Role of uncertainity in soil hydraulic properties in rainfall induced landslides

ROLE OF UNCERTAINTY IN SOIL HYDRAULIC
PROPERTIES IN RAINFALL-INDUCED LANDSLIDES








ANASTASIA MARIA SANTOSO

NATIONAL UNIVERSITY OF SINGAPORE

2011




ROLE OF UNCERTAINTY IN SOIL HYDRAULIC
PROPERTIES IN RAINFALL-INDUCED LANDSLIDES



ANASTASIA MARIA SANTOSO
(B. Eng, Institute of Technology Bandung)









A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2011

Who carves a channel for the downpour, and hacks a way for the rolling
thunder,
so that rain may fall on lands …?
Whose skill details every cloud and tilts the flasks of heaven
until the soil cakes into a solid mass and clods of earth cohere together?

The L
ORD’s reply to Job,
Job 38: 25-26, 37-38 (The Jerusalem Bible)

i


DEDICATION
To Er. Timotius Santoso and Ellen D. Widjaja, M.D.


My dear Po and Mo,
When I remember the guidance and kindness I have received during my PhD
study, I feel almost ungrateful to my professors in offering this thesis not to
them, but to you. But it cannot be otherwise
1
.
For I consider this thesis, humble though it is, not a mere product of four
years of study, but a part of my life’s work. Hence it seems right that it shall
be dedicated to those to whom I owe so much in life. For all the good things
that I have enjoyed, which of those does not come through you? A high regard
for education and learning, the will to do our best, the faith that has ever

sustained me, the maxim that we should make our own path instead of
following others’: all these things I have learnt from you.
And what parents could be more generous than you? Few parents let
their daughter go off to pursue her dreams, and an academic pursuit must have
seemed strange to entrepreneurs like you. Yet you have stood by me through
the dark days of Qualifying Examination preparation, shared my joy when my
papers were published (though you did not fail to utter your astonishment
upon knowing that publications bring no direct financial gain!), and even
managed to remain proud of me and my choices.
So I humbly hope that the close of my PhD journey may bring you
satisfaction and joy. It surely brings a great joy to me, but still greater is the
joy that comes from the privilege to remain, dearest Father and Mother,


Your little daughter,
Anastasia









1
This style of dedication was used by C.S. Lewis in his Preface to Paradise Lost. I employ it
here as it suits my purpose.

ii

ACKNOWLEDGEMENT


I would like to express my gratitude to my advisors, Professor Quek Ser Tong
and Professor Phoon Kok Kwang, for their guidance and encouragement
throughout my PhD study. Working with them has been rewarding and
enjoyable, though certainly not easy. Through many pleasant conversations
with them, I have also learnt many things beyond academic matters.
I would like to thank the examiners of my thesis, Associate Professor
Harry Tan Siew Ann (National University of Singapore), Dr. Michael Beer
(National University of Singapore), and Professor Craig H. Benson
(University of Wisconsin-Madison), for spending their valuable time reading
my thesis and making insightful suggestions. Special thanks are also due to
Dr. Beer and Dr. Goh Siang Huat (National University of Singapore) for their
kind encouragements throughout my graduate study.
I would like to thank Dr. Cheng Yonggang, not only for generously
sharing with me his knowledge on unsaturated seepage, but also for his
friendship. I have also learned much about rainfall-induced landslides from
Dr. Muthusamy Karthikeyan, and I thank him for this.
The research scholarship and the President Graduate Fellowship from the
National University of Singapore are gratefully acknowledged.
My gratitude also goes to those from my former university (Institute of
Technology Bandung) who first inspired me to pursue a doctoral study. Chief
among them is Associate Professor Sindur P. Mangkoesoebroto, who first
showed me that an academic life can be rewarding. Professor Bambang
Budiono has also encouraged me to continue my study, and Associate
Professor Indra Djati Sidi further encouraged my interest in reliability.
I cherish the warm friendship of fellow research students in the structural
and geotechnical group. I choose not to mention names, lest I forget some

dear friends. Yet one could not be left unmentioned: Ms. D.D. Thanuja
Krishanthi Kulathunga.
I am deeply grateful to my sister, Mady Naomi, M.D., and her sweet
little family. Our chats have always reminded me that there is more to life
than research and study.
Lastly, my warm gratitude goes to my dear Chris (Mr. Christian S.
Sanjaya), who has been a true friend who overlooks my failures and rejoices in
my successes.

iii
TABLE OF CONTENTS

TITLE PAGE
DEDICATION
ACKNOWLEDGMENTS

i
ii
TABLE OF CONTENTS iii
SUMMARY
viii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xvi


Chapter 1 Introduction 1

1.1. Rainfall-induced Slope Failures 1
1.2. Reliability Analysis of Unsaturated Slope 4
1.3. Objectives of Study 9
1.4. Organization of Thesis 12

Chapter 2 Literature Review 15
2.1. Uncertainty in Analysis of Rainfall-induced Landslides 15
2.2. Probability Model of Uncertain Soil Properties 21
2.2.1.Soil-Water Characteristic Curve 23
2.2.2. Soil Saturated Hydraulic Conductivity 24
2.2.3. Other Soil Properties 25
2.3. Simulation of Uncertain Soil Properties 27
2.4. Reliability Assessment 29

iv
2.4.1. Reliability Estimation Techniques 32
2.4.2. Subset Simulation 37
2.5. Concluding Remarks 38

Chapter 3 Unsaturated Seepage and Slope Stability Analysis 39
3.1. Governing Equation of Seepage Through Unsaturated Soil 41
3.1.1. Constitutive Equations of Unsaturated Soil 43
3.2. Transient Analysis of Unsaturated Seepage 46
3.2.1. Finite Element Formulation of Richards Equation 46
3.2.2. Program THFELA 49
3.3. Steady State Analysis of Unsaturated Seepage 52
3.4. Stability of Unsaturated Infinite Slope 54
3.5. Validation of Numerical Models 58
3.5.1.Validation of Finite Element Seepage Analysis 58
3.5.3. Validation of Infinite Slope Model 62

3.6. Performance Function in Probabilistic Analysis of Slope 65
3.6.1. Illustration of Multiple Failure Modes 66
3.7. Concluding Remarks 69

Chapter 4 Probabilistic Characterization of Soil Properties 70
4.1. Available Probability Models of SWCC 73
4.2. SWC Curve-Fitting 77
4.2.1. Measurement Data 77
4.2.2. SWCC Equations 78
4.2.3. Determination of Curve-Fitting Parameters 80

v
4.2.4. Statistics of SWCC Parameters 82
4.3. Lognormal Joint Probability Model of SWCC 87
4.3.1. Lognormal Random Variable 88
4.3.2. Lognormal Random Vector 90
4.4. Validation of Lognormal Random Vector Model 91
4.4.1. Normalized SWCC 91
4.4.2. Non-normalized SWCC 98
4.5. Alternate Probability Models of SWCC 99
4.6.Probability Model of Saturated Hydraulic Conductivity 100
4.6.1. Marginal Distribution of k
s
100
4.6.2. Spatial Correlation of k
s
104
4.7. Concluding Remarks 109

Chapter 5 Modified Metropolis-Hastings Algorithm for Efficient

Subset Simulation
111
5.1. Subset Simulation 114
5.2. Original Metropolis-Hastings Algorithm 117
5.3. Modified Metropolis-Hastings Algorithm 124
5.4. Verification of Modified Metropolis-Hastings Algorithm 127
5.4.1. Transition Probability 128
5.4.2. Reversibility condition 131
5.4.3. Chain-correlation 132
5.4.4. Error of estimators 134
5.5. Infinite Slope Examples 139
5.5.1. Example 1: Undrained Analysis 139

vi
5.5.2. Example 2: Transient seepage analysis 143
5.6. Concluding Remarks 145

Chapter 6 Effects of Soil Spatial Variability on Seepage and Slope
Stability
147
6.1. Steady State Seepage – Saturated Soils 151
6.1.1. Flux Boundary Problem 152
6.1.2. Head Boundary Problem 156
6.2. Steady State Seepage – Unsaturated Soils 158
6.2.1. Clayey Soil 159
6.2.2. Sandy Soil 165
6.3. Transient Seepage – Unsaturated Soils 165
6.3.1. Clayey Soil 166
6.3.2. Sandy Soil 169
6.4. Factor of Safety and Probability of Slope Failure 171

6.4.1. Factor of Safety 171
6.4.2. Probability of Slope Failure 174
6.5. Uncertain SWCC 177
6.5.1. Uncertain SWCC and Spatially Variable ks 178
6.5.2. Uncertain SWCC and Deterministic ks 183
6.6. Concluding Remarks 184

Chapter 7 Conclusions 187
7.1. Conclusions 187
7.2. Recommendations 190

vii
References 192
Appendices 206
Appendix A. SWCC Parameters of Clayey Soils 206
Appendix B. Counter Example for Modified Metropolis-Hastings
Algorithm
207
Appendix C. Pressure Head for Infiltration Flux Exceeding Saturated
Hydraulic Conductivity

209
Appendix D. List of Publications 212


viii
SUMMARY
Rainfall-induced landslide is a complex problem involving transient seepage
through unsaturated soil, and decrease in soil shear strength due to this
seepage. The problem is further complicated by the presence of fairly

significant uncertainties in the soil properties. It is essential to consider these
uncertainties for more realistic assessment of slope stability. This thesis
focuses on characterizing the uncertainties in soil-water characteristic curve
(SWCC) and the saturated hydraulic conductivity (k
s
), and investigating their
impacts on seepage and stability of unsaturated slope. These soil hydraulic
properties are among the most critical input parameters which have been
recognized in the analysis of rainfall-induced landslides.
In order to incorporate the uncertainties in the seepage and slope stability
analyses, a quantitative characterization of the uncertainties is required. A
correlated lognormal random vector containing two van Genuchten curve-
fitting parameters is proposed to characterize the uncertainty in SWCC. This
probability model is developed based on available measurement data for 5 soil
textures ranging from sandy to clayey soil. It is found that the lognormal
random vector can reproduce the measured SWCC with reasonable realism.
The spatial variability of k
s
is characterized by a stationary random field with
exponential correlation function. The marginal distribution of k
s
is derived
based on the measurement data of saturated water content. It is found that k
s

follows the lognormal distribution.
The uncertainties in soil properties create uncertainties in the pressure
head and the factor of safety of the slope. Hence, a more consistent indicator
of slope stability is the probability of slope failure (P
F

). Estimation of the

ix
probability of rainfall-induced failure requires an efficient technique which is
able to handle spatial variability and multiple potential failure modes. Among
the advanced simulation-based techniques, subset simulation is suitable for
this problem. A modified Metropolis-Hastings algorithm with reduced chain-
correlation is proposed for application with subset simulation. In the modified
algorithm, random samples are generated repetitively until the pre-candidate
sample is accepted as the candidate sample. The candidate sample is rejected
only when it lies outside the failure domain. Numerical examples are
presented to demonstrate that subset simulation with the modified algorithm
produces a more accurate estimate of P
F
over the range of random dimensions
studied, both for explicit and implicit performance function. The advantage is
more significant for smaller P
F
.
The proposed probability models and subset simulation with the
proposed modified Metropolis-Hastings algorithm are used to conduct a
probabilistic analysis of rainfall-induced landslide. It is demonstrated
numerically that probabilistic analysis accounting for spatial variability of k
s

can reproduce a shallow failure mechanism widely observed in real rainfall-
induced landslides. This shallow failure is attributed to positive pore-water
pressures developed in layers near the ground surface. In contrast,
deterministic analysis assuming a homogeneous profile cannot reproduce a
shallow failure except for the extreme case of infiltration flux being almost

equal to k
s
. This highlights a practical advantage of probabilistic analysis.
The uncertainty in SWCC causes a variation in the depth of the wetting front
and the depth of the failure surface. However, it does not change significantly
the minimum factor of safety of the slope and the probability of failure.

x
LIST OF TABLES

3.1 Parameters of infinite slope in the undrained example 67
4.1 Lognormal parameters 89
4.2 Measured versus simulated statistics from lognormal translation
for sandy soils.
93
4.3 Measured versus simulated statistics from lognormal translation
for clayey soils.
93
4.4 Statistics and distribution of k
s
obtained from simulation for
sandy clay loam.
102
4.5 Probability models of SWCC and k
s
to be used in parametric
study.
110
5.1 Example and number of samples used in each verification. 128
5.2 Final and intermediate thresholds for various values of P

F
134
5.3 Results of the 1D example. 136
5.4 Parameters of infinite slope in Example 1. 139
5.5 Results of Example 1. 140
5.6 Results of Example 2. 145
6.1 Summary of parameters of infinite slope 171


xi
LIST OF FIGURES

1.1 Illustration of change in soil matric suction (a) initial condition
(b) during dry periods (c) during rainy days (after Phoon et al.
2009).
3
2.1 Sources of uncertainty in analysis of rainfall-induced landslides. 17
3.1 Typical infinite slope with a weathered layer (after Phoon et al.
2009).
58
3.2 Comparison of transient solution from THFELA and analytical
steady state solution.
60
3.3 Comparison of numerical solution from THFELA and analytical
transient solution.
61
3.4 Results from infinite slope model with steady state seepage. 64
3.5 Results from infinite slope model with transient seepage. 64
3.6 Infinite clay slope with spatially variable undrained shear
strength.

66
3.7 Examples of realizations with failure surface located not at the
base of the slope.
68
4.1 Fitted curves based on Methods 1, 2, and 3. 81
4.2 Effect of curve-fitting parameters on SWCC curve: (a) “n” fixed
at 1.156 and (b) “a” fixed at 0.738.
82
4.3 Empirical distributions of SWCC parameters: (a)Sandy clay loam
(b)Loam (c)Loamy sand.
84
4.4 Correlation between curve-fitting parameters: (a)Sandy clay
loam (b)Loam (c)Loamy sand (d)Clay (e)Silty clay.
85

xii
4.5 Effect of negative correlation between “a” and “n”: (a)
negatively correlated “a” and “n”(b) independent “a” and “n”.
86
4.6
Correlation between 
s
and the curve-fitting parameters:
(a)Sandy clay loam (b)Loam (c)Loamy sand.
87
4.7 Empirical Cumulative Distribution Function (ECDF) of SWCC
parameters: (a) Sandy clay loam (b) Loam (c) Loamy sand (d)
Clay (e) Silty clay.
94

4.8 Curve-fitting parameters and soil water characteristic curves: (a)
Sandy clay loam (b) Loam (c) Loamy sand (d) Clay (e) Silty
clay.
96
4.9 Histogram of water content at suction of 50 kPa. 97
4.10 Non-normalized SWCC for sandy clay loam. 98
4.11 Simulated curve of hydraulic conductivity for sandy clay loam. 103
4.12 Random field representation of ln k
s
: (a) a realization of the
random field (b) averages of the random field at each layer.
108
5.1 Example of pre-candidate samples for simulation of conditional
distribution X < -1.28
.
122
5.2 Transition probability p(x,y) of original Metropolis-Hastings
algorithm with various values of initial sample x.
129
5.3 Cumulative transition probability F (x, y) with various values of
initial sample x.
130
5.4 Correlation of Markov chain samples produced by original and
modified algorithms: (a)25% quantile (b)50% quantile (c)75%
quantile.
133
5.5 Correlation of indicator function produced by original and
modified algorithms: (a) 25% quantile (b) 50% quantile (c) 75%
quantile.
134

xiii
5.6 Statistics of intermediate thresholds estimated using original and
modified algorithm for the case of c
m
= -4.26 : (a) bias of
estimator (b) coefficient of variation (c) mean square error.
136
5.7 Statistics of failure probability estimated using original and
modified algorithm: (a) bias of estimator (b) coefficient of
variation (c) mean square error.
137
5.8 Statistics of failure probability for Example 1: (a) bias of
estimator (b) coefficient of variation (c) mean square error.
143
6.1 A single realization of k
s
and the resulting pressure head profile
in flux boundary problem.
154
6.2 Computed correlation between pressure head and inverse of
conductivity.
155
6.3 Mean (m
h
) and standard deviation of pressure head (s
h
) in flux
boundary problem.
156

6.4 Mean (m
h
) and standard deviation of pressure head (s
h
) in head
boundary problem.
158
6.5 Single realization of k
s
and resulting pressure head profile in
unsaturated, steady state analysis with clayey soil and q/μ
ks
= -0.1.
160
6.6 Mean (m
h
) and standard deviation of pressure head (s
h
) in
unsaturated, steady state analysis with clayey soil and q/μ
ks
= -0.1.
161
6.7 Quantiles of pressure head in unsaturated, steady state analysis
with clayey soil and q/μ
ks
= -0.1.
163
6.8 Empirical cumulative distribution of pressure head in
unsaturated, steady state analysis with clayey soil and q/μ

ks
= -0.1
:(a) at z =2m (b) z = 4m.
163
6.9 Quantiles of pressure head in unsaturated, steady state analysis
with clayey soil and q/μ
ks
= -0.5.
164

xiv
6.10 Quantiles of pressure head in unsaturated, steady state analysis
with sandy soil and q/μ
ks
= -0.5.
165
6.11 Quantiles of pressure head obtained from unsaturated transient
seepage analysis with clayey soil and q/μ
ks
= -0.5.
168
6.12 Pressure head obtained from unsaturated transient seepage
analysis with q/k
s
= -0.5 for: (a) Clayey soil (b) Sandy soil.
169
6.13 Quantiles of pressure head obtained from unsaturated transient
seepage analysis with sandy soil and q/μ
ks
= -0.5.

170
6.14 Pressure head and factor of safety profile obtained from
deterministic analysis.
172
6.15 Quantiles of FS profile at elapsed time of: (a) 8 days (b) 12 days
(c) 20 days.
174
6.16 Relation of correlation length of k
s
and probability of rainfall-
induced slope failure at steady state.
175
6.17 Relation of correlation length of k
s
and probability of rainfall-
induced slope failure at elapsed time of: (a) 5 days (b) 8 days
(c) 12 days (d) 20 days.
176
6.18 Failure realizations obtained from analysis with k
s
as a random
field with correlation length of  = 0.1
, and: (a) deterministic
SWCC (b) random SWCC.
180
6.19 Failure realizations obtained from analysis with k
s
as a random
field with correlation length of  = 10,
and: (a) deterministic

SWCC (b) random SWCC.
181
6.20 Probability of failure estimated from analyses with deterministic
SWCC and random SWCC.
182
6.21 Typical realizations of pressure head and FS profile. 184
A.1 Empirical distributions of SWCC parameters: (a) Clay (b) Silty 206

xv
clay.
B.1 Comparison of the empirical cumulative distribution of samples
simulated using original, modified, and counter Metropolis-
Hastings algorithm.
208
C.1 (Unconditional) quantiles of pressure head obtained from
unsaturated transient seepage analysis with clayey soil and q/μ
ks

= -0.5.
210


xvi
LIST OF SYMBOLS


a
SWC curve-fitting parameter inversely related to the air-entry value
A
threshold (lower bound) of lognormal distribution

b
parameter in exponential autocorrelation function of a random field,
related to correlation length
[B] gradient matrix used in finite element formulation
c
i
intermediate threshold of conditional level i in subset simulation
c
u

soil undrained shear strength
c′ soil effective cohesion
C
KC
Kozeny-Carman empirical coefficient
C(.) autocovariance of a random field
dz
random field discretization
e
soil void ratio
E(P
̃
F
) mean of the estimated failure probability
F
i

intermediate failure events of conditional level i in subset simulation
F
failure event or failure region

FS factor of safety of the slope
FS
min
minimum factor of safety along the depth of the slope, FS
min
=
min
z
{FS(z, X)}
g(X) performance function of a system
G()
one-sided spectral density function of a random field
h
pressure head in the soil
H
total head in the soil

H
hydraulic head difference between the base of the slope and the
ground surface
{H} vector of total head at nodal points

xvii
{H}
t
vector of time derivative of total head, ∂H/∂t, at nodal points
I
F
(.) indicator function of failure
k

soil hydraulic conductivity
[k] element conductivity matrix in the finite element formulation
[k]* transformed element conductivity matrix in the finite element
formulation
k
e
conductivity of an equivalent homogeneous soil profile
k
s

soil saturated hydraulic conductivity
k
s
(z) one dimensional random field model of saturated hydraulic
conductivity
k
s,i
saturated hydraulic conductivity of element i
k
s,nl
saturated hydraulic conductivity of the topmost element / layer
[K] conductivity matrix in the finite element formulation
[K*] transformed conductivity matrix in the finite element formulation
L
depth of the slope or soil column
m
number of conditional levels in subset simulation
m
w

slope of the soil-water characteristic curve (SWCC)
M
number of terms used in spectral representation of a random field
[M] mass matrix in the finite element formulation
[M*] transformed mass matrix in the finite element formulation
MSE mean square error of the estimated failure probability
n
SWC curve-fitting parameter related to the pore size distribution
nl
number of one-dimensional element / layer within the soil column
np
number of random field discretization points within one element /
layer
N
number of samples of each conditional level in subset simulation
N
c
number of seeds in subset simulation
N/N
c

length of Markov chain used in subset simulation

xviii
N
t

total sample size of simulation
N
trial

number of regenerated pre-candidate samples in modified
Metropolis-Hastings algorithm
{N} interpolating function used in finite element formulation
p
conditional probability in subset simulation
p*(., .)

proposal probability density function (PDF) in Metropolis-Hastings
algorithm
p(., .) transition probability of a Markov chain
P
F

probability of failure
P
̃
F

estimated probability of failure
P
i

probability of failure at conditional level i
q
applied flow flux (negative q denotes infiltration)
{Q} vector of nodal flux
R(.) autocorrelation of a random field
s
element thickness
S

degree of saturation of soil
t
elapsed time
Δt
time step used in the numerical computation
T
length of the one-dimensional element (layer depth)
u
a

pore air pressure
u
w

pore water pressure
(u
a
-
u
w
)
soil matric suction
V(P
̃
F
) coefficient of variation of the estimated failure probability
X
a vector of standard normal random variables used to simulate all
uncertain input parameters
X



correlated normal random vector used to simulate SWCC
parameters (a,n)
z
elevation

xix
z
w

weathering zone parameter

acceptance probability in Metropolis-Hastings algorithm
β
slope angle measured from the horizontal
γ soil total unit weight
γ
w
unit weight of water

correlation length of a random field

normalized correlation length with respect to the depth of the slope

correlation factor of the conditional samples in subset simulation

soil volumetric water content

s

soil saturated volumetric water content

r
soil residual volumetric water content

normalized volumetric water content
λ
w

specific storage capacity

ks

mean of saturated hydraulic conductivity k
s


ln ks
mean of ln (k
s
)

(.)
target / stationary distribution of a Markov chain

product-moment correlation between SWCC parameters “a” and
“n”
ρ
X1X2
correlation between the underlying normal random variables


i

autocorrelation of the Markov chain samples (conditional samples)


i

autocorrelation of the indicator function

'
effective normal stress


total stress


- u
a
)
net stress

h

standard deviation of pressure head

ks

standard deviation of saturated hydraulic conductivity k
s

xx

ln ks
standard deviation of ln (k
s
)

soil shear strength


probability density function of a standard normal distribution

′
effective angle of internal friction with respect to changes of the
net stress

’
0

effective friction angle at ground surface
d

’
range of variation of friction angle within the weathering zone

b

angle of internal friction with respect to changes of the matric

suction

a coefficient describing the contribution of matric suction to
effective stress

soil matric suction

frequency content of a random field


1
Chapter 1. Introduction

1.1. RAINFALL-INDUCED SLOPE FAILURES
Slope failures due to prolonged or excessive rainfall are commonly
encountered, particularly in tropical countries (Rahardjo et al. 2001, Toll
2001, Okimura et al. 2010, Soralump 2010). Traditional slope stability
analyses incorporate rainfall influences by assuming that the ground water
table rises due to infiltration and this reduces the stability of the slope
(Campbell 1974). However, in many situations where shallow failures are
concerned, it has been noted that there is not much evidence of a rise in the
water table sufficient to trigger the observed slope failures (Fourie et al.
1999).
More recent studies (Gasmo et al. 2000, Rahardjo et al. 2001, Tsaparas
et al. 2002, Collins and Znidarcic 2004, Rahardjo et al. 2007, Phoon et al.
2009) explain the relation of rainfall and slope failure through the formation of
a wetted zone near the ground surface. Figure 1.1 illustrates this formation
and the resulting changes in soil pore-water pressure. Initially, the
groundwater table in the slope may be located deep below the ground surface,
causing the pore-water pressure to be negative with respect to ambient

atmospheric conditions [see Fig. 1.1(a)]. This negative pore-water pressure is
referred to as matric suction when referenced to the pore-air pressure. When
the pore-water pressure is negative, the soil is not fully saturated and it is
usually referred to as unsaturated soil. It has been recognized that matric
suction contributes towards soil shear strength and hence towards stability of

2
the slope (Fredlund and Rahardjo 1993, Lu and Likos 2004). During dry
periods, the pore-water pressures become more negative, as can be seen in Fig.
1.1(b). Thus the matric suction and the slope stability increase. During rainy
periods, the infiltration of water at the ground surface causes an increase in
pore-water pressures and a wetted zone can develop near the surface, as
depicted in Fig. 1.1.(c). This results in a decrease in the matric suction and the
slope stability. Slope failures have been attributed to the advancement of the
wetting front into the slope until it reaches a depth where it triggers failure.
This is because the shear strength provided by matric suction decreases
sufficiently to trigger the failures. These failures are usually characterized by
shallow failure surfaces. Field observations showed that for slopes in which
the water table is at significant depth, most pore-water pressure changes take
place less than 2 m from the ground surface (Tsaparas et al. 2003). It has also
been observed that many rainfall-induced landslides in Singapore are quite
shallow in nature (Phoon et al. 2009).
Rainfall-induced slope failure is a complex problem involving seepage
analysis, the transient path of infiltration from unsaturated to saturated
regimes, and both saturated and unsaturated soil strength (Collins and
Znidarcic 2004). The transient seepage through soil is governed by a
differential equation which relates the amount of flow to the change in pore-
water pressure and the change of the water storage in the soil with respect to
time.