Table Of ContentGeotechnical and Environmental Engineering Z
Z h
h a
“The authors are to be commended for bringing together the many components related a n
n g
to rain-fall induced landslides. I foresee that this book will be well-received by practicing g
p
engineers and researchers, and … university libraries.” p
L
—Delwyn G. Fredlund, Professor Emeritus, University of Saskatchewan Z i
h p
u
L
“This book concisely presents the fundamental mechanics behind rain-induced soil slope i
failures: rainfall infiltration in soil slopes, slope stability under rainfall infiltration, and hydro-
mechanical coupled deformation. The concepts and analyses are presented clearly from
R
the first principle with a strong physical sense. Some advanced topics, such as hydro-
mechanical coupled numerical analysis in unsaturated soils, are approached in a plain a
manner with hand[s]-on tutorials. The analysis of the stability of slopes with cracks is an
i
excellent addition—practitioners are aware of the vital importance of cracks but few have n
the know-how to quantify cracks and their effects. The book is therefore an excellent text
f
for graduate students and a good reference for geologists and engineers.”
a
—Limin Zhang, Hong Kong University of Science and Technology
l
l
Rainfall-induced landslides are common around the world. With global climate change,
-
their frequency is increasing and the consequences are becoming greater. Previous studies
I
assess them mostly from the perspective of a single discipline—correlating landslides with n
rainstorms, geomorphology and hydrology in order to establish a threshold prediction
d
value for rainfall-induced landslides; analyzing the slope’s stability using a geomechanical
approach; or assessing the risk from field records. u
c
This book integrates probabilistic approaches with the geotechnical modelling of slope
e
failures under rainfall conditions with unsaturated soil. It covers theoretical models of rainfall
infiltration and stability analysis, reliability analysis based on coupled hydro-mechanical d
modelling, stability of slopes with cracks, gravels and spatial heterogenous soils, and Rainfall-Induced Soil
probabilistic model calibration based on measurement. It focuses on the uncertainties S
involved with rainfall-induced landslides and presents state-of-the-art techniques and
o
methods which characterize the uncertainties and quantify the probabilities and risk of
Slope Failure
rainfall-induced landslide hazards. i
l
Lulu Zhang is a professor at Shanghai Jiao Tong University, China. S
Jinhui Li is an associate professor at Harbin Institute of Technology, China. l
o
Xu Li is an associate professor at Beijing Jiaotong University, China. Stability Analysis and Probabilistic Assessment
p
Jie Zhang is an associate professor at Tongji University, China.
e
Hong Zhu is a research assistant at Hong Kong University of Science and Technology.
F Lulu Zhang Jinhui Li Xu Li
p p
a
Jie Zhang Hong Zhu
i p
l
u
r
K27319
e
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487 ISBN: 978-1-4987-5279-4
711 Third Avenue 90000
New York, NY 10017
an informa business
2 Park Square, Milton Park
www.crcpress.com Abingdon, Oxon OX14 4RN, UK
9 781498 752794
w w w. s p o n p re s s .co m A SPON PRESS BOOK
Rainfall-Induced Soil
Slope Failure
Stability Analysis and Probabilistic Assessment
Rainfall-Induced Soil
Slope Failure
Stability Analysis and Probabilistic Assessment
Lulu Zhang p Jinhui Li p Xu Li
Jie Zhang p Hong Zhu
A SPON PRESS BOOK
All Rights Reserved. This is an authorized translation from the Chinese language edition published by Shanghai Jiao Tong
University Press.
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular
use of the MATLAB® software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2016 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20160419
International Standard Book Number-13: 978-1-4987-5286-2 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been
made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid-
ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright
holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this
form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may
rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti-
lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy-
ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the
publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://
www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For
organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for
identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Foreword xiii
Foreword xv
Preface xvii
List of symbols xix
Part I
Stability analysis methods 1
1 Introduction 3
1.1 Slope failures under rainfall and failure mechanisms 3
1.2 Recent advances and hot research topics 6
1.3 Outline of the book 8
References 8
2 Infiltration and seepage analysis in soil slopes 15
2.1 Introduction 15
2.2 Estimation of infiltration rate based on conceptual model 16
2.2.1 Mechanism of infiltration in soils 16
2.2.2 Green–Ampt model for infiltration of constant
rainfall on a level ground 17
2.2.3 Infiltration of constant rainfall on a sloping ground 19
2.2.4 Infiltration of time-varied rainfall on a sloping ground 22
2.3 Seepage analysis in unsaturated soil slopes based on
physical governing equation 27
2.3.1 Governing equation of water flow in unsaturated soil 27
2.3.2 Hydraulic properties of unsaturated soils 28
2.3.2.1 Soil–water characteristic curve 28
2.3.2.2 Coefficient of permeability function 28
2.4 Analytical solutions of the Richards equation 31
2.4.1 Analytical solution of one-dimensional infiltration
under constant rainfall 32
2.4.2 Analytical solution of one-dimensional infiltration
under time-varied rainfall 33
v
vi Contents
2.4.3 Effect of soil properties, boundary conditions,
and initial conditions 34
2.4.3.1 Saturated permeability k 34
s
2.4.3.2 Desaturation coefficient α 36
sy
2.4.3.3 Effective water content q – q 37
s r
2.4.3.4 Antecedent surface flux q 37
0
2.4.3.5 Rainfall intensity q 37
1
2.4.3.6 Thickness of soil layer L 39
2.5 Numerical analysis of the Richards equation 39
2.5.1 Standard formulations 39
2.5.2 Spatial approximation and time discretization 40
2.5.3 Nonlinear solution methods 41
2.5.4 Numerical oscillation 41
2.5.5 Rainfall infiltration boundary condition 45
2.6 Typical pore-water pressure profiles under rainfall condition 46
2.7 Soil conditions under which matric suction can be maintained 48
2.7.1 Pore-water pressure profiles under steady-state conditions 50
2.7.2 Pore-water pressure profiles under transient seepage conditions 54
2.7.2.1 Effect of air-entry value on the wetting front 54
2.7.2.2 Effect of the saturated coefficient of permeability 55
2.7.2.3 Influence of water storage coefficient 56
2.7.2.4 Effect of the groundwater boundary conditions 58
2.7.3 Geotechnical engineering implications 60
References 60
3 Stability analysis of slope under rainfall infiltration based on
limit equilibrium 65
3.1 Introduction 65
3.2 Infinite-slope stability analysis based on one-dimensional
infiltration profile 65
3.2.1 General equation of factor of safety for infinite unsaturated slope 65
3.2.2 Simplified scenarios of various seepage conditions 66
3.2.2.1 Steady-state condition with seepage parallel
slope surface 66
3.2.2.2 Transient condition with different shapes
of wetting front 68
3.2.3 Slope stability based on estimated nonlinear
unsaturated shear strength 68
3.2.3.1 Fredlund et al. nonlinear shear strength equation 69
3.2.3.2 Vanapalli et al. nonlinear shear strength equation 70
3.2.3.3 Vilar nonlinear shear strength equation 70
3.2.3.4 Khalili and Khabbaz nonlinear shear strength equation 71
3.2.3.5 Bao et al. nonlinear shear strength equation 71
Contents vii
3.3 Slope stability analysis based on limit equilibrium methods 75
3.4 Controlling factors for rainfall-induced landslides 79
3.4.1 Soil shear strength properties 79
3.4.2 Soil hydraulic properties 81
3.4.3 Rainfall characteristics 85
3.5 Spatially distributed model of hazard assessment of
rainfall-induced landslides 89
3.5.1 General methodology 90
3.5.2 Performance index 91
References 94
4 Coupled hydro-mechanical analysis for unsaturated soil slope 101
4.1 Introduction 101
4.2 Modeling of unsaturated soil based on continuity mechanics 101
4.2.1 State variables 101
4.2.2 Governing equations 103
4.2.2.1 Force equilibrium 103
4.2.2.2 Mass continuity of water phase 104
4.2.3 Formulations based on elastic constitutive model 104
4.2.3.1 Effective stress approach 104
4.2.3.2 Two stress state variables approach 107
4.2.4 Illustrative examples for elastic model 113
4.2.4.1 Consolidation of unsaturated soil 113
4.2.4.2 Heave of ground under evaporation 116
4.2.5 Formulations based on plastic constitutive models 120
4.3 Slope stability analysis based on coupled modeling 125
4.3.1 Stress analysis 125
4.3.1.1 Simplified approach 125
4.3.1.2 Fully coupled approach 128
4.3.2 Estimation of factor of safety for slope stability 129
4.4 Illustrative examples 133
4.4.1 A simple slope example based on elastoplastic
model and effective stress concept 133
4.4.2 Case study of 1976 Sau Mau Ping landslide 141
4.4.2.1 FE model 142
4.4.2.2 Soil properties 144
4.4.2.3 Results and discussion 149
4.4.3 Case study of a field test of rainfall-induced landslide 153
4.4.3.1 Site description 153
4.4.3.2 Experiment procedure 154
4.4.3.3 Numerical model 155
4.4.3.4 Soil properties 156
4.4.3.5 Results and discussion 160
References 166
viii Contents
5 Stability of soil slope with cracks 173
5.1 Introduction 173
5.2 Prediction of unsaturated hydraulic functions of cracked soil 173
5.2.1 Pore-size distribution of cracked soil 174
5.2.2 Prediction of SWCC for desiccation crack networks 174
5.2.2.1 A general method to estimate SWCC
based on the capillary law 174
5.2.2.2 SWCC for soil matrix with known pore-size distribution 176
5.2.2.3 Water retention curve for cracks 177
5.2.3 Prediction of SWCC for nondeformable cracked soil 178
5.2.4 Prediction of tensorial permeability function for
nondeformable cracked soil 179
5.2.4.1 Saturated permeability of desiccation cracks 179
5.2.4.2 Permeability function for desiccation cracks 179
5.2.4.3 Prediction of permeability function for cracked soil 181
5.2.5 Hysteresis models for SWCC and permeability function 182
5.2.6 Prediction of SWCC and permeability function
considering crack volume change 184
5.2.6.1 Desiccation-induced crack volume change 184
5.2.6.2 SWCC and permeability function for cracked
soil considering crack volume change 185
5.3 Example 186
5.3.1 Prediction of SWCC and permeability function for
cracked soils considering crack volume change 186
5.3.2 Parametric study and discussions 195
5.4 Stability of soil slope with cracks 197
5.4.1 Methodology 197
5.4.2 Results 199
References 203
6 Stability analysis of colluvium slopes 207
6.1 Introduction 207
6.2 Hydraulic properties of colluvial soils 207
6.3 Shear strength of colluvial soils 211
6.4 An example 212
6.4.1 Methodology 212
6.4.2 Seepage analysis results 213
6.4.2.1 Slopes composed of soils with high fines fractions 214
6.4.2.2 Slopes composed of colluvial soils with high
coarse fractions 219
6.4.3 Stability analysis results 221
References 224
Contents ix
Part II
Probabilistic assessment 227
7 Reliability analysis of slope under rainfall 229
7.1 Introduction 229
7.2 Fundamental concept of reliability 230
7.3 Reliability methods and applications on slope stability 233
7.3.1 First-order reliability method 233
7.3.1.1 Mean first-order second-moment method 233
7.3.1.2 Advanced first-order second-moment method 237
7.3.1.3 Spreadsheet method 242
7.3.2 Sampling methods 246
7.3.2.1 Monte Carlo simulation 246
7.3.2.2 Importance sampling 248
7.3.2.3 Latin hypercube sampling 250
7.3.2.4 Subset simulation 251
7.3.3 Response surface method 255
7.4 Uncertainties of soil properties 259
7.4.1 Index, strength, and compressibility parameters 259
7.4.2 Soil hydraulic properties 260
7.5 Effects of uncertainty of hydraulic properties on infiltration
and slope stability 269
7.5.1 Uncertainty of hydraulic parameters of CDG and CDV soils 269
7.5.2 Infiltration in CDG and CDV soil slopes 271
7.5.3 Effects of correlation of hydraulic properties on slope reliability 275
7.6 Reliability analysis of rainfall-induced slope
failure: the Sau Mau Ping landslide 277
7.6.1 Statistics of random variables 277
7.6.2 Methodology of reliability analysis 281
7.6.3 Results and discussion 281
7.6.3.1 Uncertainty of pore-water pressure
profiles and wetting fronts 281
7.6.3.2 Uncertainty of safety factor 282
7.6.3.3 Uncertainty analysis of horizontal displacement 286
7.7 Quantitative risk assessment of landslide and risk acceptance criteria 287
7.7.1 Concept of quantitative risk assessment 287
7.7.2 Method for quantitative risk assessment 288
7.7.2.1 Likelihood of landslide 288
7.7.2.2 Vulnerability analysis 289
7.7.2.3 Elements at risk 289
7.7.3 Risk acceptance criteria 290
References 293
