Influence of Stress State on Soil-Water Characteristics and Slope Stability

Abstract

A soil-water characteristic curve defines the relationship between the soil (matric) suction and either the water content or the degree of saturation. Physically, this soil-water characteristic is a measure of the water storage capacity of the soil for a given soil suction. Conventionally, the soil-water characteristic curves (SWCCs) are determined in the laboratory using a pressure plate apparatus in which vertical or confining stress cannot be applied. For investigating the influence on the stress state on the soil-water characteristics, a new stress controllable pressure plate apparatus has been developed. Effects of K0 stress conditions on the SWCCs of an 'undisturbed' volcanic soil in Hong Kong are determined and illustrated. The net normal stresses considered in the apparatus are 40 and 80 kPa, which are appropriate for many slope failures in Hong Kong. Experimental results show that the soil-water characteristic of the soil specimens is strongly dependent on the confining stress. Numerical analyses of transient seepage in unsaturated soil slopes using the measured stress-dependent soil-water characteristic curves predict that the distributions of pore-water pressure can be significantly different from those predicted by the analyses using the conventional drying SWCC. For the cut slope and the rainfall considered, the former analyses predicted a considerably lower factor of safety than that by the latter analyses. These results suggest that wetting stress-dependent soil-water characteristic curves should be considered for better and safer assessment of slope instability.

Full text

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000 / 157
I
NFLUENCE OF
S
TRESS
S
TATE ON
S
OIL
-W
ATER
C
HARACTERISTICS AND
S
LOPE
S
TABILITY
By Charles W. W. Ng,
1
Member, ASCE, and Y. W. Pang
2
A
BSTRACT
: A soil-water characteristic curve defines the relationship between the soil (matric) suction and
either the water content or the degree of saturation. Physically, this soil-water characteristic is a measure of the
water storage capacity of the soil for a given soil suction. Conventionally, the soil-water characteristic curves
(SWCCs) are determined in the laboratory using a pressure plate apparatus in which vertical or confining stress
cannot be applied. For investigating the influence on the stress state on the soil-water characteristics, a new
stress controllable pressure plate apparatus has been developed. Effects of K
0
stress conditions on the SWCCs
of an ‘‘undisturbed’’ volcanic soil in Hong Kong are determined and illustrated. The net normal stresses con-
sidered in the apparatus are 40 and 80 kPa, which are appropriate for many slope failures in Hong Kong.
Experimental results show that the soil-water characteristic of the soil specimens is strongly dependent on the
confining stress. Numerical analyses of transient seepage in unsaturated soil slopes using the measured stress-
dependent soil-water characteristic curves predict that the distributions of pore-water pressure can be significantly
different from those predicted by the analyses using the conventional drying SWCC. For the cut slope and the
rainfall considered, the former analyses predicted a considerably lower factor of safety than that by the latter
analyses. These results suggest that wetting stress-dependent soil-water characteristic curves should be considered
for better and safer assessment of slope instability.
INTRODUCTION
Rain-induced landslides pose substantial threats and over
the years have caused severe damages in many countries such
as Brazil, Italy, Japan, Malaysia, Hong Kong, and mainland
China (Fukuoka 1980; Brand 1984; Wolle and Hachich 1989;
Malone and Pun 1997). The physical process of rainfall infil-
tration into unsaturated soil slopes and the influence of infil-
trated rainwater on soil suction and hence the slope instability
have been investigated by many researchers both in the lab-
oratory (Fredlund and Rahardjo 1993) and in the field (Lim et
al. 1996; Rahardjo et al. 1998). Numerical simulations of rain-
fall infiltration have also been conducted (Anderson and Pope
1984; Lam et al. 1987; Wilson 1997; Ng and Shi 1998). As
for saturated soils, water flow through unsaturated soils is also
governed by Darcy’s law (Fredlund and Rahardjo 1993). How-
ever, there are two major differences between the water flows
in saturated and unsaturated soils. First, the ability of the un-
saturated soils to retain water varies with soil suction. Second,
the coefficient of water permeability is not a constant in un-
saturated soils but is a function of soil suction. Thus, it is
essential to determine (1) the so-called soil-water characteristic
curve (SWCC) that defines the relationship between the soil
suction and either the water content or the degree of saturation;
and (2) the water permeability function that varies with soil
suction for simulating transient seepage in unsaturated soil
slopes. Currently, it is a common practice to derive the water
permeability function from a measured saturated water per-
meability and a drying SWCC using the procedures estab-
lished by Fredlund and Xing (1994) and Fredlund et al. (1994).
The soil-water characteristic of a soil is conventionally mea-
sured by means of a pressure plate extractor in which any
vertical or confining stress is not applied and volume change
of the soil specimen is assumed to be zero. In the field, the
soil usually is subjected to a certain stress. Although it is the-
1
Assoc. Prof., Dept. of Civ. Engrg., Hong Kong Univ. of Sci. and
Technol., Clearwater Bay, Kowloon, Hong Kong.
2
M.Phil. Student. Dept. of Civ. Engrg., Hong Kong Univ. of Sci. and
Technol., Clearwater Bay, Kowloon, Hong Kong.
Note. Discussion open until July 1, 2000. To extend the closing date
one month, a written request must be filed with the ASCE Manager of
Journals. The manuscript for this paper was submitted for review and
possible publication on March 10, 1999. This paper is part of the Journal
of Geotechnical and Geoenvironmental Engineering, Vol. 126, No. 2,
February, 2000. 䉷ASCE, ISSN 1090-0241/00/0002-0157–0166/$8.00 ⫹
$.50 per page. Paper No. 20406.
oretically recognized that the stress state of a soil has some
influence on SWCC theoretically (Fredlund and Rahardjo
1993), few experimental results can be found in the literature.
Some exceptions are perhaps the publications by Vanapalli et
al. (1996, 1998, 1999), who studied the influence of the total
stress state on the SWCC of a compacted fine-grained soil
indirectly. The soil specimens were first loaded and then un-
loaded using a conventional consolidation apparatus to create
a known stress history or stress state in the specimens. Sub-
sequently, the SWCCs of the preloaded specimens were de-
termined using a traditional pressure plate apparatus, in which
the change of water content due to the variation of soil suction
was measured under almost zero-applied net normal stress ␴
⫺ u
a
. It was found that the SWCCs are significantly influenced
by the stress state for specimens compacted at initial water
contents dry of optimum.
Although the total net normal stress on the soil elements in
an unsaturated soil slope is seldom altered, the stress state at
each element is different. This may affect the soil-water char-
acteristic of these elements (i.e., the storage capacity when
subjected to various soil suctions during rainfall infiltration).
To correctly predict pore-water pressure distributions in and
the slope stability of an unsaturated soil slope, it is thus es-
sential to investigate the influence of stress state on SWCCs.
For transient flows and slope stability problems, osmotic suc-
tion is normally not very important and therefore ignored. Soil
suction is generally referred to as matric suction only.
In this paper, the influence of the stress state on the SWCC
of an ‘‘undisturbed’’ or natural, completely decomposed vol-
canic (CDV) soil is studied in the laboratory by using a newly
modified volumetric pressure plate extractor in which the total
net normal stress can be controlled one-dimensionally and ax-
ial deformation is measured. Together with measured saturated
water permeability under some appropriate effective stress
conditions using a triaxial apparatus, the measured stress-de-
pendent soil-water characteristic curves (SDSWCCs) are then
used as input hydraulic parameters for exploring their influ-
ence on soil suction distributions in and the stability of an
unsaturated soil slope subjected to various rainfall conditions.
EQUIPMENT DESIGN
An apparatus for measuring SDSWCCs of unsaturated soils
under K
0
stress conditions was developed by modifying a con-
ventional volumetric pressure plate extractor. Fig. 1 shows an

158 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000
FIG. 1. Componentsof Newly Modified Volumetric Pressure Plate Extractor
FIG. 2. Assembled Volumetric Pressure Plate Extractor
assemblage of the newly developed apparatus. An experi-
mental setup is shown in Fig. 2 together with a schematic
diagram of the apparatus illustrated in Fig. 3.
An oedometer ring equipped with a high air-entry ceramic
plate at its base is located inside an airtight chamber. Its rigid
wall is used to maintain the K
0
stress conditions. Vertical stress
␴ is applied through a loading frame to a soil specimen inside
the oedometer ring, which has a diameter of 70 mm and a
height of 20 mm. Dead weights via a loading piston are
adopted to provide the required vertical force. The airtightness
of the chamber is maintained using some rubber O-rings at
openings. To eliminate the error due to side friction between
the loading piston and the O-ring, a load cell is attached near
the end of the piston inside the airtight chamber for determin-
ing the actual vertical load applied to a soil specimen. Because
the radial deformation is zero for the K
0
stress condition, the
total volume change of the specimen is measured from the
vertical displacement of the soil specimen using a dial gauge.
An assumption of zero volume change is no longer required
in this apparatus.
Similar to the conventional volumetric pressure plate ex-
tractor, the pore-air pressure u
a
is controlled through a coarse
porous stone together with a coarse geotextile located at the
top of the specimen. The pore-water pressure u
w
is controlled
at the atmospheric pressure through the high air-entry ceramic
plate mounted at the base of the specimen. The high air-entry
ceramic plate will remain saturated if applied air pressure does
not exceed the air entry value of the plate (200 kPa). By using
the axis-translation technique (Hilf 1956), the soil suction im-
posed on the soil specimen will be the difference between the
applied air and pore-water pressures called matric suction u
a
⫺ u
w
. In addition, some attachments are employed for the pur-
pose of studying the hysteresis of the SWCCs associated with
the drying and wetting of the soil (Fig. 3). They consist of a
vapor saturator, air trap, ballast tube, and burette. The vapor
saturator is used to saturate the in-flow air to the airtight cham-
ber to prevent the soil from drying by evaporation. The air
trap is attached to collect air that may diffuse through the high
air-entry disk. The ballast tube serves as a horizontal storage
for water flowing in or out of the soil specimen. The burette
is used to store or supply water and to measure the water
volume change in the soil specimen.
LABORATORY MEASUREMENTS OF
SOIL-WATER CHARACTERISTICS
Descriptions of Soil Specimens
The soil used in this study is a CDV tuff. Soil specimens
were obtained from an undisturbed 200 ⫻ 200 ⫻ 200 mm
3
block sample excavated from a slope in Shatin, Hong Kong.
Based on Geoguide 3 (Guide 1988), the sample can be de-
scribed as a firm, moist, orangish brown, slightly sandy silt/
clay with low plasticity. Table 1 summarizes some index prop-
erties of the soil.
Testing Program and Procedures
A conventional volumetric pressure plate extractor and a
modified one were used together to determine the SWCC and
the SDSWCC of the CDV, respectively. The net normal stress
levels considered in the modified volumetric pressure plate

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000 / 159
FIG. 3. Schematic Diagram of Modified 1D Volumetric Pressure Plate Extractor
TABLE 1. IndexProperties of CDV (Sandy Silt/Clay)
Property
(1)
Value
(2)
Specific gravity (Mg/m
3
) 2.62
Maximum dry density (kg/m
3
) 1,603
Optimum moisture content (%) 22
Initial moisture content (%) 30
Gravel content (%) 4.9
Sand content (%) 20.1
Silt content (%) 36.6
Clay content (%) 37.1
Coefficient of curvature C
c
1.057
Coefficient of uniformity C
u
319.9
Liquid limit (%) 55.4
Plastic limit (%) 33.4
Plasticity index (%) 22
extractor are 40 and 80 kPa, which are appropriate for many
relatively shallow slope failures in Hong Kong.
Three undisturbed or natural specimens (70 mm in diameter
and 20 mm in height) were directly cut from the block sample
into three oedometer rings. The specimens were submerged in
deaired water inside a desiccator subjected to a small vacuum
for about 24 h for saturation. One of the specimens was then
placed in the conventional volumetric pressure plate extractor
to measure its SWCC with zero-applied stress (CDV-N1). The
remaining two specimens were used to determine the
SDSWCCs with 40-kPa (CDV-N2) and 80-kPa (CDV-N3) ver-
tically applied net normal stresses under K
0
conditions. These
two specimens were first loaded to 40- and 80-kPa applied net
normal stresses, respectively, in oedometers with free drainage
at the top and bottom for 24 h for preconsolidation purposes,
so that any change of the water contents due to applied net
normal and soil suction can be measured separately. They were
then removed from the oedometers and placed in the modified
volumetric pressure plate extractors to have their SDSWCCs
measured under a predetermined stress. The required stress
applied to each specimen was maintained throughout the tests.
To determine the drying path of the SWCC, the specimen
was subjected to an increasing value of matric suction. As the
matric suction increased, water was expelled from the soil
specimen into the ballast tube. The volume of water expelled
was measured to determine the volumetric water content at
equilibrium. Each matric suction value was maintained until
the equilibrium condition was reached. After reaching 100- or
200-kPa suction, a wetting process was then started by sub-
jecting the soil to a decreasing value of matric suction, and
water in the ballast tube was absorbed by the soil specimen.
A complete drying and wetting cycle was imposed on each
specimen during the tests. Vertical displacement of the soil
specimen was measured during the tests. A correction due to
the deformation of the loading piston was also applied. At the
end of the test, each soil specimen was oven-dried at 45⬚Cto
determine its water content. The volumetric water contents at
various matric suctions were then determined from the final
water content. Volumetric deformation was determined directly
from the readings taken by the dial gauge.
INTERPRETATIONS OF EXPERIMENTAL RESULTS
Verification of No Volume Change Assumption
Conventionally, SWCCs are determined using a pressure
plate extractor with the assumption that no volume change
takes place throughout the test. This assumption is verified
using the newly modified apparatus by comparing the mea-
sured SDSWCCs with and without considering volume
changes. For clarity, only the test results from the CDV-N2
specimen are shown in Fig. 4. Under the net normal stress of
40 kPa, there is no significant difference between the drying
paths with and without volume change corrections until the
matric suction reaches 200 kPa. The traditional method of in-
terpretation by neglecting any volume reduction clearly un-
derpredicts the volumetric water content presented in the soil
specimen. During the wetting process, the difference between
the two wetting paths does not stay constant, indicating that
some volume changes took place throughout the test. Similar
test results were also obtained from CDV-N3. Thus, volume
change corrections are applied whenever possible in this paper.

160 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000
FIG. 4. Comparison of SDSWCCs with and without Volume Change Considered for CDV-N2 Specimen
FIG. 5. Effects of Stress State on SWCCs
TABLE 2. Measured Ranges of Air-Entry Values for CDV
(Sandy Silt/Clay)
Sample identity
(1)
Applied stress
(kPa)
(2)
Estimated air-entry value
(kPa)
a
(3)
CDV-N1 0 0.8–1.5
CDV-N2 40 2–5
CDV-N3 80 6–20
a
Estimation procedures based on Vanapalli et al. (1999).
Influence of Stress State on Measurement of SWCCs
By using both the conventional and the modified volumetric
pressure extractors, SWCC and SDSWCCs are measured and
compared in Fig. 5. At the beginning of the tests under zero
suction, soil specimens loaded to a higher net normal stress
exhibit a lower initial volumetric water content. This is con-
sistent with the elastic theoretical calculations proposed by
Fredlund and Rahardjo (1993) that a reduction in volumetric
water content can be caused either by an applied load under
a constant soil suction or a change of soil suction under a
constant applied load. As the matric suction increases, the vol-
umetric water content of all specimens decreases but at dif-
ferent rates. The higher the applied load on the specimen, the
lower the rate of reduction in volumetric water content. The
point where the volumetric water content starts to decrease
significantly indicates the air-entry value of the specimen (i.e.,
the point where the soil gives up water with increasing soil
suction). Fig. 5 shows there is a general tendency for the soil
specimen subjected to higher stress to possess a larger air-entry
value. This is probably caused by the presence of a smaller
average pore size distribution in the soil specimen under the
higher applied load. Following the procedures proposed by
Vanapalli et al. (1999), the ranges of the air-entry values es-
timated from each specimen are given in Table 2.
Upon the completion of the drying phase, the tests were
continued with the wetting process. For a smaller applied load,
the volumetric water content increases more rapidly than that
from a specimen subjected to higher stress. At the end of the
tests, all three wetting curves return only to positions lower
than their original positions. There is a marked hysteresis be-
tween the drying and wetting curves for all soil specimens,

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000 / 161
FIG. 6. Permeability FunctionsComputed from Measured Soil-Water Characteristics
TABLE 3. Input Parameters for Predicting Permeability Func-
tions
Sample identity
(1)
Applied
stress
(kPa)
(2)
a
(3)
n
(4)
m
(5)
k
s
(m/s)
a
(6)
CDV-N1 (drying) 0 3.5392 0.8726 0.2726 3.01 ⫻ 10
⫺6
CDV-N1 (wetting) 0 1.4636 1.0112 0.2329 3.01 ⫻ 10
⫺6
CDV-N2 (wetting) 40 17.8684 0.6815 0.4492 2.88 ⫻ 10
⫺6
CDV-N3 (wetting) 80 18.2019 0.5225 0.3301 1.17 ⫻ 10
⫺6
a
Measured by Ng and Pang (1998).
mainly because of the different contact angles at the receding
soil-water interface during drying and at the advancing soil-
water interface during wetting. The size of the hysteresis loops
seems to be independent of the applied stress, for the range of
the net normal stresses considered, except for the one deter-
mined from the conventional volumetric pressure plate in
which volume change corrections cannot be made.
NUMERICAL SIMULATIONS
To investigate the influence of SDSWCCs on the predictions
of pore-water pressure distributions in unsaturated soil slopes
and their stability, a series of finite-element transient seepage
and limit-equilibrium analyses are carried out using SEEP/W
and SLOPE/W (SEEP/W 1998), respectively. A typical steep
unsaturated soil cut slope in Hong Kong is selected for illus-
trative purposes. The computed results from the transient seep-
age analyses are then used as input parameters for a subse-
quent limit-equilibrium analysis of the stability of the slope.
Transient Water Flow in Unsaturated Soils
Water flow through unsaturated soils is governed by Darcy’s
law (Fredlund and Rahardjo 1993). This is the same as water
flow through saturated soils. The only difference is that the
coefficient of hydraulic conductivity depends on both void ra-
tio and matric suction in the unsaturated soils. The governing
partial differential equation (Lam et al. 1987) for water flow
through a 2D unsaturated soil element is given as follows:
⭸⭸h ⭸⭸h ⭸u
w
k ⫹ k = m (1)
xyw
冉冊 冉冊 冉冊
⭸x ⭸x ⭸y ⭸y ⭸t
where h = total hydraulic head; k
x
= hydraulic conductivity in
the x-direction; k
y
= hydraulic conductivity in the y-direction;
m
w
= slope of a SWCC; and u
w
= pore-water pressure.
In this paper, the soil is assumed to be isotropic (i.e., k
x
is
equal to k
y
) in the transient seepage analyses using a computer
program called SEEP/W (SEEP/W 1998). This is an uncoupled
program in which any deformation of the soil is ignored.
Shear Strength for Saturated and Unsaturated Soils
Slope instability may be initiated by a reduction in the shear
strength of a soil. The shear strength is related to the stress
state in the soil. For limit-equilibrium analysis of a slope, the
shear strength of the soil can be simplified and represented by
a Mohr-Coulomb failure criterion proposed by Fredlund et al.
(1978) as follows:
b
␶ = c⬘ ⫹ (␴ ⫺ u )tan ␾⬘ ⫹ (u ⫺ u )tan ␾ (2)
aaw
where ␶ = shear strength; c⬘ = effective cohesion; ␾⬘ = angle
of friction; and ␾
b
= angle defining the increase in shear
strength for an increase in matric suction.
The shear strength of an unsaturated soil is governed by
two stress state variables: net normal stress ␴ ⫺ u
a
and matric
suction u
a
⫺ u
w
. For saturated soils, the stress state variable is
effective stress ␴ ⫺ u
w
,asu
a
is equal to u
w
. In the slope
stability analysis using SLOPE/W, (2) is adopted.
Input Parameters and Analysis Procedures for
Transient Seepage Analyses
Because infiltration of rainwater into the soil slope is a wet-
ting process, the measured wetting SWCC (CDV-N1) and
SDSWCCs (CDV-N2 and N3) are adopted for the transient
seepage analyses. In addition, a water permeability function
that varies with soil suction is required. For comparison, a
conventional transient analysis using a drying path of the
SWCC (CDV-N1) under zero net normal stress is also in-
cluded.
By using the measured saturated water permeability k
s
of the soil in a triaxial apparatus under appropriate stress
conditions (Ng and Pang 1998), the selected SWCC and
SDSWCCs are fitted by a highly nonlinear equation, as pro-

162 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000
FIG. 7. Finite-ElementMeshfor Slope
TABLE 4. Summary of Numerical SimulationsConducted
Series
number
(1)
Key hydraulic parameter
(2)
Type of
analysis
(3)
Rainfall
infiltration
(mm/day)
(4)
Duration
(5)
1 Drying SWCC (conventional) Steady state 10.8 —
1 Drying SWCC (conventional) Transient 236.4 24 h
1 Drying SWCC (conventional) Transient 49.2 7 days
2 Wetting SWCC and SDSWCC Steady state 10.8 —
2 Wetting SWCC and SDSWCC Transient 236.4 24 h
2 Wetting SWCC and SDSWCC Transient 49.2 7 days
posed by Fredlund and Xing (1994) for obtaining a permea-
bility function that varies with matric suction. Details of
the proposed nonlinear equation are given in Appendix I. The
input parameters for predicting the permeability functions
are summarized in Table 3. Fig. 6 shows the permeability
functions computed from the selected curves. As expected, the
soil specimen loaded to a higher net normal stress has a
lower permeability function, because the applied net normal
stress led to a smaller pore size distribution inside the soil
specimen.
For investigating the effects of SDSWCC on pore-
water pressure distributions in an unsaturated soil slope during
rainstorms, a finite-element mesh of a typical cut slope of
8.6m in height inclined 55⬚ to the horizontal in Hong Kong
is created and shown in Fig. 7. This cut slope is located
on a natural hillside. The entire soil mass in the finite-
element mesh is idealized into three different soil layers ac-
cording to their approximate stress states so that the measured
SWCC and SDSWCCs and their corresponding water perme-
ability functions can be specified. It is recognized that
the current method of specifications greatly simplifies
the actual complexity of the problem. However, computed re-
sults from the current simplified analyses are sufficient to re-
veal the important role of SDSWCC in any transient seepage
analysis.
To illustrate the influence of the SDSWCCs on pore-water
pressure distributions, two series of transient seepage analyses
are conducted. In the first series of analyses, all soil layers are
assumed to have the same drying SWCCs and their corre-
sponding water permeability functions. This series is a con-
ventional approach. In the second series of analyses, different
hydraulic properties are specified in each soil layer. The wet-
ting SWCC under 0 kPa (CDV-N1) and SDSWCCs under 40
kPa (CDV-N2) and 80 kPa (CDV-N3) applied net normal
stresses and their corresponding permeability functions are
specified, respectively, for the first, second, and third soil lay-
ers as shown in Fig. 7.
The initial ground-water conditions for each series of
transient seepage analyses are established by conducting
two steady-state analyses, in which a very small rainfall
with an intensity of 0.001 mm/day is applied on the top bound-
ary surface together with a constant hydraulic head 15 m
above the principal datum (15 mPD or sea level) specified
on the left boundary. The bottom boundary is assumed to
be impermeable, and no flux is specified along the right
boundary.
For the subsequent transient analyses, two rainfall patterns
with an average intensity of 394 and 82 mm/day are applied
on the top boundary surface in both series of analyses to
simulate a short and intensive 24-h rainfall infiltration and
a prolonged 7-day rainfall infiltration, respectively. The
rainfall intensities adopted are based on the actual 10-year
return period spanning from 1980 to 1990 (Lam and
Leung 1995). In this paper, it is assumed that the rate of in-
filtration is equal to 60% of the rainfall intensity to simulate
an average of 40% surface runoff in Hong Kong (Tung et al.
1999). The numerical simulations conducted are summarized
in Table 4.

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000 / 163
FIG. 8. Pore-Water Pressure Distributions along SectionA-A under VariousRainfall Conditions
FIG. 9. Pore-Water Pressure Distributions along SectionB-B under Various Rainfall Conditions
Input Parameters and Analysis Procedures for Slope
Stability Analyses
After obtaining the pore-water pressure distributions from
the transient seepage analyses, limit-equilibrium analyses are
then carried out to determine the factor of safety (FOS) of the
cut slope. For estimating the FOS using Bishop’s simplified
method, some basic mechanical soil parameters are needed. In
the limit-equilibrium analyses, the shear strength of the soil is
assumed to be governed by the extended Mohr-Coulomb fail-
ure criterion [i.e., (2)]. The shear-strength parameters include
an effective cohesion c⬘ of 2 kPa, an angle of friction ␾⬘ of
28⬚, and an angle indicating the rate of increase in shear
strength relative to the matric suction ␾
b
, which is equal
to 14⬚.
INFLUENCES OF SDSWCC ON PORE-WATER
PRESSURE DISTRIBUTIONS
Figs. 8–10 show the computed distributions of pore-water
pressure varying with depth at sections A-A, B-B, and C-C of
the finite-element mesh (shown in Fig. 7), respectively. It is
clear that there is a substantial difference between the initial
pore-water pressure distributions computed using the conven-
tional drying SWCCs and the unconventional wetting SWCC
and SDSWCCs in the steady-state analyses. The conventional
analysis predicts a significantly higher soil suction profile than
that computed by the unconventional analysis, because the soil
in the former analysis, in comparison with the soil in the latter
analysis, has a lower air-entry value and a faster rate of chang-
ing volumetric water content as values of soil suction increase
(Fig. 5) and a higher water permeability function (Fig. 6). In
other words, the soil under the applied stress has a stronger
capability of retaining moisture for a given soil suction be-
cause of the presence of a smaller pore size distribution, as
illustrated by a flatter SWCC (Fig. 5). The computed results
highlight the importance of considering stress effects and dry-
ing-wetting history on SWCCs.
During the short but highly intensive rainfall (i.e., 236.4
mm/day or 2.74 ⫻ 10
⫺6
m/s for 24 h), the pore-water pressure
responses at the three sections are similar in both the conven-
tional and unconventional transient analyses. Only the soil suc-
tions in the top 1–2-m of the soil are destroyed irrespective
of the magnitude of their initial values. A relatively shallow
advancing ‘‘wetting front’’ (Lumb 1975) is developed, as most

164 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000
FIG. 10. Pore-Water Pressure Distributions along Section C-C under Various Rainfall Conditions
FIG. 11. Slip Surfaces Considered in Slope Stability Analyses
of the rainfall cannot infiltrate into the soil because of rela-
tively low water permeability with respect to rainfall infiltra-
tion at high initial values of soil suction. On the contrary, the
pore-water pressure distributions predicted by the conventional
and unconventional analyses are completely different during
the 7-day low intensity prolonged rainfall (49.2 mm/day or
5.69 ⫻ 10
⫺7
m/s for 7 days), particularly at sections A-A and
B-B. Due to the relatively low initial values of suction present
in the soil, resulting in relatively high water permeability with
respect to rainfall infiltration, when the effects of the stress
state are considered, soil suctions at sections A-A and B-B
(Fig. 8 and 9) are totally destroyed by the advancement of the
wetting front to a depth of about 6 and 9 m from the ground
surface, respectively. At section C-C (Fig. 10), the advance-
ment of the wetting front is limited by the initial higher suction
values than those at sections B-B and C-C. The less intensive
but prolonged 7-day rainfall facilitates the advancement of the
wetting front into the soil to great depths and causes significant
reduction in soil suction, which would have some devastating
effects on slope stability. For the case of the initial values of
soil suction predicted using conventional drying SWCC, rain-
fall infiltration is hindered as a result of relatively low water
permeability due to the presence of high soil suction.
INFLUENCES OF SDSWCC ON SLOPE STABILITY
By using the computed pore-water pressure distributions in
the transient flow analyses, limit-equilibrium analyses are per-
formed on four selected noncircular slip surfaces, which pass
through the toe of the slope (Fig. 11). It should be noted that
these selected slip surfaces may not guarantee the minimum
FOS. They were selected only for illustrating the influence of
SDSWCCs on the FOS of some possible slips. The actual crit-
ical slip surfaces may be somewhat different.
Fig. 12 shows the variations of FOSs with elapsed time for
the four selected slip surfaces during the 7-day rainfall. It can
be seen that the limit-equilibrium analyses, which adopted the
pore-water pressures that were computed by using the con-
ventional drying SWCCs, predict substantial higher initial
FOSs at all four slip surfaces than those obtained from the
analyses using the unconventional wetting SDSWCCs. This is
attributed to the significant difference in the computed pore-
water pressure distributions (Figs. 8–10) with and without
considering the effects of the stress state and drying-wetting
history. This implies that the traditional analyses using the con-
ventional drying SWCCs may lead to unconservative designs.
Due to the presence of higher initial suction at shallow
depths, the shallower the slip surface, the larger the initial
FOS. As the time elapses, the FOS decreases but at different
rates. For the shallow slips (S1 and S2), the fall in the FOSs
is substantial when the effects of the stress state are included.
At the end of rainfall, the FOS increases with depth, opposed
to the initial safety conditions.
CONCLUSIONS
The SWCC is a measure of the water storage capacity of
the soil for a given soil suction. This is an essential hydraulic
property required for analyzing transient seepage in unsatu-
rated soils. Traditionally, the SWCCs are determined in the
laboratory using a pressure plate apparatus in which any ver-
tical or confining stress cannot be applied. It is theoretically
recognized that stress state should have some influence on soil-
water characteristics of soils. To investigate this influence, a
new stress controllable volumetric pressure plate apparatus has
been developed. Effects of K
0
stress conditions on the soil-
water characteristic on an undisturbed or natural CDV soil
were studied in the laboratory. Subsequently, the measured
SDSWCCs were adopted to derive water permeability func-

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000 / 165
FIG. 12. FOSs with Respect to Time from Beginning of 7-Day Rainfall
tions for transient seepage and limit-equilibrium analyses of a
typical unsaturated cut slope in Hong Kong under various rain-
fall conditions. Based on the experimental and the simplified
numerical studies, the following conclusions can be drawn:
• Under zero suction, soil specimens loaded to a higher net
normal stress exhibit a lower initial volumetric water con-
tent. There is a tendency to change the volumetric water
content at a slower rate as values of suction increase for
the soil loaded to a higher stress.
• There is a general and consistent trend for a soil specimen
to possess a larger air-entry value when it is subjected to
a higher stress. This is probably attributed to the presence
of smaller interconnected pores in the soil specimen under
higher applied load.
• There is a marked hysteresis between the drying and wet-
ting curves for all soil specimens tested. The size of the
hysteresis loops seems to be independent of the range of
the net normal stresses considered, except for the one de-
termined by the conventional volumetric pressure plate in
which volume change corrections cannot be made.
• Numerical analyses using the measured wetting
SDSWCCs and their derived water permeability functions
predict substantially higher (less negative) initial steady-
state pore-water pressure distributions with depth than
those computed by using the conventional drying
SWCCs. These initial high (less negative) steady-state
pore-water pressure distributions with depth leading to
higher water permeability in the ground facilitate rainfall
infiltration, which destroys soil suction to a great depth
by an advancing wetting front. This results in a substan-
tially lower FOS during a prolonged low intensity rainfall.
On the contrary, the numerical analyses suggest that only
the soil suction at the top 1–2 m of the soil would be
destroyed under highly intensive but short duration rain-
falls, irrespective of whether the stress effects on SWCC
and the drying-wetting history are considered or not.
• Based on the current experimental measurements and the
simplified numerical investigations, the stress state and
the drying-wetting history have a substantial influence on
the soil-water characteristics of unsaturated soils. During
a prolonged rainfall, analyses using wetting SDSWCCs
would predict adverse pore-water pressure distributions
with depth and lower FOSs than those from the conven-
tional analyses using drying SWCCs. The wetting
SDSWCCs should therefore be considered for better and
safer estimations of the FOS for unsaturated soil slopes.
APPENDIX I. DERIVATION OF WATER
PERMEABILITY FUNCTIONS
The general equation proposed by Fredlund and Xing
(1994) to fit the experimental results of the SWCC is given as
follows:
␪
s
␪ = C(␺) (3)
w
冋册
am
{ln[e ⫹ (␺/a ]}
where a is approximately the air-entry value in kPa; e = natural
number (2.718); n = parameter that controls the slope at the
inflection point in the SWCC; m = parameter that is related to
the residual water content; ␪
w
= volumetric water content; ␪
s
= saturated volumetric water content; ␺ = soil suction (kPa);
and
␺
ln 1 ⫹
冉冊
C
r
再冎
C(␺)=1⫺
ln(1 ⫹ 1,000,000/C )
r
where C
r
= constant related to the soil suction corresponding
to the residual water content.
With the curve-fitted SWCCs and SDSWCCs from the ex-
perimental data using (3), with the help of a computer program
called SoilVision (SoilVision 1997), the permeability function
for each characteristic curve can be derived from the measured
coefficient of saturated water permeability using the proce-
dures proposed by Fredlund et al. (1994). The required coef-
ficients of saturated water permeability of this soil were mea-
sured in a triaxial apparatus under various effective stress
conditions (Ng and Pang 1998).
The equation for computing the permeability function pro-
posed by Fredlund et al. (1994) is given as follows:
b
y
␪(e ) ⫺ ␪(␺)
y
␪⬘(e ) dy
冕
y
e
ln(␺)
k(␺)=k (4)
s
b
y
␪(e ) ⫺ ␪
s
y
␪⬘(e ) dy
冕
y
e
ln(␺ )
ave

166 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / FEBRUARY 2000
where b = ln(1,000,000); k
s
= saturated permeability (m/s); y
= dummy variable of integration representing the logarithm of
suction; and ␪⬘ = derivative of ␪
w
. The derived permeability
functions are presented in Fig. 7. As expected, the water per-
meability of the soil specimen decreases as the applied stress
increases.
APPENDIX II. REFERENCES
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321.
Fredlund, D. G., and Rahardjo, H. (1993). Soil mechanics for unsaturated
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Fredlund, D. G., and Xing, A. (1994). ‘‘Equations for the soil-water char-
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Fredlund, D. G., Xing, A., and Huang, S. (1994). ‘‘Predicting the per-
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APPENDIX III. NOTATION
The following symbols are used in this paper:
c⬘ = effective cohesion;
h = total hydraulic head;
K
0
= lateral earth pressure coefficient at rest;
k
x
= hydraulic conductivity in x-direction;
k
y
= hydraulic conductivity in y-direction;
m
w
= slope of soil-water characteristic curve;
u
a
= pore-air pressure;
(u
a
⫺ u
w
) = matric suction or soil suction if osmotic suction is
ignored;
u
w
= pore-water pressure;
␴ = total normal stress;
(␴ ⫺ u
a
) = net normal stress;
␶ = shear strength;
␾⬘ = angle of friction; and
␾
b
= angle defining increase in shear strength for increase
in matric suction.