COMPARISON OF DIFFERENT PROCEDURES TO PREDICT UNSATURATED SOIL SHEAR STRENGTH. S.K. Vanapalli and D.G. Fredlund 1

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1 COMPARISON OF DIFFERENT PROCEDURES TO PREDICT UNSATURATED SOIL SHEAR STRENGTH S.K. Vnplli nd D.G. Fredlund 1 Abstrct: Severl procedures hve been proposed in the recent yers to predict the sher strength of n unsturted soil. The soil-wter chrcteristic curve hs been used s tool either directly or indirectly in the prediction of the sher strength long with the sturted sher strength prmeters in these procedures. This pper provides comprisons between the mesured nd predicted vlues of unsturted sher strength using these procedures for three soils both for limited nd lrge suction rnges. The three soils used in the study for comprisons hve different grdtion properties, percentges of cly nd plsticity index, I p vlues. The dvntges nd limittions ssocited with predicting the sher strength of unsturted soils using the procedures is discussed in the pper. INTRODUCTION A theoreticl frmework for unsturted soil mechnics tht prllels sturted soil mechnics is vilble in terms of stress stte vribles, nmely; net norml stress, (σ n - u ), nd mtric suction, (u - uw) where σn is the norml stress, u is the pore-ir pressure n uw is the pore-wter pressure. (Fredlund nd Rhrdjo, 1993). The frmework is bsed on experimentl studies tht re costly nd time consuming. Severl dvncements hve been mde in the prediction of the engineering behvior of unsturted soils in recent yers. The soil-wter chrcteristic curve hs been found to be useful tool in the estimtion of engineering properties for unsturted soils. Exmples re the coefficient of permebility nd the sher strength functions. Sher strength forms n importnt engineering property in the design of numerous geotechnicl nd geo-environmentl structures such s erth dms, retining wlls, pvements, liners, covers, etc. Severl procedures hve been proposed in the literture during the pst five yers to predict the sher strength of n unsturted soil. 1 Deprtment of Civil Engineering, University of Ssktchewn, SK, Cnd, S7N 5A9

2 These procedures use the soil-wter chrcteristic curve s tool either directly or indirectly long with the sturted sher strength prmeters, c nd φ, to predict the sher strength function for n unsturted soil (Vnplli et l. 1996, Fredlund et l. 1996, Oberg nd Sllfors 1997, Khllili nd Khbbz 1998 nd Bo et l. 1998). The philosophy used in ech of the prediction procedures proposed by these investigtors is different. Comprisons hve been provided between predicted nd mesured vlues of sher strength for limited suction rnge for vrious soils (i.e., between to 5 kp). Escrio nd Juc (1989) mesured the soil-wter chrcteristic curves nd the sher strength of three soils prior to the time when ny proposls hd been mde for the sher strength functions. The three soils hve different grdtion properties, percentges of cly nd plsticity indices, I p. These results re used in this pper to provide comprisons between the predicted nd mesured sher strength vlues both for limited suction rnge nd lrge suction rnge. The study presented in the pper highlights the dvntges nd limittions ssocited with the vrious procedures for predicting the sher strength of unsturted soils. The simple procedures discussed in this pper re of vlue in bringing the sher strength theories for unsturted soils into engineering prctice. EQUATIONS FOR INTERPRETING THE SHEAR STRENGTH OF UNSATURATED SOILS Bishop (1959) proposed sher strength eqution for unsturted soils by extending Terzghi s principle of effective stress for sturted soils. Bishop s originl eqution cn be rrnged s shown below. τ ( σ u ) tnφ ' + ( u u )[( χ )( tn φ' )] = c' + [1] n w where: τ = sher strength of unsturted soil, c = effective cohesion, φ = ngle of frictionl resistnce, (σ n - u ) = net norml stress, (u - uw ) = mtric suction, nd χ = prmeter dependent on the degree of sturtion The vlue of χ ws ssumed to vry from 1 to, which represents the vrition from fully sturted condition to totl dry condition. Severl investigtors found limittions with respect to the quntifiction of the prmeter χ both theoreticlly nd experimentlly. Fredlund et l. (1978) hve proposed reltionship to explin the sher strength of unsturted soils in terms two independent stress stte vribles s shown below: b ( σ u ) tn φ' + ( u u ) tn φ τ = c' + [2] n w

3 The sher strength contribution due to mtric suction, φ b, ws initilly ssumed to be liner bsed on the nlysis of limited results published in the literture. Lter experimentl studies performed over lrge rnge of suction vlues hve shown tht the vrition of sher strength with respect to soil suction is non-liner (Gn et l nd Escrio nd Juc 1989). Eqution [1] cn be pplied for both the liner nd non-liner vrition of sher strength with respect to suction. Figure 1. Typicl soil-wter chrcteristic curve showing zones of desturtion. The Reltionship between the Soil-Wter Chrcteristic Curve nd the Sher Strength of Unsturted soils The soil-wter chrcteristic curve defines the reltionship between the soil suction nd either the degree of sturtion, S, or grvimetric wter content, w, or the volumetric wter content, θ (Figure 1). The soil-wter chrcteristic curve provides conceptul nd interprettive tool by which the behvior of unsturted soils cn be understood. As the soil moves from sturted stte to drier conditions, the distribution of the soil, wter, nd ir phses chnge s the stress stte chnges. A typicl soil-wter chrcteristic curve with vrious zones of desturtion re shown in Figure 1. The wetted re of contct between the soil prticles decreses with n increse in the soil suction. There is reltionship between the rte t which sher strength chnges in unsturted conditions to the wetted re of wter contct between the soil prticles or ggregtes. In other words, reltions hip exists between the soil-wter chrcteristic curve nd the sher strength of unsturted soils.

4 Different Procedures for Predicting the Sher Strength of n Unsturted Soil Vnplli et l. (1996) nd Fredlund et l. (1996) hve proposed more generl, nonliner function for predicting the sher strength of n unsturted soil using the entire soilwter chrcteristic curve (i.e., to 1,, kp) nd the sturted sher strength prmeters s shown below: τ [ { }] κ [ ' + ( σ u ) tnφ '] + ( u u ) ( Θ )( tnφ ') = n w c [3] where: κ = fitting prmeter used for obtining best-fit between the mesured nd predicted vlues, nd Θ = normlized wter content, θ w /θ s. The sher strength contribution due to suction constitutes the second prt of [Eq. 3], which is: τ κ [( u ){ ( Θ )( tn φ ')}] us = w u [4] Eqution [3] cn lso be written in terms of degree of sturtion, S, or grvimetric wter content, w, to predict the sher strength yielding similr results. The entire soil-wter chrcteristic curve dt (i.e., to 1,, kp) is required long with the sturted sher strength prmeters in the use of Eqution [3]. A best-fit soilwter chrcteristic curve cn be obtined in terms of, n, nd m prmeters using the eqution proposed by Fredlund nd Xing (1994) which is shown below: ψ ln 1 + ( ) hr 1 θw ψ = θs 1 6 m 1 n ln 1 + ψ ( ) + h ln exp 1 r where: ψ = soil suction, θ w = volumetric wter content, θ s = sturted volumetric wter content, = suction relted to the inflection point on the curve, n = soil prmeter relted to slope t the inflection point, m = soil prmeter relted to the residul wter content, nd h r = suction relted to the volumetric residul wter content, θ r [5] The sher strength contribution due to suction, tnφ b is equl to tnφ up to the irentry vlue of the soil. In other words, the conventionl eqution for estimting the sher strength of sturted soils cn be used up to the ir-entry vlue for unsturted soils. The sher strength vrition with respect to suction is liner in the boundry effect zone. The

5 sher strength contribution due to suction, tnφ b is less thn tnφ in the trnsition zone. Hence, the sher strength vrition in this zone is non-liner. The sher strength vlue grdully strts dropping t high vlues of suction nd reches sturted sher strength vlue t 1,, kp using this eqution. Eqution [3] is useful to predict the sher strength of unsturted over the entire rnge of suction vlues of to 1,, kp (i.e., from fully sturted condition to totl dry cond ition). Anlysis of experimentl results presented nd shown in the Figures 3 to 8 of this pper using Eqution [3] will be referred s Procedure 1. Vnplli et l. (1996) proposed nother eqution for predicting the sher strength of unsturted soils without using the fitting prmeter, κ. The eqution is given below: θ θ τ = c ' + ( σ ) tnφ' + ( ) w r n u u uw tnφ' θs θr [6] where: θw = volumetric wter content, θ s = sturted volumetric wter content, nd θ r = residul volumetric wter content. Eqution [6] cn lso be written in terms of degree of sturtion, S, or grvimetric wter content, w, to predict the sher strength yielding similr results. To use this eqution the residul volumetric wter content, θ r, hs to be estimted from the soil-wter chrcteristic curve. A grphicl procedure cn be used to define the residul stte of sturtion (Figure 1). The procedure involves first drwing tngent line through the inflection point on the stright-line portion of the soil-wter chrcteristic curve. The residul sturtion cn be defined s the point where the line extending from 1,, kp long the curve intersects the previous line. A computtionl technique cn lso be used to determine the residul suction vlue. More detils bout the computtionl technique re vilble in Vnplli et l. (1998). The sher strength of soil my strt to decrese beyond the residul stte conditions. Anlysis of experimentl results presented nd shown in the figures of this pper using Eqution [6] re referred s Procedure 2. Both the Procedures 1 nd 2 re consistent with the stress stte vrible pproch stisfying the continuum mechnics concepts. The form of the eqution is similr to the Fredlund et l. (1978) eqution (i.e., Eqution 2). Oberg nd Sllfors (1997) proposed n eqution for predicting the sher strength of primrily non-clyey soils such s snds nd silts. The proposed eqution cn be rerrnged s follows: ( σ u ) tnφ ' + ( u u )[( S )( tnφ ') ] τ = c' + [7] n w

6 The χ prmeter proposed by Bishop is replced by the degree of sturtion, S, in Eq. [7]. The uthor s stte tht the χ -fctor proposed by Bishop reflects the frction of the pore re tht is occupied by wter (i.e., Aw/At) which is pproximtely equl to the degree of sturtion, S. Eqution [7] hs not been experimentlly verified on soils through the mesurement of the sher strength nd the degree of sturtion t the point of filure in the specimens. Eqution [7] suggests tht there is one to one reltionship between the degree of sturtion, S, nd the re of wter contct long the sher plne in the soil. Anlysis of experimentl results presented nd shown in the figures of this pper using Eqution [7] re referred s Procedure 3. Khllili nd Khbbz (1998) hve extended Bishop s eqution (1959) (i.e., Eqution 1) for predicting the sher strength of n unsturted soil. An empiricl constnt hs been suggested for the prmeter, χ in Eqution 1 s given below: ( u uw ) f ( u u ).55 χ = [8] w b where: (u uw)f η = mtric suction in the specimens t filure conditions, = vlue equl.55 ws suggested bsed on 13 soils dt published in the literture The required prmeters for predicting the sher strength of unsturted soils bsed on Khllili nd Khbbz (1998) pproch is the ir-entry vlue, (u uw)b of the soil nd the sturted sher strength prmeters. Anlysis of experimentl results presented nd shown in the figures of this pper using Khllili nd Khbbz (1998) procedure is referred s Procedure 4. Prcticing engineers re most interested in the sher strength behvior in the trnsition zone (Figure 1). The trnsition zone lies between the ir-entry vlue nd the residul zone of sturtion (Vnplli et l. 1996). The vrition of the soil-wter chrcteristic curve behvior in the trnsition zone is liner on semi-logrithmic plot (i.e., vrition of degree of sturtion, S, or volumetric wter content, θ, or grvimetric wter content, w versus logrithm of soil suction). Bo et l. (1998) suggest nother eqution for predicting the unsturted sher strength tking into ccount of the liner vrition of the soil-wter chrcteristic curve in the trnsition zone s below: τ ( σ u ) tnφ' + ( u u )[ ξ ζ log( u u )] tnφ' = c' + [9] n w w where: ξ = log log ( u uw ) ( u u w ) r log ( u u w ) b

7 1 ζ = log ( u u w ) r log ( u u w ) b (u u w ) r = soil suction t residul wter content conditions The prmeter, ξ, represents the intercept (i.e., on the bsciss) nd the prmeter, ζ, represents the slope of the liner prt of the soil-wter chrcteristic curve respectively. Bo et l. (1998) suggests use of the expression given below for fitting the soil-wter chrcteristic curve dt. ( θw θs ) ( θ θ ) s r = ξ ζ log ( u u ) w [1] The form nd philosophy of the Eqution [9] for predicting the sher strength of unsturted soils is similr to Procedure 2 outlined in this pper. EXPERIMENTAL DATA USED IN THE ANALYSIS Escrio nd Juc (1989) mesured the sher strength of three different soils with vrying percentges of cly nd plsticity indices, I p, using modified direct sher equipment. Stticlly compcted specimens were used in the mesurement of sher strength under consolidted drined conditions with different net norml stresses. The sher strength for two soils, nmely, Mdrid gry cly nd Red silty cly ws mesured for suction rnge between to 15, kp. The sher strength for Mdrid cly snd ws mesured for suction rnge between to 5, kp. The properties of three soils used in their testing progrm re summrized in Tble 1. Tble 1. Summry of soil properties tested by Escrio nd Juc (1989). Mdrid gry cly Red silty cly Mdrid cly snd Snd (%) Silt (%) Cly (%) Liquid Limit, w L (%) Plsticity Index, Ip (%) Specific Grvity, G s Void rtio, e Escrio nd Juc (1989) hve lso mesured the soil-wter chrcteristic curves for the three soils for suction rnge between to 15, kp. The soil-wter chrcteristic curves were mesured with n pplied stress of 2 kp using clibrted springs such tht there is good contct between the specimen nd the cermic stone of the pressure plte pprtus. Figure 2 presents the fitted soil-wter chrcteristic curve dt for the entire suction rnge from to 1,, kp using Eqution 5 (Fredlund nd Xing, 1994). It should

8 be noted tht the soil-wter chrcteristic curve dt in the high suction rnge were not mesured. The soil-wter chrcteristic curve results suggest tht the ir-entry nd the residul suction vlues of the soil increses with n increse in the percentge of fines present in the soil. Tble 2 summrizes the estimtes of ir-entry vlue nd the residul suction vlue bsed on the construction procedure defined in Figure 1. 1 Degree of Sturtion (%) Mdrid cly snd Red silty cly Mdrid gry cly E+6 Soil suction, kp Figure 2. Soil-wter chrcteristic curves for three soils tested by Escrio nd Juc (1989). Tble 2. Summry of the sturted sher strength prmeters nd the soil-wter chrcteristic curve dt Mdrid gry cly Red silty cly Mdrid cly snd Air-entry vlue, (u u w ) b, kp Residul suction, ψ r, kp 4, 33, 12, Residul degree of sturtion, (%) Fitting prmeter, κ (Procedure 1 using Eqution 3) Effective cohesion, c, kp Effective ngle of internl friction, φ (degrees) Net norm l stress, (σ u ), kp Sturted sher strength, kp The comprisons between the predicted nd mesured sher strength vlues re presented using the four different procedures discussed in erlier sections (i.e., Figures 3 to 8). These comprisons re provided both for limited suction rnge nd s well s lrge suction rnge. The key informtion required for predicting the sher strength of unsturted

9 soils using the procedures, long with the sturted sher strength prmeters is summrized in Tble 2. ANALYSIS OF RESULTS Severl prmeters such s initil compction wter content nd the stress stte influence the soil-wter chrcteristic curve behvior (Vnplli et l. 1999). It would pper tht the sher strength contribution due to suction cn be more ccurtely estimted using the soil-wter chrcteristic curve tht hs been determined tking into ccount the influence of the stress stte nd the initil wter content conditions. The soil-wter chrcteristic curves re conventionlly determined in the lbortory only with the ppliction of nominl norml stress or without the ppliction of ny pplied verticl stress. Vnplli et l. (1998b) studies hve shown tht the sher strength of Indin Hed till specimens cn be predicted with resonble degree of ccurcy using the soil-wter chrcteristic curves tht hve been mesured without considering the influence of stress stte. Procedures 1 nd 2 presented in this pper were used for nlyzing the results. The Atterberg limits of the Indin Hed till were s follows: liquid limit, w L of 35.5% nd plsticity index, Ip of 18.7%. The frctions of snd, silt, nd cly were 28%, 42% nd 3% respectively. The predicted nd mesured sher strength vlues re compred for the three soils in this pper re; nmely, Mdrid gry cly, Red silty cly nd Mdrid cly snd. The sher strength of these soils were tested with different net norml stresses (Tble 2). The soil-wter chrcteristic curves mesured with 2 kp stress were used in the nlyses (Figure 1). 75 Sher strength, kp Procedure 3 Procedure 2 Procedure 4 Procedure 1 Mdrid gry cly (σ - u ) = 12 kp Soil suction, kp Figure 3. Comprison of predicted nd mesured sher strength vlues for Mdrid gry cly using different procedures for lrge suction rnge.

10 4 Sher strength, kp Procedure 3 Procedure 4 Procedures 1 nd 2 Mdrid gry cly (σ - u ) = 12 kp Soil suction, kp Figure 4. Comprison of predicted nd mesured sher strength vlues for Mdrid gry cly using different procedures for lrge suction rnge. Figure 3 shows comprisons between the predicted nd mesured sher strength vlues for Mdrid gry cly using the four different procedures discussed in the pper for suction rnge between to 15, kp. The continuous lines in the figure represent the predicted sher strength vlues nd the symbols re the mesured sher strength vlues. There is good comprison between the predicted nd mesured vlues of the sher strength for the suction rnge of to 15, kp using Procedure 1 (Figure 3). A fitting prmeter vlue of κ equl to 2.8 ws used for obtining these predictions using Eqution [3]. Figure 4 shows comprisons between predicted nd mesured sher strength vlues for limited suction rnge of to 1, kp. Procedures 2 nd 4 long with Procedure 1 provide good comprisons between the mesured nd predicted vlues of sher strength. Figure 5 shows the comprison between the mesured nd predicted sher strength vlues for Red silty cly for the suction rnge to 15, kp. Procedure 1 provides good comprisons for the suction rnge of to 15, kp. Procedures 2, 3 nd 4 do not provide good comprisons. These observtions re consistent with the erlier observtions for Mdrid gry cly.

11 1 Sher strength, kp Procedure 3 Procedure 2 Red silty cly (σ - u ) = 12 kp Procedure 1 Procedure Soil suction, kp Figure 5. Comprison of predicted nd mesured sher strength vlues for Red silty cly using different procedures for l rge suction rnge. Sher strength, kp Red silty cly (σ - u ) = 12 kp Procedure 4 Procedure 3 2 Procedure 1 Procedure Soil suction, kp Figure 6. Comprison of predicted nd mesured sher strength vlues for Red silty cly using different procedures for suction rnge between to 1,5 kp. Figure 6 shows the comprison between predicted nd mesured sher strength vlues for Red silty cly for limited suction rnge between to 1,5 kp. Procedures 3 nd 4 do not provide good comprisons. Procedure 2 provides resonbly good comprisons for suction rnge between to 1,5 kp.

12 Sher strength, kp Procedure 3 Procedure 1 Mdrid cly snd (σ - u ) = 12 kp Procedure Soil suction, kp Procedure 4 Figure 7. Comprison of predicted nd mesured sher strength vlues for Mdrid cly snd using different procedures for lrge suction rnge. Figure 7 provides comprison between the mesured nd predicted sher strength vlues for Mdrid cly snd for the suction rnge to 5, kp. Procedure 2 provides good comprison for the suction rnge of to 5, kp. Figure 8 shows the comprison between predicted nd mesured sher strength vlues for Mdrid cly snd for limited suction rnge between to 1, kp. Procedure 1, 2, nd 4 provide resonbly good comprisons. Sher strength, kp Mdrid cly snd (σ - u ) = 12 kp Procedure 3 Procedure 1 Procedures 2 nd Soil suction, kp Figure 8. Comprison of predicted nd mesured sher strength vlues for Mdrid cly snd using different procedures for suction rnge between to 1, kp.

13 Summry nd Conclusions Comprisons between the mesured sher strength nd predicted sher strength vlues for three different soils re presented. Four different procedures vilble in the literture for predicting the sher strength re used both for limited nd lrge suction rnges. Procedure 1 provides good comprisons between the mesured nd predicted sher strength vlues for limited suction rnges between to 1,5 kp for ll the three soils presented in this pper. Unsturted soil behvior is of prcticl interest in this suction rnge. Good comprisons were lso observed for two of the three soils for even for lrge suction rnge. This procedure provides better predictions in comprison to the other procedures. Figure 9 shows the reltionship between the fitting prmeter, κ, nd plsticity index, I p. Three points of κ versus I p reltionship were obtined from the study presented in this pper (Tble 2). The other two points were bsed on the studies presented by Vnplli et l. (1996) using Indin Hed nd Wulfsohn et l. (1996) using non-plstic soil. A vlue of κ equl 2.3 provided good correltion between the mesured nd predicted vlues of sher strength for Indin Hed till with plsticity index, I p, of A vlue of κ equl 1 provided good correltion between predicted nd mesured vlues of sher strength for the non-plstic soil. The fitting prmeter κ my be influenced by other prmeters such s soil structure, nture of soil (i.e., slurry consolidted, dynmiclly compcted or stticlly compcted, nturl) etc. More studies re necessry to estblish the uniqueness of this reltionship. Correltion such s shown in Figure 9 my be possible with other soil constnts. Fitting prmeter, κ Plsticity Index, I p Indin Hed till Figure 9. The reltionship between the fitting prmeter, κ, nd plsticity index, I p Procedure 2 is provides good comprisons between mesured nd predicted vlues for the three soils nlyzed in this pper for limited suction rnge between to 1,5 kp. However, the comprisons were not good for predicting the sher strength over lrge suction rnge for two soils. This my be ttributed to the possible errors in the estimtion of

14 residul suction vlue from the construction procedure using limited soil-wter chrcteristic curve dt. Procedure 3 does not provide good reltions both for limited nd s well lrge suctions rnges for the comprisons undertken in the study presented in this pper. Figure 8 shows resonble comprisons for limited suction rnge between to 2 kp for Mdrid cly snd. Procedure 4 provides resonble estimtes for predicting the sher strength of two of the three soils nlyzed in the low suction rnge but does not provide good comprisons for lrge suction rnges. The studies presented in this pper show promise of using the procedures predicting the sher strength of n unsturted soil using the soil-wter chrcteristic curve nd the sturted sher strength prmeters. More experimentl studies re necessry on different types of soils to better understnd the sher strength behvior of unsturted soils nd develop better prediction procedures. REFERENCES Bo, C.G., Gong, B. nd Zhn, L Properties of unsturted soils nd slope stbility of expnsive soil. Keynote Lecture. UNSAT 98, 2 nd Interntionl Conference on Unsturted Soils, Beijing. Wulfsohn, D., Adms, B.A. nd Fredlund, D.G Appliction of unsturted soil mechnics for griculturl conditions, Cndin Agriculturl Engineering, Vol. 38, No. 3, pp Bishop, A.W The principle of effective stress. Tecknish Ukeblnd, 16(39): Escrio, V. nd Juc Sher strength nd deformtion of prtly sturted soils. Proceedings of the 12 th Interntionl Conference on Soil Mechnics nd Foundtion Engineering, Rio de Jnerio, 2: Fredlund, D.G., Morgenstern, N.R., nd Widger, R.A The sher strength of unsturted soils. Cndin Geotechnicl Journl, 15: Fredlund, D.G. nd Rhrdjo, H Soil mechnics for unsturted soils. John Wiley nd Sons Inc., New York. Fredlund, D.G. nd Xing, A Equtions for the soil-wter chrcteristic curve. Cndin Geotechnicl Journl. 31: Fredlund, D.G., Xing, A., Fredlund, M.D., nd Brbour, S.L The reltionship of the unsturted soil sher strength to the soil-wter chrcteristic curve. Cndin Geotechnicl Journl. 33: Gn, J.K.M. nd Fredlund, D.G Multistge direct sher testing of unsturted soils. Americn Society for Testing Mterils, Geotechnicl Testing Journl, 11(2): Khllili, N. nd Khbbz, M.H A unique reltionship for the determintion of the sher strength of unsturted soils. Geotechnique, 48(5); Oberg, A. nd Sllfors, G Determintion of sher strength prmeters of unsturted silts nd snds bsed on the wter retention curve, Geotechnicl Testing Journl, GTJODJ, 2(1): 4-48.

15 Terzghi, K Theoreticl soil mechnics. Wiley Publictions, New York. Vnplli, S.K., Fredlund D.G., Pufhl, D.E. nd Clifton, A.W Model for the prediction of sher strength with respect to soil suction. Cndin Geotechnicl Journl, 33: Vnplli, S.K., Sillers, W.S., nd Fredlund, M.D The mening nd relevnce of residul wter content to unsturted soils. 51st Cnd in Geotechnicl Conference, 1998, Edmonton, pp Vnplli, S.K., Pufhl, D.E., nd Fredlund, D.G. 1998b. The effect of stress stte on the soil-wter chrcteristic curve behvior of sndy-cly till. 51st Cndin Geotechnicl Conference, 1998, Edmonton, pp Vnplli, S.K., Fredlund, D.G. nd Pufhl, D.E The influence of soil structure nd stress history on the soil-wter chrcteristics of compcted till. Geotechnique, Vol. 49: