failure of soil under water infiltration condition
TRANSCRIPT
Engineering Geology 181 (2014) 124–141
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Engineering Geology
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Failure of soil under water infiltration condition
Meen-Wah Gui a,⁎, Yong-Ming Wu b
a Dept. of Civil Engineering, National Taipei University of Technology, No 1, Sec 3, ZhongXiao E Rd., Taipei 10608, Taiwanb Formerly, Dept. of Civil Engineering, NTUT, No 1, Sec 3, ZhongXiao E Rd, Taipei 10608, Taiwan
⁎ Corresponding author. Tel.: +886 955154891; fax: +E-mail address: [email protected] (M.-W. Gui).
http://dx.doi.org/10.1016/j.enggeo.2014.07.0050013-7952/© 2014 Elsevier B.V. All rights reserved.
a b s t r a c t
a r t i c l e i n f oArticle history:Received 1 November 2013Received in revised form 1 April 2014Accepted 3 July 2014Available online 12 July 2014
Keywords:Rainfall-induced landslideWater-infiltrationLaboratory testShear strengthSuctionUnsaturated soil
To reduce andmitigate rainfall-induced landslide problems, there is a need to improve our understanding of thefailure mechanism of soil under water-infiltration condition. This study aimed at understanding the effect ofwater-infiltration on the transformation of shear stress and its eventual failure in unsaturated soil. The methodof study was via a series of advanced laboratory triaxial test of two specific types: (1) constant-suction shearingtest, and (2) shearing-infiltration test. The shearing-infiltration test results indicated that infiltration of waterreduced the matric suction of the soil by the generation of excess pore-water pressure; it however was notaccompanied by a reduction in shear strength, instead, the unsaturated soil failed under a constant shear stressapplied prior to the infiltration. Excessive deformation and the eventual softening of the soil were found to bethe main causes of water-infiltration induced failure.
886 227814518.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Rainfall has been recognized as one of the main causes of landslidesin many tropical countries. For example, Taiwan suffers from landslidesof various scales every year between the months of May and Octoberas a result of the four to five intense typhoons that strike the islandannually. According to studies conducted by the Public ConstructionCommission (Gui et al., 2008), there were about 1567 and 1718rainfall-induced roadside (excluding expressway) landslides inTaiwan in 2004 and 2005, respectively; and the cost of reconstructionwas roughly NTD3.53 billion in 2004 and NTD2.47 billion in 2005.When expressway landslides are included, the total number and costof reconstruction for the whole island every year is much greater thanthe above figures. It has been widely claimed that during rainfall,increased water content in the soil decreases the soil suction abovethe ground water table and, thus, the shear strength of the soil. Waterinfiltration can lower the shear strength to a value close to the averageshear stress along a potential failure surface and consequently trigger alandslide.
In many tropical regions the hot and humid weather coupled withhigh annual rainfall have resulted in rapidweathering of rock formationand development of a deep overburden of unsaturated residual soils(Han, 1997). Collins and Znidarcic (2004), Zhang et al. (2005), Huangand Yuin (2010), etc. have experimentally investigated the mechanism
of rainfall-induced slope failures. Lee et al. (2011) conducted two typesof instrumented laboratory tests, i.e. one-dimensional soil column andtwo-dimensional slopemodel tests, to examine the variations of suctionin an unsaturated soil under certain rainfall conditions. The triggeringphase of rainfall-induced landslides in coarse-grained soils was studiedby Sorbino and Nicotera (2013). They observed that landslides arefrequently related to rainfall events that significantly reduce matricsuction in the shallower soil layers. Godt et al. (2012) proposed anumerical framework for assessing the stability of infinite slopesunder transient variably saturated conditions; the framework includesprofiles of pressure head and volumetric water content combinedwith a general effective stress for slope stability analysis, whichcould provide a way to quantify stress changes due to rainfall andinfiltration relevant to shallow landslide initiation. Thus, it is importantto understand the evolution of soil shear stress changes due to waterinfiltration as this knowledge is not only indispensable for slope stabilityanalysis but some of the results may also be applicable to improve thecurrent design methodology and improve slope maintenance work.
The behavior of a soilwith a known initial state, a boundary conditionand a loading type because of any mechanical process, can be studiedexperimentally via the triaxial test (Terzaghi and Peck, 1967; Bishopand Henkel, 1969). Triaxial tests on unsaturated soils were usuallyconducted under various net normal stresses and matric suctions(see for example, Kim and Kim, 2010). However, the stress pathfollowed by a soil element that undergoes water infiltration andsubsequent failure in a slope is seldom modeled in laboratory testing.It is important to perform tests following the appropriate field stresspath to characterize the failuremechanism of rain-induced slope failure
Fig. 1. (a) Particle size distribution; and (b) classification of the study soil.
125M.-W. Gui, Y.-M. Wu / Engineering Geology 181 (2014) 124–141
as well as to determine the strength envelope of soil. Melinda et al.(2004) investigated the strength and deformation characteristics of are-compacted residual soil during infiltration using twomodified directshear apparatuses. They suggested that slope failure was associated tothe reduction of suction in the soil; however, the tests were conductedin a shear box device that had a pre-determined failure plane, which isthe interface of the two halves of the shear box. To verify the volumechange theory for unsaturated soil, Meilani et al. (2005) conductedtriaxial tests to study the pore-water pressure and water volumechange of re-compacted coarse kaolin under infiltration conditions.Both studies used re-compacted soils and, to guarantee failure, thesetests were conducted at a very high stress level (i.e. about 85–90%of the soil's shear strength). The shear strength and the response ofthe pore-water pressure in real intact soil, which has its in situmicro-structure unaltered, under water-infiltration process arehowever still unknown.
Detailed and fundamental studies of the evolution of shear stressdue to water infiltration of intact residual soil, which is commonlyfound in many tropical countries, have seldom been performed inlaboratory testing, and it has not been verified whether the shearstrength under a water infiltration process was similar to the shearstrength under a constant suction condition. The main aim of thisstudy is to evaluate the mechanical behavior and failure mechanismof residual soil as a result of water infiltration via a series of laboratorytriaxial tests. The evolution of the shear stress changes in the soil duringthe infiltration process is also studied. In addition, the study tries to offeran answer to the question that is often raised by engineers:
Since most of the unsaturated soil slopes were designed using theshear strength parameters of saturated soil, why has failure stilloccurred on many unsaturated soil slopes especially after a periodof rainfall even though their remaining shear strength was stillhigher than that of the saturated soil slopes?
2. Material studied
The soil used in this study was obtained from Linkou terrace, whichis situated in the northwest of Taiwan. The top formation of the terraceis a 5–15m thick brick-red lateritic soil (Chen and Yang, 1987; Chen andLiu, 1993; Bruce et al., 2006). The soil was the product of both chemicaland physical weathering, which involved varying degrees of wind, anaverage annual temperature of 20–25 °C and aminimumannual rainfallof 750 mm, on cobbles.
The study site was located at the center of the terrace with anelevation of about 251 m above sea level with a groundwater tableat about 10 m or deeper below the ground surface. Soil specimensof 5.6 cm diameter by 30 cm long were obtained from trial pits ofvarious depths. As groundwater table was not encountered at thesedepths, thus, the soil was in an unsaturated condition with an averagein situ degree of saturation of about 85%. The shear strength and thepermeability of unsaturated lateritic soil at nearby sites have beenstudied by Gui and Yu (2008) and Gui and Hsu (2009), respectively.In addition, the soil also showedhighpotential for shrinking and swellingdue to water content changes (Gui and Chu, 2005).
2.1. Soil physical properties
A series of soil physical property tests were conducted by Gui andWu (2011), and Wu (2011) to determine the soil water content(ASTM D2216-10, 2010), specific gravity (ASTM D854-10, 2010),particle size distribution (ASTM D422-63, 2002), liquid limit andplastic limit (ASTM D4318-10, 2010) of the study soil.
The initial water content of the soil ranged between 26.2% and30.6%; the average specific gravity was 2.718 with a standard deviationof 0.027; while the average void ratio was 0.889 with a standard
deviation of 0.042. The particle size distribution curves obtained areshown in Fig. 1a, which shows that the soil was composed of 12.2%sand, 86.8% silt and 1% clay; it thus has more than 50% of silt-sized par-ticles. Atterberg limits test was carried out on soil passing through sieveNo. 40. The liquid limit (LL) of the study soil ranged between 40.6% and47.7%, the plastic limit (PL) ranged between 24.6% and 32.4%; thus itsplasticity index (PI) ranged between 12.5% and 20.0% (Figure 1b). Ac-cording to the Unified Soil Classification System (USCS), the soil shouldbe classified as low plasticity clay/silt (CL/ML).
2.2. Soil water characteristic curve
Soil water characteristic curve (SWCC), also referred to as the soilmoisture retention curve, depicts the relationship between soilvolumetric water content and matric suction (Zhai and Rahardjo,2012). It is an important relationship that shows the ability of anunsaturated soil to retain water under various matric suctions and,thus, has a similar role as the consolidation curve of a saturated soilthat relates void ratio to effective stress (Fredlund and Rahardjo, 1993).A complete SWCC could be categorized into three suction ranges: lowsuction ranges between 0 kPa and 100 kPa; medium suction rangesbetween 100 kPa and 1500 kPa; and high suction ranges between1500 kPa and 1,000,000 kPa. The SWCC is commonly obtained usingthe pressure plate extractor (for low and medium suction ranges) andsalt solutionsmethod (for high suction range). In this study, the pressureplate extractor test was conducted in accordance with ASTM D6836-02(2007) and the salt solutions method was conducted in accordancewith ASTM D5298-03 (2003).
Fig. 2 shows the SWCC result of the study soil performed following adrying path on specimens of different void ratios via the pressure plateextractor and salt solutions method. The maximum matric suctionmeasured in the pressure plate extractor and the salt solutions method
126 M.-W. Gui, Y.-M. Wu / Engineering Geology 181 (2014) 124–141
was about 1200 kPa and 170,000 kPa, respectively. The vertically spreaddata at a particular matric suction were actually representing data atdifferent initial void ratios. According to Romero and Vaunat (2000),Karube and Kawai (2001), and Gallipoli et al. (2003), different degreesof saturation (in this case the water content) may occur at the samesuction because of the effect of different void ratios on the SWCC. Theinitial void ratio controls the water content but for each particularvoid ratio the SWCC was close to a smooth curve. The air-entry-value(AEV) of the study soil was found to range between 210 kPa and275 kPa; the average volumetric water content under saturationcondition θs was 47.5% while the average volumetric water contentunder residual condition θr was 1.9%. Gravimetric water content ω isrelated to the volumetric water content θw by ω = θw(1 + e) / Gs,where e andGs is the void ratio and specific gravity of the soil, respectively.
To mathematically model the SWCC, the empirical equation ofFredlund and Xing (1994) was fitted to the experimental data:
θw ¼ θs 1−ln 1þ ψ
ψr
� �
ln 1þ 106ψr
� �24
35 1
ln exp 1ð Þ þ ψaf
� �n f� �� �mf
2664
3775 ð1Þ
where θs is the saturated volumetric water content; θw is the volumetricwater content at a particular matric suction ψ; af is the fitting parameterclosely related to the air-entry value for the soil; nf is the fittingparameter related to the maximum slope of the curve; mf is thefitting parameter related to the curvature of the slope; and the lastfitting parameter, ψr, is related to the lower portion of the curve.
The equation of Fredlund and Xing (1994) forces the SWCC toconverge to zero volumetric water content when a matric suction of106 kPa is reached, seen in Fig. 2. The SWCC experimental data andthe fitted curve together with the corresponding fitting parameters,estimated using a nonlinear regression procedure, are also shown andcompared in Fig. 2.
2.3. In-situ suction
Filter paper test (Gardner, 1937)was conducted to obtain the in-situsuction of the study soil. The simple and inexpensive method has beenadopted successfully by Fawcett and Collis-George (1967), Hamblin(1981), Jiang et al. (2000), Leong et al. (2002) and others. Three stacksof Whatman No. 42 filter papers were placed between two-halvesof soil specimen inside an airtight container with a finite amount
Fig. 2. Laboratory SWCC and field s
of head-space for seven days to allow for the vapor pressure ofpore-water in the specimen, vapor pressure of pore water in the filterpaper, and partial vapor pressure ofwater in the air inside the containerto reach equilibrium (ASTM D5298-03, 2003). Once the filter paperreached equilibrium, the wet and dry masses of the paper were usedto derive the moisture content of the filter paper wf; the in-situ matricsuction ψ of the study soil was then estimated using the equationscalibrated by Leong et al. (2002):
logψ ¼ 2:909−0:0229wf for wf ¼ 47% ð2Þ
logψ ¼ 4:945−0:0673wf for wf b47%: ð3Þ
The values of the in-situ matric suction obtained for the study soilwere plotted and compared to the SWCC of the soil in Fig. 2. In general,the in-situ suctions of the study soil ranged between 40 and 90 kPa, onlytwo specimens had suction close to 170 kPa.
3. Element test setup, procedures and program
3.1. Test setup
The main method used to study the evolution of shear stressesinduced by water infiltration in a slope was via a series of advancedlaboratory element tests. The equipment used was an advanced triaxialapparatus suitable for unsaturated soil testing; it was essentially similarto the apparatus used for saturated soil, which included a triaxial cell, anaxial loading device, pore-air and pore-water pressure and volumemeasuring devices, and a computer program suitable for controllingtest sequences and recording test data. However, modification to thetriaxial pedestal for saturated soil testing had to be conducted prior toany specific triaxial test for unsaturated soil (FredlundandRahardjo, 1993).
The system used in this experiment (Figure 3) has been outlinedin Gui and Hsu (2009). Both the confining and back pressures wereprovided by two advanced digital water pressure/volume controllers(DPVCs),which have amaximumpressure of 2000 kPa and amaximumvolume of 1000 cm3. The advanced DPVC also has a minimum waterinjection rate of 0.001 mm3/s. The air pressure was provided by an airDPVC that has a maximum pressure of 2000 kPa and a maximumvolume of 2000 cm3. The pressure resolution of the DPVCs was0.48 kPa; while the volume resolution of the water DPVCs and theair DPVC was 1 cm3 and 2 cm3, respectively. The system adopted a
uction values of the study soil.
High-air entry disk
Soil specimen
De-aired Water
“O” ring
Cell pressure/volume controller
Flushing linesBack water
pressure/waterinjection
lines
Cell pressure line
Air
pres
sure
line
Integrated indicatorComputer with
Labview program
Pre
ssur
e/vo
lum
e co
ntro
llers
sig
nal l
ines
Air pressure/volume controller
Back pressure/volume controller
Servo motor
Load-cell
loading ram
Top waterpressure lines
Rubber membrane
Porous stone
Watercompartment
Note: Reaction frame not shown
Miniature PPT
Fig. 3. Advanced triaxial system used in this study.
127M.-W. Gui, Y.-M. Wu / Engineering Geology 181 (2014) 124–141
telescopic spiral ram and a server motor to replace the conventionalLVDT and axial loading device. The displacement rates of the telescopicspiral ram ranged between 0.00001 and 0.08333 mm/s. The load cellused was the Interface 1000 series loadcell with a capacity of 2.5 kNand a resolution of 0.0015 kN. A computer program, written usingLabview, was used to monitor and record the pore-water and pore-airpressures and to control the water injection rate throughout the test.
3.2. Test procedures
A series of triaxial shearing testswere performed on unsaturated soilelements that were first subjected to a prescribedmatric suction, whichwas higher than the field suction valuemeasured in the filter paper test.The test procedures used in this study can be broadly divided into threestages: (i) preparation of soil element; (ii) matric suction equalizationand consolidation of unsaturated soil element; and (iii) shearing ofsoil element.
Intact soil elements of about 112 mm in height were cut from the56 mm in diameter and 300 mm long samples that were retrievedfrom the trial pits using percussion sampler (Wu, 2011). The sampleswere not trimmed to the standard diameter of 50 mm because of theimpossibility of trimming the hard soil to obtain a smooth cylindricalsample. They were not sprayed either because spraying water wouldcause the soil elements to swell as the study soil had a very high swellingpotential (Gui and Chu, 2005).
Soil element was mounted on to the triaxial pedestal fitted with ahigh air-entry ceramic disk, which had been saturated by subjecting itto a cell pressure of 700 kPa in the triaxial cell. Air bubbles collected in
the water compartment of the pedestal were then flushed away viathe flushing line into the diffused air volume indicator (Agus et al.,2003). The soil element was then enclosed in a rubber membrane thathas a silicone rubber grommet located at mid-height using a 3-partsplit membrane stretcher. A miniature pore-water pressure transducerwas then inserted into the grommet housing and fastened usingtwo “O”-rings onto the rubber membrane to prevent water leakage.The disk in the miniature transducer was pre-saturated in a pressurechamber under a pressure of 700 kPa for 24 h before it was insertedinto the diaphragm end of the miniature transducer under water.The transducer was then subjected to several cycles of high waterpressure to dissolve any air trapped in the gap between the diskand the diaphragm, and the decreasing water pressure would forcemost of the undissolved air to flow out from the gap (Wong et al.,2001). The transducer was subsequently submerged in de-airedwater prior to its installation onto the specimen to prevent thedisk from drying out. Detailed description on the installation of theminiature pressure transducer onto soil element can be found inWong et al. (2001).
The loading cap was placed on top of the specimen and “O”-ringswere fitted around the membranes on the pedestal and the top cap.The Lucite cylinder of the triaxial cell was then installed and the cellfully filled with de-aired water. The loading piston made contact withthe top cap of the soil element at a pressure of about 3 kPa. Theconfining pressure, bottom pore-water pressure and air pressurewere then applied through the DPVCs. Matric suction was appliedto the soil element using the axis-translation technique (Hilf, 1956).The technique is conventionally used to apply matric suction (higher
Extended Mohr-Coulomb failure
envelope(ua-uw)
128 M.-W. Gui, Y.-M. Wu / Engineering Geology 181 (2014) 124–141
than the atmospheric pressure) to soil specimens in the laboratorywithout problem associated with cavitation (Richards, 1931; Hilf, 1956;Vanapalli et al., 2008). The technique basically translates the referenceorigin for the pore-water pressure from the standard atmosphericcondition to thefinal air pressure in the chamber (Vanapalli et al., 2008).
The soil element was isotropically consolidated in one stage to thedesired net confining stress (σ3 − ua) and matric suction (ua − uw)where σ3 is the applied confining pressure, and ua and uw representthe applied pore-air and pore-water pressures, respectively. To producemonotonic loading, the confining pressure, pore-water and pore-airpressures were increased gradually and simultaneously in steps of5 kPa, and at the same time the cell pressure was kept higher than thepore-water and pore-air pressures. During the matric equalization andconsolidation process, water drained out from the bottom pore-waterpressure line and the volume of water drained out was measured viathe DPVC connected to it. The matric equalization and consolidationprocesswas deemed completewhen therewas negligiblewater flowingout of the soil element; the soil element was thus in equilibrium at theapplied stress state. The stress states adopted in this study have beensummarized in Table 1.
3.3. Test program
To investigate the failure mechanism of lateritic soil due to waterinfiltration and to obtain the associated shear strength due to waterinfiltration a series of consolidated drained (CD) triaxial shearingtests and consolidated drained triaxial shearing-infiltration testswere carried out on unsaturated lateritic soil elements. For saturatedsoil element, the drained test was conducted by draining out thepore-water during the shearing process, whereas for unsaturatedsoil element, the drained test was conducted by allowing both thepore-air pressure and pore-water pressure to drain throughout thetest. Since there was no change in the pore-air and pore-water backpressures, the matric suction, (ua − uw), in the soil element remainedconstant throughout the test. Thus, the consolidated drained test isalso called the constant-suction test. In the shearing-infiltration test,soil element was first sheared to a shear stress level of 70% to 86% ofits shear strength, estimated from the corresponding constant-suctionshearing test; the shear stress was maintained and water was injecteduntil failure was reached.
3.3.1. Constant-suction shearing test programThe purpose of the constant-suction shearing test was to determine
the shear strength of the unsaturated lateritic soil. The shear strength atvarious stress states (σ− ua, ua− uw) is normally represented using theextended Mohr–Coulomb envelope (Figure 4), which can be obtainedfrom a series of constant-suction shearing tests on both the saturatedand unsaturated soil elements. The tests on the saturated soil elementsyielded the values of cohesion intercept c′ and the angle of friction ϕ′,while the tests on the unsaturated soil elements provided the value
Table 1Stress state of specimens selected for the study.
Net normal stress(σ3 − ua) (kPa)
Matric suction (ua − uw) (kPa)
0 40 100 200 300
Constant suction (CS) test
100 X X – X X200 X X X – –
400 X X – – X
Shearing-infiltration test
100 200 300
50 – – X –
100 – X X X400 – – X X
of ϕb, which is an indication of the rate of increase in shear strengthrelative to matric suction (ua − uw).
All the constant-suction shearing tests performed in this studywere single-staged tests. Soil elements obtained from the field hadan initial field suction at point O (Figure 5), which corresponded toan idealized field stress condition where they were subjected tosome suction value but at zero shear stress and zero net normal stress.All the unsaturated soil elements were first subjected to a matricsuction, which was 50 kPa higher than the final matric suction atwhich the soil element was to be tested (point A). Thereafter, the soilelement was consolidated and equilibrated to a particular net normalstress and a particular matric suction (path ABC). The path BC followedby the soil element was a wetting path since the final matric suctionwas brought from a higher (dryer) value to a lower (wetter) one. Thewetting path BC simulated the condition of a residual soil slope after arainy period where the soil above the groundwater table experienceda wetting process that caused the pore-water pressure to become “less”negative and hence a reduction in its matric suction occurred. For teston saturated soil element, the initially unsaturated soil element wasfirst brought to a saturated condition at zero net normal stress followingthe path OA′. After saturation, with a minimum B value of 0.92, the soilelement was then consolidated to a specific net normal stress followingpath A′B′ and then sheared to failure.
After the completion of the consolidation and matric equalizationprocess, the unsaturated soil element was sheared to failure followingpath CE. Wong et al. (2001) and Rahardjo et al. (2004) adopted adisplacement rate of 0.0009 mm/min, while Melinda et al. (2004)and Meilani et al. (2005) adopted a displacement shearing rate of0.004 mm/min and 0.00078 mm/min, respectively, in their shearingtests. In this study, all the soil elements were sheared under a constantaxial displacement rate of 0.0012 mm/min. Shearing began at point Cand failed at point E on the failure envelope (Figure 5). The air andwater pressures were maintained at a constant value (i.e. drainedcondition) throughout the test. Failure was defined as when a constantshear stress or at least 15% of the axial strain was attained.
3.3.2. Shearing-infiltration test programThe purpose of conducting the shearing-infiltration test was to
simulate and understand the failure mechanism of landslide inducedby water infiltration. There were two main stages in the shearing-infiltration test. The first stage of the test was to shear the soilelement under a constant suction to a pre-determined stress level.The second stage of the test was to infiltrate water from the base ofthe pedestal through the high air entry disk into the soil elementwhile maintaining the constant stress level on the specimen.
She
ar s
tres
s, τ
Net normal stress,(σ - ua)
Matric
sucti
on,
(ua-uw)f tan b
’
b
c’
c’
b
φ
φ
φ
φ
’φ
Fig. 4. Extended Mohr–Coulomb failure envelope.Drawn after Fredlund and Rahardjo (1993).
Net normal stress (σ-ua)
She
ar s
tres
s (τ
)
Mat
ric s
uctio
n
(ua-
u w)
A B
C
OFiel
d su
ctio
nD
E Shear strength
F Infil
tratio
n
Stress level(70~86% of CE)
Incr
easin
g
suct
ion
Consolidation
Reduc
ing
suct
ion
(wet
ting)
Shearing
A B
Fig. 5. Stress paths adopted in constant-suction shearing and shearing-infiltration tests.Modified after Melinda et al. (2004).
129M.-W. Gui, Y.-M. Wu / Engineering Geology 181 (2014) 124–141
Fig. 5 shows the stress path of the shearing-infiltration test, whichwas essentially similar to that of the constant-suction test, except thatthe soil elementwas not sheared to failure but to a predetermined stresslevel (point D in Figure 5). Subsequently, the soil elementwas subjectedto an infiltration process at point D whereby the matric suction wasreduced by increasing its water content, as represented by Path DFin Fig. 5. During the shearing-infiltration test, the drainage valvefor the pore-air remains open (i.e., under drained condition) whilethe drainage valve for the pore-water is closed (i.e., under undrainedcondition). Soil element eventually failed at point F under the waterinfiltration condition.
The shear stress level (Point D in Figure 5) maintained on thespecimen while the soil was being infiltrated with water was theone that ensured that the soil elementwould fail before total saturation(Han, 1997). To ensure failure at an unsaturated state, Melinda et al.(2004) sheared their specimens to a stress level of about 85–90% ofthe peak shear stress that was determined from the correspondingconstant-suction shearing test. Geoguide-7 (2008) recommended thatfor a ten-year return period rainfall, a slope should have a minimumfactor of safety of 1.4; while for the predicted worst groundwaterconditions, a slope in the consequence-to-life category 1 shouldhave a factor of safety of at least 1.1. Hence, to observe the failureof soil slope with different factors of safety, stress levels between 70and 86% were adopted in this study since the stress levels of 70% and86% corresponded to factors of safety of 1.43 and 1.16, respectively.
The infiltration processwas conducted under a constant shear stressand net normal stress. Under such circumstances the soil elementmightcreep. Creepmonitoringwas therefore conducted immediately after theshear stress reached the pre-determined stress level to observewhetherthere was any creep and to ensure that the soil elements, particularlythose under a high shear stress, did not exhibit any yielding before theinfiltration process; it thus ensured that the subsequent failure of thesoil element was solely due to water infiltration instead of creep(Melinda et al., 2004). During creep monitoring, the force actuatorwas programmed to maintain the pre-determined stress level whilethe DPVC was programmed to prevent the draining of water from andinto the soil specimen, i.e. an undrained condition of the water phasewas conducted. If there were any creep, the axial load would dropand in order to maintain the constant stress level, the ram of the forceactuator would move downward and exert a displacement (creep)on the soil element. In this study, creep monitoring was performedfor 6 h but the axial strain rate was found to be almost zero, indicatingthat creep was not present before the infiltration process.
The water infiltration process was started after the creep monitoring.Waterwas injected into the soil element using aDPVC to infusewater at a
constant rate through the water compartment located below the high airentry disk into the specimen. The rate of water infiltration was smallerthan the hydraulic conductivity of the high air entry disk. In addition,the rate was slow enough to allow the pore-water pressure to equalizein the soil element during the process of infiltration. This was assuredby comparing the reading of the back pore-water pressure to the readingof the miniature pressure transducer installed in the mid-height of thespecimen. After a few trials, a rate of 0.001mm3/swas found tobe suitablefor the study soil (Wu, 2011). The rate chosenwas 40 times (0.04mm3/s)and 25 times (0.025 mm3/s) slower than the rates adopted by Meilaniet al. (2005) and Wong et al. (2001), respectively. The volume flow rateof the 5 bar porous ceramic disk used was 0.003 mm3/s. The shear stresswas maintained at the same level as the shear stress applied duringthe creep monitoring. The matric suction in the soil specimendecreased as a result of water infiltration. In addition, the axial forceon the soil element decreased and resulted in the ram of the forceactuator to move downward in order to maintain the axial force at thepre-determined stress level.
Tests were terminated after failure of the specimen was observed.Failure was considered to have occurred when the strain rate startedto increase excessively during the shearing-infiltration test (Andersonand Sitar, 1995; Han, 1997; Melinda, et al 2004; Wong et al., 2001).
4. Results and discussion
4.1. Constant suction shearing test
A total of ten constant suction shearing tests were conductedat various combinations of net normal stress and matric suction(Table 1). A typical constant-suction shearing test result is presentedin Fig. 6, where the tests were conducted under a matric suction of300 kPa. As expected, the stress/strain curves in Fig. 6a showedthat deviatoric stress increases with the increase of net normalstress. The axial strain corresponding to the peak strength for allthe seven unsaturated specimens ranged between 7.3% and 13.8%.All the specimens eventually achieved a constant critical state strength.The mode of failure at the end of the constant-suction shearing test isshown in Fig. 7 where a rupture plane is clearly defined. As seen inFig. 6b, a constant matric suction (ua − uw = 300 kPa in this case)was maintained throughout the shearing process indicating that thechosen shearing rate was sufficiently slow to prevent any generationof excess pore-water pressure. During the shearing process waterdrained out from the specimen, as indicated by the water volumetricstrain measurement shown in Fig. 6c. The soil element subjected tothe higher net normal stress produced a higher water volumetric straincompared to the soil element subjected the lower net normal stress;both specimens produced a constant water volumetric strain at theend of the shearing.
The stress paths followed by the two soil elements during theconstant-suction test are plotted in p′ − q plot as shown in Fig. 6d.Since the constant-suction test was a drained test for the pore-air,the stress paths thus sloped at a gradient of 1 in 3 on the p′ − q plot.For over-consolidated soil, the stress path first crosses the criticalstate line but eventually reverses its direction and fails on the criticalstate line that corresponded to the critical state strength. The gradientM of the critical state line for the saturated soil was 1.025, whichcorresponded to a critical state angle of shearing ϕcv′ of 26°. Theintercept at the q-axis was 212 kPa for the two specimens testedunder 300 kPa of matric suction. Unsaturated soil elements testedunder different matric suctions have an identical value of M butwith different values of intercept along the deviatoric stress axis.Thus, at 40 kPa of matric suction the associated deviatoric interceptwas 55.24 kPa, at 100 kPa of matric suction the deviatoric interceptwas 127 kPa, and at 200 kPa of matric suction the deviatoric interceptwas 194 kPa.
Fig. 6. Constant suction shearing test results atmatric suction 300 kPa: (a) deviator stress;(b) matric suction; (c) water volumetric strain; and (d) stress path.
Fig. 7. Failure mode of specimen tested at (ua − uw) = 300 kPa and (σ3 − ua) = 400 kPaconstant-suction shearing test.
Fig. 8. Constant suction shearing test result: (a) failure envelope; and (b) angle indicatingthe rate of increase in shear strength with respect to changes in (ua − uw) when (σ− ua)is held constant, ϕb.
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Perhaps, the most commonly cited shear strength representationof unsaturated soil is the Fredlund and Rahardjo's (1993) extendedMohr–Coulomb failure envelope that was shown earlier in Fig. 4.The Mohr–Coulomb failure envelope, which was obtained from a seriesof Mohr circle of saturated soil specimens, has a peak angle of shearingϕp of 25.2° and an apparent peak cohesion intercept cp of 45.2 kPa(Figure 8a). The angle of rate of strength increase due to matric suctionϕb was obtained using the apparent cohesion intercepts obtained fromtests conducted under various matric suctions, as shown in Fig. 8b. Theϕb for the study soil was 24.5°. Hence, the extended Mohr–Coulombfailure envelope, which represents both the saturated and unsaturatedshear strength of the study soil, is given by
τ f ¼ 45:2þ σ−uað Þ tan25:2� þ ua−uwð Þ tan24:5�: ð4Þ
If all thepeak shear strength data from the constant-suction shearingtest were plotted in the three dimensional (3D) s′ − t − (ua − uw)space, as shown in Fig. 9a, instead of the kf line, one may obtain a best
Fig. 9. Constant suction shearing test result: (a) shear strength envelope at peak state; and (b) shear strength envelope at ultimate state in t − s′ − (ua − uw) space.
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fitted three dimensional kf plane; after conversion through theuse of thefollowing equations
ϕ0 ¼ sin−1 tanψ0� and c0 ¼ d
tanϕ0
tanψ0
�
whereψ′ is the angle of the kf line in the s′− t space; and d is the interceptof the kf line on the t axis. The extendedMohr–Coulomb failure envelopefor the peak strength of the study soil was then given by
τp ¼ 55þ σ−uað Þ tan24:23� þ ua−uwð Þ tan22:84� ð5Þ
with a coefficient of determination R2 of 0.994.It is possible that specimens subjected to a target suction of 40 kPa
did not have to follow an initial drying path though they were first
subjected to a suction of 90 kPa before reducing to the target suctionof 40 kPa. To evaluate the significance of this effect on the shearingresult of the study soil, the above extended Mohr–Coulomb failurecriterionwas refittedwithout the 40 kPa data points, the correspondingpeak strength equation is now given by
τp ¼ 57þ σ−uað Þ tan24:13� þ ua−uwð Þ tan22:50� ð6Þ
with a coefficient of determination R2 of 0.993. A small variation wasseen between Eqs. (5) and (6), which indicates that the suction historydid not have a significant effect on the peak strength of the study soil.Perhaps, not all the soils exhibit the influence of suction history, inparticular, the silty soil. A recent study by Hoyos et al. (2014), whostudied the residual shear strength of unsaturated silty soils via a
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series of suction-controlled ring shear tests, found that their result isvirtually independent of the suction histories experienced by the soil.
The value of cp′, ϕp′ and ϕb obtained from the 2DMohr circle diagramand the 3D kf plane were slightly different. We believe that the shearstrength parameters obtained from the 3D mean stress plot are morereliable since it is not always possible to obtain a failure envelope thatis tangential to all the Mohr circles defining the shear strength.
Likewise, the extendedMohr–Coulomb failure envelope for the criticalstate strength of the study soil, plotted in the 3D s′− t− (ua− uw) spaceof Fig. 9b, is given by
τcv ¼ 34:5þ σ−uað Þ tan22:78� þ ua−uwð Þ tan17:64� ð7Þ
with a coefficient of determinationR2 of 0.987. Similar to the case of thepeak strength envelope, had we ignored the three data points for thetests corresponded to the 40 kPa of matric suction, the equation becomes
τcv ¼ 33:6þ σ−uað Þ tan23:11� þ ua−uwð Þ tan17:74� ð8Þ
Fig. 10. Results of shearing-infiltration test: (a) deviator stress; (b) water volumetric strain; amatric suction of 100 kPa.
with a coefficient of determination R2 of 0.991. The peak angle of shearingwas only about 1.0–1.5° higher than the friction angle at criticalstate, while the corresponding apparent cohesion decreased from55 to 34.5 kPa (or 57 to 33.6 kPa from Eqs. (6) and (8)) implyingthat the peak strength of the study soil was mainly governed by theapparent cohesion.
4.2. Shearing-infiltration test results
The results of the shearing-infiltration test are presented here.Six shearing-infiltration tests were conducted under the stress statesas shown in Table 1. Fig. 10 shows the result of the specimen tested at100 kPa of matric suction and 100 kPa of net normal stress; Fig. 11shows the result of the specimens tested at 200 kPa of matric suctionand 50 and 100 kPa of net normal stresses; Fig. 12 shows the result ofthe specimen tested at 200 kPa of matric suction and 400 kPa of netnormal stresses; while Fig. 13 shows the result of the specimens testedat 300 kPa ofmatric suction and 100 and 400 kPa of net normal stresses.
nd (c) matric suction variations for specimens tested at net normal stress of 100 kPa and
Fig. 11. Results of shearing-infiltration test: (a) deviator stress; (b) water volumetric strain; and (c) matric suction variations for specimens tested at matric suction 200 kPa.
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Fig. 10a shows the result of the deviatoric stress (σ1–σ3) versus theaxial strain of the specimen tested at 100 kPa of matric suction and100 kPa of net normal stress. The soil element was initially sheared toa pre-determined stress level before water was injected into the soilelement. The deviatoric stress increased nonlinearly with axial strainuntil thepre-determined stress level, creepmonitoringwas then carriedout on the soil element but no discernible creep was observed duringthe 6-hour monitoring period.
Fig. 10b shows the volumetric strain of the pore-water recordedthroughout the shearing-infiltration test. Water volumetric strain isdefined here as the percentage of water volume change relative to theinitial total volume of the specimen. Water volumetric strain decreasedduring the initial constant-suction shearing stage because thepore-water was draining out from the specimen; the subsequentreversal (increment) of the water volumetric strain indicated thecommencement of the infiltration process where water was injectedinto the specimen. The deviatoric stress remained constant withthe increased of the axial strain as soon as water was injected into
the soil element. This was because the infiltration of water causedthe deviatoric stress on the specimen to decrease and to maintainat the pre-determined shear stress the loading ram had to movedownward. However, the deviatoric stress eventually decreasedafter mobilizing approximately 5% of its axial strain as the soil elementbegan to soften. The deviatoric stress dropped to a constant (critical)value at the end of the infiltration test. Typical failure mode of the soilelement at the end of the shearing-infiltration test is shown in Fig. 14.
For the shearing-infiltration test, the failure strain εf of the specimenwas defined at a point when the rate of the axial strain was about toreach the maximum machine allowable rate. The soil element wasinitially sheared at a rate of 0.00002 mm/s; after the commencementof the infiltration process, the specimen lost its target shear stressand in trying to maintain the target stress the loading ram had to movedownward. The axial strain rate increased non-linearly (Figure 15a)to 0.002 mm/s, which is the maximum rate allowed for the loadingram. To obtain the failure strain, tangential lines (lines “1” and “2”)are drawn along the linear portion of the bi-linear axial strain curve.
Fig. 12. Results of shearing-infiltration test: (a) deviator stress; (b)water volumetric strain; and (c)matric suction variations for specimens tested at 200 kPa ofmatric suction and 400 kPaof net normal stress.
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A vertical line (line “3”) is drawn passing through the intersection oflines “1” and “2” and the bi-linear axial strain curve. The intersectionof line “3” and the bi-linear curve (i.e. line “4”) defines the failure strainεf of the test. This definition of failure strain had been previously used byMeilani et al. (2005).
Fig. 10c shows the variation of matric suction in the soil elementthroughout the shearing-infiltration test. The recorded matric suctionremained constant during the initial constant-suction shearing test,proving that the drained shearing rate used was appropriate since noexcess pore-water pressure was generated during the shearing stage.Once the water-infiltration process was started, the water pressuresuw increased quickly causing the matric suction (ua − uw) of the soilelement to drastically decrease. The matric suction measured by themid-plane pore pressure transducer was higher than that measuredby the pore pressure transducer connected to the water compartment.This was caused by the applied pressure gradient across the height ofthe specimen that resulted in the flowing of water from the base tothe top of the soil element (Wong et al., 2001). Once a steady state
flow was attained, a constant water pressure and hence a constantmatric suction followed.
Figs. 11 and 13 show the results of shearing-infiltration test shearedunder amatric suction of 200 kPa and300 kPa, respectively. The trend ofthe results, as discussed in the preceding paragraphs, is similar to thosepresented in Fig. 10. Fig. 12 shows the result of the shearing-infiltrationtest conducted at 200 kPa of matric suction and 400 kPa of net normalstress. The variation of water volumetric strain and matric suctionwith axial strain, plotted in Fig. 12b and c, respectively, were differentfrom the corresponding plots in Figs. 10, 11 and 13. It appeared thatthere were two failures (A1 and A2) during the infiltration process.Thefirst failure, A1, occurred almost immediately afterwater infiltrationand was accompanied by the generation of positive excess pore-waterpressure (negative matric suction). The failure at A1 was determinedfollowing the failure defined earlier although it was not very obvious,as shown in Fig. 15b.
Subsequently, after more than 10% of water volumetric strainwas drawn into the specimen the second failure, A2, occurred, as shown
Fig. 13. Results of shearing-infiltration test: (a) deviator stress; (b) water volumetric strain; and (c) matric suction variations for specimens tested at 300 kPa of matric suction.
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in Fig. 12b. The matric suction decreased drastically as soon as thecommencement of water infiltration at 5.3% of axial strain andattained a constant matric suction at 6.7% of axial strain. There seemedto be a sudden drop of matric suction in the specimen at 7.6% of axialstrain and then it recovered slightly before another sudden dropoccurred at 8.6% of axial strain. It was found after the test that therewas a coarse pebble running across the slip plane of the failed specimen.The pebble not only obstructed the smooth sliding of the slip planebut also induced the sudden increase of excess pore-water pressure,which resulted in the two sudden drops of matric suction, during thesliding process.
4.3. Shear strength in relation to water infiltration
The shear stresses at failure of constant-suction and shearing-infiltration tests are compared and presented in the shear stress(σ1 − σ3)/2 versus matric suction at failure plot in Fig. 16. The plot isnot the cohesion intercept plot where the net normal stress is zero, asshown in Fig. 4; instead, they corresponded to a net normal stress of100 kPa and 400 kPa, respectively. The plot shows that the failureshear stress of the specimens failed by shearing-infiltration is higher
than that of the specimens failed by constant-suction shearing(Fig. 17). In other words, specimen subjected to shearing-infiltration process failed at a higher shear strength than the spec-imen subjected to constant-suction shearing process.
When the failure shear stresses, i.e. the shear strength, from the fiveshearing-infiltration tests are plotted in the 3D t− s′− (ua− uw) spacetogether with the extended Mohr–Coulomb envelope of peak strength(see Eq. (5)) all the points lie above the extended Mohr–Coulombenvelope of peak strength. Assuming that the infiltrated soil has thesame peak angle of shearing ϕp′ = 24.23 °, as that of the soil shearedunder constant suctions, we obtained the following failure envelopefor the shearing-infiltration soil
τ f infð Þ ¼ 93:40þ σ−uað Þ tan24:23� þ ua−uwð Þ tan16�: ð9Þ
The equation shows that the infiltrated soil has a higher cohesionintercept but with a lower angle of ϕb compared to that of the soilsheared under constant suctions. The “extra” failure shear stress, interms of cohesion intercept, encountered in the shearing-infiltrationtest is presumably associated to the seepage force generated in thespecimen as a result of water injection. The shearing-infiltration soil,
Fig. 14. Failuremode of specimen tested at (ua− uw)= 300 kPa and (σ3− ua)= 400 kPainfiltration-shearing test.
Fig. 15. Determination of failure strain for (a) a typical infiltration-shearing test; (b) thespecimen tested at 400 kPa of net normal stress and 200 of matric suction.
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though has a higher shear strength than that of the soil subjected to theconstant-suction shearing, will thus be associated to a lower factor ofsafety because of this extra component.
Figs. 18 and 19 show the stress paths of the shearing-infiltrationtest specimens conducted under an initial matric suction of 200 and300 kPa, respectively. The failure envelope shown in Figs. 18a and 19awas essentially the failure envelope obtained in Fig. 9a. The 1:1 gradientstress paths in Figs. 18b and 19b revealed that all the specimens weresheared under a drained condition (pore-air). The vertical stress pathsin Figs. 18c and 19c show that all the specimens were initially shearedunder a constant suction, 200 kPa in Fig. 18c and 300 kPa in Fig. 19c,to a stress level below the failure envelope as denoted by the openedcircles in Figs. 18b and 19b.Waterwas then injected into the specimens,causing the matric suction to decrease, as shown by the horizontalstress paths in Figs. 18c and 19c. Failure, as defined earlier by the rapidlyincreasing axial strain rate, occurs when the stress path touches orcrosses the slanting failure line, as indicated by the filled circles inFigs. 18c and 19c. The slanting failure line is, however, different fromthe Mohr–Coulomb failure envelope; it is the projection of the sectioncutting through a particular net normal stress (σ− ua) of the extendedMohr–Coulomb failure envelope (Figure 4) onto the t vs (ua − uw)space. Theoretically, failure should occur when the stress path touchesthe failure line; if failure occurred above the failure line, it was mostlikely that the shear strength of the specimen was under-estimated.The horizontal stress paths showed that infiltration alone could induceshear failure in the soil without having to have additional loading.Failure points C and D in Fig. 18c corresponded to the failure pointsA1 and A2 in Fig. 12, in which they were associated to the shearstrength at net normal stresses of 761 kPa and 890 kPa, respectively.Both failures were accompanied by negativematric suction, i.e. positivepore pressure. Hence, during the shearing-infiltration process thespecimen must have generated a significant amount of excess pore-water pressure.
4.4. Implications of the current study
Fredlund and Morgenstern (1977) suggested that any two of thethree possible normal stress variables can be used to define the stressstate of unsaturated soil. The three possible stress variables are:(i) (σ − uw), (ii) (σ − ua), and (iii) (ua − uw). Nevertheless,
Casagrande and Albert (1932) who performed a series of shear boxtests on soft soil specimens found that at failure a linear relationshipexisted between the water content and the net normal stress. Asthe measurement of the soil water content is more direct and moreeconomical than the measurement of the shear strength of the soil, itmight be useful to know the averagewater content of the soil specimensat failure. Fig. 20a shows the best fitted extended water contentenvelope of (i) saturated specimens subjected to consolidated-drainedshearing test, and (ii) unsaturated specimens subjected to constant-suction shearing test, and shearing-infiltration test. The best fittedextended water content envelope can be represented by the followinglinear equation:
wf ¼ 30:06−3:254 σ−uað Þ−1:414 ua−uwð Þ %ð Þ: ð10Þ
Relationship between water content, matric suction and meannet stress had been introduced in Vu (2002). Vu (2002) and Vu and
Fig. 16. Comparison of failure shear stress between constant-suction shearing test andshearing-infiltration test.
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Fredlund (2006) used such relationship to represent thewater contentconstitutive surface in their studies. Tarantino and ElMountassir (2013)suggested that it is possible to show that suction and degree of satura-tion or water content independently control the shear strength of thesoil. Fig. 20b presents the relationship between the water content andmean net stress at failure. The water content at failure of both thesaturated and unsaturated specimens decreased linearly with theincrease of the mean net stress. The water content of the saturatedsoil elements decreased from about 35% to 30% for mean net stressesranging between 0 and 1200 kPa, whereas the average water contentof the unsaturated soil elements decreased from 29% to 25% for thesame range of mean net stresses at failure. There was one anomalouspoint, which was the data point of the soil specimen subjected toshearing-infiltration test under a net normal stress of 400 kPa. This wasdue to the enormous amount of water (about 14%) that was drawninto the soil element prior to its second failure, as shown in Fig. 12b.
Armed with Eq. (10), the field measured water content, and thetwo stress variables, we can attempt to accurately predict whetheror not a slope is approaching failure. For accurate landslide prediction,the early landslide warning system should incorporate the monitoring
Fig. 17. Shear strength of shearing-infiltration test specimens
of the water content together with the two stress variables instead ofconcentrating in the monitoring of the slope movement. Gui (2013),who studied the triggering mechanism of a rainfall-induced landslidein Taipei through a series of numerical analysis, concluded that theamount of displacement mobilized in unsaturated soil slope dependedon the degree of saturation or the amount of water content in theslope. By the time movement in the slope was detected it would mostlikely be too late to prevent the sliding failure. There are many reliabledevices and techniques that can be used to measure in situ watercontent and with the aid of real time monitoring system, the watercontent in a slope can thus be easily and continuously monitored for amore effective andaccurate landslideprediction.However,more studiesare required to quantify the validity of Eq. (10) as the slope might havebeen subjected to wetting and/or drying paths in the field instead ofonly the wetting path as examined in this study.
Fredlund et al. (2012) suggested that soil mechanics relatedproblems can be broadly categorized into three main areas accordingto the characteristics of soils: its performance under seepage conditions,the shear strength, and the volumechange behavior,which also includesthe deformation of soils. Rainfall-induced slope instability problemshave always been treated as a shear strength problem, as explicitlyshown in the definition of the factor of safety of slope. However,contrary to our traditional belief that water infiltration reduces theshear strength of the soil and hence the stability of the slope, theabove experimental study revealed that failure due to water infiltrationwas instead triggered by excessive deformation that eventually led tomaterial softening, even without the application of additional loading.Limited by the scope of this paper, more study in this direction isrequired to further understand this issue.
5. Conclusions
A series of laboratory element tests was conducted to examinethe mechanical behavior of residual soil that was subjected to waterinfiltration. The following conclusions have been obtained:
1. The axial strain corresponding to the peak strength for all theseven constant-suction specimens ranged between 7.3% and 13.8%while the axial strain corresponding to failure for all the shearing-infiltration test specimens ranged between 5.6% and 9.2%.
with respect to shear strength envelope of peak strength.
Fig. 18. Stress path for various shearing-infiltration tests under initial (ua − uw) = 200 kPa: (a) in t − s′ − (ua − uw) space; (b) in t − s′ space; and (c) in t − (ua − uw) space.
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2. Water infiltration alone could induce shear failure in the soil withouthaving to have any additional loading.
3. Under the same initial net normal stress and matric suction, the soilsheared to failure under water infiltration condition possessed ahigher shear strength than the soil sheared to failure under a constantsuction condition.
4. A linear relation existed between the water content at failure, netnormal stress and matric suction of specimens subjected to boththe constant-suction shearing and the shearing-infiltration tests.
As the amount of soil movement is also affected by the amount ofwater content, this relation indicates that a better approach for theearly landslide warning system to predict landslide occurrenceis the one that incorporated the monitoring of field water contentand the two stress variables, instead of just depending on themonitoring of the slope movement.
5. Slope instability problems, which have always been treated as ashear strength problem, appeared to be a volume change (straindeformation) problem instead. It appears that a better method
Fig. 19. Stress path for various shearing-infiltration tests under initial (ua − uw) = 300 kPa: (a) in t − s′ − (ua − uw) space; (b) in t − s′ space; and (c) in t − (ua − uw) space.
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Fig. 20. (a) Relation betweenwater content, mean effective stress and matric suction; (b) relationship between water content andmean effective stress at failure of saturated and unsat-urated specimens.
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of reducing and/or preventing rainfall-induced landslides is tolimit/minimize the unnecessary development of deformation inthe slope rather than attempting to increase the shear strengthof the slope.
Acknowledgments
The author is grateful to the partial financial support provided by theNational Science Council under the agreements: NSC 98-2221-E-027-070
and NSC 99-2221-E-027-055. Thanks are also due to Prof. D.W. Changwho has inspired the first author to perform this study.
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