04. Effect of antecedent rainfall patterns on rainfall induced slope failure.pdf

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Effect of Antecedent Rainfall Patterns on Rainfall-Induced Slope Failure Arezoo Rahimi 1 ; Harianto Rahardjo 2 ; and Eng-Choon Leong, M.ASCE 3 Abstract: Rainfall-induced slope failure occurs in many parts of the world, especially in the tropics. Many rainfall-induced slope failures have been attributed to antecedent rainfalls. Although it has been identified as a cause of rainfall-induced slope failure, the pattern or distribution of the antecedent rainfall has not received adequate attention. In this study, parametric studies were performed by using three typical rainfall patterns, identified by analysis of available rainfall data for Singapore and two different soil types to represent high- and low-conductivity residual soils of Singapore. Antecedent rainfall patterns were applied on soil slopes and a transient seepage analysis was conducted. The computed pore-water pressures were used in stability analyses to calculate the safety factor of the slope. Results indicated that antecedent rainfall affected the stability of both high-conductivity (HC) and low-conductivity (LC) soil slopes. However, the stability of the LC soil slope was more significantly affected than the HC soil slope. Patterns of antecedent rainfall controlled the rate of decrease in factor of safety, the time corresponding to F sðminÞ and the value of F sðminÞ . Delayed rainfall pattern resulted in the lowest minimum factor of safety, F sðminÞ , for the HC soil slope, and advanced rainfall pattern resulted in the lowest F sðminÞ 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 the world. Rainfall is the most recognized triggering factor for this dis- aster, especially in tropical regions with hot and humid climatic conditions (Brand 1984; McDougall et al. 1999; Tsaparas et al. 2002; Collins et al. 2004; Chen et al. 2004; Tohari et al. 2007; Tsai et 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 unsaturated zone of soil slope, decreases matric suction, and consequently the 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 there are many relations between rainfall and slope failures, there have been some debates about the relative role of antecedent rainfall. Antecedent rainfall is the rain that falls in the days immediately preceding a landslide event (Au 1998; Rahardjo et al. 2001; Cai and Ugai 2004). Guzzetti et al. (2007) reviewed rainfall thresholds for 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 high intensity induced the majority of landslides in Hong Kong. Brand (1992) also concluded that because of the high conductivity of Hong Kong soils, the effect of antecedent rainfall on rainfall- induced slope failure was not significant. Studies in Italy showed that antecedent rainfall did not have a relation with landslides (Aleotti 2004). Pitts (1984) concluded that antecedent rainfall was not a significant factor for slope failures in Singapore. Tan et al. (1987) found that antecedent rainfall could be significant in 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 of heavy rainfall, although no rainfall occurred at the time of failure. Rahardjo et al. (2008) studied the slope responses (i.e., pore-water pressure distribution) to rainfall events through comprehensive in- strumentation of four slopes in Singapore and concluded that 5-day antecedent rainfall could affect stability of slopes in Singapore. The role of antecedent rainfall on rainfall-induced slope failure greatly depends on the permeability of soil. Although antecedent rainfall has been shown to result in slope failure, the effects of pattern or distribution of antecedent rainfall on rainfall-induced slope failures have not received adequate attention. Ng et al. (2001) studied the effect of rainfall pattern on pore-water pressure changes in slope and concluded that rainfall patterns had 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 slope failure 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 uniformly for different time periods to obtain different antecedent rainfall intensities. However, the uniform rainfall distribution may not truly 1 Project Officer, School of Civil and Environmental Engineering, Nanyang Technological Univ., Block N1, B4b-07, Nanyang Avenue, Singapore 639798. 2 Professor, School of Civil and Environmental Engineering, Nanyang Technological Univ., Block N1, 01b-36, Nanyang Avenue, Singapore 639798 (corresponding author). E-mail: [email protected] 3 Associate 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 on September 27, 2010; published online on September 29, 2010. Discussion period open until October 1, 2011; separate discussions must be submitted for individual papers. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 137, No. 5, May 1, 2011. ©ASCE, ISSN 1090-0241/2011/5-483491/$25.00. JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / MAY 2011 / 483

Transcript of 04. Effect of antecedent rainfall patterns on rainfall induced slope failure.pdf

  • 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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