Factors Controlling Instability of Homogeneous Soil Slopesunder Rainfall
H. Rahardjo1; T. H. Ong2; R. B. Rezaur3; and E. C. Leong4
Abstract: Rainfall-induced slope failure is a common geotechnical problem in the tropics where residual soils are abundant. Although thesignificance of rainwater infiltration in causing landslides is widely recognized, there have been different conclusions as to the relativeroles of antecedent rainfall to landslides. The relative importance of soil properties, rainfall intensity, initial water table location and slopegeometry in inducing instability of a homogenous soil slope under different rainfall was investigated through a series of parametricstudies. Soil properties and rainfall intensity were found to be the primary factors controlling the instability of slopes due to rainfall, whilethe initial water table location and slope geometry only played a secondary role. The results from the parametric studies also indicated thatfor a given rainfall duration, there was a threshold rainfall intensity which would produce the global minimum factor of safety. Attemptshave also been made to relate the findings from this study to those observed in the field by other researchers. Results of this parametricstudy clearly indicated that the significance of antecedent rainfall depends on soil permeability.
Soils in tropical regions commonly consist of residual soils withnegative pore-water pressure in the zone above the water table�Rahardjo et al. 1995�. The stability of residual soil slopes isstrongly influenced by climatic and hydrological changes, such asprecipitation, infiltration, evaporation, and transpiration processesas illustrated in Fig. 1. Numerous researchers �e.g., Ching et al.1984; Brand 1984, 1992; Tan et al. 1987; De Campos et al. 1988;Anderson and Zhu 1996; Cheng 1997; Rahardjo et al. 1996; Ra-hardjo 2000� have studied the causes of slope failures in tropicalregions and concluded that rainwater infiltration is the most im-portant triggering factor in the instability of slopes.
Although the significance of rainwater infiltration in causinglandslides is widely recognized, there have been different conclu-sions as to the relative roles of antecedent rainfall to landslides.Brand �1984� suggested that antecedent rainfall was not a signifi-cant factor for landslides in Hong Kong and this limited influenceof antecedent rainfall was attributed to the high permeability oflocal soils. Brand et al. �1984� suggested that the majority of
landslides in Hong Kong were induced by localized and shortduration rainfall of high intensity. Pitts �1985� also concluded thatantecedent rainfall was not thought to be significant for slopefailures in Singapore. Tan et al. �1987� reexamined Pitt’s conclu-sion and suggested that antecedent rainfall could be significant inaffecting slope stability. Wei et al. �1991� in a case study of BukitBatok landslide in Singapore found that the failure occurred aftera period of heavy rainfall and there was no rainfall at the time ofthe failure. It appears therefore that experience from differentregions has resulted in different conclusions as to the significanceof antecedent rainfall for slope instability �Morgenstern 1992�.Such mixed conclusions are probably the consequence of at-tempts to correlate the incidence of landslides to event rainfallpatterns alone rather than evaluating the relative importance ofeach controlling parameter �i.e., soil properties, rainfall intensity,initial depth of water table, and slope geometry�. Results of thisparametric study clearly indicated that the significance of ante-cedent rainfall depends on soil permeability.
The objective of this parametric study is therefore to highlightthe relative importance of each controlling parameter �i.e., soilproperties, rainfall intensity, initial depth of water table and slopegeometry� in assessing the instability of a homogeneous soil slopeunder different rainfall condition.
Methodology
The methodology for the parametric study comprised three steps:�1� choosing appropriate values for the factors affecting slopestability and designing the parametric study; �2� seepage analysis;and �3� slope stability analysis.
Designing Parametric Study
In this study the stability of a slope was assessed through thefactor of safety �dependent variable� and the factors �independentvariables� affecting the stability of a slope are considered to be
1School of Civil and Environmental Engineering, Nanyang Techno-logical Univ., Block N1, #1B-36 Nanyang Ave., 63978 Singapore�corresponding author�. E-mail: [email protected]
2School of Civil and Environmental Engineering, Nanyang Techno-logical Univ., Block N1, #1B-36 Nanyang Ave., 63978 Singapore.
3Dept. of Civil Engineering, Univ. Teknologi Petronas, Bandar SeriIskandar, 31750 Tronoh, Perak Darul Ridzuan, Malaysia.
4School of Civil and Environmental Engineering, Nanyang Techno-logical Univ., Block N1, #1B-36 Nanyang Ave., 63978 Singapore.
the soil properties, rainfall intensity, location of initial groundwa-ter table, and the slope geometry �i.e., slope angle and slopeheight�. To assess the effects and relative contribution of control-ling factors �independent variables� on the stability �dependentvariable� of residual soil slopes, a series of parametric studieswere performed on a typical geometry of a homogeneous soilslope shown in Fig. 2. Four slope heights, Hs, �5, 10, 20, and40 m�, four slope angles, � �26.6, 33.7, 45.0, and 63.4°�, fiveinitial depths of groundwater table �GWT� at the slope toe Hw,�2.5, 5, 7.5, 10, and 15 m with an inclination of 7° from thehorizon�, three soil types �namely f10,−4, f50,−5, and f100,−6�, and 13rainfall intensities Ir �0.9, 1.8, 3.6, 5.4, 9, 18, 36, 54, 80, 90, 180,360, and 900 mm/h each for 24 h duration� were used in fourseries of parametric studies.
The slope heights and angles used in this study were chosenbased on the works by Toll et al. �1999� who suggested thatvirtually all the 35 failed slopes investigated in Singapore hadslope angles greater than 27° but less than 70°, and the heights ofthose failed slopes mostly fall in the range of 5–40 m.
The three types of soils �f10,−4, f50,−5, and f100,−6� selected forthe parametric study were based on the saturated coefficient ofpermeability of typical residual soils in Singapore. The symbol fin the soil name represents “fine-grained soil”, the first subscriptafter f indicates a fitting parameter a �associated with the soil-water characteristic curve �SWCC��, and the second subscriptwith negative sign indicates the saturated coefficient of perme-ability ks of the soil. Thus the soil f10,−4, means a fine grained soil
with SWCC fitting parameter a=10 kPa and ks=10−4 m/s. Simi-lar nomenclature follow for the other two soils. The three types ofsoil selected for the study encompass almost all types of soil interms of permeability, from the boundary of good-drainage soils�i.e., ks on the order of 10−4 m/s� to the boundary of poor-drainage soils �i.e., ks on the order of 10−6 m/s�. The ks of re-sidual soils has been reported to vary in the range of 10−11–2�10−4 m/s �Winn et al. 2001�. Therefore, in general f10,−4 repre-sents a fine-grained sandy soil; f50,−5 represents a fine-grainedsilty soil; and f100,−6 represents a fine-grained clayey soil.
The shear strength parameters of the soils used in the paramet-ric study are c�=10 kPa, effective angle of internal friction, ��=26°, rate of increase in shear strength caused by matric suction,�b=26°, and unit weight of soil, �=20 kN/m3. These shearstrength parameters were chosen based on typical values of theshear strength parameters in a few Singapore sites as reported byRahardjo �2000�. Only one set of shear strength parameters and aconstant unit weight � of the soil above and below the ground-water table was used throughout the study. This was done toeliminate the effects of shear strength properties of the soils onthe factor of safety of the slope and to ensure that the changes inthe stability of the slope under different rainfall are due to thechanges in pore-water pressures, uw of the slope material ratherthan changes in shear strength properties of the slope material.Thus the changes in factor of safety of the homogenous soil slopeevaluated in this study are the reflection of changes in the con-trolling factors.
For derivation of the SWCC for the soils, the Fredlund andXing �1994� equation �Eq. �1�� with correction factor C���=1, asrecommended by Leong and Rahardjo �1997a� was used
�w = �sC���� 1
�ln�e + � �ua − uw�a
�n��m� �1�
where C����correction function defined as
C��� = 1 −
ln�1 +�ua − uw��ua − uw�r
�ln�1 +
106
�ua − uw�r� �2�
where C���=1 �following recommendation by Leong and Raha-rdjo 1997a�; �w�volumetric water content; �s�saturated volu-metric water content; a�fitting parameter related to the air-entryvalue of the soil �kPa�; n�fitting parameter related to the slope ofthe SWCC; m�fitting parameter related to the residual water con-tent; e�natural number, 2.71828. . .; �ua−uw��matric suction�kPa�; �ua−uw�r�residual matric suction corresponding to the re-sidual water content �kPa�; ua�pore-air pressure �kPa�; anduw�pore-water pressure �kPa�. Whereas for the derivation of thepermeability function of the soils, the equation proposed byLeong and Rahardjo �1997b� �Eq. �3�� was used
kw = ks�p �3�
where kw�coefficient of permeability with respect to water forunsaturated soil; ks�saturated coefficient of permeability;p�fitting parameter corresponding to the slope of the permeabil-ity function; and �= ��w /�s��dimensionless form of the SWCC.
The fitting parameters for the SWCC and permeability func-tions for the three soils are shown in Table 1. During the deriva-tion of the SWCC and permeability functions for the soils, thesoil parameters m, n, �s �saturated volumetric water content�, and
Fig. 1. Schematic representation of effect of climatic conditions onpore-water pressure profile near ground surface of slope
Fig. 2. Slope geometry and boundary conditions for homogeneoussoil slope used in parametric study
p were kept constant to reduce the number of variables associatedwith soil parameters in the study. Only the parameter a, which canbe related to air-entry value and water-entry value of a soil andthe saturated coefficient of permeability, ks, were varied �seeTable 1� based on the studies of Ong �2003� which showed thatthese two soil parameters �a, and ks� directly affect the rainwaterinfiltration. The derived SWCC and permeability function for thethree soils are shown in Fig. 3.
The rainfall intensity 9 mm/h used in the parametric studywas adopted from the intensity-duration-frequency �IDF� curvefor Singapore with a return period of 100 years �Ministry of En-vironment 1992� and the rainfall intensity 80 mm/h was adopted
from the world’s greatest rainfall intensity equation �Paulhus1965�. The other 11 rainfall intensities used in this study werechosen as a multiplicative function of the saturated coefficientpermeability of the respective soils as indicated in Table 2. In allseries of parametric studies the duration of application of rainfallto the homogeneous soil slope was 24 h.
Four series of parametric studies namely, Series A, Series B,Series C, and Series D were performed. Table 2 gives a summaryof a combination of factors controlling slope stability that werevaried and kept constant in different series of parametric studies.Within each series of parametric studies, all combinations of fac-tors �within parenthesis, see Table 2� were studied.
In Series A, with a combination of three soil types, four slopeangles, and three rainfall intensities, 36 �3�4�3� parametricstudies were performed where the slope height and the ground-water table depth were kept constant �see Table 2�. Series A stud-ies were intended to evaluate the effect of soil properties in termsof saturated coefficient of permeability and the effect of slopeangle on the stability of a homogeneous soil slope subjected todifferent rainfall. In Series B, with a combination of three soiltypes and seven rainfall intensities �multiplicative function of ks
of respective soils�, 21 parametric studies were performed wherethe slope angle, slope height, and the groundwater table depthwere kept constant �see Table 2�. Series B studies were intendedto evaluate the effect of rainfall intensity on the stability of ahomogeneous soil slope. In Series C, with a combination of threerainfall intensities and five initial groundwater table depths, 15studies were performed where the soil type, slope angle, andslope height were kept constant �see Table 2�. Series C studieswere intended to evaluate the effect of initial location of ground-water table depth on the stability of a homogeneous soil slope. InSeries D, with a combination of three rainfall intensities and fourslope heights, 12 studies were performed where the soil type,slope angle, and the groundwater table depth were kept constant�see Table 2�. Series D studies were intended to evaluate theeffect of slope height on the stability of a homogeneous soil slope.
Seepage Analysis
Each parametric study was performed in two steps. First, a seep-age analysis of the homogeneous soil slopes was performed. Thepore-water pressures obtained from the seepage analysis werethen used in the slope stability analyses to calculate the factor ofsafety, Fs, of the slope. The governing partial differential equationfor a two-dimensional transient water flow utilized in the finite-element seepage model is as follows �Fredlund and Rahardjo1993�
mw2 �w
�ht
�t=
�
�x�− kwx
�ht
�x� +
�
�y�− kwy
�ht
�y� + q �4�
where mw2 �slope of the soil-water characteristic curve; �w�unit
weight of water; ht�hydraulic head or total head; t�elapsed time;kwx�coefficient of permeability with respect to water as a func-tion of matric suction in x direction; kwy�coefficient of perme-ability with respect to water as a function of matric suction in ydirection; and q�applied boundary flux.
Eq. �4� was solved using SEEP/W software �Geo-Slope1998a�. The boundary conditions utilized for the transient seepageanalysis are shown in Fig. 2. A boundary flux, q, equal to thedesired rainfall intensity, Ir, was applied to the surface of theslope. The nodal flux, Q, was taken to be zero at the sides of theslope above the water table and at the bottom of the slope to
Table 1. Soil Parameters Used to Derive Soil-Water Characteristic Curveand Permeability Function of Different Soils for Parametric Study
SWCCparameters
Permeability functionparameters
Soil typea
�kPa� m n �s
ks
�m/s�ks
�mm/h� p
f10,−4 10 1 1 0.45 10−4 360 4
f50,−5 50 1 1 0.45 10−5 36 4
f100,−6 100 1 1 0.45 10−6 3.6 4
Fig. 3. Soil-water characteristic curves and permeability functionsfor three types of soils used in study: �a� SWCC; �b� permeabilityfunction
simulate a no flow zone �see Fig. 2�. Equal total heads, ht, wereapplied at the sides of the slope below the water table. The initialcondition for all the analyses was a hydrostatic condition with alimiting pore-water pressure of −75 kPa. The negative pore-waterpressure generated for the initial condition was based on the ini-tial depth of water table, Hw. The limit on negative pore-waterpressure �−75 kPa� was imposed to prevent the generation of un-realistic pore-water pressures. The limiting value was selectedbased on field measurements of negative pore-water pressures�Rahardjo 2000� conducted at several sites in Singapore.
Slope Stability Analysis
The shear strength equation utilized in the slope stability analysiswas the unsaturated shear strength equation to incorporate thecontribution from the negative pore-water pressure. The equationfor unsaturated shear strength is as follows �Fredlund et al. 1978�
= c� + �n − ua�tan �� + �ua − uw�tan �b �5�
where �shear strength of unsaturated soil; c��effective cohe-sion; �n−ua��net normal stress; n�total normal stress;ua�pore-air pressure; ���effective angle of internal friction;�ua−uw��matric suction; uw�pore-water pressure; and �b�angleindicating the rate of increase in shear strength relative to thematric suction. The shear strength equation �Eq. �5�� is intendedfor linear failure envelope.
The Bishop’s simplified method was adopted in the slope sta-bility analysis. This method was adopted on the premise that com-putational efforts and time for obtaining the factor of safety, Fs,are less than required by other more rigorous methods. Further-
more, comparison by Fredlund and Krahn �1977� and Ching andFredlund �1984� have shown that Bishop’s simplified method iscapable of calculating the factor of safety with accuracy near tothe more rigorous methods. The general equation to calculate thefactor of safety using Bishop’s simplified method with the incor-poration of negative pore-water pressures can be found inFredlund and Rahardjo �1993�. The slope stability analysis usingBishop’s simplified method was performed using SLOPE/W soft-ware �Geo-Slope 1998b�. The pore-water pressures, uw, obtainedfrom the transient seepage analyses using SEEP/W were exportedto SLOPE/W to be incorporated in the slope stability analyses.
Results and Discussion
The results of the parametric studies are presented in this sectionwith attention to the effects of each of the controlling factors onthe stability of the homogenous soil slope subjected to rainfall for24 h with a combination of various controlling factors. Further,the location of the GWT when the minimum factor of safety,Fs�min�, occurs in the slope after 24-h rainfall was simplified intofour different categories �e.g., I, II, III, and IV� as shown in Table3. This was done to present the results in a more meaningful andcomparable way. The criteria for each category are also shown inTable 3. Thus, subsequent discussion on the final position of theGWT when the minimum factor of safety occurs will be based onthe classification system shown in Table 3.
Effect of Soil Properties
The results from Series A parametric studies are presented in thissection. The effect of soil properties on the instability of homo-
Table 2. Summary of Combination of Factors �Independent Variables� Affecting Slope Stability Used in Parametric Study
Study series Soil typeSlope angle
� �°�
Rainfall intensityIr
�mm/h�
Slope heightHs
�m�
GWT depthHw
�m�Number of
combination
A f10,−4
f50,−5
f100,−6 26.6
33.7
45.0
63.4 9
80
1ks 10 5 36
B �f10,−4�
�f50,−5�
f100,−6
45.0
�9= 1
40ks
18= 120ks
36= 110ks
90= 14ks
180= 12ks
360=1ks
900=2.5ks
� �3.6= 1
10ks
9= 14ks
18= 12ks
36=1ks
54=1.5ks
90=2.5ks
180=5ks
� 0.9= 1
4ks
1.8= 12ks
3.6=1ks
5.4=1.5ks
9=2.5ks
18=5ks
36=10ks
10 5 21
C f50,−5 45.0 9
36
80 10
2.5
5.0
7.5
10.0
15.0
15
D f50,−5 45.0 9
36
80 5
10
20
40 5 12
Note: Within each series of parametric study, all combinations of factor levels �within parenthesis� were studied.
geneous soil slopes is shown with the focus on the saturated co-efficient of permeability ks of the soil because ks is considered toplay a dominant role in rainwater infiltration. The variation infactor of safety with time for a homogeneous soil slope of con-stant slope height Hs �10 m�, groundwater table depth Hw �5 m�subjected to rainfall intensities of 9, 80, and 1ks mm/h of respec-tive soil for 24 h with a combination of various soil types andslope angles �see Table 2� are shown in Fig. 4.
The plots in Fig. 4 show a common pattern for the minimumfactor of safety, Fs�min�, irrespective of the soil type and slopeangle, where the higher the rainfall intensity the lower the Fs�min�.This implies that the primary control on Fs�min��rainfall intensity.A comparison of the plots in Fig. 4 among the same soil type butdifferent slope angles �compare rowwise� indicates that the higherthe slope angle the lower the initial factor of safety, Fs�ini�. This
Table 3. Possible Categories of Water Table Location when Minimum Factor of Safety Occurs in Homogenous Soil Slope after 24-h Rainfall
Fig. 4. Effect of soil properties on variation of factor of safety with time �from study Series A� for homogenous soil slope of constant slope heightHs �10 m�, groundwater table depth Hw �5 m� subjected to rainfall intensity of 9, 80, and 1ks mm/h of respective soil for 24 h with �a1–a3� soiltype f10,−4, f50,−5,f100,−6, and slope angle 26.6°; �b1–b3� soil type f10,−4, f50,−5, f100,−6, and slope angle 33.7°; �c1–c3� soil type f10,−4, f50,−5, f100,−6,and slope angle 45°; and �d1–d3� soil type f10,−4, f50,−5, f100,−6, and slope angle 63.4°
implies slope angle plays a role in dictating the Fs�ini� of the slope.The effects of slope angle and rainfall intensity on slope stabilityare not described further in this section as they are dealt with inmore detail in separate sections.
A comparison of all the plots �compare columnwise� in Fig. 4shows that soil type f100,−6 with a saturated coefficient of perme-ability ks=10−6 m/s is less affected by rainfall irrespective of therainfall intensity and the slope angle. Contrarily, soil type f10,−4
and f50,−5 with ks values of 10−4 and 10−5 m/s, respectively, aregreatly affected by rainfall. For the same rainfall intensity �9 and80 mm/h� and the same slope angle �compare plots columnwise�,the rate of reduction in factor of safety, Fs, during rainfall is thefastest for soil type f10,−4 followed by soil types f50,−5 and f100,−6.The net reduction in Fs seems to be a combined function of rain-fall intensity and soil type. Furthermore, Fig. 4 also shows thatafter the rainfall ceased, the Fs for soil type f10,−4 recovered at thefastest rate, followed by soil types f50,−5 and f100,−6, regardless ofthe rainfall intensity applied to the slope.
The locations of water table when the minimum factor ofsafety, Fs�min�, occurs for all the cases examined in Series A para-metric studies are shown in Table 4. Table 4 shows that for allcases �rainfall intensity and slope angle� in Series A parametricstudies there is no mounding or relatively small mounding of thewater table �Category IV� for slopes with soil type f100,−6. How-ever, for soil types f10,−4 and f50,−5, the mounding of the watertable does occur �Categories I, II, or III� particularly under highrainfall intensity.
The above findings suggest that homogeneous soil slopes witha low saturated coefficient of permeability �ks�10−6 m/s� aresafe from short-duration rainfalls regardless of the rainfall inten-sity applied to the slopes, where a short-duration rainfall is de-fined as the “1 day” or “24-h” rainfall �Brand 1992�. However,for homogeneous soil slopes with a high saturated coefficient ofpermeability �ks�10−5 m/s� the stability of the slopes is greatlyaffected by the short-duration, high intensity rainfall. Therefore, itcan be deduced from the results that slopes with low ks �ks
�10−6 m/s� will require a long-duration rainfall in order to fail.In other words, the effect of antecedent rainfalls is more signifi-cant in affecting the stability of homogeneous soil slopes with lowks �ks�10−6 m/s� than those with high ks �ks�10−5 m/s�.
Casagrande defined that the value of 10−6 m/s for saturated
coefficient of permeability is actually the boundary of poor drain-age material �Holtz and Kovacs 1981�. Therefore, the need forlong-duration or antecedent rainfalls to fail a homogeneous soilslope with low permeability �ks�10−6 m/s� can be explained bythe fact that the time required for rainwater to infiltrate the slopewith low permeability soil is very long. Furthermore, the results�Fig. 4� also indicate that after the rainfall ceases the recovery rateof Fs for a homogeneous soil slope with low ks �ks�10−6 m/s� ismuch slower than those with high ks �ks�10−5 m/s�. This slowrecovery rate of Fs combined with the slow movement of infil-trated water into the homogeneous soil slope with a low ks resultin the failure of the slope to be related to the antecedent rainfall.
The above results and discussion indicate that the instability ofhomogenous soil slopes with a high saturated coefficient of per-meability �ks�10−5 m/s� is more likely to be affected by a short-duration rainfall, similar to those reported by Brand et al. �1984�and Brand �1992� for Hong Kong slopes with a high ks where arainfall intensity of about 70 mm/h was reported as the thresholdvalue above which landslides would likely to occur. The slopefailures reported from Hong Kong usually occur during rainfall ofshort duration or shortly after the rainfall stopped. On the otherhand, the failure of slopes with low ks �ks�10−6 m/s� is shown tobe closely related to a long-duration or antecedent rainfall. Anexample of this situation is the failure of a 40 m slope with ks
=1.9�10−8 m/s at Bukit Gombak, Singapore �Yang and Tang1997�. Yang and Tang �1997� reported that although the maxi-mum daily rainfall of 78.8 mm occurred on December 12, 1991,the slope at the site did not slip. The slope eventually slipped onDecember 28, 1991 �16 days later� with a daily rainfall of only44.5 mm. A case study on a failed slope with a low ks �ks
=1.193�10−9 m/s� reported in Rahardjo et al. �2001� also illus-trated the significance of antecedent rainfall, where the watertable of the slope rose due to a 5-day antecedent rainfall and theslope failed during a daily rainfall greater than 90 mm. Thisshows that antecedent rainfall plays a more significant role in theslope failures at sites with low ks.
Effect of Rainfall Intensity
Fig. 5 shows the plots of variation in factor of safety versuselapsed time for a homogeneous soil slope under different rainfallintensities. These plots were obtained from results of Series Bparametric study where rainfall intensity was varied as a functionof ks of respective soil; soil type was also varied; and the slopeangle, slope height, and GWT depth were kept constant �see Table2�.
Fig. 5 shows that after a rainfall event starts the factor ofsafety �Fs� will drop regardless of the soil type or the rainfallintensity �Ir� applied to the slope. The Fs will recover after therainfall stops. The magnitude and rate of reduction in Fs is di-rectly proportional to the magnitude of Ir. The higher the Ir thefaster the Fs decreases with time. Therefore, for a high Ir the slopeof the graph before the rainfall stops �i.e., the portions of thegraphs at elapsed time t�24 h� is steeper than those with a lowIr. Fig. 5 also suggests the possibility of the existence of thresholdrainfall intensity which will cause the maximum reduction in Fs
of a homogeneous soil slope. This can be observed from the graphlines that coincide with each other at high rainfall intensities. Forinstance, for soil type f10,−4 �Fig. 5�a��, the graph lines for Ir equalto 360 and 900 mm/h coincide with each other. Similar observa-tion can be made for soil type f50,−5 �Fig. 5�b��, where the graphlines for Ir equal to 90 and 180 mm/h coincide with each other.For soil type f100,−6 �Fig. 5�c�� graph lines for Ir equal to 18 and
Table 4. Categories of Water Table Location when Minimum Factor ofSafety Occurs in Series A Parametric Studies
36 mm/h almost coincide with each other. It appears that thethreshold value of rainfall intensity is larger for soils with ahigher saturated coefficient of permeability, ks.
Table 5 shows the location of water table when the minimumfactor of safety, Fs�min�, occurs for all the cases examined in SeriesB parametric studies. Generally, the mounding of water table�Categories I, II, or III� only occurs if the rainfall intensity is very
high �Ir�36 mm/h� over a duration of 24 h. This is particularlytrue for soil types f10,−4 and f50,−5. However, for slopes with soiltype f100,−6, there is no mounding or relatively small mounding ofwater table �Category IV� regardless of the rainfall intensity ap-plied to the slope �see Table 5�.
To investigate the existence of the threshold rainfall intensityin more detail and to examine the relationship between minimumfactor of safety, Fs�min�, and rainfall intensity, Ir, the minimumfactor of safety versus logarithmic of rainfall intensity for all thecases examined in Series B studies are plotted in Fig. 6. Thesemilog plot �Fig. 6� shows that generally the Fs�min� and Ir rela-tionships follow a sigmoid shape. Tangents drawn to the horizon-tal limbs and inclined portion of the sigmoid shapes give twoinflection points; an upper and a lower inflection point for each ofthe sigmoid shape �see Fig. 6�. The Fs�min� is almost constant atvery low rainfall intensities for all soil types. However, the Fs�min�starts to decrease rapidly after the upper inflection point isreached. The value of Ir when Fs�min� starts to decrease is defined
Fig. 5. Effect of rainfall intensity on variation of factor of safety withtime �from study Series B� for homogeneous soil slope of constant Hs
�10 m�, Hw �5 m�, and � �45° � subjected to rainfall for 24 h with: �a�soil f10,−4; �b� soil f50,−5; and �c� soil f100,−6
Table 5. Categories of Water Table Location When Minimum Factor ofSafety Occurs in Series B Parametric Studies
Soil type
Rainfall intensity�mm/h� f10,−4 f50,−5 f100,−6
0.8 —a —a IV
1.8 —a —a IV
3.6 —a IV IV
5.4 —a —a IV
188 IV IV IV
18 IV IV IV
36 IV II IV
54 —a I —a
90 III I —a
180 I I —a
360 I —a —a
900 I —a —a
aNot studied.
Fig. 6. Relationship between rainfall intensity and minimum factorof safety �from study Series B� for homogeneous soil slope of con-stant Hs �10 m�, Hw �5 m�, � �45° �, and three soil types f10,−4; f50,−5;f100,−6 subjected to rainfall for 24 h
as the initiating rainfall intensity, Ir�ini� �see Fig. 6�. It appears thatthe Ir�ini� for soils with a low ks is lower than those with a high ks.The Ir�ini� value for thesoils examined in this study increases in thesequence f100,−6, f50,−5, f10,−4 �i.e., soil with ks equal to 10−6, 10−5,and 10−4 m/s, respectively�. There is also a threshold value forthe Ir that could produce the maximum effect on the Fs�min�. Thisoccurs at the lower inflection point of the sigmoid curve and iscalled threshold rainfall intensity, Ir�thr� �see Fig. 6�, where theFs�min� remains constant after the Ir�thr�. The value of Ir�thr� for thesoils examined in this study also increases in the sequence: f100,−6,f50,−5, f10,−4 �i.e., soil with ks equal to10−6, 10−5, and 10−4 m/s,respectively�.
The trend in Fs�min� versus Ir relationships observed in Fig. 6can be described by a sigmoid equation of the form
Fs�min� = A +B
1 + e−�Ir−C�/D �6�
where Fs�min��minimum factor of safety; Ir�rainfall intensity;e�natural number �i.e., 2.718. . .�; and A, B, C, D�fitting param-eters. A sigmoid curve of the form of Eq. �6� fitted to the Fs�min�and Ir data for different soil types is shown in Fig. 7 with respec-tive values of the fitting parameters and coefficient of correlation.The total volume of rainfall �Vr� corresponding to Ir�ini� and Ir�thr�for each soil type is also shown in Fig. 7.
A comparison of the Ir�ini� and Ir�thr� among different soil typesreveal that soil type f10,−4 has higher Ir�ini� and Ir�thr� �11 and140 mm/h respectively, Fig. 7�a�� compared to soil type f50,−5
�8.5 and 51 mm/h, Fig. 7�b�� and soil type f100,−6 �3.8 and11 mm/h, respectively, Fig. 7�c��. This implies that a higher Ir isneeded to destabilize a homogeneous soil slope with a high satu-rated coefficient of permeability, ks. However, if the comparisonis made by considering Ir�ini� and Ir�thr� in terms of ks of the re-spective soil �i.e., �ks�, soil with the highest ks �i.e., soil typef10,−4� indicates the lowest value of Ir�ini� and Ir�thr�, while soilswith the lowest ks show the highest Ir�ini� and Ir�thr�. As an instance,for soil type f10,−4 �i.e., ks=10−4 m/s� the Ir�ini�=0.03ks and Ir�thr�=0.39ks, whereas for soil type f100,−6 �i.e., ks=10−6 m/s� theIr�ini�=0.77ks and Ir�thr�=3ks �see Figs. 7�a and c��. This suggeststhat Ir equal to 1ks will not necessarily produce the lowest valuefor the Fs�min�.
Fig. 7 indicates that for soils with a low ks �ks�10−6 m/s�,Ir 1ks is required to bring the Fs�min� to the lowest value, whilefor soils with a high ks, Ir�1ks are sufficient to bring the Fs�min� tothe lowest value. In terms of total rainfall volume, the Vr neededto destabilize a soil slope with high ks is higher than those withlow ks. For example, Vr=264 mm is needed to initiate Fs�min� todecrease for soil type f10,−4 �ks=10−4 m/s�, whereas for soil typef100,−6 �ks=10−6 m/s�Vr=264 mm is sufficient to bring the Fs�min�to the lowest value �see Fig. 7�. This suggests that more water isneeded to destabilize homogeneous soil slopes with high ks ascompared to those with low ks. The reason for this lies in the factthat the mechanisms of failure for homogeneous soil slopes witha high saturated coefficient of permeability �i.e., ks�10−5 m/s�and those with a low saturated coefficient permeability �i.e., ks
�10−6 m/s� are not the same as suggested by the categories ofwater table location when Fs�min� occurs in the slope �see Table 5�.Under intense rainfall, slopes with high ks will usually fail due tothe mounding of the water table, while slopes with low ks willdestabilize due to rainwater infiltration that causes the reductionin matric suction of the soils in the unsaturated zone above thewater table �compare Tables 3 and 5�. For a homogeneous soilslope with high ks, most of the rainwater infiltrates into the slope
and causes the slope to fail mainly due to the rise of water table.On the other hand, for a slope with low ks, the rainwater fromshort-duration rainfall �Tr�24 h� will not cause the water table torise regardless of the rainfall intensity imposed on the slope be-cause most of the rainwater will be shed off as runoff. Hence, the
Fig. 7. Relationship between rainfall intensity and minimum factorof safety �from study Series B� for homogeneous soil slope of con-stant Hs �10 m�, Hw �5 m�, and � �45° � subjected to rainfall for 24 hwith: �a� soil f10,−4; �b� soil f50,−5; and �c� soil f100,−6
threshold rainfall intensity, Ir�thr�, is lower and the reduction infactor of safety, Fs, is smaller for slopes with a low ks as com-pared to slopes with a high ks.
The existence of threshold rainfall intensity, Ir�thr�, can also beobserved from the study by Ng et al. �2001�, where they havereported that under a given rainfall duration, the rise of pore-water pressure, uw, is only significant when the return period in-creases from 10 to 100 years but not from 100 to 1,000 years. Themost plausible reason for the finding is that the rainfall intensity,Ir, with a return period of 100 years is the threshold rainfall in-tensity, Ir�thr�, for the unsaturated cut slope analyzed in the study.Therefore, any rainfall intensity, Ir, greater than that will notcause further changes to the pore-water pressure profile of theunsaturated cut slope.
Effect of Initial Water Table Location
The effects of initial groundwater table location on stability of ahomogenous soil slope is reflected through the relationship be-tween Fs�ini� and Fs�min� with Hw, shown in Fig. 8. These resultsare obtained from Series C parametric studies in which the initialdepth of water table, Hw, was varied with five different values of2.5, 5, 7.5, 10, and 15 m for a homogeneous soil slope of constantsoil type f50,−5, Hs=10 m, �=45° subjected to rainfall for 24 hwith three rainfall intensities of 9, 36, and 80 mm/h.
The relationship between Fs�ini� and Hw shown in Fig. 8 ap-pears to be linear up to a depth of 7.5 m beyond which Fs�ini�remains constant. This is because the initial pore-water pressureprofiles generated for the slope at Hw 7.5 m�same as thosegenerated when Hw=7.5 m. This is due to the limiting pore-waterpressure of −75 kPa adopted in the analyses. If this limit was notimposed in the analyses, the linear relationship between Hw andFs�ini� is expected to continue even when Hw is greater than 7.5 m�see Fig. 8�. Thus it appears that the deeper the Hw of a slope thehigher the Fs�ini� will be. Therefore, the possibility of failure for aslope with deep groundwater table subjected to rainfall is unlikelydue to the high safety margin.
Fig. 8 also shows that the reduction in factor of safety, Fs, dueto a rainfall is primarily a function of the rainfall intensity, Ir,
whereas the initial depth of water table, Hw, mainly determinesthe value of initial factor of safety, Fs�ini�. The Fs�ini� is smaller forslopes with a shallower Hw which means that the safety margin islower. Therefore, slopes with a shallow Hw are more likely to faildue to a rainfall as compared to slopes with a deep Hw. Forexample, under a 24-h rainfall with intensity of 36 mm/h, theslope with Hw=2.5 m will fail due to the rainfall but slopes withHw�5 m are theoretically safe under the same rainfall �see Fig.8�. However, if the rainfall intensity is increased to 80 mm/h,only slopes with Hw�7.5 m will be safe �see Fig. 8�. This indi-cates that therainfall intensity is more dominant than the initialdepth of water table in controlling the stability of a homogeneoussoil slope.
Table 6 shows the locations of water table when Fs�min� occursfor all the cases examined in Series C parametric studies. Theresults in Table 6 show that only slopes with a shallow water table�i.e., Hw�5 m� and under high intensity rainfall will fail due tomounding of the water table, whereby most of the reduction infactor of safety, Fs, in this study is due to rainwater infiltrationthat causes the reduction in matric suction in the unsaturated zoneabove the water table �Categories II, III, IV; see Tables 4–6�. Thisexplains why most of the residual soil slope failures in tropicalregions with a deep water table are not attributed to the moundingof the water table. For example, out of 264 slope failures in HongKong as reported by Wong and Ho �1998� only 2% was attributedto the rise in the water table.
Effect of Slope Geometry
The effect of slope geometry is evaluated in terms of slope angle��� and slope height �Hs�. The effect of slope angle on the stabil-ity of a homogenous soil slope is described first and is followedby the effects of slope height.
Effect of Slope AngleThe effect of slope angle on the stability of a homogenous soilslope is shown in Fig. 9. Fig. 9 is a plot of relationships of theinitial factor of safetyFs�ini�, minimum factor of safety, Fs�min�,with slope angle, �, for all the cases examined in Series A para-metric studies.
Fig. 9 shows that both Fs�ini� and Fs�min� bear negative linearrelationship with �. In general, the higher the slope angle, �, thelower the initial factor of safety, Fs�ini�, and the minimum factor ofsafety, Fs�min�. This is conceivable because a steep slope will yielda lower factor of safety, Fs, as compared to a flat slope. A com-parison of plots �a, b, and c� in Fig. 9 suggests that under ashort-duration rainfall �Tr�24 h� for a soil slope with a small �two requirements must be fulfilled for failure. First, the saturatedcoefficient of permeability, ks, of the soil should be high �ks
Fig. 8. Relationship between initial factor of safety and minimumfactor of safety with initial depth of groundwater table �from studySeries C� for homogeneous soil slope of constant soil type f50,−5,Hs=10 m, �=45° subjected to rainfall for 24 h with three rainfallintensities of 9, 36, and 80 mm/h
Table 6. Categories of Water Table Location When Minimum Factor ofSafety Occurs in Series C Parametric Studies
�10−5 m/s� and second the rainfall intensity, Ir, applied to theslope should be extremely high. These requirements are seldommet in many residual soil slopes in Singapore which usually havelow ks �ks�10−6 m/s�. Astatistical analysis of slope failures inSingapore �Toll et al. 1999� concluded that residual soil slopesformed in the Bukit Timah and Jurong formations in Singapore at
angles below 27° are unlikely to fail. This is in agreement withthe results obtained from the numerical analysis in this study. Infact, the results from this study show that slopes with ��32° aretheoretically safe even under extreme rainfall intensities �see Fig.9�. The results �Fig. 9� also show that slopes with low ks �ks
�10−6 m/s� but high slope angles �� up to 63°� will not failunder short-duration rainfall �Tr�24 h� even when the rainfallintensity is extremely high. This again emphasizes the importanceof long-duration or antecedent rainfall in destabilizing slopes withlow ks.
The negative linear relationships between Fs�ini�, Fs�min�, and �for all the data points in Fig. 9 can be described by a linearregression equation of the form
y = E + Fx �7�
where y�dependent variables at y axis �i.e., Fs�ini� and Fs�min� forthis plot�; x�independent variables at x axis �i.e., � for this plot�;E=y intercept �i.e., the value intersecting y axis when x=0�; andF�slope of the regression line fitted to the data points. The valuesfor the regression coefficients E, F and the corresponding coeffi-cient of correlation, r2, for all the fitted regression lines in Fig. 9are shown in Table 7.
Although the Fs�min� bears a negative linear relationship with�, the slope and intercept of the relationships are different fordifferent soil types and rainfall intensities. Table 7 shows thatwithin the same soil type, the E value corresponding to Fs�min�decreases as Ir increases. However, for different soil types but forthe same rainfall intensity, the E value corresponding to Fs�min�decreases as the ks of the soil decreases �see Table 7�. This trendsuggests that the value of regression coefficient E �i.e, the y in-tercept� is actually a function of both the rainfall intensity, Ir,applied to the slope and the soil type. Since the fitted lines arealmost parallel to each other, the magnitude of E for Fs�min� indi-cates to what extent the minimum factor of safety, Fs�min�, willdecrease from the initial factor of safety, Fs�ini�, due to a rainfallevent. For example, for Irof 36 mm/h and soil type f50,−5 themagnitude of E corresponding to Fs�min� is 1.863 while the mag-nitude of E corresponding to Fs�ini� is 3.153. Therefore, the reduc-tion in Fs from the Fs�ini� is �3.153−1.863�=1.290.
The nearly constant values for F �i.e., slope of the regressionlines� actually indicates the linear relationship between Fs�ini� andFs�min� with slope angle, �. The results obtained from the studyreveal that any increment in � will cause a reduction in the factor
Fig. 9. Relationship between slope angle and minimum factor ofsafety �from study Series A� for homogeneous soil slope of constantHs �10 m�, Hw �5 m� subjected to rainfall for 24 h with three rainfallintensities of 9, 80, and 1ks mm/h of respective soil: �a� soil typef10,−4; �b� soil type f50,−5; and �c� soil type f100,−6
Table 7. Regression Coefficients and Coefficient of Correlation forRelationships between Initial Factor of Safety and Minimum Factor ofSafety with Slope Angle
of safety, Fs. For example, the magnitude of F for correspondingFs�ini�, is −0.0232. Thus, with every increase of 1° in �, the re-duction in Fs�ini� is about 0.0232.
Effect of Slope HeightThe effect of slope height, Hs, on the stability of a homogenoussoil slope is shown in Fig. 10. These results were obtained fromSeries D parametric studies where a slope with a constant soiltype f50,−5, �=45°, Hw=5 m was subjected to three different rain-fall intensities of 9, 36, and 80 mm/h for 24 h and the slopeheight, Hs, was varied for 5, 10, 20, and 40 m.
Fig. 10 shows that initial factor of safety, Fs�ini�, decreasesexponentially as the slope height, Hs, increases. Fig. 10 suggeststhat high slopes are generally easier to fail due to the low initialfactor of safety, Fs�ini�, whereas a relatively low slope �Hs=5 m� isstable regardless of the rainfall applied �Fs�min� Fs�cri� at any rain-fall, see Fig. 10�. The reduction in factor of safety, Fs, due torainfall for a high slope is smaller and occurs at a slower rate ascompared to a low slope. This can be observed from Fig. 10where the steepness of the graph lines reduces as the slope heightincreases from 5 to 40 m. Although the reduction in Fs due torainfall for a high slope is smaller and occurs at a slower rate, theslope is more likely to fail due to the low safety margin �i.e., lowFs�ini��. For instance, under rainfall intensities of 36 and 80 mm/hwith duration of 24 h, both slopes with heights of 20 and 40 mhave theoretically failed �Fs�min��1� due to the rainfall but theslope with low Hs �5 m� remains stable.
The locations of water table when Fs�min� occurs for all thecases examined in Series D parametric studies are shown in Table8. Basically, the results indicate that mounding of the water tablewill occur �Categories I, II, and III� regardless of the slope heightif a high rainfall intensity �i.e., Ir�36 mm/h for the cases exam-ined here� is applied to the slope. However, mounding of thewater table is more severe for low slopes �i.e., Hs�10 m� and thefailure of these types of slope is mainly attributed to mounding ofthe water table. For high slopes �Hs�20 m�, failure of the slopesis primarily caused by the reduction in matric suction due toinfiltration in the unsaturated zone above the water table.
The results from Series D parametric studies suggest that theheight of a slope is important in assessing slope failures due torainfall. The triggering factor in the failure of a high slope is therainfall but the height of the slope determines the initial safetymargin of the slope. The higher the slope the lower the initialfactor of safety of the slope �see Fig. 10� and the possibility offailure of the slope due to rainfall is more likely. In addition, themechanism of slope failure for a high slope �i.e., Hs�20 m�could be attributed to the reduction in matric suction due to infil-tration in the unsaturated zone above the water table �CategoriesII, III, and IV, see Table 8� while the mechanism of failure for alow slope �i.e., Hs�10 m� is closely related to mounding of thewater table �Category I, see Table 8� particularly when the slopeis subjected to high intensity rainfalls. Although in a high slopemounding of the water table is unlikely �Category I, see Table 8�,the reduction in matric suction in the unsaturated zone above thewater table is sufficient to lead the slope to failure because thesafety margin for a high slope is very low. On the other hand, fora low slope which has a relatively high safety margin, the reduc-tion in matric suction in the unsaturated zone above the watertable may not be sufficient to cause failure of the slope. However,in low slopes mounding of the water table may take place easily,thus leading to failure of the slope during a rainfall.
Conclusions
Homogeneous soil slopes with a low saturated coefficient of per-meability �ks�10−6 m/s� are safe from short-duration rainfalls�Tr�24 h� regardless of the rainfall intensity, Ir, applied to theslopes. However, the effect of antecedent rainfalls is significant inassessing the instability of homogeneous soil slopes with low ks
�ks�10−6 m/s� than those with high ks �ks�10−5 m/s�. Forslopes with high ks �ks�10−5 m/s� the stability of the slopes isgreatly affected by the short-duration high intensity rainfalls. Inaddition, slopes with high ks will usually fail due to mounding ofthe water table, while slopes with low ks will destabilize due tothe reduction in matric suction of the soils located above thewater table.
For a given rainfall duration, Tr, there is a threshold rainfallintensity, Ir�thr�, that will produce the lowest value of minimumfactor of safety, Fs�min�. The value of Ir�thr� �in terms of mm/h�increases as the saturated coefficient of permeability, ks, of thesoil in the slope increases. Rainfall intensity, Ir, equal to 1ks doesnot necessarily produce the lowest value of the minimum factorof safety, Fs�min�. Generally, for soils with a low ks �ks
�10−6 m/s�, Ir greater than 1ks is required to bring the Fs�min� tothe lowest value, while for soils with a high ks, Ir smaller than 1ks
is sufficient to bring the Fs�min� to the lowest value.The effect of slope geometry and initial water table location
Fig. 10. Relationship between slope height and minimum factor ofsafety �from study Series D� for homogeneous soil slope of constantsoil type f50,−5, Hw �5 m�, � �45° � subjected to rainfall for 24 h withthree rainfall intensities of 9, 36, and 80 mm/h
Table 8. Categories of Water Table Location When Minimum Factor ofSafety Occurs in Series D Parametric Studies
are secondary in the rainfall-induced slope failures. The slopegeometry and the initial water table location only determine theinitial factor of safety, Fs�ini�, of the slope and thus the safetymargin. Although slopes with a higher slope angle ���, a higherslope height �Hs�, and a shallower initial depth of water table�Hw� constitute the worst combination of factors for failure, andare more likely to fail due to a rainfall event, the actual failureconditions are however very much dictated by the rainfall appliedto the slope and the properties of the soil in the slope. Therefore,when dealing with rainfall-induced slope failures, emphasisshould be on the rainfall intensity and soil properties �particularlythe saturated coefficient of permeability, ks�.
Acknowledgments
This study was supported by a research grant �Grant No. RG7/99�from the Nanyang Technological University, Singapore. The sec-ond writer acknowledges the scholarship received from the Nan-yang Technological University, Singapore.
References
Anderson, S. A., and Zhu, J. H. �1996�. “Assessing the stability of atropical residual soil slope.” Proc., 7th Int. Symp. on Landslides, K.Senneset, ed., Balkema, Rotterdam, The Netherlands, 1073–1077.
Brand, E. W. �1984�. “State-of-the-art report of landslides in SoutheastAsian.” Proc., 4th Int. Symp. on Landslides, Toronto, 17–37.
Brand, E. W. �1992�. “Slope instability in tropical areas.” Proc., 6th Int.Symp. on Landslides, D. H. Bell, ed., Balkema, Rotterdam, The Neth-erlands, 2031–2051.
Brand, E. W., Premchitt, J., and Philipson, H. B. �1984�. “Relationshipbetween rainfall and landslides in Hong Kong.” Proc., 4th Int. Symp.on Landslides, Toronto, 377–384.
Cheng, P. F. K. �1997�. “Soil infiltration prediction and its significance inslope stability.” Proc., 3rd Asian Young Geotechnical EngineersConf., T. S. Tan et al., eds., Singapore, 661–669.
Ching, R. K. H., and Fredlund, D. G. �1984�. “Quantitative comparison oflimit equilibrium methods of slices.” Proc., 4th Int. Symp. on Land-slides, Toronto, 373–379.
Ching, R. K. H., Sweeney, D. J., and Fredlund, D. G. �1984�. “Increase infactor of safety due to soil suction for two Hong Kong slopes.” Proc.,4th Int. Symp. on Landslides, Toronto, 617–623.
De Campos, L. E. P., De Sousa Menezes, M. S., and Fonseca, E. C.�1988�. “Parameter selection for stability analysis.” Proc., 2nd Int.Conf., on Geomechanics in Tropical Soils, Publications Committee of2 ICOTS, ed., Balkema, Rotterdam, The Netherlands, 241–243.
Fredlund, D. G., and Krahn, J. �1977�. “Comparison of slope stabilitymethods of analysis.” Can. Geotech. J., 14�3�, 429–439.
Fredlund, D. G., Morgenstern, N. R., and Widger, R. A. �1978�. “Theshear strength of unsaturated soils.” Can. Geotech. J., 15�3�, 313–321.
Fredlund, D. G., and Rahardjo, H. �1993�. Unsaturated soil mechanics,Wiley, New York.
Fredlund, D. G., and Xing, A. �1994�. “Equations for the soil-water char-acteristic curve.” Can. Geotech. J., 31, 533–546.
Geo-slope International. �1998a�. SEEP/W for finite element seepageanalysis, version 4, user’s guide, Calgary, Alta., Canada.
Holtz, R. D., and Kovacs, W. D. �1981�. An introduction to geotechnicalengineering, Prentice-Hall, Englewood Cliffs, N.J.
Leong, E. C., and Rahardjo, H. �1997a�. “A review of soil-water charac-teristic curve equations.” J. Geotech. Geoenviron. Eng., 123�12�,1106–1117.
Leong, E. C., and Rahardjo, H. �1997b�. “Permeability functions for un-saturated soils.” J. Geotech. Geoenviron. Eng., 123�12�, 1118–1126.
Ministry of Environment �1992�. Code of practice on surface waterdrainage, 4th Ed., Drainage Department, Republic of Singapore.
Morgenstern, N. R. �1992�. “The evaluation of slope stability—A 25 yearperspective.” Proc., Stability and Performance of Slopes and Embank-ments II, Vol. 1, Barkeley, Calif., 21–26.
Ng, C. W. W., Wang, B., and Tung, Y. K. �2001�. “Three-dimensionalnumerical investigations of groundwater responses in an unsaturatedslope subjected to various rainfall patterns.” Can. Geotech. J., 38,1049–1062.
Ong, T. H. �2003�. “Rainfall-induced slope failures: Controlling factorsand mitigation with capillary barriers.” MEng thesis, Nanyang Tech-nological Univ., Singapore.
Paulhus, J. L. H. �1965�. “Indian Ocean and Taiwan rainfalls set newrecords.” Mon. Weather Rev., 93, 331.
Pitts, J. �1985�. “An investigation of slope stability on the NTI campus,Singapore.” Applied research project No. RPI/83, Nanyang Techno-logical Institute, Singapore.
Rahardjo, H. �2000�. “Rainfall-induced slope failures.” Research Rep.No. NSTB 17/6/16, Nanyang Technological Univ., Singapore.
Rahardjo, H., Chang, M. F., and Lim, T. T. �1996�. “Stability of residualsoil slopes as affected by rainfalls.” Proc., 7th Int. Symp. on Land-slides, K. Senneset, ed., Balkema, Rotterdam, The Netherlands, 1109–1114.
Rahardjo, H., Li, X. W., Toll, D. G., and Leong, E. C. �2001�. “The effectof antecedent rainfall on slope stability.” Geotech. Geologic. Eng..19, 371–399.
Rahardjo, H., Lim, T. T., Chang, M. F., and Fredlund, D. G. �1995�.“Shear strength characteristics of a residual soil.” Can. Geotech. J.,32, 60–77.
Tan, S. B., Tan, S. L., Lim, T. L., and Yang, K. S. �1987�. “Landslideproblems and their control in Singapore.” Proc., 9th Southeast AsianGeotechnical Conf., Vol. 1, Bankok, Thailand, 25–36.
Toll, D. G., Rahardjo, H., and Leong, E. C. �1999�. “Landslides in Sin-gapore.” Proc., 2nd Int. Conf. on Landslides, Slope Stability, and theSafety of Infra-Structures, Singapore.
Wei, J., Heng, Y. S., Chow, W. C., and Chong, M. K. �1991�. “Landslideat Bukit Batok Sports Complex.” Proc., 9th Asian Conf. on Soil Me-chanics and Foundation Engineering, Vol. 1, Balkema, Rotterdam,The Netherlands, 445–448.
Winn, K., Rahardjo, H., and Peng, S. C. �2001�. “Characterization ofresidual soils in Singapore.” Journal of the Southeast Asian Geotech-nical Society, 32�1�, 1–13.
Wong, H. N., and Ho, K. K. S. �1998�. “Systematic investigation oflandslides caused by a severe rainstorm in Hong Kong.” Transactionsof the Hong Kong Institution of Engineers, 3�3�, 80.
Yang, K. S., and Tang, S. K. �1997�. “Stabilising the slope of BukitGombak.” Proc., 3rd Asian Young Geotechnical Engineers Conf. T. S.Tan et al., eds., Singapore, 589–605.
