R O C K SLOPE STABILITY Charles A. Kliche Published by Society for Mining, Metallurgy, and Exploration, Inc. © 1999 by the Society for Mining, Metallurgy, and Exploration. All rights reserved. Electronic edition published 2009. eBook Copyright.fm Page i Tuesday, December 9, 2008 4:10 PM To Alexandra Veturia Society for Mining, Metallurgy, and Exploration, Inc. (SME) 8307 Shaffer Parkway Littleton, CO, USA 80127 (303) 973-9550 www.smenet.org SME advances the worldwide minerals community through information exchange and professional development. With more than 16,000 members in 50 countries, SME is the world’s largest professional association of mineral professionals. Copyright © 1999 Society for Mining, Metallurgy, and Exploration, Inc. Electronic edition published 2009. All Rights Reserved. Printed in the United States of America No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Cover photo by Mark Kennihan from the South Dakota Department of Environment and Natural Resources used with permission of Homestake Mining Company. Figure 1.4 used with permission of Institution of Mining and Metallurgy. Figure 2.7 used with permission of authors. Figure 2.8 used with permission of International Society of Rock Mechanics. Figure 2.11 used with permission of International Society of Rock Mechanics. Figure 3.14 used with permission of U.S. Filter/Johnson Screens. Figure 10.10 used with permission of Modular Mining Systems, Inc. Figures 10.26, 10.27, 10.28, 10.29, 10.30, 10.31, 10.32, and 10.33 used with permission of Barrick Goldstrike. ISBN 978-0-87335-293-2 © 1999 by the Society for Mining, Metallurgy, and Exploration. All rights reserved. Electronic edition published 2009. Contents PREFACE xv ACKNOWLEDGMENTS xvii CHAPTER 1 BASIC CONCEPTS 1 Slope Stability as an Engineering Issue 1 Terminology 2 Slope Failure Causes and Processes 6 General Modes of Slope Failure in Rock Masses 9 Mechanical Approaches to Stability Analysis 12 References 25 CHAPTER 2 ROCK MASS PROPERTIES 27 Engineering Properties of Discontinuities 27 Shear Strength of Discontinuities 34 Geologic Data Collection 43 Hemispherical Projection Techniques 47 References 64 CHAPTER 3 GROUNDWATER 67 Groundwater Flow Within Rock Masses 68 Influence of Groundwater on Slope Stability 74 Evaluation of Groundwater Conditions in Slopes 76 Slope Dewatering 91 References 96 CHAPTER 4 THE ROCKFALL HAZARD RATING SYSTEM 99 Origins 99 Overview 100 Slope Survey and Preliminary Rating 101 Detailed Rating 103 References 110 iii © 1999 by the Society for Mining, Metallurgy, and Exploration. All rights reserved. Electronic edition published 2009. CHAPTER 5 KINEMATIC SLOPE STABILITY ANALYSIS 111 Markland Test for Plane Shear Failure 111 Markland Test for Toppling Failure 114 Friction Cone Concept 114 References 123 CHAPTER 6 KINETIC SLOPE STABILITY ANALYSIS OF PLANAR FAILURE 125 Method of Analysis for Plane Shear Failure 127 Solving Plane Shear Problems: An Example 133 References 137 CHAPTER 7 KINETIC SLOPE STABILITY ANALYSIS OF TOPPLING FAILURE 139 General Model for Toppling Failure 140 Limiting Equilibrium Analysis of Toppling on a Stepped Base 141 Example: Toppling Failure 147 References 151 CHAPTER 8 KINETIC SLOPE STABILITY ANALYSIS OF WEDGE FAILURE 153 Wedge Geometry 154 Factor-of-Safety Determination 161 Other Considerations 165 References 169 CHAPTER 9 ROCK SLOPE STABILIZATION TECHNIQUES 171 Grading 172 Controlled Blasting (Overbreak Control) 176 Mechanical Stabilization 188 Structural Stabilization 189 Vegetative Stabilization 195 Water Control 196 References 199 CHAPTER 10 GEOTECHNICAL INSTRUMENTATION AND MONITORING 201 Instrumentation to Measure Rock Deformation 201 Monitoring 220 References 230 GLOSSARY 237 INDEX 245 iv © 1999 by the Society for Mining, Metallurgy, and Exploration. 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List of Figures 1.1 The Mohr Envelope 3 1.2 Highwall slope configuration 4 1.3 Orientation of a plane 5 1.4 Transition from intact rock to rock mass 6 1.5 Pit plan with slope design sectors 7 1.6 The planar failure mode 8 1.7 The rotational failure mode 10 1.8 The wedge failure mode 11 1.9 The toppling failure mode 11 1.10 Block on an inclined plane at limiting equilibrium 12 1.11 Statics for the method of slices for rotational failure 14 1.12 Potential toppling failure when the vertical weight component, W, is outside the pivot point 16 1.13 Hypothetical histogram and probability density function of dip value for joints in a set 17 1.14 Standardized normal distribution graph and table 19 1.15 Typical PDFs for variables affecting slope stability 20 1.16 The cumulative probability distribution for dip angles 21 1.17 Distribution of friction angles for probabilistic method example 22 1.18 Determining the factor-of-safety distribution: (A) frequency distribution histogram; (B) probability density function 25 2.1 Geologic and rock slope engineering conventions for rock structure orientation 30 2.2 Conversion from bearing to azimuth and azimuth to bearing 31 2.3 First- and second-order discontinuity wall roughness 32 2.4 Possible relationships between gouge thickness and asperity size 33 2.5 Peak and residual failure envelopes for multiple inclined surfaces 35 v © 1999 by the Society for Mining, Metallurgy, and Exploration. 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Electronic edition published 2009. 2.6 Principle of and output from waviness measurements 36 2.7 Discontinuity shear resistance (τ ), against shear strain (ε ), as well as d shear normal strain (ε ), against shear strain, during shear testing along a normal typical discontinuity 37 2.8 Rock joint roughness profiles showing the typical range of JRC values associated with each 39 2.9 The tilt test utilizing two contiguous blocks or rock extracted from the same location to measure the friction angle and back-calculate the joint roughness coefficient 39 2.10 A direct shear machine 41 2.11 Suggested arrangement for a laboratory direct shear test on a single discontinuity 42 2.12 The direct shear test 43 2.13 Example discontinuity survey data sheet 46 2.14 Basic concept behind hemispherical projections: (a) inclined plane; (b) stereographic representation of inclined plane 47 2.15A Loci of planes with N–S strike and various dip angles 49 2.15B Projection of radial lines in a plane with β dip angle 49 2.15C Projection of small circles in planes with systematic dip angles 50 2.16 Locus of points of constant plunge angle, β, around the center of the reference sphere 50 2.17 Equatorial equal-angle stereonet 51 2.18 Equatorial equal-area stereonet 52 2.19 Polar equal-angle stereonet 53 2.20 Polar equal-area stereonet 54 2.21 Kalsbeek counting net 55 2.22 The geometry for the position of P on the equal-angle projection 56 2.23 The geometry for the position of P on the equal-area projection 56 2.24 The geological compass 57 2.25 Geologic structure with dip direction of 62° and dip of 51° 58 2.26A Plotting a great circle, step 1: Mark the dip direction on the overlay clockwise from the north 59 2.26B Plotting a great circle, step 2: Rotate the overlay until the dip direction mark lies at the E–W line 59 2.26C Plotting a great circle, step 3: Count inward from the dip direction, mark the dip amount, and draw the great circle 60 2.26D Plotting a great circle, step 4: Rotate the overlay back to its original position 60 2.27A Polar plot of (198°, 58°) and (210°, 75°) 61 2.27B Polar plot of 37 discontinuities in a single set 62 vi © 1999 by the Society for Mining, Metallurgy, and Exploration. All rights reserved. Electronic edition published 2009. 2.27C Contour of pole densities to determine the predominant orientation of the 37 measurements 62 2.27D Great circle representing the predominant orientation of the 37 discontinuities 63 2.28 Plot of the great circles representing A = (62°, 51°) and B = (185°, 48°) 63 3.1 Features of the hydrologic cycle 67 3.2 Simplified permeability test 68 3.3 Definition of joint conductivity, Kj 71 3.4 Groundwater patterns in a stratified slope 72 3.5 Flow net for seepage through a slope 73 3.6 Influence of water pressure on the strength of rock discontinuities 75 3.7 Hvorslev piezometer test: (A) geometry; (B) method of analysis 78 3.8 Representation of the Dupuit assumption of hydraulic gradient for a confined aquifer 82 3.9 Radial flow to a well penetrating an extensive confined aquifer 84 3.10 Type curve of the relationship between W(u) and 1/u 87 3.11 Method of superposition for solving the Theis nonequilibrium equation 89 3.12 Drawdown, s, versus t/r2 for observation well 1 89 3.13 Cooper-Jacob method for solving the Theis nonequilibrium equation 90 3.14 Effect of different coefficients of transmissivity on the shape, depth, and extent of the cone of depression 92 3.15 Pumping well and three observation wells 94 3.16 Time-drawdown curve for observation well 1 95 3.17 Drawdown versus distance from the pumped well for the three observation wells 95 3.18 Composite of depression from two pumping wells based on the principle of superposition 96 4.1 Sample RHRS field data sheet 102 4.2 Diagram for determining slope height 106 5.1 The Markland test for plane shear 112 5.2 Potential wedge failure (planes A and B) and stable wedge (planes B and C) 113 5.3 Potential plane failure and stable plane 114 5.4 The toppling failure mode showing low-dip base plane and undercutting discontinuities 115 5.5 Potential toppling failure 115 5.6 The friction cone concept for a block resting on an inclined plane 116 5.7 Stereographic representation of the friction cone concept from Figure 5.6 117 5.8 Slope for friction cone method example 119 vii © 1999 by the Society for Mining, Metallurgy, and Exploration. 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Electronic edition published 2009. 5.9A Plotting the friction cone for the example of Figure 5.8, step 1: Plot great circles representing the slope face and discontinuity and the pole of the discontinuity (P ) 120 D 5.9B Plotting the friction cone for the example of Figure 5.8, step 2: Rotate P to D a great circle on the stereonet, then measure and plot φ along the great circle on both sides of P 120 D 5.9C Plotting the friction cone for the example of Figure 5.8, step 3: Rotate P to D another great circle, then measure and plot φ 121 5.9D Friction circle of 30° around the pole of the discontinuity oriented at 143°, 45° 121 5.10 The friction cones for φ = 30° and φ = 49° for the discontinuity oriented at a 143°, 45° 122 6.1 A mass of rock that slid along a single plane 125 6.2 The planar failure mode 126 6.3 Plane shear failure plane geometry 127 6.4 Block on an inclined plane at limiting equilibrium 128 6.5 Free body diagram of the failure surface of Figure 6.3 when surcharge force is included 130 6.6 Free body diagram of the failure surface of Figure 6.3 when water forces are included 131 6.7 Free body diagram of the failure surface of Figure 6.3 when vibration force is included 131 6.8 Rock-bolt angle, θ, and rock-bolt force, T 132 6.9 Free body diagram of the failure surface of Figure 6.3 when rock-bolt forces are included 133 6.10 Slope geometry for example problem 133 6.11 Free body diagram of example problem 136 7.1 The toppling failure mode 139 7.2 General model for toppling failure 140 7.3 Conditions for sliding and toppling of a block on an inclined plane 141 7.4 Undercutting discontinuities in the highwall of a mine striking approximately parallel to the slope face 142 7.5 Forces acting on the ith column sitting on (A) a flat base and (B) a stepped base 143 7.6 Dilation process in columnar slopes on a flat base 144 7.7 Slope geometry for the toppling failure mode of columns on a stepped base 145 7.8 Moment arms, l and m, at the crest of the slope, above the crest, and below i i the crest 148 8.1 Typical wedge failure involving sliding on two discontinuities 153 8.2 Typical wedges in rock slopes 155 viii © 1999 by the Society for Mining, Metallurgy, and Exploration. 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Electronic edition published 2009. 8.3 Stereographic representation of one wedge (top) for which failure is kinematically possible and one (bottom) for which failure is not kinematically possible 156 8.4 Notation used for designating the planes and lines for wedge geometry 157 8.5 Notation of planes forming the wedge and the numbering of wedge end lines 158 8.6 Notation for calculation of rock wedge volume: (A) view of plane A; (B) looking along the line of intersection 160 8.7 Location on the stereonet of wedge weight, W; the normals N, N , and N ; i A B and angles to the normals, β (δ), δ , and δ 162 i i A B 8.8 Force polygons to determine the magnitudes of N, N , and N 163 i A B 8.9 Stereonet for wedge factor-of-safety determination, with and without cohesion 164 8.10 Water pressure distribution on a rock wedge 167 8.11 Rock-bolt force, T, and effective weight, W 168 e 9.1 Bench designed with a cross slope and back slope to drain water away from the crest and across the bench to a disposal system 173 9.2 A level catch bench in the face of a rock slope along a highway 174 9.3 A catch bench in the face of a rock slope along a highway, constructed parallel to the surface topography 174 9.4 Rock slope cut to match the dip of the beds along a highway 175 9.5 A mine highwall with overall slope angle equal to the dip of the beds 175 9.6 Mine highwall cut at an angle to match the dip of the beds, with cable bolting for additional support 176 9.7 Modified production blast design in favorable conditions 177 9.8 Typical presplit blast 178 9.9 Presplit blasting utilized to provide a stable final main highwall 179 9.10 Radial and tangential stresses at distance r from the center of a pressurized thick-walled cylinder 180 9.11 Generalized trim blast design utilizing production drills 185 9.12 A typical line drilling pattern used in conjunction with a production blast 186 9.13 Overview of line drilled holes: (A) production blasthole detonating adjacent to a line drilled hole; (B) stresses on the line drilled hole from the detonation of the blasthole 187 9.14 Chain-link wire mesh anchored at the crest and draped over a slope to prevent rockfalls from passing the toe region 190 9.15 Application of shotcrete over wire mesh and rockbolts 190 9.16 Resin-grouted threadbars used to anchor a rock wedge in an unstable cut slope 193 9.17 Grout and air-bleeding tubes inserted with a cable bolt 194 ix © 1999 by the Society for Mining, Metallurgy, and Exploration. All rights reserved. Electronic edition published 2009.