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Effect of Antecedent Rainfall Patternson Rainfall-Induced Slope
Failure
Arezoo Rahimi1; Harianto Rahardjo2; and Eng-Choon Leong,
M.ASCE3
Abstract: Rainfall-induced slope failure occurs in many parts of
the world, especially in the tropics. Many rainfall-induced slope
failureshave been attributed to antecedent rainfalls. Although it
has been identified as a cause of rainfall-induced slope failure,
the pattern ordistribution of the antecedent rainfall has not
received adequate attention. In this study, parametric studies were
performed by using threetypical rainfall patterns, identified by
analysis of available rainfall data for Singapore and two different
soil types to represent high- andlow-conductivity residual soils of
Singapore. Antecedent rainfall patterns were applied on soil slopes
and a transient seepage analysis wasconducted. The computed
pore-water pressures were used in stability analyses to calculate
the safety factor of the slope. Results indicated thatantecedent
rainfall affected the stability of both high-conductivity (HC) and
low-conductivity (LC) soil slopes. However, the stability of theLC
soil slope was more significantly affected than the HC soil slope.
Patterns of antecedent rainfall controlled the rate of decrease in
factor ofsafety, the time corresponding to Fsmin and the value of
Fsmin. Delayed rainfall pattern resulted in the lowest minimum
factor of safety,Fsmin, for the HC soil slope, and advanced
rainfall pattern resulted in the lowest Fsmin for the LC soil
slope. DOI: 10.1061/(ASCE)GT.1943-5606.0000451. 2011 American
Society of Civil Engineers.
CE Database subject headings: Rainfall; Slopes; Failures; Slope
stability; Tropical regions.
Author keywords: Rainfall pattern; Antecedent rainfall;
Rainfall-induced slope failure; Slope stability; Factor of
safety.
Introduction
Slope failure is a natural disaster that occurs in many parts of
theworld. Rainfall is the most recognized triggering factor for
this dis-aster, especially in tropical regions with hot and humid
climaticconditions (Brand 1984; McDougall et al. 1999; Tsaparas et
al.2002; Collins et al. 2004; Chen et al. 2004; Tohari et al. 2007;
Tsaiet al. 2008; Frattini et al. 2009). Tropical climate results in
the for-mation of residual soils that usually exist in unsaturated
conditions(Rahardjo et al. 1995). Rainwater infiltrates into the
unsaturatedzone of soil slope, decreases matric suction, and
consequentlythe shear strength of soil, causing slope failures
(Yoshida et al.1991; Fourie 1996; Au 1998; Crosta 2001; Kim et al.
2004;Rahardjo et al. 2005; Calvello and Cascini 2007). Although
thereare many relations between rainfall and slope failures, there
havebeen some debates about the relative role of antecedent
rainfall.Antecedent rainfall is the rain that falls in the days
immediatelypreceding a landslide event (Au 1998; Rahardjo et al.
2001; Caiand Ugai 2004). Guzzetti et al. (2007) reviewed rainfall
thresholdsfor initiation of landslides and found that many
researchers in dif-ferent parts of the world related landslides to
antecedent rainfall,
but with different durations, from 1 day to 120 days.
However,the effect of antecedent rainfall is still controversial.
Brand(1984) concluded that localized short-duration rainfalls of
highintensity induced the majority of landslides in Hong Kong.
Brand(1992) also concluded that because of the high conductivity
ofHong Kong soils, the effect of antecedent rainfall on
rainfall-induced slope failure was not significant. Studies in
Italy showedthat antecedent rainfall did not have a relation with
landslides(Aleotti 2004). Pitts (1984) concluded that antecedent
rainfallwas not a significant factor for slope failures in
Singapore. Tanet al. (1987) found that antecedent rainfall could be
significantin inducing slope instability in Singapore. The Bukit
Batok land-slide (Wei et al. 1991) was evidence that showed the
effect of ante-cedent rainfall in Singapore. The failure occurred
after a period ofheavy rainfall, although no rainfall occurred at
the time of failure.Rahardjo et al. (2008) studied the slope
responses (i.e., pore-waterpressure distribution) to rainfall
events through comprehensive in-strumentation of four slopes in
Singapore and concluded that 5-dayantecedent rainfall could affect
stability of slopes in Singapore. Therole of antecedent rainfall on
rainfall-induced slope failure greatlydepends on the permeability
of soil.
Although antecedent rainfall has been shown to result in
slopefailure, the effects of pattern or distribution of antecedent
rainfall onrainfall-induced slope failures have not received
adequate attention.Ng et al. (2001) studied the effect of rainfall
pattern on pore-waterpressure changes in slope and concluded that
rainfall patternshad a significant effect on pore-water pressure
changes. However,the stability of slope was not investigated in
this work. Therefore,the effect of antecedent rainfall pattern on
rainfall-induced slopefailure needs further investigation.
Tsaparas et al. (2002) studied the factors controlling
rainfall-induced slope failure, including antecedent rainfall. In
this study,a fixed amount of rainfall was considered and
distributed uniformlyfor different time periods to obtain different
antecedent rainfallintensities. However, the uniform rainfall
distribution may not truly
1Project Officer, School of Civil and Environmental
Engineering,Nanyang Technological Univ., Block N1, B4b-07, Nanyang
Avenue,Singapore 639798.
2Professor, School of Civil and Environmental Engineering,
NanyangTechnological Univ., Block N1, 01b-36, Nanyang Avenue,
Singapore639798 (corresponding author). E-mail:
[email protected]
3Associate Professor, School of Civil and Environmental
Engineering,Nanyang Technological Univ., Block N1, 01c-80, Nanyang
Avenue,Singapore 639798.
Note. This manuscript was submitted on January 10, 2010;
approved onSeptember 27, 2010; published online on September 29,
2010. Discussionperiod open until October 1, 2011; separate
discussions must be submittedfor individual papers. This paper is
part of the Journal of Geotechnical andGeoenvironmental
Engineering, Vol. 137, No. 5, May 1, 2011. ASCE,ISSN
1090-0241/2011/5-483491/$25.00.
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represent the actual rainfall patterns. Therefore, further
investiga-tion is needed into the actual rainfall data and their
typical patternsthat closely represent the field conditions.
The study presented in this paper focused on the effect
ofantecedent rainfall pattern on the stability of slopes. Actual
rainfalldata from various parts of Singapore were analyzed to
identifyrepeatable rainfall patterns. The identified rainfall
patterns werethen applied to two different soil types that
represent high- andlow-conductivity residual soils of Singapore. A
major rainfall eventbased on actual rainfall data was then applied
to slopes right afterthe application of the antecedent rainfall.
Two analyses, seepageand stability, were performed to study the
stability of slope sub-jected to various antecedent rainfall
patterns. Transient seepageanalysis was conducted to compute the
pore-water pressures.The computed pore-water pressures were then
used to calculatethe factor of slope safety during rainfall.
Theoretical Consideration
The seepage analysis was performed using SEEP/W
(Geo-SlopeInternational 2004a). The following water-flow governing
equationfor solving transient and two-dimensional seepage analyses
wasused in this study:
m2wwhwt
xkwx
hwx y
kwy
hwy q 1
where m2w = slope of soil-water characteristic curve; w =
unitweight of water; hw = hydraulic head or total head; t =
time;kwx = coefficient of permeability with respect to water as a
functionof matric suction in x-direction; kwy = coefficient of
permeabilitywith respect to water as a function of matric suction
in y-direction;and q = applied flux at the boundary.
Slope stability analysis was carried out in this study by
consid-ering shear strength contribution from negative pore-water
pressureor matric suction in unsaturated soil using the Fredlund et
al. (1978)equation:
c0 n ua tan0 ua uw tanb 2
where = shear strength of unsaturated soil; c0 = effective
cohesion;n ua = net normal stress; n = total normal stress; ua =
pore-airpressure; 0 = effective angle of internal friction; ua uw =
matricsuction; uw = pore-water pressure; and b = angle indicating
therate of change in shear strength relative to a change matric
suction.Bishops simplified method was used to compute factor of
safety,Fs, of slopes using Slope/W (Geo-Slope International
2004b).
Numerical Model
Slope Geometry
Fig. 1 shows the slope geometry and boundary conditions used
inthis study. One slope angle ( 30) and one slope height(Hs 15 m)
based on typical slope geometry in Singapore (Tollet al. 1999) was
examined in this study. The depth of water table,Hw, was defined as
a distance from the toe of slope to the watertable. The initial
depth of the water table, Hw, was selected tobe 2 m below the
ground surface based on typical ground waterconditions in
Singapore.
The boundary conditions used for the transient seepage
analysisare shown in Fig. 1. A boundary flux, q, equal to rainfall
intensity,Ir , was applied to the surface of the slope. The nodal
flux, Q, equalto zero was applied along the sides of the slope
above the watertable and along the bottom of the slope to simulate
no flow zone.A boundary condition equal to total head, hw, was
applied along thesides of the slope below the water table. To
achieve an initial con-dition for the homogenous soil slope, the
following procedure wasconducted.
Initial Condition
First, a very small quantity of rainfall, q was applied to the
surfaceof slope for a long duration of time to achieve a target
depth ofwater table, Hw at the toe of slope (i.e., Hw 2 m) and at
an in-clination of 5 with respect to the horizon (as shown in Fig.
1). Thepore-water pressure distributions above the water table were
plottedfor all time steps at selected sections, section x-x and
section y-y,as shown in Fig. 1. This ensured that the pore-water
pressure dis-tributions were stable and represented a steady state
condition.Although slopes with two different soil types reached the
same tar-get depth of water table (i.e., Hw 2 m), the response of
each soiltype to the applied boundary flux, q, was different. In
fact, distri-butions of the pore-water pressure above water table
were differentfor different soil types. Therefore, the initial
factors of safety, Fsini,of slopes were different. To have
comparable data, the normalizedfactor of safety, Fsn defined as the
ratio of factor of safety at eachtime step to the initial value of
factor of safety, was used to comparethe results.
Soil Properties
To study the effect of antecedent rainfall patterns on stability
ofslopes, two types of soil were considered. One soil type
wasselected to represent high-conductivity residual soils of
Singaporeand was named high-conductivity (HC) soil. The other
soiltype was selected to represent low-conductivity residual
soilsand was named low-conductivity (LC) soil. Fig. 2 shows the
soil-water characteristic curve (SWCC) and unsaturated
permeability
Fig. 1. Slope geometry and boundary conditions for a homogeneous
soil slope
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function, kw, of HC and LC soils. The Fredlund and Xing
(1994)equation with a correction factor, C 1, recommended byLeong
and Rahardjo (1997), was used to describe the SWCC ofsoils in this
study.
Saturated coefficient of permeability of HC soil, ks, was equal
to104 m=s and SWCC parameters of the soil were a 10 kPa,m 0:5, and
n 1. The saturated coefficient of permeability ofLC soil was equal
to 106 m=s. The SWCC parameters of LC soilwere a 300 kPa, m 1, and
n 1. For computation of unsatu-rated permeability function, kw,
from SWCC, the indirect pro-cedure described in Fredlund and
Rahardjo (1993) was used.
Shear strength properties of the soils used in the study
wereselected on the basis of typical shear strength properties of
soilsin Singapore (Rahardjo et al. 2007). An effective cohesion,c0
10 kPa, effective angle of internal friction, 0 26, angle
in-dicating the rate of change in shear strength relative to a
change inmatric suction, b 26, and unit weight of soil, 20
kN=m3,were used in the slope stability analyses. Shear strength
parametersof the soils were kept constant for all cases to ensure
that changes instability of the slope were only attributable to
pore-water pressure(or matric suction) changes in the soil.
Designing Rainfall Patterns and Major Rainfall
Three typical rainfall patterns were selected by analyses of
avail-able rainfall data for Singapore. Data were collected from
onlinemonitoring of rainfall at different locations in Singapore.
The du-ration associated with the different rainfall patterns was
selected torepresent antecedent rainfalls in Singapore. Three-day,
4-day, and5-day antecedent rainfall were the most repeated
durations in thecollected rainfall data. Rahardjo et al. (2008)
found that a 5-dayantecedent rainfall caused the worst pore-water
pressure profiles
in slopes in Singapore. Therefore, in this study, 5-day (i.e.,
120 h)was selected to represent the duration of the rainfall
patterns. The5-day duration was divided into equal time intervals
to distributethe antecedent rainfalls. A long duration time
interval would resultin few time intervals with very low rainfall
intensities, whichcaused difficulties in distinguishing different
rainfall patterns.On the other hand, a short-duration time interval
would result inscattered rainfall patterns that are difficult to
categorize. On thebasis of these criteria, the time interval for
distributing the rainfallwas selected to be 8 h. Each 5-day
antecedent rainfall comprised 15time intervals (i.e., 120 h=8 h).
Ng et al. (2001) selected 14-h timeintervals to distribute the
antecedent rainfall. The procedure to rec-ognize these patterns is
described here as an example for rainfalldata at Ulu Pandan Sewage
Treatment Works, in December 2006.The month of December has 31
days. Because each day is 24 h,December 2006 comprised 744 h of
rainfall data. The total amountof rainfall was computed as
follows:
rd1 rd2 rd744 675:3 mm 3
where rd = rainfall data and the subscript is time (h), e.g.,
rd1means rainfall data of first hour of the month. Data for each
8-htime interval were summed continuously as follows:
rd1 rd2 rd8 R1 mmrd9 rd10 rd16 R2 mm mm: mmrd737 rd738 rd744 R93
mm
4
Each equation represents the amount of rainfall data for onetime
interval (i.e., R1 is the rain that falls within the first 8 h
ofthe month). To obtain one antecedent rainfall, 15 time
intervalswere needed. The rainfall data of these 15 running 8-h
time inter-vals were summed as follows:
R1 R2 R15 T1 mmR2 R3 R16 T2 mm:: mm mmR79 R80 R93 T79 mm
5
Each equation represented a 5-day antecedent rainfall. For
eachof the previous equations, the percentage of the rain that fell
in eachtime interval (i.e., R1, R2;;R15) was calculated out of the
totalrainfall that fell in one antecedent rainfall (i.e., T1). To
observethe pattern of the antecedent rainfall, each of the previous
equationswas plotted so that the x-axis was the time interval and
the y-axiswas the calculated percentage of rainfall. Each of the
plots showsa unique rainfall pattern. In general, the different
patterns couldbe categorized into three different groups, as shown
in Fig. 3. Forinstance, in Fig. 3(a), rainfall started at low
intensity and graduallyincreased at the end. Fig. 3(b) shows
rainfall that started at lowintensity at the beginning of rainfall
duration, which then increasedgradually at the middle and decreased
again at the end of rainfall.Fig. 3(c) shows rainfall that started
at high intensity at the begin-ning and then decreased gradually at
the end of rainfall duration.These three patterns were selected
among all the recognized rainfallpatterns and then idealized, as
shown in the figure. The maximumcontinuous 5-day rainfall was
calculated from the available
Fig. 2. SWCC and unsaturated permeability function, kw, of the
HCand LC soil
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rainfall data and was found to be 450 mm. This value, 450
mmrainfall, was then distributed on the basis of the idealized
rainfallpatterns. It was multiplied by the idealized rainfall
percentage foreach time interval, for the three recognized rainfall
patterns. Toobtain rainfall intensity, the total rainfall in each
time intervalwas divided by 8 h. Fig. 4 shows finalized antecedent
rainfallpatterns used in this study. The first rainfall pattern was
namedDelayed Rainfall Pattern [Fig. 4(a)]. The second rainfall
pattern,which is similar to a normal distribution, was named
NormalPattern [Fig. 4(b)]. The third rainfall pattern was named
AdvancedRainfall Pattern [Fig. 4(c)].
A major rainfall was also considered in the analysis. The
dura-tion of the major rainfall was selected to be 8 h (i.e., the
sameas rainfall pattern intervals). A maximum of eight
continuoushours of rainfall of 180 mm was obtained from the
available rainfalldata. This value was divided by 8 h to calculate
the major rainfallintensity of 22:5 mm=h. The Public Utilities and
Board ofSingapore (PUB) also uses this rainfall intensity for
drainagedesigns in Singapore (PUB 2000).
Results and Discussion
Three typical antecedent rainfall patterns, namely, delayed,
normal,and advanced, were used to investigate the effect of
antecedentrainfall patterns on slope stability. The antecedent
rainfall patternswere applied to the homogenous soil slopes of two
differentsoil types, HC and LC. A major rainfall with an intensity
of22:5 mm=h for a duration of 8 h was applied to the slopes
rightafter the application of antecedent rainfall patterns. The
stabilityof the slopes was assessed through factor of safety, Fs,
calculation,and the results are presented in the following.
Effect of Antecedent Rainfall Patterns on Stabilityof Slope
Fig. 5 provides the results obtained from the numerical modeling
ofHC and LC slopes under delayed, normal, and advanced
rainfallpatterns. The results are presented in factor of safety,
Fs,versus time, t. Fig. 5(a) shows the results for HC soil slope
andFig. 5(b) shows the results for LC soil slope.
Fig. 3. Actual and idealized rainfall patterns for rainfall data
ofDecember 2006: (a) increasing intensity toward the end of
rainfall;(b) maximum intensity at the middle of rainfall; (c)
decreasing intensitytoward the end of rainfall
Fig. 4. Designed rainfall patterns: (a) delayed rainfall
pattern; (b) nor-mal rainfall pattern; (c) advanced rainfall
pattern
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Fig. 5(a) shows that the rate of decrease in factor of safety
versustime was faster for the advanced pattern, followed by the
normaland delayed patterns. The figure also shows that the minimum
fac-tor of safety, Fsmin occurred at 56, 88, and 120 h for the
advanced,normal, and delayed patterns, respectively. In other
words, the ad-vanced rainfall pattern resulted in the earliest time
for the Fsmin tooccur, compared to the normal and delayed rainfall
patterns. Thelowest Fsmin corresponded to the delayed pattern,
which was equalto 1.48, followed by the normal (Fsmin 1:51) and the
advanced(Fsmin 1:53) patterns. However, the difference in Fsmin for
allthe rainfall patterns was not significant. The rate of recovery
inthe factor of safety versus time was fastest for the delayed
pattern,followed by the normal and advanced patterns.
Fig. 5(b) shows that rate of decrease in the factor of safety
versustime was fastest for the advanced pattern, followed by the
normaland delayed patterns. The figure also shows that the
minimumfactor of safety, Fsmin occurred at 96, 112, and 120 h for
theadvanced, normal, and delayed patterns, respectively. In
otherwords, the advanced rainfall pattern resulted in the earliest
timefor the Fsmin to occur, compared to the normal and delayed
rainfall
patterns. The lowest Fsmin corresponded to the advanced
rainfallpattern, which was equal to 1.001, followed by the
normal(Fsmin 1:004) and delayed (Fsmin 1:083) rainfall
patterns.Although the lowest Fsmin corresponded to the advanced
rainfallpattern, the magnitude of Fsmin was basically the same for
all therainfall patterns; however, they occurred at different
times. Fig. 5(b)shows that the rate of recovery in factor of safety
was slower for thedelayed pattern than for the normal and advanced
patterns.
Comparison of High- and Low-Conductivity Soils
Fig. 5(c) shows that the rainfall patterns affected the rate of
reduc-tion in Fs and the time corresponding to Fsmin for both HC
and LCsoil slopes. The Fs of HC soil slope decreased by 1013% from
itsinitial value and the Fs of LC soil slope decreased to 4045% of
itsinitial value. Fig. 6 shows pore-water pressure distributions at
thecrest (section x-x) and toe (section y-y) of HC soil slope
during theapplication of antecedent rainfall of different patterns.
Fig. 6(a)shows pore-water pressure distribution for the delayed
rainfall pat-tern. The figure shows that the pore-water pressure
near groundsurface at the crest increased gradually from 38:5 kPa
att 0 h (beginning of the rainfall) to 8:5 kPa at t 120 h (atthe
end of rainfall, corresponding to Fsmin). In other words, thematric
suction of the soil decreased by 30 kPa. Fig. 6(a) also showsthat
the pore-water pressure increased from 18:5 kPa at t 0 to7:1 kPa at
t 120 h near the ground surface at the toe of slope.The reduction
in matric suction was 11.4 kPa. The maximum re-duction in matric
suction of the slope, which was at the end of rain-fall (i.e., t
120), resulted in Fsmin. This reduction in matricsuction of HC soil
slope corresponded to the first 7 m depth belowthe slope surface at
the crest. The figure shows that the position ofthe water table did
not change significantly (i.e., increased from 28to 28.83 m at the
toe of slope). This observation indicated that thereduction in
matric suction of the slope was primarily caused byinfiltration of
rainwater rather than by rising of the water table.
Fig. 6(b) shows pore-water pressure distribution associated
withthe normal rainfall pattern. The figure shows that the
pore-waterpressure near the ground surface increased from its
minimum valueof 38:5 kPa at t 0 h (at the beginning of rainfall) to
its maxi-mum value of9:85 kPa at t 88 h which corresponded to
Fsminof the slope. The increase in pore-water pressure was 74%.
Thepore-water pressures started to decrease toward negative
valuefrom t 88 h, although rainfall continued until t 120 h (endof
the rainfall). This behavior was also observed at the toe ofslope.
This is because as the rainwater infiltrated into the unsatu-rated
zone of slope, the pore-water pressures increased. Whenthe
rainwater percolated down in the slope, the matric suctiondecreased
at deeper depths and the depth of the wetting frontincreased. When
the infiltrated rainwater became less than the per-colated
rainwater, pore-water pressures started to recover. As
thepore-water pressures decreased toward negative value, the
shearstrength of soil increased and consequently the factor of
safetyof slope started to increase.
Fig. 6(c) shows pore-water pressure distributions associatedwith
the advanced rainfall pattern. The figure shows that thepore-water
pressure at the ground surface at the crest of slope in-creased
from 38:5 kPa at t 0 h (at the beginning of rainfall) to12:5 kPa at
t 56 h. The increase in pore-water pressure wasapproximately 68%.
The pore-water pressures started to decreasefrom t 64 h, although
rainfall continued until t 120 h (end ofthe rainfall). This
behavior was also observed at the toe of slope forthe same reason
for the normal rainfall pattern.
Fig. 7(a) shows infiltrated rainwater into the slope versus
timefor all the rainfall patterns at the crest of the HC soil
slope. Themaximum rainfall intensity for all the rainfall patterns
was
Fig. 5. Normalized factor of safety, Fsn, versus time, t, for
various rain-fall patterns: (a) HC soil type; (b) LC soil type; (c)
comparison of HCand LC
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8:5 mm=h, which was 2.36% of ks of HC soil slope (i.e.,ks 360
mm=h), as indicated in Fig. 4. As a result, all the rain-water
infiltrated into the slope (i.e., crest and toe), as indicatedin
Fig. 7(a). This is because rainfall intensity at all time was
muchsmaller than the saturated coefficient of permeability, ks, of
HC soilslope. Although all the rainwater infiltrated into the soil
under allthe three rainfall patterns, the amount of infiltrated
rainwater ateach time step was different, which controlled the
value ofFsmin. For HC soil, the advanced rainfall pattern that had
the high-est amount of infiltrated rainwater in the early stage was
the firstantecedent rainfall pattern to reach Fsmin (i.e., t 56 h).
The de-layed rainfall pattern that had the highest cumulative
infiltratedrainwater (i.e., 440 mm) resulted in the lowest Fsmin
(i.e.,Fsmin 1:48). The higher the amount of infiltrated
rainwater,the lower the value of Fsmin.
Fig. 8 shows pore-water pressure distributions at the crest
(sec-tion x-x) and toe (section y-y) of LC soil slopes during the
appli-cation of antecedent rainfall of different patterns. Fig.
8(a) showspore-water pressure distribution for the delayed rainfall
pattern.The figure shows that the pore-water pressure near the
ground
surface at the crest of slope increased from 141 kPa at t 0
h(beginning of the rainfall) to 0 kPa at t 120 h. The figure
alsoshows that the pore-water pressure at the toe of slope
increasedfrom 19:4 kPa at t 0 h to 0 kPa at t 32 h. The water
tablerose to the ground surface at the toe of slope (i.e., at t 32
h) androse to the middle of the slope at t 120 hours. Therefore,
thereduction in matric suction was attributed to both the
rainwaterinfiltration and the rising of water table.
Fig. 8(b) shows pore-water pressure distributions for the
normalrainfall pattern. The figure shows that the pore-water
pressure nearthe ground surface at the crest of slope increased
from 141 kPa att 0 h (beginning of the rainfall) to 0 kPa at t 64
h. However,the water table rose to its highest position at t 112 h,
whichcorresponded to Fsmin of the slope. The figure also shows
thatthe pore-water pressure at the toe of slope increased from19:4
kPa at t 0 h to 0 kPa at t 24 h. The water table roseto the ground
surface at the toe of slope (i.e., at t 32 h). Thereduction in
matric suction of the slope was primarily attributedto the rising
of water table. The same behavior was also observedfor the advanced
rainfall pattern [Fig. 8(c)].
Fig. 7(b) shows infiltrated rainwater into the slope versus
timefor all the rainfall patterns at the crest of the LC soil
slope. Thefigure shows that the changes in the rate of rainwater
infiltrationinto the soil follow the same pattern as the changes in
the rateof rainfall for all the rainfall patterns. However, for the
normalrainfall pattern, the amount of rainwater infiltration was
less thanthe amount of rainfall from t 56 h to t 88 h. This
behaviorcould be attributed to the capacity of the LC soil slope
(i.e.,ks 3:6 mm=h), which was smaller than the rainfall intensity
insome stages of the application of rainfall. This behavior wasalso
observed for the delayed pattern from t 88 h to t 120 h [Fig.
7(b)]. The figure shows that the advanced rainfall pat-tern had the
highest amount of infiltrated rainwater during its ap-plication on
the LC soil slope and was the first antecedent rainfallpattern to
reach Fsmin. In addition, it resulted in the lowest Fsmin.
Fig. 6. Pore-water pressure distribution caused by antecedent
rainfall atcrest (x-x) and toe (y-y) cross section for HC soil
type: (a) delayedrainfall pattern; (b) normal rainfall pattern; (c)
advanced rainfall pattern
Fig. 7. Rainfall and infiltration rate for antecedent rainfall
patterns atcrest of the slope: (a) HC soil slope; (b) LC soil
slope
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The delayed rainfall pattern resulted in the lowest Fsmin for
HCsoil, whereas the advanced rainfall pattern resulted in the
lowestFsmin for LC soil. On the other hand, the advanced rainfall
patternwas the first antecedent rainfall pattern to reach the Fsmin
for bothHC and LC soil slopes.
When the infiltrated rainwater became less than the
percolatedrainwater, pore-water pressures in the slope and
subsequently thefactor of safety of the slope started to recover
for all rainfall patternsand soil types. The pattern of rainfall
affects the trend of the pore-water pressure changes in the slope
and infiltration characteristicsinto the slope, especially near the
ground surface. As a result, therainfall pattern also controls the
factor of safety variation of theslope during rainfall.
Effect of Major Rainfall with Different InitialConditions on
Stability of Slope
Major rainfall was applied to the slopes right after the
application ofthe antecedent rainfall and was also applied to the
slopes without
any antecedent rainfall (i.e., no rainfall before the major
rainfallwas applied). Owing to the various antecedent rainfall
patterns ap-plied to the slope, the initial conditions (i.e.,
pore-water pressuredistributions) of the different slopes were
different at the start ofthe major rainfall. Consequently, the
antecedent rainfall patternschanged the pore-water pressure
distributions in the slope priorto the major rainfall.
Fig. 9 shows pore-water pressure distributions for HC and LCsoil
slopes at the end of antecedent rainfall and for the case
withoutany antecedent rainfall.
Fig. 9(a) shows that the antecedent rainfall with the
delayed,normal, and advanced patterns changed the initial
conditions forHC soil slope. The figure shows that the delayed
rainfall patterncaused the worst initial condition. The worst
initial condition meansthat the pore-water pressure profiles had
the highest value at thecrest and toe of the slope, which in turn
caused the lowest factorof safety. The pore-water pressure caused
by the delayed rainfallpattern near the ground surface at the crest
of slope was 8:4 kPa.This value was 22:1 kPa,24:6 kPa, and 38:4 kPa
for the nor-mal and advanced patterns and no antecedent rainfall
condition,respectively.
Fig. 9(b) shows the initial conditions caused by the
antecedentrainfall patterns for LC soil slope. The figure shows
that bothnormal and advanced rainfall patterns resulted in the same
initialcondition. The matric suction near the ground surface was30
kPafor both the normal and advanced rainfall patterns. This value
was0 kPa for the delayed rainfall pattern and 141 kPa for the
casewith no antecedent rainfall.
Fig. 10 provides the results of the numerical analyses of HCand
LC soil slopes with a major rainfall of 22:5 mm=h for 8 h.Fig.
10(a) shows the results for HC soil slope. The figure showsthat the
reduction in factor of safety attributable to the major rainfallwas
the same for all the initial conditions. For instance, the
majorrainfall decreased the factor of safety from 1.48 to 1.39 for
the
Fig. 8. Pore-water pressure distribution caused by antecedent
rainfall atcrest (x-x) and toe (y-y) cross section for LC soil
type: (a) delayed rain-fall pattern; (b) normal rainfall pattern;
(c) advanced rainfall pattern
Fig. 9. Initial conditions caused by antecedent rainfall
patterns at thestart of major rainfall: (a) HC soil type; (b) LC
soil type
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initial condition generated by the delayed rainfall pattern. The
per-centage of the reduction was approximately 6%. This
percentagewas observed for the normal and advanced rainfall
patterns. Inthe case of major rainfall (22:5 mm=h) without any
antecedentrainfall, the factor of safety decreased from 1.69 to
1.61. The per-centage of the reduction was approximately 5%. This
behaviorshows that the major rainfall had the same effect on all
the caseswith and without antecedent rainfalls for HC soil slope.
However,the role of antecedent rainfall can be observed in the
initial factor ofsafety. For example, the initial factor of safety
at the beginning ofmajor rainfall was 1.70 for the case without
antecedent rainfall andwas 1.48 for the delayed rainfall pattern.
The initial factor of safetygenerated by the delayed rainfall
pattern, 1.48, was approximately87% of its initial value (i.e.,
1.70). As a result of both the antecedentand major rainfalls, the
factor of safety of the soil slope was de-creased to 82, 87, and
87.5% of its initial value for the delayed,normal, and advanced
patterns, respectively. Therefore, the delayedrainfall pattern had
the worst effect on the stability of HC soilslope.
Fig. 10(b) provides the results for LC soil type. The
figureshows that the factor of safety at the end of application of
anteced-ent rainfalls was approximately the same (i.e., Fst120 h
1:083for the delayed, and Fst120 h 1:024 for the normal andadvanced
rainfall patterns). The figure shows that for the initialcondition
resulting from the normal and advanced rainfall patterns,the major
rainfall decreased the factor of safety of LC soil slopefrom 1.024
to a value less than one (i.e., 0.904), which reflected theunstable
condition or failure of the slope. For the initial
conditionresulting from the delayed rainfall pattern, the major
rainfalldecreased the factor of safety of the LC soil slope from
1.08 to1.01. The reduction in the factor of safety caused by the
major rain-fall for the initial condition resulting from the normal
and advancedrainfall patterns was approximately 0.12. Because the
infiltratedrainwater from the normal and advanced antecedent
rainfall pat-
terns was more than that of the delayed antecedent rainfall
pattern,the reduction in factor of safety caused by the normal and
advancedrainfall patterns was more than that of the delayed
rainfall pattern.
In the case of major rainfall without any antecedent rainfall,
thefactor of safety of LC soil slope decreased to 1.62 from its
initialFsini ( 1:82). The percentage of reduction was
approximately11%. The overall reduction in the factor of safety
(i.e., antecedentrainfall patterns and major rainfall) for LC soil
slope was approx-imately 50% for the normal and advanced rainfall
patterns and44.5% for the delayed rainfall pattern.
The major rainfall affected the stability of the LC soil
slopemore significantly than it affected the stability of HC soil
slopein the case without antecedent rainfall. This was because the
majorrainfall was 6.25 of ks (saturated coefficient of
permeability) for LCsoil, causing Fs to decrease to 89% of its
initial value. On the otherhand, the major rainfall was 0.0625 of
ks (saturated coefficient ofpermeability) for HC soil, causing Fs
to decrease to 95% of itsinitial value. Rahardjo et al. (2007) also
concluded that for low-conductivity soils (ks 106 m=s),
short-duration rainfalls withintensity greater than 1ks could bring
the slope to its lowest Fs,whereas for high-conductivity soil (ks
104 m=s), a high rainfallintensity was needed to destabilize the
slope.
The effect of antecedent rainfall patterns before the
occurrenceof major rainfall played a major role in the stability
assessment ofHC and LC soil slopes. However, its effect is more
significant in thestability assessment of LC soil slopes.
Conclusion
On the basis of this study on the effect of antecedent
rainfallpatterns on slope stability, the following conclusions can
be made:
Antecedent rainfall affected stability of both HC and LC
soilslopes by lowering the factor of safety of the slope before
theoccurrence of a major rainfall. The patterns of antecedent
rainfallcontrolled the rate of decrease in factor of safety, the
time corre-sponded to the minimum factor of safety, Fsmin, and the
valueof Fsmin. The rate of decrease in factor of safety was faster
forthe advanced rainfall pattern, followed by the normal and
delayedrainfall patterns.
The value of Fsmin was controlled by the amount of
infiltratedrainwater into the unsaturated zone of the slope. The
higher theamount of infiltrated rainwater, the lower the Fsmin of
the slope.For the HC soil slope, the delayed rainfall pattern
resulted in thelowest minimum factor of safety, Fsmin because the
amount of in-filtrated rainwater was the highest among all the
antecedent rainfallpatterns. For the LC soil slope, the advanced
rainfall patternresulted in the lowest, Fsmin because the amount of
infiltrated rain-fall was the highest among all the antecedent
rainfall patterns.
Antecedent rainfalls affected the stability of LC soil slope
moresignificantly than HC soil slope. Antecedent rainfalls could
causeup to 45% reduction in the factor of safety of LC soil slope
and upto 13% reduction in the factor of safety of HC soil slope
before theoccurrence of major rainfall.
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