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1994
Aspects of design and analysis of reinforced soildamsMohammad Reza MagharehUniversity of Wollongong
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Recommended CitationMaghareh, Mohammad Reza, Aspects of design and analysis of reinforced soil dams, Doctor of Philosophy thesis, Department of Civiland Mining Engineering, University of Wollongong, 1994. http://ro.uow.edu.au/theses/1227
ASPECTS OF DESIGN AND ANALYSIS OF
REINFORCED SOIL DAMS
A thesis submitted in fulfilment of the requirements for the award of the degree
DOCTOR OF PHILOSOPHY
from
THE UNIVERSITY OF WOLLONGONG
by
MOHAMMAD REZA MAGHAREH, BSc, MSc.
UNIVERSITY OF
DEPARTMENT OF CIVIL AND MINING ENGINEERING
July 1994
"To my late father who really was a Father and died when 1 was investigating this thesis
at the University of Wollongong. I was notable to participate in his occasional passing
ceremonies, or on the first anniversary of his passing."
"Godbless him."
STATEMENT
I here certify that the work presented in this thesis has not been submitted for a degree
to any other university or similar institution.
MOHAMMAD REZA MAGHAREH
ABSTRACT
This thesis was concerned with the design, analysis and geometrical optimisation of
reinforced soil dams (RSDs, singular RSD) and aimed to develop a computer program
for these tasks. In order to achieve this objective, the following tasks were carried out
as parts of this thesis.
(a) Comprehensive literature survey. This part included an overview of the history
of reinforced soil, its application, material components, design considerations,
construction methods, and economic considerations of reinforced soil. The
fundamentals of design and analysis of conventional earth dams were also considered.
This included the history, classification, factors governing the choice of dam type,
stability analysis, design criteria, and limitations of conventional earth dams. This
project also gave a detailed evaluation and design criteria of a number of existing
RSDs. A summary of recent investigations on the behaviour of RSDs was outlined.
This continued by considering the classification of RSDs and the forces acting on them.
(b) Stability analysis of RSDs. This part was focused on some formulae in order to
optimise the cross sectional area of RSDs. The external stability analysis of RSD was
evaluated as a whole structure based on analytical approach. Some design formulae
were given for RSD optimisation concerning the minimum base length required against
sliding, overturning, overstressing, bond failure, and rupture failure. The internal
stability of RSD was also taken into account based on a semi-empirical method. Some
empirical relationships were proposed to eliminate the tangent discontinuity which exists
in the Coherent Gravity Method formulae. These relationships reflect the non-linearity
indicated by the field data and eliminate unknown parameters existing in the formulae of
Modified Coherent Gravity Method. They also offer a better fit with the available field
observations. Relationships between the lateral earth pressure and the apparent friction
factor with the fill depth were proposed. The apparent friction factor versus the
reinforcement length were also undertaken.
i
(c) Analysis of the behaviour under seismic loads. Although many researchers have
investigated the effects of earthquakes on soil dams, many problems are still unsolved,
specially for RSDs. A comparison between the natural frequency of conventional earth
dams and RSDs were considered in this project. The practice of inserting
reinforcement into the earth dam material allows reduction in fill volume and reduction
in displacement. However, this also leads to an increase in the natural frequency of
such structures compared with conventional earth dams. This may increase the
possibility of failure. The natural frequency of RSD is increased because of its
geometry and its overall stiffness. In this project, the increases in natural frequency of
RSDs due to these two major factors were separately discussed. Formulae concerning
the magnification of the natural frequency of the structure due to reinforcement
insertion were derived, and in some cases tabulated and plotted.
(d) Development of a computer program. A computer program was developed for
geometrical optimisation and stress-strain analysis of RSD. The outcomes of the
program are (a) geometrical optimisation of RSD based on analytical and semi-
empirical formulae, and (b) stress-strain analysis of the optimised RSD based on the
finite element method.
(e) Analysis of models of RSDs. Six models of RSDs were analysed for various
heights and safety factors to find the optimum geometry. A 30m high RSD was also
analysed considering the following configurations: (a) without reinforcements, (b) with
the assumed increased stiffness of the soil fill, (c) with horizontal reinforcements, and
(d) with inclined reinforcements to evaluate the variation of stresses versus the
direction of reinforcements. It was concluded that putting reinforcements in soil dams
decreases displacements and stresses values.
ii
ACKNOWLEDGMENT M y special thanks go to the Iranian Ministry of Culture and Higher Education, because
this thesis was made possible by its scholarship.
I am also grateful to the Department of Civil Engineering, University of Wollongong
N S W , Australia for encouragement and facilities for research. I wish to record my
utmost gratitude to Dr. R. M . Arenicz for his supervision of this thesis. Also, the
comments and suggestions of Professor R. N. Chowdhury are acknowledged and
appreciated.
M y gratitude goes to m y wife, Mrs. Z. G. Haghighi for her assistance during the past
three years. I also thank Reinforced Earth Company Pty Ltd in Gosford for allowing
access to its library and sending some brochures during the initial stage of this project.
iii
TABLE OF CONTENTS
ABSTRACT i
ACKNOWLEDGMENT iii
TABLE OF CONTENTS iv
LIST OF FIGURES ix
LIST OF TABLES xv
CHAPTER ONE: INTRODUCTION, AIMS AND SCOPE 1
1.1 INTRODUCTION 1
1.2 AIMS AND SCOPE OF THE THESIS 2
1.3 THESIS OVERVIEW 3
CHAPTER TWO: PRINCIPLES OF REINFORCED EARTH 6
2.1 INTRODUCTION 6
2.2 HISTORY 7
2.3 APPLICATIONS 8
2.4 MATERIALS 14
2.4.1 Soil '. 15
2.4.2 Facing 17
2.4.3 Reinforcement 18
2.5 SOIL-REINFORCEMENT INTERACTIONS 22
2.5.1 Development of theory 22
2.5.2 Stability considerations 36
2.6 CONSTRUCTION METHODS AND STRUCTURAL SYSTEMS 39
2.7 DURABILITY 42
2.8 COSTS AND ECONOMICS 46
iv
2.9 CONCLUSIONS 49
CHAPTER THREE: EVALUATION OF SOIL D A M S 51
3.1 INTRODUCTION 51
3.2 CONVENTIONAL EARTH D A M S 52
3.2.1 History 52
3.2.2 Classification 53
3.2.3 Associated facilities 56
3.2.4 Factors governing selection of a type 56
3.2.5 Materials 57
3.2.6 Design procedure 57
3.2.7 Sections of earth dams 58
3.2.8 Limitations of conventional earth dams 62
3.3 R E I N F O R C E D SOIL D A M S 64
3.3.1 History of reinforced soil dams 64
3.3.2 Other investigations 69
3.3.3 Classification of reinforced soil dams 94
3.4 F O R C E S A C T I N G O N SOIL D A M S 98
3.4.1 External water pressure 98
3.4.2 Internal water pressure and seepage gradients 100
3.4.3 Uplift pressure 106
3.4.4 Ice pressure 107
3.4.5 Silt pressure 108
3.4.6 Weight of structure 109
3.4.7 Earthquake force 110
3.4.8 Reaction of foundation 112
3.4.9 Load combinations 114
3.5 C O N C L U S I O N S 116
v
CHAPTER FOUR: STABILITY ANALYSIS OF REINFORCED SOIL D A M S 118
4.1 INTRODUCTION 118
4.2 EXTERNAL STABILITY 119
4.2.1 Sliding 121
4.2.2 Overturning 125
4.2.3 Overstressing 130
4.3 INTERNAL STABILITY 137
4.3.1 Coefficient of lateral earth pressure 138
4.3.2 Apparent friction factor 142
4.3.3 Extension of failure zone 149
4.3.4 Reinforcement effect 150
4.3.5 Design equations 153
4.3.6 Internal erosion and piping failure 155
4.3.7 Hydraulic fracture failure 159
4.3.8 Distortional settlement 161
4.4 CONCLUSIONS 163
CHAPTER FIVE: BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOAD 165
5.1 INTRODUCTION 165
5.2 FREE H A R M O N I C VIBRATION 167
5.3 FORCED H A R M O N I C VIBRATIONS 169
5.4 DAMPING 171
5.5 N A T U R A L FREQUENCY 172
5.5.1 Stiffness function 174
5.5.2 Shape function 176
5.6 EXAMPLE 180
5.7 CONCLUSIONS 184
vi
CHAPTER SIX: COMPUTER PROGRAM 185
6.1 INTRODUCTION 185
6.2 FINITE ELEMENT FORMULAE 185
6.2.1 Elastic behaviour of soil 186
6.2.2 Inelastic behaviour of soil 188
6.2.3 Soil-reinforcement interaction 190
6.3 RSDAM COMPUTER PROGRAM 195
6.3.1 Purpose 196
6.3.2 Input data 196
6.3.3 Program operation 197
6.3.4 Output data 201
6.4 CONCLUSION 202
CHAPTER SEVEN: ANALYSIS 203
7.1 INTRODUCTION 203
7.2 GEOMETRICAL OPTIMISATION 204
7.3 NUMERICAL ANALYSIS 210
7.3.1 Loading steps 210
7.3.2 Mesh information 211
7.3.3 Material property 213
7.3.4 Stages of analysis 214
7.3.5 Displacement variation 214
7.3.6 Stress variation 215
7.3.7 Variation of the vertical facing displacement 216
7.4 CONCLUSIONS 221
CHAPTER EIGHT: CONCLUSIONS AND RECOMMENDATIONS 224
8.1 INTRODUCTION 224
8.2 PART A- THEORETICAL OPTIMISATION AND ANALYSIS 224
vii
8.2.1 Geometrical optimisation 224
8.2.2 Semi-empirical relationships 225
8.2.2 Natural frequency 227
8.3 PART B-NUMERICAL ANALYSIS 228
8.3.1 Computer program 229
8.3.1 Results of analysis 230
8.4 RECOMMENDATIONS 232
8.4.1. Reinforced soil arch dams 232
8.4.2. Cross sectional optimisation 232
8.4.3. Behaviour of reinforcement 233
8.4.4 Reinforcement width 233
8.4.5 Natural frequency 233
8.4.6 Seismic load based on dynamic analysis 234
8.4.7 Stress concentration 234
REFERENCES: Rl
APPENDICES Al
APPENDIX A- EARTH DAM FAILURES A2
APPENDIX B- TYPICAL TYPES OF DAM'S SOIL A5
APPENDIX C-ICE PRESSURE TABLES A8
APPENDIX D- BOND AND BREAK FAILURES EQUATIONS A9
APPENDIX E- RSDAM PROGRAM FLOWCHART Al 1
APPENDIX F- RUNNING THE RSDAM PROGRAM ,. A17
INTRODUCTION A17
INPUT DATA A17
OUTPUT DATA A24
EXAMPLE A30
APPENDIX G- RSDAM PROGRAM LISTING A77
viii
LIST OF FIGURES
Fig. 2.1.1 Reinforced earth components 7
Fig. 2.3.1 Reinforced soil arch 9
Fig. 2.3.2 The slot storage system 10
Fig. 2.3.3 Stepped highway structures 10
Fig. 2.3.4 Rock crushing plant 11
Fig. 2.3.5 Typical section of sea wall 11
Fig. 2.3.6 The sea wall using Z-shaped panels 11
Fig. 2.3.7 Modes of embankment reinforcing 12
Fig. 2.3.8 Critical embankment orientations 13
Fig. 2.3.9 Typical cross-section of a RSD compared with a conventional earth
dam 14
Fig. 2.3.10 Cross-section of Vallon des Bimes dam 14
Fig. 2.4.2.1 Typical examples of shapes of facing panels 18
Fig. 2.4.3.1 Typical shapes of reinforcements 19
Fig. 2.4.3.2 A reinforcement system connected to a facing panel 20
Fig. 2.4.3.3 Facing panels and reinforcement systems of various techniques 23
Fig. 2.5.1.1 Improvement in strength due to reinforcement 24
Fig. 2.5.1.2 Increase in brittleness due to reinforcement 25
Fig. 2.5.1.3 Increase in G\ due to reinforcement 25
Fig. 2.5.1.4 Coulomb analysis 26
Fig. 2.5.1.5 Comparison of theoretical and experimental results 28
Fig. 2.5.1.6 Failure condition for constant o'r 29
Fig. 2.5.1.7 Friction angle <j>r as a function of <t>and F 30
Fig. 2.5.1.8 Increase in the friction angle of soil because of reinforcement 31
Fig. 2.5.1.9 Composite Mohr envelope 31
Fig. 2.5.1.10 The LCPC interpretation 32
Fig. 2.5.1.11 The Aa'3 interpretation 33
ix
Fig. 2.5.1.12 Variation of strength with aspect ratio 34
Fig. 2.5.1.13 Variation of Aa'3 with a'3 34
Fig. 2.5.2.1 The forms of failures 37
Fig. 2.5.2.2 a) Trapezoidal distribution pressure and b) Meyerhof distribution
pressure 38
Fig. 2.5.2.3 Comparison between maximum tension stress inside reinforcement 39
Fig. 2.6.1 The cross section of Concertina Method 41
Fig. 2.6.2 A typical section of facing of a Telescope Method 42
Fig. 2.6.3 A typical section of Sliding Method 42
Fig. 2.7.1 Development of corrosion 44
Fig. 2.7.2 Loss of thickness during time for galvanised steel and unprotected
steel 45
Fig. 2.8.1 Comparison between the height of the reinforced soil structures and
the percentage of the costs of reinforced soil relative to the costs of reinforced
concrete cantilever walls 47
Fig. 2.8.2 Economy versus height of structure 47
Fig. 2.8.3 Variation of percentage of total material cost with height of structure 48
Fig. 2.8.4 Comparison between the costs of reinforced soil structures and
reinforced concrete structures 49
Fig. 3.2.2.1 General classification of dams 55
Fig. 3.2.4.1 A general view of a composite dam 57
Fig. 3.2.7.1 Cross-section of a thin core earth dam 58
Fig. 3.2.7.2 Typical sections of impervious foundation of earth dams 60
Fig. 3.2.7.3 Typical sections for shallow pervious foundation of earth dams 61
Fig. 3.2.7.4 Typical sections for deep pervious foundation 63
Fig. 3.3.1.1 Vallon des Bimes dam 65
Fig. 3.3.1.2 L'Estella D a m 65
Fig. 3.3.1.3 A general view of Taylor Draw D a m 66
x
Fig. 3.3.1.4 Front face elevation and cross-section of Taylor Draw D a m 66
Fig. 3.3.1.5 a) The cross-section of Bridle Drift dam b)Downstream elevation
after the flood 67
Fig. 3.3.1.6 a) The cross-section of the Xonxa Dam, b) Reinforcing system
designed 68
Fig. 3.3.1.7 N e w section of earth dam at Lake Sherburne 68
Fig. 3.3.1.8 N e w section of Jamesville, N e w York dam 69
Fig. 3.3.2.1 Standard sections of reinforced embankments 70
Fig. 3.3.2.2 Relationship between embankment deformation, the strain
distribution of grid and saturation degree 71
Fig. 3.3.2.3 Embankment section used in stability analysis 72
Fig. 3.3.2.4 Embankment with geocell 75
Fig. 3.3.2.5 The observed and the predicted by F E M values of stress on steel
bars... 82
Fig. 3.3.2.6 The bearing forces applied to the plates 83
Fig. 3.3.2.7 Embankment 84
Fig. 3.3.2.8 Settlement along a horizontal section in the subsoil at the ground
level 84
Fig. 3.3.2.9 Settlement profile along a vertical section 85
Fig. 3.3.2.10. Vertical and principal stress distribution 85
Fig. 3.3.2.11 Stress distribution of reinforcement 86
Fig. 3.3.2.12 The geometry and finite element mesh of the embankment 87
Fig. 3.3.2.13 Stress and strain profiles 88
Fig. 3.3.2.14 Ground surface settlement 89
Fig. 3.3.2.15 Surface horizontal displacement 89
Fig. 3.3.2.16 Reinforcement strains and forces 90
Fig. 3.3.2.17 Stranstead Abbotts Embankment 91
Fig. 3.3.2.18 Displacement distribution along ground surface 93
xi
Fig. 3.3.2.19 Pore water pressure at point B varying with time 93
Fig. 3.3.2.20 Tension distribution in the grid 94
Fig. 3.3.3.1 Cross-sections of a homogeneous fill RSD and a zoned RSD 95
Fig. 3.3.3.2 A typical cross-section of an impervious upstream shell dam 95
Fig. 3.3.3.3 A central core RSD compared to an inclined core RSD 96
Fig. 3.3.3.4 A general classification of RSDs based on material used and cross-
section shape 96
Fig. 3.3.3.5 A classification of RSDs based on their foundations 97
Fig. 3.3.3.7 A possible classification of RSDs 97
Fig. 3.3.3.6 Cross-section of an imaginary reinforced soil arch dam 98
Fig. 3.4.1.1 External water pressure acting on an earth dam 99
Fig. 3.4.1.2 External water pressure acting on a vertical downstream face RSD 99
Fig. 3.4.2.1 Seepage lines through (a) a homogeneous earth dam without
blanket (b) a homogeneous earth dam with a drainage blanket (c) a non-
homogeneous earth dam 101
Fig. 3.4.2.2 Seepage lines through: (a) a RSD without blanket (b) a RSD with a
drainage blanket (c) a zoned RSD 101
Fig. 3.4.2.3 The seepage line through a RSD compared with the seepage line
through a conventional earth dam with the same height 103
Fig. 3.4.2.4 Seepage line through the foundation of a conventional earth dam 104
Fig. 3.4.2.5 Seepage line through the foundation of a RSD 104
Fig. 4.3.5.1 A comparison between the path of water under a conventional
earth dam and a RSD with the same height 105
Fig. 3.4.3.1 Uplift pressure acting on an impervious rigid foundation dam 106
Fig. 3.4.3.2 Uplift water pressure acting on a pervious foundation dam 107
Fig. 3.4.4.1 Location of ice pressure acting on a dam 108
Fig. 3.4.5.1 Silt pressure 109
Fig. 3.4.6.1 Zoned RSD 110
xii
Fig. 3.4.7.1 The horizontal earthquake force due to water slashing 112
Fig. 3.4.7.2 The value of Cp 113
Fig. 3.4.8.1 Trapezoidal reaction of foundation 113
Fig. 3.4.8.2 Possible non-linear reaction of foundation 114
Fig. 4.1.1 Stability analysis of RSDs 118
Fig. 4.2.1 The cross section of a parametric RSD with imaginary horizontal
layers 119
Fig. 4.2.2 Forces acting on a RSD 120
Fig. 4.2.3.1 Reactions of foundation 130
Fig. 4.3.1.1 Coefficient of lateral earth pressure 139
Fig. 4.3.1.2 Comparison between the formula (for <j)=45) and the results of
observed experiments 139
Fig. 4.3.1.3 Comparison between the field data and experimental formulae 141
Fig. 4.3.2.1 Apparent friction factor 143
Fig. 4.3.2.2 Comparison between theoretical and typical values of apparent
friction factor for smooth strips 145
Fig. 4.3.2.3 Comparison between theoretical and typical values of apparent
friction factor for ribbed strips 145
Fig. 4.3.2.4 The results of pull-out tests 147
Fig. 4.3.2.5 Linear relationship between f* and the ratio H/L 148
Fig. 4.3.3.1 Effective length of reinforcing strip 150
Fig. 4.3.6.1 Piping through a homogeneous fill RSD without drainage blanket 156
Fig. 4.3.6.2 Piping through a homogeneous fill RSD with a horizontal drainage
blanket 156
Fig. 4.3.6.3 Piping through a zoned RSD 157
Fig. 4.3.6.4 Piping under a RSD 158
Fig. 4.3.6.5 Use of heavy stones in downstream side for preventing piping 158
Fig. 4.3.7.1. Idealised flow gradients in the upstream part of RSD 160
xiii
Fig. 4.3.7.2 Seepage line through a homogeneous fill RSD without drainage
blanket 160
Fig. 4.3.8.1 The distortion settlement of RSD 162
Fig. 5.2.1 a) A typical RSD divided into several imaginary layers b)the first
and the second blocks of the RSD 167
Fig. 5.3.1 The relation between N and n 171
Fig. 5.5.1 a) A typical conventional earth dam and b) a typical RSD with
vertical downstream facing 173
Fig. 5.5.1.1 Comparison between reinforced and unreinforced soil elements 175
Fig. 5.5.1.2 Variation of *F versus p for yvlys=2>.9, M=2.63 176
Fig. 5.5.2.1 Minimum slope ranges of a conventional earth dam compared to
an equivalent RSD 177
Fig. 5.5.2.2 Maximum slope ranges of a conventional earth dam compared to
an equivalent RSD 178
Fig. 5.5.2.3 Variation of (D versus Wt/H 179
Fig. 5.6.1 The illustrative example of a reinforced and a conventional earth
dam 180
Fig. 5.6.2 The illustrative example of the conventional earth dam 181
Fig. 5.6.3 Pseudo acceleration verses period, T, for various values of damping
coefficients based on four major earthquakes happened in U S A 182
Fig. 6.2.1.1 A n elastic stress-strain curve 186
Fig. 6.2.2.1 Possible elasto-plastic stress-strain curves for an element of soil
under unload-reload condition 189
Fig. 6.2.3.1 Reinforcement elements within a. RSD 190
Fig. 6.2.3.2 A typical reinforcement carrying the horizontal forces induced in
the nodal points of reinforcement 192
Fig. 6.3.3.1 Abbreviated flowchart 198
Fig. 6.3.3.2 A general view of a typical RSD showing subdivisions 200
xiv
Fig. 7.2.1 Minimum required base length versus height for a 20m high dam 206
Fig. 7.2.2 Minimum required base length versus height for a 25m high dam 208
Fig. 7.2.3 Minimum required base length versus height for a 30m high dam 209
Fig. 7.3.1 The 30m high vertical downstream earth dam 210
Fig. 7.3.1.1 Variations of seepage lines 211
Fig. 7.3.2.1 A general view of the RSD showing nodal points 212
Fig. 7.3.2.2 Positions of horizontal reinforcements 212
Fig. 7.3.2.3 Positions of inclined reinforcements 212
Fig. 7.3.5.1 The dam before loading 215
Fig. 7.3.5.2 Displacement result of the dam 217
Fig. 7.3.6.1 Variations of principal stresses acting on the elements 218
Fig. 7.3.6.2 Variations of horizontal stresses acting on the elements 219
Fig. 7.3.7.1 Variations of vertical and horizontal movements of the vertical
facing based on -0.08m base displacement 220
Fig. 7.3.7.2 Variations of vertical and horizontal movements of the vertical
facings based on 0.15m base displacement 220
Fig. IF The explanation of elements A20
Fig. 2F The consequence of the nodal points A21
Fig. 3F The cross section of a parametric RSD with imaginary horizontal layers A26
Fig. 4F The consequence of the nodal points A32
xv
LIST OF TABLES
Table 2.4.1.1 Grading restriction for non-cohesion material 16
Table 2.4.1.2 Grading restrictions for cohesive frictional material 17
Table 2.4.3.1 Degradation resistance of various synthetic fibres 19
Table 2.4.3.2 Properties of typical sheet and strip material 20
Table 2.4.3.3 Frictional properties for various strip material 20
Table 2.4.3.4 A comparison between the properties of general polymers 21
Table 2.5.2.1 Equations for calculation of the maximum tension in the
reinforcements of a vertical reinforced soil structure 38
Table 2.7.1 Corrosion allowance for metallic components exposed to various
environment 45
Table 3.2.2.1 Classification of dams based on storage and height 53
Table 3.3.2.1 Test cases 70
Table 3.3.2.2 The property of fill material... 71
Table 3.3.2.3 Analysis for the integration effect at collapse without
reinforcement 74
Table 3.3.2.4 Properties of reinforcing elements 76
Table 3.3.2.5 The summarised condition of the parameters used 77
Table 3.3.2.6 The property of foundation and embankment soil 79
Table 3.3.2.7 The constants used for finite element analysis..... 79
Table 3.3.2.8 The methods used for analysing maximum tensile force and their
formulae 80
Table 3.3.2.10 The properties of soil used in embankment 87
Table 3.3.2.11 The properties of soil used in foundation 87
Table 3.3.2.11 The results of analysis 88
Table 3.3.2.12 Summary of predictions and observations 90
Table 3.3.2.13 Physical and mechanical parameters of soils 91
Table 3.3.2.14 Computation parameters of foundation soils 92
xvi
Table 3.4.7.1 Earthquake acceleration HI
Table 3.4.9.1 Cases of load combinations 115
Table 4.2.1 Summary of the forces in sliding and overturning states 121
Table 4.2.1.1 Results of driving and resistance forces acting on RSD in sliding
situation 122
Table 4.2.2.1 Results of driving and resistance moments acting on the dam in
overturning situation 126
Table 4.2.3.1 Summary of the forces used in analysis of soil bearing capacity 131
Table 4.3.5.1 Factors of safety formulae against both break and bond failures
based on Proposed Method 154
Table 7.2.1 Final widths of the dam computed by the program 204
Table 7.2.2 Assumptions accepted during the analysis of the models 205
Table 7.3.3.1 Assumed soil properties 213
Table 7.3.3.2 Assumed concrete facing properties 213
Table 7.3.3.3 Assumed interface element properties 213
Table 7.3.3.4 Assumed reinforcement properties 214
Table L A Earth dam failures due to hydraulic problems A 2
Table 2.A Earth dam failures due to structural failures A3
Table 3.A Earth dam failures due to seepage failures A 4
Table L B Typical types of soil in or under dams A5
Table 2.B Typical types of soil in or under dams A 6
Table 3.B Soil performance in or under dams A 7
Table l.C Ice pressure A 8
Table l.D Factors of safety formulae against both break and bond failures
based on C G M A 9
Table 2.D Factors of safety formulae against both break and bond failures
based on M C G M A10
xvii
INTRODUCTION, AIMS AND SCOPE CHAPTER ONE
CHAPTER ONE
INTRODUCTION, AIMS AND SCOPE
1.1 INTRODUCTION
A significant part of the cost of any dam is associated with its design and construction.
This indicates that there is a need for a careful assessment of the cost involved. A right
type of structure with a suitable shape would reduce the cost considerably. The use of
an earth dam instead of some other types would usually reduce the cost. For example,
an earth dam can be constructed at less than half the cost of a concrete dam with equal
capacity and height. However, the use of an earth dam is restricted by its geometrical
area, weir restriction, height limitation and the availability of a sufficient amount of
earth material. These restrictions can be alleviated by the use of a reinforced soil dam
(RSD, plural RSDs) with an additional reduction in material cost. For example, at least
two RSDs may be constructed with the material needed for one earth dam.
Soil reinforcement is a reliable and suitable method for augmenting strength and
solidity of soil. Reinforced soil can be substituted for concrete and soil in the
construction. In the current form of reinforced soil, which was introduced by H. Vidal
in the 1960s, the soil is reinforced by strips located in particular directions regular in a
pattern. The concept of reinforced soil is based on making a composite structure by
frictional action between the soil and the reinforcements.
Although many researchers have been investigating the behaviour of reinforced soil,
there are still many unsolved problems in the analysis and design of RSDs. Shape,
surface properties, dimensions, strength and stiffness of the reinforcement are the main
parameters that affect the performance and behaviour of a RSD. The location,
orientation and spacing of reinforcement affects the soil reinforcement interaction.
1
INTRODUCTION, AIMS AND SCOPE CHAPTER ONE
Grading, particle size, mineral content, index properties, degree of saturation, density,
overburden pressure and state of stress are other parameters that change the behaviour
of the soil used for RSDs. The stability of RSDs under some loads such as dead load,
uplift pressure, hydrostatic pressure and, particularly, earthquake have not yet been
fully investigated. The seepage effects and the piping phenomenon in RSDs should
also be investigated. These problems clearly show the need for further research in this
area.
RSDs, based on their shape, can be classified into four groups; vertical downstream
face, vertical upstream face, inclined downstream face, and inclined upstream face.
The design and analysis of RSDs are affected by the type of dam foundation, material
homogeneity, type and shape of reinforcements, and shape and position of the core in
the zoned type. In RSDs, with a vertical downstream side, the material costs can be
reduced by eliminating the downstream material, and allowing for the construction of a
spillway on the top.
1.2 AIMS AND SCOPE OF THE THESIS
This thesis is concerned with the investigation of design and analysis of RSDs. The first
goal of the study is to contribute a better understanding for this analysis and design.
Some analytical formulae and some semi-empirical formulae are derived in order to
achieve this objective. Detailed tasks of this project may be undertaken in as follows:
(1) Literature review concerning the concept of reinforced soil and its
behaviour in RSDs.
(2) Literature review concerning the evaluation of conventional earth
dams and RSDs.
(3) Literature review concerning the soil reinforcement interaction.
(4) Literature review concerning the structural stability analysis of
RSDs.
2
INTRODUCTION, AIMS AND SCOPE CHAPTER ONE
(5) Study of the forces acting on soil dams and the behaviour of RSDs
under the forces.
(6) Classification of RSDs.
(7) Comparison of the behaviour of conventional earth dams and RSDs
under seismic loads.
(8) Consideration of the minimum required base length of RSD (against
sliding, overturning, overstressing, bond failure and break failure)
required for its geometrical optimisation.
(9) Analysis of semi-empirical relationships needed for internal stability
of reinforced soil structures.
(10) Development of a computer program (called RSDAM) for
geometrical optimisation and stress-strain analysis of RSDs.
(11) Analysis of models of RSDs using the computer program.
A major part of the project was concerned with the development of the computer
program using: (a) the analytical approach for geometrical optimisation of RSDs, and (b)
the finite element method to model the behaviour of the dam. Two-dimensional
quadrilateral elements and a general stress-strain curve are assumed in the program to
simulate the behaviour of the soil. A non-linear hyperbolic stress-strain curve is used to
represent the primary loading, while a linear response is assumed for the unloading or
reloading behaviour of the soil. The interface elements are used in the program to
permit relative movement between the soil and the concrete facing panels.
1.3 THESIS OVERVIEW
Chapter 2 gives a comprehensive literature survey on the mechanics of reinforced soil.
A n overview of the history of reinforced earth, its application, material components,
fundamental behaviour, design considerations, construction methods, and construction
cost of reinforced soil are included in this chapter.
3
INTRODUCTION, AIMS AND SCOPE CHAPTER ONE
Chapter 3 presents fundamentals of design and analysis of conventional earth dams. It
includes the history, classification, factors governing the choice of dam type, stability
analysis, design criteria, and limitations of conventional earth dams. This chapter also
considers detailed evaluation and design criteria of a number of existing RSDs. An
historical perspective, stability analysis, and a summary of recent investigations into the
behaviour of RSDs are investigated. This chapter continues by considering the
classification of RSDs and the forces acting on them. In reality, there are no major
differences between the forces acting on a RSD and the forces acting on other types of
dams. However, the behaviour of RSD and other dams is different in withstanding the
forces. The forces resulting from the weight of structure, the pressures of water, silt,
ice, seepage and earthquake are considered here.
Chapter 4 presents a stability analysis of the RSD to optimise the cross sectional area.
This includes the external stability analysis of the dam as a whole structure based on
analytical approach. Some proposed formulae are given for earth dam optimisation
concerning the minimum base length of the dams required against sliding, overturning,
overstressing, bond failure, rupture failure, hydraulic fracture failure. The semi-
empirical relationships of Coherent Gravity Method (CGM) and Modified Coherent
Gravity Method (MCGM) are taken into account. The relationships between the lateral
earth pressure and the apparent friction factor with fill depth are proposed to eliminate
the tangent discontinuity which exists in the CGM formulae and the unknown
parameters which exists in MCGM formulae. These relationships reflect the non-
linearity indicated by the field data and offer a better fit with the available field
observations The apparent friction factor versus the reinforcement length are also
undertaken in this chapter.
Chapter 5 considers the behaviour of dams under seismic loads. Although many
researchers have investigated the effects of earthquakes on dams, many problems
remain unsolved, specially for RSDs. A comparison, between the natural frequency of
conventional earth dams and RSDs, is considered in this chapter. It is shown that the
4
INTRODUCTION, AIMS AND SCOPE CHAPTER ONE
practice of inserting reinforcement into the earth dam material leads to an increase in
the natural frequency of such structures compared with conventional earth dams. This
may increase the possibility of failure. In this chapter, the increase in natural frequency
of RSD due to its geometry and its overall stiffness are discussed. Formulae concerning
the magnification of the natural frequency of the structure due to reinforcement
insertion are proposed.
Chapter 6 is concerned with the development of a computer program for optimisation
of RSDs and for stress-strain analysis based on the finite element method. The
purposes of the program are (a) the geometrical optimisation of RSDs based on
analytical and semi-empirical formulae, and (b) the stress analysis of RSDs using the
finite element method. In the finite element section, the quadrilateral elements are
assumed to model the elements of the soil and the one-dimensional bar elements are
considered to model the behaviour of reinforcements. At the beginning of this chapter,
the formulation of soil reinforcement interaction is presented.
Chapter 7 considers the analyses of six models of RSDs using the computer program for
various heights and safety factors to find the optimum base length. A 30m high RSD is
also analysed considering the following four configurations: (a) without
reinforcements, (b) with the assumed increased stiffness of the soil fill, (c) with
horizontal reinforcements, and (d) with inclined reinforcements to evaluate the
variation of stress and displacement. It is concluded that putting reinforcements within
the soil dams can decrease displacement and stress values.
Finally, Chapter 8, which contains two parts, represents a summary of main findings of
this thesis. The first part, summarises the results of the field data analysis and the
second part summarises the findings from the developed computer program.
5
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
CHAPTER TWO
PRINCIPLES OF REINFORCED EARTH
2.1 INTRODUCTION
Soil reinforcement is a modern technique for improving the mechanical properties of
soil, using the concept of frictional interaction between the soil and the reinforcement.
In the composite material consisting of soil and reinforcement, the generation of the
frictional forces between the soil and reinforcement is fundamental to its behaviour. In
these structures, the compressive and tensile stresses are borne, respectively, by the soil
and reinforcement. In fact, the contribution of reinforcement, in the reinforced earth
structure, is to unify a mass of soil by preventing its lateral displacement.
Reinforced earth is a general concept which has many applications in construction of
bridge abutments, foundations, sea walls, and dams. In some countries, e.g. United
States of America and the United Kingdom, Reinforced Earth is a trade mark and refers
to a special structure which was invented and developed by a French architect, H. Vidal,
in the early 1960s. In comparison with similar techniques, reinforced earth has many
advantages e.g. reduction in cost and ease of construction. These advantages have
caused reinforced earth to be accepted as a suitable substitution for reinforced concrete
in some structures such as, sea walls, bridge abutments and dams.
Reinforced earth is formed from two basic components, fill and reinforcements. The
reinforcement material can be wood, steel, geotextile or other materials such as
polymers. It can be used in different forms such as bar, strip, grid and sheet. Either
cohesive or non-cohesive soil can be used as the back-fill material. However, the non-
cohesive soil is preferred because of its higher internal friction angle. In a vertical
reinforced earth structure, besides the above components, another feature is necessary,
6
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
to prevent the erosion of the soil at its vertical face. This additional component, called
'facing', is usually provided by precast concrete panels, arched or plain steel sheets, or
timber. Fig. 2.1.1 shows the main components of a reinforced earth structure.
The most important considerations in the analysis and design of the reinforced earth
retaining structures are the internal stability of the composite material and the external
stability of the structure. The latter is necessary for a gravity retaining structure by a
conventional design method. In the following section of this chapter, the reinforced
earth history, its application, material components, fundamental behaviour, design
considerations, construction methods, and economy will be discussed.
Facing units Reinforcing strips
"777
Selected till
Fig. 2.1.1 Reinforced earth components
2.2 HISTORY
Although the modem technique of soil reinforcement has been developed scientifically
since the 1960s, its original concept is not new and goes back thousands of years
(Ingold, 1982). The earliest remaining structure of soil reinforcement is Al-Zigurate in
the ancient city of Ur in Iraq (1500 BC). The great wall of China, which dates back to
the third century BC, is another example of a man-made reinforced earth structure (Al-
Ashou, 1990).
7
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
After 1966, intensive research on reinforced earth began in countries such as France, the
United State of America and the United Kingdom. The first fundamental research on
behaviour, analysis and design procedures of reinforced earth wall was undertaken at the
LCPC (Laboratoir Central des Ponts et Chaussees) in 1967 (Ingold, 1982). At the same
time, similar research was continuing in the United State of America by A S C E
(American Society of Civil Engineers) and the United Kingdom. The first reinforced
earth structure of this period was built to the north of Los Angeles by the California
Department of Transportation (Caltrans) in 1972 (Hausmann, 1990). It was constructed
on a landslide area and its facing was of the sheet steel type (Chang, 1974). The large
number of international symposia and conferences, held in different parts of the world
such as USA, U K , France, Australia, Japan and India, clearly shows the universal rapid
growth of the reinforced earth technique during the past thirty years.
2.3 APPLICATIONS
Reinforced earth is a technique which can be used as a method for designing different
types of structures such as; bridge abutments; arches; tunnels; slabs; foundations;
retaining walls; sea walls; embankments and dams. Each of the above structures may
have various engineering applications in: industry; military use; housing; highway
making; railway construction and coastal protection. In the next section of this chapter,
some applications of reinforced earth will be discussed.
A successful application of a reinforced earth slab was made on State Route (SR200)
near Norristown, Pennsylvania. This slab was designed by the Reinforced Earth
Company to cover a collapsed section of foundation soil under the embankment of a
highway. The slab was constructed in the form of a low wall lm high with semi-
elliptical steel facing units forming its perimeter. In comparison with a reinforced
concrete slab, the reinforced earth slab was 25 percent cheaper.(Steiner, 1975)
8
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Another application of the soil reinforcement is the improvement of the characteristics of
the soil under the foundation. In such an application, the reinforcement is used to ensure
stability, reduce settlement and increase the bearing capacity of the foundation. In
comparison with other soil reinforcing applications, only a very small amount of research
has been done on this application of the reinforced earth in foundation engineering. This
is because the reinforced earth foundations are not economically superior to the other
soil reinforcing techniques such as, lime piles or vibroflotation (Jones, 1985).
Some laboratory and analytically investigations have been carried out by Andrawes et al
(1978) to determine the increment of the bearing characteristics resulting from the use of
reinforcement. As the result of these investigations show, the maximum bearing capacity
ratio (q/qo) was found to occur at the depth ratio (d/B, when d is the depth of the top
layer and B is the width of the footing.) of 0.4. At a depth ratio between 0.8 and 1.8,
the smooth steel is found to give a reduced bearing capacity ratio. A similar research has
been done by Bassett & Last (1978) who advocated the use of discrete reinforcements
installed at various inclinations. This system has the great advantage that it can be
installed beneath new or existing foundations, without the need for excavation.
Reinforced earth technique can be used for underground arches and tunnels. Models of
the arch and tunnel have been successfully tested. Fig. 2.3.1 shows the plane-strain arch
studied by Behnia (1972)
Fig. 2.3.1 Reinforced soil arch (after Behnia, 1972)
9
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
The largest proportion of application of reinforced earth structures are reinforced earth
walls. According to Ingold (1982), "at the end of 1978 Vidal's licences had completed
in excess of 2000 projects involving 1.3 million square meter of facing". Typical cross
sections of reinforced earth wall, shown in Figs. 2.3.2 to 2.3.4, illustrate the application
of reinforced earth in retaining walls for different structures.
Reinforced earth volume L- -X Reinforced earth volume
Fig. 2.3.2 The slot storage system (after Ingold, 1982)
Fig. 2.3.3 Stepped highway structures (after Vidal, 1970)
Reinforced earth retaining walls can also be used in marine structures. In such cases, the
structure should resist wave forces, tidal conditions and corrosion. Figs. 2.3.5 and 2.3.6
10
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
illustrate two different cross-sections of sea walls (Reinforced Earth Company
Brochures).
-777— j 1
k.-
^ = = = "
' n '1 r*i " ' Vr^ ///
"
. v** w
Fig. 2.3.4 Rock crushing plant
Tetrapods ^£3$?
§§§}§§&£>'
, , , ^ . jCi
Fig. 2.3.5 Typical section of sea wall (Reinforced Earth Company Brochures)
5m to
6m
T V 2m\
2m
f ^ = i/n\y
Fig. 2.3.6 The sea wall using Z-shapedpanels (Reinforced Earth Company Brochures)
11
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Fig. 2.3.7 shows three different purposes for using reinforcement in embankments
(Iwasaki & Watanabe, 1978). In Fig. 2.3.7a, the contribution of reinforcement is edge
stiffening and superficial slope reinforcement. Such reinforcement gives resistance to
seismic erosion and seismic shock as well as permitting heavy compaction plant to
operate close to the shoulder of embankment, hence effecting good compaction in this
sensitive area. In Fig. 2.3.7b, the main body of the embankment is reinforced by a
geogrid net. This type of reinforcement can improve the seismic stability and static
stability, especially against lateral spread of the embankment, during compaction
operation. Reinforcement of weak embankment foundation represents another
application of reinforced earth (Fig. 2.3.7c). Forsyth (1978) used similar techniques to
improve the resistance of an embankment using car tyre.
777" (a) Superficial embankment reinforcement
777 ' (b) Major embankment reinforcement
*77
77\ V7
(c) Embankment foundation reinforcement
Fig. 2.3.7 Modes of embankment reinforcing (Iwasaki & Watanabe, 1978)
The ideal and most efficient orientation for placing the reinforcement is in the
embankment along the axis of principal strain (Sims & Jones, 1979). At this orientation
12
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
a considerable increase in strength will be obtained. If, however, the reinforcement is
placed parallel with the failure plane, the strength of the embankment may be decreased.
In fact, it depends on the friction angle between the soil and the reinforcement. Fig.
2.3.8 shows these critical orientations for embankments.
^ ^
**^^ ^ ' " ^
(a) Approximate tensile strain orientation
^ «r
(b) Approximatefailure surface orientation
Fig. 2.3.8 Critical embankment orientations (Sims & Jones, 1979)
Reinforced earth can also be used in earth dam construction. The use of soil
reinforcement in the construction of earth dams allows the reduction or elimination of
the downstream slope of the structure resulting in a considerable reduction in the fill
volume. It also allows for a dam spillway to be built at the crest of the structure. In the
event of high water level during construction, it is possible to allow a portion of the flow
to spill over the unfinished dam. In comparison with the other types, RSDs also have
many other advantages e.g. structural flexibility on moderately compact foundation soils,
an increase in the speed of construction, and the integration of embankment work with
construction of reinforced earth spillway (Reinforced Earth Company Brochures). Fig.
2.3.9 compares a RSD with a conventional earth dam.
The first RSD was constructed in the Bimes Valley situated in the south of France
(Ingold, 1982; Taylor and Drioux, 1979; Cassard et al. 1979). The dam was constructed
13
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
with 9 m height and vertical downstream face using precast concrete facing units. Fig.
2.3.10 shows the cross section and the view of the Vallon des Bimes dam. More details
about RSDs will be discussed in Chapter Three.
Upstram water table -.^ ^ ^
f * ^r *
Jf j£_
Jf ^T~ S^ f ^r
f ^T ^T f
f
\ i •
i *
^ ( Downstram water table -
/// ///
Fig. 2.3.9 Typical cross-section of a RSD compared with a conventional earth dam
->^<i - - -^ * ? r > ! w
jS??: ': ^f^.:',<:-.-
y*?Xv: ••):••:•
sS^' ••'•'•'.'•'••
^f----^S^ .*<" T •
s^^ ^ r " ? •
^S^yy.yy
9m
Fig. 2.3.10 Cross-section of Vallon des Bimes dam
2.4 MATERIALS
Recognition of the material components needed for the construction of reinforced earth
structures is necessary for prediction of the behaviour and mechanics of the reinforced
soil. The availability of the material components is another major factor for constructing
reinforced earth structures. Selection of the material components depends on type of
14
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
structure and the cost. Technical requirements of the structure and the basic economics
relate to the selection of material components (Jones, 1985).
Soil, reinforcement and facing are three major components of any reinforced soil
structure. However, other features may also be required for special reinforcement
structures. For example, joining elements and capping units may be necessary as barriers
and facing in some cases (Jones, 1985).
The type of structure has an important role in the selection of material. Some materials
may be suitable for use as components of some reinforced earth structures, but may not
be suitable to be used as components of other reinforced earth structures. For example,
a 'marginal material' may be used to construct reinforced embankments. However, it
may not be suitable for the use in construction of reinforced soil walls (Jones, 1985).
2.4.1 Soil
Soil forms the major part of reinforced soil structures and it usually occupies the largest
volume within the reinforced earth structure. The increase in internal friction of soil can
normally results in the reduction of the stress and strain within the reinforced soil
structure. This may also result in reduction of the amount of soil needed for
construction. According to Jones (1985) only few types of soil can be recommended in
constructing reinforced earth structures. Generally, the soil used for the filling may be
classified into four groups: non-cohesion (or granular) material; cohesive frictional
material; cohesive fill material and waste material (Jones, 1985).
Non-cohesion materials are usually well grained material which have special properties
and granularity. They should normally be used in constructing important reinforced
earth structures with long term use, because of their high internal friction coefficients,
free drainage, less reinforcement corrosion problems and cost considerations. All non-
cohesion materials, which are suitable to be used as fill, should pass through a sieve size
125. More than ninety percent of them should not pass through the sieve size 63 mp..
15
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Recommended restrictions in the grading of non-cohesion soil are shown in Table
2.4.1.1. Density, uniformity coefficient, the friction coefficient between reinforcements
and non-cohesion material should be specified for selecting this type of material.
Table 2.4.1.1 Grading restriction for non-cohesion material (Jones, 1985)
Sieve size
125
90
10
600 tim
63 urn
2iim
Passing percentage
100
85-100
25-100
10-65
0-10
0-10
Cohesive frictional materials may also be used in the construction of some reinforced
structures. M o r e than ten percent of this type of soil should pass through the sieve size
63 mu.. Recommended restrictions in the grading of frictional cohesive soil is shown in
Table 2.4.1.2. Apart from grading, other parameters such as: uniformity coefficient;
resistivity; internal friction angle; the friction coefficient between soil and reinforcements
(the adhesion between reinforcement and fill material); soil cohesion; the index of
plasticity and liquid limit should also be considered in the design. The design life period
of the structure (long versus short term) will affect the required properties and type of
soil fill.
Cohesive soil m a y also be used as a material for reinforced soil structures, however, this
type is not suitable for long term structures, especially in the case of wet conditions.
The problem of corrosion is greater in this category of soil. Therefore, to use cohesive
soil, it is necessary to select a reinforcement with low susceptibility for corrosion. Long
term deformation is also a problem, particularly affecting construction of vertically
facing structures. Nevertheless, cohesive materials are used in the construction of some
reinforced structures, the main reason is the availability of the cohesive material on or
16
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
near to the construction site. This may reduce the costs of the reinforced earth structure.
Therefore, if the use of this type of material is more economical, it can be used provided
the material requirements are met.
Table 2.4.1.2 Grading restrictions for cohesive frictional material (Jones, 1985)
Sieve size
125
90 mm
10 mm
600 Ltm
63 Ltm
2 pm
Passing percentage
100
85-100
25-100
11-100
11-100
0-10
Waste materials may be used as a fill material in the construction of some reinforced
earth structures. For example, some industrial waste materials may be suitable for the
use as filler in the construction of non-important structures e.g. embankments. This may
help in reduction of environment problems and may be economical. For example,
pulverised fuel ash (as a light weight fill) has been used in the construction of
embankments (Jones, 1985).
2.4.2 Facing
Surface erosion of the reinforced soil structures is usually prevented by facing panels,
especially in vertical structures. The use of the facing panels can provide an attractive
architectural facing. The panels may be made of concrete, steel, timber, plastic or from
other materials. Form, size, shape and material are significant parameters which should
be considered for the designing of suitable facing panels. Examples of several shapes of
facings panels are shown in Fig. 2.4.2.1.
17
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
D O ^ Square facing panel Hexagonal facing panel Flexible facing panel Fig. 2.4.2.1 Typical examples of shapes of facing panels
2.4.3 Reinforcement
The types of materials which may be used as reinforced soil are very different. Steel,
aluminium, wood, rubber, fibre glass, concrete, some kinds of polymers, or plastics may
be used. In a general classification, the reinforcements may be divided into metallic
reinforcements and non-metallic reinforcements. Metallic reinforcements are usually
stronger than none-metallic reinforcements however, the second type is cheaper and
more flexible than the first. Non-metallic reinforcements may be made of one polymer
or combination a of polymers. The degradation resistance of various synthetic fibres is
shown in Table 2.4.3.1 (Cannon, 1976).
Shapes and properties of reinforcements vary. Strips, planks, grids, geogrids, sheets and
anchors may be used. They may be combined to create other types. Typical shapes of
reinforcements are shown in Fig. 2.4.3.1, while a system of reinforcement is shown in
Fig. 2.4.3.2.
The friction coefficient between reinforcement and soil, and the durability of
reinforcement against corrosion should be considered in selecting the reinforcement
The durability of the chosen reinforcement should be compared with the required length
of life of the reinforced structures. Some properties of strip and sheet materials are
presented in Table 2.4.3.2 and the frictional properties of various strip materials are
shown in Table 2.4.3.3.
18
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Table 2.4.3.1 Degradation resistance of
Resistance to
attack by
Fungus
Insects
Vermin
Mineral acids
Alkalis
Dry heat
Moist heat
Oxidising agents
Abrasion
Ultraviolet light
various synthetic fibres (Cannon, 1976)
Types of synthetic fibres
Polyester
Poor
Fair
Fair
Good
Fair
Good
Fair
Good
Excellent
Excellent
Polyamide
Good
Fair
Fair
Fair
Good
Fair
Good
Fair
Excellent
Good
Polyethylene
Excellent
Excellent
Excellent
Excellent
Excellent
Fair
Fair
Poor
Good
Poor
Polypropylene
Good
Fair
Fair
Excellent
Excellent
Fair
Fair
Good
Good
Good
PVC
Good
Good
Good
Good
Good
Fair
Fair
-
Excellent
Excellent
Steel bar _ J 1 " 1
Steel bar
Anchor plate
Key
Webbing Tyre
Fig. 2.4.3.1 Typical shapes of reinforcements
19
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Longitudinal reinforcements
Tranverse members
\ Facing panel
Fig. 2.4.3.2 A reinforcement system connected to a facing panel
Table 2.4.3.2 Properties of typical sheet and strip material (Jones, 1985)
Materia]
Aluminium alloy
Copper
Carbon steel (galvanised)
Stainless steel
M a x i m u m thickness to which stresses
apply (mm)
6
10
10
6-10
Basic permissible stresses
Axial
tension
mm
120
108
120 - 192
126 - 220
Shear
< " 2 >
mm 72
65
72-115
Bearing
< \ >
mm 180
163
200 -350
75-132 1 210-360
Table 2.4.3.3 Frictional properties for various strip material (Boden etal., 1978)
Effective stress
range 0-40 kPa
Effective stress
range 0 - 100 kPa
Angle of friction
of soil without
reinforcement
(<*>')
37
37
Coefficient of friction between fill and
reinforcement (p)
A
0.38
0.36
A = Galvanised mild steel
B = Stainless steel
C = Glassfibre reinforced plastic
B
0.40
0.39
C
0.53 to
0.64
0.53 to
0.64
D
0.51 to
0.58
0.51 to
0.58
E
0.36
0.37
F
0.42
0.40
D = Aluminium coated mild steel
E = Plastic coated mild steel
F = Polyester filaments in polyethylene
20
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Types of non-metallic reinforcements are usually provided by polymers. Although the
strength of the non-metallic reinforcements is lower than that for the metallic, the
applications of the non-metallic group has increased during recent years. The most
important reasons for the increased use of non-metallic reinforcements are their
avauability and low cost (John, 1987). In particular, polyamide, polyester,
polypropylene and polyethylene may be used as soil reinforcements. A comparison
between the properties of non-metallic materials is shown in Table 2.4.3.4.
Table 2.4.3.4 A comparison between the properties of general polymers (John, 1987)
Comparative properties
Strength
Elastic modulus
Strain at failure
Creep
Unit weight
Cost
RESISTANCE TO:
Stabilised U. V. light
Unestablished U. V. light
Alkalies
Fungus, vermin, insects
Fuel
Detergents
Polyester
high
high
medium
low
high
high
Polyamide
medium
medium
medium
medium
medium
medium
Polypropylene
low
low
high
high
low
low
Polyethylene
low
low
high
high
low
low
high
high
low
medium
medium
high
medium
medium
high
medium
medium
high
high
low
high
medium
low
high
high
low
high
high
low
high
The reinforcement system and the face panel of the first bar mesh reinforced wall are
shown in Fig. 2.4.3.3a This wall was constructed by Caltrans near Dunsmuir in
California in 1975 (Hausmann, 1990). The facing elements of the wall were of
concrete type and beam shaped panels. This technique was designed as Mechanically
Stabilised Embankment (Hausmann, 1990).
21
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
The Hilfiker Reinforced Soil Embankment, the Vorspann System Losinger Retained
Earth and the Georgia Stabilised Embankment are other techniques of reinforced earth
embankment with different facing panels, bar mesh geometry and construction details
(Hausmann, 1990). In the Hilfiker Reinforced Soil Embankment, which was
introduced in 1983, the precast facing panel and the reinforcements are formed by a
beam shaped and cold-drawn wire mesh, respectively. In this system, the bar mesh is
connected to the facing panels. The shape of the panel and mesh of the Hilfiker
Reinforced Soil Embankment are shown in Fig. 2.4.3.3b.
The Vorspann System Losinger Reinforced Earth represents another welded wire mesh
system with precast concrete facing. The first wall using this system was built in
California in 1981. During the period time, 1981 to 1984, about 100 walls were
constructed by using this system (Hausmann, 1990). The shape of its facing and its
wire mesh are shown in Fig. 2.4.3.3c. Also, the panel and reinforcement system of the
Georgia Stabilised Embankment system are shown in Fig. 2.4.3.3d. This system was
introduced by the Georgia Department of Transportation.
2.5 SOIL-REINFORCEMENT INTERACTIONS
2.5.1 Development of Theory
From 1966 until the present (1994), numerous tests have been undertaken to understand
the behaviour of reinforced earth and various theories have been presented to describe
reinforced soil behaviour in analytical terms. Extensive researches in this area has been
pursued by Laboratoir Central des Ponts et Chaussees (LCPC), N S W Institute of
Technology, The University of California- Los Angeles (UCLA) amongst other
researchers. Some of these works will be discussed in the following sections.
22
V. V, p
i ~""C
•U—
V
•K
s o ! ; o | : •"> -.
V
1 s vo
—1
V r V
S
7
oo
"a
+
+ +
4 <*>
--
— —
--
--
_ _
--
1 1 1 1
S
d
"«
"1
s: + + + +
+ + + +
s •»»•»
e -fc
to
a
•2
5J to
fc
"a e a to
s; o< oo fc
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
In 1966, Vidal found that if a horizontal reinforcement strip was put within the loaded
soil, the friction between the soil and reinforcement raises the lateral stress from c'3 to
tf'3 + Aa'3 in failure condition. The increase in the lateral stress (A03) increases the
bearing vertical stress of the soil from c'\ up to (a'i)r. Figure 2.5.1.1 shows the new
situation of the stresses in the Mohr's circle based on Vidal's (1966, 1969) theory, due to
reinforcement insertion within the soil.
t
Ogl y°\ y0 g+AO 3
^ C <t>
J(0\)T
- ^
Fig. 2.5.1.1 Improvement in strength due to reinforcement (based on Vidal, 1966,
1969)
Other experimental and theoretical research was conducted by Long et al. in 1972.
Figure 2.5.1.2, a plot of the deviator stress versus axial strain, shows that the reinforced
samples are brittle. The researchers concluded that the failure envelopes of reinforced
and unreinforced samples have the same angle of friction. The results from a series of
triaxial tests, carried on 100 mm diameter samples of special sand with D50= 0.15 mm
and a mean dry density of 1.67 g/cm3, are illustrated in the figure. The figure shows
that the amount of axial strain increases for unreinforced soil with same deviator stress.
Also, the additional strength of the reinforced samples results from apparent cohesion,
c'.
24
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
*-> -* VI vi
£ o
Of
2500
2000
1500
1000
500
0 0 2 4 6 8 10
Axial Strain - %
Fig. 2.5.1.2 Increase in brittleness due to reinforcement (based on Long et al, 1972)
In the LCPC cohesion theory, presented by Schlosser and Long in 1973, it was
suggested that the value of o'l is equal to the sum of passive earth pressure (Kpo'3) and
Aa'i. This means that:
oJ1 = £poJ3+Ao
J1 (2-D
25
Vertical
stress °\ 2^
(100 kN/m2) 15
10
5
0
™ M '
M
/
/
f .' , Reinforced
7 / Unreinforced
) 2 4 6 8 10
Confining pressure o y 700 kN/m )
Fig. 2.5.1.3 Increase in Cj due to reinforcement ( based on Schlosser & Long, 1973)
Reinforced
Unreinforced
25
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
They then compared this equation to the Rankine-Bell Equation for c'-(t>' soil and
concluded that:
Ao1 c =• l-rP
(2.2)
Schlosser and Long (1978) also presented a theoretical procedure to calculate c'. Fig.
2.5.1.4 shows the element which was assumed for calculating the amount of c'. In
regard to the figure and using equilibrium it can be concluded that:
F + G ' ~ A tana = c', Atan(a-0') (2.3)
where F is the sum of tensile forces induced in the reinforcements, A is the cross section
of the sample, a is the angle of failure plane, c\ and 03 are the vertical and lateral
stresses respectively, and 0' is the angle of friction of soil.
Fig. 2.5.1.4 Coulomb analysis (Schlosser & Long, 1973)
O n the other hand, because F is the sum of tensile forces in reinforcements, it can be
written as:
26
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
F=ATjma (24)
h
where h is the vertical space between reinforcements and T is the tensile force in each
reinforcement. By substituting Eq. 2.4 in Eq. 2.3 and by differentiating, the maximum
value of a'l may be given as:
K T G\=K o' +-£— (2.5) 1 P 3 h
By comparing this equation with Eq. 2.1, the Aa'i can be obtained as:
, K T A C T 1 = - £ - (2.6)
1 h
By substituting the Aa'l in Eq. 2.2, the value of c' is found as follows:
c =
T IK L. (2.7)
2h
This equation was found to be in close agreement with the experimental results which
were undertaken by Long in 1972. The comparison of the theoretical and experimental
results is shown in Fig. 2.5.1.5.
A modified version of Eq. 2.8 is:
Tr \K~
c<= V P 2h (2.8)
where r is the ratio of the plane area of the reinforcing ring to the cross sectional area of
the sample.
27
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Cohesion
(kN/m )
300
200
100-
0
experimental
theoretical
0 50 100 150 200 250
Ratio T/h (kN/m2)
Fig. 2.5.1.5 Comparison of theoretical and experimental results (Schlosser & Long,
1973)
Hausmann (1976) worked on two models, called Sigma and Tau, both considered tensile
and bond failure. The results from the two models were similar. In the Sigma model, it
was assumed that reinforcements prevented lateral expansion and, in the second model,
it was assumed that horizontal and vertical shear stresses were induced by reinforcement
into the soil. The Sigma model was analysed in two situations; when the failure happens
because of the rupture of reinforcement and, when the failure occurs due to slippage.
In former situation, it was assumed that the sum of lateral stress a'3 and the value of a'r
is equal to Ka multiplied by vertical stress a'l in failure condition. This means that:
1 r a 1 (2.9)
or
c' =K a' +K a' 1 p 3 p r
(2.10)
A comparison between this equation and Rankine-Bell's equation yields:
28
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
r 2 (2.11)
By substituting the value of G'T = aA/dy dz, Hausmann (1976) obtained that:
c ^CA^P Cr Id d
y z
(2.12)
where O" is the stress in the reinforcement, A is the cross section of reinforcement, Kp is
the coefficient of soil in passive condition and dy and dz are the dimensions of the soil
element. Fig. 2.5.1.6 shows failure condition in Sigma model in the case of constant c'r.
x • Reinforced Unreinforced
<t>'
G3 ka°l
Fig. 2.5.1.6 Failure condition for constant G'r (Hausmann, 1976)
Hausmann also considered the Sigma model when the failure happens because of lack of
bonding between soil and reinforcement. It was assumed that the friction along the
reinforcement is in linear proportion to vertical stress. This means that:
rj' = F o \ r 1
(2.13)
Substituting the o*r from Eq. 2.13 to Eq. 2.9 results in:
29
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
-^-+F = K
On the other hand, it is known that:
CT' l-sin(j>' 3__ T r
G1. 1 + sin <>' 1 T r
Substituting the CT'3/a'i from Eq. 2.15 to Eq. 2.14 results in:
(2.14)
(2.15)
(K -F-l) sin(<j>' ) = —^
(F-K -1) a
(2.16)
A series of laboratory experiments, undertaken by Hausmann, to prove his theory in
bond failure condition, indicated a suitable agreement with the LCPC theory. However,
the failures which occurred due to rupture, did not correspond very well with this
theory. Therefore, it was concluded that, at high stress level, the failure of soil is the
result of rupture of reinforcement and at low stress condition the failure may occur
because of slippage. Fig. 2.5.1.7 shows the variation of §\ due to F.
Fig. 2.5.1.7 Friction angle §r as a function ofty and F (Hausmann, 1976)
30
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
The increase in the friction angle of the soil due to failure by slippage between the soil
and reinforcement is shown in Fig. 2.5.1.8. The failure of soil because of reinforcement
rupture at high stress level, and the failure of soil because of slippage at low stress level
are shown in Fig. 2.5.1.9. The Mohr stress circle for a reinforced and unreinforced
samples, with the same lateral pressure, a'3 is shown in Fig. 2.5.1.10. This figure shows
that the effect of reinforcement is an increase from a'l to (a'i)r in the vertical stress or
the increase in the inducing cohesion, cr, of soil.
X ' . Reinforced
A—$r
03 ka G'I
> < * ,
Unreinforced
a> t?
Fig. 2.5.1.8 Increase in the friction angle of soil because of reinforcement (Hausmann,
1976)
Reinforced. x 4
J
Unreinforced
03 G\ 03 G\ a
Fig. 2.5.1.9 Composite Mohr envelope (Hausmann, 1976)
31
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Fig. 2.5.1.10 The LCPC interpretation
In 1972, Chapuis rejected the assumption that in a mass of soil with horizontal
reinforcement, the principal stresses were vertical and horizontal. It was assumed that
the horizontal and vertical planes were not able to be principal planes. Chapuis(1972)
considered that the main principal stress (a'3)r is higher than a'3 and the term, Aa'3, is
approximately equal to:
Ao%= — = — (2.17) 3 BH H
The second side of this equation is the same as that presented by Hausmann
(G'T=GA/BH). However, Aa'3 is a stress increment, whereas a'r is a stress decrement.
Chapuis also found that cohesion relates to the distribution of stress along the
reinforcement. The Aa'3 interpretation is shown in Fig. 2. 5.1.11.
32
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
X <
°3
Reinforced/?
(a3 ) r CT1
Unreinforced
1
(^l)r
Fig. 2.5.1.11 The AG'S interpretation (Chapuis, 1972)
Yang (1972) undertook the same experiments using triaxial tests on sand by using
samples with 71 mm diameter and height variations between 20 mm and 162 mm. In a
series of experiments, he investigated the reasons for the failure using strong rigid
reinforcement. It was found that the compressive strength of the samples increased
while the space between reinforcements decreased believing the samples failed at
constant effective stress ratio. It was concluded that any increase in a'l at failure
condition in the reinforced samples was due to a modified confining pressure, Aa'3, as
follows:
G. - K G~+K Aa~ 1 p 3 p 3
(2.18)
or,
Aa~ = K G.-G~ 3 a 1 3
(2.19)
Fig. 2.5.1.12 shows that the equivalent confining pressure per initial confining pressure
decreases when the aspect ratio (height / diameter) increases based on Yaung (1972).
Fig. 2.5.1.13 illustrates that the variation of the confining pressure, Aa'3, increases
linearly with the applied confining pressure, a'3. Therefore, it was concluded that the
33
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
value of Aa'3 would be constant, the equivalent of the Eq. 2.17. However, according to
Ingold (1982), there was a poor agreement between predicted and increased values.
20 Height
Diameter
10
0 0
8 12 16
Equivalent confining pressure_ 3 3
Initial confining pressure
Fig. 2.5.1.12 Variation of strength with aspect ratio (after Yang, 1972)
100
75
Increase in confining 50
pressure
Ac3(psi) 25
a
d
-
psi -= 6.9 kN/m ) /
h/d=0.57
0 10 20 30 40 50
Applied confining pressure G ? (psi)
Fig. 2.5.1.13 Variation ofAG'3 with G'3 (after Yang, 1972)
34
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
In 1985, Jones presented a theory based on principles of soil mechanic. In an element of
unreinforced soil, the value of vertical stress and lateral stress may be given as follows:
Gx=yh (2.20)
G3=KQyh (2.21)
where, y is the unit weight of soil, h is the soil depth where element is located, and Ko is
the coefficient of lateral earth pressure at the rest condition. When the element of soil
starts for expanding laterally, the coefficient of lateral earth pressure reduces from Ko to
Ka where:
K = 2 (2.22) a (l+sin<j))
Jones (1985) argued that in a compacted reinforced soil, the reinforcement doesn't
permit the soil to expand because of the friction between soil and reinforcements. This
results in creation of tensile stress and strain in any units of the reinforcement, as
follows:
(2.23)
(2.24)
(Jrp '
5 = r
*0al a r
Grp
E r
or,
5 = * 0 a l (2.25) r a E
r r
where, ar and Er are, respectively, cross sectional area and elastic modulus of
reinforcement, GT is the tensile stress in the reinforcement, and 5r is the strain of
35
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
reinforcement due to Gj. When the effective stiffness of reinforcement, ar Er, increases,
the strain in the reinforcement decreases. It was also assumed that the values of strains
in soil (er) and reinforcement (5r) are equal.
er=8r (2.26)
Thus, it was concluded that the lateral strain in the soil, er, reduces to zero when
effective stiffness of the reinforcement (ar Er) is high, and the lateral strain increases
when the effective stiffness decreases. However, the coefficient of lateral earth pressure
of the soil, Ko, decreases to Ka in the second situation (Jones, 1985).
2.5.2 Stability Considerations
Studies of the relationships between stress and strain within reinforced earth structures,
and studies of sliding, bearing, slip, tear and tension failures should be considered during
the stability considerations of reinforced soil structures. The consequential reinforced
earth structures such as walls, abutments, and dams are involved this problem. Transfer
of stress from soil to a single strip, as tensile stress, should be considered here. Two
modes of failure may occur in the reinforcements: the breaking of the reinforcements due
to tensile stresses, and the failure due to pull-out of reinforcements. Force equilibrium
and moment equihbrium have been used to calculate tension in the reinforcements. Fig.
2.5.2.1 shows the possible forms of failures in a reinforced soil structure. These will be
discussed during the following sections.
Based on the equilibrium of a reinforced soil element, the tensile force in the
reinforcement, T, is usually calculated as:
T = KGSS, (2.27) a v v h
36
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
where, Sv is the vertical space between reinforcements, Sn is the horizontal space
between them, av is the vertical stress over the soil elements and Ka is the coefficient of
lateral earth pressure in active condition.
Fig. 2.5.2.1 The forms of failures (Jones, 1985)
On the basis of Coulomb's wedge theory, the tension, Tf, in the ith layer of a vertical
reinforced soil structure is usually calculated as:
T.=—^—KyHAH (2.28) 1 (n + 1) a
where n is the number of reinforcement layers, y is unit weight of soil, Tf is the depth of
structure and AH is the vertical space between reinforcements.
Trapezoidal distribution and Meyerhof s distribution of pressure under the base of
vertical structures are shown in Figures 2.5.2.2a and 2.5.2.2b, respectively. Several
equations have been presented so far for calculation of the maximum tension in the
reinforcements of a vertical reinforced soil structure as shown in Table 2.5.2.1.
37
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
H
e = H/3
iiikkkikikki
Fig. 2.5.2.2 a) Trapezoidal distribution pressure and b) Meyerhof distribution pressure
In Table 2.5.2.1, L is the length of reinforcements, y is unit weight of soil, H is the depth
of the structure, AH is the vertical spacing between reinforcements and Ka is the
coefficient of lateral earth pressure in active condition.
Table 2.5.2.1 Equations for calculation of the maximum tension in the reinforcements
of a vertical reinforced soil structure
Rankine Eq.
Trapezoidal Distribution Eq.
Meyerhof Distribution Eq.
Coulomb Moment Balance Eq.
Elastic Analysis Eq.
Equation
T max
T max
T max
T max
T max
= K yHAH
= K yHAH(l + K A 2 ) a u j_.
K yHAH a'
(1-0.3* (^)2) a L,
n2K yHAH a1 (n2-D
= 0.35yHAH
Eq. no.
(2.29)
(2.30)
(2.31)
(2.32)
(2.33)
38
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
A comparison between Eq. 2.29 to Eq. 2.33 are shown in Fig. 2.5.2.3. The figure is
plotted based on areas of one row of reinforcement per metre width, when H is assumed
to be 5 metres. It shows that the numerical differences between these equations increase
when the vertical spacing between reinforcements rises .
Vertical spacing (mm)
1000
800
600
400
200
0 0 40 80 120 m
Area of reinforcement (mm/metre width)
Fig. 2.5.2.3 Comparison between maximum tension stress inside reinforcement (Jones,
1985)
2.6 CONSTRUCTION METHODS AND STRUCTURAL SYSTEMS
Construction of a structure is the final stage of a project. In order to reduce the
associated costs, the construction processes should be simplified as much as possible,
leading to a short construction time. For this, a number of factors ought to be
considered. Theses will be discussed in the next two sections.
According to Hambley (1979), the following considerations should be taken into
account during construction of reinforced soil structures including (a) the use of
materials obtainable and easy to work with, (b) the use of simple shape foundations, (c)
39
a= Trapezodial distribution b= Elastic analsis c= Meyerhof distribution d= Coulomb moment balance e— Rankine theory /= Coulomb wedge
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
the use of horizontal or vertical surfaces, (d) fixing reinforcement first then placing soil,
(e) avoiding small sections, (f) avoiding massive large elements, (g) considering the
stability of detailed elements of reinforced soil structure during the stages of
construction, and (h) considering the requisite distance between reinforcements.
Differential vertical settlement is another important feature which may adversely affect
the construction process. Construction methods, reinforced systems, labour and plant,
rate of construction, compaction, damage and corrosion, distortion, logistics and
constructor's construction sequences have to be considered to optimise the construction
procedure (Hambley, 1979).
There are three major methods used in the construction of reinforced soil structures: the
Concertina Method, the Telescope Method and the Sliding Method. These methods will
be discussed in the following paragraphs.
The Concertina Method was developed by Vidal (1966). The largest reinforced soil
structures have been constructed after the development of this method (Jones, 1985). In
this method, the structure of the reinforced earth wall is formed from reinforced soil with
metallic flexible faces and reinforcing material. The face of the structure is formed from
semi-elliptical cross section facing units. Each 2 5 0 m m high facing unit is typically
connected to the reinforcements by bolts which pass through the strips and the edges of
the facing units. The weight of each unit is usually 1\5kg and its length is typically up to
10m. The thickness of the unit is about 1.5 to 3mm. The facing may be settled
proportional to the soil settlement. Therefore, the settlement does not destroy the facing
units. It means that the facing will be deformed without any destruction during the
internal settlement. A cross section of this method is shown in Figure 2.6.1.
The Telescope Method (Fig. 2.6.2), was also developed by Vidal (1978). In this method
the face of the structure is made of concrete panels instead of flexible face units. The
weight of a standard concrete panel is about lOOOfcg, the sizes of panel is about
1.5mxl.5m and its thickness is 18cm. To get rid of the panels rapidly, there are 4 lugs in
40
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
each panel for connecting the fourth edges of each panel and they are rebated. The
vertical distance between luges is 75cm centre to centre and the horizontal distance
between them is lm. Settlement is achieved by horizontal gaps between the facing
panels which will be filled after gravitational settlement of the layers. Therefore, in this
method the facing panels will be fixed after the internal settlement of the soil.
Fig. 2.6.1 The cross section of Concertina Method (Vidal, 1966)
The Sliding Method (Fig. 2.6.3), was developed by Jones (1985). In this method, the
facing is formed by light weight glass reinforced cement. The weight of each facing is
only \%kg. The shape of the cross section of each facing is a hexagonal- based pyramid
22.5cm deep and 60cm across the flats. Vertical movement is provided by installation of
two rods. In this method, the differential settlement may be achieved by vertical sliding
of the facing panels. W h e n the soil is settled, the end of reinforcement may simply slide
down because of its vertical pole. This facing panel has two roles: that of protection of
soil from erosion and as a structural element A typical section of sliding method facing
is shown in Fig. 2.6.3.
41
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Fig. 2.6.2 A typical section of Telescope Method (Vidal, 1978)
Fig. 2.6.3 A typical section of Sliding Method (Jones, 1985)
2.7 D U R A B I L I T Y
The required durability of reinforced earth structures relates directly to their design life
span. The corrosion of reinforcement strips may adversely affect their durability and
hence lessens the length of life of the reinforced earth structures. Most reinforced soil
structures, their reinforcements in particular, are susceptible to corrosion. If the
42
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
question of durability is not addressed, then the structure may fail. Therefore, durability
should be considered as a function of design life.
Corrosion is a major problem which effects the durability of metallic reinforcement. The
corrosion happens under ground, its problem is not seen until the failure occurs.
Material deterioration may occur because of electrochemical, bacterial or physical
corrosion problems (Jones, 1985). All metallic reinforcements should be protected
against electrochemical corrosion. This can be done by the use of cathodic protection
systems or through electrical compatibility (Jones, 1985). Cohesive fill material is more
corrosive especially in the case of metallic reinforcement, hence it reduces the durability
of reinforcement. Therefore, non-cohesion fill material is preferable to the other types,
particularly for using in the permanent structures.
O n the basis of life span, reinforced earth structures may be classified into three
categories: temporary structures, short life structures and permanent structures. The
first category includes structures with the life span of less than 100 weeks. Durability is
not considered to be a problem for these structures. The second category are structures
with a life span of between 2 and 20 years. Durability in this category should be
considered as a minor problem. The permanent structures, with a life span of between
60 and 120 years, form the third category, and durability is a major problem for this type
of structure (Jones, 1985). Most dams are categorised in this third category because
their life span is usually more than 20 years.
Corrosion will develop in the metallic reinforcement during this period, however the rate
of corrosion development will decrease in time (Romanoff, 1959). This reduction in the
rate may be the result of the creation of an external corroded layer on the surface of the
reinforcement, acting as a protection for the underlying material. In some cases, the
corroded layer can reduce the penetration of corrosion. Therefore the actual cross
section of metallic reinforcements should be the sum of the net cross section area (to
carry the expected level of stress) and a portion of cross section area (to be sacrificed
43
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
because of corrosion). A diagram which indicates the development of corrosion versus
time is shown in Fig. 2.7.1.
Corrosion
^^^ X=Ktn
LJ > 10 years t
Fig. 2.7.1 Development of corrosion (after Romanoff, 1959)
The use of other types of metallic reinforcements may reduce corrosion. For example,
the use of galvanised steel instead of unprotected steel can decrease corrosion. A
comparison between galvanised steel and unprotected steel is shown in Fig. 2.7.2. In the
case of galvanised steel, corrosion may only happen after destruction of the protected
surface of the reinforcement. Therefore, protection of the external layer of the
reinforcement strips can increase the length of life of the reinforced soil structures.
The P H of soil, the water content, the redox potential and the soil resistivity may also
affect corrosion. In some cases, it may be desirable to use materials which are not
susceptible to corrosion or more durable than metallic reinforcements. For example, the
degradation problems of polyamide, polyester, polypropylene and polyethylene
reinforcements appears to be less extensive than the corrosion of metallic reinforcements
(Jones, 1985). Typical corrosion allowance for metallic reinforcements are shown in
Table 2.7.1.
44
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Fig. 2.7.2 Loss of thickness during time for galvanised steel and unprotected steel
(Jones, 1985)
Table 2.7.1 Corrosion allowance for metallic components exposed to various
environment (Department of Transport BE, 1978)
Aluminium alloy
Cooper
Galvanised steel
Stainless steel
Sacrificial thickness to be allowed for each surface exposed
to corrosion (mm)
Atmospheric environment
Urban, industrial,
industrial costal
0.85
0
Other
.
0.3
0
Buried in fill
Frictional
fill
0.15
0.15
0.75
0.1
Cohesive
frictional fill
0.3
0.3
1.25
0.2
45
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
2.8 COSTS AND ECONOMICS
Even one percent reduction in the construction costs of big projects can save millions of
dollars. The greatest disadvantage in the use of concrete in the construction of marine
structures, is its cost. For example, construction of a reinforced soil standard bridge
abutment, instead of the conventional piled standard bridge abutment, may reduce the
costs of the project by fifty percent (Jones, 1985).
A group of researchers in the U K have undertaken a comparison between the height of
the reinforced soil structures and the percentage of the costs of reinforced soil relative to
the costs of reinforced concrete cantilever walls. This comparison is shown in Figure
2.8.1. The figure shows that the cost of a reinforced soil structure with the height of
10m may be about 30 percent of the costs of the same structure which has been
constructed of reinforced concrete. Although the costs of reinforced earth structures
vary with the type of material, the costs of reinforced concrete structures are normally
higher than those of the reinforced earth structures. This is a conclusion which can be
drawn from Fig. 2.8.1.
The variable percentage of construction costs to the reinforced soil cost; relative to the
reinforced soil cost, versus the height of reinforced soil structure is shown in Fig. 2.8.2.
The figure shows that the costs of a reinforced soil structure with the height of 20m may
be about half the cost of a conventional structure. The figure also indicates that use of
reinforced soil is more economical in the case of high structures.
The distribution of material costs of reinforced soil structures has three major
components: the cost of reinforcement, the cost of facing and the cost of soil fill. Fig.
2.8.3 shows the variation of percentage of the total material cost with the height of
structure. This figure shows that the cost of facing reduces with the increasing the
height of structure but, the cost of soil fill and the cost of reinforcement both rise. All
three material cost components tend to stabilise with increasing the height of structure.
46
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Percentage
cost
100 -
75 ~
50
25 ~
0 T 1
15 0 5 10
Height of structure (m)
~T~
20
Fig. 2.8.1 Comparison between the height of reinforced soil structures and the
percentage of the costs of reinforced soil walls relative to the costs of reinforced
concrete walls (Jones, 1985)
100 -
Economy
0 5 10 15
Height of structure (m)
r 20
Fig. 2.8.2 Economy versus height of structure (Jones, 1985)
47
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
Prcentage
of total cost
60_
50 _
40~
30~
20~
10
0
Reinforcement
*N*. Facing elments
Soilfi.il
1 1 1 1 0 5 10 15 20
Height of structure (m)
Fig. 2.8.3 Variation of percentage of total material cost with height of structure (Jones,
1985)
Another diagram which shows the other comparison between the costs of reinforced soil
structures and reinforced concrete structures is shown in Fig. 2.8.4. This comparison is
undertaken for the construction of one (6 m high) reinforced soil wall and one (6 m high)
reinforced concrete wall. This diagram shows the cost of energy content of construction
material, process water used in the manufactured materials, the labour for manufactured
material, material transport and construction in the case of reinforced soil and reinforced
concrete structures. The process water used in the case of reinforced soil is the only
item when cost is exceeded (Jones, 1985).
48
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
120
100
80
X 60
40
20
0
reinforced soil wall X = — • xlOO
reinforced concrete wall
a f 8 h
a
d
f g h
energy content of construction material process water used in manufacture of materials despoiling of land in production of materials S(?2 - emission dust - emission labour - manufacture of materials
labour - material transport labour - construction
Fig. 2.8.4 Comparison between the costs of reinforced soil structures and reinforced concrete structures
2.9 C O N C L U S I O N S
One way to improve mechanical behaviour of soil is to use reinforcement in the soil.
The low tensile strength of the soil can be increased by reinforcement, hence the
combination of soil and reinforcement results in a new stronger material which can
withstand loads higher than the soil without reinforcement. Prevention of lateral
expansion, which is the main role of reinforcement, can decrease the lateral displacement
of soil and this increases the lateral stress. From the theoretical research and
observations concluded so far, it is obvious that the use of reinforcement in soil increases
49
PRINCIPLES OF REINFORCED EARTH CHAPTER TWO
the strength of soil mass. Some researchers claim that reinforcement increases the
cohesion of soil. Others believe that the reinforcement can increase the frictional angle of
soil. A general conclusion may be made that the effect of reinforcement in the soil is an
increase in the angle of friction in low stress levels and an increase in cohesion of soil in
high stress levels.
50
EVALUATION OF SOIL DAMS CHAPTER THREE
CHAPTER THREE
EVALUATION OF SOIL DAMS
3.1 INTRODUCTION
Earth-fill and rock-fill dams have a greater role than that of concrete dams in water
collection. According to Wolff (1985), about three - fourths of all large dams are
constructed of earth and rock-fill. The earth dam is the most important structure among
water resource structures, because it is the most economical. N o earth dam, which has
been built based on modern soil mechanic concepts, has failed. In recent years, the earth
dams are considered to be as safe as concrete dams (Singh, 1976).
The use of reinforcement in earth dams allows the reduction in displacement, stress
level, fill volume, and at the same time, increases the safety factor of the slope of the
dam. Other advantages of RSDs are: speed of construction; the flexibility of the
structure; the possibility of spillway construction in the crest of dam; and the possibility
of spilling a portion of flow over the unfinished dam. By the use of reinforcement, it is
possible to eliminate the downstream slope and reduce the upstream slope of the dam.
This results in a considerable reduction in the fill volume and the costs.
The state of stresses in RSD, the application of loads acting on dam, the lateral stresses
acting on the facing panels, and the assessment of shear stresses along the
reinforcements are not yet completely understood. The best method to be used to
analyse the internal stability of RSDs, h o w the influence of construction stages should
be simulated in the design of RSDs, and how the state of stresses should be stabilised at
the end of construction have not yet been fully answered. These should be considered
in the design criteria. In this chapter, history, classification, forces evaluation, stability
51
EVALUATION OF SOIL DAMS CHAPTER THREE
analysis, and foundation behaviour of conventional earth dams and RSDs will be
presented and discussed.
3.2 CONVENTIONAL EARTH DAMS
3.2.1 History
The date of construction of the oldest dams is not known for certain but the oldest
known earth dams were constructed about 500 B C in India (Singh, 1976). However,
Smith (1971) claims that the Sadd-el Kafara, D a m of the Pagana, which was discovered
in 1885, was built sometimes between 2950 and 2750 B C . The oldest known arch dam
was constructed in Iran (Smith, 1971). Today, there are many large rigid arch dams,
gravity dams and buttress dams in the world.
During ancient times, earth dam construction was improved. Construction
improvements were mostly undertaken by architects (Smith, 1971). By 1900 there were
less than 10 earth dams over 30m in heights (Singh, 1976). N o dam exceeding 40m in
height had been constructed until 1925 (Singh, 1976). Since 1925, the increase in the
ability of engineers to build safe and economical earth dams has led to the construction
of a greater number. From this date, the number of earth dam constructions has been
greater than in all previous history (Sherard, 1976). Causes of soil dam failures based on
Sowers (1961) is tabulated in Appendix A.
In reality, the improvements of large earth dams started after the improvement of soil
mechanics. For example, the 111m high Aswan dam with a capacity gross storage 156.2
milliard cubic meters, the 235 high Oroville dam with the gross storage 4.3 milliard cubic
meters, the 300m high Nurek dam in Russia, were all built after soil mechanic
improvements. The Nurek dam has created a reservoir with total storage 10.5 milliard
cubic meters and generation capacity of 2100MW (Singh, 1976).
52
EVALUATION OF SOIL DAMS CHAPTER THREE
Some other important earth and rock-fill dams with their capacities and heights are: the
Djatiluhur dam in Indonesia with a height of 91.5m and 7.1 million cubic meters
capacity, Beam dam with a 134m height and 32.5 million cubic meters capacity, Mica
dam with a 244m height and 32.1 million cubic meters capacity, and the Portage
Mountain dam with a 138m height and 70 milliard cubic meters capacity (Singh, 1976).
3.2.2 Classification
Dams may be classified based on: construction material; rigidity; use; structure; and
hydraulic design. A general classification of dams is shown in Fig. 3.2.2.1. O n the basis
of rigidity, dams are classified into two major categories: rigid and non-rigid. In both
categories, further classification is made with respect to construction material.
Rigid dams may be constructed from concrete, masonry, timber and even steel. The
latter two are not particularly common at the present time. Based on their structures,
types of rigid dams are arch dams, gravity dams, buttress dams or a composite of all
these.
Non-rigid dams are usually of the gravity type and made of earth or rock-fill materials.
This category is classified into two groups: earth dams and rock-fill dams. According to
U. S. Army Corps of Engineering (1982), dams may be classified based on height and
capacity storage as follows:
Table 3.2.2.1 Classification of dams based on storage and height (U. S. Army Corps of
Engineering, 1982)
Category
Small
Intermediate
Large
Storage (acre-feet)
50 < volume < 1000
1000 < volume <50,000
50,000 < volume
Height (feet)
25 < height < 40
40 < height < 100
100< height
53
EVALUATION OF SOIL DAMS CHAPTER THREE
In rigid dams the technique of construction is usually very complicated. For example, in
concrete arch dams special casings with particular arch should be used. Special casings
need professional workers, special machines and equipment for construction and
installation. These requirements cause the costs of dam construction to rise. Most parts
of the materials of a concrete dam are transported from factories to the location of the
dam. For example, reinforcement and cement are transported to the location of a
concrete dam from factories, increasing the costs of dam construction. Therefore, the
project may become un-economical.
The stages of construction in non-rigid earth dams are adaptable to the local area.
Techniques of construction are not very complex, in comparison with the concrete type.
Embankment dams do not need any casing. The need of special machines and specialist
workers is very low for the earth dam in comparison with that of the concrete dam. This
leads to a decrease of cost of dam construction. Provision of the earth dam material is
much easier than that of a concrete dam. Local materials are usually used for earth dam
or rock-fill dam construction. Therefore, the cost of the earth dam construction per unit
length (of the dam) is generally less than that of the concrete dam. For example, the cost
of a concrete work per unit volume in a concrete dam may sometimes be 20 times more
expensive than an earth work per unit volume in an earth dam (Singh, 1976).
A gravity concrete dam with the length of 500m and height of 100m may need at least 3
million cubic meters concrete and this volume of concrete needs about 1 rnillion ton
cement, which is usually an expensive material. Therefore, it is better to built an earth
dam instead of a concrete one because it is usually more none-economical and the
concrete can be used in the construction of other structures such as bridges, hospitals,
airports and buildings instead of using in dams. In conclusion, the readily availability of
the materials needed around the actual location of the earth dam, the compatibility of
earth dam with the environment, and the need for only simple technology have all gives a
better role for earth dams to be used and assisted in a reduction in the costs of earth dam
construction.
54
EVALUATION OF SOIL DAMS CHAPTER THREE
CLASSIFICATION OF DAMS
BASED ON CONSTRUCTION MATERIAL
BASED ON FLEXIBILITY
BASED ON USE
BASED ON STRUCTURE
BASED ON HYDRAULIC DESIGN _ ^ ^ _ _ _ _ _
CONCRETE DAMS
MASONRY DAMS
EARTH-FILL DAMS
ROCK-FILL DAMS
TIMBER DAMS
STEEL DAMS
MIXED DAMS
RIGID DAMS
NON-RIGID DAMS
STORAGE DAMS
FLOOD CONTROL DAMS
POWER
NAVIGATION
MULTI DAMS
PURPOSE
ARCH DAMS 1 BUTTRESS DAMS I
GRAVITY DAMS
COMPOSITE DAMS 1
OVER FLOW DAMS |
NON-OVERFLOW DAMS
MIXED DAMS Z3 Fig. 3.2.2.1 General classification of dams
55
EVALUATION OF SOIL DAMS CHAPTER THREE
3.2.3 Associated Facilities
Locks, power stations, spillways, fish ladders, baffle piers, side channels and outlet
works are the associated facilities which are normally necessary in the site plan of dams.
The costs of the associated facilities of an earth dam may be equal, or even more than,
the constructional cost of the structure. The type, shape and size of a dam influences the
location and position of power station. For example, a power station may be easily
constructed within the concrete dam, however, the construction of a power station
within an earth dam is usually a costly project.
The construction of spillway is necessary to control and regulate the outflow from the
reservoir. There may be for example free fall, side channel chute, tunnel or a glory
spillway. The constructions of spillways such as sharp crested, broad crested, or ogee
shaped on the top of concrete dams are usually recommended. These are impossible to
construct on the top of earth dams. Therefore, to discharge out-flow from the reservoir
of an earth dam, the construction of a separate spillway such as glory spillway may be
recommended.
3.2.4 Factors governing selection of a type
The shape of valley, the geological condition, the topography, the spillway location, the
foundation condition, the earthquake situation, the material availability, and, finally, the
comparative costs are factors dictating the type of dam to be constructed. For example,
the shape of dam is a function of the length and the height of the valley. If the height of
valley is more than 3 times of the length of valley and both abutments are formed from
rock or other high strength material, an arch dam may be suitable and economical, while
other types may not be economical and their constructions may even be impossible.
Gravity dams and buttresses dams are usually used in average valleys. Embankment
dams are usually suitable and economical for wide valleys with deep over-burden. A
type of composite section may be used in irregular valleys as shown in Fig. 3.2.4.1.
56
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.2.4.1 A general view of a composite dam
3.2.5 Materials
Typical types of soil in or under dams and their properties (including: permeability, shear
strength, compressibility, workability, and sensivity to seepage and piping), based on
United States Bureau of Reclamation, 1974, are shown in Appendix B.
3.2.6 Design procedure
The purpose of dam construction, the location and type of dam, the necessary types of
material for dam construction and environmental considerations are all concerns in the
initial study of the dam. Factors governing design including availability of materials, the
diversion of river, the shape of valley and the characteristics of foundation should also be
considered at this stage. The design of associated facilities, the details of construction
stages and cost calculations should be evaluated in other stages of design.
Design consideration needs evaluation and investigation about the design parameters
involved. In earth dams, design considerations are divided into three groups: factors
influencing design, factors relating to the type of earth dam, and factors affecting design
details. Factors influencing design are: availability of materials for embankment
construction; characteristic of foundation; shape and size of valley; river diversion;
location of spillway; situation of spillway; probable wave action, earthquake activity and
availability of time for construction. Factors relating to the type of earth dam are: types
of alternative earth dams; shape and size of shells and core; downstream drains and
alternative sections. Factors affecting design details include: embankment side slopes;
57
EVALUATION OF SOIL DAMS CHAPTER THREE
internal and external stability; filter zones; embankment freeboard; crest width and
chamber.
3.2.7 Sections of Earth Dams
The sections of non-homogeneous earth dams are generally formed from core and shells.
Each non-homogeneous earth dam has an impervious zone called core within its body.
This plays an important role in preventing water leakage. Non-homogeneous earth dams
include the central core types or inclined core types. The central core types are usually
suitable for both large and small earth dams, however, inclined core types are usually
suitable for low earth types. The core is constructed using clay, silt, concrete or
asphaltic materials. Sometimes, the designers choose a thin core type because of
economical considerations and the availability of materials. In this type, the thickness of
the core is less than the others. A cross-section of a thin core type is shown in Fig.
3.2.7.1.
2.5
lv^' ^t^""^ Upstream shell
10
Thin core
1P* 2
f 1 \ ^\l 7 ; 1 \ Transitions^**^
\ Downstream shell ^ v .
Fig. 3.2.7.1 Cross-section of a thin core earth dam
The significant role of shells is as a protection to both sides of the core. The shells are
normally provided from local materials. The upstream materials should be provided
from the pervious material, because the water within the upstream shell should be
58
EVALUATION OF SOIL DAMS CHAPTER THREE
followed rapidly when rapid drawdown occurs. Otherwise, the upstream shell is in
danger of cylindrical or inclined sliding. Pervious material, semi-pervious material, semi-
impervious material or even random material is usually used as external shell material. It
is necessary to place a transition layer between the core and the shell when the shell
material is obtained from coarse materials. The location of a transition layer is illustrated
in Fig. 3.2.7.1.
In homogeneous earth dams, the role of core and shell are provided by the body of dam.
In this case, the material of dam is normally chosen from impervious or semi-impervious
types. Other types are not permitted. Therefore, the use of homogeneous earth dam is
usually un-economical, unless the particular homogeneous needed material is available.
Sections of earth dams are usually chosen based on foundation type and dam height
Based on the type of foundations, dams are divided into: impervious foundations,
shallow impervious foundations and deep impervious foundations.
Typical sections for impervious foundations, according to U. S. Army Corps of
Engineers, are shown in Fig. 3.2.7.2. A central core dam with two zoned shells is
suitable in large earth dams with impervious foundation. In this case, upstream and
downstream shells are usually formed from two zones. The internal shell zones may be
chosen from random materials. The central core type, suitable for high and moderately
high dams is shown in Fig. 3.2.7.2a.
The inclined core type can provide wider area in core. This type is usually useful in
small earth dams. The inclined core type, which provides a wider working zone in the
core for low dams, is illustrated in Fig. 3.2.7.2b. A homogeneous type, requires
relatively flat slopes. This is illustrated in Fig. 3.2.7c.
59
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.2.7.2 Typical sections of impervious foundation of earth dams
In the shallow pervious foundations, the shape of the core is not different from that of
the impervious foundation. However, the core should cut the impervious foundation
layer. Cutting the impervious foundation layer is not necessary for the shells in these
cases. Three types of shallow pervious foundation dams, according to U. S. Army
60
EVALUATION OF SOIL DAMS CHAPTER THREE
Corps of Engineers, are shown in Fig. 3.2.7.3. A central core type, suitable to high and
moderately high dams, is shown in Fig. 3.2.7.3a. The inclined core type, providing a
wider working zone, in the core for low dams is illustrated in Fig. 3.2.7.3b. A modified
homogeneous type, is illustrated in Fig. 3.2.7.3c.
X P/R M\R \ p X.
Cut-off trench \ / Pervious stratum
(a)
/ P / Mf SM, SP OR P Nv
Cut-off trench \ / Pervious stratum
(b)
y^ M OR SM ^ v
Cut-off trench \ / Pervious stratum
(c)
M= impervious; P= pervious; SP= semipervious; SM= semi-impervious; R= random
Fig. 3.2.7.3 Typical sections for shallow pervious foundation of earth dams
61
EVALUATION OF SOIL DAMS CHAPTER THREE
In the deep pervious foundation dam, the core is connected to the impervious foundation
layer by a curtain wall. The curtain wall is usually chosen from clay, concrete or
asphaltic material. Typical sections for deep pervious foundations, according to U. S.
Army Corps of Engineers, are shown in Fig. 3.2.7.4. A central core type, an inclined
core type and a modified homogeneous type are shown, respectively, in Figures 3.2.7.4a
to 3.2.7.4c.
The range of slopes for the two shells of earth dams is determined, based on internal
friction coefficients of soil, types of materials and their unit weight, the plane zones of
sliding in the shells and a safety factor. The range of upstream slope is usually about
2.5-3 horizontal per 1 vertical. This range is usually about 2-2.5 horizontal per 1 vertical
in the downstream slope.
3.2.8 limitations of Conventional Earth Dams
Although, there are many reasons for preferring earth dams, the use of earth dams is
limited because of some restrictions including: weir limitation; spillway limitation; power
house limitation; outlet restriction and the large amount of material needed for
construction of conventional earth dams.
The crest of concrete dam is usually used as spillway in overflow conditions, however
the use of the crest on the top of an earth dam as spillway is impossible. The
construction of conventional earth dam is economical only if there is a suitable hill, to be
used as spillway, near the dam's location. Otherwise, a costly spillway arrangement is
needed to be built for the earth dam. This limits the use of earth dam in any location.
The construction of a power house in the body of concrete dams is possible, however
this is impossible in the body of earth dams. The power house needs to be located
independently. The separate construction of the power house increases the cost of dam
project.
62
EVALUATION OF SOIL DAMS CHAPTER THREE
Curtain wall Deep pervious
foundation
(a)
(b)
MORSM
Curtain wall Deep pervious
foundation
(c)
M= impervious; P= pervious;
SP= semipervious;
SM- semi-impervious;
R= random
Fig. 3.2.7.4 Typical sections for deep pervious foundation
63
EVALUATION OF SOIL DAMS CHAPTER THREE
Finally, another important problem connected with the construction of the earth dam is a
great amount of material needed. A concrete dam with the length of 1000m and height
of 100m needs about one million cubic metres concrete. However, the volume of a
conventional earth dam needs at least 22 million cubic metres of soil for the same
construction. This means that the volume of work in the construction of the earth dam
may be 20 times that of the construction of concrete dam. Therefore, the volume of
earth material in the conventional earth dams should be reduced.
3.3 REINFORCED SOIL DAMS
3.3.1 History of reinforced soil dams
As shown in Chapter two, the first RSD was constructed in the Bimes Valley near
Hyeres situated in the south of France. The dam was constructed with 9 m high vertical
downstream face using precast concrete facing units. A general view of the Vallon des
Bimes dam is shown in Fig. 3.3.1.1. A cross-section of the dam has been shown in
Chapter two (Fig. 2.3.7.2). Much larger dam, called the L'Estella Dam, was
constructed in Estelle with a maximum height of 29.5m as shown in Fig. 3.3.1.2.
The most complex dam built of reinforced earth is the Taylor Draw Dam, on the White
River in Colorado (USA), which is 380m in length, and with a flowrate of its spillway
which can reach 1850 m3/s (Reinforced Earth Company Brochures). The vertical
downstream side of dam has allowed construction of spillway on the top of its central
section which has been formed by reinforced earth. A core of impervious material was
used in the foundation to control the water penetration of foundation. T w o vertical
drainage zones, upstream and downstream drainage zones, were used in its reinforced
earth area to control the water penetration in its body. A thin layer of impervious soil
and a reinforced concrete slab topped the reinforced earth zone, to prevent water
penetration from the crest. It has been estimated that the construction of this dam by
reinforced earth could save about 1.5 million dollars (Reinforced Earth Company
64
EVALUATION OF SOIL DAMS CHAPTER THREE
Brochures). The general view, front face elevation and typical cross section of Taylor
Draw D a m are shown in Figures 3.3.1.3. and 3.3.1.4a & b, respectively.
Fig. 3.3.1.1 Vallon des Bimes dam (Reinforced Earth Company Brochures)
Filter
Impervious zone
i;ni;iiimninnimnn!
ft'*^y*YO':'i.i.i.i.i.i.:
29.5 m
^v
Fig. 3.3.1.2 L'Estella Dam (after Taylor & Drioux, 1979)
65
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.3.1.3 A general view of Taylor Draw Dam (Reinforced Earth Company
Brochures)
1616.5 m 1616.8 m 1620 m
M -7—r-
(a)
16m 22.5m
Fig. 3.3.1.4 Front face elevation and cross-section of Taylor Draw Dam (after
Reinforced Earth Company Brochures)
Pells (1977) has reported that the techniques of using downstream zones of reinforced
rock-fill in the completion of three embankment dams (Bridle Drift, Xonxa and Lesapi
Dams) in South Africa were not successful. In the case of Xonxa D a m a major failure
developed, while at the Bridle Drift and Lesapi dams minor failures occurred when
66
EVALUATION OF SOIL DAMS CHAPTER THREE
floods passed over the partially constructed dams (Pells, 1977). The cross section of
Bridle Drift dam is shown in Fig. 3.3.1.5.a, its downstream elevation after the flood is
shown in Fig. 3.3.1.5.b. The cross section of the Xonxa dam and the reinforcing
system designed for the rock-fill at the Xonxa dam are shown in Figs. 3.3.1.6a & b,
respectively.
Fig. 3.3.1.5 a) The cross-section of Bridle Drift dam b)Downstream elevation after the
flood (after Pells, 1977)
Reinforced earth can also be used for increasing the height of existing dams using a
double-faced structure. A good example of this application is the earth dam at Lake
Sherburne in Montana (USA). This dam is 60 years old and rises to a height of 26m. In
1983 it was topped with a double-faced reinforced earth wall 7.3m wide and 350m
long, increasing the reservoir holding capacity to approximately 200 million cubic
metres. The reinforced earth solution was 3 5 % less expensive than the other methods
67
EVALUATION OF SOIL DAMS CHAPTER THREE
for raising the dam (Reinforced Earth Company Brochures). The cross section of dam
is shown in Fig. 3.3.1.7.
Fig. 3.3.1.6 a) The cross-section of the Xonxa Dam, b) Reinforcing system designed
(Pells, 1977)
Fig. 3.3.1.7 New section of earth dam at Lake Sherburne (Reinforced Earth Company,
1988)
68
EVALUATION OF SOIL DAMS CHAPTER THREE
The use of reinforced earth is also possible for earth dam restoration. According to the
Reinforced Earth Company, the uncertain condition of the Jamesville (a 100 years old
dam) in N e w York, was repaired by reinforced soil. The stability of this dam, was
improved because reinforced earth zone was added to the old dam, which had a height
of 15m and the capacity of 8,000,000, cubic metre in water retaining. The resulting
cross section of the dam is shown in Fig. 3.3.1.8 (Reinforced Earth Company
Brochures).
Reinforced concrete spillway cap
Heavy stone filling^5== Existing
dam
//>/// ////////////////
Bed rock
Fig. 3.3.1.8 New section of Jamesville, New York dam (Reinforced Earth Company
Brochures)
3.3.2 Other Investigations
According to Miki et al. (1988), a sequence of experiments were directed on test
embankments in order to establish a suitable design method for this type of structure.
The embankments were 3 m high with 1:0.7 slope, variable length and spacing of grid
laying as shown in Table 3.3.2.1 and Fig. 3.3.2.1. They were subjected to a severe test
of 15 mm/hr rain.
Three types of grid laying and three types of grid layers were used. The surface and
internal displacement were measured, using inclinometers and displacement gauges.
The foil strain gauges attached to the grids measured the strains on polymer grids. The
degree of saturation was determined from the moisture distribution inside the
embankment. The manometers inserted in the embankment measured the depth of
69
EVALUATION OF SOIL DAMS CHAPTER THREE
ground water. The properties of soil fill used within the reinforced embankment are
shown in Table 3.3.2.2.
Table 3.3.2.1 Test cases (after Miki et al; 1988)
Test case
Case 0.0
Case 1.3
Case 2.3
Case 3.3
Case 3.1
Case 3.2
Case 3.3
Grid laying
length L
0
1
2
3
3
3
3
Grid laying
layer N
0
3
3
3
1
2
3
8m
2 m 2.1 m 3.64 m
3 m
\j s \> s
Foil strain gauge
s s s (a) Case 3.1
3 m
1 m
i 1 m /" i i i i i
Polymer grid i i i i
1 m
(b) Case 3.2
2.6 m
2.5 m
Fig. 3.3.2.1 Standard sections of reinforced embankments (after Miki et al; 1988)
The grids (Table 3.3.2.1 Cases 3.1, 3.2 and 3.3) have a length of 3m and different
number of layers: 1, 2 or 3, called Case 3.1, 3.2 and 3.3, were tested. The relationships
70
EVALUATION OF SOIL DAMS CHAPTER THREE
between embankment deformation, the strain distribution of grid and the degree of
saturation are illustrated in Fig. 3.3.2.2.
Table 3.3.2.2 The property offi.il material (after Miki et al; 1988)
Natural water content
Specific gravity
Gravel fraction
Sand fraction
Silt fraction
Clay fraction
Maximum grain size
Uniformity coefficient
Optimum moisture content
Maximum dry density
Permeability
22.4 - 24.3 (%)
2.7
1 - 2 (%)
70 - 74 (%)
12 - 20 (%)
9 - 12 (%)
4.76 (mm)
5.5 -15.9
17 - 18.6 (%)
1.64- 1.70 (t/m3)
1.5 -1.6 X 10 -4 (cm/s)
Case 1.3
Case 2.3
Case 3.3
Sr(%)
Sr(%)
Sr(%)
Case 3.1
Case 3.2
Case 3.3
Sr(%) - Degree of saturation
Sr(%)
Sr(%)
Sr(%)
Fig. 3.3.2.2 Relationship between embankment deformation, the strain distribution of
grid and saturation degree (after Miki et al; 1988)
71
EVALUATION OF SOIL DAMS CHAPTER THREE
In the case of 1 layer used, the horizontal displacement of the top slope increased
quickly when the accumulated rainfall reached 110mm. The slope was eroded for a
depth of 5 0 0 m m at the time of 2 1 0 m m rainfall. In the case of both 2 and 3 layers, there
was only surface erosion without any sliding, the accumulative reached the final
rainfall of test. The basic equations that were used to evaluate the internal stability of
the reinforced embankment were:
M +AM FS = -* r-
M,
(3.1)
and
AM =Y(7\y.) r *->K riJiJ
(3.2)
where Mr and Md are, respectively, the resisting and driving moments of soil mass,
AMr is the resisting moment due to grid reinforcements, Tri is the pull-out resisting
forces due to /th layer of grid reinforcement, and y/ is the vertical distance of the ith
layer of grid to the centre of slip circle as shown in Fig. 3.3.2.3.
y. y
.o
y
O'
r
Fig. 3.3.2.3 Embankment section used in stability analysis (after Miki et al; 1988)
72
EVALUATION OF SOIL DAMS CHAPTER THREE
Tn is calculated by the smaller value of either the allowable tensile strength, Ta, of
grid, or the pull-out grid resistance Tpi which can be equated as:
r?.=2a/tan(J,L. {33)
where, ai is the vertical stress on the z'th layer grid, L; is the boarding length of /th layer
grid, and the constant 2 represents both sides of the grid.
The researchers were concerned that the safety factor, FS* (obtained by substituting the
value of Tji in Equation 3.22 with the tension, T, which is equal to multiplying grid
strain e; by stiffness J) is found to be smaller than the FS (obtained by Equation 3.21
with pull-out resistance force Tn). It was concluded that the grid and earth integrated
into a rigid body with a decreased deformation of the grid reinforcement. The
differences of both factors of safety can be calculated as:
AFS = FS - FS* =*ACIL (3.4) Md
where, L L and R are the length and radius of slip circle, Md is the driving moment of
soil mass, and A C is the increase of an apparent cohesion.
The rate of increase of apparent cohesion, Rc, was determined by the following
equation:
R =£±AC c C
where, C is the cohesion coefficient, and A C is the increase of apparent cohesion. The
results of computation for FS*, FS, and Rc for different types of reinforcement are
shown in Table 3.3.2.3.
73
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EVALUATION OF SOIL DAMS CHAPTER THREE
It was also concluded that in the testing, with the grids laying 0.75m vertically spaced,
Case 1.3, with the rates of laying length to embankment height L/H<0.33, the external
stability governs, and for Case 2.3 where UH>0.67, the internal stability governs the
overall stability of the embankment. As a result of interaction between the grids and
fill material, the deformation of the reinforced zone is decreased when the grids are laid
horizontally in several layers. Also, the analysis of the embankment as an elasto-plastic
body was done by finite element method analysis, and the results were in close
agreement with those of the tests. Therefore, it was concluded that the finite element
method is suitable for analysing the reinforcing mechanism in the embankment (Miki et
al., 1988).
Dean and Lothian (1990) used a geocell mattress, illustrated in Fig. 3.3.2.4, to
overcome problems encountered in the construction of a 9 m embankment over an area
of variable soft deposits. It was expected that the underlying soft layers would reached
plastic failure mode under the pressure of the embankment constructed without
reinforcement. In this case the embankment would not be able to bear the internal
strain and would fail in the centre. The application of geocell mattress was expected to
prevent the failure by reducing the settlement and internal stresses.
Fig. 3.3.2.4 Embankment with geocell (after Dean and Lothian; 1990)
75
EVALUATION OF SOIL DAMS CHAPTER THREE
Preventing slip failure and transverse rupture were also expected to be other benefits of
reinforcing the embankment base. However, the mattress did not behave as predicted.
It is still considered that the use of a geocell mattress is economical compared to other
solutions and it can reduce the time of construction (Dean and Lothian, 1990).
Koga et al. (1988a) used non-woven fabric nets and steel bars in 14 cases of model
shaking tests of embankments to investigate the seismic resistance of an embankment
constructed on an inclined ground. A steel box of 2 m high, 8 m long and lm wide was
used for the model of a bed slope. The properties of reinforcement used are shown in
Table 3.3.2.4 and the summarised condition of the parameters used are shown in Table
3.3.2.5.
Table 3.3.2.4 Properties of reinforcing elements (Koga et al, 1988a)
Type
Non woven fabrics
Plastic net
Steel bar
Properties
Nylon 70%, Polyester 30%, Thickness .2 m m
Polyethylene 100%, Grid 2.5 #2.5 m m
Pianowire, diameter 3.5 m m
The kind of reinforcement, the spacing between them, the slope surface gradient, and
the existence of benches on a bed slope were varied during the experiments. It was
assumed that Poisson's ratio v is 0 for reinforcements. Also, the reinforcement ratio, R,
which represents the ratio of strength increase of a reinforced soil to an unreinforced
one at a specified reference strain, was defined as:
R= —^ (3.6) a3QAH
where, £ 3 ^ is average horizontal tensile strain of the reinforced soil, E is the Young
modulus of reinforcements, t is the thickness of reinforcements, a30 is the horizontal
confining pressure, and A H is the spacing between the reinforcements.
76
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EVALUATION OF SOIL DAMS CHAPTER THREE
The tests were conducted under sinusoidal wave loading, starting from 4 Hz and 210
sec, while the acceleration was increased step by step. After each step, the tensile
force in reinforcement and the acceleration were recorded.
During the tests, the embankment model was sliding along a slip surface and its crest
was settling under the large acceleration. The deformation of reinforced embankments
were less than the unreinforced ones for some slope gradients and the value of crest
settlement became less when the spacing of non-woven fabrics became smaller. The
settlement of the embankment with plastic nets as reinforcement, which has larger
tensile stiffness, was less than that where non-woven fabrics in the same spacing was
used. The deformation of embankments also decreased when the reinforcements were
overlapped on their slope surface. The embankment settlement and deformation also
became less when the reinforcements were fixed to the bed slope. The deformation of
the embankments became larger when the slope became steeper (Koga et al., 1988a).
Fukuoka and Goto (1988) had investigated design and analysis of steel bars with anchor
plates used to strengthen the high embankment on soft foundation. A n embankment
was constructed (10m in thickness) on soft ground, mainly used for rice fields. The
steel bar reinforcing method was used to reduce deformation at the ground surface and
to strengthen the embankment.
The preconsolidation pressure a'p and effective overburden pressure a'v both increase
with depth. The dimensions of bearing plates used as anchors were 250x300x9 mm.
The diameter of the steel bars were 22 mm, placed at 500 mm horizontally and 600 mm
vertically. The properties of soil used in the embankment and foundation are shown in
Table 3.3.2.6, while the constants used for finite element method (FEM) analysis are
shown in the Table 3.3.2.7. The formulae and the resulting tensile force in the
reinforcements are shown in Table 3.3.2.8. Fig. 3.3.2.5 shows the observed values, and
the predicted values by F E M of stresses on steel bars. Fig. 3.3.2.6 shows the bearing
78
EVALUATION OF SOIL DAMS CHAPTER THREE
forces applied to the plates. These forces were calculated from the tensile forces on the
tensile bars.
Table 3.3.2.6 The property of foundation and embankment soil (Fukuoka and Goto,
1988)
Soft clay
Embankment
1
m
17
20
Unconfined compressive
kN strength qu (—~-)
mz
20 for 0 < Z <3m
20 + 6.6 (Z-3) for 3m < Z
_
Coefficient of
consolidation
(Cv'xl07)
3.3(m2/s)
_
C
kN
m
-
10
<t>*
-
30
Table 3.3.2.7 The constants used for finite element analysis (Fukuoka and Goto, 1988)
Unit weight of submerged soil (kN/m*)
Poisson's ratio v
Coefficient of earth pressure K
Coefficient of deformation E (MN/m2)
Embankment
20
0.3
0.43
10
As
10
0.3
0.43
Ac
.33
0.5
Therefore, based on experiments done by Fukuoka and Goto (1988), reinforced steel
bars with gravel compaction piles can be used to strengthen high embankments on soft
foundation and to reduce their displacement. The largest tensile force in the bars occur
at the lower layer and its ratio to that in the middle layer was about 2. The analysis of
reinforced earth embankment done by F E M was in good agreement with the results
from the field experiments (Fukuoka and Goto, 1988).
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EVALUATION OF SOIL DAMS CHAPTER THREE
Upper bar
Middle bar
Lower bar
7.0 m
Stress 10 r~
(kN/m2) 5
0
-5 -10
Upper bar
Stress 5 (kN/m 2) 0
-10
-20
-30
A——A
Middle bar
Stress Q -
(kN/m2) .10
-20
-30
-40
-50
Yield point (-35)
Lower bar
O Bank height 4.2m 122 days after
• Bank height 4.2m (Predicted by FEM)
A Bank height 7.0m 193 days after
A Bank height 7.0m (Predicted by FEM)
Fig. 3.3.2.5 The observed and the predicted by FEM values of stress on steel bars (after
Fukuoka and Goto, 1988)
82
EVALUATION OF SOIL DAMS CHAPTER THREE
7.0 m
Middle bar
Lower bar 4.2 m
Plate
Stress on
plate (kN)
10
0
-10
-20
-30
-40
-50
-60
~Q — >
—
-
¥ \
\
N. i
\
o- -
\'
.o'\
O"
1 JF
, Ny
\
^o~*
Middle
o—
Lower
Fig. 3.3.2.6 The bearing forces applied to the plates (after Fukuoka and Goto, 1988)
Koga et al. (1988b) used the finite element method to study the behaviour of reinforced
soil by a geogrid system with particular reference to an embankment on soft soil. The
geometry of the embankment and its material properties are shown in Fig. 3.3.2.7. The
use of geogrid within the embankment allows higher compaction to be achieved, hence
a reduction in the width of the embankment, and economical construction are the
results. The stiffness of the reinforced soil embankment may be increased and the
amount of settlement may be reduced by the use of a geogrid mattress in the
embankment.
The behaviour of the individual elements containing soil, reinforcement and interface
elements were analysed and the results were as shown in Figures 3.3.2.8 and 3.3.2.9.
Fig. 3.3.2.8 shows the settlement profile along a horizontal section in the subsoil at the
ground level. Fig. 3.3.2.9 shows the settlement profile along a vertical section at the
centre of the embankment. The vertical stress (Cy) and the maximum principal stress
83
EVALUATION OF SOIL DAMS CHAPTER THREE
distribution along the horizontal section at the top level of subsoil, below the
reinforcement, are plotted in the Figures 3.3.2.10a and b, respectively. As shown in the
Fig. 3.3.2.10a, the distributions of vertical stress for the three cases are the same. Also,
based on the results shown in Fig. 3.3.2.10b, the use of grid reinforcement reduces the
maximum tensile stress up to about 50%. The stress distribution in the reinforcement is
shown in Fig. 3.3.2.11. Therefore, provision of geogrid reinforcement reduces the
settlement profile.
15m
5m Clay E=300 t/m2
, 14m
1 E=10 t/m2
v=0.4 7
¥=1.8 t/m
v=0.45
82m
:L
2
Y=1.6 t/m
Gravel 9 E=15 t/m v=0.3 9
T=0.8 t/m
Fig. 3.3.2.7 Embankment (after Koga et al, 1988b)
10
Settlement 0
Distance from centre line
20 t 3p ty40(m) 12-^ Grid 2
Grid 1 No grid
Fig. 3.3.2.8 Settlement along a horizontal section in the subsoil at the ground level
(after Koga etal 1988b)
84
EVALUATION OF SOIL DAMS CHAPTER THREE
0 Settlement
0
Depth 10 _.
20
(m)
<m%
No grid
Fig. 3.3.2.9 Settlement profile along a vertical section (after Koga et al, 1988b)
Distance from centre line
10 20 30 40 (m)
0
Stresses
(t/m )
10 -
20
30 J
j . i
Gridl
No grid
(a) Vertical stress
Tension 10 -•
Stresses
(t/m ) 0
10 ~t
No grid
Grid 2
(m)
Gridl
Compression
(b) Principal stress
Fig. 3.3.2.10. Vertical and principal stress distribution (after Koga etal; 1988b)
85
EVALUATION OF SOIL DAMS
Tension
4000 -
Stresses
m2, °
4000 ~
Compression
" »--__Hjj^--s_
• — ^ o ^ m >
Lower 1 1
10
Middle
s W ^ _ y
i 20
Upper
^ T M ^ \ ^
"T -^^p— 30 (m) j
Fig. 3.3.2.11 Stress distribution of reinforcement (after Koga et al; 1988b)
The behaviour of a reinforced embankment on soft ground was investigated by Hird et.
al (1990). The numerical modelling of the embankment was evaluated using the
computer program CRISP. The geometry and finite element mesh of the embankment
is shown in Fig. 3.3.2.12.
Constant pore suction was assumed to exist within the embankment. A summary of
input parameters, including the property of the foundation and embankment soils, is
shown in Tables 3.3.2.10 and 3.3.2.11. Fig. 3.3.2.13 shows the effective vertical stress,
preconsolidation pressure, over-consolidation ratio, effective horizontal stress and
undrained shear strength within the foundation. As shown in Fig. 3.3.13.d, the
computed shear stress under undrained conditions is seen after the predicted strength.
The tensile modulus of the reinforcement, which was assumed to be linear elastic
material, was taken as 450 kN/m. The results of six analyses are shown in Table
3.3.2.11 and the distribution of the settlement of the original ground surface and surface
displacement are plotted in Figs. 3.3.2.14 and 3.3.2.15, respectively. At least 7 0 % of
the settlement occurred in the clay layer. Fig. 3.3.2.16 shows the distribution of
reinforcement strains and forces. It can be seen in the figure that the results of Analysis
No. 4 was in good agreement with pattern.
86
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.3.2.12 The geometry and finite element mesh of the embankment (Hird et al,
1990)
Table 3.3.2.10 The properties of soil used in embankment (Hird et al, 1990)
Embankment
Fill
E' (kN/m2)
15000
•
V
0.3
C*
0
<&•
30
y(kN/m2)
20
Table 3.3.2.11 The properties of soil used in foundation (Hird et al, 1990)
Foundation
Peat
Clay
X
2.8
0.25
K
0.56
0.05
M
1.7
1.2
r
16.5
3.2
<
V
0.14
0.3
y(kN/m2)
11.4
16.2
87
EVALUATION OF SOIL DAMS CHAPTER THREE
Effective vertical stress (kN/m2) 0 W 20 30 40 50 60 0Y~
Depth (m) 6
8'
10-
Overconsolidation ratio 0 2 4 6 8 10 12
Preconsolidation Pressure
Beneath working 'lateform Depth
Outside working plate form
10-
Beneath working ' plateform
Outside working plateform
0
2
4
Depth (m)
6
8
10-
Effective horizontal stress (kN/m2) 0 10 20 30 40 50 60
1—T
Beneath working plateform
Depth
Outside working plateform
8
id-
i—r
Undrained shear strength (kN/m2) 0 5 10 15 20 25 30 0~
2
4 (m) 6
Outside working plateform
T
Beneath working plateform
Shear stresses computed by
CRISP
Fig. 3.3.2.13 Stress and strain profiles (Hird et al, 1990)
Table 3.3.2.11 The results of analysis (Hird et al, 1990)
Analysis
No
1
2
3
4
5
6
Embankment
Representation
Equivalent vertical loading
Equivalent vertical loading
Elements added in layers
Elements added in layers
Elements added in layers
Elements added in layers
Embankment
Suction
Not applicable
Not applicable
High
High
Low
Low
Foundation
Clay
Drained
Undrained
Drained
Undrained
Drained
Undrained
88
EVALUATION OF SOIL DAMS CHAPTER THREE
Toe Distance from embankment toe (m)
2.5 -Settlement (m)
No.l
Fig. 3.3.2.14 Ground surface settlement (Hird et al, 1990)
Distance from embankment toe (m)
0.5-
Horizontal displacement (m)
Fig. 3.3.2.15 Surface horizontal displacement (Hird et al, 1990)
The prediction of the results and the observations are summarised in Table 3.3.2.12.
Based on these results, the reinforcements appear to play a minor role in increasing the
stability of the embankment. Another analysis, conducted by later authors on the effect
of lack of the reinforcement, showed that although the horizontal displacement will be
increased up to 15%, the vertical displacement would remain constant (Hird, 1990).
89
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.3.2.16 Reinforcement strains and forces (Hird et al, 1990)
Table 3.3.2.12 Summary of predictions and observations (Hird et. al, 1990)
Item
Settlement (mm) on centre-line
Maximum horizontal displacement of Inclinometer A (mm).
Depth (m)
Maximum horizontal displacement of Inclinometer B (mm).
Depth (m)
Maximum Reinforcement tension (kN/m)
and Strain (%).
Distance from centre-line.
Maximum excess pore water pressure (kN/m2) in peat (0-3.5m
depth)
Maximum excess pore water pressure (kN/m2) in clay (3.5-
10m depth)
Predicted
Value
2000 + 350
430 + 90
1.8 + 0.5
500 + 70
2.5 + 0.5
12.2 + 2
2.7 + 0.4
10 + 0.5
Assumed
zero
80 + 80
Observed
Value
2250
270
2.9
300
3
2.3
8
20
90
The effect of reinforcement in an embankment was predicted and analysed using the
finite element method and Biot's consolidation theory, and compared with the measured
one by Yin Zong Ze (1990). The cross section of the embankment, called Stranstead
Abbotts Embankment, is shown in Fig. 3.3.2.17, while the physical and mechanical
parameters of soils are shown in Table 3.3.2.13.
90
EVALUATION OF SOIL DAMS CHAPTER THREE
Grey clay,
k
Brown
Peat
Gravel
1m
Fig. 3.3.2.17 Stranstead Abbotts Embankment (Yin Zong Ze, 1990)
Table 3.3.2.13 Physical and mechanical parameters of soils (Yin Zong Ze, 1990)
Soils
1-Fill
2- Sand
3- Brown clay
4- Peat
5- Grey clay
7
kN
m 3
19
19
16
10.5
16
C'
kN
m2
20
0
0
0
0
0>
20
35
33
25
33
Cu
kN
m2
15
14
40
W
(%)
64-127
400 - 605
35-37
my
2
m . ^MN
0.24 - 0.87
1.08 - 6.33
0.38 - 1.27
Cy
MN
1.7 - 3.7
2.7-31.4
8.4 - 22
The elliptical and parabolical yield surfaces, based on stress-strain relationship, were
developed and the following equations were presented.
F+-hep,P vl a
(3.13) M, {{P+Pr) i-«j; vl
aq
G M2(P + Pr) -q)
(3.14)
where, P, q and G are defined as follows:
91
EVALUATION OF SOIL DAMS CHAPTER THREE
p_al + a2 + <T3
3
q = [(a, - a 0 ) + (a0 -a,) + (CT3-a1) '1 " 2 / , v " 2 "3-
(3.75)
(3.76)
G=KGPa^n
a
(3.17)
in which, Pa is the atmospheric pressure, KQ, n, h, t, a, Mj, M2 and Pr are parameters
determined from triaxial drain tests and for the embankment foundation soils. These
parameters and AT are shown in Table 3.3.2.14.
Table 3.3.2.14 Computation parameters of foundation soils (Yin Zong Ze, 1990)
Soils
Brown clay
Peat
Grey clay
KG 20
10
20
n
0.7
1
0.7
Pr 0
0
0
M]
1.5
1.6
1.5
M2 1.3
1.1
1.3
h
6
5
6
t
0.5
1
0.5
a
0.1 0.1
0.1
K .004
.01 .004
The thickness, the average Young modulus and the Poison's ratio of the grid was
assumed to be 3 mm, 150 MPa, and 0.3, respectively. The comparison of computation
results with the data measured on site, including vertical and horizontal displacement
distribution along ground surface, pore water pressure at point B, and tension
distribution in the grid are shown in Fig. 3.3.2.18 to 3.3.2.20, respectively.
As shown in Fig. 3.3.2.18, the computed and measured vertical and horizontal
displacements were close to each other. Fig. 3.3.2.19 shows that the results of the
computed pore water pressure were not in close agreement with the measured ones.
Fig. 3.3.2.20 shows that the measured tensile distribution in the grid was lower than the
computed one (Yin Zong Ze, 1990).
92
EVALUATION OF SOIL DAMS CHAPTER THREE
(a) vertical
-©-
(b) horizontal
End of construction
18 months after
computed measured
Fig. 3.3.2.18 Displacement distribution along ground surface (Yin Zong Ze, 1990)
u(m
40^
30-
20~
0 1
0
fm2)
f t
f i S * f t i *
J > ) t / t
J *
f * It It
\ Computed
i \
\\ Measured
1 S \ ^ S
V. ** x
1 1
20 40
i
60 t(day)
Fig. 3.3.2.19 Pore water pressure at point B varying with time (Yin Zong Ze, 1990)
93
EVALUATION OF SOIL DAMS CHAPTER THREE
Tension (kN/m)
20
10 — ^y^7 - • "
0
End of construction
18 months after
• o o
computed
° W\ o v\
measured ©
Fig. 3.3.2.20 Tension distribution in the grid (Yin Zong Ze, 1990)
3.3.3 Classification of Reinforced soil dams
An understanding of the general behaviour of RSD is necessary for the selection of a
suitable RSD for a particular site. Categorising RSDs allows for the classification and
recognition of their general behaviour. General and possible classifications of RSDs,
based on their construction will be considered in the following paragraphs.
3.3.3.1 General Classification
Based on the material used, RSDs can be classified into two main groups: homogeneous
fill types and zoned types. Typical cross-sections of a homogeneous fill RSD and a
zoned RSD are shown in Fig. 3.3.3.1. The components of RSDs are soil,
reinforcements and facing panels.
Zoned RSDs can be further divided into impervious upstream shell types and central
impervious core types. In the later, shown in Fig. 3.3.3.1a, the central core should
made from impervious materials such as clay, clayey silt or clay mixtures for water
retardation. Fig. 3.3.3.2 shows the cross-section of an impervious upstream shell dam.
94
EVALUATION OF SOIL DAMS CHAPTER THREE
Unreinforced shell
Impervious core
Filter
Reinforced shell
Filter
(a) Zoned RSD (b) Homogeneous fill RSD
Fig. 3.3.3.1 Cross-sections of a homogeneous fill and a zoned RSDs
Impervious upstream shell
Facing panels
Downstream reinforced soil shell
Fig. 3.3.3.2 A typical cross-section of an impervious upstream shell dam
Another classification can be made with respect to the form of the core, including
central core RSDs and inclined core RSDs. A central core RSD is illustrated in Fig.
3.3.3.3a, while a RSD with inclined core is shown in Fig. 3.3.3.3b. All these types can
be further divided into four groups which are, vertical upstream face, vertical
downstream face, vertical both sides and inclined both sides as shown in Fig. 3.3.3.4.
In the cases of the vertical face of dams, the use of facing panels is necessary to prevent
erosion of soil and to facilitate the connection of reinforcements.
95
EVALUATION OF SOIL DAMS CHAPTER THREE
Upstream shell
Reinforced earth shell Reinforced earth shell
Upstream shell
Inclined impervious core
(a)
Central impervious core
(b)
Fig. 3.3.3.3 A central core RSD compared to an inclined core RSD
CLASSIFICATION OF RSDs BASED O N THEIR
SECTIONS
H O M O G E N E O U S FILL TYPES
Vertical
upstream
face
Vertical
downstr
eam face
Vertical
both
faces
Inclined
both
faces
ZONED TYPES
IMPERVIOUS UPSTREAM SHELL TYPES
Vertical
upstream
face
Vertical
downstr
eam face
Vertical
both
faces
Inclined
both
faces
IMPERVIOUS INTERNAL C O R E TYPES
CENTRAL C O R E TYPES
Vertical
upstream
face
Vertical
downstr
eam face
Vertical
both
faces
ZL INCLINED C O R E TYPES
Inclined
both
faces
Vertical
upstream
face
Vertical
downstr
eam face
Vertical
both
faces
Inclined
both
faces
Fig. 3.3.3.4 A general classification of RSDs based on material used and cross-section
shape.
96
EVALUATION OF SOIL DAMS CHAPTER THREE
The foundations of RSDs can be classified as soft foundation and rigid foundation. The
behaviour of RSDs is different in these two situations. Based on the type of foundation
soil, RSDs are classified as shown in Fig. 3.3.3.5. Other classifications may also be
considered based on hydraulic design and use. For example, based on hydraulic design,
RSDs may be classified into over-flow types and non over-flow types similar to
conventional earth dams (for more detail see Chapter 1).
CLASSIFICATION OF RSDs BASED O N FOUNDATION SOIL
SOFT FOUNDATION TYPES RIGID FOUNDATION TYPES
S H A L L O W SOFT FOUNDATION
TYPES
DEEP SOFT FOUNDATION
TYPES
Fig. 3.3.3.5 A classification of RSDs based on their foundations
3.3.3.2 Possible Classification
Although most RSDs are of the gravity type, there is no reason to claim that reinforced
soil arch and buttress dams can not be built in the future. As an illustrated example, the
cross section of an imaginary reinforced earth arch dam is shown in Fig. 3.3.3.6. In
this case, reinforcement may stabilise the structure by increasing the strength of the soil
and connect the facing panels of two sides. Therefore, the RSDs can be, potentially,
classified as gravity, arch or buttress types as shown in Fig. 3.3.3.7.
CLASSIFICATION OF RSDs
GRAVITY TYPES
BUTTRESS TYPES
ARCH TYPES
Fig. 3.3.3.7 A possible classification of RSDs
97
EVALUATION OF SOIL DAMS CHAPTER THREE
*r —
TA
/r^i
m
H — y.~
Fig. 3.3.3.6 Cross-section of an imaginary reinforced soil arch dam
3.4 FORCES ACTING ON SOIL DAMS
A n understanding of the forces acting on soil dams is essential for the analysis and
design of the structures. Actually, there are no main differences between the forces
acting on RSDs and the forces acting on other types of dams. However, the behaviour
of RSDs and other dams in withstanding forces is different. The forces resulting from
water pressure, silt pressure, ice pressure, earthquake pressure, foundation reaction,
seepage and the weight of structure all act on a RSD. In subsequent sections these
forces will be discussed separately, and the combinations of the loads (including usual
loading, unusual loading and critical loading) will be described.
3.4.1 External water pressure
Upstream and downstream hydrostatic pressures (Vj and V-j) and the weight of water
on the upstream and downstream sides (Wj and W2) of soil dams are external water
pressures which act on the dam. A schematic diagram illustrating the external water
pressures acting on an earth dam is shown in Fig. 3.4.1.1. The weight of water on the
upstream (or downstream) side is zero when the upstream (or downstream) face is
vertical as shown in Fig. 3.4.1.2. The value of the downstream water pressure is low,
consequently the effect of downstream water pressure can be ignored during the
analysis of soil dams.
98
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.4.1.1 External water pressure acting on an earth dam
Fig. 3.4.1.2 External water pressure acting on a vertical downstream face RSD
Referring to Fig. 3.4.1.1, the external water pressures are calculated as follows:
r2
V, Y #i
_ 'w 1 (3.18)
Y #o _ ' w 2
(3.19)
W, Y Hf
_ 'w 1 1 2tan0
(3.20)
1
Y #o 2 2tan0^
(3.21)
where H 7 and //2 are the depths of water on upstream and downstream sides,
respectively, 01 and 92 are the angles of upstream and downstream side slopes and yw
is the unit weight of water. Locations of Vl and Vl are respectively at Hj/3 and #2/3
99
EVALUATION OF SOIL DAMS CHAPTER THREE
from the bottom of the reservoir, and the locations of W] and W2 from the upstream
and downstream toes of dam (Xj and X2) are respectively calculated as follows:
H, _2_
3tan6, X2=TZ^~ <3-23)
3.4.2 Internal water pressure and seepage gradients
Seepage is the gradual motion of water through the soil causing driving force acting on
the particles of soil dams. If the value of seepage force (transmitted to a soil particle) is
greater than the resultant of the resistance force, an unstable condition occurs for the
particle. In conventional homogeneous earth dams, seepage appears on the downstream
slope regardless of the impermeability of the soil. The downstream slope is finally
affected by seepage to a height of approximately one third of water depth in the
reservoir (USBR, 1977).
The upper limits of seepage through two conventional homogeneous earth dams (one
with a horizontal drainage blanket and one without drainage blanket) and a non-
homogeneous earth dam are shown in Figs. 3.4.2.1a to 3.4.2.1c, respectively.
Similar to conventional earth dams, seepage occurs through the RSDs. The upper limit
of seepage lines through two homogeneous fill RSDs (one with a horizontal drainage
blanket, and one without drainage blanket) and a zoned RSD are shown in Figs. 3.4.2.2a
to 3.4.2.2c, respectively.
100
EVALUATION OF SOIL DAMS CHAPTER THREE
^
Seepage line
H2=Hj/3
(a)
Seepage line
Horizontal drainage blanket
Seepage line
Filter
H;
H2
(c)
Fig. 3.4.2.1 Seepage lines through (a) a homogeneous earth dam without any blanket (b) a homogeneous earth dam with a drainage blanket (c) a non-homogeneous earth
dam
Fig. 3.4.2.2 Seepage lines through: (a) a RSD without any blanket (b) a RSD with a
drainage blanket (c) a zoned RSD
101
EVALUATION OF SOIL DAMS CHAPTER THREE
On the basis of Darcy's law, the discharge of seepage flow in unit of time is proportional
to (a) the coefficient of permeabihty for the soil, k, (b) the hydraulic gradient, i, or the
rate of loss of head, dh/dl, and (c) the gross area of soil which the flow takes place. The
seepage flow, Q, is usually given as follows:
Q = kiA (3.24)
On this basis, the velocity of seepage flow, V, in unit of time is proportional to the
coefficient of permeabihty for soil and the hydraulic gradient as follows:
V = -ki (3.25)
The combination of Darcy's law with the continuity equation leads to:
—+— = 0 (3.26) dx dy
where u and v are the velocity components in both x and y directions. The Laplacian
equation of seepage for steady condition is usually formulated as follows:
___|+___| = 0 (3.27) dx2 dy2
where, ty=-kh is the flow potential.
It should be noted that the slope of seepage line through a RSD is normally steeper than
the slope of seepage line through a conventional earth dam (with the same condition),
because the base length of RSD is normally less than the base length of the conventional
earth dam as compared in Fig. 3.4.2.3. This causes an increase in the rate of loss of
head, dh/dl Hence, the hydraulic gradient, i, increases, because i=dh/dl. The increase
102
EVALUATION OF SOIL DAMS CHAPTER THREE
in the hydraulic gradient causes an increase in the seepage flow and seepage velocity,
because both are linearly proportional to the hydraulic gradient (See Eqs. 3.24 and 3.25).
A n increase in the seepage velocity through the RSD fill causes an increase in the driving
force acting on the particles of dams. For any particle of soil under the upper limit of
seepage line, the value of seepage force should be less than the value of resistance force
divided by an appropriate safety factor to avoid the occurrence of unstable conditions for
the soil particle.
Fig. 3.4.2.3 The seepage line through a RSD compared with the seepage line through a
conventional earth dam with the same height
Seepage may also emerge through the foundation of the conventional earth dams as
shown in Fig. 3.4.2.4. The motion of water through the foundation soil causes a force
which acts on the soil particles. Referring to Fig. 3.4.2.4, if the value of seepage force,
F3, (transmitted to the soil particle Q is greater than the weight, W, of particle C, an
unstable condition occurs for the particle C.
Similarly, seepage may also emerge through the RSD foundation as shown in Fig.
3.4.2.5. If the value of F3 is greater than the particle weight, W, an unstable condition
occurs in the downstream side.
103
EVALUATION OF SOIL DAMS CHAPTER THREE
H2 3
%
W Pervious foundation
Seepage line
~~ I B h - > — - -
(a)
Fig. 3.4.2.4 Seepage line through the foundation of a conventional earth dam
0
A
W 1
Pervious foundation Sgepage ^
(a) **
H2 rF3
c\-w
H2 l i s Seepage line- /W
(b) *lw
Fig. 3.4.2.5 Seepage line through the foundation of a RSD
104
EVALUATION OF SOIL DAMS CHAPTER THREE
Cutoff trenches are normally used to reduce the seepage force under the dams as seen in
Figs. 3.4.2.4b and 3.4.2.5b. The use of cutoff trench causes an increase in the length of
seepage line. The increase in the seepage line causes a decrease in the hydraulic gradient
i causing a reduction in the seepage flow and seepage velocity. Reduction of seepage
velocity causes a reduction in the driving force transmitted to the particle.
A comparison between the path of water under a conventional earth dam and under a
RSD with the same heights is shown in Fig. 3.4.2.6. Since the length of water path under
the RSD is normally less than the length of water path under the conventional earth dam,
as shown in Fig. 3.4.2.6, the hydraulic gradient (i-dh/dl) under the RSD is more than the
hydraulic gradient under the conventional earth dam. Hence, the seepage force under a
RSD is more than the seepage force under a conventional earth dam with the same
condition.
_..-_.. Reinforced soil dam
Hy
\Seepage line under reinforced soil dam / Vs. \ /
Conventional earth dam
Ho
Seepage line under conventional earth dam
Fig. 4.3.5.1 A comparison between the path of water under a conventional earth dam
and a RSD with the same height
Similarly, an increase of seepage velocity through the foundation of RSD causes an
increase in the driving force acting on the foundation particles. For any particle of soil
under the dam, the value of seepage force should be less than the value of resistance
force divided by an appropriate safety factor to avoid the occurrence of unstable
conditions for the particle. More detail will be presented in Sec. 4.3.5.
105
EVALUATION OF SOIL DAMS CHAPTER THREE
3.4.3 Uplift pressure
Uplift pressure is an internal water pressure which should be discussed here. Based on
the types of foundations, the magnitude of the uplift pressure may vary. The
commonly assumed distribution of the uplift force, acting under a dam, is shown in Fig.
3.4.3.1. The value of uplift water pressure and its distance to the toe of dam will be
equal to:
U = JUa + UhWh
2
X = _W*(2Ua+Uh)
6U
(3.28)
(3.29)
If the dam is built on impervious rigid foundation, as shown in Fig. 3.4.3.1, the values
of U a and U^, are calculated as follows:
a 'w 1 (3.30)
Ub = V * 2 <3-31>
in which W D is the width of dam at the base, and y w is the unit weight of water.
Fig. 3.4.3.1 Uplift pressure acting on an impervious rigid foundation dam
106
EVALUATION OF SOIL DAMS CHAPTER THREE
If the dam is built on pervious foundation, as shown in Fig. 3.4.3.2, the values of Ua
and Ub are calculated as follows:
U = a
H l-< gl- H2>*V,
ab
g, -(//, -H2)Lh b L
r w ab
L U = L +L\ + WU ab a b b
(3.31)
(3.32)
(3.33)
where, L a is the weighted distance from the beginning of upstream apron to the
upstream face of dam, Lb is the weighted distance from the beginning of downstream
apron to the downstream face of dam, Lab is the weighted length of path from the
beginning of upstream apron to the end of downstream apron, and y w is the unit weight
of water.
Hi ^^^m
Ua
1 h- 1 Vl 'h
~R2
ub x -
I I 1 1 1 Lfth 1 I 1
Fig. 3.4.3.2 Uplift water pressure acting on a pervious foundation dam.
3.4.4 Ice pressure
The magnitude of ice pressure can be calculated based on solar energy, ice thickness
and earth temperature. The table which shows the value of ice pressure, based on these
107
EVALUATION OF SOIL DAMS CHAPTER THREE
three factors, is illustrated in Appendix C. The position of ice pressure / acting on a
dam is shown in Fig. 3.4.4.1.
Fig. 3.4.4.1 Location of ice pressure acting on a dam
3.4.5 Silt pressure
According to the United States Bureau of Reclamation, the horizontal component of silt
pressure acting on a dam is assumed to be equivalent to that of liquids weighting 35
percent of the hydrostatic pressure, while the vertical pressure is equivalent to 90
percent. However, in silt retention dams, both components are calculated by Rankine's
formulas as follows:
V = s
y #2tan2 (45-|) 's s 2 (3.34)
y H2
' s s W =• s tan 9,
(3.35)
where Vs and Ws are horizontal and vertical components of silt pressure respectively, as
shown in Fig. 3.4.5.1, Hs is the depth of silt, $ is the angle of internal friction of silt
material, ys is the submerged unit weight of silt, and 01 is the angle of upstream side
slope.
108
EVALUATION OF SOIL DAMS CHAPTER THREE
Fig. 3.4.5.1 Silt pressure
3.4.6 Weight of structure
In homogeneous fill dams, the weight of structure per unit length of dam is calculated
by the multiplication of cross sectional area of dam by the unit weight of material as
follows:
W= Ay m
(3.36)
where, Wis weight, A is the cross sectional area of dam and ym is its unit weight.
In zoned types (Fig. 3.4.6.1), the weight of each area should be calculated separately.
The sum of the weights results in the total weight of the structure per unit length as
follows:
W. = A. y . i i ' mi
(3.37)
W= IW. (3.38)
where, W is the total weight of unit length of the dam, W( is the weight of each part of
dam cross section, and ym; is its unit weight. The location of W should be obtained
based on static equilibrium of the cross section.
109
EVALUATION OF SOIL DAMS CHAPTER THREE
•S^^H, y J—1
/^ Wi A JcV
—
Fig. 3.4.6.1 Zoned RSD
3.4.7 Earthquake force
The forces due to earthquakes are classified as direct and indirect (slashing). Direct
force is the result of inertia force of an earthquake acting on the body of dam, while
indirect force represents hydrodynamic forces acting on the upstream side of dam.
These two forces are evaluated in the following sections, while a comparison between
the natural frequency of RSDs and conventional soil dams will be presented in Chapter
Five.
3.4.7.1 Direct force
The static method and response expectra method are two methods for analysing the
direct effect of an earthquake acting on soil dams. In static analysis, it is assumed that
a horizontal force, equal to a portion of the acceleration due to gravity, acts on the
centre of gravity of dam. This force is calculated as follows:
F = (—)(ag) = Wa (3J9> 8
where W is the weight of dam, g is the acceleration due to gravity, and a is the
earthquake acceleration specified for the dam site and the surrounding area. The force
should be calculated separately for each zone of dam, when the cross section of dam
contains several zones. This force should also be checked separately for the horizontal
layers of dam. Generally in this method, the acceleration considered does not indicate
110
EVALUATION OF SOIL DAMS CHAPTER THREE
the duration of shaking (or the frequency of earthquake), which is usually necessary for
determination of the acceleration period and the natural frequency of dam.
In the response expectra method, the magnitude of earthquake acceleration, a, is
calculated with reference to the acceleration, frequency and duration of forces acting on
the dam. Based on the work done by Schnable and Seed (1983) and accepted by the
United States Bureau of Reclamation, the value of a is calculated for two situations: the
maximum credible earthquake (MCE) and the operating basis earthquake (OBE). Both
M C E and O B E are considered in the design of dams. The O B E is obtained based on
probabilistic and statistic approaches. There should be no permanent damage under the
OB E , and the dam should be able to resume operation after an earthquake. Under the
M C E , it should not cause the release of water from the reservoir (National Research
Council (U.S.) Panel on Regional Networks, 1990).
According to the National Research Council, the earthquake record for the region, the
length and the depth of all major faults, the types of foundation material (soil or rock)
and the distance of dam from the faults are parameters to be considered at the first stage
of the determination of maximum credible acceleration. The amount of earthquake
force, the maximum stress in the dam and the material strength required to resist these
stresses are considered as the second stage of this method. The magnitude of
earthquake acceleration, a, in the M C E and O B E are shown in Table 3.4.7.1 (National
Research Council (U.S.) Panel on Regional Networks, 1990). The numbers shown in
the first column of this table are usually represented on seismic zone maps.
Table 3.4.7.1 Earthquake acceleration
Region
0
1
2
3
MCE
o* o.i/? 0-2*
0-3*
O B E
o* .05*
o-i* 0.2*
Note: * = acceleration due to gravity
111
EVALUATION OF SOIL DAMS CHAPTER THREE
3.4.7.2 Indirect force
Referring to Fig. 3.4.7.1, the magnitude of horizontal earthquake force due to water
slashing is normally calculated from the following equation.
V =0.726 C Xy Y e p 'wJ
(3.40)
where, Ve is the magnitude of horizontal forces above the elevation considered, A, is the
earthquake intensity, y is the vertical distance from the reservoir water table to the
elevation considered, Cp is determined from the curve shown in Fig. 3.4.7.2 by
reference the values of y/h and a, which is the angle between the upstream slope and
vertical line shown in this figure, and the height of water in the upstream side of the
dam, h. The position of Ve is at 0.41y above the elevation considered.
Fig. 3.4.7.1 The horizontal earthquake force due to water slashing
3.4.8 Reaction of foundation
The linear reaction of foundation is usually assumed to have a trapezoidal distribution
as shown in Fig. 3.4.8.1. The upstream and downstream sides of the trapezoidal
pressure are calculated as follows:
/, o-iUL (1..5L) a W7 W,
(3.41)
112
EVALUATION OF SOIL DAMS CHAPTER THREE
b wb wb (3.42)
where, Z F V is the sum of vertical forces acting on the dam without uplift force, 7LFn is
the sum of horizontal forces acting on the dam, WD is the width of dam in the top level
of foundation, and e is eccentricity, which is a function of ZFy/ZFh and its location.
Fig. 3.4.7.2 The value ofCp (US Bureau of Reclamation, 1977)
Fig. 3.4.8.1 Trapezoidal reaction of foundation
113
EVALUATION OF SOIL DAMS CHAPTER THREE
Several non-linear foundation reactions may also be assumed for the distribution of
foundation reaction of RSDs. The exact reaction of foundation is not fully understood.
A possible non-linear reaction of foundation is shown in Fig. 3.4.8.2.
R a
Rb
Fig. 3.4.8.2 Possible non-linear reaction of foundation
3.4.9 Load Combinations
The combination of forces acting on a RSD should be considered in order to understand
the critical state of loading combinations. According to United State Bureau of
Reclamation (USBR), the three following combinations should be considered for
analysing the critical state of stresses and strains due to the forces acting on dams;
including usual loading, unusual loading and critical loading.
In usual loading, forces due to upstream and downstream hydrostatic pressure, ice and
silt pressure and the weight of dam are considered for purpose of analysing the
behaviour of dam. In this case, the level of water should be considered in both normal
and maximum situations. In unusual loading analysis, the maximum upstream
hydrostatic force, downstream hydrostatic force, weight of dam and the silt force are
considered. In critical loading analysis, usual and unusual load combinations are
analysed in consideration of the maximum force due to an earthquake. The cases of
load combinations m a y be summarised as shown in Table 3.4.9.1.
114
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Extreme loading
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EVALUATION OF SOIL DAMS CHAPTER THREE
3.5 C O N C L U S I O N S
The construction costs of earth dams are much lower than these of concrete types such
as arch dams, buttress dams and gravity dams. However, the impossibility of spillway
construction on the crest of earth dams, the great amount of material needed for
constructing an earth dam, and the high costs of incorporating outlets and power
stations into the body of earth dams are restrictions which should be considered in the
selection of earth dams.
The insertion of reinforcement within earth dams reduces the restriction on the great
amount of earth work needed for construction of the earth dam. At least two RSDs may
be constructed using the material of one conventional earth dam with the same heights.
Reductions in fill volume, stress level, and displacement result from the use of
reinforcement inside earth dams. The structural flexibility, increase of safety factor,
elimination of downstream zone, reduction in upstream slope, and decrease in the time
needed for RSD construction should be considered as advantages of using
reinforcement in earth dam construction. The stiffness of RSD fill material is increased
due to the presence of reinforcement. The use of geogrid in earth dam construction
allows higher compaction to be achieved, resulting in a reduction in the width of earth
dam, and a more economic construction.
The design and analysis of reinforced earth embankments and soil dams (based on the
researches done so far) by the finite element method seems to be in a close agreement
with the observed behaviour. It is, therefore, an useful tool for further research in this
area.
The selection of an appropriate RSD for a particular site can be assisted by the use of a
classification system based on consideration of c o m m o n behaviour of dams. In this
chapter general and possible classifications of RSDs based on their components and
types have been considered in regards to external stability and internal stability
analysis. RSDs, based on the material used, have been classified into two basic groups:
116
EVALUATION OF SOIL DAMS CHAPTER THREE
homogeneous fill types and zoned types. Components, properties and types of both
groups have also been considered.
The identification of forces acting on RSD is fundamental to a study of the behaviour of
RSD. In reality, there are no differences between the forces acting on a RSD and the
forces acting on other types of dams. However, the behaviour of RSD and other dams
in withstanding the forces are different. The forces due to water pressure, silt pressure,
ice pressure, earthquake pressure, foundation reaction, seepage and the weight of
structure are the main forces acting on a RSD.
117
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
CHAPTER FOUR
STABILITY ANALYSIS OF REINFORCED SOIL DAMS
4.1 INTRODUCTION
The stability analysis of RSDs, which may be classified as shown in Fig. 4.1.1, should
be accurately evaluated regarding its two main parts: internal stability and external
stability. Sliding, overturning and over-stressing should be carefully thought about in
external stability analysis. The failures due to reinforcement failure, and lack of bond
between the soil and reinforcement should be considered in the internal stability
evaluation. The minimum required base length for a no failure state due to sliding,
overturning, over-stressing should also be considered in order to optimise the geometry
of dam. In this chapter, the external stability of RSDs based on an analytical approach,
and the internal stability analysis based on semi-empirical methods will be evaluated.
It is assumed that the whole reinforced soil structure acts as a unit in external stability
analysis.
S T A B I L I T Y A N A L Y S I S O F RSDs
SLI]
EXTERNAL STABILITY OF RSDs
DING OVERTURNING OVER-STRESSING OF SOIL
INTERNAL STABILITY OF RSDs
REINFORCEMENT STABILITY
BOND STABILITY
Fig. 4.1.1 Stability analysis of RSDs
118
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.2 EXTERNAL STABILITY
Sliding, overturning, and overstressing should be considered in the external stability
analysis of RSDs. These should also be evaluated for each layer of the dam. For
evaluation, the cross-section of a parametric RSD with vertical downstream facing is
assumed to be as shown in Fig. 4.2.1, illustrating its cross section with imaginary
horizontal layers. During analysis, it is assumed that the height of the dam is a constant
parameter fixed with respect to the flow-rate of water in the river. The ratio of the crest
width to base width of the dam is assumed to be expressed by a constant parameter
h=Wt/Wb. For simplification, the average unit weight of the dam is assumed to be
another constant parameter called ys. Fig. 4.2.2 shows the forces, their locations and
their directions, acting on the RSD.
w t
M 1
AT 1
AT
/ 1
r
i
M 1
^ •^ ..
—
wb
\Hi H2 V
. A
Hi
r
3
H
*
Fig. 4.2.1 The cross section of a parametric RSD with imaginary horizontal layers
119
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Fig. 4.2.2 Forces acting on a RSD
In the cases of sliding and overturning, the weight of the water, and the weight of silt,
both acting on the upstream side of dam (or a layer of dam as shown in Fig. 4.1), and
the weight of dam (or the layer), should be considered as resistance forces. The
upstream hydrostatic force, ice force, direct and indirect forces of earthquake and the
horizontal force of silt pressure should be considered as driving forces acting on dam
(or the layer). Downstream hydrostatic forces can be neglected in the stability analysis
of dam, while the weight of water acting on the vertical downstream side of dam (or the
layer) is zero. For sliding and overturning evaluations, the summarised states of the
forces under the four cases of load combinations including usual loading, unusual
loading, and the two cases of extreme loading (Case 1 and Case 2) are shown in Table
4.2.1.
120
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Table 4.2.1 Summary of the forces in sliding and overturning states
Forces:
1-Upstream hydrostatic force
2-Downstream hydrostatic force
3-Uplift pressure
4-Weight of water acting on
upstream side of dam
5-Weight of dam
6-Ice pressure • *
7- Weight of silt
8-Silt pressure
9-Earthquake force (direct force)
10-Earthquake force (indirect force)
Neg. = Negligible
Vl
V2
U
Wj
W
Vl
Ws
Vx E
Ve
Usual
loading
Drv.
Neg.
Drv.
Res.
Res.
Drv.
Res.
Drv.
-
.
Unusual
loading
Drv.
Neg.
Drv.
Res.
Res.
_
Res.
Drv.
-
_
Drv. = Driving Force
Extreme
loading
(case 1)
Drv.
Neg.
Drv.
Res.
Res.
Drv.
Res.
Drv.
Drv.
Drv.
Extreme
loading
(case 2)
Drv.
Neg.
Drv.
Res.
Res.
-
Res.
Drv.
Drv.
Drv.
Res. = Resistance Force
4.2.1 Sliding
Failure due to sliding will occur, if:
where XZ>/ and IRi are, respectively, the sum of driving and resisting forces acting on
RSD dam, and p is the coefficient of friction between its layers, between the RSD dam
and its foundation, or between the layers of the foundation. Actually, u can be
expressed as:
a) p= tan fa between the layers of RSD dam
b) p= tan 5 between the dam and its foundation
c) p= tan fa between the layers of foundation
121
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
where <t>r and fa are, respectively, angles of internal friction of soil within the dam and
within its foundation, and tan8 is angle of friction between the dam and its foundation.
The RSD dam will fail theoretically if:
2ZD. ^ L > - ^ - (42)
£/?. SF ( ' i s
where SFS is a greater than 1 safety factor against sliding failure. Referring to Fig.
4.2.2, the sum of driving forces, £Df, the sum of resistance forces, ZJ?/, and the results
of the sum of driving forces divided by the sum of resistance forces, HDf/LRi, for the
four cases of loading, can be illustrated as shown in Table 4.2.1.1.
Table 4.2.1.1 Results of driving and resistance forces acting on RSD in sliding situation
•LD;
ZRi
x*.
Usual loading
Vl + Vl+Vs
W+Wi+Wg-U
V+VT + V l i s W + W.+W -U 1 s
Unusual
loading
Vi + Vs
W+Wi+Ws-U
V +v
W + W.+W -U 1 s
Extreme loading
(Case 1)
Vl+Vl+Vs + E+Ve
W+ Wi + Ws -U
V+VT+V +E+V l i s e W + W.+W -U
1 s
Extreme loading
(Case 2)
Vj+ Vs+ E+Ve
W+ W] + Ws -U
V.+V +E + V Is e W + W.+W -U
1 s
As can be seen from Table 4.2.1.1, the critical loading at the time of sliding, is Case 1
of the extreme loading because, in this state, the sum of the driving forces is maximum.
The sum of resistance forces in the all states is equivalent. This clearly shows that Case
1 of the extreme loading is the critical state of loading. Therefore, by replacing the left
side of Eq. 4.2 with the extreme loading, the following result (for no base sliding) will
be expressed:
122
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
W+W.+W • 1 s
-U
V+VT + V +E+V l i s e
> SF s V
(4.3)
in which SFS is a greater than 1 safety factor for no sliding, p is the coefficient of
friction expressed previously, and W, W], WSf U, V]f Vjt Vs, E and Ve are the forces
shown in Fig. 4.2.2 6.1b. Separation of the variables, which are a function of the width
of the crest, Wt, and/or the width of the base, WD, in the left side of the equation, results
in the following expression for a no sliding situation.
(W+W.+W -U)\i-SFE 1 £ *—>V+V +VT + V (4.4)
SF I s l e s
or
(W+W.+W -U)\i-SF E 1 S. _ §— > v (4.5)
SF s
where Vis the sum of all the horizontal forces acting on the dam except the direct force of earthquake. By factoring W from the left side of Eq. 4.5, the following expression
can be written.
(l + P+X-a>)p-SFa W s— > V (4.6)
SF s
where, E
W (4.7)
p . V f o - ^ w (4.8) W H2(\+%)y
123
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Ws "s^-^sub X = W = H2{1 + ™
y} = ILjhw + hw2)'Yw (4J0) W H(l + )ys
( ;
where, W, is the weight of RSD dam (or the layer), Wj and Ws are, respectively, the
weight of water and silt on its upstream side (or the layer), E is the direct force of
earthquake acting on the dam (or the layer), U is the uplift pressure acting on the dam
(or the layer), ys is the average unit weight of the dam (or the layer), yw and ysub are,
respectively, the unit weights of the water and the silt on the upstream side of the dam
(or the layer) and, finally, H, hw and Hs are, respectively, the height of dam (or the
layer), the height of water and the height of the silt on the upstream side of dam (or the
layer).
Assume;
(l + P + X-x>)v.-SFa m = — (4.11)
SF s
Substituting Eq. 4.11 in 4.6, yields the following:
mW>V (4.12)
Since,
(Wt + Wb)Hys Wh(l + Wls (4J3) 2 2
substituting W from Eq. 4.13 to Eq. 4.12 and solving for Wb results in the following
condition for a no sliding failure state:
V i b Hy
(4.14)
124
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
where £l\ is a factor expressed as the following equation:
^ ((l + ^+X-v)[i-SFa)(l + ^) Ql= ISF— (4J5)
s
where p, %, D, p, SFs, £ are factors expressed before. Since, these are dimensionless
parameters, Q.\ is a dimensionless factor in conventional static analysis (because
earthquake acceleration, a, is a dimensionless factor in such analysis), while in
dynamic analysis, €1\ linearly depends on the earthquake acceleration, a.
4.2.2 Overturning
Referring to Fig. 4.2.2, in stability analysis of RSD against overturning, the sum of
driving moments and resistance moments in the critical state of loading should be
calculated. In each layer, the point of rotation is the common point of the base line of
the layer with the vertical line of downstream facing. The sum of the driving moments
divided by the sum of the resisting moments, in the four cases of loadings, are
calculated and compared in Table 4.2.2.1.
Failure of RSD dam due to overturning occurs, if:
ZD.h. l-±>l (4.16)
ZRx. i i
Regarding to the safety factor for no overturning failure, the sum of overturning
moments divided by the sum of resistance moments should be less than the inverse of
the safety factor.
X D.h. i ±—LL<-±- (4.17)
ZR.x. SF i i o
where SF0 is a greater than 1 safety factor for no overturning failure.
125
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Table 4.2.2.1 Results of driving and resistance moments acting on the dam in
overturning situation
Loading case
Usual loading
Unusual loading
Extreme loading (Case 1)
Extreme loading (Case 2)
The sum of driving moments divided by the sum of
resistance moments
(iD.h.) ^ i i
V i i)
V fu + V7 hT + V h + Ux 1 1 II s s u Wx + W.x, + W x
11 s s Vh, + V h + Ux 1 1 s s u Wx + W.x, + W x
11 s s V h, +VThT + V h +Ehr, + V h +Ux 1 1. I I s s E e e u Wx + W.x,+W x
11 s s Vh,+V h +Ehr7 + V h +Ux 1 L s s E e e u Wx + W. x.+W x
1 1 s s
As can be seen from Table 4.2.2.1, Case 1 of the extreme loading is the critical state of
the load combinations, because in this state, the sum of driving moments is maximum
while the sum of resistance moments is constant. Therefore, for no overturning failure
the following expression should be met.
Wx + W.x.+W x 11 s s
Vh,+VThT + Vh +Ehr + Vh+Uxit 11 II s s E e e u
>SF (4.18)
Separation of the variables, which are functions of the width of crest and / or base of
the dam in the left side of the above, results in the following condition for no
overturning failure.
Wx + Wxxx+Wsxs -(EhE +Uxu)SFo>SFoMh (4.19)
126
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
in which,
Mh -<v 1vv JVv.VW (4-20)
Since the safety factor against overturning failure, SFD, is a positive number, the
following expression should be met for no overturning failure.
Wx W U , W J C . JE%„ Hr [ 1 + — ^ + - £ - £ - ( — E - + — ^ ) S F ]>M, (4.21)
SF Wx Wx Wx Wx o h o
Referring to Fig. 4.2.2, the horizontal distance from the centre of gravity of the dam (or
the layer) to its toe, x, and the horizontal distances from the centre of gravity of the
water and the silt, both on the upstream side of the dam (or the layer) to the toe of dam
(or the layer), xj and xs, can be calculated as follows:
x = W2+WWU+W
2 WAl+^+Z,2) - t t b b _ b ^ T (4 22)
3(Wf + Wb) 3(1 + $)
(l-c> x,=WAl- w) (4.23) 1 bK riff
3J7
(l-x)h x =WA1- -&•) (4.24) s bK 2>H
The distance of the result of uplift pressure, xu, to the toe of the dam is shown in Fig.
4.2.2. The ratio of the horizontal distance of the centre of gravity of the water on
upstream side, the ratio of the horizontal distance of the centre of gravity of the silt, ,
and the ratio of the horizontal distance of the result of uplift pressure, all to the
horizontal distances of the centre of gravity of dam, (Pi, X\ and v\) can be calculated
as follows:
x, (l + %)QH-hw+h^) (425)
1 x (l + ^+%2)H
x (l + x)(3H-h +h$) tJ^ y = s ___K s s*J (4.26) 1 x (\+%+%2)H
127
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
X (l + %)(2h +h )
x a+$+e)(hw+hw2)
Substituting the values of x, pi, X\ and -oi from Equations 4.22, 4.25, 4.26 and 4.27 in
Equation 4.21 results in the following expression for no overturning failure state.
WAl + %+^2)(l+W +XX -vx>.SF -ahFSFnlx) W-£ i -1 1—Q £—Q > M, (4.28)
3(1 + |)SF h
where hE is the vertical distance of the centre of gravity of dam to the base level, x, x],
xs, are horizontal distances shown in Fig. 6.2, and a, 0 and % are the parameters
calculated from Equations 4.7 to 4.9. Substituting the value of W from Eq. 4.13 in 4.28
results in the following condition for no overturning failure state:
r2, W, £(l + l; + ¥)(l + Wl + XX1-vv1SFo-ahESFo/x) Mh (4.29)
6SF Hy o s
Referring to Fig. 6.2, the value of hE can be calculated as follows:
2HW+HWU H(2c\ + \)
h 1 b_=H(li; + l) Q) 3(Wt + Wb) 3(^ + 1)
Substituting the values of x from Eq. 4.22 and hE from Eq. 4.30 in 4.29, and solving
for W&, results in:
m^W2 + m2Wb + m^ > 0 (4.31)
where,
(l+jc+x2)(l + j3p1 +%%i -x>v, SF ) tr,=: - — M H 1 A A 1 I—QL (4.32) 1 6SF
o
128
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
aH(l + 2t) m2=
y — — (4.33)
Mu m3=--^
tL- (4.34) Hy s
in which Mh is calculated from Eq. 4.20, m$ is a negative value depending on the
moments due to the forces acting on dam, Mh, the dam height, H, and the unit weight,
ys of the dam. Since £;, P, Pi, x, Xh v, t)l and SFo are dimensionless positive values as
explained before, mj should be a dimensionless value. Finally, based on Eq. 4.33, m2
is a negative value, because a, H and % are positive values. Since, H was assumed to
be a constant parameter for a particular site and £, is a dimensionless constant
parameter, m2 is a parameter which linearly depends on earthquake acceleration, a.
Therefore, m2 is a constant factor in conventional static analysis, while in dynamic
analysis W 2 depends linearly on the earthquake acceleration, a.
Solution of 4.31 for W b results in the following equations:
-mn +J(mn -4m.m~) W = 2 V 2 1_3_ (435)
bl 2mx
~ m 2 ~\^m2 ~^m\m'x) W = ___________ ______ (4.36) b\ 2nu
Since m2 and m j are negative values, Wbl is always a positive value and WD2 is
always a negative value when ml is a positive value. Therefore, the correct solution of
4.31 is only Wbl calculated from Eq. 4.35, because Wb should always be a positive
value. Therefore, for no overturning failure state, the following condition should be
met.
- m 0 +J(m~ -4m,m-.) W =
2 V 2 1 _ _ (4J7) b 2mx
129
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.2.3 Overstressing
Based on the type of soil used, the reaction of the foundation may change. Actually,
the form of foundation reaction force is not exactly understood. Linear distribution and
several types of non-linear distribution may be assumed. The linear reaction of the
foundation of a RSD is shown in Fig. 4.2.3.1a. T w o simple forms of non-linear
reactions of foundation are shown in Fig. 4.2.3.1b & c.
miuun. j.muuu-*a
Wi
R
(a) (b) (c)
Fig. 4.2.3.1 Reactions of foundation
The following horizontal and vertical forces are considered in overstressing analysis
including: upstream hydrostatic force, force due to silt pressure, force due to ice
pressure, the two forces of earthquake (direct force and indirect force), weight of dam,
weight of water on the upstream side in normal and maximum situations, and weight of
silt on the upstream side. These should be considered in the four loading cases (usual,
unusual and two cases of extreme loadings). The role of these forces acting on a dam
for overstressing analysis is shown in Table 4.2.3.1, while direction and location of the
forces were shown in Fig. 4.2.2.
130
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Table 4.2.3.1 Summary of the forces used in analysis of soil bearing capacity
Forces:
1-Upstream hydrostatic force
2-Downstream hydrostatic force
3-Weightofdam
4-Weight of water acting on upstream side of dam
5- Weight of water acting on downstream side of dam
6-Ice pressure
7-Weight of silt
8-Horizontal force due to silt pressure
9-Earthquake force (direct force)
10-Earthquake force (indirect force)
Vl
V2
W
Wi
W2
VI
Ws
Vs
E
Ve
Usual loading
Driv.
Neg.
Driv.
Driv.
0
Driv.
Driv.
Driv.
-
-
Unusual loading
Driv.
Neg.
Driv.
Driv.
0
-
Driv.
Driv.
-
-
Extreme
loading
(case 1)
Driv.
Neg.
Driv.
Driv.
0
Driv.
Driv.
Driv.
Driv.
Driv.
Extreme
loading
(case 2)
Driv.
Neg.
Driv.
Driv.
0
-
Driv.
Driv.
Driv.
Driv.
Neg. = Negligible Drv. = Driving Force
4.2.3.1 Linear Reaction
Referring to Fig. 4.2.3.1a, and based on the equilibrium of the forces, the two following
equations can be written:
wh
(R+Ru)-?- = ZR, a V 2 R W£ (R,-R )WU2 ___£__£_+_____£—aL-b_+1D h =2-R x
2 6 l l l l
(4.38)
(4.39)
where Ra and Rb are, respectively, the upstream and downstream values of foundation
reaction and £_?i, L/?f, xi, and ID; hi are the sum of vertical loads, the sum of
resistance moments and the sum of driving moments, respectively. The solution of
131
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Eqs. 4.38 and Eq. 4.39, yields Ra and Rb being the upstream and downstream sides of
the foundation reaction as following equations:
(6ZR.x.-2Wh2ZR.-6ZD.h.) R = LJ OIL Li_ (4A0) a Wb2
(-6ZR.x.+4Wuj:R.+61D.h.) R = LJ ____! L±- (4A1) a Wb2
For no overstressing failure, the values of Ra and Rb should both be a positive number
smaller than the ratio of allowable bearing capacity, R*, over the factor of safety, SFb-
Therefore the following expressions should be met.
0<R <— (4.42) a SFb
0 <RU<— (4-43) b SFb
Substitutions of Ra and Rb from 4.40 and 4.41 to 4.42 and 4.43, respectively, yields the
following expressions:
-2 l— ZR.x. + ZD. h.<0 (4.44) 3 — i i — i i
* WUZR. W2R ,, _ - b l+Y,R.x.-<ZD.h.—2 <0 (4.45)
3 i i ' * 6SFb
b±-L+2^R.x..^D.h. <0 (4.46) 3 — i i — i i
2W,_/.. whR* ,AA^ h l-ZR.x.+lD.h.--b < 0 (4-47) 3 i i * i i 6SFb
132
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Solution of the set of conditions (Eqs. 4.44 to 4.47) results in the following expressions
for no overstressing failure:
W2R* —- > 0 (4.48) 6SFb
WUJ,R. —- l- > 0 (4.49)
3
W.^R. 2W2R* --2 l- - < Q (4.50)
3 6 ^
Conditions 4.48 and 4.49 are always met because all terms (Wb, R* and -_J?j) of the
equations are positive. However, for fulfilling condition 4.50, the following condition
should be met.
W, > b l (4.51) b /?*
Substitution of the sum of vertical loads acting on the dam, YRi, from Table 4.2.1.1 to
Eq. 4.51 results in:
(W+W.+W)SFU W > : 1 _____ (4.52) b /?*
or,
yq+p+x)-. (4J3) b R*
where p and % are dimensionless factors, respectively, shown in Equations 4.8 and 4.9.
Substituting Whom Eq. 4.13 in 4.53 results in the following equation for no failure.
Wb(l-p)>W{p (4-^4)
where
133
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
HySF(l+$+x) p = —s__o (455) V 2R* ' '
4.2.3.2 Non-linear Reaction
Similar to the above procedure (linear reaction), other procedures are evaluated based
on the non-linear reaction of foundation. Referring to Fig. 4.3b and 4.3c, the
foundation reaction is assumed to be a parametric polynomial curve of two degree as
follows:
R = ax2 +bx + c (4.56)
where R is the function of reaction, and x is the distance from the left side of the dam at
base level as shown in Fig. 4.3b and c. After calculation, it can be found that the
following equations should be met for fulfilling the vertical equilibrium equation.
-6HR. 3R 3RU a = —^r
±+—4-+—%- (4.57)
w? wr w£ b b b
61/?. AR 2RU b= l &- &• (4.58)
W2 WL W, wb b b c = R (4.59) a
where Ra and Rb are, respectively, the upstream and downstream value of foundation
reaction, and X/?/, IRj x(, and XD; hi were shown in Tables 4.2 and 4.3.
The following equation should be met for the fulfilment of moment equilibrium
equation around the toe.
aW* bwl cW2 tA</.. — - £ - + _ _ _ - + _ k - ^ R . x . - Z D . h . (4.60) 12 6 2 l l l l
There are five unknown variables (a, b, c, Ra and Rb) in four equations (Eqs., 4.57 to
4.60). Another equation is needed for the solution of the set of equations. The fifth
134
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
equation can be written to describe the shape of the reaction of foundation. For
example, the following conditions can be written for Figs 4.3b, 4.3c, respectively.
dR For x = 0: — = 0 -» fo = 0 (4.61a)
dx For x = Wu: — = 0 -> b = -2aWu (4.61b)
b dx b
The solution of the set of equations (Eqs. 4.57 to 4.60, and 4.61a) leads to the
following results.
-TRi 4(2ZR-x.-lD.h.) \ = ^ + ll
2 ll (4.62a)
a Wb Wb
5Y Ri S(2ZR.x.-2ZD.h.) R = ______ J___I_L^1____ (4.62b) b Wu w2
b wb Also, the solution of the set of equations (Eqs. 4.57 to 4.60 and 4.61b) leads to the
following results.
-4YJ?,' 8(X#.x.-_D.fc.) R = * ± R i + ^ i i ^ n> (463a)
a Wb W2
».2__.____(_^5l_2 (4.63b) b 2Wb W
2
Substituting the values of Ra and Rb, Equations 4.62a and b, in Equations 4.42 and
4.43 results in the following conditions for no failure:
-YRi ACZR:X.-2ZD.h) R* 0<R _ _ _ _ _ + i-l L _ _ < _ — (4.64)
a Wu Wn SF, b b2 b
0 </.,= — LJ--5 —- <-—- (4.65) b wt rf SFb
135
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Solution of 4.64 and 4.65 leads to:
CLR:X.-lDh) R* 0< L L , — L J - < T T — (4-66)
W2 2SFb
X*, R* 0< L< (4.67)
W b SFb
The left side of 4.67 is always met, and for meeting the right side, the following
condition should be considered:
SFUZR-Wu >—-
l- (4.68) b R*
For complying with 4.68, which is similar as 4.51, the following expression should be
met:
Wb(l-p)>Wfp (4.69)
where p has been defined by Eq. 4.55. Also, for meeting Eq. 4.66, the two following
conditions should be concerned for no failure:
(__/?.*.-XD./j.) 0< l l , l l (4.70)
W£ b
(lR.x.-TD.h) R* i i < _ L ; — (4.71) W2 25F, wb b
ZR.x. For meeting 4.70, the ratio of resistance moments over driving moments, — ^ should
i i
be greater than 1, which has been fulfilled for no overturning failure (See Eq. 4.16).
Also, for fulfilling 4.71, the following condition should be met:
\Yl > LJ i i b (4.72) b R*
136
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.3 INTERNAL STABILITY
The internal stability of reinforced earth structures can be analysed using methods based
on conventional principles of soil mechanics (Rankine and Coulomb-type of analysis). It
has become known, however, that certain theoretical assumptions of these methods have
not been supported by observations. In particular, since reinforcement changes the state
of stress within soil, the direction of principal stresses are no longer vertical and
horizontal, and the ratio of the vertical stress to the horizontal stress is not constant
(Arenicz & Chowdhury, 1987). This, together with other field data regarding the bond
between soil and embedded reinforcement, has led to the development of semi-empirical
methods, with one of them (proposed by McKittrick and Schlosser in 1978) being
adopted as a recommended design method by the Reinforced Earth Company. The
method, the Coherent Gravity Method (CGM), was structured around a set of bi-linear
functions, which represent and interpret field data in a simplified manner. Some
modifications to this method were suggested by Arenicz and Chowdhury in 1987,
Modified Coherent Gravity Method (MCGM), to reflect field observations more closely.
Factors of safety against tensile and bond failure of reinforcements are needed for design
purposes. The apparent friction factor, the coefficients of lateral earth pressure, and the
maximum tension line are needed to establish the safety factor formulae. The field data
on which both the CGM and the MCGM are based, is re-examined and analysed in order
to assess and reduce discrepancies between methods; their assumptions and field
observations. Therefore, the apparent friction factor, coefficient of lateral earth pressure
and the maximum tension line will be considered here. O n this basis, new empirical
formulae will be proposed for design purposes.
The assumptions accepted in CGM are that,
(a) the failure surface of the reinforced earth model is of a bi-linear shape
originating at the toe of the wall,
137
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
(b) the maximum force in the reinforcement occurs at some distance from the
facing panels,
(c) the coefficient of earth pressure varies linearly between Ko at the top of wall
to Ka at the depth of 6m, and
(d) the friction factor between the soil and reinforcements varies between fo near
the top to/* at 6m depth.
4.3.1 Coefficient of Lateral Earth Pressure
In the CGM, the coefficient of lateral stress is assumed to be a bi-linear function of the
fill depth, as shown in Fig. 4.3.1.1. It can be seen that, for y<6m, the lateral earth
pressure coefficient varies linearly from Ko to Ka and, for y>6m, it remains constant and
equal to Ka. This has been formulated as Eq. 4.73a & b, suggested by Schlosser (1978).
K = \ ' '' +Ka for, y<6m 6 ' " 0 JU" ^yj"y (4.73)
K for, y > 6m a J J
where K is the coefficient of the lateral earth pressure, Ka and Ko are the coefficients of
the lateral earth pressure in active and at rest conditions, respectively, and y is the depth
of soil fill above the level considered. A comparison between Eq. 4.73 (for § = 45) and
the field data of the experiments is shown in Fig. 4.3.1.2.
The main problem regarding the Schlosser equation is that the results of observations
indicate a non-linear change of K with fill depth (Baquelin, 1978, Arenicz & Chowdhury,
1987). The tangent discontinuity of Eq. 4.73 at y=6m can not be justified in terms of
stress state in a non-stratified soil fill, nor can it be supported by the field data.
138
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
T y = 6m \
y
Ka K0 ^ K 1
/
Fig. 4.3.1.1 Coefficient of lateral earth pressure
2.5-
2.0-
1.5-
K/K a
i.o-
0.5-
o.o -\ t
•.
N
)
Schlosser's Formula
. [ •
10
Depth (m)
t
20
• Asahigaoka
• Granton
• Gringy
* Lille |
• Silvermine
• (7c/a j
* Vicksbourg
Fig. 4.3.1.2 Comparison between the formula (for §=45) and the results of observed
experiments
To eliminate discontinuity and allow for a non-linear change of K, as observed, the
following function was proposed by Arenicz and Chowdhury (1987):
K = dlKa + $y(d2K0-dlKa) (4.74)
139
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
where, P is a constant equal to 0.75, d} and d2 are dimensionless coefficients that
change depending on boundary conditions. The previous equation was derived assuming
a non-linear decrease of K from KQ for y=0 to Ka for y = °°, with the lower limit
effectively reached for y=7m (Arenicz & Chowdhury, 1987).
There is, however, a practical problem associated with this proposal. In order to be used
for design purposes, the two unknown parameters it contains (dj and d_) have to be
determined. Based on the comparison between the theoretical and observed variation of
K/Ka with the fill depth, illustrated in Fig. 4.3.3.1, both dj and d2 have been suggested
to have a value of 1. On the other hand, different values have been suggested to
conform to the measurements taken in Lille abutment (d]=0.25 & d2=1.92) and
Dunkerque wall (dj=0.6 & d2=2.8). Therefore, Eq. 4.74 cannot be used for design
calculations since the actual determination of the two parameters for such a purpose
have not been addressed.
The analysis of the results of the field investigations suggests that, in order to eliminate
some of the problems described above, Eq. 4.74 should be altered to:
Ka+$yd1(K0-Ka) for, y<6m
„=J ' (4.75)
K for, y>6m a
v.
where,
<L --i-I+l (4.76) 1 36 3
and, p is the constant equal to 1.2.
The assumptions accepted in the new formulae are the same as these accepted in the
MCGM, except that for any depth of backfill exceeding 6m (instead of 7m) the value of
K remains constant. This gives a better agreement between the proposed function and
the interpolated average of observed data than in the MCGM, as shown in Fig. 4.3.1.3.
140
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
2.0-
KJKa ' i
1.6-
1.2-
f) S-
• The average of interpolated data of the experiments
Schlosser, 1978
- - - - Arenicz & Chowdhury, 1987
K<+ """ """ Proposed Equation
V'"-o.
t/.o~. ' 1 ' 1 ' 1 ' 1 • 1 • I • 1
0 2 4 6 8 10 12 14 Depth (m)
Fig. 4.3.1.3 Comparison between the field data and experimental formulae.
It should be noted that there is no tangent discontinuity in the proposed equation
because:
dK(y) = dK(y)
dy dy
y -> 6 + y->6~
= K(6) (4.77)
A comparison between Eq. 4.75, Schlosser (1978) formula, the formula of Arenicz and
Chowdhury (1987), and the average of the field data is shown in Fig. 4.3.3. It can be
seen from Fig. 4.3.1.3 that Eq. 4.75 offers a better fit with the average of observed data
than the alternative formulae.
141
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.3.2 Apparent Friction Factor
It has been known that both the length of reinforcement and the overburden pressure can
affect the apparent coefficient of friction between soil and reinforcement. Although
some formulae have been proposed to describe these effects, there are still problems
regarding their application in design. In the following paragraphs, frictional formulae
reflecting the influence of vertical pressure and strip length will be presented and
analysed. On this basis, some new formulae are proposed.
4.3.2.1 Vertical Pressure Effect
According to Schlosser and Segrestin (1979), the apparent friction factor for smooth and
ribbed strips, its variation with depth shown in Fig. 4.3.2.1, can be calculated as follows:
I) For smooth strips:
/* = 0.4 (4.78)
U) For ribbed strips:
* / =
y(tan(])-/0) +
— ~ + /0 for, y<6m (4.79)
tantj) for, y>6m
in which,
/0*=1.2 1ogCM (4.80)
and Cu is uniformity coefficient, fo* is the apparent friction factor at the top of
reinforced earth zone, (j> is internal angle of friction of the soil, and y is the depth of soil.
The figure shows clearly that Eq. 4.79 has a tangent discontinuity at y=6m, which
cannot be justified in terms of physical interaction between the soil and reinforcement
Also, Figures 4.3.2.2 and 4.3.2.3 shown a significant disparity (on the conservative side)
between Eq. 4.79 and the field data.
142
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
t y = 6m
>
/• /„
1
y
X i
Ribbed strip
Smooth strip
f
Fig. 4.3.2.1 Apparent friction factor
To address these problems, Arenicz and Chowdhury (1987) suggested the following:
I) For smooth strips:
/* = tan\|/+ct-),(n-tan\|/) (4.81)
H) For ribbed strips:
/* = tan<|>+ay(m/0-tan(|>) (4.82)
where f* is the apparent friction coefficient between soil and reinforcement, \\f is the
angle of friction between soil and reinforcement measured in direct shear box, y is the
depth, fo* is calculated from Eq. 4.80, a is an empirical coefficient suggested to be 0.6,
n and m are maximum value factors, respectively, for smooth and ribbed strips.
As shown in Figures 4.3.2.2 and 4.3.2.3, their formulae (Equations 4.81 & 4.82) have
eliminated the tangential discontinuity but remains conservative. Although these
formulae are in closer agreement with the experimental results in comparison with
143
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Schlosser's proposals, a significant disparity still remains. Hence, the following
modifications in the calculation of the apparent friction factor are proposed.
I) For smooth strips:
/ =
tan\|/ + sl(2.4-tan\|/) for, y<6m
tan\|/ for, y>6m
(4.83)
II) For ribbed strips
* tan(j) +0.9^^(3.85^-tan(j)) for, y<6m
tan<|) for, y > 6m
(4.84)
where „; is calculated from Eq. 4.76. It should be noted that there is no tangent
discontinuity in Equations 4.83 and 4.84 because:
3/*(y) _ff*(y) By dy
y -» 6 + y -> 6~
= f*(6) (4.85)
A comparison between the proposed Equations 4.83 and 4.84, Schlosser and Segrestin's
formulae (1979), Arenicz and Chowdhury's formulae (1987), and typical values of the
apparent friction factor based on observations is shown in Figures 4.3.2.2 and 4.3.2.3.
The figures illustrate that Equations 4.83 and 4.84 eliminates the problem of tangential
144
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
discontinuity, reflects the non-linearity suggested by the field data, and offers a closer
agreement with the observations.
8-1
f* •
6-
4-
2-
A Observed (After Schlosser & Elias, 1978)
Schlosser and Segreston, 1979
Arenicz & Chowdhury, 1987 — - Proposed formula (Eq. 4.83)
U 1 • 1 • 1 • ! • 1 • 1 ' 1
0 2 4 6 8 10 12
Depth (y) 'm'
Fig. 4.3.2.2 Comparison between theoretical and typical values of apparent friction
factor for smooth strips
f* 8-i
2-
0 0
A Observed (After Schlosser & Elias, 1978)
Schlosser & Segrestin, 1979
Arenicz & Chowdhury, 1987 — - Proposed Formula (Eq. 4.84)
~r 2
-r 4
T-6 8
T— 10
Depth (y) 'm'
12
Fig. 4.3.2.3 Comparison between theoretical and typical values of apparent friction
factor for ribbed strips
145
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.3.2.2 Strips length effects
The length of strips appears to have an important effect on the value of apparent friction
coefficient as found by several tests carried out in the U S A and France. Based on the
results of pull-out tests in Satolas in France (Alimi et al, 1973) and in California (Chang
& Forsyth, 1977) for smooth strips, there appears to be a non-linear relationship
between the strip length and the apparent friction coefficient. The result of the tests are
shown in Fig. 4.3.2.4.
Arenicz and Chowdhury (1987), have suggested the calculation of the effect of length of
reinforcement strips as follows:
/*=/*(l-aL) (4.86)
where / is the apparent friction coefficient between soil and reinforcements, fc is the
maximum value of /*, L is the length of reinforcement strips and a is a constant
suggested to be 0.72.
There are two points that ought to be made regarding this equation. Firstly, it does not
relate the value of/* to the height (H) of reinforcement earth wall, even though the field
tests results (Fig. 4.3.2.4) indicate that/* depends on H. Secondly, the value of f* is
unknown and appears to change with the depth of fill. Since no method of detennining
the value of fc* has been proposed by Arenicz and Chowdhury (1987), the equation
cannot effectively be used for design purposes.
An analysis of the results of the field tests, shown in Fig. 4.3.2.4, indicates that although
the relationship between the apparent friction factor/* and the length of reinforcement L
is non-linear - as confirmed by others (Alimi et. al, 1973; Chang and Forsyth, 1977;
Arenicz and Chowdhury, 1987) - there is a linear relationship between/* and the ratio of
H/L, as illustrated in Fig. 4.3.2.5 based on the same field data.
146
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Results of pull-out tests at Satolas (France)
2.2 ~\
f* 1.8 -
1.4 -
1.0 -
0.6 -
0.2 H=2m
1——T 6 7
~i——
8 L 9
Results of pull-out tests at Highway 39 Wall (USA)
1.5 -i
f* 1.2-
0.9-
0.6-
0.3-
0.0 — T 2 L 5
Fig. 4.3.2.4 The results of pull-out tests
From Fig. 4.3.2.5, the apparent friction coefficient/* decreases linearly with the increase
in ratio H/L. This relationship can be written as:
* H
f* = f -m(—) JC >
(4.87)
where m is the tangent of the lines.
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STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.3.3 Extension of failure zone
Observations and measurements taken from the existing structures, which remain in a
state of safe equilibrium, can only identify the position of a potential failure surface. This
surface is commonly assumed to coincide with the maximum tension line, ie. the line
passing through the loci of maximum tension in reinforcement strips.
For a number of existing reinforced earth structures with vertical facings, the shape and
position of the maximum tension line has been determined through field observations. In
general, they are curvilinear and located between 0.1H to 0.3H away from the face of
structure. To facilitate empirical design, Schlosser (1978) suggested a simple bi-linear
function (Fig. 4.3.3.1), with a tangential discontinuity at 0.5H, to represent the observed
maximum tension lines. Therefore, the required length of the strips, L, can be calculated
as follows.
L = L +0.3H for y<— (4.88) e 2
L = L +0.6#-0.6y for y > — (4.89) e J J J 2
where, H is the height of the reinforced earth structure, Le is the effective length of the
reinforcing strips and, y is the depth of soil from the top.
Later, Arenicz and Chowdhury (1987), suggested a modification to the Schlosser
proposal, which eliminated tangent discontinuity and reflected field observations more
closely. This was achieved by proposing the following function:
_L = \r2-(±)2-a (4.90)
H V H
where r is radius of cylindrical failure surface, x is distance from facing panels to the
point of maximum tension in reinforcements and y is the thickness of the soil fill above
149
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
the strip considered. Based on Eq. 4.90, therefore, the required length of the strips, L,
can be calculated as follows:
L=L +x e
(4.91)
where Le is calculated (as will be discussed in the following section) and:
x = H(^r2-(jj)2-a) (4.92)
H
r
H/2
0.3H '
L
Le
Fig. 4.3.3.1 Effective length of reinforcing strip
4.3.4 Reinforcement Effect
4.3.4.1 Bond Failure
The friction force between soil and reinforcements,//, can be calculated as follows:
/. =2B.L f a Jf i eJ v
(4.93)
150
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
where 5/ is the total width of reinforcements at level i, Le is the effective length of the
reinforcing strips, /* is the friction factor between soil and reinforcement, and o*v is the
vertical stress acting on the reinforcements. On the other hand, the pull out force, fa can
be calculated as follows:
/ = KSVTSTJG Ja V H v
(4.94)
where K is the coefficient of lateral earth pressure, Sy and Sjj are vertical and horizontal
spacings between reinforcements, respectively, and GV is the vertical stress. At the time
of bond failure, the following equation can be written considering the safety factor:
FS, a (4.95)
where FS§ is the safety factor against bond failure. Substituting ff and fa from
Equations 4.93 and 4.94 in Eq. 4.95 and solving for Le results in the following equation:
L = e
KSySHFS^
IB.f* r
(4.96)
Substituting K from Eq. 4.75, /* from Eq. 4.83 and 4.84 to Eq. 4.96, results in the
following:
I) for smooth strips:
L =< e
[*«+I-2H<WvV5* 2B. [tan y + d^ (2.4 - tan \|/)]
K S-,,STjFS. a V H § 2_5.tan\|/
i Y
for, y < 6m
for, y>6m
(4.97)
II) for ribbed strips:
151
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
e
»y [ * a + 1 . 2 ^ l ( „ Q - * a ) ] V ^
2B. [tan<|> + 0.9y dl (3.85 - tan <)))]
K S,rSrjFS± a V H §
2i5.tan(l) i Y
/or, y < 6 m
/or, y < 6 m
(4.98)
where L e is the effective length of the reinforcements, Sy and S H are the vertical and
horizontal spacings between reinforcements, respectively, Ka and Ko are the coefficients
of lateral earth pressure in active and at rest conditions, respectively, FS§ is the safety
factor against bond failure, B{ is the total width of reinforcements at level i, d\ is
calculated from Eq. 4.76, y is the depth of soil, \|/ is the angle of friction between soil and
reinforcement measured in the direct shear box, and § is the internal angle of friction of
soil.
4.3.4.2 Reinforcement Failure
At the time of failure due to the rupture of reinforcing strips, the following equation can
be written:
A/ ________
FS y
f. a (4.99)
where, fa is the force given by Eq. 4.94, FSy is the safety factor against rupture failure of
reinforcement, As is the cross sectional area of the reinforcement, and/y is the ultimate
tension in a unit area of reinforcement. Substituting fa from Eq. 4.94 for Eq. 4.99
provides a solution for the cross section area, As, as follows:
A -s
KS SrjO SF v H v s
/_.
(4.100)
Substituting the value of K from Eq. 4.75 to Eq. 4.100 leads to the following equations
for no failure due to the rupture of the reinforcement:
152
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
A = \ s
[K +1.2ydAK -K )]S„SrjO FS 1 a 1 o a V H v y
— for, y < 6m
K SvS„c FS <4M1>
a V H v y , — — for, y<6m U
where S y and Sfj are vertical and horizontal spacings between reinforcements,
respectively, Ka and K o are coefficients of lateral earth pressure in active and at the rest
conditions, respectively, FSy is the safety factor against rupture failure,/y is the ultimate
tension in a unit area of reinforcement, d\ is calculated from Eq. 4.76, c v is vertical
stress on the reinforcement, y is the thickness of soil in the level considered.
4.3.5 Design Equations
In the design of reinforced earth structures, factors of safety against both break and bond
failures have to be calculated. In current practice, this is usually carried out through
design formulae derived from the static equilibrium, which incorporates the empirical
functions discussed in the previous sections of this chapter. The sets of formulae derived
by Arenicz and Chowdhury (1987) for the C G M and the M C G M are given in Appendix
D for comparison with the alternative design formulae based on the semi-empirical
functions proposed in this chapter (given in Table 4.3.5.1).
In table 3.4.5.1, A/ is the total cross-section of reinforcement at level i, ot is the
allowable tensile stress for the reinforcement, y is the thickness of soil fill above the strip
considered, Lt is the length of reinforcement strip at level i, y is the total unit weight of
reinforced soil fill, Ka is the coefficient of active earth pressure, K o is the coefficient of
lateral earth pressure at rest, dj is calculated from Eq. 4.76, Sv and SH are, respectively,
the vertical and horizontal spacing of the reinforcement, 5; is the total width of
reinforcement at level i, H is the height of reinforced earth structure, <|> is the angle of
internal friction of soil fill, and y is the angle of friction between soil and reinforcement.
153
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STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.3.6 Internal erosion and piping failure
Piping is the removal of soil particles by percolating water causing creation of channels
through the soil. As mentioned in Sec. 3.4.2, seepage flow through the soil exerts force
on the soil particles. If this force is greater than the resultant of resistance forces, the
particles start to move. The resistance forces acting on the last particle (which is at the
end of a flow path) are minimum. Therefore the removal of particle firstly occurs there.
After removing the last particle, this process will be repeated for the next particles.
Continuation of this process leads to creation of a channel through the soil. This process
is normally accelerated for the next particles, because the seepage force is increased due
to decrease of the seepage path length.
The type of RSD is an important factor in the prevention of internal erosion and
occurrence of piping failure. For example, the piping may affect the stability of
downstream facing panels in homogeneous fill RSDs without drainage blanket. However,
piping does not directly affect the downstream facing panels in zoned RSDs.
Construction of drainage blanket has an important role in the prevention of piping. In
the following sections, these will be further discussed as: (a) piping in homogeneous fill
RSD without drainage blanket, (b) piping in homogeneous fill RSD with drainage
blanket, (c) piping in zoned RSD, and (d) piping under RSD.
(a) Piping in homogeneous fill RSD without drainage blanket. In homogeneous
fill RSD without drainage blanket, the effect of seepage force on the last particle is nearly
a horizontal force, Fp, at the downstream side of dam. This force acts on the facing
panels, which are below the upper line of seepage, toward the downstream side as
shown in Fig. 4.3.6.1. If the upper seepage limit is assumed to act at about one third of
the height, this force m a y be represented as a push-out force and is given as:
V2
F = f 3 C , p A — (4.107) p h dv 2
155
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
where V is the seepage velocity calculated from Eq. 3.25, C j is the drag shape
coefficient relating to the shape of facing panel suggested to be 2 for the square shapes
(Streeter and Wylie, 1979), p is the density of water, and A is the cross sectional area of
the facing panels. This force should be considered in calculation of cross sectional area
of reinforcement needed against break failure.
Hi y
y^' yS \ -
S? S\f y)*h i#\_
't' Particle C
Hj/3
Fig. 4.3.6.1 Piping through a homogeneous fill RSD without drainage blanket
(b) Piping in homogeneous fill RSD with drainage blanket. Referring to Fig.
4.3.6.2, in homogeneous fill RSD with a horizontal drainage blanket, the seepage force,
Fp, does not act on the facing panels. This force may cause water to percolate through
the drainage blanket. This should be considered in the design of drainage blanket which
is beyond the scope of this project.
Draniage blanket
particle C
Fig. 4.3.6.2 Piping through a homogeneous fill RSD with a horizontal drainage blanket
156
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
(c) Piping in zoned RSD. Seepage lines through a zoned RSD is shown in Fig
4.3.6.3. Similar to the Case (b), the piping force, Fp, does not act on the facing panels.
However, this force should be considered as external force acting on the reinforced soil
zone when there is no filter between the reinforced zone and the core. The stability of
reinforced soil zone should be checked against this force. If a filter is constructed
between the core and reinforced soil zone, this force may be ignored.
(d) Piping under RSD As the seepage force percolates upward under RSD at the
downstream side, it tends to uplift the soil particle (See Fig. 4.3.6.4). This force reduces
the effective weight of particle C. W h e n the seepage force exceeds the weight of
particle, then the piping failure starts and particle C floats out. If particle C floats out,
the length of water path is reduced. Reduction of the path length increases the driving
force, Fp. This causes the floating out of the next particle. Continuation of this process
leads to rapid creation of a channel under the dam. This should be considered in the
design of foundation of RSDs which is beyond the scope of this project.
H,
Hn
(a)
(b)
Reinforced soil zone
Filter
Draniage blanket
Reinforced soil zone
Draniage blanket
Fig. 4.3.6.3 Piping through a zoned RSD
157
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
Fig. 4.3.6.4 Piping under a RSD
The use of cutoff trenches under the RSD and the use of heavy stones on downstream
side may prevent the piping failure through the foundation (see Fig. 4.3.6.5). Using
heavy stones on the downstream side causes an increase in the vertical stress acting on
the particles. This prevents piping. Using cutoff trenches increases the length of seepage
line, this means prevention of piping. Detailed evaluation of these solutions are beyond
the scope of this thesis.
Reinforced soil dam
Heavy stones
H-
Seepage line under reinforced soil dam
Fig. 4.3.6.5 Use of heavy stones in downstream side for preventing piping
158
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
4.3.7 Hydraulic fracture failure
The shearing strength of fill material is reduced when pore water pressure occurs in the
soil mass. The increase in pore water pressure may lead to hydraulic fracture failure.
According to Singh (1975), pore water pressure may occur in earth dams under three
stages: (a) during the earth dam construction, (b) under steady seepage, and (c) during
or after a quick drawdown. The first one is the result of weak compaction of fill
material. The second one occurs after the reservoir is full of water for a certain time.
The last one occurs when the reservoir is emptied rapidly.
Three flow gradients may occur in the upstream side of RSD as shown in Fig. 4.3.7.1.
After a quick drawdown, the seepage reverses and flows towards the upstream side.
Reversed seepage lines through a RSD at rapid drawdown situation are shown in Fig.
4.3.7.2.
The total pore water pressure, u, is normally calculated as follows:
u = B [a3 +A (cx -CT3)] (4.108)
where A and B are Skempton's pore pressure coefficients, determined based on triaxial
test, and "1-0*3 is the deviator stress difference. When the pore pressure is more than
minimum principal stress, the soil mass is increased in volume and may be floated out as
a dense liquid with a unit weight more than the submerged unit weight of soil.
Therefore, the minimum principal stress should always exceed the pore water pressure at
any infinitesimal element of the soil to prevent hydraulic fracture failure.
According to Mitchell (1983), upward gradient can be expected when lateral flow
gradients conform to the slopes. In some cases (Case c in Fig. 4.3.7.2), this gradient
reaches to a critical hydraulic gradient, ic which is the hydraulic gradient at a point
where water exits out of the soil fill. The hydraulic gradient is normally given as:
i --^-cose. (4.109) C y 1
'w
159
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
where y is the submerged unit weight of soil mass, y w is the unit weight of water, and
61 is the upstream slope angle as shown in Figs. 4.3.7.2.
(a) Hydrostatic pressure
(b) Drawdown
(c) Artesian pressure
u
u
u-yh 'w
u < y h 'w
u> y h 'w
Fig. 4.3.7.1. Idealised flow gradients in the upstream part of RSD
Upstream water table (level 1)
Reversed seepage lines
H
Upstream water table (level
\
Seepage line
H,
Fig. 4.3.7.2 Seepage line through a homogeneous fill RSD without drainage blanket
160
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
When the hydraulic gradient reaches its critical value, a continued erosion of the slope
may occur leading to hydraulic fracture failure. This phenomenon may be seen in the
case of rapid drawdown. Therefore, the upstream slope of dam should be as flat as
practicable to prevent hydraulic fracture failure in rapid drawdown. This slope may be
given as:
8. -Arc cos Y * 'w c
y SF (4.110)
where SF is the safety factor against hydraulic fracture failure. Since,
tan6- = H
wb-wt (4.111)
Therefore, for no hydraulic fracture failure, the minimum required base length of dam
may be calculated as:
wb>-H
tan /
Arc cos Y i 'w c Y SF
T + W > (4.112)
4.3.8 Distortional settlement
Distortional settlement, which usually causes the appearance of cracks in conventional
earth dams, is also a major problem for RSDs. Foundation character and construction
method affect the distortional settlement. The foundation may suffer under the forces
acting on dam, causing the creation of cracks. The construction method has also an
important role in the reduction of settlements in RSD. Maximum compaction should be
obtained when the dam is being constructed. Using thinner layers during the compaction
causes better compaction, which leads to a reduction of settlement. A rapid construction
of earth dams may cause post-distortional settlement after construction. T w o main
161
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
reasons for considering the distortional settlement are: to ensure that the distortional
strains are sufficiently low to prevent internal cracking and, the compressive stresses are
greater than the water pressure at any location to prevent hydraulic fracture failure.
Original reinforced soil dam ^>*
Deformed reinforced soil dam ^ , - '
^ g g j g l l l l ^ ^
5
Bd
-'-- — •-- - h j
H
W
Fig. 4.3.8.1 The distortion settlement of RSD
Referring to Fig. 4.3.8.1, the distortional settlement, 5, of RSD may be calculated as:
6 = 5 _ + 5 / (4.113)
where 67 is the foundation settlement and 8j is the dam compression which may be
calculated as:
§j=\r\m ACT =]/?m zyd =m y — „ JU v v Jv v ' z v ' 9
(4.114) z v • 2
in which m v is the compression modulus of the compacted reinforced soil fill. Hence,
the vertical strain may be estimated as:
162
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
8 , m yH E =-^= —* (4.115) v // 2
For average settlements, the base extensional strain may be approximated as:
2J(W2+b2) E -i JL__ ____ C4.-Z76;
Therefore, the distortional strain under plain strain is:
_ e ___._____!_______! v h H H
To prevent distortional cracks, the distortional strain should be less than the maximum
distortional strain, ^max, which causes rupture in reinforced soil sample, tested in
laboratory condition.
4.4 C O N C L U S I O N S
The stability analysis of RSD should be accurately addressed from the point of view of
internal and external stability. The external stability of RSD has been evaluated, based
on an analytical approach. In external stability analysis, it has been assumed that the
whole reinforced soil structure acts as a unit.
To optimise the geometry of these dams, the functions of minimum required base
length for no failure state due to sliding, overturning, and overstressing have been
presented in the first part of this chapter.
Soil reinforcement is a modern technique for improving the mechanical properties of
soil, using the concept of frictional interaction between soil and reinforcement. In the
composite material (consisting of soil and reinforcement) the generation of frictional
forces between soil and reinforcement is fundamental to its behaviour. The mechanisms
163
STABILITY ANALYSIS OF REINFORCED SOIL DAMS CHAPTER FOUR
involved in this process are, however, not yet fully understood. Various analytical
theories developed so far are still not in satisfactory agreement with the observed
behaviour of reinforced earth structures; which necessitates the use of empirical
relationships in current design practice.
Some of the theories developed so far, their relationships and the field data on which
they were based, have been analysed in the second part of this chapter and, subsequently,
modified. Empirical formulae reflecting the observed behaviour of reinforced earth
structures were suggested.
The semi-empirical relationships suggested in this chapter have eliminated the tangential
discontinuity existing in the formulae of the CGM. They have reflected the non-linearity
indicated by the field data, have eliminated unknown parameters existing in formulae of
the MCGM, and have offered a closer agreement with available field observations.
In regards to the apparent friction factor, (which is fundamental to design of reinforced
earth structures), a linear relationship between the factor and the ratio of fill depth to
strip length has been discovered in the analysis of the field data.
On the basis of the coefficient of lateral earth pressure, apparent friction factor, and the
maximum tension line, the formulae for calculation of the factor of safety against tensile
failure FSy, and the bond failure of reinforcements FS(j), have been proposed.
164
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
CHAPTER FIVE
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOAD
5.1 INTRODUCTION
Earthquakes, a world wide problem, act on structures as a kind of dynamic force. In
the past, many dams have been damaged by earthquakes e.g. the Sheffield dam in the
U S A failed as a resulted of the Santa Barbara earthquake in 1925. About nine cases of
damage and/or even failure were reported from 1930 to 1946 (Ambraseys 1960). The
range of side slopes of these nine earth dams were from 2 to 3.5 horizontal to 1 vertical.
The failure of the Hebgen dam in Montana in the U S A was the result of another
earthquake which occurred in 1959. Slope sliding, settlement, slumping, longitudinal
cracks and even the complete wash-out of earth dams were some of the results of the
earthquakes (Singh, 1976). The 1939 Ojika Earthquake in Japan resulted in 12
complete dam failures. More than half of these failures occurred during the 24 hour
period after the earthquake. The sandy soil embankments suffered the greatest damage.
However, there were no total failures in clay soils embankments. It is well known that
crest settlement and formation of cracks are the most frequent types of damage to dams
as a result of earthquake. Cracks may cause damage to outlets of tunnels resulting in
leakages. Blockage of the outlets, piping and even overtopping, may also appear after
an earthquake.
The failure of the earth dam may be the result of relative dam displacement caused by
major fault movement in the foundation soil, loss of freeboard due to differential
tectonic ground movement, slope failures induced by ground motions. Other factors
deserving consideration are the sliding of the dam on weak foundation materials, piping
165
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
failure through cracks induced by ground motions, overtopping of dam due to slides or
rock-falls into the reservoir and failure of the spillway or outlet works (Seed, 1983).
In an earthquake, the earth moves in an approximately random manner in both
horizontal and vertical directions. Variation of acceleration due to earthquake is a
function of time (Newmark, 1965). The velocity and displacement caused by the
earthquake can be calculated by integration from the acceleration-time function.
At least, two relationships have been formulated by Richter (1958) and Bath (1966)
between the magnitude of earthquake, M on the Richter Scale, and the energy released
from the earthquake shock, E in Ergs, as follows:
log E= 11.4 +1.5 M (5.1)
log E = 12.24 + 1.44 M (5.2)
Regarding the second equation, the energy released by an earthquake of the magnitude
7 on the Richter Scale is equal to 7.2 x 1 0 2 0 Ergs or 9 times the energy released by the
Hiroshima atom bomb. The energy released by an earthquake of the magnitude 8 on the
Richter Scale is equal to 241 times as this bomb. The El-Centro earthquake, which
occurred in California, on the M a y 1940 is one of the strongest earthquakes recorded.
It is known that the maximum ground acceleration of the earthquake was 0.32g, the
maximum ground velocity was about 0.35 m/s, and the maximum ground displacement
was 0.21 m (Newmark, 1965).
Although many researchers have investigated the behaviour of conventional earth dam
under seismic load, many problems still remained unknown in this regard (Wahlstorm
1974; Wolff 1985;). The behaviour of RSD under seismic loads is another problem
which should be studied. Seismic resistance of reinforced soil dams and embankments
may be tested by the shaking table tests (Koga et al. 1988a), or may be modelled
numerically by the finite element methods. However, evaluating the natural frequency of
166
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
the RSD is a very simple method for addressing the maximum safe proportion of
reinforcement needed for a RSD. Comparison between the natural frequency of
conventional earth dam and RSD is the aim of this chapter.
5.2 FREE HARMONIC VIBRATION
Fig. 5.2.1a shows a typical RSD divided into several imaginary layers. Each layer may
be considered to act as a block for the purpose of dynamic analysis: the first and the
second blocks of the dam are shown in Fig. 5.2.1b.
w t
•4 • m y e * g \ x x
g X X X
g • / / g X X X
m * * *
- • - ^
\ X X
g X X _x
wb r
(a)
in? 1 ?2
i
i -
Hi
r
^^ N. l
First layer Second Layer
W W • i i
i
a / — •* \ X X \ X
X X X X \
1 1
iff. / 1 fe2 /, . ,—-J-' N' S' -' -' \ S
' /
model of internal resistance
(b)
Fig. 5.2.1 a) A typical RSD divided into several imaginary layers b)the first and the
second blocks of the RSD
It is assumed that a load Fi is acting on a block and then is suddenly removed. The
motion of the block, neglecting damping effects of soil under the load, can be
expressed by the following equation:
m4-£+F.=0 dt1 V
(5.3)
167
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
in which y is the vertical displacement of the block at time t, m is mass, m = Wl g, and
¥\ is the force necessary to keep the block in its place. Substitution of F, = K y in the 1 sJ
above equation, in which Ks is the spring constant of soil, results in the following:
dt
The general solution of the above expression is usually written as follows:
y = cx s i n ( r ^ ) + c2 cos(r^J-) (5.5)
in which c\ and C2 are constants. Since, y=0 when t=0, C2 should also be zero and the
solution of Eq. 5.5 is:
K y = c1sin(?AM-) (5.6)
1 V m
The dimension of the term IK lm is 1/sec, because the term tjK lm has no
dimension. Substitution of cj and IK lm with a and co, respectively, results in the
following:
y = asm((at) (5.7)
in which a is the amplitude of a sinusoidal harmonic vibration and co is the angular
velocity which can be represented by a vector of length a which rotates with a constant
angular velocity around the equilibrium position of the centre of gravity of the block.
In fact, the vibrations are damped because of the internal resistance of the soil.
Therefore, the amplitude will decrease over time until Vibration stops completely. Thus
Eq. 5.3 may be modified as follows:
d2y m—%-+F, + F,=0 (5.8)
dt2 d 2
168
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
in which Fj is the damping force, which could be described in terms of c^, the
damping coefficient, as follows:
Fd=
c4 (5-9> Substitution of 5.9 in 5.8 yields;
dt2 d dt s
or;
^+2A.-^ + co2y = 0 (5.11) dt1 dt
in which X, the damping ratio, is related to c^ as follows:
\ = ^L (5.12) 2m
In this case, the amplitude of sequential cycles have the ratio:
a n + 1 _ e-<K a n
(5.13)
in which x is the period of the vibration which may be related to the circular frequency,
co, as follows:
T = 2TC
__. (5.14)
5.3 FORCED HARMONIC VIBRATIONS
Impulses causing vibrations are repeated frequently. In this case, the sinusoidal
periodic impulse and the associated equation of motion are represented as follows:
F= FjSint.Gy) (5.15)
169
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
— ^ + ( 0 02 y = a1_0
2sin(co10 (5.16) dt
where COQ is the natural frequency of the system consisting of a block and spring and aj
is a ratio of Fj and Ks:
F. 0.--1- (5.17)
1 K s
The solution of Eq. 5.16 is:
y = N [sin(co10-«cos(C000] (5.18)
in which the amplification factor, is given by:
_V=- —5L- f5.i9j d-nl)
where n is the ratio between the frequency of the periodic impulse to the natural
frequency of the block, coi/coo- The relationship between N and n can be plotted as
illustrated in Fig. 5.3.1. The figure shows clearly that if the frequency of the periodic
impulse is equal to the natural frequency of the block (n=l), resonance of vibrations
occurs and the magnification factor reaches infinite. The first term of Eq. 5.18
represents a forced vibration with an amplitude N and a circular frequency a>\. The
second term of the equation is a forced vibration with circular frequency COQ and
amplitude -nN.
170
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
N
al
0
HAZARD ZONE
Fig. 5.3.1 The relation between N and n
5.4 D A M P I N G
The infinite value of magnification factor N at n=l is theoretically correct for the ideal
case of an undamped system. However, since damping occurs, N is not infinite even for
n=l. With the inclusion of damping, the equation of motion can be modified as
follows:
1 a v av ? 2 —^-+2X,^-+coty = fl1cotsin(co10 dt1 dt U i U 1
(5.20)
where X is the damping ratio given by Eq. 5.12. In this case, the amplitude is
maximum when:
1 a = a l2_.f_W
%i 4 coQ
(5.21)
and the magnitude of circular frequency associated with this amplitude at resonance is
given by:
171
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
<» = c o n l 1 " ^ — > 2 (5-22)
res 0A/ 2 fi>0
5.5 NATURAL FREQUENCY
It is of considerable interest to estimate the natural frequency of any structure which may
be subjected to dynamic forces such as those due to an earthquake. The analysis and
design of such a structure must recognise the possibility of resonance during an
earthquake. This will require selection of the appropriate design earthquake and a
comparison of the natural frequency of the structure with the frequency characteristics of
the design earthquake.
This chapter is concerned with the development of a simple approach for the estimation
of the natural frequency of a RSD. The method is developed by considering the overall
stiffness of such a composite structure in terms of the stiffness of the unreinforced mass
and that of the reinforcing elements.
A conventional earth dam and a RSD will be shown schematically in Fig. 5.5.1a and b.
Each of these may by subdivided into imaginary layers which are horizontal. It is
assumed that any such layer acts as an individual block. It is also assumed that the
natural frequency of a system of soil layers is:
0 K w
where, k is the stiffness of the spring assumed to be in the system, W is the weight of
the system of the structure assumed, g is the gravity acceleration and COQ is the natural
frequency of the system.
172
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
mi y 1
Ai i i
^
WM (a)
\ni 1
p\ I 1
ft
m? / 1
/ • > ^
I 1 **
H
(b)
Fig. 5.5.1 a) A typical conventional earth dam and b) a typical RSD with vertical
downstream facing
Referring to Fig. 5.5.1, the weight of the conventional earth dam, Wj, and the weight
of the RSD, W2, may be calculated as follows:
Wl = ^+wh^Hh
W, _(^2_^_2____
(5.24)
(5.25)
in which h is dam height, wtj and w g are the crest widths of both dams, wbJ and wjj2
are the base widths of both dams as shown in Fig. 5.5.1, and y\ and 72 we,
respectively, the average unit weights of the soil in the conventional earth dam and in
IheRSD.
The unit weight of the soil material used within the RSD, Y2, is calculated as follows:
y2=|3Yr+(l-p)Y1 (5.26)
173
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
in which yr is the unit weight of reinforcement and P is the proportion by weight of the
reinforcement used within the RSD to the total weight of the dam. Substitution of
Equations 5.24 to 5.26 in 5.23, and finding the ratio of natural frequency of RSD per
natural frequency of conventional earth dam gives:
co
co ^ - - c p x ¥ (5.27)
01
where
2— L L + m1 +«H
H 1 1
I 2-^ + m, H
(5.28)
¥ =
[p-_. + (l-P)]
h (5.29)
[P__ + (1_P)]
in which COQI and COQ2 are, respectively, the natural frequencies of both conventional
and reinforced soil dams, m\ and nj are respectively the slopes of upstream and
downstream of the conventional dam as shown in Fig. 5.5.1, mj is the upstream slope
of the RSD, kj and ki are, respectively, the spring constants for the elastic support in
both conventional and RSDs. In reality, (p is a function of geometry of dams, and V is
a function of the overall stiffness of materials of dams.
5.5.1 Stiffness Function
In order to find ¥, it is necessary to find the proportion of spring constant of reinforced
soil to the spring constant of the soil, fc?A/- Referring to Fig. 5.5.1.1, the ratio of the
174
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
spring constant of the reinforced soil, > to the spring constant of the unreinforced soil,
k], can be expressed as follows:
b, (ErAr+EsAs)/0-5(wt2+^ kl <VVV°-5(",i+"M)
(5.30)
or,
(1+ p—^)M K _
s
U + P)
(5.31)
where Er is the elastic modulus of the reinforcements strips, Es is the elastic modulus
of soil, P is the ratio between Ar and As which are, respectively, the cross-section area
of reinforcement strips and the cross-section area of soil element as shown in Fig.
5.5.1.1, and Mis a dimensionless factor equal to (w . + w,,) / (w ~ + Wuy )•
Reinforcement strip
d
EA / r
W////////////K
EA s s
a- Reinforced soil element
Soil elements
b- Unreinforced soil element
Fig. 5.5.1.1 Comparison between reinforced and unreinforced soil elements
Substitution of Eq. 5.31 in Eq. 5.29 gives:
¥ =
[p(l + p-f)Af + (l-pz)] E s
(5.32)
[p(l + P ) - ^ + (l-pZ)]
175
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
Eq. 5.32 shows that ¥ is a function of (a) the ratio of the reinforcement used within the
soil, P, (b) the ratio of elastic modulus of reinforcements strips to elastic modulus of
soil E/Es, (c) the ratio of the unit weight of reinforcement to the unit weight of soil
Yj/yj, and (d) the ratio of the middle width of conventional earth dam to the middle
width of RSD. The variation of *F versus p for Yr/Ys=3-9, M=2.63 and the various
Ej/Es is shown in Fig. 5.5.1.2. This figure clearly represents that by increase the
proportion of the reinforcement used within the RSD leads to an increase in the
function of material, T.
Fig. 5.5.1.2 Variation of*¥ versus >fory/is-3.9, M=2.63
5.5.2 Shape Function
Inclination of upstream and downstream slopes of conventional earth dams depends on
the internal friction angle of soil, unit weight of material used, plane zones of sliding in
the slopes, and the safety factor (Sherard, 1963; Janbu, 1973; Singh, 1976). However,
the minimum value for small earth dams, shown in Fig. 5.5.2.1, is about 2:1 in both
176
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
upstream face and down stream face (United States Bureau of Reclamation, 1977).
Assuming the upstream slope inclination of the equivalent RSD with vertical
downstream facing is 1.5:1 as shown in Figures 5.5.2.2 and 5.5.2.3, the substitution of
the minimum values in the function of geometry, Eq. 5.28, gives:
<P mm
2-*-+4 H
2-*-+1.5 H
(5.33)
- '
I* r
l
2
Upstream
Wt i * — *
, V
1
• ' /
/Reinforced
/ soil dam
wb
- 3
2
1
Downstream
M
1
7
H
Fig. 5.5.2.1 Minimum slope ranges of a conventional earth dam compared to an
equivalent RSD
The maximum slope inclination of the earth dams, shown in Fig. 5.5.2.1, is about 4:1 in
upstream face and about 2.5:1 in downstream face (United States Bureau of
Reclamation, 1977). Therefore, substitution of the maximum values in the function of
geometry, Eq. 5.28, gives:
w 2 — + 6.5 H
max
n (5.34)
+ 1.5
177
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
where, <pmi'n and (Pmax are, respectively, the minimum and the maximum values of the
function of geometry.
,_ *
IH_
r
i
-'" i
4
Upstream
Wt v*-*
, -jr
i
1 lr /Reinforced
soil dam
wb
t
* • s 2.5
>. 1
Downstream ' - ,
fo|
1
H
_
Fig. 5.5.2.2 Maximum slope ranges of a conventional earth dam compared to an
equivalent RSD
Therefore, the value of cOQ2/tO0b Eq- 5.21, can be expressed as:
co Tmax Q)
02
01
<cp . V ^min
(5.35)
Equations 5.34 and 5.35 show that the minimum and maximum values of the function of
geometry, cp-^ and cpm/„, are functions of the ratio of the crest width of dam to dam
height, W/H. Variations of (pmin and (praax versus W/H is shown in Fig. 5.5.2.3. This
figure illustrates that the maximum value of cpmin and (pmax happens when Wt/H is
zero. This means that both cpm/n and (p,^ are maximum when H is maximum, or the
maximum values of both <?min and (p,-^ happen when the RSD is compared with the
total conventional earth dam.
The values of shape functions, (p, are calculated and shown in Table 5.1 for three (20m,
25m and 30m high) dams with a crest width 5m and various side slopes to find the
effect of dam shape on natural frequency. Table 5.1 shows clearly that replacing a
178
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
conventional dam by a RSD causes increase in the value of shape function. The
increase in the shape function leads to the increase of natural frequency of the structure.
Fig. 5.5.2.3 Variation o/cp versus Wt/H
Table 5.1 The values of shape functions, q>, for various side slopes
Conventional
Earth Dams
US-DS
2:1-2:1
2.5:1-2:1
2.5:1 - 2.5:1
3:1 -2:1
3:1-2.5:1
3.5:1-2:1
3.5:1-2.5:1
4:1-2:1
4:1-2.5:1
Reinforced soil
dam
US-DS
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
1.5:1-0:1
Shape
functions, <p
(H=20 m )
1.500 (cpm7-~)
1.581
1.658
1.658
1.732
1.732
1.803
1.803
1.871 (cpw/7r)
Shape
functions, cp
(H=25 m)
1.522 (cpm,-„)
1.606
1.686
1.686
1.762
1.762
1.835
1.835
1.906 (qw)
Shape
functions, cp
(H=30 m )
1.537 (cpm/„)
1.624
1.706
1.706
1.784
1.784
1.859
1.859
1.931 (qw)
US = Upstream slope DS = Downstream slope
179
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
5.6 E X AMPLE
As an illustrative example, the natural frequency of the RSD, shown in Fig. 5.6.1, is
compared to the natural frequency of the conventional earth dam, shown in the same
figure. Assume the elastic modulus of reinforcement, Er, is 2xl08 kN/m2; the elastic
modulus of dense soil, Es, is 50000 kN/m2; the unit weight of reinforcement, yr, is 78
kN/m3; the unit weight of soil, ys, is 20 kN/m3 and the ratio of reinforcement weight
used within the dam to that of soil, p, is 0.02.
1*
1
2.5
1 Jpstreaml S
tJ»L
1 X
r Reinforced soil dam
i 1 50m
140m
2
Downstream
j
1
tl rl
r
30
<
Fig. 5.6.1 The illustrative example of a reinforced and a conventional earth dam
Based on Fig. 5.5.1.2, the value of *F is 2.21, because E/Es=4000, Yr/Ys=3-9 and
M=[0.5x(140+5)]/[0.5x(50+5)]=2.63. Regarding Table 5.1, the values of (p is 1.624
(because the upstream and downstream slopes are, respectively, 2.5:1 and 2:1 for the
conventional earth dam, and are 1.5:1 and 0:1, respectively, for the RSD). Replacing
these values in 5.27 yields the following:
—^ = 2.21 x 1.624 = 3.59 (5.35)
180
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
From Eq. 5.35 it appears that the value of natural frequency of the RSD is more than 3.5
times the value of natural frequency of the conventional earth dam. The natural
frequency of the conventional earth dam is calculated from Eq. 5.23.
Referring to Fig. 5.6.2, the stiffness of the soil within the conventional earth dam, k, is
assumed to be calculate as follows:
E A pH E AHx 1 fc = — £ — = f - s
L Jo A L
(5.36)
Fig. 5.6.2 The illustrative example of the conventional earth dam
For the conventional earth dam shown in Fig. 5.6.2, k=50000xdH/dL=20690 kN/m.
Substituting the values of (a) weight of the conventional dam, W, (b) stiffness of the soil
within the conventional earth dam, k, and (c) acceleration due to gravity, g=9.8 m/s2, in
Eq. 5.21 results in.
CO 20690 [kNImlm] 9.8 [mis1] ^ 2 1 6 §ec-i
01 -'(5 + l40x30) [ m2 ]x20 [kNIm3]
(5.37)
181
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
From Eq. 5.35, the natural frequency of the RSD can be expressed as follows:
coQ2 =3.59x2.16 = 7.75 Sec"1 (5.38)
Pseudo acceleration verses period, T, for various values of damping coefficients based
on four major earthquakes which occurred in the U S A is shown in Fig. 5.6.3. It is
assumed that such earthquakes acts on the conventional earth dam as shown in Fig.
5.6.1. Since the earthquake frequency is 20.94 sec-1 for maximum acceleration of such
earthquakes, the value of ngj can be calculated as:
co "01 =
01 _ 2.16
co 0 20.94
= 0.1 (5.39)
\ccelaration
4
3
2
0
iffs*0
__ 0.05
S s^ Damping 7 t
^l_d • --S_3 a—.
0 10 ~„ Period (sec) ™
Fig. 5.6.3 Pseudo acceleration verses period, T,for various values of damping
coefficients based on four major earthquakes happened in USA (After Adely, 1987)
Regarding Eq. 5.38, the ratio of the natural frequency of the RSD to earthquake
frequency, nQ2, is calculated as follows:
182
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
10 CY) 7 75 nm = —^- = — — = 0.37 (5.40) 02 „ 0 20.94
As seen from Fig. 5.6.3, the ratio between the natural frequency of the RSD to the
earthquake frequency, COQ2/COO, is less than 0.5. Referring to Fig. 5.3.1, this does not
cause the phenomenon of resonance in the structure which could lead to a significant
damage of the structure. However, if the value of P is increased to 0.05, then \\f is 4.77
(See Fig. 5.5.1.2). O n this basis, the ratio of natural frequency of the RSD to that of
conventional earth dam is:
—^- = 4.77x1.624 = 7.75 (5.41) ffl01
Therefore,
co02 = 7.75 x 2.16 = 16.73 Sec"1 (5.42)
In this situation the value of nryi will be:
%l = ii73_080 (5A3) 02 „ 0 20.94
which is very close to resonance situation regarding Fig. 5.3.1. To prevent the
resonance phenomenon in this example, the proportion of the reinforcement used in the
above example should be kept below 3% .
Again, if the value of p is increased to 0.11, then Eq. 5.32 yields \jr=9.45. On this basis,
the ratio of natural frequency of the RSD to that of the conventional earth dam is:
—Q2- = 9.45 x 1.624 = 15.35 (5.44)
%1
Therefore,
coQ2 = 15.35 x 2.16 = 33.16 Sec"1 (5-45)
In this situation the value of nrj2 will be:
183
BEHAVIOUR OF SOIL DAMS UNDER SEISMIC LOADS CHAPTER FIVE
C002 33.16 _ co R n - = - ^ = = 1.58 (546) 0 2 co0 20.94 (J' '
which is far enough from the resonance situation (See Fig. 5.3.1). Again, to prevent the
resonance phenomenon, the proportion of reinforcement used in the dam should be kept
higher than 11% (ignoring cost). Therefore, to prevent resonance in the RSD, the
proportion of reinforcements used within the dam should be sufficient to result in a
considerable reduction or increase in the value of cp (Less than 4% or more than 10% in
the above example). Using reinforcements with low stiffness such as polymers results in
a considerable decrease in the values of cp
5.7 CONCLUSIONS
Construction of a RSD would normally lead to a considerable cost savings. However, it
is necessary to calculate the natural frequency of such a dam to find its behaviour under
earthquake force. Knowledge of the natural frequency of the structures can assist
designers in assessing the potential for the resonance phenomenon in the structure,
which may result in its total destruction. The practice of inserting reinforcement into
the earth dam material allows reduction in fill volume, reduction in displacement, and
increases the safety factor. However, this also leads to an increase in the natural
frequency of such structures compared with conventional earth dams which may
increase the possibility of failure.
In reality, the natural frequency of RSD is increased because of its geometry and its
overall stiffness. In this chapter, the increases in natural frequency of RSD due to these
two major factors have been separately discussed. Formulae concerning the
magnification of the natural frequency of the structure due to reinforcement insertion
have been derived, and in some cases tabulated and plotted.
184
COMPUTER PROGRAM CHAPTER SDl
CHAPTER SIX
COMPUTER PROGRAM
6.1 INTRODUCTION
A computer program is developed as part of thesis based on the calculation of the
forces acting on RSD (Chapter 3), the equations of stability analysis (Chapter 4), and
the formulae of soil-reinforcement interaction which will be explained in this chapter.
The purpose of the program is to assist a designer in geometrical optimisation and
stress-strain analysis of RSDs.
6.2 FINITE ELEMENT FORMULAE
The finite element method is now widely used as a numerical solution method for the
systems of partial differential equations describing the mechanical behaviour of
material. The deformation of soil, the flow of fluids and the natural behaviour of
metals are some of the fields in which mechanical effects can be simulated by this
method. A RSD, which covers the three materials, can also be analysed by this method.
The following section presents equations representing the elastic and/or elasto-plastic
behaviour of such a system.
The state of stress inside soil normally varies from point to point. Although the stresses
within the soil are not necessary elastic, it is helpful to describe the elastic behaviour of
the soil before any explanation of the plastic response or elasto-plastic behaviour of a
soil mass. Such an analysis is normally based on consideration of the internal forces
acting on an infinitesimal element of soil mass. These will be further explained in the
following sections.
185
COMPUTER PROGRAM CHAPTER SIX
6.2.1 Elastic behaviour of soil
Fig. 6.2.1.1 shows an elastic stress-strain curve. Initially the relationship between
stress and strain is linear (OA in this figure), but become non-linear after point A.
When the soil is unloaded, the stress-strain relationship follows the same path but in the
reverse direction to the origin even though the path is not linear.
Fig. 6.2.1.1 An elastic stress-strain curve
The relationship between the stress components, ox, cy, xxy, acting on a soil element,
based on elastic deformation in a two dimensional form, are usually formulated as
follows:
3c? <K -*+__-_/r
dy
da dx *y _ = F
(6.1)
(6.2) d y a x y
where Fx and Fy are, respectively, the body forces per unit volume in directions x and
y. The direct strains of the element, EX, £ V and y^, are usually calculates as follows:
Bd
x ax (6.3)
186
COMPUTER PROGRAM CHAPTER SIX
5 d
y a y
dd dd Y = — ^ + — * • r*y a JC a y
(6.4)
(6.5)
The relationship between the strains and the normal stresses are normally represents as:
a vo\, (6.6)
(6.7)
£ = X
c — y
Y
£ £
x , y E
X 2(1 + v)
E (6.8)
These equations can be shown in matrix form as follows:
y
'xy
1
F
1
-V
0
-v 0
1 0
0 2(1+ v)
X
a x
c y X
xy
(6.9)
or,
xy (1-v2)
1 v 0
v 1 0
0 0 0.5(l-v)
which can be written as:
x
Y xy
(6.10)
to-MM (6.11)
In the case of saturated soil, the effective stresses, a*x, a*y, are defined instead of the
stresses, ax, oy as follows:
187
COMPUTER PROGRAM CHAPTER SIX
CT = G -u (6.12) A. ^
CT = CT - M (6.75J y y
where « is pore water pressure which discussed before (Sec. 4.3.6). This is known as
Terzaghi's principle of effective stress which states that the change in soil stress is due
to change in effective stress. In this case, Eq. 6.11 changes to:
{a'}-[A'] {e} (6.14)
in which [A'] includes elastic moduli E' and v' rather than E and v.
6.2.2 Inelastic behaviour of soil
Familiarity with plasticity theory is necessary to find how soil deformations can be
modelled. The shape of stress-strain curves is an important factor for predicting the
deformation of the soil. M a n y investigations are being undertaken to understand how
the deformation of a soil mass can be predicted. A possible stress-strain curve for an
element of soil under an unload-reload condition is shown in Fig. 6.2.2.1a, while
Figures 6.2.2.1b to 6.2.2. Id show the simplify models of Fig. 6.2.2.1a.
188
K .© Sst
©
"© © © < I
© ©
-_V
©
•*s,
-s_
<*> Ss
©
s <s)
S3
>!
h ••si
SO
SO
-S
SO
©
•—-a
-©
©
a, CN
CN VO
COMPUTER PROGRAM CHAPTER SIX
From Fig. 6.2.2.1a, it can be seen that the relationship between stress and strain is not
elastic. If the element is unloaded beyond point B, the unload path is not reversible but
the path BC will be followed. If the element is loaded again, the path CD will be
followed. Since the reverse path beyond B, BC, is nearly parallel to the origin path of
primary loading path, OA, as shown in Fig. 6.2.2.1a, the figure may be simplified to
Fig. 6.2.2.1b to Fig. 6.2.2. Id. In these figures it is assumed that the unload-reload
paths are the same and linear.
6.2.3 Soil-reinforcement interaction
In a RSD, shown in Fig. 6.2.3.1, it is assumed that compressive forces are induced in
the soil mass as active forces while, tensile forces are induced in the reinforcements due
to the frictional bond between the soil and the reinforcements as reaction forces. The
finite element method will be used to model the soil deformation, to find the tensile
stress within the reinforcements, and to predict the level of bond between the soil and
reinforcements. To simplify the problem, it is assumed that the loading generates a
group of nodal forces at the contact points between the soil and reinforcement. These
forces cause some deflections within the soil and reinforcements.
Fig. 6.2.3.1 Reinforcement elements within a RSD
190
COMPUTER PROGRAM CHAPTER SIX
For a no bond failure state, the soil deflections should be compatible with the
deflections of the nodal points. In this condition, the reinforcement and soil would
require to be combined by joining or spring elements, modelling the slip behaviour
between soil and reinforcement (Goodman et al, 1968). In the following sections, the
soil reinforcement interaction will be discussed for a layer of reinforced soil.
Following this, the interaction will be extended to the whole structure.
Each reinforcement, Fig. 6.2.3.2, carries the horizontal forces induced in the nodal
points of the reinforcement. The displacement relative to the first node, AT is
calculated as shown in the following equation assuming constant cross-section area of
reinforcement, Ar, and constant stiffness of the reinforcement, Er:
n 2 F*Lr.
• 1 ' l
A r=-—i (6.15) 1 ErAr
in which LF.r is the sum of the nodal points, and ll. is the length of reinforcement
from the first nodal point to the assumed nodal point. Therefore, the nodal
displacements relative to the first node, p, are calculated as follows:
p.-0
= A. -A. (6.16)
P2= A2" A1 p3=A3-A1
The relationship representing the displacement of the soil nodes, As., which are parallel
to the reinforcement nodes, being caused by the active forces, may be calculated as
follows:
n _ F?LS.
i EsAs
191
COMPUTER PROGRAM CHAPTER SIX
?S • in which XF. is the sum of the active forces at the nodes, L. is the length of soil
elements, Es is the Young modulus of the soil elements, and As is the cross section area
of soil elements.
Fig. 6.2.3.2 A typical reinforcement carrying the horizontal forces induced in the nodal
points of reinforcement
For no bond failure, the difference between the displacement of the nodal points of soil
elements and the displacement of the nodal points of reinforcement elements should be
zero. The difference can be expressed as:
-r Tr ?S rS ^F!L. J^FfU.
5. = A r _ A * ______ L_L i i i £rAr
(6.18) s As _ M
Since lengths of reinforcement elements are equal to lengths of soil elements, the above
equation yields to:
8. =Ar-A* = ^ - L L_L (6.19)
ErAr S AS EM
192
COMPUTER PROGRAM CHAPTER SIX
This assumes that the force on reinforcement nodes should be equal and opposite to the
force acting on the corresponding soil nodes and results in:
Substituting this equation to Eq. 6.19 yields:
8. = < — r - r + — r - r ) £ ^ ^ ErAr ESAS i i
(6.21)
This can be written as follows:
{8/} = A{IF.L.} (6.22)
in which;
A = (ESAS -ErAr)
ErArEsAs (6.23)
Eq. 6.23 can be given in matrix form as follows:
= A
0 0 0 0 0
0 1 1 1 1 0 1 2 2 2
0 1 2 3 3 0 1 2 3 4
Flh F 2 L2 F3L3
FALA F5 L5 (6.24)
From equilibrium:
F 1 L 1 + F 2 L 2 + F 3 L 3 + F 4 L 4 + F 5 L 5 = ° C6.25)
Addition of this equation into the above matrix results in:
193
COMPUTER PROGRAM CHAPTER SIX
0
= A
0 0 0 0
0
1
0 1 1
1
1
1
0 1 2
2
2
1
0 1 2
3
3
1
0 . . 1 . . 2 . .
3 . . 4 . .
1 1 1 0
F.L 1 1
FiLi F3 L3 F4L4
F5L5
- A l
(6.26)
or; F1L1 F 2 L 2 F 3 L 3
F 5 L 5
- A l
1
A
0 0 0 0 0 0 1 1 1 1 0 1 2 2 2
0 1 2 3 3 0 1 2 3 4
1 1 1 1 1 1 1 0 0
(6.27)
The solution of this matrix yields a group of nodal forces from a given set of
differential displacements together with the chosen distances between the nodal points.
The set of soil displacement can be obtained from the solution of the soil stiffness
matrix under the external forces as:
[*]{As} = {F) (6.28)
in which [K\ is the stiffness matrix of soil mass, {As} is the vector of nodal
displacement in soil, and {F} is the external force acting on whole elements.
For a number of reinforcements, if the stiffness of reinforcements is assumed to be
constant, the displacements of the nodes can be formulated as:
Ar. U
n r r
_ FT.lL. . 1 U lJ i = l J
ErAr
(6.29)
194
COMPUTER PROGRAM CHAPTER SIX
in which i is the number of nodal points assumed in a reinforcement and j is the number
of reinforcements assumed in the whole structure. The nodal displacements of the soil
elements are calculated as follows:
n 2 F?.LS..
Af. = __L__! (6.30) ij EsAs
In this case, the difference between the displacement of the nodal points of soil
elements and the displacement of nodal points of reinforcement elements can be
expressed as:
8..= (—-—+ ——)_.F..L.. (6.31) V ErAr ESAS lJ lJ
On the other hand, from equilibrium;
2^2 =° (6.32) SF3I3-O
Therefore, for each;", the equation 6.32 can be repeated and solved.
6.3 RSDAM COMPUTER PROGRAM
The program, R S D A M , has been compiled using Fortran 77 and contains two main
sub-programs. The first includes 15 subroutines and optimises the geometry of a RSD.
Then, the dam is divided into several incremental elements in order to perform the
analysis by the second part, which includes 13 subroutines and computes the stresses
and displacements within the elements of the dam, based on two dimensional finite
element formulation.
195
COMPUTER PROGRAM CHAPTER SIX
6.3.1 Purpose
The purposes of the program are: (a) to optimise the geometry of RSD and (b) to find
the stresses and strains inside the dam. Firstly, the program allows for the geometrical
optimisation of RSD and the necessitate reinforcement used within the dams based on
the formulae of external and internal stability analysis presented in Chapter 4.
Secondly, it allows for the calculation of the stresses and strains within the dam, based
on plain strain analysis. It should be noted that although the program is particularly
adapted to RSDs, it may also be used for a variety of reinforced earth walls and
embankments with only a small change in the configuration of the program.
6.3.2 Input Data
In the program, the information regarding dam geometry, loading, safety factors, fill
material, reinforcement, facing panel, and foundation material are used as input data.
Geometrical data covers the dam height, the initial width of crest and the initial width
of base. Final widths are calculated by the program. Loading data covers the height of
water acting on the upstream side of the dam, the height and unit weight of silt settled
on the upstream side of dam, the height of water acting on the downstream side of dam,
a possible ice force, and the coefficient of earthquake acceleration. The safety factor
data includes those against sliding, overturning, over-stressing, bond failure and rupture
failure.
Fill material data contains unit weight, angle of internal friction, elastic modulus,
Poisson's ratio, unload-reload coefficient, coefficient of uniformity of fill materials
used within the dam and the frictional coefficient between the soil and the
reinforcement. Reinforcement data covers width and the admissible tension of
reinforcements used. Facing panel data contains the width and length of facing panels,
and the number of reinforcements connected to each facing panel. Foundation material
data covers allowable bearing capacity of foundation soil. The other input data are as
196
COMPUTER PROGRAM CHAPTER SIX
follows: the method of internal stability analysis, the number of nodal points in x-
direction, the number of fixed nodal points in y-direction, and possible displacements
of base nodal points. More detail together with the input data of an example of a 20m
high RSD is shown in Appendix F.
6.3.3 Program Operation
The program written by the author contains two main sub-programs which are further
described below. A n abbreviated flowchart for the program is shown in Fig. 6.3.3.1,
with more details included in Appendix E. A guide for running the program is
presented in Appendix F, while the listing of program is included in Appendix G.
6.3.3.1 First main sub-program
The first main sub-program serves to control calling subroutines (INPUTD, O U T P U T ,
H O R F O R C E , V E R F O R C E , DIST, B E A O P T M , SLIDOPTM, O V T U O P T M ,
O V S T O P T M , C G M , M C G M , N C G M , NOFAIL, REINAREA, M E S H ) , the processes
of iterations of calculation, preparing output data for graphical figures, and preparing
material properties. These will be explained in the subsequent paragraphs.
During the execution of the first sub-program, the dam is divided into several layers.
The number of layers is equal to the ratio of dam height to panels height. Every layer
is taken from the top of dam to a specified layer depth.
The horizontal forces acting on each layer of the RSD, including upstream hydrostatic
force, downstream hydrostatic force, the horizontal force due to silt pressure, and the
direct and indirect forces of earthquake are calculated in Subroutine H O R F O R C E .
Layer weight, uplift force, and the weights of the water and silt both acting on the
upstream side of layer are calculated in Subroutine V E R F O R C E .
197
COMPUTER PROGRAM CHAPTER SIX
START THE FIRST MAIN SUB-PROGRAM (SOB
I CALL INPUTDATA
I r, f
LOOP -m~ S M _ 1 T Q NUMBER OF LAYERS-.
T PROCESS OF THE FRST MAIN
SUB-PROGRAM (SOB)
CALL MESH
T END THE FIRST MAIN SUB-PROGRAM (SOB)
I START THE SECOND MAIN SUB-PROGRAM (MAINI!
J LOOP
N=l TO NUMBER OF ITERATION FOR LODING STEP
T PROCESS OF THE SECOND MAIN
SUB-PROGRAM (MAINI)
T -.--__-.
END THE SECOND MAIN SUB-PROGRAM (MAINI)
Fig. 6.3.3.1 Abbreviated flowchart
198
COMPUTER PROGRAM CHAPTER SIX
On the basis of the forces acting on each layer, the layer is analysed by the program.
The effective distances from the forces to the point of rotation including the horizontal
distances for the vertical forces, and the vertical distances for the horizontal forces
acting on the layers, are calculated in Subroutine DIST.
Regarding the external stability analysis of the layers, the minimum required base
width of the layer is checked in Subroutines B E A O P T M , SLIDOPTM, O V T U O P T M ,
and O V S T O P T M against sliding, overturning, bearing capacity, and overstressing
failure states, respectively.
Internal stability analysis of the layers can be analysed based on CGM, MCGM, or N e w
Coherent Gravity Method included in Subroutines C G M , M C G M , or N C G M ,
respectively (for detailed methods see Chapter 4). The choice of the method which will
be used is optional.
Subroutine R E I N A R E A computes the minimum required cross-sectional area of the
reinforcements. The area should be designed considering the rupture failure and talcing
into account to the methods of internal stability analysis. Minimum required
reinforcement lengths within the layers of the dam against bond failure are calculated in
this subroutine based on equations of the three methods mentioned above. The
optimum net weights of reinforcements within the dam at different levels and the
optimum net total weights of the reinforcements are calculated based on the methods in
this subroutine. In Subroutine O P T M , the base widths are compared and the minimum
required to prevent failure is determined.
Subroutine M E S H serves to subdivide the optimum geometry of the dam into
incremental four-node elements, and to prepare input data for the second main sub
program. The number of nodal points, the number of elements including interface
elements, the coordination of nodal points, and the slopes of the dam facings are
calculated at this stage. More detailed properties of the material used within the dam,
the position of forces acting on the nodal points, the locations of reinforcements, and
199
COMPUTER PROGRAM CHAPTER SIX
the boundary condition, required as input data for the second main program, are
prepared at this stage. A general view showing the subdivisions of a typical RSD is
illustrated in Fig. 6.3.3.2.
Fig. 6.3.3.2 A general view of a typical RSD showing subdivisions
6.3.3.2 Second main sub-program
The second main sub-program serves to control the calling subroutines (NDF,
E B T E D A , T S S M , SSMILV, T A N E S H , E S M , SBE, SIE, VSE, STIE, S E E P A G E ,
PSTMS), and the processes of iterations of calculation. This is further explained in the
subsequent section.
Subroutine N D F computes the structure of the stiffness matrix. The initial stresses
within the dam, due to its weight is calculated by Subroutine E B T E D A . Subroutine
T S S M assembles the results in the stiffness matrix. The equations representing the
stiffness matrix and loading vectors are solved in Subroutine SSMILV. The stresses
and strains of two dimensional elements are computed in Subroutine T A N E S H .
Subroutine E S M computes the stress-strain matrix. Principal stresses and maximum
shear stresses for material elements are calculated in Subroutine P S T M S . The stiffness
of reinforcement are computed in Subroutine SBE. The stiffness of interface elements
are computed in Subroutine SIE. Subroutine STIE calculates the stresses in interface
200
COMPUTER PROGRAM CHAPTER SIX
elements. Subroutine S E E P A G E computes the equivalent seepage level due to pore
water pressure changes within the dam. Ultimately, Subroutine V S E models the
material properties used within the dam.
A two-dimensional quadrilateral element has been used in the program to represent the
soil behaviour, while a general stress-strain curve is assumed in order to model the
behaviour of the soil within the dam. A non-linear hyperbolic stress-strain curve is
used in the program to represent the primary loading, while a linear response is
assumed for the unloading or reloading behaviour of the soil.
One dimensional interface elements have been used in the program to permit relative
movement between the soil and the concrete facings. Interface elements, which have
no thickness, have been defined by four nodes, with each of two pairs having the same
coordinates. The interface elements response has been modelled in the program
considering linear or hyperbolical variation of the shear stress with shear displacement
until a specified shear strain is reached.
6.3.4 Output Data
Output data contains two main parts, called D A M L O U T and D A M 2 . 0 U T , which will
be explained in the following two sections:
6.3.4.1 First Part
The output data consists of the minimum required base width of the cross-sectional area
of RSDs to prevent the failures due to sliding, overturning, over-stressing, insufficient
bond, and rupture. The optimised base width is printed out based on the minimum
required base length for no failures.
In this part, the results of analysis are printed out after each iteration. The output data
includes (a) the numbers and the heights of layers, (b) the depths of the water and the
silt acting on the upstream side of the layers, (c) the values of the base width of the
201
COMPUTER PROGRAM CHAPTER SIX
layers, (d) the weight of layers, (e) the weight of water and silt acting on the upstream
side of layers, (f) the values of hydrostatic force, (g) the silt force, (h) the ice force, and
(i) the direct and indirect forces of earthquake acting on the layers. The optimum
required crest and base widths of the dam are computed by the program. The main
output data in this part represents the minimum required base width of the layers versus
sliding, overturning, overstressing, rupture failure and lack of bond. If any of these
failures is likely to occur, the program will stop and a massage describing the mode of
failure will be shown in the output data file. The detailed output for the example of
RSD with the height of 20m is shown in Appendix F.
6.3.4.2 Second Part
In the second part, the nodal point data and element data are printed out in
D A M 2 . 0 U T . The results of analysis include (a) the horizontal and vertical
displacements of nodal points, (b) the horizontal, vertical and principal stresses within
the elements, and (c) the maximum shear stresses for material elements. These are
printed out after each iteration. The values of stresses in the reinforcements are
included in this part, too. The output for the second part of example of the 20m high
RSD is shown in Appendix F.
6.4 CONCLUSION
In this chapter, the RSD dam has been divided into several layers which have been
separately analysed based on the proposed equations governing sliding, overturning,
and overstressing as the equations of external stability analysis, and the equations
governing bond failure and rupture failure as internal stability analysis equations of the
dam. The formulae of soil-reinforcement interaction has also been presented in this
chapter. A computer program has been developed based on these equations for: (a)
optimisation of a parametric RSD, and (b) the analysis of the optimised RSD based on
the finite element method.
202
ANALYSIS CHAPTER SEVEN
CHAPTER SEVEN
ANALYSIS
7.1 INTRODUCTION
Six models of RSDs, with the heights of 20m, 25m, and 30m have been analysed for
safety factors equal to 1 and 1.5. The purpose of analysis of these models was to find
the variation of the minimum required base width of dam (or the layers) versus the dam
height for various safety factors to find the geometrical optimisation of these dams. It
was found that increases in the safety factors cause a non-linear increase in the
minimum required base length of RSD (or the layers of dam). Also, the increase in the
height of dam leads to a non-linear increase in the minimum required base length of
dam (or the layers of dam) to maintain stability. Although these effects are small when
the safety factors are equal to 1, they increase greatly when the safety factors increase
from 1 to 1.5. This will be discussed in greater detail in Sec. 7.2.
In addition, the 30m high RSD has been analysed by the program in order to find the
variation of stresses and deformations. The dam was analysed under plane strain
conditions in the following four configurations: (a) without reinforcements, (b) with an
assumed increased stiffness of the soil fill (due to the presence of reinforcement), (c)
with horizontal reinforcement, and (d) with inclined reinforcements. It was found that
placing reinforcement within the dams, can reduce the displacement and stress values in
the dam fill. Changing the direction of reinforcement results in further reduction of
these values. Also, it was found that the analyses of dams based on the soil stiffness
increase is much less effective than the analyses which include the existence of
reinforcement in soil fill. This is given in greater detail in Sec. 7.3.
203
ANALYSIS CHAPTER SEVEN
7.2 G EOMETRICAL OPTIMISATION
Initially, a 20m high RSD was analysed using the RSDAM Program under the two
following conditions. Firstly, it was assumed that the safety factors against internal and
external modes of failures were equal to 1, and then, in second part, it was assumed that
the safety factors were equal to 1.5.
For both these safety factors, the following data were assumed: (a) the levels of water
in upstream side and in downstream side of the dam of, respectively, 20m and 2m; (b)
the height of silt acting on the upstream of 6m; (c) the unit weight of the silt of 15
kN/m?; (d) the unit weight of the reinforced earth soil of 20 kN/m?; (e) the coefficient
of earthquake acceleration of 0.15; (f) the allowable bearing capacity of foundation soil
of 700 kN/m2; (g) the internal angle of friction of soil of 35 degree, and (h) the
coefficient of uniformity of soil of 200.
Each 60 mm wide reinforcement was also assumed to be connected to one lxlm facing
panel, and the allowable tension of reinforcements was assumed to be 240 MN/m2 in
both conditions. Initial widths of the crest and the base of the dam were assumed to be
4m and 10m, respectively. The final widths of the dam base and crest, computed by the
program, are shown in Table 7.2.1. The minimum required base width to prevent bond
failure was also assumed to be calculated based on the New Coherent Gravity Method
(See Chapter 4).
Table 7.2.1 Final widths of the dam computed by the program
Final crest width
Final base width
Safety factors = 1
6m
17.4m
Safety factors = 1.5
6m
32m
The minimum required base widths of the layers versus height of the 20m high dam
(for safety factors equal to 1 and 1.5) are shown in Fig. 7.2.1. This figure shows that
204
ANALYSIS CHAPTER SEVEN
the increase in the safety factor leads to an increase in the minimum required base
width of the dam (or the layers). This figure also shows that the minimum required
base width of the layers appears to be governed by:
(a) the sliding failure in about the bottom half of dam when safety
factor is 1.
(b) the bond failure in about the top half of dam when safety factor is 1.
(c) the sliding failure in about the bottom two third of dam when safety
factor is 1.5.
(d) the bond failure in about the top one third of dam when safety
factor is 1.5.
In a similar way, four other RSDs with the heights of 25m and 30m, and safety factors 1
and 1.5 have been analysed in order to find the effect of dam height versus the
optimum required base width. Different assumptions made during the analysis of these
dams are shown in Table 7.2.2. Also, it has been assumed that the levels of upstream
water were equal to the heights of dams.
Table 7.2.2 Assumptions accepted during the analysis of the models
Model No.
Height (m)
Safety factor against sliding
Safety factor against overturning
Safety factor against over-stressing
Safety factor against bond failure
Safety factor against rupture failure
1
25
2
25
1.5
1.5
1.5
1.5
1.5
3
30
1
1
1
1
1
4
30
1.5
1.5
1.5
1.5
1.5
205
ANALYSIS CHAPTER SEVEN
Height (m)
30 -
20 -
10 -i
0 -c
Q ^
)
Height (m)
30 -
20 -
20 -
rt .
0
5F=i
____ Bond failure
^^- Overstressing
_ _ Overturning
!L . Sliding
20 40 60
Minimum required base width (m)
SF=1.5
Bond failure
"•L Overstressing
"*L "L , Overturning
\ ta Sliding
20 40 60 Minimum required base width (m)
80
1
80
Fig. 7.2.1 Minimum required base length versus height for the 20 m high dam
206
ANALYSIS CHAPTER SEVEN
The minimum required base widths of the layers versus height for 25m and 30m high
dams are shown in Figs. 7.2.2 and 7.2.3, respectively. As indicated by these figures,
the increase in the height of dam leads to an increase of the minimum required base
width of the dam (or the layers). The changes are small when safety factors are equal
to 1, while the changes increase greatly when the safety factors increase to 1.5.
The minimum required base width of the layers appears to be governed by:
(a) the sliding failure in about the bottom half of dam when safety
factor is 1.
(b) the bond failure in about the top half of dam when safety factor is 1.
(c) the sliding failure in about the bottom two third of dam when safety
factor is 1.5.
(d) the bond failure in about the top one third of dam when safety
factor is 1.5.
(e) the overstressing failure in the base when safety factor is 1.5 only
for 30m high dam.
As a result, for no failure (due to sliding, overturning, overstressing and bond failure),
the minimum required base widths of the layers of dams should be checked against the
minimum required base width for no bond failure in about the top one third of the dam
when safety factor is 1.5. These should also be checked against the required base
length for no sliding failure in the remaining part of the dam when safety factor is 1.5.
Over-stressing failure needs to be considered when the height of dam reaches 30m and
factor of safety is 1.5.
207
ANALYSIS CHAPTER SEVEN
Height (m)
30 -
20 ~l\ V
-
10 -
n •=
0
Height (m)
30 ~
20 -
10 -
o
0
SF=1
___ Bond failure
^^ Overstressing
L ___ Overturning
\ J L Sliding
20 40 60
Minimum required base width (m)
SF=1.5
Bondfailure
±M ^^Overstressing
it Tl ^^.Overturning
4* Ti Sliding
20 40 60
Minimum required base width (m)
- -+ 80
i \
80
Fig. 7.2.2 Minimum required base length versus height for a 25 m high dam
208
ANALYSIS CHAPTER SEVEN
SF=1
Bondfailure
Overstressing
verturning
Sliding
20 40 60
Minimum required base width (m)
80
0
SF=1.5
Bondfailure
Overstressing
Overturning
Sliding
20 40 60
Minimum required base width (m)
80
Fig. 7.2.3 Minimum required base length versus height for a 30 m high dam
209
ANALYSIS CHAPTER SEVEN
7.3 NUMERICAL ANALYSIS
It was assumed that the 30m high earth dam with vertical downstream face was built on
a rigid foundation, with the base width of the dam to be 40.4m. Two 0.2m thick
concrete facings are assumed to be on both side slopes of the dam, as shown in Fig.
7.3.1.
5.4m
30m
Concrete facings
Rigid Foundation
40.4m
Fig. 7.3.1 The 30m high vertical downstream earth dam
For the static analysis, it was assumed that the dam was constructed on rigid foundation
hence there was no horizontal nor vertical movements at the dam base level. In time-
history analysis it was, however, assumed that the dam base had moved proportional to
0.15m and -0.08m base displacements.
7.3.1 Loading steps
The dam has been analysed under loadings which included the weight, hydrostatic
pressure, seepage, and earthquake. The horizontal and the vertical forces, due to
upstream hydrostatic pressure, were calculated and applied to the upstream nodal points
210
ANALYSIS CHAPTER SEVEN
(Nodal points 155 to 165 in Fig. 7.3.2.1), while the downstream hydrostatic pressure
was assumed to be zero. The height of its water was assumed to be 30m in maximum
condition. The variations of top seepage lines were assumed to be as illustrated in Fig.
7.3.1.1. The coefficient of earthquake acceleration, based on static method, was taken
to be 0.2g in the calculation of the earthquake force acting on the nodal points. T w o
increments of earthquake displacement acting on the base of dam were applied to the
dam using time-history analysis.
Fig. 7.3.1.1 Variations of seepage lines
7.3.2 Mesh information
Number of four-external nodal elements including interface elements, but excluding
reinforcement elements was 140 as shown in Fig. 7.3.2.1. The total number of nodes
considered in the analyses was 165, and the number of interface elements was 20. The
positions of horizontal and the inclined reinforcements used are shown in Figs. 7.3.2.2
and 7.3.2.3, respectively.
211
ANALYSIS CHAPTER SEVEN
Fig. 7.3.2.1 A general view of the RSD showing nodal points
• i" ,• _ Horizontal reinforcements
i * >
i \
Fig. 7.3.2.2 Positions of horizontal reinforcements
-, U . - V-X-^S-S S S. Inclined reinforcements
Fig. 7.3.2.3 Positions of inclined reinforcements
212
ANALYSIS CHAPTER SEVEN
7.3.3 Material property
The assumed properties of the soil, concrete facings, interface elements, and
reinforcements are shown in Table 7.3.3.1 to Table 7.3.3.4, respectively.
Table 7.3.3.1 Assumed soil properties
Unit weight
Angle of internal friction
Cohesion of the soil
Initial tangent exponent
Initial unload-reload exponent
Loading coefficient
Unloading coefficient
Ratio of measured strength at failure to ultimate
strength
Minimum initial tangent modulus
Bulk modulus exponent
Bulk modulus coefficient
Tangent modulus at failure
16 kN/m3
35 degrees
0
0.5
0.5
300
500
0.8
' 1 MN/m2
0.2
250
50 MN/m2
Table 7.3.3.2 Assumed concrete facing properties
Unit weight
Young modulus
Poisson's ratio
24 kN/m3
25 GN/m2
0.2
Table 7.3.3.3 Assumed interface element properties
Interface cohesion
Interface friction angle between soil and concrete
Initial shear stiffness
Failure shear stiffness
Initial normal stiffness
Failure normal stiffness
0
25 degree
40 kN/m2
lkN/m2
1 GN/m2
1 kN/m2
213
ANALYSIS CHAPTER SEVEN
Table 7.3.3.4 Assumed reinforcement properties
Unit weight
Young modulus
Poisson's ratio
78 kN/m3
250 GN/m2
0.2
7.3.4 Stages of analysis
The 30m high RSD was analysed by the program in the following stages: (a) without
reinforcements, (b) assuming increased stiffness of the soil due to the presence of
reinforcements, (c) with horizontal reinforcement strips, and (d) with inclined
reinforcements. The results are given in the following sections.
7.3.5 Displacement variation
In the first stage, the dam was analysed without reinforcements. After the analysis, it
was found that significant horizontal displacements appeared in the nodal points of the
dam due to the action of forces such as weight, hydrostatic force, seepage force and
earthquake. Locations of the nodal points of the dam before loading and after loading
are shown, respectively, in Figures 7.3.5.1 and 7.3.5.2a.
In the second stage, the dam was re-analysed under conditions assuming increased
stiffness of the soil (used within the dam) due to the presence of reinforcements.
Similarly to the first stage, the soil and the concrete facings formed the only dam
materials. It was assumed that the effect of the reinforcement insertion increases the
stiffness of the soil material proportional to the ratio of the cross-sectional area of
reinforcements to unit area of soil. It was found that although the displacements values
were reduced, a considerable horizontal displacement still appeared in the dam, due to
the forces acting on the dam as shown in Fig. 7.3.5.2b.
In the third stage, the dam was re-analysed again with horizontal reinforcements as
illustrated in Fig. 7.3.5.2a. The result of the deformed dam was plotted in Fig.
214
ANALYSIS CHAPTER SEVEN
7.3.5.2c. W h e n this figure is compared with Figures 7.3.5.2b and 7.3.5.2a, it is shown
clearly that the horizontal displacements of the nodal points are reduced. Therefore,
horizontal displacements can be decreased by inserting horizontal reinforcements
within the dam.
As the final stage of displacement analyses, the dam was re-analysed once more with
inclined reinforcements as shown in Fig. 7.3.5.2.b. It was found that inserting inclined
reinforcements still decreases the displacements even more than the other stages. Fig.
1.3.5.26. shows the deformation of the dam (with inclined reinforcements) after the
analysis.
Fig. 7.3.5.1 The dam before loading
7.3.6 Stress variation
Stress variation should be considered in the analysis of reinforced earth structures to
locate the high stress levels. The variation of principal stresses, due, to the forces
acting on the dam in the four stages of analysis has been contoured and plotted in
Figures 7.3.6.1a to d. These clearly show that using reinforcement within the earth
dam with vertical downstream face reduces the maximum principal stress acting on the
elements to more than half of the maximum principal stress of the dam without
215
ANALYSIS CHAPTER SEVEN
reinforcement. Moreover, the use of inclined reinforcements reduces the value of the
maximum principal stress.
The changes to the horizontal stresses due to the forces acting on the dam for the four
stages of analyses are also pictured in Figures 7.3.6.2a to 7.3.6.2d supporting the
conclusion that the use of reinforcement leads to a reduction of horizontal stress level
after using reinforcement within the dam.
7.3.7 Variation of the vertical facing displacement
Vertical and horizontal movements of the vertical facing (nodal points 1 to 12 shown in
Fig. 7.3.2.1) affect stresses within reinforcements. Such displacements are plotted in
Fig. 7.3.7.1 and Fig. 7.3.7.2 regarding the four steps of analysis (a) without
reinforcements, (b) with increased stiffness of the soil fill, (c) with horizontal
reinforcement strips, and (d) with inclined reinforcements strips. Figure 7.3.7.1 shows
the variations of the facing movements based on -0.08 m base displacement, while
Figure 7.3.7.2 shows the variations based on 0.15 m base displacement.
These figures clearly show that the horizontal movement of the vertical facing is
maximum in Case a (dam without reinforcement) while the magnitude of horizontal
displacement is minimum in Case d (dam with inclined reinforcements). As shown in
Fig. 7.3.7.1, the maximum value of horizontal movement is about 0.63m in Case a at a
height equal to about 27m above the base. It is only about 0.28m in Case d and about
0.36m in Case c (dam with horizontal reinforcements) near to the dam crest. Similar
conclusions can be made by referring to Fig. 7.3.7.2.
The minimum value of vertical displacement is associated with Case a, while the
maximum value is with Case b (increased stiffness of the soil fill). Fig. 7.3.7.1b
indicates that the maximum value of vertical displacement, which is about 0.20 m,
happens at height 24m from the base for Case b, while it is 0.15m for Case c.
Maximum value of vertical displacement, which is about 0.10m, occurs near the crest.
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30 A. m
20..
Height
10..
-0.6 -0.4 -0.2 0
Horizontal Displacement
-0.2 -0.1 0 0.1
Vertical Displacement
Fig. 7.3.7.1 Variations of vertical and horizontal movements of the vertical facing based on -0.08 m base displacement
-0.5 -0.3 -0.1 +0.1 +0.3
Horizontal Displacement
-0.2 -0.1 0 0.1
Vertical Displacement
Fig. 7.3.7.2 Variations of vertical and horizontal movements of the vertical facings
based on 0.15m base displacement
220
ANALYSIS CHAPTER SEVEN
7.4 CONCLUSIONS
Results of the analysis of the six models of RSDs indicate that an increase in the safety
factor leads to an increase in the minimum required base length of the RSD (or the
layers of the dam). Also, an increase in the height of dam leads to an increase in the
minimum required base length of dam (or the layers of dam). The changes are small
when the safety factor is 1, but they increase considerably when the safety factor
increases to 1.5. This is most noticeable in the minimum required base length for no
overstressing failure when the safety factor is equal to 1.5.
The presence of reinforcement also leads to a reduction in displacement and stress
level. A 30m high RSD with vertical downstream facing was analysed assuming the
following four stages: (a) without reinforcements, (b) with increased stiffness of the
soil fill, (c) with horizontal reinforcement embedded within the fill, and (d) with
inclined reinforcement within the fill. It was found that inclusion of reinforcement
within the dam material could reduce the vertical and horizontal displacements of the
dam. Changing the direction of reinforcements could also result in further reduction in
the displacements of the nodal points of the dam.
In the first stage, the dam was analysed without reinforcements within the dam. After
the analysis, it was found that significant horizontal displacements appeared in the
nodal points due to the action of forces such as weight, hydrostatic force, seepage force
and earthquake. Locations of the nodal points of before loading and after loading were
shown in this chapter.
In the second stage, the dam was re-analysed under conditions assuming increased
stiffness of the soil used within the dam due to the presence of reinforcements.
Similarly to the first stage, the soil and the concrete facings formed the only dam
materials. It was assumed that the effect of reinforcement insertion increases the
stiffness of soil material proportional to the ratio of the cross-sectional area of
reinforcements to unit area of soil. It was found that although the displacements values
221
ANALYSIS CHAPTER SEVEN
were reduced, a considerable horizontal displacement still appeared in the dam, due to
the forces acting on it.
In the third stage, the dam was re-analysed again with horizontal reinforcements. It
was shown that the horizontal displacements of the nodal points are considerably
reduced.
In the fourth stage, the dam was re-analysed once more with inclined reinforcements.
It was found that inserting inclined reinforcements still decreases the displacements
even more than the other stages. The deformations of dams after the analyses were
shown in this chapter.
The variation of maximum principal stress, due to the forces acting on the dam, in the
four stages of analysis has also been contoured and plotted in this chapter. These show
that using reinforcement within the earth dam with vertical downstream face reduces
the maximum principal stress acting on the elements to more than half of the maximum
principal stress of dam without reinforcement. The use of inclined reinforcements still
reduces the value of the maximum principal stress.
The changes to the horizontal stresses due to the forces acting on the dam for the four
stages of analyses have also been pictured in this chapter supporting the conclusion that
the use of reinforcement leads to a reduction of horizontal stress level by using
reinforcement within the dam.
Vertical and horizontal displacements of the vertical facing have been plotted in this
chapter regarding the four steps of analysis. The variations of facing movements based
on -0.08m and 0.15m base displacements are shown in this chapter (Sec. 7.3.7). It was
concluded that the horizontal displacement of the vertical facing is maximum in Case a
(dam without reinforcement) while the magnitude of horizontal displacement is
minimum in Case d (dam with inclined reinforcements). The maximum value of
horizontal movement is about 0.63m in Case a at a height equal to about 27m above the
222
ANALYSIS CHAPTER SEVEN
base. It is only about 0.28m in Case d and about 0.36m in Case c (dam with horizontal
reinforcements) near to the dam crest.
The minimum value of vertical displacement is associated with Case a, while the
maximum value is with Case b (increased stiffness of the soil fill). It has been shown
that the maximum value of vertical displacement, which is about 0.20m, happens at
height 24m from the base for Case b, while it is 0.15m for Case c. Maximum value of
vertical displacement, which is about 0.10m, happens near the crest.
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CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
CHAPTER EIGHT
CONCLUSIONS AND RECOMMENDATIONS
8.1 INTRODUCTION
Conclusions and implications of the results of the investigations on the design on RSDs
are presented in this chapter. Part A deals with (a) the semi-empirical formulae obtained
from analysing the field data, (b) the theoretical formulae obtained from the analytical
investigation, and (c) the formulae of the natural frequencies of RSDs. Part B outlines
the main features of the computer program based on these formulae and its application in
the design of RSDs.
8.2 PART A- THEORETICAL OPTIMISATION AND ANALYSIS
The work presented in this part can be classified into three categories:
- Theoretical formulae in geometrical optimisation of RSDs.
- Semi-empirical formulae in the design of reinforced soil structures.
- The formulae of the natural frequency of RSDs.
Several investigations have been performed in each category. The results from the
developed computer program concern the overall behaviour of RSDs.
8.2.1 Geometrical optimisation
The aim of research was to find the theoretical formulae in the geometrical optimisation
of RSDs. Initially, in this thesis (Chapter Three), general and possible classifications of
RSDs based on their types and components have been considered. RSDs, based on the
material used, can be classified into homogeneous fill types and zoned types. The
components, properties and types of homogenous fill and zoned RSDs have all been
considered.
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CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
The identification of the forces acting on RSD is also fundamental to study this
behaviour. Although there are no major differences between the forces acting on RSD
and the forces acting on other types of dams, the behaviour of RSD and other dams are
different in withstanding the forces. The main forces assumed to act on a RSD are those
due to water pressure, silt pressure, ice pressure, earthquake pressure, foundation
reaction, seepage and the weight of the structure. In Chapter Three, the forces acting on
a RSD were individually discussed, and, at the end, the combination of the loads
(including usual loading, unusual loading and critical loading) were defined.
This was followed by the stability analysis of RSDs which was addressed from the point
of view of both internal and external stabilities. In Chapter Four, the external stability of
RSDs was evaluated based on the analytical approach. Sliding, overturning, and
overstressing were considered in the external stability analysis. In the external stability
analysis, it was assumed that the whole reinforced soil structure acts as a unit. To
optimise the geometry, the formulae of minimum required base length for no failure due
to sliding, overturning, and overstressing was proposed and evaluated separately for the
dam and its layers.
8.2.2 Semi-empirical relationships
The research undertaken in this area was concerned with the analysis of the field data
using the concept of frictional interaction between soil and reinforcement. Various
analytical theories developed so far are not in sufficient conformity with the observed
behaviour of reinforced earth structures. This necessitated the use of empirical
relationships in the current design practice. Some of these relationships and the field
data, on which the previous experimental formulae were based, were re-analysed in this
thesis. N e w proposed semi-empirical formulae reflecting the observed behaviour of
reinforced earth structures have been suggested. The proposed formulae make
adjustments to exiting formulae based on the field observations. The findings,
corresponding to the investigations performed, are n o w summarised.
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CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
The internal stability of the reinforced earth structures can be analysed using methods
based on conventional principles of soil mechanics. It has been known, however, that
certain theoretical assumptions, accepted in these methods, were not supported by the
observations. In particular, since reinforcement changes the state of stress within soil,
the directions of principal stresses are no longer vertical and horizontal, and the ratio of
the vertical stress to the horizontal stress is not constant. This, together with other field
data regarding the bond between soil and embedded reinforcement, have led to the
development of the semi-empirical methods. One of the methods termed CGM,
proposed by McKittrick and Schlosser in 1978, was adopted as a recommended design
method by Reinforced Earth Company and the French Code. This method has been
structured around a set of bi-linear functions representing and interpreting the field data
in a somewhat simplified way. Some modifications to the method were later suggested
by Arenicz and Chowdhury in 1987, in order to reflect the field observation more
closely.
The proposed semi-empirical relationships suggested in this thesis (Chapter Four) have
eliminated the tangent discontinuity existing in the formulae of the CGM, and have
reflected the non-linearity indicated by the field data. Also, the proposed relationships
have eliminated unknown parameters existing in the formulae of the MCGM, and have
offered a better fit with the available field observations.
A linear relationship between the apparent friction factor and the ratio of fill depth to
strip length was discovered by analysing the field data. Formulae for calculation of the
safety factor against the tensile failure and bond failure of reinforcements have been
proposed regarding the formulae of lateral earth pressure coefficient, apparent friction
factor, and maximum tension line.
8.2.2 Natural frequency
The resonance phenomenon in the structure can be prevented by the designer's
familiarity of the natural frequency of the structure. Although the practice of inserting
226
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
reinforcement within earth dams allows reduction in fill volume, displacement, and stress
level, this causes an increase in the natural frequency of RSDs compared with the
conventional earth dams. This leads to an increase of the natural frequency of the
structure which may result in the possibility of total destruction of such dams.
Therefore, the calculation of the natural frequency of RSDs is necessary to find their
behaviour under earthquake forces.
Chapter Five discussed that the natural frequency of a RSD may be more critical than the
natural frequency of a corresponding conventional earth dam. This is because of the two
major functions: (a) the geometrical function concerning the change in dam geometry
and (b) the overall stiffness function concerning the change in the dam's flexibility.
Formulae concerning the major functions were derived and in some cases plotted. The
following general suggestions have been proposed in order to prevent resonance in
RSDs:
a) The volume of reinforcements used within the dams should be calculated
based on the formulae of the natural frequency of RSDs. Any additional increase in the
volume of reinforcement may result in the extreme situation of resonance in the structure
under an earthquake condition.
b) Using reinforcements with low stiffness such as polymers can yield a
considerable decrease in the value of the geometry function of the dams compared with
reinforcements with high stiffness
c) The effect of geometry in increasing or decreasing the natural frequency has
been found as shape coefficient and has been tabulated in Chapter Five. As a result,
inserting reinforcement within earth dams causes a decrease of the dam width and at the
same time, causes an increase in the natural frequency of the dam.
8.3 PART B NUMERICAL ANALYSIS
The state of stresses inside a soil mass normally varies from point to point. In reality, the
situation of stresses within the soil is not elastic. However, it is helpful to describe the
227
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
elastic behaviour of the soil before giving the explanation of the plastic response or
elasto-plastic behaviour of a soil mass. The equations representing the elastic and/or the
plastic behaviours of the soil were modelled in the program. The deformation of the
soil, the concrete facing panels, and the natural behaviour of the reinforcements were
simulated by the finite element program.
In the body of RSDs it is assumed that some forces (normally compressive forces) are
induced in the soil mass as acting forces, while some forces (normally tensile forces) are
induced in the reinforcements considering the frictional bond between the reinforcements
and the soil as reaction forces. The finite element method has been used to model the
soil deformation, to find the tensile stress within the reinforcements, and to predict the
behaviour of the bond between the soil and reinforcements. It is assumed that the
loadings cause a group of nodal forces in contact point between the soil and
reinforcements. The forces cause some deflections within the soil and reinforcements.
For a no bond failure state, the soil deflections should be compatible with the deflections
of nodal points. In this condition, the reinforcement and soil would need to be combined
by joining or spring elements modelling the slip behaviour between soil and
reinforcement. Each reinforcement carries the horizontal forces induced in the nodal
points of reinforcements.
For no bond failure, the difference between the displacement of nodal points of soil
elements and the displacement of the nodal points of reinforcement elements should be
zero. It is assumed that the displacements, due to force on nodal points within
reinforcements, should be equal and opposite to the displacements due to the forces
acting on the corresponding soil nodes. The set of soil displacement equations has been
met by a solution of the soil stiffness matrix under the external forces assuming the
stiffness of reinforcements are constant. The difference between the displacements of
nodal points of soil elements and the displacements of nodal points of reinforcement
elements were formulated in Chapter Six.
228
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
8.3.1 Computer Program
The program, RSDAM, written by the author as a part of the investigations, has two
main sub-programs. The purpose of the program is (a) geometrical optimisation of
RSDs and (b) evaluation of stresses and strains inside the dam increments. The
optimisation includes the fill volume optimisation of material and the reinforcement
volume optimisation. It should be noted that the program is particularly adapted to
RSDs, however, it may also be used for a variety of reinforced earth walls and
embankments.
The first sub-programs including 15 subroutines optimises the geometry of RSDs based
on semi-experimental formulae. Also, the dam is subdivided into several increments in
order to be prepared for the analysis by the second part. The second, including 13
subroutines, computes the stresses and displacements within the elements of the dam
based on the two dimensional finite element formulation.
8.3.1 Results of Analysis
Results of the analyses of six RSD models, presented in Chapter Seven, show that an
increase in the safety factor leads to an increase in the minimum required base length of
these RSDs (or the layers of dams). Also, an increase in the height of these dams leads
to an increase of the base length of the dams (or the layers of the dams). In this case, the
changes are small when the safety factor is equal to 1, but the changes increase
considerably, when the safety factor increases from 1 to 1.5. The greatest increase is
seen in the minimum required base length for a no overstressing failure state.
A 30m high RSD with vertical downstream facing was analysed by the program under
the four following stages: (a) without reinforcements; (b) assuming increased stiffness of
the soil due to inserting reinforcements; (c) with horizontal reinforcements; and (d) with
inclined reinforcements. It was found that the addition of reinforcements within the
dams can reduce the vertical and horizontal displacements. Changing the direction of
229
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
reinforcements may result in further reduction in the displacements of the nodal points of
dam. In some cases, the changes of the stress levels are more than 50%.
In the first stage, the dam was analysed without any reinforcements within the dam.
After the analysis, it was found that significant horizontal displacements appeared in
the nodal points of dam due to the action of forces such as weight, hydrostatic force,
seepage force and earthquake.
In the second stage, the dam was re-analysed under conditions assuming increased
stiffness of the soil used within the dam due to the presence of reinforcements. It was
assumed that the effect of reinforcement insertion increases the stiffness of the soil
material proportional to the ratio of the cross-sectional area of reinforcements to the
unit area of soil. It was found that although the displacements values were reduced, a
considerable horizontal displacement still appeared in the dam, due to the forces acting
on dam.
In the third stage, the dam was re-analysed again with actual horizontal reinforcements.
It was shown that the horizontal displacements of the nodal points were considerably
reduced.
As the final stage of displacement analyses, the dam was re-analysed once more with
inclined reinforcements within the dam. It was found that inserting inclined
reinforcements still decreases the displacements even more than the other stages.
Locations of the nodal points of the dam before loading and after loadings were shown
in Chapter Seven.
The variation of principal stresses, due to the forces acting on the dam in the four stages
of analysis were contoured and plotted in Chapter Seven. These showed that using
reinforcement within the dam face reduced the maximum principal stress acting on the
elements of dam to more than half of the maximum principal stress of the dam without
reinforcement. The use of inclined reinforcements reduced the value of the maximum
principal stress more than the other cases.
230
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
The changes to the horizontal stresses due to the forces for the four stages of analyses
were also pictured in the chapter supporting the conclusion that the use of
reinforcement leads to a reduction of horizontal stress level within the dam.
Vertical and horizontal displacements of the vertical facing were also plotted in Chapter
Seven regarding the four steps of analysis. The variations of the facing movements
based on -0.08m and 15m base displacements were shown in the chapter.
It was shown that the horizontal displacement of the vertical facing is maximum in the
case dam without reinforcement, while the magnitude of horizontal displacement was
minimum in the case dam with inclined reinforcements. The maximum value of
horizontal movement was about 0.63m in the case dam without reinforcement at a
height equal to about 27m above the base. It was only about 0.28m in case dam with
inclined reinforcements and about 0.36m in case dam with horizontal reinforcements
near to the dam crest.
The minimum value of vertical displacement is associated with case dam without
reinforcement, while the maximum one is with Case b (increased stiffness of the soil
fill). It was shown that the maximum value of vertical displacement, which is about
0.20m, occurs at height 24m from the base for this case, while it is 0.15m for the case
dam with horizontal reinforcements. The maximum value of vertical displacement,
which is about 0.10m, occurs near the crest.
8.4 RECOMMENDATIONS
8.4.1. Reinforced soil arch dams
Although most RSDs are of the gravity type, there is no reason to claim that the
reinforced soil arch dam and the reinforced soil buttress dam can not be built in the
future. In these cases, the reinforcement may stabilise the structure by increasing the
strength of the soil and by connecting the facing panels of two sides. Therefore, it
would be of considerable interest to investigate the possibility of construction of arch
231
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
and buttress RSDs and, to construct experimental and numerical models of them to find
their behaviour under the forces acting on dams.
8.4.2. Cross sectional optimisation
A stability analysis of the RSD based on an analytical approach and a semi empirical
method was presented in Chapter 4 to optimise the cross sectional area. Some proposed
formulae were given for optimisation of the RSD to minimise the base length against
sliding, overturning, overstressing, bond failure, and rupture failure. Since the main
aim of this thesis was to develop a computer program for the design and analysis of
RSD, it is recommended that some hydraulic (experimental) models of the RSD be
constructed to compare the results of the experimental models to the results of the
analysis based on this computer program.
8.4.3. Behaviour of reinforcement
There is a difference between the behaviour of reinforcements used within the reinforced
soil walls and within the RSD. As indicated in Chapter 4, most reinforced soil theories
(eg. Vidal's Theory (1966), CGM (1978), and MCGM 1987)) claim that inserting
reinforcement within the soil induces a tension force in the reinforcement. The
experiments done so far (explained in Chapter 4) support this theory. It should be noted,
however, that the forces acting on the reinforced soil walls are usually perpendicular to
the reinforcement directions. While, the directions of forces acting on RSD are not
perpendicular to the reinforcement direction. Therefore, forces acting on the
reinforcement seem not to be pure tension. This needs further investigation in the
future.
8.4.4 Reinforcement width
The width of reinforcement has an important role in apparent friction factor. The
optimum width of reinforcement in RSD, and the relationship between the reinforcement
232
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
and the height of structure are questions which are not fully answered yet. Therefore, it
is recommended that a numerical and/or an experimental model be used to conduct
further study of these aspects.
8.4.5 Natural frequency
In Chapter Five, the natural frequency of RSD and that of conventional earth dam were
theoretically calculated and compared. It was concluded that inserting reinforcement
increases the natural frequency of the structure which may increase the possibility of
failure. It was also concluded that the natural frequency of RSD is increased because of
two major factors: (a) its geometry and (b) its overall stiffness. Comparison between
both natural frequencies using some experimental models to compare the results of
experiments with the results of theory presented in Chapter Five might lead to new
findings.
8.4.6 Seismic load based on dynamic analysis
The computer program presented in this project can analyse RSD based on static analysis
or time history analysis. However, it is an alternative to model the RSD based on
dynamic analysis. The program can be modified based on dynamic analysis.
8.4.7 Stress concentration
In Chapter Seven, it was shown that there is a stress concentration at the toe of a 30
high RSD with vertical downstream side. A n increase in the RSD height increases the
rate of stress concentration at the toe of RSD. This may be the reason why the
maximum heights of RSDs constructed so far are not more than 30m. The effect of
height increase on the stress concentration of RSD needs more investigation. It seems,
for example, that using buttresses at the downstream side of RSD may reduce the stress
concentration at the toe. Therefore, it is recommended that the stress concentration of
233
CONCLUSIONS AND RECOMMENDATIONS CHAPTER EIGHT
RSD is taken into account to find the relationship between height and stress
concentration at the toe of RSD.
234
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Singh B., (1976), "Earth and rockfill dams", Nauchandi, Meerut: Sarita Prakashan.
Smith, A. K. C. S, & P. L., Bransby, (1976), "The failure of reinforced earth wall by
overturning", Geotechnique 26, No. 2, pp. 376-381.
Smith N., (1971), "A history of dams", P. Davis, London.
Sowers G. B. & Sowers G. F., (1970), "Introductory soil mechanics and foundations",
New York, Macmillan.
Sowers G. F., (1979), "Introductory soil mechanics and foundations: Geotechnical
engineering", New York, Macmillan.
Steiner, R. S., (1975), "Reinforced earth bridges highway sinkhole" Civil Engineering,
ASCE, July, pp. 54-56.
Streeter V. L., and Wylie E. B. (1979), "Fluid mechanics", McGraw-Hill, USA.
Taylor, J. P. and Drioux, J. C, (1979), "Utilisation de la terra arme'e dans le domaine
des barrages", Proceedings of the International Conference on Soil Reinforcement; Paris,
Vol. 2, pp 373 - 378.
Terre Armee International, (1987), "Quay walls built underwater", Australian and
Canadian Prototypes, Technical Report, N o M 6 .
R8
REFERENCES
United State Committee on Large Dams and Committee on Failures and Accidences to
Large Dams, (1975), " Lessons from dam incidents, USA", A S C E and U S C O L D , N e w
York.
United States Bureau of Reclamation, (1977), "Design of small dams", United States
Department of the Interior, Bureau of Reclamation, 2nd edition, Washington, D. C ,
U.S. Government Printing Office.
Vidal, H., (1966), "Diffiusion restpeinte de la terre armee" Institute Technique du
Batement et des Trovause Publics, pp 888-939 No. 223-4.
Vidal, H., (1969), "The principle of reinforced earth", Highway Res. Rec, No. 282, pp.
1-16.
Vidal, H., (1978), "The development and future of reinforced earth" Proceedings of the
Symposium on Earth Reinforcement, Pittsburgh, Pennsylvania, pp. 1-61.
Vidal H., (1986), "A brief history of terre armee (Reinforced Earth)", Reinforced Earth
Company, Technical Report No. 635.
Wahlstorm, E., (1974), "Dams, dams foundations, and reservoir sites", Elsevier
Scientific Publishing Co.
Wolff T. F., (1985), "Analysis and design of embankment dam slopes: A probabilistic
approach", Ann Arbor, Michigan.
Wu P. and R. J. H. Smith, (1990), "Reinforced earth marine wall experienced in Canada
and United Kingdom", Proceedings of the International Conference On Performance of
Reinforced Soil Structures, British Geotechnical Society.
R9
REFERENCES
Yamanouchi, T., (1970), "Experimental study on the improvement of the bearing
capacity of soft ground by laying a resinous net", Proceedings of the Symposium on
Foundations on Interbended Sands, Australia, Commonwealth Scien. & Indus. Res.
Orgn. pp. 144-150.
Yang, Z, (1972), "Strength and deformation characteristics of reinforced sand" Ph.D.
Thesis, U C L A .
Yin Zong Ze, (1990), "Effect of reinforcement in embankment", Performance of
reinforced soil structures, British Geotechnical Society.
RIO
APPENDICES
Al
EARTH DAM FAILURES APPENDIX A
APPENDIX A- EARTH DAM FAILURES
Table 1A- Earth dam failures due to hydraulic problems (Sowers, 1961)
Form
Overtopping
Wave erosion
Toe erosion
Gulling
General characteristics
Flow over embankment, washing out dam
Nothing of upstream face by waves, currents
Erosion of toe by outlet
discharge
Rainfall erosion of dam face
Causes
Inadequate spillway capacity
Clogging of spillway with debris
Insufficient freeboard due to settlement, skimpy design
Lack of riprap, too small riprap
Spillway too close to dam
lack of sod or poor surface drainage
Preventive measures
Spillway designed for maximum flow
Maintenance, trash booms, clean design
Allowance for
freeboard and settlement in design; increase crest height or add flood parapet
Properly design riprap
Training wall
sod, fine riprap; surface drains
A2
EARTH DAM FAILURES APPENDIX A
Table 2.A- Earth dam failures due to structural failures (Sowers, 1961)
Form
Found ation slide
Upstre am slope
Downs tream slope
Flow
side
General characteristics
Sliding of entire dam, one face or both faces in opposite directors, with bulging of foundation
Slide in upstream face with little or no bulging in foundation below toe
Slide in downstream face
Collapse and flow of soil
in either upstream or downstream direction
Causes
Soft or weak
foundation
Excess water pressure in confined sand or silt seams
Steep slope
Weak embankment
soil
Sudden drawdown of
pond
Steep slope
Weak slope
Loss of soil strength by seepage pressure or saturation by
seepage or rainfall
Loose embankment
soil at low cohesion, triggered by shock,
vibration seepage, or foundation movements
Preventive measures
Flatten slope; employ broad berms; remove weak material; stabilise
soil
drainage by deep drain trenches with protective filters; relief wells
Flatten slope or employ berm at toe
Increase compaction;
better soil
Flatten slope, rock berms; operating rales
flatten slope or employ berm at toe
Increase compaction;
better soil
core internal drainage with protective filters; surface drainage
Adequate compaction
A3
EARTH DAM FAILURES APPENDIX A
Table 3. Earth dam failures due to seepage failures (Sowers, 1961)
Form
Loss of water
Seepage erosion or
piping
General characteristics
Excessive loss of water from reservoir /or occasionally increased
seepage or increased groundwater levels near reservoir.
Progressive internal erosion of soil from downstream side of dam or foundation
toward the upstream side to
form an open conduit or
pipe.
Often leads to a washout of
a section of the dam.
Causes
Pervious reservoir rim or bottom.
Pervious dam foundation.
Pervious dam
Leaking conduits.
Settlement cracks in dam.
Shrinkage cracks in dam.
Settlement cracks in
dam.
Shrinkage cracks in dam
Pervious seams in
foundation
Pervious seams, roots,
etc., in dam.
Preventive measures
Banked reservoir with
compacted clay or chemical admix: grout
seams, cavities.
Use foundation cutoff; grout; upstream blanket
Impervious core.
Watertight joints; water stops; grouting.
Remove compressible foundation, avoid sharp changes in abutment
slope, compact soil at high moisture.
Use low plasticity clays for core, adequate
compaction.
Remove compressible foundation, avoid sharp
changes, internal
drainage with protective
filters.
L o w plasticity soil;
adequate compaction;
internal drainage with
protective filters.
Foundation relief drain
with filter; cutoff.
A4
TYPICAL TYPES OF DAM"S SOIL APPENDIX B
APPENDIX B- TYPICAL TYPES OF DAM'S SOIL
Table LB Typical types of soil in or under dams (U. S. Bureau of Reclamation, 1974) Typical names of soil groups
Well graded gravels, gravel sand mixture, little or no fines
Poorly graded gravels, gravel sand mixtures, little
or no fines
Silty gravels, poorly graded gravel - sand - silt mixture s
Clayey gravels, poorly
graded gravel, clay mixtures
Well graded sands, gravel sands, little or no fines
Poorly graded sands,
gravelly sands, little or no fines
Silty sands, poorly graded sand - silt mixtures
Clayey sands, poorly graded sand- clay mixtures
Inorganic silts and very fine sands, rock flour, silty or clayey fine sands with slight plasticity
Inorganic clay of low to
medium plasticity, gravelly clays, sandy clays, silty
clays, lean clays
Organic silts and organic silt
- clays of flow plasticity
Inorganic silts, micaceous or
diatom aceous fine sandy or
silty soils, elastic silts
Inorganic clay of high plasticity, fat clays
Organic clays of medium to
high plasticity
Group
symbols
G W
GP
G M
GC
sw
SP
SM
SC
ML
CL
OL
M H
CH
OH
Seepage important
1
2
3
4
6
5
7
8
9
10
Seepage not
important
1
3
4
6
2
5
7
8
9
10
11
12
13
14
Permanent
reservoir
Positive cutoff or blanket
Positive cutoff or blanket
Core trench to none
None
Positive cutoff or upstream blanket and toe drains
Positive cutoff or
upstream blanket and toe
drains
Upstream blanket and toe drains
None
Positive cutoff or
upstream blanket and toe drains
None
None
None
None
None
Flood water retarding
Control only within volume acceptable plus pressure relief if required
Control only within volume acceptable plus pressure relief if required
None
None
Control only within volume acceptable plus pressure relief if required
Control only within volume acceptable plus pressure relief if required
Sufficient control to
prevent dangerous seepage piping
None
Sufficient control to prevent dangerous seepage piping
None
None
None
None
None
Note: No. 1 is considered the best
A5
TYPICAL TYPES OF DAM'S SOIL APPENDIX B
Table 2.B Typical types of soil in or under dams (U. S. Bureau of Reclamation, 1974)
Group
symbols
GW
GP
GM
GC
SW
SP
SM
sc
ML
CL
OL
MH
CH
OH
Homogeneous
embankment
-
-
2
1
-
-
4
3
6
5
8
9
7
10
Core
-
-
4
1
-
-
5
2
6
3
8
9
7
10
Shell
1
2
-
-
3 if gravelly
4 if gravelly
-
-
-
-
-
-
-
-
Resistance to piping
Good
Good
Poor
Good
Fair
Fair to poor
Poor to very poor
Good
Poor to very poor
Good to fair
Good to poor
Good to poor
Excellent
Good to poor
Note: No. 1 is considered the best
A6
TYPICAL TYPES OF DAM'S SOIL APPENDIX B
Table 3.B Soil performance in or under dams (Bureau of Reclamation, 1974)
Group
symbols
GW
GP
GM
GC
SW
SP
SM
sc
ML
CL
OL
MH
CH
OH
Permeability
when compacted
Pervious
Very pervious
Semipervious to
impervious
Impervious
Pervious
Pervious
Semipervious to
impervious
Impervious
Semipervious to
impervious
Impervious
Semipervious to
impervious
Semipervious to
impervious
Impervious
Impervious
Shear strength
when compacted
and saturated
Excellent
Good
Good
Good to fair
Excellent
Good
Good
Good to fair
Fair
Fair
Poor
Fair to poor
Poor
Poor
Compressibility
when compacted
and saturated
Negligible
Negligible
Negligible
Very low
Negligible
Very low
Low
Low
Medium
Medium
Medium
High
High
High
Workability as
a construction
material
Excellent
Good
Good
Good
Excellent
Fair
Fair
Good
Fair
Good to Fair
Fair
Poor
Poor
Poor
A7
ICE PRESSURE TABLES APPENDIX C
APPENDIX C- ICE PRESSURE TABLES
Table l.C Ice pressure (kN/m) (
Vertical shores, solar energy considered
Ice
thickness
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Air temperature increase( C)
9 18 27
0
17
31
43
54
64
74
84
94
104
114
124
134
0
35
58
64
86
96
106
116
126
136
146
158
166
0
60
90
115
130
140
150
160
170
180
190
200
210
(US Bureau of Reclamation, 1977)
Vertical shores, solar energy considered
Ice
thickness
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Air temperature increase( C)
9 18 27
0
26
50
62
82
100
115
130
145
160
175
190
205
0
50
83
112
129
146
163
180
197
214
231
246
265
0
110
160
180
202
218
234
250
266
282
296
314
330
Vertical shores, solar energy neglected
Ice
thickness
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Air temperature increase( C)
9 18 27
0
10
20
30
40
50
60
70
80
90
100
110
120
0
16
29
41
52
63
74
85
96
107
118
129
140
0
30
55
75
80
103
114
125
136
147
158
169
180
Vertical shores, solar energy neglected
Ice thickness
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Air temperature increase( C)
9 18 27
0
19
37
54
70
85
100
115
130
145
160
175
190
0
20
39
67
84
101
118
135
152
169
186
203
220
0
60
95
120
140
163
180
197
214
231
248
265
282
A8
BOND AND BREAK FAILURES EQUATIONS APPENDIX D
APPENDIX D- BOND AND BREAK FAILURES EQUA TIONS
Table l.D Factors of safety formulae against both break and bond failures based on
CGM DESIGN
EQUATIONS
FSy
(for both smooth and ribbed strips)
FS(|)
(for smooth strips)
FS<>
(for ribbed strips)
C G M (McKITTRICK, 1978)
yiK0+(Ka-K0)i]ysvsH
i yK yS Sv ' aJ v H O.SB.(L.-0.3H)
i i '
[Kn+(K -Kn)^-]S ST, 0 a 0y6J v H
O.%B.(L.-0.3H)
K S Srr a v H O.SB.[L.-0.6(H-y)]
[K~+(K -Kn)2-]S Srr 0 a 0 g v H
0.8_S.[L.-O.6(ff-y)]
K S SJJ a v H
2B.(L.-0.3H)[f*(l-^)+^ tan(|>]
[Kn+(K -Kn)^]S Srr L 0 a 0 6 v H
2_S.(L.-0.3//)tan<|>
K S Srr a v H
2B.[L.-0.6(H-v)][/J(l-^) + tan<j>]
[Kn+(K -Kn)?-]S Srr 1 0 a 0^6J v H
2B.[L.-0.6(H-y)] tan(J)
[K^+iK -K~)-]S Srr L 0 a 0 g v H
CONDITION
for (0 < y < 6m)
for (y < 6m)
for (0 < y < 6m & 0 < y < 0.5H)
for (y > 6m & 0 < y < 0.5H)
for (0 < y < 6m & 0.5H < y < H)
for (y > 6m &
0.5H < y < H)
for (0 < y < 6m & 0 < y < 0.5H)
for (y > 6m & 0 < y < 0.5H)
for (0 < y < 6m &
0.5H<y<H)
for (y > 6m & 0.5H<y<H)
A9
BOND AND BREAK FAILURES EQUATIONS APPENDIX D
Table 2.D Factors of safety formulae against both break and bond failures based on
MCGM DESIGN
EQUATIONS FSy (for both smooth and ribbed strips)
FS<> (for smooth strips)
FS<b (for ribbed strips)
MCGM (ARENICZ & CHOWDHURY, 1987)
Ai°t«-Ka^ i
j[Ka+o.6y(K0 -Ka)]ySvSH
2B. [L. -j(2.6H)2 -y2 + 2.3H][tan\\r + 0.6 (1.5- tan\|/)]
y[K +o.6y(K„-K )] S 5„ 'a 0 a v H
2B. [L. -•y/(2.6//)2-y2 + 2.3H][ton$ + 0.6y(l.lf*- tan (J))]
[K +o.6y(Kn-K )]S Srr a 0 a v H
A10
RSDAM PROGRAM FLOWCHART APPENDIX E
APPENDIX E- RSDAM PROGRAM FLOWCHART
c START SOB \
CALL INPUDATA
__ 1 . S^* LOOP
- - " -8^C^N=1 TO NUMBER OF
1 LA1
CALL VERFORCE
1 CALL HORFORCE
'
\ CALL DIST
\
fERsJ)
CALL BEAOPTM
• CALL SLIDOPTM
• CALL OVERTOPTM
1 3ALL OVERSTOPTM
/ \. Y \ K K = 1 / " ^ ~
I N
/ \.Y \ KK=2 /*""
I N
CALL NCGM • 1—z
CALL CGM
CALL MCGM
X All
RSDAM PROGRAM FLOWCHART APPENDIX E
? CALL OPTM
• CALL NOFAIL
r { CALL REINAREA
} r
^END LOOP) S X
r" - CALL MESH
1
- IDAM1.UUT1
^ ~S
S^—>. C^JEIN0 SOB^>
( DAM.IN ] • V J C3TART FEM >
v_ C
;SS 8 Br^^=l TO NUMBEF
\ "START MAINT_>
VI " •
CALL NDF
• CALL EBTEDA
1 LOOP
. OF ITERATIC
/ X Y ^ K C = 3 y~*
NY-_«
—© N FOR LODING SI
*"" CALL SEEPAGE
'EP^
OT>
A12
RSDAM PROGRAM FLOWCHART APPENDIX E
i ? \ Y
<KC=5y>~*~
Nl
CALL TSSM
1
CALL NDF
— r a
CALL SSMILV |
• CALL TANESH
• C^END LOOP
1
-©
-- 1 DAM2.UUTI
A13
RSDAM PROGRAM FLOWCHART APPENDIX E
CALL TSSM
I CALL SSMILV
I CALL TANESH
T LOOP
•j8***C N=l TO NUMBER OF ELEMENTS
T CALL PSTMS
\
CALL VSE
T ^JDLOOp
LOOP N=l TO NUMBER OF REINFORCEMENTS
T CALL SBE
A14
RSDAM PROGRAM FLOWCHART APPENDIX E
? ([^START TSSM
1 z> • >v^J=l TO NUMBER OF ELEMENTS^
\
CALL SIE
\
(END LOOP)
' -®*K^N^2- TO NUMBER OF REINFORCEMENTS^
1 CALL SBE
(END LOOP)
(RETURN)
A15
RSDAM PROGRAM FLOWCHART APPENDIX E
CALL ESM
T CALL PSTMS
T CALL PSTMS |
CALL VSE
1 END LOOP.
N=l TO NUMBER OF INTERFACE ELEMENTS
T CALL STIE
A16
RUNNING THE RSDAM PROGRAM APPENDIX F
APPENDIX F- RUNNING THE RSDAM PROGRAM
INTRODUCTION
It is possible to find the minimum base length required for a RSD to prevent the
following modes of failures: sliding, overturning, overstressing, bond failure, and rupture
failure. A computer program, called RSDAM, has been developed based on the
calculations of the forces acting on RSD (presented in Chapter 3), the equations of
stability analysis of RSD (presented in Chapter 4), and the formulae of soil-reinforcement
interaction (presented in Chapter 6). The purpose of the program is to assist a designer
in geometrical optimisation of RSDs and their analysis. This program has been compiled
using Fortran 77 and contains two main sub-programs.
The first main sub-program includes 15 subroutines and optimises the geometry of RSDs.
At the end of this main sub-program, a dam is divided into several incremental elements
in order to perform the analysis by the second main sub-program. The second main sub
program includes 13 subroutines and computes the stresses and displacements within the
elements of the dam based on two dimensional finite element formulation. It should be
noted that although the program is particularly adapted to RSDs, it may also be used for
a variety of reinforced earth walls and embankments with a small change in the
configuration of the program. A guide to this program will be presented here and, as
illustrative example, a model of a RSD with a height of 2 0 m will be analysed.
INPUT DATA
In the program, the information regarding dam geometry, loading, safety factor, fill
material, reinforcement, facing panel, and foundation material are used as input data.
This information, which is asked by the program at the time of running, will be explained
in the following stages:
A17
RUNNING THE RSDAM PROGRAM APPENDIX F
a) First stage
The first stage covers the dam height, the upstream and downstream water tables, the
upstream silt height and, the initial widths of the crest and base as follows:
HEIGHT OF DAM =? UPSTREAM WATER TABLE =? DOWNSTREAM WATER TABLE =? HEIGHT OF SILT =? INITIAL TOP WIDTH OF DAM =? INITIAL BASE WIDTH OF DAM =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
(m) (in) (m) (m) (m) (m)
b) Second stage
The second stage covers the unit weight of silt, the average unit weight of dam, and the
safety factors against the modes of failures (sliding, overturning, overstressing, bond
failure, and rupture failure) as follows:
UNIT WEIGHT OF SILT =? (KN/m3) AVERAGE UNIT WEIGHT OF DAM =? (KN/m3) ***************************************************** SAFETY FACTOR AGAINST SLIDING =? SAFETY FACTOR AGAINST OVERTURNING =? SAFETY FACTOR AGAINST BOND FAILURE =? SAFETY FACTOR AGAINST OVER-STRESSING =? SAFETY FACTOR AGAINST RUPTURE FAILURE =? FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
c) Third stage
The third stage covers the ice force (which should be obtained by referring to Table CI
presented in Appendix C), and the coefficients of direct and indirect forces of earthquake
acceleration (see Chapter Three) as follows:
A18
RUNNING THE RSDAM PROGRAM APPENDIX F
ICE FORCE =? (KN) INITIAL COEFFICIENT OF EARTHQUAKE ACCELERATION =? COEFFICIENT OF INDIRECT FORCE OF EARTHQUAKE =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
d) Fourth stage
The fourth stage covers the width, height and thickness of facing panel as follows:
WIDTH OF FACING PANEL =? HEIGHT OF FACING PANEL =? THICKNESS OF FACING PANEL =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
(m) (m) (m)
e) Fifth stage
The fifth stage covers the width, unit weight, allowable tension and the number of
reinforcements connected to a facing panel as follows:
WIDTH OF REINFORCEMENTS =? (m) UNIT WEIGHT OF REINFORCEMENTS =? (KN/m3) ALLOWABLE TENSION OF REINFORCEMENTS =? (KN/m2) NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2 .
f) Sixth stage
The sixth stage covers the allowable bearing capacity of foundation soil, internal friction
angle, and uniformity coefficient of the dam soil as follows:
ALLOWABLE BEARING CAPACITY OF FOUNDATION SOIL =? (KN/m2) ANGLE OF INTERNAL FRICTION OF DAM SOIL =? (DEGREE) COEFFICIENT OF UNIFORMITY OF DAM SOIL =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2 .
A19
RUNNING THE RSDAM PROGRAM APPENDIX F
g) Seventh stage
The seventh stage covers the selection of the method, which the internal stability analysis
of the dam is based, as follows:
1- INTERNAL STABILITY ANALYSIS BASED ON COHERENT GRAVITY METHOD 2- INTERNAL STABILITY ANALYSIS BASED ON MODIFIED COHERENT GRAVITY METHOD 3- INTERNAL STABILITY ANALYSIS BASED ON NEW COHERENT GRAVITY METHOD
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
h) Eighth stage
The eighth stage covers a question for mesh generation of dam. The number of nodal
points in x-direction of dam should be determined here. The number of the nodal points
in y-direction is calculated by the program and equal to the ratio of dam height per facing
panel height.
NUMBER OF
1-2-
STATIC
NODAL POINTS
ANALYSIS =? TIME HISTORY
IN
ANALYSIS =
X-
-?
-DIRECTION =?
The explanation of elements and the consequence of nodal points are shown in Figures
IF and 2F respectively.
Interface elements Thickness = 0~
Facing Panels
m*, Interface elements Thickness = 0
Facing Panels
Fig. IF The explanation of elements
A20
RUNNING THE RSDAM PROGRAM APPENDIX F
2n
n
4
3
mn
n+1 2n+l 3n+l 4n+l 5n+l 6n+l 7n+l
(m-l)n+l
Fig. 2F The consequence of the nodal points
i) Ninth stage
The ninth stage covers the facing panel properties as follows:
UNIT WEIGHT OF FACING PANELS =? YOUNG'S MODULUS OF FACING PANELS =? POISSON'S RATIO OF FACING PANELS =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
(KN/m3) (KN/m2)
j) Tenth stage
The tenth stage covers the soil properties for finite element analysis as follows:
UNIT WEIGHT OF THE MATERIAL =? (KN/m3) COHESION OF THE MATERIAL =? (KN/m2) FRICTION ANGLE =? (DEGREE) LATERAL EARTH PRESSURE COEFFICIENT AT REST =? INITIAL TANGENT MODULUS EXPONENT =? INITIAL TANGENT MODULUS COEFFICIENT =? FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2 **************************************************** UNLOAD-RELOAD MODULUS COEFFICIENT =? MIN. INITIAL TANGENT MODULUS FOR NON-ELASTIC MATERIALS =? BULK MODULUS EXPONENT =? BULK MODULUS COEFFICIENT =? YOUNG'S MODULUS =? POISSON'S RATIO =? FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
(KN/m2)
(KN/m2)
A21
RUNNING THE RSDAM PROGRAM APPENDIX F
k) Eleventh stage
The eleventh stage covers the number of fixed nodes in y-direction, x-direction, both x
and y directions and z-rotation as follows:
NUMBER NUMBER NUMBER NUMBER
OF OF OF OF
NODAL NODAL NODAL NODAL
FIXED FIXED FIXED FIXED
POINTS POINTS POINTS POINTS
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
IN IN IN
Y-X-X
-DIRECTION =? -DIRECTION =? AND Y DIRECTIONS =?
AGAINST ROTATING =?
I) Twelfth stage
The twelfth stage covers the numbers of fixed nodes in y-direction, if any, as follows:
NODAL NUMBERS AGAINST Y-MOVEMENT =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
m) Thirteenth stage
The thirteenth stage covers the number of fixed nodes in x-direction, if any, as follows:
NODAL NUMBERS AGAINST X-MOVEMENT =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
n) Fourteenth stage
The fourteenth stage covers the numbers of fixed nodes in both y and x-direction, if any,
as follows:
NODAL NUMBERS AGAINST BOTH Y AND X-MOVEMENT =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
A22
RUNNING THE RSDAM PROGRAM APPENDIX F
o) Fifteenth stage
The fifteenth stage covers the nodal numbers of fixed nodes against rotation, if
follows:
NODAL NUMBERS AGAINST ROTATIONS =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
p) Sixteenth stage
The sixteenth stage covers the numbers and the elastic modulus of reinforcements
installed within the dam as follows:
NUMBER OF REINFORCEMENTS =? ELASTIC MODULUS OF THE REINFORCEMENTS =? (KN/m2)
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
q) Seventeenth stage
The seventeenth stage covers the nodal numbers, and cross-section area of these
reinforcements together with the angle between reinforcements and a horizontal line as
follows:
NODAL ANGLE CROSS-
NUMBERS OF THE BETWEEN THE
Nth REINFORCEMENT = Nth REINFORCEMENT AND
-SECTIONAL AREA
FOR CHANGING DATA FOR CONTINUE TYPE
= ? HORIZONTAL
OF THE Nth REINFORCEMENT =?
TYPE 1 2
LINE =?
r) Eighteenth stage
The eighteenth stage covers the displacement of the base nodes, if time history analysis
has been chosen in the eightieth stage, as follows:
A23
RUNNING THE RSDAM PROGRAM APPENDIX F
DISPLACEMENTS OF BASE NODAL POINTS =? DELTA(X) AND DELTA(Y) OF NODE J =? DELTA(X) AND DELTA(Y) OF NODE J+NMP =?
FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
s) Nineteenth stage
The nineteenth stage covers the phreatic surface at the present and at the new levels as
follows:
NUMBER OF PHREATIC SURFACE END POINTS =? X-COORDINATE OF NODE J =? PRESENT LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT NODE J =? NEW LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT NODE J =? FOR CHANGING DATA TYPE 1 FOR CONTINUE TYPE 2
OUTPUT DATA
Output data contains two files, called D A M L O U T and D A M 2 . 0 U T , which will be
explained in the following two sections:
a) First Section
Initially the values of the input data will be printed out in the D A M L O U T file for
checking the input data as follows:
A24
RUNNING THE RSDAM PROGRAM APPENDIX F
HEIGHT OF DAM = m
UPSTREAM WATER TABLE = m DOWNSTREAM WATER TABLE = m HEIGHT OF SILT = m TOP WIDTH OF DAM = m BOTTOM WIDTH OF DAM = m
UNIT WEIGHT OF WATER = KN/m3 UNIT WEIGHT OF SILT = KN/m3 AVERAGE UNIT WEIGHT OF DAM = KN/m3
SAFETY FACTOR AGAINST SLIDING = SAFETY FACTOR AGAINST SLIDING = SAFETY FACTOR AGAINST BOND FAILURE = SAFETY FACTOR AGAINST OVER-STRESSING = SAFETY FACTOR AGAINST RUPTURE FAILURE =
ICE FORCE =
COEFFICIENT OF EARTHQUAKE ACCELERATION =
KN
COEFFICIENT OF INDIRECT FORCE OF EARTHQUAKE =
WIDTH OF FACINGS = HEIGHT OF FACINGS = WIDTH OF REINFORCEMENTS = UNIT WEIGHT OF REINFORCEMENTS =
NUMBER OF REINFORCEMENTS CONNECTED TO A
ALLOWABLE BEARING CAPACITY OF SOIL = ANGLE OF INTERNAL FRICTION OF SOIL =
ALLOWABLE TENSION OF REINFORCEMENTS = COEFFICIENT OF UNIFORMITY OF SOIL =
m m m KN/m3
FACING PANEL =
KN/m2 DEGREE
KN/m2
THE NAME OF THE METHOD WHICH THE INTERNAL STABILITY ANALYSIS IS BASED
Then, the output results of analysis for optimisation of the RSD are printed out in
D A M L O U T . In this stage the dam has been divided into several layers. Each layer is
taken from the crest to a specified depth as shown in Fig. 3F. The first layer is
considered as the whole dam and the second layer means the dam from its crest to the
depth of the first facing panel near the base.
A25
RUNNING THE RSDAM PROGRAM APPENDIX F
w ,
/ '" "
r
<
_
wb
#2 ! ^1
T
Fig. 3F The cross section of a parametric RSD with imaginary horizontal layers
The output data includes:
- the height of the layer,
- the depth and weight of water and silt acting on the upstream side of
the layer,
- the base width of the layer,
- the weight of the layer,
- the hydrostatic force acting on the layer,
- the silt force acting on the layer,
- the ice force acting on the layer,
- the direct and indirect forces of earthquake acting on the layer,
- the rrtinimum required base width of dam for no sliding, overturning,
overstressing, rupture failure and lack of bond,
- the optimum required base width of the dam
- the minimum required length of reinforcement
- the minimum net thickness of reinforcement needed for each layer
- the minimum cross-section area of each reinforcement
- the minimum net volume of each reinforcement
- and the minimum net weight of the reinforcements
If any failure in the above output data occurs, the program will stop and a massage
describing the mode of failure will be shown in output data file. These stages are iterated
A26
RUNNING THE RSDAM PROGRAM APPENDIX F
in the first layer (whole dam) analysis until the base width of the RSD is optimised.
Then, the above operation is repeated and printed out for other layers of the dam. In
these layers, the base length of the layer should be compared with the rninimum required
base lengths of the layer. The above output-data are printed out as follows:
**************************************************** LAYER NO. = ****************************************************
HEIGHT OF LAYER = UPSTREAM WATER TABLE = DOWNSTREAM WATER TABLE = HEIGHT OF SILT = TOP WIDTH OF LAYER = BOTTOM WIDTH OF LAYER = RATIO OF TOP WIDTH TO BOTTOM WIDTH =
WEIGHT OF LAYER = WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER = WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER = UPLIFT PRESSURE ACTING ON THE LAYER = HYDROSTATIC FORCE ACTING ON LAYER = ICE FORCE ACTING ON LAYER = SILT FORCE ACTING ON LAYER = INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER = BEARING CAPACITY FAILURE WILL NOT HAPPEN
rn m rn rn m m
=
MIN. REQUIRED BASE LENGTH FOR NO SLIDING = MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING = MIN. REQUIRED BASE LENGTH FOR NO OVER-STRESSING = MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE =
MIN. REQUIRED BASE LENGTH FOR NO FAILURE =
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL
MIN. REQUIRED LENGTH OF REINFORCEMENT = MIN. NET THICKNESS OF REINFORCEMENT = WIDTH OF REINFORCEMENT =
MIN. CROSS SEC. AREA OF REINFORCEMENT = MIN. NET VOLUME OF REINFORCEMENT = MIN. NET WEIGHT OF REINFORCEMENT =
*
*
KN KN KN KN KN KN KN KN KN
m m m m
m
1
m mm cm
cm2/m2 AREA m3/m2 AREA Kq/m2 AREA
b) Second Section
In this section, the numbers of nodal points, soil elements, interface elements,
reinforcements, and loading steps are printed out in DAM2.0UT as follows:
A27
RUNNING THE RSDAM PROGRAM APPENDIX F
NUMBER NUMBER NUMBER NUMBER NUMBER
OF OF OF OF OF
NODAL POINTS = ELEMENTS = REINFORCEMENTS = INTERFACE ELEMENTS = LOADING STEPS =
This is followed by the reinforcement installation and the loading steps as follows:
STAGE No.
* *
NO. OF ITERATION
* *
CONSTRUCTION TYPE
* *
The material properties are printed out as follows:
MATERIAL
* *
GAMMA
* *
COHESION
* *
PHI
* *
TENS. STRENGTH
* *
KO
* *
In addition, the coordinates of the nodal points are printed out as follows:
COORDINATES OF NODAL POINTS
NODAL POINT X-COORDINATE
* * * *
Y-COORDINATE
* *
The boundary conditions of dam is also printed out in D A M 2 . 0 U T as follows:
NODES WITH BOUNDARY RESTRAINTS
NO x-MOVEMENT =
NO Y-MOVEMENT =
NO X OR Y MOVEMENT = * * *
* *
* * *
A28
RUNNING THE RSDAM PROGRAM APPENDIX F
This is followed by the data representing dam geometry, including the number of soil
element, followed by the four numbers representing the number of nodes of this element.
A number representing the type of element materiel is also printed out after the numbers
of nodes as follows:
ELEMENT DATA ELEMENT No. I J K L MATERIAL
* * * * * * * * * * * *
The specification of the reinforcement instalation and/or loading step is printed out in the
next stage as follows:
**************************** STAGE NUMBER 1
******************** THE FOLLOWING
REINFORCEMENT No.
* *
* ********
*************************
******* REINFORCEMENTS
I
* *
J
* *
*********** ARE ADDED
DISP. TC
******* HEREIN
ACTIVATE
* *
or
***************************************************** STAGE NUMBER 2
*****************************************************
FORCE AND/OR DISPLACEMENT LOADING IS SPECIFIED FOR THIS INCREMENT
NODE X-LOAD Y-LOAD NODE X-LOAD Y-LOAD
* * * * * * * * * * * *
The results of analysis, including the coordinates of the nodal points, and the horizontal
and vertical displacements of nodal points are printed out here as follows:
A29
RUNNING THE RSDAM PROGRAM APPENDIX F
DISPLACEMENT
NODAL POINT
* *
X
* *
RESULTS
Y
* *
FOR STAGE 1
TOTAL UX
* *
TOTAL UY
* *
PORE PRESS
* *
The coordinates of the middle of soil element, the horizontal stress, the vertical stress
and the principal stresses within the elements, and the maximum shear stresses for soil
elements are printed out as follows:
ELEM NO
* *
STRESSES VALUES
X Y
* * * *
FOR STAGE
SIGMA X
* *
1
SIGMA Y
* *
TAU XY
* *
SIGMA 1
* *
SIGMA 3
* *
Then the interface element results are printed out as follows:
INTERFACE ELEMENT RESULTS FOR STAGE 1
ELEM NO X Y NORMAL STRESS SHEAR STRESS NORMAL STIFF SHEAR STIFF
* * * * * * * * * * * * * *
Finally, the value of tension in the reinforcements are printed out as follows:
REINFORCEMENT RESULTS FOR STAGE 1
REIN. NUM. I J TYPE COMPR FORCE INCR COMPR STIFFNESS COSA
**** * * ** * * * * * * * *
EXAMPLE
The input data and output data for the example of the 20m high RSD is presented here.
A30
RUNNING THE RSDAM PROGRAM APPENDIX F
Input Data
The input data of a RSD with 20 m height are as follows:
HEIGHT OF DAM =20 UPSTREAM WATER TABLE =20 DOWNSTREAM WATER TABLE = 2 HEIGHT OF SILT = 6 INITIAL TOP WIDTH OF DAM = 2 INITIAL BASE WIDTH OF DAM =10
(m) (m) (m) (m) (m) (m)
UNIT WEIGHT OF SILT = 18 AVERAGE UNIT WEIGHT OF DAM =20
**************************************
SAFETY FACTOR AGAINST SLIDING = 2 SAFETY FACTOR AGAINST OVERTURNING = 2 SAFETY FACTOR AGAINST BOND FAILURE =3 SAFETY FACTOR AGAINST OVER-STRESSING = SAFETY FACTOR AGAINST RUPTURE FAILURE
(KN/m3) (KN/m3)
************
2 = 3
ICE FORCE = 0 (KN) INITIAL COEFFICIENT OF EARTHQUAKE ACCELERATION =0.2 COEFFICIENT OF INDIRECT FORCE OF EARTHQUAKE =0.2
WIDTH OF FACING PANELS = 1 HEIGHT OF FACING PANELS = 2 THICKNESS OF FACING PANELS = 0.2
(m) (m) (m)
WIDTH OF REINFORCEMENTS =0.08 (m) UNIT WEIGHT OF REINFORCEMENTS = 78 (KN/m3) ALLOWABLE TENSION OF REINFORCEMENTS = 24 0000 (KN/m2) NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL = 1
ALLOWABLE BEARING CAPACITY OF FOUNDATION SOIL = 900 (KN/m2) ANGLE OF INTERNAL FRICTION OF DAM SOIL =35 (DEGREE) COEFFICIENT OF UNIFORMITY OF DAM SOIL = 150
1-2-3-
INTERNAL INTERNAL INTERNAL
STABILITY STABILITY STABILITY
ANALYSIS ANALYSIS ANALYSIS
BASED BASED BASED
ON ON ON
COHERENT GRAVITY METHOD MODIFIED COHERENT GRAVITY METHOD NEW COHERENT GRAVITY METHOD = 3
NUMBER OF NODAL POINTS IN X-DIRECTION 11
A31
RUNNING THE RSDAM PROGRAM APPENDIX F
Therefore, the consequence of the nodal points of this example is as shown in Fig. 4F.
ll
10
9
8
4
3
2
33 55 77 99 22, 44
i l l \
34 12 23
\ \ \ \ \ w \ 7 7_r
\ \ \ W ^ x \ \ \ \ \ ^
-, 113
M v 117 \ \ \ \ \ ^
45 56 67 78 89 • ;;;
100
Fig. 4F- The consequence of the nodal points
UNIT WEIGHT OF FACING PANELS =24 (KN/m3) YOUNG'S MODULUS OF FACING PANELS = 2500000 (KN/m2) POISSON'S RATIO OF FACING PANELS =0.2
UNIT WEIGHT OF THE MATERIAL =20 (KN/m3) COHESION OF THE MATERIAL = 0 (KN/m2) FRICTION ANGLE =35 (DEGREE) LATERAL EARTH PRESSURE COEFFICIENT AT REST =0.5 INITIAL TANGENT MODULUS EXPONENT =0.5 INITIAL TANGENT MODULUS COEFFICIENT = 3 00 **************************************************** UNLOAD-RELOAD MODULUS COEFFICIENT = 5 00 MIN. INITIAL TANGENT MODULUS FOR NON-ELASTIC MATERIALS = 1000 (KN/m2) BULK MODULUS EXPONENT =0.2 BULK MODULUS COEFFICIENT =250 YOUNG'S MODULUS = 50 00 (KN/m2) POISSON'S RATIO =0.1
NUMBER NUMBER NUMBER NUMBER
OF OF OF OF
NODAL NODAL NODAL NODAL
FIXED FIXED FIXED FIXED
POINTS POINTS POINTS POINTS
IN Y-DIRECTION = 0 IN X-DIRECTION = 0 IN X AND Y DIRECTIONS = AGAINST ROTATING = 0
= 11
NODAL NUMBERS AGAINST BOTH Y AND X-MOVEMENT = 1 12 23 34 45 56 67 78 89 100 111
A32
RUNNING THE RSDAM PROGRAM APPENDIX F
NUMBER OF REINFORCEMENTS =10 ELASTIC MODULUS OF THE REINFORCEMENTS = 250000000 (KN/m2)
Since the number of reinforcements are specified to be 10, the input data in regard to the
specifications of the reinforcements are asked 10 times as follows:
NODAL NUMBERS OF THE 1th REINFORCEMENT = 1 111 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT =
NODAL NUMBERS OF THE 2th REINFORCEMENT = 2 112 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT = **************************************************** NODAL NUMBERS OF THE 3th REINFORCEMENT = 3 113 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT =
NODAL NUMBERS OF THE 4th REINFORCEMENT = 4 114 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT = **************************************************** NODAL NUMBERS OF THE 5th REINFORCEMENT = 5 115 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT =
NODAL NUMBERS OF THE 6th REINFORCEMENT = 6 116 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT = **************************************************** NODAL NUMBERS OF THE 7th REINFORCEMENT = 7 117 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT =
NODAL NUMBERS OF THE 8th REINFORCEMENT = 8 118 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT = **************************************************** NODAL NUMBERS OF THE 9th REINFORCEMENT = 9 119 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT =
NODAL NUMBERS OF THE 10th REINFORCEMENT = 10 120 ANGLE BETWEEN THE Nth REINFORCEMENT AND HORIZONTAL LINE = 0 CROSS-SECTIONAL AREA OF THE Nth REINFORCEMENT = ****************************************************
Then the input data in regard to the displacements of the base nods are asked as follows:
A33
RUNNING THE RSDAM PROGRAM APPENDIX F
DISPLACEMENTS OF BASE DELTA(X) AND DELTA(Y) DELTA(X) AND DELTA(Y)
DISPLACEMENTS OF BASE DELTA(X) AND DELTA(Y)
DELTA(X) AND DELTA(Y)
NODAL POINTS OF NODE 1 = OF NODE 12 =
NODAL POINTS OF NODE 23 =
OF NODE 34 = **********************************.
DISPLACEMENTS OF BASE
DELTA(X) AND DELTA(Y) DELTA(X) AND DELTA(Y)
DISPLACEMENTS OF BASE DELTA(X) AND DELTA(Y)
DELTA(X) AND DELTA(Y) *********************
DISPLACEMENTS OF BASE
DELTA(X) AND DELTA(Y)
DELTA(X) AND DELTA(Y)
DISPLACEMENTS OF BASE DELTA(X) AND DELTA(Y)
NODAL POINTS OF NODE 45 = OF NODE 56 =
NODAL POINTS OF NODE 67 = OF NODE 78 =
3. 0
0 0
V *
0 0
0 0
I (
.1
1
1 t *
1 1
1 1
*****************
NODAL POINTS OF NODE 89 =
OF NODE 100 =
NODAL POINTS OF NODE 111 =
0 1 : 0.1
= 0.]
)
0
0 0
0 0
0 0
0
0
0
Since the number of phreatic surface end points are specified to be 2, the input data in
this regard are asked 2 times as follows:
NUMBER OF PHREATIC SURFACE END POINTS = 2
X-COORDINATE OF NODE J = 0
PRESENT LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT NODE
NEW LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT NODE J =
NUMBER OF PHREATIC SURFACE END POINTS = 2
X-COORDINATE OF NODE J = 6 PRESENT LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT NODE
NEW LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT NODE J =
J =
0
J = 0
2
20
Output Data
The output data contains two files, called D A M l . O U T and DAM2.0UT, which will be
explained in the following two sections:
A34
RUNNING THE RSDAM PROGRAM APPENDIX F
a) First Section (Dam 1.out)
Initially the input data of this example (printed out in the D A M L O U T file for checking)
are presented as follows:
***************************************************** * * * * INPUT DATA *
* * *
* * *****************************************************
HEIGHT OF DAM = 20.0000 m UPSTREAM WATER TABLE = 20.0000 m DOWNSTREAM WATER TABLE = 2.00000 m HEIGHT OF SILT = 6.00000 m TOP WIDTH OF DAM = 2.00000 m BOTTOM WIDTH OF DAM = 20.0000 m
UNIT WEIGHT OF WATER = UNIT WEIGHT OF SILT = AVERAGE UNIT WEIGHT OF DAM =
SAFETY FACTOR AGAINST SLIDING = SAFETY FACTOR AGAINST SLIDING = SAFETY FACTOR AGAINST BOND FAILURE = SAFETY FACTOR AGAINST OVER-STRESSING = SAFETY FACTOR AGAINST RUPTURE FAILURE =
ICE FORCE =
10.0000 KN/m3 18.0000 KN/m3 20.0000 KN/m3
2.00000 2.00000 3.00000 2.00000 3.00000
0.000000
COEFFICIENT OF EARTHQUAKE ACCELERATION = 0.200000 COEFFICIENT OF INDIRECT FORCE OF EARTHQUAKE = 0.200000
WIDTH OF FACINGS = HEIGHT OF FACINGS = WIDTH OF REINFORCEMENTS = UNIT WEIGHT OF REINFORCEMENTS =
NUMBER OF REINFORCEMENTS CONNECTED TO A
ALLOWABLE BEARING CAPACITY OF SOIL = ANGLE OF INTERNAL FRICTION OF SOIL =
ALLOWABLE TENSION OF REINFORCEMENTS = COEFFICIENT OF UNIFORMITY OF SOIL =
INTERNAL STABILITY ANALYSIS IS BASED ON
NUMBER OF LAYERS =
1.00000 2.00000 0.800000E-01 78.0000
FACING PANEL =
900.000 35.0000
240000. 150.000
KN
m m m KN/m3
1
KN/m2 DEGREE
KN/m2
NEW COHERENT GRAVITY METHOD
10
A35
RUNNING THE RSDAM PROGRAM APPENDIX F
Then the output data of this example for stability analysis and optimisation of the whole
dam (printed out in the DAM LOUT file) are presented as follows:
***************************************************** * * * * * OUTPUT
*****************************************************
LAYER NO.= 1 ITERATION NO.= 1
HEIGHT OF LAYER= 20.0000 m UPSTREAM WATER TABLE= 2 0.0000 m DOWNSTREAM WATER TABLE= 2.0000 0 m HEIGHT OF SILT= 6.00000 m TOP WIDTH OF LAYER= 6.00000 m BOTTOM WIDTH OF LAYER= 2 0.0000 m
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.300000
WEIGHT OF LAYER= 5200.00 KN WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 1400.00 KN WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 22 6.80 0 KN UPLIFT PRESSURE ACTING ON THE LAYER= 2200.00 KN
HYDROSTATIC FORCE ACTING ON LAYER= 2000.00 KN ICE FORCE ACTING ON LAYER= 0.000 00 0 KN SILT FORCE ACTING ON LAYER= 87.8 0 07 KN INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 116.160 KN DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 1040.00 KN
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= 76.1570 MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= 50.402 0 MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= 42.3742 MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= 16.5226
MIN. REQUIRED BASE LENGTH FOR NO FAILURE= 76.1570 m FOR NO FAILURE BASE LENGTH SHOULD BE INCREASED
m m m m
A36
RUNNING THE RSDAM PROGRAM APPENDIX F
gggggggg@ggggg@@ggggg@@g@g@gg@g@gggg@@gg@gg@gg@g(a@g@g *****************************************************
OUTPUT
***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= ITERATION NO.
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
1 2
20.0000 20.0000 2.00000 6.00000 6.00000 76.1570
m m m m m m
0.787847E-01
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE=
16431.4 7015.70 1136.54 8377.27
2000.00 0.000000 87.8007 116.160 3286.28
KN KN KN KN
KN KN KN KN KN
70.4086 43.4634 34.3741 16.5226
m m m m
70.4086 m
A37
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggg@ggggg@@ggggggggg@ggggggggggggggggggg@@ggggg@g ***************************************************** * * * * * OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= ITERATION NO.
1 3
20.0000 20.0000 2.00000 6.00000 6.00000 73.2828
m m m m m m
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.818746E-01
WEIGHT OF LAYER= 1585 6.6 KN WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 6728.28 KN WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 1089.98 KN UPLIFT PRESSURE ACTING ON THE LAYER= 8061.11 KN
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= 70.4829 m MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= 43.5895 m MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= 34.4680 m MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= 16.5226 m
MIN. REQUIRED BASE LENGTH FOR NO FAILURE^ 70.4829 m
2000.00 0.000000 87.8007 116.160 3171.31
KN KN KN KN KN
A38
RUNNING THE RSDAM PROGRAM APPENDIX F
gggggggggggggggggggg@@g@ggggg@gg@ggggggg@ggg@@ggggggg *****************************************************
* OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= ITERATION NO.:
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
1 4
20.0000 20.0000 2.00000 6.00000 6.00000 71.8829
m m m m m m
0.834691E-01
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING--MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE=
15576.6 6588.29 1067.30 7907.11
2000.00 0.000000 87.8007 116.160 3115.31
KN KN KN KN
KN KN KN KN KN
70.5213 43.6543 34.5166 16.5226
70.5213
m in m m
m
A39
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg ***************************************************** * * * * * OUTPUT *
***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= 1 ITERATION NO.= 5
HEIGHT OF LAYER= 2 0.0000 m UPSTREAM WATER TABLE= 2 0.0000 ro DOWNSTREAM WATER TABLE= 2.00000 m HEIGHT OF SILT= 6.0000 0 m TOP WIDTH OF LAYER= 6.00000 m BOTTOM WIDTH OF LAYER= 71.2021 m
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.842672E-01
WEIGHT OF LAYER= 1544 0.4 KN WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 6520.21 KN WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 1056.27 KN UPLIFT PRESSURE ACTING ON THE LAYER= 7832.23 KN
HYDROSTATIC FORCE ACTING ON LAYER= 2 000.00 KN ICE FORCE ACTING ON LAYER= 0.000000 KN SILT FORCE ACTING ON LAYER= 87.8007 KN INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 116.160 KN DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 3 088.08 KN
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= 7 0.5406 MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= 43.68 67 MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= 34.5410 MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= 16.5226
m m m m
MIN. REQUIRED BASE LENGTH FOR NO FAILURE= 70.5406 m
A40
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *******************************************************
* OUTPUT * * * _ ******************************,*****.**************,*, ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= ITERATION NO.=
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE: HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
20.0000 20.0000 2.00000 6.00000 6.00000 70.8713
m m m m m m
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.846604E-01
WEIGHT OF LAYER= 15374.3 KN WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 6487.13 KN WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 1050.92 KN UPLIFT PRESSURE ACTING ON THE LAYER= 7795.85 KN
HYDROSTATIC FORCE ACTING ON LAYER= 2 000.00 KN ICE FORCE ACTING ON LAYER= 0.000000 KN SILT FORCE ACTING ON LAYER= 87.8007 KN INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 116.160 KN DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 3074.85 KN
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= 70.5501 m MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= 43.7027 m MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= 34.5530 rn MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= 16.5226 m
MIN. REQUIRED BASE LENGTH FOR NO FAILURE= 70.5501
A41
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
OUTPUT
***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= ITERATION NO.:
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
1 7
20.0000 20.0000 2.00000 6.00000 6.00000 70.7107
m m m m m m
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.848528E-01
WEIGHT OF LAYER= 15342.1 KN WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 6471.07 KN WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 1048.31 KN UPLIFT PRESSURE ACTING ON THE LAYER= 7778.18 KN
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
2000.00 0.000000 87.8007 116.160 3068.43
KN KN KN KN KN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= 43.7105 MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING^ 34.5589 MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= 16.5226
70.5547 m m m m
MIN. REQUIRED BASE LENGTH FOR NO FAILURE: 70.5547 m
A42
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * *
* * ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.= ITERATION NO.=
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
20.0000 20.0000 2.00000 6.00000 6.00000 70.6327
m m m m m m
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.849465E-01
WEIGHT OF LAYER= 15326.5 WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 64 63.27 WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 1047.05 UPLIFT PRESSURE ACTING ON THE LAYER= 7769.60
HYDROSTATIC FORCE ACTING ON LAYER= 2 000.00 ICE FORCE ACTING ON LAYER= 0.00 00 00 SILT FORCE ACTING ON LAYER= 87.8007 INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 116.16 0 DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 3 065.31
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= 70.5570 MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= 43.7143 MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= 34.5618 MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= 16.5226
MIN. REQUIRED BASE LENGTH FOR NO FAILURE= 7 0.557 0
KN KN KN KN
KN KN KN KN KN
m
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT^ MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
m m m m
16.5226 33.8737 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT= MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
13.5495 0.223872E-01 1.74620
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
After calculation of the stability analysis and optimisation of the RSD, the output data of
this example for the other layers of the dam (printed out in the DAMLOUT file) are
presented as follows:
A43
RUNNING THE RSDAM PROGRAM APPENDIX F
g@g@@g@gggggggg@g@gggg@@ggggg@ggg@ggggggg@g@ggg@g@gg@ *****************************************************
* OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
18.0000 m 18.0000 m 0.000000 m 4.00000 m 6.00000 m 64.1694 m
0.935025E-01
WEIGHT OF LAYER= 12 63 0.5 WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= 5235.25 WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= 465.355 UPLIFT PRESSURE ACTING ON THE LAYER= 5775.25
HYDROSTATIC FORCE ACTING ON LAYER= 1620.00 ICE FORCE ACTING ON LAYER= 0.000000 SILT FORCE ACTING ON LAYER= 3 9.0225 INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 94.0896 DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= 2 526.10
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE=
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
KN KN KN KN
KN KN KN KN KN
60.2596 39.2878 24.7662 17.3078
60.2596 rn
m m m m
1 17.3078 30.4864 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT: MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
12.1945 0.211061E-01 1.64627
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A44
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg • i * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^
* OUTPUT * *
* * *****************************************************
LAYER NO.= -3
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
16.0000 16.0000 0.000000 2.00000 6.00000 57.7062
0.103975
m m m m m m
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER: WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER: DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE:
10193.0 4136.49 116.339 4616.49
1280.00 0.000000 9.75563 74.3424 2038.60
KN KN KN KN
KN KN KN KN KN
56.2094 40.1675 18.2379 17.9998
m m m m
56.2094 m
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT WIDTH OF REINFORCEMENT=
MIN. CROSS SEC. AREA OF REINFORCEMENT: MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
10.8396 0.195111E-01 1.52187
17 27 8.
.9998
.0990 00000
cm2/m2 m3/m2 KN/m2
m mm cm
AREA AREA AREA
A45
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
14.0000 14.0000
0.000000 0.000000 6.00000 51.2429
0.117089
m m m m m m
8014.00 3167.00 0.000000 3587.00
980.000 0.000000 0.000000 56.9184 1602.80
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER: WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER: DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE:
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
KN KN KN KN
KN KN KN KN KN
50
50.4058 38.1480 13.5319 18.6025
.4058 m
m m m m
18.6025 23.7116 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT= MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
9.48464 0.176438E-01 1.37622
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A46
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE: HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
12.0000 12.0000 0.000000 0.000000 6.00000 44.7796
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.133990
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE=
m m m m m m
6093.56 2326.78
0.000000 2686.78
720.000 0.000000 0.000000 41.8176 1218.71
KN KN KN KN
KN KN KN KN KN
43.3298 32.9942 9.90900 19.1190
m m m m
43.3298
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
ro
19.1190 20.3242 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT--MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
8.12969 0.155432E-01 1.21237
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A47
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.:
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
10.0000 10.0000 0.000000 0.000000 6.00000 38.3164
0.156591
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER: WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER: DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE:
m m m m m m
4431.64 1615.82
0.000000 1915.82
500.000 0.000000 0.000000 29.0400 886.327
KN KN KN KN
KN KN KN KN KN
36.2484 27.7815 7.01611 19.5520
m m m m
36.2484
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL: MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
m
19.5520 16.9369 !. 00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT= MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
6.77475 0.132460E-01 1.03319
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A48
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * *
* *
* ***************************************************** gggggggggggggggggggggggggggg@@@g@@@@g@g@g@@ggg@gggggg LAYER NO.= n
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
8.00000 8.00000 0.000000 0.000000 6.00000 31.8531
0.188365
m m m m m m
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE:
3028.25 1034.12
0. 000000 1274.12
320.000 0.000000 0.000000 18.5856 605.649
KN KN KN KN
KN KN KN KN KN
29.1578 22.4771 4.70376 19.9035
m m m m
29.1578 m
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
1 19.9035 13.5495 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT: MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
5.41980 0.107873E-01 0.841409
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A49
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * * * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggggggggggggggg
LAYER NO.
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE= HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
RATIO OF TOP WIDTH TO BOTTOM WIDTH=
6.00000 6.00000
0.000000 0.000000 6.00000 25.3898
0.236315
m m m m m m
1883.39 581.694 0.000000 761.694
180.000 0.000000 0.000000 10.4544 376.678
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING= MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE=
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL: MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
KN KN KN KN
KN KN KN KN KN
22
22.0509 17.0239 2.87675 20.1753
.0509 m
m m m m
20.1753 10.1621 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT= MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
4.06485 0.820093E-02 0.639673
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A50
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg ***************************************************** * * * OUTPUT *
***************************************************** gggggggggggggggggggggggggggggggggggggggg@@@@@gg@g@ggg
LAYER NO.=
HEIGHT OF LAYER= UPSTREAM WATER TABLE= DOWNSTREAM WATER TABLE: HEIGHT OF SILT= TOP WIDTH OF LAYER= BOTTOM WIDTH OF LAYER=
4.00000 4.00000 0.000000 0.000000 6.00000 18.9265
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.317015
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER: WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE:
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING MIN. REQUIRED LENGTH OF REINFORCEMENT= MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
m m m m m m
997.062 258.531 0.000000 378.531
80.0000 0.000000 0.000000 4.64640 199.412
KN KN KN KN
KN KN KN KN KN
14.9101 11.3263 1.47904 12.2295
14.9101 m
m m m m
PANEL= 12.2295 5.87985 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT= MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
2.35194 0.287630E-02 0.224351
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
A51
RUNNING THE RSDAM PROGRAM APPENDIX F
ggggggggggggggggggggggggggggggggggggggggggggggggggggg *****************************************************
* OUTPUT * * * ***************************************************** ggggggggggggggggggggggggggggggggggggggggg@@g@@@@g@@@g
LAYER NO.= 10
HEIGHT OF LAYER= 2.00000 UPSTREAM WATER TABLE= 2.00 000 DOWNSTREAM WATER TABLE= 0.0000 00 HEIGHT OF SILT= 0.0 00 000 TOP WIDTH OF LAYER= 6.00000 BOTTOM WIDTH OF LAYER= 12.4633
RATIO OF TOP WIDTH TO BOTTOM WIDTH= 0.481415
WEIGHT OF LAYER= WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER: WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= UPLIFT PRESSURE ACTING ON THE LAYER=
HYDROSTATIC FORCE ACTING ON LAYER= ICE FORCE ACTING ON LAYER= SILT FORCE ACTING ON LAYER= INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=
BEARING CAPACITY FAILURE WILL NOT HAPPEN
MIN. REQUIRED BASE LENGTH FOR NO SLIDING= MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= MIN. REQUIRED BASE LENGTH FOR NO OVERSTRESSING: MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE=
MIN. REQUIRED BASE LENGTH FOR NO FAILURE:
m m m m m m
369.265 64.6327
0. 000000 124.633
20.0000 0.000000 0.000000 1.16160 73.8531
KN KN KN KN
KN KN KN KN KN
7.67795 5.32100 0.493391 7.54333
7.67795
m m m m
NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL= MIN. REQUIRED LENGTH OF REINFORCEMENT^ MIN. NET THICKNESS OF REINFORCEMENT= WIDTH OF REINFORCEMENT=
7.54333 2.14445 8.00000
m mm cm
MIN. CROSS SEC. AREA OF REINFORCEMENT= MIN. NET VOLUME OF REINFORCEMENT= MIN. NET WEIGHT OF REINFORCEMENT=
0.857782 0.647053E-03 0.504701E-01
cm2/m2 AREA m3/m2 AREA KN/m2 AREA
b) Second Section (Dam2.out)
Then the values of the analysis by the finite element method (printed out in the
DAM2.0UT file) are presented as follows:
A52
RUNNING THE RSDAM PROGRAM APPENDIX F
REINFORCED EARTH DAM ANALYSIS
STAGE
1 2 3 4 5
NUMBER NUMBER NUMBER NUMBER
NO.
MATERIAL
1 2
OF OF OF OF
OF
NODAL POINTS = 121 ELEMENTS = 100 INTERFACE ELEMENTS = 2 0 LOADING STEPS = 5
ITERATION CONSTRUCTION TYPE
1 1 1 1 1
GAMMA
24.00 20.00
REINFORCEMENT INSTALLATION HYDROSTATIC FORCE
SILT FORCE EARTHQUAKE FORCE OR DISPLACEME
SEEPAGE LINE VARIATION
COHESION PI TEN. STRGTH
0.00 0.00 0.00 0.00 35.00 0.00
K0
0.000 0.500
COORDINATES OF NODAL POINTS
NODAL POINT X-COORDINATE Y-COORDINATE
1 2 3 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 34 35 36 37 38 39 40 41 42 43
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.2O0 0.200 0.200 0.200 0.200 0.200 0.200
11.910 10.832 9.755 8.677 7.599 6.522 5.444 4.366 3.288 2.211
0.000 2.000 4 .000 6.000 8.000
10.000 12.000 14.000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000
10.000 12.000 14 .000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000
A53
RUNNING THE RSDAM PROGRAM APPENDIX F
44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
1.133 23.610 21.456 19.301 17.147 14.993 12.838 10.684 8.530 6.376 4.221 2.067 35.320 32.088 28.856 25.624 22.392 19.160 15.928 12.696 9.464 6.232 3.000 47.020 42.711 38.403 34.094 29.785 25.476 21.168 16.859 12.550 8.242 3.933 58.730 53.344 47.957 42.571 37.185 31.799 26.412 21.026 15.640 10.253 4.867 70.430 63.967 57.504 51.041 44.578 38.115 31.652 25.189 18.726 12.263 5.800 70.430 63.967 57.504 51.041 44.578 38.115 31.652 25.189 18.726 12.263 5.800 70.630 64.167 57.704 51.241
20.000 0.000 2.000 4.000 6.000 8.000
10.000 12.000 14.000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000
10.000 12.000 14.000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000 10.000 12.000 14 .000 16.000 18.000 20.000 0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000 0.000 2.000 4 .000 6.000 8.000
10.000 12.000 14 .000 16.000 18.000 20.000 0.000 2.000 4.000 6.000
A54
RUNNING THE RSDAM PROGRAM APPENDIX F
115 116 117 118 119 120 121
NO X OR Y MOVEMENT 111
44.778 38.315 31.852 25.389 18.926 12.463 6.000
1 1 23
8.000 10.000 12.000 14.000 16.000 18.000 20.000
34 45 56 67 78 89 100
ELEMENT DATA ELEMENT
1 2 3 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 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
I
23 24 25 26 27 28 29 30 31 32 100 101 102 103 104 105 106 107 108 109 12 13 14 15 16 17 18 19 20 21 34 35 36 37 38 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 56 57 58
J
24 25 26 27 28 29 30 31 32 33
101 102 103 104 105 106 107 108 109 110 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 46 47 48 49 50 51 52 53 54 55 57 58 59
K
13 14 15 16 17 18 19 20 21 22 90 91 92 93 94 95 96 97 98 99 2 3 4 5 6 7 8 9 10 11 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 42 43 44 46 47 48
L
12 13 14 15 16 17 18 19 20 21 89 90 91 92 93 94 95 96 97 98 1 2 3 4 5 6 7 8 9 10 23 24 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 43 45 46 47
MATERIAL
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
A55
RUNNING THE RSDAM PROGRAM APPENDIX F
54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
59 60 61 62 63 64 65 67 68 69 70 71 72 73 74 75 76 78 79 80 81 82 83 84 85 86 87 89 90 91 92 93 94 95 96 97 98 111 112 113 114 115 116 117 118 119 120
60 61 62 63 64 65 66 68 69 70 71 72 73 74 75 76 77 79 80 81 82 83 84 85 86 87 88 90 91 92 93 94 95 96 97 98 99 112 113 114 115 116 117 118 119 120 121
49 50 51 52 53 54 55 57 58 59 60 61 62 63 64 65 66 68 69 70 71 72 73 74 75 76 77 79 80 81 82 83 84 85 86 87 88
101 102 103 104 105 106 107 108 109 110
48 49 50 51 52 53 54 56 57 58 59 60 61 62 63 64 65 67 68 69 70 71 72 73 74 75 76 78 79 80 81 82 83 84 85 86 87
100 101 102 103 104 105 106 107 108 109
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1
*************************************************** STAGE NUMBER 1
THE FOLLOWING 10 REINFORCEMENTS ARE ADDED HEREIN
REINFORCEMENT NUMBER I J
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9
10
111 112 113 114 115 116 117 118 119 120
A56
RUNNING THE RSDAM PROGRAM APPENDIX F
STRESSES VALUES FOR STAGE 1
ELEM X Y SIGMA SIGMA TAU SIGMA SIGMA NO X Y XY 1 3
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
0 0 0 0 0 0 0 0 0 0 5 5 4 4 3 3 2 2 1 0
16 15 13 12 10 8 7 5 4 2
28 25 22 20 17 14 11 9 6 3
39 35 31 27 24. 20. 16, 12. 9. 5.
50. 45. 40. 35. 31. 26. 21. 16. 11. 6.
61. 55. 49. 43. 37. 31.
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.79
.25
.71
.17
.63
.09
.55
.01
.47
.94
.95
.34
.72
.10
.49
.87
.26
.64
.02
.41
.12
.43
.73
.04
.35
.65
.96
.27
.57
.88
.28
.51
.74
.97 ,20 ,43 ,66 ,89 ,12 ,35 ,45 ,60 76 .91 06 21 37 52 67 82 62 69 77 84 92 99
1. 3, 5, 7, 9.
11, 13. 15. 17. 19. 1. 3. 5. 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1. 3 5 7 9
11 13, 15 17, 19, 1. 3. 5, 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11.
.00 ,00 .00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 00 ,00 00 .00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 8 7 5 3 1 1 1 1 1 9 8 6 4 3 1 1 1 9 8 7 6 5 3 2 1 8 7 6 6 5 4 3. 2 1 9 5. 4 4. 3, 3, 2. 2. 1, 1. 3, 1. 1. 1. 1. 1. 8.
.000E+00
.OOOE+00
.000E+00
.000E+00
.OOOE+00
.000E+00
.000E+00
.000E+00
.OOOE+00
.000E+00 •913E+02 .678E+02 .463E+02 .272E+02 .072E+02 .925E+01 .059E+01 .298E+01 .366E+01 .280E+01 .533E+02 .456E+02 .309E+02 .154E+02 .914E+01 .153E+01 .423E+01 .709E+01 .158E+01 .623E+01 .180E+02 .064E+02 .877E+01 .894E+01 .865E+01 .725E+01 .364E+01 .918E+01 .523E+01 .463E+01 .733E+01 .758E+01 .788E+01 .059E+01 .337E+01 .698E+01 .984E+01 .979E+01 .849E+01 .250E+00 .405E+01 .861E+01 .273E+01 .650E+01 .103E+01 .605E+01 .276E+01 .911E+01 209E+01 822E+00 888E+01 697E+01 514E+01 316E+01 079E+01 369E+00
0 0 0 0 0 0 0 0 0 0 3 3 2 2 2 1 1 1 6 2 3 2 2 2 1 1 1 9 6 3 2 2 1 1 1 1 1 7 5 2 1 1 1 1 1. 9 7. 5 3, 1 1. 9 8, 7. 6, 5 4, 3, 2. 7, 3. 3, 3. 2, 2. 1.
.OOOE+00
.000E+00
.000E+00
.000E+00
.OOOE+00
.000E+00
.OOOE+00
.000E+00
.OOOE+00
.000E+00
.826E+02
.356E+02
.926E+02
.543E+02
.145E+02
.785E+02
.412E+02
.060E+02
.733E+01
.560E+01
.065E+02
.913E+02
.618E+02
.307E+02
.983E+02
.631E+02
.285E+02
.417E+01
.315E+01
.245E+01
.359E+02
.128E+02
.975E+02
.779E+02
.573E+02
.345E+02
.073E+02
.836E+01
.045E+01
.926E+01
.747E+02
.552E+02
.358E+02
.212E+02 , 067E+02 .396E+01 ,969E+01 .957E+01 .697E+01 .850E+01 ,081E+02 .722E+01 .547E+01 ,301E+01 .207E+01 .211E+01 .552E+01 .822E+01 417E+01 ,644E+00 776E+01 395E+01 029E+01 632E+01 158E+01 674E+01
0 0 0 0 0. 0 0 0. 0. 0, 0, 0, 0. 0. 0, 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 0. 0. 0. 0. 0. 0. 0 0. 0. 0. 0. 0 0, 0. 0 0, 0 0, 0, 0. 0. 0. 0. 0 0, 0, 0, 0. 0, 0 0, 0 0, 0, 0, 0,
•O00E+00 •000E+00 .000E+00 .000E+00 .000E+00 .000E+00 .000E+00 .OOOE+00 ,000E+00 .000E+00 .000E+00 .000E+00 ,000E+00 .000E+00 .000E+00 .000E+00 .000E+00 .000E+00 .OOOE+00 .000E+00 ,000E+00 .000E+00 ,000E+00 .000E+00 .000E+00 .000E+00 .000E+00 .000E+00 .OOOE+00 .000E+00 .000E+00 •000E+00 .000E+00 •000E+00 •000E+00 .OOOE+00 •000E+0O .OOOE+00 .OOOE+00 •000E+00 •000E+00 .OOOE+00 •OO0E+00 •000E+00 •000E+00 •OOOE+00 .OOOE+00 •OOOE+OO •000E+00 •000E+00 •000E+00 •000E+00 •000E+00 .OOOE+00 •000E+00 .OOOE+00 .000E+00 .OOOE+00 •000E+00 •000E+O0 .000E+00 .000E+00 OOOE+00 .000E+00 .000E+00 .000E+00
0 0 0 0 0. 0 0. 0 0 0 3 3. 2. 2 2. 1 1. 1 6 2 3 2 2. 2 1. 1 1. 9. 6. 3 2 2 1 1. 1. 1 1. 7 5. 2 1. 1 1 1 1. 9 7 5 3 1 1 9 8 7 6 5 4 3 2 7 3 3 3 2 2 1
.000E+00
.000E+00
.000E+00
.000E+00
.000E+00
.000E+00
.000E+00 •OOOE+00 •000E+O0 •OOOE+00 •826E+02 •356E+02 •926E+02 •543E+02 •145E+02 •785E+02 •412E+02 •060E+02 •733E+01 •560E+01 •065E+02 .913E+02 •618E+02 •307E+02 •983E+02 .631E+02 .285E+02 •417E+01 •315E+01 .245E+01 •359E+02 .128E+02 •975E+02 .779E+02 .573E+02 •345E+02 •073E+02 .836E+01 .045E+01 .926E+01 .747E+02 •552E+02 .358E+02 .212E+02 .067E+02 .396E+01 .969E+01 .957E+01 .697E+01 .850E+01 .081E+02 .722E+01 .547E+01 . 301E+01 .207E+01 .211E+01 .552E+01 .822E+01 .417E+01 .644E+00 .776E+01 .395E+01 .029E+01 .632E+01 .158E+01 .674E+01
0 0 0 0 0. 0 0. 0, 0. 0. 1. 1. 1. 1. 1. 8. 7. 5, 3. 1, 1. 1. 1, 1. 9. 8, 6. 4. 3. 1, 1. 1. 9, 8, 7, 6 5. 3 2. 1 8. 7. 6. 6. 5 4 3 2 1 9 5 4 4 3 3 2 2 1 1 3 1 1 1 1 1 8
•000E+00 •000E+00 •000E+00 .000E+00 •000E+00 •000E+00 .000E+00 •000E+00 .000E+00 •000E+00 .913E+02 •678E+02 463E+02 •272E+02 .072E+02 .925E+01 059E+01 .298E+01 366E+01 .280E+01 533E+02 .456E+02 309E+02 .154E+02 914E+01 .153E+01 .423E+01 •709E+01 158E+01 •623E+01 •180E+02 .064E+02 •877E+01 •894E+01 .865E+01 •725E+01 •364E+01 .918E+01 •523E+01 •463E+01 •733E+01 .758E+01 •788E+01 .059E+01 .337E+01 .698E+01 .984E+01 .979E+01 .849E+01 .250E+00 .405E+01 . 861E+01 .273E+01 .650E+01 .103E+01 .605E+01 .276E+01 .911E+01 .209E+01 .822E+00 .888E+01 .697E+01 .514E+01 .316E+01 .079E+01 .369E+00
A57
RUNNING THE RSDAM PROGRAM APPENDIX F
87 88 89 90 91 92 93 94 95 96 97 98 99 100
26. 20. 14, 8
67, 60, 54 47 41 34 28 22 15 9
,07 .15 .22 .30 .30 .84 .37 .91 .45 .98 .52 .06 .59 .13
13. 15. 17. 19. 1. 3. 5. 7. 9
11. 13 15 17 19
.00 00 .00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00
6. 6. 6.
-1. 0. 0 0 0. 0 0 0 0 0 0
108E+00 077E+00 .795E+00 .516E+O0 •OOOE+00 •OOOE+00 •OOOE+00 •000E+00 .OOOE+00 .OOOE+00 .000E+00 .000E+00 .OOOE+00 .OOOE+00
1, 1. 1. -3 0 0 0 0. 0 0 0 0 0 0
222E+01 215E+01 •359E+01 •032E+00 •000E+00 •OOOE+00 .000E+00 .000E+00 .OOOE+00 .000E+00 .000E+00 .OOOE+00 .OOOE+00 .000E+00
0. 0. 0, 0. 0. 0. 0 0 0 0. 0 0 0 0
.000E+00 000E+00 .000E+00 , OOOE+00 .OOOE+00 .000E+00 .OOOE+00 .OOOE+00 .000E+00 .OOOE+00 .OOOE+00 .OOOE+OO •000E+00 .OOOE+00
1 1 1 -1 0 0. 0 0 0 0 0 0 0 0
.222E+01
.215E+01 •359E+01 •516E+O0 •000E+00 .OOOE+00 .000E+00 .OOOE+00 .OOOE+00 .OOOE+00 .OOOE+00 .000E+00 .OOOE+00 .OOOE+00
6, 6. 6,
-3. 0. 0. 0 0. 0 0. 0 0 0 0
108E+00 077E+00 795E+00 •032E+00 .OOOE+00 •OOOE+00 .OOOE+00 •000E+00 .OOOE+00 •000E+00 .OOOE+00 .OOOE+00 .000E+00 .OOOE+00
INTERFACE ELEMENT RESULTS FOR STAGE
EM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
NO X
0. 0. 0. 0. 0. 0. 0. 0 0. 0
67 60 54 47 41 34 28 21 15 9
.20
.20
.20 ,20 .20 .20 .20 .20 .20 .20 .20 .74 .27 .81 .35 .88 .42 .96 .49 .03
Y
1. 3. 5. 7. 9,
11. 13. 15, 17, 19, 1 3, 5 7 9 11 13 15 17 19
NORMAL STRESS SHEAR
00 00 ,00 .00 .00 .00 ,00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
7, 0, 0 2 , 0 1 0 4 0. 4 8 1 1 1 1 1 1 1 7 1
823E+00 .000E+00 .OOOE+00 •049E+00 •000E+00 .257E+00 .OOOE+00 .657E-01 .000E+00 .657E-02 .513E-01 .524E+00 .243E+00 .478E+00 .350E+00 .187E+00 .676E+00 .676E+00 .451E-01 .304E+00
0. 0. 0, 0 . 0, 0. 0. 0. 0. 0 0 0. 0
o. 0 0 0 0 0 0
STRESS
000E+00 000E+00 .OOOE+00 000E+00 .000E+00 .OOOE+00 .OOOE+00 •000E+00 •OOOE+00 .000E+00 •OOOE+00 •000E+00 .OOOE+00 •OOOE+00 .OOOE+00 .OOOE+00 .000E+00 .OOOE+00 .OOOE+00 .OOOE+00
NORMAL STIFF
1. 1. 1. 1. 1. 1. 1 1. 1. 1 1 1 1 1 1 1 1 1 1 1
000E+08 000E+02 .000E+02 OOOE+08 .000E+02 .000E+08 .000E+02 .OOOE+08 •000E+02 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .000E+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08
SHEAR STIFF
4. 1, 1. 4. 1 4 1 4 1. 4 4 4 4 4 4 4 4 4 4 4
OOOE+03 .OOOE+02 .000E+02 .000E+03 .000E+02 .000E+03 .000E+02 .000E+03 .000E+02 .000E+03 .000E+03 .000E+03 .00OE+O3 .000E+03 .OOOE+03 .000E+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03
REINFORCEMENT RESULTS FOR STAGE 1
REIN. NUM.
1 2 3 4 5 6 7 8 9
10
I
1 2 3 4 5 6 7 8 9
10
J
111 112 113 114 115 116 117 118 119 120
TYPE COMPR FORCE
1 0.000000E+0Q 1 0.O0O0OOE+OO 1 0.000000E+00 1 0.OOO0OOE+O0 1 O.OOOOOOE+00 1 0.0O000OE+O0 1 0.000000E+00 1 0.OOOOO0E+00 1 0.00O0O0E+O0 1 O.OOOOOOE+00
INCR COMPR
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
OOE+00 00E+00 OOE+00 OOE+00 00E+00 00E+00 OOE+00 00E+00 OOE+00 OOE+00
STIFFNESS
6.7500 6.7500 6.7500 6.7500 6.7500 6.7500 6.7500 6.7500 6.7500 6.7500
00E+05 OOE+05 00E+05 OOE+05 OOE+05 00E+05 00E+05 OOE+05 OOE+05 OOE+05
A58
RUNNING THE RSDAM PROGRAM APPENDIX F
*************************************************** STAGE NUMBER 2
FORCE AND/OR DISPLACEMENT LOADING IS SPECIFIED FOR THIS STAGE
NODE
111 113 115 117 119 121
-2. -3. -2 -1 -8 0
X-LOAD
. 00000E + 02
.20000E+02
.40000E+02
.60000E+02
.00000E+01
.OOOOOE+OO
-6. -1. -7. -5 -2 0
Y-LOAD
. 50000E+02
.00000E+03
.80000E+02
.20000E+02
.60000E+02
.00000E+00
NODE
112 114 116 118 120
0
-3. -2. -2. -1 -4 0.
X-LOAD
.60000E+02
.80000E+02
.0OO00E+02
.20000E+02
.OOO00E+01
.OOOOOE+00
-1 -9 -6. -3 -1 0
Y-LOAD
.20000E+03
.00000E+02
.50000E+02
.90000E+02
.30000E+02
.00000E+00
DISPLACEMENT RESULTS FOR STAGE 2
NODAL POINT
1 2 3 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 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
X
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20
11.91 10.83 9.75 8.68 7.60 6.52 5.44 4.37 3.29 2.21 1.13
23.61 21.46 19.30 17.15 14.99 12.84
Y
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00
TOTAL UX
0.00000E+00 -9.66641E-03 -2.25790E-02 -3.06625E-02 -3.78562E-02 -4.33966E-02 -4.72485E-02 -4.93257E-02 -4.98057E-02 -4.87903E-02 -4.86997E-02 0.00000E+00 -9.65705E-03 -2.25741E-02 -3.06547E-02 -3.78522E-02 -4.33936E-02 -4.72473E-02 -4.93254E-02 -4.98057E-02 -4.87909E-02 -4.86996E-02 0.00000E+00
-9.65728E-03 -1.97643E-02 -3.06544E-02 -3.78521E-02 -4.33935E-02 -4.72472E-02 -4.93253E-02 -4.98057E-02 -4.87910E-02 -4.86996E-02 0.OOOOOE+00
-9.95573E-03 -2.02009E-02 -2.90837E-02 -3.77028E-02 -4.41208E-02 -4.85027E-02 -5.08358E-02 -5.11112E-02 -4.98042E-02 -4.84247E-02 0.OOOOOE+00
-1.25726E-02 -2.21393E-02 -3.09764E-02 -3.84480E-02 -4.51733E-02
TOTAL UY
0.OOOOOE+00 -1.22706E-03 -9.08989E-04 -1.24448E-03 -1.27741E-03 -1.38915E-03 -1.30659E-03 -1.30794E-03 -1.17737E-03 -1.15954E-03 -1.25621E-03 0.00OOOE+00 6.55410E-04
-1.85596E-04 -3 .63533E-04 -7.14513E-04 -8.49476E-04 -1.07506E-03 -1.12469E-03 -1.26667E-03 -1.26971E-03 -1.16573E-03 0.00000E+00 -2.39635E-03 -4.06288E-03 -4.74494E-03 -4.89627E-03 -4.46839E-03 -3.63578E-03 -2.72890E-03 -1.69778E-03 -9.93194E-04 -9.81562E-04 0.OOOOOE+00 9.01700E-06 -2.03284E-04 -9.70777E-04 -1.91997E-03 -2.62305E-03 -2.94632E-03 -2.71885E-03 -2.08639E-03 -1.03563E-03 -3.70832E-04 0.O0O0OE+O0 -2.76861E-03 -4.24053E-03 -4.75471E-03 -4.87349E-03 -4.89617E-03
PORE PRESS 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A59
RUNNING THE RSDAM PROGRAM APPENDIX F
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121
10. 8. 6. 4. 2.
35. 32. 28. 25. 22. 19. 15. 12. 9. 6. 3 .
47. 42, 38. 34. 29. 25. 21. 16. 12 8 3 58 53 47 42 37 31 26 21 15 10 4
70 63 57 51 44 38 31 25 18 12 5
70 63 57 51 44 38 31 25 18 12 5
70 64 57 51 44 38 31 25 18 12 6
68 53 38 22 07 32 09 86 62 39 16 93 70 46 23 00 02 .71 .40 ,09 ,79 ,48 .17 ,86 .55 .24 .93 .73 .34 .96 .57 .18 .80 .41 .03 .64 .25 .87 .43 .97 .50 .04 .58 .11 .65 .19 .73 .26 .80 .43 .97 .50 .04 .58 .11 .65 .19 .73 .26 .80 .63 .17 .70 .24 .78 .31 .85 .39 .93 .46 .00
12. 14. 16. 18. 20. 0. 2. 4. 6. 8.
10. 12. 14. 16. 18. 20. 0. 2. 4. 6. 8.
10. 12. 14. 16. 18, 20. 0. 2. 4. 6. 8.
10. 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8
10 12 14 16 18 20 0 2 4 6 8
10 12 14 16 18 20
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .00 00 .00 .00 ,00 .00 .00 .00 .00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
-4. -5. -5. -5. -4. 0.
-1. -2. -3. -4. -4. -5. -5. -5. -5. -4. 0.
-1. -2. -3. -4, -4 -5. -5. -5 -5 -4 0
-9 -2 -3 -4 -4 -5 -5 -5 -5 -4 0
-8 -2 -3 -3 -4 -4 -5 -5 -4 -4 0
-1 -2 -3 -3 -4 -4 -4 -4 -4 -4 0
-9 -2 -3 -3 -4 -4 -4 -4 -4 -4
99906E-02 25863E-02 28276E-02 09024E-02 83737E-02 00000E+00 28875E-02 45714E-02 33215E-02 05170E-02 61660E-02 08548E-02 36319E-02 38874E-02 16189E-02 84485E-02 00O00E+O0 •30506E-02 •44252E-02 •45416E-02 •19100E-02 •72777E-02 •09291E-02 .35281E-02 .40132E-02 .15180E-02 •84739E-02 •00000E+00 .19290E-03 •18989E-02 .29591E-02 .16002E-02 .71757E-02 .05278E-02 .22017E-02 .29021E-02 .07735E-02 .81074E-02 .OOOOOE+00 .61350E-03 .20175E-02 .11377E-02 .85978E-02 .43546E-02 .81436E-02 .01491E-02 .06764E-02 .99556E-02 .72268E-02 .OOOOOE+00 .00216E-02 .26582E-02 .08441E-02 .80129E-02 .35467E-02 .73717E-02 .94188E-02 .98763E-02 .88108E-02 .62745E-02 .OOOOOE+00 .70039E-03 .25526E-02 .07110E-02 .78746E-02 .34164E-02 .72559E-02 .93277E-02 .98066E-02 .87788E-02 .62688E-02
-4. -3. -2. -1. -2. 0.
-4. -8. -1. -1. -1. -9. -7. -5. -2. -2. 0.
-7. -1. -1. -1. -1. -1. -1. -9, -4. -4. 0.
-1, -2. -2 . -2 -2. -2 -2 -1 -7 -1 0
-1 -2 -3 -4 -4 -3 -3 -2 -1 -2 0
-1 -2 -3 -4 -4 -3 -3 -2 -1 -2 0
-9 -2 -3 -4 -4 -3 -3 -2 -1 -2
53903E-03 82648E-03 64485E-03 27354E-03 72025E-04 0O000E+00 86885E-03 54078E-03 06540E-02 12751E-02 07864E-02 69127E-03 69882E-03 14939E-03 33852E-03 31698E-04 00000E+00 67479E-03 35124E-02 74231E-02 91577E-02 88400E-02 68891E-02 39573E-02 .53121E-03 62503E-03 .66477E-04 .OOOOOE+00 .13967E-02 .03076E-02 •60613E-02 .88770E-02 .88405E-02 .62180E-02 .16085E-02 .57274E-02 .90649E-03 .18001E-03 .OOOOOE+00 .08538E-02 .57712E-02 .64069E-02 .17358E-02 .21101E-02 .84662E-02 .16737E-02 .27137E-02 .25233E-02 .11478E-03 .00000E+00 .04194E-02 .55744E-02 .64992E-02 .19180E-02 .23611E-02 .87059E-02 .19003E-02 .29617E-02 .28778E-02 .40937E-03 .OOOOOE+00 .95582E-03 .51590E-02 .62534E-02 .18383E-02 .24221E-02 .88787E-02 .21539E-02 .32645E-02 .32006E-02 .73496E-03
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 .00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A60
RUNNING THE RSDAM PROGRAM APPENDIX F
STRESSES VALUES FOR STAGE 2
3LEM NO
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
0 0 0 0 0 0 0 0 0 0 5 5 4 4 3 3 2 2 1 0
16 15 13 12 10 8 7 5 4 2
28 25 22 20 17 14 11. 9 6. 3.
39. 35. 31. 27. 24, 20. 16. 12. 9. 5.
50. 45. 40. 35. 31. 26. 21. 16. 11. 6.
61. 55. 49. 43. 37. 31.
X
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.79
.25
.71
.17
.63
.09
.55
.01
.47
.94
.95
.34
.72
.10
.49
.87
.26
.64
.02
.41
.12
.43
.73
.04
.35
.65
.96
.27
.57
.88
.28
.51
.74
.97 ,20 .43 ,66 ,89 ,12 35 45 60 76 91 06 21 37 52 67 82 62 69 77 84 92 99
1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13, 15 17, 19 1. 3 5, 7. 9,
11. 13, 15. 17. 19. 1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11.
Y
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00 ,00 .00 ,00 ,00 .00 .00 .00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
3 -8 1
-1 -5 -4 -2 -3 1 1 2 1 1 1 1 9 7 5 3 1 1 1 1 1 1 9 7 5 3 1 1 1 1 1 1 9 7 5 3 1 1 1 1. 1. 9. 8, 6. 4, 2, 9. 1. 1. 1. 1. 9. 7. 6. 4. 2. 4. 1. 1. 1. 1. 8. 7.
SIGMA X
.425E+01
.259E+00
.207E+00
.516E+01
.698E+00
.660E+00
.515E+00
.660E-01
.669E+00
.983E+00
.057E+02
.784E+02
.501E+02
.274E+02
.080E+02
.027E+01
.243E+01
.504E+01
.655E+01
.412E+01
.760E+02
.696E+02
.534E+02
.345E+02
.140E+02
.354E+01
.357E+01
.391E+01
.545E+01
.708E+01
.649E+02
.491E+02
.383E+02
.240E+02
.084E+02
.091E+01
.128E+01
.096E+01
.098E+01
.493E+01
.609E+02
.438E+02 •266E+02 •127E+02 •800E+01 •343E+01 .774E+01 .840E+01 .754E+01 .495E+00 534E+02 .382E+02 238E+02 077E+02 234E+01 659E+01 189E+01 663E+01 542E+01 747E+00 102E+02 260E+02 204E+02 062E+02 818E+01 046E+01
3 3 3 2 1 9 3 7 -9 -4 4 3 2 2 2 1 1 1 6 2 3 3 2 2 2 1 1 9 6 3 3 2 2 2 1 1 1 8 5. 2 2 2 2, 1, 1, 1, 1, 8. 4. 1. 2. 2, 1. 1. 1. 1. 9. 7. 4. 1. 1. 1. 1. 1. 1. 9.
SIGMA Y
.807E+02
.384E+02
.346E+02
.462E+02
.592E+02
.194E+01
.256E+01
.324E+00
.207E+00
.274E+00
.035E+02
.500E+02
.995E+02
.571E+02
.146E+02
.767E+02
.389E+02
.033E+02
.606E+01
.529E+01
.363E+02
.200E+02
.887E+02
.539E+02
.161E+02
.754E+02
.355E+02
.678E+01
.228E+01
.078E+01
.012E+02
.690E+02
.466E+02
.204E+02
.934E+02
.633E+02 •274E+02 •994E+01 •435E+01 .757E+01 .744E+02 .441E+02 •127E+02 •872E+02 •623E+02 •396E+02 •152E+02 •275E+01 •790E+01 900E+01 399E+02 .171E+02 919E+02 643E+02 390E+02 150E+02 506E+01 425E+01 332E+01 185E+01 486E+02 660E+02 589E+02 424E+02 202E+02 760E+01
1 -5 3 -1 1
-1 1 5 -9 3 2 2 2 1 1 7 3 1 -8 -8 3 2 2 2 1 1 5 2 -4 -1 2 2. 2 1. 1 1 7. 3 2. -1 2. 2. 1. 1. 1 1. 7 . 3 . 2.
-1. 1, 1. 1, 1. 9. 6. 4. 2 .
-3, -1. 7. 1, 9, 7, 6. 4.
TAU XY
.299E+02
.963E+01
.144E+01
.228E+01
.458E+01
.673E+00
.971E+00
.418E+00
.227E+00
.925E+00
.799E+01
.608E+01
.285E+01
.651E+01
.145E+01
.410E+00
.856E+00
.038E+00
.889E-01
.505E-01
.041E+01
.771E+01
.412E+01
.055E+01 •565E+01 .054E+01 .962E+00 .107E+00 .740E-01 .106E+00 .940E+01 .501E+01 .202E+01 .889E+01 .579E+01 .205E+01 •786E+00 .587E+00 .479E-01 .231E+00 •574E+01 •249E+01 .870E+01 .569E+01 •285E+01 •016E+01 •187E+00 .709E+00 •223E-01 .288E+00 .611E+01 •660E+01 506E+01 .208E+01 .363E+00 .926E+00 731E+00 479E+00 .099E-01 716E+00 708E+00 154E+01 719E+00 909E+00 009E+00 600E+00
4 3 3 2 1 9 3 1 6 3 4 3 3 2 2 1 1 1 6 2. 3 3. 2 2. 2. 1 1 9 6. 3 3 2. 2. 2 1 1 1. 9 5 2 2 2 2 1. 1. 1. 1 8 4 1 2. 2 1. 1 1 1. 9 7. 4 1 1 1 1. 1 1 9
SIGMA 1
.240E+02
.484E+02
.375E+02
.467E+02
. 605E+02
.197E+01
.268E+01
.012E+01
.942E+00
.874E+00
.074E+02
.539E+02
.029E+02
.591E+02
.158E+02
.773E+02
.391E+02
.033E+02
.609E+01 •536E+01 .419E+02 .250E+02 •929E+02 .573E+02 •184E+02 .767E+02 •361E+02 •689E+01 •229E+01 .087E+01 .072E+02 .740E+02 •509E+02 .239E+02 .962E+02 .653E+02 .285E+02 •027E+01 .435E+01 .768E+01 .799E+02 .489E+02 .166E+02 .904E+02 .647E+02 •414E+02 •163E+02 •315E+01 •790E+01 •917E+01 •428E+02 .204E+02 •951E+02 •668E+02 .408E+02 •162E+02 •573E+01 •447E+01 .333E+01 •225E+01 . 501E + 02 .691E+02 •612E+02 .440E+02 .213E+02 .836E+01
-9 -1 -1 -1 -6. -4 -2 -3. -1 -6. 2 1. 1. 1 1 8 7 5. 3 1, 1. 1. 1 1. 1. 9, 7. 5, 3. 1, 1. 1. 1. 1. 1. 8. 7, 5. 3, 1. 1, 1. 1. 1. 9. 8. 6. 4. 2 9 1. 1 1 1 9 7 6 4 2 4 1 1 1 1 8 6
SIGMA 3
.026E+00
.823E+01
.733E+00
.573E+01
.978E+00
.689E+00
.626E+00
.164E+00
.448E+01
.165E+00
.019E+02 •745E+02 •466E+02 .253E+02 067E+02 •964E+01 •221E+01 •501E+01 •652E+01 .406E+01 .705E+02 .647E+02 .493E+02 311E+02 116E+02 .220E+01 .301E+01 .381E+01 .545E+01 .699E+01 •588E+02 441E+02 •340E+02 •204E+02 •055E+02 •896E+01 022E+01 •063E+01 098E+01 •481E+01 •553E+02 •390E+02 •227E+02 •096E+02 •553E+01 •165E+01 •667E+01 •801E+01 .754E+01 •324E+00 •505E+02 .348E+02 .206E+02 .052E+02 .053E+01 .538E+01 .123E+01 .641E+01 •542E+01 .354E+00 .087E+02 .229E+02 .181E+02 .046E+02 .709E+01 .970E+01
A61
RUNNING THE RSDAM PROGRAM APPENDIX F
87 88 89 90 91 92 93 94 95 96 97 98 99
100
26 20 14 8. 67 60 54 47 41 34 28 22 15 9
.07 ,15 .22 ,30 .30 .84 .37 ,91 .45 .98 .52 .06 .59 .13
13 15, 17 19. 1 3. 5 7. 9
11. 13. 15 17. 19
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
5 3 2
-2 -1 -2 -1 -1 -1 -1 -1 -1 -6 -2
.317E+01
.903E+01
.684E+01
.82OE+O0 •294E+03 .624E+03 •543E+03 .800E+03 .792E+03 .647E+03 .394E+03 .090E+03 .941E+02 •581E+02
7 5 4 3 3 6 4
-1 -1 -1 -1 -1 -1 -5
.541E+01
.845E+01
.347E+01
.446E+00
.188E+03
.170E+02
.195E+01
.323E+02
.734E+02
.802E+02
.858E+02
.733E+02
.289E+02
.211E+01
3 1
-3 -2 1 7 5 6 5 5 4 3 2 5
.286E+00
.579E+00
.548E-01
.423E+00
.225E+03
.571E+02
.262E+02
.011E+02
.752E+02
.339E+02
.421E+02
.398E+02
.285E+02
.756E+01
7 5 4 4 3 7 2 6 1
-6 -4 -6 -4 -3
.589E+01
.858E+01
.348E+01
.274E+00
.502E+03
.851E+02
.007E+02 •176E+01 .016E+01 .449E+00 .129E+01 .104E+01 .807E+01 .712E+01
5 3 2
-3 -1 -2. -1 -1 -1. -1 -1. -1 -7. -2.
•27OE+01 .890E+01 •683E+01 . 647E+00 •607E+03 .793E+03 .702E+03 .994E+03 .976E+03 .821E+03 .538E+03 .202E+03 .749E+02 •731E+02
INTERFACE ELEMENT RESULTS FOR STAGE 2
ELEM NO X Y NORMAL STRESS SHEAR STRESS NORMAL STIFF SHEAR STIFF
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20
0 0. 0 0. 0 0
o. o. 0 0 67 60. 54 47 41. 34 28. 21. 15. 9.
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.74
.27
.81
.35
.88
.42
.96
.49
.03
1 3 5 7 9
11. 13 15. 17 19 1. 3. 5 7 9. 11 13 15 17, 19,
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
1 0 0 0 0 0 0 2. 7 2 6 1. 1 1 1 9 7. 5 3. 8.
•914E+01 •000E+00 .000E+00 .000E+00 .OOOE+00 •000E+00 .000E+00 .794E-01 .264E-06 .841E+00 .376E+01 .348E+02 .395E+02 .287E+02 .109E+02 .078E+01 .134E+01 .234E+01 .343E+01 .941E+00
-6 0 0 0 0 0 0
-4 -7 9 2 4 7
-1 -2 -3 -3 -3 -4 -4
.104E+00 •000E+00 .000E+00 .000E+00 .000E+00 •000E+00 .OOOE+00 •071E+00 .729E-03 .214E-01 .947E+00 .288E+00 .248E-01 .841E+00 .917E+00 .309E+00 •146E+00 .205E+00 .072E+00 .390E+00
1 1. 1 1. 1 1 1 1. 1 1. 1 1 1 1 1 1 1 1 1 1
.000E+08 •000E+02 •000E+02 .000E+02 .000E+02 •000E+02 .000E+02 .OOOE+08 .OOOE+08 .000E+08 •OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .000E+08 .000E+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08
4. 1. 1 1 1 1. 1 1. 1 4 4 4 4 4 4 4 4 4 4 4
.OOOE+03
.000E+02 •000E+02 .000E+02 . 000E + 02 •00OE+02 •000E+02 •OOOE+02 •000E+02 •000E+03 .OOOE+03 •000E+03 .OOOE+03 .000E+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03
REINFORCEMENT RESULTS FOR STAGE 2
REIN. NUM. I J TYPE COMPR FORCE INCR COMPR STIFFNESS
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9
10
111 112 113 114 115 116 117 118 119 120
1 1 1 1 1 1 1 1 1 1
0 2 -1 3 1 1 4 1 6
-7
. OOOOOOE + 00
.293917E+01
.781573E+01
.272714E+01
.238929E+01
.338003E+01
.986394E+00
.327693E+00
.361865E-01
.737335E+00
0 3. -2 4 1 1 7 1 9
-1
.000000E+00
.398396E-05
. 639368E-05
.848465E-05
.835451E-05
.982227E-05
.387251E-06 •966953E-06 .424984E-07 •146272E-05
6 6 6 6 6 6 6 6 6 6
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
A62
RUNNING THE RSDAM PROGRAM APPENDIX F
*************************************************** STAGE NUMBER 3
FORCE AND/OR DISPLACEMENT LOADING IS SPECIFIED FOR THIS INCREMENT
NODE X-LOAD Y-LOAD NODE X-LOAD Y-LOAD
111 113 115 117 119 121
-2. -2. 0 0, 0. 0.
•90000E+01 •00000E+01 .00000E+00 •00000E+00 •OOOOOE+00 .00000E+00
-3. -2 0. 0 0 0
•50000E+02 .30000E+02 .00000E+00 •OOOOOE+00 .00000E+00 .OOOOOE+00
112 114 116 118 120 0
-3. 0 0. 0. 0 0.
•90000E+01 .00000E+00 •OOOOOE+00 •00000E+00 •00000E+00 •00000E+00
-4. 0 0 0. 0 0.
.70000E+02
.00O00E+O0
.OOOOOE+00 •OOOOOE+00 .OOOOOE+00 •O0000E+O0
DISPLACEMENT RESULTS FOR STAGE 3
NODAL POINT
1 2 3 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 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
X
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o. o. o.
11. 10, 9. 8. 7. 6. 5. 4. 3, 2. 1.
23. 21. 19. 17, 14. 12.
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20
.20 ,20 .20 .91 .83 .75 ,68 .60 ,52 .44 .37 .29 .21 .13 .61 .46 30 .15 99 84
Y
0 2 4 6 8
10 12 14 16 18 20 0 2 4 6 8
10 12. 14 16 18. 20 0. 2. 4 6. 8,
10. 12, 14. 16. 18, 20, 0, 2. 4. 6. 8.
10. 12. 14. 16. 18. 20. 0. 2. 4. 6. 8.
10.
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00 ,00 ,00 .00 ,00 .00 ,00 .00 ,00 .00 ,00 ,00 00 .00 .00 00 .00 00 00 .00 00 00 00 00 00 .00 00 00
0 -9 -2 -3 -3 -4 -4 -4 -4 -4 -4 0
-9 -2 -3 -3 -4 -4 -4 -4 -4 -4 0
-9 -1 -3. -3 -4 -4 -4 -4. -4. -4 0.
-1. -2 -2. -3. -4. -4, -5. -5, -4, -4. 0,
-1, -2. -3, -3. -4.
TOTAL UX
.00000E+00
.29390E-03
.19444E-02
.01371E-02
.74785E-02
.31643E-02
.71013E-02
.92201E-02
.97055E-02
.86902E-02 •86042E-02 .00OOOE+00 •28491E-03 •19394E-02 .01294E-02 .74745E-02 •31613E-02 .71000E-02 .92197E-02 .97056E-02 .86908E-02 .86040E-02 .OOOOOE+00 .28519E-03 .96293E-02 .05217E-02 .77371E-02 .32834E-02 .71404E-02 .92197E-02 .97056E-02 ,86909E-02 .86040E-02 .0OOO0E+O0 .00224E-02 ,00712E-02 ,89665E-02 .75792E-02 .40031E-02 83894E-02 07271E-02 .10059E-02 97033E-02 83290E-02 OOOOOE+00 24844E-02 20844E-02 08603E-02 83266E-02 50499E-02
0 -1 -9 -1 -1 -1 -1 -1 -1. -1 -1. 0, 6
-1. -3. -7 -8 -1. -1. -1. -1. -1 0
-2. -4 -4. -4. -4 -3. -2. -1. -9. -9 0 2. -1 -9 -1. -2 -2 -2 -2 -1 -3, 0
-2, -4, -4 -4. -4.
TOTAL UY
.OOOOOE+00
.18995E-03 •15243E-04 .24498E-03 .28584E-03 .38940E-03 . 30786E-03 .30355E-03 .17423E-03 .15420E-03 •25308E-03 .00000E+00 .21295E-04 •74961E-04 •58022E-04 .00258E-04 .42770E-04 .06666E-03 .12138E-03 .26153E-03 .26626E-03 .15984E-03 •OOOOOE+00 .36644E-03 .00443E-03 •69558E-03 •85242E-03 •43172E-03 .60508E-03 •70312E-03 .67655E-03 •77095E-04 •71149E-04 .OOOOOE+00 .10586E-05 .70920E-04 .31043E-04 •88057E-03 . 58690E-03 .91427E-03 .69032E-03 .06131E-03 •01416E-03 53036E-04 •OOOOOE+00 •77175E-03 .24640E-03 •74626E-03 •85546E-03 .87224E-03
PORE PRESS 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A63
RUNNING THE RSDAM PROGRAM APPENDIX F
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121
10. 8. 6. 4. 2.
35. 32. 28. 25. 22. 19. 15. 12. 9. 6. 3.
47. 42. 38. 34. 29. 25. 21. 16. 12. 8. 3.
58, 53 47. 42 37. 31 26 21 15 10 4
70 63 57 51 44 38 31 25 18 12 5
70 63 57 51 44 38 31 25 18 12 5
70 64 57 51 44 38 31 25 18 12 6
68 53 38 22 07 32 09 86 62 39 16 93 70 46 23 00 02 71 40 09 79 48 .17 .86 ,55 ,24 ,93 ,73 .34 .96 .57 .18 .80 .41 .03 .64 .25 .87 .43 .97 .50 .04 .58 .11 .65 .19 .73 .26 .80 .43 .97 .50 .04 .58 .11 .65 .19 .73 .26 .80 .63 .17 .70 .24 .78 .31 .85 .39 .93 .46 .00
12. 14. 16. 18. 20. 0. 2. 4. 6. 8.
10. 12. 14. 16. 18. 20. 0. 2. 4. 6. 8.
10, 12. 14, 16, 18, 20, 0. 2. 4. 6 8 10 12. 14 16 18 20 0 2 4 6 8
10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8
10 12 14 16 18 20
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .00 ,00 .00 ,00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
-4.98724E-02 -5.24739E-02 -5.27205E-02 -5.08004E-02 -4.82780E-02 0.OOOOOE+00 -1.28039E-02 -2.44456E-02 -3.32206E-02 -4.03993E-02 -4.60460E-02 -5.07354E-02 -5.35174E-02 -5.37782E-02 -5.15151E-02 -4.83529E-02 0.00000E+00 -1.31414E-02 -2.44302E-02 -3.44561E-02 -4.18091E-02 -4.71638E-02 -5.08136E-02 -5.34147E-02 -5.39039E-02 -5.14126E-02 -4.83777E-02 0.OOOOOE+00 -9.51986E-03 -2.20710E-02 -3.29632E-02 -4.15022E-02 -4.70628E-02 -5.04151E-02 -5.20924E-02 -5.27945E-02 -5.06686E-02 -4.80091E-02 0.OOOOOE+00 -9.02932E-03 -2.24031E-02 -3.10573E-02 -3.83935E-02 -4.41852E-02 -4.80221E-02 -5.00446E-02 -5.05730E-02 -4.98524E-02 -4.71282E-02 0.OOOOOE+00 -9.61286E-03 -2.20318E-02 -3.03283E-02 -3.76442E-02 -4.33172E-02 -4.72262E-02 -4.93128E-02 -4.97761E-02 -4.87106E-02 -4.61747E-02 0.OOOOOE+00 -9.31813E-03 -2.19202E-02 -3.01840E-02 -3.74979E-02 -4.31833E-02 -4.71092E-02 -4.92217E-02 -4.97068E-02 -4.86786E-02 -4.61691E-02
-4.51294E-03 -3.80039E-03 -2.61947E-03 -1.24981E-03 -2.51793E-04 0.00000E+00 -4.82731E-03 -8.49374E-03 -1.06176E-02 -1.12435E-02 -1.07579E-02 -9.66440E-03 -7.67385E-03 -5.12595E-03 -2.31563E-03 -2.10179E-04 0.OOOOOE+00 -7.57060E-03 -1.33447E-02 -1.72698E-02 -1.90489E-02 -1.87690E-02 -1.68428E-02 -1.39250E-02 -9 .50689E-03 -4 . 60414E-03 -4.45818E-04 0.OOOOOE+00 -1.18685E-02 -2 .04748E-02 -2.59546E-02 -2.87019E-02 -2.86998E-02 -2.61296E-02 -2 .15580E-02 -1.56973E-02 -7.88600E-03 -1.16161E-03 0.OOOOOE+00 -1.20427E-02 -2.72880E-02 -3.71329E-02 -4.18080E-02 -4.19582E-02 -3.83186E-02 -3.15888E-02 -2.26721E-02 -1.25009E-02 -2.10052E-03 0.OOOOOE+00 -1.18640E-O2 -2.74047E-02 -3.73599E-02 -4.20412E-02 -4 .22279E-02 -3.85657E-02 -3.18159E-02 -2.29191E-02 -1.28545E-02 -2 .39550E-03 0.OOOOOE + 00 -1.13540E-02 -2.70067E-02 -3.71466E-02 -4.19766E-02 -4.22920E-02 -3.87371E-02 -3.20679E-02 -2.32210E-02 -1.31769E-02 -2.72084E-03
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A64
RUNNING THE RSDAM PROGRAM APPENDIX F
STRESSES VALUES FOR STAGE 3
ELEM NO
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 5. 5. 4. 4. 3 , 3. 2. 2. 1, 0.
16. 15. 13. 12. 10 8 7 5 4 2
28 25 22 20 17 14 11 9 6 3
39 35 31 27 24 20 16 12 9 5
50 45 40 35 31 26 21 16 11 6 61 55 49 43 37 31
X
10 10 10 10 10 10 10 10 10 10 79 25 71 17 .63 .09 .55 .01 .47 .94 .95 .34 .72 .10 .49 .87 .26 .64 .02 .41 .12 .43 .73 .04 .35 .65 .96 .27 .57 .88 .28 .51 .74 .97 .20 .43 .66 .89 .12 .35 .45 .60 .76 .91 .06 .21 .37 .52 .67 .82 .62 .69 .77 .84 .92 .99
1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11. 13, 15, 17, 19. 1 3. 5 7 9
11 13. 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7 9 11 13 15 17 19 1 3 5 7 9
11
Y
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .00 00 .00 .00 .00 ,00 ,00 ,00 .00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
3. -6. 7.
-1. -5. -4. -2. -3. 1. 2. 2. 1. 1. 1. 1. 9. 7. 5, 3. 1. 1. 1. 1, 1. 1. 9. 7. 5 3 . 1. 1 1 1 1 1 9 7 5 3 1 1 1 1 1 9 8 6 4 2 9 1 1 1 1 9 7 6 4 2 4 1 1 1 1 8 7
SIGMA X
627E+01 916E+00 708E-01 493E+01 784E+00 589E+00 554E+00 439E-01 614E+00 015E+00 062E+02 789E+02 501E+02 274E+02 080E+02 029E+01 244E+01 503E+01 653E+01 .413E+01 758E+02 •694E+02 .535E+02 .345E+02 •140E+02 .354E+01 •357E+01 •391E+01 •545E+01 .708E+01 .646E+02 •488E+02 .380E+02 .239E+02 .083E+02 .090E+01 .127E+01 .096E+01 .097E+01 .493E+01 .604E+02 .438E+02 .266E+02 . 126E + 02 .795E+01 .340E+01 .773E+01 .841E+01 .755E+01 .515E+00 .589E+02 .399E+02 .243E+02 .078E+02 .220E+01 .651E+01 .187E+01 .665E+01 .544E+01 .771E+00 .257E+02 .369E+02 .238E+02 .060E+02 .754E+01 .005E+01
3. 3. 3. 2. 1. 9. 3. 6.
-9. -4. 4. 3. 2. 2. 2. 1. 1. 1. 6. 2. 3. 3. 2. 2. 2. 1. 1. 9. 6. 3. 3. 2. 2. 2 1 1 1 8 5 2 2 2 2 1 1 1 1 8 4 1 2 2 1 1 1 1 9 7 4 1 1 1 1 1 1 9
SIGMA Y
793E+02 378E+02 340E+02 457E+02 587E+02 153E+01 218E+01 958E+00 557E+00 419E+00 036E+02 501E+02 996E+02 571E+02 147E+02 768E+02 389E+02 033E+02 610E+01 532E+01 361E+02 198E+02 888E+02 539E+02 161E+02 754E+02 .355E+02 .682E+01 .230E+01 .079E+01 .007E+02 .687E+02 •463E+02 •202E+02 .933E+02 .633E+02 .274E+02 .997E+01 .438E+01 .758E+01 .727E+02 .429E+02 .120E+02 .868E+02 .620E+02 .394E+02 .152E+02 .276E+01 .793E+01 .903E+01 .514E+02 .187E+02 .914E+02 .639E+02 .386E+02 .147E+02 .494E+01 .422E+01 .335E+01 .189E+01 .845E+02 .895E+02 .659E+02 .435E+02 .201E+02 .725E+01
1. -5. 2.
-1. 1.
-6. 1. 5.
-9. 4. 2 . 2. 2. 1. 1. 7. 3 . 1.
-8. -8. 3 . 2 , 2, 2 . 1. 1. 5 . 2
-4 . -1 2 2 2 1 1 1 7 3 2 -1 2 2 1 1 1 1 7 3 2
-1 1 1 1 1 9 6 4 2
-2 -1 1 1 9 7 5 4
TAU XY
214E+02 475E+01 871E+01 014E+01 314E+01 399E-01 227E+00 859E+00 519E+00 012E+00 758E+01 618E+01 288E+01 653E+01 146E+01 418E+00 861E+00 047E+00 979E-01 613E-01 036E+01 748E+01 .409E+01 056E+01 .567E+01 .057E+01 .987E+00 •127E+00 •591E-01 •100E+00 •914E+01 .492E+01 .186E+01 .882E+01 .577E+01 .206E+01 .807E+00 .611E+00 .681E-01 .219E+00 .589E+01 .234E+01 .852E+01 .546E+01 .271E+01 .011E+01 .186E+00 .724E+00 .376E-01 .281E+00 .936E+01 .720E+01 .490E+01 .177E+01 .066E+00 .772E+00 .682E+00 .480E+00 .985E-01 .710E+00 .232E+01 .369E+01 .381E+00 .436E+00 .778E+00 .427E+00
4 . 3. 3 . 2. 1. 9. 3. 1. 7. 3. 4. 3. 3. 2. 2. 1 . 1. 1. 6. 2. 3. 3. 2. 2. 2. 1. 1. 9. 6. 3. 3. 2, 2, 2. 1. 1 1 9 5 2 2 2 2 1 1 1 1 8 4 1 2 2 1 1 1 1 9 7 4 1 1 1 1 1 1 9
SIGMA 1
179E+02 463E+02 365E+02 461E+02 598E+02 153E+01 222E+01 021E+01 066E+00 940E+00 074E+02 540E+02 030E+02 592E+02 159E+02 774E+02 391E+02 033E+02 613E+01 538E+01 416E+02 247E+02 929E+02 573E+02 185E+02 768E+02 361E+02 692E+01 231E+01 087E+01 .067E+02 •737E+02 .505E+02 .237E+02 •961E+02 .653E+02 .285E+02 .030E+01 .439E+01 .770E+01 .784E+02 .477E+02 .159E+02 .899E+02 .644E+02 .412E+02 .162E+02 .316E+01 .794E+01 .920E+01 .553E+02 .223E+02 .946E+02 .663E+02 .403E+02 .159E+02 .559E+01 .444E+01 .335E+01 .228E+01 .870E+02 .929E+02 .679E+02 .449E+02 .211E+02 .795E+01
-2. -1. -1. -1. -6. -4. -2. -3. -1. -6. 2. 1. 1. 1. 1. 8. 7. 5. 3. 1. 1. 1. 1. 1. 1. 9. 7. 5. 3. 1. 1, 1. 1. 1. 1. 8 7 5 3 1 1 1 1 1 9 8 6 4 2 9 1 1 1 1 9 7 6 4 2 4 1 1 1 1 8 6
SIGMA 3
375E+00 540E+01 684E+00 532E+01 828E+00 593E+00 597E+00 597E+00 501E+01 344E+00 024E+02 750E+02 467E+02 253E+02 068E+02 966E+01 221E+01 500E+01 651E+01 406E+01 702E+02 646E+02 494E+02 311E+02 117E+02 220E+01 300E+01 380E+01 544E+01 .699E+01 .586E+02 .438E+02 •338E+02 .204E+02 .055E+02 .894E+01 •021E+01 •063E+01 •097E+01 .481E+01 .547E+02 .390E+02 .227E+02 .095E+02 .552E+01 .163E+01 .667E+01 .801E+01 .755E+01 .345E+00 .551E+02 .363E+02 .211E+02 .054E+02 .049E+01 .534E+01 .122E+01 .643E+01 .544E+01 .382E+00 .232E+02 .336E+02 .218E+02 .046E+02 .654E+01 .935E+01
A65
RUNNING THE RSDAM PROGRAM APPENDIX F
87 88 89 90 91 92 93 94 95 96 97 98 99 100
26. 20. 14. 8
67. 60 54. 47 41 34 28 22 15 9
,07 ,15 ,22 .30 .30 ,84 .37 .91 .45 .98 .52 .06 .59 .13
13, 15, 17, 19, 1. 3. 5, 7. 9. 11 13. 15 17 19
.00 ,00 .00 ,00 ,00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00
5. 3 2. -2 -8 -2 -1 -1 -1 -1 -1 -1 -6 -2
.307E+01 •903E+01 .686E+01 •802E+00 •771E+02 .501E+03 .718E+03 .926E+03 .861E+03 .674E+03 .400E+03 .088E+03 .921E+02 .575E+02
7 5 4 3 4 5 -2 -1 -1 -1 -1 -1 -1 -5
•520E+01 •837E+01 •347E+01 •480E+00 •167E+03 •799E+02 .082E+02 .359E+02 .483E+02 .609E+02 .788E+02 .731E+02 .306E+02 .304E+01
3 1
-3 -2 1 7 5 6 5 5 4 3 2 5
.202E+00 •560E+00 •449E-01 •413E+00 .122E+03 .315E+02 •669E+02 .409E+02 .988E+02 .425E+02 •447E+02 .385E+02 .280E+02 .727E+01
7 5 4 4 4 7
-1. 6 4 1
-3 -6 -4 -3
•565E+01 •850E+01 .348E+01 .300E+00 .405E+03 •447E+02 .907E+01 •995E+01 •033E+01 •356E+01 •398E+01 •149E+01 .962E+01 .809E+01
5 3 2 -3 -1 -2 -1. -2 -2 -1 -1 -1 -7. -2
•261E+01 •891E+01 .686E+01 .622E+00 .115E+03 .666E+03 .907E+03 .131E+03 . 050E+03 .848E+03 •545E+03 .200E+03 •731E+02 .724E+02
INTERFACE ELEMENT RESULTS FOR STAGE 3
ELEM NO X Y NORMAL STRESS SHEAR STRESS NORMAL STIFF SHEAR STIFF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0. 0. 0. 0. 0. 0 0 0. 0 0
67 60 54 47 41 34 28 21 15 9
• 20 .20 .20 .20 .20 .20 .20 .20 .20 .20 .20 .74 .27 .81 .35 .88 .42 .96 .49 .03
1. 3 . 5. 7 9
11. 13 15 17 19 1 3 5 7. 9 11 13 15 17 19
.00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
2. 2 4 3 1. 8 2 2 0 2 9 1 1 1 1 9 7 5 3 8
.206E+01 •499E-02 •462E-02 •277E-02 .925E-02 •132E-03 •021E-03 .703E-01 .OOOE+00 .854E+00 .059E+01 .754E+02 .550E+02 .306E+02 .108E+02 .037E+01 .100E+01 .222E+01 .343E+01 .992E+00
-5. 5. 4. 3. 2. 2. 2.
-4.
o. 9 1 4
-2 -3 -3 -3 -3 -3 -4 -4
975E+00 •592E-03 .583E-03 .673E-03 .978E-03 .613E-03 •238E-03 •069E+00 .000E+00 .557E-01 .221E+00 .422E-01 •306E+00 •097E+00 •387E+00 .485E+00 •199E+00 .201E+00 .059E+00 .387E+00
1. 1. 1. 1. 1. 1. 1. 1. 1. 1 1 1 1 1 1 1 1 1 1 1
000E+08 OOOE+08 .OOOE+08 .OOOE+08 OOOE+08 •OOOE+08 .OOOE+08 •OOOE+08 .000E+02 .OOOE+08 •OOOE+08 .OOOE+08 •OOOE+08 •OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08
4 4 4 4 4 4 1 1 1 4 4 4 4 4 4 4 4 4 4 4
•OOOE+03 .OOOE+03 •000E+03 .OOOE+03 •000E+03 .OOOE+03 .000E+02 .000E+02 .OOOE+02 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03
REINFORCEMENT RESULTS FOR STAGE 3
REIN. NUM. I J TYPE COMPR FORCE INCR COMPR STIFFNESS
1 2 3 4 5 6 7 8 9
10
1 2 3 4 5 6 7 8 9
10
111 112 113 114 115 116 117 118 119 120
1 1 1 1 1 1 1 1 1 1
0 1.
-1 3. 1 1 5 1 8
-7.
.000000E+00
.635870E+01
.637198E+01
.167185E+01
.305019E+01
.285954E+01
.331912E+00
.083230E+00
.405101E-01
.811441E+00
0 -9 2
-1. 9 -7 5
-3 3 -1
.000000E+00
.748852E-06
.138899E-06
.563400E-06
.791111E-07
.710914E-07
.118782E-07
.621681E-07
.027017E-07
.097869E-07
6. 6. 6. 6 6 6 6 6 6 6
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
.750000E+05
A66
RUNNING THE RSDAM PROGRAM APPENDIX F
*************************************************** STAGE NUMBER 4
FORCE AND/OR DISPLACEMENT LOADING IS SPECIFIED FOR THIS INCREMENT
NODE X-LOAD Y-LOAD NODE X-LOAD Y-LOAD
1 23 45 67 89 111
1. 1. 1. 1. 1. 1.
•0OOOOE-•00000E-•00000E-•00000E-•00000E-.00000E-
-01 -01 -01 -01 •01 -01
0. 0. 0 0. 0 0.
•OOOOOE+00 •00000E+00 .O00O0E+O0 .00000E+00 .00000E+00 •OOOOOE+00
12 34 56 78 100
0
1 1. 1 1. 1 0.
.00000E-01
.00000E-01
.00000E-01 •00000E-01 .00000E-01 .00000E+00
0 0 0 0 0 0,
•00000E+00 •00000E+00 •OOOOOE+00 •OOOOOE+00 .00000E+00 •00000E+00
DISPLACEMENT RESULTS FOR STAGE 4
NODAL POINT
1 2 3 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 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
X
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20
11.91 10.83 9.75 8.68 7.60 6.52 5.44 4.37 3.29 2.21 1.13
23.61 21.46 19.30 17.15 14.99 12.84
Y
0. 2. 4 6. 8
10, 12 14. 16 18 20 0 2 4 6 8
10 12 14 16. 18 20 0 2 4 6 8
10 12. 14 16 18 20. 0. 2. 4, 6. 8.
10. 12. 14, 16. 18. 20. 0. 2. 4. 6. 8.
10.
.00 ,00 .00 ,00 .00 ,00 .00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 .00 ,00 .00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 00 ,00 00 00 00 00
TOTAL
ux 1.00000E-01 9.07302E-02 7.81036E-02 6.99333E-02 6.25979E-02 5.68958E-02 5.29159E-02 5.07664E-02 5.02681E-02 5.12356E-02 5.11215E-02 1.00000E-01 9.07393E-02 7.81087E-02 6.99409E-02 6.26020E-02 5.68987E-02 5.29171E-02 5.07667E-02 5.02681E-02 5.12350E-02 5.11216E-02 1.00000E-01 9.07390E-02 8.04188E-02 6.95487E-02 6.23394E-02 5.67766E-02 5.28766E-02 5.07668E-02 5.02681E-02 5.12349E-02 5.11216E-02 1.00000E-01 8.99889E-02 7.99503E-02 7.10626E-02 6.24508E-02 5.60168E-02 5.16156E-02 4.92572E-02 4.89513E-02 5.02114E-02 5.14681E-02 1.00000E-01 8.75187E-02 7.79215E-02 6.91459E-02 6.16811E-02 5.49549E-02
TOTAL UY
0.OOOOOE+00 -1.18993E-03 -9.18942E-04 -1.24981E-03 -1.29476E-03 -1.40099E-03 -1.32273E-03 -1.31741E-03 -1.19000E-03 -1.17508E-03 -1.28636E-03 0.00000E+00 6.17085E-04
-1.79756E-04 -3.65719E-04 -7.07965E-04 -8.51873E-04 -1.07585E-03 -1.13445E-03 -1.27581E-03 -1.27872E-03 -1.16176E-03 0.00000E+00
-2.36892E-03 -4.00997E-03 -4.70419E-03 -4.86381E-03 -4.44613E-03 -3.62526E-03 -2.73185E-03 -1.71259E-03 -1.02000E-03 -1.05233E-03 0.00000E+00 1.85673E-05
-1.73438E-04 -9.31039E-04 -1.87593E-03 -2.57767E-03 -2.90473E-03 -2.68546E-03 -2.06130E-03 -1.01557E-03 -3.86103E-04 0.OOOOOE+00
-2.76985E-03 -4.24341E-03 -4.74190E-03 -4.84963E-03 -4.86557E-03
PORE PRESS 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 o.oo 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A67
RUNNING THE RSDAM PROGRAM APPENDIX F
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121
10.68 8.53 6.38 4.22 2.07
35.32 32.09 28.86 25.62 22.39 19.16 15.93 12.70 9.46 6.23 3.00
47.02 42.71 38.40 34.09 29.79 25.48 21.17 16.86 12.55 8.24 3.93 58.73 53.34 47.96 42.57 37.18 31.80 26.41 21.03 15.64 10.25 4.87 70.43 63.97 57.50 51.04 44.58 38.11 31.65 25.19 18.73 12.26 5.80
70.43 63.97 57.50 51.04 44.58 38.11 31.65 25.19 18.73 12.26 5.80
70.63 64.17 57.70 51.24 44.78 38.31 31.85 25.39 18.93 12.46 6.00
12.00 14.00 16.00 18.00 20.00 0 .00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00
5.01235E-02 4.75069E-02 4.72379E-02 4.91217E-02 5.15530E-02 1.00000E-01 8.71994E-02 7.55594E-02 6.67868E-02 5.96053E-02 5.39565E-02 4.92608E-02 4.64668E-02 4.61870E-02 4.84186E-02 5.14975E-02 1.00000E-01 8.68657E-02 7.55828E-02 6.55567E-02 5.82047E-02 5.28439E-02 4.91871E-02 4.65741E-02 4.60669E-02 4.85297E-02 5.14833E-02 1.00000E-01 9.04917E-02 7.79473E-02 6.7062OE-02 5.85198E-02 5.29576E-02 4.95947E-02 4.79039E-02 4.71816E-02 4.92753E-02 5.18608E-02 1.00000E-01 9.09838E-02 7.76183E-02 6.89717E-02 6.16478E-02 5.58468E-02 5.20025E-02 4.99615E-02 4.94093E-02 5.00919E-02 5.27413E-02 1.00000E-01 9.04120E-02 7.80181E-02 6.97451E-02 6.24321E-02 5.67430E-02 5.27929E-02 5.06762E-02 5.01977E-02 5.12136E-02 5.36933E-02 1.00000E-01 9.07058E-02 7.81291E-02 6.98888E-02 6.25787E-02 5.68778E-02 5.29112E-02 5.07676E-02 5.02677E-02 5.12471E-02 5.36999E-02
-4.50502E-03 -3.79170E-03 -2.61203E-03 -1.24678E-03 -2.64942E-04 0.O00O0E+O0
-4.82784E-03 -8.49295E-03 -1.06162E-02 -1.12404E-02 -1.07522E-02 -9.65906E-03 -7.66991E-03 -5.12343E-03 -2.31428E-03 -2.20945E-04 0.00000E+00 -7.57676E-03 -1.33525E-02 -1.72744E-02 -1.90520E-02 -1.87697E-02 -1.68383E-02 -1.39208E-02 -9.50649E-03 -4.60827E-03 -4.57878E-04 0.00000E+00
. -1.18765E-02 -2.04895E-02 -2.59725E-02 -2.87127E-02 -2.87074E-02 -2 .61335E-02 -2.15537E-02 -1.56950E-02 -7.89169E-03 -1.17720E-03 0.00000E+00 -1.20472E-02 -2.73009E-02 -3.71541E-02 -4.18358E-02 -4.19748E-02 -3.83296E-02 -3.15938E-02 -2.26665E-02 -1.25058E-02 -2.12310E-03 0.00000E+00
-1.18721E-02 -2.74264E-02 -3.73949E-02 -4.20797E-02 -4.22532E-02 -3.85750E-02 -3.18156E-02 -2.29109E-02 -1.28532E-02 -2.41761E-03 0.OOOOOE+00 -1.13617E-02 -2.70279E-02 -3.71813E-02 -4.20153E-02 -4.23179E-02 -3.87469E-02 -3.20678E-02 -2.32129E-02 -1.31752E-02 -2.74217E-03
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 o.oo 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0. 00 0 . 00 0 .00 0 .00 0 . 00 0. 00 0.00 0. 00 0 .00 0.00 0.00 0. 00 0 .00 0 . 00 0.00 0. 00 0.00
A68
RUNNING THE RSDAM PROGRAM APPENDIX F
STRESSES VALUES FOR STAGE 4
ELEM
NO
21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
0
0 0 0 0 0 0 0 0 0 5 5 4 4 3 3 2 2 1 0
16 15 13 12 10 8 7 5 4 2
28 25 22 20 17 14 11. 9. 6. 3,
39. 35. 31. 27. 24. 20. 16. 12. 9. 5.
50. 45. 40. 35. 31. 26. 21. 16. 11. 6.
61. 55. 49. 43. 37. 31.
X
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.79
.25
.71
.17
.63
.09
.55
.01
.47
.94
.95
.34
.72
.10
.49
.87
.26
.64
.02
.41
.12
.43
.73
.04
.35
.65
.96
.27
.57
.88 ,28 .51 .74 .97 20 43 66 89 12 35 45 60 76 91 06 21 37 52 67 82 62 69 77 84 92 99
1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13. 15. 17. 19, 1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11.
Y
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00 ,00 ,00 ,00 ,00 ,00 .00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
3 -6 1
-1 -5 -3 -1 1 1 2 2 1 1 1 1 9 7 5 3 1 1 1 1 1 1 9 7 5 3 1 1 1 1 1 1 9. 7. 5. 3. 1. 1. 1. 1. 1. 9. 8. 6. 4. 2 . 9. 1. 1. 1. 1. 9. 7. 6. 4. 2. 4. 1. 1. 1. 1. 8. 6.
SIGMA
X
.635E+01
.936E+00 •582E+00 .454E+01 .736E+00 .396E+00 .291E+00 .773E-01 .758E+00 .040E+00 .063E+02 .790E+02 .502E+02 .276E+02 .082E+02 .043E+01 .251E+01 .512E+01 .668E+01 .376E+01 .758E+02 .695E+02 .536E+02 .346E+02 .141E+02 .361E+01 .363E+01 .392E+01 .538E+01 .679E+01 .646E+02 .488E+02 .380E+02 .239E+02 .083E+02 .091E+01 .128E+01 .095E+01 ,090E+01 .478E+01 •604E+02 438E+02 266E+02 126E+02 791E+01 336E+01 770E+01 839E+01 753E+01 532E+00 590E+02 400E+02 243E+02 078E+02 213E+01 643E+01 180E+01 659E+01 545E+01 821E+00 258E+02 370E+02 239E+02 060E+02 745E+01 997E+01
3 3 3 2 1 9 3 9
-7 -3 4 3 2 2 2 1 1 1 6 2 3 3 2 2 2 1 1 9 6 3 3 2 2 2 1 1 1. 9. 5. 2. 2. 2. 2. 1. 1. 1. 1. 8. 4. 1. 2. 2. 1. 1. 1. 1. 9. 7. 4. 1. 1. 1. 1. 1. 1. 9.
SIGMA Y
.820E+02
.406E+02
.369E+02 •484E+02 .614E+02 .400E+01 .437E+01 .113E+00 .383E+00 .176E+00 .037E+02 .502E+02 .997E+02 .572E+02 .148E+02 .769E+02 .390E+02 .034E+02 .611E+01 .527E+01 .361E+02 .198E+02 .888E+02 .539E+02 .162E+02 .755E+02 .356E+02 .683E+01 .226E+01 .073E+01 .007E+02 .687E+02 .463E+02 .202E+02 .933E+02 •633E+02 •275E+02 .004E+01 •443E+01 •759E+01 .728E+02 .430E+02 .121E+02 868E+02 620E+02 394E+02 152E+02 281E+01 802E+01 911E+01 517E+02 189E+02 915E+02 639E+02 387E+02 148E+02 493E+01 423E+01 341E+01 198E+01 846E+02 898E+02 661E+02 437E+02 202E+02 730E+01
1 -5 2 -8 1 4 3 6
-1 4 2 2 2 1 1 7 3 1
-8 -6 3 2 2 2 1 1 6 2 -2 -9 2 2 2 1 1 1 7, 3 3.
-1, 2, 2. 1. 1. 1. 1. 7. 3. 3 .
-1. 1. 1. 1. 1. 9. 6. 4. 2.
-2. -1. 1. 1. 9. 7. 5. 4.
TAU XY
.199E+02
.338E+01
.744E+01
.992E+00
.206E+01
.208E-01
.729E-01
.599E+00
.040E+01
.642E+00
.753E+01
.614E+01
.284E+01
.652E+01
.148E+01
.473E+00
.907E+00
.055E+00
.202E-01
.257E-01
.034E+01
.746E+01
.409E+01
.056E+01
.570E+01
.062E+01
.077E+00
.246E+00
.896E-01
.092E-01 •913E+01 •492E+01 •185E+01 •883E+01 •579E+01 .210E+01 •872E+00 •710E+00 •913E-01 •090E+00 •586E+01 •231E+01 •850E+01 545E+01 273E+01 014E+01 234E+00 796E+00 271E-01 227E+00 927E+01 713E+01 483E+01 174E+01 053E+00 793E+00 729E+00 548E+00 187E-01 653E+00 220E+01 358E+01 281E+00 332E+00 738E+00 410E+00
4 3 3 2 1 9 3 1 8 4 4 3 3 2 2 1 1 1 6 2 3 3 2 2 2 1 1 9 6 3 3. 2 2. 2. 1. 1. 1. 9, 5, 2, 2, 2. 2. 1. 1. 1. 1. 8. 4. 1. 2. 2. 1. 1. 1. 1. 9. 7. 4. 1. 1. 1. 1. 1. 1. 9.
SIGMA 1
.196E+02
.487E+02
.391E+02
.487E+02
.622E+02
.400E+01
.438E+01
.261E+01
.547E+00
.757E+00
.075E+02
.541E+02
.031E+02
.593E+02
.160E+02
.775E+02
.392E+02
.034E+02
.614E+01
.530E+01
.416E+02
.247E+02
.929E+02
.573E+02
.185E+02
.768E+02 •362E+02 •695E+01 •227E+01 •079E+01 •067E+02 •737E+02 •505E+02 •237E+02 •961E+02 .653E+02 .285E+02 039E+01 444E+01 768E+01 .785E+02 477E+02 159E+02 899E+02 644E+02 412E+02 162E+02 322E+01 803E+01 926E+01 555E+02 224E+02 947E+02 663E+02 404E+02 159E+02 559E+01 446E+01 342E+01 235E+01 871E+02 930E+02 681E+02 451E+02 212E+02 800E+01
-1 -1 -6 -1 -6 -3 -1 -3 -1 -5 2 1 1 1 1 8 7 5 3 1 1 1 1 1 1 9 7 5 3 1 1 1 1. 1. 1. 8. 7. 5. 3. 1, 1. 1, 1, 1, 9. 8, 6. 4. 2. 9, 1. 1. 1. 1. 9. 7. 6. 4. 2. 4. 1. 1. 1. 1, 8, 6.
SIGMA 3
.162E+00
.495E+01
.481E-01
.485E+01
. 602E + 00
.398E+00
.295E+00
.324E+00
.417E+01
.892E+00
.025E+02
.751E+02
.468E+02
.255E+02
.069E+02
.979E+01
.228E+01
.510E+01
.665E+01
.372E+01
.702E+02
.646E+02
.494E+02
.311E+02
.117E+02 •225E+01 •304E+01 •381E+01 •538E+01 •674E+01 •586E+02 •438E+02 •338E+02 •204E+02 •055E+02 •894E+01 •020E+01 •060E+01 •089E+01 •469E+01 •548E+02 •390E+02 •227E+02 •095E+02 •548E+01 •159E+01 •663E+01 •798E+01 •752E+01 •378E+00 •552E+02 364E+02 212E+02 054E+02 043E+01 526E+01 114E+01 636E+01 545E+01 458E+00 234E+02 337E+02 219E+02 046E+02 647E+01 927E+01
A69
RUNNING THE RSDAM PROGRAM APPENDIX F
87 88 89 90 91 92 93 94 95 96 97 98 99
100
26. 20. 14. 8.
67. 60, 54 47 41 34 28 22 15 9
07 .15 ,22 ,30 .30 .84 .37 .91 .45 .98 .52 .06 .59 .13
13. 15. 17. 19. 1. 3. 5 7. 9. 11 13 15 17 19
00 .00 .00 .00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00
5. 3, 2,
-2. -8 -2 -1 -1 -1 -1 -1 -1 -7 -2
.297E+01
.896E+01
.686E+01
.765E+00
.698E+02 •490E+03 .710E+03 •923E+03 .869E+03 .689E+03 .410E+03 .095E+03 .070E+02 .736E+02
7. 5. 4 3. 4 5 -2 -1 -1 -1 -1 -1 -1 -5
•523E+01 •835E+01 •352E+01 •568E+00 •170E+03 .811E+02 .062E+02 .341E+02 .513E+02 .639E+02 .781E+02 .763E+02 .323E+02 .227E+01
3. 1
-2 -2 1 7 5 6 6 5 4 3 2 6
.231E+00
.615E+00 •622E-01 •338E+00 •116E+03 .301E+02 .629E+02 .415E+02 .000E+02 .480E+02 .487E+02 .392E+02 .343E+02 .237E+01
7 5 4 4 4 7 -1 7 3 1
-3 -6 -4 -3
•569E+01 •849E+01 •352E+01 •338E+00 .406E+03 .459E+02 .887E+01 .213E+01 .753E+01 .264E+01 .204E+01 .470E+01 .894E+01 .591E+01
5. 3. 2
-3 -1 -2 -1 -2 -2 -1 -1 -1 -7 -2
•252E+01 .883E+01 .686E+01 .534E+00 .106E+03 .654E+03 .897E+03 .129E+03 .058E+03 .865E+03 .556E+03 .207E+03 .904E+02 .900E+02
INTERFACE ELEMENT RESULTS FOR STAGE 4
ELEM NO X Y NORMAL STRESS SHEAR STRESS NORMAL STIFF SHEAR STIFF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0, 0. 0. 0, 0 0. 0 0. 0. 0
67 60 54 47 41 34 28 21 15 9
.20
.20
.20 ,20 .20 .20 .20 .20 .20 .20 .20 .74 .27 .81 .35 .88 .42 .96 .49 .03
1. 3. 5, 7, 9
11. 13. 15 17. 19 1 3 5 7 9 11 13 15 17 19
.00
.00 ,00 .00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
2 . 2. 0, 0, 3. 1. 2, 1. 3. 2 9 1 1 1 1 9 7 5 3 9
169E+01 499E-02 .000E+00 .0O0E+00 •918E-01 .498E+00 .237E+00 •015E+00 •725E-07 •481E+00 •040E+01 •757E+02 •554E+02 •305E+02 .108E+02 •037E+01 •100E+01 .204E+01 •315E+01 •085E+00
-5, 7. 0. 0.
-1. -2. 9 -4 -2 7 1 3 -2 -3 -3 -3 -3 -3 -3 -4
.972E+00
.556E-03 •000E+00 •OOOE+00 •501E-02 •998E-02 •060E-04 •071E+00 •611E-03 .363E-01 •196E+00 •579E-01 •458E+00 •263E+00 •520E+00 .532E+00 •152E+00 .147E+00 .999E+00 .342E+00
1. 1. 1. 1. 1. 1 , 1. 1, 1. 1. 1. 1. 1 1 1 1 1 1 1 1
OOOE+08 OOOE+08 000E+02 000E+02 .OOOE+08 OOOE+08 OOOE+08 OOOE+08 OOOE+08 .000E+08 •000E+08 •000E+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08
4 • 4. 1. 1, 4 4 4. 1 1. 4 4 4 4 4 4 4 4 4 4 4
OOOE+03 OOOE+03 000E+02 000E+02 •OOOE+03 •000E+03 •000E+03 .000E+02 •000E+02 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .000E+03 .000E+03 .OOOE+03 .OOOE+03
REINFORCEMENT RESULTS FOR STAGE 4
NUM.
1 2 3 4 5 6 7 8 9
10
I
1 2 3 4 5 6 7 8 9
10
J
111 112 113 114 115 116 117 118 119 120
TYPE
1 1 1 1 1 1 1 1 1 1
COMPR FORCE
O.OOOOOOE+00 1.646934E+01 -1.719676E+01 3.000217E+01 1.297475E+01 1.215547E+01 3.149264E+00 -8.278439E-01 2.521005E-01 -7.751091E+00
0, 1. -1 -2. -1 -1 -3 -2 -8 8
INCR COMPR
•O0OOOOE+00 .639128E-07 •221895E-06 .473593E-06 .117587E-07 .043081E-06 .233552E-06 .831221E-06 .717179E-07 .940697E-08
6. 6, 6. 6. 6 6 6 6 6 6
STIFFNESS
•750000E+05 •750000E+05 .750000E+05 .750000E+05 .750000E+05 .750000E+05 .750000E+05 .750000E+05 .750000E+05 .750000E+05
A70
RUNNING THE RSDAM PROGRAM
:***************,*******«****»*,*,*********** STAGE NUMBER
SEEPAGE LOADING IS SPECIFIED FOR THIS INCREMENT
NUMBER OF WATER LEVEL CHANGES SPECIFIED
X-COORD OF BOUNDARY
PRESENT LEVEL
NEW LEVEL
0.00 6.00
2.00 20.00
O.OO 0.00
DISPLACEMENT RESULTS FOR STAGE 5
NODAL POINT
1 2 3 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 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
X
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20
11.91 10.83 9.75 8.68 7.60 6.52 5.44 4.37 3.29 2.21 1.13
23.61 21.46 19.30 17.15 14.99 12.84
y
0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00 12.00 14.00 16.00 18.00 20.00 0.00 2.00 4.00 6.00 8.00
10.00
TOTAL UX
1.00000E-01 9.18048E-02 8.12350E-02 7.55360E-02 7.13068E-02 6.85893E-02 6.67098E-02 6.54552E-02 6.49130E-02 6.56933E-02 6.68319E-02 1.00000E-01 9.18134E-02 8.12406E-02 7.55434E-02 7.13113E-02 6.85931E-02 6.67121E-02 6.54564E-02 6.49136E-02 6.56939E-02 6.68319E-02 1.00000E-01 9.18131E-02 8.35508E-02 7.62569E-02 7.10488E-02 6.84710E-02 6.66717E-02 6.54565E-02 6.49135E-02 6.56938E-02 6.68320E-02 1.00000E-01 9.32471E-02 8.60010E-02 7.91981E-02 7.30601E-02 6.82883E-02 6.52204E-02 6.35424E-02 6.35009E-02 6.49777E-02 6.68722E-02 1.00000E-01 9.44769E-02 8.83178E-02 8.10120E-02 7.41486E-02 6.78647E-02
TOTAL UY
0.OOOOOE+00 -1.07595E-03 -8.07301E-04 -1.08613E-03 -1.11719E-03 -1.25857E-03 -1.28305E-03 -1.36982E-03 -1.31898E-03 -1.30157E-03 -1.31771E-03 0.OOOOOE+00 5.17785E-04
-2.65887E-04 -4.99654E-04 -8.52247E-04 -9.85142E-04 -1.17807E-03 -1.22645E-03 -1.35443E-03 -1.42151E-03 -1.42605E-03 0.00000E+00
-2.47771E-03 -3.78615E-03 -4.14875E-03 -4.19436E-03 -3.65968E-03 -3.44588E-03 -3.83093E-03 -3.36798E-03 -2.60641E-03 -1.82659E-03 0.00000E+00 -1.20963E-03 -2.14154E-03 -3.28552E-03 -4.36388E-03 -5.08759E-03 -6.10823E-03 -6.42548E-03 -5.07781E-03 -3.53701E-03 -2.55833E-03 0.00000E+00
-4.20731E-03 -6.58483E-03 -7.48384E-03 -7.68276E-03 -7.58165E-03
PORE PRESS
-2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-2.60 -0.60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-2.60 -0.60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-2.60 -0.60 0.00 0.00 0.00 0.00
-6.33 -1.10 0.00 0.00 0.00
-5.40 -3.40 -1.40 0.00 0.00 0.00
A71
RUNNING THE RSDAM PROGRAM APPENDIX F
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121
10, 8. 6, 4. 2
35, 32 28. 25, 22 19, 15. 12. 9. 6 3. 47 42 38 34 29 25 21 16 12 8 3 58 53 47 42 37 31 26 21 15 10 4
70 63 57 51 44 38 31 25 18 12 5
70 63 57 51. 44 38. 31 25. 18. 12, 5.
70, 64. 57. 51, 44, 38, 31, 25. 18, 12. 6,
.68 ,53 ,38 .22 .07 ,32 .09 .86 .62 .39 .16 .93 .70 .46 .23 .00 .02 .71 .40 .09 .79 .48 .17 .86 .55 .24 .93 .73 .34 .96 .57 .18 .80 .41 .03 .64 .25 .87 .43 .97 .50 .04 .58 .11 .65 .19 .73 .26 .80 .43 .97 .50 .04 .58 ,11 .65 .19 ,73 ,26 ,80 ,63 ,17 .70 ,24 ,78 ,31 .85 ,39 ,93 ,46 ,00
12. 14, 16, 18. 20. 0. 2. 4. 6. 8.
10. 12 14. 16. 18 20. 0 2 4. 6 8
10 12 14 16 18 20 0 2 4 6 8
10 12 14 16 18 20 0 2 4 6 8 10 12. 14 16 18 20 0. 2 4 6. 8
10, 12 14 16, 18, 20, 0. 2. 4. 6. 8.
10. 12. 14. 16. 18. 20,
.00 ,00 ,00 ,00 .00 ,00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 .00 .00 ,00 ,00 ,00 .00 ,00 ,00 .00 ,00 ,00 ,00 .00 ,00 ,00 .00
6. 6 6. 6 6 1. 9 8. 8. 7 6. 6 6 6. 6 6 1 9 8 7 7 6 6 6 6 6 6 1 9 8 7 7 6 6 6 6 6 6 1 9 8 7 7 6 6 6 6 6 6 1. 9 8 7 7 6 6 6 6. 6 6 1 9. 8. 7. 7. 6. 6. 6. 6. 6. 6
.32008E-02
.11789E-02
.15591E-02
.39281E-02
.68473E-02
.00000E-01
.40924E-02
.67067E-02
.01941E-02
.39547E-02
.84105E-02
.36379E-02
.05436E-02
.02732E-02
.30577E-02 •67719E-02 .00000E-01 .06950E-02 .39196E-02 .74659E-02 .23426E-02 .79900E-02 .43003E-02 .13024E-02 .02685E-02 .28223E-02 .67176E-02 .00000E-01 .27749E-02 .29353E-02 .55651E-02 .04660E-02 .73166E-02 .49633E-02 .30257E-02 .17194E-02 .33985E-02 .68180E-02 .00000E-01 .17702E-02 .01520E-02 .41461E-02 .03833E-02 .80989E-02 .65959E-02 .51982E-02 .41095E-02 .43814E-02 .71369E-02 .00000E-01 .15420E-02 .11914E-02 .54173E-02 •12121E-02 .84923E-02 .66270E-02 .53769E-02 •48494E-02 .56618E-02 •79471E-02 .00000E-01 •17823E-02 .12486E-02 ,54891E-02 .12791E-02 .85623E-02 ,67052E-02 54558E-02 •49162E-02 .56908E-02 •79513E-02
-7 -7 -6. -4 -2 0 -5 -9 -1. -1. -1. -1 -1. -8. -6 -3. 0
-8. -1. -1 -1. -1. -1 -1 -1 -8 -3 0
-1 -2 -2 -2 -2 -2 -2 -1 -1 -4 0
-1 -2 -3 -4 -4 -3 -3 -2 -1 -5 0
-1 -2 -3 -4 -4 -3 -3 -2 -1 -6 0 -1 -2 -3 -4 -4 -3 _3 -2 -1 -6
.58374E-03
.58667E-03
.46377E-03
.52293E-03
.78183E-03
.OOOOOE+00
.76020E-03 •99426E-03 •24827E-02 •33147E-02 •30489E-02 •21143E-02 •05080E-02 .66246E-03 •06968E-03 •18198E-03 .OOOOOE+00 .20939E-03 •41376E-02 •81046E-02 •99713E-02 •98823E-02 •84056E-02 •59691E-02 .23020E-02 .20758E-03 .88243E-03 .OOOOOE+00 •23045E-02 •11158E-02 •65622E-02 .90729E-02 .90176E-02 .66936E-02 •27845E-02 .77785E-02 .10669E-02 .79952E-03 .00000E+00 .21430E-02 .75558E-02 .74787E-02 .20374E-02 .20004E-02 .83609E-02 .21034E-02 .41502E-02 .51544E-02 .88470E-03 .OOOOOE+00 .20742E-02 .78792E-02 .78735E-02 .22951E-02 .21232E-02 .83714E-02 .21593E-02 .43796E-02 .55508E-02 .13539E-03 .00000E+00 .15520E-02 .74729E-02 .76603E-02 .22377E-02 .21933E-02 .85353E-02 .23838E-02 .46424E-02 .58374E-02 .42996E-03
0. 0. 0. 0. 0,
-8. -6, -4, -2. -0. 0. 0. 0. 0 , 0. 0,
-11. -9, -7. -5. -3. -1. 0, 0. 0. 0. 0,
-13, -11. -9. -7, -5. -3. -1, 0, 0. 0. 0
-16. -14. -12 -10. -8 -6 -4 -2 -0 0 0
-19 -17 -15 -13 -11 -9 -7 -5 -3 -1 0
-19 -17 -15 -13 -11 -9 -7 -5 -3 -1 0
00 .00 00 .00 .00 20 .20 .20 .20 .20 00 .00 00 00 .00 00 ,00 .00 00 .00 00 00 .00 00 .00 .00 00 ,80 ,80 ,80 ,80 80 ,80 .80 ,00 ,00 ,00 .00 ,60 .60 .60 .60 .60 .60 .60 .60 .60 .00 .00 .40 .40 .40 .40 .40 .40 .40 .40 .40 .40 .00 .40 .40 .40 .40 .40 .40 .40 .40 .40 .40 .00
A72
RUNNING THE RSDAM PROGRAM APPENDIX F
STRESSES VALUES FOR STAGE 5
SIGMA SIGMA TAU SIGMA SIGMA X Y XY 1 3
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
0 0 0 0 0 0 0 0 0 0 5 5 4 4 3 3 2 2 1 0
16 15 13 12 10 8 7 5 4 2 28 25 22 20 17 14 11 9 6 3.
39. 35, 31, 27, 24. 20. 16. 12. 9. 5.
50. 45. 40. 35. 31. 26. 21. 16. 11. 6.
61. 55. 49. 43. 37. 31.
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.79
.25
.71
.17
.63
.09
.55
.01
.47
.94
.95
.34
.72
.10
.49
.87
.26
.64
.02
.41
.12
.43
.73
.04
.35
.65
.96
.27
.57
.88 ,28 ,51 ,74 ,97 20 43 66 89 12 35 45 60 76 91 06 21 37 52 67 82 62 69 77 84 92 99
1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7 9
11 13 15 17 19 1 3 5 7. 9
11. 13. 15. 17. 19. 1, 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11. 13. 15. 17. 19. 1. 3. 5. 7. 9.
11.
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
3 -9 -8 -1 -9 -4 -8 7 3 -9 2 1 1 1 1 9 8 5 3 1 1 1 1 1 1 9 8 5 3 1 1 1 1 1 9 8. 6. 4. 3. 1. 1. 1. 1. 1. 9. 7. 6. 4. 2. 1. 1. 1. 1. 1. 1. 7. 5. 3. 2. 5. 1. 1. 1. 1. 1. 7.
•678E+01 .314E+00 •181E-01 .614E+01 .962E+00 .140E+00 .637E-01 .760E-01 .721E-01 .046E-01 .112E+02 .735E+02 .443E+02 .234E+02 .049E+02 .951E+01 .634E+01 .919E+01 .504E+01 .269E+01 .862E+02 .658E+02 .433E+02 .249E+02 .083E+02 .862E+01 .330E+01 .720E+01 .644E+01 .772E+01 .779E+02 .537E+02 .344E+02 •143E+02 .724E+01 .223E+01 .565E+01 .942E+01 ,278E+01 .670E+01 .734E+02 580E+02 357E+02 145E+02 310E+01 542E+01 020E+01 402E+01 778E+01 123E+01 698E+02 567E+02 443E+02 255E+02 008E+02 605E+01 658E+01 996E+01 358E+01 799E+00 320E+02 517E+02 446E+02 294E+02 056E+02 985E+01
3 3 3 2 1 1 8 5 3 1 4 3 2 2 2 1 1 1 6 2 3 3 2 2 2 1 1 9 6 3 3 2 2 2 1 1. 1. 8. 5. 2. 2. 2. 2. 1. 1. 1. 1. 7. 4. 2. 2. 2. 1. 1. 1. 1. 8. 6. 4. 1. 1. 1. 1. 1. 1. 9.
.726E+02
.330E+02 •335E+02 .457E+02 .760E+02 .405E+02 .779E+01 .039E+01 .243E+01 .325E+01 .142E+02 .493E+02 .969E+02 .558E+02 .139E+02 •912E+02 .607E+02 .081E+02 .488E+01 .350E+01 .557E+02 .256E+02 .864E+02 .490E+02 .125E+02 .845E+02 .487E+02 .616E+01 .222E+01 .166E+01 .206E+02 .782E+02 .462E+02 .135E+02 .852E+02 ,591E+02 ,261E+02 .806E+01 .406E+01 .926E+01 913E+02 520E+02 126E+02 801E+02 518E+02 299E+02 083E+02 987E+01 635E+01 019E+01 686E+02 283E+02 942E+02 603E+02 308E+02 054E+02 607E+01 733E+01 109E+01 194E+01 916E+02 951E+02 691E+02 443E+02 176E+02 363E+01
1 -5 3
-1 1
-6 6 1
-1 1 2 1 1 1 8 5 5 5 3 8 1 1 1 1 1 7 3 2 1
-3 8 1 1 1 1 8 3
-2. -6. -5. -3. 1. 3. 4. 5. 5. 3. 8.
-1. -1. -5. -5. -3. -1. 6. 1. 1. 2.
-1. -1. 2. 9.
-3. -3. -1. 1.
.158E+02
.438E+01
.051E+01
.377E+01
.357E+01
.178E+00
.962E+00
.491E+00
.746E+00
.584E+00
.084E+01
.976E+01
.715E+01
.304E+01
.303E+00
.988E+00
.742E+00
.271E+00
.092E+00
.482E-01
.573E+01
.704E+01
.702E+01
.512E+01
.223E+01
.916E+00
.986E+00
.119E+00
.457E+00
.176E-01
.818E+00
.000E+01
.070E+01
.119E+01
.063E+01
.251E+00
.372E+00
.987E-02
.962E-01
.989E-01
.088E+00
.099E+00 583E+00 .758E+00 166E+00 054E+00 990E+00 930E-01 637E+00 300E+00 231E+00 490E+00 237E+00 169E+00 314E-01 605E+00 455E+00 733E-01 700E+00 942E+00 169E+00 481E-01 967E+00 625E+00 292E+00 498E+00
4 3 3 2 1 1 8 5 3 1 4 3 2 2 2 1 1 1 6 2 3 3 2 2 2 1 1 9 6 3. 3 2. 2. 2 1, 1. 1, 8, 5, 2. 2, 2. 2, 1. 1. 1. 1. 7. 4. 2. 2. 2. 1. 1. 1. 1. 8. 6. 4. 1. 1. 1. 1. 1. 1. 9.
.086E+02
.414E+02
.363E+02
.464E+02
.770E+02
.407E+02
.833E+01
.043E+01
.253E+01
.342E+01
.163E+02
.515E+02
.988E+02
.571E+02
.145E+02
.916E+02
.611E+02
.086E+02
.519E+01
.357E+01
.572E+02
.274E+02
.884E+02
.508E+02
.139E+02
.852E+02
.489E+02
.627E+01
.230E+01
.167E+01
.211E+02
.790E+02 ,472E+02 ,148E+02 .864E+02 .599E+02 .263E+02 .806E+01 409E+01 929E+01 913E+02 520E+02 127E+02 804E+02 523E+02 303E+02 086E+02 989E+01 650E+01 037E+01 689E+02 287E+02 944E+02 603E+02 308E+02 055E+02 614E+01 733E+01 126E+01 251E+01 916E+02 952E+02 698E+02 451E+02 178E+02 379E+01
7 -1 -3 -1 -1 -4 -1 7 2 -1 2 1 1 1 1 9 8 5 3 1 1 1 1 1 1 9 8 5 3, 1, 1, 1. 1, 1, 9, 8, 6, 4, 3 . 1. 1. 1, 1. 1. 9. 7. 5. 4. 2. 1. 1. 1. 1. 1. 1. 7. 5. 3 . 2 . 5. 1. 1. 1. 1. 1. 7.
.444E-01
.774E+01
.580E+00
.686E+01
.095E+01
.404E+00
.407E+00
.312E-01
.773E-01
.080E+00
.091E+02
.713E+02
.424E+02
.221E+02
.042E+02
.912E+01
.590E+01
.863E+01
.473E+01
.263E+01
.848E+02
.640E+02
.413E+02
.231E+02
.069E+02
.790E+01
.305E+01
.708E+01 ,636E+01 .771E+01 ,774E+02 ,529E+02 ,334E+02 ,130E+02 .597E+01 .135E+01 547E+01 942E+01 275E+01 667E+01 734E+02 580E+02 356E+02 142E+02 265E+01 495E+01 987E+01 400E+01 764E+01 105E+01 695E+02 563E+02 441E+02 255E+02 008E+02 596E+01 651E+01 996E+01 341E+01 237E+00 319E+02 517E+02 440E+02 286E+02 055E+02 969E+01
A73
RUNNING THE RSDAM PROGRAM APPENDIX F
87 88 89 90 91 92 93 94 95 96 97 98 99 100
26. 20. 14. 8.
67. 60. 54. 47 41 34 28 22 15 9
07 15 .22 ,30 ,30 ,84 .37 .91 .45 .98 .52 .06 .59 .13
13. 15. 17. 19. 1. 3 5. 7 9 11 13 15 17 19
00 00 .00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00
5. 3. 2.
-1. -4. -1, -8. -9, -9 -1 -1 -9 -6 -2
457E+01 650E+01 372E+01 .863E+00 .967E+02 .768E+03 .685E+02 .199E+02 .173E+02 .002E+03 .058E+03 .727E+02 .438E+02 .378E+02
7 , 5. 4. 3 . 4. 6
-1 -6 -1 -1 -1 -9 -8 -8
169E+01 495E+01 004E+01 .953E+00 .272E+03 .784E+02 .142E+02 .521E+01 .009E+02 .485E+02 .426E+02 .708E+01 .094E+01 .607E+01
2. 1. -1 -2. 9 5 3 3 2 3 3 3 2 5
.883E+00
.455E+00
.570E+00
.278E+00
.604E+02
.167E+02
.041E+02
.186E+02
.961E+02
.320E+02
.407E+02 •210E+02 •117E+02 . 012E+01
7 5, 4 4 4 7 -6 4 -4 -3 -2 8 -1 -7
.216E+01
.507E+01 ,019E+01 .739E+00 •458E+03 .831E+02 .889E+00 •047E+01 .823E+00 .455E+01 •973E+01 .001E+00 .022E+01 .101E+01
5, 3. 2,
-2. -6, -1 -9. -1 -1 -1 -1 -1 -7 -2
410E+01 638E+01 357E+01 649E+00 .828E+02 ,872E+03 .758E+02 .026E+03 .013E+03 .116E+03 .171E+03 .078E+03 .146E+02 .529E+02
INTERFACE ELEMENT RESULTS FOR STAGE 5
ELEM
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20
NO X
0. 0. 0. 0. 0. 0. 0. 0, 0. 0,
67 60 54 47 41 34 28 21 15 9
20 20 20 20 20 .20 ,20 .20 ,20 .20 .20 .74 .27 .81 .35 .88 .42 .96 .49 .03
Y
1. 3. 5. 7. 9.
11. 13. 15. 17. 19 1 3 5 7 9
11 13 15 17 19
NORMAL STRESS SHEAR
00 00 00 .00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
2. 0. 0. 0. 0, 1. 2, 2 0, 4 9 1 1 1 1 9 7 5 3 9
389E+01 000E+00 OOOE+00 OOOE+00 OOOE+00 .478E-01 .097E+00 .133E+00 .000E+00 .322E-01 .006E+01 .750E+02 .541E+02 .295E+02 .101E+02 .076E+01 .328E+01 .314E+01 .020E+01 .297E+00
-5. 0. 0. 0. 0. 2. -1 -4 0
-3 4
-1 -4 -4 -2 -8 -4 -1 -4 -4
STRESS
991E+00 000E+00 OOOE+00 .000E+00 .000E+00 .373E+00 .450E+00 .200E+00 .000E+00 .171E+00 .767E-01 .700E+00 .839E+00 .398E+00 .560E+00 .897E-01 .402E-01 .924E+00 .230E+00 .377E+00
NORMAL STIFF
1. 1. 1. 1. 1. 1. 1. 1. 1, 1 1 1 1 1 1 1 1 1 1 1
OOOE+08 000E+02 OOOE+02 OOOE+02 000E+02 OOOE+08 OOOE+08 .000E+08 OOOE+02 .000E+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .OOOE+08 .000E+08 .OOOE+08 .OOOE+08
SHEAR STIFF
4. 1. 1. 1. 1. 1. 4. 1. 1. 1. 4. 4 4 4 4 4 4 4 4 4
OOOE+03 000E+02 000E+02 OOOE+02 000E+02 000E+02 000E+03 000E+02 OOOE+02 .OOOE+02 .OOOE+03 .000E+03 .OOOE+03 .000E+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03 .OOOE+03
REINFORCEMENT RESULTS FOR STAGE 5
NUM.
1 2 3 4 5 6 7 8 9 10
I
1 2 3 4 5 6 7 8 9
10
J
111 112 113 114 115 116 117 118 119 120
TYPE
1 1 1 1 1 1 1 1 1 1
COMPR FORCE
0.000000E+00 1.516247E+01 -9.161447E+00 3.167562E+01 1.866586E+01 1.821873E+01 3.136692E+00 -4.022528E-01 -2 .177604E+00 1.640831E+00
0. -1, 1 2. 8 8
-1 6
-3 1
INCR COMPR
000000E+00 936103E-06 .190417E-05 .479181E-06 .431263E-06 .982606E-06 .862645E-08 .305054E-07 .599562E-06 .391396E-05
6. 6. 6. 6. 6. 6 6 6 6 6
STIFFNESS
750000E+05 750000E+05 .750000E+05 .750000E+05 .750000E+05 •750000E+05 .750000E+05 .750000E+05 .750000E+05 .750000E+05
A74
RSDAM PROGRAM LISTING APPENDIX G
APPENDIX G- RSDAM PROGRAM LISTING
Q ******************************************************************
C C * PROGRAM FOR C * C * (A) GEOMETRICAL OPTIMISATION OF REINFORCED EARTH DAMS C * C * AND * C C * (B) STRESS-STRAIN ANALYSIS WITHIN REINFORCED EARTH DAMS * C Q ******************************************************************
COMMON /MESH1/ PJ(99),KS(15,3),NIT(15),X11(1000),Y11(1000),NUS(15) &,TEJ(99),IB(35,3),JDN(99),STF(99),X(999),Y(999),MOD(99,15),IC(200) &,ALPHA(99),EZ(99),AO(99),FR(99),GAM(99)
C COMMON /MESH2/ XPB(99),BC(99),PHI(99),XXP(99),COHE(99),EIMN(99), & TN(99),HCF(99),ULF(99),IDN(99),GUE(99),REDJ(99) ,BR(35,9) /COJ(99) , & FRJ(99),XI(10 00),Y1(10 00),FX1(100)
C COMMON /MESH3/ IDT(99),STI(99),STS(99),STN(99),FX(10 0),FY(100),NMP & ,HIZ,HWIZ/GSUB,HSIZ,AKA,ALFA,CP,WT,WBIZ/TF
C DIMENSION Vl(lOO) ,VS(100) ,VE(100) ,V(100) ,E(100) ,W1(100) ,AKISI(100) DIMENSION H1(100),HS(100),RU(100),ANU(100),AMH(100),U(100),XK(100) DIMENSION WB(IOO),ANU1(100),SV(100),WR(100),AN(100),HE(100),Z(100) DIMENSION WS(100),W(100),H(100),HW(100),HW2(100),HI(10 0),DOV(100) DIMENSION AM(IOO),AM1(100),AM2(100),AM3(100),DELTA(100),D1(100) DIMENSION XX{100),XXI(100),XX2(100),XX3(100),XX4(100),XX5(100) DIMENSION XX6(100),XX7(100),AK1(100),AK2(100),AK3(100),VR(100) DIMENSION CMM(IOO),FST(100),AS(100),WEIGG(100),CC(100),ZZ(100) DIMENSION BET(IOO),BET1(100),SIG(100),SIGl(100),DD(100)
OPEN (UNIT=5,FILE='DAM1.OUT',STATUS='OLD') OPEN (UNIT=9,FILE='DAM.IN',STATUS='NEW')
_, ****************************************************************** C * MAIN PROGRAM c ******************************************************************
CALL INPUDATA(H(1),HW(1),HW2{1),HS(1),WT,WB(1),GW,GSUB,GS,SFS,SFO k ,SFB/SFOS,SFY,VI,ALFA,CP/Bl,B2,B,UR,N,RSTAR/FEE/FY,CU,KK,P,TF) FEEl=FEE/57.3248 EE=(45-FEE/2) EEl=EE/57.2958 AKA=(tan(EEl))**2 AK0=AKA*(1+SIN(FEE1)) AK=SFS/(tan (FEED ) XJ=H(1)/B2 J=XJ IF (XJ.GT.J) J=J+1 WRITE (5,19) WRITE (5 , *) 'NUMBER OF LAYERS= ' -J
WRITE (5,19) NMP=J+1 HIZ=H{1) HWIZ=HW(1) HSIZ=HS(1) IF (H(l).LE.15) THEN WT=H(1)/5+3 ELSE
WT=6 END IF 1 = 1
C WRITE (6,19) C WRITE (8,19) A75
RSDAM PROGRAM LISTING APPENDIX G
50 ZZ(1)=0 AKISI(I)=WT/WB(I) AN(I)=1+AKISI(I) CALL OUTPUT(I,H(I),HW(I),HW2(I),HS (I) ,WT,WB(I),AKISI(I)) CALL VERFORCE(Wl(I) ,WB(I) ,WT,HW(I),HW2(I),U(I),GW, H(I) ,WS(I) ,HS(I) 5c ,GSUB,W(I) ,GS,BET(I) ,SIG(I) , ANU (I) ) CALL HORFORCE(VI(I),GW,HW(I),VS(I),GSUB,HS(I),EE1,VE(I),CP,ALFA, & E(I),W(I),V(I),VI) CALL DIST(HKI) , HW( I) , HI (I) , HS (I) , HE (I) ,AMH(I) , VI (I) , VI, VS (I) , & VE(I)) CALL BEAOPTM(DOV(I),RSTAR,H(I),GS,BET(I),SIG(I),AKISI(I)) CALL SLIDOPTM(AMd) , BET (I) ,SIG(I) ,ANU(I) , AK, ALFA, XX (I) ,V(I) ,AN(I) , Sc H(I) ,GS) CALL OVTUOPTM(AKISI(I),H(I),BET1(I),HI(I),SIG1(I),HS(I),CMM(I), & BET(I),SIG(I),AM1(I),AM2(I),AM3(I),SFO,ALFA,AMH(I),GS,DELTA(I), & XXI(I),XX2(I),HW(I),HW2(I),ANU(I),ANU1(I)) CALL OVSTOPTM(AKKI) , RSTAR, SFOS, AN (I) ,H(I) ,GS,BET(I) ,SIG(I) , CC (I) , & AKISI(I) ,AK2(I),ALFA,AMH(I),AK3(I),DD(I),XX4(I) ,XX5(I),RU(I) , & XX7(I),WT) IF(ZZ(I).LT.XX(I)) ZZ(I)=XX(I) IF(ZZ(I) .LT.XXKI) ) ZZ(I)=XX1(I) IF(ZZ(I).LT.XX2(I)) ZZ(I)=XX2(I) IF(ZZ(I).LT.XX7(I)) ZZ(I)=XX7(I)
Q ****************************************************************** C * CHECK FOR NO BOND FAILURE OF REINFORCEMENTS WITHIN A * C * LAYER OF A REINFORCED EARTH DAM Q ******************************************************************
Z(I)=H(I) F0ST=1.2*ALOG10(CU) IF (KK.EQ.l) THEN GO TO 12 ELSE IF (KK.EQ.2) THEN GO TO 13 ELSE GO TO 14 END IF END IF
12 CALL CGM(Z(I),FST(I),FEE1,FOST,XK(I),AKA,AK0,XX3(I),Bl,B2,SFB,N,B, &H(D) IF(ZZ(I).LT.XX3(I)) ZZ(I)=XX3(I) GO TO 15
13 CALL MCGM(FSTd) ,Z(I) , FOST, FEE1, XK (I) ,AKA,AK0,XX3 (I) , Bl, B2 , SFB, N, B &,H(D) IF(ZZ(I).LT.XX3(I)) ZZ(I)=XX3(I) GO TO 15
14 CALL NCGM(Z(I),D1(I),FST(I),FEE1,FOST,XK(I),AKA,AK0,XX3(I),B1,B2, &SFB,N,B,H(1))
15 IF(ZZ(I).LT.XX3(I)) ZZ(I)=XX3(I) CALL NOFAIL(ZZ(I),WB(I)) IF (I.EQ.l) THEN IF (WB(1).LT.ZZ(l)) THEN WB(1)=ZZ(1) GO TO 50 END IF IF (WB(l)-ZZ(l).GT.0.1) THEN WB(1)=(WB(1)+ZZ(1))/2 GO TO 50 END IF END IF CALL REINAREA(SV(I) ,Z(I),GS,AS(I),XK(I) ,SFY,Bl,B2,N,FY,XX6(I) ,B, &XX3(I),VR(I),WR(I) ,UR,H(I)) WEIGG(1)=0 WEIGG(I+1)=WEIGG(I)+WR(I) IF(I.LT.XJ)THEN 1=1 + 1 H(I)=H(1)-(I-1)*H(1)/XJ HW(I)=HW(1)-(I-1)*H(1)/XJ HW2(I)=HW2(1)-(I-1)*H(1)/XJ HS(I)=HS(1)-(I-1)*H(1)/XJ WB(I)=WT+(WB(1)-WT)*H(I)/H(1)
A76
RSDAM PROGRAM LISTING APPENDIX G
ELSE C WRITE (8,*) 'TOTAL WEIGHT OF REINFORCEMENTS=',WEIGG(I+l)
GO TO 999 END IF WBIZ=WB(1) IF(O.GT.HSd) ) HS(I)=0 IF(O.GT.HWd) ) HW(I)=0 IF(0.GT.HW2(I)) HW2(I)=0 GO TO 50
999 CALL MESH 121 FORMAT (7 F 10.2) 19 FORMAT (/)
STOP END
p ******************************************************************
C * SUBROUTINE FOR INPUT DATA C ******************************************************************
SUBROUTINE INPUDATA(H,HW,HW2,HS,WT,WB, GW, GSUB, GS,SFS,SFO,SFB,SFOS &/SFY,VI,ALFA,CP,Bl,B2,B,UR,N,RSTAR,FEE,FY,CU,KK,P,TF) WRITE (*,11) WRITE (* * ) • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' WRITE (*,*)'HEIGHT OF DAM=? (m)• READ (*,*) H WRITE (*,*)'UPSTREAM WATER TABLE=? (m)' READ (*,*) HW WRITE (*,*)"DOWNSTREAM WATER TABLE=? (m)' READ (*,*) HW2 WRITE (*,*)'HEIGHT OF SILT=? (ra) ' READ (*,*) HS WRITE (*,*)'INITIAL TOP WIDTH OF DAM=? (m) ' READ (*,*) WT WRITE (*,*)'INITIAL BASE WIDTH OF DAM=? (m)' READ (*,*) WB GW=10. WRITE ( *,*) ' FOR CHANGING DATA TYPE 1 WRITE ( * , *) 'FOR CONTINUE TYPE 2 READ ( * , *) P IF (P.EQ.l) GO TO 1 WRITE (*,11) WRITE (* *) •*****************************************************' WRITE (*',*)'UNIT WEIGHT OF SILT=? (KN/m3)' READ (*,*) GSUB WRITE (*,*)"AVERAGE UNIT WEIGHT OF DAM=? (KN/m3 READ (*,*) GS WRITE (* * ) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * WRITE {*',*) 'SAFETY FACTOR AGAINST SLIDING=? READ (*,*) SFS WRITE (*,*)'SAFETY FACTOR AGAINST OVERTURNING=? READ (*,*) SFO WRITE (*,*)'SAFETY FACTOR AGAINST BOND FAILURE=? READ ( *,*) SFB WRITE (*,*)'SAFETY FACTOR AGAINST OVER-STRESSING=? READ ( *,*) SFOS WRITE (*,*)'SAFETY FACTOR AGAINST RUPTURE FAILURE=? READ (*,*) SFY WRITE (*,*)"FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ (*,*) P IF (P.EQ.l) GO TO 2 WRITE (*,11) WRITE (* *) •**************************************************' WRITE (*',*) 'ICE FORCE=? 'KN> READ (*,*) VI WRITE (*,*)'INITIAL COEFFICIENT OF EARTHQUAKE ACCELARATION=? READ (*,*) ALFA WRITE (*,*) 'COEFFICIENT OF INDIRECT FORCE OF EARTHQUAKE=? READ (*,*) CP WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( *,*) P IF (P.EQ.l) GO TO 3
********* '
A77
RSDAM PROGRAM LISTING APPENDIX G
WRITE (*,11) WRITE (*,*)"**************************,*»,***»****»**************,
4 WRITE (*,*)"WIDTH OF FACING PANELS=? lm) READ (*,*) Bl WRITE (*,*)'HEIGHT OF FACING PANELS=? (m) READ ( *,*) B2 WRITE (*,*) 'THICKNESS OF FACING PANELS=? (m) READ (*,*) TF WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( *,*) P IF (P.EQ.l) GO TO 4 WRITE (*,11) WRITE (*,*)'*****************************************************,
5 WRITE (*,*)"WIDTH OF REINFORCEMENTS=? (m) READ ( *,*) B WRITE (*,*) 'UNIT WEIGHT OF REINFORCEMENTS=? (KN/m3) READ (*,*) UR WRITE (*,*)'ALLOWABLE TENSION OF REINFORCEMENTS=? (KN/m2) READ ( *,*) FY WRITE (*,*)'NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL=? & READ ( *,*) N WRITE ( * , *) " FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( *,*) P IF (P.EQ.l) GO TO 5 WRITE (*,11) WRITE (*,*) ' *****************************************************•
6 WRITE (*,*)'ALLOWABLE BEARING CAPACITY OF FOUNDATION SOIL=? (KN/m2 &) * READ (*,*) RSTAR WRITE (*,*)'ANGLE OF INTERNAL FRICTION OF SOIL=? (DEGREE) READ ( *,*) FEE WRITE (*,*)'COEFFICIENT OF UNIFORMITY OF SOIL=? READ ( *,*) CU WRITE ( *,*) ' FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( *,*) P IF (P.EQ.l) GO TO 6 WRITE (*,11) WRITE (* * ) • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * '
7 WRITE (*,*) '1- INTERNAL STABILITY ANALYSIS BASED ON COHERENT GRAVI &TY METHOD WRITE (*,*) '2- INTERNAL STABILITY ANALYSIS BASED ON MODIFIED COHER &ENT GRAVITY METHOD' WRITE (*,*) '3- INTERNAL STABILITY ANALYSIS BASED ON NEW COHERENT G &RAVITY METHOD READ (*,*) KK WRITE (* * ) ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (* , *) 'FOR CONTINUE TYPE 2 READ ( *,*) P IF (P.EQ.l) GO TO 7 WRITE (*,11)
11 FORMAT (/1111 /7 / / / /1111111111•/) 19 FORMAT (/)
WRITE (5,*)'ggggggggggggggggggggggggggggggggggggggggggggggggggggg WRITE (5 * ) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * WRITE (5,*)'* * WRITE (5,*) '* WRITE (5,*)'* INPUT DATA * WRITE (5,*)"* WRITE (5,*)'* WRITE (5 *) '***************************************************** WRITE (5,*)"@g@gggggggggggggggggggggggggggggggggggggggggggggggggg
WRITE (5,*)'HEIGHT OF DAM= WRITE (5,*)'UPSTREAM WATER TABLE= WRITE (5,*) "DOWNSTREAM WATER TABLE= WRITE (5,*)'HEIGHT OF SILT= WRITE (5,*) 'TOP WIDTH OF DAM=
,H, 'm ' ,HW,' m' ,HW2,' m' ,HS,' m' ,WT,' m'
A78
RSDAM PROGRAM LISTING APPENDIX G
WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE &,N WRITE WRITE WRITE WRITE WRITE WRITE WRITE
5,*)'BOTTOM WIDTH OF DAM= 5,19) 5,*)"UNIT WEIGHT OF WATER= 5,*)"UNIT WEIGHT OF SILT= 5,*)'AVERAGE UNIT WEIGHT OF DAM= 5,19) 5,*)'SAFETY FACTOR AGAINST SLIDING= 5,*)'SAFETY FACTOR AGAINST SLIDING= 5,*)"SAFETY FACTOR AGAINST BOND FAILURE= 5,*)'SAFETY FACTOR AGAINST OVER-STRESSING= 5,*)'SAFETY FACTOR AGAINST RUPTURE FAILURE 5,19) 5,*) 'ICE FORCE=
',WB,' m'
',GW,' KN/m3' ',GSUB, ' KN/m3' ',GS,' KN/m3'
' ,SFS ' ,SFS ' ,SFB ',SFOS ' ,SFY
19) • VI, KN'
*)'COEFFICIENT OF EARTHQUAKE ACCELARATION= ",ALFA *)"COEFFICIENT OF INDIRECT FORCE OF EARTHQUAKE=',CP 19) *) 'WIDTH OF FACINGS= • , Bl,
5,*)'HEIGHT OF FACINGS= ',B2, 5,*) 'WIDTH OF REINFORCEMENTS= ',B, ' 5,*) 'UNIT WEIGHT OF REINFORCEMENTS= ' ,UR,
m' m' n" KN/m3'
m
19) *)"NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL=
19) *)'ALLOWABLE BEARING CAPACITY OF SOIL= *)"ANGLE OF INTERNAL FRICTION OF SOIL= 19) *)"ALLOWABLE TENSION OF REINFORCEMENTS= *)'COEFFICIENT OF UNIFORMITY OF SOIL=
RSTAR," KN/m2 FEE,' DEGREE'
",FY,' KN/m2 " ,CU
(5,19) IF (KK.EQ.l) WRITE (5,*)"INTERNAL STABILITY ANALYSIS IS BASED ON C
COHERENT GRAVITY METHOD" IF (KK.EQ.2) WRITE (5,*)'INTERNAL STABILITY ANALYSIS IS BASED ON M MODIFIED COHERENT GRAVITY METHOD' IF (KK.EQ.3) WRITE (5,*)'INTERNAL STABILITY ANALYSIS IS BASED ON N &EW COHERENT GRAVITY METHOD' RETURN END
19
C C C C
SUBROUTINE OUTPUT(I,H,HW,HW2,HS,WT,WB,AKISI) WRITE (5,*) 'ggggggggggggggggggggggggggggggggggggggggggggggggggggg WRITE (5 *) ****************************************************** WRITE (5,*)'* * WRITE ( 5 , * ) '* * WRITE (5,*) '* OUTPUT * WRITE (5,*)'* * WRITE (5,*) "* * WRITE (5 *) ****************************************************** WRITE (5,*) 'ggggggggggggggg@@g@ggggggggggggggggggggggggggggggggg@ WRITE (5,19) WRITE (5,*) 'LAYER NO.= ',I WRITE (5,19) WRITE (5,*) 'HEIGHT OF LAYER= ',H,' m* WRITE (5,*)'UPSTREAM WATER TABLE= ',HW,' m' WRITE (5,*) "DOWNSTREAM WATER TABLE= ',HW2, ' m' WRITE (5,*)'HEIGHT OF SILT= ',HS,' m' WRITE (5,*) "TOP WIDTH OF LAYER= ",WT, " m' WRITE (5,*)'BOTTOM WIDTH OF LAYER= ',WB,' m' WRITE (5,19) WRITE (5,*)"RATIO OF TOP WIDTH TO BOTTOM WIDTH=',AKISI WRITE (5,19) FORMAT (/) RETURN END ****************************************************************** * SUBROUTINE FOR CALCULATION OF HORIZONTAL FORCES ACTING ON * * A REINFORCED EARTH DAM * ****************************************************************** SUBROUTINE HORFORCE(VI,GW,HW,VS,GSUB, HS,EE1,VE,CP,ALFA,E,W,V,VI) Vl=GW*HW**2/2
A79
RSDAM PROGRAM LISTING APPENDIX G
c
c
C
VS=GSUB*HS**2*(TAN(EEl))**2/2 VE=0.726*CP*ALFA*GW*HW**2 E=ALFA*W V=V1+VI+VS+VE WRITE (5,19) WRITE (5,*)'HYDROSTATIC FORCE ACTING ON LAYER= \V1,'KN' WRITE (5,*) "ICE FORCE ACTING ON LAYER= ',VI,'KN' WRITE (5,*)"SILT FORCE ACTING ON LAYER= ',VS,'KN' WRITE (5, *) 'INDIRECT FORCE OF EARTHQUAKE ACTING ON LAYER=' ,VE, 'KN' WRITE (5,*)'DIRECT FORCE OF EARTHQUAKE ACTING ON LAYER= ',E,'KN'
C WRITE (5,19) C WRITE (5,*)'SUM OF HORIZENTAL FORCES EXCEPT DIRECT FORCE OF EARTHQ C &UAKE=',V,' KN'
WRITE (5,19) 19 FORMAT (/)
RETURN END
n ****************************************************************** C * SUBROUTINE FOR CALCULATION OF VERTICAL FORCES ACTING ON A C * REINFORCED EARTH DAM *
****************************************************************** SUBROUTINE VERFORCE(Wl,WB,WT,HW, HW2,U,GW,H,WS,HS,GSUB,W,GS,BET,SIG Sc ,ANU) W1=(WB-WT)*HW**2*GW/(2*H) WS=(WB-WT)*HS**2*GSUB/(2*H) W=(WT+WB)*H*GS/2 U=GW*(HW+HW2)*WB/2 WRITE (5,*) 'WEIGHT OF LAYER= ',W, 'KN' WRITE (5,*)'WEIGHT OF WATER ON UPSTREAM SIDE OF LAYER= ',Wl,'KN' WRITE (5,*)'WEIGHT OF SILT ON UPSTREAM SIDE OF LAYER= ',WS,'KN' WRITE (5,*)'UPLIFT PRESSURE ACTING ON THE LAYER= ',U,"KN' BET=W1/W S1G=WS/W ANU=U/W RETURN END ******************************************************************
SUBROUTINE FOR CALCULATION OF THE DISTANCES OF THE C * FORCES ACTING ON A LAYER OF A C * REINFORCED EARTH DAM * Q ******************************************************************
SUBROUTINE DIST(HI,HW,HI,HS,HE,AMH,VI,VI,VS,VE) Hl=HW/3 HI=HW HE=0.4*HW AMH=Vl*Hl+VI*HI+VS*HS/3+VE*HE
C WRITE (5,19) C WRITE (5,*)'SUM OF DRIVING MOMENTS= ',AMH,' KN-m' C WRITE (5,19) 19 FORMAT (/)
RETURN END
Q ****************************************************************** C * SUBROUTINE FOR NO BEARING CAPACITY FAILURE STATE Q ******************************************************************
SUBROUTINE BEAOPTM(DOV,RSTAR,H,GS, BET,SIG,AKISI) DOV=2*RSTAR/(H*GS*(1+BET+SIG)) IF(AKISI.GT.DOV)THEN WRITE (5,*)'BEARING CAPACITY FAILURE WILL HAPPEN' ELSE WRITE (5,*)'BEARING CAPACITY FAILURE WILL NOT HAPPEN' END IF WRITE (5,19)
19 FORMAT (/) RETURN END n ****************************************************************** C * SUBROUTINE FOR NO SLIDING FAILURE STATE WITHIN A C * LAYER OF REINFORCED EARTH DAM ****************************************************************** SUBROUTINE SLIDOPTM(AM,BET,SIG, ANU, AK,ALFA,XX,V,AN,H,GS)
A80
RSDAM PROGRAM LISTING APPENDIX G
AM=(1+BET+SIG-ANU-(AK*ALFA))/AK IF(AM.LE.O) THEN WRITE (5,*)'WARNING; SLIDING MAY HAPPEN' WRITE (5,19) END IF XX=2*V/(AM*AN*H*GS) WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO SLIDING= ",XX," & m"
19 FORMAT (/) RETURN END
Q ****************************************************************** C SUBROUTINE FOR NO OVERTURNING FAILURE STATE WITHIN * c * A LAYER OF REINFORCED EARTH DAM * Q ******************************************************************
SUBROUTINE OVTUOPTM(AKISI,H,BET1,HI,SIG1,HS,CMM,BET,SIG,AMI,AM2, & AM3 , SFO, ALFA, AMH, GS, DELTA, XXI, XX2 , HW, HW2 , ANU, ANU1) BET1=(1+AKISI)*(3*H-H1+H1*AKISI)/((1+AKISI+AKISI**2)*H) SIG1=(1+AKISI)*(3*H-HS/3+HS*AKISI/3)/((1+AKISI+AKISI**2)*H) IF (HW.EQ.0.AND.HW2.EQ.0) THEN ANU1=0 ELSE ANU1=(1+AKISI)*(2*HW+HW2)/((1+AKISI+AKISI**2)*(HW+HW2)) END IF CMM=(1+BET*BET1+SIG*SIG1-ANU*ANU1*SF0) AM1=(1+AKISI+AKISI**2)*CMM/(6*SFO) AM2=(-1)*ALFA*H*(1+2*AKISI)/6 AM3=(-1)*AMH/(H*GS) DELTA=AM2 **2-4*AMl*AM3 IF (DELTA.LT.O) THEN IF (AMI.LT.O) THEN WRITE (5,19) WRITE (5,*) "NO ANSWER FOR THE EQUATION OF OVERTURNING FAILURE' WRITE (5,*) "FOR NO OVERTURNING FAILURE, MINIMUM BASE LENGTH SHOUL &D BE INCREASED" WRITE (5,*) END IF ELSE XX1=(AM2 +DELTA* * 0.5)/(-2 *AM1) XX2=(-1*AM2+DELTA**0.5)/(2*AM1) IF (AMI.LT.O)THEN WRITE (5,*) XX1,'<MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING<' , & XX2,' m' ELSE WRITE (5,*)"MIN. REQUIRED BASE LENGTH FOR NO OVERTURNING= ",XX2 &, " m' END IF END IF
19 FORMAT (/) RETURN END
Q ****************************************************************** C * SUBROUTINE FOR NO OVER-STRESSING FAILURE STATE WITHIN * C * A LAYER OF A REINFORCED EARTH DAM * Q ******************************************************************
SUBROUTINE OVSTOPTM(AK1,RSTAR,SFOS,AN,H,GS,BET,SIG,CC,AKISI,AK2, & ALFA,AMH,AK3,DD,XX4,XX5,RU,XX7,WT) AKl=RSTAR/SFOS-AN*H*GS*(1+BET+SIG)12 CC=H*(2*AKISI+1)/(3*(AKISI+1)) AK2 = -3 *AN*H*GS*ALFA*CC AK3=-6*AMH DD=AK2**2-4*AK1*AK3 IF (DD.LT.O) THEN WRITE (5,*) "NO ANSWER FOR THE EQUATION OF OVER-STRESSING FAILURE' ELSE IF (AK1.EQ.0) THEN XX5=-AK3/AK2 WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO OVER-STRESSING=',XX5, &' m' GO TO 99 END IF
A81
RSDAM PROGRAM LISTING APPENDIX G
XX4=(AK2+DD**0.5)/(-2*AKl) XX5=(-1*AK2+DD**0.5)/(2*AK1) IF (AK1.LT.O)THEN WRITE (5,*) XX4,'<MIN. REQUIRED BASE LENGTH FOR NO OVER-STRESSING< &', XX5,' rn' ELSE WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO OVER-STRESSING=',XX5, &' m' END IF
99 END IF RU=H*GS*SFOS*(1+BET+SIG)/(2*RSTAR) XX7=WT*RU/(1-RU) IF (XX7.LT.0) THEN WRITE (5,19) WRITE (5,*)'OVER-STRESSING FAILURE WILL HAPPEN' PRINT *,'ERROR: BEARING CAPACITY OF FOUNDATION SOIL IS VERY LOW' WRITE (5,*)'BEARING CAPACITY OF FOUNDATION SOIL IS VERY LOW' WRITE (5,19) STOP ELSE WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO OVER-STRESSING=',XX7, &' m' END IF
19 FORMAT (/) RETURN END
Q ****************************************************************** C * SUBROUTINE FOR NO BOND FAILURE OF REINFORCEMENTS WITHIN A * C * LAYER OF A REINFORCED EARTH DAM * C * BASED ON COHERENT GRAVITY METHOD * Q ******************************************************************
SUBROUTINE CGM(Z,FST,FEE1,FOST,XK,AKA,AKO,XX3,Bl,B2,SFB,N,B,H) IF (Z.LE.6)THEN FST=Z*(tan(FEEl)-FOST)/6+FOST XK=Z*(AKA-AKO)/6+AKO ELSE FST=tan(FEEl) XK=AKA END IF XX3=XK*B1*B2*SFB/(2*N*FST*B) IF (Z.LE.H/2)THEN XX3=XX3+0.3*H ELSE XX3=XX3+0.6*(H-Z) END IF WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= ',XX3, &' m' WRITE (5,19)
19 FORMAT (/) RETURN END
C ****************************************************************** C * SUBROUTINE FOR NO BOND FAILURE OF REINFORCEMENTS * C * WITHIN A LAYER OF A REINFORCED EARTH DAM * C * BASED ON MODIFIED COHERENT GRAVITY METHOD * Q ******************************************************************
SUBROUTINE MCGM(FST,Z,FOST,FEE1,XK,AKA,AKO,XX3,Bl,B2,SFB,N,B,H) FST=((0.6)**Z)*(1.7*F0ST-tan(FEEl))+tan(FEED XK=((0.75)**Z)*(AKA-AKO)+AKA XX3=XK*B1*B2*SFB/(2*N*FST*B) XX3=XX3+H*((6.76-(Z/H)**2)**0.5-2.3) WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= ',XX3, &' m' WRITE (5,19)
19 FORMAT (/) RETURN END Q ****************************************************************** C * SUBROUTINE FOR NO BOND FAILURE OF REINFORCEMENTS * C * WITHIN A LAYER OF A REINFORCED EARTH DAM C * BASED ON NEW COHERENT GRAVITY METHOD *
A82
RSDAM PROGRAM LISTING APPENDIX G
Q ****************************************************************** SUBROUTINE NCGM(Z,Dl,FST,FEE1,FOST,XK,AKA,AKO,XX3,Bl,B2,SFB,N,B,H) IF (Z.LE.6)THEN Dl=Z**2/36-Z/3+l FST=tan(FEEl)+0.9**Z*D1* (3 . 85*F0ST-tan(FEED) XK=1.2**Z*D1*(AKA-AKO)+AKA ELSE FST=tan(FEEl) XK=AKA END IF XX3=XK*B1*B2*SFB/(2*N*FST*B) XX3=XX3+H*((6.76-(Z/H)**2)**0.5-2.3) WRITE (5,*) 'MIN. REQUIRED BASE LENGTH FOR NO BOND FAILURE= ',XX3, &' m' WRITE (5,19)
19 FORMAT (/) RETURN END
r» * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C * SUBROUTINE FOR CHECK OF MINIMUM REQUIRED BASE LENGTH C * FOR NO FAILURE Q ******************************************************************
SUBROUTINE NOFAIL(ZZ,WB) IF (ZZ.LE.WB) THEN WRITE (5,*) 'MIN. REQUIRED BASE LENGTH FOR NO FAILURE= ',ZZ,' m' ELSE WRITE (5,*)'MIN. REQUIRED BASE LENGTH FOR NO FAILURE= ",ZZ,' m' WRITE (5, * ) ' FOR NO FAILURE BASE LENGTH SHOULD BE INCREASED' WRITE (5,19) END IF
19 FORMAT (/) RETURN END
£, ****************************************************************** C * SUBROUTINE FOR CALCULATION OF THE CROSS SECTION AREA OF C * REINFORCEMENTS WITHIN A LAYER OF C * A REINFORCED EARTH DAM
****************************************************************** SUBROUTINE REINAREA(SV,Z,GS,AS,XK,SFY,Bl,B2,N,FY, XX6, B,XX3,VR,WR,
ScUR,H) SV=Z*GS AS=XK*SV*SFY*B1*B2*10000/(N*FY) XX6=AS/(B*100) VR=AS*XX3*N/(10000*B1*B2) WR=VR*UR WRITE (5,19) WRITE (5,*) 'NUMBER OF REINFORCEMENTS CONNECTED TO A FACING PANEL=' Sc, N WRITE (5,*) 'MIN. REQUIRED LENGTH OF REINFORCEMENT= &,XX3,' m' WRITE (5,*)'MIN. NET THICKNESS OF REINFORCEMENT= Sc,XX6*10, " mm" WRITE (5,*) 'WIDTH OF REINFORCEMENT= &,B*100,' cm" WRTTF (5 19) WRITE (5!*)'MIN. CROSS SEC. AREA OF REINFORCEMENT= ',AS*N/(B1*B2) Sc, ' cm2/m2 AREA' WRITE (5,*) "MIN. NET VOLUME OF REINFORCEMENT= ',VR,' & m3/m2 AREA' WRITE (5,*)'MIN. NET WEIGHT OF REINFORCEMENT= ',WR,' & KN/m2 AREA'
19 FORMAT (/) RETURN END
c ****************************************************************** C * SUBROUTINE FOR MESH GENERATION r ******************************************************************
C
SUBROUTINE MESH COMMON /MESH1/ PJ(99),KS(15,3),NIT(15),Xll(1000),Yll(1000),NUS(15) &,TEJ(99),IB(35,3),JDN(99),STF(99),X(999),Y(999),MOD(99,15),IC(200) &,ALPHA(99),EZ(99),AO(99),FR(99),GAM(99)
A83
RSDAM PROGRAM LISTING APPENDIX G
COMMON /MESH2/ XPB(99),BC(99),PHI(99),XXP(99),COHE(99),EIMN(99), & TN(99),HCF(99),ULF(99),IDN(99),GUE(99),REDJ(99),BR(35,9),COJ(99), & FRJ(99),X1(1000),Y1(1000),FX1(100) COMMON /MESH3/ IDT(99),STI(99),STS(99),STN(99),FX(IOO),FY(100),NMP &. ,HIZ,HWIZ, GSUB, HSIZ, AKA, ALFA, CP, WT, WBIZ , TF WRITE (*, *) ***************************************************** ' WRITE (9,*)'REINFORCED EARTH DAM ANALYSIS' WRITE (*,*) 'NUMBER OF NODAL POINTS IN X-DIRECTION=? READ (*,*) NUP NNP=NUP*NMP NUMEL=(NUP-1)*(NMP-1) NUMJT=2*(NMP-1) NUMBA=0 NBEAM=0 NBTYPE=0 NMOD=0 NC=5 INIT=1 IHORIZ=0 ITRD=2 ILIST=1 IOUT=0 WRITE(9,5010) NNP,NUMEL,NUMJT,NUMBA,NBEAM,NBTYPE,NC,NMOD,INIT, & IHORIZ,ITRD,ILIST,IOUT GW=10 PATM=100 WRITE(9,5015) GW,PATM NMAT=3 NNNNN=1 NUMSOL=NMAT-NNNNN IATYP=0 INOSLIP=0 WRITE(9,502 0) NMAT,NUMSOL,0,1,0,0,0,0,IATYP,INOSLIP DO 2 0 N=1,NC+1 KS(N,2)=0 KS(N,3)=0 MOD(1,N)=0 KS(1,1)=5 NIT(1)=1 NIT(N)=1 NUS(N)=1 IF (N .EQ. 1) WRITE(9,5040) KS(N,1),KS(N,2),KS(N,3),NIT(N),NUS(N), & MOD(1,N),'REINFORCEMENT INSTALATION' IF (N .EQ. 2) THEN KS(N,1)=9 END IF IF (N -EQ. 3) THEN KS(N,1)=9 WRITE(9,5040) KS(N,1),KS(N,2),KS(N,3),NIT(N),NUS(N),MOD(l,N), Sc 'HYDROSTATIC FORCE' ENDIF IF (N .EQ. 4) THEN KS(N,1)=9 WRITE(9,5040) KS(N,1),KS(N,2),KS(N,3),NIT(N),NUS(N),MOD(1,N), & 'SILT FORCE' ENDIF IF (N .EQ. 5) THEN WRITE(*,*) '1- STATIC ANALYSIS=? & 2- TIME HISTORY ANALYSIS=? READ (*,*) ZEL IF (ZEL .EQ. 1) THEN KS(N,D=9 WRITE(9,504 0) KS(N,D,KS(N,2),KS(N,3),NIT(N),NUS(N),MOD(l,N) , & 'EARTHQUAKE FORCE' END IF IF (ZEL .EQ. 2) THEN KS(N,D=8 WRITE(9,5040) KS(N,1),KS(N,2),KS(N,3),NIT(N),NUS(N),MOD(l,N), & 'EARTHQUAKE FORCE OR DISPLACEMENT' END IF ENDIF
A84
RSDAM PROGRAM LISTING APPENDIX G
IF (N .EQ. 6) THEN KS(N,1)=3 WRITE(9,504 0) KS(N,1),KS(N,2),KS(N,3),NIT(N),NUS(N),MOD(l,N), & 'SEEPAGE LINE VARIATION' ENDIF IF (N .EQ. NC+1) GO TO 100
2 0 CONTINUE 100 WRITE (*,*) •***************FACING PANELS PROPERTY***************'
DO 160 N=l,NUMSOL IF (N .EQ. 1) THEN ZTZ=0 WRITE(*,*) 'UNIT WEIGHT OF FACING PANELS=? (KN/m3) READ(*,*) GAM(N) COHE(N)=0 PHI(N)=0 TN(N)=0 AO(N)=0 XXP(N)=0 HCF(N)=0 ULF(N)=0 FR(N)=0 EIMN(N)=0 XPB(N)=0 BC(N)=0
2 WRITE (*,*) 'YOUNG,S MODULUS OF FACING PANELS= (KN/m2) READ (*,*) EZ(N) WRITE (*,*) 'POISSON,S RATIO OF FACING PANELS READ (*,*) GUE(N) WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ (*,*) P IF (P.EQ.l) GO TO 2 WRITE (*,11) ELSE WRITE (*,*) *********************SOIL PROPERTY*******************'
1 WRITE {*',*) 'IS THE MATERIAL DRAINED? WRITE (*,*) '0-NO
& 1-YES READ(*,*)ZTZ IF (ZTZ.EQ.l) IDN(N)=1 IF (ZTZ.EQ.0) IDN(N)=0 , WRITE(*,*) "UNIT WEIGHT OF THE MATERIAL=? (KN/m3) READ(*,*) GAM(N) WRITE '(*,*) 'COHESION OF THE MATERIAL=? (KN/m2) READ(*,*) COHE(N) mPPRFF)' WRITE (*,*) "FRICTION ANGLE=? (Ub^Ktuj READ (* *) PHI(N)
c WRITE '(*,*) 'MIN. ALLOWABLE VALUE OF MINOR PRINCIPAL STRESS=? c READ (*,*} TN(N)
TN(N)=0 WRITE (*,*) "LATERAL EARTH PRESSURE COFFICIENT AT REST=? READ (*,*) AO(N) WRITE (*,*) 'INITIAL TANGENT MODULUS EXPONENT=? READ (*,*) XXP(N) WRITE (*,*) 'INITIAL TANGENT MODULUS COEFFICIENT? READ (*,*) HCF(N) WRITE (*,*) "FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( * , *) P IF (P.EQ.l) GO TO 1 WRITE (*,11) ENDIF WRITE(9,5080) IDN(N),GAM(N),COHE(N),PHI(N),TN(N),AO(N),XXP(N), & HCF(N)
SITE if;)1!™^********************************** — **; 21 WRITE (*,*) 'UNLOAD-RELOAD MODULUS COFFICIENT=?
READ (*,*) ULF(N) PR (jj) -l WRITE"(*,*)'MIN. INITIAL TANGENT MODULUS FOR NON-ELASTIC MATERIALS Sc =? (KN/m2) '
A85
RSDAM PROGRAM LISTING APPENDIX G
READ (*,*) EIMN(N) WRITE (*,*) "BULK MODULUS EXPONENT=? READ (*,*) XPB(N) WRITE (*,*) 'BULK MODULUS COEFFICIENT? READ (*,*) BC(N) WRITE (*,*) 'YOUNG,S MODULUS=? (KN/m2) ' READ (*,*) EZ(N) WRITE (*,*) 'POISSON,S RATIO=? READ (*,*) GUE(N) WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE ( *,* ) 'FOR CONTINUE TYPE 2 READ ( *,*) P IF (P.EQ.l) GO TO 21 WRITE (*,11) ENDIF ALPHA(N)=0 WRITE(9,5100) ULF(N),FR(N),EIMN(N),XPB(N),BC(N),EZ(N),GUE(N), Sc ALPHA (N)
160 CONTINUE DO 170 N=NUMSOL+l,NMAT JDN(N)=0 COJ(N)=0 WRITE (*,*)"FRICTION COFICIENT BETWEEN FACING PANELS AND SOIL=? READ (*,*) PJ(N) TEJ(N)=0 IDT(N)=0 WRITE(9,5085) JDN(N),COJ(N),PJ(N),TEJ(N),IDT(N) STI(N)=4000 STS(N)=100 STN(N)=100000000 STF(N)=100 FRJ(N)=0 REDJ(N)=0 WRITE(9,5090) STI(N),STS(N),STN(N),STF(N),FRJ(N),REDJ(N)
17 0 CONTINUE X(1)=0 X(NUP)=WBIZ X(NMP)=0 X(NNP)=WT Y(1)=0 Y(NUP)=0 Y(NMP)=HIZ Y(NNP)=HIZ K=l DO 190 N=1,NNP,NMP IF(N .EQ. 1) THEN WRITE(9,5120) N,0,0 WRITE(9,5120) N+NMP-1,0,HIZ GO TO 190 ENDIF IF(N .EQ. NMP+1 .OR. N .EQ. 2*NMP+D THEN WRITE(9,5120) N,TF,0 WRITE(9,5120) N+NMP-1,TF,HIZ GO TO 190 ENDIF IF(N .EQ. NNP-2*NMP+1 .OR. N .EQ. NNP-3*NMP+1) THEN WRITE(9,5120) N,WBIZ-TF,0 WRITE(9,512 0) N+NMP-1,WT-TF,HIZ GO TO 190 ENDIF IF(N .EQ. NNP-NMP+1) THEN WRITE(9,5120) N,WBIZ,0 WRITE(9,5120) N+NMP-1,WT,HIZ GO TO 190 ENDIF WRITE(9,5120) N,TF+(WBIZ-2*TF)*K/(NUP-5),0 WRITE(9,5120) N+NMP-1,TF+(WT-2*TF)*K/(NUP-5),HIZ K=K+1 19 0 CONTINUE 3 4 0 WRITE(*,*)•******************************************************' 3 WRITE (*,*) "NUMBER OF NODAL FIXED POINTS IN Y-DIRECTION=?
A86
RSDAM PROGRAM USTING APPENDIX G
READ (* , *) NOY WRITE (*,*) 'NUMBER OF NODAL FIXED POINTS IN X-DIRECTION=? READ (*,*) NOX WRITE (*,*) "NUMBER OF NODAL FIXED POINTS IN X AND Y DIRECTIONS=?' READ (*,*) NOXY WRITE (*,*) 'NUMBER OF NODAL FIXED POINTS AGAINST ROTATING=? READ (* , * ) NOROT WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE ( *,*) 'FOR CONTINUE TYPE 2 READ (*,*) P IF (P.EQ.l) GO TO 3 WRITE (*,11) WRITE(9,5020) NOY,NOX,NOXY,NOROT WRITE ( * * ) •******************************************************' IF(NOY .EQ. 0) GO TO 4 00
4 WRITE (*,*) 'NODAL NUMBERS AGAINST Y-MOVEMENT=? READ (*,*) (IC(N),N=l,NOY) WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ (*,*) P IF (P.EQ.l) GO TO 4 WRITE (*,11) WRITE(9,5020) (IC(N),N=l,NOY)
400 IF(NOX .EQ. 0) GO TO 460 5 WRITE (*,*) 'NODAL NUMBERS AGAINST X-MOVEMENT=?
READ (*,*) (IC(N),N=l,NOX) WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ (*,* ) P IF (P.EQ.l) GO TO 5 WRITE (*,11) WRITE(9,5020) (IC(N),N=l,NOX)
460 IF(NOXY .EQ. 0) GO TO 510 6 WRITE (*,*) 'NODAL NUMBERS AGAINST BOTH X- AND Y- MOVEMENTS=?
READ (*,*) (IC(N),N=l,NOXY) WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ (*,*) P IF (P.EQ.l) GO TO 6 WRITE (*,11) WRITE(9,5020) (IC(N),N=1,NOXY)
510 IF(NOROT.EQ.0) GO TO 520 7 WRITE (*,*) 'NODAL NUMBERS AGAINST ROTATIONS=?
READ (*,*) (IC(N),N=1,NOROT) WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( * , *) P IF (P.EQ.l) GO TO 7 WRITE (*,1D WRITE(9,5020) (IC(N),N=1,NOROT)
C 520 IF(NUMEL.EQ.O) GO TO 660
DO 570 N=1,NUMEL IF (N .EQ. 1) THEN WRITE(9,5020) N,(2*NMP+D,(2*NMP+2),(NMP+2),(NMP+1),NMAT WRITE(9,5020) N+NMP-2,3*NMP-1,3*NMP,2*NMP,2*NMP-1,NMAT ENDIF IF (N .EQ. NMP) THEN WR1TE(9,5020) N,(NUP-2)*NMP+1,(NUP-2)*NMP+2,(NUP-3)*NMP+2, &(NUP-3)*NMP+1,NMAT WRITE(9,5020) N+NMP-2,NNP-NMP-1,NNP-NMP,NNP-2*NMP,NNP-2*NMP-1,NMAT ENDIF IF (N -EQ. 2*NMP-1) THEN WRITE(9,5020) N,NMP+1,NMP+2,2,1,1 WRITE(9,502 0) N+NMP-2,2*NMP-1,2*NMP,NMP,NMP-1,1 ENDIF K=2 DO 571 II=2,NUP-4 IF(N .EQ. (K+1)*NMP-K) THEN WRITE(9,5020)N,(K+1)*NMP+1,(K+l)*NMP+2,K*NMP+2,K*NMP+1,2 WRITE (9, 5020 )N+NMP-2, (K + 2)*NMP-1, (K + 2)*NMP, (K+l) *NMP, (K+D*NMP-1,2
A87
RSDAM PROGRAM LISTING APPENDIX G
ENDIF K=K+1
571 CONTINUE IF(N .EQ. (NUP-2)* (NMP-D+1) THEN WRITE(9,5020) N,(NUP-1)*NMP+1,(NUP-1)*NMP+2,(NUP-2)*NMP+2, &(NUP-2)*NMP+1,1 WRITE(9,5020) N+NMP-2,NNP-1,NNP,NNP-NMP,NNP-NMP-1 1 ENDIF
570 CONTINUE C C REINFORCEMENTS INSTALATION C 660 WRITE (*,*) '**************************************************** 8 WRITE (*,*) 'NUMBER OF REINFORCEMENTS=?
READ ( *,*) NUMBAR IF(NUMBAR .EQ. 0) GO TO 960 WRITE (*,*) 'ELASTIC MODULUS OF THE REINFORCEMENTS=? (KN/m2) READ (*,*) HJ WRITE (*,*) 'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( *,* ) P IF (P.EQ.l) GO TO 8 WRITE (9,514 0) NUMBAR WRITE (*,11) WRITE (*,*) ***************************************************** DO 68 0 N=l,NUMBAR
9 WRITE (*,*) 'NODAL NUMBERS OF THE ', N,'th REINFORCEMENT=? READ (*,*) IB(M,1),IB(M,2) WRITE (*,*) 'ANGLE BETWEEN REINFORCEMENT AND HORIZONTAL LINE=? READ (*,*) ZAVIEH WRITE (*,*) 'CROSS-SECTIONAL AREA OF THE ',N,'th REINFORCEMENT=? READ ( *,*) HK WRITE (*,*)'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ (*,*) P IF (P.EQ.l) GO TO 9 WRITE (*,11) IB(M,3)=1 ZAV=ZAVIEH/57.2958 WRITE(9,5140) N,(IB(M,I),1=1,3),COS(ZAV),SIN(ZAV),0,HJ*HK,0
680 CONTINUE C C CALCULATION OF GRAVITY FORCE C 960 IF(NUMBAR .EQ. 0) WRITE (9,5140) NUMBAR
WRITE f * *) ******************************************************' DO 918 1=0,NUP-1 DO 919 J=1,NMP Xl(i*NMP+j)=0 Y(j)=HIZ*(j-l)/(NMP-l) X(I*NMP+J)=X(I*NMP+1)-(X(I*NMP+1)-X((I+1)*NMP))*Y(J)/HIZ
919 CONTINUE 918 CONTINUE
DO 980 1=0,NUP-1 DO 982 J=1,NMP Xl(i*NMP+j)=0 IFU.EQ.O .OR. I.EQ.l .OR. I.EQ.NUP-1 .OR. I.EQ.NUP-2) THEN Yl(I*NMP+j)=-l*TF*HIZ*GAM(l)/(NMP-1) IF(J .EQ. 1 .OR. J .EQ. NMP) Yl(I*NMP+j)=Y1(I*NMP+j)12 GO TO 982 ENDIF IF(I .gt. 1 .AND. I. It. NUP-2) THEN IF(J .EQ. 1) THEN Yl(I*NMP+j)= -1*(X( (I + 1)*NMP+J+D-X( (1-1) *NMP+J + 1) +X ( (I + l)*
Sc NMP+J)-X( (I-1)*NMP+J) ) *HIZ*GAM(2)/ (8* (NMP-1) ) GO TO 982 ENDIF IF(J .EQ. NMP) THEN Yl(I*NMP+j)= -1*(X((I+1)*NMP+J)-X((1-1)*NMP+J)+X((I+l)*NMP+J-1
&)-X((I-1)*NMP+J-1))*HIZ*GAM(2)/(8*(NMP-1)) GO TO 982
A88
RSDAM PROGRAM LISTING APPENDIX G
ELSE Yl(I*NMP+j)= -1*(X((I+1)*NMP+J+1)-X((1-1)*NMP+J+1)+X((I+1)*NMP &+J-1)-X((1-1)*NMP+J-1))*HIZ*GAM(2)/(4*(NMP-1))
ENDIF ENDIF
982 CONTINUE 980 CONTINUE 979 WRITE(*,*)'*****************************************************
DO 1915 I=1,NNP,2 IF (I .EQ. NNP) THEN GO TO 850 ENDIF
1915 CONTINUE C C CALCULATION OF HYDROSTATIC FORCE C 850 WRITE(9,5010) NMP
DO 290 1=1,NMP HWW=HWIZ-(i-1)*HIZ/(NMP-1) FX(I)=-GW*HWW*HIZ/(NMP-1) IF (I .EQ. 1 .OR. I .EQ. NMP) FX(I)=FX(I)12 IF (FX(I) .GT. 0) FX(I)=0 XWW=(WBIZ-WT)/(NMP-1) FY(I)=-1*GW*HWW*XWW IF (I .EQ. 1 .OR. I .EQ. NMP) FY(I)=FY(I)/2 IF (FY(I) .GT. 0) FY(I)=0
290 CONTINUE DO 291 1=1,NMP,2 IF (I .EQ. NMP) THEN WRITE(9,5160) NNP-NMP+I,FX(I),FY(I) GO TO 857 ENDIF WRITE (9,5160) NNP-NMP+I,FX(I),FY(I),NNP-NMP+I+1,FX(I+l),FY(I+D
291 CONTINUE C C CALCULATION OF SILT FORCE C 857 WRITE(9,5010) NMP
DO 390 1=1,NMP HSS=HSIZ-(i-1)*HIZ/(NMP-1) FX(I)=-GSUB*HSS*HIZ*AKA/(NMP-1) IF (I .EQ. 1 .or. I .EQ. NMP) FX(I)=FX(I)12 IF (FX(I) .GT. 0) FX(I)=0 XWW=(WBIZ-WT)/(NMP-1) FY(I)=-1*GSUB*HSS*XWW IF (I .EQ. 1 .OR. I .EQ. NMP) FY(I)=FY(I)12 IF (FY(I) .GT. 0) FY(I)=0
39 0 CONTINUE DO 391 I=1,NMP,2 IF (I .EQ. NMP) THEN WRITE(9,5160) NNP-NMP+I,FX(I),FY(I) GO TO 858 ENDIF WRITE (9,5160) NNP-NMP+I,FX(I),FY(I),NNP-NMP+I+1,FX(I+l),FY(I+l)
391 CONTINUE C C EARTHQUAKE FORCE OR DISPLACEMENT C 858 IF (ZEL .EQ. 2) GO TO 1117
DO 299 I=NNP-NMP+1,NNP HWW=HWIZ-(1-1)*HIZ/(NMP-1) FX1(I)=-0.72 6*CP*ALFA*GW*HWW*HWW*HIZ/(NMP-1) IF (I .EQ. NNP-NMP+1 .OR. I .EQ. NNP) FX1(I)=FX1(I)12 IF (FX1(I) .GT. 0) FX1(I)=0
299 CONTINUE 820 WRITE(9,5010) NNP
DO 1919 1=1,NNP,2 X11(I)=ALFA*Y1(I) Y11(I)=ALFA*X1(I) Xll(I+1)=ALFA*Y1(I+l) Y11(I+1)=ALFA*X1(I+1)
A89
RSDAM PROGRAM LISTING APPENDIX G
IF (I .GT. NNP-NMP) THEN X11(I)=FX1(I)+X11(I) X11(I+1)=FX1(I+1)+X11(I+1) ENDIF IF (I .EQ. NNP) THEN WRITE(9,5160) I,Xll(I),Yll(I) GO TO 1117 ENDIF WRITE(9,5160) I,Xll(I),Yll(I),I + l,Xll(I + l), Yll(I + l)
1919 CONTINUE C 1117 IF (ZEL .EQ. 1) GO TO 859
WRITE (*,*) 'DISPLACEMENTS OF BASE NODAL POINTS^' WRITE (9,5133) NUP DO 123 J=1,NNP+1-NMP,2*NMP
22 WRITE (*,*) 'DELTA(X) & DELTA(Y) OF NODE', J,'= READ (*,*) X1(I),Y1(I) IF (J .EQ. NNP+1-NMP) GO TO 860 WRITE (*,*) 'DELTA(X) & DELTA(Y) OF NODE', J+NMP,'= READ (*,*) Xll(I),Yll(I) WRITE (*,*) 'FOR CHANGING DATA TYPE 1 WRITE (*,*)'FOR CONTINUE TYPE 2 READ ( * , *) P IF (P.EQ.l) GO TO 22 WRITE (*,11)
860 IF (J .EQ. NNP+1-NMP) THEN WRITE(9,5160) J,XI(I),Yl(I) GO TO 859 ENDIF WRITE (9,5160) J,X1(I),Y1(I),J+NMP,X11(I) ,Y11(I)
123 CONTINUE C C VARIATION OF SEEPAGE FORCE C 859 WRITE (*,11)
WRITE ( * *) - j * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1
WRITE (9,5010) 1 WRITE (*,*) 'NUMBER OF PHREATIC SURFACE SEGMENT END POINTS=?' READ (*,*) NWAT WRITE (9,5010) NWAT DO 124 J=1,NWAT WRITE (*,*) 'X-CORDINATE OF NODE', J,'= ' READ (*,*) XI(J) WRITE (*,*) 'PRESENT LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE & AT NODE', J,'= READ (*,*) Xll(J) WRITE (*,*) 'NEW LEVEL (Y-COORDINATE) OF THE PHREATIC SURFACE AT &NODE', J,'= READ (*,*) Yll(J) WRITE (*,11) WRITE(9,5165) XI(J),Xll(J),Yll(J)
124 CONTINUE 11 FORMAT {1111111111111111111111) 19 FORMAT (/) 5000 FORMAT(20A4) 5010 FORMAT(15I5) 5015 FORMAT(2F10.4) 5020 FORMAT(16I5) 5040 FORMAT(6I3,2X,1A3 0) 5060 FORMAT(40I2) 5080 FORMAT(II0,7D10.5) 5085 FORMAT(I10,3D10.5,I10) 5090 FORMAT(6D10.5) 5100 FORMAT(8D10.5) 5120 FORMAT(110,6D10.4) 5130 FORMAT(515,5D10.4) 5131 FORMAT(4D10.3) 5132 FORMAT(2D10.3) 5133 FORMAT(2I5) 514 0 FORMAT(4I5,2F10.5,2D10.5,F10.5) 5160 FORMAT(2(I10,2D10.2))
A90
RSDAM PROGRAM LISTING APPENDIX G
5165 FORMAT(3D10.2) 522 0 FORMAT(3X,I4,lP2D14.5,4X,I4,2D14.5) 1050 RETURN
END C Q ****************************************************************** C * C * MAIN PROGRAM * C * * Q ******************************************************************
c COMMON /TWO/ GIS(900,5),B(2000),DF(2000) ,X(999),Y(999),PD(999) ,
& BM(900),ET(900),PP(999),DIX(999),DIY(999),IL(900,5),NA(2 000), Sc IC(200) ,NP(60) ,LE(30,2) ,KC(15,3) , NUT (15) , NUS (15) COMMON /THREE/ E(40),AO(40),FR(40),GAM(40),XB(40),BF(40),PI(40), 6c XP(40) ,CE(40) ,EN(40) ,TN(40) ,AL(40) , HC (4 0 ) ,UL(40) ,IDR(40) ,GUE(40) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40),PJ(40), Sc TJ(40) ,SC,CSA,SNA,CM,DC,IB(100,3) ,ITP,IDT(40) ,STI(40) ,STF(40) , Sc SFK40) ,SFF(40) , INO, JDN(40) ,REJ(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3),P(10),Q(4),STCR(3) Sc ,R,DEl,DE2,VOL,GAMW,PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP,NN, NTP, Sc SLT,MOD(40,15) COMMON /SEVEN/ XW(30),FL(30),PL(30),SNL(2,4) COMMON /EIGHT/ 1D(8),IDS(900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD k ,NXY,NRT,IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP,IHZ,1ST,NUP,NBR,NMT, k NNP2,NSL,NOP COMMON /NINE/ NBEAM,NBTYP COMMON /TEN/ N1T,N2T,N3T,N4T DIMENSION VS(IOOOOO),HEDCS(15) OPEN (5,FILE='dam.in',STATUS='OLD') OPEN (6,FILE='dam2.out',STATUS='OLD') READ(5,1000) (HED(I),1=1,20)
10 00 FORMAT(20A4) READ(5,1010) NNP,NEL,NJT,NBR,NBEAM,NBTYP,NC,NMOD,INT,IHZ, ITD
1010 F0RMAT(15I5) READ(5,1015) GAMW,PATM
1015 FORMAT(2F10.4) READ(5,102 0) NMT,NSL,NAP,NCT,N1T,N2T,N3T,N4T,ITP,INO
1020 FORMAT(16I5) WRITE(6,20 00) (HED(I),1=1,20),NNP,NEL,NJT,NMT
2000 FORMAT(//1H1,4X,20A4,//10X, 'NUMBER OF NODAL POINTS = ' ,I10/10X, 'NU MBER OF ELEMENTS = ',I14/10X,'NUMBER OF INTERFACE ELEMENTS = ',14) WRITE(6,2010) NC
2010 FORMAT(1OX,'NUMBER OF LOADING STEPS = ',16) DO 2 1=1,NNP
2 IDS(I)=2 NDOF=0 DO 3 1=1,NNP
3 NDOF=NDOF+IDS(I) IDS(NNP)=NDOF+l-lDS(NNP) N1=NNP-1 DO 4 1 = 1, Nl J=N1+1-I
4 IDS(J)=IDS(J+1)-IDS(J) NNP2=NDOF DO 5 1=1,NMT MOD(I,1)=0
5 CONTINUE GO TO 140 DO 10 J=1,NC READ(5,1060) (MOD(I,J),1=1,NMT)
1060 FORMAT(40I2) 10 CONTINUE 140 WRITE(6,2080) 2080 FORMAT(//3X,'MATERIAL',7X,'GAMMA',5X,'COHESION',10X,"PI",4X, & "TEN. STRGTH',7X,'K0'/) DO 2 0 N=1,NSL READ(5,1080) IDR(N),GAM(N),CE(N),PI(N),TN(N),AO(N),XP(N),HC(N) 1080 FORMAT(110,7D10.5) READ(5,1090) UL(N),FR(N),EN(N),XB(N),BF(N),E(N),GUE(N),AL(N)
A91
RSDAM PROGRAM LISTING APPENDIX G
1090 FORMAT(8D10.5) WRITE(6,2100) N,GAM(N),CE(N),PI(N),TN(N),AO(N)
2100 FORMAT(4X,I4,4X,4F13.2,F12.3) IDT(N)=0
2 0 CONTINUE READ(5,112 0) N,X(N),Y(N),PP(N),PD(N)
200 READ(5,1120) N,X(N),Y(N),PP(N) , PD (N) 1120 FORMAT(II0,6D10.4)
L=L+1 LM1=L-1 DUM=DFLOAT(N-LMl) DX=(X(N)-X(LM1))/DUM DY=(Y(N)-Y(LM1))/DUM DELP=(PP(N)-PP(LM1))/DUM DELT=(PD(N)-PD(LMl))/DUM LM1=L-1 X(L)=X(LM1)+DX Y(L)=Y(LM1)+DY PP(L)=PP(LM1)+DELP PD(L)=PD(LM1)+DELT L=L + 1 WRITE(6,2200)
2200 FORMAT(//1H1,4X, ' ** ERROR **: NODAL POINT DATA INPUT INCORRECTLY') STOP
300 WRITE(6,2220) 2220 FORMAT(///5X, 'COORDINATES OF NODAL POINTS'
k //11X, 'NODAL POINT',6X, 'X-COORDINATE',6X, 'Y-COORDINATE'/) DO 33 0 M=1,NNP WRITE(6,2240) M,X(M),Y(M)
2240 FORMAT(11X,15,2(9X,F7.3)) 33 0 CONTINUE 340 READ(5,1020) NY,NX,NXY,NRT
IM=NY+1 IN=NY+NX IO=IN+l IP=IN+NXY IOO=IP+NXY+l IPP=IOO+NRT-l IF(NX .EQ. 0) GO TO 460 READ(5,1020) (IC(N),N=IM,IN) WRITE(6,2300) (IC(N),N=IM,IN)
2300 FORMAT (//5X, 'NO X-MOVEMENT M0I5/18X, 10I5/18X, 10I5/18X, 1015 k /18X,10I5/18X,10I5)
420 DO 360 N=IM,IN IC(N)=IDS(IC(N))
3 60 CONTINUE 460 IF(NXY .EQ. 0) GO TO 510
READ(5,1020) (IC(N),N=IO,IP) WRITE(6,2320) (IC(N),N=IO,IP)
2320 FORMAT(//5X, "NO X OR Y MOVEMENT',10I5/18X, 10I5/18X,10I5/18X, 1015 k /18X,10I5/18X,10I5)
480 1=0 DO 490 N=IO,IP 1=1 + 1 IC(N)=IDS(IC(N)) IC(IP+I)=IC(N)+1
490 CONTINUE 510 IF(NRT.EQ.O) GO TO 520
READ{5,1020) (IC(N),N=IOO,IPP) WRITE(6,2130) (IC(N),N=IOO,IPP)
2130 FORMAT(5X,'NO Z-ROTATION',20I5/23X,20I5/23X, 2015) 490 DO 500 N=IOO,IPP
IC(N)=IDS(IC(N))+2 500 CONTINUE 520 IF(NEL.EQ.O) GO TO 660
N=0 540 READ(5,1020) M,(IL(M,I),1=1,5) 560 N=N+1
IF(NEL-M) 600,640,540 600 WRITE(6,2340) 2340 FORMAT(/1H1,4X,'*** ERROR *** : INCORRECT ELEMENT DATA INPUT')
A92
RSDAM PROGRAM LISTING APPENDIX G
STOP 64 0 WRITE(6, 236 0)
2360 FORMAT(//5X,'ELEMENT DATA' & /5X, 'ELEMENT',8X, 'I',5X, 'J',5X, 'K',5X, 'L',4X, 'MATERIAL'/) DO 65 0 M=1,NEL
^nn WRITE(6,2380) M, IL (M, 1) , IL (M, 2 ) , IL (M, 3 ) , IL (M, 4 ) , IL (M, 5) 2380 FORMAT(8X,I4,3X,4I6,8X,I4,6X,I4) 650 CONTINUE 660 IF(NBR .EQ. 0) GO TO 700
DO 680 N=1,NBR READ(5,1140) M, (IB(M,I),1=1,3), (BR(M,I),1 = 1,5)
114 0 FORMAT(4I5,2F10.5,2D10.5,F10.5) 680 CONTINUE
WRITE(6,2400) 24 00 FORMAT(/5X,'REINFORCEMENT DATA'/'REINFORCEMENT',5X,'I',5X,'J",4X,
k "TYPE",5X, "PRESTRESS' ,5X, 'DISP TO'/4X, 'NUMBER',38X, 'ACTIVATE'/) WRITE(6,2420) (N,(IB(N,I),1=1,3),BR(N,3),BR(N,5),N=l,NBR)
2420 FORMAT(7X,I4,10X,I5,3X,I5,4X,1PD10.3) 700 CALL NDF
DO 710 N=1,NNP DIX(N)=0 DIY(N)=0
710 CONTINUE 725 CONTINUE
CALL EBTEDA(VS) DO 1001 MQ=1,NC WRITE(6,2440) MQ
2440 FORMAT(//5X, ****************************** */5x, 'STAGE NUMBER',13) DO 760 1=1,NMT
760 CONTINUE KSB=1 DO 780 I=1,NNP2 DF(I)=0
780 CONTINUE IF(KC(MQ,1).NE.3 .AND. KC(MQ,2).NE.3 .AND.KC(MQ,3).NE.3) GO TO 880 CALL SEEP
880 IF(KC(MQ,1).NE.5 .AND. KC(MQ,2).NE.5 .AND.KC(MQ,3).NE.5) GO TO 960 READ(5,1020) NCARDS WRITE(6,2560) NCARDS
2560 FORMAT(///5X,'THE FOLLOWING',13,' REINFORCEMENTS ARE ADDED' klI'REINFORCEMENT NUMBER',5X,'I',5X,'J',5X,'DISP. TO ACTIVATE'/) DO 900 N=l,NCARDS READ(5,114 0) M, (IB(M,I) ,1 = 1,3) , (BR(M,I),1 = 1,5) WRITE(6,242 0) M,(IB(M,I),1=1,2),BR(M,5) BR(M,6)=DIX(IB(M,1)) BR(M,7)=DIX(IB(M,2)) BR(M,8)=DIY(IB(M,1)) BR(M,9)=DIY(IB(M,2))
900 CONTINUE NBR=NBR+NCARDS CALL NDF
960 IF(KC(MQ,1).NE.8 .AND. KC(MQ,2).NE.8 .AND. KC(MQ,3).NE.8 .AND. k KC(MQ,1).NE.9 .AND. KC(MQ,2).NE.9 .AND. KC(MQ,3).NE.9) GO TO 999 WRITE(6,2600)
2600 FORMAT(///5X,'FORCE AND/OR DISPLACEMENT LOADING IS SPECIFIED FOR T &HIS INCREMENT'//3X,'NODE',8X,'X-LOAD',8X,'Y-LOAD',4X,'NODE',8X,"X-&LOAD',8X,'Y-&LOAD'/)
965 READ(5,1020) NUMNDE NCARDS=(NUMNDE-1)12 + 1 DO 980 1=1,NCARDS READ(5,1160) M,X1,Y1,N,X2,Y2 WRITE(6/2620) M,X1,Y1,N,X2,Y2
2 62 0 FORMAT(3X,I4,lP2D14.5,4X,I4,2D14.5) NY1=IDS(M)+1 NX1=NY1-1 DF(NX1)=DF(NX1)+X1 DF(NY1)=DF(NY1)+Y1 CONTINUE
999 NSP=NUS(MQ) NUP=NUT(MQ) NQ=1
A93
RSDAM PROGRAM LISTING APPENDIX G
970 CALL TSSM(VS) CALL SSMILV(VS) CALL TANESH IF(NQ .GE. NUP) GO TO 1100 NQ=NQ+1 GO TO 970
1001 CONTINUE STOP END
0********************************************************************* SUBROUTINE EBTEDA(VS)
Q* ******************************************* * *********************** * COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999) ,PD(999) ,
k BM(900),ET(900),PP(999),DIX(999),DIY(999),IL(900,5),NA(2000), & IC(200),NP(60),LE(30,2),KC(15,3),NUT(15),NUS(15) COMMON /THREE/ E(40),AO(40),FR(40),GAM(40),XB(40),BF(40),PI(40), Sc XP(40) ,CE(40) ,EN(40) ,TN(40) ,AL(40) ,HC(40) ,UL(40) ,IDR(40) ,GUE(40) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40) , PJ(40), k TJ(40) ,SC,CSA,SNA,CM,DC,IB(10 0,3),ITP,IDT(4 0) ,STI(4 0) ,STF(40) , k SFK40) ,SFF(4 0) , INO, JDN(40) ,REJ(40) COMMON /FIVE/ SE (10,10),ST (3,10),HED(2 0),D(3,3),P(10),Q(4) ,STCR(3) Sc ,R,DEl,DE2,VOL,GAMW,PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP, NN, NTP, Sc SLT,MOD(4 0,15) COMMON /EIGHT/ ID(8) ,IDS(900) ,N,MQ,NC,NQ,NSN,NX,NY,INT,ITD, NL,NMOD Sc ,NXY,NRT, IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP, IHZ , 1ST, NUP, NBR, NMT, Sc NNP2,NSL,NOP COMMON /NINE/ NBEAM,NBTYP COMMON /TEN/ NIT,N2T,N3T,N4T DIMENSION VS(1) IF(NEL.EQ.O) RETURN MQ=1 NQ=1 NTP=0 NUP=1 NSP=1 KSB=1 DO 40 N=1,NEL DO 2 0 M=l,5 GIS(N,M)=0
2 0 CONTINUE MTP=IL(N,5) IF (MTP -GT. NSL) GO TO 160 GNU=AO(MTP)/(l+AO(MTP)) IF (GNU.GT.0.49 .AND. GNU.LE.0.5) THEN GNU=0.49 ELSE IF (GNU.GT.0.5 .AND. GNU.LT.0.51) THEN GNU=0.51 END IF IF (MTP.EQ.NAP .OR. MTP.EQ.NIT .OR. MTP.EQ.N2T .OR. MTP.EQ.N3T k .OR. MTP.EQ.N4T) THEN ET(N)=1 ELSE ET(N)=1.D5 END IF BM(N)=ET(N)/(3*(1-2*GNU)) GO TO 180
160 STS(N)=1.D8 STN(N)=1.D8
4 0 CONTINUE DO 60 N=1,NNP2 DF(N)=0
60 CONTINUE DO 80 N=1,NNP DIX(N)=0 DIY(N)=0 80 CONTINUE CALL TSSM(VS) CALL SSMILV(VS) CALL TANESH 240 NN=0
A94
RSDAM PROGRAM LISTING APPENDIX G
INU=0 IF(NEL.EQ.O) GO TO 57 0 DO 12 0 N=1,NEL MTP=IL(N,5) IF(MTP .GT. NSL) GO TO 560 PPAVG=(PP(IL(N,1))+PP(IL(N,2))+PP(IL(N,3))+PP(IL(N,4)))*0.25*GAMW IF(IL(N,1) .EQ. IL(N,4)) PPAVG=(PP(IL(N,1))+PP(IL(N,2))
Sc +PP(IL(N,3) ) )*GAMW/3 IF(INT .EQ. 1) GO TO 280 DO 100 1=1,4 Q(I)=GIS(N,I)
100 CONTINUE CALL PSTMS GO TO 460
280 Q(4)=0 IFdDR(MTP) .EQ. 1) GO TO 300 IF(IHZ .EQ. 0) GO TO 3 80 GO TO 340
300 GIS(N,2)=GIS(N,2)-PPAVG IF(IHZ .EQ. 1) GO TO 320 GIS(N,l)=AO(MTP)*GIS(N,2) GO TO 4 00
320 GIS(N,1)=GIS(N,1)-PPAVG 340 DO 360 1=1,3
Q(I)=GIS(N,I) 3 60 CONTINUE
CALL PSTMS GO TO 460
380 GIS(N,l)=AO(MTP)*(GIS(N,2)-PPAVG)+PPAVG 400 GIS(N,3)=0
DO 410 1=1,3 410 Q(I)=GIS(N,I)
CALL PSTMS 4 60 CALL VSE
GIS(N,4)=Q(4) GIS(N,5)=DMAX1(SIG1,GIS(N,5))
120 CONTINUE 570 IF(NJT .EQ. 0) GO TO 640
INU=0 DO 62 0 N=1,NJT XC=(X(IL(N,1))+X(IL(N,2)))12 YC=(Y(IL(N,1))+Y(IL(N,2)))12 PPAVG=(PP(IL(N,1))+PP(IL(N,2)))*0.5*GAMW IF(INU .GT. 0) GO TO 580 WRITE(6,2040) (HED(I),1=1,20)
2040 FORMAT(//1H1,4X,20A4//5X,"INITIAL INTERFACE STRESSES' k //"ELEM NO',3X,"X",3X,"Y",2X,"NORM. STRESS',2X,'SHEAR STRESS",2X, Sc'NORM. STIFF',2X, 'SHEAR STIFF'/) INU=60 GO TO 600
580 INU=INU-1 600 WRITE(6,2060) N,XC,YC,(GIS(N,I),1=1,2),STN(N),STS(N)
2060 F0RMAT(I4,1X,2F7.2,1P5D12.3) 62 0 CONTINUE 64 0 IF(NBR .EQ. 0) GO TO 72 0
WRITE(6,2080) (HED(I),1=1,20) 2080 FORMAT(//1H1,4X,2 0A4 //5X,'INITIAL REINFORCEMENT STRESSES'
& //5X,'REINFORCMENT',5X,'I',5X,'J',4X,'TYPE',3X,'COMPR FORCE',3X, Sc • COMPRESSION' , 5X, ' STIFFNESS ' / ) DO 680 N=1,NBR MTP=IB(N,3) CALL SBE IF(INT .EQ. 0) GO TO 660 DC=0 CM=BR(N,3)
660 WRITE(6,2100) N,(IB(N,I),1=1,3),CM,DC,SC 2100 FORMAT(9X,I4,2(2X,I4),4X,14,1P3D14.6,0P2F10.5,6X,14) 680 CONTINUE 720 IF(INT.EQ.O) GO TO 760 755 INT=0 760 NTP=0
A95
RSDAM PROGRAM LISTING APPENDIX G
RETURN END
p* ****************************************** * ************************ *
SUBROUTINE SSMILV(VS) p* ******************************************************************* *
COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999) ,Y(999) ,PD(999) , Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) ,DIY(999) ,IL(900,5) ,NA(2000) , Sc IC(200),NP(60),LE(30,2),KC(15,3) , NUT (15) , NUS (15) COMMON /THREE/ E(40), AO (40),FR(40),GAM(40),XB(40),BF(40) , PI(40) , Sc XP(40) ,CE(40) ,EN(40) ,TN(40) ,AL(40) ,HC(40) ,UL(40) ,IDR(40) ,GUE(40) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40),PJ(40), & TJ(40),SC,CSA,SNA,CM,DC,IB(100,3),ITP,IDT(40),STI(40),STF(40), Sc SFK40) ,SFF(40) ,INO,JDN(40) ,REJ(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3),P(10),Q(4) , STCR(3) Sc ,R,DE1,DE2,V0L,GAMW,PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP,NN,NTP, Sc SLT,MOD(40,15) COMMON /SEVEN/ XW(30),FL(30),PL(30),SNL(2 , 4 ) COMMON /EIGHT/ ID(8) ,IDS (900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD
Sc ,NXY,NRT,IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP,IHZ,IST,NUP,NBR,NMT, Sc NNP2,NSL,NOP COMMON /NINE/ NBEAM,NBTYP COMMON /TEN/ N1T,N2T,N3T,N4T DIMENSION VS(1) NEQ=NNP2 NEQQ=NEQ-1 ILL=1 NAJP=NA(1) DO 140 J=2,NEQ NAJ=NA(J) JK=NAJ-J IF=1-JK+NAJP IF(IF .GE. J) GO TO 120 IF1=IF+1 KF=JK+IF KL=NAJ-1 AA=0 DO 100 K=KF,KL NAI=NA(IF) CC=VS(K)/VS(NAI) AA=AA+VS(K)*CC VS(K)=CC IF=IF+1
100 CONTINUE VS(NAJ)=VS(NAJ)-AA
120 ILL=ILL+1 NAJP=NAJ
14 0 CONTINUE DO 160 N=1,NEQQ N1=N+1 I1=N1+1 KL=N NAIP=NA(N) DO 240 I=N1,NEQ NAI=NA(I) II=I1-NAI+NAIP 11=11+1 KL=KL+1 NAIP=NAI
240 CONTINUE DO 260 I=N,NEQ NAI=NA(I) B(I)=B(I)/VS(NAI!
2 60 CONTINUE J=NEQ NAJ=NA(NEQ) DO 32 0 I=1,NEQQ NAJP=NA(J-D JKA=NAJP+1 II=J-NAJ+JKA IF(II .GE. J) GO TO 300
A96
RSDAM PROGRAM LISTING APPENDIX G
KL=J-1 BB=B(J) DO 280 K=II,KL B(K)=B(K)-VS(JKA)*BB JKA=JKA+1
280 CONTINUE 300 J=J-1
NAJ=NAJP 32 0 CONTINUE
RETURN END
0********************************************************************* SUBROUTINE TSSM(VS) C*********************************************************************
COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999),PD(999), Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) ,DIY(999) ,IL(900,5),NA(2000), Sc IC(200) ,NP(60) ,LE(30,2) ,KC(15,3) , NUT (15) , NUS (15) COMMON /THREE/ E(40),AO(40),FR(40),GAM(40),XB(40),BF(40),PI(40), Sc XP(40) ,CE(40) ,EN(40) ,TN(40) ,AL(40) ,HC(40) ,UL(40) ,IDR(40) ,GUE(40) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40),PJ(40), Sc TJ(40) ,SC,CSA,SNA,CM,DC, IB (100, 3) , ITP,IDT(40) , STI (40) ,STF(40) , Sc SFI (40) ,SFF(40) , INO, JDN(40) , RE J ( 4 0 ) COMMON /FIVE/ SE(10,10),ST(3,10),HED(2 0),D(3,3),P(10),Q(4),STCR(3) Sc ,R,DEl,DE2,VOL,GAMW,PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3 , TEP,NN,NTP,
k SLT,MOD(40,15) COMMON /SEVEN/ XW(30),FL(30),PL(30),SNL(2,4) COMMON /EIGHT/ ID(8),IDS(900) ,N,MQ,NC,NQ,NSN, NX,NY, INT, ITD,NL,NMOD Sc ,NXY,NRT, IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP, IHZ , 1ST, NUP, NBR, NMT, Sc NNP2,NSL,NOP COMMON /NINE/ NBEAM,NBTYP COMMON /TEN/ NIT,N2T,N3T,N4T DIMENSION VS(1) DO 2 0 1=1,NSN VS(I)=0
2 0 CONTINUE IFL=0 IST=0 IF(NBR .EQ. 0) GO TO 160 DO 14 0 N=1,NBR IF(DABS(BR(N,4)-0) .LE. l.D-6) GO TO 140 ID(1)=IDS(IB(N,1)) ID(3)=IDS(IB(N,2)) ID(2)=ID(1)+1 ID(4)=ID(3)+1 MTP=IB(N,3) CALL SBE DO 120 1=1,4 IROW=ID(I) DO 12 0 J=l,4 ICOL=ID(J) IFdCOL .LT. IROW) GO TO 12 0 IADR=NA(ICOL)-(ICOL-IROW) VS(IADR)=VS(IADR)+SE(I,J)
120 CONTINUE 14 0 CONTINUE 160 IM=NY+NX+NXY+NXY+NRT
IF(INT .EQ. 1) GO TO 17 0 IF(KC(MQ,1).EQ.8 .OR. KC(MQ,2) .EQ.8 .OR. KC(MQ, 3) .EQ.8) GO TO 260
170 DO 240 M=1,IM J=IC(M) DF(J)=0 IF(J .EQ. 1) GO TO 200 ISTRT=NA(J-1)+1 IEND=NA(J)-1 IFdSTRT .GT. IEND) GO TO 2 00 DO 180 IADR=ISTRT,IEND VS(IADR)=0
18 0 CONTINUE 200 VS(NA(J))=1
IF(J .EQ. NNP2) GO TO 240
A97
RSDAM PROGRAM LISTING APPENDIX G
JSTRT=J+1 KTR=0 DO 22 0 ICOL=JSTRT,NNP2 KTR=KTR+1 IADR=NA(ICOL)-KTR
24 0 CONTINUE 260 DO 280 I=1,NNP2
B(I)=DF(I) 28 0 CONTINUE
DO 400 M=1,IM J=IC(M) FDJ=DF(J) JSTRT=J+1 KTR=0 DO 3 60 ICOL=JSTRT,NNP2 KTR=KTR+1 IADR=NA(ICOL)-KTR CONTINUE
380 VS(NA(J))=1 4 0 0 CONTINUE
DO 420 M=1,IM J=IC(M) B(J)=DF(J)
42 0 CONTINUE RETURN END
£********************************************************************* SUBROUTINE NDF
£********************************************************************* COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999) ,PD(999) ,
Sc BM(900),ET(900),PP(999) ,DIX(999) ,DIY(999) ,IL(900,5),NA(2000), & IC(200),NP(60),LE(30,2),KC(15,3),NUT(15),NUS(15) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40),PJ(40), S: TJ(40) ,SC,CSA,SNA,CM,DC, IB (100, 3) ,ITP,IDT(40) , STI (40) ,STF(40) , k SFK40) ,SFF(40) , INO, JDN(40) ,REJ(40) COMMON /EIGHT/ ID(8),IDS(900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD
Sc ,NXY,NRT,IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP,IHZ,IST,NUP,NBR,NMT, Sc NNP2,NSL,NOP COMMON /NINE/ NBEAM,NBTYP DO 10 J=1,NNP2 NA(J)=J
10 CONTINUE IF(NBR .EQ. 0) GO TO 180 DO 40 N=1,NBR ID(1)=IDS(IB(N,1)) ID(3)=IDS(IB(N,2)) ID(2)=ID(1)+1 ID(4)=ID(3)+1 IDMIN=ID(1) DO 2 0 1=2,4 IDMIN=MIN0(IDMIN, ID(I) )
2 0 CONTINUE DO 30 1=1,4 NA(ID(I) )=MIN0 (IDMIN,NA(IDd) ) )
3 0 CONTINUE 4 0 CONTINUE 18 0 IDIADR=1
DO 60 J=2,NNP2 IDIADR=IDIADR+J-(NA(J)-l) NA(J)=IDIADR
60 CONTINUE NA(1)=1 NSN=NA(NNP2) WRITE(6,202 0) NSN RETURN
2020 FORMAT(/////5X,'SIZE OF STIFNESS MATRIX = ',17) END
Q********************************************************************* SUBROUTINE ESM
n******************************************************************** * COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999) ,PD(999) ,
A98
RSDAM PROGRAM LISTING APPENDLX G
Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) ,DIY(999) , IL (900 , 5) , NA (2000 ) , Sc IC(2 00) ,NP(60) ,LE(30,2) ,KC(15,3) , NUT (15) , NUS (15) COMMON /THREE/ E(40),AO(40),FR(40),GAM(40),XB(40),BF(40),PI(40), Sc XP(40) ,CE(40) ,EN(40) ,TN(40) ,AL(40) ,HC(40) ,UL(40) , IDR(40) ,GUE(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(2 0),D(3,3),P(10),Q(4),STCR(3) Sc ,R,DEl,DE2,VOL,GAMW,PATM COMMON /EIGHT/ ID(8),IDS(900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD Sc ,NXY,NRT,IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP,IHZ,IST,NUP,NBR,NMT, Sc NNP2,NSL,NOP COMMON /TEN/ NIT,N2T,N3T,N4T DIMENSION SS(4),TT(4) DATA SS/-1,1,1,-1/,TT/-1,-1,1,1/ MTP=IL(N,5) DFAC=ET(N)/(l-GUE(N)*GUE(N)) D(1,D=DFAC D(1,2)=GUE(N)*D(1,1) D(2,D=D(1,2) D(2,2)=D(1,1) D(3,3)=DFAC*(1-GUE(N))/2
15 DO 20 J=l,10 P(J)=0 DO 20 1=1,10 SE(I,J)=0
2 0 CONTINUE I=IL(N,1) J=IL(N,2) K=IL(N,3) L=IL(N,4) VOL=X13*Y24-X24*Y13 IF(VOL .LE. 0) RETURN IF(MTP .NE. NCT) GO TO 3 0 DTAVG=(PD(I)+PD(J)+PD(K)+PD(L))/4 IF(I .EQ. L) DTAVG=(PD(I)+PD(J)+PD(K))/3 DE1=(D(1,1)+D(1,2))*(1+GUE(N))*DTAVG*AL(MTP) DE2=(D(2,1)+D(2,2))*(1+GUE(N))*DTAVG*AL(MTP)
30 IF(1ST .EQ. D GO TO 120 DO 100 11=1,4 S=SS(II)*0.577 T=TT(II)*0.577 XJ=VOL+S*(X34*Y12 - X12*Y34)+T*(X23*Y14 - X14*Y23) XJAC=XJ/8 SM=1-S SP=1+S TM=1-T TP=1+T FAC=XJAC XS=0.25*(-TM*X(I)+TM*X(J)+TP*X(K)-TP*X(L)) YS=0.25*(-TM*Y(I)+TM*Y(J)+TP*Y(K)-TP*Y(L)) XT=0.25*(-SM*X(I)-SP*X(J)+SP*X(K)+SM*X(D) YT=0.25*(-SM*Y(I)-SP*Y(J)+SP*Y(K)+SM*Y(L)) XC=-2*(T*SM*SP*XS-S*TM*TP*XT)/XJAC YC= 2*(T*SM*SP*YS-S*TM*TP*YT)/XJAC DO 40 IM=1,3 D1=D(IM,1)*FAC D2=D(IM,2)*FAC D3=D(IM,3)*FAC
4 0 CONTINUE DO 60 IM=1,10 D1=ST(1,IM) D2=ST(2,IM) D3=ST(3,IM)
60 CONTINUE IF(INT .EQ. 0) GO TO 100 DUM=-GAM(MTP)*FAC P(2)=P(2)+0.25*DUM*SM*TM P(4)=P(4)+0.25*DUM*SP*TM P(6)=P(6)+0.2 5*DUM*SP*TP P(8)=P(8)+0.25*DUM*SM*TP P(10)=P(10)+DUM*SM*SP*TM*TP
100 CONTINUE IF(IST .EQ. 0) GO TO 160
A99
RSDAM PROGRAM LISTING APPENDIX G
120 DO 140 IM=1,3 STCR(IM)=0 D1=D(IM,1) D2=D(IM,2) D3=D(IM,3) Tl=( Dl*Y24-D3*X24)/VOL T2=(-D1*Y13+D3*X13)/VOL T3=(-D2*X24+D3*Y24)/VOL T4=( D2*X13-D3*Y13)/VOL
14 0 CONTINUE RETURN
160 DO 180 NM=1,2 LM=10-NM MM=LM+1 SEMM=SE(MM,MM) DO 180 IM=1,LM DUM=SE(IM,MM)/SEMM P(IM)=P(IM)-DUM*P(MM) DO 180 JM=1,LM SE(IM,JM)=SE(IM,JM)-DUM*SE(MM,JM)
180 CONTINUE DO 200 IM=1,4 KM=IDS(IL(N,IM))+l JM=KM-1 MM=2*IM LM=MM-1 DF(JM)=DF(JM)+P(LM) DF(KM)=DF(KM)+P(MM)
2 00 CONTINUE RETURN END
p * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
SUBROUTINE SBE Q*********************************************************************
COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999),PD(999), Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) ,DIY(999) ,IL(900,5),NA(2000), Sc IC(200),NP(60),LE(30,2),KC(15,3) , NUT (15) , NUS (15) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40) , PJ(40) , & TJ(40),SC,CSA,SNA,CM,DC,IB(100,3) ,ITP,IDT(40),STI(40),STF(40) , Sc SFK40) ,SFF(4 0) , INO, JDN(4 0) ,REJ(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3),P(10),Q(4),STCR(3) Sc ,R,DEl,DE2,VOL,GAMW,PATM COMMON /EIGHT/ ID(8),IDS(900) ,N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL, NMOD Sc ,NXY,NRT,IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP,IHZ,IST,NUP,NBR,NMT, Sc NNP2,NSL,NOP I=IB(N,D I1=IDS(I)+1 12=11-1 J=IB(N,2) J1=IDS(J)+1 J2=J1-1 SNA=BR(N,2) CSA=BR(N,1) SC=BR(N,4) IF(MTP .EQ. 1) GO TO 120 DISPXI=DIX(I)-BR(N,6) DISPXJ=DIX(J)-BR(N,7) DISPYI=DIY(I)-BR(N,8) DISPYJ=DIY(J)-BR(N,9) IF(NQ .NE. NUP .OR. 1ST .NE. 1) GO TO 80 DISPXI=DISPXI-B(I2) DISPXJ=DISPXJ-B(J2) DISPYI=DISPYI-B(ID DISPYJ=DISPYJ-B(Jl)
80 IF (I.EQ.J) THEN COMPR=DISPXI*CSA+DISPYI*SNA ELSE COMPR=(DISPXI-DISPXJ)*CSA+(DISPYI-DISPYJ)*SNA END IF IF(MTP .EQ. 3) GO TO 100 IF(COMPR .LT. BR(N,5)-1.0D-6) SC=0
A100
RSDAM PROGRAM LISTING APPENDIX G
GO TO 12 0 100 IF(-COMPR .LT. BR(N,5)-1.OD-6) SC=0 14 0 IF (I.EQ.J) THEN
DC=B(I2)*CSA+B(I1)*SNA ELSE DC=(B(I2)-B(J2))*CSA+(B(I1)-B(J1))*SNA END IF IF(DABS(BR(N,4)-0) .LT. l.D-6) DC=0 CM=BR(N,3)+DC*SC IF(NQ .EQ. NUP) BR(N,3)=CM RETURN END
Q********************************************************************* SUBROUTINE SIE
Q* ******************************************************************* * COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999),PD(999),
Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) ,DIY(999) ,IL(900,5),NA(2000), Sc IC(200),NP(60),LE(30,2),KC(15,3) , NUT (15) , NUS (15) COMMON /FIVE/ SE(10,10),ST(3,10) ,HED(2 0) ,D(3,3),P(10),Q(4) ,STCR(3) Sc ,R,DEl,DE2,VOL,GAMW,PATM COMMON /EIGHT/ ID(8),IDS(900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD Sc ,NXY,NRT, IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP, IHZ , 1ST, NUP, NBR, NMT, Sc NNP2,NSL,NOP DIMENSION BC(4,4),COSIN(2,2) DO 2 0 J=l,8 DO 20 1=1,8 SE(I,J)=0
20 CONTINUE I=IL(N,1) J=IL(N,2) DELY=Y(J)-Y(I) DELX=X(J)-X(I) VOL=DSQRT(DELY* * 2 +DELX* *2 ) IF(VOL .LE. 0) RETURN CKS=STS(N)*VOL/6 CKN=STN(N)*VOL/6 DO 40 11=1,4 IN=2*II IS=IN-1 DO 4 0 JJ=1,4 JN=2*JJ JS=JN-1 SE(IS,JS)=CKS*BC(II,JJ) SE(IN,JN)=CKN*BC(II,JJ)
4 0 CONTINUE IF(DELY -EQ. 0) RETURN COSIN(1,1)=DELX/VOL COSIN(l,2)=DELY/VOL COSIN(2,l)=-COSIN(l, 2) COSIN(2,2)=COSIN(l,D DO 100 M=l,4 MT2=2*M DO 60 1=1,8 J=MT2-1 TEMP=SE(I,J) DO 60 K=l,2 SE(I,J)=TEMP*COSIN(1,K)+SE(I,MT2)*COSIN(2,K) J=J+1
60 CONTINUE DO 80 1=1,8 J=MT2-1 TEMP=SE(J,I) DO 80 K=l,2 SE(J,I)=TEMP*COSIN(1,K)+SE(MT2,I)*COSIN(2,K) J=J+1
80 CONTINUE 100 CONTINUE
RETURN END
Q******: SUBROUTINE VSE
:***************************************************************
A101
RSDAM PROGRAM LISTING APPENDIX G
o********************************************************************* COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999),PD(999),
Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) ,DIY(999) ,IL(900,5),NA(2000), Sc IC(200),NP(60),LE(30,2),KC(15,3) , NUT (15) , NUS (15) COMMON /THREE/ E(40),AO(40),FR(40),GAM(40) ,XB(40),BF(40) ,PI(40), Sc XP(40) ,CE(40) ,EN(40) ,TN(40) ,AL(40) ,HC(40) ,UL(40) ,IDR(40) ,GUE(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(2 0),D(3,3),P(10),Q(4),STCR(3) Sc ,R,DE1,DE2,V0L,GAMW,PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP,NN,NTP,
Sc SLT,MOD(40,15) COMMON /EIGHT/ ID(8),IDS(900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD Sc ,NXY,NRT, IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP, IHZ , 1ST, NUP, NBR, NMT, Sc NNP2,NSL,NOP COMMON /TEN/ NIT,N2T,N3T, N4T IF(MTP.NE.NCT.AND.MTP.NE.NAP.AND.MTP.NE.NIT.AND.
ScMTP.NE.N2T.AND. DABS (XP (MTP)-0 ) . GT . 1 . D-5 . AND . ScMTP.NE.N3T.AND.MTP.NE.N4T) GO TO 20 ET(N)=E(MTP) BM(N)=ET(N)/(3*(1-2*GUE(MTP))) SL=0 Q(4)=0 GIS(N,5)=0 SLT=0
5 RETURN 20 IF (NQ .EQ. NUP) THEN
SG3=SIG3 ELSE SG3=(PSG3+SIG3)/2 RD=(((PSG1+SIG1)/2)-SG3)/2 END IF PH=PI(MTP)*1.745329251994329D-2 RDF=(2*CE(MTP)*DCOS(PH)+2*SG3*DSIN(PH))/(1-DSIN(PH)) IF(SG3 .GE. 0) GO TO 50 IF(DABS(SG3) .GE. TN(MTP)) GO TO 40 PHIT = DATAN2 (CE(MTP),TN(MTP)) RDFT = ((2*DSIN(PHIT))*(TN(MTP)+SG3))/(1-DSIN(PHIT)) RDF = DMINKRDFT, RDF) GO TO 50
40 RDF=2*RD 50 IF (RDF.GT.l.D-5) THEN
SL=(2*RD)/RDF ELSE SL=1 END IF MQM=MQ+NN IF (SG3.GT.0) THEN BM(N)=BF(MTP)*PATM*(SG3/PATM)**XB(MTP) IF (PI(MTP).GE.0.1) THEN STRSS=(SG3+CE(MTP)/DTAN(PH))/PATM ELSE STRSS=(SG3+CE(MTP)*5.73D2)/PATM END IF STST=SL*STRSS**0.2 5 SLT=Q(4)/STRSS**0.25 IF (SL.GE.l .AND. MOD(MTP,MQM).EQ.0) THEN ET(N)=E(MTP) ELSE IF (SL.GE.SLT .OR. MOD(MTP,MQM).EQ.1) THEN EI=HC(MTP)*PATM*(SG3/PATM)**XP(MTP) EI=DMAX1(EI,EN(MTP)) FRSL=FR(MTP)*SL IF (FRSL.LT.l) THEN ET(N)=((1-FRSL)**2)*EI ELSE ET(N)=E(MTP) ENDIF ELSE IF (SL.LE.0.75*SLT .OR. MOD(MTP,MQM).EQ.2) THEN EI=UL(MTP)*PATM*(SG3/PATM)**XP(MTP) ET(N)=DMAX1(EI,EN(MTP)) ELSE EI=HC(MTP)*PATM*(SG3/PATM)**XP(MTP) EI=DMAX1(EI,EN(MTP))
A102
RSDAM PROGRAM LISTING APPENDIX G
FRSL=FR(MTP)*SLT IF (FRSL.LT.l) THEN ETL=((1-FRSL)**2)*EI ELSE ETL=E(MTP) ENDIF ETL=DMAX1(ETL,E(MTP)) EI=UL(MTP)*PATM*(SG3/PATM)**XP(MTP) ETH=DMAX1(EI,EN(MTP)) ET(N)=4*((SL-0.75*SLT)*ETL+(SLT-SL)*ETH)/SLT END IF ELSE IF (NQ.LT.NUP .AND. PSG3.GE.0) THEN BM(N)=BM(N)/4 ELSE BM(N)=0 END IF IF (DABS(SG3).GE.TN(MTP)) THEN IF (NQ.LT.NUP .AND. PSG3.GE.0) THEN ET(N)=ET(N)/4 ELSE ET(N)=E(MTP) END IF STST=Q(4) SLT=1 ELSE STST=SL*STRSS**0.25 SLT=Q(4)/STRSS* * 0.2 5 IF (FRSL.LT.l) THEN ETL=((1-FRSL)**2)*EN(MTP) ELSE ETL=E(MTP) ENDIF ETL=DMAX1(ETL,E(MTP)) ETH=EN(MTP) ET(N)=((SL-0.75*SLT)*ETL+(SLT-SL)*ETH)/(0.2 5*SLT) END IF END IF END IF Q(4)=DMAX1(Q(4),STST) SLT=DMAX1(SLT,SL) ET(N)=DMAX1(ET(N),E(MTP)) BM(N)=DMIN1(BM(N),1.7D1*ET(N)) SIG5=GIS(N,5) IF (SIG1.GT.SIG5 .AND. PI(MTP).GT.2.2) THEN BM(N)=DMAX1(BM(N),(2-DSIN(PH))*ET(N)/(3*DSIN(PH))) ELSE IF (SIG1.LE.SIG5 .AND. PI(MTP).GE.1.6) THEN TEMPV=(1-DSIN(PH))*(5-5**DSIN(PH)) BM(N)=DMAX1(BM(N),(4+TEMPV)*ET(N)/(3*(4-TEMPV))) ELSE BM(N)=1.7D1*ET(N) END IF RETURN END
0* ******************************************************************* * SUBROUTINE STIE
0* ******************************************************************* * COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999),PD(999),
Sc BM(900) ,ET(900) ,PP(999) ,DIX(999) , DIY (999 ) , IL (9 00 , 5) , NA (2 000 ) , Sc IC(2 00) ,NP(60) ,LE(30,2) ,KC(15,3) , NUT (15) , NUS (15) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40) , FJ(40),PJ(40),
Sc TJ(40) ,SC,CSA,SNA,CM,DC,IB(10 0,3) ,ITP,IDT(40) ,STI(40) ,STF(40) , Sc SFI(40) ,SFF(40) , INO, JDN(40) ,REJ(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3),P(10),Q(4) ,STCR(3)
& ,R,DEI,DE2,VOL,GAMW,PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP,NN,NTP,
Sc SLT, MOD (4 0,15) I=IL(N,1) J=IL(N,2) MTP=IL(N,5) SLN=DSQRT(DELX**2+DELY**2)
A103
RSDAM PROGRAM LISTING APPENDIX G
CSN=DELX/SLN SNE=DELY/SLN DO 2 0 K=l,4 K1=K*2 K2=K1-1 L=IL(N,K) L1=IDS(L)+1 L2=L1-1 P(KD=-B(L2) *SNE+B(L1) *CSN P(K2)= B(L2)*CSN+B(L1)*SNE
2 0 CONTINUE RDN=0.5*(P(8)-P(2)+P(6)-P(4)) RDS=0.5*(P(7)-P(1)+P(5)-P(3)) DO 30 11=1,3
30 Q(II)=GIS(N,II) 60 AA = 0.5
IF(INT .EQ. 1 .OR. NQ .EQ. NUP) AA=1 Q(l) = GIS(N,1) - AA*STN(N)*RDN IF (INT.EQ.l .AND. JDN(MTP).EQ.1) Q(1)=Q(1)-PPAVG IF (INT.EQ.l .AND. IHZ.EQ.O) THEN Q(2)=0 ELSE Q(2) = GIS(N,2) - AA*STS(N)*RDS END IF
100 IF (MTP.EQ.INO .OR. MTP.EQ.ITP) THEN SL=0 SLT=0 Q(3)=0 GOTO 150 END IF IF (Q(l).GT.-TJ(MTP)) THEN STN(N)=SFI(MTP) PH=PJ(MTP)*1.74532925D-2 IF (Q{1).GT.0) THEN SHRST=CJ(MTP)+Q(1)*DTAN(PH) IF (PJ(MTP).GE.0.1) THEN STRSS=(Q(1)+CJ(MTP)/DTAN(PH))/PATM ELSE STRSS=(Q(1)+CJ(MTP)*5.73D2)/PATM END IF ELSE SHRST=(TJ(MTP)+Q(D)*CJ(MTP)/TJ(MTP) END IF SL=DABS(Q(2))/SHRST STST=SL * STRSS * * 0.2 5 Q(3)= DMAX1(Q(3),STST) SLT=Q(3)/STRSS**0.25 MQM=MQ+NN IF (NQ.LT.NUP .AND. GIS(N,1).GT.-TJ(MTP)) THEN STN(N)=DMAX1(SFF(MTP),STN(N)*REJ(MTP) ) STS(N)=DMAX1(STF(MTP),STS(N)*REJ(MTP)) ELSE STN(N)=SFF(MTP) STS(N)=STF(MTP) END IF END IF
150 IF (NQ -NE. NUP) GO TO 210 DO 200 11=1,3
200 GIS(N,II)=Q(ID 210 IF (INT.EQ.l) RETURN 230 IFdTD .LE. 0 .AND. NQ .NE. NUP) RETURN
WRITE(6,2000) N,XC,YC,Q(1),Q(2),STN(N),STS(N) RETURN
2000 F0RMAT(I4,2F8.2,1P4D13.3) END c********************************************************************* SUBROUTINE SEEP c********************************************************************** COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999),Y(999),PD(999), & BM(900),ET(900),PP(999),DIX(999),DIY(999),IL(900,5),NA(2000), Sc IC(200),NP(60),LE(30,2),KC(15,3),NUT(15),NUS(15)
A104
RSDAM PROGRAM LISTING APPENDIX G
COMMON /THREE/ E(40),AO(40),FR(40),GAM(40),XB(40) , BF(40) , PI(40 ) , Sc XP (4 0 ) , CE (4 0 ) , EN (4 0 ) , TN ( 4 0 ) , AL (4 0 ) , HC (4 0) , UL (4 0 ) , IDR (4 0 ) , GUE (40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3),P(10),Q(4) ,STCR(3)
Sc , R, DEI, DE2, VOL, GAMW, PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP,NN,NTP,
Sc SLT, MOD (40,15) COMMON /SEVEN/ XW(3 0),FL(3 0),PL(30),SNL(2 , 4) COMMON /EIGHT/ ID(8),IDS(900),N,MQ,NC,NQ,NSN,NX,NY,INT,ITD,NL,NMOD
k ,NXY,NRT, IFL,KSB,MTP,NAP,NCT,NSP,NEL,NJT,NNP,IHZ,1ST,NUP,NBR,NMT, Sc NNP2,NSL,NOP COMMON /TEN/ NIT,N2T,N3T,N4T WRITE(6,2000)
2000 FORMAT(///5X,'SEEPAGE LOADING IS SPECIFIED FOR THIS INCREMENT') READ(5,1000) NCODE
1000 FORMAT(16I5) IF(NCODE .NE. 0) GO TO 60 DO 40 N=1,NNP PTEM=PP(N)+PD(N) IF(PTEM .GE. 0) GO TO 2 0 PD(N)=-PP(N) PP(N)=0 GO TO 40
2 0 PP(N)=PTEM 4 0 CONTINUE
GO TO 2 00 60 READ(5,1000) NWAT
WRITE(6,1020) NWAT 1020 FORMAT(6D10.2)
READ(5,1020) (XW(I),PL(I),FL(I),1=1,NWAT) WRITE(6,2040) (XW(I),PL(I),FL(I),1=1,NWAT)
2 04 0 FORMAT(5X,F10.2,7X,F10.2,3X,F10.2) DO 180 N=1,NNP DO 8 0 1=2,NWAT IF(DABS(X(N)-XW(I)) .LT. l.D-5) GOTO 100 IF(X(N) .LT. XW(I)) GO TO 120
80 CONTINUE GO TO 140
100 TFL=FL(I) TPREL=PL(I) GO TO 140
120 IM1=I-1 DELX=DABS(XW(I)-XW(IM1) ) DELF=FL(I)-FL(IM1) DELP=PL(I)-PL(IM1) DX=DABS(X(N)-XW(IM1)) TFL=(DX/DELX)*DELF+FL(IM1) TPREL=(DX/DELX)*DELP+PL(IM1)
14 0 PD(N)=TFL-TPREL IF(TFL .LT. TPREL) GO TO 160 IF(Y(N) .GT. TFL) PD(N)=0 IF(Y(N) -GE. TPREL .AND. Y(N) .LE. TFL) PD(N)=TFL-Y(N) GO TO 180
160 IF(Y(N) .GE. TPREL) PD(N)=0 IF(Y(N) -GE. TFL .AND. Y(N) .LT. TPREL) PD(N)=Y(N)-TPREL
180 PP(N)=PP(N)+PD(N) 200 DO 300 N=1,NEL
MTP=IL(N,5) ,mrs _ IF(MTP GT. NSL .OR. MTP .EQ. NCT.OR.MTP.EQ.NAP .OR. MTP .EQ. Sc N1T.OR.MTP.EQ.N2T.OR.MTP.EQ.N3T.OR.MTP.EQ.N4T) GO TO 300 DO 210 1=1,2 DO 210 J=l,4 SNL(I,J)=0
210 CONTINUE II = IL(N,D JJ=IL(N,4) DO 220 1=1,4 n ^r 24 0 H=(SNL(1,1)+ SNL(1,2)+SNL(1,3)+ SNL(1, 4))* 0 . 2 5 V=(SNL(2,D+SNL(2,2)+SNL(2,3)+SNL(2,4))*0.25 IF(II -NE. JJ) GO TO 260 H=(SNL(1,1)+SNL(1,2)+SNL(1,3)+SNL(1, 4)) /3 V=(SNL(2,l)+SNL(2,2)+SNL(2,3)+SNL(2,4))/3
A105
RSDAM PROGRAM LISTING APPENDIX G
260 DO 280 J=l,4 IF(II .EQ. JJ .AND. J .EQ. 4) GO TO 300 J2=IDS(IL(N,J))+l J1=J2-1 DF(J1)=DF(J1)+H DF(J2)=DF(J2)+V
280 CONTINUE 3 00 CONTINUE
WRITE(6,2060) 2060 FORMAT(//5X,'THE CUMULATIVE EQUIVILENT NODAL FORCES GENERATED AT T
ScHE SPECIFIED DEGREES'/5X, ' OF FREEDOM TO SIMULATE THE SPECIFIED PHR ScEATIC LEVEL CHANGES FOLLOW' //5X, ' NODE ', 8X, ' X-FORCE ', 8X, ' Y-FORCE '// ) DO 32 0 1=1,NNP IY=IDS(I)+1 IX=IY-1 IF(DABS(DF(IX)).LT. l.D-4 .AND. DABS(DF(IY)).LT. l.D-4) GO TO 320 WRITE(6,2080) I,DF(IX),DF(IY)
2080 F0RMAT(5X,I4,1P2D15.6) 32 0 CONTINUE
RETURN END
p* ******************************************************************* *
SUBROUTINE PSTMS Q*********************************************************************
COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3),P(10),Q(4),STCR(3) Sc , R, DEI, DE2, VOL, GAMW, PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1,SIG3,TEP,NN,NTP, Sc SLT,MOD(40,15) CNTR=(Q(l)+Q(2))/2 HL=(Q(l)-Q(2))/2 RD=DSQRT(HL**2+Q(3)**2) SIG1=CNTR+RD SIG3=CNTR-RD RETURN END
Q**************************************** ******************** ********* SUBROUTINE TANESH
Q* ************************************** ****************************** COMMON /TWO/ GIS(900,5),B(2000),DF(2000),X(999) ,Y(999),PD(999),
Sc BM(900) ,ET (900) , PP (999) , DIX (999) , DIY (999) , IL (900,5 ) ,NA (2000) , & IC(200) ,NP(60) , LEO 0,2) , KC (15 , 3 ) , NUT (15) , NUS (15 ) COMMON /THREE/ E(40),AO(40),FR(40),GAM(40),XB(40),BF(40),PI(40), Sc XP(40) ,CE(40),EN(40) ,TN (40 ) , AL (40 ) , HC ( 40 ) , UL (40 ) ,IDR(40) ,GUE(40) COMMON /FOUR/ BR(100,9),STS(199),STN(199),CJ(40),FJ(40),PJ(40), & TJ(40),SC,CSA,SNA,CM,DC,IB(100,3),ITP,IDT(40),STI(40),STF(40), & SFK40) ,SFF(40) ,INO,JDN(40) ,REJ(40) COMMON /FIVE/ SE(10,10),ST(3,10),HED(20),D(3,3) , P(10),Q(4),STCR(3) Sc , R, DEI, DE2, VOL, GAMW, PATM COMMON /SIX/ RD,SL,RDF,HL,PH,SG3,PSG1,PSG3,SIG1, SIG3 , TEP,NN,NTP, Sc SLT, MOD (40, 15) COMMON /NINE/ NBEAM,NBTYP COMMON /TEN/ N1T,N2T,N3T,N4T IF(INT .EQ. 1 -OR. NQ .LT. NUP) GO TO 120 INU=0 J=l DO 100 N=1,NNP IX=IDS(N) IY=IX+1
20 DIX(N)=DIX(N)+B(IX) DIY(N)=DIY(N)+B(IY)
4 0 IFdNU .GT. 0) GO TO 6 0 WRITE(6,2000) MQ,NQ,NUP
2000 FORMAT(//5X,'DISPLACEMENT RESULTS FOR STAGE',13,4X,'ITERATI ScON' 12 ' OF',I2//5X, 'NODAL',5X, 'X',7X,'Y',9X, 'TOTAL',9X, 'TOTAL',9X Sc, 'PORE' /5X, 'POINT' ,25X, ' UX' ,12X, ' UY ' , 10X, 'PRESS' ) INU=1000 GO TO 80
60 INU=INU-1 80 CONTINUE
WRITE(6,2020) N, X (N) , Y(N) , DIX(N),DIY(N),PP(N) 2020 FORMAT(5X,I5,2F8.2,1P2D14.5,OPF11.2)
A106
RSDAM PROGRAM LISTING APPENDIX G
100 CONTINUE 120 IST=1
NN=1 IF(NQ .NE. NUP .OR. MQ .EQ. NC .OR. KSB .LT. NSP) NN=0 INU=0 IF(NEL.EQ.O) GO TO 610 DO 600 N=1,NEL MTP=IL(N,5)
6 00 CONTINUE 610 IF(NJT .EQ. 0) GO TO 680
INU=0 DO 660 N=1,NJT IF(INT .EQ. 1) GO TO 64 0 IF(ITD .LE. 0 .AND. NQ .NE. NUP) GO TO 640 IF(INU .GT. 0) GO TO 62 0 WRITE(6,2080) MQ,NQ,NUP
2080 FORMAT(//5X, 'INTERFACE ELEMENT RESULTS FOR STAGE',13 , 4X, Sc' ITERATION' ,12, 'OF' ,12//'ELEM NO' ,2X, 'X' ,5X, 'Y' ,2X, 'NORMAL STRESS' Sc,2X, "SHEAR STRESS" ,2X, 'NORMAL STIFF', 2X, ' SHEAR STIFF'/) INU=200 GO TO 64 0
620 INU=INU-1 640 CALL STIE 6 60 CONTINUE 680 IF(NBR .EQ. 0 .OR. INT .EQ. 1) GO TO 740
IFdTD .LE. 0 .AND. NQ .NE. NUP) GO TO 700 WRITE(6,2100) MQ,NQ,NUP
2100 FORMAT(//5X, 'REINFORCEMENT RESULTS FOR STAGE',13 , 4X, Sc' ITERATION' ,12, ' OF' ,I2//5X, 'REIN. NUM. ' ,4X, 'I' ,4X, ' J' ,4X, 'TYPE' , Sc3X, "COMPR FORCE' , 4X, ' INCR COMPR', 5X, ' STIFFNESS'/)
700 DO 720 N=1,NBR MTP=IB(N,3) CALL SBE IF(ITD .LE. 0 .AND. NQ .NE. NUP) GO TO 720 WRITE(6,212 0) N,(IB(N,I),1=1,3),CM,DC,SC
2120 FORMAT(9X,14,2(2X,I4),4X, 14,1P3D14.6,0P2F10.5,6X, 14 ) 720 CONTINUE 740 RETURN
END
A107