Modulus−suction−moisture relationship for compacted soils

Modulus–suction–moisture relationship forcompacted soils

Auckpath Sawangsuriya, Tuncer B. Edil, and Peter J. Bosscher

Abstract: The ultimate parameter of interest in engineering design of compacted subgrades and support fills for highways,railroads, airfields, parking lots, and mat foundations is often the soil modulus. Modulus of compacted soils depends notonly on dry unit weight and moisture but also on matric suction and soil structure (or fabric) resulting from the compac-tion process. However, these relationships in the as-compacted state (i.e., immediately after compaction) have not yet beenextensively explored. This paper presents an experimental laboratory study of the shear modulus – matric suction – mois-ture content-dry unit weight relationship using three compacted subgrade soils. Compacted subgrade specimens were pre-pared over a range of molding water contents from dry to wet of optimum using enhanced, standard, and reduced Proctorefforts. A nondestructive elastic wave propagation technique, known as bender elements, was used to assess the shearwave velocity and corresponding small-strain shear modulus (Go) of the compacted subgrade specimens. The matric suc-tions were measured with the filter paper method. An empirical relation that takes into account the effect of compactionconditions is proposed for the Go – matric suction – molding water content relationship of compacted subgrade soils.

Key words: modulus, moisture, suction, bender elements, shear wave velocity, compacted soils.

Resume : Le parametre ultime d’ingenierie qui est d’interet dans le calcul d’ingenieur des infrastructures compactees etdes remblais de soutien pour les autoroutes, les voies ferrees, les aeroports, les aires de stationnement, et les nattes defondations est souvent le module du sol. Le module des sols compactes dependent non seulement du poids volumique secet de la teneur en eau mais aussi de la succion matricielle et de la structure du sol (ou fabrique) resultant du processus decompactage. Cependant, ces relations dans l’etat tel que compacte (c.-a-d. immediatement apres compactage) n’ont pasencore ete abondamment explorees. Cet article presente un etude experimentale en laboratoire de la relation module decisaillement – succion matricielle – teneur en eau – poids volumique sec en utilisant ces sols d’infrastructure compactes.Des echantillons d’infrastructure compactes ont ete prepares dans une large plage de teneurs en eau de moulage en partantdu cote sec au cote mouille de l’optimum et en utilisant des efforts Proctor augmentes, standard, et reduits. Une techniquede propagation d’ondes elastiques non destructives au moyen de languettes piezoceramiques a ete utilisee pour evaluer lavitesse de l’onde de cisaillement et le module correspondant de cisaillement a faible deformation (Go) des specimensd’infrastructure compactes. Les succions matricielles ont ete mesurees avec la methode du papier filtre. On propose unerelation empirique qui prend en compte l’effet des conditions de compactage pour la relation Go – matrice de succion –teneur en eau de moulage des sols d’infrastructure compactes.

Mots-cles : module, humidite, succion, elements piezoceramiques, vitesse de l’onde de cisaillement, sols compactes.

[Traduit par la Redaction]

Introduction

Currently, typical earthwork compaction acceptancecriteria are based on the specified target dry unit weight ofthe placed earthen materials achieved through appropriatemoisture content and compaction energy. According to thisapproach, achieving a certain dry unit weight using anappropriate level of compaction energy, assures attainment

of an optimum level of structural properties, minimizes theavailable pore space, and limits future moisture contentchanges and consequent property degradation. In importantprojects, various laboratory and field tests are employed torelate the achieved level of compaction to mechanical prop-erties such as modulus.

One of the potential approaches for rapidly and directlyassessing soil modulus, both in the laboratory and the field,is to employ the small-strain modulus tests. The small-strainmodulus of soils is routinely measured in earthquakeengineering. In pavement engineering, the application ofsmall-strain modulus tests to assess the modulus of pave-ment materials and structural variability for pavementperformance has increased dramatically (Kim and Stokoe1992; Souto et al. 1994; Kim et al. 1997; Chen et al. 1999;Nazarian et al. 1999; Fiedler et al. 2000; Yesiller et al.2000; Zeng et al. 2002; Nazarian et al. 2003; Sawangsuriyaet al. 2005; Edil and Sawangsuriya 2005). The main advant-age of small-strain modulus tests is the ability to noninva-sively and nondestructively assess the modulus of pavement

Received 30 May 2007. Accepted 25 February 2008. Publishedon the NRC Research Press Web site at cgj.nrc.ca on 7 July2008.

A. Sawangsuriya. Road and Pavement Design Branch, Bureauof Materials, Analysis and Inspection, Department of Highways,Bangkok, Thailand.T.B. Edil1 and P.J. Bosscher.2 Geological EngineeringProgram, Department of Civil and Environmental Engineering,University of Wisconsin, Madison, WI 53706, USA.

1Corresponding author (e-mail: [email protected]).2Deceased.

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materials at the surface or under a free-field condition (i.e.,near-zero confining pressure). Laboratory test methods arealso available for small-strain modulus tests that can repro-duce similar results to those measured in the field.

Unsaturated soil behavior plays a significant role in themechanical properties of compacted pavement subgrades.Typical compaction specifications require that subgradesoils be compacted in the field at or near optimum watercontent and at a specified percentage of the laboratory maxi-mum dry unit weight (i.e., relative compaction). Conse-quently, compacted subgrade soils are in an unsaturatedstate during construction. In unsaturated soil mechanics,matric suction is an important parameter that governs thestate of stress and represents the difference between thefree energy of the water in the soil and that of pure waterin a free surface condition. However, matric suction is notroutinely quantified in geotechnical engineering practice.Furthermore, there is no unique relationship betweenmodulus and dry unit weight alone. Similar modulus underthe same stress condition can correspond to several valuesof dry unit weight depending on current moisture contentand matric suction. In view of recent increased interest inimplementing modulus-based monitoring of compactionsuch as the use of stiffness gauges and intelligent compac-tion, a relationship among shear modulus, dry unit weight,moisture content, and matric suction is developed for dif-ferent soil compositions and compaction conditions. Under-standing the influence of these factors on modulus is likelyto enhance the implementation of the small-strain modulusin monitoring the mechanical property quality of subgradesduring earthwork construction monitoring (i.e., in the as-compacted state). The objective of this study is to investi-gate the small-strain shear modulus as a function of matricsuction, dry unit weight, and moisture content for threetypes of compacted subgrade soils at their initial compactionstate. Factors that influence the relationship are addressed.Based on the limited data available, a mathematical modelis also developed for the shear modulus – matric suction –moisture compaction energy relationship of compacted sub-grades.

Review of past studies

Three factors — dry unit weight, moisture content ordegree of saturation, and compaction conditions (i.e., com-paction efforts, method of compaction), have been shown toaffect the modulus of the compacted subgrade for a givensoil (Shackel 1973). In general, the modulus increases withthe dry unit weight but decreases as the molding moisturecontent increases. The difference in compaction conditionscauses alterations in soil structure and hence the modulus.

Because of its rapid and simple approach, nondestructiveseismic waves are often employed, and the P- and (or)S-wave velocities are monitored to determine the small-strain Young’s and (or) shear moduli when the total massdensity is known. Many studies reported the correlation ofwave velocities and small-strain moduli with the dry unitweight, water content, degree of saturation, and strengthparameters (Sheeran et al. 1967; Marinho et al. 1996;Nazarian et al. 1999, 2003; Yesiller et al. 2000; Ooi andPu 2003; Yuan and Nazarian 2003). Besides dry unit

weight, moisture content or degree of saturation, and com-paction conditions, matric suction also governs the modu-lus behavior of compacted soils, which are typically in anunsaturated state (Edil et al. 1981). Matric suction is thepotential energy of soil water created by capillary tensionbetween soil particles and pore water and surface adsorp-tive forces. Matric suction constitutes about 40%–75% oftotal suction in fine-grained soils (Sivakumar Babu et al.2005).

Both dry unit weight and moisture content reflect the cur-rent physical state of the soil, while matric suction definesthe state of stress in unsaturated soils and varies with thechanges in moisture content. Since modulus is sensitive tothe state of stress within a subgrade and the matric suctionimpacts the state of stress, it is crucial to understand theinfluence of matric suction on modulus. Past research sug-gested that the modulus of unsaturated soils is strongly in-fluenced by matric suction and a good correlation was alsoobserved between modulus and matric suction (Sauer andMonismith 1968; Edil 1973; Fredlund et al. 1977; Edil etal. 1981; Khoury et al. 2003; Yang et al. 2005). Therefore,the matric suction should be treated as an independentparameter in establishing the relationship among shearmodulus, matric suction, dry unit weight, and moisturecontent.

Properties of test soilsDisturbed samples of a lean clay (CL), a silt (ML), and a

clayey sand (SC) collected from Red Lake Falls, Minnesota;Red Wing, Minnesota; and Anaheim, California, respec-tively, were selected for this study. The CL soil has thehighest plasticity and percent fines, while the SC soil hasthe lowest plasticity and percent fines. These soil samplesrepresent typical pavement subgrades and cover a reasonablerange in composition. The classification, index properties,and compaction characteristics of the test soils are summar-ized in Table 1.

Testing program

Specimen preparationSoil samples were air dried until friable and then pulver-

ized with a mallet. After measuring the moisture content ofthe processed and air-dried soil, a calculated amount ofwater was added to obtain the predetermined molding watercontent. Subsequently, the moist soil sample was sealed in aplastic bag for 24 h to allow the moisture content to equili-brate prior to compaction.

Moisture-equilibrated samples of all three soils were com-pacted in a standard Proctor mold (103.5 mm in diameterand 116.4 mm high). All specimens were compacted in threelayers using the standard Proctor hammer having a 24.4 Nrammer dropped from a height of 305 mm. The SC soil wascompacted with three levels of compaction energy: reducedProctor effort, standard Proctor effort, and enhanced Proctoreffort. These correspond to the number of hammer blowsper layer at 15, 25, and 35, respectively. The resulting com-paction energies per unit volume of soil used for reducedProctor effort, standard Proctor effort, and enhanced Proctoreffort are 357, 594, and 832 kN�m/m3, respectively. Theother two soils, namely CL and ML, were prepared with

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only standard Proctor effort. In each case, a series of fivespecimens were compacted over a range of molding watercontents: 4% dry of optimum (opt–4%), 2% dry of optimum(opt–2%), 2% wet of optimum (opt+2%), 4% wet of opti-mum (opt+4%), and at optimum (opt). The resulting dryunit weights and moisture contents of the test soils in termsof their compaction curves are given in Fig. 1.

Small-strain shear modulus experiment

Bender element test systemThe small-strain shear modulus of the compacted speci-

mens was determined based on a shear wave propagationtechnique using bender elements. A pair of bender elementswas employed to generate and receive the shear wave. Thesebender elements were supported in a custom-made housingdesigned as a bolt-clamp anchoring system. Detailed infor-mation on this bender element system is given in Sawang-suriya et al. (2006).

The instrumentation system for the bender element testconsists of two main components: a signal generator and adigital oscilloscope. A signal generator produces the outputsignal in the form of a square pulse to a transmittingbender element. This signal is generated and controlled us-ing LabVIEW 7 Express, a graphical programming lan-guage by National Instruments that drives a multifunctionNational Instruments PCI-6014 data acquisition board. Theamplitude of the square pulse varied from ±10 to ±50 V toenhance the response of the bender element – soil system.The square input signal was used in this study because itgives a clear response regardless of soil modulus and is ad-vantageous when the resonant frequency in the bender ele-ment – soil system is unknown (Kawaguchi et al. 2001;Lee and Santamarina 2005). Jovicic et al. (1996) provide agood explanation for selection of the input signal. The A 2-channel digital oscilloscope, PICO ADC200 high speedanalog-to-digital converter, with a maximum sampling rateof 50 megasamples per second and a resolution of 8 bitswas used to display and collect the signals from both thetransmitting and the receiving bender elements. Tensampled signals were stacked to improve the signal-to-noiseratio.

Test procedureA pair of bender elements was mounted to the sides of the

specimen at the mid-height in diametrically opposite posi-tions. The shear wave propagating in the horizontal (diamet-rical) direction with soil particles vibrating in a horizontalplane (Shh) was monitored and the travel time of the Shh-wave(ts,hh) was measured across the diameter of the specimen(i.e., in the horizontal plane). The Shh-wave was evaluatedbecause the soil fabric tended to be more uniform andhomogenous in this propagation plane than in the verticalplane. In addition, this Shh-wave coincides with the planeof isotropy in an assumed cross-anisotropy medium(Pennington et al. 1997). For the cross-anisotropy case, thehorizontal plane is an isotropic plane with symmetry alongthe vertical axis. To avoid the near-field component (San-chez-Salinero et al. 1986; Viggiani and Atkinson 1995),the first arrival of shear wave was taken as the point ofzero crossing after first inflection of the received signal(Fig. 2), which corresponds to the first arrival of shear

Fig. 1. Compaction data of test soils. Dashed lines represent prede-termined compaction curves. Enh Proc, enhanced Proctor; Std Proc,standard Proctor; Red Proc, reduced Proctor; ZAV, zero air voids;Gs, specific gravity.

Table 1. Properties of test soils.

PropertiesLean clay(Red Lake Falls, Minn.)

Silt(Red Wing, Minn.)

Clayey sand(Anaheim, Calif.)

Sample designation USCSa CL ML SCAASHTOb A-7–6 (23) A-4 (0) A-2–4 (0)Liquid limit 42 28 28Plastic index 24 11 14Sand (%) 8.9 11.9 59Silt (%) 63.8 82.4 23Clay (%) 27.3 5.7 18Fines (%) 91.1 88.1 41Specific gravity 2.73 2.69 2.70Optimum moisture content (%)c 22.0 13.5 13.5Maximum dry unit weight (kN/m3)c 15.8 17.9 18.5

aLetters in sample designation refer to Unified Soil Classification System (USCS) soil symbol.bAmerican Association of State Highway and Transportation Officials (AASHTO) soil classification.cASTM D 698 (Method A).

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wave based on experimental and numerical studies (Vig-giani and Atkinson 1995; Kawaguchi et al. 2001; Lee andSantamarina 2005). The travel distance is taken as the tip-to-tip distance (L) between bender elements (Dyvik andMadshus 1985; Viggiani and Atkinson 1995). Lastly, thevelocity of Shh-wave is computed as Vs,hh = L/ts,hh. Know-ing Vs,hh and the total mass (bulk) density of the specimen(�), the corresponding small-strain shear modulus in thehorizontally isotropic plane from Shh-wave (Go,hh) can bedetermined using the following equation:

½1� Go;hh ¼ �V2s;hh

Note that the soil fabric is assumed to be uniform andhomogenous in this horizontal plane. Furthermore, if thesoil is assumed to be cross-anisotropic, this Go,hh representsthe shear deformation in the horizontally isotropic plane andcan be used to determine the elastic parameters. Sawang-suriya (2006) studied the influence of the soil fabric orstructure of the compacted kaolinite specimens on Go. Theshear moduli were measured from the dry to wet side ofoptimum compaction moisture contents. The shear modulimeasured longitudinally were consistently lower than thosemeasured diametrically. The shear moduli measured diamet-rically showed minor variation regardless of polarization(Sawangsuriya 2006). The fabric or inherent anisotropy ofsmall-strain modulus of compacted soils is beyond thescope of this study. However, this issue could be neglected

by the selection of the horizontal plane for wave propaga-tion.

Matric suction determinationThe filter paper technique was employed to measure

matric suction. The filter paper method was performed inaccordance with ASTM D 5298 (ASTM 2003). This methodwas selected because: (i) it is capable of measuring a widerange of matric suctions (i.e., from 10 kPa to 10 MPa), (ii)it is relatively simple and inexpensive, and (iii) it has beenwidely used in geotechnical engineering practice (Fredlundand Rahardjo 1993; Houston et al. 1994; Melgarejo et al.2002; Sivakumar Babu et al. 2005).

The filter paper disks used in this study were WhatmanNo. 42, ashless quantitative Type II. A stainless steel retain-ing ring with a diameter of 73 mm and a height of 25 mmwas used to trim two test specimens from the compactedsoil specimen. Trimming was carefully performed so thatthe retaining ring could slide over the soil specimen withminimum effort. The top and bottom of the specimen weretrimmed flush with the retaining ring. After trimming wascompleted, the retaining ring was removed, and the gravi-metric water content was determined from the excess soil.To measure the matric suction, three initially dry filterpapers were sandwiched between the two trimmed speci-mens. The center filter paper was used for suction measure-ment, while the outer filter papers were used to protect thecenter filter paper from soil contamination. To ensure goodcontact between the specimen and the filter paper, a lightmass was applied on the top of the specimen. The twospecimens sandwiching the filter papers were kept in sealeddouble-layered containers and stored inside an insulatedchest to avoid any moisture loss and to minimize fluctua-tions of the room temperature. An equilibrium period of atleast 7 d was allowed for the specimens, filter paper, andthe air in the sealed container to reach equilibrium.

At the end of the equilibration period, the filter paperswere removed from the soil specimen, and the wet mass ofthe center filter paper was measured. The measurementprocess was completed within a few seconds to avoid mois-ture loss from the filter paper. Subsequently, the moisturecontents of the filter paper and the soil were individually de-termined. The matric suction of the specimen was obtainedfrom the calibration curve using the filter paper moisturecontent. The calibration curve represented by two equations(i.e., different sensitivities of the filter paper response in thehigher and lower suction range) is usually appropriate formeasuring matric suction with Whatman No. 42 filter paper(Leong et al. 2002). Although many calibration curves forthe same filter paper are available in the literature (Hamblin1981; Chandler et al. 2002; Leong et al. 2002), the bilinearequation suggested in ASTM D 5298 was used in this studyto relate the filter paper water content to the equivalent suc-tion of the soil specimen. Leong et al. (2002) also indicatedthat the Whatman No. 42 filter paper can be used with theASTM D 5298 equation to reliably obtain matric suction ofthe soil via the contact method.

In addition to the filter paper technique, the thermal dissi-pation sensor technique was employed as an alternative testwith which to compare the matric suction measured with thefilter paper technique. The thermal dissipation sensor is a

Fig. 2. Shh-wave traces of the silt (ML) soils compacted with stan-dard Proctor effort.

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device for measuring matric suction both in the laboratoryand in the field. Although this sensor has been increasinglyemployed in the field applications (Fredlund et al. 1992;Phene et al. 1992; Shuai and Fredlund 2000; Flint et al.2002; Nichol et al. 2003; Tan et al. 2004), no standard testprocedure is currently available. Similar to other indirectmethods, the accuracy of the suction measurements usingthe thermal dissipation sensor are highly dependent on thecalibration. Proper calibration is required for each sensorprior to deployment. Detailed description of suction meas-urements with the filter paper technique and the thermal dis-sipation sensor are given by Sawangsuriya (2006).

Experimental results

Shear wave time seriesAn example of Shh-wave traces is presented in Fig. 2 for

the ML soil compacted at various molding water contentsusing standard Proctor effort. Traces of the Shh-wave for theSC soil compacted with enhanced Proctor, standard Proctor,and reduced Proctor efforts, and for the CL soils compactedwith standard Proctor effort are given in Sawangsuriya(2006). The repeatability of the Shh-wave measurement isalso presented in Sawangsuriya (2006).

Matric suctionFigure 3 shows the plot of matric suction versus molding

water content for three types of compacted soils. The matricsuctions obtained from all test soils varied from 10 kPa to10 MPa for the range of molding water contents from 4%dry of optimum to 4% wet of optimum. In general, matricsuction decreases as molding water content increases. TheML soil exhibits the lowest matric suctions, while the matricsuctions of the CL soil are the highest at a given moisturecontent. The results for the SC soil compacted with threelevels of compaction energy indicate that the SC specimenscompacted with standard Proctor effort exhibit higher matricsuctions than those compacted with reduced or enhancedProctor efforts. Consistent trends were also observed in suc-tion measurements using the thermal dissipation sensors onthe identical specimens. Results suggest that the influenceof molding water content on suction is more significantthan that of compaction energy.

To provide some indication of the reliability of the filterpaper technique, the matric suction as measured by the filterpaper technique is compared with that measured by the ther-mal dissipation sensor. The results indicate that both methodsagree fairly well for the specimens compacted on the wetside of the optimum moisture content (see Fig. 3). However,larger discrepancies, as much as an order of magnitude,were observed for the specimens compacted on the dryside of the optimum moisture content curve. A scatter plotcomparison is shown in Fig. 4. This discrepancy can beexplained by the degree of contact between the soil specimenand the suction measurement device. Good contact betweenthe soil specimen and the filter paper or between the soilspecimen and the thermal dissipation sensor might be diffi-cult to achieve for the specimen compacted on the dry sideof the optimum moisture content. Fredlund and Rahardjo(1993) also indicated that the degree of contact is an impor-tant factor in suction measurements using these methods.

In addition, the hysteresis of the thermal dissipation sensor(Feng et al. 2002) might cause the discrepancy in suctionmeasurement. Although it is not possible to confirm theaccuracy of these methods because both of them provideindirect measurements of matric suction, the matric suc-tions measured with both methods fall within a reasonablesuction range (e.g., 10–1000 kPa) for typical compactedsoils (Olson and Langfelder 1965). The repeatability ofmatric suction measurements was given in Sawangsuriya(2006).

Modulus–suction–moisture relationshipThe relationships among shear modulus, matric suction,

moisture content, and dry unit weight for three types of soils(SC, ML, and CL) are presented in Fig. 5. Typical variationof dry unit weight with moisture content (i.e., bell-shapedcompaction curve) for these soils is shown in Fig. 5a. Theeffect of compaction energy on the optimum moisture con-tent of SC soil is shown in Fig. 5a. In general, soils withhigher plasticity exhibit smaller dry unit weight and higheroptimum moisture content than soils with lower plasticity atthe same compactive effort. For the same compaction

Fig. 3. Matric suction versus molding water content of three com-pacted soils: (a) clayey sand (SC), (b) silt (ML), (c) lean clay (CL).Enh Proc, enhanced Proctor; Std Proc, standard Proctor; Red Proc,reduced Proctor; FP, filter paper; TDS, thermal dissipation sensor.

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energy, the SC soil has the highest dry unit weight. The CLsoil exhibits the smallest dry unit weight but the highestoptimum moisture content. Although both SC and ML soilsare low plasticity soils (plasticity index (PI) = 11~14) andshow the same optimum moisture content, the SC soilexhibits a higher dry unit weight than the ML soil.

The plot of shear modulus versus dry unit weight isshown in Fig. 5b. No particular trend was observed betweenshear modulus and dry unit weight. Moreover, the maximumshear modulus did not correspond to the maximum dry unitweight. This observation is consistent with the study bySheeran et al. (1967).

As shown in Fig. 5c, the difference in suction between theSC and ML soils is greatest at lower molding water con-tents. These relationships suggest that the initial conditionsof the specimen (i.e., molding water content and level ofcompaction energy) have influence on the soil microstruc-ture and thus on the matric suction. Similar observationswere also made by Olson and Langfelder (1965). The SCsoil compacted with standard Proctor effort had higher suc-tion than that compacted with enhanced and reduced Proctorefforts. The CL soil has the highest matric suction, whereasthe matric suction of the ML soil is the lowest at a givenmoisture content. Although these curves are similar to thesoil water characteristic curve (SWCC), they are not theSWCC because each point on the curve represents a differ-ent microstructure (Graham et al. 2001). In addition, thespecimens compacted at varying moisture contents do notbelong to a single SWCC but are points on a series of sepa-rate SWCCs that are unique for each molding water content(Wan et al. 1995). Each molding water content generates aunique soil structure that in turn has its own SWCC. As aresult, a point for a given molding water content would rep-resent one point on the SWCC for a given initial condition.

The variation of shear modulus with matric suction andmolding water content is presented in Fig. 5d and Fig. 5e,respectively. In general, the shear modulus increases as ma-tric suction increases and molding water content decreases.For the same compaction energy, the shear modulus of theCL soil is the lowest and that of the SC soil is the highest.Similar observations were also obtained for the undisturbedsubgrade samples collected from a highway pavement(Khoury et al. 2003). Results obtained can be explained bythe fact that the matric suction is considered as the state ofstress within a subgrade, which directly and mainly controlsthe mechanical property (i.e., shear modulus) of unsaturatedsoils. Edil (1973) indicated that matric suction represents thecombined effects of the forces holding the water in the soil,which are controlled by the same factors that control the netinteraction forces between the soil particles. Therefore, withthe exception of cementation bonds, the matric suction canbe expected to include implicitly the effects of the funda-mental interaction forces that influence the deformationcharacteristics of the soils.

Proposed empirical relationSince the matric suction plays an important role in the

mechanical properties of unsaturated soils and the relation-ship between shear modulus and matric suction exhibitssome promising trends, as depicted in Fig. 5d, the shearmodulus – matric suction relationship was selected for fur-ther analysis.

The shear modulus of a given compacted soil depends pri-marily on matric suction and to a lesser degree on moldingwater content and dry unit weight. To incorporate the effectsof molding water content into the shear modulus – matricsuction relationship, the shear modulus was normalized withrespect to molding water content. Once a soil is compacted,variations in dry unit weight are shown to exert a relativelysmall effect on the modulus (Edil and Sawangsuriya 2005),and hence the dry unit weight was not included in the corre-lation. Figure 6 illustrates the semilogarithmic correlationbetween the normalized shear modulus and matric suction.The linear regression analysis was performed on each soilcomposition as well as on the SC soil compacted with dif-ferent levels of compaction energy. A good correlation wasobtained with R2 ranging from 0.82 to 1.00 in each case.The correlation also suggests that there is a dependency ofthe normalized shear modulus – matric suction relationshipon soil composition and compaction energy. A generalmathematical model between the normalized shear modulusand matric suction for different soil composition and soilscompacted with different levels of compaction energy canbe expressed as follows:

½2� Go

w¼ �log � �

where Go is the small-strain shear modulus, w is the mold-ing water content, j is the matric suction, and a and b arefitting parameters dependent on soil composition and thelevel of compaction energy.

The correlation in eq. [2] was examined further to takeinto account the effect of compaction energy. The normal-ized shear modulus (Go/w) was divided by the compactionenergy ratio (x), which is defined as the ratio of compaction

Fig. 4. Comparison between matric suction measured by the filterpaper technique and matric suction measured by the thermal dissi-pation sensor.

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energy achieved by the enhanced or reduced Proctor effortto the compaction energy achieved by the standard Proctoreffort. Figure 7 shows the plot of the normalized Go/w withrespect to compaction energy ratio (x) versus j for the SCsoil compacted with three different levels of compaction en-ergy. The plot indicated that each regression line became

parallel and offset by a constant value, which might be dueto the offset in molding water content of soils compactedwith different compaction energies. To take into account themolding water content offset, the Go/(w �) was normalizedwith respect to the optimum moisture content ratio (u),which is defined as the ratio of the optimum moisture con-

Fig. 5. Small-strain shear modulus – matric suction – molding water content – dry unit weight relationship for clayey sand (SC), lean clay(CL), and silt (ML) soils. Enh Proc, enhanced Proctor; Std Proc, standard Proctor; Red Proc, reduced Proctor; ZAV, zero air voids; Gs,specific gravity.

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tent obtained from the enhanced or reduced Proctor effort tothe optimum moisture content obtained from the standardProctor effort. Figure 8 shows the plot of the normalizedGo/(w x u) as a function of j for the SC soil. Based onthe regression analysis on all SC data combined, an R2 of0.98 was obtained. Notice that the fitting parametersderived from the new regression equation are very close tothose derived from the regression equation of SC soil com-pacted with standard Proctor energy. Finally, eq. [2] can berewritten in a new form, which takes into account theeffect of compaction conditions and soil composition

½3� Go

w�!¼ �log � �

or

½4� Go ¼ wE

Estd

wopt

wopt;std

� �ð�log � �Þ

where � is the compaction energy ratio, E is the compactionenergy achieved by enhanced or reduced Proctor effort, Estdis the compaction energy achieved by standard Proctoreffort, ! is the optimum moisture content ratio, wopt is theoptimum moisture content obtained from enhanced orreduced Proctor effort, wopt,std is the optimum moisture con-tent obtained from standard Proctor effort, and a and b arefitting parameters associated with soil composition.

Generalized modulus relationshipThe modulus – suction – moisture content (Go–j–w) rela-

tionship shown in Fig. 6 was further modified to develop amore generalized relationship covering different types ofsoils and compaction energies. To take into account the soilcomposition and compaction energy, the modulus, dry unitweight, and moisture content were normalized with respectto their values obtained at the optimum moisture contentbased on the standard Proctor effort, which are referred toas the modulus ratio, the dry unit weight ratio, and the mois-ture content ratio hereafter in this study. As shown inFig. 9a, the moisture content ratio correlates well with thematric suction in a simple linear semilogarithmic form withR2 = 0.85. This relationship can effectively take into accountthe difference in soil composition and compaction energy(compare with Fig. 5c). In Fig. 9b, the modulus ratiodivided by the dry unit weight ratio is plotted against themoisture content ratio. A reasonably good correlation isalso observed for this relationship with R2 = 0.80. Both themodulus ratio and moisture content ratio incorporate theinfluence of soil composition on this relationship. The dryunit weight ratio was introduced in the correlation toaccount for the compaction energies. For a given soil withthe same moisture content but different compaction ener-gies, both dry unit weight and modulus can be different asdepicted in Figs. 5a and 5e, respectively. Lastly, the rela-tionships depicted in Figs. 9a and 9b are combined by plot-

Fig. 6. Normalized shear modulus versus matric suction. Enh Proc,enhanced Proctor; Std Proc, standard Proctor; Red Proc, reducedProctor; Go, small-strain shear modulus; w molding water content;j, matric suction..

Fig. 7. Normalized Go/(w x) versus matric suction for clayey sand(SC) soil. Enh Proc, enhanced Proctor; Std Proc, standard Proctor;Red Proc, reduced Proctor; x, compaction energy ratio.

Fig. 8. Normalized Go/(wx u) versus matric suction for clayey sand(SC) soil. !, optimum moisture content ratio.

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ting the modulus ratio divided by the moisture content anddry unit weight ratios against the matric suction as shownin Fig. 9c. Although there is some dispersion of the data, itis less scattered at high matric suctions (compared withFig. 6) and the relationship has an overall R2 = 0.70. Theeffects of all of the compaction parameters (i.e., soil compo-sition, molding water content, and compaction energy) onthe Go–j relationship are also incorporated into this rela-tionship.

The relationship shown in Fig. 9b was further evaluatedfor other compacted fine-grained subgrade soils whose stiff-ness and (or) modulus and compaction parameters arereported in the literature. The more generalized relationshipshown in Fig. 9c could not be evaluated because there wasno matric suction measurement available in the literature.The stiffness and (or) modulus of these soils were measuredusing a variety of testing methods such as seismic test, resil-ient modulus test, soil stiffness gauge, and Briaud compac-tion device (Nazarian et al. 2002; Butalia et al. 2003; Liand Qubain 2003; Ooi and Pu 2003; Ooi et al. 2004; Briaudet al. 2006). Similar to Fig. 9b, the modulus ratio is plottedagainst the moisture content ratio, and the results are shown

in Fig. 10. Again, the dry unit weight ratio was used to takeinto account the effect of compaction energy. The modulusratio decreases by as much as one half of the modulus ratioat optimum moisture content with standard Proctor compac-tion for soils compacted wet of optimum. It increases asmuch as 2.5 times the modulus ratio at the optimum mois-ture content with standard Proctor compaction for soils com-pacted dry of optimum. However, the modulus of thecompacted soil decreases at very low moisture contents(i.e., less than 0.6 of the standard Proctor optimum moisturecontent). Within this small moisture content range, there is alarge dispersion in the data, which might be attributed tomatric suction and (or) soil fabric (i.e., spatial arrangementof both discrete and compound particles) particularly forclay soils where the particle orientation is very important inexplaining the mechanical properties (Edil 1973). A general-ized modulus–moisture relationship for compacted soils isshown in Fig. 10, however, a considerable dispersion of thedata are indicated. For example, for a given soil with 14%optimum water content, when molding water contents rangefrom 2% dry of optimum to 4% wet of optimum, w/wopt,stdcorresponding to these water contents are 0.85 and 1.3,respectively. From Fig. 10, (G/Gopt,std)/(�/�opt,std) changesfrom about 0.7 to 2.5 for the soil compacted at 2% dry ofoptimum. On the other hand, (G/Gopt,std)/(g/gopt,std) changesfrom about 0.1 to 0.8 for the soil compacted at 4% wet ofoptimum.

Summary and conclusions

An experimental investigation of the shear modulus –matric suction – moisture content – compaction energy rela-tionship using three compacted subgrade soils is presentedbased on the limited data available. Compacted subgradespecimens were prepared over a range of molding watercontents from dry to wet of optimum using enhanced, stand-

Fig. 9. Generalized modulus – suction – moisture content (Go–j–w)relationship of test soils. �, dry unit weight; �opt,std, dry unit weightat the optimum moisture content based on the standard Proctor ef-fort.

Fig. 10. Generalized modulus–moisture relationship of compactedsoils.

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ard, and reduced Proctor efforts. A nondestructive elastic-wave propagation technique known as bender elements wasused to assess the shear wave velocity and correspondingsmall-strain shear modulus (Go) of the compacted subgradespecimens. The matric suction was measured with the filterpaper method and a thermal dissipation sensor.

The Go–j–w relationship of soils prepared at the initialcompaction condition is developed in this study. Based onthe experimental investigation, an empirical Go–j–w-dryunit weight relationship is developed for compacted soils.At the as-compacted state, modulus normalized with mois-ture content correlates semilogarithmically with matric suc-tion. A generalized Go–j relationship is also developed toincorporate all compaction parameters considered during theconstruction (i.e., soil composition, molding water content,and compaction energy). This general relationship is basedon normalized modulus, normalized moisture content, andnormalized dry unit weight by their values at optimummoisture content at standard Proctor effort.

AcknowledgementThis paper is dedicated to the memory of our co-author

Prof. Peter J. Bosscher.

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