Engineering Geology 141–142 (2012) 124–140

Contents lists available at SciVerse ScienceDirect

Engineering Geology

j ourna l homepage: www.e lsev ie r .com/ locate /enggeo

Variability of residual soil properties

Harianto Rahardjo a,⁎, Alfrendo Satyanaga b, Eng-Choon Leong c, Yew Song Ng d, Henry Tam Cheuk Pang d

a School of Civil & Environmental Engineering, Nanyang Technological University, Block N1, 01b-36, Nanyang Avenue, 639798, Singaporeb School of Civil & Environmental Engineering, Nanyang Technological University, Block N1, B4c-10, Nanyang Avenue, 639798, Singaporec School of Civil & Environmental Engineering, Nanyang Technological University, Block N1, 01c-80, Nanyang Avenue, 639798, Singapored Building Technology Department, Housing & Development Board, HDB Hub 480, Lorong 6, Toa Payoh, 310480, Singapore

⁎ Corresponding author. Tel.: +65 67905246; fax: +E-mail address: chrahardjo@ntu.edu.sg (H. Rahardjo

0013-7952/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.enggeo.2012.05.009

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 February 2012Received in revised form 15 May 2012Accepted 19 May 2012Available online 28 May 2012

Keywords:Residual soilCoefficient of variationParticle size distributionSoil–water characteristic curveShear strength

Rainfall-induced slope failures are commonly observed in residual soil. Due to weathering, the residual soilproperties vary with depths, especially in tropical countries, such as: Singapore. Therefore, it is importantto characterize the properties of residual soil with depth. Index properties, soil–water characteristic curveand saturated and unsaturated shear strength tests were carried out on residual soils from sedimentaryJurong Formation, Bukit Timah Granite and Old Alluvium in Singapore. The variations of residual soil proper-ties in Singapore were determined from the laboratory test results and evaluated as a function of soil inherentvariability. Typical, upper and lower bounds of soil properties for the residual soils in Singapore weredescribed using confidence interval approach and coefficient of variation (COV) in this paper. The variations inresidual soil properties can be incorporated in design based on risk or reliability approach. The COV of indexand engineering properties of residual soils in Singapore indicate that residual soils from Bukit Timah GraniteandOld Alluviumare coarser than residual soil from sedimentary Jurong Formation. The particle size distributionof residual soil from Old Alluvium is more uniform than that from Bukit Timah Granite. On the other hand, theparticle size distribution of residual soil from Bukit Timah Granite is more uniform than that from sedimentaryJurong Formation. The shear strengths of residual soils from Bukit Timah Granite and Old Alluvium are higherthan that from sedimentary Jurong Formation.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Residual soils can be found in many parts of the world especiallyin those areas where slope failures due to rainfall frequently happen.Thick layers of residual soil are commonly found in tropical regionswith warm to hot climate. The residual soil is the final product of thein-situ mechanical and chemical weathering of underlying rocks,which have lost their original rock fabrics (Wesley, 1990). The mostimportant characteristic of residual soils is the low strength due to thedestruction of the bonds and the cementation of the material from theweathering processes. Residual soils are also difficult to test due totheir heterogeneity (Lumb, 1965; Wesley, 1990; Faisal, 2000; Brand,1985). Residual soils are usually found unsaturated, since they areoften observed above the ground water table where the pore waterpressures are negative (Rahardjo et al., 1995). In certain cases, theyappear to have high shear strength, but as they reach saturation theshear strength reduces significantly with zero or very small effectivecohesion (Lumb, 1965). Residual soils also tend to have higher porosityand higher permeability as compared to their parental rock materials.The characteristics of residual soils often cause instability of slopes

65 67910676.).

rights reserved.

during infiltration, especially in tropical areas where severe rainfallevents are common (Lumb, 1965; Brand, 1985; Rahardjo et al., 2007).

The characteristics of residual soil tend to varywith depths due to thedifferent degrees ofweathering and the variation in properties of residualsoil with depth becomes unpredictable (Faisal, 2000). The variabilityof soil properties also causes difficulty in slope stability analyses wheresoil data are limited. Therefore, it is desirable to have tools to estimatesoil heterogeneity in a quantitative schemewhich is appropriate for engi-neering design. In addition, it is important to develop a guideline toestimate the variability of residual soil with depth. Classical statisticalprocedures have beenwidely used to assess the variability of soil proper-ties from multiple point field measurements (Biggar and Nielsen, 1976;Bresler, 1989; Brejda et al., 2000). Statistical characterization involvesparameter estimation such as the mean, distribution and variance.The use of these techniques assumes that observations in the field areindependent of one another, regardless of their location. However,many studies in various disciplines such as hydrology (Holawe andDutter, 1999; Ali et al., 2000), geology (Davis, 1986), mining (Isaaks andSrivastava, 1989), environmental science (Vereeckern et al., 2000) andsoil science (Bhatti et al., 1991; Dasselaar, et al., 1998), showed thatvariability of soil data tends to be correlated across the area. Therefore,classical statistical methods may be inadequate for the establishment ofprobable range of soil properties relative to the location of samples(Vauclin et al., 1983; Goderya et al., 1996).

Fig. 1. Location of investigated slopes in Singapore for the period of 2006 until 2009.

125H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

Phoon and Kulhawy (1999a) developed a method to quantify thevariability of soil across space. They observed that the uncertaintiesin the variability of soil are caused by three factors, i.e. inherentvariability, measurement error and transformation uncertainty. Theinherent variability results from the geological processes (weatheringprocess). The measurement error is related to equipment, operatorand testing procedure. The uncertainties due to these two factorscan be minimized by collecting more samples (Kulhawy, 1992). Thetransformation uncertainty occurs during analyses of field or labora-tory test results using empirical methods. The method has been eval-uated and verified that it can be used to quantify the variability of soilproperties for geotechnical design (Phoon and Kulhawy, 1999b). Themost important property in unsaturated soil is soil–water characteris-tic curve (SWCC) (Fredlund and Rahardjo, 1993). Measurement ofSWCC is time-consuming, especially for clayey soils. Therefore,many attempts have been carried out to estimate SWCC from soil

Fig. 2. Grain size distribution of residual so

properties (e.g. Chin et al., 2010) or using a probabilistic model ofthe SWCC fitting parameters (e.g. Phoon et al., 2010).

In Singapore, residual soils are also characterized based on rockformation and degree of weathering (Winn et al., 2001; Leong et al.,2002). Residual soils from Bukit Timah Granite have mainly silty par-ticles with clay material and they are usually medium to highly plas-tic. On the other hand, residual soils from sedimentary JurongFormation have mainly clayey particles with sand or silt materialand they are usually medium to highly plastic. The density of residualsoil from Bukit Timah Granite ranges from 1.6 to 2.4 Mg/m3, with anaverage density of 1.8 Mg/m3, whereas the density of residual soilfrom sedimentary Jurong Formation ranges from 1.6 to 2.2 Mg/m3,with an average density of 2.0 Mg/m3. The specific gravity of the re-sidual soils can range from as low as 2.4 to as high as 2.75.

Based on a study by Leong et al. (2002), residual soils from BukitTimah Granite have a narrow range of average effective angle of shearingresistance,ϕ′, from 29° to 30°whereas the range of averageϕ′ of residualsoils from sedimentary Jurong Formation is larger, from 27° to 35°. Thelarger range of average ϕ′ of residual soils from sedimentary JurongFormation is attributed to the more variable parent rock types. The ϕb

values for residual soils from sedimentary Jurong Formation are in therange of 23° to 35° (Lim et al., 1996; Winn et al., 2001). The ranges ofsaturated coefficients of permeability for residual soils from Bukit TimahGranite and sedimentary Jurong Formation are in the order of 10−10 to10−5 m/s and 10−11 to 10−6 m/s, respectively (Leong et al., 2002).

The main objective of this paper is to discuss the variability ofsaturated and unsaturated soil properties with depth for residual soilsin Singapore. The range of soil properties (index and engineering prop-erties) that can be used for geotechnical engineering design is pres-ented in this paper. Techniques from Phoon and Kulhawy (1999a) areadopted and modified to be applicable to residual soils in Singapore.In addition, the range of soil–water characteristic curve (SWCC)variables and properties for residuals soil in Singapore is presented inthis paper. The SWCC variables are calculated fromSWCCfitting param-eters using Zhai and Rahardjo (2012) equation.

2. Geology of Singapore

The Singapore island is situated around 15m above sea level (PWD,1976). The climatic condition of Singapore is characterized by uniform

il from sedimentary Jurong Formation.

Fig. 3. Grain size distribution of residual soil from Bukit Timah Granite.

126 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

temperature and pressure, high humidity and particularly, abundantrainfalls. The tropical climate of this island can be divided into twomain seasons, the wetter Northeast Monsoon season from Decemberto March and the drier Southwest Monsoon season from June toSeptember (National EnvironmentAgency, 2011). During theNortheastMonsoon season, moderate to heavy rainfalls usually occur betweenDecember and January, lasting from1 to 3 days at a stretch. Theweatheris relatively drier in February until end of March. The maximum rainfallusually occurs between December and January, whereas July is noted asthe driest month (National Environment Agency, 2011).

Fig. 4. Grain size distribution of re

The geology of Singapore consists essentially of three formations:(i) igneous rocks of granite (Bukit Timah Granite) in the center andnorthwest, (ii) sedimentary rocks (Jurong Formation) in the west, and(iii) a semi-hardened alluvium (Old Alluvium) which covers olderrocks beneath in the east of Singapore (PWD, 1976). Fig. 1 shows asimplified geology map that outlines the distribution of the three majorgeological formations of Singapore. The oldest rocks in Singapore proba-bly come from the Palaeozoic era, which ended about 225 million yearsago (PWD, 1976). Granite occurs in two separate masses. The largerone is found in the central and northern areas, the smaller one in north

sidual soil from Old Alluvium.

Fig. 5. Distribution of soil particle with depth for residual soil from A. sedimentary Jurong Formation, B. Bukit Timah Granite and C. Old Alluvium.

127H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

eastern parts of Singapore. Granite or igneous rocks underlie the BukitTimah Nature Reserve and the Central Catchment Area in the center ofthe island. The granite in Singapore, according to radioactive age determi-nation, is more than 200 million years old. The sedimentary rocks ofJurong Formation form extensive areas in southern, south western andwestern parts of Singapore. These variations of conglomerate, sandstoneand shale are also observed on the islands to the south and west. Thesemi-hardened Old Alluvium was deposited by an ancient river system,probably in the Pleistocene epoch, during a low stand of the sea.According to PWD (1976), Old Alluvium contains a clayey coarse angularsand with stringers of subrounded pebbles up to 4 cm in diameter. Fine-grained beds are also present, usually as small lenticular bodies. Thepebbles within the Old Alluvium are mainly quartz, but rhyolite, chert,and argillite pebbles are also observed.

Fig. 6. Coefficient of variation of inherent variability (COVw) of soil particle distributionwith depth for residual soil from Jurong Formation, Bukit Timah Granite and OldAlluvium.

3. Soil investigation

Soil samples were collected from 30 slopes in Singapore. The soilsamplings were divided into three batches. Each batch consisted of 10numbers of sampling from 10 different slopes. The slopes are locatedin three different rock formations in Singapore, i.e.: sedimentary JurongFormation, Bukit Timah Granite and Old Alluvium (Figure 1). Soil

128 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

samples were collected using a Mazier sampler. The drillings of eachborehole were carried out by rotary boring with foam to obtain thehigh quality Mazier samples. PVC tubes are used to store the samples.

There were two criteria for ending the drillings. Firstly, if the SPTof the soil within the borehole was higher than 50, the drilling wasstopped. Secondly, if the drillings already achieved 5 m depth belowthe reduced level at the toe of the slope, the drilling was also stopped.Rock coring must be performed if the sampler hit the hard layer(SPT>50). The samples were waxed properly to maintain the naturalwater content inside the PVC tube. All samples were stored insidea curing room with constant humidity to maintain the natural condi-tion of the soil samples.

All samples were extruded from PVC tube and trimmed accordingto the required dimension. Index and engineering property testswere carried out only for selected depths due to time limitation.Index properties consisted of specific gravity (ASTM D854-02, 2002),Atterberg limits (ASTM D4318-00, 2000), and grain size distributiontests (ASTM D422-63, 2002). The engineering properties consisted ofsaturated and unsaturated tests, such as soil–water characteristiccurve (SWCC) tests; saturated and unsaturated triaxial tests. Consoli-dated undrained triaxial tests with pore–water pressuremeasurementswere selected for saturated triaxial tests (ASTM D4767-04, 2004).

Fig. 7. Distribution of liquid limit with depth for residual soil from A. sedim

SWCC is an important soil property in unsaturated soil mechanics.It relates water content to the matric suction (ua–uw) of a soil. Matricsuction is applied to the specimen using the axis-translation tech-nique (Hilf, 1956). The magnitude of the matric suction is the differ-ence between the applied air pressure and water pressure on thespecimen. SWCC tests were performed in Tempe cell and pressureplate (ASTM D6838-02, 2008) apparatuses. The main part of theTempe cell and pressure plate is the high-air entry ceramic plate.Prior to the test, the ceramic plate needs to be saturated in a desicca-tor with de-aired distilled water. There must be a good contactbetween the soil specimen and the ceramic plate to ensure thewater flow between specimen and the plate is continuous. Whenequilibrium is reached, that is, when the change in weight of thesoil specimen is negligible, a higher pore–air pressure is then applied.The test using the Tempe cell can be performed up to a matric suctionof 100 kPa because the maximum air-entry value of the ceramic diskis 1 bar or 100 kPa. The pressure plate is used for the application ofmatric suction up to 1500 kPa.

Consolidated drained triaxial tests on unsaturated soil speci-mens were carried out using the modified triaxial cell (Fredlundand Rahardjo, 1993). The modified triaxial apparatus is capable ofcontrolling pore–air and pore–water pressures in the soil specimen

entary Jurong Formation, B. Bukit Timah Granite and C. Old Alluvium.

129H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

independently using the axis-translation technique in order toachieve the desired matric suction. Pore–water pressure was mea-sured and controlled through a saturated ceramic disk with a 5 bar ofair-entry value. The triaxial cell was connected to a GDS digital pres-sure/volume control (DPVC) for applying the cell pressure, pore–water pressure and axial strain. A low shearing rate of 0.0009 mm/min was adopted to ensure fully drained conditions for both the airand water phases, and to prevent pore–water pressure from buildingup (Rahardjo et al., 2004a).

4. Mathematical model

Due to the weathering process, soil properties vary vertically andhorizontally. However, Elkateb et al. (2003) observed that the vari-ability of soil properties is not random, but is gradual and it followsa pattern that can be quantified using certain relationships, wheresoil properties are treated as random variables. As described, one fac-tor that causes the uncertainty of soil variability is the inherent soilvariability. The probable range of soil properties with depth can beobtained by calculating the standard deviation of the inherent soil

Fig. 8. Distribution of plastic limit with depth for residual soil from A. sedim

variability (SDw) for every depth. In this study, the inherent soil var-iability was obtained by calculating the mean of soil properties forevery depth. Then standard deviation of the inherent soil variability(SDw) for every depth was calculated using Eq. (1) (Phoon andKulhawy, 1999a). The soil properties for residual soil used in thisstudy are summarized in Appendices 1 to 3.

SDw ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n−1

X1i¼n

w zið Þ½ �2vuut ð1Þ

where:

SDw standard deviation of the inherent soil variabilityn number of data pointsw(zi) fluctuation at depth zi

The comparison of the variability of residual soil fromdifferent forma-tion was carried out by comparing the coefficient of variation of the

entary Jurong Formation, B. Bukit Timah Granite and C. Old Alluvium.

130 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

inherent soil variability (COVw) of each formation. The calculation ofCOVw is useful because it can describe the characteristics of residual soilprovided the residual soil is located in the same geological formation(Tang, 1984; Phoon and Kulhawy, 1999a). The COVw was obtained bynormalizing SDw with respect to the mean of soil properties (Phoonand Kulhawy, 1999a) as follows:

COVw ¼ SDw

tð2Þ

where:

COVw coefficient of variation of the inherent soil variabilityt mean of soil properties

In this paper, the inherent soil variability was also called typicalsoil properties. The upper and lower bounds of soil properties withdepth were obtained using confidence interval approach (Harr,1987). The selection of design parameters associated with a 90%level of confidence are commonly used in practice (Elkateb et al.,2003). Therefore, this approach was also used in this study. The lowerand upper bounds of the soil properties were associated with a 90%level of confidence from typical soil property variation with depth for re-sidual soils in Singapore.

Fig. 9. Distribution of natural water content with depth for residual soil from A.

5. Index properties

5.1. Grain size distribution

Grain size distributions (GSD) of residual soils from sedimentaryJurong Formation (JF), Bukit Timah Granite (BTG) and Old Alluvium(OA) were compiled according to their formation. The lower and upperbound GSD data from each formation were fitted using Fredlund's(2000) equation for unimodal grain size distribution (Eq. (1)). TypicalGSD data were calculated based on the average of percentage passingof each particle diameter and fitted using Fredlund's (2000) equation.

F dð Þ ¼ 1

ln exp 1ð Þ þ agrd

� �ngr� �mgr

2664

3775 1−

ln 1þ drd

� �

ln 1þ drdm

� �0BB@

1CCA

726664

37775 ð3Þ

where:

d particle diameter (mm)agr the point of inflection in the Fredlund equationngr parameter related to the steepest slopemgr the shape of the curve near the fines regiondr amount of fine particlesdm minimum diameter (mm)

sedimentary Jurong Formation, B. Bukit Timah Granite and C. Old Alluvium.

Fig. 10. Coefficient of variation (COV) of liquid limit and plastic limit for residual soilfrom Jurong Formation, Bukit Timah Granite and Old Alluvium.

Fig. 11. Distribution of void ratio with depth for residual soil from A. sedimentary Jurong Formation, B. Bukit Timah Granite and Old Alluvium.

Fig. 12. Coefficient of variation (COV) of void ratio for residual soil from Jurong Formation,Bukit Timah Granite and Old Alluvium.

131H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

A. sedimentary Jurong Formation, B. Bukit Timah Granite and C. Old Alluvium.

132 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

Typical upper and lower bounds of GSD for residual soils from JF,BTG and OA are shown in Figs. 2 to 4. The minimum percentage offine particles for residual soils from JF, BTG and OA are 38%, 20% and

Fig. 13. Distribution of effective cohesion with depth for residual soil from

Fig. 14. Coefficient of variation (COVw) of inherent variability of effective cohesion forresidual soil from Jurong Formation, Bukit Timah Granite and Old Alluvium.

23%, respectively. The maximum percentages of fine particles forresidual soils from JF, BTG and OA are similar, which are about 95%.Typical percentages of fine particles for residual soils from JF, BTGand OA are 65%, 58% and 60%. In general, residual soils from BTGand OA are coarser than residual soils from JF. The distribution offine particles for residual soils from BTG and OA is similar with onlysmall percentages of gravel being observed in the GSD from thesetwo residual soils. However, more percentages of clay particles andless percentages of silt particles are found in residual soils from OAas compared with those from BTG. Some residual soils from BTGalso have GSD with bimodal characteristics (gap-graded soils).

The distribution of soil particles for various depths of residual soilsfrom JF, BTG and OA is also plotted and shown in Fig. 5. Typical, upperand lower bounds of the soil particle distributions are calculated follow-ing procedures explained in Section 4. Fig. 5A shows that the typicalpercentage of sand and fine particles for residual soils from JF increaseslinearly with depth from ground surface (silty clay) until 7 m depth(clayey sand). However, the percentages of sand and fine particles forresidual soils from JF are about constant for depths from 7 m to 14 m.Fig. 5A also shows that the typical residual soil from JF is classified asa coarse-grained soil (i.e., percentage of sand is higher than 50%) fordepths greater than 7 m.

The percentage of sand increases non-linearly with depth in a simi-lar trend with the percentage of fine particles for residual soil from BTG(Figure 5B). The percentage of sand for residual soil from BTG increases

Fig. 15. Distribution of effective friction angle with depth for residual soil from A. sedimentary Jurong Formation, B. Bukit Timah Granite and C. Old Alluvium.

133H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

significantly from ground surface until 2 m depth and starts to increasegradually at greater depths. Similar to residual soils from JF, typical re-sidual soils from BTG are also classified as a coarse-grained soil fordepths greater than 7 m (Figure 5B). However, the percentage of sandfor residual soils from BTG increases at depths greater than 7 m. There-fore, typical residual soils from BTG at various depths are coarser thantypical residual soils from JF.

The percentage of sand also increases non-linearly for residualsoils from OA (Figure 5C). However, the percentage of sand increasesmore drastically with depth as compared with the percentage of clay.On the other hand, the percentage of silt for residual soils from OA de-creases with depth. As it can be seen in Fig. 5C, the percentages ofsand and clay for residual soils from OA are higher at greater depths.In addition, typical residual soils fromOA are classified as a fine-grainedsoil from ground surface until 14 m depth. Fig. 5C also shows that thepercentage of clay for residual soils from OA is higher than that forresidual soils from JF and BTG.

The variation of the COV of inherent variability (COVw) of soilparticle distribution is plotted versus the mean of soil particle distribu-tion (percentage of sand and clay) as shown in Fig. 6. The COVw of allresidual soils relatively decrease with increasing mean of soil particledistribution. Typical ranges of COVw for residual soils from JF, BTG andOA are 3–47%, 5–34% and 15–38%, respectively. The range of COVw for

residual soils from BTG is narrower than that for residual soils from JF.This indicates that the particle size distribution of residual soils fromBTG is more uniform than that from JF.

The heterogeneity of residual soils from JF is also indicated inFig. 5A where the boundary of soil particle distribution for residualsoils from JF varies with depth. This happens because residual soilsfrom BTG were formed only from one type of rock, granite. On theother hand, residual soils from JF were formed from different typesof rock, i.e. mudstone, siltstone, sandstone, shale and conglomerate.Fig. 6 also shows that the COVw for residual soils from OA is narrowerthan that for residual soils from BTG. This indicates that the particlesize distribution of residual soils from OA is more uniform than thatfrom BTG. This can be attributed to the fact that residual soil fromBTG is older than that from OA (Dames and Moore, 1983).

5.2. Water content, liquid limit and plastic limit

The distribution of liquid limit (LL), plastic limit (PL) and naturalwater content (w) of residual soils from JF, BTG and OA at variousdepths is plotted and shown in Figs. 7, 8 and 9, respectively. Typical,upper and lower bounds of the LL, PL and wn are calculated followingthe procedures explained in Section 4. Figs. 7 to 9 show that typicalLL, PL and wn for residual soils from JF, BTG and OA decrease non-

Fig. 16. Coefficient of variation of inherent variability (COVw) of effective friction anglefor residual soil from Jurong Formation, Bukit Timah Granite and Old Alluvium.

Fig. 17. Distribution of ϕb angle with depth for residual soil from A. sedimen

134 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

linearly with depth from ground surface until 14 m depth. These canbe understood since the percentages of clay for residual soils from JF,BTG and OA decrease with depth from ground surface until 14 mdepth. However, the decrease in LL, w and PL with depth forresidual soil from JF is not as significant as that for residual soils fromBTG and OA. This may be caused by the less weathering of residualsoils from JF as compared to that of residual soils from BTG and OA.Similar observation was also shown in the study by Rahardjo et al.(2004b). Figs. 7A, 8A and 9A show that the boundaries of LL, PL andw for residual soils from JF vary with depth. These trends are not ob-served in residual soils from BTG and OA (Figures 7B, 7C, 8B, 8C, 9Band 9C). These are related to the fact that the boundary of soil particledistribution for residual soils from JF also varies with depth. Figs. 8and 9 show that natural water contents of residual soils from JF, BTGand OA are very close to their plastic limits throughout the depth indi-cating the unsaturated condition of the residual soils (Fredlund andRahardjo, 1993).

The variations of COVw of LL and PL for residual soils from JF, BTGand OA are plotted and shown in Fig. 10. No trends are observed forthe mean of LL and PL in Fig. 10. The mean values of LL for residualsoils from JF, BTG and OA vary from 41% to 45%, from 41% to 51%

tary Jurong Formation and B. Bukit Timah Granite and C. Old Alluvium.

Fig. 18. Coefficient of variation (COV) of ϕb angle for residual soil from Jurong Forma-tion, Bukit Timah Granite and Old Alluvium.

135H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

and from 51% to 55%, respectively. The mean values of PL for residualsoils from JF, BTG and OA vary from 20% to 22%, from 31% to 37% andfrom 36% to 40%, respectively. The typical ranges of COVw of LL (5% to33%) and PL (12% to 30%) for residual soils from JF are wider than thetypical ranges of COVw of LL (15% to 32%) and PL (24% to 31%) forresidual soils from BTG. These indicate that the variabilities of LL andPL, which correspond to the boundary of LL and PL, are higher for resid-uals soil from JF than those for residual soil fromBTG. The typical rangesof COVw of LL (5% to 33%) and PL (12% to 31%) for residual soils from JF,BTG and OA are in agreement with the typical ranges of COVw of LL (7%to 39%) and PL (6% to 34%) for fine-grained soils as shown in Phoon andKulhawy (1999a).

5.3. Void ratio

Weathering process of rock formation in Singapore resulted in theporous structure of residual soil. Fig. 11 shows that typical void ratio

Fig. 19. Drying soil–water characteristic curve of res

of residual soils from JF, BTG and OA is high near ground surface anddecreases with depth. As a result, total density increases with depthsince water and air occupy more space in the upper part of residualsoils from JF, BTG and OA. The decreasing void ratio with depth forall residual soils is non-linear as shown in Fig. 11. The typical andthe boundary values of void ratio for various depths are calculatedfollowing the procedure in Section 4.

The variation of void ratio also reflects the variation of degree ofweathering. As shown in Fig. 11, the decreasing trend of void ratioof residual soils from JF is not as obvious as that of residual soilsfrom BTG. On the other hand, the void ratio of residual soils fromBTG decreases in a less significant manner as compared to that ofresidual soils from OA. This corresponds to the decreasing trends ofsoil particle distribution of residual soils from JF, BTG and OA whichoccur due to the fact that the residual soil from JF is the weatheringproduct of different types of rock. Fig. 11 also shows that the rangein void ratio for residual soils from OA (0.47 to 0.75) is higher thanthat for residual soils from JF (0.3 to 0.78) and BTG (0.3 to 0.75).These can be attributed to the higher percentage of clay for residualsoils from OA than that for residual soils from JF and BTG.

The variations of the COVw of void ratio for residual soils from JF, BTGand OA are plotted in Fig. 12. No trends are observed for the mean ofvoid ratio in Fig. 12. The mean values of void ratio for residual soilsfrom BTG and OA vary from 0.49 to 0.6 and from 0.5 to 0.8, respectively.The mean value of void ratio for residual soils from JF is relativelyconstant around 0.52. The typical ranges of COVw of void ratio for resid-ual soils from JF (15% to 44%) are wider than the typical ranges of COVw

of void ratio for residual soils fromBTG (16% to 33%). These indicate thatthe variabilities of void ratio for residual soils from JF are higher thanthose for residual soils from BTG. On the other hand, the typical rangesof COVw of void ratio for residual soils from BTG are wider than thetypical ranges of COVw of void ratio for residual soils from OA (3% to10%). These also indicate that the variabilities of void ratio for residualsoils from BTG are higher than those for residual soils from OA.

6. Shear strength of residual soil

6.1. Effective cohesion

Shear strength properties are important geotechnical parameters.However, the weathering process resulted in the variation of effectivecohesion (c′), effective friction angle (ϕ′) and ϕb angle with depth for

idual soil from sedimentary Jurong Formation.

Fig. 20. Drying soil–water characteristic curve of residual soil from Bukit Timah Granite.

Fig. 21. Drying soil–water characteristic curve of residual soil from Old Alluvium.

136 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

residual soils in Singapore. Therefore, it is important to quantifythe shear strength properties of residual soils at various depths. Thetypical and the boundary values of the c′, ϕ′ and ϕb are plotted inFigs. 13, 15 and 17, respectively. Typical c′ of residual soils from JFdecreases with depth although the decrease in c′ for residual soilsfrom JF is not as significant as that of residual soils from BTG and OA

Table 1Range of SWCC properties of residual soil in Singapore calculated using the Zhai and Rahar

Soil Air-entry value (kPa) Saturated w

Sedimentary Jurong Formation 1 to 116 0.3 to 0.60Bukit Timah Granite 0.8 to 25 0.21 to 0.61Old Alluvium 5 to 25 0.24 to 0.5

(Figure 13). This occurs since the percentages of fine particles for resid-ual soils from JF, BTG and OA also decrease with depth. The typical c′value of residual soils from BTG is higher than that of residual soilsfrom JF since residual soils from BTG are coarser than that from JF.

The relationships between COVw and mean of c′ for residual soilsfrom JF, BTG and OA are shown in Fig. 14. The mean c′ values for

djo (2012) equation.

ater content Residual suction (kPa) Residual water content

1500 to 18,000 0.025 to 0.100106 to 12,000 0.015 to 0.09842 to 12,000 0.009 to 0.098

137H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

residual soils from JF, BTG and OA vary from 11 kPa to 14 kPa, 8 kPa to12.5 kPa and 18 kPa to 24 kPa, respectively. The COVw of c′ forresidual soils from JF is wider than that for residual soils from BTG andOA. This can happen because the degree of weathering for residualsoils from JF is more variable than that for residual soils from BTG andOA. Fig. 14 shows that the range of COVw of c′ for residual soils fromBTG is similar to that for residual soils from OA.

6.2. Effective friction angle

The effective friction angle (ϕ′) of residual soils from JF, BTG andOA increases with depth (Figure 15) as the percentage of sandincreases with depth (Figure 5). The increasing trend of ϕ′ for residualsoils from JF is similar to that for residual soils from BTG and OA. Thistrend is different from the trend observed in Fig. 13 where the decreasein c′ for residual soils from JF is not as significant as that of residual soilsfrom BTG and OA. This can be attributed to the fact that the effectivefriction angle is affected by texture, size and distribution of particles insoil. The typical mean line and the upper and lower boundaries of theeffective friction angle for residual soils from BTG are higher thanthose for residual soils from JF. These are due to the fact that the particlesizes of residual soil fromBTG are larger than those of residual soils fromJF. Fig. 15 also shows that the particle size of residual soil from OA issimilar to that of residual soil from BTG since the typical mean lineand boundaries of residual soils from OA are similar to that of residualsoils from BTG.

Fig. 16 shows that the range of mean ϕ′for residual soils from JF(28° to 35°) is lower than that for residual soils from BTG (33° to42°). This suggests that the particle size of residual soils from JF isfiner than that of residual soils from BTG. On the other hand, therange of mean value of ϕ′ for residual soils from BTG is similar tothat for residual soils from OA (35° to 41°). This indicates that thereis similarity in the majority of particle size distribution betweenresidual soils from BTG and those from OA. The range of COVw forresidual soils from JF is much wider than that for residual soilsfrom BTG (Figure 16). This verifies the fact that the shear strengthof residual soils from JF in a saturated condition is more diversethan that of residual soils from BTG. In other words, residual soilsfrom JF are more heterogeneous in nature. The ranges of COVw of ϕ′for residual soils from JF (4° to 14°) are in agreement with the rangesof COVw of ϕ′ for silt and clay (4° to 12°) as observed in Phoon andKulhawy (1999a). On the other hand, the ranges of COVw of ϕ′ forresidual soils from BTG and OA (7° to 15°) are in agreement withthe ranges of COVw of ϕ′ for sand (5° to 11°) as shown in Phoonand Kulhawy (1999a).

6.3. Angle indicating the rate of increase in shear strength relative tomatric suction

The variations of typical ϕb angle with depth for residual soils(Figure 17) show a similar trend with those observed in the variationsof ϕ′ (Figure 15). Typical ϕb angle for all residual soils increases withdepth due to the higher contents of coarser particles in the greaterdepths. Typical ϕb angle for residual soils from BTG is slightly higherthan that for residual soils from JF, indicating that ϕb angle of soilswith a high percentage of coarse particles (residual soil from BTG)is higher than that of soils with a high percentage of fine particles(residual soil from JF). On the other hand, typical ϕb angle for residualsoils from OA is similar to that for residual soils from BTG, which issimilar to the trend observed in the comparison of the variation of ϕ′between residual soils from BTG and JF.

Fig. 18 shows that the range of mean value of ϕb for residual soilsfrom JF (25° to 31°) is lower than that for residual soils from BTG (28°to 32.5°). On the other hand, the range of mean value of ϕ′ for resid-ual soils from BTG is similar to that for residual soils from OA (30° to32.5°). These correspond to the variation of mean value of ϕ′ for

residual soils from JF, BTG and OA. The range of COVw of ϕb for residualsoils from JF is wider than that for residual soils from BTG (Figure 18).This can be attributed to the higher variability of degree of weatheringof residual soils from JF as compared to that of residual soils from BTG.

6.4. Soil–water characteristic curve

Soil–water characteristic curve (SWCC) defines the relationshipbetween water content and suction of soil. The SWCC of residual soilsfrom JF, BTG and OA are compiled and shown in Figs. 19, 20 and 21,respectively. The SWCCs of residual soils were plotted in terms of nor-malized volumetric water content (Θw) versus matric suction (ua–uw).The normalized volumetric water content can be defined with respectto the residual water content of residual soil as shown in Eq. (1).

Θw ¼ θw−θrθs−θr

ð4Þ

whereΘw is the normalized volumetric water content, θw is the volumet-ric water content at particularmatric suction, θr is the residual volumetricwater content and θs is the saturated volumetric water content.

The following equation (Fredlund and Xing, 1994) was used tobest fit the SWCC data:

θw ¼ C ψð Þ θsln eþ ua−uw

a

� �nh in om ð5Þ

where θw is the calculated volumetric water content, C(ψ) is correc-tion factor, (ua–uw) is matric suction (kPa), and e is natural number(2.71828…).

The a, n, and m are fitting parameters. Leong and Rahardjo (1997)suggested using a correction factor C(ψ) of 1. The upper and lowerbounds of normalized SWCC together with the typical SWCC for eachformation were subsequently drawn based on Eq. (2) with C(ψ)=1.The typical SWCC was obtained by taking a mean value of volumetricwater content for each matric suction within the upper bound andlower bound of SWCC for residual soils in Singapore. Then, the meanvalue of volumetric water content was fitted using Fredlund and Xing(1994) equation with a correction factor C(ψ)=1 as suggested byLeong and Rahardjo (1997). Zhai and Rahardjo (2012) developed equa-tions to describe the SWCC parameters (air-entry value or AEV, residualsuction, and residual water content) without using the graphical meth-od. Therefore, the SWCC parameters for the residual soils from JF, BTGand OA are determined using the Zhai and Rahardjo (2012) equations(Eqs. (6) to (8)).

AEV ¼ a � 0:13:72 �1:31nþ1 1−e

− m3:67

� �n �m � ln10 ð6Þ

ψr ¼ 10θi−θwþs1� log að Þ−s2� log ψð Þ

s1−s2 ð7Þ

θr ¼ θi−s1 � logψr− logað Þ ð8Þ

where:

θi ¼θs

1:313m ð9Þ

s1 ¼ θi−θrlogψr− loga

ð10Þ

s2 ¼ θr−θwlogψ− logψr

ð11Þ

ψr is residual suction, θs is saturated volumetric water content and θr isresidual volumetric water content.

138 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

The SWCC parameters are summarized in Table 1. It can be observedthat the ranges of AEV for residual soils fromBTG and OA arewider thanthose for residual soils from JF. It can be attributed to the greater varia-tion of pore sizes of residual soils from BTG and OA as compared to thatof residual soils from JF. Typical AEVs of residual soils from BTG and OAare lower than that of residual soils from JF indicating the pore size ofresidual soils from BTG and OA is bigger than that observed in residualsoils from JF. This is also supported by the lower saturated water con-tent and the steeper slope of SWCC of residual soils from BTG and OAthan those of residual soils from JF. Table 1 also shows that typical resid-ualwater content and suction of residual soils fromBTG and JF are lowerthan those of residual soils from JF.

7. Conclusions

In general, the COV of typical index properties (soil particle size,liquid limit, plastic limit and void ratio) for residual soils from JF iswider than that for residual soils from BTG, whereas the COV of typicalindex properties of residual soils from BTG is wider than those of residualsoils from OA. These trends indicate that the particle size distribution ofresidual soils from OA is more uniform than that of residual soils fromBTG and JF. The variation of index properties with depth also indicatesthat residual soils from OA and BTG are coarser than residual soils fromJF. In addition, the percentage of sand for residual soils from OA, BTG

Depth(m)

Soil type USCS % Sand % Silt % Clay w (%

1 Silty clay CL 0 48 52 201 Silty clay CH 4 30 66 291 Silty clay CL 2 41 57 121 Silty clay NA 2 37 61 NA1 Silty clay NA 10 35 55 NA1 Silty clay NA 8 31 61 NA1 Silty clay NA 12 30 58 NA2 Silty clay NA 15 30 55 NA2 Silty clay NA 14 28 58 NA2 Silty clay CL 16 35 49 192 Silty clay NA 8 42 50 NA3 Silty clay CL 17 32 51 103 Silty clay CH 13 31 56 283 Sandy clay CL 28 25 47 184 Silty clay CL 25 32 43 104 Silty clay CL 17 35 48 184 Silty clay CL 22 39 39 174 Clayey silt NA 22 41 37 NA4 Clayey silt NA 23 46 31 NA4 Silty clay CH 24 35 41 204 Silty clay CL 21 37 42 165 Sandy clay CL 36 31 33 185 Silty clay CH 28 35 37 225 Silty clay CL 24 40 36 145 Silty clay CL 33 31 36 175 Silty clay CH 19 40 41 235 Silty clay CL 20 42 38 135 Clayeysilt NA 24 43 33 NA6 Sandy clay NA 35 31 34 NA6 Sandy clay CL 44 25 31 186 Sandy clay NA 47 27 26 NA6 Clayey silt NA 29 38 33 NA7 Sandy silt NA 45 34 21 NA7 Sandy silt NA 47 30 23 NA7 Sandy clay CL 47 25 28 189 Sandy clay NA 40 29 31 NA9 Sandy silt NA 48 33 19 NA9 Silty sand NA 51 27 22 NA12 Sandy silt CL 47 35 18 1314 Sandy clay CL 42 29 29 814 Sandy silt CH 44 35 21 2414 Silty sand SM 53 25 22 18

Appendix 1. Summary of soil properties for residual soils from sedime

and JF increases with depth resulting in the lower value of void ratio ina greater depth for residual soils in Singapore.

The variations of engineering properties (effective cohesion, ef-fective friction angle and ϕb) with depth for residual soils from JF,BTG and OA indicate that typical pore size of residual soils fromBTG is similar to that of residual soils from OA, but is larger thanthat of residual soils from JF. Residual soils from BTG and OA arealso observed to have a higher shear strength than that of residualsoils from JF. The COV of typical engineering properties of residualsoils from JF is wider than that of residual soils from BTG, whereasthe COV of typical engineering properties of residual soils from OAare shown to be similar to that for residual soils from BTG. Thesetrends indicate that the distribution of pore size within residualsoils from BTG is similar to that within residual soils from OA, butit is more uniform than that within residual soils from JF.

Acknowledgements

This work was supported by a research grant from a collaborationproject between the Housing and Development Board and NanyangTechnological University (NTU), Singapore. The authors gratefully ac-knowledge the assistance of the Geotechnical Laboratory staff, Schoolof Civil and Environmental Engineering, NTU, Singapore during theexperiments and data collections.

) PL (%) LL (%) e c′ (kPa) ϕ′(o) ϕb(o)

23 48 0.32 9 33 3327 53 0.53 14 30 NA16 37 0.76 19 25 18NA NA NA NA NA NANA NA NA NA NA NANA NA NA NA NA NANA NA NA NA NA NANA NA 0.52 13 32 20NA NA NA NA NA 3421 36 NA NA NA NANA NA NA NA NA NA20 32 0.69 8 36 3626 55 0.37 12 31 2617 45 0.48 18 29 2215 39 0.31 8 33 NA20 46 0.42 9 30 NA24 43 0.55 11 29 NANA NA 0.44 10 35 35NA NA 0.57 14 31 2323 54 NA NA NA NA18 32 NA NA NA NA21 41 0.43 10 37 NA27 50 0.52 11 33 NA15 38 0.58 14 29 NA21 47 0.31 7 35 NA25 51 0.58 12 33 NA16 31 0.61 16 31 NANA NA NA NA NA NANA NA NA NA NA 2421 43 0.5 12 34 34NA NA NA NA NA 25NA NA NA NA NA 34NA NA NA NA NA NANA NA NA NA NA NA21 43 0.5 12 34 NANA NA NA NA NA 26NA NA NA NA NA 35NA NA NA NA NA NA16 32 0.34 8 35 2314 41 0.41 6 38 3826 54 0.52 9 32 2320 30 0.55 16 31 NA

ntary Jurong Formation in Singapore

139H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

Appendix 2. Summary of soil properties for residual soils from Buk

it Timah Granite in Singapore

Depth (m) Soil type USCS % Sand % Silt % Clay w (%) PL (%) LL (%) e c′ (kPa) ϕ′(o) ϕb(o)

5 Sandysilt MH 43 35 22 43 45 54 0.61 15 40 385 Sandy silt ML 44 35 21 21 23 35 0.42 5 31 NA5 Sandy silt ML 43 34 23 34 36 45 0.55 8 35 NA5 Sandy silt ML 52 23 25 41 42 52 0.58 14 41 NA5 Sandy silt NA 51 26 23 NA NA NA NA NA NA NA6 Sandy silt NA 43 33 24 NA NA NA 0.52 9 36 396 Silty sand SM 51 30 19 32 33.3 43.6 NA NA NA 236 Silty sand NA 53 25 22 NA NA NA NA NA NA 246 Sandy silt NA 49 30 21 NA NA NA NA NA NA 297 Silty sand NA 54 30 16 NA NA NA NA NA NA 307 Silty sand NA 55 25 20 NA NA NA NA NA NA 417 Sandy silt ML 45 34 21 31 32 43 0.51 9 36 3110 Silty sand NA 59 30 11 NA NA NA NA NA NA 2210 Silty sand SM 55 27 18 31 34 42 0.49 8 37 3712 Silty sand SM 60 32 8 25 26 37 0.37 4 34 2412 Silty sand SM 56 31 13 36 38 46 0.59 12 40 4014 Silty sand SM 61 31 8 16 22 28 0.32 2 32 2214 Silty sand SM 58 29 13 30 31 41 0.49 8 39 3314 Silty sand SM 55 34 11 44 42 54 0.63 12 41 415 Sand ysilt MH 43 35 22 43 45 54 0.61 15 40 385 Sand ysilt ML 44 35 21 21 23 35 0.42 5 31 NA5 Sand ysilt ML 43 34 23 34 36 45 0.55 8 35 NA5 Sand ysilt ML 52 23 25 41 42 52 0.58 14 41 NA5 Sand ysilt NA 51 26 23 NA NA NA NA NA NA NA6 Sand ysilt NA 43 33 24 NA NA NA 0.52 9 36 396 Siltysand SM 51 30 19 32 33.3 43.6 NA NA NA 236 Siltysand NA 53 25 22 NA NA NA NA NA NA 246 Sand ysilt NA 49 30 21 NA NA NA NA NA NA 297 Siltysand NA 54 30 16 NA NA NA NA NA NA 307 Siltysand NA 55 25 20 NA NA NA NA NA NA 417 Sand ysilt ML 45 34 21 31 32 43 0.51 9 36 3110 Silty sand NA 59 30 11 NA NA NA NA NA NA 2210 Silty sand SM 55 27 18 31 34 42 0.49 8 37 3712 Silty sand SM 60 32 8 25 26 37 0.37 4 34 2412 Silty sand SM 56 31 13 36 38 46 0.59 12 40 4014 Silty sand SM 61 31 8 16 22 28 0.32 2 32 2214 Silty sand SM 58 29 13 30 31 41 0.49 8 39 3314 Silty sand SM 55 34 11 44 42 54 0.63 12 41 41

Depth (m) Soil type USCS % Sand % Silt % Clay w (%) PL (%) LL (%) e e c′ (kPa) ϕ′(o) ϕb(o)

0.5 Clayey silt MH 3 41 56 25 29 53 0.76 15 30 210.5 Clayey silt MH 8 47 45 40 41 65 0.81 33 41 412 Clayey silt MH 17 45 38 28 30 53 0.65 15 31 242 Clayey silt MH 30 22 48 46 48 68 0.71 28 40 383.5 Sandy clay CH 37 33 30 25 27 52 0.62 13 34 253.5 Clayey silt MH 25 24 51 47 50 66 0.64 27 38 383.5 Clayey silt NA 33 28 39 NA NA NA NA NA NA NA4.5 Clayey silt CH 34 27 39 21 26 51 0.57 9 34 NA5 Clayey silt NA 30 25 45 NA NA NA NA NA NA NA5 Clayey silt NA 43 25 32 NA NA NA NA NA NA NA6.5 Silty sand SM 50 22 28 25 28 48 0.53 12 33 226.5 Clayey silt MH 32 18 50 31 35 56 0.53 20 36 NA6.5 Sandy silt MH 39 28 33 48 48 68 0.56 26 39 398 Sandy silt NA 36 28 36 NA NA NA NA NA NA NA8 Clayey silt NA 41 16 43 NA NA NA NA NA NA NA8.5 Sandy clay CL 45 27 28 24 27 49 NA NA NA NA8.5 Silty sand SM 51 16 33 36 39 56 0.51 NA NA NA8.5 Silty sand SM 35 20 45 42 45 65 0.55 NA NA NA9.5 Sandy clay CH 42 19 39 28 29 50 0.58 NA NA NA9.5 Sandy silt MH 48 21 31 40 45 63 0.51 NA NA NA13.5 Silty sand SM 56 13 31 21 26 45 0.47 21 36 2313.5 Sandy silt MH 49 11 40 34 36 58 0.50 23 42 42

Appendix 3. Summary of soil properties for residual soils from old alluvium in Singapore

140 H. Rahardjo et al. / Engineering Geology 141–142 (2012) 124–140

References

Ali, A., Abtew, W., Van Horn, S., Khanal, N., 2000. Temporal and spatial characterizationof rainfall over Central and South Florida. Journal of the American Water ResourcesAssociation 36 (4), 833–848.

ASTM D422-63, 2002. Standard Test Method for Particle Size Analysis of Soils.ASTM D4318–00, 2000. Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity

Index of Soils.ASTM D4767-04, 2004. Standard test method for consolidated undrained triaxial

compression test for cohesive soils.ASTM D6838-02, 2008. Standard Test Methods for the Soil–Water Characteristic Curve

for DesorptionUsingHangingColumn, Pressure Extractor, ChilledMirrorHygrometer,or Centrifuge.

ASTM D854–02, 2002. Standard Test Methods for Specific Gravity of Soil Solids byWater Pycnometer.

Bhatti, A.U., Mulla, D.J., Koehler, F.E., Gurmani, A.H., 1991. Identifying and removingspatial correlation from yield experiment. Soil Science Society of America Journal55, 1523–1528.

Biggar, J.W., Nielsen, D.R., 1976. Spatial variability of the leaching characteristics of afield soil. Water Resources Research 12 (1), 78–84.

Brand, E.W., 1985. Geotechnical engineering in tropical residual soils. Proc. 1st Interna-tional conference Geomechanics in Tropical Lateritic and Saprolitic Soils, Brazilia,Brazil, 3, pp. 23–91.

Brejda, J.J., Moorman, T.B., Smith, J.L., Karlen, D.L., Allan, D.L., Dao, T.H., 2000. Distributionand variability of surface soil properties at a regional scale. Soil Science Society ofAmerica Journal 64, 974–982.

Bresler, E., 1989. Estimation of statistical moments of spatial field averages for soilproperties and crop yields. Soil Science Society of America Journal 53, 1645–1653.

Chin, K.B., Leong, E.C., Rahardjo, H., 2010. A simplified method to estimate the soil–watercharacteristic curve. Canadian Geotechnical Journal 47 (12), 1382–1400.

Dames, Moore, 1983. Mass rapid transit system Singapore. Detailed Geotechnical StudyInterpretative Report. 204 pp.

Dasselaar, A.P., Corre, W.J., Prieme, A., Klemedtsson, A.K., Weslien, P., Stein, A.,Klemedtsson, L., Oenema, O., 1998. Spatial variability of methane, nitrous oxide andcarbon dioxide emissions from drained grasslands. Soil Science Society of AmericaJournal 62, 810–817.

Davis, J., 1986. Statistics and Data Analysis in Geology. John Wiley & Sons, New York.Elkateb, T., Chalaturnyk, R., Robertson, P.K., 2003. An overview of soil heterogeneity:

quantification and implications on geotechnical field problems. Canadian GeotechnicalJournal 40, 1–15.

Faisal, H.A., 2000. Unsaturated tropical residual soils and rainfall induced slope failuresin Malaysia. Unsaturated Soils for Asia. Balkema, Rotterdam, pp. 41–52.

Fredlund, D.G., 2000. The 1999 R.M. Hardy Lecture: The implementation of unsaturatedsoil mechanics into geotechnical engineering. Canadian Geotechnical Journal 37,963–986.

Fredlund, D.G., Rahardjo, H., 1993. Soil Mechanics for Unsaturated Soils. John Wiley &Sons, Inc., New York. 517 pp.

Fredlund, D.G., Xing, A., 1994. Equations for the soil–water characteristic curve. CanadianGeotechnical Journal 31, 533–546.

Goderya, F.S., Dhab, M.F., Woldt, W.E., Bogradi, I., 1996. Spatial patterns analysis of fieldmeasured soil nitrate. In: Rouhani, S., Srivastava, R.M., Desbaratas, A.J., Cromer, M.V.,Jonson, A.I. (Eds.), Geostatistics for Environmental and Geotechnical Applications:ASTM Publications, STP 1283, pp. 248–261.

Harr, M.E., 1987. Reliability-based design in civil engineering. McGraw-Hill BookCompany, New York, N.Y.

Hilf, J.W., 1956. An investigation of pore–water pressure in compacted cohesive soils.PhD Dissertation, Tech. Memo. No. 654, U. S. Department of the Interior, Bureauof Reclamation, Design and Construction Div., Denver, CO, 654 pp.

Holawe, F., Dutter, R., 1999. Geostatistical study of precipitation in Austria: time andspace. Journal of Hydrology 219, 70–82.

Isaaks, E.H., Srivastava, R.M., 1989. An Introduction to Applied Geostatistics. OxfordUniversity Press, New York.

Kulhawy, F.H., 1992. On evaluation of static soil properties. In: Seed, R.B., Boulanger, R.W.(Eds.), Stability and Performance of Slopes and Embankments II (GSP 31). AmericanSociety of Civil Engineers, New York, pp. 95–115.

Leong, E.C., Rahardjo, H., 1997. Review of soil–water characteristic curve equations.Journal of Geotechnical and Geoenvironmental Engineering 123 (12), 1106–1117.

Leong, E.C., Rahardjo, H., Tang, S.K., 2002. Characterisation and engineering propertiesof Singapore residual soils. Proc. International Workshop on Characterisation andEngineering Properties of Natural Soils, Singapore, 2, pp. 1279–1304.

Lim, T.T., Rahardjo, H., Chang, M.F., Fredlund, D.G., 1996. Effect of rainfall on matricsuction in a residual soil slope. Canadian Geotechnical Journal 33, 618–628.

Lumb, P., 1965. The residual soils of Hong Kong. Geotechnique 15, 180–194.National Environment Agency, 2011. Meteorological Services Data. National Environment

Agency, Singapore.Phoon, K.K., Kulhawy, F.H., 1999a. Characterization of geotechnical variability. Canadian

Geotechnical Journal 36 (4), 612–624.Phoon, K.K., Kulhawy, F.H., 1999b. Evaluation of geotechnical variability. Canadian

Geotechnical Journal 36, 625–639.Phoon, K.K., Santoso, A., Quek, S.T., 2010. Probabilistic analysis of soil–water characteristic

curves. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 136 (3),445–455.

PWD, 1976. Geology of the Republic of Singapore. Public Works Department, Singapore.Rahardjo, H., Lim, T.T., Chang, M.F., Fredlund, D.G., 1995. Shear strength characteristics

of a residual soil in Singapore. Canadian Geotechnical Journal 32, 60–77.Rahardjo, H., Ong, B.H., Leong, E.C., 2004a. Shear strength of a compacted residual soil

from consolidated drained and constant water content triaxial tests. CanadianGeotechnical Journal 41 (3), 421–436.

Rahardjo, H., Aung, K.K., Leong, E.C., Rezaur, R.B., 2004b. Characteristics of residual soilsin Singapore as formed by weathering. Engineering Geology 73 (1–2), 157–169.

Rahardjo, H., Satyanaga, A., Leong, E.C., Ng, Y.S., Foo, M.D., Wang, C.L., 2007. Slopefailures in Singapore due to rainfall. Proc. 10th Australia New Zealand Conferenceon Geomechanics, Brisbane, Australia, 2, pp. 704–709.

Tang,W.H., 1984. Principles of probabilistic characterization of soil properties. In: Bowles,D.D., Ko, H.-Y. (Eds.), Probabilistic Characterization of Soil Properties: Bridge BetweenTheory and Practise. American Society of Civil Engineers, Atlanta, pp. 74–89.

Vauclin,M., Vieira, S.R., Vachaud, G., Nielsen, D.R., 1983. The use of co-krigingwith limitedfield soil observation. Soil Science Society of America Journal 47, 175–184.

Vereeckern, H., Doring, U., Handelauf, H., Jaekel, U., Hasagen, U., Neuendorf, O.,Schwarze, H., Seidemann, R., 2000. Analysis of solute transport in a heterogeneousaquifer: the Krauthausen field experiment. Journal of Contaminant Hydrology 45,329–358.

Wesley, L.D., 1990. Influence of structure and composition on residual soils. Journal ofGeotechnical Engineering 116, 589–603.

Winn, K.K., Rahardjo, H., Peng, S.C., 2001. Characterization of residual soils in Singapore.Journal of the Southeast Asian Geotechnical Society 1, 1–13.

Zhai, Q., Rahardjo, H., 2012. Determination of soil–water characteristic curve variables.Computer and Geotechnics. 42, 37–43.