resilient behavior of compacted subgrade soils under

Construction

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Construction and Building Materials 21 (2007) 1470–1479

and Building

MATERIALS

Resilient behavior of compacted subgrade soils underthe repeated triaxial test

Daehyeon Kim a,*, Jong Ryeol Kim b,1

a Indiana Department of Transportation (INDOT), Research and Development, 1205 Montgomery Street, West Lafayette, IN 47906, USAb Department of Civil Engineering, Chonnam National University 300 Yongbong-Dong, Buk-Gu, Kwangju 500-757, South Korea

Received 21 March 2006; accepted 10 July 2006Available online 14 September 2006

Abstract

Subgrade soils are very important materials to support highways. Resilient modulus (Mr) has been used for characterizing stress-strain behavior of subgrades subjected to repeated traffic loadings. Recently the repeated triaxial test procedure has been upgradedthrough AASHTO T 307. Since the testing procedure is still complex, the testing has not been widely implemented in practice. In orderto evaluate resilient behavior of compacted subgrades soils, the repeated triaxial test and the unconfined compressive test as well as somefundamental property tests were conducted. In this study, the applicability of a simplified procedure with a confining pressure of 13.8 kPaand deviator stresses of 13.8, 27.6, 41.4, 55.2, 69 and 103.4 kPa was investigated on the typical sandy–silty–clay and silty–clay subgradesoils encountered in Indiana. The results obtained from the simplified procedure are comparable with those obtained from AASHTO T307 which calls for 15 combinations of stresses. This shows the simplified procedure to be feasible and effective for design purpose. Somesoils compacted wet of optimum moisture content showed an excessive permanent deformation. This phenomenon was investigated bythe comparison of the unconfined compressive test and the repeated triaxial test results. For soils exhibiting excessive permanent defor-mation, use of deformed length is desirable for more accurate calculation of Mr. Usually the soils compacted dry of optimum shows thelargest Mr for sandy–silty–clay soils due to capillary suction, but it is not necessarily true for silty–clay soils. A predictive model to esti-mate regression coefficients k1, k2, and k3 using 11 soil variables obtained from the soil property tests and the standard Proctor compac-tion tests was developed. The predicted regression coefficients compare well with measured ones.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Resilient modulus; Silty–clay soils; Predictive model; Soil properties; Regression coefficients; Permanent deformation

1. Introduction

1.1. Background and research objective

Since the ‘‘AASHTO Guide for Design of PavementStructures’’ in 1986 recommended highway agencies touse a resilient modulus (Mr) value obtained from arepeated triaxial test for the design of pavements, numer-ous efforts have been made in obtaining more accurate,

0950-0618/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.conbuildmat.2006.07.006

* Corresponding author. Tel.: +1 765 463 1521; fax: +1 765 497 1665.E-mail addresses: [email protected] (D. Kim), jrkim@chonna-

m.ac.kr (J.R. Kim).1 Tel.: +82 62 530 1654; fax: +82 62 530 1650.

straightforward, and appropriate Mr values which are rep-resentative of field conditions. In the past or even in thepresent, most highway agencies have used the CaliforniaBearing Ratio (CBR) to characterize subgrades in thedesign of pavements and to correlate it with the resilientmodulus. CBR, however, is a static property that cannotaccount for the actual response of the subgrade under thedynamic loads of moving vehicles [1].

Although the AASHTO design guide requires designersto use one resilient modulus value representative for agiven subgrade considering seasonal variation, it is not easyto obtain the resilient modulus by performing a standardrepeated triaxial test due to its complex, time-consumingand costly testing procedure [2–4]. Due to its complexity

mailto:[email protected]



Dev

iato

r st

ress

Strain (%)

Mr

εrεa

Fig. 1. Definition of resilient modulus for a confining and a deviatorstress.

D. Kim, J.R. Kim / Construction and Building Materials 21 (2007) 1470–1479 1471

and difficulty, many correlations have been made betweenMr values from the repeated triaxial test and measurementsobtained from nondestructive field testing methods, such asthe Cone Penetration Test (CPT), the Dynamic Cone Pen-etration Test (DCPT), the Falling Weight Deflectometer(FWD), and the Plate Load Test (Plate Load Test). Ofthese methods, CPT is one of the most frequently usedmethods due to its economy, reliability and repeatability[1]. Also, at small strain levels (i.e. less than 0.1%), somelaboratory tests such as unconfined compression test [5–7] and static triaxial test [8] were suggested to find somealternatives to the repeated triaxial test. A simplified testingprocedure was also suggested by decreasing the number ofconfining and deviator stresses [2].

It is noted that the AASHTO Design guide recommendshighway agencies to use representative confining and devi-ator stresses in subgrade layers under traffic loading condi-tions. Therefore, it is necessary to investigate the range ofconfining and deviator stresses resulting from the trafficloadings and to account for such reasonable stress levelsin the repeated triaxial test. Over- or underestimation ofthe stress levels in the subgrades will lead to erroneousresilient modulus results [9]. Through a repeated triaxialtest, as one resilient modulus corresponding to the repre-sentative confining and deviator stress is needed for a givensubgrade in designing a pavement, the complex testing pro-cedure can be simplified for practical design purposes.

The current standard test method to determine the resil-ient modulus is described in the AASHTO T 307-99 whichhas recently been upgraded from AASHTO T 294-94 andAASHTO T 274. Most literature is limited to AASHTOT 294-94 and AASHTO T 274, so no literature on the eval-uation of AASHTO T 307-99 appears to be available. InAASHTO T 307-99, field conditions are simulated by con-ditioning and postconditioning (i.e., main testing). Condi-tioning consists of 500–1000 load applications at aconfining stress of 41.4 kPa and a deviator stress of27.6 kPa. In addition, main testing is performed at threelevels of confining stresses (in the order of 13.8, 27.6 and41.4 kPa) for which each five levels of deviator stresses(13.8, 27.6, 41.4, 55.2 and 69 kPa) are applied, resultingin 15 steps of load applications. It classifies soil types intotypes 1 and 2 materials. Granular soils and cohesive soilsare categorized as types 1 and 2, respectively. This testapplies the same procedure for both granular and cohesivesubgrades and is done under a drained condition only.

There have been two research projects [10,7] on the resil-ient modulus tests focusing on the evaluation of the resil-ient behavior of typical subgrade soils in Indiana and itsimplementation. In order to achieve more realistic designof subgrade, the Indiana Department of Transportation(INDOT) has required the resilient modulus to be used.For most of new alignment and reconstruction of the road-way, the repeated triaxial test results are required on com-pacted samples at moisture contents (OMC and twopercent greater than OMC). However, the repeated triaxialtests are being performed by only several specialized labo-

ratories due to its complex and difficult procedure. Thecomplexity and difficulty of performing the repeated triax-ial test prevented INDOT and others from performing therepeated triaxial test as a routine test. For small projects,the CBR test is performed and an empirical correlation isused to convert CBR to Mr.

In this study, an attempt to simplify the procedure of thestandard resilient modulus test (AASHTO 307-99 orAASHTO 294-94) is made for typical compacted subgradesoils. The objective of this study is to simplify the existingrepeated triaxial test procedure, to evaluate the resilientbehavior of Indiana subgrades and to develop a predictivemodel for estimation of the resilient modulus, allowingconstruction of a database on the resilient modulus andhelping engineers in the evaluation of Mr.

1.2. Resilient modulus

Resilient modulus is an important material property ofsubgrade soils and is an input parameter in the design ofpavements. It is based on the recoverable strains after a ser-ies of combination of confining and deviator stresses in therepeated triaxial test is applied to a soil specimen in orderto take into account nonlinear behavior of subgrade soilsunder the traffic loadings. Resilient modulus is defined as:

M r ¼rd

er

ð1Þ

where Mr is the resilient modulus, rd is the repeated devia-tor stress, er is the recoverable axial strain.

An idealized schematic for a confining stress and a devi-ator stress is shown in Fig. 1 where ea is the irrecoverableaxial strain and er is the recoverable axial strain. An under-lying assumption in Fig. 1 is that so long as the deviatorstress applied is not in excess of the shear strength of thesoil, only recoverable strain occurs after a numerous num-ber of repetitions. However, this assumption may not be

1472 D. Kim, J.R. Kim / Construction and Building Materials 21 (2007) 1470–1479

true for all soils subjected to the traffic loading. For somecohesive soils, excessive permanent strain can often beobserved while performing the repeated triaxial test evenunder the typical traffic loading condition (i.e., 80 kN (18kips) single axle load). As indicated in Eq. (1), the largerthe recoverable deformation, the smaller the resilient mod-ulus (i.e., weak subgrade). This indicates that if the recov-erable deformation is quite large, even the continuouselastic deformation can damage to the integrity of the high-ways as a result of repeated loading.

In AASHTO T307, Mr is calculated using the originallength of the specimen tested. For soils having small per-manent deformation, this would be acceptable, but for soilsshowing larger permanent deformation, the use of thedeformed length of the specimen and corrected area wouldbe helpful for more accurate Mr to be obtained. Also, it isintuitively noticed from Eq. (1) that typical range of therecoverable strain level measured during the repeated triax-ial test is on the order of 10�3–10�4, which suggests howaccurately a measurement of displacement is required.

1.3. Resilient behavior of soils

In general, the resilient modulus of subgrades is affectedby the following factors: deviator stress; confining pressure;water content and dry density; method of compaction;thixotropy; and freeze-thaw cycles. The resilient modulusof cohesive soils is mainly a function of the applied devia-tor stress (i.e., little effect of confining pressure), when asingle confining stress level is considered [11]. On the otherhand, the resilient modulus of granular materials increaseswith increasing confining pressure. For cohesive subgrades,there is a general consensus that at low levels of repeateddeviator stress, the resilient modulus decreases significantlyas the deviator stress increases, while at greater levels ofdeviator stress, the resilient modulus either decreasesslightly or reaches constant values [6,12,13]. Generally,there is a breakpoint resilient modulus corresponding tothe resilient modulus at a deviator stress of 41.4 kPa [12].This breakpoint characterizes the behavior of these soilsunder repeated loads and might be different depending onthe subgrades.

It appears that there is some disagreement betweenresearchers on confining pressure for cohesive subgrades.It is noted that Lee et al. [14] obtained considerably differentvalues for different confining stresses, while others showedlittle effect of confining stresses on the modulus of cohesivesoils [6]. It is also noted that Thompson and Robnett [12] intheir study used zero confining pressure with change in devi-ator stress. As such, the effect of confining pressure on resil-ient modulus of cohesive subgrades has not beenthoroughly studied based on very careful investigation ofdrainage mechanism during testing and detailed soil typesdepending on clay contents and moisture contents.

Most researchers have shown that there is little effect ofmoisture content on resilient modulus of granular sub-grades [6,15], while there is significant effect of water con-

tent on resilient modulus of cohesive subgrades (i.e. thehigher the moisture content, the less the resilient modulus)[6].

1.3.1. Mr in the design

Although Mr values are obtained from a repeated triax-ial test, the final design Mr value for a certain subgrade isdetermined through an additional step. It is generallyknown that moisture and freeze-thaw cycles significantlyaffect the subgrade support capability and their effectsshould be taken into account [3]. In the AASHTO designguide, seasonal or monthly Mr values are required toaccount for the monthly variations of Mr values. Elliotand Thornton [3] suggested a method to account for themonthly variations of Mr values based on the relationshipsbetween Mr and moisture contents, and moisture contentsand months. But their methodology was not very sophisti-cated as the effect of temperature was not taken intoaccount. According to the study done by Lee et al. [14],the average Mr value for four frozen Indiana soils wasobtained. Based on climatic data in Indiana, they suggesteda tentative representation of subgrade Mr throughout theyear. The Mr starts to increase in December and a highMr is maintained until March. Mr decreases abruptly inApril due to thawing, being followed by five months of athaw recovery period. Once the seasonal variation in Mr

is estimated, the effective roadbed resilient modulus (i.e.,Design Mr) can be obtained following the procedure spec-ified in AASHTO design guide.

2. Testing program

A total of eleven soils (four sandy–silty–clay and sevensilty–clay) encountered in Indiana were used in the testingprogram. The testing program consisted of the sieve analy-sis, the Atterberg’s limit test, the standard Proctor compac-tion test, the unconfined compressive test, and the repeatedtriaxial test. Fig. 2 shows the particle size distribution andTable 1 shows material properties of these soils. The soils(I65-146, I65-158, I65-172 and Dsoil) are sandy–silty–claysoils and the rest of the soils in Table 1 are silty–clay soils.

For each soil, the standard Proctor compaction testswere conducted. Three samples for the repeated triaxialtesting were made at different water contents which aredry of optimum (95% relative compaction), optimum(100% relative compaction), and wet of optimum (95% rel-ative compaction). After the repeatability of the repeatedtriaxial test and unconfined test was ensured, the main test-ing was performed. Throughout the paper, dry of opti-mum, optimum and wet of optimum correspond to 95%relative compaction (dry side), 100% compaction, 95% rel-ative compaction (wet side), respectively. A wide range ofwater content was used to account for the possible rangeof lower and upper bounds of Mr values. Note that the per-cent relative compaction is defined as the percentage of thedry unit weight (cd) divided by the maximum dry unitweight (cdmax) in the compaction curve.

San

d Li

mit

Silt

Lim

it

Cla

y Li

mit

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00010.0010.010.1110Particle Diameter (mm)

Per

cen

t F

iner

I65-146 I65-158 I65-172 Dsoil #1 #2 #3 #4 SR 19 US 41 Bloomington

Fig. 2. Particle size distribution for soils used.

Table 1Material properties for soils used

Soil Gravel (%) Sand (%) Silt (%) Clay (%) LL (%) PI (%) AASHTO USCS

I65-146 8 34 40 18 18.5 5.2 A-4 CL–MLI65-158 8 38 44 10 18.2 4.6 A-4 CL–MLI65-172 16 33 33 18 24.2 14.7 A-6 CL–MLDsoil 0 17 61 22 26 6.2 A-4 CL–ML#1soil 0.3 4.8 52.3 42.6 50 23 A-7-6 CH#2soil 2.6 20.5 52.7 24.2 39 16 A-6-12 CL#3soil 8.7 20.6 62.6 8.1 40 15 A-6-10 CL#4soil 2.5 23.2 59.8 14.5 43 21 A-7-6 CLSR19 3.2 21.5 55.4 19.9 33 16 A-6-10 CLUS41 0.9 19.6 58.1 21.4 28 9 A-4-6 CLBloomington 0.3 3.2 60.6 35.9 46 26 A-7-6 CL

Note: LL, liquid limit; PI, plasticity index; AASHTO, American Association of State Highway Transportation Officials; USCS, unified soil classificationsystem; CL, clay with low plasticity; CH, clay with high plasticity; CL–ML, silty clay.


For preparation of a sample for a repeated triaxial test,a compaction mold, specially constructed, with a diameterof 7.1 cm and a height of 15.2 cm was used. Five layers ofcompaction were done with the same compaction energy asthe standard Proctor compaction test. Compaction curvesfor all of the soils tested are shown in Fig. 3. As can bein Fig. 3, for sandy–silty–clay soils the dry unit weight isin the range of 18.5–20 kN/m3 and the optimum water con-tent ranges between 9% and 13%, while for silty–clay soilsthe dry unit weight ranges from 15 to 18 kN/m3 and theoptimum water content ranges between 12% and 23%.

An automated repeated triaxial test device made byGeocomp. Corp. was used for the repeated triaxial test.Air pressure was used for applying a confining pressure.

After a specimen is put into a triaxial chamber, therepeated triaxial test is begun. The repeated triaxial test iscompleted after a series of loading combinations as speci-fied in AASHTO T307.

3. Discussion of test results

3.1. Proposed simplified procedure vs. AASHTO T307

As mentioned previously, the current AASHTO T307calls for 15 steps of repeated loading. The primary reasonfor that is to apply the traffic loading in a wide range cov-ering the typical loadings. In the design of pavements, resil-ient modulus values of subgrades corresponding to the

10

12

14

16

18

20

22

24

0.00 5.00 10.00 15.00 20.00 25.00 30.00

Water content, w (%)

Dry

un

it w

eig

ht

(kN

/m3)

I65-146I65-158I65-172Dsoil#1soil#2soil#3soil#4soilSR19US41Bloomington

Fig. 3. Compaction curves for soils used.


representative stress levels on top of the subgrades areimportant because these values should be used for designparameters. Generally, the level of confining stress on topof the subgrades induced by 80 kN (18 kips) EquivalentSingle Axle Load (ESAL) would be about 13.8–27.6 kPa[3]. In our study, several multi-layered elastic analyses fortypical cross-sections using ELSYM5 showed the13.8 kPa as a minimum confining pressure for typical Indi-ana roads [16]. Therefore, one attempt was made to makethe procedure quicker and easier. As a consequence, it wasdetermined that a confining stress of 13.8 kPa and deviatorstresses of 13.8, 27.6, 41.4, 55.2 and 69 kPa were appropri-ate for the simplified Mr procedure. Note that the proposedsimplified procedure consists of five steps while the currentprocedure requires 15 steps.

Fig. 4a and b show the comparisons of the Mr valuesbetween the simplified and the AASHTO procedures,where those soils were compacted at optimum moisturecontents for I65-158 and I65-172. It is clearly seen inFig. 4a and b that the higher the confining stress, the higherthe resilient modulus value, which is the typical behavior ofsubgrade soils. In Fig. 4a the number of repetition in theconditioning stage and the main testing was the same asthe one in the AASHTO T307, while in Fig. 4b the numberof repetitions both in the conditioning stage and the maintesting stage was reduced by half the number as perAASHTO T307. The Mr values obtained from the twomethods are in good agreement (R2 = 0.9 for Fig. 4a andR2 = 0.76 for Fig. 4b). This means that the simplified pro-cedure can be appropriately used for estimation of Mr val-ues in place of the current repeated triaxial test method,AASHTO T 307.

3.2. Mr values for dry, OMC and wet water contents

In general, the repeated triaxial test is performed at opti-mum moisture content (OMC) or ±2% of the OMC. In thefield, however, compaction control is conducted by thepercent relative compaction with respect to the standardProctor compaction curve. Ninety-five percent relative

compaction is usually incorporated for compaction controlof subgrades, which allow some cases where water contentsexist dry of optimum or wet of optimum. In order toaccount for such field conditions, the repeated triaxial testwas performed on soils compacted dry of optimum, opti-mum and wet of optimum. It should be noted that the dif-ference in water contents between them is considerablylarge, approximately 5–12%, which is dependent on theshape of the compaction curve.

It is very important to distinguish the meaning of stiff-ness and strength of the soil. The resilient modulus of sub-grade soil does not represent its strength but stiffness. Forinstance, a soil having a higher strength than the other doesnot necessarily show higher stiffness; it may show eitherhigher or lower stiffness. Table 2 shows the measured Mr

values for soils compacted dry of optimum, optimum andwet of optimum at a confining stress of 13.8 kPa and adeviator stress of 41.4 kPa. This indicates that subgradesoil must be compacted adequately at near the optimummoisture content in order for the subgrade to better sup-port the highways.

3.3. Sandy–silty–clay soils

As indicated in Table 2, for all of the four sandy–silty–clay soils tested, the highest Mr value is observed in thesoils compacted dry of optimum, and the lowest Mr valuein soils compacted wet of optimum. Although the dry unitweight of the dry sample is smaller than the OMC sample,the value of Mr is higher. This appears to be caused by cap-illary suction. Capillary suction contributes to increase inthe effective stress by pulling particles towards one anotherand thus increasing particle contact force, resulting inhigher Mr values.

Fig. 5a–d are the unconfined compressive test results forOMC, dry and wet samples for I65-146, I65-158, I65-172and Dsoil, respectively. The unconfined compressive(UC) tests were done to understand why the permanentstrain (which will be discussed in a later section) occursexcessively for some wet samples, and to understand if

I65-158 OMC Sample

25000

50000

75000

100000

125000

150000

0.0 30.0 60.0 90.0 120.0

Deviator stress (kPa)


Mr

(kP

a)M

r (k

Pa)

Conf. = 41.4 kPa

Conf. = 27.6 kPa

Conf. = 13.8 kPa

Conf. = 13.8 kPa(simplified)

I65-172 OMC Sample

25000

50000

75000

100000

125000

150000

0 30 60 90 120

Conf. = 41.4 kPa

Conf. = 27.6 kPa

Conf. = 13.8 kPa

Conf. = 13.8 kPa(simplified)

a

b

Fig. 4. Comparison of Mr (a) between the simplified (500 repetitions for conditioning and 100 repetitions for main testing) and the AASHTO procedures,(b) between the simplified (250 repetitions for conditioning and 50 repetitions for main testing) and the AASHTO procedures.

Table 2Measured Mr values for dry, OMC and wet samples (rc = 13.8 kPa,rd = 41.4 kPa)

Soil Mr values (kPa)

Dry OMC Wet

Sandy–silty–clay soils I65-146 94,060 22,940 20,310I65-158 109,400 76,560 27,370I65-172 115,210 66,410 17,960Dsoil 84,660 64,190 13,760

Silty–clay soils #1soil 114,570 86,790 84,560#2soil 92,690 121,090 16,760#3soil 99,560 129,720 11,260#4soil 78,880 73,760 11,840SR19 172,690 157,870 12,990US41 166,920 99,900 16,380Bloomington 94,630 93,000 13,970


there is any indication of effect of peak strength, stiffness ofUC test and permanent strain on resilient behavior. As sta-ted previously, the repeatability of the UC test was ensuredprior to the main testing. For all of the four sandy–silty–clay soils, the highest stiffness is observed in the dry sampleand the peak strength is also observed in the dry sample,except for I65-158 OMC sample. From Fig. 5b and c,dry samples of I65-158 and Dsoil show slightly larger stiff-ness than OMC samples. The same trend in the repeatedtriaxial test is also evidenced in Table 2.

3.4. Silty–clay soils

As shown in Table 2, the seven silty–clay soils have aslightly different resilient behavior compared with thesandy–silty–clay soils. The difference in Mr for silty–claysoils between dry samples and OMC samples are smallerthan that for sandy–silty–clay soils. Some OMC samplesshow higher Mr values than dry samples. This indicatesthat the effect of dry unit weight on resilient behavior inthe silty–clay soils becomes more pronounced than in thesandy–silty–clay soils and the effect of suction appears todecrease in the silty–clay soils. Similarly observed in thesandy–silty–clay soils, the wet samples in the silty–clay soilsshow considerably lower Mr values than dry and OMCsamples, which means that the soils are very weak due tothe higher degree of saturation and thus can be used forthe lowest limit (i.e., spring) of Mr values for subgrades.

3.5. Permanent deformation behavior

Permanent deformation behavior is not considered inthe calculation of Mr values. This is because the permanentstrain is very small for most of the subgrade soils. For mostof the soils tested, the small permanent deformationsoccurred, especially for dry and OMC samples. However,some samples compacted wet of optimum exhibited an

0

50

100

150

200

250

300

Axi

al S

tres

s (k

Pa)

Axi

al S

tres

s (k

Pa)

Axi

al S

tres

s (k

Pa)

Axi

al S

tres

s (k

Pa)

146omc

146dry

146wet

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9Axial Strain (%)Axial Strain (%)

Axial Strain (%) Axial Strain (%)

158omc158dry158wet

0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 80

50

100

150

200

250

300

172omc172dry172wet

0

5

10

15

20

25

30

35

40

dsoil omcdsoil drydsoil wet

a b

c d

Fig. 5. Unconfined compressive test results for dry, OMC, wet samples for (a) I65-146, (b) I65-158, (c) I65-172 and (d) Dsoil.


excessive permanent deformation while performing arepeated triaxial test. This caused a significant difficultyto run a repeated triaxial test up to the final step. Some-times it was impossible to run a repeated triaxial test tothe end because of the sudden failure of the sample. Mostof the failure was observed to be bulging failure, not shearfailure. As can be seen in Fig. 5a–d, the peak strengths ofthe wet samples occur at a permanent strain of about sevenpercent and the stress ratio of the highest deviator stress(i.e., 69 kPa) in the repeated triaxial test to the peakstrength are in the range of 50–70%. This explains why

00 1 2 3 4 5 6

3

6

9

12

15

18

21

Step

Per

man

ent

stra

in (

%)

Fig. 6. Permanent strains for I65-146 wet sample in the conditioning stage(step 1) in the 5th step.

the permanent strain occurs excessively in the wet samples.The AASHTO T307 calls for shear test for samples greaterthan 5% permanent strain. However, it is not practical notto evaluate Mr values for the soils exhibiting excessive per-manent deformation. The maximum permanent strain wasset as 20% so that Mr values can be obtained even for thosesoils with excessive permanent strain.

Fig. 6 presents the results of the repeated triaxial test forI65-146 wet sample in the conditioning stage (step 1) and inthe 5th step, respectively. It was observed in Fig. 6 thateven in the conditioning stage the permanent strainoccurred to about 10% and the permanent strainapproached to about 18% and the testing was terminated

Permanent strain (9.8%) for wet sample

0

10000

20000

30000

40000

50000

0 20 40 60 80


Mr

(kP

a)

Original length

Deformed length

Fig. 7. Mr values for original length and deformed length.


in the 5th step. A comparison was made of the resilientmodulus between using the original length and using thedeformed length for I65-158 soil, as shown in Fig. 7. Thepermanent strain of about 10% occurred in the repeated tri-axial test and the difference in Mr values using the originaland deformed lengths are approximately eight percent.This implies that it would be more accurate to calculatethe Mr values using the deformed length.

3.6. A predictive model for Mr values

Generally, resilient behavior of subgrade soils can bedescribed by the Uzan model [17] known as the universalmodel, taking into account confining and deviator stresses.The predicted Mr values can be obtained from the follow-ing equation:

Table 3Predictive model for estimation of Mr values considering 11 soil variables

log k1 = 6.660876 � 0.22136 · OMC � 0.04437 · MC � 0.92743 · MCR � 0.0%sand � 0.04349 · %SILT � 0.01832 · %Clay + 0.027832 · LL � 0.01665 · P

k2 = 3.952635 � 0.33897 · OMC + 0.076116 · MC � 2.45921 · MCR � 0.0646sand + 0.002321 · %SILT + 0.011056 · % CLAY + 0.077436 · LL � 0.05367

k3 = 2.634084 + 0.124471 · OMC � 0.09277 · MC + 0.366778 · MCR � 0.011sand � 0.00512 · % SILT � 0.00492 · %clay � 0.05083 · LL + 0.018864 · PI

y = 0.7908x + 118.04

R2 = 0.8338

0

400

800

1200

1600

2000

0 400 800 1200 1600 2000Measured k1

Pre

dic

ted

k1

y = 1.1365x - 0.4071

R2 = 0.5136

-1.4

-0.9

-0.4

0.1

0.6

-1.4 -0.9 -0.4 0.1 0.6

Measured k3

Pre

dic

ted

k3

a

c

Fig. 8. Comparison between (a) predicted k1 and measured k1, (b) predicted k

measured Mr values.

M r ¼ k1pa

hpa

� �k2 rd

pa

� �k3

ð2Þ

where k1, k2, k3, is the regression coefficients; h the sum ofprincipal stresses; pa the reference pressure 100 kPa �1 kgf/cm2 � 2000 psf � 14.5 psi; and rd is the deviatorstress in the same unit as pa.

As noticed in Eq. (2), the major limitation of Uzan’smodel is that it cannot take into account the different typesof subgrade soils [18]. In order to overcome such limita-tion, a predictive model based on the all the repeated triax-ial test data for 11 soils, as shown in Table 3, the materialcoefficients k1, k2, and k3 were developed through multipleregression analyses in terms of 11 soil variables, which canbe easily obtained in the sieve analysis, Atterberg’s Limittest, and standard Proctor compaction test. As shown in

6133 · DD + 10.64862 · %comp + 0.328465 · SATU � 0.04434 ·I (R2 = 0.85)

2 · DD + 6.012966 · %comp + 1.559769 · SATU + 0.020286 · %· PI (R2 = 0.81)

68 · DD � 1.32637 · %comp + 1.297904 · SATU � 0.01226 · %(R2 = 0.76)

y = 0.7458x + 0.0699

R2 = 0.7466

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5

Measured k2

Pre

dic

ted

k2

y = 1.1365x

R2 = 0.8472

0

50000

100000

150000

200000

0 50000 100000 150000 200000

Measured Mr (kPa)

Pre

dict

ed M

r (k

Pa)

b

d

2 and measured k2, (c) predicted k3 and measured k3, (d) predicted Mr and


Table 3, the coefficient of determination, R2, for k1, k2, andk3 are reasonable to estimate the resilient modulus once thesoil variables are known. The variables are the following:OMC, MC (moisture content), MCR (moisture contentratio = moisture content/optimum moisture content), DD(dry density), SATU (degree of saturation), % sand (per-cent sand in particle size distribution curve), % CLAY (per-cent sand in particle size distribution curve), LL (liquidlimit) and PI (plasticity index).

Fig. 8a–c are the comparisons between measured andpredicted regression coefficients and Fig. 8d is the compar-ison between measured and predicted resilient values for675 data points for 45 samples tested. Predicted regressioncoefficients and resilient modulus values are reasonablycomparable to measured ones considering the wide rangeof water contents adopted in this study (Se/Sy = 0.45,R2 = 0.85). This predictive model can be readily used inthe estimation of Mr values in design phase of roadconstruction.

4. Conclusions

In this study, four sandy–silty–clay and seven silty–clayIndiana subgrade soils were used to evaluate resilientbehavior of these soils. The following can be drawn fromthis study.

(1) The simplified procedure suggested compares wellwith the existing repeated triaxial test procedure. Thiscan significantly reduce the time required for therepeated triaxial test with reasonable accuracy.

(2) For some soils, excessive permanent strains occurredwhile testing. This is because the stress ratio of thedeviator stress to the peak strength of those soils werequite large and permanent strain to reach the peakstrength is quite large, approximately 7%.

(3) The largest Mr values are observed in the dry samplesfor sandy–silty–clay soils due to the capillary suctionwhile the largest Mr values are observed either in thedry or OMC sample for silty–clay soils. The smallestMr values obtained from wet samples can be used asthe limit of Mr in spring.

(4) The current repeated triaxial test uses the originallength of the specimen, but the deformed length dur-ing testing should be used for more accurate calcula-tion of Mr.

(5) A predictive model was developed using the 11 vari-ables easily obtained from physical property testsand the standard Proctor test. The predicted regres-sion coefficients and resilient moduli compare wellwith the measured ones.

5. Recommendations

The current repeated triaxial test cannot take intoaccount the long term Mr values due to a limited number

of repeated loadings applied to the specimen. The longterm Mr values are especially needed for rehabilitation. Astudy on the long term Mr values is recommended.

Acknowledgements

The authors are grateful to the Federal HighwayAdministration/Indiana Department of Transportation/Joint Transportation Research Project (Project: SPR2633) for supporting this research. They are obliged tothe Study Advisory Committee members: VincentDrnevich (Purdue); Kumar Dave, Samy Noureldinand Nayyar Zia (INDOT); Val Straumins (FHWA).Also, appreciation is extended to Tommy Nantung ofINDOT Research Division for his support and encour-agement.

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resilient behavior of compacted subgrade soils under

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