Effect of delayed backfill in Open Stope methods.pdf

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E F F E C T OF D E L A Y E D B A C K F I L L ON O P E N S T O P E M I N I N G M E T H O D S

by

CRISTIAN ANDRES CACERES DOERNER

B.Sc, Universidad de Chile, 1997

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF

T H E REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

T H E FACULTY OF GRADUATE STUDIES

MINING ENGINEERING

T H E UNIVERSITY OF BRITISH COLUMBIA

March 2005

Cristian Andres Caceres Doerner, 2005


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Abstract i i

A B S T R A C T

Open stoping is comprised of large rectangular voids separated by intervening pillars soas to minimize the size of the exposed surface and thereby reducing the potential for w a l lslough and in turn external dilution.

These pillars provide support to the exposed w a l l ; however, they result in ore loss andincreased costs such as having to establish slots for blasting. Longhole mining methods suchas A v o c a or longhole retreat as practiced at the Musselwhite mine of Placer Dome employs100% extraction with the use of fill walls to provide support to the adjacent stope.

Transverse open stoping also practiced at Musselwhite employs cemented rock f i l ladjacent to a mined stope. The question is how to account for the overall stope w a l l stabilitywhen the adjacent support is ba ck f i l l . The ba ck f i l l does not provide the same support as thatof a rock pillar, however, due to the increased use of fill abutments one has to develop amethodology that accounts for this reduced overall support element as it does reduce theoverall stope surface exposed.

It has been shown in this thesis that the ba ck f i l l w a l l does not provide the same overallstability to an individual stope as would avail itself i f the stope had rock abutments.

This is the focus of this study in order to establish design criteria to enable one toemploy existing methods for stope design such as the Stability Graph by augmenting inputparameters that have been calibrated through f ield measurements, analytical assessments,numerical modeling and laboratory testing to evaluate the effect of mining adjacent to abackfilled stope.

S i l l pillars are employed at the Musselwhite mine to allow for multiple mining horizonswith unconsolidated b a c k f i l l placed immediately above the intervening s i l l . These s i l l s can becomprised of unmined ore when the economics are such as to negate their mining oralternatively they are replaced by a constructed s i l l mat to allow for mining underneath bynon-entry methods and thereby containing the overlying ba ck f i l l .

Numerical studies were conducted to investigate modeled results of mining under acemented r o c k f i l l s i l l mat and to develop criteria for s i l l mat design. The results obtainedfrom this analysis can be extrapolated to other operations that utilize b a c k f i l l as part of the


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Abstract i i i

mining sequence. Design curves were developed for the stability of s i l l mats for variousstope configurations and cemented r o c k f i l l strength properties

This, coupled with defining the effect of mining adjacent to b a c k f i l l , forms the focus ofthis thesis.


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Tableof Contents

T A B L E OF CONTEN TS

AB S T RACT "T A B L E O F CONTENTS IVLIST O F T AB L E S VIITA BL E OF FIGURES VIIIA C K N O W L E D G M E N T S XI1 INTRODUCTION 1

1.3 BACKGROUND 21.4 THESIS OVERVIEW 31.5 CONTRIBUTIONS MADE BY THESIS 3

2 TH E MU SSELWH I TE MINE 52.1 INTRODUCTION 52.2 GEOLOGY 6

2.2.1 Regional Geology 62.2.2 Mine Geology 72.3 UNDERGROUND MINING METHODS 9

2.3.1 Avoca 92.3.2 Transverse Retreat Open Stoping 102.3.3 Drilling and Blasting Methods 102.3.4 Ore Handling 112.3.5 Ground Support / /2.3.5.1 Development Support 122.3.5.2 Stope support - Stope backs and walls 122.3.6 Backfill 132.3.6.1 M i n i n g Underneath Backf il l - C R F Sill Mats 142.3.6.2 M i n i n g Adjacent to Backf il l 14

2.4 EQUIPMENT 163 REVIEW OF DESIGN ME T H O DO L O G IE S 17

3.1 BACKFILL 173.1.1 Purpose of Backfill. / 73.1.2 Types of Backfill 19

3.1.2.1 Rockf il l 203.1.2.2 Uncemented Rockf il l - U R F 203.1.2.3 Cemented Rockf il l with Portland cement Slurry - C R F 21

3.1.3 Backfill Properties 213.1.4 Parameters Affecting Cemented Rockfill Strength 26

3.2 VERTICAL LOAD ON CEMENTED ROCKFILL SILL MA T PILLARS 283.2.1 Sill Mat Pillar Definition 283.2.2 Background - Loads Acting by Unconsolidated Material 293.2.3 Maximum Horizontal Pressure on the Walls of the Stope 313.2.4 Coefficient of Lateral Earth Pressure 33

3.2.4.1 Categories of Lateral Earth Pressure 333.2.4.2 Calculating Lateral Earth Pressure Coefficients 35

3.2.5 Maximum Vertical Load Exerted by Backfill on the Floor of the Stope 383.2.5.1 Terzaghi's Formulation 393.2.5.2 Blight's Formulation for Inclined Stopes 393.2.6 Vertical Load of Unconsolidated Material as a Function of the Material's Height 403.2.6.1 The Janssen Method - Silo Theory 403.2.6.2 The Reimbert Method - Silo Theory 41

3.3 STABILITY OF CEMENTED ROCKFILL SILL MATS-ANALYTICAL SOLUTION 42


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Table of Contents v

3.3.1 Caving Failure 423.3.2 Flexural Failure 433.3.3 Sliding Failure : 443.3.4 Rotational Failure 443.3.5 Strength Properties 44

3.4 EMPIRICAL STABILITY DESIGN METHODS 453.4.1 The Stability Graph Method1 463.4.2 The Stability Graph Method - Radius Factor* 48

3.5 SOFTWARE AND DEVICE UTILIZED 493.5.1 Flac2D - Two Dimensional Explicit Finite Difference Method*' 493.5.2 Map3D - Three Dimensional Boundary Element Method*2 503.5.3 NeuroShell Predictor - Neural Networksfl 513.5.4 Unwedge - Underground Wedge Stability Analysis*4 523.5.5 Dips - Graphical and Statistical Analysis of Orientation Data *4 533.5.6 Methods Ground Control Assessment - Cavity Monitoring System Surveys*5 53

4 DAT AB AS E 554.1 INTACT STRENGTH 554.2 FABRIC ANALYSIS 564.3 ROCK MASS ANALYSIS 584.4 STRESS 604.5 NUMERICAL MODELING - CONSTITUTIVE MODELS AND MA TERJAL PROPERTIES 604.6 EMPIRICAL STOPE DESIGN - MUSSEL WHITE'S STABILITY DA TABASE 614.7 STATISTICAL ANALYSIS OF THE MUSSELWHITE DATABASE 63

5 DESIGN GUIDELINES FO R C E M E N T E D R OC K F I L L SILL MAT S 665.1 INTRODUCTION 665.2 LOAD OF BACKFILL 66

5.2.1 Vertical Stress Comparison using different Coefficients of Lateral Earth Pressure 705.3 VERTICAL STRESS USING NUMERICAL MODELING 71

5.3.1 Introduction 715.3.2 Stress Distribution as a Function of Stope Dip Angle 745.3.3 Vertical Stress as a Function of Stope Span 755.3.4 Vertical Stress as a Function of Rockfdl 'sDensity 765.3.5 Vertical Stress as a Function of Rockfdl's Friction Angle 765.3.6 Comparison of Analytical and Numerical Methods to Determine Vertical Stress 775.3.7 Proposed Analytical Equation for Inclined Stopes 79

5.4 STABILITY OF CEMENTED ROCKFILL SILL MATS 805.4.1 Introduction 805.4.2 Sill Mat Strength - Friction and Cohesion (c) 815.4.3 Backfill Load. 825.4.4 Proposed Rotational Analytical Formulation 82

5.5 FAILURE MODES-NUMERICAL MODELING SOLUTION 855.5.1 Model Construction 855.5.2 Constitutive Equations - Strain Softening 865.5.3 Model Execution 875.5.4 Caving Failure 885.5.5 Flexural Failure 885.5.6 Sliding Failure 895.5.7 Rotational - Crushing Failure 905.5.8 Rotational Breaking Failure 905.5.9 Sill Mat Design Curves 91

6 E F F E C T OF DE L A Y E D BA C K F I L L ON OPEN STOPING 976.1 INTRODUCTION 976.2 BACKFILL AS LOCAL SUPPORT 97


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Table of Contents vi

6.3 USE OF THE STABILITY GRAPH METHOD 996.4 QUANTIFYING THE EFFECT OF BACKFILL ON LONG HOLE OPEN STOPING 1006.5 UP DA TING MUSSEL WHITE 'S STABILITY GRAPH 1006.6 NEURAL NETWORK TRAINING AND RESULTS 104

6.6.1 Relative Importance of Inputs 1046.6.2 Neural Network Predictions 107

6.7 EFFECT OF BACKFILL IN STABILITY OF OPEN STOPES - NUMERICAL MODELING ANALYSIS 1106.7.1 Radius Factor Behavior with Stope Strike Length 1126.7.2 Horizontal Displacement Behavior considered with Stope Strike Length /156.7.3 Design Curves - Avoca Mining Method 116

7 CONCLUSIONS AND RECOMMENDATIONS 1208 FUTURE W O R K 125R E F E R E N C E S 128APPENDIX A 134PROPOSED A N A L Y T I C A L EQUATION TO DE T E RMIN E V E RT ICAL L O AD O F BA C K F I L L . . . . 134APPENDIX B 138PROPOSED A N A L Y T I C A L EQUATION TO DE T E RMIN E ROTATIONAL SILL M A T FAILUREMODES 138APPENDIX C + 139IN T E RFACE E L E ME N T S 139


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List of Tables vii

LIST OF T A B L E STable 2-1: Support strength properties 11Table 2-2: Development support 12Table 2-3: Mobile Equipment List 16Table 4-1: Mean uniaxial compressive strength, standard deviation and ISRM hardness55Table 4-2: Mean Young's Modulus (E) and Mean Poisson's Ratio (v) 56Table 4-3: RMR and Q' of a typical foorwall stope 59Table 4-4: Typical RMR ranges for the different Musselwhite rock types 59Table 4-5: Musselwhite's far field stress state 60Table 4-6: Mohr-Coulomb stress-strain and strength parameters for backfill and hostrock 61Table 4-7: Updated Musselwhite stability database 63Table 5-1: Example of Musselwhite's geometry, rockfill loading, and sill mat strengthproperties 86Table 6-1: Average and standard deviation for the Musselwhite's stability database. 102


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Tableof Figures viii

T A B L E O F FIGURES

Figure 2-1: Location of Musselwhite mine 5Figure 2-2: Long section of Musselwhite orebody 5Figure 2-3: Geological cross-section through the T-Antiform Northern Iron Formation6Figure 2-4: Geological cross-section showing the Wa, T , C and S zones 7Figure 2-5: Longitudinal retreat open stoping -- Mining adjacent to backfill 9Figure 2-6: Transverse open stoping -- Mining adjacent to backfill 10Figure 2-7: Cemented rockfill sill mats constructed: 275, 300 and 375 mLevels 14Figure 3-1: Purposes of backfilling 18Figure 3-2: Mohr-Coulomb failure envelope for a cohesive fill material 24Figure 3-3: Mohr-Coulomb failure envelope for a cohesionless fill material 25Figure 3-4: Angle of repose for cohesionless fill material 26Figure 3-5: Sill mat pillar cross-section 28Figure 3-6: Natural angle of repose of the material (left) and the oblique, normal andtangential components of the force (right) 29Figure 3-7: Vertical stress at increasing depth for a confined material 31Figure 3-8: Pressure on a horizontal slice of thickness 5z 31Figure 3-9: Relationship of earth pressures to wall movements 35Figure 3-10: Comparison of at-rest earth and active earth pressure coefficients 35Figure 3-11: Differential slice in a silo 40Figure 3-12: Mathews Stability Graph (Mathews et al., 1981) 46Figure 3-13: Modified Stability Graph (Porvin and Milne, 1992) 47Figure 3-14: Modified Stability Graph with support (Nickson, 1992) 47Figure 3-15: E L O S dilution design method (Clark, 1998) 48Figure 3-16: Empirical estimation (a) of wall slough (ELOS) expressed in terms ofRadius Factor (b) 49Figure 4-1: Equal area stereonet representing the three major joint sets 57Figure 4-2: Wedge formed on the back of a drift running north-south 58Figure 4-3: Geological section obtained using Vulcan database 60Figure 4-4: Statistical Analysis on Musselwhite stability database 64Figure 5-1: Coefficient of lateral earth pressure A" for cohesionless material 67Figure 5-2: Comparison of analytically and numerically determined coefficients oflateral earth pressure 68Figure 5-3: Coefficient of lateral earth pressure obtained using numerical modeling andbest fit curve derived 69Figure 5-4: Coefficient of lateral earth pressure obtained using numerical modeling andbest fit curve derived for the rockfill friction angle range 69Figure 5-5: Horizontal vs. vertical stress at different rockfill friction angles 70Figure 5-6: Vertical stress comparison for different K values 71Figure 5-7: 25 meters (5 layers) and 35 meters (7 layers) of unconsolidated backfilldeposited in the stope 73Figure 5-8: Vertical stress distribution along span at different stope dips 74Figure 5-9: Stress contour for a stope dipping at 70 degrees 75Figure 5-10: Vertical stress at various stope spans for different rockfill heights 75Figure 5-11: Vertical stress vs. rockfill density at varying rockfill heights 76


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Tableof Figures i x

Figure 5-12: Vertical stressvs. rockfill height at varying frictionangles 77Figure 5-13: Vertical stress over rockfill height comparing analytical and numericalresults 78Figure 5-14: Vertical stress versus stope span using different methods 78Figure 5-15: Vertical stress for a 10 meter stope span using different methods 79Figure 5-16: Analytical vs. numerical modeling comparison for different stope dipangles SOFigure 5-17: Geometry, strength and stress component and failure modes in a sill matpillar gFigure 5-18: Rotational failure considering shear strength in the hangingwall of the sillmat gFigure 5-19: Rotational failure considering shear strength in the hangingwall of the sillFigure 5-20: Factor of safety for sill mat failure modes 84Figure 5-21: Strain softening model - cohesion example 87Figure 5-22: Caving failure mode - planar and semi circular crack 88Figure 5-23: Sill mat flexural failure mode - grid elements and plasticity state 89Figure 5-24: Sill mat sliding failure mode - grid elements and plasticity state 89Figure 5-25: Sill mat rotational crushing failure mode - grid elements and plasticitystateFigure 5-26: Sill mat rotational breaking failure mode - grid elements and plasticitystate 91Figure 5-27: Sill mat stability for 90 - No strength onHW (xt = 0%) 92Figure 5-28: Sill mat stability for 90 - 50% sill mat strength on HW (x, = 50%) 92Figure 5-29: Sill mat stability for 90 - 100% sill mat strength onHW (T, = 100%) 92Figure 5-30: Sill mat stability for 85 - No strength onHW (xt = 0%) 93Figure 5-31: Sill mat stability for 85 - 50% sill mat strength on HW (x, = 50%) 93Figure 5-32: Sill mat stability for 85 - 100% sill mat strength on HW (x, = 100%) 93Figure 5-33: Sill mat stability for 80 - No strength on HW (xt = 0%) 94Figure 5-34: Sill mat stability for 80 - 50% sill mat strength on HW (xt = 50%) 94Figure 5-35: Sill mat stability for 80 -100% sill mat strength onHW (xt = 100%) 94Figure 5-36: Sill mat stability for 75 - No strength onHW (x, = 0%) 95Figure 5-37: Sill mat stability for 75 - 50% sill mat strength on HW (xt = 50%) 95Figure 5-38: Sill mat stability for 75 -100% sill mat strength onHW (xt = 100%) 95Figure 6-1: Horizontal stress versus rockfill height at different stope spans 98Figure 6-2: Stope adjacent to rock(isolated) or backfill abutment(s) - Modified fromAtlas Copco Drawing 99Figure 6-3: Stability Graph update - longitudinal stope data (AVOCA) 101Figure 6-4: Stability Graph update - transverse stope data 102Figure 6-5: Stability Graph update - transverse and longitudinal stope data 103Figure 6-6: Relative importance of inputs onstope stability for stopes dippingmorethan 90 degrees (footwalls) VFigure 6-7: Relative importance of inputs on stope stability for stope dips under 90degrees (hangingwalls) 1 rJ C R F S ill Mats225 Level

250 Level

5 Level \ 100m*5 Level \ 100m* / \ 330 Level\ 330 Level375 Level

4.00 L ( V P I425 Level

Figure 2-7: Cemented rockfill sill mats constructed: 275, 300 and 375 mLevels

2.3.6.2 MiningAdjacent to BackfillStopes are mined upwards, using sub-level open stoping methods. The ore is mucked on

the floor of b a c k f i l l material and deposited on thelevel below. The broken ore is normallyremotely mucked on the bottom s i l l . R o c k f i l l material is dumped, using either scoops or


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Chapter 2 - The Musselwhite Mine 15

trucks, from the top s i l l to the point just before the hanging w a l l exposure would exceed itspredicted maximum stable span.

The longitudinal retreat and transverse open stoping methods both require periodicplacement of b a c k f i l l to support the stope walls.

This mine operation consists sequentially of: blasting; mucking; and b a c kf i l l i ng . Slotraises are dri l led and blasted at the end of each stope to create the free face needed forsubsequent production blastholes. Remote scoops are utilized to muck ore from the blastedstopes. Use of remote-control mucking improves both safety and productivity.

R o c k f i l l used for filling mined stopes comes from underground waste development, orfrom open pit rock material. Open pit r o c k f i l l material is crushed and screened to a maximumsize of 10 cm, providing crushed rock dimensions consistent with strength guidelines formixing with cement (< 5% for primary stopes; < 8-10% for s i l l mat pillars). The material isdropped down a raise fill to the underground batching plant, where it is discharged through achute and onto a truck or scoop. Cemented slurry is then applied with spray bars to meetshear and tensile strength requirements.

Maintaining a high quality b a c k f i l l product is crucial to the safety and efficiency of themining operation, while maximizing ore recovery, and leaving behind minimal ore pillars.


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Chapter 2 - The Musselwhite Mine 16

2.4 EquipmentMobile equipment in use is summarized by table 2-3.

Table 2-3: Mobile Equipment List

Type of Equipment Make/Model Number of UnitsDrilling EquipmentProduction drills Tamrock Solo 1000 Sixty 2Development drills Tamrock Minimatic H205D 3Bolters Tamrock Robolt H320-30C 3Miscellaneous drills MacLean Blockholer 1

Boart B C I - 2 1Production Scoops3 yd" Tamrock EJC-130 18yd J Tamrock Toro T500D 39yd J Tamrock Toro T650D 511 yd J Tamrock Toro 0011 1Production Trucks30 tonne Tamrock EJC 430 140 tonne Tamrock Toro 40D 9Ancillary EquipmentExplosives loader Tamrock A L B 4 5 2Scissor lift Teledyne SL6-812 3Boom truck Teledyne 1Grader Caterpillar M-120 1Personnel vehicle Toyota Landcruiser 17B u l k explosives truck I C I U-101-1 1

This chapter reviewed Musselwhite's mining methods, types of support, handling of oreand waste materials, and types of equipment in current use. The next chapter will discussdesign methodologies in current use.


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Chapter 3 - Review of Design Methodologies 11

3 R E V I E W O F D E S I G N M E T H O D O L O G I E SThis review of pertinent, existing literature is sub-divided into the following topics:

- uses, types, and properties of b a c k f i l l ;- vertical load exerted by r o c k f i l l ;- analytical s i l l matdesign;- empirical stability graph methods; and- software utilized in the analysis.

3.1 BackfdlB a c k f i l l is an increasingly important component of underground mining operations

around the world. F o l l o w i n g is a brief overview of current methods of b a c k f i l l technology,focusing on r o c k f i l l . R o c k f i l l is the principal ba ck f i l l material used at the Musselwhiteoperation.

Disposal of b a c k f i l l underground not only reduces the environmental impact andfootprint, but also provides the basis of an engineering material that can be used to improveboth the ground conditions, and the economics of mining. Carefully engineered andefficiently operated ba ck f i l l systems can significantly enhance the productivity of a givenmining operation. On the other hand, badly engineered ba ck f i l l system can become a seriousimpediment to mining operations and, in the worst case scenario, compromise safety.

Whether composed of tailings, al luvia l sand, or coarse r o c k f i l l , ba ck f i l l can be treated asa special form of so i l . Therefore, several of soil's mechanical properties and relationships canbe applied to b a c k f i l l . Note that mechanical and cure properties of fill deposited undergroundmay vary considerably, depending upon the fill material's intrinsic properties, the method ofpreparation, and the location and condition o f the mine environment.

3.1.1 Purpose ofBackfdlB a c k f i l l has multiple purposes, as indicated in figure 3-1. The primary purposes are to

improve hangingwall stability, and to permit increased ore extraction. Other importantapplication purposes include dilution control and regional support. Although much less


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Chapter 3 - Review of Design Methodologies 1 8

common, some interesting applications might include ventilation improvement, fire control,and environment protection (De Souza, et al., 1998).

Pur pose of backf i l l ing

Figure 3-1: Purposes of backfilling

For w a l l stability using ba ck f i l l , the objective is not to transmit rock stresses, but toreduce the uncontrollable convergence of rock mass so that the rock itself w i l l retain its loadcarrying capacity, and in turn, decrease cracking propagation of crown pillars and abutments(Barrett et al. , 1978). This also helps to prevent cave-ins and roof falls, minimize surfacesubsidence, and enhance pillar recovery (Coates, 1981). The ultimate result is lessdeterioration of ground conditions in the mine, and thus operation and safety are improvedoverall.

A d d i n g small percentages of ordinary Portland cement provides cohesive strength, andself-support when exposed in vertical faces to adjacent pillar mining, as w e l l as to the miningconducted below. The self-supporting nature of ba ck f i l l permits higher recovery of pillars.This, in turn, allows greater exploitation of the mining reserves, and improves the economicso f the mining operation. Increased ore recovery results in a longer mine l i fe .


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In some mining methods, b a c k f i l l forms a working platform for mine personnel andequipment. B a c k f i l l must be capable of supporting this traffic. Cement is usually not requiredi n such an application.

Depositing b a c k f i l l underground directly reduces the quantity of waste to be disposed ofon the surface. This results in direct operating and capital cost benefits, and reduces futurerehabilitation costs.

Nantel (1998) initiated a trend now common in Canada, where environmentalauthorizations for future underground mines require the return of the maximum availablequantity of mine wastes to the underground operation. This trend has reached its l o g i c a l l i m i t ,as seen in the recent Australian government recommendation to approve a project for theproposed Jabiluka uranium mine, which is encircled by the world famous Kakadu NationalPark (inscribed on the W o r l d Heritage L i s t ) . For this project, a maximum percentage ofm i l l i n g wastes are required to be re-deposited underground.

Research by Yu (unpublished) and Stone (1993) provides a good background referencesource regarding the placement of cemented r o c k f i l l , typical strength characteristics and itsapplications.

3.1.2 Types ofBackfillHassani and Archibald (1998) stated that b a c k f i l l refers to any waste materials re-

deposited into voids mined either for disposal or some other engineering task. Thesematerials include waste development rock, deslimed and whole m i l l tailings, quarried andcrushed aggregate and al luvia l or aeolian sands. Other exotic b a c k f i l l components mayinclude ice and salt. The waste materials are often combined with cement or other pozzolanic(volcanic ash) binders to improve their strength properties.

The three most common ba ck f i l l types are:

- Hydraulic backfill Deslimed m i l l tailings slurry, with densities up to70%cw (i.e., concentration of solids by weight) the coarser fractions aredeposited underground as hydraulic ba ck f i l l and the slimes rejected to thesurface dam;


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- Rock/ill Surface or underground waste rock, crushed to amaximum size -- can be deposited as is or combined with cemented hydraulicba ck f i l l slurry, or cement water slurry; and

- Paste backfill Total m i l l tailings filtered or thickened to approx.80%cw, to which cement and water is added, achieving required rheologicaland strength characteristics. (Note: pastefill is a type of b a c k f i l l in current use,although this thesis does not deal specifically with pastefill.)

3.1.2.1 RockfdlR o c k f i l l can be grouped into unconsolidated and consolidated types of material. The

latter comprises binding mixtures that achieve the required strength for a given purpose.Consolidated, or cemented, r o c k f i l l (CRF) includes classified or unclassified aggregate,

mixed with a variety of types and quantities of binder materials. T y p i c a l l y , unconsolidated,or uncemented, r o c k f i l l ( U R F ) is pre-mixed with cement binder, usually in slurry form, priorto its entry into the stope, forming a reasonably homogenous material at that time.Consolidated r o c k f i l l is commonly employed in large exposures where undermining canoccur, future exposure of fill walls is expected, and significant resistance to w a l l movementis desired. The r o c k f i l l stiffness so achieved produces significant advantages to operationsseeking ground control at sites subject to high ground stresses.

U R F also facilitates an inexpensive method of disposing of development waste orsurface open pit waste.

3.1.2.2 Uncemented Rockfdl - URFU R F is waste material deposited without additives. Although U R F has a limited ground

support capability because of its minimal resistance to closure, U R F w i l l prevent w a l l slough.The free standing height capacity of such fill is negligible. U R F is used when the filled stopewon't be exposed to future pillar recovery operations. In this case, stopes surrounding thefilled stope w i l l have been mined and filled before pillar recovery. U R F is generally used forv o i d f i l l i ng and to provide some measure of passive w a l l support to resist localized ground


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Chapter 3 - Review ofDesign Methodologies 21

movement. It is a relatively low cost f i l l medium, which is both expedient and relatively easyto place insitu.

3.1.2.3 CementedRockfill withPortland cementSlurry - CRFA variation on cemented rock b a c k f i l l widely used in Canada makes use of crushed

waste rock and Portland cement slurry aggregated at rates of approximately 5% cement byweight. Consequently, the overall sizing curve is low in fines content (i.e., size distribution ofr ock f i l l ) . This reduces the workability of the deposited ba ck f i l l and demands higher cementaggregation to provide equivalent strength performance. The technique is currently in use atthe Musselwhite mine, where a surface batching plant produces slurry, which is thendelivered via boreholes to an underground mixing plant.

Note that CRT yields a higher strength fill, demanding lower quantities of cementingagents in comparison to cemented hydraulic fill materials (including pastefill). Aggregatedwith equivalent binder components, C R F exhibits uniaxial compressive strengths that can betwo to three times higher than consolidated hydraulic fill (including pastefill). C R F rockf i l l salso exhibit higher moduli of elasticity, cohesion, and friction angle characteristics thanhydraulic fill mixtures (including pastefill) composed of similar cement contents.

3.1.3 Backfill PropertiesR o c k f i l l particles are in constant contact with each other, i.e., particles do not collide but

rather r o l l , rub, and scrape against one another. This type of stress is called frictional stress,as opposed to collisional or kinetic stress, which occurs in more diluted solutions.

When granular material does not move or f low to any extent, the only force acting on thegrains is gravity. Basic engineering theory states that for any f lu id , the total stress at thebottom of a granular pile of height hwould be:

P = p-g-h 3-1

Where:gP

is the acceleration of gravity; andis the bulk density of the r o c k f i l l material.


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Theoretically, the total stress at the bottom of the waste f i l l is a normal stress along thevertical direction (h), and therefore is an isostatic pressure, solely resulting from the weightof the r o c k f i l l pile. In practice this is not true. In fact, beyond a sufficient height of ther o c k f i l l column, the pressure reaches a maximum value and w i l l not increase further,regardless of the height of the f i l l . This occurs because r o c k f i l l supports frictional shearstress, even in a static situation. Additionally, if side walls exist within the stope, they cansupport the extra weight of the r o c k f i l l column. And so, the total stress at the bottom of ther o c k f i l l pile is a combination of normal stress and shear stress.

In order to predict the ground support capacity of a ba ck f i l l system, it is essential to firstdefine, and to understand, the significant properties of the fill material. Since most fillmaterial can be defined as either granular or fine-grained soils, evaluation of any fill propertyinvolves the principles of s o i l mechanics. However, s o i l mechanics alone cannot describe allof the properties of cemented fill. Aggregation of cement and other pozzolans to a fill,transforms the fill from natural material, e.g., s o i l , to an engineered material, making theprocess of characterizing fill properties more complex. Extensive evaluation of the effects ofcement aggregation is therefore necessary.

Existing detailed studies and laboratory work examine cemented fills and the propertiessignificant in their design. Laboratory testing indicates that the relevant properties ofcemented fill (Knissel and Helms, 1983) are:

- strength (i.e., uniaxial compressive strength);- deformation behavior;- cohesion and angle of internal friction;- density and porosity; and- consistency of the mixture.

A s with uncemented fill, strength is the principle concern in cemented fills. Certainproperties of the fill material including friction angle, density, and porosity, have the sameeffect on cemented fill strength as on uncemented fill strength.

Cement aggregation improves the strength properties of ba ck f i l l material. The mostevident increase in strength of a cemented fill over an uncemented fill is in shear strength.


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Cement bonds formed between f i l l particles produce a cohesive component in the f i l l ' sshear strength, absent in an uncemented f i l l .


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The relationship between shear stress and normal stress is commonly referred to as theMohr-Coulomb relationship for frictional shear stress.

In its basic form, it is:

r = c + < r - t a n ^ 3-2Where:

- x is the fictional shear stress ( M P a , psi, etc.);- rjn is the normal frictional stress ( M P a , psi, etc.); and- c is the cohesion of the material ( M P a , psi, etc.).

Cohesion, c, is a known material property (describing the cohesive state of grains)normally negligible in uncemented f i l l material, and (j) is the angle of repose (i.e., the angle ofinternal friction of the material).

The following figure describes equation 3-2:

Frictional Stress: Mohr-Coulomb Plane

reV) T = c + On tan((|))

ShSh

\ ()) = Friction Angle

c = cohesive shear0 Normal Stress an

Figure 3-2: Mohr-Coulomb failure envelope for a cohesive fill material

A t y i e l d , the higher the frictional stress, the higher the shear stress. The moreinterconnected the particles, i.e., the more cohesive, and/or the higher the angle of friction,the higher the shear stress, as indicated in figure 3-2.


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The Mohr-Coulomb law described by equation 3-2 and portrayed in figure 3-2, is ayielding law asserting that a material w i l l y i e l d by shearing on a surface element i f x attains acritical value defined by equation 3-2. This linear relationship is sometimes called the " y i e l dline". Below the y i e l d line, the material response w i l l be r ig id or elastic and w i l l not typicallyundergo strain, and if it does it is merely elastic strain. Elastic strain is negligible inuncemented r o c k f i l l material.

Figure 3-3 portrays the Mohr-Coulomb envelope for a cohesionless f i l l material. If theshear stress is increased for a given normal stress so that the stress state of the materialremains at y i e l d , then plastic strain, i.e., yielding, w i l l result. A state of stress cannot existabove the Mohr-Coulomb y i e l d line. When y i e l d stress is reached, particles w i l l simply slideover one another.

Figure 3-3: Mohr-Coulomb failure envelope for a cohesionless fill material

In this case, shear stress of the r o c k f i l l material is due solely to the frictional componentand is mobilized by the normal stress.

Frictional Stress: Mohr -Coul omb Plane

0 Normal Stress On


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The angle of repose (or angle of internal friction) is evident in the following figure:

Figure 3-4: Angle of repose for cohesionless fill material

The angle of repose, portrayed in figure 3-4, is low when grains are smooth, coarse, orrounded, and high for sticky, sharp, irregular, or very fine particles. T y p i c a l l y , it is between15 and 50 degrees. Musselwhite rockf i l l friction angles range from 35 to 40 degrees.

3.1.4 ParametersAffecting Cemented RockfillStrengthThe following parameters are considered essential to f inal r oc k f i l l strength (Kuganathan,

et al. , 2001):- maximum size of the aggregate;- grading of the aggregate;- binder content of the mix; and- water content of the mix.

Suitable grading of the aggregate is important, not only to reduce porosity, i.e., the v o i dratio of the fill, but also to increase the number of rock to rock contacts per unit area. Thestrength of the fill depends on the number of cement bonds that develop at these contactpoints. The strength and quality of C R F depends on how w e l l the r oc k f i l l particles are coatedwith the cement slurry before they are deposited in the stope. In a w e l l controlled operation,


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the resultant f i l l w i l l exclude uncemented r o c k f i l l pockets, and a nearly homogeneous CRFf i l l mass is thus achievable.

In the majority of underground mining operations reviewed, sized r o c k f i l l aggregate ismixed with cement slurry, typically at a cement content of 5 to 6 percent, by weight(cw), anda pulp density of 50 to 60%(cw). This type of fill may exert active pressure on contact withstope walls, providing not only ground support but also improvement in the inherent w a l lrock strength. In the case of consolidated r o c k f i l l , there normally occurs no drainageproblem, and a high fill quality can often be achieved if the materials are mixed properly.W i t h these r o c k f i l l materials however, segregation control can be difficult, and qualitycontrol may be variable. In this regard, Stone (1993) presents a methodology for theoptimization of mix designs for cemented r o c k f i l l , and suggests laboratory evaluations forverification of the design parameters. Furthermore, a program of quality control testing andperformance monitoring is outlined to improve the reliability of the design.

Segregation of consolidated rockf i l l is often unavoidable but can be minimized when filloperations are w e l l planned and closely monitored.


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3.2 Vertical Load on CementedRockfdl Sill Mat Pillars3.2.1 SillMat Pillar Definition

S i l l pillars are ore blocks left between working levels in an underground mine to supportthe overlying mine b a c k f i l l , during removal of the underlying ore. Steeply dipping ore bodiesshould be mined bottom up but for economic reasons and/or because of stability constraints(i.e., underhand cut and fill), upper ore levels are usually mined first. S i l l pillars arecommonly used in steeply dipping ore zones of limited width.

A typical situation is portrayed in figure 3-5:

B a c k f i l l

S i l l Mat P i l l a r

Stope

Figure 3-5: Sill mat pillar cross-sectionAccordingly, mineable values in the ore generally make it economically feasible to mine

the s i l l pillar. It is necessary to create an artificial s i l l , which w i l l support the overlyingunconsolidated fill, after the stope below is mined. Such s i l l mats can be constructed fromeither cemented r o c k f i l l or hydraulic and paste b a c k f i l l material.

In analyzing s i l l mat stability, the strength of ba ck f i l l necessary to maintain stability is afunction of the stresses generated within and around the s i l l mat and the fill mass.

These stresses are caused by:- self-weight of the s i l l mat;- vertical load of unconsolidated b a c k f i l l ;- blast damage/abrasion; and- ground movements.


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Th e most significant design loading used in this thesis is the weight of the f i l l material.Th e stresses generated by this weight are a function of f i l l density, f i l l friction angle, height,and span.

A number of methods have been proposed for analyzing the stability of cemented s i l lmats. These generally use free standing w a l l or two-dimensional stope stability concepts.Mitchell's (1981) approach is reviewed in this chapter.

3.2.2 Background- LoadsActing by UnconsolidatedMaterialWhen b a c k f i l l material is dumped onto a horizontal surface, it heaps into a volume

conical in shape, forming a specific angle with the horizontal plane. This angle ischaracteristic of each type of material and is called the natural angle of repose of thematerial. This is the angle of internal friction. If the material is dumped into a confined spacesuch as that of a stope, it w i l l exert pressure on the walls and on the floor of the stope. Theresultant thrust, due to the friction of the material on the walls, is oblique in relation to thesurface of the walls. This thrust has two components, one, N , normal to the w a l l , and theother, T, parallel to the w a l l (Reimbert, 1976).

The normal pressure is also called lateral thrust (figure 3-6):

Figure 3-6: Natural angle of repose of the material (left) and the oblique, normal andtangential components of the force (right)


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The material's angle of friction on the walls is termed and the correspondingcoefficient of friction is tan As a function of the oblique thrust Q defined above, the twocomponents N and T are:

N = Q-cosfT = Q-sm'

Therefore:

T = N-tan.fi 3-5

Where T is the load balanced by the friction corresponding to the thrust N .A t a given depth of the stope, the load, i.e., total vertical pressure, is the difference

between the total weight of the ba ck f i l l material and the total load offset by the friction of thematerial on the walls.

In situ measurements tell us that pressure increases with depth. However, because of thefriction of the material on the walls, the pressure on the stope floor is merely a fraction of theweight of the confined material. Furthermore, at great depths the pressure reaches a constantmaximum value (Reimbert, 1976). The curve representing pressure (plotting depth on the x-axis, and pressure on the y-axis) is asymptotic parallel to the x-axis, in correspondence withthe maximum vertical pressure (portrayed in figure 3-7).

3-33-4
http://-tan.fi/http://-tan.fi/http://-tan.fi/


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Vertical Stress at Deothfor Confined Material

V

cSery

/ Maximum Vertical Pressure

Depthz

Figure 3-7: Vertical stress at increasing depth for a confined material

3.2.3 Maximum Horizontal Pressure on the Walls of the StopeA behavior similar to that portrayed by figure 3-7, can be inferred from the curve

representing the lateral thrust on the walls. This curve is asymptotic parallel to the x-axiswhere the y-axis plots maximum thrust.

The value of the maximum horizontal thrust can be determined by the following method(figure 3-8):

z

1

* L

t

Figure 3-8: Pressure on a horizontal slice of thickness 8z


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Chapter 3 - Review ofDesien Methodologies 21

The weight of a horizontal slice of thickness dz in the interior of the stope is:

S-dz-y 3-6Where:

- S = internal area o f the cross-section of the stope;- y = unit weight of the ba ck f i l l material; and- dz = thickness of the horizontal slice.

The weight exerts a lateral pressure on the walls over the entire perimeter:

crx{z)-P-dz 3.7

Where:- CTx(z) = lateral thrust at a depth z; and- P = internal perimeter of the stope.

Pressure increases with depth up to the maximum (7_Mx, at which point the friction onthe walls balances the actual weight o f the slice considered. Therefore:

x_Max -P-dz-tan(p'=S-dz-r 3-8

From which the value of the maximum thrust can be determined:

cr = r ' S 3-9X - M a x P-tanp'Note that, for stopes of sufficient strike length (i.e., in theory, infinite), the hydraulic

radius S/P tends toward one half the span of the stope (see equation 3-9). Equation 3-10indicates the maximum lateral thrust within a stope of sufficiently long strike:

a = y L 3-10xx Max ,

2 tan cpWhere:


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- L = stope span.U p to this point in the analysis, only the maximum lateral thrust has been derived

analytically. Determining the stability of C R F s i l l mats deals with the vertical load exerted onthe top of the s i l l . The coefficient of lateral earth pressure implies a relationship between thevertical and horizontal pressures. This relationship is considered next.

3.2.4 Coefficient of Lateral Earth PressureEstimating lateral earth pressures is not a t r iv ia l problem. Nor is it a new problem.

Couplet and Coulomb developed their theories in 1726 and 1776 (respectively), and Rankinedeveloped his theory in 1857. Flexural movement of the structure must occur for thepredictions of these theories to be v a l i d , and whether it is translation/rotation into, or out of,the s o i l mass in question, active (or passive) lateral earth pressure w i l l develop.

The coefficient of lateral earth pressure implies a constant relationship between theaverage horizontal, OH , and vertical, oy, stresses, independent of the geometry of the fillvolume. While there is no physical reason for such a relationship to hold, in practice, routineindustrial calculations indicate that the results implied by this relationship are reasonablyaccurate empirically.

Equation 3-11 portrays this relationship (the coefficient of lateral earth pressure):

K = 3"n

3.2.4.1 Categories of Lateral Earth PressureThere are three categories of lateral earth pressure and each depends upon the movement

experienced by the vertical w a l l upon which the pressure is acting.These categories are:

- active earth pressure;- passive earth pressure; and- at-rest earth pressure.


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A c t i v e pressure develops when the w a l l is free to move outward. E.g., a retaining w a l lwhere the s o i l mass may stretch sufficiently to mobilize its shear strength. On the other hand,i f the w a l l moves into the s o i l , then the s o i l mass is compressed sufficiently to mobilize itsshear strength where passive pressure develops.

This problem might occur along the section of the w a l l that is below grade, on theopposite w a l l from that of the higher section.

In order to develop full active pressure or full passive pressure, the w a l l must move. Ifthe w a l l does not move sufficiently, fu l l pressure w i l l not develop. If full active pressure doesnot develop behind a w a l l , then the pressure w i l l be higher than the expected active pressure.Significant movement is necessary to mobilize the full passive pressure. This is illustrated infigure 3-9.

Most earth retaining problems involve the movement of the structure away from the so i lmass, known as the "active condition". Terzaghi (1920) demonstrated the significance oflateral earth pressures developed on structures that experience no movement, and termedthem "at-rest earth pressures". Note the at-rest condition, portrayed by figure 3-9(b), wherethe w a l l rotation is equal to zero (i.e., the condition for zero lateral strain).

Figure 3-9 shows that:- as the w a l l moves away from the so i l b a c k f i l l (see figure 3-9(c)), the active

condition develops and the lateral pressure against the w a l l decreases withw a l l movement, until the minimum active earth pressure force is reached;

- as the w a l l moves toward (i.e., into) the so i l b a c k f i l l (see figure 3-9(a)), thepassive condition develops and lateral pressure against the w a l l increases withw a l l movement until maximum passive earth pressure is reached - theintensity of the active/passive horizontal pressure, which is a function of theapplicable earth pressure coefficient, depends on w a l l movement, as it affectsthe degree of shear strength mobilized in the surrounding s o i l ; and

- at-rest pressure develops when the w a l l experiences no lateral movement,which typically occurs when the w a l l is restrained from movement, as in thecase of a stope (see figure 3-9(b)).


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Figure 3-9: Relationship of earth pressures to wall movements

Coefficient of Lateral Earth PressureK

- Ko at rest

- Ka active

20 25Friction Angle (deg) 35 40

Figure 3-10: Comparison of at-rest earth and active earth pressure coefficients3.2.4.2 CalculatingLateralEarth Pressure Coefficients

Lateral earth pressure is related to vertical earth pressure by coefficients, termed asfollows:

- active earth pressure coefficient ( K a ) ;- passive earth pressure coefficient ( K p ) ; and- at-rest earth pressure coefficient ( K o ) .

Lateral earth pressure is equal to vertical earth pressure multiplied by the appropriateearth pressure coefficient.


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Since s o i l ba ck f i l l is typically granular material, such as crushed rock, sand, silty sand,sand with gravel, etc., the ba ck f i l l material that exerts pressure on the w a l l can be treated ascoarse-grained non-cohesive material.

3.2.4.2.1 Active andPassive Earth Pressure CoefficientsWhen discussing active and passive lateral earth pressure, there are two relatively

straightforward classical theories (among others) in widespread use: Rankine earth pressure,and Coulomb earth pressure.

The Rankine theory assumes that:there is no adhesion or friction between the w a l l and s o i l ;lateral pressure is limited to vertical walls;failure (in the backfill) occurs as a sliding wedge along an assumed failureplane defined by (j);lateral pressure varies linearly with depth, and the resultant pressure is locatedone-third of the height above the base of the w a l l ; andthe resultant force is parallel to the ba ck f i l l surface.

there is friction between the w a l l and s o i l and accounts for this by using a s o i l -w a l l friction angle of 8 (8 ranges from 12 to 2cp/3 and a 5 equal to 23 iscommonly used);lateral pressure is not limited to vertical walls; andthe resultant force is not necessarily parallel to the ba ck f i l l surface because ofthe s o i l -w a l l friction value 5.

The Rankine active and passive earth pressure coefficients for a horizontal ba ck f i l lsurface are calculated as follows:

The Coulomb theory is similar to the Rankine theory, except that:

(Active) Ka =1 - sin(fz))1 + sin(c )= tan2 (45-^/2) 3-12


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(Passive) -> Kp = 1 + sin(^)1 - sin(^) tan2 (45 + ^/2) 3-13

The Coulomb active and passive earth pressure coefficients are more complexexpressions that depend on the angle of the back w a l l , the s o i l -w a l l friction value, and theangle of the ba ck f i l l . The Coulomb active and passive earth pressure coefficient for thespecific case of a vertical back w a l l angle and horizontal ba ck f i l l surface (not shown) yieldsresults equivalent to the Rankine method (equations 3-12 and 3-13).

3.2.4.2.2 At-Rest CoefficientGenerally, at-rest earth pressure is the horizontal component of the in situ stress state, or

the horizontal pressure acting on an earth retaining structure. At-rest lateral earth pressurescan be shown to be some multiple of the vertical stress at any point, illustrated in thefollowing ratio (Terzaghi, 1920):

A more specific definition is offered by Bishop (1958): "The coefficient of earthpressure at-rest, is the ratio of the lateral to the vertical effective stresses in a s o i lconsolidated under the condition of no lateral deformation, the stresses being principalstresses with no shear stress applied to the planes on which these stresses act" or:

3-14

Where:is the horizontal pressure;

K ois the vertical pressure; andis the coefficient of earth pressure at-rest.

3-15

Where:- a'h is the horizontal principal effective stress; and


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- a'v is the vertical principal effective stress.

Existing published relationships depend upon the soil's engineering values to calculatethe at-rest earth pressure coefficient. One common earth pressure coefficient for the at-restcondition used with granular s o i l is called the "Neutral Earth Pressure Method", derived byTschebotarioff(1973):

K = 3-160 l-v

Where:- v is the Poison's ratio.

The assumption is that the force of gravity affects the elastic mass of material andtherefore lateral movement is prevented.

A n alternate solution for Ko can be found via Jaky's (1944) equation:

Ko=l-sm(0) 3-17

Where:-


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Chapter 3 - Review of DesignMethodologies 39

y _Max 2-#-tan(^)3-19

3.2.5.1 Terzaghi's FormulationAnother approach to estimating the vertical load exerted by b a c kf i l l material is found in

Terzaghi et. al. (1948). Terzaghi derives a solution to the first order linear differentialequation:

5 ^dy r

2-c 2 K a tan0 3-20

Where:is cemented r ock f i l l cohesion.

For cohesionless soils, the solution to the first order differential equation yields theequation for maximum vertical stress:

y_Max (*) =2 - . K - t a n ( 0 )

3-21

3.2.5.2 Blight's Formulationfor InclinedStopesB l i g h t (1984) proposed an approximate solution for the stresses in an inclined planar

stope. This solution applied to the design of inclined rectangular stopes, produces theequation:

y _Max 2-K- tan(^) sin(/7) 3-22

Where:P is the inclination of stope.


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3.2.6 Vertical Load ofUnconsolidatedMaterial as aFunction oftheMaterial's HeightEmploying themaximum vertical load rather than the actual vertical load, dependent

upon the height of the b a c k f i l l , overestimates the strength required to withstand the load on as i l l mat. This in turn leads to an increase in cost. For that reason the preferable application ofvertical loads is as afunction of the ba ck f i l l height.

There arenumerous formulations of silo theory, two of which arediscussed here. S i lotheory only applies to vertical silos and thus is not va l id for inclined stopes. S i lo theory,however, canenhance ourunderstanding ofhow vertical stresses act within open stopes.Janssen's method, developed in 1895, and Reimbert's method, developed in 1953 (andsubsequently further developed in 1976), are discussed next.

3.2.6.1 TheJanssen Method- Silo TheoryJanssen's method isbased on theequilibrium of a thin horizontal slice, expressed as a

differential equation (3-23).

Figure 3-11: Differential slice in a silo

da K tan(^) tr + :--y = ody HR 3-23


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This yields a solution of the form:

C T ( Z ) = y HRK-tan() 1-expK-ian(


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Chapter 3 - Review of Design Methodologies

A i is the characteristic abscissa corresponding to the s i lo .

42

The characteristic abscissa is defined as:

Ai = 2-Ln tan(^) K 3-27

Combining equations 3-26 and 3-27, yields:

( n tan(^) K- z2 T Z

- i - i+ 1 3-28

V J

3.3 Stability of CementedRockfill Sill Mats -Analytical SolutionOne of the key components of s i l l mat stability, analyzed previously, is the vertical load

exerted by the b a c k f i l l material. The vertical load is a crucial input parameter of the s i l l matstability analytical solution. The specific modes relevant here are: block caving, flexuralfailure, block sliding (shear failure parallel to the hanging w a l l within the fill), and rotationfailure (tensile/shear failure of the roof as it rotates away from the flat dipping hanging wall).Schematics of these failure modes can be found in Chapter 5.

3.3.1 Caving FailureAssuming that caving would extend to a stable arch height L/2 (for a semi-circular arc),

all unreinforced s i l l s would form a depth, d > L/2, and caving would occur when ( M i t c h e l l ,1991):

L-y>S-a,/Tc 3-29

Where:tensile strength of the cemented s i l l ;unit weight of the material; andstope span.


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The driving forces represented by the weight w of the arc of radius L/2 are defined as:

w = 8 r 3-30S i l l mat tensile strength ah over the entire hanging w a l l to footwall span L, represents

the resisting force. The factor of safety (F.S.) is derived by the forces resisting movementover the driving forces:

F.S.= 8 - C T ,y-n-L 3-31

3.3.2 Flexural FailureA wide, thin s i l l mat is susceptible to flexural failure due to the relatively low tensile

strength of cemented b a c k f i l l . Using standard flexural formulae for a fixed-end uniformly-loaded beam, failure is predicted when ( M i t c h e l l , 1991):

> 2-(crt+crc)w

3-32

or:

> 2-(


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3.3.3 Sliding FailureFrom equilibrium, block sliding of the s i l l as a result of side shear failure occurs when

( M i t c h e l l , 1991):

(av+d-y)>2-f - ^ , d \

sin 2(/3)3-34

Where:

Pshear strength of the cemented s i l l ; anddip of the stope.

3.3.4 Rotational FailureRotational failure is most l ik e ly to occur when the shearing resistance at the hanging

w a l l contact is too low, as a result of poor quality hanging w a l l rock and/or low dip angles.Separation subsequently occurs. For low dip angles, an approximate prediction can be madeby assuming the s i l l mat tensile failure results in a complete separation in hanging w a l lcontact (i.e., a gap forms).

Rotational failure develops when ( M i t c h e l l , 1991):

( cr v + d y) > d a. 3-352 L (L - d cot(/3)) sin2 (J3)

Technically, this formula has an embedded factor of safety of 2.0. The formula shouldtherefore be of the form:

(av+d-y)>d2 -a. 3-36

L-(L-^-cot( /3))-s in 2 ( /3)

3.3.5 Strength PropertiesTh e tensile strength of the f i l l is crucial in its capacity to resist damage due to blast

vibration, and to resist failure where undercutting is effected. Tensile strength of the f i l l is


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limited to, and is primarily a function of, binder content. Resistance to blast vibration damageis a function of dynamic tensile strength, which can be approximated as 5% to 15% ofunconfined compressive strength. A r i o g l u (1983) concluded that tensile strength of cementedaggregate fill occurs at approximately 15% of U C S . Smith (1982) concluded that tensilestrength of cemented tailings fill occurs at approximately 12% of U C S .Y u (unpublished) states that the actual strength of CRF placed in a mine w i l l beapproximately 2/3 of the laboratory value that is obtained from standard 6 inch diameterconcrete test cylinders, but w i l l be about 90% of the value obtained from 12-inch diametercylinders.

For stability analysis of C R F s i l l mats, this study uses a tensile strength of 10% of U C S .A l l other strength properties were obtained using Mohr-Coulomb stress strength criteria.

Th e strength properties used to calculate the factors of safety are obtained by theanalytical equations:

Cohesion, c US_ ^ + ^ 3 3 ?2 2

Tensile Strength,


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3.4.1 TheStability Graph Method^The Stability Graph Method for open stope design was in i t i a l ly proposed by Mathews, et

al. (1981), depicted in figure 3-12, and subsequently modified by Potvin (1988), using 242case histories (176 unsupported, 66 supported) and by redefining some of the adjustmentfactors. The result was the modified stability number N ' . The influence of cable bolt supportwas re-examined by Potvin & M i l n e (1992), depicted in figure 3-13, and Nickson (1992),figure 3-14, to arrive at the M o d i f i e d Stability Graph. Stability was qualitatively assessed asbeing: stable, potentially unstable, or caved.

Research at the University of B r i t i s h Columbia (1988) quantified the degree of slough bythe introduction of the term "Equivalent Linear Overbreak/Slough," E L O S , (Clark, 1998) asdepicted in figure 3-15. E m p i r i c a l estimation of w a l l slough employs:

- Stability Number N (or N ' , i.e., modified); and- Adjusted Rock Mass Rating with respect to the Hydraulic Radius (Clark,

1998).

1 0 0 0

0 .1 -I 1 1 1 1 10 5 10 15 20 25

Shape Factor, S (m)Figure 3-12: Mathews Stability Graph (Mathews et al., 1981)


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Chapter 3 -Review of Design Methodologies 4 2

1000

0 5 10 15 20 25H y d r a u l i c R a d i u s , HR (m)

Figure 3-13: Modified Stability Graph (Potvin and Milne, 1992)

H Y D R A U L I C R A D IU S , HR (m)

Figure 3-14: Modified Stability Graphwith support (Nickson, 1992)


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Numbers showing measured ELOS values

0.1 L - 1 ' ' 10 5 10 15 20

H Y D R A U L I C R A D I U S (m)Figure 3-15: E L O S dilution design method (Clark, 1998)3.4.2 TheStability Graph Method- Radius Factorf

The Stability Graph, later augmented by Mah (1997), was first introduced in terms ofRadius factor, by M i l n e (1997). Radius factor accounts for complex mining geometrieswhereas Hydraulic Radius is restricted to rectangular surfaces (Area/Perimeter). The radiusfactor has the same form as hydraulic radius; however, instead of being based on the averageo f four measurements of the supporting abutments, several measurements are taken at smallangular increments, as shown in figure 3-16(b). This allows greater f le x ib i l i t y in assessingthe geometry of the support potential at a specific point on the surface ( M i l n e , 1997),involving complex shapes, providing "weightings" (i.e., RF values).

The Stability Number N ' employed in figure 3-16(a) is similar to that of figure 3-15.The only significant difference is in the calculation of stope surface geometry, which

employs the radius factor parameter.t from "Pakalnis et a l . " , (1998).


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MODIFIED STABILITY GRAPH (ELOS) - 9 6 0 D S

l i i l l l i o ! I! n i t i>

Figure 3-16: Empirical estimation (a) of wall slough (ELOS) expressed in terms ofRadius Factor (b)

3.5 Software and Device Utilized3.5.1 Flac2D - TwoDimensional Explicit Finite Difference Method*1

Flac20 (version 4.0) is the numerical modeling tool used in this study to examine theload exerted by b a c k f i l l . Flac2D (Fast Lagrangian Analysis of Continua) is a two-dimensionalexplicit finite difference program used in engineering mechanics computations.

The program can simulate the behavior of structures built of s o i l , rock, or othermaterials, which may undergo plastic f low when their y i e l d limits are reached. Materials arerepresented by elements, or zones, which form a grid that can be adjusted to fit the shape ofthe object to be modeled.

Each element behaves according to a prescribed linear or nonlinear stress/strain law inresponse to the applied forces or boundary restraints.

The material can y i e l d and f low and, i f set to do so, the grid can deform and move thematerial that is represented. Plastic collapse and f low are modeled very accurately using theexplicit Lagrangian calculation scheme and the mixed-discretion zoning techniques inFlac2D. Flac2D is also the numerical modeling tool used to derive the design charts forstability of the CRF s i l l mat. Flac2D is an effective tool for modeling non-linear gravity


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driven materials l i ke uncemented and cemented r o c k f i l l . W i t h i n appropriate quality controlguidelines, the material (of required strength for a self-weight supported structure l ike theC R F s i l l mat) should behave as an inelastic material, once cured. Even so, the two

2D

dimensional version of Flac w i l l overestimate results given that the third dimension isconsidered to be infinite, and therefore Flac is considered to provide a conservativeestimate.

A t Musselwhite, the stope strike length, where s i l l mats were constructed, is typicallythree or more times greater than the stope height, and the use of plain-strain numericalmodeling is effective and practical, for understanding its behavior. An essential aspect ofmodeling b a c k f i l l using Flac lies in the fact that ba ck f i l l is deposited as a material with noin i t i a l stress state. The only stress comes from its own weight, which allows the distributionof vertical loads to be a function of Hangingwall (HW) and Footwall (FW) host-rock/backfillinteractions, and b a c k f i l l properties.

Another important feature of Flac2D, for the purpose of this analysis, is its capacity todisplay actual deformations of grid zones caused by material failure under different stressstates and material properties. The explicit, time-marching solution permits analysis ofprogressive failure and collapse, significant phenomena in studies of mine design.

It is also possible to perform parametric studies, conveniently, by restarting the analysisat a previous state. Results are given in Chapter 5.

t l technical source: Itasca Consulting Group L t d . (2002)3.5.2 Map3D - Three Dimensional Boundary Element Method^2

Map3D is a comprehensive, fully three-dimensional rock stability analysis package.Map3D can construct models as w e l l as analyze and display displacements, strains, stresses,and strength factors. Map3D is effective for modeling rock engineering design problemsinvolving both large tabular orebodies and irregular massive excavations.

The program features:- full three-dimensional stress analysis;- tabular stress analysis with yielding pillars;- elastic, non-linear, creep and thermal/fluid f low options;- fault slip and fracture analysis capability;


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- simulation of s t i f f dykes, weak schist zones and b a c k f i l l ;- external loading effects;- structural support placement; and- seismic database visualization.

Models may be made of rock slopes, open pits, tunnels, fractures, and undergroundexcavations, with yielding (i.e., non-linear) zones of different moduli (e.g., s t i f f dykes or softore zones) and loads resulting from steady-state thermal/fluid f l o w. Excavations can beintersected by multiple discrete faults (i.e., non-planar and gouge filled) that slip and open.Map3D can simulate ground support elements such as arches, steel sets, props, thick liners,chalks, strong ba ck f i l l , etc.

Map3D is based on three-dimensional boundary element formulation. Both displacementdiscontinuity and force discontinuity (fictitious force) formulations are available in thesoftware package. Special proprietary elements are used for simulation of thermal/fluid f lowand non-linear effects. Because automated lumping is built into the program, Map3D canaccommodate more than 300,000 elements (and over 1,000,000 degrees of freedom) usingmerely desktop computers. Larger models can be created as required..

t2 technical source: M i n e Modeling Pty L t d . (2004)Map3D-SV (standard version), release 5.0, is used in this study to calculate the

displacements on the stope w a l l for different strike lengths. The results and analysis are giveni n Chapter 6.

3.5.3 NeuroShellPredictor - NeuralNetworksfS

Neural network technology mimics the brain's own problem solving system. Just ashumans apply knowledge gained from past experience to new problems or situations, aneural network takes previously solved examples to b u i l d a system of "neurons" that makesnew decisions, classifications, and forecasts.

A Neural network looks for patterns within training sets of data, then learns thesepatterns, and develops the ability to correctly classify new patterns, or to make forecasts andpredictions. Neural networks excel at problem diagnosis, decision making, prediction,


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classification, and other problems where pattern recognition is vi ta l but precisecomputational answers are not required.

The neural network begins by evaluating linear relationships between the inputs and theoutput. Weights are assigned to the links between the input and output neurons. After thoserelationships are identified, neurons are added to the "hidden layer", so that non-linearrelationships can then be searched for. Input values in the first layer are multiplied by theweights and passed to the second (hidden) layer. Neurons in the hidden layer "fire," i.e,produce outputs that are based on the sum of the weighted values passed to them. The hiddenlayer passes values to the output layer in the same fashion, and the output layer produces thedesired results, i.e., its predictions.

The network "learns" by re-adjusting the weights between layers. The answers thenetwork produces are continually compared with the correct answers, and each time theconnecting weights are adjusted slightly in the direction of the correct answers. Additionalhidden layer neurons are added as needed to isolate structures in the data set.

Eventually, if the problem can be learned, a stable set of weights evolves and w i l lproduce useable answers for all sample decisions, or predictions. The real power of neuralnetworks becomes evident when the trained network is able to produce useable results fordata that the network has never "seen" before.

t3 technical source: Ward System Group Inc. (1997)NeuroShell Predictor version 5.1 is used in this study to compare E L O S (Equivalent

Linear Overbreak Slough) data for transverse primaries, or isolated stopes, againstlongitudinal stopes, where b a c k f i l l is adjacent to the exposed w a l l . Results are given inChapter 6.

3.5.4 Unwedge - Underground WedgeStabilityAnalysis*4

Unwedge (version 2.2) is a three-dimensional stability analysis and visualizationprogram for underground excavations in rock, containing intersecting structuraldiscontinuities. Safety factors are calculated for potentially unstable wedges so that supportrequirements can be modeled using various types of pattern and spot bolting, and shotcrete.Unwedge can perform safety factor analysis, in accordance with reinforcements employed,and interpret the results.


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The graphical data interpreter provides a r i c h set of tools, including 3D animation,providing for convenient display of wedges surrounding the excavation.

Unwedge incorporates enhanced support models for bolts, shotcrete, and supportpressures, and has the ability to optimize tunnel orientation. There is also an option toexamine different combinations of three joint sets based on a list of multiple joint sets.Unwedge uses a new analysis engine based on Goodman and Shi's block theory, includingthe ability to evaluate induced stress around the excavation and its effects on stability.Unwedge includes new strength models such as Barton-Bandis and Power Curve, and theability to improve the scaling and sizing of wedges.

t4 technical source: Rocscience Inc.(2004)Unwedge is used in this study to represent structural blocks, and support pattern

performance in a typical production tunneling scenario.

3.5.5 Dips - Graphical and StatisticalAnalysis of Orientation Data 14Dips is designed for the interactive analysis of orientation-based geological data and

allows the user to analyze and visualize structural data, following the same techniques usedi n manual stereonets. Additionally, it has several computational features, such as statisticalcontouring of orientation clustering, mean orientation and confidence calculation, clustervariability, and qualitative and quantitative feature attribute analysis.

Dips is designed for analysis of parameters related to the engineering analysis of rockstructures, however, the free format of the Dips data f i le permits analysis of any orientation-based data (Rocscience Inc., 2004).

+4 technical source: Rocscience Inc.(2004)Dips version 5.0 is used in this study in the modeling of Musselwhite's fabric analysis

(see 4.2).

3.5.6 Methods Ground ControlAssessment - Cavity MonitoringSystemSurveysfSOptech's Cavity Monitoring System (CMS) is an advanced, reflectorless, laser-based

auto scanning system that provides efficient and accurate measurement of dangerous andinaccessible cavities. C M S collects thousands of data points per minute. The data is used to


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determine stope volume and stope dilution, sloughing/backfill volumes and minemeasurements, and to create detailed profiles of pillars, orepasses, raises, drifts, anddrawpoints. M i n e surveyors obtain detailed 3D survey data images of undergroundproduction stopes. M i n e planners use the data to determine the exact area mined, andquantify volumes of mined/unmined ore. Geologists use the data to match month endreconciliation. Rock mechanics then use the data to predict rock failure (e.g., hangingwalland footwall).

After a set of blast rings is designed, blasted, excavated and surveyed, the results arecompared to the original blast design. The results are then analyzed for tonnage of lost ore(underbreak), tonnage of waste rock or unplanned dilution (overbreak), and accuracy ofgrades sent to the m i l l (reconciliation). Ultimately, the results are analyzed for the success, orlack of success, of d r i l l in g and blasting, and to predict dilution in future stopes (Optech Inc.).

t5 technical source: Optech Incorporated.(2004)


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Chapter 4 - Database 55

4 D A T A B A S E4.1 IntactStrength

A total of 32 additional uniaxial compressive strength tests were carried out, augmentingthe existing 12 results on both iron formation and intermediate-mafic/felsic volcanic rocks.Four more samples of the iron formation were tested with extensometers, allowing for elasticmodulus determination. The tests were performed as recommended in the I S R M SuggestedMethods (Brown, E.T. (Editor), 1981). The test result averages are presented in Table 4-1and Table 4-2.

Table 4-1: Mean uniaxial compressive strength, standard deviation and ISRM hardness

Rock TypeIron Formation Number ofSamples

UCS(MPa)

Standard Deviation(MPa)

ISRM Hardness

4ea 7 194 46 V e r y Strong Rock - R54 f 12 92 31 Strong Rock - R44e 3 116 15 V e r y Strong Rock - R54b 5 156 46 V e r y Strong Rock - R5

4e4f 3 86 11 Strong Rock - R4Intermediate-MaficVolcanic

A V o l 9 181 43 V e r y Strong Rock - R5Intermediate-FelsicVolcanic

B V o l 5 117 22 V e r y Strong Rock - R5


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Chapter 4 - Database

Table 4-2: Mean Young's Modulus (E) and Mean Poisson's Ratio (v)

56

Rock Type Young Modulus Standard Poisson's ratio StandardE Deviation V Deviation

(GPa) (GPa) () ()4ea 84 13 0.21 0.034f 72 7 0.21 0.02

A V o l 85 N / A 0.23 N / AB V o l 79 N / A 0.24 N / A

The tests were performed using an electro-hydraulic servo-controlled s t i f f testingmachine, used for comparing the various physico-mechanical properties of rocks underdifferent conditions of loading to I S R M standards.

4.2 FabricAnalysisGenerally, three joint sets are prominent in all rock types: parallel to the ore,

perpendicular to the ore, and flat. Some random, typically vertical, faulting also exists asdoes the 4f (garnet-biotite-schist), which is also vertical and parallel to the ore zone. Astructurally intense domain seems to be characteristic of the B V o l (footwall drift) in whichthe three prominent joint sets exist, except with tighter spacing, resulting in blocky ground.The A V o l has characteristically tight foliation (north-south, vertically dipping), which rangesin spacing from below one centimeter to five centimeters, or more. Flat and crosscuttingjoints in the A V o l are spaced from one to two meters or more as opposed to the B V o l .Ground conditions at the back of the A V o l are generally very good. Because there is tightfoliation, the walls are prevented from buckling.

The ore zone consists of three predominant joint sets in dip/dip direction, globalorientation format:

8 3 / 90 (north-south, vertical joints);- 75 / 177 (east-west, vertical joints); and

25/210 (flat jointing).


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Figure 4-1 portrays the equal area projection stereonet, obtained by employingRocscience's Dips program on the three major joint sets.

Figure 4-1: Equal area stereonet representing the three major jointsets

In the ore zone, the three joint sets typically have an average spacing of 1 - 1.5 meters.The joint sets have slightly rough surfaces and little or no separation with hard joint w a l lrock. In the B V o l , the joints are typically spaced more tightly and have thin chloritic-coatedsurfaces.

There is the potential for wedge or block failures in these areas, both when drifting andwhen longholing. Wedge failures may occur at the hangingwall or the back of the open stope.Wedges in the drifts are normally supportable with standard 1.8 meter (#6) support.

Figure 4-2 portrays a 10-tonne wedge, supported by standard 1.4 meter by 1.4 meterpattern, fully-grouted resin rebar. The factor of safety for the standard bolting patternemployed at Musselwhite produces a high degree of confidence. Stability analysis waseffected using Rocscience's Unwedge program on three major joint sets (previously defined)with 1 meter spacing each, considering no cohesion and a 35 degree friction angle for thejoint sets' i n f i l l i n g material. The tunnel trends to the north.


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U N M E D C E - S T A B I L I T Y A N A L Y S I S

lit U . I ' M

P e i c s p o o t rue u i i < t |

/ 01

I J ' .K1 - f K . L MP A I fOMHiT O V.Q13HIIM I.HIUrl Kik'i\T O H O TftT J"

> S U c t button to lnat l 1 '*ujior't ( C E S C 1 to ox it)

Figure 4-2: Wedge formed on the back of a drift running north-south

Failures in the open stope due to random faulting and jointing produce the potential forunplanned dilution. Some failures of up to 4.5 meters deep have been observed occasionally,due to the poor hangingwall rock mass quality 4f, which runs parallel to the hangingwall.

4.3 Rock Mass AnalysisBieniawski's Geomechanics Classification (1976), or the Rock Mass Rating ( R M R ) , of

the stopes varies between 40% - 70% for the hanging w a l l , 60% - 80% for the footwall, 65%- 70% for the back of the stope, and 70% - 75% for the ore itself. Table 4-3 illustrates anexample of the RMR where R4 rock strength represents uniaxial compressive strengthbetween 100 and 250 M P a , and the Rock Quality Designation ( R Q D ) provides a quantitativeestimate of rock mass quality from d r i l l core logs. R Q D is defined as the percentage of intactcore pieces longer than 100 mm (4") within the total length of the core. Barton's TunnelingQuality Index Q, was also measured, or derived, for each stope, to estimate its stability anddetermine the approximate degree of hangingwall and footwall slough.


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Table 4-3: R M R and Q' of a typical footwall stopeParameter Description Rating (%)Strength R4 12% R Q D 60-70% 12-14

Joint Spacing 0.25-0.5m 11-17Joint Condition Slightly rough/smooth 15-17Ground Water D ry 10

Total R M R 60-70%Total Q' 5.9-18.0

The following table summarizes the average range of Rock Mass Rating (Bieniawski,1976) for the different rock types found at Musselwhite throughout the l i fe of the mine.

Table 4-4: Typical R M R ranges for the different Musselwhite rock types

Rock Type BVol AVol 4f 4bStrength 120(240 MPa)

12(180 MPa)

12(100 M P a )

12(150 MPa)

RQD 18(75-90)18

(75-90)17-10

(50-90)17-10

(50-90)

Spacing 18-13(0.3-lm)

18-13(0.3-lm)

11-8(50-300mm)

11-8(50-300mm)

Condition 17-12(tight-sep


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Some of the RMR points were derived by interpreting geological sections using theV u l c a n geological database. Thus, the contact rock type and thickness was associated withthe R M R range in each case (see Table 4-4).

Figure 4-3: Geological section obtained usingVulcan database

4.4 StressT h e f o l l o wi ng table summarizes the stress state of Musselwhite orebodies at a depth of

500 meters (Arjang et. al., 1997):Table 4-5: Musselwhite's far field stress state

Type In-situ Stresses e.g., at 500mCThMax(E-W) 2.5 x a v M P a / m depth 3 8 M P a0-hMin(N-S) 1.5 xaV M P a / m depth 2 3 M P a

rjv(Vertical) 0.03 M P a / m depth 1 5 M P a

4.5 Numerical Modeling - Constitutive Models andMaterial PropertiesT w o different constitutive models were used to characterize both material types, host

rock and b a c k f i l l . Host rock material was assigned an elastic and isotropic model. This modelprovides the simplest representation of material behavior. The model is v a l i d for


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homogeneous, isotropic, continuous materials that exhibit linear stress-strain behavior.B a c k f i l l material was represented by the Mohr-Coulomb model, which is the conventionalmodel used to represent shear failure in soils and rocks.

Table 4-6: Mohr-Coulomb stress-strain and strength parameters for backfill and hostrock

Parameter Rockfill Host RockUnit weight (kJN/m3), y 19.67 26.48Cohesion (MPa), c 0.0 -Friction angle (degree), 37.0 -Tensile strength(MPa), at 0.0 -Young modulus (MPa), E 300.0 74,000Poisson's ratio ( ), v 0.25 0.22Bulk modulus (MPa), K 200 44,047Shear modulus (MPa), S 120 30,327

4.6 EmpiricalStopeDesign - Musselwhite's Stability DatabaseThe stability of underground excavations at Musselwhite is determined by three

components:- characterization o f the surrounding rock mass;- geometry and relative orientation of the opening; and- induced stress-state about the opening.

The first component is the identification and quantification of the rock mass properties,e.g., rock type, support, R M R , and/or Barton's Tunneling Quality Index Q. The secondcomponent is the size of the planned opening and the dip of the stope, i.e., strike length andslanted height of the opening. From this, the hydraulic radius (or radius factor) of theexposed w a l l is determined. The third aspect considered is the degree of relaxation of thestope w a l l and the major principal stress (versus minor principal stress) about the opening.The modified stability number N ' is adjusted for the new stress conditions.

B y identifying and quantifying rock mass properties and the planned geometry it ispossible to derive empirically the stability of the stope, using the M o d i f i e d Stability Graph


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(Potvin, 1998) and/or determining the amount of w a l l slough using the Equivalent LinearOverbreak Slough ( E L O S ) Graph (Clark, 1998).

Table 4-7 portrays Musselwhite's mine stability database, comprised of the 69 stopesinvestigated. For each stope, the following data are indicated: length, height, dip, R M R , andE L O S , for both hangingwall and footwall. The E L O S value was calculated by comparing thed r i l l layout and/or geological block model with the C M S survey profile for each stope. Thefollowing table was derived specifically for this study:


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Chapter 4 - Database

Table 4-7: Updated Musselwhite stability database

63

L HHW Dip Positive Di p ^ R M R QHW N'HW H W E L 0 S HFW D i P m Positive Dippw H.R.pw R M R QFW N' F W E L 0 SS100T535 20.5 44.5 74.4 74.4 7.0 60.0 5.9 9.4 0.8 47.3 -65.0 115.0 7.2 70.0 18.0 35.9 0.5S100t515 20.0 44.5 81.6 81.6 6.9 70.0 18.0 32.0 0.6 45.2 -77.1 102.9 6.9 70.0 18.0 35.9 0.4S100T495 20.0 42.0 81.0 81.0 6.8 70.0 18.0 31.7 0.5 42.5 -77.5 102.5 6.8 60.0 5.9 11.8 0.6S100T475 20.0 42.0 81.0 81.0 6.8 70.0 18.0 31.7 0.5 42.1 -80.0 100.0 6.8 70.0 18.0 35.9 0.3S100T455 20.0 42.0 81.0 81.0 6.8 70.0 18.0 31.7 0.4 42.6 -76.6 103.4 6.8 70.0 18.0 35.9 0.3S100T435 20.0 42.0 85.7 85.7 6.8 70.0 18.0 33.9 0.6 42.1 -84.6 95.4 6.8 70.0 18.0 35.9 0.3S125T570 42.5 36.5 79.1 79.1 9.8 55.0 3.4 5.8 1.4 36.4 -80.0 100.0 9.8 70.0 18.0 35.9 0.4S150T625 25.0 54.0 80.6 80.6 8.5 55.0 3.4 6.0 1.5 54.1 -80.0 100.0 8.5 70.0 18.0 35.9 0.5S150T600 25.0 52.0 80.2 80.2 8.4 45.0 1.1 1.9 2.6 53.9 -72.0 108.0 8.5 70.0 18.0 35.9 0.4S150L510SZ 40.0 32.2 -88.0 92.0 8.9 70.0 18.0 35.9 0.4 33.1 76.8 76.8 9.0 55.0 3.4 5.6 1.4S175L610 47.5 29.0 75.0 75.0 9.0 70.0 18.0 29.0 0.4 28.4 80.7 80.7 8.9 45.0 1.1 2.0 2.3S175L505SZ 22.5 23.4 -79.4 100.6 5.7 70.0 18.0 35.9 0.4 24.3 71.4 71.4 5.8 60.0 5.9 9.0 0.7S175L940 12.5 30.5 68.3 68.3 4.4 70.0 18.0 26.0 0.3 28.7 -81.1 98.9 4.4 70.0 18.0 35.9 0.3S175940CZ 12.5 30.2 67.8 67.8 4.4 70.0 18.0 25.8 0.3 28.3 -81.2 98.8 4.3 70.0 18.0 35.9 0.3S200T785 20.0 32.8 90.0 90.0 6.2 50.0 1.9 3.9 1.7 32.8 90.0 90.0 6.2 55.0 3.4 6.8 0.8S200L455 15.0 32.2 -83.0 97.0 5.1 70.0 18.0 35.9 0.4 32.3 82.0 82.0 5.1 60.0 5.9 10.6 0.5S225T888 20.0 57.4 77.0 77.0 7.4 70.0 18.0 29.9 0.4 57.2 -77.8 102.2 7.4 70.0 18.0 35.9 0.3S225T842 22.5 54.4 80.0 80.0 8.0 45.0 1.1 1.9 1.6 54.4 -80.0 100.0 8.0 70.0 18.0 35.9 0.2M250L250 17.0 22.0 64.9 64.9 4.8 45.0 1.1 1.5 2.0 20.0 -83.9 96.1 4.6 70.0 18.0 35.9 0.3M250T110 35.0 27.0 82.0 82.0 7.6 60.0 5.9 10.6 0.9 30.8 -60.3 119.7 8.2 60.0 5.9 11.8 0.5M250T090 20.0 49.5 78.5 78.5 7.1 70.0 18.0 30.6 0.4 50.3 -74.6 105.4 7.2 70.0 18.0 35.9 0.3S250T980 22.5 49.3 86.5 86.5 7.7 60.0 5.9 11.3 0.8 49.3 -86.5 93.5 7.7 70.0 18.0 35.9 0.5S250T957 22.5 50.5 83.8 83.8 7.8 55.0 3.4 6.2 1.0 50.4 -85.4 94.6 7.8 60.0 5.9 11.8 0.7S250T935 17.5 52.0 83.6 83.6 6.5 60.0 5.9 10.8 0.7 52.0 -84.0 96.0 6.5 70.0 18.0 35.9 0.4S250L820 32.5 29.0 78.4 78.4 7.7 45.0 1.1 1.9 2.0 28.6 -82.9 97.1 7.6 60.0 5.9 11.8 0.6S250L820 72.5 28.5 85.0 85.0 10.2 45.0 1.1 2.1 1.8 28.5 -84.0 96.0 10.2 55.0 3.4 6.8 0.9S250L735 35.5 46.0 -86.8 93.2 10.0 55.0 3.4 6.8 0.7 46.0 86 8 66.8 10.0 70.0 18.0 34.4 0.4S250L735 37.5 44.0 90.0 90.0 10.1 55.0 3.4 6.8 0.9 44.3 83.4 83.4 10.2 70.0 18.0 32.8 0.4S250L550 80.0 39.7 -87.6 92.4 13.3 70.0 18.0 35.9 0.5 39.9 83.6 83.6 13.3 60.0 5.9 10.8 0.4M2 7 5 L4 4 0 C Z 50.0 27.5 73.7 73.7 8.9 55.0 3.4 5.4 1.0 27.2 -76.0 104.0 8.8 55.0 3.4 6.8 0.8M275L440 17.5 23.1 74.6 74.6 5.0 55.0 3.4 5.4 0.8 22.6 -79.5 100.5 4.9 60.0 5.9 11.8 0.6M275L350 20.0 23.5 72.4 72.4 5.4 55.0

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