influence of stress state on soil-water characteristics and slope stability

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INFLUENCE OF STRESS STATE ON SOIL-WATER CHARACTERISTICS AND

SLOPE STABILITY

By Charles W. W. Ng,1 Member, ASCE, and Y. W. Pang2

ABSTRACT: A soil-water characteristic curve defines the relationship between the soil (matric) suction andeither the water content or the degree of saturation. Physically, this soil-water characteristic is a measure of thewater storage capacity of the soil for a given soil suction. Conventionally, the soil-water characteristic curves(SWCCs) are determined in the laboratory using a pressure plate apparatus in which vertical or confining stresscannot be applied. For investigating the influence on the stress state on the soil-water characteristics, a newstress controllable pressure plate apparatus has been developed. Effects of K0 stress conditions on the SWCCsof an ‘‘undisturbed’’ volcanic soil in Hong Kong are determined and illustrated. The net normal stresses con-sidered in the apparatus are 40 and 80 kPa, which are appropriate for many slope failures in Hong Kong.Experimental results show that the soil-water characteristic of the soil specimens is strongly dependent on theconfining stress. Numerical analyses of transient seepage in unsaturated soil slopes using the measured stress-dependent soil-water characteristic curves predict that the distributions of pore-water pressure can be significantlydifferent from those predicted by the analyses using the conventional drying SWCC. For the cut slope and therainfall considered, the former analyses predicted a considerably lower factor of safety than that by the latteranalyses. These results suggest that wetting stress-dependent soil-water characteristic curves should be consideredfor better and safer assessment of slope instability.

INTRODUCTION

Rain-induced landslides pose substantial threats and overthe years have caused severe damages in many countries suchas Brazil, Italy, Japan, Malaysia, Hong Kong, and mainlandChina (Fukuoka 1980; Brand 1984; Wolle and Hachich 1989;Malone and Pun 1997). The physical process of rainfall infil-tration into unsaturated soil slopes and the influence of infil-trated rainwater on soil suction and hence the slope instabilityhave been investigated by many researchers both in the lab-oratory (Fredlund and Rahardjo 1993) and in the field (Lim etal. 1996; Rahardjo et al. 1998). Numerical simulations of rain-fall infiltration have also been conducted (Anderson and Pope1984; Lam et al. 1987; Wilson 1997; Ng and Shi 1998). Asfor saturated soils, water flow through unsaturated soils is alsogoverned by Darcy’s law (Fredlund and Rahardjo 1993). How-ever, there are two major differences between the water flowsin saturated and unsaturated soils. First, the ability of the un-saturated soils to retain water varies with soil suction. Second,the coefficient of water permeability is not a constant in un-saturated soils but is a function of soil suction. Thus, it isessential to determine (1) the so-called soil-water characteristiccurve (SWCC) that defines the relationship between the soilsuction and either the water content or the degree of saturation;and (2) the water permeability function that varies with soilsuction for simulating transient seepage in unsaturated soilslopes. Currently, it is a common practice to derive the waterpermeability function from a measured saturated water per-meability and a drying SWCC using the procedures estab-lished by Fredlund and Xing (1994) and Fredlund et al. (1994).

The soil-water characteristic of a soil is conventionally mea-sured by means of a pressure plate extractor in which anyvertical or confining stress is not applied and volume changeof the soil specimen is assumed to be zero. In the field, thesoil usually is subjected to a certain stress. Although it is the-

1Assoc. Prof., Dept. of Civ. Engrg., Hong Kong Univ. of Sci. andTechnol., Clearwater Bay, Kowloon, Hong Kong.

2M.Phil. Student. Dept. of Civ. Engrg., Hong Kong Univ. of Sci. andTechnol., Clearwater Bay, Kowloon, Hong Kong.

Note. Discussion open until July 1, 2000. To extend the closing dateone month, a written request must be filed with the ASCE Manager ofJournals. The manuscript for this paper was submitted for review andpossible publication on March 10, 1999. This paper is part of the Journalof Geotechnical and Geoenvironmental Engineering, Vol. 126, No. 2,February, 2000. qASCE, ISSN 1090-0241/00/0002-0157–0166/$8.00 1$.50 per page. Paper No. 20406.

JOURNAL OF GEOTECHNICA

J. Geotech. Geoenviron. E

oretically recognized that the stress state of a soil has someinfluence on SWCC theoretically (Fredlund and Rahardjo1993), few experimental results can be found in the literature.Some exceptions are perhaps the publications by Vanapalli etal. (1996, 1998, 1999), who studied the influence of the totalstress state on the SWCC of a compacted fine-grained soilindirectly. The soil specimens were first loaded and then un-loaded using a conventional consolidation apparatus to createa known stress history or stress state in the specimens. Sub-sequently, the SWCCs of the preloaded specimens were de-termined using a traditional pressure plate apparatus, in whichthe change of water content due to the variation of soil suctionwas measured under almost zero-applied net normal stress s2 ua. It was found that the SWCCs are significantly influencedby the stress state for specimens compacted at initial watercontents dry of optimum.

Although the total net normal stress on the soil elements inan unsaturated soil slope is seldom altered, the stress state ateach element is different. This may affect the soil-water char-acteristic of these elements (i.e., the storage capacity whensubjected to various soil suctions during rainfall infiltration).To correctly predict pore-water pressure distributions in andthe slope stability of an unsaturated soil slope, it is thus es-sential to investigate the influence of stress state on SWCCs.For transient flows and slope stability problems, osmotic suc-tion is normally not very important and therefore ignored. Soilsuction is generally referred to as matric suction only.

In this paper, the influence of the stress state on the SWCCof an ‘‘undisturbed’’ or natural, completely decomposed vol-canic (CDV) soil is studied in the laboratory by using a newlymodified volumetric pressure plate extractor in which the totalnet normal stress can be controlled one-dimensionally and ax-ial deformation is measured. Together with measured saturatedwater permeability under some appropriate effective stressconditions using a triaxial apparatus, the measured stress-de-pendent soil-water characteristic curves (SDSWCCs) are thenused as input hydraulic parameters for exploring their influ-ence on soil suction distributions in and the stability of anunsaturated soil slope subjected to various rainfall conditions.

EQUIPMENT DESIGN

An apparatus for measuring SDSWCCs of unsaturated soilsunder K0 stress conditions was developed by modifying a con-ventional volumetric pressure plate extractor. Fig. 1 shows an

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FIG. 1. Components of Newly Modified Volumetric Pressure Plate Extractor

FIG. 2. Assembled Volumetric Pressure Plate Extractor

assemblage of the newly developed apparatus. An experi-mental setup is shown in Fig. 2 together with a schematicdiagram of the apparatus illustrated in Fig. 3.

An oedometer ring equipped with a high air-entry ceramicplate at its base is located inside an airtight chamber. Its rigidwall is used to maintain the K0 stress conditions. Vertical stresss is applied through a loading frame to a soil specimen insidethe oedometer ring, which has a diameter of 70 mm and aheight of 20 mm. Dead weights via a loading piston areadopted to provide the required vertical force. The airtightnessof the chamber is maintained using some rubber O-rings atopenings. To eliminate the error due to side friction betweenthe loading piston and the O-ring, a load cell is attached nearthe end of the piston inside the airtight chamber for determin-ing the actual vertical load applied to a soil specimen. Because

158 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGI


the radial deformation is zero for the K0 stress condition, thetotal volume change of the specimen is measured from thevertical displacement of the soil specimen using a dial gauge.An assumption of zero volume change is no longer requiredin this apparatus.

Similar to the conventional volumetric pressure plate ex-tractor, the pore-air pressure ua is controlled through a coarseporous stone together with a coarse geotextile located at thetop of the specimen. The pore-water pressure uw is controlledat the atmospheric pressure through the high air-entry ceramicplate mounted at the base of the specimen. The high air-entryceramic plate will remain saturated if applied air pressure doesnot exceed the air entry value of the plate (200 kPa). By usingthe axis-translation technique (Hilf 1956), the soil suction im-posed on the soil specimen will be the difference between theapplied air and pore-water pressures called matric suction ua

2 uw. In addition, some attachments are employed for the pur-pose of studying the hysteresis of the SWCCs associated withthe drying and wetting of the soil (Fig. 3). They consist of avapor saturator, air trap, ballast tube, and burette. The vaporsaturator is used to saturate the in-flow air to the airtight cham-ber to prevent the soil from drying by evaporation. The airtrap is attached to collect air that may diffuse through the highair-entry disk. The ballast tube serves as a horizontal storagefor water flowing in or out of the soil specimen. The buretteis used to store or supply water and to measure the watervolume change in the soil specimen.

LABORATORY MEASUREMENTS OFSOIL-WATER CHARACTERISTICS

Descriptions of Soil Specimens

The soil used in this study is a CDV tuff. Soil specimenswere obtained from an undisturbed 200 3 200 3 200 mm3

block sample excavated from a slope in Shatin, Hong Kong.Based on Geoguide 3 (Guide 1988), the sample can be de-scribed as a firm, moist, orangish brown, slightly sandy silt/clay with low plasticity. Table 1 summarizes some index prop-erties of the soil.

Testing Program and Procedures

A conventional volumetric pressure plate extractor and amodified one were used together to determine the SWCC andthe SDSWCC of the CDV, respectively. The net normal stresslevels considered in the modified volumetric pressure plate

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FIG. 3. Schematic Diagram of Modified 1D Volumetric Pressure Plate Extractor

TABLE 1. Index Properties of CDV (Sandy Silt/Clay)

Property(1)

Value(2)

Specific gravity (Mg/m3) 2.62Maximum dry density (kg/m3) 1,603Optimum moisture content (%) 22Initial moisture content (%) 30Gravel content (%) 4.9Sand content (%) 20.1Silt content (%) 36.6Clay content (%) 37.1Coefficient of curvature Cc 1.057Coefficient of uniformity Cu 319.9Liquid limit (%) 55.4Plastic limit (%) 33.4Plasticity index (%) 22

extractor are 40 and 80 kPa, which are appropriate for manyrelatively shallow slope failures in Hong Kong.

Three undisturbed or natural specimens (70 mm in diameterand 20 mm in height) were directly cut from the block sampleinto three oedometer rings. The specimens were submerged indeaired water inside a desiccator subjected to a small vacuumfor about 24 h for saturation. One of the specimens was thenplaced in the conventional volumetric pressure plate extractorto measure its SWCC with zero-applied stress (CDV-N1). Theremaining two specimens were used to determine theSDSWCCs with 40-kPa (CDV-N2) and 80-kPa (CDV-N3) ver-tically applied net normal stresses under K0 conditions. Thesetwo specimens were first loaded to 40- and 80-kPa applied netnormal stresses, respectively, in oedometers with free drainageat the top and bottom for 24 h for preconsolidation purposes,so that any change of the water contents due to applied netnormal and soil suction can be measured separately. They werethen removed from the oedometers and placed in the modifiedvolumetric pressure plate extractors to have their SDSWCCsmeasured under a predetermined stress. The required stressapplied to each specimen was maintained throughout the tests.

To determine the drying path of the SWCC, the specimenwas subjected to an increasing value of matric suction. As the



matric suction increased, water was expelled from the soilspecimen into the ballast tube. The volume of water expelledwas measured to determine the volumetric water content atequilibrium. Each matric suction value was maintained untilthe equilibrium condition was reached. After reaching 100- or200-kPa suction, a wetting process was then started by sub-jecting the soil to a decreasing value of matric suction, andwater in the ballast tube was absorbed by the soil specimen.A complete drying and wetting cycle was imposed on eachspecimen during the tests. Vertical displacement of the soilspecimen was measured during the tests. A correction due tothe deformation of the loading piston was also applied. At theend of the test, each soil specimen was oven-dried at 457C todetermine its water content. The volumetric water contents atvarious matric suctions were then determined from the finalwater content. Volumetric deformation was determined directlyfrom the readings taken by the dial gauge.

INTERPRETATIONS OF EXPERIMENTAL RESULTS

Verification of No Volume Change Assumption

Conventionally, SWCCs are determined using a pressureplate extractor with the assumption that no volume changetakes place throughout the test. This assumption is verifiedusing the newly modified apparatus by comparing the mea-sured SDSWCCs with and without considering volumechanges. For clarity, only the test results from the CDV-N2specimen are shown in Fig. 4. Under the net normal stress of40 kPa, there is no significant difference between the dryingpaths with and without volume change corrections until thematric suction reaches 200 kPa. The traditional method of in-terpretation by neglecting any volume reduction clearly un-derpredicts the volumetric water content presented in the soilspecimen. During the wetting process, the difference betweenthe two wetting paths does not stay constant, indicating thatsome volume changes took place throughout the test. Similartest results were also obtained from CDV-N3. Thus, volumechange corrections are applied whenever possible in this paper.


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FIG. 4. Comparison of SDSWCCs with and without Volume Change Considered for CDV-N2 Specimen

FIG. 5. Effects of Stress State on SWCCs

Influence of Stress State on Measurement of SWCCs

By using both the conventional and the modified volumetricpressure extractors, SWCC and SDSWCCs are measured andcompared in Fig. 5. At the beginning of the tests under zerosuction, soil specimens loaded to a higher net normal stressexhibit a lower initial volumetric water content. This is con-sistent with the elastic theoretical calculations proposed byFredlund and Rahardjo (1993) that a reduction in volumetricwater content can be caused either by an applied load undera constant soil suction or a change of soil suction under aconstant applied load. As the matric suction increases, the vol-umetric water content of all specimens decreases but at dif-ferent rates. The higher the applied load on the specimen, thelower the rate of reduction in volumetric water content. Thepoint where the volumetric water content starts to decreasesignificantly indicates the air-entry value of the specimen (i.e.,the point where the soil gives up water with increasing soilsuction). Fig. 5 shows there is a general tendency for the soilspecimen subjected to higher stress to possess a larger air-entryvalue. This is probably caused by the presence of a smalleraverage pore size distribution in the soil specimen under the

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J. Geotech. Geoenviron.

TABLE 2. Measured Ranges of Air-Entry Values for CDV(Sandy Silt/Clay)

Sample identity(1)

Applied stress(kPa)

(2)

Estimated air-entry value(kPa)a

(3)

CDV-N1 0 0.8–1.5CDV-N2 40 2–5CDV-N3 80 6–20

aEstimation procedures based on Vanapalli et al. (1999).

higher applied load. Following the procedures proposed byVanapalli et al. (1999), the ranges of the air-entry values es-timated from each specimen are given in Table 2.

Upon the completion of the drying phase, the tests werecontinued with the wetting process. For a smaller applied load,the volumetric water content increases more rapidly than thatfrom a specimen subjected to higher stress. At the end of thetests, all three wetting curves return only to positions lowerthan their original positions. There is a marked hysteresis be-tween the drying and wetting curves for all soil specimens,

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mainly because of the different contact angles at the recedingsoil-water interface during drying and at the advancing soil-water interface during wetting. The size of the hysteresis loopsseems to be independent of the applied stress, for the range ofthe net normal stresses considered, except for the one deter-mined from the conventional volumetric pressure plate inwhich volume change corrections cannot be made.

NUMERICAL SIMULATIONS

To investigate the influence of SDSWCCs on the predictionsof pore-water pressure distributions in unsaturated soil slopesand their stability, a series of finite-element transient seepageand limit-equilibrium analyses are carried out using SEEP/Wand SLOPE/W (SEEP/W 1998), respectively. A typical steepunsaturated soil cut slope in Hong Kong is selected for illus-trative purposes. The computed results from the transient seep-age analyses are then used as input parameters for a subse-quent limit-equilibrium analysis of the stability of the slope.

Transient Water Flow in Unsaturated Soils

Water flow through unsaturated soils is governed by Darcy’slaw (Fredlund and Rahardjo 1993). This is the same as waterflow through saturated soils. The only difference is that thecoefficient of hydraulic conductivity depends on both void ra-tio and matric suction in the unsaturated soils. The governingpartial differential equation (Lam et al. 1987) for water flowthrough a 2D unsaturated soil element is given as follows:

h h uwk 1 k = m (1)x y wS D S D S D

x x y y t

where h = total hydraulic head; kx = hydraulic conductivity inthe x-direction; ky = hydraulic conductivity in the y-direction;mw = slope of a SWCC; and uw = pore-water pressure.

In this paper, the soil is assumed to be isotropic (i.e., kx isequal to ky) in the transient seepage analyses using a computerprogram called SEEP/W (SEEP/W 1998). This is an uncoupledprogram in which any deformation of the soil is ignored.

Shear Strength for Saturated and Unsaturated Soils

Slope instability may be initiated by a reduction in the shearstrength of a soil. The shear strength is related to the stress



TABLE 3. Input Parameters for Predicting Permeability Func-tions

Sample identity(1)

Appliedstress(kPa)

(2)a

(3)n

(4)m(5)

ks

(m/s)a

(6)

CDV-N1 (drying) 0 3.5392 0.8726 0.2726 3.01 3 1026

CDV-N1 (wetting) 0 1.4636 1.0112 0.2329 3.01 3 1026

CDV-N2 (wetting) 40 17.8684 0.6815 0.4492 2.88 3 1026

CDV-N3 (wetting) 80 18.2019 0.5225 0.3301 1.17 3 1026

aMeasured by Ng and Pang (1998).

state in the soil. For limit-equilibrium analysis of a slope, theshear strength of the soil can be simplified and represented bya Mohr-Coulomb failure criterion proposed by Fredlund et al.(1978) as follows:

bt = c 9 1 (s 2 u )tan f9 1 (u 2 u )tan f (2)a a w

where t = shear strength; c9 = effective cohesion; f9 = angleof friction; and fb = angle defining the increase in shearstrength for an increase in matric suction.

The shear strength of an unsaturated soil is governed bytwo stress state variables: net normal stress s 2 ua and matricsuction ua 2 uw. For saturated soils, the stress state variable iseffective stress s 2 uw, as ua is equal to uw. In the slopestability analysis using SLOPE/W, (2) is adopted.

Input Parameters and Analysis Procedures forTransient Seepage Analyses

Because infiltration of rainwater into the soil slope is a wet-ting process, the measured wetting SWCC (CDV-N1) andSDSWCCs (CDV-N2 and N3) are adopted for the transientseepage analyses. In addition, a water permeability functionthat varies with soil suction is required. For comparison, aconventional transient analysis using a drying path of theSWCC (CDV-N1) under zero net normal stress is also in-cluded.

By using the measured saturated water permeability ks

of the soil in a triaxial apparatus under appropriate stressconditions (Ng and Pang 1998), the selected SWCC andSDSWCCs are fitted by a highly nonlinear equation, as pro-

FIG. 6. Permeability Functions Computed from Measured Soil-Water Characteristics


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FIG. 7. Finite-Element Mesh for Slope

posed by Fredlund and Xing (1994) for obtaining a permea-bility function that varies with matric suction. Details ofthe proposed nonlinear equation are given in Appendix I. Theinput parameters for predicting the permeability functionsare summarized in Table 3. Fig. 6 shows the permeabilityfunctions computed from the selected curves. As expected, thesoil specimen loaded to a higher net normal stress has alower permeability function, because the applied net normalstress led to a smaller pore size distribution inside the soilspecimen.

For investigating the effects of SDSWCC on pore-water pressure distributions in an unsaturated soil slope duringrainstorms, a finite-element mesh of a typical cut slope of8.6m in height inclined 557 to the horizontal in Hong Kongis created and shown in Fig. 7. This cut slope is locatedon a natural hillside. The entire soil mass in the finite-element mesh is idealized into three different soil layers ac-cording to their approximate stress states so that the measuredSWCC and SDSWCCs and their corresponding water perme-ability functions can be specified. It is recognized thatthe current method of specifications greatly simplifiesthe actual complexity of the problem. However, computed re-sults from the current simplified analyses are sufficient to re-veal the important role of SDSWCC in any transient seepageanalysis.

To illustrate the influence of the SDSWCCs on pore-waterpressure distributions, two series of transient seepage analysesare conducted. In the first series of analyses, all soil layers areassumed to have the same drying SWCCs and their corre-sponding water permeability functions. This series is a con-ventional approach. In the second series of analyses, differenthydraulic properties are specified in each soil layer. The wet-ting SWCC under 0 kPa (CDV-N1) and SDSWCCs under 40kPa (CDV-N2) and 80 kPa (CDV-N3) applied net normalstresses and their corresponding permeability functions are

162 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN


TABLE 4. Summary of Numerical Simulations Conducted

Seriesnumber

(1)Key hydraulic parameter

(2)

Type ofanalysis

(3)

Rainfallinfiltration(mm/day)

(4)Duration

(5)

1 Drying SWCC (conventional) Steady state 10.8 —1 Drying SWCC (conventional) Transient 236.4 24 h1 Drying SWCC (conventional) Transient 49.2 7 days2 Wetting SWCC and SDSWCC Steady state 10.8 —2 Wetting SWCC and SDSWCC Transient 236.4 24 h2 Wetting SWCC and SDSWCC Transient 49.2 7 days

specified, respectively, for the first, second, and third soil lay-ers as shown in Fig. 7.

The initial ground-water conditions for each series oftransient seepage analyses are established by conductingtwo steady-state analyses, in which a very small rainfallwith an intensity of 0.001 mm/day is applied on the top bound-ary surface together with a constant hydraulic head 15 mabove the principal datum (15 mPD or sea level) specifiedon the left boundary. The bottom boundary is assumed tobe impermeable, and no flux is specified along the rightboundary.

For the subsequent transient analyses, two rainfall patternswith an average intensity of 394 and 82 mm/day are appliedon the top boundary surface in both series of analyses tosimulate a short and intensive 24-h rainfall infiltration anda prolonged 7-day rainfall infiltration, respectively. Therainfall intensities adopted are based on the actual 10-yearreturn period spanning from 1980 to 1990 (Lam andLeung 1995). In this paper, it is assumed that the rate of in-filtration is equal to 60% of the rainfall intensity to simulatean average of 40% surface runoff in Hong Kong (Tung et al.1999). The numerical simulations conducted are summarizedin Table 4.

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Input Parameters and Analysis Procedures for SlopeStability Analyses

After obtaining the pore-water pressure distributions fromthe transient seepage analyses, limit-equilibrium analyses arethen carried out to determine the factor of safety (FOS) of thecut slope. For estimating the FOS using Bishop’s simplifiedmethod, some basic mechanical soil parameters are needed. Inthe limit-equilibrium analyses, the shear strength of the soil isassumed to be governed by the extended Mohr-Coulomb fail-ure criterion [i.e., (2)]. The shear-strength parameters includean effective cohesion c9 of 2 kPa, an angle of friction f9 of287, and an angle indicating the rate of increase in shearstrength relative to the matric suction fb, which is equalto 147.

INFLUENCES OF SDSWCC ON PORE-WATERPRESSURE DISTRIBUTIONS

Figs. 8–10 show the computed distributions of pore-waterpressure varying with depth at sections A-A, B-B, and C-C ofthe finite-element mesh (shown in Fig. 7), respectively. It isclear that there is a substantial difference between the initial



pore-water pressure distributions computed using the conven-tional drying SWCCs and the unconventional wetting SWCCand SDSWCCs in the steady-state analyses. The conventionalanalysis predicts a significantly higher soil suction profile thanthat computed by the unconventional analysis, because the soilin the former analysis, in comparison with the soil in the latteranalysis, has a lower air-entry value and a faster rate of chang-ing volumetric water content as values of soil suction increase(Fig. 5) and a higher water permeability function (Fig. 6). Inother words, the soil under the applied stress has a strongercapability of retaining moisture for a given soil suction be-cause of the presence of a smaller pore size distribution, asillustrated by a flatter SWCC (Fig. 5). The computed resultshighlight the importance of considering stress effects and dry-ing-wetting history on SWCCs.

During the short but highly intensive rainfall (i.e., 236.4mm/day or 2.74 3 1026 m/s for 24 h), the pore-water pressureresponses at the three sections are similar in both the conven-tional and unconventional transient analyses. Only the soil suc-tions in the top 1–2-m of the soil are destroyed irrespectiveof the magnitude of their initial values. A relatively shallowadvancing ‘‘wetting front’’ (Lumb 1975) is developed, as most

FIG. 8. Pore-Water Pressure Distributions along Section A-A under Various Rainfall Conditions

FIG. 9. Pore-Water Pressure Distributions along Section B-B under Various Rainfall Conditions


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FIG. 10. Pore-Water Pressure Distributions along Section C-C under Various Rainfall Conditions

of the rainfall cannot infiltrate into the soil because of rela-tively low water permeability with respect to rainfall infiltra-tion at high initial values of soil suction. On the contrary, thepore-water pressure distributions predicted by the conventionaland unconventional analyses are completely different duringthe 7-day low intensity prolonged rainfall (49.2 mm/day or5.69 3 1027 m/s for 7 days), particularly at sections A-A andB-B. Due to the relatively low initial values of suction presentin the soil, resulting in relatively high water permeability withrespect to rainfall infiltration, when the effects of the stressstate are considered, soil suctions at sections A-A and B-B(Fig. 8 and 9) are totally destroyed by the advancement of thewetting front to a depth of about 6 and 9 m from the groundsurface, respectively. At section C-C (Fig. 10), the advance-ment of the wetting front is limited by the initial higher suctionvalues than those at sections B-B and C-C. The less intensivebut prolonged 7-day rainfall facilitates the advancement of thewetting front into the soil to great depths and causes significantreduction in soil suction, which would have some devastatingeffects on slope stability. For the case of the initial values ofsoil suction predicted using conventional drying SWCC, rain-fall infiltration is hindered as a result of relatively low waterpermeability due to the presence of high soil suction.

INFLUENCES OF SDSWCC ON SLOPE STABILITY

By using the computed pore-water pressure distributions inthe transient flow analyses, limit-equilibrium analyses are per-formed on four selected noncircular slip surfaces, which passthrough the toe of the slope (Fig. 11). It should be noted thatthese selected slip surfaces may not guarantee the minimumFOS. They were selected only for illustrating the influence ofSDSWCCs on the FOS of some possible slips. The actual crit-ical slip surfaces may be somewhat different.

Fig. 12 shows the variations of FOSs with elapsed time forthe four selected slip surfaces during the 7-day rainfall. It canbe seen that the limit-equilibrium analyses, which adopted thepore-water pressures that were computed by using the con-ventional drying SWCCs, predict substantial higher initialFOSs at all four slip surfaces than those obtained from theanalyses using the unconventional wetting SDSWCCs. This isattributed to the significant difference in the computed pore-water pressure distributions (Figs. 8–10) with and withoutconsidering the effects of the stress state and drying-wettinghistory. This implies that the traditional analyses using the con-ventional drying SWCCs may lead to unconservative designs.

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FIG. 11. Slip Surfaces Considered in Slope Stability Analyses

Due to the presence of higher initial suction at shallowdepths, the shallower the slip surface, the larger the initialFOS. As the time elapses, the FOS decreases but at differentrates. For the shallow slips (S1 and S2), the fall in the FOSsis substantial when the effects of the stress state are included.At the end of rainfall, the FOS increases with depth, opposedto the initial safety conditions.

CONCLUSIONS

The SWCC is a measure of the water storage capacity ofthe soil for a given soil suction. This is an essential hydraulicproperty required for analyzing transient seepage in unsatu-rated soils. Traditionally, the SWCCs are determined in thelaboratory using a pressure plate apparatus in which any ver-tical or confining stress cannot be applied. It is theoreticallyrecognized that stress state should have some influence on soil-water characteristics of soils. To investigate this influence, anew stress controllable volumetric pressure plate apparatus hasbeen developed. Effects of K0 stress conditions on the soil-water characteristic on an undisturbed or natural CDV soilwere studied in the laboratory. Subsequently, the measuredSDSWCCs were adopted to derive water permeability func-

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FIG. 12. FOSs with Respect to Time from Beginning of 7-Day Rainfall

tions for transient seepage and limit-equilibrium analyses of atypical unsaturated cut slope in Hong Kong under various rain-fall conditions. Based on the experimental and the simplifiednumerical studies, the following conclusions can be drawn:

• Under zero suction, soil specimens loaded to a higher netnormal stress exhibit a lower initial volumetric water con-tent. There is a tendency to change the volumetric watercontent at a slower rate as values of suction increase forthe soil loaded to a higher stress.

• There is a general and consistent trend for a soil specimento possess a larger air-entry value when it is subjected toa higher stress. This is probably attributed to the presenceof smaller interconnected pores in the soil specimen underhigher applied load.

• There is a marked hysteresis between the drying and wet-ting curves for all soil specimens tested. The size of thehysteresis loops seems to be independent of the range ofthe net normal stresses considered, except for the one de-termined by the conventional volumetric pressure plate inwhich volume change corrections cannot be made.

• Numerical analyses using the measured wettingSDSWCCs and their derived water permeability functionspredict substantially higher (less negative) initial steady-state pore-water pressure distributions with depth thanthose computed by using the conventional dryingSWCCs. These initial high (less negative) steady-statepore-water pressure distributions with depth leading tohigher water permeability in the ground facilitate rainfallinfiltration, which destroys soil suction to a great depthby an advancing wetting front. This results in a substan-tially lower FOS during a prolonged low intensity rainfall.On the contrary, the numerical analyses suggest that onlythe soil suction at the top 1–2 m of the soil would bedestroyed under highly intensive but short duration rain-falls, irrespective of whether the stress effects on SWCCand the drying-wetting history are considered or not.

• Based on the current experimental measurements and thesimplified numerical investigations, the stress state andthe drying-wetting history have a substantial influence onthe soil-water characteristics of unsaturated soils. Duringa prolonged rainfall, analyses using wetting SDSWCCswould predict adverse pore-water pressure distributionswith depth and lower FOSs than those from the conven-

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tional analyses using drying SWCCs. The wettingSDSWCCs should therefore be considered for better andsafer estimations of the FOS for unsaturated soil slopes.

APPENDIX I. DERIVATION OF WATERPERMEABILITY FUNCTIONS

The general equation proposed by Fredlund and Xing(1994) to fit the experimental results of the SWCC is given asfollows:

usu = C(c) (3)w F Ga m{ln[e 1 (c/a ]}

where a is approximately the air-entry value in kPa; e = naturalnumber (2.718); n = parameter that controls the slope at theinflection point in the SWCC; m = parameter that is related tothe residual water content; uw = volumetric water content; us

= saturated volumetric water content; c = soil suction (kPa);and

cln 1 1S DCrH JC(c) = 1 2

ln(1 1 1,000,000/C )r

where Cr = constant related to the soil suction correspondingto the residual water content.

With the curve-fitted SWCCs and SDSWCCs from the ex-perimental data using (3), with the help of a computer programcalled SoilVision (SoilVision 1997), the permeability functionfor each characteristic curve can be derived from the measuredcoefficient of saturated water permeability using the proce-dures proposed by Fredlund et al. (1994). The required coef-ficients of saturated water permeability of this soil were mea-sured in a triaxial apparatus under various effective stressconditions (Ng and Pang 1998).

The equation for computing the permeability function pro-posed by Fredlund et al. (1994) is given as follows:

b yu(e ) 2 u(c) yu9(e ) dyE yeln(c)

k(c) = k (4)s byu(e ) 2 us yu9(e ) dyE yeln(c )ave

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where b = ln(1,000,000); ks = saturated permeability (m/s); y= dummy variable of integration representing the logarithm ofsuction; and u9 = derivative of uw. The derived permeabilityfunctions are presented in Fig. 7. As expected, the water per-meability of the soil specimen decreases as the applied stressincreases.

APPENDIX II. REFERENCES

Anderson, M. G., and Pope, R. G. (1984). ‘‘The incorporation of soilwater physics models into geotechnical studies of landslide behavior.’’Proc., 4th Int. Symp. on Landslides, Vol. 4, 349–353.

Brand, E. W. (1984). ‘‘Landslides in south Asia: A state-of-art report.’’Proc., 4th Int. Symp. on Landslides, Vol. 1, 17–59.

Fredlund, D. G., Morgenstern, N. R., and Widger, R. A. (1978). ‘‘Theshear strength of unsaturated soil.’’ Can. Geotech. J., Ottawa, 15, 313–321.

Fredlund, D. G., and Rahardjo, H. (1993). Soil mechanics for unsaturatedsoils. Wiley, New York.

Fredlund, D. G., and Xing, A. (1994). ‘‘Equations for the soil-water char-acteristic curve.’’ Can. Geotech. J., Ottawa, 31, 521–532.

Fredlund, D. G., Xing, A., and Huang, S. (1994). ‘‘Predicting the per-meability functions for unsaturated soils using the soil-water charac-teristic curve.’’ Can. Geotech. J., Ottawa, 31, 533–546.

Fukuoka, M. (1980). ‘‘Landslides associated with rainfall.’’ Geotech.Engrg. J., 11, 1–29.

Guide to rock and soil descriptions (GEOGUIDE). (1998). GeotechnicalControl Office, Public Works Department of Hong Kong, Hong Kong.

Hilf, J. W. (1956). ‘‘An investigation of pore-water pressure in compactedcohesive soils,’’ PhD dissertation, Tech. Memo. No. 654, U.S. Dept.of the Interior, Bureau of Reclamation, Design and Construction Di-vision, Denver.

Lam, C. C., and Leung, Y. K. (1995). ‘‘Extreme rainfall statistics anddesign rainstorm profiles at selected locations in Hong Kong.’’ Tech.Note No. 86. Royal Observatory, Hong Kong.

Lam, L., Fredlund, D. G., and Barbour, S. L. (1987). ‘‘Transient seepagemodel for saturated-unsaturated soil systems: A geotechnical engineer-ing approach.’’ Can. Geotechn. J., Ottawa, 24, 565–580.

Lim, T. T., Rahardjo, H., Chang, M. F., and Fredlund, D. G. (1996).‘‘Effect of rainfall on matric suctions in residual soil slope.’’ Can.Geotech. J., Ottawa, 33, 618–628.

Lumb, P. B. (1975). ‘‘Slope failures in Hong Kong.’’ Quarterly J. ofEngrg. Geol., 8, 31–65.

Malone, A. W., and Pun, W. K. (1997). ‘‘New engineering tools for land-slip risk control.’’ Proc., 2nd Int. Symp. on Struct. and Found. in Civ.Engrg., Hong Kong, C. K. Shen, J. S. Kuang, and C. W. W. Ng, eds.,1–27.

Ng, C. W. W., and Pang, Y. W. (1998). ‘‘Lai Ping road landslide inves-tigation—Specialist testing of unsaturated soils.’’ Tech. Rep., Geo-technical Engineering Office of the Hong Kong Special AdministrativeRegion, Hong Kong.

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Ng, C. W. W., and Shi, Q. (1998). ‘‘A numerical investigation of thestability of unsaturated soil slopes subjected to transient seepage.’’Comp. and Geotechnics, 22, 1–28.

Rahardjo, H., Leong, E. C., Gasmo, J. M., and Deutscher, M. S. (1998).‘‘Rainfall-induced slope failures in Singapore: Investigation and re-pairs.’’ Proc., 13th Southeast Asian Conf., Vol. 1, 147–152.

SEEP/W (Version 4) for finite element seepage analysis and SLOPE/Wfor slope stability analysis. (1998). Geo-slope International, Canada.

SoilVision (version 1.2). (1997). Soilvision Systems Ltd., Sask., Sas-kachewan, Canada.

Tung, Y. K., Ng, C. W. W., and Liu, J. K. (1999). ‘‘Lai Ping road landslideinvestigation—Three dimensional groundwater flow computation.’’Tech. Rep.—Part I, Geotechnical Engineering Office of the Hong KongSpecial Administrative Region, Hong Kong.

Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E., and Clifton, A. W. (1996).‘‘Model for the prediction of shear strength with respect to soil suc-tion.’’ Can. Geotech. J., Ottawa, 33, 379–392.

Vanapalli, S. K., Pufahl, D. E., and Fredlund, D. G. (1998). The effectof stress state on the soil-water characteristic behavior of a compactedsandy-clay till.’’ Proc., 51st Can. Geotech. Conf., 81–86.

Vanapalli, S. K., Pufahl, D. E., and Fredlund, D. G. (1999). ‘‘The effectof soil structure and stress history on the soil-water characteristics ofa compacted till.’’ Geotechnique, London, 49(2), 143–159.

Wilson, G. W. (1997). ‘‘Surface boundary flux modeling for unsaturatedsoils.’’ Unsaturated soil engineering practice, Geotech. Spec. Publ. No.68, ASCE, New York, 38–65.

Wolle, C. M., and Hachich, W. (1989). ‘‘Rain-induced landslides in south-eastern Brazil.’’ Proc., 12th Int. Conf. Soil Mech. and Found. Engrg.,Vol. 3, 1639–1644.

APPENDIX III. NOTATION

The following symbols are used in this paper:

c9 = effective cohesion;h = total hydraulic head;

K0 = lateral earth pressure coefficient at rest;kx = hydraulic conductivity in x-direction;ky = hydraulic conductivity in y-direction;

mw = slope of soil-water characteristic curve;ua = pore-air pressure;

(ua 2 uw) = matric suction or soil suction if osmotic suction isignored;

uw = pore-water pressure;s = total normal stress;

(s 2 ua) = net normal stress;t = shear strength;

f9 = angle of friction; andfb = angle defining increase in shear strength for increase

in matric suction.

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influence of stress state on soil-water characteristics and slope stability

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