Table Of ContentR 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
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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.
All rights reserved. Electronic edition published 2009.
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
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© 1999 by the Society for Mining, Metallurgy, and Exploration.
All rights reserved. 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
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© 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.
All rights reserved. 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
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© 1999 by the Society for Mining, Metallurgy, and Exploration.
All rights reserved. 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
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© 1999 by the Society for Mining, Metallurgy, and Exploration.
All rights reserved. Electronic edition published 2009.
