-

69m height ranges. There is a slight trend of increasing percentage of gravity dam

failures with height. Arch, buttress and multi-arch dams are shown to be more likely to

have failures in the 15-39m height range.

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Table 2.14. Percent of concrete & masonry dam fails vs population for height

Dam Height (m) Type 15-19 20-29 30-39 40-49 50-59 60-69 Unknown ALL

NUMBER OF FAILURES PG 3 - 1 2 1 3 - 10 PG(M) 3 6 3 7 - 1 1 21 VA 2 - - - - 1 - 3 VA(M) 1 1 1 - - - - 3 CB 3 1 - - - - - 4 CB(M) 1 1 1 - - - - 3 MV - 1 1 - - - - 2 MV(M) - - - - - - - - All concrete

8 2 2 2 1 4 - 19

All masonry

5 8 5 7 - 1 1 27

NUMBER OF FAILURES/POPULATION(1) (%) Gravity 0.7 0.6 0.7 2.5 0.4 2.6 N/A 0.9 Arch 3.4 0.6 1.0 - - 1.7 N/A 0.8 Buttress 4.6 2.7 1.9 - - - N/A 2.4 Multi-Arch

- 4.5 5.6 - - - N/A 2.0

All 1.2 0.8 0.9 1.9 0.3 2.2 N/A 1.0 Note (1) Population height ranges from ICOLD(1979) extrapolated to population in ICOLD(1984).

Table 2.15. Percent of concrete & masonry accidents vs population for height

Dam Height (m) Type

15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-149 150-199 >200 Unknown NUMBER OF SIGNIFICANT ACCIDENTS

PG 4 7 3 3 3 2 1 2 2 3 - 2 6 PG(M) - 4 3 1 3 1 - 2 1 - - - - VA - 2 13 9 12 5 6 3 4 16 5 6 4 VA(M) - - - - - - - - - - - - - CB 1 1 - - 1 - - 1 - 1 1 - 2 CB(M) - - - - 1 - - - - - - - - MV 1 2 2 4 1 1 1 2 - - - - 1 MV(M) - - 2 - - - - - - - - - - All concrete 6 12 18 16 17 8 8 8 6 20 6 8 13 All masonry - 4 5 1 4 1 8 2 1 - - - -

NUMBER OF ACCIDENTS/POPULATION(1) (%) Gravity 0.5 1.1 1.0 1.1 2.5 2.0 1.2 6.7 7.1 4.7 - 35.8 N/A Arch - 1.2 12.5 11.8 18.8 8.3 15.3 7.9 12.8 22.5 24.8 76.6 N/A Buttress 1.1 1.4 - - 8.9 - - 11.2 - 25.0 no pop - N/A Multi-Arch 3.0 8.9 22.3 35.8 22.3 89.4 29.8 44.7 - - - - N/A All 0.6 1.3 2.9 3.6 6.3 3.9 6.0 9.0 9.3 14.4 21.5 55.0 N/A

Note (1) Population height ranges from ICOLD(1979) extrapolated to population in ICOLD(1984).

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Figure 2.15 shows the height distribution for the world population at 1984. There

appears to be an exponential like drop in numbers of dams per 10m height range. There

were 26.8% of large dams in the range 20-29m; dropping to 0.6% at 110-119m; and to

0.4% at 140-149m. Note that the range 15-19m had 22.7% due to the smaller height

range (5m c.f. 10m).

Note: No failures for dams 70m or higher

0 1 2 3 4 5 6

15-19

20-29

30-39

40-49

50-59

60-69

(m)

Failures/Population (%)

AllGravityArchButtressMulti-Arch

Figure 2.14. Height of failed dams - failures/population (%)

Page 94: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.61

22.7

26.8

16.7

10.2

7.1

4.9

2.9

2.4

1.6

0.9

0.6

0.5

0.6

0.4

0.6

0.3

0.8

0.0 5.0 10.0 15.0 20.0 25.0 30.0

15-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

100-109

110-119

120-129

130-139

140-149

150-199

>200

Unknown(m)

Percent of Dams

Figure 2.15. World dams - height ranges for all concrete & masonry dams

2.3.4 Age at Failure

Figure 2.16 to Figure 2.18 show the age at failure for all, concrete gravity and masonry

gravity dams. T2 (during first filling) is the most common time for failure to occur.

Concrete gravity dams do appear to have proportionally fewer failures during first

filling than do masonry gravity dams.

The term first filling may be misinterpreted and as such a further analysis was carried

out. All failed dams were assessed to see whether they had failed at their maximum

water level, and whether this was the first time such a level had been reached. The

results of this analysis are given in Table 2.20.

Of the 46 dams assessed 29 had failed at their highest level ever recorded; four were not

at the highest level recorded; and there were 13 cases with insufficient information. For

Page 95: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.62

the unknown cases four were during a flood and can be assumed to be at or near the

highest water level. Of the four that did not fail at their highest recorded water level:

• Bayless (B) had been at the same level the year prior when sliding had also occurred

(Bayless (A));

• Bouzey (B) had been 0.1m higher for over a year;

• Meihua had overtopped by 0.3m previously (0.8m higher than during failure); and

• Leguaseca failed at a low reservoir storage. This multi-arch structural failure was due

to concrete deterioration in the acidic reservoir water.

From this analysis it is clear that the majority of failures have occurred when the

reservoir was at its highest recorded level (which could be defined as ‘first fill’). Note

however, that several of these dams failed at water levels the same or slightly higher

than those previously recorded. The water levels were often reached during a rapid stage

of first filling or during flood. Of those dams where information was available, most

failed within two days of reaching their final water level and several failed within six

hours.

Table 2.16, Table 2.17 and Figure 2.21 show the age at failure versus year

commissioned for various failure modes. Foundation piping failures generally occurred

in the first three years. Exceptions to this were Puentes, Bacino di Rutte and Austin (A).

Puentes, which was commissioned in 1790, failed in first fill which took 11 years.

Bacino di Rutte failed due to piping in the foundation. During first fill a crack appeared

under the dam which was filled. The dam was emptied and the silt removed 13 years

later. The dam failed during refilling of the reservoir. Austin (A) failed due to a

combination of scour, piping and sliding during overtopping at the highest water level

the dam had experienced.

Foundation sliding occurred in less than five years in all but two cases. Zerbino dam

failed after ten years due to scour and sliding during overtopping. Xuriguera failed after

42 years, unfortunately no further details on the failure were available.

Structural sliding was more evenly distributed with five failures occurring after ten

years. One structural tensile/shear failure occurred after 80 years (Khadakwasla Dam

Page 96: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.63

that failed during overtopping due to an upstream dam failure). There are a number of

dams with unknown failure modes. Most of these failed during overtopping events (see

Figure 2.22). Most of the failures that occurred after five years were due to overtopping

(12 compared to 6 non-overtopping). Prior to five years of age non-overtopping failures

were more prevalent (21 compared to 4).

Figure 2.23 shows the age at failure versus year commissioned for different dam types.

Masonry dams appear to have failed at all ages. Concrete dams, with the exception of

the three below, have failed within ten years of commissioning. There is insufficient

information on the exceptions to determine why they failed at a later time.

Kohodiar (India) - Combined concrete gravity/earthfill dam, unknown failure mode.

Xuriguera (Spain) - Concrete gravity dam apparently failed by foundation sliding.

Hauser Lake II (USA) - Concrete gravity dam with no failure information.

Table 2.16. No. of dam foundation sliding & piping failures vs age at failure

Sliding Piping Age at Failure Grav.

Arch Butt. Total Grav.

Arch Butt. Total

T1 During construction

- - - - - - - -

T2 During first fill 3 1 - 4 4 1 3 8 T3 0-5 years 1 - 1 2 - - - - T4 5-10 years 1 - - 1 - - - - T5 10-20 years - - - - - 1 - 1 T6 40-50 years 1 - - 1 - - - - ALL 6 1 1 8 4 2 3 9

Page 97: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.64

Table 2.17. No. of structural (shear or tensile) failures vs age at failure

Age at Failure Grav. Arch Butt. Multi-Arch Total T1 During construction 1 - - - 1 T2 During first fill 1 - 2 1 4 T3 0-5 years - 1 - - 1 T4 5-10 years 2 - - - 2 T5 10-20 years 2 - - - 2 T6 20-30 years - - - 1 1 T7 30-40 years - - - - - T8 40-50 years 1 - - - 1 T9 >50 years 1 - - - 1 ALL 8 1 2 2 13

Page 98: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.65

0 5 10 15 20 25 30 35 40 45

T1 (during const'n)

T2 (first fill

T3 (<5 yrs)

T4 (5-10yrs)

T5 (10-20yrs)

T6 (20-30yrs)

T7 (30-40yrs)

T8 (40-50yrs)

T9 (>50yrs)

T10 (>5yrs, timeunknown)

T11 (unknown)

Percent of Dams

Failure

Accident

Major Repair

Figure 2.16. Age at incident - all dams

Page 99: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.66

Figure 2.24 and Figure 2.25 show age at significant incident versus year commissioned

for different dam types. As expected the accidents/major repairs tend to occur mostly

after 1915. Older incidents are less likely to be recorded. Accidents and major repairs

appear to occur at a later stage than that of failures. The distribution of ages to incident

for both masonry and concrete dams appears to be similar.

Table 2.18 gives the breakdown of incidents in all types of concrete and masonry dams.

0 5 10 15 20 25 30 35

T1 (during const'n)

T2 (first fill

T3 (<5 yrs)

T4 (5-10yrs)

T5 (10-20yrs)

T6 (20-30yrs)

T7 (30-40yrs)

T8 (40-50yrs)

T9 (>50yrs)

T10 (>5yrs, timeunknown)

T11 (unknown)

Percent of Dams

Failure

Accident

Major Repair

Figure 2.17. Age at incident - concrete gravity dams

Page 100: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.67

0 5 10 15 20 25 30 35 40 45

T1 (during const'n)

T2 (first fill

T3 (<5 yrs)

T4 (5-10yrs)

T5 (10-20yrs)

T6 (20-30yrs)

T7 (30-40yrs)

T8 (40-50yrs)

T9 (>50yrs)

T10 (>5yrs, time unknown)

T11 (unknown)

Percent of Dams

Failure

Accident

Major Repair

Figure 2.18. Age at incident - masonry gravity dams

Figure 2.19, Figure 2.20 and Table 2.18 show the time to significant incidents for dams.

The data is presented as the number of incidents in a time period divided by the

population of dams that had survived that time period. The population was taken from

ICOLD (1979) and extrapolated to 1983 dam numbers.

First filling is still the predominant failure time. There appears to be a slight rise in the

rate of failures with time (ignoring T2). After 40 years of age there is a jump in the

failure rate. It should be noted that the older age groups are represented by a small

population

Page 101: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.68

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11

Time to Significant Incident

Inci

dent

s/Po

pula

tion

(%)

FailuresAccidentsMajor Repairs

Figure 2.19. Time to significant incident - gravity dam incidents/population (%)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11

Time to Significant Incident

Inci

dent

s/Po

pula

tion

(%)

FailuresAccidentsMajor Repairs

Figure 2.20. Time to significant incident - all dam incidents/population (%)

Page 102: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.69

Table 2.18. Time to significant incident - incident/population of dams surviving

period (%)

Failures Grav Arch Butt MA Total

Tot 0.90 0.75 2.24 1.87 0.99 T1 0.09 - - - 0.07 T2 0.32 0.25 1.60 0.93 0.41 0-5 0.03 0.13 0.66 - 0.09 5-10 0.16 - - - 0.12 10-20 0.13 0.19 - - 0.13 20-30 0.12 - - 1.52 0.14 30-40 - - - - - 40-50 0.32 0.53 - - 0.32 >50 0.32 - - - 0.24 T10 - - - - - T11 - 0.13 - - 0.02

Accidents Grav Arch Butt MA Total

Tot 1.54 10.69 2.88 14.02 3.47 T1 0.14 0.63 0.64 - 0.26 T2 0.41 2.39 0.32 5.61 0.86 0-5 0.27 1.16 0.99 0.95 0.49 5-10 0.03 - - - 0.02 10-20 0.22 0.19 - - 0.19 20-30 0.25 - - - 0.19 30-40 0.08 0.38 1.09 - 0.18 40-50 0.11 0.53 - - 0.16 >50 0.32 0.53 - - 0.32 T10 0.21 2.06 0.33 3.81 0.62 T11 0.09 4.03 0.32 5.61 0.90

Major Repairs Grav Arch Butt MA Total

Tot 2.06 0.13 3.53 - 1.78 T1 0.06 - 0.64 - 0.09 T2 0.12 - 0.32 - 0.11 0-5 0.18 - - - 0.13 5-10 0.10 - - - 0.07 10-20 0.39 - - - 0.29 20-30 0.37 - 0.87 - 0.33 30-40 0.31 - - - 0.24 40-50 0.43 - 1.49 - 0.41 >50 0.64 0.53 1.49 - 0.65 T10 0.72 - 1.32 - 0.62 T11 0.09 - 0.32 - 0.09

T1: During construction; T2: During first fill; T10: >5 years, else unknown; T11: Unknown.

Page 103: Shear Strength of Rock

Page 2.70

Table 2.19. Time to significant incident

No. Failures Accidents Major Repairs PG PG(M) CB CB(M) VA VA(M) MV ALL PG PG(M) CB CB(M) VA MV(M) ALL PG PG(M) CB VA ALL TOTAL

T1 2 1 - - - - - 3 4 1 1 1 5 - 12 2 - 2 - 4 21 T2 3 8 3 2 2 - 1 19 11 3 1 - 19 - 40 2 2 1 - 5 63 T3 1 - 1 1 - 1 - 4 6 3 3 - 9 - 22 6 - - - 6 32 T4 1 4 - - - - - 5 1 - - - - - 1 2 1 - - 3 9 T5 1 2 - - - 1 - 4 4 1 - - 1 - 6 7 2 - - 9 19 T6 - 2 - - - - 1 3 1 3 - - - - 4 5 1 1 - 7 14 T7 - - - - - - - 0 1 - 1 - 1 - 3 3 1 - - 4 7 T8 1 2 - - - 1 - 4 - 1 - - 1 - 2 3 1 1 - 5 11 T9 1 2 - - - - - 3 1 2 - - 1 - 4 3 3 1 1 8 15 T10 - - - - - - - 0 6 1 1 - 16 2 28 16 8 4 - 28 56 T11 - - - - 1 - - 1 3 - 1 - 32 - 42 3 - 1 - 4 47

10 21 4 3 3 3 2 46 38 15 8 - 85 2 164 52 19 11 1 83 294

Page 104: Shear Strength of Rock

Page 2.71

Table 2.20. Details of dam failure water levels

Dam Name Dam

Type

Year

Com.

Year

Fail

Fail

Type

Fail

Mode

MWL

(m)

Height

at fail

(m)

Highest

record

level?

Height

above previous

Time

(hrs)

Comments

Torrejon-Tajo PG 1967 1965 Fa SH DNA

Zerbino PG 1925 1935 Faf S/SC 10 15 Y ≈5m >FSL

Large flood caused overtopping.

Mohamed V PG 1966 1963 Fb ? DNA

Elwha River PG 1912 1912 Ff P 31 31 Y 1st fill 240 Failure occurred 10 days after pond was first filled.

Xuriguera PG 1902 1944 Ff S

Bayless (A) PG 1909 1910 Ff S 12.5 12.5 Y 1st fill 48 Failed 2 days after spillway began discharging.

Bayless (B) PG 1909 1911 Ff S 12.5 12.5 N <6 Was at this level previous year when failure A occurred. Failed at 2-2:30 on day the reservoir filled.

St Francis PG 1926 1928 Ff S 61 61 Y 1st fill 170 Gradual first fill.

Hauser Lake II PG 1911 1969 ? ? DNA

Kohodiar PG/TE 1963 1983 ? ? DNA

Fergoug I PG(M) 1871 1881 Fa SC >43 Y Flood due to failure of Habra dam.

Fergoug II PG(M) 1885 1927 Fa SC? >43 Y Flood due to failure of Habra dam.

Sig PG(M) 1858 1885 Fa SC? Y Flood due to failure of Cheurfas dam.

Santa Catalina PG(M) 1900 1906 Fa ?

Cheurfas PG(M) 1884 1885 Fb ? Y 1st fill

Granadillar PG(M) 1930 1933 Fb ?

Bouzey PG(M) 1881 1895 Fb T 19.7 19.6 N 0.1m >1 year Had been at 19.7m for over a year previously.

Khadakwasla PG(M) 1879 1961 Fb T/SH 28 32.7 Y* 3.9m 4 Flood due to failure of Panshet dam.

Page 105: Shear Strength of Rock

Page 2.72

Dam Name Dam Type

Year Com.

Year Fail

Fail Type

Fail Mode

MWL

(m)

Height at fail

(m)

Highest record

level?

Height above

previous

Time (hrs)

Comments

* Overtopped by 2.7m and failed when overtopping had receded to 1.8m.

Habra (B) PG(M) 1872 1881 Fba T/SH 33 36.9 Y Overtopping.

Angels PG(M) 1895 1895 Ff P

Tigra PG(M) 1917 1917 Ff S 27.1 26.7 Y 1.1m 0.5 Spillway section overtopped by 1.1m. Whole dam overtopped by 0.15m.

Austin (A) PG(M) 1893 1900 Ff SC/P/S 20.7 24.1 Y 0.4m Flood overtopped dam by 3.4m.

Puentes PG(M) 1791 1802 Ffb P >47 47 Y 1st fill* *1st fill took 11yrs. Dam filled from 22-47m in final 4 mths.

Kundli PG(M) 1924 1925 Fm ? Y 1st fill Rapid 1st fill due to floods.

Chickahole PG(M) 1966 1972 Fm T 27.4 26 ? Flood rise of 1.5m immediately prior to failure.

Gallinas PG(M) 1910 1957 Fm/Fa ? Y Overtopped by record flood.

Lynx Creek PG(M) 1891 1891 Fm ? Flood.

Pagara PG(M) 1927 1943 Fmb T? 28.7 30 Y 1.3m <12 Overtopped by 0.4m in flood.

Habra (A) PG(M) 1871 1872 Fmb T/SH 33 Y Flood after 1st fill.

Habra (C) PG(M) 1881 1927 Fmb T/SH 33 37 Y Flood overtopped, largest since repair.

Elmali I PG(M)/TE 1892 1916 Fa ? Overtopped.

Lower Idaho Falls

ER/PG(M) 1914 1976 Fa ? Y Overtopped from upstream failure of Teton.

Vaughn Creek VA 1926 1926 Ff P 17 17 Y 1st fill 48

Malpasset VA 1954 1959 Ff S 66 65.7 Y* 3 * Just previously exceeded this by ≈ 0.1m for 3 hours.

Moyie River VA 1924 1926 Ffa SC 14 16-18 Y 2-4m Storm and upstream dam failure flood overtopped dam.

Page 106: Shear Strength of Rock

Page 2.73

Dam Name Dam Type

Year Com.

Year Fail

Fail Type

Fail Mode

MWL

(m)

Height at fail

(m)

Highest record

level?

Height above

previous

Time (hrs)

Comments

Meihua VA(M) 1981 1981 Fb 21.5 N Previously overtopped by 0.3m (0.8m > than at failure).

Bacino di Rutte VA(M) 1952 1965 Ff D/P 12 Y* <48 * Highest since sediment removed. Dam had been filling for 2 days.

Ashley CB 1908 1909 Ff P 17 17 Y 1st fill >1 Just spilling when pipe failed.

Stony Creek CB (Ambursen)

1913 1914 Ff P 13 13 ? Unsure how long at this level or if it had been higher. Dam in service 6 months.

Komoro CB 1927 1928 Ff S/P No suggestion of high water level.

Overholser CB (Ambursen)

1920 1923 Ffa SC Y Overtopped in flood.

Austin (B) CB(M) 1915 1915 Fba SH Y 3 Highest since rebuilt.

Vega de Tera CB(M) 1956 1959 Fm T/C 33 33 Y 1.75m <0.5 Previous year was at 31.25m. Flood had just completed 1st fill. “The dam reportedly was breached at the moment of topping of the crest”

Selsfors CB/TE 1943 1943 Ff P 20 18.2 Y 1st fill ≈ 6

Gleno MV 1923 1923 Fb T/C 32 32 Y 1st fill 1 month Had been at full supply level for ≈ 1 month.

Leguaseca MV 1958 1987 Fb T/C N “low reservoir storage”

Page 107: Shear Strength of Rock

Page 2.74

T3T4T5

T6

T7

T8

T9

0

10

20

30

40

50

60

70

80

90

100

1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

Year Commissioned

Age

(yea

rs)

Structural

Structural (T1 or T2)

Fndn Sliding

Fndn Sliding (T1 or T2)

Fndn Piping

Fndn Piping (T1 or T2)

Unknown

Unknown (T1 or T2)

T1- During constructionT2- First Fill

Figure 2.21. Failure mode: age at failure versus year commissioned (all dams)

Page 108: Shear Strength of Rock

Page 2.75

T9

T8

T7T6

T5T4T30

10

20

30

40

50

60

70

80

90

100

1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000Year Commissioned

Age

(yea

rs)

?

Over Topping

Non-Over Topping

T1- During constructionT2- First Fill

Figure 2.22. Over topping: age at failure versus year commissioned (all dams)

Page 109: Shear Strength of Rock

Page 2.76

T9

T8

T7

T6

T5

T4T3

0

10

20

30

40

50

60

70

80

90

100

1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

Year Commissioned

Age

(yea

rs)

Concrete Gravity

Masonry Gravity

Concrete Buttress

Masonry Buttress

Concrete Arch

Masonry Arch

Concrete Multi-Arch

T1- During constructionT2- First Fill

Figure 2.23. Dam type: age at failure versus year commissioned

Page 110: Shear Strength of Rock

Page 2.77

0

10

20

30

40

50

60

70

80

90

100

1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

Year Commissioned

Age

(yea

rs)

Fail - Concrete GravityFail - Masonry Gravity

Fail - OtherAcc/MR - Concrete Gravity

Acc/MR - Masonry GravityAcc/MR - Other

Figure 2.24. Age at significant incident versus year commissioned

Page 111: Shear Strength of Rock

Page 2.78

0

10

20

30

40

50

60

70

80

90

100

1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Year Commissioned

Age

(yea

rs)

Fail - Concrete Gravity

Fail - Masonry GravityFail - Other

Acc/MR - Concrete GravityAcc/MR - Masonry Gravity

Acc/MR - Other

Figure 2.25. Age at significant incident versus year commissioned

Page 112: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.79

2.3.5 Incident Causes

Table 2.21 shows that failures in the foundation are much more common in concrete

dams than in masonry dams (47% compared to 19% and 68% compared to 22% when

combined failure types, Ff, Ffa and Ffb, are included). Failures due to the dam body or

materials are more common in masonry dams.

Table 2.21. Failure types

Dam Type Ff Fb Fa Fm Ffa Ffb Fbm Fba Unknown PG 5 1 1 1 2

PG(M) 3 4 5 4 1 3 1 VA 1 2

VA(M) 1 1 1 CB 3 1

CB(M) 1 1 1 MV 2

Total Concrete

9 (47)

3 (16)

1 (5)

- 4 (21)

- - - 2 (11)

Total Masonry

5 (19)

5 (19)

5 (19)

6 (22)

- 1 (4)

3 (11)

2 (7)

-

Total All 14 (30)

8 (17)

6 (13)

6 (13)

4 (9)

1 (2)

3 (7)

2 (4)

2 (4)

NOTE: Figures in brackets are percentages for each dam type.

Tables D1 to D3 in Appendix D give the incident causes for all dams, concrete gravity

dams and masonry gravity dams respectively. These have been derived from the ICOLD

failure causes terminology shown in Section 2.2.3.8.

Table 2.22 to Table 2.24 show the most common causes of incidents to all dams,

concrete gravity dams and masonry gravity dams respectively. It should be noted that

the ‘percentage of dams’ column can total more than 100% since there can be more than

one cause for each incident.

Page 113: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.80

Table 2.22. Main causes of incidents in all dams

Rank Code Description No % of Dams FAILURES

1 3.4.6 Overtopping 10 22 2 3.4.2 Uplift 8 17 3 1.1.4 seepage in the foundation 7 15 4 1.1.5 piping through the foundation 6 13 5 4.7.1 excess rates of flow 6 13

ACCIDENTS 1 1.1.4 seepage in the foundation 16 9 2 4.8 local scour 16 9 3 1.1.5 piping through the foundation 13 7 4 4.7.1 excess rates of flow 13 7 5 4.11.6 discharge equipment malfunction 10 6

MAJOR REPAIRS 1 1.2.3 freezing and thawing 53 20 2 1.3.4 external temperature variation 28 11 3 1.2.2 reaction between concrete & environment 22 8 4 1.2.8 concrete permeability 22 8 5 3.2.2 reaction between masonry & environment 22 8

Overtopping, uplift and foundation seepage and piping are the most common causes of

failure for all dams combined. Foundation problems (shear and seepage) are the major

cause of failures for concrete gravity dams. Masonry gravity dams have more failures

due to overtopping. Seepage and flow problems are the main causes of accidents whilst

concrete reactions, temperature and freeze-thaw cause the most major repairs. These

types of major repairs tend to cause only surficial damage.

Page 114: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.81

Table 2.23. Main causes of incidents in concrete gravity dams

Rank Code Description No % of Dams FAILURES

1 1.1.3 shear strength in the foundation 4 40 2 1.1.4 seepage in the foundation 4 40 3 1.3.2 Uplift 2 20 4 4.7.1 excess rates of flow 2 20

ACCIDENTS 1 1.1.5 piping through the foundation 8 18 2 1.1.4 seepage in the foundation 7 16 3 4.6 due to structural behaviour 7 16 4 4.7.1 excess rates of flow 5 11 5 4.11.6 discharge equipment malfunction 5 11

MAJOR REPAIRS 1 1.2.3 freezing and thawing 40 24 2 1.2.2 reaction between concrete & environment 15 9 3 1.2.8 concrete permeability 15 9 4 1.3.2 Uplift 15 9 5 4.2.12 concrete erosion by abrasion 13 8

Table 2.24. Main causes of incidents in masonry gravity dams

Rank Code Description No % of Dams FAILURES

1 3.4.6 Overtopping 8 38 2 3.4.2 Uplift 7 33 3 2.3.9 upstream dam collapse 5 24 4 3.5.2 tensile stresses 5 24

ACCIDENTS 1 3.4.2 Uplift 6 35 2 3.5.2 tensile stresses 3 18 3 3.1.4 seepage in foundation 2 12 4 3.2.8 mortar permeability 2 12 5 3.2.9 masonry construction (including order) 2 12

MAJOR REPAIRS 1 3.2.2 reaction between masonry & environment 20 51 2 3.2.8 mortar permeability 10 26 3 3.1.4 seepage in foundation 8 21 4 3.2.3 freezing and thawing 8 21 5 3.4.1 hydrostatic, silt and ice pressure 5 13

Page 115: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.82

When all the dams were analysed together, similar incident codes were grouped

together to better distinguish the main causes of incidents. Only ‘significant incidents’

were included. The incidents were separated into those with soil foundations and those

with rock or unknown foundations. Figure 2.26, Table 2.25 and Table 2.26 show the

results of this analysis. Table 2.25 only shows results for failures of dams with soil

foundations. There were only three dam accidents where the dam was known to have a

soil foundation. The results show that piping was the predominant cause of failure for

dams with soil foundations.

For dams with rock or unknown foundations, the major cause of failure was overtopping

followed by shear strength of the foundation. Piping was the sixth most common cause

of failure with five cases noted. The causes of accidents for dams with rock or unknown

foundations were seepage, scour, piping, permeability in the concrete and tensile

stresses in the dam body. Major repairs were caused by reactions of the

masonry/concrete with the environment, concrete/masonry permeability and

construction methods.

Table 2.25. Main failure causes for dams with soil foundations

Rank ICOLD Codes Description No % of Dams

1 1.1.5, 3.1.5, 4.1.5 internal erosion in the foundation (piping)

6 67

2 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 2 22 2 1.1.9, 3.1.9, 4.1.8 foundation preparation 2 22

Page 116: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.83

Table 2.26. Main significant incident causes for dams with rock or unknown

foundations

Rank ICOLD Codes Description No % of Dams

FAILURES 1 1.3.7, 3.4.6 overtopping 12 32 2 1.1.3, 3.1.3, 4.1.3 shear strength in the foundation 8 22 3 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 7 19 3 1.4.2, 1.5.2, 3.5.2 tensile stresses in the concrete/masonry 7 19 5 4.7.1 excess rates of flow (3 due to overtopping) 6 16 6 1.1.5, 3.1.5, 4.1.5 internal erosion in the foundation (piping) 5 14 6 1.2.6, 1.3.6 shear strength of concrete/masonry 5 14

ACCIDENTS 1 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 18 11 2 4.8 local scour 15 9 3 1.1.5, 3.1.5, 4.1.5 internal erosion in the foundation (piping) 13 8 3 1.2.8, 3.2.8, 4.2.6 permeability in the concrete/masonry 13 8 3 1.4.2, 1.5.2, 3.5.2 tensile stresses in the concrete/masonry 13 8

MAJOR REPAIRS 1 1.2.2, 3.2.2,

4.2.2, 4.4.1 reaction between concrete/masonry & environment

21 26

2 1.2.8, 3.2.8, 4.2.6 permeability in the concrete/masonry 16 20 2 1.2.9, 1.2.10,

3.2.9, 4.2.7 method of construction (including cooling) 16 20

4 1.2.3, 3.2.3, 4.2.3 freezing and thawing 12 15 5 1.2.11, 3.2.10,

3.3.2, 4.2.10 structural joints in concrete/masonry 10 12

6 1.1.4, 3.1.4, 4.1.4 seepage in the foundation 9 11

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Analysis of Concrete and Masonry Dam Incidents Page 2.84

Failure modes for incidents involving the foundation will be discussed further in

Section 2.3.8. For the failures in the dam structure the following was noted:

• The numbers of structural failures attributed to ‘poor construction’ and ‘design

flaws’ were similar. There was difficulty in separating design and construction

problems as, in many cases, both contributed to the failure.

• Only one concrete gravity dam failed due to an inadequacy in the structure. The dam

(Torrejon-Tajo, Spain) failure cause was traced to organics present in the aggregate,

and filling of the dam by a flood during construction before the concrete had fully

set.

• Overtopping preceded 5 of the failures.

• The majority of the failure cases were masonry gravity dams, probably reflecting the

quality of construction and materials.

Page 118: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.85

0 5 10 15 20 25 30 35

fndn shear strength

fndn seepage

fndn piping

overtopping

excess flow rates

local scour

upstream dam fail

tensile stresses

structural joints

mat shear strength

mat tensile strength

compressive strength

construction method

mat permeability

enviro & mat reaction

freeze/thaw

Percent of Incidents

Failure

Accident

Major Repair

Figure 2.26. Causes of significant incidents (rock & unknown foundations)

Page 119: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.86

0 1 2 3 4 5 6 7

fndn seepage

fndn piping

fndn preparation

uplift

overtopping

shape of dam

structural joints

mechanical strength

discharge malfunction

Number of Incidents

Failure

Accident

Figure 2.27. Causes of significant incidents (soil foundations)

2.3.6 Monitoring and Surveillance Data

2.3.6.1 Using ICOLD Terms

Overtopping was the most common failure warning type followed by dam leakage and

no warning. However, as can be seen from Table 2.27 it is masonry dams which are

most susceptible to overtopping. Dam leakages followed by cracking were the most

prevalent warning in accidents. Major repairs tended to have been prompted by dam

leakage or concrete deterioration. It appears that the accidents and major repairs tend to

have a ‘structural’ warning that can be noticed, whereas the failure warnings are more

difficult to notice. Figure 2.28 and Figure 2.29 show the warning types for concrete

gravity dam and all dam incidents respectively.

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Analysis of Concrete and Masonry Dam Incidents Page 2.87

Table 2.27 to Table 2.29 show the warning types for failures, accidents and major

repairs for each dam type. It should be noted here that there can be more than one

warning type per dam failure.

From Section 2.3.5, it appears that the accidents and major repairs generally occur

where there has been obvious signs of distress (e.g. surficial damage, uplift records,

seepage monitoring). Whether these problems may signal potential instability in the

dam is questionable. For example, it is unlikely that cavitation damage in a spillway will

lead to failure of the dam. Failures have occurred where it is likely that little warning

was given or where the least amount was known, that is, in the foundation.

0 5 10 15 20 25 30 35 40 45

None

Foundation piping

Foundation leak

Dam leak

Move, horizontal

Move, vertical

Cracking

AAR

Conc. deterioration

Scour

Overtopping

Downstream slide

Uplift develop

Percent of Incidents

FailureAccidentMajor Repair

Figure 2.28. Warning types - gravity dams

Page 121: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.88

0 5 10 15 20 25 30 35 40

None

Foundation piping

Foundation leak

Dam leak

Move, horizontal

Move, vertical

Cracking

AAR

Conc. deterioration

Scour

Overtopping

Downstream slide

Uplift develop

Percent of Incidents

FailureAccident

Major Repair

Figure 2.29. Warning Types - All Dams

Page 122: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.89

Table 2.27. Warning types vs dam type - failures

Warning Type PG

PG(M) CB CB(M) VA VA(M) MV Total

None 1 3 - 1 - - 1 6 Foundation piping - 2 1 - 2 - - 5 Foundation leak 1 1 1 - 3 - - 6 Dam leak 3 2 2 - - 1 1 9 Move, horizontal 2 2 - - 1 - - 5 Move, vertical - - 1 - - - - 1 Cracking 2 - 1 - 1 1 1 6 AAR - - - - - 1 - 1 Conc deteriorate - - - - - - 2 2 Scour - 2 - - - - - 2 Overtopping 1 11 1 1 1 1 - 16 Downstream slide - - - - - - - - Uplift develop - - - - - 1 - 1 Unknown 4 2 - 1 - - - 7

Total 14 25 7 3 8 5 5 67

Table 2.28. Warning types vs dam type - accidents

Warning Type PG

PG(M)

CB

CB(M) VA

MV MV(M) Total

None 1 - 1 - 2 - - 4 Foundation piping 5 - 1 - 1 - - 7 Foundation leak 7 1 1 - - - - 9 Dam leak 6 9 1 - 2 - - 18 Move, horizontal 3 1 - - 3 - - 7 Move, vertical 2 2 - - 4 - - 8 Cracking 3 5 2 - 4 - - 14 AAR - - - - - - - 0 Conc deteriorate - - 1 - - - - 1 Scour 3 1 - - - - - 4 Overtopping 2 2 - 1 - - - 5 Downstream slide 3 - - - - - - 3 Uplift develop 2 1 - - 1 - - 4 Unknown 20 4 4 - 77 17 2 124

Total 57 26 11 1 94 17 2 208

Page 123: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.90

Table 2.29. Warning types vs dam type - major repairs

Warning Type PG

PG(M)

CB

CB(M) MV MV(M) Total

None - - - - - - - Foundation piping 1 1 - - - - 2 Foundation leak 7 4 - - - - 11 Dam leak 17 10 4 - - - 31 Move, horizontal 1 - 1 - - - 2 Move, vertical - - - - - - - Cracking 9 1 6 - - - 16 AAR 4 - 1 - - - 5 Conc deteriorate 18 7 2 - - - 27 Scour 2 - - - - - 2 Overtopping 2 - - - - - 2 Downstream slide 4 - - - - - 4 Uplift develop 3 1 - - - - 4 Unknown 110 21 21 2 6 1 161

Total 178 45 35 2 6 1 267

2.3.6.2 Details of Warnings

Warnings prior to dam failures are very important as they allow for the possibility of

either preventing the failure if detected early enough or, importantly, they allow time for

people downstream to be notified and evacuated. A warning, even a few hours prior to

failure, can have a major effect on loss of life. Table 2.31 was created to describe each

of the failures and their warnings. A subjective warning rating was given to each failure.

The ratings were taken as to whether a dam failure had a sufficient warning which could

have led to people downstream being advised of the impending failure. Table 2.31 also

includes information on the failure type and failure mode.

Many of the dam failures had limited information and as such could not be given a

warning rating. Table 2.30 shows the results for this analysis.

Page 124: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.91

Table 2.30. Warning ratings for failed dams

Warning Rating Number of Dams Yes 10 No 1

Maybe 9 Dam failure upstream 5

Flood 5 Unknown 16

Ashley Dam was the only dam where the failure signs were deemed insufficient to

allow a warning to be given. There was some seepage 1.5 to 2 hours prior to failure but,

the time was insufficient to allow for a warning to be given. Failure occurred through

the alluvial foundation. Selsfors Dam had a small seepage 4.25 hours prior to collapse.

The seepage increased slowly for 0.5 hour and then rapidly. The signs may have been

enough to give a limited warning.

An important note to come from this analysis is that most of the warnings comprised a

rapid increase in flow prior to failure. Quantity of flow appears not to be as critical.

Table 2.32 shows a similar analysis for significant accidents. Most of the accidents gave

signs of problems developing. Blackbrook II did not, as the accident was caused by an

earthquake. Bhandardara Dam which went close to failure through the dam body had

insufficient warning. Cracking occurred quickly at a flood level slightly higher than that

recorded previously.

Page 125: Shear Strength of Rock

Page 2.92

Table 2.31. Details of dam failures and descriptions of warnings

Dam Name Dam Type

Fail Type

Fail Mode

Failure Description Warning Description Warning Rating

Torrejon-Tajo PG Fa SH Failure of outlet gate. No details available ?

Zerbino PG Faf S/SC Scour due to overtopping, followed by foundation failure (sliding or overturning)

No details available, but some warning issued - “Despite warnings, the flood drowned 100 people”. Large scour occurred in power plant tunnel in 1928 (same rock).

M

Mohamed V PG Fb ? No details available No details available ?

Elwha River PG Ff P Piping through alluvial sand and gravel during construction of cutoff. Dam was completed and reservoir part filled before cutoff construction.

Leakage into caisson for cutoff. Failed in 1.5 hours.

M

Xuriguera PG Ff S No details available No details available ?

Bayless (A) PG Ff S Left half of dam moved 450mm downstream at base, 790mm at top by sliding on foundation.

Landslide left abutment downstream, large leakage 4.5-15m downstream of dam 12 days before dam failed.

Y

Bayless (B) PG Ff S Rapid failure of most of dam by sliding and overturning. Previous failure 8 months before. No remedial action taken.

Y

St Francis PG Ff S Sudden failure in foundation due to “softening of conglomerate” or sliding on existing landslide or foliation surface in schist.

Foundation seepage measured as reservoir rose to 1-2ft3/sec (30-60l/sec) or 6-9hrs before failure water level recorder dropped 0.1m in ½ hour before failure. (There is a suggestion that this was due to the tilting of the dam, but in any case it would have acted as a warning.) Some evidence of cracking in foundation 2 months before failure (due to landslide in abutment).

Y/M

Hauser Lake II

PG ? ? No details available. No details available. ?

Kohodiar PG/TE ? ? No details available. No details available. ?

Fergoug I PG(M) Fa SC 50m spillway section scoured by flood and failed. Flood caused by failure of Habra dam upstream. DF

Page 126: Shear Strength of Rock

Page 2.93

Dam Name Dam Type

Fail Type

Fail Mode

Failure Description Warning Description Warning Rating

Fergoug II PG(M) Fa SC? 125m section failed during flood. Flood caused by failure of Habra dam upstream. DF

Sig PG(M) Fa SC? Overtopped in flood. Founded on gravel. Flood caused by failure of Cheurfas dam upstream 2 hours before.

DF

Santa Catalina PG(M) Fa ? Overtopping. No details available. No details available. ?

Cheurfas PG(M) Fb ? No details available. ICOLD cite piping in foundation as cause, but failure in dam, which is inconsistent.

No details available. ?

Granadillar PG(M) Fb ? Failure of dam due to inadequate cross section. No data available. ?

Bouzey (B) PG(M) Fb T Sudden tensile/compressive and overturning failure. Failure surface slope gently 3.5m from upstream face, then steeply. Crush and shear marks near downstream face.

Dam had leaked badly in foundation and moved up to 0.34m downstream 11 years before failure. Repairs had been carried out 3 years before, and crest deflection 25mm observed. No warning immediately before failure.

Y

Khadakwasla PG(M) Fb T/SH Failure in masonry. Tensile/compression probably enhanced by stress concentration due to sudden change in foundation elevation.

Dam was overtopped for 4 hours prior to failure, and was vibrating. Flood due to failure of Panshet dam upstream 7 hours prior to breach.

DF

Habra (B) PG(M) Fba T/SH Sudden failure in masonry during flood. No warning immediately before failure (flood). F

Angels PG(M) Ff P Piping in (soil?) foundation. No data available. ?

Puentes PG(M) Ffb P Piping failure through alluvium in foundation. Leakage from fndn noted just over 0.5hr prior to failure. Just prior to failure there was a large explosion from the discharge wells and a large increase in leakage. It is said that the dam emptied in 1hr. A messenger was sent to warn the town of Lorca when the leakage was first noted (by bike) but was overtaken by the flood wave.

M

Tigra PG(M) Ff S Sliding on weak shale (?) seam in foundation under flood level. Dam overtopped by 0.15m only so overtopping itself unlikely to be critical re scour, but may have affected uplift inside dam.

Dam went overtopped ½ hour before failure. F

Austin (A) PG(M) Ff SC/P/S

Sliding on weak seam in foundation of two 80m long sections of the spillway, moved downstream 20m.

Whirlpools in storage 1 year before, 2m scour at toe of spillway section of dam. Failed in 3 minutes

Y

Page 127: Shear Strength of Rock

Page 2.94

Dam Name Dam Type

Fail Type

Fail Mode

Failure Description Warning Description Warning Rating

during flood of record.

Kundli PG(M) Fm ? Failure attributed to “green” uncured lime mortar masonry. No data available. ?

Chickahole PG(M) Fm T Sudden tensile/overturning failure. Flood rise of 1.5m immediately prior to failure.

No warning immediately prior to failure. Cracking of dam occurred during consolidation grouting of foundation.

M

Gallinas PG(M) Fm/Fa ? Overtopped and “washed out” (no details). No data available. “Early warnings … credited with preventing loss of life”.

M

Lynx Creek PG(M) Fm ? Failure in masonry in flood. No details available. ?

Pagara PG(M) Fmb T? Overtopping. No additional details. No data available. ?

Habra (A) PG(M) Fmb T/SH Sudden failure in foundation or masonry during overtopping by flood.

No warning immediately before failure (“large leakage” in dam on first filling but had reduced).

Y

Habra (C) PG(M) Fmb T/SH Sudden failure in masonry during flood. Flood no details about any warnings but, “reportedly did not result in a loss of human lives because of adequate advance warnings”.

F

Elmali I PG(M)/TE

Fa ? Overtopped. No data available. No data available. ?

Lower Idaho Falls

ER/PG(M)

Fa ? Overtopped due to failure of Teton dam upstream. Failure of Teton dam 96km upstream. DF

Vaughn Creek VA Ff P Foundation piping and arch concrete failure. Considerable flow below west abutment, followed by settlement and sliding of abutment and in a short time, its overturning.

Some seepage in abutment on first filling. Very large and serious leakage just before failure through abutment.

Y

Malpasset VA Ff S Sudden shear failure in foundation controlled by geology and uplift.

Failure very rapid. Seepage in abutment on first filling 15 days, and more 2 days before failure. 17mm displacement of dam base compared to estimated 10mm.

M

Moyie River VA Ffa SC Spillway scoured and undermined left abutment dam left standing.

No details available, but scour should have been evident.

F

Meihua VA(M) Fb ?

Page 128: Shear Strength of Rock

Page 2.95

Dam Name Dam Type

Fail Type

Fail Mode

Failure Description Warning Description Warning Rating

Bacino di Rutte

VA(M) Ff D/P Foundation seepage and movement causing crack to open upstream of dam on first filling. Crack sealed. Dam operated for 13 years, but failed when sediment removed from reservoir and dam refilled. Failure was piping initiated along crack, giving breach 12m by 2m into which dam collapsed.

Prior seepage, observation of cracks in foundation, and displacement.

Y

Ashley CB Ff P Piping failure in fine sand with a little clay and gravel, 6m deep below cutoff.

Seepage in foundation noted 1.5-2 hours before piping failure.

N

Stony Creek CB Ff P Piping in foundation followed by settling of dam, cracking and collapse of dam.

Large leakage through weep holes in floor of the dam 24 hours before flow developed rapidly in last 20 minutes before failure.

Y

Komoro CB Ff S/P Failure due to softening of volcanic ash in foundation. Unclear whether piping, sliding or both.

No details available. ?

Overholser CB Ffa SC Overtopping. Scour of abutment. No details available. ?

Austin (B) CB(M) Fba SH Flood destroyed 20 gates of masonry dam, and filled tailrace and draft tubes with debris.

Flooding F

Vega de Tera CB(M) Fm T/C Structural failure of masonry buttress. No warning noted. “Heavy leakage” occurred through masonry but may have been unrelated.

M

Selsfors CB/TE Ff P Piping in foundations fluvioglacial sand, followed by collapse of dam into void.

Small seepage into abutment 4.25 hours prior to failure, increased slowly for 0.5 hour, then rapidly.

M/N

Gleno MV Fb T/C Rapid structural failure of multiple buttress arch dam attributed to weakness in poor quality supporting masonry.

Leakage through dam and on the cut off between dam and foundation during and after construction. Leakage increased markedly in the days before failure up to 50l/sec.

Y

Leguaseca MV Fb T/C Structural failure of an arch due to concrete deterioration in acidic reservoir water.

No details available (concrete deterioration). M

Page 129: Shear Strength of Rock

Page 2.96

Table 2.32. Details of dam significant accidents and descriptions of warnings

Dam Name Dam Type

Fail Type

Fail Mode

Hd/ W

Failure Description Warning Description Warning

Rating

Bingham PG Fa SC ? Spillway failed by overturning due to piping and erosion of the weathered foundation rock.

No details available. ?

Wilbur PG Fa ST ? Overtopping of dam caused damage to power station downstream. Dam was not damaged.

Flood F

Upper Glendevon

PG Ff/Fb P 1.32 Leakage of 25l/sec on first filling, giving high uplift. Leakage through foundation of 25l/sec on first filling.

Y

Mequinenza PG Ff S 0.6 Weak bedding surfaces in limestone, lignite and marl exposed during construction, led to strengthening works being built before the dam was completed.

Horizontal and vertical movements anticipated but did not occur because dam was strengthened before completion.

Y

Aguilar PG Ff P 1.25 Piping of clay filled joint in limestone foundation giving leakage of 50l/sec.

Leakage in joint in foundation of 50l/sec. Y

Villagarcia PG Ff P ? Leakage and piping through rock foundation of up to 100l/sec on first filling.

Leakage up to 100l/sec in foundations Y

Hales Bar PG Ff P 1.61 Leakage through karst limestone foundation, reaching 47600l/sec (47.6m3/sec) 27 years after construction. Many attempts to stop leakage failed, dam abandoned 51 years after construction.

Leakage up to 47600l/sec, whirlpools in reservoir, boils downstream.

Y

Woodbridge (A)

PG Ff P ? Piping of alluvial foundation. No details available. ?

Zardezas PG Ff S ? Foundation slide during construction. No details available. ?

Don Marco PG Ff S 1.44 Scour of foundations due to spillway, and sliding of dam on weak zone in foundation rock.

Sliding of dam, erosion of downstream foundation.

Y

Castrelo PG Ff S ? Landslide from abutment onto power station outlet. Landslide in abutment. Y

Burrinjuck (C)

PG Ffa S 1.57 Rock slide in spillway channel partly damaged outlet works. No details available. ?

Page 130: Shear Strength of Rock

Page 2.97

Dam Name Dam Type

Fail Type

Fail Mode

Hd/ W

Failure Description Warning Description Warning

Rating

Great Falls Generating Station (A)

PG Ff P ? Leakage through a narrow ridge in reservoir which increased from 560l/sec on first filling, to 12600l/sec over 20 years. Leakage was through limestone interbedded with shale.

Leakage began at 560l/sec, increasing steadily each year at 640l/sec/year to 14 years after filling, and 840l/sec/year to 12600l/sec, 24 years after filling. Leakage was from 19 areas.

Y

Dworshak PG Fm CR/L 1.25 Thermal cracking which developed to give up to 380l/sec leakage into the drainage gallery.

Cracking prior to initial filling, remained small for 9 years, then suddenly opened to give 380l/sec leakage.

M

Jandula PG(M) Fa T/SH ? Overtopped by flood to a depth of 0.15m. Flood overtopping. F

New Croton PG(M) Fa CR 1.5 Cracking of spillway concrete due to vibration by floodwater over flashboards on top of the dam.

Flood, cracking in spillway, vibration and leakage up to 9l/sec.

F

Blackbrook II PG(M) Fb CR 1.25 Earthquake caused cracking of parapit wall. Temporary increase in foundation seepage.

Cracking of dam, increased foundation seepage and earthquake itself.

N

Mulshi PG(M) Fb L/SH ? Leakage through dam increased to 42l/sec, analysis showed inadequate stability. Mortar quality was an issue.

Leakage through dam increased from 3.6l/sec 28 years after construction to 42l/sec 11 years later.

Y

Thokarwadi PG(M) Fb L/SH ? Fine cracks right through dam on abutments. 200l/sec leakage from weep holes drilled low down on downstream face.

Fine cracks through dam on abutments. 200l/sec flow from weep holes drilled in downstream face near foundation.

Y

Walman PG(M) Fb L/SH ? Leakage at many places, maximum 280l/sec. Leakage at many places up to 280l/sec. Y

Bhandardara PG(M) Fb T/SH 1.15 Cracking of dam due to tensile failure of masonry under slightly higher flood level from previously. Also greatly increased leakage in dam. Dam must have gone very close to collapse.

Leakage through dam for 43 years less than 1.8l/sec. Suddenly increased to 870l/sec at dam/foundation interface and 150mm diameter hole in dam “as a powerful jet” (1 day after flood level reached). Cracking of dam located from upstream to downstream face.

N

Gela (A) PG(M) Fb L/SH ? “Considerable seepage” through dam into inspection gallery. “Considerable seepage” through dam into inspection gallery.

Y

Page 131: Shear Strength of Rock

Page 2.98

Dam Name Dam Type

Fail Type

Fail Mode

Hd/ W

Failure Description Warning Description Warning

Rating

El Gasco (A) PG(M) Fba ? Flood overtopped dam, saturated clay and rock filling between two outer masonry walls.

No data available. ?

Bouzey (A) PG(M) Ff S 1.66 135m length of dam slid up to 0.34m downstream. Foundations disturbed up to 3m below dam.

Spring discharges in foundation 50-75l/sec 2 ¼ years before accident, increasing to 230l/sec after accident.

Y

Shirawata PG(M) Fmb L/SH ? Leakage through dam increased to 600l/sec 10 years after construction. Mortar quality was an issue.

Leakage through dam increased from first filling to 600l/sec 10 years after construction.

Y

Olef CB Fbm CR Tensile cracking of buttress dam during curing of concrete in construction.

Cracking of concrete. Y

Estremera CB Ff P “High leakage” through alluvial foundation with solution of gypsum.

“High leakage” through foundation. Y

Ayers Islands CB Fm CR/L Concrete deterioration by freeze-thaw until a hole formed in buttress slab concrete.

Concrete deterioration, hole formed, leakage of dam.

M

Austin (C) CB(M)/PG(M)

Fa ST Spillway piers destroyed during flood and hollow concrete dam section partly destroyed.

Flood. Dam previously damaged and foundations scoured.

F

Austin (D) CB(M)/PG(M)

Faf SC/P Scour and piping of foundation of hollow concrete dam caused collapse of 60m of dam.

Flood. Dam previously damaged and foundations scoured.

Y

Umberumba VA Fa SC/L Overtopped by flood, scour of downstream toe, leakage under dam.

No details available. (Flood) F

Idbar VA Ff P High seepage and piping of limestone foundation which had not been grouted. Dam was abandoned.

Leakage, piping of foundation. Y

Vajont VA Fa S Massive landslide in reservoir caused overtopping of dam by many metres (>100m). Dam remained intact.

Movements in landslide accelerating with time.

M

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Analysis of Concrete and Masonry Dam Incidents Page 2.99

2.3.7 Remedial Measures

‘Abandonment of the dam’ and ‘reconstruction with a new design’ were the most

common remedial measures for failures. For accidents, reconstruction of deteriorated

zones in appurtenant works and water tightening treatment in the foundations were the

most common. Repairing concrete/masonry facing or reconstructing the deteriorated

concrete/masonry was the most frequent remedial method for major repairs. Figure 2.30

shows the most common remedial measures vs incident type. shows the number of

dams within each remedial measure category. Table 2.33 shows the number of dams

within each remedial measure category.

Page 133: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.100

0 5 10 15 20 25 30 35

Reconstruction(same design)

Reconstruction(same design)

Not available

Scheme abandoned

Foundationwatertightening

Drain and filterconstruction

Concretewatertightening

Concrete facing

Reconstruction(deteriorated zones)

Grouting

Dam shape correction

Appurtenant surfacerepair

Appurtertenant Reconst.(deteriorated zones)

Percent of Incidents with Remedial Measure

Failure

Accident

Major Repair

Figure 2.30. Most common remedial measures - all dam incidents

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Analysis of Concrete and Masonry Dam Incidents Page 2.101

Table 2.33. Remedial measures - all dam incidents

Failures Accidents Major Repairs All Incidents Remedial Measure Number %* Number %* Number %* Number %*

Of a general nature: Investigation 1 2 8 5 19 7 28 6 Monitoring 0 0 9 5 14 5 23 5 Lowering of reservoir level 1 2 10 6 11 4 22 5 Overall reconstruction (same design)_ 5 11 0 0 0 0 5 1 Reconstruction with new design 10 22 3 2 2 1 15 3 None 1 2 8 5 7 3 16 3 Not available 1 2 11 6 8 3 20 4 Scheme abandoned 15 33 5 3 1 0 21 4

In foundations: Water tightening treatment 0 0 20 11 24 9 44 9 Drain & filter construction or repair 0 0 15 9 23 9 38 8 Strengthening by grouting or other methods 0 0 10 6 6 2 16 3 Filling in of fractures & cavities 1 2 2 1 1 0 4 1 Anchoring 1 2 0 0 2 1 3 1

In concrete and masonry dams: Water tightening treatment 1 2 15 9 28 11 44 9 Drain construction or repair 1 2 1 1 14 5 16 3 Thermal protection (exc. facing) 0 0 0 0 7 3 7 1 Facing 0 0 9 5 56 21 65 13 Reconstruction of deteriorated zones 5 11 10 6 35 13 50 10 Execution of joints 0 0 3 2 5 2 8 2 Strengthening by grouting 0 0 9 5 21 8 30 6 Strengthening by anchoring 2 4 7 4 11 4 20 4 Strengthening by shape correction 4 9 8 5 3 1 15 3

In appurtenant works: Discharge increase 1 2 8 5 7 3 16 3 Construction of additional appurtenant work 1 2 2 1 1 0 4 1 Overall reconstruction of appurtenant works 0 0 2 1 6 2 8 2 Partial reconstruction with strengthening 0 0 5 3 6 2 11 2 Shape correction of surfaces contacting flow 0 0 3 2 5 2 8 2 Aeration devices: construction or capacity inc. 0 0 0 0 2 1 2 0 Repair of surfaces contacting flow 0 0 8 5 19 7 27 6 Slope protection & stabilisation 0 0 2 1 1 0 3 1 Const., modification & repair of valves & gates 0 0 10 6 4 2 14 3 Establish. & update rules for gate & valve ops 0 0 0 0 2 1 2 0 Reconstruction of deteriorated zones 1 2 19 11 8 3 28 6 Abandonment of appurtenant work 0 0 0 0 1 0 1 0

In reservoir: Reforestation 0 0 2 1 0 0 2 0 Torrent training 0 0 5 3 0 0 5 1 Sediment discharge diversion 0 0 1 1 0 0 1 0 Slope regularisation, protection & strengthening 0 0 2 1 0 0 2 0 Water tightening 0 0 4 2 1 0 5 1 Dredging 0 0 2 1 2 1 4 1

Downstream of Dam: Draining 0 0 2 1 0 0 2 0 Slope regularisation, protection & strengthening 0 0 2 1 2 1 4 1 TOTAL 52 242 365 659 Note: (*) Percent of dams (of particular incident type) with particular remedial measure

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Analysis of Concrete and Masonry Dam Incidents Page 2.102

2.3.8 Geology

2.3.8.1 Geology of Dam Foundations Experiencing Incidents

In previous databases and analyses the dam foundation geology has been simply

described using categories of soil and/or rock. Since a large proportion of failures have

occurred due to deficiencies in the foundation, an improved analysis would be to

classify what type of soil or rock the dam was founded on, and then assess whether

certain foundation types are more susceptible to failure.

The aim of this section is to assess the geology of the foundations of dams that have

failed with particular reference to those that have undergone failure due to sliding or

piping in the foundation. There are 65 dams in the database that have experienced

foundation incidents, of which there are 19 failures 25 accidents and 25 (16 of which

were ‘significant’) major repairs. Table 2.34 and Table 2.35 list the dams that have had

failures or accidents (respectively) due to deficiencies in the foundation.

Figure 2.31 shows the age to failure for dams with failure in the foundation. Times to

failure and accidents in the foundation tend to be confined to less than five years. Major

repairs have occurred up to 45 years after commissioning. Failures due to the foundation

have occurred mainly in dams constructed prior to 1940.

Figure 2.32 shows the foundation geology types for incidents occurring in the

foundation. Limestone, shale, granite and alluvium are the most common foundation

geology types for dam foundations that have had accidents. Shale, limestone, sandstone

and alluvium are the most common for major repairs. However, there are a large

number of foundation major repairs (27%) with unknown foundation geologies.

The two main foundation failure modes are:

(a) Sliding on/in the Foundation

Table 2.34 and Table 2.35 show that sliding is most prevalent in interbedded

sedimentary sequences particularly with shale, and in schistose metamorphic where

weaknesses could be expected. The tuff and conglomerate (and shale for Bayless Dam)

were noted to have softened when wet. In the case of Malpasset the rock type played

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Analysis of Concrete and Masonry Dam Incidents Page 2.103

some role in the failure but it was predominately due to uplift pressure and a fault zone.

In the case of Zerbino Dam the failure occurred along the foliations of the schist. There

are no cases of dam sliding associated with igneous rocks. Overtopping preceded four of

the foundation sliding cases.

Table 2.34. Geology for dams with failure in the foundation

Dam Name Dam Type

Year Failed

Failure Mode*

Fndn Material**

Geology

FAILURES Bayless (A) PG 1910 Slide R Shale Sandstone Bayless (B) PG 1911 Slide R Shale Sandstone St Francis PG 1928 Slide R Conglomerate Schist Xuriguera PG 1944 Slide R Unknown Austin (A) PG(M) 1900 Slide R Shale Limestone Dolomite

Tigra PG(M) 1917 Slide R Shale Sandstone Malpasset VA 1959 Slide/Uplift R Gneiss Komoro CB(M) 1928 Slide/Piping R Tuff

Elwha River PG 1912 Piping S/R Fluvioglacial Conglomerate Angels PG(M) 1895 Piping S Unknown Puentes PG(M) 1802 Piping S Alluvium Sandstone

Vaughn Creek VA 1926 Piping (abt) S/R Residual Conglomerate Ashley CB 1909 Piping S Fluvioglacial Selsfors CB 1943 Piping S/R Fluvioglacial

Stony River CB 1914 Piping S Alluvial Shale Bacino di Rutte VA(M) 1965 Deformation/Piping R Dolomite

Zerbino PG 1935 Scour/Slide R Schist Hornfeld Moyie River VA 1926 Scour R Unknown Overholser CB 1923 Scour R Unknown

*Piping failure through abutment denoted by (abt). **Note: S= Soil; R= Rock

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Table 2.35. Geology for dams with accidents in the foundation

Dam Name Dam Type

Year Failed

Failure Mode*

Fndn Material**

Geology

Castrelo PG - Slide R Granite Don Marco PG 1975 Slide R Unknown Mequinenza PG 1966 Slide R Limestone Lignite

Zardezas PG 1932 Slide R Sandstone Limestone Conglomerate Bouzey (A) PG(M) 1884 Slide R Sandstone

Dobra VA 1954 Slide R Unknown Aguilar PG 1963 Piping R Limestone

Great Falls (A) PG 1945 Piping R Shale Limestone Hales Bar PG 1964 Piping R Limestone Shale Kawamata PG 1966 Piping ? Unknown

Upper Glendevon PG 1956 Piping R Andesite Agglomerate Siltstone Villagarcia PG 1961 Piping R Granite

Woodbridge (A) PG - Piping S Alluvial Idbar VA 1959 Piping R Limestone Schist

Estremera CB 1955 Piping S Alluvial Logan Martin PG/TE 1964 Piping R Dolomite Limestone

Koshibu PG 1969 Piping/Leakage R Granite Bingham PG - Piping/Scour R Unknown

Austin (D) CB(M) 1937 Scour/Piping R Limestone Shale Dolomite Saulspoort PG 1988 Scour R Sandstone Siltstone Dolerite

Albigna PG - Deformation R Granite Santa Maria VA 1968 Deformation R Granite

Gerlos VA 1964 Deformation R Unknown Kariba VA 1958 Leakage R Unknown

Kolnbrein VA 1978 Uplift/Tension/Leakage R Gneiss *Piping failure through abutment denoted by (abt). **Note: S= Soil; R= Rock

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(b) Piping through the Foundation

Piping has tended to occur in soils namely alluvium, fluvioglacial and residual.

Although large concrete dams are generally not built on soil foundations, smaller

structures such as weirs are. Where foundations were rock, piping failure was through

the abutment of the dam. The abutment is defined by ICOLD(1978) as ‘that part of the

valley side against which the dam is constructed’ (i.e. zones L2 and L4 of Figure 2.2 in

Section 2.2.4.9). A disproportionately high number of piping failures occurred in

buttress and arch dams. This is likely to be due to the high hydraulic gradients in the

foundations/abutments of these types of dams. Note, the scouring associated with

Overholser Dam was also through the abutment. When accidents are included limestone

becomes notably more prevalent.

0

10

20

30

40

50

60

1880 1900 1920 1940 1960 1980 2000Year Commissioned

Age

Fail - SlideFail - PipingFail - OtherAcc - SlideAcc - PipingAcc - Other

Xuriguera

Austin (A)

Bacino di RutteZerbino

Figure 2.31. Foundation incidents age, type and year commissioned - all dams

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Analysis of Concrete and Masonry Dam Incidents Page 2.106

(45%)

0 5 10 15 20 25

Sandstone

Shale

Siltstone

Conglomerate

Sedimentary

Limestone

Agglomerate

Gneiss

Schist

Hornfeld

Lignite

Dolomite

Dolerite

Andesite

Basalt

Granite

Volcanic Ash

Alluvial

Residual

Unknown

Percent of Dams

FAIL (19)ACC (25)MR* (16)

Note(*) Significant incidents only

Figure 2.32. Foundation incidents geology - all incidents

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Analysis of Concrete and Masonry Dam Incidents Page 2.107

2.3.8.2 Geology of the Population of Dams

As discussed above a large proportion of concrete dam failures have occurred in the

foundation. ICOLD (1974, 1983 and 1995) and USCOLD (1975 and 1988) have only

assessed the foundation of dams as soil or rock. Little work has been done in attempting

to compare foundation geology to likelihood of failure. This would allow comparison of

the geology of those dams experiencing incidents to the geology of the population of

dams allowing identification of those with disproportionately high or low number of

incidents.

To gain a better understanding of which foundation geology is likely to cause problems

a population of dams was required. The difficulty in doing this was finding populations

of concrete and masonry dams where the geology of dams could reasonably be attained.

The following populations were chosen:

• USBR;

• Australia/New Zealand; and

• Portugal.

Descriptions of the populations are given below. The results of the analysis are shown

in Table 2.36 and Table 2.37. It should be noted that where a dam has two foundation

geology types both are included in the tables. This results in the total number of dams

being less than the total number of foundation geology types in Table 2.36 and Table

2.37. The percentage figures are calculated as the number of occurrences of a particular

geology type divided by the number of dams (and not the total number of geology

types). The figures therefore represent the percentage of dams with a particular geology

type.

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(a) USBR Large Concrete Dams

The USBR large concrete dam population was chosen for its good information on

geologies. The main sources being:

• USBR (1996) Large Concrete Dams Online Database;

• USBR SEED Reports;

• USBR database Dam Safety Information System; and

• personal communication with USBR personnel.

The results of the analysis on the dams are shown in Table 2.36. The results are in

percent per dam type. The number of dams is given in italics. The predominant

foundation types were granite (25%) and sandstone (22%). The total number of

unknowns was six.

(b) Australian and New Zealand Dams

The Australia/New Zealand population of dams was taken primarily from the ANCOLD

dam register with more detailed information provided by the sponsors of the research

project. Other information was taken from ICOLD Congresses, the ANCOLD Bulletin

and other journals. The major New Zealand dam owners (besides ECNZ who were a

sponsor) were contacted and the following companies provided information:

• Contact Energy Ltd

• Central Electric Ltd

• Egmont Electricity Ltd

• Marlborough Electric Ltd

Table 2.36 gives the breakdown of foundation geology types. The most common

foundation geology types were sandstone (26%) and granite (14%).

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(c) Portuguese Dams

The Portuguese population was taken from LNEC (1996). The results are given in Table

2.36 in a similar method to above. There were 52 dams on rock foundations; 1 on a

soil/rock foundation and 1 unknown. The most common geology types were granite

(50%), schist (30%) and sandstone (19%).

The populations from Australia, New Zealand, the USBR and the Portuguese population

have been added into one population, which is presented in Table 2.37. Sandstone

(24%) and granite (24%) were the most common foundation geology types. 2% of the

dam population had soil, namely alluvium, foundations.

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Page 2.110

Table 2.36. Foundation geology for Australia, New Zealand, Portugal and USBR (percent and number for each group)

AUSTRALIA/NEW ZEALAND PORTUGAL USBR Grav Arch Butt MA ALL Grav Arch Butt MA ALL Grav Arch Butt ALL

Total Dams 97 42 10 3 152 28 20 4 2 54 21 7 31 59 Sandstones 24 23 36 15 20 2 26 40 21 6 15 3 25 1 19 10 24 5 43 3 16 5 22 13 Shale 8 8 5 2 7 10 0 10 2 14 1 3 1 7 4 Siltstone 5 5 14 6 20 2 9 13 0 0 Conglomerate 10 4 3 4 0 5 1 14 1 10 3 8 5 Limestone 5 2 1 2 50 1 2 1 5 1 13 4 8 5 Claystone 3 3 7 3 4 6 0 0 Mudstone 4 4 10 1 3 5 0 0 Chert 2 2 2 1 2 3 0 0 Breccia 2 2 1 2 0 0 Dolomite 5 1 3 1 3 2 Tillite 2 1 1 1 0 0 Marl 5 1 2 1

Schist 7 7 7 3 7 10 21 6 30 6 75 3 50 1 30 16 14 3 6 2 8 5 Quartzite 7 7 12 5 10 1 33 1 9 14 4 1 5 1 4 2 14 1 6 2 5 3 Gneiss 7 7 5 7 5 1 2 1 3 1 2 1 Phylitte 2 2 2 1 2 3 7 2 5 1 25 1 7 4 0 Slate 3 3 7 3 4 6 0 0 Hornfels 0 5 1 2 1 5 1 2 1 Argillite 1 1 1 1 0 0

Granite 21 20 5 2 14 22 43 12 65 13 50 2 50 27 24 5 14 1 29 9 25 15 Basalt 4 4 5 2 10 1 5 7 50 1 2 1 14 3 29 2 10 3 14 8 Tuff 9 9 5 2 20 2 9 13 0 5 1 3 1 3 2

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AUSTRALIA/NEW ZEALAND PORTUGAL USBR Grav Arch Butt MA ALL Grav Arch Butt MA ALL Grav Arch Butt ALL

Dolerite 8 8 5 2 7 10 0 0 Rhyolite 4 4 5 2 4 6 0 5 1 10 3 7 4 Andesite 3 3 5 2 10 1 4 6 0 0 Porphyry 2 2 1 2 0 6 2 3 2 Diorite 1 1 2 1 1 2 0 5 1 3 1 3 2 Granodiorite 2 2 1 2 4 1 2 1 0 Greenstone 1 1 1 1 0 5 1 3 1 3 2 Agglomerate 1 1 1 1 0 3 1 2 1 Pumice 1 1 1 1 0 0

Volcanic Ash 0 0 0 Alluvium 2 2 1 2 0 5 1 14 1 3 2 Glacial 5 1 2 1 Residual 1 1 1 1 0 0 Unknown 20 19 14 6 50 5 67 2 21 14 18 5 9 5 0

Grav - Gravity; Butt - Buttress; MA - Multi-Arch

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Table 2.37. Foundation geology for Australia, New Zealand, Portugal & USBR

dams - totalled Figures

Gravity Arch Buttress Multi-Arch ALL Total Dams 125 93 21 5 265 Sandstone 27 34 25 23 29 6 24 63 Shale 8 10 3 3 5 1 5 14 Siltstone 4 5 6 6 10 2 5 13 Conglomerate 1 1 8 7 5 1 3 9 Limestone 1 1 6 6 20 1 3 8 Claystone 2 3 3 3 2 6 Mudstone 3 4 5 1 2 5 Chert 2 2 1 1 1 3 Breccia 2 2 1 2 Dolomite 1 1 1 1 1 2 Tillite 1 1 0 1 Marl 1 1 0 1

Schist 13 16 12 11 14 3 20 1 12 31 Quartzite 6 8 9 8 10 2 20 1 7 19 Gneiss 6 7 2 2 3 9 Phylitte 3 4 2 2 5 1 3 7 Slate 2 3 3 3 2 6 Hornfels 1 1 1 1 1 2 Argillite 1 1 0 1

Granite 30 37 26 24 14 3 24 64 Basalt 6 7 5 5 14 3 20 1 6 16 Tuff 8 10 3 3 10 2 6 15 Dolerite 6 8 2 2 4 10 Rhyolite 4 5 5 5 4 10 Andesite 2 3 2 2 5 1 2 6 Porphyry 2 2 2 2 2 4 Diorite 2 2 2 2 2 4 Granodiorite 2 3 1 3 Greenstone 2 2 1 1 1 3 Agglomerate 1 1 1 1 1 2 Pumice 1 1 0 1

Alluvium 2 3 5 1 2 4 Glacial 1 1 0 1 Residual 1 1 0 1 Unknown 19 24 6 6 24 5 40 2 14 37

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Analysis of Concrete and Masonry Dam Incidents Page 2.113

2.3.9.3 Geology - Comparison Between Incidents and Population

The following assesses the foundation geology more likely to cause foundation piping

and stability problems. This has been based on the statistics of failures and accidents

and the “population” assumed in Table 2.37. Due to the limited number of foundation

failures that have occurred and the potential inaccuracies introduced by adopting Table

2.37 as a world population, care should be exercised here and the information taken as

qualitative only.

Figure 2.33 to Figure 2.35 gives the number of incidents in each geology type for: all

dams; concrete gravity dams; and masonry gravity dams respectively. From these

figures it becomes evident that soil foundations - most particularly alluvial soils are over

represented in the foundation incidents. The alluvial soils have a tendency to pipe under

the high gradients imposed. No dam has been reported to have failed by sliding on

alluvial soils. Normally a large concrete or masonry dam would not be built on a soil

foundation. It is interesting that sandstone does not appear to be over represented when

the population is taken into account. Failures tend not to occur in sandstone alone but

only when the sandstone is interbedded with shales. Shale and limestone (often

interbedded) have a high incidence for failing. The limestone has a high proportion of

accidents generally due to excessive leakage through dissolution. Another point of note

is that no incidents have occurred in basalt foundations.

Figure 2.36 to Figure 2.39 give the number of incidents in each geology type over the

population of dams in the same geology. The population was estimated using the figures

from Table 2.37 and the estimated world population of dams at 1983 (the available

ICOLD world population data cutoff). For gravity dams conglomerate, limestone,

dolomite and alluvium foundations stand out. Dams with limestone foundations appear

to be very susceptible to accidents. The figures for arch and buttress dams are based on

small failure populations and should therefore be looked at with caution. Dolomite and

gneiss stands out for arch dams whilst alluvium and shale are notable in buttress dams.

Figure 2.40 gives a clear indication of which foundation geology types have a tendency

to slide or pipe fail. Soils (particularly alluvial and fluvioglacial) and limestones are

more likely to have piping problems. Shale (interbedded with other sedime ntary units)

has a greater tendency to be involved with sliding failure because of the likely presence

Page 147: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.114

of weaknesses in the bedding such as bedding surface shears. These conclusions agree

with the general knowledge regarding the geology types (e.g. as described in Fell et al,

1992).

Page 148: Shear Strength of Rock

Page 2.115

0

5

10

15

20

25

30

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Perc

ent o

f Pop

ulat

ion.

0

1

2

3

4

5

6

7

8

9

Num

ber of Dam

s.ALL - FAIL

ALL - ACC

ALL - POP

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.33. Geology for incidents in the foundation and dam population – all dams

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Page 2.116

0

5

10

15

20

25

30

35

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Perc

ent o

f Pop

ulat

ion.

0

1

2

3

4

5

6

7

Num

ber of Dam

s.

PG - FAIL

PG - ACC

Gravity - POP

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.34. Geology for incidents in the foundation and dam population – concrete gravity dams

Page 150: Shear Strength of Rock

Page 2.117

0

5

10

15

20

25

30

35

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Perc

ent o

f Pop

ulat

ion.

0

1

2

3

4

Num

ber of Dam

s.PG(M) - FAIL

PG(M) - ACC

Gravity - POP

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.35. Geology for incidents in the foundation and dam population – masonry gravity dams

Page 151: Shear Strength of Rock

Page 2.118

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Inci

dent

s/Po

pula

tion

(%).

ALL - Fail

ALL - Acc

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.36. Foundation geology type as a percentage of the geology population – all dams

Page 152: Shear Strength of Rock

Page 2.119

0.0

5.0

10.0

15.0

20.0

25.0

30.0

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Inci

dent

s/Po

pula

tion

(%)

Gravity - Fail

Gravity - Acc

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.37. Foundation geology type as a percentage of the geology population – gravity dams

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Page 2.120

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Inci

dent

s/Po

pula

tion

(%).

Arch - Fail

Arch - Acc

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.38. Foundation geology type as a percentage of geology population – arch dams

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Page 2.121

0.0

5.0

10.0

15.0

20.0

25.0

Sandstone

Shale

Siltstone

Conglom

erate

Lim

estone

Dolom

ite

Schist

Gneiss

Hornfels

Granite

Basalt

Dolerite

Andesite

Agglom

erate

Alluvium

Residual

Unknow

n

Inci

dent

s/Po

pula

tion

(%).

Buttress - Fail

Buttress - Acc

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.39. Foundation geology type as a percentage of geology population – buttress dams

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Page 2.122

0

1

2

3

4

5

6

7

Granite

Sandstone

Schist

Basalt

Shale

Siltstone

Conglom

erate

Gneiss

Lim

estone

Andesite

Dolom

ite

Hornfels

Agglom

erate

Alluvial

Residual

Unknow

n

Num

ber

of D

ams

0

5

10

15

20

25

30Percent of Population of D

ams

Fail - PipingFail - SlidingAcc - PipingAcc - SlidingPopulation

Note: Population based on Australia, New Zealand, Portugal and USBR

Figure 2.40. Foundation incident geology and population – mode of failure/accident

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Analysis of Concrete and Masonry Dam Incidents Page 2.123

2.3.9 Other Design Factors in Failed Dams

Due to the limited information no conclusions could be drawn for the following factors.

(a) Post-Tensioning

No dam that failed was found to have been post-tensioned. The dams where there is no

information tend to be older dams (generally masonry) where post-tensioning is

unlikely.

(b) Gallery and Drains

Of the 46 dam failures, information could be found on the gallery and drains for 21

dams. Of these, only Zerbino Dam had drains present. The gallery was 4m above the

base of the dam with drains to the concrete-rock interface. Zerbino overtopped by 3m

causing erosion of the weak foundation rock at the toe, which resulted in foundation

sliding. It is not known what effect, if any, the drains had on the failure.

(c) Foundation Grouting

Of the 46 dam failures, information could be found on the foundation grouting for 20

dams. Of these, 2 dams had curtain grouting; three dams had consolidation grouting;

and one (Vega de Tera) had both. These dams are shown in

Table 2.38. The foundations of the other 14 failed dams were not grouted.

Table 2.38. Failed dams with grouted foundation

Dam Name

Dam Type

Grout Type

Foundation Geology

Failure Comments

Cheurfas PG(M) curtain limestone Failed in dam body Austin (B) PG(M) curtain limestone/shale/

dolomite Seepage softened fndn prior to sliding - grouting inadequate

Zerbino PG consolidation hornfeld/schist Overtopped by 3m with toe erosion then sliding

Chickahole PG(M) consolidation gneiss Failed in dam body Bacino di

Rutte VA(M) consolidation dolerite Concrete failure due to fndn

movement Vega de Tera CB(M) both gneiss/schist Failed in dam body

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Analysis of Concrete and Masonry Dam Incidents Page 2.124

(d) Shear Key

Bouzey Dam was the only failed dam found to have a shear key. The failure occurred

within the body of the dam.

(e) Radius of Curvature

Where information on the radius of curvature for failed gravity dams was available (15),

all but two dams had straight sections. Tigra Dam and St Francis Dam had radii of

curvature of 1000m and 152m respectively.

(f) Valley Shape

18 failed dams were found with information on the valley shape. The gradient of the

valley sides ranged from 0.06 to 2.0 (H/L) for gravity dams and 0.6 to 1.3 for arch

dams. The averages were 0.72 and 0.84 respectively.

Table 2.39 shows the ratio of crest length to dam height for both failed dams (where

information was available) and the population of dams. The structural height, Hd, was

used for the failed dams. The population from ICOLD as described in Section 2.2.6 was

used for the comparison. Dams with composite embankment sections were omitted from

both the failure and population analyses. The data shows that the failures were in

relatively wide valleys (L1/Hd≥3.1 for gravity dams) where three-dimensional effects

are unlikely to make a significant impact to the strength of the dams.

Elwha River Dam, a gravity dam which pipe failed, had a very narrow valley (11m)

with reasonably steep sides. However the failure was likely to be mainly due to the

alluvial foundation. No conclusive results were attained from this analysis.

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Analysis of Concrete and Masonry Dam Incidents Page 2.125

Table 2.39. Crest length/height for failed dams and population

DAM FAILURES POPULATION TYPE Number Range Mean Number Range Mean Gravity 27 3.1-53 13.2 2887 0.3-182(1) 10.1 Arch 5 2.9-4.3 3.6 663 0.2-29 3.8

Buttress 6 6.0-26 13.2 232 1.0-131 10.1 Multi-Arch 2 3.5-6.8 5.1 82 2.0-47 9.2

Note (1) 80% of the population of gravity dams has a crest length/height greater than 3.1.

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(g) Upstream/Downstream Slopes

Table 2.40 shows the upstream and downstream slopes for the failed dams where the

information was available. Of the 15 gravity dams in the table, 13 had vertical or near

vertical upstream slopes. On the downstream face the concrete gravity dams ranged

from 0.55:1 (H:V) to 1:1. The masonry gravity dams ranged from 0.38:1 to 3:1. The

arch dams ranged from near vertical to 0.32:1.

Table 2.40. Upstream and downstream slopes for failed dams

Failure Mode Dam Name Dam Type Upstream (xH:1V)

Downstream (yH:1V)

Foundation Dam Bayless (A) PG 0 1 S Bayless (B) PG 0 1 S Elwha River PG 0 0.75 P St. Francis PG 0 1 S Zerbino PG 0.05 0.55 S/SC Angels PG(M) 0 0.6 P Austin (A) PG(M) 0 0.38 SC/P/S Bouzey PG(M) 0 1 T Chickahole PG(M) 0.1 0.7 T Habra (A) PG(M) 0.3 0.8 T/SH Habra (B) PG(M) 3 1 T/SH Habra (C) PG(M) 3 1 T/SH Khadakwasla PG(M) 0.05 0.4 T/SH Puentes PG(M) 0 0.6 P Tigra PG(M) 0 0.67 S Malpasset VA 0 0 S Moyie River VA 0 0.06 SC Vaughn Creek VA 0 0.2 P Bacino di Rutte VA(M) 0.12 0.12 D/P Gallinas VA(M) 0 0.32 ? Meihua VA(M) 0 0 SH Ashley CB 1 0.5 P Stony Creek CB 1 0.15 P Vega de Tera CB(M) 0.05 0.75 T/C Austin (B) CB(M) 0 1 SH Gleno MV 0.85 0.1 T/C

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Analysis of Concrete and Masonry Dam Incidents Page 2.127

(h) Dam Height/Base Width (Hd/W)

Table 2.41 shows the dam structural height and height of water at failure over base

width (Hd/W and hwf/W respectively) for the failed dams where the information was

available. Figure 2.1 in Section 2.2.4.9 shows the definition of these terms. The Hd/W

and/or hwf/W ratios give an indication of the stability and hydraulic gradient of the

dams. A high Hd/W or hwf/W indicates a slender dam with potentially a high hydraulic

gradient. These are common for arch dams. The definitions for the failure modes are

given in Sections 2.4.2 and 2.4.3.

Dams that failed by piping generally had soil foundations. Those with alluvial

foundations had hwf/W ratios of 0.6 to 1.1. Vaughn Creek, an arch dam which pipe

failed through its extremely to highly weathered conglomerate abutment, had a ratio of

3.0. Austin (A), the only dam to have pipe failure through rock (weathered) had a hwf/W

of 1.2. Gravity dams that failed by sliding had hwf/W ratios of 1.2 to 2.1. Of these,

Zerbino Dam (hwf/W=2.1) was the only dam known to have drainage. Malpasset Dam,

an arch dam, had a hwf/W of 5.8.

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Analysis of Concrete and Masonry Dam Incidents Page 2.128

Table 2.41. Hd/W for failed dams

Dam Name Dam Type Hd/W hwf/W Failure Mode Foundation Dam

Bayless (A) PG 1.6 1.6 S Bayless (B) PG 1.6 1.6 S Elwha River PG 1.4 0.6 P St. Francis PG 1.2 1.2 S Zerbino PG 1.7 2.1 S/SC Austin (A) PG(M) 1.0 1.2 SC/P/S Bouzey PG(M) 1.7 1.7 T Cheurfas PG(M) 1.0 ? Chickahole PG(M) 1.3 1.0 ? Fergoug I PG(M) 1.3 ? Fergoug II PG(M) 1.3 Habra (A) PG(M) 1.3 T/SH Habra (B) PG(M) 1.3 1.2 T/SH Habra (C) PG(M) 1.3 1.4 T/SH Khadakwasla PG(M) 1.8 2.0 T/SH Puentes PG(M) 1.1 1.1 P Tigra PG(M) 1.5 1.5 S Malpasset VA 6.0 5.8 S Moyie River VA 7.0 SC Vaughn Creek VA 4.3 3.0 P/D Gallinas VA(M) 3.1 3.2 ? Meihua VA(M) 18.3 17.5 SH Ashley CB 1.2 1.1 P Stony River CB 1.0 0.9 P Vega de Tera CB(M) 2.0 1.8 T/C Austin (B) CB(M) 0.7 1.2 SH Gleno MV 1.1 1.1 T/C

(i) Stability Analyses

Gulan (1995) and Rich (1995) collated information for 13 concrete gravity dams that

had failed by either sliding or overturning through their foundations or the concrete

mass. Of the 13 cases, nine failures were back analysed to determine the shear strength

properties of either the foundation or concrete. Table 2.42 shows the results from the

analyses, which have been checked and some adjustments to the cohesion results made.

The results are quoted as c=0, φ or c, φ=0. Actual strengths are between these limits.

The results for Khadakwasla Dam have been omitted as the analysis technique was not

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Analysis of Concrete and Masonry Dam Incidents Page 2.129

valid for the failure mode. The failure plane for Khadakwasla Dam was 6m below the

base of the dam.

An additional analysis was carried out for Bhandardara Dam, an 82m high gravity dam

in India. The dam suffered extensive cracking, from an elevation of 39m at the upstream

face to the toe, and came close to failure. The dam has been extensively investigated

and several papers describe the accident including: Murthy et. al. (1976 & 1979); and

Kulkarni & Kulkarni (1994). Two simple analyses were carried out: the first assuming a

horizontal failure at the elevation where the cracking initiated; and the second assuming

an angled crack from the location of crack initiation to the toe. The results from the

analyses have been included in the tables and figures below.

Table 2.43 shows the reanalysed stresses along the failure planes. As can be seen seven

of the dams had tensile stresses, up to -280KPa at the heel of the dam. Bhandardara

Dam, a concrete gravity structure, experienced up to -440kPa tension.

Table 2.42. Back analysed shear strengths for failed dams (mod. from Rich, 1995)

Name Dam Type

Failure φ′ (°)

C′ (KPa)

Foundation Concrete

Austin (A) PG(M) Foundation sliding

49 0

0 120

limestone rubble limestone in portland cement-mortar

Bouzey (1st)

PG(M) Foundation sliding

40 0

0 110

sandstone & schist

masonry in lime-mortar

Bouzey (2nd)

PG(M) Through concrete

34 0

0 75

sandstone & schist

masonry in lime-mortar

El Habra (3rd)

PG(M) Foundation sliding

46 0

0 605

int. sandstone & clay

rubble masonry in lime-mortar

Tigra PG(M) Foundation sliding

48 0

0 195

stratified sandstone

rubble masonry in lime-mortar

Bayless PG Foundation sliding

43 0

0 300

int. sandstone & shale

cyclopean concrete

St. Francis PG Foundation sliding

41 0

0 155

mica schist & conglomerate

portland cement

Bhandardara (horizontal)

PG Severe cracking - tension & shear

>46 0

0 >1015

basalt rubble masonry

Bhandardara (angled)

PG severe cracking - tension & shear

>71 0

0 >480

basalt rubble masonry

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Table 2.43. Calculated normal stresses along the failure plane of back analysed

gravity dams

Name Dam Type

σn Upstream (KPa)

σn Downstream (KPa)

Austin PG(M) -20 +210 Bouzey (1st) PG(M) -20 +265 Bouzey (2nd) PG(M) -10 +220 El Habra (3rd) PG(M) -280 +735 Tigra PG(M) +25 +355 Bayless PG -155 +425 St. Francis PG +35 +355 Bhandardara (horizontal) PG -440 +1085 Bhandardara (angled) PG -50 +320

The average stresses acting along the failure planes have been calculated using the

forces on each dam provided by Rich (1995). Figure 2.41 and Figure 2.42 compare the

ANCOLD guidelines (ANCOLD, 1991) to the failure stresses of the nine failure cases.

It was assumed that shear strength only acted in the region of compression along the

failure plane. The figures show that the failure stresses were much lower than those

recommended by ANCOLD for initial assessments. The likely reason for this is the

existence of continuous defects through or below the dam. The friction angle and

cohesion suggested by ANCOLD assumes no continuous defects. The results show the

importance of having a good geotechnical model for the dam and a good bond at the

dam/foundation interface.

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0200400600800

10001200140016001800

0 100 200 300 400 500 600

σn (kPa)

τ (kPa)

ANCOLD Bayless Austin

Bouzey I HabraSt Francis Tigra

Figure 2.41. Average failure stresses for dams with failure through the foundation

0

500

1000

1500

2000

2500

0 200 400 600 800 1000σn (kPa)

τ (kPa)

ANCOLD

Bhandardara (horizontal) Bhandardara (angled)

Figure 2.42. Average failure stresses for Bhandardara Dam

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Analysis of Concrete and Masonry Dam Incidents Page 2.132

2.4 METHOD OF FIRST ORDER PROBABILITY ASSESSMENT

2.4.1 Probability of Failure

2.4.1.1 Introduction

This section describes an attempt to develop a ‘first’ estimate of the annual probability

of failure of concrete and masonry dams based on the history of dam failures. ‘Average’

annual probabilities of failure have been assessed for all concrete and masonry dam

types. These probabilities have been further refined for concrete and masonry gravity

dams.

The initial or ‘average’ annual probability of failure was calculated as the number of

dam failures, using the history of failures, over an estimate of the population of dams.

The cut off year for the population of dams was taken as 1992 as the latest ICOLD

statistics on failures (ICOLD, 1995) go up to this time. Dams were separated using the

following categories:

(a) Dam type: gravity, arch, buttress, multi-arch;

(b) year commissioned;

(c) age at failure (0-5 years and >5 years); and

(d) Concrete or masonry (gravity dams).

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2.4.1.2 Population of Dams

The total number of concrete and masonry dams as at 1992 (excluding China) is shown

in Table 2.44. Since the ICOLD world population data for post 1983 was not available,

the population for the period 1983-1992 was estimated as shown in the table below.

Table 2.44. Number of dams as at 1992

Year Commissioned

Number of Dams

Reference

1700-1799 37 ICOLD (1983) 1800-1899 167 ICOLD (1983) up to 1977 4446 ICOLD (1984) 1978-1982 217 ICOLD (1984) 1983-1992 434 estimated as 2 x 1978-82

Total 5097

Dams were divided into gravity, arch, buttress and multi-arch dams. Where a dam was

described as a composite section an assessment of the category best describing the dam

was made. The population was also split according to age (year commissioned) to

account for progress in the methods used for dam construction. The breakdown of the

population of dams into dam types and year commissioned was performed using a

computer database created by the author using ICOLD (1979). The database comprised

the concrete and masonry dams from the 26 countries with the largest dam populations.

These countries included all those that had experienced failures (excluding China).

Table 2.45 shows the percentage split for population of dams according to dam type and

year commissioned.

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Table 2.45. Population of dams by dam type and year commissioned

Year Commissioned

Gravity (%)

Arch (%)

Buttress (%)

Multi-Arch (%)

<1900 2.7 0.2 0.0 0.1 1900-1909 2.5 0.4 0.1 0.1 1910-1919 4.7 0.7 0.5 0.2 1920-1929 8.3 2.2 0.6 0.4 1930-1939 7.5 1.7 0.5 0.2 1940-1949 7.4 1.4 0.6 0.3 1950-1959 16.9 3.8 1.9 0.4 1960-1969 17.3 4.8 1.6 0.3 1970-1977 7.8 1.5 0.4 0.2

1977-1983(1) 81.1 12.0 6.0 0.9 Note (1) Data from ICOLD (1983)

For dams commissioned during the period 1978 to 1982 the distribution of concrete and

masonry dam types was taken from ICOLD (1983). Dams commissioned between 1983

and 1992 were assumed to have a similar distribution of dam types. Table 2.46 shows

the number of dams as at 1992 calculated from Table 2.44 and Table 2.45.

Table 2.46. Number of dams (excluding China) in the population

Year Commissioned

Gravity Arch Buttress Multi-Arch Total

1700-1799 34 2 0 1 37 1800-1899 152 10 1 4 167 1900-1909 109 17 4 3 133 1910-1919 205 31 21 11 267 1920-1929 362 94 27 18 501 1930-1939 327 75 20 11 433 1940-1949 321 62 28 12 422 1950-1959 738 164 85 17 1004 1960-1969 757 208 71 13 1049 1970-1977 339 67 18 8 433 1978-1982 176 26 13 2 217 1983-1992* 352 52 26 4 434

Total 3872 808 314 103 5097 Note (1) Estimated as 2 x 1977-1982

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2.4.1.3 Dam Year

As most failures occur prior to five years after commissioning (Douglas et al, 1998) the

failure probabilities were broken into: less than or equal to five years of age; and greater

than five years of age. Equations 1 and 2 were used to calculate the number of dam

years for dams less than or equal to five years, and for dams greater than five years of

age respectively.

Y n≤ = ×5 5 (2.1)

( )Y yi> = −∑5 5 (2.2)

where,

n = total number of dams

yi = age of individual dam in years

2.4.1.4 Probabilities of Failure

Annual probabilities (number of failures/number of dam years) and straight probabilities

of failure (number of failures/number of dams) were calculated from the database of

failures and the population of dams.

A distinction was made between dams commissioned prior to, and those commissioned

after 1930. This represents the historical change to a better understanding of uplift

pressures and materials properties for dams. Categories without failures have been

denoted as ‘NF’.

The probabilities were recalculated for the various failure modes. The following failure

modes were used:

• All modes (Table 2.47 and Table 2.48)

• Sliding (Table 2.49 and Table 2.50)

• Piping (Table 2.51 and Table 2.52)

• Through the dam body (Table 2.53 and Table 2.54)

Table 2.55 and Table 2.56 show the number of failures with unknown failure modes.

Table 2.55 shows those unknowns where failure during overtopping was known to have

occurred.

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Table 2.47. Annual probability of failure (1992, exc. China) - all failure types

Year Gravity Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 5.9E-03 NF 1.2E-04 NF NF NF 1800-1899 6.6E-03 3.8E-04 6.0E-04 NF NF NF 1900-1909 3.7E-03 2.2E-04 4.2E-04 NF NF NF 1910-1919 2.0E-03 1.4E-04 2.5E-04 NF 4.5E-04 4.2E-04 1920-1929 1.1E-03 8.9E-05 1.7E-04 4.2E-03 NF 3.2E-04 1930-1939 6.1E-04 NF 5.4E-05 NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 1.2E-03 1.9E-04 3.3E-04 1960-1969 5.3E-04 1.2E-04 2.0E-04 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 7.7E-03 NF 3.2E-03

1983-1992(3) NF NF NF NF NF NF 1700-1929 2.8E-03 1.9E-04 3.3E-04 2.6E-03 8.9E-05 2.5E-04

1930-1992(3) 2.0E-04 2.6E-05 5.5E-05 6.2E-04 5.8E-05 1.5E-04 Total(3) 7.9E-04 1.1E-04 1.8E-04 1.0E-03 7.0E-05 1.8E-04

Year Buttress Multi-Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 4.7E-02 NF 2.7E-03 NF NF NF 1910-1919 1.9E-02 NF 1.2E-03 NF NF NF 1920-1929 1.5E-02 NF 1.1E-03 1.1E-02 NF 8.3E-04 1930-1939 NF NF NF NF NF NF 1940-1949 7.3E-03 NF 7.7E-04 NF NF NF 1950-1959 2.4E-03 NF 3.2E-04 NF 1.8E-03 1.6E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF

1983-1992(3) NF NF NF NF NF NF 1700-1929 1.9E-02 NF 1.2E-03 5.4E-03 NF 3.2E-04

1930-1992(3) 1.6E-03 NF 2.5E-04 NF 5.1E-04 4.3E-04 Total(3) 4.5E-03 NF 5.8E-04 2.0E-03 2.0E-04 3.7E-04

Year All Concrete & Masonry Comm. 0-5 years(1) >5 years Total

1700-1799 5.4E-03 NF 1.1E-04 1800-1899 6.0E-03 3.5E-04 5.5E-04 1900-1909 4.5E-03 1.8E-04 4.3E-04 1910-1919 3.0E-03 1.6E-04 3.4E-04 1920-1929 2.8E-03 6.4E-05 2.7E-04 1930-1939 4.6E-04 NF 4.1E-05 1940-1949 4.7E-04 NF 5.0E-05 1950-1959 4.0E-04 6.2E-05 1.1E-04 1960-1969 3.8E-04 8.7E-05 1.4E-04 1970-1977 NF NF NF 1978-1982 9.2E-04 NF 3.8E-04

1983-1992(3) NF NF NF 1700-1929 3.6E-03 1.6E-04 3.6E-04

1930-1992(3) 3.6E-04 3.9E-05 9.0E-05 Total(3) 1.1E-03 9.7E-05 2.1E-04

Notes (1) Assumes dam years =

number of dams * five years life

(2) NF - No Failure (3) Assumes number of dams

constructed in 1983-1992 = 2 * number of dams in 1978-1982

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Table 2.48. Probability of failure (as at 1992, exc. China, non-annualised) -

all failure types

Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 3.0E-02 NF 3.0E-02 NF NF NF 1800-1899 3.3E-02 5.3E-02 8.5E-02 NF NF NF 1900-1909 1.8E-02 1.8E-02 3.7E-02 NF NF NF 1910-1919 9.8E-03 9.8E-03 2.0E-02 NF 3.3E-02 3.3E-02 1920-1929 5.5E-03 5.5E-03 1.1E-02 2.1E-02 NF 2.1E-02 1930-1939 3.1E-03 NF 3.1E-03 NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 6.1E-03 6.1E-03 1.2E-02 1960-1969 2.6E-03 2.6E-03 5.3E-03 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 3.8E-02 NF 3.8E-02 1983-1992 NF NF NF NF NF NF 1700-1929 1.4E-02 1.6E-02 3.0E-02 1.3E-02 6.5E-03 2.0E-02 1930-1992 1.0E-03 6.6E-04 1.7E-03 3.1E-03 1.5E-03 4.6E-03

Total 3.9E-03 4.1E-03 8.0E-03 5.0E-03 2.3E-03 7.3E-03

Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 2.4E-01 NF 2.4E-01 NF NF NF 1910-1919 9.4E-02 NF 9.4E-02 NF NF NF 1920-1929 7.5E-02 NF 7.5E-02 5.5E-02 NF 5.5E-02 1930-1939 NF NF NF NF NF NF 1940-1949 3.6E-02 NF 3.6E-02 NF NF NF 1950-1959 1.2E-02 NF 1.2E-02 NF 5.9E-02 5.9E-02 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 9.3E-02 NF 9.3E-02 2.7E-02 NF 2.7E-02 1930-1992 7.7E-03 NF 7.7E-03 NF 1.5E-02 1.5E-02

Total 2.2E-02 NF 2.2E-02 9.7E-03 9.7E-03 1.9E-02

Year All Concrete & Masonry Comm. 0-5 years >5 years Total

1700-1799 2.7E-02 NF 2.7E-02 1800-1899 3.0E-02 4.8E-02 7.8E-02 1900-1909 2.2E-02 1.5E-02 3.7E-02 1910-1919 1.5E-02 1.1E-02 2.6E-02 1920-1929 1.4E-02 4.0E-03 1.8E-02 1930-1939 2.3E-03 NF 2.3E-03 1940-1949 2.4E-03 NF 2.4E-03 1950-1959 2.0E-03 2.0E-03 4.0E-03 1960-1969 1.9E-03 1.9E-03 3.8E-03 1970-1977 NF NF NF 1978-1982 4.6E-03 NF 4.6E-03 1983-1992 NF NF NF 1700-1929 1.8E-02 1.4E-02 3.2E-02 1930-1992 1.8E-03 1.0E-03 2.8E-03

Total 5.3E-03 3.7E-03 9.0E-03

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Table 2.49. Annual probability of failure (as at 1992, excluding China) - sliding

failures

Year Gravity Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 1.3E-03 NF 4.6E-05 NF NF NF 1900-1909 3.7E-03 1.1E-04 3.2E-04 NF NF NF 1910-1919 9.8E-04 NF 6.3E-05 NF NF NF 1920-1929 5.5E-04 4.5E-05 8.3E-05 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 1.2E-03 NF 1.6E-04 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF

1983-1992(3) NF NF NF NF NF NF 1700-1929 1.2E-03 2.7E-05 8.8E-05 NF NF NF

1930-1992(3) NF NF NF 3.1E-04 NF 4.9E-05 Total(3) 2.6E-04 1.3E-05 4.1E-05 2.5E-04 NF 3.1E-05

Year Buttress Multi-Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 7.5E-03 NF 5.6E-04 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF

1983-1992(3) NF NF NF NF NF NF 1700-1929 3.7E-03 NF 2.5E-04 NF NF NF

1930-1992(3) NF NF NF NF NF NF Total(3) 6.5E-04 NF 8.3E-05 NF NF NF

Year All Concrete & Masonry Comm. 0-5 years(1) >5 years Total

1700-1799 NF NF NF 1800-1899 1.2E-03 NF 4.2E-05 1900-1909 3.0E-03 9.1E-05 2.6E-04 1910-1919 7.5E-04 NF 4.9E-05 1920-1929 8.0E-04 3.2E-05 8.9E-05 1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 2.0E-04 NF 2.7E-05 1960-1969 NF NF NF 1970-1977 NF NF NF 1978-1982 NF NF NF

1983-1992(3) NF NF NF 1700-1929 1.1E-03 2.2E-05 8.1E-05

1930-1992(3) 5.1E-05 NF 8.2E-06 Total(3) 2.8E-04 1.0E-05 4.1E-05

Notes (1) Assumes dam years =

number of dams * five years life

(2) NF - No Failure (3) Assumes number of dams

constructed in 1983-1992 = 2 * number of dams in 1978-1982

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Table 2.50. Probability of failure (as at 1992, excluding China, non-annualised) -

sliding failures

Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 6.6E-03 NF 6.6E-03 NF NF NF 1900-1909 1.8E-02 9.2E-03 2.7E-02 NF NF NF 1910-1919 4.9E-03 NF 4.9E-03 NF NF NF 1920-1929 2.8E-03 2.8E-03 5.5E-03 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF 6.1E-03 NF 6.1E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 5.8E-03 2.3E-03 8.1E-03 NF NF NF 1930-1992 NF NF NF 1.5E-03 NF 1.5E-03

Total 1.3E-03 5.2E-04 1.8E-03 1.2E-03 NF 1.2E-03

Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF

1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF

1910-1919 NF NF NF NF NF NF 1920-1929 3.8E-02 NF 3.8E-02 NF NF NF 1930-1939 NF NF NF NF NF NF

1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF

1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF

1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1.9E-02 NF 1.9E-02 NF NF NF

1930-1992 NF NF NF NF NF NF Total 3.2E-03 NF 3.2E-03 NF NF NF

Year All Concrete & Masonry Comm. 0-5 years >5 years Total

1700-1799 NF NF NF 1800-1899 6.0E-03 NF 6.0E-03 1900-1909 1.5E-02 7.5E-03 2.2E-02

1910-1919 3.7E-03 NF 3.7E-03 1920-1929 4.0E-03 2.0E-03 6.0E-03

1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 1.0E-03 NF 1.0E-03

1960-1969 NF NF NF 1970-1977 NF NF NF

1978-1982 NF NF NF 1983-1992 NF NF NF 1700-1929 5.4E-03 1.8E-03 7.2E-03

1930-1992 2.5E-04 NF 2.5E-04 Total 1.4E-03 3.9E-04 1.8E-03

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Table 2.51. Annual probability of failure (as at 1992, excluding China) - piping

failures

Year Gravity Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 5.9E-03 NF 1.2E-04 NF NF NF 1800-1899 1.3E-03 NF 4.6E-05 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 9.8E-04 NF 6.3E-05 NF NF NF 1920-1929 NF NF NF 2.1E-03 NF 1.6E-04 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF 1.9E-04 1.6E-04 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF

1983-1992(3) NF NF NF NF NF NF 1700-1929 7.0E-04 NF 3.8E-05 1.3E-03 NF 8.3E-05

1930-1992(3) NF NF NF NF 5.8E-05 4.9E-05 Total(3) 1.6E-04 NF 1.8E-05 2.5E-04 3.5E-05 6.1E-05

Year Buttress Multi-Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 NF NF NF NF NF NF

1800-1899 NF NF NF NF NF NF 1900-1909 4.7E-02 NF 2.7E-03 NF NF NF

1910-1919 9.4E-03 NF 6.1E-04 NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF

1940-1949 7.3E-03 NF 7.7E-04 NF NF NF 1950-1959 NF NF NF NF NF NF

1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF

1978-1982 NF NF NF NF NF NF 1983-1992(3) NF NF NF NF NF NF 1700-1929 7.5E-03 NF 4.9E-04 NF NF NF

1930-1992(3) 7.8E-04 NF 1.2E-04 NF NF NF Total(3) 1.9E-03 NF 2.5E-04 NF NF NF

Year All Concrete & Masonry Comm. 0-5 years(1) >5 years Total

1700-1799 5.4E-03 NF 1.1E-04 1800-1899 1.2E-03 NF 4.2E-05 1900-1909 1.5E-03 NF 8.6E-05

1910-1919 1.5E-03 NF 9.7E-05 1920-1929 4.0E-04 NF 3.0E-05

1930-1939 NF NF NF 1940-1949 4.7E-04 NF 5.0E-05 1950-1959 NF 3.1E-05 2.7E-05

1960-1969 NF NF NF 1970-1977 NF NF NF

1978-1982 NF NF NF 1983-1992(3) NF NF NF 1700-1929 1.1E-03 NF 6.1E-05

1930-1992(3) 5.1E-05 9.8E-06 1.6E-05 Total(3) 2.8E-04 5.1E-06 3.6E-05

Notes (1) Assumes dam years =

number of dams * five years life

(2) NF - No Failure (3) Assumes number of dams

constructed in 1983-1992 = 2 * number of dams in 1978-1982

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Table 2.52. Probability of failure (as at 1992, excluding China, non-annualised) -

piping failures

Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 3.0E-02 NF 3.0E-02 NF NF NF 1800-1899 6.6E-03 NF 6.6E-03 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 4.9E-03 NF 4.9E-03 NF NF NF 1920-1929 NF NF NF 1.1E-02 NF 1.1E-02 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF 6.1E-03 6.1E-03 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 3.5E-03 NF 3.5E-03 6.5E-03 NF 6.5E-03 1930-1992 NF NF NF NF 1.5E-03 1.5E-03

Total 7.7E-04 NF 7.7E-04 1.2E-03 1.2E-03 2.5E-03

Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF

1800-1899 NF NF NF NF NF NF 1900-1909 2.4E-01 NF 2.4E-01 NF NF NF

1910-1919 4.7E-02 NF 4.7E-02 NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF

1940-1949 3.6E-02 NF 3.6E-02 NF NF NF 1950-1959 NF NF NF NF NF NF

1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF

1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 3.7E-02 NF 3.7E-02 NF NF NF

1930-1992 3.8E-03 NF 3.8E-03 NF NF NF Total 9.5E-03 NF 9.5E-03 NF NF NF

Year All Concrete & Masonry Comm. 0-5 years >5 years Total

1700-1799 2.7E-02 NF 2.7E-02 1800-1899 6.0E-03 NF 6.0E-03 1900-1909 7.5E-03 NF 7.5E-03

1910-1919 7.5E-03 NF 7.5E-03 1920-1929 2.0E-03 NF 2.0E-03

1930-1939 NF NF NF 1940-1949 2.4E-03 NF 2.4E-03 1950-1959 NF 1.0E-03 1.0E-03

1960-1969 NF NF NF 1970-1977 NF NF NF

1978-1982 NF NF NF 1983-1992 NF NF NF 1700-1929 5.4E-03 NF 5.4E-03

1930-1992 2.5E-04 2.5E-04 5.0E-04 Total 1.4E-03 2.0E-04 1.6E-03

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Table 2.53. Annual probability of failure (as at 1992, excluding China) -

tension/shear failures through dam body

Year Gravity Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 2.6E-03 2.4E-04 3.2E-04 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF 4.5E-05 4.1E-05 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 2.6E-04 6.0E-05 9.8E-05 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 7.7E-03 NF 3.2E-03

1983-1992(3) NF NF NF NF NF NF 1700-1929 4.6E-04 8.0E-05 1.0E-04 NF NF NF

1930-1992(3) 6.8E-05 1.3E-05 2.2E-05 3.1E-04 NF 4.9E-05 Total(3) 1.6E-04 4.6E-05 5.9E-05 2.5E-04 NF 3.1E-05

Year Buttress Multi-Arch Comm. 0-5 years(1) >5 years Total 0-5 years(1) >5 years Total

1700-1799 NF NF NF NF NF NF

1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF

1910-1919 9.4E-03 NF 6.1E-04 NF NF NF 1920-1929 NF NF NF 1.1E-02 NF 8.3E-04 1930-1939 NF NF NF NF NF NF

1940-1949 NF NF NF NF NF NF 1950-1959 2.4E-03 NF 3.2E-04 NF 1.8E-03 1.6E-03

1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF

1978-1982 NF NF NF NF NF NF 1983-1992(3) NF NF NF NF NF NF 1700-1929 3.7E-03 NF 2.5E-04 5.4E-03 NF 3.2E-04

1930-1992(3) 7.8E-04 NF 1.2E-04 NF 5.1E-04 4.3E-04 Total(3) 1.3E-03 NF 1.7E-04 2.0E-03 2.0E-04 3.7E-04

Year All Concrete & Masonry Comm. 0-5 years(1) >5 years Total

1700-1799 NF NF NF 1800-1899 2.4E-03 2.2E-04 3.0E-04 1900-1909 NF NF NF

1910-1919 7.5E-04 NF 4.9E-05 1920-1929 4.0E-04 3.2E-05 6.0E-05

1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 2.0E-04 3.1E-05 5.4E-05

1960-1969 1.9E-04 4.3E-05 7.1E-05 1970-1977 NF NF NF

1978-1982 9.2E-04 NF 3.8E-04 1983-1992(3) NF NF NF 1700-1929 7.2E-04 6.5E-05 1.0E-04

1930-1992(3) 1.5E-04 2.0E-05 4.1E-05 Total(3) 2.9E-04 4.0E-05 6.8E-05

Notes (1) Assumes dam years =

number of dams * five years life

(2) NF - No Failure (3) Assumes number of dams

constructed in 1983-1992 = 2 * number of dams in 1978-1982

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Table 2.54. Probability of failure (as at 1992, excluding China, non-annualised) -

tension/shear failures through dam body

Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 1.3E-02 3.3E-02 4.6E-02 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF 2.8E-03 2.8E-03 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 1.3E-03 1.3E-03 2.6E-03 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF 3.8E-02 NF 3.8E-02 1983-1992 NF NF NF NF NF NF 1700-1929 2.3E-03 7.0E-03 9.3E-03 NF NF NF 1930-1992 3.3E-04 3.3E-04 6.6E-04 1.5E-03 NF 1.5E-03

Total 7.7E-04 1.8E-03 2.6E-03 1.2E-03 NF 1.2E-03

Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF

1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF

1910-1919 4.7E-02 NF 4.7E-02 NF NF NF 1920-1929 NF NF NF 5.5E-02 NF 5.5E-02 1930-1939 NF NF NF NF NF NF

1940-1949 NF NF NF NF NF NF 1950-1959 1.2E-02 NF 1.2E-02 NF 5.9E-02 5.9E-02

1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF

1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1.9E-02 NF 1.9E-02 2.7E-02 NF 2.7E-02

1930-1992 3.8E-03 NF 3.8E-03 NF 1.5E-02 1.5E-02 Total 6.4E-03 NF 6.4E-03 9.7E-03 9.7E-03 1.9E-02

Year All Concrete & Masonry Comm. 0-5 years >5 years Total

1700-1799 NF NF NF 1800-1899 1.2E-02 3.0E-02 4.2E-02 1900-1909 NF NF NF

1910-1919 3.7E-03 NF 3.7E-03 1920-1929 2.0E-03 2.0E-03 4.0E-03

1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 1.0E-03 1.0E-04 2.0E-03

1960-1969 9.5E-04 9.5E-04 1.9E-03 1970-1977 NF NF NF

1978-1982 4.6E-03 NF 4.6E-03 1983-1992 NF NF NF 1700-1929 3.6E-03 5.4E-03 9.0E-03

1930-1992 7.5E-04 5.0E-04 1.3E-03 Total 1.4E-03 1.6E-03 2.9E-03

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Table 2.55. Number of failures during overtopping where the failure mode was

unknown

Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF 3 3 NF NF NF 1900-1909 NF 1 1 NF NF NF 1910-1919 NF 1 1 NF 1 1 1920-1929 NF NF NF 1 NF 1 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 NF 5 5 1 1 2 1930-1992 NF NF NF NF NF NF

Total NF 5 5 1 1 2

Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF

1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF

1910-1919 NF NF NF NF NF NF 1920-1929 1 NF 1 NF NF NF 1930-1939 NF NF NF NF NF NF

1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF

1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF

1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1 NF 1 NF NF NF

1930-1992 NF NF NF NF NF NF Total 1 NF 1 NF NF NF

Year All Concrete & Masonry Comm. 0-5 years >5 years Total

1700-1799 NF NF NF 1800-1899 NF 3 3 1900-1909 NF 1 1

1910-1919 NF 2 2 1920-1929 2 NF 2

1930-1939 NF NF NF 1940-1949 NF NF NF 1950-1959 NF NF NF

1960-1969 NF NF NF 1970-1977 NF NF NF

1978-1982 NF NF NF 1983-1992 NF NF NF 1700-1929 2 6 7

1930-1992 NF NF NF Total 2 6 8

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Table 2.56. No. of failures where the failure mode was unknown (no overtopping)

Year Gravity Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 1 NF 1 NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF 1 1 NF NF NF 1920-1929 1 NF 1 NF NF NF 1930-1939 1 NF 1 NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 1 1 2 NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1960-1982 NF NF NF NF NF NF 1960-1992 1 1 2 NF NF NF 1700-1929 2 1 3 NF NF NF 1930-1992 2 1 3 NF NF NF

Total 4 2 6 NF NF NF

Year Buttress Multi-Arch Comm. 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF NF NF 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1960-1982 NF NF NF NF NF NF 1960-1992 NF NF NF NF NF NF 1700-1929 NF NF NF NF NF NF 1930-1992 NF NF NF NF NF NF

Total NF NF NF NF NF NF

Year All Concrete & Masonry Comm. 0-5 years >5 years Total

1700-1799 NF NF NF 1800-1899 1 NF 1 1900-1909 NF NF NF 1910-1919 NF 1 1 1920-1929 1 NF 1 1930-1939 1 NF 1 1940-1949 NF NF NF 1950-1959 NF NF NF 1960-1969 1 1 2 1970-1977 NF NF NF 1978-1982 NF NF NF 1983-1992 NF NF NF 1960-1982 NF NF NF 1960-1992 1 1 2 1700-1929 2 1 4 1930-1992 2 1 2

Total 4 2 6

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2.4.1.5 Gravity Dams - Separation of Concrete and Masonry Dams

The ICOLD(1984) population for gravity dams does not distinguish between dams

made of concrete and those made of masonry. An estimate was made for the population

taking into account the history of dam building and the USA population of dams. Dams

of cyclopean concrete construction were assumed to be concrete.

According to Smith (1972), Schnitter (1994) and Lewis (1988) the first concrete dams

were completed in the 1870’s in Australia and the USA; the 1890’s in India; and the

1900’s in Great Britain. The distribution of concrete and masonry gravity dams in the

USA was taken from the 567 concrete and masonry dams in the US Inventory of dams

(1994) and is presented in Table 2.57.

Table 2.57. Distribution of concrete and masonry gravity dams in the USA

Year Commissioned

Concrete (%)

Masonry (%)

Pre 1900 68.4 31.6 1900-1909 76.5 23.5 1910-1919 93.7 6.3 1920-1929 96.3 3.7 1930-1939 98.3 1.7 1940-1949 100 0 1950-1959 98.9 1.1 1960-1969 100 0 1970-1979 100 0 1980-1989 100 0 1990-1992 100 0

Table 2.57 was not used directly as this was likely to be biased towards concrete dams

due to the modern nature of USA dams compared to much of the rest of the world. It is

also possible that some dams denoted as ‘gravity’, and therefore assumed to be

concrete, in the US database are masonry. Some countries such as India, which has

approximately 3.2% of the world concrete and masonry dam population (ICOLD,

1994), commonly use masonry to construct their dams due to material availability and

expense. Table 2.58 shows the distribution chosen for the analysis. It was found that the

probabilities of failure were not sensitive to the assumptions in the concrete/masonry

distribution for the post 1960 period.

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Table 2.61 to Table 2.64 show the annualised probabilities of failure for concrete and

masonry dams for the various failure modes. Table 2.65 and Table 2.66 show the

number of failures with unknown failure modes. Table 2.65 shows those unknowns

where failure during overtopping was known to have occurred. A distinction was made

between dams commissioned prior to, and those commissioned after 1930. This

represents the historical change to a better understanding of uplift pressures and

materials properties for gravity dams. Table 2.59 summarises the annualised

probabilities of failure using this distinction. As there were a number of categories

without failures (denoted ‘NF’) a ‘maximum’ annual probability (assuming one failure

to have occurred over the number of dam years) has been calculated and included in the

last row of Table 2.59.

Table 2.51 gives suggested average annualised probabilities of failure for concrete and

masonry gravity dams based on Table 2.59. Unknowns were accounted for by

distributing them evenly through the three dam failure modes (foundation sliding and

piping and failure within the dam body). This allowed for the total probability to be

equal to the sum of the three modes. The probabilities have been rounded down (to one

decimal place) to account for the assumptions in the analysis. In particular, the

population used was that in existence as at 1992 and many dams are likely to have been

decommissioned prior to this time or omitted from the ICOLD database and hence not

included in the population. A larger population would result in lower probabilities of

failure. This was checked for validity by assuming a larger population and re-running

the analysis. Where no failures have occurred the suggested value is lower than that for

the case where one failure had occurred.

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Table 2.58. Distribution of concrete and masonry gravity dams chosen for analysis

Year Commissioned

Concrete (%)

Masonry (%)

Pre 1900 0/30 100/70 1900-1909 60 40 1910-1919 75 25 1920-1929 90 10 1930-1939 90 10 1940-1949 95 5 1950-1959 95 5 1960-1969 97.5 2.5 1970-1979 97.5 2.5 1980-1989 97.5 2.5 1990-1992 97.5 2.5

Note (1) 1700-1799/1800-1899

Table 2.59. Summary of annualised probabilities of failure for gravity dams (exc.

China)

Concrete Gravity Masonry Gravity Failure Mode

Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1700-1929 1.0E-03 9.3E-05 1.5E-04 5.2E-03 3.4E-04 5.4E-04 All Modes 1930-1992 1.4E-04 1.4E-05 3.5E-05 1.6E-03 2.4E-04 4.2E-04

1700-1929 6.7E-04 7.0E-05 1.1E-04 1.5E-03 NF 6.0E-05 Foundation Sliding 1930-1992 NF NF NF NF NF NF

1700-1929 3.4E-04 NF 2.2E-05 1.5E-03 NF 6.0E-05 Foundation Piping 1930-1992 NF NF NF NF NF NF

1700-1929 NF NF NF 7.3E-04 1.6E-04 1.8E-04 Within Dam Body 1930-1992 7.1E-05 NF 1.1E-05 NF 2.4E-04 2.1E-04

1700-1929 3.3E-04 2.3E-05 2.2E-05 7.3E-04 3.1E-05 3.0E-05 Max. No Fails(1) 1930-1992 7.0E-05 1.4E-05 1.1E-05 1.6E-03 2.4E-04 2.1E-04

1700-1929 - - - - 6 6 Unknown (O/T) 1930-1992 - - - - - -

1700-1929 - 1 1 3 - 3 Unknown 1930-1992 2 2 4 2 - 2

Note (1) Assuming 1 failure (for where no failures have occurred)

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Table 2.60. Suggested values for annualised probabilities of failure for gravity

dams (excluding China)

Concrete Gravity Masonry Gravity Failure Mode

Year Commissioned 0-5 years >5 years 0-5 years >5 years

pre 1930 N/A 6.4E-052 N/A 3.2E-042 All Failures 1930-present 1.3E-042 1.2E-052 1.5E-032 2.4E-042

pre 1930 N/A 5.0E-052 N/A 6.0E-051 Foundation Sliding PSA 1930-present 2.0E-051 4.0E-061 5.0E-041 2.0E-051

pre 1930 N/A 7.0E-061 N/A 6.0E-052 Foundation Piping PPA 1930-present 2.0E-051 4.0E-061 5.0E-041 2.0E-051

pre 1930 N/A 7.0E-061 N/A 2.0E-042 Within Dam Body PBA 1930-present 9.0E-052 4.0E-061 5.0E-041 2.0E-042

Note: (1) No failures, probability estimated lower than that for one failure. (2) Probability rounded down to account for smaller than actual population used in the analysis.

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Table 2.61. Annualised probabilities of failure for gravity dams - all failures

Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF 5.9E-03 NF 1.2E-04 1800-1899 NF NF NF 7.5E-03 5.5E-04 7.9E-04 1900-1909 3.0E-03 3.7E-04 5.2E-04 NF 2.7E-04 2.6E-04 1910-1919 1.3E-03 8.9E-05 1.7E-04 3.8E-03 2.7E-04 5.0E-04 1920-1929 6.0E-04 4.9E-05 9.0E-05 5.4E-03 4.4E-04 8.1E-04 1930-1939 NF NF NF 6.0E-03 NF 5.3E-04 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 5.3E-04 6.1E-05 1.5E-04 NF 2.4E-03 1.9E-03 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 1.0E-03 9.2E-05 1.5E-04 5.1E-03 3.4E-04 5.4E-04 1930-1992 1.4E-04 1.4E-05 3.4E-05 1.6E-03 2.4E-04 4.2E-04

Total 2.9E-04 4.3E-05 7.5E-05 4.0E-03 3.3E-04 5.2E-04

Table 2.62. Annualised probabilities of failure for gravity dams - sliding failures

Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF 1.9E-03 NF 6.6E-05 1900-1909 3.0E-03 3.7E-04 5.2E-04 NF NF NF 1910-1919 NF NF NF 3.8E-03 NF 2.5E-04 1920-1929 6.0E-04 4.9E-05 9.0E-05 NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 6.7E-04 6.9E-05 1.1E-04 1.5E-03 NF 6.0E-05 1930-1992 NF NF NF NF NF NF

Total 1.2E-04 2.6E-05 3.7E-05 1.0E-03 NF 5.2E-05

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Table 2.63. Annualised probabilities of failure for gravity dams - piping failures

Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF 5.9E-03 NF 1.2E-04 1800-1899 NF NF NF 1.9E-03 NF 6.6E-05 1900-1909 NF NF NF NF NF NF 1910-1919 1.3E-03 NF 8.3E-05 NF NF NF 1920-1929 NF NF NF NF NF NF 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 NF NF NF NF NF NF 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1700-1929 3.3E-04 NF 2.2E-05 1.5E-03 NF 6.0E-05 1930-1992 NF NF NF NF NF NF

Total 5.8E-05 NF 7.5E-06 1.0E-03 NF 5.2E-05

Table 2.64. Annualised probabilities of failure for gravity dams - dam body

tension/shear failures

Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF 1.9E-03 2.7E-04 3.3E-04 1900-1909 NF NF NF NF NF NF 1910-1919 NF NF NF NF NF NF 1920-1929 NF NF NF NF 4.4E-04 4.1E-04 1930-1939 NF NF NF NF NF NF 1940-1949 NF NF NF NF NF NF 1950-1959 NF NF NF NF NF NF 1960-1969 2.7E-04 NF 4.9E-05 NF 2.4E-03 1.9E-03 1970-1977 NF NF NF NF NF NF 1978-1982 NF NF NF NF NF NF 1983-1992 NF NF NF NF NF NF 1960-1982 1.6E-04 NF 3.6E-05 NF 1.8E-03 1.4E-03 1960-1992 1.3E-04 NF 3.4E-05 NF 1.8E-03 1.3E-03 1700-1929 NF NF NF 7.3E-04 1.6E-04 1.8E-04 1930-1992 7.0E-05 NF 1.1E-05 NF 2.4E-04 2.1E-04

Total 5.8E-05 NF 7.5E-06 5.0E-04 1.6E-04 1.8E-04

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Table 2.65. Number of failures during overtopping where failure mode was

unknown

Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1700-1799 NF NF NF NF NF NF 1800-1899 NF NF NF NF 4 4 1900-1909 NF NF NF NF 1 1 1910-1919 NF NF NF NF 1 1

Total NF NF NF NF 6 6

Table 2.66. Number of failures where failure mode was unknown

Concrete Gravity Masonry Gravity Year Commissioned 0-5 years >5 years Total 0-5 years >5 years Total

1800-1899 NF NF NF 2 NF 2 1910-1919 NF 1 1 NF NF NF 1920-1929 NF NF NF 1 NF 1 1930-1939 NF NF NF 1 NF 1 1960-1969 1 1 2 NF NF NF 1930-1992 1 1 2 1 NF 1

Total 1 2 3 4 NF 4

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2.4.2 General Approach for Estimating the Probability of Failure for

Individual Gravity Dams

Not all dams can be considered as ‘average’. Corrections can be made to the average

probabilities so that they can be used for particular dams. The following describes a

method to assess multiplication factors for concrete and masonry gravity dams that can

be applied to the ‘average’ probabilities from the previous section for better or worse

than ‘average’ dams. The method is for gravity dams that have a straight axis (no

curvature) and are not post-tensioned.

Where a dam is constructed of masonry but can be shown to be of a quality comparable

to that of a good concrete gravity dam, the average annual probability may be taken as

somewhere between that for masonry and that for concrete.

Where a dam has been raised and the full supply level (FSL) increased, the dam should

be treated as a ‘new’ dam and the age of the dam calculated from this time. That is, the

dam should fall back into the 0-5 years category. This stems from the Section 2.3.4 that

showed that dams have generally failed at or just above their highest recorded water

level.

If the dam is of good design, is very well drained, has good uplift monitoring AND the

dam foundation has been assessed by a suitably qualified rock mechanics practitioner

and found to easily satisfy present day standards then a reduction factor, fred, of between

0.9 and 0.1 can be used. This factor should be applied to the annual probability of

failure in Equation 2.6. This factor can NOT be applied to dams with soil foundations

and should NOT be used for initial dam screening assessments where the data available

and the level of investigation and analysis are limited.

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2.4.3 Details of the Method for Estimating the Probability of Failure for

Individual Gravity Dams

The following summarises the suggested procedure for estimating the annual probability

of failure of a concrete or masonry gravity dam. The annual probability of failure of the

dam, P, should be calculated as the sum of the probabilities of failure for sliding, piping

and through the dam body.

• Sliding through the foundation:

Step (1) Determine the average annual probability of failure, PSA, from Table 2.51 in

Section 2.4.1.5.

(2) Determine the multiplication factor for sliding on a soil or rock foundation,

fSF, from Table 2.72 in Section 2.4.4.1.

(3) If the foundation is rock go to Step (4), if it is soil go to Step (5).

(4) Determine the geology type factor, fSG, from

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Table 2.75 in Section 2.4.4.2, then go to Step (6)

(5) fSG = 1.0

(6) Determine the structural height/width factor, fH/W, from Table 2.77 in Section

2.4.4.4.

(7) Determine the other observations factor, fO, from Section 2.4.4.5.

(8) Determine the surveillance factor, fS, from Table 2.78 in Section 2.4.4.6.

(9) Calculate the probability of a foundation sliding failure as:

P P f f f f fS SA SF SG H W O S= × × × × ×/ (2.3)

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• Piping through the foundation:

Step (1) Determine the average annual probability of failure, PPA, from Table 2.51 in

Section 2.4.1.5.

(2) Determine the multiplication factor for piping on a soil or rock foundation,

fPF, from Table 2.72 in Section 2.4.4.1.

(3) If the foundation is rock go to Step (4), if it is soil go to Step (5).

(4) Determine the geological environment, fGE, factor from Section 2.4.4.3, then

go to Step (6).

(5) fGE = 1.0

(6) Determine the structural height/width factor, fH/W, from Table 2.77 in Section

2.4.4.4.

(7) Determine the other observations factor, fO, from Section 2.4.4.5.

(8) Determine the surveillance factor, fS, from Table 2.78 in Section 2.4.4.6.

(9) Calculate the probability of a foundation piping failure as:

P P f f f f fP PA PF GE H W O S= × × × × ×/ (2.4)

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• Failure through the dam body:

Step (1) Determine the average annual probability, PBA , of failure from Table 2.51 in

Section 2.4.1.5.

(2) Determine the structural height/width factor, fH/W, from Table 2.77 in Section

2.4.4.4.

(3) Determine the other observations factor, fO, from Section 2.4.4.5.

(4) Determine the surveillance factor, fS, from Table 2.78 in Section 2.4.4.6.

(5) Calculate the probability of a failure through the dam body as:

P P f f fB BA H W O S= × × ×/ (2.5)

• Total annual probability of failure:

( )BPSred PPPfP ++= (2.6)

where,

fred = Reduction factor, only applied when conditions described in Section

2.4.2 are satisfied.

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2.4.4 Gravity Dam Probability Multiplication Factors

The following outlines the basis for assigning the multiplication factors. The factors,

where possible, have been based on the failure statistics in the previous sections. Where

necessary the accident statistics have been used to assist in developing the

multiplication factors. It should be noted however, that most of the dam accidents were

‘theoretical’ (eg. a calculation was performed that indicated the dam was unsafe and it

was anchored) and as such of little value to this exercise.

2.4.4.1 Soil/Rock Foundation Factor, fSF and fPF

The probability of a dam failing through the foundation is highly dependent on whether

the foundation is soil and/or rock. An estimation of the multiplication factors for sliding

and piping of gravity dams on soil and rock foundations is outlined below.

The percentage of soil and rock foundations in the world population was estimated from

the USBR, Australia/New Zealand, and Portugal populations (Table 2.67 to Table 2.69)

and is shown in Table 2.70. It is recognised that this may be a somewhat biased sample

but there was no way of practically obtaining data for a larger population.

Table 2.67. Foundation types - USBR

Foundation Gravity Arch Buttress Multi-Arch Total Rock 18 31 6 - 55 Soil 1 - 1 - 2 Soil and Rock 2 - - - 2 Total 21 31 7 - 59

Table 2.68. Foundation types - Australia/New Zealand

Foundation Gravity Arch Buttress Multi-Arch Total Rock 84 40 6 1 131 Soil - - - - 0 Soil and Rock 3 - - - 3 Total 87 40 6 1 134

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Table 2.69. Foundation types - Portugal

Foundation Gravity Arch Buttress Multi-Arch Total Rock 26 20 4 2 52 Soil - - - - 0 Soil and Rock 1 - - - 1 Unknown 1 - - - 1 Total 28 20 4 2 54

Table 2.70. Gravity dam foundation types - combined

Foundation Number % Rock 128 94.1 Soil 1 0.7 Soil and Rock 6 4.4 Unknown 1 0.7 Total 136 100

The number of failures (both sliding and piping) in a particular foundation type is

shown below.

Table 2.71. Foundations for gravity dam failures by sliding or piping

Foundation Piping Sliding PG PG(M) PG PG(M)

Rock 5 2 Soil 2

Soil and Rock 1 Total 1 2 5 2

To determine the factors for soil and rock the following assumptions were made:

• All piping failures occurred through the soil section of the foundation.

• Combined soil/rock (S/R) foundations are taken as soil.

• Unknown foundation types are rock.

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The factors were calculated as:

fpercent of failures

percent of population= (2.7)

For example, the factor for piping through soil foundations is:

f PF = =100%51%

19 6.

. (2.8)

Where there are no failures (0%) the factor is zero. To overcome this problem it was

assumed that 1% of all foundation failures would occur on this particular foundation

type. The results of this analysis are shown in Table 2.72. Table 2.72 shows that the

factor for sliding on rock is greater than that for soil. This can be justified by the fact

that no sliding failures have occurred on soil. It is likely that engineers have taken the

soil into account in the dam design whereas, there may be defects which drastically

reduce the foundation strength, in a rock foundation that may be overlooked in the

design. Historically no gravity dam piping failures have occurred in rock foundations. A

number of accidents have occurred as shown in Table 2.73. It is likely that there is

sufficient warning of the progression of piping through rock foundations to allow for

action to be taken to prevent failure.

Table 2.72. Gravity dam factors for piping and sliding failure on soil and rock, fSF

and fPF

Foundation Piping, fPF Sliding, fSF Rock 0.01* 1.1

Soil or Soil and Rock 19.6 0.2* * These values were derived by assuming 1% failures.

Table 2.73. Foundation types - accidents

Piping Sliding Foundation PG PG(M) PG PG(M)

Rock 9 1 5 1 Soil 1

Soil and Rock Unknown 1

Total 11 1 5 1

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2.4.4.2 Geology Types - Sliding on Rock, fSG

Some rock types are more likely to have weaknesses in the foundation (Fell et al, 1992),

so a geology type factor has been included. The geology population was calculated from

a weighted average of the representative populations from the USBR, Australia/New

Zealand and Portugal. The population for the whole of the USA was assessed by

considering the overall geology map of the USA and comparing the distribution of

geology types west of longitude 100°W (where the USBR population lies) with that east

of longitude 100°W. A weighted average population was created using the number of

gravity dams in the respective countries as given in ICOLD (1984) as weighting factors.

Equation 2.9 shows the method used. Table 2.74 gives the weighting factors used in the

analysis. Table 2.76 shows the weighted population and the number of sliding failures

in each foundation. The calculated and adopted sliding factors are also included. Table

2.75 shows a summary of the factors adopted. Where there is a high chance of a through

going defect beneath the dam a factor of 3 should be used. The following points should

be noted:

• There were three failures in sandstone/shale foundations and none in sandstone

alone.

• There was one failure in a combined limestone/dolomite foundation.

GG G G

G G G=

+ +1 1 2 2 3 3

1 2 3

α α α (2.9)

where,

G is the weighted geology type population

G1, G2 and G3 are the geology type populations for each region

α1, α2 and α3 are the weighting factors

Table 2.74. Weighting factors used for weighted average (ICOLD (1984) dam

population)

Population α Australia/ New Zealand 81 Portugal 27 USA 528

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Table 2.75. Adopted gravity dam factors for sliding on a rock foundation, fSG

Geology Type Multiplication Factor

Comments

shale, claystone sandstone with shale interbeds limestone with shale interbeds default for sandstone

3

Where a dam is known to be on sandstone but it can not be proved that no shale/claystone exists then the default of 3 should be taken.

Mudstone, siltstone, Conglomerate Schist, gneiss, phyllite, slate Hornfels, limestone, dolomite

1.5

Mudstone and siltstone represent a transition from shale to sandstone. Others based on failure statistics.

Granite Granodiorite

0.3

A low factor has be deemed appropriate as there have been no sliding failures on granite yet there exists a large population of dams.

Others

0.9 Where it can be proved that the dam foundation comprises ONLY sandstone 0.9 can be used else, a factor of 3 should be taken

Page 196: Shear Strength of Rock

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Table 2.76. Gravity dam factors for sliding on a rock foundation

Failures Factors Geology Type

Population % No. % Calculated Adopted

Comments

Total 100 13 100 Sandstones 21.1 3 23.1 1.1 0.9 No sandstone only failures

so treated as no failures Shale 8.0 4 30.8 3.9 3 Based on failure data, includes

shale & sandstone Siltstone 0.5 0.0 0.0 1.5 Assumed transitional between

shale & sandstone Conglomerate 3.6 1 7.7 2.1 1.5 Based on failure data Limestone 3.6 1 7.7 2.1 1.5 Based on failure data Claystone 0.3 0.0 0.0 3 Similar properties to shale Mudstone 0.4 0.0 0.0 1.5 Assumed transitional between

shale & sandstone Chert 0.2 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1 Breccia 0.2 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1 Dolomite 3.6 1 7.7 2.1 1.5 Based on failure data Marl 3.6 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1 Schist 11.4 2 15.4 1.4 1.5 Based on failure data Quartzite 0.8 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1 Gneiss 0.7 0.0 0.0 1.5 Similar properties to schist Phylitte 0.5 0.0 0.0 1.5 Similar properties to schist Slate 0.3 0.0 0.0 1.5 Similar properties to schist Hornfels 3.3 1 7.7 2.4 1.5 Based on failure data Argillite 0.1 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1

Granite 20.1 0.0 0.0 0.3 Factor would be 0.4 assuming 1 failure

Basalt 5.0 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Tuff 2.4 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Dolerite 0.8 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Rhyolite 1.9 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Andesite 0.3 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Porphyry 0.2 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Diorite 3.4 0.0 0.0 0.9 No fails so adjusted such that Σ (Pop × Factor) ≈ 1

Granodiorite 0.3 0.0 0.0 0.3 Similar properties to granite Greenstone 3.4 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1 Agglomerate 0.1 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1 Pumice 0.1 0.0 0.0 0.9 No fails so adjusted such that

Σ (Pop × Factor) ≈ 1

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2.4.4.3 Geology Type - Piping on Rock, fGE

As there have been no piping failures of concrete dams on rock foundations it was

decided to take all factors as unity. Another factor, which takes account of problem

geological environments, was used as a better indicator of variations of likelihood of

failure from the average. The environments considered for this were those that allowed

for the possibility of open joints and include:

• Granitic foundations with sheet joints;

• very steep sided narrow valleys with likely stress relief joints parallel to the ground

surface;

• sedimentary sequences with stress relief effects;

• very weak erodible volcanics; and

• limestone or dolomite. (Reference Fell, MacGregor and Stapledon, 1992)

The factor should be chosen on a site by site basis but should not exceed 2. The

minimum multiplication factor should be 1. The default value (where the environment is

unknown) should also be taken as 1.

2.4.4.4 Height on Width Ratio, fH/W

The structural height to width ratio (hd/W) is used to take account of the

stockiness/slenderness of the gravity dam. Hence the hd/W ratio offers a first order

guide to the relative likelihood of failure by sliding and within the body of the dams. A

database of hd/W ratios was collected from the Australia/New Zealand, USBR

populations and from selected ICOLD international conferences (Questions 26, 30, 45,

52, 56, 59, 65). Where found, dams with any curvature were excluded. Figure 2.43 and

Figure 2.44 show scatter plots of hd/W versus year commissioned and hd respectively

for the population and failed dams. Failures are scattered amongst the population,

although the majority appear to be more concentrated above the average hd/W ratio. The

hd/W population does not show any correlation with year commissioned. However, as hd

increases hd/W approaches approximately 1.2. It was decided to apply factors as shown

in Table 2.77 and Figure 2.45. These factors have been derived by dividing the

percentage of failures (due to sliding or in the dam body) by the percentage of the

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Analysis of Concrete and Masonry Dam Incidents Page 2.165

population in each hd/W range, in a similar manner to those for sliding and piping in

Section 2.4.4.1.

Table 2.77. Multiplication factors for structural height/width ratio of gravity dams,

fH/W

hd/W <1.0 1.0-1.19 1.2-1.39 1.4-1.59 1.6-1.79 1.8-1.99 Factor 0.1 0.5 0.9 1.3 3 6

Page 199: Shear Strength of Rock

Page 2.166

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

Year Commissioned

hd/W

.

Population - Concrete Gravity

Population - Masonry Gravity

Population - Unknown Gravity

Failure - Sliding

Failure - Body

Figure 2.43. hd/W versus year commissioned

Page 200: Shear Strength of Rock

Page 2.167

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0 20 40 60 80 100 120 140 160 180 200

hd

hd/W

.

Population - Concrete GravityPopulation - Masonry GravityPopulation - Unknown GravityFailure - SlidingFailure - Body

Figure 2.44. hd/W versus hd

Page 201: Shear Strength of Rock

Page 2.168

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

hd/W

Fact

or (%

Fai

lure

s/%

Pop

ulat

ion)

.Sliding

Body

Combined

Suggested

Figure 2.45. hd/W factors

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Analysis of Concrete and Masonry Dam Incidents Page 2.169

2.4.4.5 Other Observations, fO

This section allows for a multiplication factor to be applied for observed conditions or

special features of the dam. These features will vary with each dam and must be

assessed on a dam by dam basis. The minimum value for any dam should be 0.9 (no

signs of distress, no or very little leakage). The default value should be 1.0. Conditions,

which would warrant a higher multiplication factor (up to a maximum of 10), include:

• Sudden increases in seepage through the dam or foundation

• Cracking (of a nature that could effect the dam’s stability)

• High or non-linear uplift pressures (also blocked drains)

• Alkali aggregate reaction (AAR) or alkali silica reaction (ASR)

• Extensive calcite deposits

• Large/non-linear dam movements

2.4.4.6 Surveillance, fS

Historically, unlike embankment dams, most gravity dams have failed with only a short

amount of warning. This warning may be enough to warn people downstream but, is

usually insufficient to enable the dam to be saved from failure. However dams will

sometimes begin to show some signs of problems developing, allowing intervention (eg

by controlling the water level, or by remedial works). Hence it is considered reasonable

to apply a factor to allow for the quality of monitoring and surveillance. Table 2.78

shows the multiplication factors recommended. The multiplication factors have been

modified from those given by Foster et al (1998) for embankment dams.

Table 2.78. Monitoring and surveillance multiplication factors, fS

Surveillance Embankment Dam Factor

Factor fS

Inspections annually 2.0 1.5 Inspections monthly 1.2 1.1 Irregular seepage observations, inspections weekly 1.0 1.0 weekly seepage monitoring, weekly inspections 0.8 0.9 Daily monitoring of seepage, daily inspections 0.5 0.8

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2.4.5 Results

Figure 2.46 and Figure 2.47 show the potential ranges for the annual probabilities of

failure for various cases. The ‘average’ dam has been taken as a dam that has: a geology

type factor, fSG, of 0.9; a height to width ratio, hd/W, of 1.3; and the remaining

multiplication factors as unity. A number of dams that have failed have been plotted

together with dams from the Australia/New Zealand population and USBR population

of concrete and masonry gravity dams. None of the dams plotted have the fred reduction

factor, as it could not be proven that they satisfied the criteria described above. Where

unknown, multiplication factors were taken as their default or unity. For the most

common type of dam (commissioned after 1930, greater than five years in age and on a

rock foundation) the potential average probabilities using the method range from 4 x 10-

8 to 1 x 10-3.

ANZ damfailed dammin USBR dammaximum 'average'

1E-81E-71E-61E-51E-41E-31E-21E-11E+0

post 1930/<5 years/soil fndn

post 1930/<5 years/rock fndn

post 1930/>5 years/soil fndn

post 1930/>5 years/rock fndn

pre1930/>5 years/soil fndn

pre1930/>5 years/rock fndn

Probability of Failure

Figure 2.46. Range of annual probability of failure for concrete gravity dams

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Analysis of Concrete and Masonry Dam Incidents Page 2.171

1E-81E-71E-61E-51E-41E-31E-21E-11E+0

post 1930/<5 years/soil fndn

post 1930/<5 years/rock fndn

post 1930/>5 years/soil fndn

post 1930/>5 years/rock fndn

pre1930/>5 years/soil fndn

pre1930/>5 years/rock fndn

min'average'failed damsmaximum

Probability of Failure

Figure 2.47. Range of annual probability of failure for masonry gravity dams

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2.5 DISCUSSION AND CONCLUSIONS

Most of the results have been discussed in Section 2.3. Below is a brief discussion of

the major components of CONGDATA.

• Year commissioned

The data shows a distinct increase in incidents for all concrete/masonry dam types in the

1920’s. Another peak occurred in the 1960’s for concrete gravity and concrete arch

dams. There were no failures in gravity dams commissioned between 1930 and 1963.

Based on the population data there appears to be a reduction in the failure rate with

time. Buttress and multi-arch dams show some various peaks due to their limited

populations.

• Height

No concrete or masonry dams greater than 70m are reported to have failed. Failures in

masonry gravity dams appear to be concentrated below 50m in height. Concrete gravity

dams tend to be spread out more. Accidents and more particularly major repairs are

more evident in greater height concrete dams than masonry gravity dams. This however,

is likely to be due to the lower height at which masonry dams are constructed.

The ratio of failures to population does not exhibit any major trend. There appears to be

a higher percentage of failures to population in the 40-49m and 60-69m height ranges.

Arch, buttress and multi-arch dams are shown to be more likely to have failures in the

15-39m range.

• Age at failure

There is a large proportion of dams that have failed during first filling. An analysis of

the water levels at failure show most dams failed at their highest recorded water level.

Several of these were only slightly higher than that recorded previously. There appears

to be a slight rise in the rate of failures with time (ignoring first filling). After 40 years

of age there is a jump in the failure rate. It should be noted that the older age groups are

Page 206: Shear Strength of Rock

Analysis of Concrete and Masonry Dam Incidents Page 2.173

represented by a small population. Concrete gravity dams of less than five years age

appear to have a greater chance of failure compared to older concrete gravity dams.

Masonry gravity dams are more evenly distributed throughout the ages.

A noticeable problem with the accident/major repair data is its bias to the post 1920’s

whereas failures occur much further back. This can be put down to a lack of detailed

dam information in the period prior to 1920. Large dam failures would still have been

published during these times.

Piping tends to occur early in a dams life (<5 years, with one exception). Sliding of the

foundation also tends to occur early but is not as restricted as piping. Structural

problems seem to be more likely than foundation problems with age. Concrete dams

have a tendency to fail at younger ages than masonry dams. Most older (masonry) dam

failures have overtopping as a component. Unfortunately there is usually little

information as to the actual mode of failure.

• Incident causes

Foundation problems (sliding, leakage and piping) are the main causes of failure to

concrete dams, overtopping tends to play a bigger part in the failure of masonry dams.

Accidents and major repairs are more likely to come about due to surficial damage to

the dam structure or noticeable uplift or leakage in the foundation.

Piping is the main cause of failure for dams with soil foundations. Overtopping and

foundation shear strength are the main causes of failure for dams with rock or unknown

foundations.

• Warning types

Overtopping was the most common failure warning type. This was mainly due to the

masonry gravity dams which are more susceptible to overtopping failure. This could be

due to the poorer quality downstream face of masonry dams which can be eroded during

overtopping events and/or the higher permeability of masonry dams which results in a

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more rapid increase in uplift pressures. For accidents, and even more so for major

repairs, the warning signs tend to be visual damage of the dam or excessive leakage.

An analysis of all dam failures showed that, where information was available, most had

some warning which could have resulted in the warning and evacuation of residents

downstream. Often the warning was a sudden increase in the amount and rate of

leakage.

• Remedial measures

Where a dam has failed it is usually abandoned or reconstructed with a new design. In

the case of accidents and major repairs it is most common that the damaged section is

replaced with no effect to the dam structure as a whole.

• Geology

Soils and limestones are more likely to have piping problems. The alluvial soils have a

tendency to pipe under the high gradients imposed. No dam has been reported to have

failed by sliding on alluvial soils. Normally a large concrete or masonry dam would not

be built on a soil foundation.

Shale (interbedded with other sedimentary units) has a greater tendency to be involved

with sliding failure because of the likely presence of weaknesses in the bedding such as

bedding surface shears. It is interesting that sandstone does not appear to be over

represented when the population is taken into account. Failures tend not to occur in

sandstone alone but only when the sandstone is interbedded with shale. Shale and

limestone (often interbedded) have a high incidence for failing. The limestone has a

high proportion of accidents generally due to excessive leakage through dissolution.

Another point of note is that no incidents have occurred in basalt foundations. These

conclusions agree with the general knowledge regarding the geology types (e.g. as

described in Fell et al, 199211).

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• Other design factors

The factors in Section 2.3.9 suffered from a lack of information. Generally these could

only be obtained if a dam’s cross section was available. From the data collected it

appears that the failed dams suffered from a lack of ‘good engineering’. Very few dams

were found with galleries (1 dam); drainage (1 dam); grout curtains (4 dams);and shear

keys (1 dam). The downstream slopes appeared to be too steep. Six gravity failures had

downstream slopes of 0.6:1 (H:V) or less. Failed dams, particularly gravity dams, were

usually located in relatively wide valleys or were composite sections with earthfill

dams. Three dimensional effects are unlikely to have contributed any strength in these

cases. hwf/W ratios ranged from 0.6 to 2.1 with an average of 1.35.

Generally, unlike embankment dams, concrete and masonry dams are analysable and

hence can readily be checked for stability. The major unknowns for these dams lie in the

foundation where sliding and piping failures can occur.

Section 2.4 gives a method for assessing the first order probability of failure of masonry

or concrete gravity dams. The method accounts for dam age, year commissioned and

type; failure mode; foundation geology; height to width ratio; and monitoring and

surveillance. General probabilities of failure for arch, buttress and multi-arch dams,

based on failure and population statistics, are included.

The author cautions that this approach should only be used as a first order

approximation of the annual probabilities of failure. It is clearly very approximate, and

suffers from being based on small numbers of failures, and limited quality data. Where

significant decisions on dam safety are being made, detailed deterministic and/or

probabilistic methods should be used.

The results from the analysis of CONGDATA are subject to the limitations mentioned

earlier. Whilst all care has been taken in compiling data, it should be remembered that

the information in CONGDATA has come from numerous sources, not all of which

could be validated. The analysis of dams in CONGDATA does not take into account

such things as: surveillance; quality of construction; and quality of geological

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Analysis of Concrete and Masonry Dam Incidents Page 2.176

description. It is therefore recommended that this work be used in a qualitative sense

only.

Page 210: Shear Strength of Rock

The Strength of Intact Rock Page 3.1

3 THE SHEAR STRENGTH OF INTACT ROCK

3.1 INTRODUCTION

The application of the Hoek-Brown criterion (Hoek & Brown, 1980) to intact rock and

rock masses is common in slope engineering, so it is important that it is validated in

both applications, and that the uncertainty of its predictions are well understood. This

chapter presents a detailed analysis of the application of the criterion to laboratory test

data on intact rock and suggests modifications that provide improved predictions of

triaxial strength based on easily measured material properties.

The data consists of 4507 test results from 511 sets obtained from the literature and

original laboratory test reports.

Page 211: Shear Strength of Rock

The Strength of Intact Rock Page 3.2

3.2 FAILURE CRITERIA FOR INTACT ROCK

Equation 3.1 presents a generalised criterion where a1, a2, etc are material properties.

Figure 3.1 presents a generalised failure criterion in the σ′1-σ′3 plane and shows the

locations of the unconfined compressive strength, σc, Brazillian strength, σBt, uniaxial

tensile strength, σut and pure tensile strength,σpt.

,....),,,,(fn0 21321 aaσσσ= (3.1)

Sigma 3 / Sigma C

Sig

ma

1 / S

igm

a C

-1

0

1

2

3

-0.25 0.00 0.25 0.50

σc

σpure t

σuniaxial t

σBrazillian t

Figure 3.1. Generalised failure criterion

There are two approaches to the selection of a failure criterion for intact rock,

theoretical and empirical. The base of the most commonly adopted theoretical

approaches are those of Coulomb:

φστ tannc += (3.2)

or Griffith’s (1924) criterion for fracture initiation:

( ) ( )312

31 8 σσσσσ +−=− t (3.3)

σ′3/σc

σ′1/σc

Page 212: Shear Strength of Rock

The Strength of Intact Rock Page 3.3

Most practical engineering relies on a linear Mohr’s envelope being fitted to

experimental data or to the relevant portion of a theoretical or empirical criterion.

Notwithstanding this it is becoming increasingly common for computer software to be

able to deal directly with one or more non-linear criteria. Thus while the limits and

pitfalls of linearisation are well understood, it is now important to assess the accuracy of

non-linear criteria.

It is well known that the theoretical criteria do not accurately predict the failure strength

of rock and often rely on parameters that are difficult to measure (Ramamurthy et al,

1988, Andreev, 1995, Parry, 1995). Figure 3.2 by Johnston & Chiu (1984) shows that

equations based on the work by Griffith provide poor fits to Melbourne mudstone. For

these reasons many criteria have been developed that seek to capture the important

elements of measured rock strengths or seek to modify theoretical approaches to

accommodate experimental evidence, several of these empirical criteria are listed in

Table 3.1. Most of these share a reasonably similar structure and all have elements that

are likely to fail at the extremes.

Figure 3.2. Comparison of test results with theoretically based failure criteria

(Johnston & Chiu, 1984)

The requirements of a good rock shear strength criterion are: that the criterion is a good

predictor of strength at the stresses of interest (if not all confining stresses); that it is

mathematically simple and preferably based on dimensionless parameters; and that it

Page 213: Shear Strength of Rock

The Strength of Intact Rock Page 3.4

can also be used for rock mass (Hoek, 1983). Many of these criteria have been

developed with high (underground) stresses and hard rocks in mind. As such many do

not acurately predict shear strengths at low (or negative) stresses. For example, Mogi

(1966) states Equation 3.6 “is applicable to the middle part of curves, but it deviates

from observed values at an initial part and later ductile part of curves”. This is a

problem where estimates of the strength of rock at low stresses (say slopes or dams) are

required.

Figure 3.3 shows that the Hoek-Brown shear strength criterion provides a poor fit to

Melbourne mudstone. This is mainly due to the exponent being set at 0.5 in the Hoek-

Brown equation. This is likely a direct result of the equation being created for hard

rocks.

Figure 3.3. Comparison of Hoek-Brown criterion (solid) and Johnston criterion

(dashed) for Melbourne mudstone (Johnston, 1985)

An inspection of Table 3.1 shows that equations (3.6), (3.9), (3.12), (3.14) and (3.15) do

not algebraically reduce to the unconfined compressive strength, σc, when the minor

principal stress, σ′1, is zero. Similarly, (3.6), (3.7), (3.9), (3.10), (3.14) and (3.15) fail to

predict strengths in the tensile range (some completely and others at particular

reasonably expected constant values) whilst (3.5) recommends a tensile cutoff due to it

overestimating σt.

Page 214: Shear Strength of Rock

The Strength of Intact Rock Page 3.5

Equations (3.6), (3.7), (3.10) and (3.14) indicate ∞→′′ →031 3σσσ dd which implies a

friction angle of 90° at σ′3 = 0.

Equation 3.8 represents straight line (Coulomb type) fits to lab data. As the rock

strength envelope is known to be curved this equation could only be expected to predict

the correct shear strengths over very narrow ranges.

As is discussed elsewhere in this thesis, (3.4) is unsuitable for rock mass as it does not

allow for a tensile strength of zero and hence can not be sensibly extended into the

strength of rock mass or rockfill.

The unconfined compressive strength, σc, is widely used and is a useful index for rock

strength. Only Equations (3.8), (3.10), (3.11) and (3.15) can be non-dimensionalised by

σc. This aids in the presentation and grouping of data with various unconfined

compressive strengths.

Table 3.2 shows the various exponents suggested (or obtained by regression) by the

authors for their particular criterion. A power function of unity would imply a straight

line (Coulomb). Smaller power functions will generally imply that the criterion has a

higher curvature at very low stresses.

Page 215: Shear Strength of Rock

Page 3.6

Table 3.1. Various intact rock failure criteria

Reference Equation Constants Development UCS Tensile strength

3.4 Balmer (1952)

Sheorey et al (1989)

b

tc

′+=′

σσσσ 3

1 1

b = 0.411 to 0.828

(ignoring samples controlled

by defects orientated 15-75°

to the load axis)

Sheorey et al used tests on

sandstone and shale plus

literature. 23 sets in total of

which 11 had no UCS

recorded, 6 of which were

also defect controlled.

σc -σt

3.5 Fairhurst (1964) ( ) ( )312

31 σσσσ ′+′+=′−′ BA

= 12

12

2mA tσ

( )212 −= mB tσ

1+= tcm σσ

Based on an empirical

generalisation of Griffith

allowing for all n = σc/σt

possibilities.

b b a± +2 42

b b a± +2 42

Note a tensile cut-off is

recommended

3.6 Hobbs (1966)

Mogi (1966) n

c 331 σασσσ ′+′+=′ α - f(rock type)

n – 0.38 to 0.73 (Mogi)

Developed using triaxial

tests on intact rock and

literature results.

σc (n>0) undefined

3.7 Murrel (1965)

Hobbs (1970) A

c F 31 σσσ ′+=′ F, A

Non-linear empirical

adjustment to Coulomb.

Hobbs (1970) found that his

earlier equation (3.6) did not

fit new test data.

σc (A>0) −

σ cA

F

1

(undefined for most A)

Page 216: Shear Strength of Rock

Page 3.7

Reference Equation Constants Development UCS Tensile strength

3.8 Bodonyi (1970)

31 σσσ ′+=′ ac

or

cc

aσσ

σσ 31 1

′+=

A Straight line fit to lab test

data σc

− σ c

a

3.9 Franklin (1971) ( )ba 3131 σσσσ ′+′+′=′ a, b 0 Undefined

Page 217: Shear Strength of Rock

Page 3.8

Reference Equation Constants Development UCS Tensile strength

3.10 Bieniawski (1974)

Yudhbir et al (1983)

α

σσ

σσ

′+=

cc

k 31 1

412 triaxial samples used to

determine constants:

α ≈ 0.75 (Bieniawski)

α ≈ 0.65 (Yudhbir et al)

k - varies with rock

type from 2 to 5(see

Table 3.2. Empirical

estimates of exponents

for the equations in

Table 3.1

Equation Parameter Exponent for rock

3.4 b 0.411 to 0.828

3.6 n 0.38 to 0.73

3.8 N/A 1

3.10 α 0.75 (Bieniawski, 1974)

0.65 (Yudhbir et al., 1983)

3.11 α 0.5

3.12 β 0.38 (tuff only)

3.13 B 0.5 – 0.81 (Johnston & Chiu, 1984)

( )2log0172.01 cσ− (Johnston, 1985)

3.14 α 0.8

Non-dimensional form of

Murrell (1965). Note that k

has become dependent on σc

as ( )1−= AcFk σ

σc (α>0)

ασ

1

1

kc

(undefined for most α)

Page 218: Shear Strength of Rock

Page 3.9

Reference Equation Constants Development UCS Tensile strength

3.11 Hoek & Brown (1980a)

( ) 212

331 cci sm σσσσσ +′+′=′

or

21

331

+

′+

′=

′sm

ci

cc σσ

σσ

σσ

mi – depends on rock type

s = 1

Developed using curve

fitting to extensive triaxial

data on hard rock.

s0.5σc

= σc (s=1) 2

42 smm icci +−σσ

3.12 Adachi et al (1981)

qp

pp′

=′′

0 0

αβ

or

( )β

β σσασσ

′+′

=′−′ −

32 311

031 p

q = (σ1-σ3)

p = (σ1+2σ3)/3

po = 0.1MPa (unit stress)

α,β = strength parameters

tuff: α = 1.76 and β = 0.38.

Based on triaxial test results

plotted on a log-log graph.

The equation is from Hobbs

(1966).

Porous tuff was used to

represent soft rock.

β

β

α −

1

1

31.0

(MPa)

0123

11

. −

αβ β

(MPa)

3.13 Johnston & Chiu (1984)

Johnston (1985)

B

cc BM

+

′=

′131

σσ

σσ

M = f(rock type and σc)

B = f(rock type) – 1984

see Table 3.4.

( )2log0172.01 cB σ−=

(Johnston, 1985)

Developed empirically for

soft rocks after Hoek &

Brown was shown to give a

poor fit.

σc − BM cσ

Page 219: Shear Strength of Rock

Page 3.10

Reference Equation Constants Development UCS Tensile strength

3.14

Ramamurthy et al (1985)

Ramamurthy et al (1988)

Rao et al (1988)

α

σσσσσ

′+′=′3

331cB

B - function of rock

type/quality ≈ 1.8 to 3.54

α - slope of log-log curve of

(σ′1-σ′3)/σ′3 and σc/σ′3 ≈

0.75 to 0.85 (0.8 usually

taken)

Modified Mohr-Coulomb to

become non-linear.

Empirical work done using

testing on 4 sandstones plus

100 sets from literature.

Extended for anisotropy and

rock mass in 1988.

0 (α<1)

Bσc (α=1)

Undefined (α>1)

0 (α<1)

( )ασ1

Bc −

( )K7

151

31 ,,1,=α

else undefined

3.15 Yoshida et al (1990)

b

cc sa

1

331

+

′+′=′

σσσσσ

or

b

ccc

sa

1

331

+

′+

′=

′σσ

σσ

σσ

a = 1.3 to 8.3

s = 0.01 to 0.78

b = 1 to 3.3 (tuff = 7.2)

1/b = 0.3 to 1 (tuff = 0.14)

Proposed for geologic

materials exhibiting time

dependent softening e.g. soft

rocks.

Data came from 16 rock sets

from the literature.

aσcsb

Page 220: Shear Strength of Rock

The Strength of Intact Rock Page 3.11

Table 3.2. Empirical estimates of exponents for the equations in Table 3.1

Equation Parameter Exponent for rock

3.4 b 0.411 to 0.828

3.6 n 0.38 to 0.73

3.8 N/A 1

3.10 α 0.75 (Bieniawski, 1974)

0.65 (Yudhbir et al., 1983)

3.11 α 0.5

3.12 β 0.38 (tuff only)

3.13 B 0.5 – 0.81 (Johnston & Chiu, 1984)

( )2log0172.01 cσ− (Johnston, 1985)

3.14 α 0.8

3.15 1/b 0.3 – 1.0 (tuff = 0.14)

Table 3.3. Suggested values of constant k (Yudhbir et al, 1983 and Bieniawsi,

1974)

Rock Type k

Norite, granite, quartzdiorite, chert 5

Quartzite, sandstone, dolerite 4

Siltstone, mudstone 3

Tuff, shale, limestone 2

Table 3.4. Values of M and B for a range of materials (Johnston, 1991)

Material UCS

(MPa)

M B

Soft clay 0.02 2.5 0.97

Stiff clay 0.2 3.5 0.91

Soft rock 2.0 5.1 0.81

Soft rock 20 7.2 0.68

Hard rock 100 9.0 0.57

Hard rock 200 9.8 0.52

Page 221: Shear Strength of Rock

The Strength of Intact Rock Page 3.12

Given the variability typical of rock test results it is likely that any one criteria is as

suitable overall as any of the alternatives. The Hoek-Brown empirical failure criterion

(Hoek & Brown, 1980) was developed in the early 1980s for intact rock and rock

masses, it has been subject to continual refinement for rock masses. For intact rock its

form has not changed and is given in Equation 3.16.

5.0

331 1

+

′+′=′

c

ic

mσσσσσ (3.16)

In common with most of the empirical failure criteria, the Hoek-Brown criterion is

formulated in terms of σ′1 and σ′3 and is independent of σ′2. The author does not

consider this a major impediment for practical purposes.

It is the author’s experience that the Hoek-Brown criterion forms the basis of virtually

all the non-linear criteria now used by practising engineers. Further it forms the basis

for the almost universal extension into rock mass strength. It thus has been adopted as

the basis of examination for the rest of this Chapter. Further, for these reasons it is

important to establish that the criterion does accurately represent actual intact rock

behaviour.

Page 222: Shear Strength of Rock

The Strength of Intact Rock Page 3.13

3.3 LABORATORY TEST DATABASE FOR INTACT ROCK

A large database of test results has been assembled for a wide variety of rocks; tests

include uniaxial tensile strength, Brazilian tensile strength, unconfined compressive

strength and triaxial compression and tension. Many of the results were sourced from

Sheorey (1997), Hoek and Brown (1980), Shah (1992) and Johnston (1985) and

checked against original sources where possible. Further test information from other

sources was obtained. Full details of the data are contained in the Appendix. At present,

the data consists of 4507 test results forming 511 sets.

In addition to the principal stresses, and to aid in the examination of the data, the

information in Table 3.5, about the rock samples, was obtained where possible.

Page 223: Shear Strength of Rock

The Strength of Intact Rock Page 3.14

Table 3.5. Intact rock database descriptors

Database heading Description

Set Set number (1-511)

Test Test number within set

D? "*" denotes σ′1<4.4σ′3 – from Sheorey (1997) method of denoting

ductile behaviour

R G – good range of σ′3 ( cσσσ 3.0min3max3 ≥′−′ );

P – poor range σ′3 ( cσσσ 3.0min3max3 <′−′ )

s3 Minimum principal stress, σ′3 (MPa)

s1 Maximum principal stress, σ′1 (MPa)

Name/location Specific rock name or location of source

Rock type General geological group term

mi98 Published Hoek et al (1998) mi value for the rock type

orientation: BP/weak Orientation relative to bedding or planes of weakness (if any)

moisture Sample moisture condition

diam Sample diameter (mm)

h/d Sample height to diameter ratio

poros Porosity of sample (%)

grain size Sample mean grain size (mm)

B/T/D Comment on behaviour of sample under load based on an observation of

the stress-strain curves, options were:.Brittle/Transitional/Ductile

strain rate Test strain rate (%/second)

comments Other comments on test, sample or test type

Reference Quoted original reference for data

Source Source of data for database::

- original - original reference used

- SH_A.1. - Sheorey (1997) Table A1

- SH_A.2.- Sheorey (1997) Table A2

- Doruk - Doruk (1991)

- Shah - Shah (1992)

Page 224: Shear Strength of Rock

The Strength of Intact Rock Page 3.15

3.4 AN ANALYSIS OF THE ANALYSIS OF DATA

When confronted with a set of data, there are a number of questions that have to be

addressed:

• What data should be included in the analysis?

• What equation should be fitted?

• What method of fitting should be adopted?

It is of little value undertaking a comprehensive test program or detailed analysis of the

results if the methodology is flawed. In fact, parameters determined can vary from very

conservative to quite the opposite, both situations have consequences in analysis and

design.

Turning to the first question, the data included is that described in the previous section.

It has been common practice for researchers fitting empirical failure criterion to intact

rock to exclude results thought to exhibit ductile behaviour; this approach has been

adopted by Hoek and Brown (1981), Shah (1992), Johnston (1985) and Sheorey (1997).

In general these researchers have adopted the brittle-ductile transition suggested by

Mogi (1966). The Equation is given by:

34.3 σ ′=C (3.17)

There is some confusion in the literature regarding Equation 3.17. Sheorey (1997) has

assumed C to be the difference in the maximum and minimum principal stresses (i.e.

31 σσ ′−′ ) whilst the other authors have assumed C to be the maximum principal stress,

1σ ′ . Mogi (1966) defined C as the ‘compressive strength’ but did not define it in relation

to principal stresses. Mogi (1973) however, defines C as 31 σσ ′−′ . Therefore it is

assumed that the brittle-ductile transition, given by Mogi (1966), is:

331 4.3 σσσ ′=′−′ or 31 4.4 σσ ′=′ (3.18)

Page 225: Shear Strength of Rock

The Strength of Intact Rock Page 3.16

The exclusion of ductile data would be appropriate if (i) only brittle behaviour was of

interest, (ii) the boundary was clear and (iii) the failure criterion was disjoint across the

transition. In the case of a criterion based solely on Griffith’s theory, exclusion of

ductile tests results would be appropriate. It is not necessary, is counter productive and

is arbitrary, for an empirical criterion. Research (Evans et al., 1990, Mogi, 1966 and

1973, Scott & Nielsen, 1991, Rutter & Hadizadeh, 1991, Hoshino et al, 1972) shows

that the transition is not well defined for all rocks, is often curved and certainly occurs

over a wide range of stresses. Gustkiewicz (1985) found that “the value of [the brittle

ductile transition] pressure cannot be seen distinctly on the curve of strength versus

confining pressure”. Research by others (Evans et al., 1990) also showed that the failure

envelope is not necessarily disjoint at the brittle-ductile transition. Thus an appropriate

criterion can model strength on both sides of the transition.

Triaxial tests with stresses around the brittle-ductile transition should be checked to

ascertain that they actually reached their maximum stress. Often the triaxial apparatus

(or sample) will not allow sufficient strain for this to happen and thus the result should

be ignored.

Sheorey (1997) only uses data points where σ′1>4.4σ′3 and data sets where there are at

least 5 data points.

Doruk (1991) uses the following criteria to decide whether a data set is acceptable:

• Each data set must have major and minor principal stresses at failure.

• Only the results of effective or drained uniaxial and triaxial compression tests at

room temperature are used.

• Each data set must contain at least three triaxial test results.

• Only results in the brittle range (defined as σ′1≥ 3.4σ′3 and σ′3≤ σc) were used.

Doruk (1991) divides the data sets used into the following classes:

Page 226: Shear Strength of Rock

The Strength of Intact Rock Page 3.17

• Class 1: ≥ 5 ‘well fitted’ data points with cσσσ 3.0min3max3 ≥′−′

• Class 2: ≥ 5 ‘scattered’ data points with cσσσ 3.0min3max3 ≥′−′

• Class 3: ≥ 5 ‘well fitted’ data points with cσσσ 3.0min3max3 <′−′

• Class 4: < 5 ‘well fitted’ data points with cσσσ 3.0min3max3 ≥′−′

• Class 5: < 5 ‘scattered’ data points with cσσσ 3.0min3max3 ≥′−′

• Class 6: < 5 ‘well fitted’ data points with cσσσ 3.0min3max3 <′−′

• Class 7: Data sets which contain ‘very scattered’ data points

In the current work as many test results as possible have been included and only results

for which there is true ductile behaviour (no ma ximum definable σ′1 or where there is

significant doubt as to their accuracy) have been excluded.

Columns in the rock strength database show the number of points and whether the data

has a good range of σ3 (i.e. cσσσ 3.0min3max3 ≥′−′ ) or a poor range of σ′3 (i.e.

cσσσ 3.0min3max3 <′−′ ). The effect of the number of tests in a data set is investigated in

the analysis.

There are several forms of the Hoek-Brown criterion that can be adopted for data

analysis, these include Equation 3.16 and:

−≤′′=′

−>′

+

′+′=′

ic

icc

ic

m

mm

σσσσ

σσσσ

σσσ

331

3

5.0

331

for

for 1 (3.19)

( ) 23

231 ccim σσσσσ +′=′−′ (3.20)

( ) ( )2331 log5.0log ccim σσσσσ +′=′−′ (3.21)

Equation 3.16 is strictly the Hoek-Brown criterion, but is undefined for σ′3 less than

approximately -σc/mi. Equation 3.19 ensures that the criterion is defined over the full

range of σ′3. Equations 3.20 and 3.21 are linearisations of the criterion. The impact of

adopting these different forms is discussed at the end of this section.

Page 227: Shear Strength of Rock

The Strength of Intact Rock Page 3.18

The method of least squares is very widely adopted in fitting models to data; there are

often very sound statistical reasons to so do. Shah (1992) suggests that the simplex

method with the function (observed-predicted)2 is a better method than least squares. In

fact, the method presented by Shah is least squares, the simplex is purely a numerical

method to optimise some function, in this case minimising the sum of squared

differences (ie errors). It has been verified that the resulting parameter estimates are the

same as those from other robust least squares procedures.

If the departure of the measured σ′1 from the predicted σ′1 (ie the error) is normally

distributed with a variance that is independent of the predictor variables (here σ′3), then

the predictions obtained with least squares, either with a simplex or otherwise, will be

uniform minimum variance unbiased estimators; this is highly desirable. But

consideration of data with multiple measurements of σut or σBt will indicate that straight

least squares is not appropriate for fitting the Hoek-Brown criterion.

Consider an experimental program with multiple measurements of σut, it is clear that if a

failure criterion is to be fitted to the test data it is desirable that the estimated tensile

strength should be the average of these measurements (ie the fitted curved should pass

through the middle of the measured values). Equation 3.16 is not defined for measured

values of σut less than the fitted value (ie larger tensile strengths) and this forces many

fitting methods to fit the maximum measured (ie most negative) tensile strength as the

estimated tensile strength. Equation 3.19 overcomes this problem, but reference to

Figure 3.1 shows that the slope of the equation to the left of the estimated σut is much

less than that to the right; the figure is drawn for an mi of 8 and the slope to the right is

much steeper for higher mi. Given that a general least squares approach assesses the

error as the observed σ′1 (ie zero) minus the predicted σ′1, then data a given distance to

the right of the estimated σut will have a much larger “error” than data the same distance

to the left. Thus a standard least squares procedure will result in a very poor fit at low

stresses and force a small σut and high mi, ie the opposite effect to adopting Equation

3.16.

A resolution of the above problem comes about by recognising that in a uniaxial tensile

strength test, the controlled variable is σ′1 and the measured variable is σ′3, thus the real

Page 228: Shear Strength of Rock

The Strength of Intact Rock Page 3.19

error is observed σ′3 minus the predicted σ′3. But this error is scaled in σ′3 and needs to

be adjusted if it is to have equal status with measurements in σ′1. It is suggested that

scaling by mi is a convenient and accurate approach. Given this it is recommended that a

least squares procedure be used where the error is defined as:

( )( )

′−≤′×′−′′−>′′−′

3133

3111

3for predicted measured3for predicted measuredσσσσσσσσ

im (3.22)

This has been found to provide very good fits for a wide variety of data.

It is the author’s experience that the method of parameter estimation can, and often

does, have a large impact on parameters derived from experimental data but the effect is

often camo flaged by the variability of test data. Table 3.6 and Figure 3.4 show the

results of analysis of a simulated test program with results generated for a material with

a Hoek-Brown failure criterion, σc and mi are both normally distributed with

mean/standard deviation of 10/2 MPa and 12/2 respectively. Results generated were 10

uniaxial tensile strength tests, 20 unconfined compressive strength tests, and 4 each

triaxial strength tests at confining pressures of 1, 2, 5, 10, 20, 40 and 80 MPa. Thus

there were 58 data points in all, simulating a very comprehensive test program from

which it should be possible to determine accurate estimates of material properties.

The entire generated data and selected fits are shown on Figure 3.4a. It can be seen that,

with two exceptions, the methods provide a reasonable fit for the majority of the data.

But reference to Figure 3.4b shows that most methods provide a very poor fit to the data

at low stresses, that is over the stress range of interest in slope analysis.

Page 229: Shear Strength of Rock

Page 3.20

Table 3.6. Results of different regression methods on artificial data

Case Equation Fitting method Number σc (MPa) mi r2 (%)

1 Actual data 58 10.0 12.0 na

2 Normal equation 3.16 Least squares 58 14.9 7.75 97.88

3 Extended equation 3.19 Least squares 58 8.46 15.6 99.12

4 Extended equation 3.19 Modified least squares, Eqn 3.22 58 10.7 12.0 99.00

5 Adopting known σc and normal equation 3.16 Least squares 58 na 5.21 91.69

6 Excluding σt results and normal equation 3.16 Least squares 48 9.53 13.7 99.06

7 Excluding σc & σt results and normal equation 3.16 Least squares 28 6.20 21.4 98.80

8 Stress difference squared 3.20 Least squares 58 3.97 35.2 95.53

9 Stress difference squared and known σc 3.20 Least squares 58 na 13.8 95.47

10 Stress difference squared 3.20 Least sum of absolute differences 58 9.18 15.4 95.45

11 Logarithms 3.21 Least squares 58 8.09 4.12 55.97

12 Logarithms and excluding σt results 3.21 Least squares 48 9.67 12.2 95.00

Page 230: Shear Strength of Rock

The Strength of Intact Rock Page 3.21

Sigma 3 (MPa)

Sig

ma

1 (M

Pa)

0

50

100

150

200

250

-10 10 30 50 70

UCS miArtificial data 10.012.0Normal eqn & LS14.97.75Extended eqn & LS 8.4615.5Ext eqn & mod LS 10.712.0Fix UCS & LS 10.05.21Excl Sc or St & LS 6.1921.4DS^2 & LS 3.9735.2Log & LS 8.094.12

Not shownExcl St & LS 9.5213.7DS^2 with UCS fixed 10.013.8DS^2 & Least abs sum 9.1815.4Log with excl St 9.6712.2

Sigma 3 (MPa)

Sig

ma

1 (M

Pa)

0

10

20

30

40

-2 0 2 4 6

UCS miArtificial data 10.012.0Normal eqn & LS14.97.75Extended eqn & LS 8.4615.5Ext eqn & mod LS 10.712.0Fix UCS & LS 10.05.21Excl Sc or St & LS 6.1921.4DS^2 & LS 3.9735.2Log & LS 8.094.12

Not shownExcl St & LS 9.5213.7DS^2 with UCS fixed 10.013.8DS^2 & Least abs sum 9.1815.4Log with excl St 9.6712.2

Figure 3.4. Fits to artificial data (a) full range (b) low stress range

UCS mi Artificial data 10.0 12.0 Normal eqn & least squares 14.9 7.75 Extended eqn & least squares 8.46 15.5 Extended eqn & modified least squares 10.7 12.0 Fixed UCS and least squares 10.0 5.21 Excluding σc or σt and least squares 6.2 21.4 (σ1 - σ3)2 and least squares 3.97 35.2 Logarithm and least squares 8.09 4.12

UCS mi Artificial data 10.0 12.0 Normal eqn & least squares 14.9 7.75 Extended eqn & least squares 8.46 15.5 Extended eqn & modified least squares 10.7 12.0 Fixed UCS and least squares 10.0 5.21 Excluding σc or σt and least squares 6.2 21.4 (σ1 - σ3)2 and least squares 3.97 35.2 Logarithm and least squares 8.09 4.12

Page 231: Shear Strength of Rock

The Strength of Intact Rock Page 3.22

The following comments are offered on the various analyses undertaken, listed in the

same order as in Table 3.6.

1. The generated data, the author considers that this is a reasonable representation

of a comprehensive test program in a moderately variable unit.

2. The strict application of least squares to Equation 3.16, ie the usual form of the

Hoek-Brown criterion, results in the uppermost curve in Figure 3.4b. The criterion

cannot be evaluated for σ′3 less than the estimated tensile strength. This results in large

estimates of σut and σc and thus a low mi. From 5 to 80 MPa the curve passes through

the middle of the data. Below 1 MPa the estimated strength is nearly 50% higher than

the true strength even though the regression r2 is nearly 98%. This problem could be

partially fixed by including only the average measured tensile strength in the analysis

but this ignores considerable readily obtained and economic data and disguises the true

variability.

3. Least squares applied to Equation 3.19 results in vastly improved parameter

estimation but the lower slope to the left of the estimated σut produces a low estimate of

σut and thus somewhat low estimated σc and high estimated mi. A good fit overall with

the highest r2, but approximately 15% underestimate of true strength for low σ3.

4. Modified least squares, Equation 3.22, applied to Equation 3.19 results in

accurate estimation of the parameters and does so in almost all circumstances. The fact

that r2 is slightly less than for method 3 is a necessary consequence of the treatment of

variability of the measured tensile strengths.

5. Least squares applied to Equation 3.16 with σc fixed at the average of the test

results. It might be thought that knowing one property should help with estimating a

second unknown property, this is not the case here. The problem in 2 above is now

magnified to produce almost the worst fit imaginable. It shows that an r2 of over 90%

can be obtained with a fit that bears only a passing relationship to the data.

Page 232: Shear Strength of Rock

The Strength of Intact Rock Page 3.23

6. Least squares applied to either Equation 3.16 or 3.19, with the tensile strength

test results excluded, results in a good fit. Again the problem is that good economic data

is ignored and the fit at low stress will be more variable.

7. Least squares applied to either Equation 3.16 or 3.19 with both the tensile and

unconfined compression test results excluded. In this case more than half the data is

ignored and, in the present case, the fit at low σ′3 is more than 30% out. This is a

random error and the fit could be low or high. The problem with this approach is that it

is poorly controlled at the stresses of interest in slope analysis.

8. Least squares applied to Equation 3.20. This is a common form of fitting the

Hoek-Brown criterion to data and estimating σc and mi. This method virtually

minimises “errors” to the fourth power, hence the lowish r2, and dramatically

overweights the larger values of σ′1. Errors in parameter estimates are not predictable,

but in this example, estimated σc and mi are 40% and 300% of the true values

respectively, even though the corrupted r2 is over 95%. Over most of the range of the

test results it is a very good fit but not over that portion of interest in slope design. It is

not recommended.

9. As for 8 above but with σc fixed at the mean value, in contrast to 5 above this

results in a good fit across the range but relies on a good estimate of σc and increased

faith that this accurately represents triaxial behaviour.

10. Least sum of absolute differences applied to Equation 3.20. This in large

measure compensates for the overweighting of large σ′1 values of method 8. The

resulting estimates are good.

11. Least squares applied to Equation 3.21, again a common form of fitting the

Hoek-Brown criterion. As for Equation 3.16 this equation is not defined for σ′3 less than

σpt. This method has major problems fitting any data which includes a moderate spread

of tensile testing.

Page 233: Shear Strength of Rock

The Strength of Intact Rock Page 3.24

12. Least squares applied to Equation 3.21 with the tensile strength test results

excluded. A robust method weighted to low stress results and good for slope analysis

but unable to take advantage of economic and readily available data.

From Table 3.6 it can be seen that r2 is not a useful indicator of accuracy of estimates of

the parameters and that these estimates can vary widely depending on the method of

analysis. Methods with r2 in excess of 95% and that model the data very well over most

of the range have estimates of σc varying from 3.97 to 14.9 MPa and mi from 7.75 to

35.2 and this is for artificial data that follows exactly the criterion with only test

variability. Thus many of these methods are very poor estimators of strength in the low

stress region that is of interest in slope analysis.

Page 234: Shear Strength of Rock

The Strength of Intact Rock Page 3.25

3.5 HOEK-BROWN CRITERION FOR INTACT ROCK

Modified least squares, Equation 3.22, was combined with the extended formulation of

the Hoek-Brown criterion, Equation 3.19, to estimate σc and mi for all test data in the

database. Discussion in the previous section indicates that the fit is poorly controlled at

low stresses for sets with little data, particularly σc and σt. Small changes in the data can

lead to wildly varying estimates of both σc and mi, in general with σc becoming very

small and mi very high but with the fit being almost identical over the range of the test

results. In fact for many data sets σc and mi are not independent but σc→0 as mi→∞.

The best solution to this issue is to place plausibility limits on the parameters. A number

of limits were considered and the following ones adopted:

• As all the test results were taken from materials described as rock, σc was limited

to be not less than 1 MPa.

• Published values of mi fall in the range of 4 to 33 (Hoek & Brown, 1998). As will

be discussed later mi is very closely related to the ratio -σc/σut, reference to the figures

in Lade (1993) indicates that this ratio varies from less than 2 to over 50. This limits mi

to the range 1 to 50. Further mi is related to the angle of friction at σ′3=0 (ie φ0), which

is of great interest in slope analysis. It was considered that φ0 should be limited to the

range of 15 to 65°, which for the Hoek-Brown criterion further limits mi to the range 1.4

to 40.

The process was completed for 475 data sets involving 3779 test results. The results of

the analysis are provided in Figure 3.5 to Figure 3.8. Figure 3.5 shows a “box and

whisker” plot of the values of mi estimated from the data, mitest, against the values of mi

provided in Hoek & Brown (1998) and Hoek et al (1995), mipub. Several such figures are

presented in this chapter, the whiskers show the range of test results, the box shows the

upper and lower quartiles and the bar the median value. Also shown on this figure is a

linear regression between published mipub and mitest weighted for the number of data

points supporting each estimate. The regression equation is:

ipubitest mm 441.058.7 += (3.23)

Page 235: Shear Strength of Rock

The Strength of Intact Rock Page 3.26

This is a very poor relation, r2=16.4%, between mi determined on the basis of actual

testing and that obtained from the literature.

Page 236: Shear Strength of Rock

Page 3.27

mi from literature, mipub

mi f

rom

fitti

ng H

B e

quat

ion,

mite

st

0

10

20

30

40

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Figure 3.5. mi from literature against mi from test results and Hoek-Brown Equation

Page 237: Shear Strength of Rock

The Strength of Intact Rock Page 3.28

Figure 3.6 presents mitest against rock type ordered in increasing mipub, it can be seen that

it is difficult to ascribe a single or even small range to mi on the basis of rock type. It

should be remembered that 50% of the test data falls outside the range indicated by the

box for each rock type, thus for example 50% of the values for sandstone fall below 11

or above 19, and for granite below 19 or above 31.

Page 238: Shear Strength of Rock

Page 3.29

mite

st

0

10

20

30

40

Cla

ysto

nF

irecl

ayG

reen

sto

Mud

ston

eS

erpe

nti

Sch

ist

Sha

leC

halk

Chl

oriti

Lim

esto

nM

arbl

eS

iltst

onS

late

Bio

calc

aD

olom

iteA

nhyd

ritS

alt

Coa

lT

uff

Pyr

ocla

sR

hyol

iteA

plite

Bas

alt

Lam

prop

hT

rach

iteA

gg tu

ffG

reyw

ack

Whi

nsto

nA

ndes

iteD

iaba

seD

oler

iteQ

uart

zdo

San

dsto

nG

rani

te1

Nor

iteQ

uart

zit

Dun

iteE

clog

iteG

abbr

oP

erid

oti

Am

phib

olD

iorit

eQ

uart

zdi

Gra

nodi

oG

neis

sG

rani

te

Figure 3.6. Rock type against mi from test results and Hoek-Brown equation

Page 239: Shear Strength of Rock

The Strength of Intact Rock Page 3.30

Figure 3.7 presents the σc determined from fitting the Hoek-Brown equation against the

σc determined from σc testing or, at least, as reported in the literature from which the

data was obtained. Several figures in this chapter are presented in this style. The upper

and lower dashed lines represent 1.5 and 0.67 times the reported σc values. Further, the

symbols represent the number of test results used to determine the fit, a small cross is 4

or less data points, a small circle is 7 or less, large circle is 12 or less and a square is

more than 12 data points. It can be seen that virtually all the data lies in a very narrow

band, such that the fitted σc is quite close to the reported σc.

Figure 3.8 is a similar presentation to Figure 3.7 except that it presents fitted tensile

strength versus reported tensile strength. It can be seen that the fitting method adopted

provides a very good estimate of σt for those data sets which do have reported tensile

strengths. Most of the other methods fail for such data, so much so that often

practitioners are forced to ignore the valuable information available from inexpensive

tensile testing. This is particularly a problem as such data forms a good control on the

failure envelope over the low stress range (Lade, 1993).

In summary the proposed method results in good fits of the Hoek-Brown criterion to the

data and, in particular, results in good fits in the low stress region. It appears that

published values of the parameter mi might be quite misleading as mi does not appear to

be related to rock type.

Page 240: Shear Strength of Rock

Page 3.31

Unconfined compressive strength (MPa)

UC

S fr

om H

B e

quat

ion

(MP

a)

1

4

710

40

70100

400

7001000

1 4 7 10 40 70 100 400 7001000

Figure 3.7. Unconfined compressive strength against that predicted by the Hoek-Brown equation

Page 241: Shear Strength of Rock

Page 3.32

Tensile strength (MPa)

Tens

ile s

treng

th fr

om H

B e

quat

ion

(MP

a)

0.1

0.4

0.71.0

4.0

7.010.0

40.0

70.0100.0

0.1 0.4

0.7 1.0

4.0 7.0

10.040.0

70.0100.0

Figure 3.8. Uniaxial tensile strength against that predicted by the Hoek-Brown equation

Page 242: Shear Strength of Rock

The Strength of Intact Rock Page 3.33

3.6 GENERALISED CRITERION FOR INTACT ROCK

There are a number of concerns regarding the formulation of the Hoek-Brown criterion:

• Several authors, including Johnston (1985), note that soil, soft rock, and brittle

rock form a continuum and thus a failure criterion should be able to accommodate the

linear or near linear behaviour observed in soils and soft rocks. Fixing the exponent at a

half means that at best the criterion is a poor model of soft rocks. This is not surprising

as it was developed for brittle rocks but it is a limitation which is often overlooked by

practitioners who apply it to all rocks. Further it is a severe limitation on the extension

of the criterion to rock mass strength.

• Lade (1993) in comparing the theories and the evidence regarding rock strength

criteria finds that an appropriate criterion should have three independent characteristics

– the opening angle, the curvature and the tensile strength. The fixed exponent on the

Hoek-Brown criterion limits it to modelling only two of these characteristics. In fact as

often used, mi is varied to model the curvature over the stress range of the test results

and neither the opening angle nor the tensile strength are modelled. Lade also states that

it may be an advantage to include the tensile strength in determination of material

parameters as it stabilises the fit at low stresses. This is particularly important for slope

analysis.

If the exponent, α, is allowed to vary the Hoek-Brown criterion can model widely

varying curvatures and opening angles. It is also able to include an accurate

representation of the tensile strength. This “generalised” Hoek-Brown criterion for

intact rock has been applied to the full data set. As would be expected, adding an extra

parameter or property always improves the fit but has many other benefits as well.

The equation becomes:

−≤′′=′

−>′

+

′+′=′

ic

icc

ic

m

mm

σσσσ

σσσ

σσσσ

α

331

33

31

for

for 1 (3.24)

Page 243: Shear Strength of Rock

The Strength of Intact Rock Page 3.34

The modified least squares, Equation 3.22, is adopted.

The limits, given above for fitting the Hoek-Brown criterion, are also placed on the

parameters. For the generalised criterion these become, σc>1, mi in the range 1 to 50,

and α mi in the range 0.7 to 20 (this is the equivalent limit on φ0). In addition, α is

limited to the range 0.2 to 1.

Allowing α to vary provides the ability to obtain a much better fit over the low stress

range which is of greatest interest in slope analysis.

The results of the analysis are presented in a series of figures. Figure 3.9 presents a box

and whisker plot of mi determined from the data against the published values of mi.

Again it can be seen that there is little relationship between the two. Likewise, there was

found to be no relationship between mi and rock type.

Page 244: Shear Strength of Rock

Page 3.35

mi from literature

mi f

rom

fitti

ng e

quat

ion

0

10

20

30

40

50

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Figure 3.9. mi from literature against mi from test results and generalised equation

Page 245: Shear Strength of Rock

The Strength of Intact Rock Page 3.36

The slope of the generalised criterion at σ′3=0 is 1+α mi, and is related to φ0 by:

( )( )( )451atan2 5.00 −+= imαφ (3.25)

If a classification of samples, say by mi or rock type, is predictive of the triaxial

envelope at low stresses then it will be apparent on a plot of that classification against α

mi. Figure 3.10 and Figure 3.11 present plots of α mi against published mi and rock type

respectively. From Figure 3.10 it can be seen that published mi is not a good predictor of

the triaxial envelope at low stress. Examination of Figure 3.11 shows that there is a

weak correlation of rock type with α mi in that fine grained rocks tend to have the

lowest values, medium to coarse grained higher and rocks with tightly interlocked

crystals the highest. It is not believed that the relationship is strong enough to be used

predictively.

Page 246: Shear Strength of Rock

Page 3.37

mi from literature

alph

a*m

i fro

m fi

tting

equ

atio

n

0

5

10

15

20

25

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Figure 3.10. mi from literature against α mi from test results and generalised equation

Page 247: Shear Strength of Rock

Page 3.38

Alp

ha*m

i

0

5

10

15

20

Cla

ysto

nF

irecl

ayG

reen

sto

Mud

ston

eS

erpe

nti

Sch

ist

Sha

leC

halk

Chl

oriti

Lim

esto

nM

arbl

eS

iltst

onS

late

Bio

calc

aD

olom

iteA

nhyd

ritS

alt

Coa

lT

uff

Pyr

ocla

sR

hyol

iteA

plite

Bas

alt

Lam

prop

hT

rach

iteA

gg tu

ffG

reyw

ack

Whi

nsto

nA

ndes

iteD

iaba

seD

oler

iteQ

uart

zdo

San

dsto

nG

rani

te1

Nor

iteQ

uartz

itD

unite

Ecl

ogite

Gab

bro

Per

idot

iA

mph

ibol

Dio

rite

Qua

rtzd

iG

rano

dio

Gne

iss

Gra

nite

Figure 3.11. Rock type against α mi from test results and generalised equation

Page 248: Shear Strength of Rock

The Strength of Intact Rock Page 3.39

Figure 3.12 presents the σc obtained from fitting the generalised equation against the

reported σc. It can be seen that virtually all the data lies in a very narrow band, such that

the fitted σc is quite close to the reported σc. As would be expected the overall

correlation is better than that shown on Figure 3.7.

Page 249: Shear Strength of Rock

Page 3.40

Unconfined compressive strength (MPa)

UC

S fr

om fi

tting

equ

atio

n (M

Pa)

1

4

710

40

70100

400

7001000

1 4 7 10 40 70 100 400 7001000

Figure 3.12. Unconfined compressive strength against that predicted by generalised equation

Page 250: Shear Strength of Rock

The Strength of Intact Rock Page 3.41

Figure 3.13 presents the fitted tensile strength versus reported tensile strength. It can be

shown that the uniaxial tensile strength σut is bound as:

( )1+−

≤<−i

cut

i

c

mmσ

σσ (3.26)

Page 251: Shear Strength of Rock

Page 3.42

Tensile strength (MPa)

Tens

ile s

treng

th fr

om H

B e

quat

ion

(MP

a)

0.1

0.4

0.71.0

4.0

7.010.0

40.0

70.0100.0

0.1 0.4

0.7 1.0

4.0 7.0

10.040.0

70.0100.0

Figure 3.13. Uniaxial tensile strength against that predicted by generalised equation

Page 252: Shear Strength of Rock

The Strength of Intact Rock Page 3.43

Table 3.7 presents the errors involved in adopting –σc/(mi+1) as σt. For simplicity the

lower bound has been adopted in plotting Figure 3.8 and Figure 3.13, the error in doing

this is quite small. It should be noted that it is likely that many of the reported σt are

likely to be Brazilian tensile strengths.

Table 3.7. Error in approximating σut as -σc/(mi+1)

α mi Error (%)

1 All 0

0.8 All <7.6

0.5 1 19

0.5 >8 <10

0.4 1 23

0.4 >9 <10

The fit in Figure 3.13 is extremely good. Figure 3.12 and Figure 3.13 provide

considerable confidence that the fitted curves provide a very good model of triaxial

strength at low stresses. In both cases the unexplained variance of the generalised fits is

about half that of the Hoek-Brown fits.

Figure 3.14 presents a plot of α against mi as determined for each data set from the

generalised criterion. Also shown on the figure are hyperbolae showing lines of constant

α mi, ie φ0, for 15° to 65°. Inspection of the figure shows that the constraints on mi, α

and α mi did not often limit the regression procedure.

Page 253: Shear Strength of Rock

Page 3.44

mi

Alp

ha

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50

φ0 1525

35 45 55 65φ0

Figure 3.14. α against mi

Page 254: Shear Strength of Rock

The Strength of Intact Rock Page 3.45

An interesting and useful observation from Figure 3.14 is that there appears to be a

relationship between α and mi. Such a relationship is derived in the next section and is

shown on Figure 3.14. It is often thought that the curvature of the strength envelope, ie

α against mi in the current context, should be greater for strong rocks than weak rocks.

The data set and analysis do not support this contention. Figure 3.15 shows the

relationship between α and mi plotted for the data divided into four categories

depending on the σc. It can be seen that the relationship is independent of strength. High

strength rocks can have linear flat failure envelopes and low strength rocks can have

steep curved envelopes. Thus σc is a truly independent parameter in a rock failure

criterion.

Page 255: Shear Strength of Rock

Page 3.46

mi

alph

a UCS<= 40

0.0

0.5

1.0

0 20 4040<UCS<=100

0 20 40

100<UCS<=200

0.0

0.5

1.0

0 20 40200<UCS

0 20 40

Figure 3.15. α against mi categorised by σc

Page 256: Shear Strength of Rock

The Strength of Intact Rock Page 3.47

A consequence of allowing α to vary at all, is that a failure envelope with a high φ0 can

have a low φ at high stresses and thus failure envelopes for different rocks normalised

on σc, can cross at high stresses. This cannot happen with α fixed at 0.5 in which case

all envelopes cross only once at σc. Figure 3.16 shows a family of curves, normalised by

σc, for various mi and the α typical of the relationship shown on Figure 3.14. It can be

seen that the mi equals 40 curve crosses the mi equal 10 and 3 curves at 1.4 and 2.5

times σc respectively. This implies that high frictional strength at low stresses is often

associated with low frictional strength at higher stresses. Figure 3.17 shows some

examples of test data that illustrate this point.

Sigma 3 / Sigma C

Sig

ma

1 / S

igm

a C

-2

0

2

4

6

8

10

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

mi 40

10

3

1

Figure 3.16. Family of failure envelopes

Page 257: Shear Strength of Rock

Page 3.48

Sigma 3 / Sigma C

Sig

ma

1 / S

igm

a C

0

2

4

6

8

10

12

14

16

18

20

-1 0 1 2 3 4 5

Set 382 SandstoneSet 305 GraniteSet 425 Gabbro

Figure 3.17. Results showing failure envelopes crossing

Page 258: Shear Strength of Rock

The Strength of Intact Rock Page 3.49

A relationship between α and mi implies that the triaxial failure envelope can be

estimated from σc and either mi or σt, with α being determined by the relationship. Thus

there are no more parameters to be determined than for the usual Hoek-Brown criterion.

The parameters can be based on simple testing and provide a more accurate prediction

of strength than published mi values, particularly in the low stress region typical of

slopes.

Page 259: Shear Strength of Rock

The Strength of Intact Rock Page 3.50

3.7 GLOBAL PREDICTION

A single equation could be fitted to the entire database on the following assumptions:

• The value of σc obtained from fitting the generalised Hoek-Brown criterion is the

best estimate of σc for each data set.

• A reasonable estimate of |σt | is obtained for each data set by dividing σc by the

value of mi obtained by fitting the generalised Hoek-Brown criterion.

Figure 3.12 and Figure 3.13 show that the above assumptions are quite reasonable for

those cases where there is data to confirm them. On this basis mi can be set to –σc/σt and

Equations 3.19 and 3.24 can be rewritten as:

α

σσ

σσ

σσ

′−+

′=

tcc

331 1 (3.27)

−++

′−+

′=

′cmba

tcc

t

c

σσ

σσ

σσ

σσ 0exp1

331 1 (3.28)

Equation 3.27 is equivalent to the Hoek-Brown criterion but with an exponent not

necessarily equal to 0.5. Equation 3.28 is equivalent to the generalised Hoek-Brown

criterion. The exponent of Equation 3.28 is a general function that varies from a to b

with a midpoint at –m0 and a variable length of step. These equations can be fitted to the

entire data set using Equation 3.22.

Two of the data sets produced extremely large residuals and were ignored in reanalysis.

Fitting Equation 3.27, ie a constant exponent, resulted in α being estimated as 0.439 and

an r2 of 83.5%. This is a reasonable fit when the range of rocks to which it applies is

considered. Examination of the residuals reveals that a better fit will be possible as the

residual is a function of mi. This is illustrated on Figure 3.18, for mi<10 the residuals are

positive and increase with σ′1. The residuals gradually reduce until for mi greater than

40 they are predominantly negative. This is strong evidence that α is not constant.

Page 260: Shear Strength of Rock

Page 3.51

Sigma 1 / Sigma c

Res

idua

l for

glo

bal r

egre

ssio

n w

ith c

onst

ant a

lpha

<= 5

-10

-5

0

5

10

0 5 10 15 20

(5,10]

0 5 10 15 20

(10,20]

0 5 10 15 20

(20,30]

-10

-5

0

5

10

0 5 10 15 20(30,40]

0 5 10 15 20> 40

0 5 10 15 20

Number under graph is estimated ratio of-Sigma c / Sigma t

Figure 3.18. Residuals for global fit with α constant against σ′3/σc categorised by -σc/σt

Page 261: Shear Strength of Rock

The Strength of Intact Rock Page 3.52

Fitting Equation 3.28 resulted in the following estimate for the exponent:

( )( )455.7exp108585.14032.0 im++=α (3.29)

This equation is shown on Figure 3.14 and models the results of the analysis of the

individual data sets very well. This analysis resulted in an r2 of 94.8%, which is

extremely good for such a global fit. The residuals are plotted on Figure 3.19, there is

no or little trend with mi or σ1 and it can be seen that this is a much better fit than

Equation 3.27 and Figure 3.18.

Page 262: Shear Strength of Rock

Page 3.53

Sigma 1 / Sigma c

Res

idua

l for

glo

bal r

egre

ssio

n w

ith v

aria

ble

alph

a

<= 5

-10

-5

0

5

10

0 5 10 15 20

(5,10]

0 5 10 15 20

(10,20]

0 5 10 15 20

(20,30]

-10

-5

0

5

10

0 5 10 15 20

(30,40]

0 5 10 15 20

> 40

0 5 10 15 20

Number under graph is estimated ratio of-Sigma c / Sigma t

Figure 3.19. Residuals for global fit with variable α against σ′3/σc categorised by -σc/σt

Page 263: Shear Strength of Rock

The Strength of Intact Rock Page 3.54

Figure 3.20 shows a three dimensional plot of the failure criterion described by

Equations 3.28 and 3.29, ie σ′1 as a function of σ′3 and mi (ie –σc/σt). It can be seen that

for mi<8 the failure envelope is close to linear and then becomes more curved. The ridge

at mi equals 8 is well supported in the data and may reflect “more” or “less” than

Griffith behaviour.

Page 264: Shear Strength of Rock

Page 3.55

Figure 3.20. Three dimensional plot of global fit

Page 265: Shear Strength of Rock

The Strength of Intact Rock Page 3.56

Figure 3.21 and Figure 3.22 show slices through the model for high and low stress

ranges respectively with the equation for the midrange of each slice also shown. Thus

the upper left subgraph on Figure 3.21 presents all the σ1 versus σ3 data, normalised by

σc, for sets with σc/|σt |<=5 together with the equation for σc/|σt |=3. Figure 3.21 provides

the data for σ′3 up to three times σc and Figure 3.22 for σ′3 to half of σc. It can be seen

that the fits are very good. The ridge at high stress and mi=8 are apparent on Figure 3.21

with uniform behaviour at low stress seen on Figure 3.22.

Page 266: Shear Strength of Rock

Page 3.57

Sigma 3 / Sigma c

Sig

ma

1 / S

igm

a c

<= 5

0

5

10

15

0 1 2 3

(5,10]

0 1 2 3

(10,20]

0 1 2 3

(20,30]

0

5

10

15

0 1 2 3

(30,40]

0 1 2 3

> 40

0 1 2 3

Number under graph isestimated ratio of

-Sigma c / Sigma t

Figure 3.21. σ′1/σc with fits for variable α against σ′3/σc categorised by -σc/σt for high stress

Page 267: Shear Strength of Rock

Page 3.58

Sigma 3 / Sigma c

Sig

ma

1 / S

igm

a c

<= 5

0

1

2

3

4

5

0.0 0.1 0.2 0.3 0.4 0.5

(5,10]

0.0 0.1 0.2 0.3 0.4 0.5

(10,20]

0.0 0.1 0.2 0.3 0.4 0.5

(20,30]

0

1

2

3

4

5

0.0 0.1 0.2 0.3 0.4 0.5

(30,40]

0.0 0.1 0.2 0.3 0.4 0.5

> 40

0.0 0.1 0.2 0.3 0.4 0.5

Number under graph isestimated ratio of

-Sigma c / Sigma t

Figure 3.22. σ′1/σc with fits for variable α against σ′3/σc categorised by -σc/σt for low stress

Page 268: Shear Strength of Rock

The Strength of Intact Rock Page 3.59

Figure 3.23 presents α against mi including Equation 3.29 and showing those data for

which there is actual, not estimated, values for both σc and σt. It can be seen that these

sets are distributed similarly to those for which at least one of these parameters has been

estimated by fitting the generalised Hoek-Brown criterion.

Page 269: Shear Strength of Rock

Page 3.60

mi

Alp

ha

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50

Data with compressive and tensile strengthsOther data

Figure 3.23. α against mi showing cases with measured or reported σ′3 and σt

Page 270: Shear Strength of Rock

The Strength of Intact Rock Page 3.61

3.8 COMPARISON OF CRITERIA

A comparison of the various criterion as fitted to the database is provided in Table 3.8.

The variance explained approximates r2. As would be expected, the generalised Hoek-

Brown criterion provides by far the best fit, r2 of 99.5%, as it has three parameters and

is fitted to the individual data sets. None the less, the fit obtained is considerably better

than the fit obtained by the Hoek-Brown criterion (ie with α fixed at 0.5) , r2 of 98.9%.

The unexplained variance for the generalised criterion is less than half that of the Hoek-

Brown criterion with α of 0.5.

Table 3.8. Comparison of predictions

Variable/prediction Variance Variance

explained

σ′1/σc 16.93 0

Global regression with α constant 2.78 83.6

Hoek-Brown with published mi 2.00 88.2

Global regression with α variable 0.846 95.0

Hoek-Brown fitted to individual sets 0.186 98.9

Generalised Hoek-Brown fitted to individual sets 0.077 99.5

The above methods compare different ways of fitting triaxial data, ie different criteria

applied to actual triaxial data. Table 3.8 also allows a comparison of three methods of

prediction of triaxial strength that are not based on having actual data but are based on

parameters estimated in some other manner. The methods are discussed in the following

points:

• Prediction based on global equation with variable α. This method is based on

Equations 3.28 and 3.29 and estimates of σc and σt. It has an r2 of 95.0% when used to

predict the test results in the database. The accuracy of the predictions are illustrated on

Figure 3.21 and Figure 3.22.

• Prediction based on global equation with constant α. This method, based on

Equation 3.27, is the least accurate of the three and is not discussed further.

Page 271: Shear Strength of Rock

The Strength of Intact Rock Page 3.62

• Prediction based on published values of mi. This method is based on Equation

3.19 with values of mi estimated from those widely published in the literature. The

method has an r2 of 88.2% when used to predict the test results in the database. On

average this method predicts the strengths well but with considerably more scatter than

that from the global equation. Figure 3.24 and Figure 3.25 present the data categorised

by published mi, these figures are in a similar form and can be compared to Figure 3.21

and Figure 3.22. It is clear from the figures that at low published mi the triaxial strength

is under predicted and at high published mi it is over predicted. In effect what this means

is that triaxial strength is poorly predicted by published mi values and the method is

predicting the average strength for all tests.

Page 272: Shear Strength of Rock

Page 3.63

Sigma 3 / Sigma c

Sig

ma

1 / S

igm

a c

<= 7

0

5

10

15

0 1 2 3

(7,9]

0 1 2 3

(9,18]

0 1 2 3

(18,19]

0

5

10

15

0 1 2 3

(19,24]

0 1 2 3

> 24

0 1 2 3

Categorised by publishedvalues of mi

Figure 3.24. σ′1/σc with fits for published mI against σ′3/σc categorised by mI for high stress

Page 273: Shear Strength of Rock

Page 3.64

Sigma 3 / Sigma c

Sig

ma

1 / S

igm

a c

<= 7

0

1

2

3

4

5

0.0 0.1 0.2 0.3 0.4 0.5

(7,9]

0.0 0.1 0.2 0.3 0.4 0.5

(9,18]

0.0 0.1 0.2 0.3 0.4 0.5

(18,19]

0

1

2

3

4

5

0.0 0.1 0.2 0.3 0.4 0.5

(19,24]

0.0 0.1 0.2 0.3 0.4 0.5

> 24

0.0 0.1 0.2 0.3 0.4 0.5

Categorised bypublished values

of mi

Figure 3.25. σ′1/σc with fits for published mI against σ′3/σc categorised by mI for low stress

Page 274: Shear Strength of Rock

The Strength of Intact Rock Page 3.65

3.9 SYSTEMATIC ERROR IN HOEK-BROWN CRITERION

If α for a particular rock is not equal to 0.5 then there is a systematic error in fitting the

Hoek-Brown criterion to any triaxial test results obtained on that rock. The error is

illustrated on Figure 3.26, two data sets are shown, the upper one is for σc, mi and α of

30 MPa, 24 and 0.4 respectively and the lower one for 8 MPa, 5 and 0.8. The different

σc were chosen to separate the curves, and the mi and α are typical combinations

determined in the analysis of the entire database. The solid lines represent the Hoek-

Brown fits to these data. The residuals are shown on the bottom graph, if α is less than

0.5 then there are negative residuals at both the low and high end of the range of σ′3

tested with positive residuals in the middle range. The sign of the residuals is reversed if

α is greater than 0.5. While the fits in the upper graph might look satisfactory for

engineering purposes, the errors in estimates of σc and mi can be significant. Table 3.9

shows the parameters estimated from fitting the Hoek-Brown criterion to these data, it

can be seen that errors in the estimates vary from one half to five times the correct

values. Thus the parameters of this model cannot be considered material properties.

These errors are discussed in more detail below.

Sigma 3 (MPa)

Sig

ma

1 (M

Pa)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Res

idua

l (M

Pa)

-20

-10

0

10

20

0 5 10 15 20 25 30 35

Figure 3.26. Pattern of residuals for Hoek-Brown fits

Page 275: Shear Strength of Rock

The Strength of Intact Rock Page 3.66

Table 3.9. Errors in fitting Hoek-Brown criterion to materials with α ≠ 0.5

Actual parameters

Material σc mi α r2 (%)

Upper 30.0 24.0 0.4 100.0

Lower 8.0 5.0 0.8 100.0

Parameters determined by fitting Hoek-Brown criterion

Material Estimated σc Estimated mi r2 (%)

Upper 33.0 11.7 99.65

Lower 3.94 48.5 97.47

Consider programs of triaxial testing on rocks with σc equal to 3 MPa, and mi and α of

(a) 40 and 0.4 and (b) 4 and 0.8. Both are weak rocks and their triaxial strength could be

of interest in design of a large rock slope. Further consider that different test programs

are undertaken in which the maximum σ′3 is determined by the capacity of the triaxial

apparatus. The following test programs could result:

• Program A - 12 stages to a maximum σ′3 of 10 MPa,

• Program B - 10 stages to 5 MPa (ie omitting the last two stages),

• Program C - 8 stages to 3 MPa,

• Program D - 6 stages to 1.5 MPa, and

• Program E - 4 stages, including UCS, to 0.7 MPa.

If there was no variability in the test apparatus or material, and measurement was

perfect, the test results would be as shown on Figure 3.27, that is there is no sample or

test error. Quite different envelopes result if the Hoek-Brown criterion is fitted to these

test programs. The estimated σc and mi are given in Table 3.10. Estimated σc varies

from 1.66 to 4.20 MPa and mi from 8.0 to 29.6 with very high r2.

Page 276: Shear Strength of Rock

The Strength of Intact Rock Page 3.67

Table 3.10. Variation of σc and mi with σ3max for exact simulated results

Material (a) σc = 3 MPa, mi = 40 and α = 0.4

Program σ′3max

(MPa) Stages Estimated σc Estimated mi r2 (%)

A 10 12 4.20 11.5 99.43

B 5 10 3.77 14.2 99.41

C 3 8 3.47 16.9 99.38

D 1.5 6 3.22 20.3 99.52

E 0.7 4 3.07 23.4 99.74

Material (b) σc = 3 MPa, mi = 4 and α = 0.8

Program σ′3max

(MPa) Stages Estimated σc Estimated mi r2 (%)

A 10 12 1.66 29.6 97.96

B 5 10 2.23 17.5 98.65

C 3 8 2.59 12.6 98.96

D 1.5 6 2.85 9.60 99.46

E 0.7 4 2.96 8.01 99.85

Page 277: Shear Strength of Rock

Page 3.68

Sigma 3

Sig

ma

1

0

5

10

15

20

25

30

35

40

-2 0 2 4 6 8 10 12

Artificial data forsc=3 MPa, mi=40 and alpha=0.4

Sigma 3

Sig

ma

1

0

5

10

15

20

25

30

35

40

-2 0 2 4 6 8 10 12

Artificial data forsc=3 MPa, mi=4 and alpha=0.8

Figure 3.27. Hoek-Brown fits to artificial data

Page 278: Shear Strength of Rock

The Strength of Intact Rock Page 3.69

The dashed lines on Figure 3.27 show the envelopes fitted to cases A, C and E. It is

emphasised that while the upper line for material (a) and the lower line for material (b)

(ie Case E) do not look like good fits, they are in fact very good fits for the 4 test results,

below σ′3 equal 0.7 MPa, that form their basis with r2 of 99.74% and 99.85%

respectively. Such results might erroneously be taken to support the contention that the

material was well modelled by the Hoek-Brown criterion. It can be concluded that the

estimated parameters are as much a function of the test program as of the material

tested. These errors would generally be obscured by the material variability but they are

still present.

Figure 3.28 and Table 3.11 present the results of analysis of data set 434, a sandstone, in

which the analysis has assumed different maximum possible σ′3. This further illustrates

the errors that can occur if a Hoek-Brown envelope is fitted to material for which α

does not equal 0.5. Depending on the test program, estimates of σc obtained by fitting

the generalised criterion vary from 85.4 to 57.7 MPa and of mi from 6.35 to 13.1,

variations of 150% and 205%. If the Hoek-Brown criterion is fitted, the estimates vary

from 23.8 to 55.5 MPa (230%) and 31 to 138 (445%). Again the r2 determined for the

fits are very good.

Table 3.11. Variation of σc and mi with σ′3max for data set 434

For generalised Hoek-Brown criterion

σ′3max (MPa) N Estimated σc Estimated mi Estimated α r2 (%)

All data 20 85.4 6.71 0.75 99.70

400 16 59.2 13.1 0.65 99.63

200 9 57.7 13.0 0.66 99.50

100 5 64.1 6.35 0.87 98.18

For Hoek-Brown criterion

σ′3max (MPa) N Estimated σc Estimated mi r2 (%)

All data 20 23.8 138 97.00

400 16 35.1 75.2 98.49

200 9 44.9 49.7 98.20

100 5 55.5 31.0 93.99

Page 279: Shear Strength of Rock

Page 3.70

Sigma 3

Sig

ma

1

0

500

1000

1500

2000

2500

0 100 200 300 400 500 600 700

Sigma 3

Sig

ma

1

0

500

1000

1500

2000

2500

0 100 200 300 400 500 600 700

Figure 3.28. Hoek-Brown fits to actual data

Page 280: Shear Strength of Rock

The Strength of Intact Rock Page 3.71

Figure 3.29 shows the residuals from fitting the Hoek-Brown criterion to data sets with

σc less than 20 MPa plotted against σ′3 divided by the maximum test σ′3. There are four

graphs showing cases where the estimated α from fitting the generalised criterion is (a)

less than 0.4, (b) between 0.4 and 0.6, (c) between 0.6 and 0.8 and (d) greater than 0.8.

On each graph the residuals have been fitted with a quadratic relationship. It can be seen

that these residuals conform almost perfectly to those predicted on Figure 3.26. This is

very strong evidence that the Hoek-Brown model is not appropriate. Figure 3.30 shows

the residuals obtained from fitting the generalised Hoek-Brown criterion. It can be seen

that these show little or no trend.

Page 281: Shear Strength of Rock

The Strength of Intact Rock Page 3.72

Data with estimated UCS less than 20 MPa

Sigma 3 / Maximum test sigma 3

Res

idua

l fro

m fi

tting

HB

equ

atio

n

Alpha <= .4

-30

-20

-10

0

10

20

30

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Alpha (.4,.6]

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Alpha (.6,.8]

-30

-20

-10

0

10

20

30

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Alpha > .8

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Figure 3.29. Residuals for Hoek-Brown fits for weak rock against σ′3/σ′3max

categorised by α

Page 282: Shear Strength of Rock

The Strength of Intact Rock Page 3.73

Data with estimated UCS less than 20 MPa

Sigma 3 / Maximum test sigma 3

Res

idua

l fro

m fi

tting

gen

eral

equ

atio

n

Alpha <= .4

-30

-20

-10

0

10

20

30

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Alpha (.4,.6]

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Alpha (.6,.8]

-30

-20

-10

0

10

20

30

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Alpha > .8

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Figure 3.30. Residuals for generalised fits for weak rock against σ′3/σ′3max

categorised by α

Page 283: Shear Strength of Rock

The Strength of Intact Rock Page 3.74

3.10 APPLICATION TO SLOPE ENGINEERING

In general the triaxial strength of intact rock is not particularly important in the analysis

or design of rock slopes, even large rock slopes. The maximum depth of the failure

surface for even a 500 m high slope is generally only 100 to 150 m deep, and thus the

maximum σ′3 of interest is around 4 MPa. The relative contribution of the triaxial

component of strength for various rocks (ie σc, mi and α) and overburden stresses is

given in Table 3.12. It can be seen that for high φ0 rocks triaxial strength is generally

significant, even for quite low slopes and high strength, but for most of these situations

intact rock strength will not be critical except in forming the basis of rock mass strength.

For low φ0 rocks triaxial strength is important for low strength or high stress conditions

and it is these situations for which intact strength may be critical in design.

Table 3.12. Triaxial component of strength

σc σ′3

High φ0 case

mi = 50, α = 0.4

%

Low φ0 case

mi = 0.8, α = 0.9

%

300 4.0 24 2.3

100 4.0 59 6.9

30 4.0 140 23

10 4.0 280 68

3 4.0 570 230

300 0.5 3.4 0.3

100 0.5 9.8 0.9

30 0.5 29 2.9

10 0.5 70 8.6

3 0.5 160 29

Table 3.13 and Figure 3.31 provide a comparison of different methods of predicting the

triaxial strength of low strength rocks at low stress. The predicted strengths are

compared with the measured strengths for all cases in the database for which σc is less

than 20 MPa and σ′3 is between 0 and 5 MPa (excluding UCS test results). The

variances of the residuals scaled on σc are given in Table 3.13 and the scaled residuals

Page 284: Shear Strength of Rock

The Strength of Intact Rock Page 3.75

plotted on Figure 3.31. In general the order of accuracy of the various prediction

methods is the same as discussed for the overall predictions. It is of interest to note that

the global generalised equation (r2 of 88.6%) is almost as accurate a prediction of the

triaxial strength of these rocks as that obtained by fitting the Hoek-Brown criterion

directly to triaxial test data (r2 of 90.3%). This reflects the fact that there is abundant

evidence that α does not equal 0.5 for a large proportion of the rocks tested – see Figure

3.14 and thus there will be systematic errors at low stress.

Table 3.13. Comparison of predictions for weak rocks at low stress

Variable/prediction Variance Variance

explained %

σ′1/σc 7.69 0

Global regression with α constant 1.91 75.1

Hoek-Brown with published mi 1.99 74.1

Global regression with α variable 0.88 88.6

Hoek-Brown fitted to individual sets 0.74 90.3

Generalised Hoek-Brown fitted to individual sets 0.12 98.5

The above situation arises because the range of σ′3 over which the tests were performed

hardly ever corresponded to 5 MPa and thus there were almost always systematic errors

at the lower stresses tested. It is sometimes argued that the solution to this is to test over

a range of σ′3 that represents the field conditions, but this is hardly ever possible as

generally the one set of testing is used to design low and high slopes. Further for a given

slope different portions of the failure surface are at different stresses. Another solution

is to determine the parameters as a function of stress, but this virtually defeats the

purpose of adopting a non-linear failure envelope and confirms they are not a material

property.

Page 285: Shear Strength of Rock

The Strength of Intact Rock Page 3.76

Sigma 3

Gen

eral

ised

HB

-5

0

5

10

0 2 4

Sigma 3

HB

-5

0

5

10

0 2 4

Sigma 3

Glo

bal

-5

0

5

10

0 2 4

Sigma 3

Glo

bal w

ith fi

xed

alph

a

-5

0

5

10

0 2 4

Sigma 3

HB

and

pub

lishe

d m

i

-5

0

5

10

0 2 4

Figure 3.31. Residuals against σ′3 for various fits

Page 286: Shear Strength of Rock

The Strength of Intact Rock Page 3.77

A useful approximation of the effective stress parameters, c0 and φ0, at low stress can be

obtained in the following manner. Equation 3.26 can be rearranged to provide an

estimate of mi based on σc and σt as:

t

ci

t

c mσσ

σσ <≤−1 (3.30)

In addition, α can be estimated from Equation 3.29, φo is given by Equation 3.25 and:

( )( )5.00 12 ic mc ασ += (3.31)

The writers do not argue that this approximation is a substitute for triaxial testing but, in

the absence of such testing, the approximation should be more accurate than other

methods of estimation such as using σc and published values of mi. Further it results in a

linear failure envelope which is exact at the origin and as such is convenient to use in

many slope stability programs.

Page 287: Shear Strength of Rock

The Strength of Intact Rock Page 3.78

3.11 CONCLUSION

This chapter presented an overview of the strength of intact rock. It was demonstrated

that the method of fitting the criterion to the test data has a major effect on the estimates

obtained of the material properties. The results of a recent analysis of a large database of

test results demonstrated that there are inadequacies in the Hoek-Brown empirical

failure criterion as currently proposed for intact rock and, by inference, as extended to

rock mass strength. The parameters mi and σc are not material properties if the exponent

is fixed at 0.5. Published values of mi can be misleading as mi did not appear to be

related to rock type. The Hoek-Brown criterion can be generalised by allowing the

exponent to vary. This change resulted in a better model of the experimental data. The

most accurate method of estimating mi and α is through using triaxial tests on intact

rock. The recommended method for regression of the data is modified least squares,

Equation 3.22, combined with the extended formulation of the generalised criterion,

Equation 3.24. The equations are repeated below.

( )( )

′−≤′×′−′′−>′′−′

3133

3111

3for predicted measured3for predicted measuredσσσσσσσσ

im (3.22)

−≤′′=′

−>′

+

′+′=′

ic

icc

ic

m

mm

σσσσ

σσσ

σσσσ

α

331

33

31

for

for 1 (3.24)

Analysis of individual data sets indicated that the exponent, α, is a function of mi which

is, in turn, closely related to the ratio of σc/σt. A regression analysis of the entire

database provided a model to allow the triaxial strength of an intact rock to be estimated

from a reliable measurement of its uniaxial tensile and compressive strengths. The

method proposed is the most accurate of those methods that do not require triaxial

testing and is adequate for preliminary analysis. An analysis was presented that showed

applying the Hoek-Brown criterion to most rocks results in systematic errors. Simple

relationships for triaxial strength that are adequate for slope design were presented.

Page 288: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.1

4 THE SHEAR STRENGTH OF ROCKFILL

4.1 OUTLINE OF THIS CHAPTER

The work by Marsal (1973) on the shear strength of rockfill showed that the strength of

rockfill may vary directly with normal effective stress, dry density, particle roughness,

particle crushing strength and inversely with grain size, uniformity of grading, and

particle shape.

The aim of this Chapter is to verify and extend this work using an extensive literature

review and an analysis of a triaxial shear strength database which has been collected

from the literature, and from organisations who have carried out testing for dams and

other projects.

In the context of this Chapter the term rockfill encompasses both material of alluvial

origin and that of blasted quarry origin. The differentiation between the two can be

made by looking at parameters such as angularity.

This Chapter also comprises part of the larger study that is investigating rock mass

strength. The author believes that it is reasonable to assume that a compacted rockfill is

representative of a poor quality rock mass as defined by Hoek and Brown (1980). The

author has therefore used the data collected in this report to create a lower bound for the

Hoek-Brown criterion.

This Chapter presents a summary of the main factors affecting rockfill strength from the

literature; the triaxial shear strength database; statistical results from the database; and

several shear-strength criteria for rockfill using Hoek-Brown and other methods.

Page 289: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.2

4.2 FACTORS AFFECTING THE SHEAR STRENGTH OF

ROCKFILL

The author believes that the shear strength of rockfill at a particular confining stress

may be seen as the combination of a basic friction angle (shearing between rock

surfaces), φb, plus a dilation component less an amount caused by asperity or particle

crushing/shearing and reorientation of particles. In terms of friction angle:

crushφφφ −+= ib (4.1)

Dilation ceases to occur at the critical confining pressure as defined by Seed and Lee

(1967).

Marsal (1973) found that the shear strength of rockfill may vary directly with normal

effective stress, dry density, particle roughness, particle crushing strength and inversely

with grain size, uniformity of grading, and particle shape. The following discussion

centres on what factors have been found to affect the shear strength of rockfill. An

attempt is made to relate these factors to the equation above.

4.2.1 Confining Pressure

Several authors have shown the shear strength curve for rockfill is non-linear,

particularly at low confining pressures (triaxial: Leslie, 1963, Marachi et al, 1969, Leps,

1970, Bertacchi & Bellotti, 1970, Penman et al., 1982 and Indraratna et al., 1993; direct

shear: Dobr & Rozsypal, 1974 and Anagnosti & Popovic, 1982; plane strain: Al-

Hussaini, 1983). This would be consistent with the theory that as normal stress is

increased dilation is suppressed and therefore shear strength increase is reduced. Indeed,

Boughton (1970) found “some indication … that the limiting value of φ as σ′3 increases

is the value for the surfaces of the individual rock pieces” or φb in Equation 4.1.

The effect of a curved strength envelope has a large impact on the stability analysis of

rockfill dams where shallow slip surfaces are shown by the analysis to be critical using

traditional average c-φ analysis. These failure surfaces are not found in practice and this

Page 290: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.3

is likely to be due to the high frictional strength of rockfill at the low confining

pressures acting near the surface.

Figure 4.1 shows a curved envelope together with various c-φ representations. The

tangent friction angle, φt, is defined as the slope of the tangent to the curved shear

strength envelope at a given normal stress. The secant friction angle, φsec, is defined as

the slope of the tangent from the origin to the Mohr’s circle for a particular normal

stress (Equation 4.2). It is this secant friction angle that is most commonly quoted when

test results are published.

+−

= −

31

311sec sin

σσσσ

φ (4.2)

Where the Mohr-Coulomb parameters are taken as c = 0 and φ = φsec the shear strength

will be underestimated for normal stresses less than σn2 and over estimated for stresses

greater than σn2. Where the Mohr-Coulomb parameters are taken as c = ct and φ = φt the

strength will be overestimated at confining pressures less than the normal stress at the

tangent point. Where ct is taken as zero, and φ = φt, as sometimes is done by designers,

the strength will be significantly underestimated. This shows the importance of using a

non-linear strength criterion or stress dependent parameters e.g. a bi-linear strength

envelope.

Page 291: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.4

φsec

φt

σn2

τ

σn

τ0<τenv<τt

Failureenvelope

τt =τenv<τ0

τenv<τt<τ0

Assumes φ = φt

and c = 0

Tangent to circlethrough origin =secant to failureenvelope

Tangent to failureenvelope

Figure 4.1. Methods for representing the shear strength envelope

As is typical in the literature, this report uses φ = φsec in its discussion unless otherwise

stated.

Marachi et al (1969) carried out large scale triaxial tests on highly angular argillite,

crushed basalt and rounded amphibolite and found that φ does not appear to decrease

significantly beyond σn = 4.5MPa. Note that they did not perform tests beyond a

confining pressure of 4.5MPa. Figure 4.2 and Figure 4.3 show curved strength

envelopes from triaxial and direct shear tests respectively which support this.

Indraratna and his co-workers (Indraratna et al., 1993, 1998, Indraratna, 1994)

performed tests on greywacke rockfill and basalt ballast. They found that the shear

strength of the failure envelope was highly curved for confining stresses of less than

500kPa. Penman et al (1982) found a similar result for confining stresses below 400kPa.

Indraratna found that the shear strength could be approximated by a linear Mohr-

Coulomb criterion at stresses higher than 1.5MPa (as compared to the Marachi value of

4.5MPa above). Figure 4.4 shows the variation of φsec with σn on a log scale presented

by Indraratna et al. (1993). The figure also shows a lower limit to the shear strength of

rockfill proposed by Indraratna et al (1993).

Page 292: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.5

Figure 4.2. Variation of secant friction angle, φsec, with respect to cell confining

stress, σ′3, for (a) dense and (b) medium dense crushed basalt from triaxial tests

(Al-Hussaini, 1983)

0.5

1.0

1.5

2.0

2.5

0.5 1.0 1.5 2.0

σn (MPa)

τ/σn

1

1

2a

2b

45

6

73

2b

2b

crushed quarry rockfillgravel rockfill

1 marble2a limestone (0.15 x 0.15m)2b limestone (0.07 x 0.07m)3 mica & phyllite4 sandstone-claystone-marl flysch5 claystone-marl flysch6 crystalline schist7 sandstone

Figure 4.3. Average strength of rockfills from large-scale direct shear tests

(Anagnosti & Popovic, 1982)

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Figure 4.4. Variation of secant friction angle, φ sec, with normal stress σn

(Indraratna et al., 1993)

4.2.2 Particle Strength

The strength of the individual particles could be expected to have some effect on the

shear strength of rockfill. Where the confining pressure, σ′3, is low compared to the

particle (or unconfined compressive) strength, σc, it could be expected that variations in

particle strength would have minimal effect on the shear strength. The only exception to

this is if it could be shown that σc affects φb. It has been shown however that φb

generally falls within a narrow range for defects in rocks which have not been

tectonically sheared. As σ′3/σc decreases, dilation will be the main contributor to

increased shear strength. As σ′3/σc increases, failure of particles could be expected

through crushing shearing and/or splitting, and thus a reduction in dilation would take

place leading to lower shear strength.

Particle strength should therefore play a major role with higher strength particles

generally leading to higher strength rockfill. Hirshfeld et al (1973) found the curvature

of the shear strength envelope to be more distinct for weak particles. This would be due

to the rapid reduction in dilation with increase in confining stress. A reduction in

dilation for high strength particles could be expected at much higher stresses than weak

particles.

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Anagnosti and Popovic (1982) found for crushed rocks, there is a large drop in shear

strength up to normal stresses of 1MPa for strong rockfills (Figure 4.5) with a much

smaller drop for weaker flysch materials (Figure 4.6). It is likely that tests were not

carried out at low enough confining pressures to capture the curvature in the flysch

material.

Figure 4.5. Shear strength and grain size curves for crushed (a) limestone and (b)

marble (Anagnosti and Popovic, 1982)

Figure 4.6. Shear strength and grain size curves for crushed flysch sandstone-marl

rockfill (Anagnosti and Popovic, 1982)

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4.2.3 Uniformity Coefficient

Generally, it could be expected that a poorly-graded rockfill (low uniformity coefficient,

cu, Equation 4.3), would have a higher strength than a well-graded rockfill assuming a

constant void ratio for both. A well-graded material would be more likely to reduce the

amount of dilation required due to the ‘gaps’ in the gravel matrix being filled with

smaller particles. However, Marachi et al (1969) claim that if both rockfills were

compacted to their maximum density then the well graded material could be expected to

be stronger as it would have the greater density.

10

60

dd

cu = (4.3)

Where, d60 is the particle size for which 60% is finer.

Chiu (1994) using data by Marsal (1967) found that the effect of cu on the shear strength

of rockfill was more pronounced for low σ′3, with little effect at high σ′3. cu affects

dilation however, at higher σ′3 that dilation may have been retarded. Sarac & Popovic

(1985) found that the failure envelope was more curved for narrowly graded materials.

Al-Hussaini (1983) found strength increased with cu but felt it may also have been

affected by maximum particle size. Anagnosti & Popovic (1982) found for gravels there

is a marked drop in strength for the high strength limestone below σ′3=1MPa possibly

due to dilational effects below σ′3=0.4MPa caused by the uniform grading (Figure 4.7).

The well-graded and weaker material does not show this effect (Figure 4.8).

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Figure 4.7. Shear strength and grain size curves for different gradings of

limestone gravel (Anagnosti and Popovic, 1982)

Figure 4.8. Shear strength and grain size curves for (a) crystalline schist and (b)

sandstone gravels (Anagnosti and Popovic, 1982)

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4.2.4 Density

When comparing the degree of compaction of rockfill relative density or void ratio can

be used. Where materials of the same rock type and grading characteristics are tested

dry density may be used as it will be related to relative density. Dry density or void ratio

will not be a good parameter to use where different types and gradings of rockfills are

compared.

Rockfill with a higher relative density has been found to have a higher shear strength

(Boughton, 1970, Leps, 1970, Marsal, 1973, Williams & Walker, 1984, Sarac &

Popovic, 1985, Tosun et al., 1999). The shape of the Mohr-Coulomb failure envelope is

also affected. Initially dense rockfill shows a marked curvature showing a distinct drop

in the friction angle whereas an initially loose sample shows minimal curvature and

drop in friction. The two curves tend to merge at very high confining pressures. This is

consistent with the behaviour of granular soils which reach the critical state or constant

volume/void ratio at large strains. Marachi et al (1969) indicate that the curves continue

as a straight line whose projection passes through the origin. This is likely due to the

dense material requiring dilation at low stresses to fail. At higher confining stresses

dilation is restrained and particle shearing/crushing occurs resulting in a lower angle of

friction. Initially loose material will require much less dilation as particles have more

freedom to move (e.g. rotation) during shearing. Thus without the dilation there will be

a minimal drop in the friction angle.

Al-Hussaini (1983) found that dense crushed basalt has a higher strength than medium

dense crushed basalt. Dobr & Rozsypal (1974) tested basalt at different dry densities in

direct shear. They found that the strength increases with density but, the strength

difference reduces with confining pressure. Chui (1994) also found little difference at

high confining pressures. Alva-Hurtado et al. (1981) found the opposite with the

difference in strengths increasing with confining pressure.

Zeller et al (1957), as reported in Marachi et al (1969), performed triaxial tests on

scalped rockfill samples for Goscheoenalp Dam in Switzerland. The confining pressure

for all tests was 88kPa. It should be noted that the scalping method used did not result in

parallel gradations. Zeller’s results (Figure 4.9 and Figure 4.10) show a decrease in

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The Shear Strength of Rockfill Page 4.11

friction angle of approximately 50° to 40° for an initial porosity increase of 8% for all

dry rockfill samples (dmax of 10mm to 100mm).

Figure 4.9. Scalped rockfill gradings (Marachi et al, 1969)

Figure 4.10. Strength porosity relationships with σ3 = 88kPa (Marachi et al, 1969)

Marachi et al (1969) tested rockfill material from Pyramid Dam. They found a drop in

friction angle of approximately 4° for an increase in void ratio of 0.3.

Nakayama et al. (1982) found that the friction angle was reduced with an increase in the

void ratio (Figure 4.11). There is no indication in the paper as to what the confining

pressure or method of assessing φ was. Boughton (1970) and Anagnostic & Popovic

(1985) found a similar result although, as might be expected, Anagnostic & Popovic

(1985) found the effect was more noticeable at low confining pressures and low Cu.

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40

41

42

43

44

45

0.25 0.3 0.35 0.4 0.45 0.5e

φ

triaxial - green schist - 12% -4.76mm triaxial - green schist - 18% -4.76mm

triaxial - quartz schist - 13% -4.76mm triaxial - quartz schist - 20% -4.76mm

direct shear - quartz schist - 18% -4.76mm direct shear - quartz schist - 25% -4.76mm

direct shear - green schist - 17% -4.76mm

Figure 4.11. Void ratio vs angle of friction (modified from Nakayama et al., 1982)

4.2.5 Maximum Particle Size

There is some conjecture as to the effect of the maximum particle size on the shear

strength of rockfill. It is generally accepted that the shear strength decreases with

particle size (Marachi et al., 1969 & 1972, Marsal, 1973, Chui, 1994). However, some

researches claim no effect (Charles et al., 1980) or the opposite effect (Anagnosti &

Popovic, 1981). Some data from Marsal is tabulated below.

The effect of maximum particle size should be considered as two issues:

(I) the effect of increasing maximum particle diameter, dmax with constant sample

diameter, D; and

(II) the effect of increasing dmax with constant dmax/D ratio.

(both assuming constant sample height to sample diameter, H/D ratio)

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The Shear Strength of Rockfill Page 4.13

4.2.5.1 Increasing dmax with Constant D

Marsal (1973) performed tests on basalt rockfill (the results of the tests are tabulated

below). The results show an increase in friction angle of 3-4% for a change in dmax/D

from 0.07 to 0.18. At high normal stresses (3.9MPa) the effect is more limited (0.3°).

Table 4.1. Increase in φ with dmax/D from Marsal (1973) data for different σn

Source Rock Type D (mm)

Cu

Cc σn (MPa)

dmax1/D

dmax2/D (φ2 - φ1)/φ2 (%)

Marsal (1973) Basalt 1130 A 11 - 18 5.21 – 0.55 0.8 0.07 0.18 3 Marsal (1973) Basalt 1130 A 11 - 18 5.21 – 0.55 1.6 0.07 0.18 4 Marsal (1973) Basalt 1130 A 11 - 18 5.21 – 0.55 3.9 0.07 0.18 0.3

Note: dmax1, φ1 and dmax2, φ2 are the maximum particle sizes and secant friction angle for sample one and sample two respectively.

4.2.5.2 Increasing dmax with Constant dmax/D

Thiers & Donovan (1981) present Figure 4.12 to estimate the shear strength of rockfill

at field scale. The figure plots the angle of internal friction versus maximum particle

size. It should be noted that all the samples tested had a constant dmax/D ratio.

Table 4.2. Reduction in φ with particle size, dmax, from Marsal (1973) data

Source Rock Type dmax/D Cu

Cc σn (MPa)

dmax1 (mm)

dmax2 (mm)

(φ1 - φ2)/φ2 (%)

Marsal (1973) Silicified conglomerate .18 A 10 1.72 3.92 38.1 200 7 Marsal (1973) Granitic -gneiss .18 SA 14 1.30 3.92 38.1 200 20 Note: dmax1, φ1 and dmax2, φ2 are the maximum particle sizes and secant friction angle for sample one and sample two respectively.

Figure 4.12. Friction angle vs maximum particle size (Thiers & Donovan, 1981)

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4.2.6 Silt and Sand Fines versus Gravel and Larger Particle Content

The percent of material passing 2mm is believed to affect the shear strength of rockfill.

At the point where the failure shear surface does not incorporate gravel to gravel contact

it could be expected that the shear strength of the finer particles would be the sole

control on the shear strength of the material. Large triaxial tests for silty gravels were

carried out by the USBR (1966). Tests were carried out at 0, 35, 50 and 65% gravel

content. Shear strengths were found to be similar for the 0 and 35% gravel content tests.

Shear strengths increased considerably at 50% and 65% gravel content. Further tests on

clayey gravels found that the shear strength increased considerably between 42 and 50%

gravel content. Other conclusions that were reached included:

• Clayey and silty gravel show the shear strength is unaffected by gravel contents

below 35%.

• Sandy gravel shows an increase in gravel gives an increase in strength up to a

maximum of 50% gravel

• At 50% gravel content, silty gravel and clayey gravel strengths significantly increase.

• At 65% gravel content the silty gravel has similar shear strength to the sandy gravel.

Data from USBR (1966) and USBR (1961) for silty gravel and clayey gravel are plotted

on Figure 4.13 and Figure 4.14 respectively. Trend lines (logarithmic) have been plotted

on the curves to show the general trends of the data. They should not be used for design.

Marsal (1976) reports two triaxial tests each on rockfill-silt and rockfill-sand mixtures

and compares these to a test on rockfill only. The clean rockfill and 10% sand-rockfill

mixtures had a φ of 34.1° whilst the 30% sand-rockfill had a φ of 39°. Marsal (1976)

attributes the difference to the lower initial void ratio in the 30% sand-rockfill mixture.

The 10% silt-rockfill mixture showed a decrease in φ to 28.8° whilst the 30% silt-

rockfill mixture had the strength properties of the silt.

Nakayama et al. (1982) performed triaxial and direct shear tests on schist gravels

(quartz schist and green schist) with maximum particle size of 63.5mm at Inamura

Rockfill Dam. It was found that the friction angle was reduced with an increase in the

percent of –4.76mm particles (Figure 4.15).

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30

35

40

45

50

55

60

65

70

75

80

0.0 0.2 0.4 0.6 0.8 1.0

σ′3 (MPa)

φ

38% gravel53% gravel67% gravel

Figure 4.13. Effect of gravel content on φ for silty gravel based on USBR (1966)

30

32

34

36

38

40

42

44

46

48

50

0.0 0.1 0.2 0.3 0.4

σ′3 (MPa)

φ

26% gravel42% gravel55% gravel68% gravelLog. (26% gravel)Log. (42% gravel)Log. (55% gravel)Log. (68% gravel)

Figure 4.14. Effect of gravel content on φ for clayey gravel based on USBR (1961)

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The Shear Strength of Rockfill Page 4.16

35

40

45

50

10 15 20 25 30

-4.76mm content (%)

φ

direct shear - quartz schist - e=0.28direct shear - quartz schist - e=0.39

Figure 4.15. –4.76mm content vs secant angle of friction (Nakayama et al., 1982)

4.2.7 Particle Angularity

The strength of highly angular rockfill could be expected to be higher than that for a

rounded rockfill at similar relative density and low confining pressures. This is due in

some part to the interlocking effect of the angular particles and also increased dilation.

At high stresses the effect may not be as prominent and may be the opposite. An angular

rockfill may allow for stress concentrations that cause breakage of the particles at high

confining pressures reducing dilation and leading to a lower overall rockfill strength

than the rounded particles with less stress concentrations.

The shape co-efficient, Cf, is often used to describe the shape of particles and is given in

Equation 4.4. The shape coefficient is the volume of n particles of gravel over the

equivalent volume of n spheres of diameter D.

∑∑=

n

n

f

D

VC

03

0

(4.4)

Bertacchi & Berlotti (1970) found that serpentinite (UCS = 100-150MPa, laminar

surfaces, sharp edges, Cf = 0.11) gives higher friction angles than tonalite (UCS =

150MPa, irregular rough surfaces, Cf = 0.17) due to the irregularity in the shape of the

serpentinite particles. Sarac & Popovic (1985) found a similar result but the effect was

less with higher confining pressures.

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4.2.8 Other Factors

The type of shear test is believed to have an influence over results. Generally plane

strain tests in the literature (Al-Hussaini, 1983 – dense crushed basalt, Barton &

Kjærnsli, 1981, Charles & Watts, 1980) give higher friction angles, φ′ps, than triaxial

shear tests, φ′ax. Tests by Marsal et al (1967) and Marsal (1973) discussed by Charles

(1991) showed φ′ at failure is greater in the plane strain tests by up to 8° for the same

minor principal stress. The Danish Code of Practice (Steensen-Bach, 1989) gave:

axps φφ ′=′ 1.1 (4.5)

Whilst Wroth (1984) gives:

axps φφ ′=′ 98 (4.6)

McWilliam (2001), working with the author, used published data to show that the ratio

between φ′ps and φ′ax varied from 1.02 to 1.1 (c.f. 1.125 from equation 4.6). The ratio

varied with material type and confining pressure.

The triaxial test provides a correct value of φ as it incorporates the intermediate

principal stress, σ′2 (=σ′3). In a plain strain test, strain is prevented in the direction of

σ′2. Where the popular Mohr-Coulomb criterion is used the intermediate stress is

ignored which leads to a miscalculation of φ. It is a common misconception that using

the Mohr-Coulomb derived φ from plain strain tests gives a better correlation to field

values and should therefore be used in preference to the φ from triaxial tests. The

backanalysis of failures have traditionally been carried out in two dimensions. This

procedure ignores σ′2 in the same manner as in the derivation of φ from the plane strain

lab tests. Thus, the plain strain φ and the back calculated φ are both incorrect but, as

they have similar errors in their derivation they tend to give similar results. The author

recommends the use of the φ derived from triaxial tests for design.

The shear strength of rockfill may decrease with moisture content (Frassoni et al., 1982,

Chui, 1994, Marsal, 1967). This is probably related to the drop in unconfined

compressive strength for some intact rocks.

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4.2.9 Summary of Factors Affecting the Secant Friction Angle

Table 4.3 shows a summary of the factors affecting the secant friction angle discussed

in this section. The most significant effects on the secant friction angle appear to be

caused by confining pressures, density and maximum particle size. There is also a

substantial effect on φsec at high percentages of material finer than gravel. Minor effects

on the secant friction angle are caused by angularity and the uniformity coefficient.

Table 4.3. Summary of factors affecting the secant friction angle

Parameter Effect on φsec with increase in parameter

Comment

Confining pressure Decrease Significant effect. The rate of decrease in φsec will drop with increasing confining

pressure

Unconfined compressive strength of intact rock

Increase Effect will depend on the ratio of confining stress to compressive strength

Uniformity coefficient Decrease Minor effect and may reverse if samples are compacted to the ir maximum density

prior to testing

Density Increase

Maximum particle size (assuming the ratio of maximum particle size to

sample diameter is constant)

Decrease

Ratio of maximum particle size to sample diameter

Increase

Angularity Increase The effect will be most noticeable with highly angular material

Percent finer than gravel size in sample Decrease The effect will not be significant at low percentages. At high percentages strength will approach that of the finer material.

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4.3 SHEAR STRENGTH CRITERIA

Table 4.5 shows a number of rockfill shear strength equations from the literature. The

equations are numbered in the first column of the table. The criteria are empirical

having been based on laboratory tests of rockfill.

De Mello (1977) proposed Equation 4.8 as suitable for representing the curved strength

envelope. Charles & Watts (1980) also used this form of equation. Indraratna et al.

(1993) developed a non-dimensional form of Equation 4.8 for both shear stress and

principal stress plots (Equations 4.9 and 4.11). Charles (1991) gives values for the

constants A and B in the De Mello (1977) equation (Table 4.4).

Table 4.4. Parameters obtained using De Mello (1977) (Charles, 1991)

ID A B

Sandy gravel .95 4.4 .81

Soft rockfill .95 4.2 .75

Soft rockfill .70 1.4 .90

Indraratna et al. (1998) also uses Equation 4.12 to describe the shear strength of basalt

ballast.

Doruk (1991) created a modified version of the Hoek-Brown criterion by removing the

s component and thus rendering the unconfined compressive strength of the rock mass

to zero. (Equation 4.13)

Sarac & Popovic (1985) analysed a large number of large scale (0.7x0.7x0.4 to

1.9x2.9x1.5m) direct shear tests carried out at the Institute for Geotechnics and

Foundation Engineering, Sarajevo (Equation 4.10). The materials tested were generally

limestone, sandstone, serpentinite and slate and were from a mixture of sources

including: natural; rock debris; and quarry rockfill. The tests were generally carried out

for materials for embankment dams over stress ranges between 0.05 to 2.0MPa. Figure

4.17 shows the test results.

Page 307: Shear Strength of Rock

Page 4.20

Table 4.5. Various shear strength criteria for rockfill

Eq Reference Equation Parameters Development

4.8 De Mello (1977)

Charles & Watts (1980) B

nAστ = A, B see Table 4.4 Empirical curved envelope.

4.9 Indraratna et al (1993)

Indraratna (1994)

b

c

n

c

a

=

σσ

στ

a,b = 0.25,0.83 (lower bound, σn=0.1-1MPa)

a,b = 0.71,0.84 (upper bound, σn=0.1-1MPa)

a,b = 0.75,0.98 (lower bound, σn=1-7MPa)

a,b = 1.80,0.99 (upper bound, σn=1-7MPa)

Non-dimensionalised form of (4.8). Note that if A in (4.8) is independent of σc then a is not independent of σc.

4.10 Sarac & Popovic (1985) ( )BnA 0max σστ =

A increases with σc↑, Cu↑, γ ↑, d50 ↑

≈ 0.7 to 1.5 (Figure 4.19,Figure 4.20)

B increases with σc↑, Cu↑, γ ↓

≈ 0.419 to 0.911 (Figure 4.18)

σ0 = 1MPa

Developed from large-scale direct shear tests (up to σn = 2MPa) on quarry rockfill and natural gravels. Various sedimentary rocks were used.(Figure 4.17)

4.11 Indraratna et al (1993)

Indraratna (1994)

β

σσ

ασσ

′=

cc

31

α,β = 0.4,0.62 (lower bound, 0.1 to 1MPa)

α,β = 0.78,0.65 (upper bound, 0.1 to 1MPa)

α,β = 2.71,0.96 (lower bound, 1 to 7MPa)

α,β = 3.58,0.90 (upper bound, 1 to 7MPa)

Alternative of (4.9) for principal stresses

4.12 Indraratna et al (1998) ba 3

3

1 σσσ ′=

′′

a, b = 84.98,-0.49 (gradation A)

a, b = 125.17,-0.56 (gradation B)

Developed empirically for two gradations of ballast

Undefined at σ′3 = 0

4.13 Doruk (1991) c

a

c

σσ

σσ

′+′=′ 3

31 m, a

Developed from Hoek-Brown by setting the rockfill compressive strength to zero (i.e. s = 0).

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4.4 DATABASE OF TRIAXIAL SHEAR TESTS

The author has collated a database of large-scale triaxial shear tests. The database has

over 989 individual triaxial shear tests from 307 sets of data. The information in the

database has been collected from selected quality published papers and reports and from

unpublished laboratory reports from organisations that have carried out high quality

testing for dams and other projects. There is an assumption inherent in collating a large

amount of data that all data sets are of equal quality. The dangers of making this

assumption were mitigated to some degree by using the quality sources stated above.

Although virtually all tests were accepted, there were some that were rejected. Tests that

were carried out at a very high strain rate were rejected. As were results where the

strength of the sample was estimated due to the test reaching the strain limit of the

testing apparatus prior to attaining the maximum strength of the sample. Table 4.6

shows the parameters recorded in the database. The complete database is contained in

Appendix F on a CD-ROM that is appended to this thesis.

Table 4.7 summarises the basic statistics of the data. The triaxial cells used for tests

ranged from a diameter of 50.8mm to a diameter of 1130mm. The maximum particle

size in the tests ranged from 4.8mm to 200mm. The minimum particle size in the tests

ranged from 0.0035mm to 40mm. Note that many tests recorded a minimum particle

size of ‘less than’ a particular diameter.

40% of tests had zero fines (% passing 0.075mm) content whilst 80% of the tests had a

fines content of no more than 5%. 10% of the triaxial tests had fines contents in excess

of 20%. The largest fines content for a test in the database was 45%. Note that the

uniformity coefficient and the coefficient of curvature are very high for tests where

fines have been added to a large diameter rockfill.

18.7% of the triaxial tests were on basalt material whilst 14.9% were on granite, 8.2%

sandstone and 3.9% limestone. Many tests did not give the rock type of the material

tested.

49% of the samples tested were considered angular (with an angularity rating = 8).

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Table 4.6. List of parameters in triaxial shear strength database

Parameter Description Case Test number within database Reference Data source Data set Identifying number given for each set of tests performed. Taken from

reference where given. Test Test number within data set Site Place of origin of material or location (e.g. dam name) Origin Source of gravel size particles (e.g. crushed, blasted, alluvial etc.) Type Rock particle type (e.g. sandstone etc) UCS (MPa) Unconfined compressive strength of individual particles UCS* (MPa) Includes UCS estimated where not given (see Section 4.5.1) Ang Angularity of particles from: angular; sub-angular; sub-rounded; rounded Ang rat A value from 1 (rounded) to 8 (angular) based on a description of the

rockfill given in reference. (0 = not given) Ds (mm) Sample diameter Hs (mm) Sample height Fines (%) Percent of material finer than 0.075mm Fines* (%) Includes estimated fines where not given (see Section 4.5.1) dmin (mm) Minimum particle size d10 (mm) Diameter corresponding to 10% finer d30 (mm) Diameter corresponding to 30% finer d50 (mm) Diameter corresponding to 50% finer d60 (mm) Diameter corresponding to 60% finer d90 (mm) Diameter corresponding to 90% finer dmax (mm) Maximum particle size cu

Coefficient of uniformity: 10

60

dd

cu =

cc Coefficient of curvature:

6010

230

ddd

cc =

Grav (%) Gravel content (defined as percent of material greater than 2mm diameter)

rd Relative density γd (kN/m3) Dry unit weight emin Minimum void ratio emax Maximum void ratio ei Initial void ratio ei

* Includes estimated void ratio where not given (see Section 4.5.1) n Porosity Bg Breakage co-efficient (Marsal) GS Specific gravity w (%) Moisture content S (%) Degree of saturation σ′3 Minimum principal effective stress σ′1 Maximum principal effective stress εaf Axial strain at failure εvf Volumetric strain at failure Brit Type of failure (B-brittle, T-transitional, D-ductile). Qualitative term

based on the stress-strain curves (if given) presented in the reference. φsec Secant friction angle (calculated) σn Normal stress on failure plane (calculated) σ1-σ3 Principal stress difference (calculated) σ1/σ3 Principal stress ratio (calculated)

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Table 4.7. Summary of basic statistics from the rockfill database

Parameter Minimum Average Maximum

Sample diameter (mm) 50.8 332 1130.3

Minimum particle size (mm) 0.0035 3.6 40

d10 (mm) 0.001 4.3 53

d30 (mm) 0.01 9 90

d50 (mm) 0.09 16 100

d60 (mm) 0.22 20 110

Maximum particle size (mm) 4.8 59 200

Fines content (%) 0 4.1 45

Uniformity coefficient, cu 1.3 81 3243

Coefficient of curvature, cc 0.04 2 16.9

Unconfined compressive strength of intact rock particles (MPa) 25 153 761

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4.5 DATABASE ANALYSIS

This section describes the qualitative and quantitative (using statistical methods)

analysis of the rockfill database. Analyses using both the secant friction angle and

principal stresses were carried out. A final analysis using the Hoek-Brown criterion was

performed as part of the development of a criterion for rock mass strength.

4.5.1 Analysis Methodology

The database contained missing information for some of the test results. If a parameter

used in the statistical analysis was missing for a particular test, that test result was

generally ignored. However, to increase the number of tests, certain assumptions were

made prior to the analysis. These are:

Where an unconfined compressive strength of the intact rock was not given and

reasonable estimates could be made, it was estimated into three groupings of 40, 100

and 200MPa rocks based on a description of the rock type, degree of weathering and

also the origin of the material. These samples were placed. The effect of including these

data sets was evaluated during the statistical analysis.

Where the minimum particle size, dmin, was recorded as ‘less than’ a particular diameter

the following table was used to estimate dmin for the analysis.

Minimum particle size given, dmin Minimum particle size used, dminhat

<0.075 (and d10>0.075) 0.01

<0.075 (and d10≤0.075) 0.005

<0.02 0.005

<0.005 (and d10>0.003) 0.001

<0.005 (and d10≤0.003) 0.0005

Where an initial void ratio was not given it was calculated from one of the following

equations (in order of preference):

n

ne

−=

1 (4.17)

Page 317: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.30

( )minmaxmax eeDee r −−= (4.18)

1−=d

wsGe

γγ

(4.19)

where

e = void ratio

n = porosity

emax = maximum void ratio

emin = minimum void ratio

Dr = relative density (%)

γw = unit weight of water (kN/m3)

γd = dry unit weight (kN/m3)

Gs = specific gravity (assumed = 2.7 if not given)

4.5.2 Secant Friction Angle, φsec, Versus Normal Stress, σn

Relationships between secant friction angle, φsec, and normal stress, σn, were

investigated using the rockfill shear strength database. This relationship was chosen as it

is commonly used in the literature and practice to present and analyse data. The results

are discussed in detail below however, it should be noted at the outset that the fits

obtained using this statistical analysis were inferior to those obtained using a

relationship of maximum principal stress, σ′1, versus minor principal stress, σ′3. This is

of particular importance at both low and high confining stress, σ′3.

4.5.2.1 General Assessment of Database

Figure 4.21 to Figure 4.27 show plots of φsec vs σn with σn plotted on a logarithmic

scale. These plots are discussed in turn below. Note that these analyses were carried out

for the complete data sets. No parameter (e.g. σc) was estimated for these plots. Where a

specific parameter has been investigated a small ‘+’ symbol on a figure represents a test

result where the parameter is unknown (except for Figure 4.21).

Page 318: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.31

q Figure 4.21 φsec vs σn: This figure shows that φsec has a range of approximately 25°

for any given value of σn. This shows that the bounds given by Indraratna et al

(1993) (equating to a range of about 15°) for this type of plot do not indicate the full

range of φsec possible. Their upper bound appears to be too conservative whilst the

lower bound, although providing a better fit, has several test results below it. The

gradient of the bounds does not appear to be steep enough to adequately describe the

variation in φsec relative to σn.

q Figure 4.22 φsec vs σn sorted on angularity rating: The addition of angularity rating

does not assist greatly with improving the prediction of φsec vs σn. The figure shows

that angular rockfill (angrat = 7 or 8) generally lies above sub-angular material

(angrat = 5 or 6). However, rounded material (angrat = 1 or 2) lies roughly in the

centre of the data with angular material lying both above and below the data.

q Figure 4.23 φsec vs σn sorted on rock type = basalt: This was plotted to see the

amount of variability there was within one class of rock type. Basalt is used as

railway ballast, road base and dam rockfill. A basalt rockfill might be expected to lie

at the higher strength end of all rockfills. Although the figure shows this to be true

there is still a 10°-15° range in φsec for the material for any given σn.

q Figure 4.24 φsec vs σn sorted on coefficient of uniformity, cu: The figure shows that

cu does not appear to be a very good additional predictor with data for each cu range

generally being well and evenly spread. It could be argued that the lower strength

rockfills predominately have high cu values (>12). However, these types of rockfills

are spread throughout the full strength range.

q Figure 4.25 φsec vs σn sorted on maximum particle size, dmax: This data is also quite

scattered although there appears to be a tendancy for high dmax rockfills to result in a

higher strength than small dmax rockfills.

q Figure 4.26 φsec vs σn sorted on percent fines content: The rockfills with a high fines

content (>20%) generally have a lower φsec. Much of the other data, particularly

with fines less than 10% is well scattered.

Page 319: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.32

q Figure 4.27 φsec vs σn sorted on unconfined compressive strength, σc: Rockfills with

a σc of less than 100MPa appear to have lower strengths than those greater than

100MPa. It is difficult to discern any real difference in the results for rockfills with

strengths of 100-200MPa and greater than 200MPa.

A general conclusion from the analysis of the graphs may be made that the factors

described above do have some effect on the shear strength of rockfill, although none of

them stands out as being substantially better than the others as a predictor. It is unwise

to estimate strength based solely on these graphs due to the interrelationship between

the various factors in the tests. A better statistical analysis is to perform a global

analysis of the data using all these factors and assessing whether they are statistically

significant. This is performed in the next section.

Page 320: Shear Strength of Rock

Page 4.33

Sigma n (kPa)

Phi

sec

ant (

deg)

20

30

40

50

60

70

80

10 40 70 100 400 700 1000 4000 7000

Figure 4.21. Secant friction angle, φ sec vs normal stress, σn

Approximate location of bounds from

Indraratna et al (1993) - see Figure 4.4.

Page 321: Shear Strength of Rock

Page 4.34

Sigma N (kPa)

Phi

sec

(deg

)

20

30

40

50

60

70

80

10 40 70 100

400

700

1000

4000

7000

1000

0

angrat=1 or angrat=2angrat=3 or angrat=4angrat=5 or angrat=6angrat=7 or angrat=8

Figure 4.22. Secant friction angle, φ sec vs normal stress, σn, sorted on angularity rating

Note a ‘+’ symbol indicates the angularity rating is unknown for that particular test

Page 322: Shear Strength of Rock

Page 4.35

Sigma n (kPa)

Phi

sec

(deg

)

20

30

40

50

60

70

80

10 40 70 100

400

700

1000

4000

7000

1000

0

type="basalt"type="basalt r"type="basalt1"

Figure 4.23. Secant friction angle, φ sec vs normal stress, σn, sorted on rock type = basalt

Note a ‘+’ symbol indicates the material is not basalt or is unknown for that particular test

Page 323: Shear Strength of Rock

Page 4.36

Sigma n (kPa)

Phi

sec

(deg

)

20

30

40

50

60

70

80

1040

70100

400700

10004000

700010000

cu<=2cu<=6cu<=12cu>12

Figure 4.24. Secant friction angle, φ sec vs normal stress, σn, sorted on coefficient of uniformity, cu

Note a ‘+’ symbol indicates the coefficient of uniformity is unknown for that particular test

Page 324: Shear Strength of Rock

Page 4.37

Sigma N (kPa)

Phi

sec

(deg

)

20

30

40

50

60

70

80

10 40 70 100

400

700

1000

4000

7000

1000

0

dmax<=20dmax<=50dmax<=100dmax>100

Figure 4.25. Secant friction angle, φ sec vs normal stress, σn, sorted on maximum particle size, dmax

Note a ‘+’ symbol indicates dmax is unknown for that particular test

Page 325: Shear Strength of Rock

Page 4.38

Sigma n (kPa)

Phi

Sec

(deg

)

20

30

40

50

60

70

80

10 40 70 100

400

700

1000

4000

7000

1000

0

fines<=0fines<=5fines<=10fines<=20fines>20

Figure 4.26. Secant friction angle, φ sec vs normal stress, σn, sorted on percent fines (passing 0.075mm) content

Note a ‘+’ symbol indicates the fines content is unknown for that particular test

Page 326: Shear Strength of Rock

Page 4.39

Sigma n (kPa)

Phi

sec

(deg

)

20

30

40

50

60

70

80

10 40 70 100

400

700

1000

4000

7000

1000

0

ucs>=200ucs>=100ucs>0

Figure 4.27. Secant friction angle, φ sec vs normal stress, σn, sorted on unconfined compressive strength of the rock substance, UCS (MPa)

Note a ‘+’ symbol indicates the UCS of the intact particles is unknown for that particular test

Page 327: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.40

4.5.2.2 Statistical Analysis of Database

A non-linear statistical analysis was carried out on the database. The estimation method

used was least squares. An analysis of the form shown below was found to be the most

effective for relating φ to σn.

cnba σφ ′+=′ (4.20)

The analysis resulted in the following constants:

( ) ( )1500459.02756.0172.0267.043.36 −+−+−−= UCScFINESANGa c (4.21)

( ) ( )150408.02105.5549.027.1051.69 −−−−++= UCScFINESANGb c -0.408 (4.22)

3974.0−=c (4.23)

where,

( )5−= ratingangularityANG for angularity rating >5.5; otherwise 0

FINES = percentage of fines passing 0.075mm (%)

cc = coefficient of curvature

UCS = unconfined compressive strength of the rock substance (MPa)

This function resulted in a variance explained of just 61.7%. It should be noted that the

addition of the uniformity coefficient, cu, and the maximum and minimum particle sizes,

dmax and dmin, did not result in a better fit to the data. As the φ vs σn curve is

unconstrained at both low and high σn it is unlikely that a reasonable fit will be found

regardless of the function used. Due to the relatively poor statistical results it was

decided to proceed with an analysis using principal stresses.

Page 328: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.41

4.5.3 Maximum Principal Stress, σ′1, versus Minimum Principal Stress, σ′3

The analysis using φsec vs σn gave poor results. In this section principal stresses are

used. These are constrained at σ′3=0, σ′1=0. A non-linear statistical analysis was carried

out on the database. The estimation method used was least squares. An analysis of the

form shown in Equation 4.24 was found to be the most effective for relating σ′1 to σ′3.

ασσ 31 ′=′ RFI (4.24)

An initial analysis on the whole database (988 data sets) found (Variance explained =

97.13%):

RFI = 4.7002

α = 0.8972

To determine which parameters affected RFI, the analysis was carried out iteratively.

The analysis was carried out using a parameter in the database as a predictor of RFI

(e.g. σc). After each analysis the residuals were plotted against the parameters in the

database. Where a trend was noted for a particular parameter another analysis was

carried out using that additional parameter. The analysis resulted in the following

equations (based on 869 data sets and with a variance explained = 98.82%):

8726.0=α

UCSFINESdANGe RFIRFIRFIRFIRFIRFI 30598.01568.10027.048763.03491.6max

+−−+=

(4.25)

ie e

RFI+

=1

1 (4.26)

0otherwise angular, if 1 ==ANGRFI (4.27)

maxmaxdRFI d = (mm) (4.28)

( )

( )20Fines

20Fines

1 −

+=

ee

RFI FINES where fines is in % (4.29)

( )

( )110UCS

110UCS

1 −

+=

ee

RFIUCS where UCS is in MPa (4.30)

Page 329: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.42

Equation 4.29 and 4.30 are effectively smooth “step” functions that are ameniable to

equation solving routines.

Figure 4.28 shows the variation of RFIe with initial void ratio. This shows that an

increase in initial void ratio will lead to a decrease in σ′1 and shear strength.

Highly angular rockfill (angularity rating = 8) showed an increase in strength. There

was no noticeable trend for less angular rockfill (angularity rating ≤ 7) and hence

Equation 4.27 was chosen.

The strength of the rockfill (σ′1) was found to be proportional to the maximum particle

size (Equation 4.28).

The unconfined compressive strength, σc, was found to have a limited effect on the

strength of the rockfill. Generally strengths below a σc of 100MPa had similar strengths,

as did those with σc greater than 120MPa. Equation 4.30 acts as a switch at a σc around

110MPa. Below a σc of 110MPa the function rapidly approaches zero and above a σc of

110MPa the function rapidly approaches unity (Figure 4.29).

The fines content was found to only affect the strength of the rockfill where the fines

content was greater than approximately 20%. Equation 4.29 acts as a switch at a fines

content around 20%. Below a fines content of 20% the function rapidly approaches zero

and above a fines content of 20% the function rapidly approaches unity (Figure 4.30).

Page 330: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.43

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Void Ratio

RFIe

Figure 4.28. RFIe versus void ratio

0

0.2

0.4

0.6

0.8

1

50 60 70 80 90 100 110 120 130 140 150

UCS (MPa)

RFIUCS

Figure 4.29. RFIUCS versus unconfined compressive strength

Page 331: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.44

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 40

FINES (%)

RFIFINES

Figure 4.30. RFIFINES versus percent fines

The residuals versus unconfined compressive strength, maximum particle size, initial

void ratio, angularity and fines content are shown on Figure 4.31 to Figure 4.35

respectively. These figures shown no discernible trend from which it can be assumed

that the equations provided above are reasonable over the range of the data.

Figure 4.36 shows the residuals plotted against sample diameter. The lack of any major

trend in the data suggests that sample diameter does not have a large effect on rockfill

strength at least up to diameters of about 1.2m. This suggests that the process of scaling

using parallel grading lines when testing rockfill for use in the field is valid and should

not affect the results. Note however, that if fines are increased due to the scaling

strength (σ′1) may be reduced.

Figure 4.37 to Figure 4.41 show the effect that a change in unconfined compressive

strength, angularity, fines content, maximum particle size and initial void ratio have on

σ′1 respectively.

Page 332: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.45

Figure 4.42 shows the data used in the analysis together with lines representing RFI=7

(approximate upper bound), RFI=4.7 (approximate best estimate) and RFI=3

(approximate lower bound). Figure 4.43 shows the same plot with all the data in the

database plotted. It shows that the bounds are still reasonable and that the data left out

of the analysis (due to insufficient information) would not have changed the results

significantly. Figure 4.44 shows the same plot for a stress range (σ′3) up to 1.5MPa.

Page 333: Shear Strength of Rock

Page 4.46

-3

-2

-1

0

1

2

3

0 100 200 300 400 500 600 700 800

UCS (MPa)

Res

idua

ls (M

Pa)

Figure 4.31 Residuals versus unconfined compressive strength of intact rock

Page 334: Shear Strength of Rock

Page 4.47

-3

-2

-1

0

1

2

3

0 50 100 150 200 250

Dmax (mm)

Res

idua

ls (M

Pa)

Figure 4.32. Residuals versus dmax

Page 335: Shear Strength of Rock

Page 4.48

-3

-2

-1

0

1

2

3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Void Ratio

Res

idua

ls (M

Pa)

Figure 4.33. Residuals versus void ratio

Page 336: Shear Strength of Rock

Page 4.49

-3

-2

-1

0

1

2

3

0 1 2 3 4 5 6 7 8 9

Angularity Rating

Res

idua

ls (M

Pa)

2 - Rounded4 - Sub-rounded6 - Sub-angular8 - Angular

Figure 4.34. Residuals versus angularity rating

Page 337: Shear Strength of Rock

Page 4.50

-3

-2

-1

0

1

2

3

0 5 10 15 20 25 30 35 40

Fines (%)

Res

idua

ls (M

Pa)

Figure 4.35. Residuals versus fines content

Page 338: Shear Strength of Rock

Page 4.51

-3

-2

-1

0

1

2

3

0 200 400 600 800 1000 1200

Sample diameter (mm)

Res

idua

ls (M

Pa)

Figure 4.36. Residuals versus sample diameter

Page 339: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.52

0

5

10

15

20

0 1 2 3 4 5σ3 (MPa)

σ1

(MPa)

UCS = 50MPa

UCS = 110MPa

UCS = 200MPa

Angularity = 7Fines = 0%dmax = 60Void ratio = 0.4

Figure 4.37. Effect of unconfined compressive strength on σ′1

0

5

10

15

20

0 1 2 3 4 5σ3 (MPa)

σ1

(MPa)

Angularity = 7

Angularity = 8

UCS = 100 MPaFines = 0%dmax = 60Void ratio = 0.4

Figure 4.38. Effect of angularity on σ′1 (7 = sub-angular to angular; 8 = angular)

Page 340: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.53

0

5

10

15

20

0 1 2 3 4 5σ3 (MPa)

σ1

(MPa)

Fines = 40%

Fines = 20%

Fines = 0%

UCS = 100 MPaAngularity = 7dmax = 60Void ratio = 0.4

Figure 4.39. Effect of fines content on σ′1

0

5

10

15

20

0 1 2 3 4 5σ3 (MPa)

σ1

(MPa)

dmax = 200

dmax = 100

dmax = 5

UCS = 100 MPaAngularity = 7Fines = 0%Void ratio = 0.4

Figure 4.40. Effect of maximum particle size on σ′1

Page 341: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.54

0

5

10

15

20

0 1 2 3 4 5σ3 (MPa)

σ1

(MPa)

e = 0.8

e = 0.5

e = 0.2

UCS = 100 MPaAngularity = 7Fines = 0%dmax = 60

Figure 4.41. Effect of initial void ratio on σ′1

Page 342: Shear Strength of Rock

Page 4.55

0

5

10

15

20

25

30

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

σ3 (MPa)

σ1 (MPa) RFI = 7

RFI = 3

RFI = 4.7

Figure 4.42. σ′1 vs σ′3 showing data used in analysis and RFI relationship

Page 343: Shear Strength of Rock

Page 4.56

0

5

10

15

20

25

30

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

σ3 (MPa)

σ1 (MPa) RFI = 7

RFI = 3

RFI = 4.7

Figure 4.43. σ′1 vs σ′3 showing all data and RFI relationship

Page 344: Shear Strength of Rock

Page 4.57

0

2

4

6

8

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

σ3 (MPa)

σ1 (MPa)

RFI = 7

RFI = 3

RFI = 4.7

Figure 4.44. σ′1 vs σ′3 showing all data and RFI relationship (σ′3 up to 1.5MPa)

Page 345: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.58

4.5.3.1 Secant Friction Angle Versus Normal Stress

Figure 4.37 to Figure 4.41 are replotted as curves for φsec vs σn by using the following

equations:

′+′′−′

= −

33

331sec sin

σσσσ

φ α

α

RFIRFI (4.31)

13seccos +′= ασφσ RFIn (4.32)

Table 4.8 shows the variation in φsec due to changes in various parameters for σn=1MPa

and 0.5MPa. These give some idea of the influence of different parameters on the secant

friction angle. Note that these friction angles are based on assumptions as shown on

Figure 4.45 to Figure 4.49. The values chosen for the parameters are realistic upper and

lower bounds from the database.

Table 4.8. Changes in φsec on Figure 4.45 to Figure 4.49 for σn=1MPa and σn =

0.5MPa

σn = 0.1MPa σn = 0.5MPa σn = 1MPa Parameter Value

φsec (°)

Change in φ with

increase in parameter

φsec (°)

Change in φ with

increase in parameter

φsec (°)

Change in φ with

increase in parameter

50 46.8 42.2 40.3 σc (MPa)

200 48.1 +1.3

43.6 +1.4

41.8 +1.5

1-7 46.7 42.2 40.3 Angularity rating

8 48.8 +2.1

44.4 +2.2

42.6 +2.3

0 46.7 42.2 40.3 Fines content (%)

20 43.9 -2.8

39.1 -3.1

36.9 -3.4

50 47.0 42.4 40.4 Maximum particle size

(mm) 200 44.8 -2.2

40.3 -2.1

38.3 -2.1

0.2 49.9 45.5 43.7 Initial void ratio

0.6 43.5 -6.4

36.4 -9.1

34.2 -9.5

Page 346: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.59

30

35

40

45

50

0 2 4 6 8σn (MPa)

φsec

UCS = 50MPa

UCS = 200MPa

Angularity = 7Fines = 0%dmax = 60Void ratio = 0.4

Figure 4.45. Effect of unconfined compressive strength on φ sec

30

35

40

45

50

0 2 4 6 8σn (MPa)

φsec

Angularity = 7

Angularity = 8

UCS = 100MPaFines = 0%dmax = 60Void ratio = 0.4

Figure 4.46. Effect of angularity on φ sec (7 = sub-angular to angular; 8 = angular)

Page 347: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.60

20

25

30

35

40

45

50

0 2 4 6 8σn (MPa)

φ

Fines = 0%

Fines = 20%

Fines = 40%

UCS = 100MPaAngularity = 7dmax = 60Void ratio = 0.4

Figure 4.47. Effect of fines content on φsec

30

35

40

45

50

0 2 4 6 8σn (MPa)

φ

dmax = 5

dmax = 100

dmax = 200

UCS = 100MPaAngularity = 7Fines = 0%Void ratio = 0.4

Figure 4.48. Effect of maximum particle size on φsec

Page 348: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.61

20

25

30

35

40

45

50

0 2 4 6 8σn (MPa)

φ

e = 0.2e = 0.4

e = 0.6

UCS = 100MPaAngularity = 7Fines = 0%dmax = 60

Figure 4.49. Effect of initial void ratio on φ sec

4.5.4 Hoek-Brown Criterion

The author considers that rockfill could represent a very poor quality rockmass. As such

an analysis of the database using the Hoek-Brown criterion was performed. The results

from this analysis could then be used as a lower bound rock mass strength estimator.

The statistical analysis was carried out for data where the UCS was known. This

resulted in a sample of 409 triaxial tests. Two approaches were used: one where the

variables are σ′3 and the dependent variable σ′1; and the other where the variables are

σ′3/σc and the dependent variable σ′1/σc. Similar analyses to those discussed previously

were carried out i.e. non-linear, quasi-Newton with a loss function of (observed –

predicted)2. A further analysis was carried out where the estimated values of the UCS of

the intact rock were used where no UCS was recorded for the sample.

The ability of the Hoek-Brown criterion to estimate the shear strength of rockfill (and

subsequently poor quality rock mass) was performed by assuming typical Hoek-Brown

parameters of s = 0 and a = 0.6. This was compared with a further analyses where a was

defined as a parameter. The results from the analyses are shown in Table 4.9.

Page 349: Shear Strength of Rock

The Shear Strength of Rockfill Page 4.62

Table 4.9 and Figure 4.50 show that if the recommended Hoek-Brown parameters are

used a poor fit results. Due to the enforced curvature (a = 0.6), σ′1 is overpredicted at

low σ′3 and under predicted at high σ′3. Much better fits (Table 4.9 and Figure 4.50) are

obtained where a was a parameter. These analyses showed that an a of 0.90 to 0.95 was

much more suitable for rockfill. Similarly to intact rock, the interrelation between a and

mb is also illustrated by the results in Table 4.9.

The conclusion from the point of view of rock masses is that a is too constrained in the

current Hoek-Brown criterion. Modifications need to be made such that the exponent, a,

towards a value of 0.90-0.95 for poor quality rockfill.

A look at the forms of the equations used shows that the method of fitting is very

important to the results obtained. In this case, non-dimensionalising the equations

resulted in a better variance explained.

Table 4.9. Results from the statistical analysis of the rockfill database using the

Hoek-Brown equation

Form of equation Data sets mb a Variance explained

6.0

331 0

+

′+′=′

c

bc

mσσ

σσσ 405

σci known 0.42929

0.6

(input) 88.95%

a

c

bc

m

+

′+′=′ 03

31 σσ

σσσ 405

σci known 2.40706 0.89999 97.40%

6.0

331 0

+

′+

′=

cb

cc

mσσ

σσ

σσ

405

σci known 0.75486

0.6

(input) 90.93%

a

cb

cc

m

+

′+

′=

′0331

σσ

σσ

σσ

405

σci known 2.71833 0.94877 98.73%

a

c

bc

m

+

′+′=′ 03

31 σσ

σσσ

988

σci estimated where

unknown

2.39551 0.8954 97.42%

Page 350: Shear Strength of Rock

Page 4.63

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

σ3/σ c

σ1/σc

6.0

331 75486.0

+=

ccc σσ

σσ

σσ

94877.0

331 71833.2

+=

ccc σσ

σσ

σσ

Figure 4.50. Statistical analysis results using Hoek-Brown formula and for a = 0.6 and a = 0.95

Page 351: Shear Strength of Rock

Page 4.64

4.6 CONCLUSION

This chapter presented an overview of the strength of rockfill. An analysis of a large

database of test results was used to develop two new shear strength equations, one

relating the secant friction angle and normal stress and the other the principal stresses.

The equation for principal stresses provided a much better fit to the data and is

recommended. Of the parameters statistically investigated, the unconfined compressive

strength, particle angularity, fines content, maximum particle size and void ratio were

found to have the most significant effect on the shear strength of rockfill.

An analysis using the database and the Hoek-Brown criterion demonstrated that the

criterion provided a poor fit to the rockfill data due to the restrictions placed on the

exponent a of approximately 0.6. A good fit was obtained where a was free to vary up

to unity (a value of 0.9 to 0.95 was obtained). This has important implications for the

use of the Hoek-Brown criterion for very poor quality rock masses.

Page 352: Shear Strength of Rock

Empirical Rock Slope Design Page 5.1

5 EMPIRICAL ROCK SLOPE DESIGN

5.1 INTRODUCTION

Due to the complexity of rock masses, a number of researchers have attempted to

correlate rock slope design with rock mass parameters. Many of these methods have been

subsequently modified by others and are now currently being used in practice for

preliminary and sometimes final design. This chapter presents a review of the more

commonly used empirical rock slope design methods. The historical development of these

methods and the data used to support them is discussed. A number of case studies are

assessed using the different methods. Finally, a new relationship between the Geological

Strength Index, GSI, slope height and stable slope angle is presented for use in the design

of cuts in rock masses in dry conditions or under moderate water pressures.

Page 353: Shear Strength of Rock

Empirical Rock Slope Design Page 5.2

5.2 REVIEW OF THE ROCK MASS RATING SYSTEMS

There are several empirical rock mass rating techniques that can be utilised in the design

of slopes. These include:

• RMR - Rock mass rating (Bieniawski, 1976 & 1989)

• MRMR - Mining rock mass rating (Laubscher, 1977 & 1990)

• RMS - Rock mass strength (Selby, 1980)

• SMR - Slope mass rating (Romana, 1985)

• SRMR - Slope rock mass rating (Robertson, 1988)

• CSMR - Chinese system for SMR (Chen, 1995)

• GSI - Geological strength index (Hoek et al. 1995)

• M-RMR - Modified rock mass classification (Ünal, 1996)

• BQ - Index of rock mass basic quality (Lin, 1998)

The majority of methods require the determination of a basic rock mass rating. The rating

is usually calculated as the summation of a number of rating values that account for intact

rock strength, block size, defect condition and possibly groundwater. A number of the

methods then adjust this value based on such factors as defect orientation, excavation

method, weathering, induced stresses and the presence of major planes of weakness.

Table 5.1 compares a number of these methods. The numbers show the range of

weightings possible for each component of the rating system, whilst an asterix, ‘*’, shows

which parameters are taken into account in each method. It should be noted that the

different rock mass rating systems use varying methods to account for each parameter.

The MRMR and M-RMR adjustment factors are multipliers whilst the adjustment factors

for the other methods are added to the basic rock mass rating. The maximum value of 141

for CSMR assumes a slope height of 50m. The numbers shown in brackets, ‘( )’, in Table

5.1 represent negative values.

Table 5.1. Comparison of weightings for various rock mass rating methods

Page 354: Shear Strength of Rock

Empirical Rock Slope Design Page 5.3

Method RMR76 RMR89 MRMR RMS SMR CSMR M-RMR SRMR GSIIntact strength 0-15 0-15 0-20 5-20 0-15 0-15 0-15 0-30 0-15Block size 8-50 8-40 0-40 8-30 8-40 8-40 0-40 8-40 8-50

- Spacing * * * * * * * * *- RQD * * * * * * * *

Defect condition 0-25 0-30 0-40 3-14 0-30 0-30 0-30 0-30 0-25- Persistence * * * * * * * * *- Aperture * * * * * * * * *- Roughness * * * * * * * *- Infilling * * * * * * * *- Weathering * * * * * * *

Ground water 0-10 0-15 * 1-6 0-15 0-15 0-15 - 10Defect orientation (60)-0 (60)-0 63-100% 5-20 (60)-0 (60)-0 (12)-(5)

- Strike * * * * *- Dip * * * * * *- Slope dip – defect dip * *

Excavation method - - 80-100% - (8)-15 (8)-15 80-100% - -Weathering - - 30-100% 3-10 - - 60-115% - -Induced stresses - - 60-120% - - - - - -Major plane of weakness - - - - - - 70-100% - -

TOTAL RANGE (52)-100 (52)-100 0-120 25-100 (60)-115 (63)-141 (7)-105 8-100 18-100

BA

SIC

RO

CK

MA

SS R

AT

ING

AD

JUST

ME

NT

S - -

Note values in brackets are negative

5.2.1 Methods for Estimating the Basic Rock Mass Rating

The basic rock mass rating attempts to capture the main features of a rock mass that, in the

context of this report, affect the shear strength of the rock mass and subsequently the

stability of slopes in that rock mass.

5.2.1.1 The Rock Mass Rating, RMR, and Geological Strength Index, GSI

Bieniawski’s (1973, 1975, 1976, 1989) rock mass rating (RMR) is probably the most

commonly used rock mass rating system for estimating rock mass strength. Initially

created to assess the stability and support requirements of tunnels, it has been found to be

useful in assessing the strength of rock masses for slope stability. Table 5.2 shows the

rating method of Bieniawski (1989). It should be noted that the weighting of the

parameters has changed slightly over the years since its development. Wherever the RMR

is referred to in this document, the subscript will refer to the year of publication of that

version. For example, RMR76, refers to the RMR published by Bieniawski (1976).

Hoek et al (1995) modified the RMR so as to make it more applicable to assessing the

strength of rock masses. The result of this was the Geological Strength Index (GSI). Table

5.3 shows the components and ratings from the GSI.

Page 355: Shear Strength of Rock

Empirical Rock Slope Design Page 5.4

The GSI is based on RMR76 and is calculated by summing the ratings for each parameter

and adding 10. A rating value of 10 is added as the GSI assumes water conditions to be

dry. No corrections are made for joint orientation as it is assumed to be favourable. Hoek

et al. (1995) believe that joint orientation and water conditions should be assessed during

the analysis.

Hoek et al. (1995) allow for the use of RMR89 to estimate the GSI by using GSI = RMR89

– 5. The author warns that RMR89 should be used with caution as it can lead to a GSI

difference of up to 10 when compared with the GSI derived as above. Hoek (2000)

provides another method of estimating GSI using Figure 5.1.

This chapter is primarily concerned with the estimate of the strength of large rock masses

and the subsequent correlation with slope angles. The GSI is made up of several

components: intact rock strength; rock quality designation (RQD); defect spacing; and

joint condition (water is already set to dry). All these components can be affected by

scale and thus must be considered carefully when designing for very large rock masses. A

larger discussion of the applicability of using the GSI for rock slopes is contained in

Chapter 6.

Page 356: Shear Strength of Rock

Empirical Rock Slope Design Page 5.5

Table 5.2. Rock mass rating (Bieniawski, 1989)

Page 357: Shear Strength of Rock

Empirical Rock Slope Design Page 5.6

Table 5.3. Geological strength index, GSI (Hoek et al, 1995)

5.2.1.2 Mining Rock Mass Rating, MRMR

Laubscher (1977, 1984 and 1990) developed a classification system, based on

Bieniawski (1973), that gave a basic rating from 0 (very poor) to 100 (very good) (Table

5.4 and Table 5.5). The system changes some of the weightings of parameters and alters

the method of determining joint spacing and condition compared to Bieniawski (1973).

Laubscher assesses the rock joint spacing for one, two or three “continuous” joint

systems. “A joint is continuous if its length is greater than one diameter of the excavation

or 3m. It is also continuous if it is less than 3m but it is displaced by another joint – that

is, the joints are features that define blocks of ground.” Joints logged from boreholes are

placed in three 30° dip ranges. “Experience” is used to divide these ranges into further

joint sets.

MRMR was specifically developed for use in the assessment of support for underground

openings and there is ambiguity in the assessment of MRMR when dealing with slopes.

For poor and very poor quality rock masses (MRMR<40) the MRMR can be largely

influenced by the evaluation of joint spacing and joint/water conditions. The appropriate

evaluations are very difficult to assess when only borehole data is available and clearly

requires a large degree of judgement even when exposures are available.

Page 358: Shear Strength of Rock

Empirical Rock Slope Design Page 5.7

Figure 5.1. Estimate of GSI based on geological descriptions. (Hoek, 2000)

Page 359: Shear Strength of Rock

Empirical Rock Slope Design Page 5.8

Table 5.4. MRMR (Laubscher, 1977)

RQD (%) 100-91 90-76 75-66 65-56 55-46 45-36 35-26 25-16 15-6 5-0

Rating 20 18 15 13 11 9 7 5 3 0

IRS (MPa) 141-136 135-126 125-111 110-96 95-81 80-66 65-51 50-36 35-21 20-6 5-0

Rating 10 9 8 7 6 5 4 3 2 1 0

Defect spacing Depends on number of defect sets and spacing

Rating 30.................................................................................................................................. 0

Defect condition 45° .......................................................See Table ........................................................5°

Rating 30.................................................................................................................................. 0

Groundwater

Inflow/10m length 0 25 l/min 25 – 125 l/min 125 l/min

Joint water pressure/σ1 0 0.0 - 0.2 0.2 - 0.5 0.5

Description dry moist Moderate pressure Severe problems

Rating 10 7 4 0

Table 5.5. Defect condition rating for MRMR (Laubscher, 1977)

Parameter Description Percentage adjustment to maximum rating of

30

Joint expression

(Large-scale)

Wavy unidirectional 90-99

Curved 80-89

Straight 70-79

Joint surface

(Small-scale)

Striated 85-99

Smooth 60-84

Polished 50-59

Alteration zone Softer than wall rock 70-99

Joint filling Coarse hard-sheared 90-99

Fine hard-sheared 80-89

Coarse soft-sheared 70-79

Fine soft-sheared 50-69

Gouge thickness < irregularities 35-49

Gouge thickness > irregularities 12-23

Flowing materials > irregularities 0-11

Page 360: Shear Strength of Rock

Empirical Rock Slope Design Page 5.9

5.2.1.3 Rock Mass Strength, RMS

Selby (1980, 1982, 1987, 1993 and Moon & Selby, 1983) developed the RMS system

based on correlations between RMS and stable slope angles of natural rock outcrops. The

slopes were located in New Zealand, Antarctica, the Namib Desert and the margins of the

Central plateau of southern Africa. The geology included sedimentary sequences and

metamorphic (quartzite, gneiss, schist and marble) and igneous (dolerite, basalt and

granite) rock masses.

The RMS is calculated in a similar way to RMR with a summation of rating parameters

for intact rock strength, weathering, defect spacing, aperture, defect orientation relative to

the slope, defect continuity and groundwater flow (Table 5.6).

Orr (1992) found an approximate (r2 = 0.88) correlation between RMS and RMR88:

1302.288 −= RMSRMR (5.1)

Selby uses natural slopes in his database, and thus the slopes have been exposed over

geological time. These slopes could therefore be seen to be conservative when compared

to slopes in a pit with a limited design life. Selby breaks the natural slopes into small

sections (generally bedding layers) and assesses the slope angle of these. The slope

angles of these segments of limited height are generally structurally controlled (slaking

mudstones may be an example of an exception) in practice and thus not applicable to

correlations with rock mass.

Schmidt and Montgomery (1996) modified the RMS for application to deep-seated

bedrock landsliding in sedimentary rocks. They examined a total of 61 slopes, of which

17 were rockslides. The slopes were in the Eocene Chuckanut Formation, which

comprises a fluvial sequence of interbedded sandstone and siltstone/mudstone. Schmidt

and Montgomery note that there were distinct planes of weakness at lithological contacts.

The sandstone and siltstone/mudstone layers showed distinct differences in strength.

Table 5.6. RMS Classification and Ratings (mod. Selby, 1980)

Intact strength (N-type Schmidt

100-60 60-50 50-40 40-35 35-10

Page 361: Shear Strength of Rock

Empirical Rock Slope Design Page 5.10

Hammer ‘R’)

Rating 20 18 14 10 5

Weathering unweathered slightly

weathered

moderately

weathered

highly

weathered

completely

weathered

Rating 10 9 7 5 3

Defect spacing >3m 3-1m 1-0.3m 0.3-0.05m <0.05m

Rating 30 28 21 15 8

Defect orientation

very favourable

steep dips into slope, cross

defects interlock

favourable

moderate dips into slope

fair

horizontal dips, or nearly vertical

(hard rocks only)

unfavourable

moderate dips out of slope

very unfavourable

steep dips out of slope

Rating 20 18 14 9 5

Defect aperture <0.1mm 0.1-1mm 1-5mm 5-20mm >20mm

Rating 7 6 5 4 2

Defect continuity none continuous few continuous continuous, no infill

continuous, thin infill

continuous, thick infill

Rating 7 6 5 4 1

Groundwater outflow

none trace slight <25

l/min/10m2

moderate 25-125

l/min/10m2

great >125

l/min/10m2

Rating 6 5 4 3 1

The main changes to the RMS were in the defect orientation parameter. Schmidt and

Montgomery (1996) state that defects with moderate dips into the slope should have a

higher rating than those with steep dips into the slope. Steep dips into the slope are more

likely to cause toppling and so this change appears reasonable. They also give steep dips

out of the slope a higher rating than moderate dips out of the slope. This appears to

contradict what would be expected.

An important point to note is that Schmidt and Montgomery’s data appears to be based on

translational slides and hence structurally controlled rather than on rotational rock mass

slides. This would be backed up by their statement that “the vast majority of deep-seated

rockslides … occur on hillslopes inclined at 15° to 35°”. Schmidt and Montgomery also

state that the low RMS values associated with rockslides are due to the intact rock and

defect orientation parameters.

Page 362: Shear Strength of Rock

Empirical Rock Slope Design Page 5.11

Based on their data, Schmidt and Montgomery claim that the RMS “successfully

discriminates localised areas of low rock mass strength within a landscape exhibiting

deep-seated rockslides”. However, as this data appears defect controlled it is not

considered to be reliable for use with a rock mass rating and hence this author cannot

come to the same conclusion. Also, the method could only apply in bedded rocks given its

database.

5.2.1.4 Slope Rock Mass Rating, SRMR

Robertson et al (1987), using back analysis of slopes at Island Copper Mine in British

Columbia, found that the RMR and MS (Hoek-Brown correlation to RMR) were poor

predictors of the strength of rock masses for weak rock masses. They developed the

Island Copper Rock Mass Rating (ILC-RMR) which modified RMR for RMR values less

than 40. As this method did not allow for consistency in strength assessment (i.e. different

rock mass rating methods above and below RMR = 40), Robertson (1988) proposed the

SRK Geomechanics Classification of rock masses (SRMR), shown in Table 5.7.

Robertson (1988) defines weak rock masses as those with shear strength parameters less

than:

c′ = 0.2 MPa

φ′ = 30°

This being equivalent to a jointed specimen having an unconfined compressive strength,

UCS, of less than 0.7MPa. Robertson gives three cases where rock mass strength can be

this low (or combinations of these).

1. Where the intact rock is very weak or soil-like.

2. Where there is an intense number of defects that allow the material to fail along

random stepped surfaces.

Page 363: Shear Strength of Rock

Empirical Rock Slope Design Page 5.12

3. Where there is sufficient freedom of rotation in the mass to allow intact material to

rotate to allow for the formation of a failure surface. Note, rotation/freedom increases

with equidimensional, rounded intact particles with weak infill or voids.

The SRMR varies from RMR74 in the following ways:

• Groundwater is ignored as it is assumed that groundwater is a destabilising force and

does not influence the rock mass strength. The maximum groundwater factor (15) has

been added to the intact rock factor.

• For material in the ‘soil strength’ range additional classes and ratings have been

added (S1-S5).

• The RQD has been replaced with a ‘handled’ RQD (HRQD). This is in effect a

disturbed RQD where the material has been “firmly twisted and bent but without

substantial force or use of any tools or instruments”. High RQD values will therefore

not be assigned for weak or weakly cemented rock. Note that the RQD should only be

applied to hard rock masses and as such, if properly recorded, should be equivalent

to HRQD. The HRQD suffers from the same problems as RQD when using it for large

slopes.

• Discontinuity spacing is substituted with ‘handled’ discontinuity spacing in a similar

manner to HRQD.

• The discontinuity condition parameters stay unchanged except that the rating is limited

to less than or equal to ten for mat1erial with intact rock strength less than or equal to

R1. This is to stop weak rock being given a high discontinuity condition rating.

Table 5.7. SRK Geomechanics Classification or Slope Rock Mass Rating (SRMR)

PARAMETER RANGES OF VALUES

Is50

(MPa)

> 10 4 - 10 2 - 4 1 – 2 For this low range

UCS test is preferred

<1

Strength of intact rock material

UCS

(MPa)

R5

>250

R4

100-250

R3

50-100

R2

25-50

R1

5-25

R1

1-5 S5 S4 S3 S2 S1

Page 364: Shear Strength of Rock

Empirical Rock Slope Design Page 5.13

Rating 30 27 22 19 17 15 10 6 2 1 0

Handled RQD (%) 90-100 75-90 50-75 25-50 <25

Rating 20 17 13 8 3

Handled (mm) discontinuity spacing

>2000 600-2000 200-600 60-200 <60

Rating 20 15 10 8 5

Condition of discontinuities

Rock > R1

Very rough surfaces

Not continuous

No separation

Unweathered rock wall

Rock > R1

Slightly rough surfaces

Separation < 1mm

Slightly weathered walls

Rock > R1

Slightly rough surfaces

Separation < 1mm

Highly weathered walls

Rock ≥ R1

Slickensided surfaces

OR

Gouge < 5mm

OR

Separation 1 – 5mm

Continuous

Rock < R1

Soft gouge > 5mm thick

OR

Separation > 5mm

Continuous

Rating 30 25 20 10 0

The SRMR system was found to give similar rating values as the ILC-RMR for the Island

Copper Mine. Therefore, Robertson (1988) concludes that Robertson et al (1987)

correlations with rock strength can be used with the SRMR. The SRMR or SRK-RMR

system was also checked using Getchell Mine, Nevada. Table 5.8 shows the correlations

given by Roberston (1988). Figure 5.2 shows these correlations as Mohr-Coulomb

strength curves. It can be seen that for SRMR = 20-25 the results seem invalid for normal

stresses less than about 700kPa (for values less than this it implies that higher SRMR

values give lower strengths). The author does not know the normal stresses acting on the

Island Copper Mine Slopes. Table 5.8 and Figure 5.2 show that the correlations vary a

considerable amount with sites and thus the rating system may need refining. Robertson

cautions that more case histories are required before the data in Table 5.8 can be used

with confidence.

Table 5.8. SRMR strength correlation (Robertson, 1988)

Strength Parameters

Island Copper Mine Getchell Mine Rock

Mass

Class

SRMR c′

(kPa)

φ′ c′

(kPa)

φ′

IVa 35-40 86 40 - -

Page 365: Shear Strength of Rock

Empirical Rock Slope Design Page 5.14

30-35 72 36 - -

25-30 69 34 48 30 IVb

20-25 138 30 48 26

Va 15-20 62 27.5 48 24

Vb 5-15 52 24 14 21

0

200

400

600

800

1000

0 200 400 600 800 1000σn (kPa)

τ (k

Pa)

35-40

30-35

25-30

20-25

15-20

5-15

0

200

400

600

800

1000

0 200 400 600 800 1000σn (kPa)

τ (k

Pa)

35-40

30-35

25-30

20-25

15-20

5-15

Figure 5.2. SRMR strength correlation (a) Island Copper Mine (b) Getchell Mine

(Robertson, 1988)

5.2.1.5 Modified Rock Mass Classification, M-RMR

Ünal (1996) developed the M-RMR from the RMR method with additional features for

better characterisation of weak, stratified, anisotropic and clay bearing rock masses. The

method was based on investigations carried out at a borax mine and two coal mines. The

geology at the borax mine comprised laminated and bedded limestone with continuous

beds (varying from 2m to 9m in thickness) of consolidated clay. Stability was affected by

the presence of water. The coal mines consisted of lignite with associated coal measure

rocks (marl, claystone, mudstone) and clayey limestone.

The rating is given below. IUCS, IRQD, IJC, IJS, IGW and IJO are the ratings for σc, RQD,

joint condition, joint spacing, groundwater and joint orientation respectively. Table 5.9

and Table 5.10 show the ratings for IJC. The tables appear very extensive however, as

they are based on a very limited database the author believes these should not be used for

general application. Fc is the weathering coefficient and Ab and Aw are the adjustment

factors for blasting and major planes of weakness respectively. The factors are discussed

further in the rating adjustment section.

Page 366: Shear Strength of Rock

Empirical Rock Slope Design Page 5.15

( )( )JOGWJSJCRQDUCScwb IIIIIIFAARMRM +++++=­ (5.2)

515.0856.0 cUCSI σ= (5.3)

For RQD>10:

RQDI RQD 173.07.2 += (5.4)

For RQD≤10:

RQDI RQD 443.0= (5.5)

187.093.3 SJS JI = (5.6)

WGW eI 03.015 −= (5.7)

Where, w = Inflow of groundwater per 10m of tunnel length (lt/min)

(Note, damp = 0-10; wet = 10-20; dripping = 20-35; flowing >35)

For ICR≤5:

12−=JOI (5.8)

Where, ICR = Intact core recovery (%)

For 5<ICR<25:

75.1335.0 −= ICRI JO (5.9)

For ICR≥25:

5−=JOI (5.10)

( )200515.02 6.00015.0 −+= −

dIdC eIF (5.11)

Where, Id-2 = Slake durability index

Page 367: Shear Strength of Rock

Empirical Rock Slope Design Page 5.16

Table 5.9. Joint condition index IJC (Ünal, 1996)

Intact core recovery Condition JJC

No filling 10 ICR < 5

Filling 0

No filling, RQD = 0 13

No filling, 0 < RQD < 10 17

No filling, RQD ≥ 10 22

Filling ≥ 5mm (soft) 0

Filling ≥ 5mm (hard) 4

Filling 1 - 5mm (soft) 8

Filling 1 - 5mm (hard) 11

5 ≤ ICR ≤ 25

Filling < 1mm 14

No filling ( )DACRW ××++

Filling ≥ 5mm (soft) 0

Filling ≥ 5mm (hard) ( )DC ×+2

Filling 1 - 5mm (soft) ( )DC ×+4

Filling 1 - 5mm (hard) ( )DC ×+6

ICR > 25

Filling < 1mm ( )DC ×+8

It is interesting to note that IJO is calculated from the intact core recovery from boreholes.

Ünal (1996) indicates that Bieniawski’s (1989) adjustments should be used where field

surveys are available.

Page 368: Shear Strength of Rock

Empirical Rock Slope Design Page 5.17

Table 5.10. Ratings for joint condition parameters (Ünal, 1996)

Parameter Condition Rating Parameter Condition Rating

Unweathered 8 Very low 3.5

Slightly weathered 7 Low 3

Moderately weathered 6 Medium 2

Highly weathered 4 High 1.5

Very highly weathered 2

Continuity

C

Very high 1

Weathering

W

Decomposed 0 0.0 - 0.01mm 4

Undulating, very rough 8 0.01 - 1.0mm 3

Undulating, rough 6 1.0 - 5.0mm 2

Undulating, slightly rough 4

Aperture

A

>5mm 0

Undulating, smooth 2 None 1

Undulating, slickensided 1 0 - 1mm 4

Planar, very rough 4 1-5mm, hard 3.5

Planar, rough 3 1-5mm, soft 3

Planar, slightly rough 2 >5mm, hard 2

Planar, smooth 1

Filling

F

>5mm, soft 0

Roughness

R

Planar, slickensided 0

5.2.1.6 Basic Quality, BQ

The BQ system was introduced as a “forced standard” in China in 1995 (Lin, 1998). It

was developed using an extensive database of projects around China. A number of

numerical analysis techniques were used to assess the data including: reliability analysis;

stepwise regression (dynamic cluster analysis and expert system); and stepwise

discriminative analysis (dynamic cluster analysis and expert system). The final equation

chosen to represent a rock mass is shown below.

22 9786.2760492.10064.01130.5469212.10451.41 vvccvc KKKBQ −+−++−= σσσ (5.12)

where,

velocityseismicintact velocityseismicinsitu

=vK

σc = unconfined compressive strength of the intact rock

Page 369: Shear Strength of Rock

Empirical Rock Slope Design Page 5.18

Although this equation is called “precise” it should be noted that other parameters were

found to have some importance including rock unit weight and average defect spacing.

There is also no statistical data presented to support the formula.

Table 5.11 shows the rock classes. There are no correlations to rock mass properties

provided in the paper.

Table 5.11. The basic quality, BQ, rock mass classes (Lin, 1998)

Page 370: Shear Strength of Rock

Empirical Rock Slope Design Page 5.19

5.2.2 Adjustment Factors to basic rock mass ratings

Most of the empirical rating methods apply adjustment factors to their basic rock mass

rating. These adjustment factors account for such things as defect orientation, excavation

method, weathering, induced stresses and major planes of weakness.

Bieniawski (1976 and 1989) applies the adjustments by subtracting them from the rock

mass rating.

Table 5.1 shows that the defect orientation adjustment can dominate the RMR. If the

defect orientations are deemed “very unfavourable” an adjustment of -60 is required to

the basic rock mass rating. Even for defect orientations denoted as “fair” this adjustment

is -25. There is no guideline as to what “very unfavourable” means. Bieniawski (1989)

recommends the use of the Romana (1985) SMR corrections for slopes.

Romana used the same basic rock mass rating as RMR89 but developed new adjustment

factors for joint orientation and blasting to account for the lack of guidelines in the RMR

methods. The equation for SMR is shown below. The joint orientation weighting includes

a factor for the difference between joint dip and slope angle, F3. This requires an iterative

approach for design. Table 5.12 and Table 5.13 show the adjustment ratings.

432189 FFFFRMRSMR +−= (5.13)

Romana (1985) developed his factors not only for rock mass failures but also for wedge

and planar failure. A rock mass rating method should not be used for these two cases as

they are defect controlled and can be assessed using such measures as stereographic

projection. Even if the method was applicable, the ratings for planar failure are

questionable. F2 depends on defect dip and must account for the defect shear strength

however, the method seems to assume that friction angles are quite high. For example,

bedding surface shears may attain strengths of φ′ below 12° yet these would be given a

‘very favourable’ rating of 0.15.

Page 371: Shear Strength of Rock

Empirical Rock Slope Design Page 5.20

Table 5.12. Adjustment rating for joints (after Romana, 1985)

Case Very

Favourable

Favourable Fair Unfavourable Very

unfavourable

P sj αα −

T o180−− sj αα

>30°

30°-20°

20°-10°

10°-5°

<5°

P/T ( )21 sin1 sjF αα −−= 0.15 0.4 0.7 0.85 1.00

P jβ <20° 20°-30° 30°-35° 35°-45° >45°

P jF β22 tan= 0.15 0.4 0.7 0.85 1.00

T F2 1.00 1.00 1.00 1.00 1.00

P sj ββ − >10° 10°-0° 0° 0°-(-10°) <-10°

T sj ββ − <110° 110°-120° >120° - -

P/T F3 0 -6 -25 -50 -60

P - Planar failure αs - Slope dip direction αj - Defect dip direction

T - Toppling failure βs - Slope dip βj - Defect dip

Table 5.13. Adjustment Rating for methods of excavation of slopes (after Romana,

1985)

Method Natural

Slope

Presplitting Smooth

Blasting

Blasting or

Mechanical

Defficient

Blasting

F4 +15 +10 +8 0 -8

Figure 5.3 shows the problem with attempting to predict structurally controlled failures

with rock mass ratings. The example shows a defect dipping out of the slope at 60°. The

dip direction is within 15° of the dip direction of the slope. The intact rock has a high

strength and there are no other defects. The defect shown is unweathered, fairly tight and

slightly rough. By inspection, this is an unstable slope however, the SMR rates it as ‘II

Good’ (Table 5.14).

Page 372: Shear Strength of Rock

Empirical Rock Slope Design Page 5.21

Table 5.14. Tentative description of SMR classes (after Romana, 1985)

SMR 0-20 21-40 41-60 61-80 81-100

Class V IV III II I

Description Very Bad Bad Normal Good Very Good

Stability Completely Unstable

Unstable Partially Stable

Stable Completely Stable

Failures Big planar or soil like

Planar or big wedges

Some joints or many wedges

Some blocks None

Support Reexcavation Important/

Corrective

Systematic Occasional None

Figure 5.3. Example of Planar Failure Case with High SMR

The CSMR method (Chen, 1995) is based on the SMR method. The CSMR applies a

discontinuity condition factor, λ, that describes the conditions of the controlling

discontinuity on which the ratings F1, F2 and F3 are based (Table 5.15). This factor ranges

from 0.7 to 1.0. The CSMR method also assumes that the SMR method is applicable for a

slope height of 80m but must be adjusted for other slope heights, H, using the slope height

factor, ξ. The relationship for ξ, based on an extensive survey and rigorous analysis of

slopes in China, is shown in Figure 5.4. With the addition of the two new factors, the

equation for CSMR is defined as:

432176 FFFFRMRCSMR +×−×= λξ (5.14)

60°

UCS rating = 15 (300MPa) RQD rating = 20 (100%) Spacing rating = 20 (> 2m) Condition rating = 25 Groundwater rating = 15 (dry) F1 = 0.7 (15°) F2 = 1.0 F3 = -60 F4 = +10 (presplitting) SMR = 63

Page 373: Shear Strength of Rock

Empirical Rock Slope Design Page 5.22

H4.3457.0 +=ξ (5.15)

where, H = Slope height in metres

Table 5.15. Discontinuity condition factor λ (Chen, 1995)

λ Defect Condition

1.0 Faults, long weak seams filled with clay

0.8 to 0.9 Bedding planes, large scale joints with gouges

0.7 Joints, tightly interlocked bedding planes

0

2

4

6

8

10

1 10 100 1000

H (m)

ξ

Figure 5.4. Slope height, H, vs slope height factor, ξ (after Chen, 1995)

The CSMR has been based on the SMR and thus has similar problems. CSMR

acknowledges the affect of slope height. It is the authors view that height should not be

grouped with the rock mass rating (a defacto strength estimate) but should be addressed

during the stability analysis where it will contribute to the stresses acting.

Laubscher (1977) adjusts his MRMR for weathering; field and induced stresses; change

in stress due to mining; orientation and type of excavation with respect to geological

structures; and blasting effects. The multipliers were developed primarily for

underground excavations but are also used for slopes.

Page 374: Shear Strength of Rock

Empirical Rock Slope Design Page 5.23

Ünal (1996) uses corrections for weathering, blasting and major planes of weakness.

Table 5.16 and Table 5.17 show the adjustment factors Ab and Aw for blasting and major

planes of weakness respectively.

( )( )JOGWJSJCRQDUCScwb IIIIIIFAARMRM +++++=­ (5.16)

Table 5.16. Blasting adjustment, Ab (Ünal, 1996)

No blasting 1.0

Smooth blasting 0.95

Fair blasting 0.90

Poor blasting 0.85

Very poor blasting 0.80

Table 5.17. Major plane of weakness adjustment, Aw (Ünal, 1996)

No major weakness zones 1.0

Stiff dykes 0.90

Soft ore zones 0.85

Host rock/ore contact zones 0.80

Folds; synclines; anticlines 0.75

Discrete fault zones 0.70

It is not understood why the RQD rating is adjusted for weathering whilst the joint

spacing rating is not. It is felt that ideally Aw should not be used in a rock mass

classification system for slopes. If major planes of weakness exist they should be

considered individually during the analysis phase.

MRMR, RMS and M-RMR contain an adjustment for weathering. The author believes that

weathering should not be used as an adjustment factor in the estimation of rock mass

strength. The effect of weathering is to alter the intact strength and defect condition

parameters over geological time. ‘Present day’ weathering condition should already have

been accounted for in the strength of the rock substance. Where further weathering may be

expected within the design life of a slope, the parameters for intact strength and defect

condition could be adjusted. However, the extent of these effects needs to take into

account the scale of influences versus the scale of the slope. That is, surficial weathering

Page 375: Shear Strength of Rock

Empirical Rock Slope Design Page 5.24

may not extend into the slope to such a degree as to affect the strength of the rock mass

along the shear failure surface.

The excavation method adjustment (MRMR, SMR, CSMR and M-RMR) was originally

designed for support of underground excavations where it has obvious implications. The

method of excavation may affect low height slopes, however large slopes are unlikely to

be affected by blasting (with regard to rock mass failure). The author believes that the

rock mass involved in the failure is usually remote to the region affected by blasting.

Blasting may affect the stability of benches. However, failures of slopes of this scale can

be expected to be caused by failure along structure and not through rock mass due to the

low stresses acting. Hoek et al (2002) suggest that destressing can have a significant

affect on the strength of rock masses for slopes. Where blasting or destressing is believed

to have affected the rock mass to a large degree, then these affects should be accounted

for in the assigning of weightings for block size (smaller) and joint condition (persistence

and aperture) and not as an adjustment factor.

The author believes that the best currently available rock mass rating for slope design is

the GSI (Hoek et al, 1995). The GSI is relatively simple to use and accounts for the major

factors that affect rock mass strength (block size and strength and defect condition).

Reducing the GSI can incorporate affects due to destressing and blasting. The effect of

groundwater should be included in the analysis as a stress and the effect of major

structures should be analysed separately.

Page 376: Shear Strength of Rock

Empirical Rock Slope Design Page 5.25

5.3 A REVIEW OF SLOPE DESIGN METHODS WHICH ARE

BASED ON ROCK MASS RATINGS

5.3.1 Correlations with Shear Strength Parameters and Slope Angles

Bieniawski (1976) and Robertson (1988) provided estimates of cohesion and friction

angle values for different RMR and SRMR ranges respectively that could be used for

slope stability analysis. Robertson’s (1988) shear strength correlations (Table 5.8) were

based on the back analysis of failed slopes in weak rock masses at two mine sites.

Bieniawski’s (1976) shear strength correlations (Table 5.18) were based on experience

working with underground excavations, slopes and foundations. Cited published case

studies included: a cable jacking test in highly weathered to friable gneiss and schist

bedrock (Pells, 1975); a 50m high toppling slope failure induced by base shearing

through weak decomposed amphibolite; and slopes (stable and one failure) consisting of

dolerite, shale and melaphyre (Bieniawski, 1975). The cases reported comprised failures

in very poor quality rock masses.

Table 5.18. Rock mass properties for RMR76 (Bieniawski, 1976)

RMR76 <20 21-40 41-60 61-80 81-100

Rock mass cohesion (kPa) <100 100-150 150-200 200-300 >300

Rock mass friction angle (°) <30 30-35 35-40 40-45 >45

Laubscher (1977) presents a table of stable slope angles versus MRMR independent of

slope height (Table 5.19). These slope angles were based on Laubscher’s 20 years of

experience working predominately in metamorphic and volcanic rocks of varying quality,

taking in the whole range of possible MRMR values. Laubscher (1977) mentions an

example of a pit slope with MRMR of 12 that failed at a slope angle of 45°. A stable

slope angle was found at 35°, which corresponds with the value in Table 5.19. No

information with regard to the slope’s height, geology or failure mode was provided.

Page 377: Shear Strength of Rock

Empirical Rock Slope Design Page 5.26

Table 5.19. Stable slope angle versus MRMR (Laubscher, 1977)

MRMR 81-100 61-80 41-60 21-40 0-20

Slope Angle ±75 ±65 ±55 ±45 ±35

Abrahams and Parsons (1987) performed a statistical analysis of Selby’s RMS data and

developed the following relationship:

( ) 072.141681.2degrees −= RMSAngleSlopeStable (5.17)

The data has a narrow spread of RMS (approximately 55 to 90) and yet, the slope angles

predicted by the equation range from approximately 5° to 90° for their RMS data. The

line of best fit to Selby’s data indicates a slope angle of -74° for a “very weak” rock

mass (RMS=25). This is not meaningful and is likely due to the lack of “weak” and “very

weak” rock masses (RMS<50) in the data. Selby (1980) divided the slopes he assessed

into sections of similar geology, generally with slope heights less than 40m. This resulted

in short lengths of slopes under different stresses being compared. Slope angles for low

slope heights are likely to be governed by the dip of defects and less so the strength of

rock mass where the intact rock strength is high enough to prevent intact rock failure.

These aspects may account for some of the scatter in the data and subsequent poor

statistical results.

Orr (1992) proposed the following relationship between RMR (converted from RMS)

and slope angle as the limit of long term stability, using the data on Figure 5.5. Orr (1992)

states that the equation is for slopes up to 50m high and with RMR values of between 20

and 77.

( ) 71ln35angle Slope −= RMR (5.18)

Page 378: Shear Strength of Rock

Empirical Rock Slope Design Page 5.27

Figure 5.5. RMR versus slope angle (Orr, 1996)

Romana (1985) correlated SMR with stability class. Of the 28 slopes (ignoring the six

toppling failures) presented by Romana (1985) only six had failed and only one of those

was a rock mass failure (“soil like failure”), the others were planar or wedge failures

(Table 5.20). The highest known slopes tested against SMR by Romana were up to 62m

in calcareous slopes and all were stable or partially stable (Jordá et al., 1999). Slope

heights less than 40m are invariably controlled by structure (Duran and Douglas, 1999)

and hence there is very little if any published rock mass failure data supporting the

Romana (1985) SMR correlation.

Page 379: Shear Strength of Rock

Empirical Rock Slope Design Page 5.28

Table 5.20. Case records for SMR (after Romana, 1985)

Rock Excavation method SMR Failures

Limestone Presplitting 85 None

Sandy marl Natural slope 84 None

Limestone Presplitting 77 3 small blocks

Gneiss Presplitting 72-75 Small wedges during construction

Limestone Blasting 74 None

Dolestone Blasting 64-76 Small planes during construction

Limestone Smooth blasting 61-73 None

Marl Smooth blasting 71 None

Limestone Blasting 70 Small blocks

Sandstone/Siltstone Natural slope 68 Small blocks

Limestone Deficient blasting 59 Many blocks

Marl/Limestone Mechanical excavation 55 “Local problems”

Gypsum rock Natural slope 52 Some wedges (1m3)

Claystone/Sandstone Blasting 47 Big wedge (15m3)

Claystone Mechanical excavation 46 Surface erosion

Sandstone/Marl Blasting 43 Many wedges

Limestone Deficient blasting 40 Many failures

Gypsum Rock Natural slope 31-43 Big wedge (100m3)

Sandy marl Mechanical excavation 32 Blocks, mud flows

Sandstone/Marl Blasting 30 Big planar failure during construction

Limestone Blasting 29 Several wedges (50m3)

Marl Smooth blasting 36 Almost total planar failure after weathering

Volcanic tuff/Diabase Blasting 30 Big planar failure

Marl Blasting 16 Total planar failure after weathering

Marl Blasting 42 Small wedges

Marl Blasting 17 Total planar failure after weathering

Marl Blasting 43 Small wedges

Slate/Greywacke Mechanical excavation 17 Soil like failure

The CSMR uses the same stability class correlation as SMR. Figure 5.6 shows

correlations between observed behaviour (ESMR) and SMR and CSMR for 44 slopes

with heights ranging from 8 to 42m. Chen (1995) uses a similar method proposed by

Collado and Gili (1988) to determine ESMR. The ESMR is derived from estimates of the

factor of safety from field engineers and the following empirical equation:

Page 380: Shear Strength of Rock

Empirical Rock Slope Design Page 5.29

15.0

5.52100

−−=

FESMR

where, F = Factor of safety

All points falling on the 45° line would represent a good correlation. Although the CSMR

has slightly less scatter than the SMR, both methods can be seen to have a poor

correlation.

Figure 5.6. Observed cases (ESMR) vs (a) SMR, (b) CSMR (Chen, 1995)

Moon et al (2001) found that rock mass classification techniques (RMR, SMR and RMS),

used for slope angle estimation, perform poorly for weak rock masses where failure

occurs through intact rock, rather than solely along defects.

Page 381: Shear Strength of Rock

Empirical Rock Slope Design Page 5.30

Tsiambaos & Telli (1991) compare the RMR and SMR systems for limestone slopes.

They found that the RMR system leads to an underestimation of the stability conditions

(i.e. the actual rock conditions are better than predicted) of limestone cuts whilst the SMR

was a better predictor. It should be noted that the only stability problems the slopes had

were rock falls that were structurally controlled.

Of the methods presented, Robertson’s (1988) approach has the most merit as it was

developed specifically for slopes and is based on slope failures in weak rock masses.

Unfortunately, only two slopes have been used and hence c′ and φ′ values are only

available for two specific rock masses. Other methods presented have limited value as

they are based on either long-term natural slopes that are often structurally controlled;

stable slopes; or slopes of only limited height.

5.3.2 Available Slope Performance Curves

Slope performance curves provide a valuable tool in the design process where rock mass

failure plays a strong control in the stability of slopes. The curves are derived from the

performance of stable and unstable slopes plotted on a slope angle versus slope height

plot. The curves are often site specific and take into account the impact of existing

failures, the remaining time frame for mining and the acceptable risks to the mining

operation.

Extending slope design curves from being a site specific tool to a general tool must be

treated with caution. Early attempts at doing this include Lane (1961) and Fleming et al

(1970 for slopes in shale, Coates et al (1963) for “incompetent rock” slopes, Shuk (1965)

for natural slopes, Lutton (1970) and Hoek (1970) for general rock excavations.

Hoek and Bray (1981) present a collection of data, from mines, quarries, dam foundation

excavations and highway cuts, on stable and unstable slopes in hard rock (Figure 5.7).

The plot also shows a curve representing the highest and steepest slopes that have

successfully been excavated in hard rock (note that many failures have occurred in flatter

slopes). This line can therefore be used as a guide as to the upper bound heights and slope

angles that can be considered in slope design.

Page 382: Shear Strength of Rock

Empirical Rock Slope Design Page 5.31

McMahon (1976) attempted to group similar rock masses together and came up with

correlations (based on log-log graphs) relating slope length, L, with slope height, H

(Equations 5.19 and 5.20 and Table 5.21).

baLH = (5.19)

( )angle slope tanHL = (5.20)

Figure 5.7. Upper bound slope height versus slope angle curve for rock masses

(Hoek & Bray, 1981)

Page 383: Shear Strength of Rock

Empirical Rock Slope Design Page 5.32

Table 5.21. Parameters for McMahon’s (1976) slope relationship

Rock mass type a B

Massive granite with few joints 139 0.28

Horizontally layered sandstone 85 0.42

Strong but jointed granite and gneiss 45 0.47

Jointed partially altered crystalline rocks 16 0.58

Stable shales 8.5 0.62

Swelling shales 2.4 0.75

Figure 5.8 shows the data from McMahon (1976) replotted on a slope height versus slope

angle curve. The relationships from Table 5.21 are also plotted on the graph. It can be

seen from the figure that the relationships provide a poor fit to a lot of the data,

particularly the stronger rock masses. The curves also tend toward about 10° which is not

supported by the data. It should also be noted that only the data for shale was near limit

equilibrium and so the curves for the other rock mass types represent conservative (by an

unknown amount) boundaries.

Haines and Terbrugge (1991) took this technique further and tried to correlate slope

design curves with rock mass ratings. The Haines and Terbrugge (1991) slope design

methodology makes use of the MRMR empirical rock mass strength assessment as

presented by Laubscher (1977 and 1990). The slope design methodology is presented in

Figure 5.9 and again in Figure 5.10, replotted on the basis of slope angle versus slope

height and with contours of MRMR presented. Haines & Terbrugge (1991) divide the

graph into three design zones where: (1) classification alone may be adequate; (2)

marginal on classification alone; and (3) slopes require additional analysis.

Page 384: Shear Strength of Rock

Empirical Rock Slope Design Page 5.33

0

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60 70 80 90

Slope angle

Hei

ght (

m).

Massive granite with few joints

Horizontally bedded sandstonesStrong but jointed granite and gneiss

Jointed partially altered rocks

Horizontally bedded stable shalesSwelling shales

Clay shale

Jointed & altered

Sandstone and shalestrong granite and gneiss

Figure 5.8. Slope angle versus slope height with regression curves (modified after

McMahon, 1976)

Case studies were utilised by Haines & Terbrugge (1991) to evaluate the design curves.

It is noted that several of the cases presented related to slopes for feasibility studies that

had at the time not been excavated. The cases of excavated slopes have been presented in

Figure 5.10. The MRMR values, grouped into intervals, are presented by the use of

different symbols. Three aspects of the Haines & Terbrugge (1991) design curves are of

concern:

Page 385: Shear Strength of Rock

Empirical Rock Slope Design Page 5.34

Firstly, the data does not appear to indicate the validity of the design curves presented.

Vertical design lines could have been equally appropriate, i.e. independent of slope

height. This is in keeping with the use of MRMR for open pit slopes, as originally

proposed by Laubscher (1977), shown in Table 5.19.

Secondly, the shape of the interpreted design curves does not appear valid. The curves

are broadly convex in shape and nearly linear for slope heights of up to 100m. This is at

odds with the wide body of experience, which suggests a concave shape is appropriate.

In addition, the experience presented in Figure 5.11 suggests a predominant curvature

would be expected for slope heights up to 100m. Finally, the curves are not asymptotic

and indicate a continuing reduction in slope angle with slope height is required.

Thirdly, none of the case studies presented by Haines & Terbrugge (1991) related to

unstable slopes. Moreover, a third of the cases related to road cuttings where typically a

high degree of conservatism is utilised. As such the design curves have a large element of

conservatism built into them.

Figure 5.9. Slope height vs slope angle for MRMR (Haines & Terbrugge, 1991)

Page 386: Shear Strength of Rock

Empirical Rock Slope Design Page 5.35

20

4060

80100

0

50

100

150

200

250

20 30 40 50 60 70Slope angle (deg)

Slop

e H

eigh

t (m

) .

0-10

10-20

20-30

30-40

40-50

50-60

60-70

Classification alonemay be adequate

Marginal onclassification alone

Slopes requireadditional analysis

MRMR

MRMRValues

Figure 5.10. Haines & Terbrugge (1991) slope design replotted on basis of slope

angle versus slope height showing Haines & Terbrugge (1991) slope data.

Page 387: Shear Strength of Rock

Empirical Rock Slope Design Page 5.36

5.3.3 Pells Sullivan Meynink Slope Performance Curves

Through the utilisation of aggressive designs within interim pits and documentation of

stable and failed slopes, slope performance curves have been established at several

mining operations by Pells Sullivan Meynink Pty Ltd, consulting geotechnical engineers

and engineering geologists, to aid in the slope design process. They indicate that the

methodology has been of enormous benefit in slope design for mining operations where

multiple open pits are developed in similar geotechnical conditions, a poor rock mass is

present and rock mass failures have been the predominant control on slope stability.

Figure 5.11 presents six case studies where slope performance curves were developed on

the basis of the site specific stability.

Pells Sullivan Meynink (pers. com. Alex Duran) indicate that the methodology has been

of particular use in operations where multiple shallow pits have been developed and

where no geotechnical studies were available. Although these curves are not presented

the shapes of the curves are in keeping with those presented in Figure 5.11.

Three key regions can be defined on the slope performance curves in Figure 5.11. The

three regions and the division within the slope angle versus slope height plot are in

keeping with typical rock mass strengths for poor quality rock masses and the concept of

a curved strength envelope.

Region 1: Typically negligible rock mass failures occur for slope heights of less

than 40m. This is in keeping with findings of a survey of 54 mining operations

which indicated generally stable pits for slope heights less than 45m (Swindells,

1990). This is anticipated since for these heights, i.e. low stress levels, rock mass

strengths typically have a high friction angle. Typical slip-circle analyses indicate

steep slopes can be achieved for these slope heights. The experience of the author

and that of Pells Sullivan Meynink personnel indicates unstable slopes in Region 1

are invariably controlled by structure except where very poor rock mass conditions

are encountered.

Page 388: Shear Strength of Rock

Empirical Rock Slope Design Page 5.37

Figure 5.11. Slope performance curves for case studies (Duran & Douglas, 1999)

0

50

100

150

200

250

20 30 40 50 60 70Slope angle (deg)

Slop

e H

eigh

t (m

) .

Case 1

Case 2

Case 3

Case 4

Case 6

Case 9

1

2

3

4

6

9

After Figure 7,Hoek & Bray (1981)

Numbers refer tocases in Table 2

Solid symbolsrepresent unstable

slopes

Upper bound from Hoek & Bray (1981) – see Figure 5.7

Slope performance

curves

Numbers refer to cases in Table 5.22

Solid symbols represent unstable slopes as does the symbol x

Page 389: Shear Strength of Rock

Empirical Rock Slope Design Page 5.38

Region 2: For slopes above 40m in height rock mass failures become apparent in

poor quality rock masses. The design curves display a pronounced concave

curvature with a reduction in the overall slope angle for increasing slope height.

This curvature is in keeping with that indicated by Hoek & Bray (1981) and with

typical slip circle analyses. The curvature of the design curves conform to a curved

rock mass strength envelope. Back analyses indicate the use of a fixed friction angle

and cohesion provides a poor fit. Whilst back analyses using a decreasing friction

angle and increasing cohesion, with increasing slope height (i.e. increasing stress

level), provides a better fit to the curves. It should be noted the design curves are

roughly sub-parallel and with curves further to the right representing better rock

mass conditions.

Region 3: For slope heights above 90m the curves show a trend of becoming

asymptotic to a given slope angle. This is in keeping with the fact that at higher

stress levels the curved envelope approaches a straight line and a constant friction

angle is implied.

Page 390: Shear Strength of Rock

Empirical Rock Slope Design Page 5.39

5.4 ANALYSIS OF CASE STUDY DATA

5.4.1 Case Studies Used

Table 5.22 summarises the case studies that were made available to the author by Pells

Sullivan Meynink Pty Ltd. Each ‘case’ represents a particular open pit mine. Each mine

may have several stable/unstable slopes in the database. Where this situation exists the

different slopes are denoted a, b, c etc. Case 5 was obtained separately from Glastonbury

(2002).

A total of 13 cases with 37 slopes, of which 21 were stable and 16 had failed, was made

available. All failures were considered to have had a rock mass failure component.

Table 5.22. Summary of slope data from case studies

Geology Mine

Case

Height

(m)

Slope

angle

(°)

MRMR

interval

GSI

interval

Water Stable

Saprolite/Basalt 1a 70 49 20-30 40-50 none yes

Saprolite/Basalt 1b 41 50 20-30 40-50 none no

Saprolite/Basalt 1c 41 55 20-30 40-50 none no

Saprolite/Basalt 1d 46 55 20-30 40-50 none no

Saprolite/Basalt 1e 57 49 20-30 40-50 none no

Saprolite/Basalt 2a 58 50 30-40 50-60 none yes

Saprolite/Basalt 2b 60 48 30-40 50-60 none yes

Saprolite/Basalt 2c 60 52 30-40 50-60 none yes

Volcanoclastics 3a 20 39 10-20 30-40 mod no

Volcanoclastics 3b 40 32 10-20 30-40 mod yes

Volcanoclastics 3c 60 31 10-20 30-40 mod yes

Talc chlorite schist 4a 70 44 30-40 40-50 mod no

Talc chlorite schist 4b 120 35 30-40 40-50 mod no

Talc chlorite schist 4c 120 38 30-40 40-50 mod no

Talc chlorite schist 4d 150 31 30-40 40-50 mod yes

Talc chlorite schist 4e 150 35 30-40 40-50 mod yes

Argillite 5a 250 42 30-40 50-60 mod no

Page 391: Shear Strength of Rock

Empirical Rock Slope Design Page 5.40

Table 5.22. Summary of slope data from case studies (cont.)

Geology Mine

Case

Height

(m)

Slope

angle

(°)

MRMR

interval

GSI

interval

Water Stable

Argillite 5b 107 37 30-40 50-60 mod yes

Argillite 5c 80 38 30-40 50-60 mod yes

Schist 6a 70 45 20-30 40-50 mod no

Schist 6b 95 45 20-30 40-50 mod no

Mudstone/siltstone 7 38 39 40-50 50-60 none yes

Breccia 8 200 65 60-70 70-80 none yes

Faulted breccia 9a 78 32 20-30 40-50 high yes

Faulted breccia 9b 50 34 20-30 40-50 high yes

Faulted breccia 9c 77 37 20-30 40-50 high no

Faulted breccia 9d 60 40 20-30 40-50 high no

Sheared siltstone 10a 97 36 20-30 40-50 mod yes

Siltstone 10b 157 48 50-60 60-70 none yes

Siltstone 10c 60 53 50-60 60-70 none yes

Siltstone 11 110 48 30-40 40-50 none no

Shale 12a 29 39 10-20 30-40 mod yes

Shale 12b 37 28 10-20 30-40 mod yes

Shale 12c 30 40 10-20 30-40 mod no

Shale 12d 45 26 10-20 30-40 mod no

Granodiorite breccia 13a 40 75 50-60 70-80 none yes

Granodiorite breccia 13b 90 80 50-60 70-80 none yes

5.4.2 Correlations of MRMR, SRMR and RMS with GSI

Data from 12 of the case studies have been used to provide correlation’s between three

rating methods (MRMR, SRMR and RMS) and GSI (Table 5.23 and Figure 5.12). The

data from Selby (1980) has also been used for the correlation between RMS and GSI and

is plotted on Figure 5.12.

Table 5.24 and Table 5.25 show the data used to determine the GSI for the case studies.

Table 5.26, Table 5.27 and Table 5.28 show the data used to determine the MRMR,

Page 392: Shear Strength of Rock

Empirical Rock Slope Design Page 5.41

SRMR, and RMS for the case studies respectively. Best estimate data was used for all

case studies and interpolation used to choose ratings for each parameter.

Some assumptions were made in assessing SRMR for the author’s case studies, based on

the intact strength and character of borehole core, to assess handled RQD and spacing.

Table 5.23. Correlation between rating methods – author’s case studies

MINE

CASE

Rock Unit GSI MRMR SRMR RMS

1 Saprolite/Basalt 41 22 42 58

2 Saprolite/Basalt 52 36 49 74

3 Volcanoclastics 37 15 35 59

4 Talc chlorite schists 45 30 47 69

6 Schist 44 22 45 51

7 Mudstone/Siltstone 57 43 49 76

8 Breccia 76 65 97 98

9 Faulted breccia 49 24 57 71

10a Sheared siltstone 48 24 51 54

10c Siltstone 68 54 63 80

11 Siltstone 46 35 55 63

12 Shale 39 18 41 52

13 Granodiorite breccia 73 55 83 85

GSI was chosen since it provides a measure of the basic rock mass quality. Correlation

with the other rating systems was not considered appropriate in view of the rating

adjustments required. The correlations exhibit a good fit, even though there is limited data

for the correlations with MRMR and SRMR.

Page 393: Shear Strength of Rock

Empirical Rock Slope Design Page 5.42

GSI = 0.78MRMR + 25.22

R2 = 0.94

GSI = 0.67SRMR + 15.10

R2 = 0.84GSI = 1.07RMS - 22.39

R2 = 0.82

0

20

40

60

80

100

0 20 40 60 80 100Rating

GSI

MRMR

SRMR

RMS

Figure 5.12. Correlations of GSI with MRMR, SRMR, RMS rating (mod. Duran and

Douglas, 2002).

Page 394: Shear Strength of Rock

Empirical Rock Slope Design Page 5.43

Table 5.24. Summary of best estimate GSI data for mine cases

MINE

CASE Rock Unit UCS RQD Spacing

Defect

Condition GSI

value 3MPa 46% 0.6m Table 5.25 1

a-e

Saprolite/

Basalt rating 1.3 9.3 11.2 9.8 41

value 5MPa 56% 2m Table 5.25 2

a-c

Saprolite/

Basalt rating 1.5 11 20 9.7 52

value 13MPa 45% 0.1m Table 5.25 3

a-c Volcanoclastics

rating 2.2 9.1 6.1 9.6 37

value 30MPa 25% 1m Table 5.25 4

a-e

Talc chlorite

schists rating 3.8 6.1 14.6 11.1 45

value 12MPa 65% 0.1m Table 5.25 6

a-b Schist

rating 2.1 12.6 6.1 12.6 44

value 5MPa 75% 1m Table 5.25 7

Mudstone/

Siltstone rating 1.5 14.6 14.6 16.7 57

value 150MPa 98% 5m Table 5.25 8 Breccia

rating 11.4 19.5 11.8 23.3 76

value 60MPa 50% 0.5m Table 5.25 9

a-d

Faulted

breccia rating 6.4 9.9 10.3 12.8 49

value 23MPa 90% 2m Table 5.25 10

a

Sheared

siltstone rating 3.1 17.7 20 16.7 68

value 23MPa 70% 0.5m Table 5.25 10

b-c Siltstone

rating 3.1 13.6 10.3 10.8 48

value 11 Siltstone

rating

RMR from Q = 1.3 and

44ln9 += QRMR 46

value 18MPa 40% 0.1m Table 5.25 12

a-d Shale

rating 2.7 8.3 6.1 12.1 39

Page 395: Shear Strength of Rock

Empirical Rock Slope Design Page 5.44

Table 5.25. Summary of defect condition for GSI

MINE

CASE Rock Unit

Length

(m)

Separation

(mm) Roughness Infilling Weathering

1 Saprolite/Basalt 5 0-1 smooth soft High

2 Saprolite/Basalt 5 0-1 smooth soft High

3 Volcanoclastics 20 0-1 slickensided soft moderate

4 Talc chlorite schists 10 1-5 smooth soft fresh

6 Schist 20 1-5 smooth hard fresh

7 Mudstone/Siltstone 5 0-1 smooth hard fresh

8 Breccia 2 <1 rough hard fresh

9 Faulted breccia 15 1-5 slightly rough soft fresh

10a Sheared siltstone 15 1-5 smooth soft fresh

10c Siltstone 5 0-1 smooth hard fresh

11 Siltstone

12 Shale 10 1-5 slightly rough hard moderate

Page 396: Shear Strength of Rock

Page 5.45

Table 5.26. Summary of best estimate of Laubscher’s MRMR data for mine cases

Adjustments Mine

Case UCS RQD

Defect set

spacing Defect condition* RMR

Weathering Orientation Blasting MRMR

3MPa 46% 0.6m/0.8m/5m wavy/smooth undulose/soft medium slight 1 year poor good conventional 1

1 8 15 13 37 0.9 0.75 0.9 22

5MPa 56% 2m/5m/10m curved/smooth undulose/soft medium slight 4 years good good conventional 2

2 10 22 11 45 0.96 0.9 0.92 36

13MPa 45% 0.1m/2m/5m straight/smooth planar/soft medium slight 1 year topple poor 3

3 8 12 8 31 0.9 0.65 0.85 15

30MPa 25% 1m/2m/5m slight undulating/slickensided undulose/soft fine nil poor fair 4

4 12 18 9 43 1 0.8 0.88 30

12MPa 65% 0.1m/2m/2m slight undulating/smooth-rough planar/non soft med nil very poor fair conventional 6

3 10 11 11 35 1 0.7 0.9 22

5MPa 75% 1m/5m/5m straight/rough planar/no filling nil good good conventional 7

1.5 12 21 17 51 1 0.9 0.94 43

150MPa 98% 5m/5m/5m slight undulating/rough undulose/non soft medium nil good good conventional 8

16 15 25 20 76 1 0.9 0.94 65

60MPa 50% 0.5m/2m/5m straight/smooth to rough/gouge nil fair poor 9

6 8 16 3 33 1 0.85 0.85 24

Page 397: Shear Strength of Rock

Page 5.46

Table 5.26. Summary of best estimate of Laubscher’s MRMR data for mine cases (cont.)

Adjustments Mine

Case UCS RQD

Defect set

spacing Defect condition* RMR

Weathering Orientation Blasting MRMR

23MPa 70% 0.5m/0.8m/1m curved/slickensided undulose/non soft medium nil very poor poor 10a

3 10 11 16 40

1 0.7 0.85 24

23MPa 90% 2m/2m/5m curved/smooth stepped/non soft coarse nil very good pre-split 10b,c

3.5 14 20 22 59

1 0.95 0.97 54

nil fair fair conventional 11 RMR from Q = 1.3 and 44ln9 += QRMR 46

1 0.85 0.9 35

18MPa 40% 0.1m/2m/5m slight undulating/smooth-rough, planar/hard med. nil topple poor 12

3 6 12 11 32

1 0.65 0.85 18

*large scale/small scale/infilling

Page 398: Shear Strength of Rock

Page 5.47

Table 5.27. Summary of best estimate of SRMR data for mine cases

Mine

Case Rock unit UCS

Handled

RQD Spacing

Defect

Condition SRMR

value 3MPa 34.50% 0.3 to 0.4m R1 1 Saprolite/Basalt

rating 15 7 10 10 42

value 5MPa 28% 1 to 2m R1 2 Saprolite/Basalt

rating 15 8.5 15 10 49

value 13MPa 22.50% 0.08m schist R1 3 Volcanoclastics

rating 15 3 7 10 35

value 30MPa 25% 1 to 2m R2, Slickensided surfaces 4 Talc chlorite schists

rating 19 3 15 10 47

value 12MPa 48.75% 0.08m schist R1 6 Schist

rating 17 10.5 7 10 45

value 5MPa 37.50% 0.5 to 2m R1 7 Mudstone/Siltstone

rating 16 8 15 10 49

value 150MPa 98% 5 R4, rough, not continuous 8 Breccia

rating 27 20 20 30 97

value 60MPa 40% 0.5 to 2m R3, slightly rough - gouge 9 Faulted breccia

rating 22 8 15 12 57

Page 399: Shear Strength of Rock

Page 5.48

Table 5.27. Summary of best estimate of SRMR data for mine cases (cont.)

Mine

Case Rock unit UCS

Handled

RQD Spacing

Defect

Condition SRMR

value 23MPa 52.50% 0.4 to 0.6m R1 10a Sheared siltstone

rating 19 10.5 11 10 51

value 23MPa 90% 2 R1 10b,c Siltstone

rating 19 18.5 15 10 63

value 11 Siltstone

rating

SRMR estimated using MRMR and multiplying by average

SRMR/MRMR ratio for all cases (=1.2) 55

value 18MPa 30% 0.08 to 0.5m R1 12 Shale

rating 17 6 8 10 41

Page 400: Shear Strength of Rock

Page 5.49

Table 5.28. Summary of best estimate of RMS data for mine cases

Defect Mine

Case Rock unit UCS

Weathering Spacing Orientation Aperture Length Water RMS

value 3MPa high 0.6m unfavourable 0-1mm 5m none 1 Saprolite/Basalt

rating 5 5 21 9 6 6 6 58

value 5MPa high 2m favourable 0-1mm 5m none 2 Saprolite/Basalt

rating 5 5 28 18 6 6 6 74

value 13MPa moderate 0.1m favourable 0-1mm 20m slight 3 Volcanoclastics

rating 5 7 15 18 6 4 4 59

value 30MPa fresh 1m unfavourable 1-5mm 10m slight 4 Talc chlorite schists

rating 10 10 25 9 5 6 4 69

value 12MPa fresh 0.1m unfavourable 1-5mm 20m mod 6 Schist

rating 5 10 15 9 5 4 3 51

value 5MPa fresh 1m very favourable 0-1mm 5m trace 7 Mudstone/Siltstone

rating 5 10 25 20 6 5 5 76

value 150MPa fresh 5m very favourable <1mm 2m none 8 Breccia

rating 18 10 30 20 7 7 6 98

value 60MPa fresh 0.5m fair 1-5mm 15m moderate 9 Faulted breccia

rating 14 10 21 14 5 4 3 71

Page 401: Shear Strength of Rock

Page 5.50

Table 5.28. Summary of best estimate of RMS data for mine cases (cont.)

Defect Mine

Case Rock unit UCS

Weathering Spacing Orientation Aperture Length Water RMS

value 23MPa fresh 0.5m very unfavourable 1 to 5mm 15m slight 10a Sheared siltstone

rating 5 10 21 5 5 4 4 54

value 23MPa fresh 2m very favourable 0 to 1mm 5m trace 10b,c Siltstone

rating 5 10 28 20 6 6 5 80

value 25MPa fresh 0.05-0.3m fair <1mm few none 11 Siltstone

rating 5 10 15 14 7 6 6 63

value 18MPa moderate 0.1m favourable 1 to 5mm 10m mod 12 Shale

rating 5 7 10 18 5 4 3 52

Page 402: Shear Strength of Rock

Empirical Rock Slope Design Page 5.51

5.4.3 General Assessment of the Parameters in GSI

The GSI calculated from RMR (GSIRMR) contains ratings for UCS, RQD, defect spacing

and defect condition. This section uses the case study data to assess how well these

individual ratings differentiate rock mass strength. Figure 5.13 shows GSI versus slope

height for both failed and stable slopes from the case studies. A general observation

shows that the failed slopes are gathered at the lower end of the ratings. Figure 5.14 to

Figure 5.17 show the same graph as Figure 5.13 with defect spacing rating, defect

condition rating, RQD rating and UCS rating substituted for GSI respectively. The RQD

and spacing ratings (which essentially are both substitutions for block size) both appear

to differentiate between the rock masses well and have the failed slopes toward the lower

rating values. The defect condition rating appears to group most rock masses in the case

studies together. The UCS rating does not appear to differentiate between the failed and

stable slopes. This is not suprising as slope failure will generally occur along defects

unless the intact rock strength is very low due to the low stress environment.

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100GSI Rating

H (m

).

FailedStable

Figure 5.13. GSI versus slope height for failed and stable slopes

Page 403: Shear Strength of Rock

Empirical Rock Slope Design Page 5.52

0

50

100

150

200

250

0 5 10 15 20 25 30Spacing Rating

H (m

).

FailedStable

Figure 5.14. GSI defect spacing rating versus slope height for failed and stable

slopes

0

50

100

150

200

250

0 5 10 15 20 25

Defect Rating

H (m

).

FailedStable

Figure 5.15. GSI defect condition rating versus slope height for failed and stable

slopes

Page 404: Shear Strength of Rock

Empirical Rock Slope Design Page 5.53

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18 20RQD Rating

H (m

).

FailedStable

Figure 5.16. GSI RQD rating versus slope height for failed and stable slopes

0

50

100

150

200

250

0 2 4 6 8 10 12 14UCS Rating

H (m

)

FailedStable

Figure 5.17. GSI UCS rating versus slope height for failed and stable slopes

Page 405: Shear Strength of Rock

Empirical Rock Slope Design Page 5.54

5.4.4 Development of Generalised Slope Design Curves

5.4.4.1 Use of MRMR in Haines and Terbrugge Method

Table 5.22 shows the MRMR’s that have been evaluated for the case studies. Each case

has been allotted into a MRMR interval owing to the uncertainties in assessing a rigorous

value.

The data presented by Haines & Terbrugge (1991) and the new case studies (Figure 5.10

and Table 5.22 respectively) have been combined into one database.

The author (Duran & Douglas, 1999) presented cases 1-10 and the Haines & Terbrugge

(1991) design methodology in Figure 5.18. Several of the cases do not confirm the Haines

& Terbrugge design curves. For cases 1, 2, 6 and 8 the Haines & Terbrugge curves are

conservative for these mining operations. In cases 4 and 9 however, the design curves

would have indicated the use of steeper slopes. For these two latter cases there are

additional factors which affected the overall stability of slopes. For case 4 structure made

a significant contribution to the failure. Whilst for case 9, groundwater played a critical

role.

5.4.4.2 Revised Method Using MRMR

Figure 5.19 presents design curves that have been defined by the author (Duran &

Douglas, 1999) on the basis of the available data. An upper bound design curve has been

suggested which relates to MRMR values greater than 40. This is based on the experience

of Duran & Douglas (1999) as no rock mass failures have been observed in slopes that

are comprised of good, or better, rock mass quality. This observation was previously

related by Robertson (1988) who indicated that stability was almost exclusively

controlled by structure where MRMR was greater than 40.

It must be stressed that these design curves are based on slopes in mining operations,

where some instability is acceptable and slopes need only to stand up over short time

frames of up to two years. Appropriate reductions in slope angles could be utilised where

a conservative design is required.

Page 406: Shear Strength of Rock

Empirical Rock Slope Design Page 5.55

It should be noted that cases 4 and 9 were treated as exceptions in defining the design

curves. This clearly reinforces that in the design of rock slopes there needs to be a careful

assessment of the influence of structure and groundwater in defining an acceptable design.

5.4.4.3 Method Based on the Use of the Geological Strength Index, GSI

The case studies discussed above together with additional data from Haines and

Terbrugge (1991) and Selby (1980) have been used to create slope design curves based

on GSI. Slope height versus slope angle was plotted for two ground water conditions, dry

and moderate pressures. Moderate water pressures are defined as where the piezometric

surface reaches the surface at a distance of 4 x the slope height. This is taken from Hoek

and Bray’s (1981) circular failure slope chart No. 3. Figure 5.20 and Figure 5.22 show

the data and the author’s proposed design curves for dry and moderate water pressures

respectively. Where failure occurred predominantly through the rock mass the data is

presented as a solid symbol. Figure 5.20 does not contain a curve for GSI = 30 due to a

lack of data. It could be assumed that this curve would lie 10-15° to the right of the curve

for GSI = 40 based on the curves in Figure 5.22.

The slope design curves for various ranges of MRMR presented in the previous section

(Figure 5.19) have been used as the basis for deriving the GSI slope design curves. These

curves have been assessed for GSI values of 40 and 50, utilising the author’s correlation.

The author’s design curves provide a very good fit of the data.

Slope designs using strength estimates estimated by Bieniawski (1976), assuming no

rating adjustment for orientation, are presented on Figure 5.21 and Figure 5.23 based on

stability charts from Hoek and Bray (1981) and assuming a Factor of Safety of one. As

readily evident, Bieniawski’s strength estimates are too high. Robertson (1988) provided

estimates of shear strength for back-analyses of failures. Using the correlation of SRMR

with GSI presented earlier, Robertson’s rock mass strengths were assessed for GSI

values of 30 and 40, Figure 5.21 and Figure 5.23. Robertson (1988) suggested rock mass

failure in slopes was unlikely for an SRMR of greater than 35 (GSI≈40) and this is

confirmed by the data presented in Figure 5.21 and Figure 5.23. The strengths estimated

by Robertson (1988), if correlated to GSI, appear to overestimate slopes angles for dry

slopes. For moderate water pressures the curves are similar to the author’s curves for

Page 407: Shear Strength of Rock

Empirical Rock Slope Design Page 5.56

heights greater than 150m for lower heights, the author’s curves predict flatter stable

slope angles.

20

40

60

80

100

0

50

100

150

200

250

20 30 40 50 60 70Slope angle (deg)

Slop

e H

eigh

t (m

) .

0-10

10-20

20-30

30-40

40-50

50-60

60-70

MRMR

Solid symbolsrepresent unstable

slopes

Solid symbolsrepresent unstableslopes as do thesymbols + x

Haines &TerbruggeMRMRcurves

Figure 5.18. Haines & Terbrugge (1991) slope design curves & slope data (Figure

5.10) with additional case studies (Duran & Douglas, 1999)

Page 408: Shear Strength of Rock

Empirical Rock Slope Design Page 5.57

0

50

100

150

200

250

20 30 40 50 60 70Slope angle (deg)

Slop

e H

eigh

t (m

) .

0-10

10-20

20-30

30-40

40-50

50-60

60-70

MRMR

> 4030

20 Solid symbolsrepresent unstable

slopes

MRMR =Solid symbolsrepresent unstableslopes as do thesymbols + xS S

H

H

=Significant contributionto failure from structure.

=High water pressures inslope

S

H

Figure 5.19. Suggested slope design curves for MRMR (Duran & Douglas, 1999)

Page 409: Shear Strength of Rock

Empirical Rock Slope Design Page 5.58

0

50

100

150

200

250

10 20 30 40 50 60 70 80 90

Slope Angle (deg)

Slop

e H

eigh

t (m

).

20-3030-4040-5050-6060-7070-8080-90

GSI

GSI ≈ 40

GSI ≈ 50

Solid symbols represent unstable slopes

Figure 5.20. Slope height vs slope angle case study data and the author’s proposed

design curves for a dry slope

Page 410: Shear Strength of Rock

Empirical Rock Slope Design Page 5.59

0

50

100

150

200

250

10 20 30 40 50 60 70 80 90

Slope Angle (deg)

Slop

e H

eigh

t (m

).

20-30

30-40

40-50

50-60

60-70

70-80

80-90

GSI

GSI≈30 GSI≈40

RMR≈30

RMR<20

Robertson (1988)

RMR≈50

Bieniawski (1979)

Author's curvesGSI≈40GSI≈50

Solid symbols represent unstable slopes

Figure 5.21. Slope height vs slope angle case study data and a comparison of design

curves for a dry slope

Page 411: Shear Strength of Rock

Empirical Rock Slope Design Page 5.60

0

50

100

150

200

250

10 20 30 40 50 60 70 80 90

Slope Angle (deg)

Slop

e H

eigh

t (m

).

20-30

30-40

40-50

50-60

60-70

70-80

80-90

GSI

S

= Solid symbols represent unstable slopes= Significant contribution to failure from structure= High water pressures in slope

S

H

H

H

S

GSI ≈ 30

GSI ≈ 40

GSI ≈ 50

Figure 5.22. Slope height vs slope angle case study data and the author’s proposed

design curves for moderate pressures

Page 412: Shear Strength of Rock

Empirical Rock Slope Design Page 5.61

0

50

100

150

200

250

10 20 30 40 50 60 70 80 90

Slope Angle (deg)

Slop

e H

eigh

t (m

).

20-30

30-40

40-50

50-60

60-70

GSI

GSI≈30 GSI≈40

RMR≈30

RMR<20

Robertson

RMR≈50

Bieniawski

= Solid symbols represent unstable slopes= Significant contribution to failure from structure= High water pressures in slope

S

H

H

H

S S

Author'scurves

GSI≈40

GSI≈50

GSI≈30

Figure 5.23. Slope height vs slope angle case study data and a comparison of design

curves for moderate pressures

Page 413: Shear Strength of Rock

Empirical Rock Slope Design Page 5.62

5.5 CONCLUSION

A rock mass rating system should provide a measure of the basic quality/strength of the

rock mass. Aspects such as ground water, excavation method, slope height and orientation

of structure should not be included in the rock mass rating and should be taken account of

during analysis.

Correlation of GSI with several other rock mass ratings indicates a good correlation and

would suggest GSI is an adequate indicator of basic rock mass quality for rock slopes.

Slope design curves have been developed based on a number of stable and unstable open

pit mine slopes. Shear strength estimates for rock slopes that were proposed by

Bieniawski (1976) are too high for values of GSI below 40. The design curves using

strength estimates proposed by Robertson (1988) predict steeper angles than the author’s

design curves.

Most slopes will be structurally controlled and therefore a rock mass rating system will

not be applicable for most slope design. Empirical slope design using rock mass rating

systems should only be considered for slopes in rock masses with GSI values lower than

about 45 and only after any potential structurally controlled failures have been

investigated. The method should only be applied at the preliminary stage or as a site

specific tool to complement detailed mapping and analysis.

Page 414: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.1

6 THE SHEAR STRENGTH OF ROCK MASSES

6.1 INTRODUCTION

This chapter contains a discussion of current methods of predicting rock mass strength

and develops modifications to the Hoek-Brown strength criterion that account for the

results in the previous chapters. The author has concentrated mainly on developing the

criterion for use at low confining stresses (e.g. slopes) however, the resulting criterion

should be applicable for the full stress range.

A rock mass criterion should only be used where “there are a sufficient number of

closely spaced discontinuities that isotropic behaviour involving failure on

discontinuities can be assumed” (Hoek and Brown, 1997). Such a situation for slopes is

illustrated on Figure 6.1, it should be noted that the concept of closely spaced should be

defined in terms of the scale of the failure surface.

Figure 30 : Heavily jointed rock mass

Figure 6.1. Heavily jointed rock mass

Slope failures in which the failure surface is entirely through the rock mass are not

common. This is due to the low stresses typically acting in a slope. Failure through the

rock mass usually requires large scale (relative to the slope in question) defects

concentrating stresses into regions of weak rock mass. For example a long vertical joint

or subvertical fault may lead to over stressing of weak material at the toe of the slope

(Figure 6.2). In this case a rock mass criterion is only applicable to the region of rock

mass at the toe of the slope.

Page 415: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.2

‘long’subvertical

joint

Rock massfailure at toe of

slope

Figure 6.2. Example of shear failure through rock mass at the toe of a slope -

Nattai Escarpment Failure

Page 416: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.3

6.2 ESTIMATING THE SHEAR STRENGTH OF A ROCK MASS

As mine slopes become larger (stresses increasing), the necessity to account for the

strength of rock masses in design increases. This section discusses different techniques

to determine the strength of a rock mass.

6.2.1 Predicting Rock Mass Strength from Discontinuities

Initial methods of determining the shear strength of rock mass relied on using intact and

rock joint strengths. This section briefly describes current methods for estimating rock

joint strengths and the problems with extending these for use with rock masses.

The two most commonly used approaches to estimating discontinuity strength are those

by Patton (1966) and Barton and his co-workers (Barton, 1971a-c, 1973, 1976, Barton

and Bandis, 1982, 1990, Barton and Choubey, 1977). Patton (1966) showed that the bi-

linear equation presented below could be used to estimate the shear strength of

discontinuities.

)tan( ibn += φστ (6.1)

The problem with this equation is that the dilation angle, i, is stress dependent and also

scale dependent. There is also some conjecture as to how the basic friction angle, φb,

should be measured. The author believes that the basic friction angle should not be

measured on artificially polished or otherwise artificially modified samples. The

reasoning for this is that φb should represent the minimum friction angle that a

discontinuity could reasonably be expected to attain in the field. Therefore the best way

to determine φb would be to measure the friction angle at high strain or to use the

approach suggested by Hencher (1995) where the shear test results are corrected for

dilation using the equations below and plotted to find the slope of the curve (φb).

( ) iii nc cossincos σττ −= (6.2)

( ) iiinnc cossincos τσσ += (6.3)

Page 417: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.4

where, τc and σnc are the corrected shear strength and normal stresses respectively.

There is, at present, no definitive way of measuring the dilation angle, i, for field scale

discontinuities. The approach by McMahon (1985) or similar, where asperities are

measured for a certain wavelength (or interlimb angle) of the defect are used to predict

i, is probably the best current approach.

Bandis et al (1981) developed the following shear strength criterion for discontinuities:

+

= b

nn

JCSJRC φ

σστ 10logtan (6.4)

Where,

JRC = Joint roughness coefficient

JCS = Joint compressive strength

This equation was developed based on 100mm long discontinuities and as such can be

expected to resonably predict shear strengths on this scale. Barton and Bandis (1982)

presented the following formulae to predict JRC and JCS for field scale samples.

002.0

00

JRC

nn L

LJRCJRC

= (6.5)

003.0

00

JRC

nn L

LJCSJCS

= (6.6)

where,

JRCn = Joint roughness coefficient for a discontinuity of length Ln

JCSn = Joint compressive strength for a discontinuity of length Ln

JRC0 = Joint roughness coefficient for a discontinuity of length L0

JCS0 = Joint compressive strength for a discontinuity of length L0

These equations are now widely used to predict the shear strength of discontinuities in

the field. However, there appears to be a problem with the form of the equations. Figure

Page 418: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.5

6.3 shows a plot of JRCn vs JRC0 for discontinuity lengths varying from 1m to 100m. It

is clear from this figure that the general trend of the equation must be incorrect. For

example, for a discontinuity length of 100m a JRC0 of 8 would imply a JRCn of

approximately 2.65 whereas, a JRC0 of 20 would imply a JRCn of 1.26. This implies

that two discontinuities identical in every respect except small-scale roughness would

have reversed larger scale roughness. Clearly this is wrong. It is understood that this

equation was developed on small-scale models and therefore the author suggests that

this equation may only be appropriate for joint lengths in the region of 1m. For larger

joint lengths/block sizes, and high JRC0, the scaling equations are clearly unsuitable.

This has important implications where at least part of the failure surface is controlled by

long joints or where the block size of the rock mass is in excess of 1m.

Some early studies (e.g. Bray, 1966) suggested that the strength of a rock mass could be

estimated as the lowest strength envelope of the individual discontinuities in the rock

mass (assuming that the strength of the intact material is relatively high). This could be

true where the failure of the rock mass was purely due to sliding along discontinuities.

However, this theory does not account for any interlocking or rotation of the intact rock

blocks in the rock mass. Any interlocking of the rock mass would require a dilation of

the mass to fail and hence an increase in strength. The shear strength of the individual

discontinuities in the rock mass could therefore be seen only as a lower bound to the

shear strength of the rock mass and not much use in design.

Where failure is partly through intact rock it has been suggested that the strength of the

rock mass could be estimated as a combination of the joint and intact rock strengths

(e.g. John, 1962, 1969, Einstein et al, 1983).

Brown (1970) showed that failure through a rock mass is more complex than the

methods above suggest. Brown (1970) tested models of rock masses and found that:

• At low confining stresses collapse was possible due to block movement involving

the opening of joints and dilation of the mass. He found this mode “of probable

practical significance in studying the behaviour of large masses of jointed rock in

which the unit rock block is small compared with the dimensions of the mass as a

whole as, for example, in deep open cut mines.”

Page 419: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.6

• Axial cleavage of the rock blocks (gypsum plaster in the models) occurred at low

confining stresses.

• Where failure occurred at low confining pressures through the model material or as

a combined shear and tension failure the strengths were lower than theories

developed from intact rock and rock joints would suggest.

The prediction of the strength of discontinuities on the field scale is, at best,

approximate. When applied, the predicted strengths of these discontinuities can only be

used to give a lower bound envelope to the shear strength of rock masses. Failure modes

for rock masses are more complex than simple shearing along defects and through intact

rock, particularly at low confining stresses. It is for these reasons that researchers have

taken an empirical approach to estimating the shear strength of rock masses.

Page 420: Shear Strength of Rock

Page 6.7

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16 18 20

JRC0 (for L0 = 0.1m)

JRC

n

JRC JRCLLn

nJRC

=

00

0 02 0.

Ln = 1m

2m

5m

10m

20m

50m100m

65.2m1008

m1.0

0

0

=

==

=

n

n

JRCLJRC

L

26.1

m100

20m1.0

0

0

=

=

==

n

n

JRC

L

JRCL

= Example point

Figure 6.3. Assessment of Barton and Bandis (1982) JRC0 vs JRCn

Page 421: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.8

6.2.2 Predicting Rock Mass Strength using Empirical Formulae

Yudhbir et al (1983), Ramamurthy et al (1994) and Sheorey (1997) (Equations 6.7 to

6.9 respectively) present rock mass criteria that have been developed as extensions of

strength criteria for intact rock. The modification process has typically been based on

model tests, small sample testing and limited experience. The criteria all assume a non-

zero unconfined compressive strength, σcm, and hence tensile strength, σtm, for the rock

mass. These criteria would therefore be expected to overpredict the strength for poor

quality rock masses at the low stresses common to failure surfaces in slopes.

αα

σσ

σσσσ

σσ

′+=′

′+=

ccm

cm

c

bba 31

31 or (6.7)

mb

cmma

′+′=′3

331 σσ

σσσ (6.8)

mb

tmcm

′+=′

σσ

σσ 31 1 (6.9)

where, α, am, bm are constants

6.2.3 Predicting Rock Mass Strength using the Hoek-Brown Criterion

The most commonly and almost exclusively used strength criterion for rock mass, over

the last two decades, is the Hoek-Brown empirical rock mass failure criterion, the most

general form of which is given in Equation 6.10. Hoek and Brown (1980) developed

this criterion, as there was no suitable alternate empirical strength criterion. The

equation, which has subsequently been updated by Hoek and Brown (1988), Hoek et al.

(1992) and Hoek et al. (1995), was based on their criterion for intact rock discussed

earlier in this paper. Although initially developed for hard rock masses, this criterion is

now used for all types of rock masses and stress regimes. The only ‘rock mass’ tested

and used in the original development of the Hoek-Brown criterion was 152mm core

samples of Panguna Andesite from Bougainville in Papua New Guinea (Hoek and

Brown, 1980) together with rock mass models (Brown, 1970). Hoek and Brown (1988)

later noted that it was likely this material was in fact ‘disturbed’. The validation of the

Page 422: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.9

updates of the Hoek-Brown criterion have been based on experience gained whilst using

this criterion. To the author’s knowledge the only data published supporting this

experience has been two slopes cited by Hoek et al (2002).

a

cbc sm

+

′+′=′

σσσσσ 3

31 (6.10)

The parameters mi and mb are intact and mass material parameters; a and s are

parameters that depend on the rock mass characteristics; and σc is the uniaxial

compressive strength of the intact rock. Estimating the parameters, mb, s and a in the

Hoek-Brown criterion is done by correlation with rock mass rating parameters. The

most current of these is the Geological Strength Index (GSI) (Hoek, 1994). The

correlations with GSI were modified by Hoek et al (2002) to allow for a continuous

transition at GSI=25 and to introduce a rock mass disturbance factor, D. These

equations are given in Table 6.1.

Table 6.1. Estimation of Hoek-Brown co-efficients

Parameter Hoek et al (pre 2002) Hoek et al (2002)

mb

=28

100exp

GSImm

i

b

−−=

DGSI

mm

i

b

1428100exp

GSI>25

=9

100exp

GSIs

s

GSI<25 0=s

−−

=D

GSIs

39100

exp

GSI>25 5.0=a

a GSI<25

20065.0

GSIa −=

( )32015

61

21 −− −+= eea GSI

Page 423: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.10

A summary of all the changes to the equations for estimating the shear strength of rock

masses using the Hoek-Brown criterion was presented by Hoek (2002) and is

reproduced here as Figure 6.6.

Hoek and Brown (1980) introduced the material parameter mi. Figure 6.4 gives an

example from Hoek (1999) of how to estimate mi based on rock type. Hoek and his co-

workers have presented numerous variations of this table. Chapter 3 on intact rock has

shown that rock type is a poor predictor of mi and as such a discussion of these

variations has not been provided here.

Hoek (1997) provides Figure 6.5 to determine the GSI directly. The GSI tables have

been modified several times up to Hoek et al (2002). These modifications will be

discussed in the following sections. Hoek et al (1995) say that the GSI may also be

calculated using Bieniawski’s (1976 and 1989) rock mass rating (RMR), GSIRMR, or

Barton’s (1974) Q-system, GSIQ.

Page 424: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.11

Figure 6.4. Values of the parameter mi for intact rock (Hoek, 1999)

Page 425: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.12

Figure 6.5. Estimation of GSI (Hoek, 1997)

Page 426: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.13

Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002)

Page 427: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.14

Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) (cont.)

Page 428: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.15

Note 1: These are corrected Balmer equations. The original equations were incorrect.

Figure 6.6. History of the Hoek-Brown criterion (Hoek, 2002) (cont.)

Page 429: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.16

6.3 A DISCUSSION OF THE HOEK-BROWN CRITERION WITH

PARTICULAR REFERENCE TO SLOPES

6.3.1 Calculation of GSI

GSIRMR and GSIQ are derived from the rating parameters for several rock mass

properties (Equations 6.11 and 6.12).

( )∑ +++= conditiondefect spacingdefect strengthintact Ratings RQDGSIRMR (6.11)

44log9 +

=

a

r

neQ J

JJ

RQDGSI (6.12)

where Jr = joint roughness number

Jn = joint set number

Ja = joint alteration number

The RMR was derived for and on the basis of a data set of underground tunnels that

were of the order of 10 to 20m in span (Bieniawski, 1989). The Q-system was

developed in a similar way. It can be expected from this that the RMR and Q-system

could be expected to be reasonable indicators of rock mass properties for underground

tunnels and caverns. Where a slope is in the order of several hundred meters high,

ranges of values for each parameter in the RMR system begin to lose meaning. This is

discussed further below for each component of the GSI.

6.3.1.1 Intact Strength

It is well known that intact rock exhibits a strength scale effect. This scale effect exists

up to block sizes of at least one metre. Figure 6.7 shows this effect. The author suggests,

that this should be considered when assigning a rating for intact rock strength.

Page 430: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.17

Figure 6.7. Scale effect of Intact Rock (Hoek and Brown, 1980)

6.3.1.2 RQD

Since the RQD is based on a fixed length of 100mm of drill core, the ability of the RQD

to give meaningful information reduces as slopes get larger. Roof stability of a 10m

diameter tunnel is likely to be affected by a reduction in RQD. However, for slopes

several hundred meters high the RQD (particularly estimated from borehole data) has

questionable value. On the scale of a large pit slope it is highly unlikely that all the

defects encountered in boreholes would be of significance to the overall rock mass

stability. The defect sets controlling stability for a large rock slope could be expected to

have a spacing far in excess of 100mm because the closely spaced ones are unlikely to

be persistent. If only these defects are taken into account in the GSI then a rating of 20

(the highest possible) will always apply for RQD. There is a general correlation between

RQD and defect spacing and as such the need for both spacing and RQD in the method

is questioned.

Page 431: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.18

6.3.1.3 Defect spacing

Most systems refer to the term ‘joint’. The author believes that the term ‘defect’ is more

appropriate as all types of defects including bedding planes, shears, faults, lithological

contacts (and not just joints) will interact to form blocks in a rock mass.

The defect spacing suffers from a similar problem to that of the RQD. The maximum

spacing interval is “greater than 3m” and “greater than 2m” for Bieniawski (1976) and

Bieniawski (1989) respectively. A defect spacing of this size would result in large

blocks which would have a much lower probability of forming blocks that would fall

out of a 10m diameter tunnel roof. When assessing loading of rock mass around the

tunnel, stress concentrations would generally be confined within single blocks and so a

maximum GSI parameter would be applicable. However, for a large rock slope the

region of over stressed rock can be expected to comprise several of these blocks. The

critical defect spacing may be much larger than 3m. Thus, a maximum GSI parameter

may not be suitable. Figure 6.8 shows blocks from a 400m high slope failure. A tunnel

of 15m span is unlikely to have rock mass strength problems with a block size as big as

those in the figure.

6.3.1.4 Joint condition

The analyst must take into account the ‘large scale’ (i.e. scale of rock mass) defect

characteristics as well as those on the small scale. This is similar to considering both the

basic friction angle, φb, and the field roughness, i, from Patton’s (1966) shear strength of

defects formula. The thickness of defect infilling and defect roughness should be

considered proportionately to the size of the rock blocks in the slope. Figure 6.9 shows

two defects, on the small scale (borehole) defect A would have a high rating and defect

B a low rating. However, when one looks at the large scale (large slope), defect A would

be expected to have a lower strength.

Page 432: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.19

Figure 6.8. Slope failure block size

Very roughSmooth

Very rough

Smooth&

infilled

Defect A

Defect B

Figure 6.9. Effect of scale on defect properties

6.3.1.6 GSI from Bartons Q-System

Hoek et al. (1995) also offer a method of using the Q-system developed by Barton et al.

(1974) to estimate GSI. The system includes RQD, joint number, Jn, joint roughness and

joint alteration. RQD/Jn represents block size. This system suffers in a similar way to

RMR in its over reliance on RQD for large rock masses.

Page 433: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.20

6.3.1.7 GSI from published figures

Figure 6.5 shows estimates of GSI provided by Hoek (1997). The main components

affecting the strength of the rock mass are covered (ie structure and surface conditions).

It is not clear how scale is to be interpreted on this figure. The author believes that GSI

should be interpreted as being on the scale of the rock mass under assessment. Using

judgement the user can estimate the condition of their rock mass at the scale of their

slope. For example, a ‘blocky’ rock mass at a scale of 10m is vastly different to a

‘blocky’ rock mass at the scale of 500m. Smaller relative block size leads to more

freedom for block rotation and a greater chance for mass failure. Liao & Hencher

(1997) showed that relative block size was critical in deciding the mode of failure. The

smaller the block size (when compared to slope height) the more likely rock mass

failure would be the dominant failure mechanism.

The author recommends the use of Figure 6.5 for calculations of GSI for slopes. The use

of GSIRMR and GSIQ from boreholes should only be used for preliminary strength

estimates. It should be remembered that the key to the structure column is ‘degree of

interlocking’. The degree of interlocking should be assessed on the scale of the slope

under consideration. For example, the rock mass controlling the slopes for an ultimate

pit may be considered interlocked whilst the rock mass may be considered as very well

interlocked on the scale of individual benches of the same slope. It should also be

remembered that “where block size is of the same order as that of the structure being

analysed, the Hoek-Brown criterion should not be used. The stability of the structure

should be analysed by considering the behaviour of blocks and wedges defined by

intersecting structural features” (Hoek, 1997).

6.3.1.8 A Note on Schistose Rocks

Hoek et al (1998) presented Figure 6.10 as a new version of the GSI estimation table

(Figure 6.5). This new figure allows for the estimation of GSI for sheared rock masses.

The author does not agree with this new extension to GSI. This extension to GSI

contradicts the basic premise of a rock mass as defined in the Hoek-Brown criterion:

Page 434: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.21

“The Hoek-Brown failure criterion is only applicable to intact rock or to

heavily jointed rock masses which can be considered homogeneous and

isotropic. In other words the properties of these materials are the same in

all directions.

The criterion should not be applied to highly schistose rocks such as

slates…The strength of the discontinuities should be analysed in terms of a

shear strength criterion such as that published by Barton (1976).”

(Hoek et al, 1995)

One reason that Hoek et al (1998) gave for extending the GSI table was that the

empirical equation for estimating the modulus of deformation of the rock mass, Ed, from

the GSI and σci developed by Hoek and Brown (1997), overestimated Ed in schistose

rocks.

= 4010

1010

GSIci

dEσ

(6.13)

The conclusion by Hoek et al (1998) was that GSI must therefore be lower for schistose

rocks.

The author has, together with his Kung (2001), collated a number of case studies from

the literature where rock mass deformability has been measured. The results from the

case studies, together with data presented by Bieniawski (1978) and Serafim and Pereira

(1983) are shown in Figure 6.11 and Table 6.2. The error bars acknowledge the

variation of Ed in the test results. The uncertainty in GSI was due both to the variability

of the rock masses and also the conversion from published RMR values to GSI. Figure

6.12 shows a plot of Ed as measured in the field versus Ed predicted from the equaton

above using the published unconfined compressive strengths. Figure 6.11 and Figure

6.12 show that there is, not suprisingly, a large amount of scatter in the data. Also, a lot

of the data is over predicted by the above equation.

Page 435: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.22

Figure 6.10. GSI Table (Hoek et al, 1998)

Page 436: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.23

Table 6.2. Rock mass deformability case studies

Reference Rock type GSI Ed (GPa) Type of In-situ Testing

Santiago J.L. (1986) Claystone 34 (30-63) 1.6 Pile Loading Test

Georgiadis M. (1986) Mudstone 49 (40-49) 1.8 Dilatometer Test

Gifford A.B. (1986) Claystone 53 (44-62) 4.40 (0.51-8.28) Plate Bearing Test

Pavlakis M. (1980) Siltstone 39 (23-60) 0.11 (.05-.17) Pressuremeter Test

Poulton M.M. (1986) Sandstone 67 (54-79) 0.3 (0.25-0.36) Plate Loading Test

Schultz R.A. (1995) Basalt 60 (51-79) 25 (10-40) Jointed Block Test

Sandstone 3.9 (2.2-5.6) Flat Jack Test Cheng Y. (1993)

Sandstone 75 (55-87)

3.7 (2.3-5.1) Plate Loading Test

Giovanni B. (1993) Limestone 79 (63-91) 37.5 (32.5-42.5) Plate Loading Test

Mcdonald P. (1993) Basalt 39 (30-74) 1.39 (.2-4.6) Pressuremeter Test

Granodiorite 52 3.8

Granite 55 2.5

Siltstone 60 14

Tuff 75 11

Marble 76 18

Goodman Jack Test

Sandstone 46 (35-57) 7.5 (5-10)

Granite 48 (41-55) 17.5 (15-20)

Siltstone 68 (64-71) 25 (20-30)

Littlechild B.D. (2000)

Marble 78 (71-84) 15 (10-20)

Cross-Hole Geophysics Test

Sandstone 60 (55-65) 6.6

Shale 63 (58-68) 13.8

Shale 72 (67-77) 13.8

Mudstone 75 (70-80) 5

Bieniawski Z.T. (1990)

Shale 75 (70-80) 12.4

MPBX

35 (30-40) 4

42 (37-47) 8

43 (38-48) 10

45 (40-50) 7

62 (58-68) 9

64 (59-69) 8

50 (45-55) 13

55 (50-60) 13

57 (52-62) 18

67 (62-72) 24

70 (65-75) 20

75 (70-80) 13

75 (70-80) 15

80 (75-85) 33

Ribacchi R. (1984) Granite

80 (75-85) 35

Plate Loading Test

Page 437: Shear Strength of Rock

Page 6.24

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100GSI

Ed

(GPa

).

Bieniawski (1978)

Serafim & Pereira (1983)

Santiago (1986)

Georgiadis (1986)

Gifford (1986)

Pavlakis (1980)

Poulton (1986)

Schultz (1995)

Cheng (1993)

Giovanni (1993)

McDonald (1993)

Littlechild (2000)

Bieniawski (1990)

Ribacchi (1984)

UCS = 100MPa

UCS = 10MPa

( ) 40101010

−= GSIcdE

σ

Figure 6.11. Ed versus GSI case study data and Hoek et al (1995) equation for σ c ≥ 100MPa and σ c = 10MPa

Page 438: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.25

The author believes that the fact that the modulus of a schistose rock is over predicted

by an empirical equation does not justify the extension of GSI to these types of rocks.

The manner in which Figure 6.10 has been extended is also questionable. The author

does not believe that there is a continuum between “poorly interlocked, heavily broken

rock mass” and “thinly laminated or foliated” rock masses with “closely spaced

schistosity”. Therefore extrapolating the lines of equal GSI across this boundary can not

be justified.

The author has decided to adopt the Hoek et al (1995) position and omit highly

schistose rock from the rock mass criterion.

0

10

20

30

40

50

60

0 10 20 30 40 50 60Ed test (MPa)

Ed p

red

Figure 6.12. Ed test from case studies versus Ed pred from Hoek et al (1995)

equation

Page 439: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.26

6.3.2 Estimation of Parameters from GSI

6.3.2.1 The Rock Mass Disturbance Factor, D

The rock mass disturbance factor, D, was introduced by Hoek et al (2002) to account for

the degree of disturbance to which the rock mass has been subjected by blast damage

and stress relaxation. It varies from zero for undisturbed insitu rock masses to unity for

very disturbed rock masses. Table 6.3 shows the suggested values for D for slopes.

Table 6.3. Guidelines for estimating disturbance factor D (Hoek et al, 2002)

Description of rock mass Suggested value for D

Small scale blasting in civil engineering slopes results in modest

rock mass damage, particularly if controlled blasting is used.

However, stress relief results in some disturbance.

D = 0.7

Good blasting

D = 1.0

Poor blasting

Very large open pit mine slopes suffer significant disturbance

due to heavy production blasting and also due to stress relief

from overburden removal.

In some softer rocks excavation can be carried out by ripping

and dozing and the degree of damage to the slopes is less.

D = 1.0

Production blasting

D = 0.7

Mechanical excavation

The introduction of D was in response to published experience using the Hoek-Brown

criterion. Sjöberg et al (2001) and Pierce et al (2001) stated that the Hoek-Brown

criterion overestimated the strength of rock masses based on experience with mine

slopes. The author (Douglas and Mostyn, 1999) agrees with these findings and

discusses this further on in the chapter. Sjöberg et al (2001) claimed that the equations

(6.14 and 6.15) presented by Hoek and Brown (1988) for ‘disturbed’ rock masses were

more appropriate. Hoek et al (2002) in response modified their formulas for the

parameters mb and s, using D such that they could reduce to the Hoek and Brown (1988)

formulas (Table 6.1).

−=

14100exp RMR

mm

i

b (6.14)

Page 440: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.27

=6

100exp

RMRs (6.15)

Prior to excavation, the only tools available to the designer are boreholes and possibly

surface exposures. The model that is developed can therefore only be considered as

preliminary (see Section 6.3.1 for discussion). De-stressing and blasting of the rock

mass may reduce the interlocking of the rock mass in the original model however, the

author does not believe a ‘catch all’ parameter ‘D’ is appropriate.

Different types of rock masses with different stress histories will be affected differently

when subjected to blasting and destressing affects. Good quality blasting should not

affect a large region of rock mass. This region is likely to be remote to the failure

surface. If it is considered that this is not the case or that de-stressing will affect the rock

mass the GSI can be reduced accordingly. The GSI is considered the appropriate

parameter as it is meant to be a representation of the degree of interlocking of the rock

mass as per Hoek et al (1995).

The reduction of the GSI should follow an observational type approach. Changes to the

rock mass (interlocking and defect surface conditions) due to blasting and de-stressing

can be predicted using past experience in the particular rock mass under consideration.

As excavation proceeds mapping of exposed surfaces should show whether these

predictions are reasonable or whether they need to be modified.

The author has not used the disturbance factor, D, in this thesis. Instead, where analysis

is performed the GSI at the time of interest (i.e. the time of slope failure or pit wall

completion) is used.

6.3.2.2 The Variation of the Hoek-Brown Parameters with GSI

Figure 6.13 shows the variation of the Hoek-Brown parameters mb/mi, a and s with GSI

based on Hoek et al (2002) and D = 0. It should be noted that if the Hoek (1997) table,

Figure 6.5, is used then the minimum and maximum values of GSI are 5 and 80

respectively (Table 6.4). mb/mi, which mainly accounts for friction, varies gradually

from unity as could be expected for a rock mass. The value of s (which mainly accounts

for cohesion) diminishes rapidly with a reduction in GSI thus, indicating a rapid

Page 441: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.28

reduction in compressive strength and an even more rapid reduction in tensile strength

as the quality of the rock mass decreases. This is as expected. As rock mass defects

become more cohesive it would be expected that s would be non-zero so as to avoid

zero compressive strength. But GSI reduces for increasing cohesion and if s is predicted

from GSI then s approaches zero not a finite value. This may be why the Hoek-Brown

criterion will underpredict the shear strength of clayey bench slopes. It should be

remembered at this point that the initial Hoek-Brown criterion was developed for hard

rocks and has only recently been accepted for use with very poor quality rock masses by

Hoek and Brown (1997). Thus, it could be expected that the experience with using the

criterion for poor quality rock masses (particularly for slopes) would be limited.

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100GSI

mb/m

i; s;

a

mb/mis

a

mb/misa

Figure 6.13. Variation of a, s and mb/mi with GSI

Page 442: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.29

Table 6.4. Maximum and minimum values of Hoek-Brown parameters using

Figure 6.10

Parameter Minimum

GSI = 5

Maximum

GSI = 80

mb/mi 0.034 0.49

s 0.000026 0.11

a 0.62 0.50

The value of a remains relatively constant and has a maximum value of 0.62 (Table

6.4). This is not consistent with what is known about compacted rockfill strength (a

material that could represent a lower bound to poor quality rock masses) where an a of

0.95 would be expected (Chapter 4). Chapter 3 on intact rock indicates that a actually

varies from 0.2 to 1.0, with a reasonable estimate of 0.4 to 0.95 depending on mi. Thus it

is not correct at two limits presented in this thesis. Where the intact rock approaches that

of a soft rock or hard soil the curvature is much less pronounced than an exponent of

0.65 would suggest (Johnston & Chiu, 1984).

As has been shown for intact rock (Chapter 3), fixing or limiting a has a very large

impact on the estimation of the other parameters (mb and s) and therefore a cannot

simply be changed without addressing the other parameters as well.

Page 443: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.30

6.4 VALIDATION OF THE HOEK-BROWN CRITERION

This section describes some analyses performed in order to assess the ability of the

Hoek-Brown criterion to predict the shear strength of rock mass.

6.4.1 Chichester Dam

The first case analysed was Chichester Dam, a 41m high concrete gravity dam

constructed in the 1920’s. The dam was upgraded with drainage holes and post

tensioning due to a perceived weakness in the foundation. The foundation consisted of

interbedded tuffaceous sandstone and thin shale layers. The best estimate GSI for the

foundation was 75. Unfortunately the analysis of the foundation (assuming no post

tensioning and drainage) using the distinct element program UDEC found that the

stresses beneath the dam were insufficient to give meaningful bounds on the Hoek-

Brown criterion. Note that sliding of the dam along bedding surfaces was a potential

failure mode. It was decided at this point to direct attempts at validating the criterion

toward higher stressed rock mass such as large failed slopes.

6.4.2 Nattai North Escarpment Failure

The Nattai North escarpment failure is located 80km south west of Sydney. The failure,

with a total volume of 14 million cubic meters and height ranging between 200 and

300m, is one of the largest rock mass failures to have occurred in Australia in modern

times. The failure has been well documented with studies in the area by Kotze & Pells

(1980), McGregor (1980), Cunningham (1986) and Pells et al (1987). Figure 6.2 shows

a photograph and diagram of the failure.

Figure 6.14 shows the escarpment stratigraphy consists of Hawkesbury Sandstone

overlying sandstones and claystones of the Narrabeen Group which in turn overlies the

Illawarra Coal Measures. Of most interest to stability considerations are the weaker

more fractured, and finer grained claystone and siltstone known as the Wombarra

Claystone and the 2.7m thick Bulli Coal Seam.

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Figure 6.14. Typical section of the Nattai North failure (Pells et al, 1987)

Persistent vertical defects dipping at approximately 84° out of the slope together with

bedding planes dipping 5° into the slope, resulted in large pillars that were prevented

from sliding or toppling. The pillars were supported on the highly stressed weaker

Wombarra Claystone. These conditions are believed to be sufficient to cause shearing

through the claystone and failure of the escarpment under natural processes. It is

believed that the failure was triggered by mining of coal seams beneath the escarpment.

The mining is suspected to have caused further fracturing to the claystone and stress

concentrations at the toe (Pells et al, 1987). Figure 6.15 gives a general illustration of

the failure mode. Shearing occurs through the claystone at the base of the pillars. The

base of the pillars slide out and the mass collapses (Cunningham, 1986).

The failure of the escarpment at Nattai North is seen as predominately shear failure

along defects (natural and mining induced) and through rock mass. The nature of the

defects in the claystone lend themselves well to the description of rock mass by Hoek

(1980) and hence the Hoek-Brown empirical rock mass failure criteria.

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a) Pre-mining: failure mayoccur as a natural process ifthe vertical joints arecontinuous and the base rockis of poor quality.

b) De-pillaring proceeds toward theescarpment. Vertical joints open andextend to form continuous joints.Fracturing of the Wombara claystoneis occurring.

c) Massive columns areformed. Yielding and shearingat the base is initiated.

d) Shearing through of base andcomplete failure.

Fracturing of WombaraClaystone due to highshear stress. Furtherfracturing due to tensilestrain.

Highly stressed

Fractured due tohigh shear andtensile stresses.

Coal seamshownexaggerated.

Figure 6.15. Illustration of the failure mechanism at Nattai North (Helgstedt,

1997)

The geometry and rock mass properties of the failure were estimated using data from

Cunningham (1986), McGregor (1980), Kotze and Pells (1980) and Richmond and

Smith (1979). The strength and deformation properties of the intact rock were estimated

from Bhattacharya (1976) and Evans (1978) who had performed testing on similar rocks

in a different area. The author validated as much of the information as possible during

surface field mapping (both on top and at the toe) of the landslide.

The properties used in the analysis are shown in Table 6.5 and Table 6.6. Table 6.7

shows the GSI estimated for the claystone where rock mass failure was deemed to have

occurred.

Helgstedt (1997) carried out numerical modelling of the failure under the supervision of

the author and Garry Mostyn using the distinct element code UDEC.

Two series of runs were made, with and without mining. The slope was modelled as two

units comprising sandstones and claystones. The geometry of the slope and cliff line

prior to failure was reconstructed using the Burragorang 1:25000 topographical map.

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All parameters adopted for the model were ‘best estimate’ average values. Extreme but

possible values were chosen for the sensitivity analysis. During modelling the material

parameters (marked with an asterix in Table 6.6) were progressively reduced until

failure occurred. The stresses at failure were then obtained along the shear surface

through the claystone.

Due to computational constraints, the actual spacing for the joint sets and bedding

planes could not be implemented in UDEC in areas remote to the zone of shearing.

However, the true spacing for most of the slope was not required to model the

mechanism of slope failure. Three different areas needing different spacing were

recognised and are outlined below. Stresses of 3.5+0.055z and 1.6+0.034z MPa were

used as the upper and lower bounds respectively for σ1 (horizontal stress).

The base of the slope in the Wombarra Claystone and lower section of the Scarborough

Sandstone (‘rough’ zone) required a spacing as close to actual as possible. Due to the

failure mechanism being one of shear failure both along discontinuities and through

intact rock, ‘randomly’ oriented fictitious joints having intact rock strength were added.

It should be noted that although the ficticious joints are given intact rock strengths, once

they fail UDEC assumes their strength to reduce to zero rather than that expected for a

rock joint in claystone/sandstone.

The section above the failing base required continuous vertical joints to permit the

mechanism of failure to be modelled. The presence of these vertical joints was

confirmed by the author during field mapping. For simplicity bedding plane spacing

was made equal to the vertical joint spacing. Away from the failure the joint spacing

was increased. The purpose of modelling this area was purely to reduce any edge effects

in the model.

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Table 6.5. Joint orientation, spacing and persistence for Nattai North

Parameter Applied to Upper

bound

Adopted

value

Lower

bound

vertical joints 87.9 84 75.6 Apparent Dip

(°) bedding - -5 -

vertical joints 20,40,150,250 14,30,125,250 8,20,100,250 Apparent spacing

(m)

(finest to roughest)

Bedding

discontinuities 20,40,110,180 14,30,90,180 8,20,70,180

Discontinuity

persistence all discontinuities - continuous -

Table 6.6. Summary of parameters used for the Nattai North Escarpment Failure

Adopted initial value Parameter

Sandstone Claystone

Density (kg/m3) 2560 2650

Young’s modulus, E (GPa) 14.4 10.5

Shear modulus, G (GPa) 5.54 4.04

Bulk modulus, K (GPa) 12.00 8.75

Poissions ratio 0.3

Friction angle of intact material (°)* 40 35

Cohesion of intact material (MPa)* 6 5

Tensile strength of intact material, σti (MPa)* 0.75 0.6

Normal stiffness, Kn (GPa/m) 50

Shear stiffness, Ks (GPa/m) 25

Defect friction angle (°)* 32 28

Defect cohesion (MPa)* 0.025 0.03

In-situ in plane horizontal stress, σ1 (MPa) 2.5+0.044z (where z = depth)

In-situ out of plane horizontal stress, σ2 (MPa) 1.2+0.026z

In-situ vertical stress, σ3 (MPa) 0.026z

* Changed globally for sensitivity analysis.

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Table 6.7. Summary of Hoek-Brown parameters for Nattai using RMR and the

Hoek-Brown chart

GSI

source

RMR89 Hoek-Brown Chart

(Hoek, 1997)

Estimate LB BE UB LB BE UB

GSI 55 61 69 49 45 55

mi 4 6.5 9 4 6.5 9

LB = Lower bound; BE = Best estimate; UB = Upper bound

The results of the analysis using UDEC correlated well with the assumed failure mode.

Average shear and normal stresses along the failure zone are presented in Table 6.8. The

mode of failure did not change where mining was modelled however, the shear zone

was found to extend deeper into the toe of the slope.

Table 6.8. UDEC output: average shear and normal stresses along the predicted

failure plane

Average stress along failure

zone (MPa) Case

Strength parameters

used Normal

stress

Shear

stress

Best estimate of all values, no mining 0.8 x best estimate 1.21 1.39

Lower bound in-situ stresses, no mining 0.7 x best estimate 1.16 1.32

Upper bound in-situ stresses, no mining 1.3 x best estimate 1.26 1.63

Best estimate of all values, mining 1.4 x best estimate 1.96 1.90

6.4.3 Katoomba Escarpment Failure

The Katoomba (or Dogface Rock) escarpment failure is located at Katoomba in the

Blue Mountains west of Sydney. The main failure occurred on the 28th January 1931.

Smaller failures have been recorded through to July 1977. The total volume of all

failures comprises approximately 75000 to 100000m3. The depth to the failure surface

was up to 280m. The failure has been documented by Pells et al (1987). Figure 6.16

shows a photograph from after the failure.

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Figure 6.16. Katoomba Escarpment Failure (photo courtesy Mrs Gwen Silvey of

the Blue Mountains Historical Society)

The geology and mode of failure was similar to that of the Nattai Escarpment failure.

The rocks were part of the Narrabeen Group with hard competent sandstones (Banks

Wall Sandstone and Burramoko Head Sandstone) overlying weaker material (including

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Hartley Vale Claystone, Victoria Pass Claystone, Beauchamp Falls Shale). Bedding

planes were near horizontal and joints in the sandstones persistent and subvertical.

Figure 6.17 shows an example of the vertical defects in the sandstone.

Figure 6.17. Katoomba Escarpment Failure, column prior to collapse (photo

courtesy Mrs Gwen Silvey of the Blue Mountains Historical Society)

No site specific testing was carried out on the materials and so all parameters were

estimated from testing on similar rocks in other areas (Evans, 1978 and Bhattacharyya,

1976). Table 6.9 shows the material properties used and Table 6.10 shows the

estimation of the GSI.

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Table 6.9. Summary of parameters used for the Katoomba Escarpment Failure

Adopted initial value Parameter

Sandstone Claystone

Density (kg/m3) 2560 2650

Young’s modulus, E (GPa) 14.4 10.5

Shear modulus, G (GPa) 5.9 3.86

Bulk modulus, K (GPa) 8.57 12.5

Poissions ratio 0.22 0.36

Friction angle of intact material (°)* 38 33

Cohesion of intact material (MPa)* 15 12.9

Tensile strength of intact material, σti (MPa)* 1.91 1.61

Defect friction angle (°)* 32 28

Defect cohesion (MPa)* 0.025 0.03

In-situ in plane horizontal stress, σ1 (MPa) 2.5+0.044z (where z = depth)

In-situ out of plane horizontal stress, σ2 (MPa) 1.2+0.026z

In-situ vertical stress, σ3 (MPa) 0.026z

Table 6.10. Summary of Hoek-Brown parameters for the Claystone in the

Katoomba Escarpment Failure using RMR and the Hoek-Brown chart

GSI

source

RMR89 Hoek-Brown Chart

(Hoek, 1997)

Estimate LB BE UB LB BE UB

GSI 28 50 69 48 53 58

mi 4 6.5 9 4 6.5 9

Tarua (1997) carried out the numerical modelling under the supervision of the author

and Garry Mostyn using the distinct element code UDEC. As the mode of failure and

geology/geometry was simlar, the analysis was carried out in the same manner as that

for the Nattai Escarpment failure.

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6.4.4 Aviemore Dam Insitu Shear Tests

Aviemore Dam, constructed between 1963 and 1968, is located on the Waitaki river,

185km south west of Christchurch, New Zealand. The dam is comprised of both a

340m long, 57m high concrete gravity section and a 350m long, 49m high earth

embankment section (Read et al, 1996). During construction eight large-scale in-situ

shear tests were carried out on the foundation in order to determine the strength of the

concrete/rock interface for stresses relevant to those induced by the proposed dam.

The dam is founded on silty to sandy greywacke of Mesozoic age and coal measure

sediments of Tertiary age. However all in-situ tests were carried out on greywacke rock.

The rock mass is closely jointed, veined, and often is crushed and sheared. Read et al

(1996) identified three semi-orthogonal joint sets as follows:

• joints sub-parallel to bedding, 150°-190°/75°NE-75°SW (strike/dip)

• joints striking approximately perpendicular to bedding, 100°-120°/70°NW-90°

• joints striking approximately perpendicular to bedding, 080°-110°/30°-50°SW

The range of the orientation for the joint sets is very wide and in addition several other

randomly orientated joints are present. Read et al (1996) stated that a statistical analysis

gives the impression that the overall jointing pattern at Aviemore was random. The most

common spacing has been found to be between 60 and 200mm (Read et al, 1996). Most

of the joints were found to have a slightly wavy profile, were rough to smooth and

closed with a persistence of a few metres. Moreover sheared and crushed zones occur,

although these are very widely spaced at the location of the in-situ shear tests.

Read et al (1996) mapped approximately 350 defects on available outcrops. The

outcrops were considered similar to the rock mass in the tests based on photos and other

documents. By scrutinising old photos and documents Read et al (1996) concluded that

the tested rock mass was of similar quality to that covered by the joint survey. A

summary of this survey is shown in Table 6.11. The GSI was estimated using the results

of this survey and is shown in Table 6.12.

Figure 6.18 illustrates the setup and dimensions of the tests at Aviemore. One test block

(0.76mx1.8m) and one reaction (anchor) block (0.9mx1.8m) were cast directly onto

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clean rock foundations (Foster & Fairless, 1994). The vertical load was applied to the

blocks using stressed bars anchored into the rock foundation. An ungrouted length of

4.9m was used for at least two of the tests. Freyssinet flat jacks were used to force the

blocks apart as constant vertical load was maintained on the test blocks. Six tests were

performed using a horizontally acting thrust and two using an inclined thrust acting at a

downward angle through the centre of the blocks. The latter two test results were not

used.

Table 6.11. Summary of the Joint Properties from the Joint Survey carried out by

Read et al (1996)

Persistence of joints (m) 0-0.75 0.75-1.5 1.5-2.5 2.5-3.5 3.5-4.5 4.5-7 7-(15) % per metre interval 27 30 19 13 9 5 0.5

Defect types shear/ fault

joint bedding schistosity /foliation

% 10 84 6 0 Aperture (mm) >200 60-200 20-60 6-20 2-6 <2 tight

% 0 0 0 1 2 97 0 Nature of infill clean surface stain. non-cohesive cemented

% 12 72 1 12 Roughness polished slickensided smooth rough defined

ridges small steps

% 0 1 58 35 4 1

Table 6.12. Hoek Parameters for Aviemore Shear Tests using RMR, and the

Hoek-Brown Chart

GSI

Source RMR

Hoek-Brown Chart

(Hoek, 1997)

Estimate UB BE LB UE BE LB

GSI 52 43 31 40 35 30

mi 15 12 10 15 12 10

σc (MPa) 50 35 20 50 35 20

Foster & Fairless (1994) stated that all tests failed through the rock mass,

approximately 50-100mm below the rock-concrete contact, involving failure of several

defects. During the test both the test block and the reaction block failed at the same

time. Foster & Fairless (1994) analysed the failures and proposed that both blocks

failed at the same τ/σN ratio and that the σ-ε curves should have been similar. Since the

σ-ε curves were similar it was likely that vertical force had been transferred between

the blocks via the stiff jack.

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Foster and Fairless (1994) adjusted the vertical stresses on the test and reaction blocks

assuming that vertical forces were transferred from the reaction block to the test block

due to differential displacement. The values were adjusted to yield similar τ/σN ratios

for the reaction and the test blocks.

Helgstedt (1997) carried out the numerical modelling under the supervision of the

author and Mr Garry Mostyn using the distinct element code UDEC. The modelling

was used to investigate whether the assumptions of Foster and Fairless (1994) were

reasonable. The general model behaviour was studied to see if it agreed with

observations from the real tests and to confirm the theory that vertical stress had been

transferred between the blocks through the Freyssinet jack. The failure stresses from the

model were not used.

Figure 6.18. Direct Shear Test Set up (Foster & Fairless, 1994)

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The defects in the rock mass were created by Monte Carlo generation. The joints were

assumed to be randomly orientated with a negative exponentially distributed joint trace

length. The distribution of the discontinuities in space was assumed to be random.

These assumptions were verified against the data from the joint survey and data

presented by Read et al (1995 and 1996). Figure 6.19 illustrates the mesh generated for

one of the UDEC models. The actual true joint frequency was only modelled close to

the simulated test and reaction blocks, joints were more widely spaced in the far field.

The vertical load applied by stressed bars, anchored in the rock below the shear tests, at

Aviemore was simulated in the UDEC model by applying vertical loads at the top of the

blocks. This simplification is however not likely to influence the results. The horizontal

load from the Freyssinet jack was simulated by four blocks as can be seen in Figure

6.20 (between the test and reaction block). The left and right blocks represent

pressurised sides of the jack. A pressure was exerted in the vertical slot between these

blocks. The upper and lower blocks represent the casing of the jack. The two horizontal

cracks dividing the upper and lower blocks from the left and right blocks were given

zero friction angle and cohesion, but very high tensile strength. This allows the left and

right blocks to slide freely in a horizontal direction, while simultaneously, the simulated

jack can act as a rigid device capable of transferring moment.

The parameters that were used for the numerical model are given in Table 6.13 and

Table 6.14.

The general displacement (vertical and horizontal) behaviour matched the behaviour of

the field tests. The assumptions of Foster and Fairless (1994) were validated as vertical

stress was shown to be transferred through the jack and failure occurred simultaneously

in the reaction and test blocks. The statistically generated models were run several

times. All with results similar to that discussed above.

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Table 6.13. Intact material parameters

Material Tensile

strength

(MPa)

Cohesion

(MPa)

Friction

angle

(°)

Bulk

Modulus

(MPa)

Shear

Modulus

(MPa)

Density

(t/m3)

Concrete blocks 5 15 45 25000 10400 2.4

Jack and stressed bars 200 400 0 133333 80000 7.6

Intact rock 3 8 45 20000 18000 2.2

Table 6.14. Defect and Interface Material Parameters

Material Tensile

strength

(MPa)

Cohesion

(MPa)

Friction

angle

(°)

Normal

Stiffness

(MPa)

Shear

Stiffness

(MPa)

Conc-steel interface 0 0 45 50000 30000

Conc-rock interface 5 15 50 25000 15000

Jack casing interface 200 0 0 2500000 1500000

Press. void in jack 0 0 0 2500000 1500000

Defects in rock mass 0 0 44 15000 5000

6.4.5 Discussion of the Results of the Analysis

The Hoek-Brown criterion, together with Figure 6.5 to estimate GSI, was used to

estimate the shear strength of the rock mass. Balmer’s method was used to convert from

principal stresses to shear and normal stresses. Figure 6.21 shows a plot of the ratio of

calculated shear strength, τin-situ, versus the shear strength estimated from GSI for the

cases. The results show that the Hoek-Brown criterion provides a reasonable estimate of

the strength at the Nattai Escarpment. The Aviemore insitu shear tests show the

predicted strength using the Hoek-Brown criterion to range from 0.8 to 1.2 times the

computed strength from the shear tests. The Hoek-Brown criterion predicts twice the

strength as that calculated using UDEC for the Katoomba escarpment failure. However

this may be due to the lack of site specific strength data at Katoomba. The GSI

estimated from the RMR was noticeably higher than that estimated using Figure 6.5 for

the Aviemore insitu shear tests and Nattai escarpment failure. Thus, the strengths

estimated using RMR would lead to an overprediction of the strength of the rock mass

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Figure 6.19. Example of mesh used (Helgstedt, 1997)

Figure 6.20. Close up of the simulated jack (Helgstedt, 1997)

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

σn (MPa)

τ in-

situ

/ τta

ble

Katoomba escarpment failure

Aviemore shear tests

Nattai escarpment Failure

Figure 6.21. Back analysis results using Figure 6.5 for GSI

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6.5 A NEW ESTIMATION OF ROCK MASS STRENGTH

6.5.1 Development of a Modified Criterion

As discussed earlier the Hoek-Brown criterion is virtually universally accepted. It also

appears to give reasonable results if used in conjunction with Figure 6.5 to estimate

GSI. The current method of calculating the parameters m and a appears to be flawed at

the limits of intact rock (Chapter 3) and rockfill (Chapter 4). It has therefore been

decided to modify this criterion so that it incorporates some of the results presented in

this thesis rather than to develop a completely new approach.

The terminology used for the modified criterion is outlined below.

α

σσ

σσσ

+

′+′=′ s

m

cici

331 (6.15)

For intact rock (GSI=100):

s = si

m = mi

α = αi

For rock mass (GSI<100):

s = sb

m = mb

α = αb

In general, σci is the unconfined compressive strength, σc, of the intact rock; unless the

scale of the discontinuities affects the strength of the blocks in the rock mass under

consideration.

The author proposes to use the form of the Hoek-Brown criterion and to modify the

method of calculating the parameters α, s and m. The basic assumption is that the rock

mass parameters will be factored versions of the intact parameters developed in Chapter

3.

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6.5.1.1 Exponent ‘α’

Hoek and Brown (1980) restricted α to 0.5. Hoek (1994) modified this for GSI<25 to

allow α to vary up to a theoretical maximum of 0.65 (but actually 0.625 for a minimum

GSI of 5) using the equation below.

200/65.0 GSI−=α (6.16)

This equation resulted in a ‘step’ at GSI = 25 from 0.525 to 0.5. Hoek et al (2002)

eliminated this step by modifying the equation for all GSI values to:

( )32015

61

21 −− −+= ee GSIα (6.17)

This equation results in a maximum α of 0.62 using a minimum GSI of 5.

Chapter 3 has shown that α is not fixed at 0.5, and can vary considerably for intact rock.

A rock mass can be considered a transitional material between intact rock and soil. At

the soil limit it is expected that α would approach unity (Mohr-Coulomb material). A

statistical analysis of 929 triaxial tests on rockfill given in Chapter 4 showed that αb for

rockfill is approximately 0.9 and that mb≈2.5.

If the results of Chapter 3 are used for intact rock then a modification to the current

Hoek-Brown equation is required where αb is not restricted to a range of 0.5 to 0.65,

and is a function of mb and GSI. It is assumed that as the rock mass approaches a soil

like material that αb will approach 0.9 and mb will approach 2.5.

6.5.1.2 Parameter ‘m’

Hoek and Brown provide estimates of mi based on rock type however, as discussed in

Chapter 3, rock type is a poor predictor of mi. The parameter mi should be estimated

using triaxial tests on intact rock samples or can be approximately estimated as σci/σti.

This method may also be appropriate for intact soil-like materials (clays). Limited Al-

Hussaini (1981) found that the “unconfined compression strength obtained was about 5

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to 10 times larger than the tensile strength” for samples of high and low plasticity clay

and sandy clay. Fang and Fernandez (1981) found that the ratio of σc/σt was between

15-28 for clays at their optimum moisture content and 3-7 for air dried samples. These

ratios from the literature fall within the authors suggested mi range.

There is some limited information in the literature that shows that mi = σc/σt, for intact

soil-like materials (clays), is within the range found for intact rock (between 4 and 40)

(Al-Hussaini, 1981 and Fang and Fernandez, 1981). However, the information in the

literature is insufficient for the author to make a definitive judgement on whether the

author’s criterion can be applied to clays. As the criterion is empirical and has been

developed for rock using triaxial tests on rock samples the author does not recommend

the extrapolation and use of the criterion for clays.

The parameter m (in association with the exponent α) predominately affects the friction

angle of the rockmass. Therefore as GSI drops it can be expected that the rockmass will

become less interlocked and the frictional strength of the rockmass will reduce

(predominately through a reduction in dilation). The parameter mb should therefore

reduce from mi to a limiting value as a function of GSI. The limiting value for a non-

cohesive rockmass could be taken as 2.5 from the analyses of rockfill discussed earlier.

6.5.1.3 Parameter ‘s’

The parameter s contributes predominately to the cohesiveness of the rock mass. Thus,

as GSI decreases s should also decrease as per the Hoek-Brown criterion. The limiting

value should be zero where the ‘soil-like’ rock mass is non-cohesive.

Once a rock mass no longer behaves as ‘intact’ it can be expected that cohesion and thus

s should decrease rapidly with a decrease in GSI. Hoek and Brown use an exponential

drop in s versus GSI as shown in the following equation.

( )

=9

100exp

GSIs (6.18)

Hoek and Brown consider a well-interlocked rock mass to have a GSI of 80. Therefore,

s may be close to unity in the region of GSI equal to 80-100.

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The Hoek-Brown criterion was developed for hard rock masses. As such, at the ‘soil

limit’ (GSI→ 0) the parameter s in the Hoek-Brown equation approaches zero. This is

reasonable for a non-cohesive or frictional rock mass. However, where the rock mass is

controlled by cohesion (i.e. the rock mass is controlled by the clay in the mass) this

assumption is incorrect. The author believes that where there is sufficient clay material

in the rock mass such that there is no rock to rock contact during shearing the shear

strength of the soil should be used. The Hoek-Brown criterion is inappropriate, as the

properties of the intact rock (e.g. σc) will have at the most a minor effect on the strength

of the mass. The cohesive soil limit is not considered in this thesis.

6.5.2 Development of the Equations to Estimate the Parameters in the

Hoek-Brown Criterion

The previous section discussed the development of modifications to the parameters of

the Hoek-Brown criterion. These were based on the author’s work on intact rock,

rockfill and rock masses. The bounds have been well quantified in this thesis however,

due to the limited information available about failures and the addition of a variable α

dependent on m, it meant good quality triaxial tests were needed to provide equations

for intermediate rock masses. The analysis of triaxial testing on rock mases could also

give confidence to the theory developed in the previous section. Habimana et al (2002)

published four sets of triaxial tests on quartzitic sandstone. These were part of an

extensive laboratory testing programme carried out by the rock mechanics laboratory of

the Swiss Federal Institute of Technology Lausanne (EPFL) for the hydroelectric power

plant of Cleuson-Dixence and the reconnaissaince gallery for the Lotschberg Tunnel in

the Swiss Alps. New sampling techniques were developed to ensure as little disturbance

as possible. To the author’s knowledge, these are the best set of published triaxial tests

on rock mass available. The quartzitic sandstone had varying degrees of tectonic

crushing. Habimana et al (2002) classified the rocks used into four GSI groupings (GSI

= 15, 25, 50 and 80). Figure 6.22 shows the triaxial test results for each GSI data set.

The samples were tested perpendicular to anisotropic planes (if any) to induce rock

matrix failure. Habimana et al (2002) noted that the degree of anisotropy decreased with

an increase in tectonic crushing. At a low GSI the material was considered isotropic.

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Each data set was analysed statistically using the Hoek-Brown equation. Figure 6.23

shows the Habimana et al (2002) data together with the author’s statistical fits. During

this analysis the loss function used in the statistical analysis had to be modified to allow

the solution to converge and to avoid local minimums outside the bounds of the Hoek-

Brown parameters i.e.

0 ≤ s ≤ 1

0 ≤ m ≤ 40

0 ≤ α ≤ 1

The results of the statistical analyses are shown in Table 6.15.

Table 6.15. Results of statistical analysis of Habimana et al (2002) test data

GSI m s α σc

(MPa)

Variance explained

(%)

15 2.46 0 0.84 16 93.4

25 3.9 0.016 0.65 16 99.3

50 14 0.10 0.62 16 99.996

80 20 0.7 0.55 16 93.3

Table 6.15 was used together with the discussion and models in the preceding section to

develop equations for the parameters sb, αb and mb.

6.5.2.1 A New Equation for ‘mb’

The results for the parameter mb showed that a linear equation gave the best fit to the

data. The best-fit equation (variance explained = 95.5%) was:

4

GSImb = (6.19)

If this line was extrapolated to GSI = 100 then mb = 25. The equation was therefore

rewritten as:

Page 464: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.51

100GSI

mm ib = (6.20)

Figure 6.24 shows this equation together with the data used.

A lower limit of mb was set at 2.5 as indicated from the analysis of rockfill. Thus the

equation becomes:

=5.2

100max

GSImm

i

b (6.21)

Page 465: Shear Strength of Rock

Page 6.52

0

20

40

60

80

100

0 5 10 15 20σ′3 (MPa)

σ′1

GSI = 15

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 25

0

20

40

60

80

100

0 5 10 15 20σ′3 (MPa)

σ′ 1

GSI = 50

0

20

40

60

80

100

0 5 10 15 20σ′3 (MPa)

σ′ 1

GSI = 80

Figure 6.22. Test results for tectonised quartzitic sandstone (Habimana et al, 2002)

Page 466: Shear Strength of Rock

Page 6.53

0

20

40

60

80

100

0 5 10 15 20σ′ 3 (MPa)

σ′1

GSI = 15

0

20

40

60

80

100

0 5 10 15 20σ′3 (MPa)

σ′1

GSI = 25

0

20

40

60

80

100

0 5 10 15 20σ′ 3 (MPa)

σ′1

GSI = 50

0

20

40

60

80

100

0 5 10 15 20σ′ 3 (MPa)

σ′1

GSI = 80

Figure 6.23. The author’s statistical fits to Habimana et al (2002) data

Page 467: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.54

The linear relationship is different in form to the exponential Hoek-Brown relationship:

( )

=28

100exp

GSImm ib (6.22)

The author does not see this as a problem as:

• Frictional strength may not decrease as rapidly with GSI as indicated by the Hoek-

Brown equation for mb.

• α is no longer almost constant and as it is directly related to mb, the Hoek-Brown

equation will not be appropriate.

• An exponential relationship is not supported by the data.

0

5

10

15

20

25

0 20 40 60 80 100GSI

m b

Figure 6.24. mb versus GSI

6.5.2.2 A New Equation for ‘sb’

The results from the statistical analysis of the Habimana et al (2002) data showed a

rapid decrease of s with a decrease in GSI as predicted in the discussion in Section

6.5.1.3. Therefore an exponential relationship, similar to the Hoek-Brown relationship

for s, was deemed appropriate. One issue raised from the test results was the relatively

high value for s for a GSI of 80. This result was taken to indicate the possibility of a

Page 468: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.55

plateau in the value of s at high GSI. This can be justified by the argument that at high

GSI (>85) the rockmass is very strongly interlocked and thus the cohesive strength is

similar to that of intact rock. This is supported by the GSI table by Hoek (1999) that

includes a new row for ‘intact or massive’ rock that has a GSI ranging from 80 upwards

for very good defect quality (Figure 6.25).

Figure 6.25. GSI for an intact or massive rock structure (Hoek, 1999)

A statistical analysis of the data in Table 6.15 using an exponential curve together with

a plateau (maximum) of s = 1 for GSI>85 was performed and produced the following

equation (variance explained = 99.97%):

( )

=1

1585exp

min

GSI

sb (6.23)

This relationship is plotted on Figure 6.26 together with the data used.

Page 469: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.56

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100GSI

s b

Figure 6.26. sb versus GSI

6.5.2.3 A New Equation for ‘αb’

The exponent, αb, varies with GSI and mb. The limits, as discussed in Section 6.5.1.1,

on αb are:

GSI = 100, αb = αi

GSI → 0, αb → 0.90

A statistical analysis of the data using these limits produced the following equation

(variance explained = 83.3%).

( )

−−+=

i

biib m

m3075exp9.0 ααα (6.24)

Figure 6.27 shows the relationship for αb together with the data. It should be noted that

for this analysis mi was taken as that extrapolated from the equation derived earlier for

mb. The exponent for intact rock, αi, was also estimated from the test data.

Page 470: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.57

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100GSI

α b

Figure 6.27. αb versus GSI

Figure 6.28 shows the relationship plotted on a m versus α curve (Figure 6.29 shows an

example of the transition from intact rock to rock mass). Plotted on this curve is a

relationship between mi and αi (Equation 6.25). This relationship is a slight

modification to that derived in Chapter 3 (Equation 6.26). This was done to allow the

curve to pass through α = 1 when mi = 0.

++=

7exp1

2.14.0

ii m

α (6.25)

++=

455.7exp1

08585.14032.0

ii m

α (6.26)

Figure 6.30 shows that the modification does not affect the results significantly.

Figure 6.27 and Figure 6.28 show that the increase in α occures rapidly over a short

range of mb. This increase starts at approximately mi/4 or GSI ≈ 20-25. Interestingly this

is very similar to the Hoek et al (1995) relationship for a where a remains constant for

GSI approximately 25-100 and increases below a GSI of 25.

Page 471: Shear Strength of Rock

Page 6.58

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40

m

α

m i = 40

m i = 20

6

m i = 10

4

( )

−−+=

i

biib m

m3075exp9.0 ααα

+

+=

7exp1

2.14.0

ii m

α

Figure 6.28. Graphical representation of the equations for α and m

Page 472: Shear Strength of Rock

Page 6.59

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40

m

α

Intact sampleGSI = 100

m i , αi

Mass samplem b = function of GSI

αi = function of m b (GSI)

Transition curve fromGSI =100 to GSI = 0

Rock mass limitGSI = 0

Relationship between m i

and αi for intact rocks

Figure 6.29. Transition of α and m from intact rock to rock mass

Page 473: Shear Strength of Rock

Page 6.60

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40 45 50m i

α i

ai

ainew

αi

αinew

+

+=

455.7exp1

08585.14032.0

ii m

α

++=

7exp1

2.14.0

iinew m

α

Figure 6.30. Original and modified relationships for α i and mi

Page 474: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.61

6.5.2.4 The Overall Equation

Figure 6.32 shows the original plots of data together with curves developed using the

preceding equations. These curves provide a good fit to the data. For a GSI of 50 there

is a slight underestimation of the strength and for a GSI of 25 there is a slight

overestimation of the strength. A look at the original test curves presented by Habimana

et al (2002) (Figure 6.31) shows that there is a larger gap between GSI = 25 and 50 than

could be expected for a regular transition from an intact rock to a weak rockmass.

Habimana et al (2002) claim that their estimates of GSI are within ±5. It may be that the

gap is due to a slight error in the estimation of GSI.

Figure 6.31. Shear strength curves for tectonised quartzitic sandstone (Habimana

et al, 2002)

A final global statistical analysis of all the data was performed using the general Hoek-

Brown criterion together with the equations developed in this section. This was carried

out to check whether any errors were introduced due to each parameter equation being

derived seperately and then being recombined into the Hoek-Brown equation. Figure

6.33 shows the plots for GSI = 15, 25, 50 and 80 provide good fits to the data (variance

explained 95.6%).

Figure 6.34 and Figure 6.35 show non-dimensional example plots of the shear strength

criterion for an mi of 40 and an mi of 4 respectively for GSI varying from 10 to 100.

Page 475: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.62

Figure 6.36 and Figure 6.37 compare the author’s modified criterion with that of the

current Hoek-Brown criterion for an mi of 40 and an mi of 4 respectively. The plots

show that the modified criterion gives a higher strength in the compressive region for an

mi of 4. For an mi of 40, the modified criterion gives a lower strength for a GSI of 100, a

similar strength for a GSI of 80 and a higher strength for a GSI of 10. There is a larger

relative drop in strength between GSI 100 and 80 for the Hoek-Brown criterion

compared with the modified criterion. This is in accordance with the discussion in

Section 6.5.2.2. It should be noted that the two criteria use different methods of

approximating mi.

Page 476: Shear Strength of Rock

Page 6.63

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 15

0

20

40

60

80

100

0 5 10 15 20 25σ′3 (MPa)

σ′1

GSI = 25

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 50

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 80

Figure 6.32. Results of analysis of Habimana et al (2002) data using the new equation and parameters from equations

Page 477: Shear Strength of Rock

Page 6.64

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 15

0

20

40

60

80

100

0 5 10 15 20 25σ′3 (MPa)

σ′1

GSI = 25

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 50

0

20

40

60

80

100

0 5 10 15 20 25σ′ 3 (MPa)

σ′1

GSI = 80

Figure 6.33. Results of global analysis of Habimana et al (2002) data using new equations

Page 478: Shear Strength of Rock

Page 6.65

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

σ′3/σc

σ′1/σc

GSI = 10

GSI = 40

GSI = 60

GSI = 80

GSI = 100

α

σσ

σσ

σσ

+

′+

′=

′s

m

cicici

331

Figure 6.34. Non-dimensionalised plot of new shear strength curves for mi = 40 and varying GSI

Page 479: Shear Strength of Rock

Page 6.66

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

σ′3/σc

σ′1/σc

GSI = 10

GSI = 40

GSI = 60

GSI = 80

GSI = 100

α

σσ

σσ

σσ

+

′+

′=

′s

m

cicici

331

Figure 6.35. Non-dimensionalised plot of new shear strength curves for mi = 4 and varying GSI

Page 480: Shear Strength of Rock

Page 6.67

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

σ′3/σc

σ′1/σc

Hoek 2002

Author's criterion

α

σσ

σσ

σσ

+

′+

′=

′s

m

cicici

331

Figure 6.36. Comparison of the author’s criterion and the Hoek-Brown criterion (Hoek, 2002) for mi = 40

Page 481: Shear Strength of Rock

Page 6.68

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

σ′3/σc

σ′1/σc

Hoek 2002

Author's criterion

α

σσ

σσ

σσ

+

′+

′=

′s

m

cicici

331

Figure 6.37. Comparison of the author’s criterion and the Hoek-Brown criterion (Hoek, 2002) for mi = 4

Page 482: Shear Strength of Rock

The Shear Strength of Rock Masses Page 6.69

6.5.3 Summary of Method

The basic form of the shear strength equation remains unchanged from the Hoek-Brown

criterion.

α

σσ

σσσ

+

′+′=′ s

m

cici

331 (6.27)

For intact rock m = mi and α = αi. These should preferably be measured from triaxial

tests on intact rock samples. Alternatively an approximation can be made using the

uniaxial compressive strength, σci, and tensile strength, σti, of the intact rock and the

equations below.

ti

ciim

σσ

= (6.28)

++=

7exp1

2.14.0

ii m

α (6.29)

The estimation of mb, αb and sb can be made using the following equations:

=5.2

100max

GSImm

i

b (6.30)

( )

−−+=

i

biib m

m3075exp9.0 ααα (6.31)

( )

=1

1585exp

min

GSI

sb (6.32)

The equations presented by Hoek et al (2002) (Figure 6.6) can be used to estimate the

cohesion, c, and friction angle, φ, of the rock mass, as the form of the Hoek-Brown

equation has not been changed.

Page 483: Shear Strength of Rock

Conclusions and Recommendations Page 7.1

7. CONCLUSIONS AND RECOMMENDATIONS

7.1 CONCLUSIONS

This thesis is divided into two sections. The first section of this thesis (Chapter 2)

describes the creation and analysis of a database on concrete and masonry dam

incidents known as CONGDATA. The second and main section of this thesis (Chapters

3-6) had its origins in the results of Chapter 2 and the general interests of the author. It

was found that failure through the foundation was common in the list of dams analysed

and that information on how to assess the strength of the foundations of dams on rock

masses was limited. This section applies to all applications of rock mass strength such

as the stability of rock slopes.

7.1.1 The Analysis of Concrete and Masonry Dams

The author has collected a far more extensive database on concrete and masonry dam

incidents (CONGDATA) than has previously been attempted

Generally, unlike some failure modes for embankment dams, e.g. internal erosion and

piping, the stability of concrete and masonry dams is analysable and hence can readily

be checked. The major unknowns for these dams lie in the foundation where sliding and

piping failures can occur. It is for this reason that foundation problems (sliding, leakage

and piping) are the main causes of failure to concrete dams. Overtopping tends to play a

bigger part in the failure of masonry dams, possibly reflecting limited understanding of

floods when they were built. It should be noted that the actual failure mode for

‘overtopping’ failures was often unknown.

Foundation shear strength is the main cause of failure for dams with rock or unknown

foundations. Shale (interbedded with other sedimentary units) has a greater tendency to

be involved with sliding failure because of the likely presence of weaknesses in the

bedding such as bedding surface shears. Shale and limestone (often interbedded) have a

high incidence of failure. The limestone has a high proportion of accidents generally

due to excessive leakage through dissolution.

Page 484: Shear Strength of Rock

Conclusions and Recommendations Page 7.2

An analysis of the water levels at failure show most dams failed at their highest

recorded water level (regardless of the age of the dam). Several of these were only

slightly higher than that recorded previously. The database showed that, where

information was available, most dam failures had some warning that could have

resulted in the warning and evacuation of residents downstream. Often the warning was

a sudden increase in the amount and rate of leakage. The actual volume of leakage was

not as significant a guide. This indicates that although a dam may have performed

satisfactorily in the past, increases in water level (above historical maxima) should be

treated with caution and the dam sufficiently monitored as the water level rises.

Piping is the main cause of failure for concrete and masonry dams with soil

foundations. The alluvial soils have a tendency to pipe under the high gradients

imposed. No gravity dam has been reported to have failed by sliding on alluvial soils.

Piping tends to occur early in a dam’s life (<5 years, with one exception).

From the data collected it appears that the failed dams suffered from a lack of ‘good

engineering’. Very few dams were found with galleries (1 dam); drainage (1 dam);

grout curtains (4 dams); and shear keys (1 dam). The downstream slopes appeared to be

too steep. Six gravity failures had downstream slopes of 0.6:1 (H:V) or less. Failed

dams, particularly gravity dams, were usually located in relatively wide valleys or were

composite sections with earthfill dams. Three-dimensional effects are unlikely to have

contributed any strength in these cases. hwf/W ratios ranged from 0.6 to 2.1 with an

average of 1.35.

The author has used the analysis of CONGDATA and a ‘population’ database to

develop a method for assessing the first order probability of failure of masonry or

concrete gravity dams. The method accounts for dam age, year commissioned and type;

failure mode; foundation geology; height to width ratio; and monitoring and

surveillance. General probabilities of failure for arch, buttress and multi-arch dams,

based on failure and population statistics, are included.

The author cautions that this approach should only be used as a first order

approximation of the annual probabilities of failure. It is clearly very approximate, and

suffers from being based on small numbers of failures, and limited quality data. Where

Page 485: Shear Strength of Rock

Conclusions and Recommendations Page 7.3

significant decisions on dam safety are being made, detailed deterministic and/or

probabilistic methods should be used.

Whilst all care has been taken in compiling the data in CONGDATA, it should be

remembered that the information in CONGDATA has come from numerous sources, not

all of which could be validated. The analysis of dams in CONGDATA does not take

into account such things as: surveillance; quality of construction; and quality of

geological description. It is therefore recommended that this work be used in a

qualitative sense only.

7.1.2 The Shear Strength of Intact Rock

An overview of the strength of intact rock has been presented. It was demonstrated that

the method of fitting the criterion to the test data has a major effect on the estimates

obtained of the material properties. The results of a recent analysis of a large database

of test results demonstrated that there are inadequacies in the Hoek-Brown empirical

failure criterion as currently proposed for intact rock and, by inference, as extended to

rock mass strength. The parameters mi and σc are not material properties if the exponent

is fixed at 0.5. Published values of mi can be misleading as mi is not related to rock type.

The Hoek-Brown criterion can be generalised by allowing the exponent to vary. As

expected, this change resulted in a better model of the experimental data. The most

accurate method of estimating mi and α is through using triaxial tests on intact rock.

The recommended method for regression of the data is modified least squares, Equation

7.1, combined with the extended formulation of the generalised Hoek-Brown criterion,

Equation 7.2. The equations are repeated below.

( )( )

′−≤′×′−′′−>′′−′

3133

3111

3for predicted measured3for predicted measuredσσσσσσσσ

im (7.1)

−≤′′=′

−>′

+

′+′=′

ic

icc

ic

m

mm

σσσσ

σσσ

σσσσ

α

331

33

31

for

for 1 (7.2)

Page 486: Shear Strength of Rock

Conclusions and Recommendations Page 7.4

Analysis of individual data sets indicated that the exponent, α, is a function of mi which

is, in turn, closely related to the ratio of σc/σt. A regression analysis of the entire

database provided a model to allow the triaxial strength of an intact rock to be estimated

from a reliable measurement of its uniaxial tensile and compressive strengths. The

method proposed is the most accurate of those methods that do not require triaxial

testing and is adequate for preliminary analysis. An analysis was presented that showed

applying the Hoek-Brown criterion to most rocks results in systematic errors. Simple

relationships for triaxial strength that are adequate for slope design were presented.

7.1.3 The Shear Strength of Rockfill

A general overview of the shear strength of rockfill is presented. An analysis of a large

database of test results was used to develop two new shear strength equations, one

relating the secant friction angle and normal stress (Equation 7.3) and the other the

principal stresses (Equation 7.4). The parameters can be found using equations 4.21-

4.23 and 4.25-4.30 in Chapter 4 respectively. The equation for principal stresses

provided a much better fit to the data and is recommended. The equations presented

effectively give the mean strengths of the data. Graphs are provided showing the range

of strengths and the affect of various parameters on the shear strength of rockfill. Of the

parameters statistically investigated, the unconfined compressive strength, particle

angularity, fines content, maximum particle size and void ratio were found to have the

most significant effect on the shear strength of rockfill.

cnba σφ ′+=′ (7.3)

ασσ 31 ′=′ RFI (7.4)

7.1.4 Empirical Slope Design

A review of current empirical methods of slope design using rock mass characterisation

has also been presented. The findings highlighted the lack of well tested methods.

Current slope design methods were based on limited databases with no failures and

slopes of limited height. Many of the methods were incorrectly advocated for

structurally controlled slopes. The author has presented new slope design curves, based

Page 487: Shear Strength of Rock

Conclusions and Recommendations Page 7.5

on slopes that have had rock mass failure components, that can be used for preliminary

slope design.

7.1.5 The Shear Strength of Rock Masses

The Hoek-Brown criterion is the most commonly used strength criterion for rock mass

and has thus been the main subject of this section of the thesis. The author has

examined the appropriateness of the equation for predicting strengths at the two limits

of rock mass (intact rock and rockfill). A study of the strength of intact rock using a

large database of triaxial tests shows that the exponent, a, in the Hoek-Brown criterion

should vary from about 0.2 to 0.9. The study of a database of 988 triaxial tests on

rockfill shows that, if it is assumed a rockfill is representative of a very poor quality

rock mass, the exponent, a, should approach 0.9 to 0.95 (with mi approximately 2.4-2.7)

as GSI approaches zero. The current Hoek-Brown criterion assumes for most rock

masses a is 0.5 and limits a to approximately 0.62 for a very poor quality rock mass. A

problem with simply modifying a is that a and mi (or mb) are interrelated.

The author has developed a new method of determining the parameters in the Hoek-

Brown criterion to overcome these problems. It is strongly suggested that the intact rock

parameters mi & ai should be obtained using triaxial testing and statistical methods

discussed in Chapter 3. The author has provided approximate methods of determining

mi and ai where no triaxial test results are available. Equations have been derived for

rock mass to address the limit (ab ≈0.95, mb ≈2.5, sb =0) of very poor quality rock

masses. The equations developed allow for a reduction in mb from mi (and associated

increase from ab from ai) and sb from si to this limit. A summary of the method is

presented below.

The basic form of the shear strength equation remains unchanged from the Hoek-Brown

criterion.

α

σσ

σσσ

+

′+′=′ s

m

cici

331 (7.5)

Page 488: Shear Strength of Rock

Conclusions and Recommendations Page 7.6

For intact rock m = mi and α = αi. These should preferably be measured from triaxial

tests on intact rock samples. Alternatively an approximation can be made using the

uniaxial compressive strength, σci, and tensile strength, σti, of the intact rock and the

equations below.

ti

ciim

σσ

= (7.6)

++=

7exp1

2.14.0

ii m

α (7.7)

The estimation of mb, αb and sb can be made using the following equations:

=5.2

100min

GSImm

i

b (7.8)

( )

−−+=

i

biib m

m3075exp9.0 ααα (7.9)

( )

=1

1585exp

min

GSI

sb (7.10)

The equations presented by Hoek et al (2002) can be used to estimate the cohesion, c,

and friction angle, φ, of the rock mass, as the form of the Hoek-Brown equation has not

been changed.

Page 489: Shear Strength of Rock

Conclusions and Recommendations Page 7.7

7.2 RECOMMENDATIONS FOR FURTHER RESEARCH

7.2.1 The Analysis of Concrete and Masonry Dams

The analysis of CONGDATA and the method for predicting probabilities of failure of

concrete and masonry dams is based on field data of varying quality. Further detailed

analysis of new incidents would improve the confidence in the conclusions presented in

this thesis. Further detailed information on the geology of the foundations of dams

would allow a better prediction of the likelihood of failure. Research into the

effectiveness of monitoring and warning systems using the outcomes from this thesis

would be of value.

The author believes that it is better to do a probabilistic analysis of stability modelling

uncertainty in the geology, shear strengths of the foundation and foundation pore

pressures (uplift) as modified by grouting and drainage.

Where large defects exist below a dam the shear strength in the foundation will be

governed by these defects. As discussed in Section 7.2.2 the shear strength of field scale

defects is still poorly understood. Further work in this area is required. Studies could

examine large-scale failures, preferably with insitu shear tests and laboratory scale shear

tests for comparison. However, these would be limited in number and quality.

Alternatively studies could use numerical modelling to look at the effect of increasing

the scale of defects. The use of the program PFC which models the movement and

interaction of circular particles by the distinct element method has shown some promise

in this area.

7.2.2 The Shear Strength of Rock Masses

The methods presented for estimating the shear strength of intact rock and rockfill are

based on substantial databases. These provide good bounds on the shear strength of rock

masses. The development of the equations for estimating the strength of the transitional

rock masses is based on a limited amount of field and laboratory data. Further analysis

and reporting of well-documented failures and lab testing of rock masses of varying

quality would improve the confidence in the results presented in this thesis and would

also provide a better understanding of the degree of uncertainty in the results obtained

Page 490: Shear Strength of Rock

Conclusions and Recommendations Page 7.8

by the equations presented in this thesis. The publishing of more data on failures would

also assist in improving the slope design curves presented in this thesis.

The equations for rock masses provided in this paper are principally for cohesionless

rock masses. Further work could be carried out to assess cohesive rock masses.

Modifications to the parameter s based on cohesive properties of the rock mass would

allow the Hoek-Brown criterion to better model these types of rock masses at low

confining stresses. This would be of value for predicting strengths for pit slope benches.

The effect of the intermediate principal stress, σ′2, could be incorporated into the

equations for intact rock and ultimately rock masses. The use of Lade’s (1993) work

would be of benefit here.

Page 491: Shear Strength of Rock

Appendix Page A.1

APPENDIX A: CONGDATA DATABASE

The full CONGDATA database is contained on the accompanying CD-ROM.

APPENDIX B: DAM LIST - FAILURES

Table B1. Dam list - failures

Dam Name Country Dam Type Year Commissioned

Year Failed

Hlf (m)

Kohodiar India PG/TE 1963 1983 36

Zerbino Italy PG 1925 1935 16

Mohamed V Morocco PG 1966 1963 62

Torrejon-Tajo Spain PG 1967 1965 62

Xuriguera Spain PG 1902 1944 42

Bayless (A) USA PG 1909 1910 17

Bayless (B) USA PG 1909 1911 17

Elwha River USA PG 1912 1912 51

Hauser Lake II USA PG 1911 1969 40

St Francis USA PG 1926 1928 62

Cheurfas Algeria PG(M) 1884 1885 42

Fergoug I Algeria PG(M) 1871 1881 43

Fergoug II Algeria PG(M) 1885 1927 43

Habra (A) Algeria PG(M) 1871 1872 40

Habra (B) Algeria PG(M) 1872 1881 40

Habra (C) Algeria PG(M) 1881 1927 40

Sig Algeria PG(M) 1858 1885 21

Bouzey France PG(M) 1881 1895 26

Chickahole India PG(M) 1966 1972 30

Khadakwasla India PG(M) 1879 1961 33

Kundli India PG(M) 1924 1925 45

Pagara India PG(M) 1927 1943 30

Tigra India PG(M) 1917 1917 28

Santa Catalina Mexico PG(M) 1900 1906 15

Granadillar Spain PG(M) 1930 1933 22

Puentes Spain PG(M) 1791 1802 69

Elmali I Turkey PG(M)/TE 1892 1916 23

Angels USA PG(M) 1895 1895 16

Austin (A) USA PG(M) 1893 1900 21

Lower Idaho Falls USA ER/PG(M) 1914 1976 15

Page 492: Shear Strength of Rock

Appendix Page A.2

Dam Name Country Dam Type Year Commissioned

Year Failed

Hlf (m)

Lynx Creek USA PG(M) 1891 1891 15

Komoro Japan CB 1927 1928 16

Selsford Sweden CB/TE 1943 1943 21

Ashley USA CB 1908 1909 18

Overholser USA CB 1920 1923 17

Vega de Tera Spain CB(M) 1956 1959 35

Austin (B) USA CB(M) 1915 1915 20

Stony River USA CB(M) 1913 1914 15

Gleno Italy MV 1923 1923 35

Leguaseca Spain MV 1958 1987 20

Malpasset France VA 1954 1959 66

Moyie River USA VA 1924 1926 16

Vaughn Creek USA VA 1926 1926 20

Meihua China VA(M) 1981 1981 22

Bacino di Rutte Italy VA(M) 1952 1965 15

Gallinas USA VA(M) 1910 1957 32

Page 493: Shear Strength of Rock

Appendix Page A.3

APPENDIX C: DAM LIST - POPULATION OF DAMS

Table C1. Dam list - USBR population

Dam Name Type Year Commissioned

Height (m)

Altus PG 1945 33.5

American Falls PG 1927 31.5

Angostura PG 1949 58.8

Black Canyon PG 1924 55.8

Brantley PG 1988 33.5

Camp Dyer PG 1929 24.1

Canyon Ferry PG 1954 68.6

Elephant Butte PG 1916 91.7

Folsom PG 1956 103.6

Friant PG 1942 97.2

Grand Coulee PG 1942 167.6

Jackson Lake PG 1911 20

Keswick PG 1950 47.9

Kortes PG 1951 74.4

Marshall Ford PG 1942 84.7

Nimbus PG 1955 26.5

Olympus PG 1949 21.3

Savage Rapids Diversion PG 1921 13.1

Shasta PG 1945 183.5

Upper Stillwater PG 1988 88.4

Yellowtail Afterbay PG 1965 21.9

Bartlett CB/MV 1939 94

Coolidge (BIA) CB/MV 1928 75.9

Minidoka CB 1906 26.2

Pueblo CB 1975 76.2

Red Bluff Diversion CB 1963 15.8

Stony Gorge CB 1928 42.4

Thief Valley CB 1932 22.3

Anchor VA 1960 63.4

Arrowrock VA 1915 106.7

Buffalo Bill VA/PG 1910 106.7

Clear Creek VA 1914 25.6

Crystal VA 1976 98.5

Deadwood VA 1931 50.3

East Canyon VA 1966 79.2

Page 494: Shear Strength of Rock

Appendix Page A.4

Dam Name Type Year Commissioned

Height (m)

East Park VA 1910 42.4

Flaming Gorge VA 1964 153

Gerber VA 1925 26.8

Gibson VA 1929 60.7

Glen Canyon VA 1964 216.4

Hoover VA 1936 221.4

Horse Mesa VA 1927 93

Hungry Horse VA 1953 171.9

Monticello VA 1957 92.7

Mormon Flat VA 1926 68.3

Morrow Point VA 1968 142.6

Mountain Park VA 1975 40.5

Nambe Falls VA 1976 45.7

Owyhee VA/PG 1932 127.1

Parker VA 1938 97.5

Pathfinder VA(M) 1909 65.2

Santa Cruz VA 1929 46

Seminoe VA 1939 89.9

Stewart Mountain VA 1930 63.1

Swift VA 1967 62.5

Theodore Roosevelt VA(M) 1911 108.5

Warm Springs VA 1919 32.3

Wild Horse VA 1967 33.5

Yellowtail VA 1966 160

Page 495: Shear Strength of Rock

Appendix Page A.5

Table C2. Dam list - Australia/New Zealand population

Dam Name Type Year Commissioned

Height (m)

Bendora VA 1961 47 Cotter PG 1915 31 Lower Molongolo PG 1994 32 Scrivener PG 1963 33 Wrights PG 1989 16 Avon PG 1927 72 Back Creek VA 1937 15 Borenore Creek VA 1928 18 Bundanoon VA 1960 35 Burrinjuck PG 1928 93 Captains Flat PG 1939 19 Carcoar VA 1970 58 Cataract PG 1907 56 Chichester PG 1923 44 Coeypolly Creek No I VA 1932 19 Cordeaux PG 1926 67 Crookwell PG 1937 16 Danjera CB 1971 36 Deep Creek PG 1961 21.3 Dunn Swamp VA 1930 16 Flat Rock Creek VA 1933 16 Fountaindale VA 1915 15 Glenquarry Cut PG 1974 18 Greaves Creek VA 1942 19 Guthega PG 1955 33.5 Happy Jack PG 1959 76.2 Hume PG 1936 Ingleburn MV 1933 16 Island Bend PG 1965 48 Junction Reefs MV 1897 19 Keepit PG 1960 55 Lake Medlow VA 1907 21 Lake Rowlands CB 1953 25 Lithgow No 2 VA 1907 26 Loyalty Road PG 1995 30 Maldon Weir PG 1968 20 Manly PG 1892 20 Medway VA 1964 25 Middle Cascade (No 1) VA 1915 15 Molong PG 1987 16

Page 496: Shear Strength of Rock

Appendix Page A.6

Dam Name Type Year Commissioned

Height (m)

Mooney Upper VA 1961 28 Moore Creek VA 1898 19 Murray 2 VA 1968 42.7 Nepean PG 1935 82 Oaky River PG 1956 18 Oberon CB 1949 35 Parramatta VA(M) 1857 15 Porters Creek PG 1968 18 Puddledock Creek VA 1928 19 Redbank Creek VA 1899 15 Rylstone VA 1953 20 Suma Park VA 1962 35 Tallowa PG 1976 43 Tantangara PG 1960 45.1 Timor VA 1961 22 Tumut 2 PG 1961 46.3 Tumut 3 Pipeline PG 1971 34.7 Tumut Pond VA 1959 86.3 Umberumberka PG 1914 41 Upper Cordeaux No 2 VA 1915 22 Warragamba PG 1960 142 Warragamba Weir PG 1940 21 Wellington VA 1933 15 Winburndale PG 1936 22 Woodford Creek VA 1928 16 Woronora PG 1941 74 Wyangla PG 1971 85 Atiamuri PG 1958 46 Aviemore PG 1968 57 Clyde PG 1993 105 Lake Onslow VA 1982 17 Mangahao No. 1 PG 1926 36 Mangahao No. 2 PG 1924 32 Marslin VA 1982 19 Roxburgh PG 1956 70 Waihopai VA 1927 34 Waitaki PG 1934 37 Whakamaru PG 1956 Beardmore PG 1972 17 Boggabilla Weir PG 1991 16 Burdekin Falls PG 1987 55 Burton Gorge PG 1992 34

Page 497: Shear Strength of Rock

Appendix Page A.7

Dam Name Type Year Commissioned

Height (m)

Cedar Pocket PG 1984 20 Chinaman PG 1993 19 Cooloolabin PG 1979 20 Copperfield PG 1984 40 Dumbleton PG 1992 15 Ibis PG 1906 16.5 Julius MV 1976 38 Koombooloomba PG 1961 52 Kroombit PG 1992 23 Lake Manchester PG 1916 38 Leslie PG 1965 33 Little Nerang PG 1961 47 Moogerah VA 1961 37 North Pine PG 1975 46 Rifle Creek VA 1929 21 Somerset PG 1955 50 Theresa Creek PG 1982 19 Tinaroo Falls PG 1958 47 Greenstone Ck Dam VA 1969 20 Wappa PG 1961 20 Wuruma PG 1969 46 Aroona PG 1955 26.2 Barossa VA 1902 36 Beetaloo PG 1890 31 Clarendon Weir PG(M) 1896 15 Middle River PG 1968 20 Mount Bold VA 1938 58 Myponga VA 1962 52 Sturt VA 1966 41 Ullabidinie PG 1914 22 Ulbana PG 1911 11.1 Warren PG 1916 26 Yeldulknie PG 1913 17 Bowden 1984 18 Catagunya PG 1962 49 Clark VA 1949 67 Cluny PG 1967 30 Craigbourne PG 1986 25 Devils Gate VA 1969 84 Gordon VA 1974 140 Henty PG 1988 23 Lake Margaret PG 1918 17

Page 498: Shear Strength of Rock

Appendix Page A.8

Dam Name Type Year Commissioned

Height (m)

Liapootah PG 1960 40 Meadowbank CB 1966 43 Mount Paris CB 1936 18 Pine Tier PG 1953 39 Repulse VA 1968 42 Ridgeway VA 1919 59 Trevallyn PG 1954 33 Clover CB 1956 20 Dartmouth PG 1980 25 Evansford PG 1887 17 Glenmaggie PG 1927 37 Goulburn Weir PG 1891 15 Hume Weir 1919 Junction CB 1945 26 Lauriston CB 1941 33 Lower Stoney Creek PG 1875 21 Maroondah PG 1927 46 Mt Cole PG 1903 28 Nicholson River CB 1976 16 Rocklands PG 1953 28 Swingler PG 1977 18 Yallourn Storage CB 1961 21 Canning PG 1940 70 Conjurunup PG 1992 Harvey PG 1916 24 Kununurra Diversion 1963 20 Mundaring PG 1902 71 New Victoria PG 1991 52 Serpentine Pipehead PG 1957 16 Wellington PG 1933 37

Page 499: Shear Strength of Rock

Appendix Page A.9

Table C3. Dam list - Portugal population

Dam Name Type Year Commissioned

Height (m)

Alto Cavado PG 1964 29

Alem da Fazenda PG 1967 20

Carrapatelo PG 1972 57

Corgas PG 1991 25

Cova do Viriato PG 1962 28

Fratel PG 1973 43

Monte Novo PG 1982 30

Penha Garcia PG 1980 25

Pocinho PG 1982 49

Raiva PG 1981 36

Ranhados PG 1986 41

Regua PG 1973 42

Torrao PG 1988 70

Touvedo PG 1996 43

Valeira PG 1975 48

Gameiro PG/TE 1960 20

Andorinhas PG(M) 1945 25

Burgaes PG(M) 1940 30

Covao do Ferro PG(M) 1956 35

Freigil PG(M) 1955 17

Guilhofrei PG(M) 1938 49

Idanha PG(M) 1949 54

Lagoa Comprida PG(M) 1958 29

Poio PG(M) 1932 18

Povoa PG(M) 1928 32

Vale do Rossim PG(M) 1956 27

Penide PG(M) 1951 15

Caia CB/PG/TE 1967 52

Roxo CB/PG/TE 1968 49

Miranda CB 1961 80

Pracana CB 1951 60

Odivelas MV/TE 1972 55

Aguieira MV 1981 89

Alto Lindoso VA 1993 110

Bravura VA 1958 41

Cabril VA 1954 136

Caldeirao VA 1996 39

Page 500: Shear Strength of Rock

Appendix Page A.10

Dam Name Type Year Commissioned

Height (m)

Fagilde VA 1984 27

Fronhas VA 1984 62

Funcho VA 1991 49

Picote VA 1958 100

Varosa VA 1976 76

Vilarinho das Furnas VA 1972 94

Alto Rabagao VA/PG 1964 94

Bemposta VA/PG 1964 87

Castelo do Bode VA/PG 1951 115

Covao do Meio VA/PG 1953 25

Venda Nova VA/PG 1951 97

Alto Ceira VA 1949 36

Bouca VA 1955 65

Canicada VA 1955 76

Salamonde VA 1953 75

Santa Luzia VA 1942 76

Page 501: Shear Strength of Rock

Appendix Page A.11

APPENDIX D: CAUSES OF INCIDENTS

Table D1. Causes of incidents - all dams

Cause Fail Acc. Major Repairs

Total Cause Fail Acc. Major Repairs

Total

1.1.1 1 2 3 3.1.2 1 1 2

1.1.2 1 8 4 13 3.1.3 3 1 2 6

1.1.3 5 5 2 12 3.1.4 2 3 9 14

1.1.4 7 16 7 30 3.1.5 5 1 6

1.1.5 6 13 1 20 3.1.9 2 1 1 4

1.1.5.1 4 2 6 3.1.12 1 2 3

1.1.5.2 1 1 2 3.2 1 1

1.1.6 1 1 3.2.2 3 1 22 26

1.1.8 1 2 3 3.2.3 9 9

1.1.9 1 1 2 3.2.5 3 3

1.1.10 1 1 3.2.6 4 1 5

1.1.11 4 3 7 3.2.7 4 1 5

1.1.12 3 4 7 3.2.8 3 10 13

1.1.14 1 1 3.2.9 3 2 1 6

1.2.1 6 13 19 3.2.10 3 3

1.2.2 1 6 22 29 3.3.2 1 1 2 4

1.2.3 1 6 53 60 3.4.1 5 5

1.2.5 1 1 2 3.4.2 8 6 1 15

1.2.6 1 1 3.4.3 1 1

1.2.7 1 1 3.4.4 4 4

1.2.8 9 22 31 3.4.5 1 1

1.2.9 9 17 26 3.4.6 10 10

1.2.10 3 4 7 3.5.1 2 2 4

1.2.11 7 13 20 3.5.2 5 3 1 9

1.2.13 1 2 3 3.5.3 1 1

1.3.1 1 4 5 3.5.4 1 1 2

1.3.2 4 3 15 22 3.5.5 1 3 4

1.3.3 6 1 7 3.7.2 1 1

1.3.4 4 28 32 4.1.5 2 2

1.3.5 5 16 21 4.1.8 0

1.3.7 3 1 4 4.2.1 1 1

1.3.7.2 1 1 4.2.2 1 1

1.3.7.3 1 1 4.2.3 6 6

1.4.1 1 1 2 4.2.4 1 1

1.4.2 8 8 4.2.5 1 1 2

Page 502: Shear Strength of Rock

Appendix Page A.12

Cause Fail Acc. Major Repairs

Total Cause Fail Acc. Major Repairs

Total

1.4.3 1 1 2 4.2.6 1 1

1.4.4 1 1 2 4.2.7 1 2 3

1.4.6 1 2 3 4.2.8 4 1 5

1.4.7 2 3 5 4.2.9 1 2 3

1.5.1 1 2 2 5 4.2.10 1 1

1.5.2 2 4 6 12 4.2.12 3 13 16

1.5.4 2 3 5 4.2.13 2 12 14

1.5.5 2 2 4.4.2 1 1

1.5.6 1 1 4 6 4.4.3 1 1

1.6.1 2 2 4.4.4 3 1 4

1.7.1 1 1 4.5.1 1 1

1.7.2 8 8 4.5.5 4 4

2.3.9 5 5 4.6 1 10 5 16

4.6.1 1 1 4.9.1 2 2 4

4.6.2 1 1 2 4.9.2 2 2 4

4.6.3 1 1 4.11.1 1 1

4.7.1 6 13 10 29 4.11.6 10 6 16

4.7.2 4 1 5 4.11.7 1 4 5

4.7.3 1 1 4.12.6 1 1

4.7.4 1 1 5.1 5 5

4.7.6 1 1 2 5.3 4 1 5

4.7.7 1 1 5.4 9 2 11

4.7.8 4 9 13 6.1 1 1

4.7.9 1 3 4 6.2 5 2 7

4.8 2 16 6 24 Total 121 283 450 854

Page 503: Shear Strength of Rock

Appendix Page A.13

Table D2. Causes of incidents - PG dams

Cause Fail Acc. Major Repairs

Total Cause Fail Acc. Major Repairs

Total

1.1.1 1 1 4.1.5 2 2 1.1.2 2 2 4 4.1.8 0 1.1.3 4 3 1 8 4.2.1 1 1 1.1.4 4 7 5 16 4.2.2 1 1 1.1.5 1 8 1 10 4.2.3 6 6 1.1.5.1 1 2 3 4.2.4 1 1 1.1.5.2 1 1 4.2.5 1 1 2 1.1.6 1 1 4.2.7 1 2 3 1.1.9 1 1 4.2.8 1 1 2 1.1.10 1 1 4.2.9 1 1 1.1.11 1 3 4 4.2.12 1 13 14 1.1.12 4 4 4.2.13 11 11 1.2.1 8 8 4.4.3 1 1 1.2.2 1 15 16 4.4.4 1 1 1.2.3 1 40 41 4.5.1 1 1 1.2.5 1 1 4.5.5 4 4 1.2.7 1 1 4.6 1 7 4 12 1.2.8 2 15 17 4.6.2 1 1 1.2.9 2 11 13 4.7.1 2 5 10 17 1.2.10 1 3 4 4.7.2 1 1 2 1.2.11 1 7 8 4.7.3 1 1 1.3.1 4 4 4.7.4 1 1 1.3.2 2 2 15 19 4.7.6 1 1 1.3.4 1 6 7 4.7.7 1 1 1.3.5 1 2 3 4.7.8 9 9 1.3.7 1 1 4.7.9 2 2 1.4.1 1 1 4.8 4 3 7 1.4.6 2 2 4.9.1 1 1 2 1.5.1 1 1 2 4 4.9.2 2 2 1.5.2 1 1 3 5 4.11.1 1 1 1.5.4 1 1 4.11.6 5 4 9 1.5.5 2 2 4.11.7 4 4 1.5.6 4 4 4.12.6 1 1 1.6.1 2 2 5.1 2 2 1.7.1 1 1 5.3 2 2 1.7.2 8 8 5.4 2 2 4 3.1.4 1 1 6.1 1 1 3.2.2 1 1 6.2 3 1 4 3.2.8 1 1 Total 19 82 263 364

Page 504: Shear Strength of Rock

Appendix Page A.14

Table D3. Causes of incidents - PG(M) dams

Cause Fail Acc. Major Repairs

Total Cause Fail Acc. Major Repairs

Total

1.1.3 1 1 3.2.9 3 2 1 6

1.1.5 1 1 3.2.10 3 3

1.2.2 1 1 3.3.2 1 2 3

1.2.3 1 1 3.4.1 5 5

1.2.8 1 1 3.4.2 7 6 1 14

1.3.1 1 1 3.4.3 1 1

1.3.3 1 1 3.4.4 4 4

1.3.7 1 1 2 3.4.6 8 8

1.4.7 1 1 3.5.1 2 2 4

1.5.6 1 1 3.5.2 5 3 8

2.3.8 1 1 3.5.3 1 1

2.3.9 5 5 3.5.4 1 1

3.1.12 1 2 3 3.5.5 1 3 4

3.1.2 1 1 2 3.7.2 1 1

3.1.3 3 1 1 5 4.2.8 1 1

3.1.4 1 2 8 11 4.6 1 1

3.1.5 4 1 5 4.6.2 1 1

3.1.9 2 1 1 4 4.7.1 2 1 3

3.2 1 1 4.7.8 1 1

3.2.2 3 1 20 24 4.7.9 1 1

3.2.3 8 8 4.8 1 1

3.2.5 2 2 4.9.1 1 1

3.2.6 4 1 5 4.11.6 1 1

3.2.7 4 1 5 5.3 1 1

3.2.8 2 10 12 5.4 2 2

Total 62 39 80 181

Page 505: Shear Strength of Rock

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