EFFECTS OF DRY DENSITY AND GRAIN SIZE DISTRIBUTION ON …

161

i) Lecturer, School of Urban Development, Queensland University of Technology, Brisbane, Australia.ii) Associate Professor, University of Tokyo, Department of Civil Engineering, Tokyo, Japan (uchimura＠civil.t.u-tokyo.ac.jp).

The manuscript for this paper was received for review on March 10, 2008; approved on December 2, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

Fig. 1. Typical soil-water characteristic curves

161

SOILS AND FOUNDATIONS Vol. 50, No. 1, 161–172, Feb. 2010Japanese Geotechnical Society

EFFECTS OF DRY DENSITY AND GRAIN SIZE DISTRIBUTIONON SOIL-WATER CHARACTERISTIC CURVES OF SANDY SOILS

CHAMINDA PATHMA KUMARA GALLAGEi) and TARO UCHIMURAii)

ABSTRACT

The soil-water characteristic curve (SWCC) of soil plays the key roll in unsaturated soil mechanics which is a rela-tively new êld of study having wide applications particularly in Geotechnical and Geo-environmental Engineering. Toencourage the geotechnical engineers to apply unsaturated soil mechanics theories in routine practice, numericalmethods, based on the SWCC and saturated soil properties, have been developed to predict unsaturated permeabilityfunction and unsaturated shear strength properties which are expensive and time consuming to measure in laborato-ries. Further, several methods have been proposed to predict the SWCC in order to avoid di‹culties in measuring theSWCC in laboratories. It is time consuming and it may require special techniques or apparatus to measure the SWCCin laboratories. However, it is important to have laboratory measured data of SWCCs to enhance and verify theproposed numerical methods. Hence, employing a Tempe pressure cell apparatus, the present study aims to investigatethe eŠects of dry density and grain-size distribution on the SWCCs of sandy soils. Drying and wetting SWCCs were ob-tained for four sandy soils with diŠerent dry densities. The test data were best-ˆtted using the Fredlund and Xing(1994) equation and found that the ˆtting parameter, a, increases linearly with increasing the air-entry value of theSWCC and the ˆtting parameter, m, decreases with increasing the residual suction of the SWCC. The results revealedthat soils with a low density have lower air-entry value and residual suction than soils with a high dry density. Further,the maximum slope of drying SWCC and hysteresis of drying and wetting SWCCs decrease with increasing density ofsoil. The air-entry value, residual suction, and hysteresis (the diŠerence between the drying and wetting SWCCs) tendsto decrease when the eŠective D10 of the soil increases. A soil with uniform grain-size distribution (the steeper slope ingrain-size distribution) has a less hysteresis and a greater slope of drying SWCC than those of a non-uniform soil.

Key words: dry density, grain-size distribution, hysteresis of suction, model ˆtting, soil-water characteristic curve(IGC: F4)

INTRODUCTION

The relationship between water content and suction ofa soil is termed as the soil-water characteristic curve(SWCC). The most commonly used form of water con-tent is volumetric water content (Houston et al., 1999), uw

(deˆned as the volume of water in the soil divided by thetotal volume of soil, Vw/V ). The degree of saturation, S,is also used sometimes as a measure of water content forthe SWCC. The suction used for the SWCC is usually thematric suction, ua-uw (deˆned as the diŠerence betweenthe pore-air pressure and the pore-water pressure in thesoil), but the total suction is occasionally used as well.

Figure 1 illustrates typical drying and wetting SWCCs.The air entry value, AEV or ca, refers to the matric suc-tion that must be exceeded before air recedes into thepores of the soil during drying process (Brooks and Corey1964, 1966). As suction increases from zero to the AEVof the soil, the volumetric water content, uw, is nearlyconstant. Then the water content steadily decreases to the

residual water content, ur, as matric suction increases be-yond the AEV. The residual water content is the watercontent at residual state, at which water phase is discon-tinuous. The suction corresponding to the residual water

162

Fig. 2. Grain-size distributions of test materials

162 GALLAGE AND UCHIMURA

content is called residual soil suction. cr. Absorption anddesorption curves refer to the wetting and drying proc-esses, respectively. The diŠerence in water content at thesaturation between drying and wetting processes is theresidual (trapped) air content. The water-entry value, cw,on the wetting SWCC, is deˆned as the matric suction atwhich the water content starts to increase signiˆcantlyduring the wetting process.

In Fig. 1, the SWCC during wetting process is not thesame as that in drying process. This is referred to as hys-teresis, i.e., the soil's ability under similar suction to havetwo diŠerent water contents when the soil is being wettedor dried. For a speciêd suction value, the soil being wet-ted has less water content than the soil being dried. Suchhysteresis is due to the following. Within a group of soilgrains or aggregate, pores of various sizes exist that canbe visualized as many interconnecting bottlenecks. Thesmallest pores at the outermost of an aggregate governsthe maximum matric suction (or air entry value) of a par-ticular aggregate. Since the pore sizes are not uniformthrough an aggregate, larger pores can be found insidethe aggregate. These pores does not control or aŠect airentry value of the aggregate. They have the tendency toretain water if they are surrounded by pores of smaller di-ameter when the soil is being dried under constant matricsuction. However, these larger pores don't contain waterwhen the soil has been previously dried prior to beingwetted under similar matric suction. Hence, soil at dryingalways has greater water content than the soil at wetting(Orense, 2003).

A number of empirical models or equations have beendeveloped to describe the highly nonlinear SWCC (e.g.,van Genuchten, 1980; Mualem, 1986; Rossi and Nimmo,1994; Fredlund and Xing, 1994; Assouline et al., 1998;Aubertin et al., 1998). Among these equations, the vanGenuchten (1980) equation and the Fredlund and Xing(1994) equation were found to be the best SWCC modelsfor a variety of soils (Leong and Rahardjo, 1997).

The soil-water characteristic curve is central to the be-havior of an unsaturated soil (e.g., Fredlund and Ra-hardjo, 1993; Barbour, 1998). The SWCC can be relatedto other properties describing the behavior of the soil,such as the unsaturated coe‹cient of permeability (Fred-lund et al., 1994) and the shear strength (Vanapalli et al.,1996). Therefore, to encourage geotechnical engineers toimplement unsaturated soil mechanics theory in routinepractice, a number of methods for prediction of theSWCC have been developed (e.g., Gupta and Larson,1979; Arya and Paris, 1981; Haverkamp and Parlange,1986; Fredlund et al., 1997) to avoid time and moneyconsumption in measuring the SWCC in laboratories.The method proposed by Fredlund et al. (1997) uses thepore distribution in soil obtained from grain size distribu-tion curve to obtain the SWCC. The methods proposedby Arya and Paris (1981) and Gupta and Larson (1979)use statistical approach to predict SWCC using percen-tages of sand, silt and clay and bulk density. They con-ducted regression analyses using the cubic spline methodon experimental data to predict the SWCC. Any of these

previous studies has not investigated quantitatively theeŠects of grain size distribution and density on hysteresisof drying and wetting SWCCs, and ˆtting parametersused in respective methods. Therefore, it is important toconduct such a quantitative investigation to enhance thepredictive methods of the SWCC.

In this study, drying and wetting SWCCs for foursandy soils were obtained in the laboratory using a Tempepressure cell and the experimental data were ˆtted usingthe Fredlund and Xing (1994) equation. The obtained ˆt-ting parameters are correlated to the soil parameterswhich governs the shape of the drying SWCC. The eŠectsof dry density and grain size distributions of soils on theirdrying and wetting hysteresis and SWCCs parameters arethen discussed.

TEST MATERIALS AND APPARATUS

Test MaterialsFour diŠerent materials, namely Edosaki sand, Inage

sand, Tsukuba River sand, and Chiba soil, were em-ployed in the experimental work of this study. Edosakiand Inage sands were procured from two diŠerent naturalslopes in Ibaraki and Chiba Prefectures (Japan), respec-tively. Tsukuba River sand was obtained from a river bedin Tsukuba area in Ibaraki prefecture (Japan). Chiba soilwas excavated from a railway embankment in Chibaprefecture (Japan).

Wet sieving analysis and hydrometer tests were per-formed on Edosaki sand, Inage sand, and Chiba soil asthese materials contain ˆnes (particles ˆner than 0.075mm) contents of 17.1, 18.0, and 36z, respectively. Drysieving analysis was performed on Tsukuba River sand.These sieve and hydrometer analyses were conducted us-ing JGS (Japanese geotechnical Society) standard testmethod. The grain-size distributions of the four soils areshown in Fig. 2. Other basic soil properties such asspeciˆc gravity, maximum void ratio, minimum void ra-tio, compaction properties, and plasticity index weremeasured for the four soils using JGS standard testmethod and are shown in Table 1. These soils were classi-êd in accordance with the Uniêd Soil ClassiˆcationSystem using JGS standard test method and it was found

163

Table 1. Basic properties of test materials

Properties Edosakisand

Inagesand

TsukubaRiversand

Chibasoil

Speciˆc gravity, Gs 2.75 2.72 2.71 2.72

Mean Grain size, D50 [mm] 0.22 0.15 0.55 0.14

Coe‹cient ofuniformity,Uc＝D60/D10

17.10 18.00 4.50 54.40

Coe‹cient of gradation,Cc＝(D30)2/(D10*D60)

3.97 4.50 0.94 1.95

Sand content, [z] 83.60 73.53 98.00 64.00

Fines content, [z] 16.40 26.47 2.00 36.00

Plastic index NP NP NP 2.26

Maximum void ratio, emax 1.59 1.35 0.96 1.74

Minimum void ratio, emin 1.01 0.84 0.52 1.11

Fig. 3. Schematic diagram of Tempe pressure cellFig. 4. Saturation check of the high air-entry ceramic disk embedded

in the base plate of Tempe pressure cell

163EFFECTS OF DENSITY AND GRAIN SIZE ON SUCTION

that Edosaki sand, Inage sand, and Chiba soil were siltysand whereas Tsukuba River sand was well-graded.

Test ApparatusThe schematic diagram of the Tempe pressure cell

which was used in the laboratory to obtain soil-watercharacteristic curves of tests materials is shown in Fig. 3.This apparatus was designed and manufactured in thelaboratory. It consists of a brass cylinder with the innerdiameter of 50 mm and the height of 60 mm, a base plateon which a high air-entry (300 kPa) ceramic disk is em-bedded, and a top cap. A soil specimen is placed on thehigh air entry ceramic disk inside the retaining brass-cylinder of the Tempe pressure cell. A tube connected tothe base plate (underneath the high air entry disk) allowsin and out water ‰ow of the soil specimen. Air pressure issupplied through the tube connected to the top cap. Thetop and the bottom plate are fastened together during thetest. It is worthy to note that this Tempe pressure cell issimilar to a conventional one which can not be used to

apply conˆning pressure and to measure possible soilvolume change. However, in the conventional Tempepressure cell, the change in water content in the sample ismeasured by weighing or measuring the amount of out/in ‰ow during the test and therefore, the evaporation ofwater could lead to inaccurate water content calculation.In the Tempe pressure cell used in this study, change inwater content in the soil sample is measured by weighingthe assembly of the apparatus and therefore, the evapora-tion of out/in ‰ow water does not aŠect the calculation ofsoil water content.

TEST METHOD

The test procedure of the Tempe pressure cell mainlyinvolved saturation of the ceramic disk, sample prepara-tion, and obtaining drying and wetting SWCCs.

Saturation of the Ceramic DiskA test was started by saturating the high air-entry cer-

amic disk and the associated measuring system (the com-partment between the ceramic disk and the base plate, thetube connected to the base plate). In order to saturate theceramic disk and the associated system, ceramic disk em-bedded base plate was immersed in a vacuum cylinderand left for one day. During this time, tapping was doneto the cylinder in order to expel the trapped air in thewater and the disk itself.

After this process, a check was made to ensure the satu-ration of the associated system following the proceduredescribed by Huang (1994). To do the check, the fullysaturated system (the ceramic disk, the compartment be-low the ceramic disk, and the tube connected to the baseplate) was connected to a pore pressure transducer by thetube connected to the base plate. The surface of the cer-amic disk was then wiped using a soft dry paper and thereading of the pressure transducer was observed withtime. The saturation of the disk and the associated systemwas considered perfect when a negative pore-water pres-sure of about 60¿70 kPa was observed after drying thesurface of the disk by a soft dry paper (Huang, 1994).Otherwise, the described process of saturation was con-

164

Fig. 5. Saturation of the specimen


ducted again. Figure 4 shows the typical result of satura-tion check of the ceramic disk and the associated system.After conˆrming the saturation, the water was ‰ushedthrough the bottom of the ceramic disk in order tosaturate the upper portion of the disk which dried-upduring the saturation-check.

Sample PreparationAfter the saturation check of the disk and the associ-

ated system, the base plate was connected to a water tankto maintain the saturation of the disk and the associatedsystem. The brass-cylinder was then mounted andfastened to the base plate. Before sample preparation wasstarted, the soil was oven-dried and the mass of the soilrequired to achieve the target density was computed. Thesoil was then mixed with water to achieve the gravimetricwater content of 10z (for all tests). After closing the lineconnecting the base plate and the water tank and wipingout the surface of the ceramic disk, the required amountof soil was placed cylinder and compacted to the targetdensity (moist tamping technique). Then the preparedspecimen was saturated by sending water through thebase plate as shown in Fig. 5. During the saturation, theweight of the assembly (the base plate, cylinder, and thespecimen) was measured (after removing the excess waterfrom the surface of the specimen) time to time. When theconstant weight of the assembly was observed, the topcap was mounted and tightened. Generally the saturationof the sample took 2¿3 days.

Obtaining Drying and Wetting Soil-water CharacteristicCurves

The Tempe pressure cell was connected to a system asshown in Fig. 3. The water level of the water collectingtank was maintained at the middle height of the soil speci-men and the tank was always vented to atmospheric pres-sure (pore-water pressure in the sample (uw) was assumedto be zero throughout the test). As ˆrst step, without ap-plying any air-pressure (air-pressure in the specimen (ua)is zero) into the specimen, the weight of the assembly wasmeasured until constant weight was observed. The con-

stant weight of the assembly corresponding to zero suc-tion (ua-uw＝0) was recorded. Then the air-pressure (ua)was increased to another value (i.e., 0.5, 1.0, 2.0, 3.0,5.0, 7.0, 10.0, 20.0, 50.0, 100.0, 200.0 kPa) through theinlet tube on the top plate and the outlet tube located atthe base plate allowed water to drain out to the water col-lecting tank, which was opened to atmospheric pressure,and its water level was maintained at the middle height ofthe soil specimen. When the air pressure was applied,water was draining from the specimen through the highair-entry disk until the equilibrium was reached. When e-quilibrium was ensured (the assembly reached a constantweight) the weight of the assembly was noted (corre-sponding air-pressure was equal to the suction (ua-uw) asthe water pressure was maintained atmospheric). Duringthe weighting of the assembly, both tubes (inlet and out-let) were closed. The procedure was then repeated at ahigher applied air pressure (i.e., higher matric suction)and the drying process was stopped at the suction of 200kPa (applied air pressure 200 kPa).This apparatus cannot be used to obtain SWCC for the suction greater than300 kPa as the air entry value of the used ceramic disk is300 kPa.

The wetting process was simulated by decreasing the airpressure from 200 kPa keeping the water pressure at theconstant value of zero. Once the air pressure wasdecreased, water ‰owed into the cell through the disk un-til the equilibrium was reached. The weight of the assem-bly was noted when it reached the equilibrium. Thisprocedure was repeated at lower water pressure (i.e., low-er matric suction).

When the specimen reached zero matric suction in thewetting process (i.e., water pressure was equal to the airpressure), the assembly was disconnected from the systemand the water content corresponding to zero suction onwetting was measured by oven-drying the soil specimen.This water content together with previous change inweight of the assembly was used to back-calculate thewater contents corresponding to the other suction values.The suctions were then plotted against their corre-sponding water contents to obtain the SWCCs.

RESULTS AND DISCUSSION

The Fredlund and Xing (1994) equation which wasused in this study to ˆt the SWCC test data can be writtenas follows:

uw＝« us

sln [e＋(c/a)n]tm$«1－ ln (1＋c/cr)ln (1＋106/cr)$ (1)

where uw in the volumetric water content; us is the saturat-ed volumetric water content; a is a soil parameter relatedto the AEV of the soil (kPa); n is a soil parameter relatedto the slope between the AEV and the residual suction onthe SWCC; m is a parameter related to the residual watercontent portion of the curve; e is the natural number2.71828 . . .; c is any soil suction (kPa); cr is the residualsoil suction (kPa) corresponding to the residual watercontent, ur.

165

Table 2. Fredlund and Xing (1994) best-ˆt parameters

Drydensity[g/cm3]

Residualsuction[kPa]

Fredlund and Xingbest-ˆt parameters

Cr a [kPa] m n

Inage sand 1.35Drying 11.749 4.834 0.218 9.956

Wetting 4.805 1.818 0.154 20

Tsukuba sand 1.35Drying 5.087 2.293 0.203 5.087

Wetting 2.465 0.970 0.164 20

Edosaki sand

1.22Drying 6.525 2.233 0.443 6.893

Wetting 6.558 1.273 0.552 2.927

1.35Drying 10.130 3.320 0.403 5.453

Wetting 6.086 1.674 0.400 5.512

1.50Drying 11.255 3.979 0.291 6.845

Wetting 6.095 1.863 0.254 6.964

Chiba soil

1.25Drying 11.913 3.696 0.195 10.729

Wetting 3.039 0.642 0.163 6.406

1.35Drying 12.283 5.115 0.162 12.283

Wetting 2.348 1.315 0.116 1.315

1.42Drying 19.555 7.123 0.130 14.099

Wetting 6.416 1.282 0.126 6.137

Fig. 6. Soil-water characteristic curves of Inage sand for dry densityof 1.35 g/cm3


Fredlund and Xing (1994) model has the following ad-vantages over the van Genuchten model:

(1) Provides a good ˆt for general soils over the entiresuction range of 0 to 106 kPa.

(2) Since there are three ˆtting parameters (a, m, n)better data ˆtting can be obtained (van Genuchtenmodel has only two ˆtting parameters).

(3) Some ˆtting parameters used in FX model havephysical meaning: a has unit of pressure and closelyrelated to AEV of soil, n controls the slope of theSWCC curve.

The ˆtting parameters in Eq. (1) (a, n, m) describe theshape of the SWCC. To best-ˆt the experimental data,these parameters can be obtained by the least square op-timization method using experimental data and nonlinearcurve-ˆtting algorithms as explained by Fredlund andXing (1994).

Soil-water Characteristic Curves of Test MaterialsDrying and wetting soil-water characteristic curves

(SWCCs) for the four test materials were obtained using aTempe pressure cell in the laboratory. Inage and Tsukubasand samples with dry density of 1.35 g/cm3, Edosakisand samples with dry densities of 1.22, 1.35, and 1.50g/cm3, and Chiba soil samples with dry densities of 1.25,1.35, and 1.42 g/cm3 were used in this experimental pro-gram. The experimental data were best-ˆt using the equa-tion Eq. (1) proposed by Fredlund and Xing (1994). Thisequation provides a good ˆt for sand, silt, and silt soilsover entire suction range from 0 to 106 kPa. The air-entryvalue, residual suction, maximum slope, and ˆttingparameters (a, m, n) of SWCCs were obtained using theSoilVision computer software (SoilVision systems Ltd.Ver. 4.14). The obtained ˆtting parameters and residualsuction values of SWCCs are listed in Table 2.

The experimental data and the best-ˆt SWCC results oftest materials for diŠerent densities are shown in Figs.6–13. The results show that the best-ˆt SWCCs using theFredlund and Xing (1994) equation closely describes theSWCC data of test materials. The best-ˆt parameters ofthe Fredlund and Xing (1994) are further discussed in thisstudy.

The laboratory obtained drying SWCCs are diŠerenteach other due to the eŠects of the grain-size distributionand the initial dry density. The diŠerences of the SWCCsare determined by the diŠerences of the SWCCparameters such as the air-entry value, ca, residual suc-tion, cr, and the slope of SWCC. In this study, an at-tempt was made to correlate the SWCC parameters to theˆtting parameters (a, n, and m) of the Fredlund and Xing(1994) equation. As Shown in Fig. 14, the air-entryvalues, ca, and the ˆtting parameter, a, are closely relatedand have an apparent linear relationship. The greater theca value, the greater the a value. Similarly, the residualsuction values, cr, are related to the ˆtting parameter m(Fig. 15) such a way that the larger the cr value, thesmaller the m value. These ˆndings are consistent withLeon and Rahardjo (1997) and Hong et al. (2004).

The maximum slope of SWCC was obtained by extend-

ing the steepest straight portion of the SWCC as shown inFig. 16. Two points on the extended line were selectedand the corresponding water content and suction valueswere used in the following equation to calculate the maxi-mum slope of the SWCC.

The maximum slope of the SWCC＝u1－u2

log Øc2

c1»

(2)

The maximum slope of drying SWCC was plotted againstthe ˆtting parameter n as shown in Fig. 17. A clear corre-lation can not be observed between these two. However,Hong et al. (2004) observed that the steeper the slope of

166

Fig. 7. Soil-water characteristic curves of Tsukuba sand for dry den-sity of 1.35 g/cm3

Fig. 8. Soil-water characteristic curves of Edosaki sand for dry densityof 1.22 g/cm3

Fig. 9. Soil-water characteristic curves of Edosaki sand for dry densityof 1.35 g/cm3

Fig. 10. Soil-water characteristic curves of Edosaki sand for dry den-sity of 1.50 g/cm3

Fig. 11. Soil-water characteristic curves of Chiba soil for dry densityof 1.25 g/cm3



the SWCC, the larger the parameter n. Note, the valuesshown within brackets in Figs. 14, 15 and 17 are the ini-tial dry density values for which the drying SWCCs wereobtained.

EŠects of the Initial Dry Density on Soil-water Character-istic Curves

The initial dry density of silty soils has some signiˆcanteŠects on the soil-water characteristic curve as shown inFigs. 18 and 19. In order to observe the eŠects of the ini-tial density on the SWCC parameters, the laboratory ob-tained drying SWCCs of Edosaki sand and Chiba soil for

167


Fig. 14. Fitting parameter a in Fredlund and Xing (1994) equation ver-sus air-entry (AEV) of drying SWCCs of test materials (the valuesshown in brackets are initial dry density)

Fig. 15. Fitting parameter m in Fredlund and Xing (1994) equationversus residual suction of drying SWCCs of test materials (thevalues shown in brackets are initial dry density)

Fig. 16. The maximum slope of the soil-water characteristic curve

Fig. 17. Fitting parameter n in Fredlund and Xing (1994) equationversus slope of drying SWCCs of test materials (the values shown inbrackets are initial dry density)

Fig. 18. EŠects of dry density on drying SWCCs for Edosaki sand


the diŠerent dry densities are considered. As the initialdry density of silty soil increases, the air entry value of thesoil increases (Fig. 20). As shown in Fig. 21, the high-density specimens de-saturate at a slower rate than thelow-density specimens. As a result, the high-density

specimens have higher water contents than the low-den-sity specimens at matric suctions beyond their air entryvalues (Figs. 18 and 19). Therefore, the residual suction,cr, increases eventually with the increase in the initial drydensity (Fig. 22). These ˆndings are consistent with theresults of Croney and Coleman (1954). For comparison,the AEV is plotted with void ratio and relative density asshown in APPENDIX A and found the same R2 value for

168

Fig. 19. EŠects of dry density on drying SWCCs for Chiba soil

Fig. 20. The variation of the air-entry value (AEV) with the dry den-sity of sand

Fig. 21. The variation of the slope of drying SWCC with the dry den-sity of sand

Fig. 22. The variation of the residual suction with the dry density ofsand


linear correlation which is obtained by plotting AEV withdry density.

Aitchison (1960) pointed out that the matric suction (ua

-uw) obeys a simple capillary model as follows:

ua－uw＝2Ts

Rs(3)

Where Ts＝the surface tension force of water (N/m)Rs＝Radius of curvature of meniscus (m)

With the increase of density of a soil sample, the size andthe number of pores in the soil matrix reduces. As aresult, the radius of curvature of meniscus decreases andthe corresponding suction increases. Therefore, the suc-tion required for air to enter into the soil matrix (air-entryvalue) increases. Similarly, for the same volumetric watercontent, the higher the initial density is the greater thesuction value. Increasing in the initial density of a soilsample, the permeability of soil is decreased. This canlead to slower the de-saturation process and also to in-crease the air-entry value and the residual suction.

Croney and Coleman (1954) further revealed that theeŠect of initial water content on the drying curves of in-compressible soils has similar eŠect, as was illustrated bythe initial dry densities. An increase in the initial watercontent of the soil results in a decrease in the air entryvalue. This can be attributed to the large pore sizes in thehigh initial water content mixtures. This soils drainquickly at relatively low matric suctions. As a result, thewater content in the soil with the large pores is less thanthe water content in the soil with the small pores at matricsuctions beyond the air entry value. In other wards, soilswith low initial water content (or small pore sizes) requirea large matric suction value in order to commence de-saturation. There is then a slower rate of water drainagefrom the pores.

In this study, the hysteresis between the drying andwetting SWCCs is quantiêd as shown in Fig. 23, wherethe area between the drying and wetting SWCCs as com-puted on logarithm scale over the suction range from 0.1to 106 kPa. First, drying and wetting SWCC data were ˆt-ted using Eq. (1) and corresponding ˆtting parameterswere obtained. Then, the two curves were integrated overthe suction range of 0.1 to 106 kPa. The diŠerence of thetwo integrated values would give the hysteresis as shownin the following equation:

169

Fig. 23. The deˆnition of hysteresis of the soil-water characteristiccurves

Fig. 24. The variation of the hysteresis with the dry density of sand

Fig. 25. The variation of air-entry value and residual suction of dryingSWCC with grain-size parameter D10

Fig. 26. The variation of slope of drying SWCC with the slope ofgrain-size distribution curve


Hysteresis＝

106

f0.1

(uw)dryingdc－

106

f0.1

(uw)wettingdc (4)

where, (uw)drying is Eq. (1) ˆtted for drying data, (uw)wetting isEq. (1) ˆtted with wetting data, c is suction.

Water content is unit less quantity and suction has theunit of pressure. Therefore, as shown in Eq. (4), the hys-teresis could have the unit of pressure and in this study, itis kPa.

As shown in Fig. 24, the hysteresis associated with thehigh-density specimens is less than the hysteresis exhibit-ed by the low-density specimens. The possible reasons forthis behavior may be less pore-volume and greater capil-lary potential created by the denser soil sample.

EŠects of Grain Size Distributions on Soil-water Charac-teristic Curves

Since the SWCC depends on the pore-size distributionof the soil, it is directly related to the grain-size distribu-tion. Holtz and Kovacs (1981) assumed that the averagepore-diameter is about 20z of the mean grain-size, D10,hence, the attempt was made in this study to relate D10 ofa soil to its SWCC parameters. To examine the eŠects ofD10 on SWCC parameters, the drying SWCCs obtainedfor the four test materials with initial dry density of 1.35

g/cm3 were considered. It could be reasonable to com-pare with the same value of density as their speciˆc gravi-ty (Gs) are similar (2.71¿2.75). Further, AEV, residualsuction, and hysteresis were correlated with D10, D30, D50,D60, and Uc ( see APPENDIX B) and found that D10

would give better correlation with AEV, residual suction,and hysteresis.

As shown in Fig. 25, both the AEV and the residualsuction correlate well with the D10 of the soils. The AEVand the residual suction decrease with the increase in theD10. The larger the D10 the coarser the soils, the coarsegrained soils have bigger voids and hence, air can easilyenter into the soil skeleton (small AEV). It can also beseen in Fig. 24 that the diŠerence between the residualsuction and the AEV decrease with the increase in the D10.From Figs. 25 and 26, it can be extracted that the maxi-mum slope of drying SWCC increases with the increase inthe D10.

Figure 26 depicts the relationship between the maxi-mum slope of the drying SWCC and the slope of grain-size distribution curve of sandy soils. The results showthat a steep slope of drying SWCC is caused by a steepgrain size distribution curve. This observation indicates

170

Fig. 27. The eŠects of the slope of grain-size distribution on hysteresis

Fig. 28. The eŠects of D10 on hysteresis


that the drying SWCC is closely related to the grain sizedistribution of the soil. Because of this strong correlationbetween the drying SWCC and the grain size distributioncurve, many empirical methods have been developed topredict the drying SWCC directly from the grain-size dis-tribution of the soil (Fredlund et al., 1997).

Figures 27 and 28 show how the hysteresis of SWCCs isaŠected by the slope of grain size distribution curve andthe grain-size parameter, D10, respectively. The resultssuggest that the hysteresis between the drying and thewetting SWCCs decreases with increasing the slope of thegrain size distribution curve of the soils. It can be furtherdecreased by increasing the grain-size parameter, D10. Auniform particle distribution (i.e., a steep slope of grain-size distribution) creates uniform pore-sizes and hencethe diŠerence between water contents in drying and wet-ting at the same suction decreases (less histeresis). Withincreasing grain size (D10), the numbers of bigger poresincrease and the number of smaller pores which sig-niˆcantly aŠect the hysteresis of drying and wettingSWCCs decrease. Hence, the increase in D10 may reducethe diŠerence between the drying and wetting SWCCs.

CONCLUSIONS

In the present study, drying and wetting soil-watercharacteristic curves were investigated for four sandysoils. The experimental data of SWCCs obtained fromTempe pressure cell were best-ˆtted using the Fredlundand Xing (1994) equation. The ˆtting parameters andSWCC's parameters were then correlated. The eŠects ofdry density and the grain-size distribution on the SWCC'sparameters and the hysteresis in drying and wettingSWCCs were investigated. Accordingly, the followingconclusions were drawn.

(1) The ˆtting parameter, a, exhibits a linear relation-ship with the air-entry of drying SWCC. a increaseswith increasing the air-entry value,

(2) As the residual suction of drying SWCC increases,the ˆtting parameter, m, may decrease. The ˆttingparameter, n, does not exhibit any clear correlationwith the maximum slope of drying SWCC.

(3) Both the air-entry value and the residual suction ofdrying SWCC may increase as dry density of sandysoil increases. However, the area between dryingand wetting SWCCs (i.e., hysteresis) seems todecrease with increasing dry density of soils.

(4) A coarse-grained soil has a lower air-entry value,lower residual suction than a ˆne-grained soil.

(5) The SWCC of a uniform soil has a steeper slopethan that of a less uniform soil. In other word, thesteeper the slope of grain-size distribution curve thegreater the slope of the SWCC.

(6) A uniform coarse-grained soil has a smaller hyste-resis than a less uniform, ˆne-grained soil.

ACKNOWLEDGEMENT

The authors gratefully acknowledge the PromotingFundamental Transport Technology Research of theJapan Railway Construction, Transport and TechnologyAgency (JRTT), and Grants-in-Aid for ScientiˆcResearch of the Japan Society for the Promotion ofScience (JSPS) for the ˆnancial support for this study.The ˆrst author acknowledges the scholarship receivedfrom the Ministry of Education, Science and Culture,Government of Japan (MONBUSHO) for reading doc-toral degree at the University of Tokyo, Japan.

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APPENDIX A

Fig. AA1. The variation of air-entry value of drying SWCC with ini-tial void ratio

Fig. AA2. The variation of air-entry value of drying SWCC with ini-tial relative density

APPENDIX B

Fig. AB1. The variation of air-entry value of drying SWCC withgrain-size parameters


Fig. AB2. The variation of air-entry value of drying SWCC withcoe‹cient of uniformity

Fig. AB3. The variation of residual suction of drying SWCC withgrain-size parameters

Fig. AB4. The variation of hysteresis of drying SWCC with grain-sizeparameters

EFFECTS OF DRY DENSITY AND GRAIN SIZE DISTRIBUTION ON …

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