Research Article Effects of Density and Moisture Variation

Research ArticleEffects of Density and Moisture Variation on DynamicDeformation Properties of Compacted Lateritic Soil

Weizheng Liu,1 Shuai Qu,1 Zhihong Nie,1 and Junhui Zhang2

1School of Civil Engineering, Central South University, Changsha 410075, China2School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410114, China

Correspondence should be addressed to Zhihong Nie; [email protected]

Received 8 December 2015; Accepted 17 February 2016

Academic Editor: Philip Eisenlohr

Copyright © 2016 Weizheng Liu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A series of repeated load triaxial tests were conducted in this study to investigate the influences of compaction density andpostcompaction moisture variation on the dynamic elastic modulus (𝐸𝑑) and plastic permanent strain (PPS) of compacted lateriticsoil. Specimens were compacted at optimum moisture content (OMC) and three degrees of compaction (90%, 93%, and 96%).Then the specimens were dried or wetted to different moisture contents (OMC, OMC ± 3%, OMC ± 6%, and OMC + 9%) prior totesting for𝐸𝑑 and PPS. Results show that moisture content has greater influence on the𝐸𝑑 and PSS than compaction degree, and theincrease in moisture content leads to a decrease of 𝐸𝑑 and an increase of PPS. Furthermore, an empirical relationship between 𝐸𝑑and applied cyclic stress (𝜎𝑑) is developed that incorporates density and moisture variations.Three different evolution types of PPSwith number of load cycles, plastic stable, plastic creep, and incremental collapse, are identified as the increase of moisture content.In addition, the critical dynamic stress (𝜎𝑑𝑐) separating stable and unstable deformation is determined based on the shakedownconcept. The envelope curves of 𝜎

𝑑𝑐-moisture of lateritic soil with different degrees of compaction are also determined to provide

reference for the pavement design.

1. Introduction

In the field construction, subgrade soils are generally com-pacted at or near optimum moisture content (OMC) andmaximum dry density (MDD), and as such the compactedsubgrade is usually present in an unsaturated condition.However, during the service life of a subgrade, the moisturecontent at the time of compaction is not constant and firstlychanges to an equilibrium water content (EPC) and thenfluctuates along the EPC due to the seasonal environmen-tal factors such as groundwater table variation, rainwaterinfiltration, and evaporation [1–5]. Several recent studieshave shown that variations in moisture content significantlydegrade the engineering properties of compacted subgrade[6–9] and contribute to the deterioration and prematurefailure of pavements. It is evident that proper considerationto the effect of moisture variation should be given in realisticpavement design and analysis.

Lateritic soils are widely distributed in tropical andsubtropical regions such as south China, in which lateritic

soils are extensively used as fill materials for the subgradeconstruction of highway and railway due to the expandingurbanization and deficiency in good quality crushed aggre-gate. Nevertheless, lateritic soils possess special propertieswith high plasticity and high water sensitivity [10], which canlead to significant moisture variation of compacted subgradewith the seasonal environmental factors. Considerable stud-ies have been carried out on the effect of moisture variationon the shear strength and static modulus of lateritic soil [11–15]. It was observed that an increase in moisture contenttypically decreased the matric suction and hence decreasedthe shear strength and static modulus. Although dynamicdeformation properties including resilient stiffness and accu-mulated permanent deformation are closely related to theservice performance of operated subgrade, particularly underhigh-speed and heavy-axle traffic loading, limited researchwork has been performed on dynamic elastic modulus (𝐸𝑑)and plastic permanent strain (PPS) of lateritic soil. Fall et al.[16] investigated the evolution of permanent and reversibledeformation of the three laterites under various cyclic stress

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016, Article ID 5951832, 11 pageshttp://dx.doi.org/10.1155/2016/5951832

2 Advances in Materials Science and Engineering

levels. Samb et al. [17] indicated that the moisture contentseemed to affect the values of the resilient modulus in asensitive way. Parreira and Goncalves [18] and Mu et al. [19]found that resilient modulus decreased as the increase ofmoisture content and there was often a strong correlationbetween matric suction and resilient modulus. Throughvarying moisture contents at compaction, Liao et al. [20],Liu et al. [21], and Zhang et al. [22] evaluated the effect ofmoisture variation on the critical dynamic stress. However, itshould be pointed out that laboratory specimens compactedat different moisture contents cannot accurately simulatethe field conditions, in which subgrades were compacted atunique moisture content and then subjected to postcom-paction moisture changes. Few studies have addressed thevariations of dynamic elastic modulus and plastic permanentdeformation of compacted lateritic soil with postcompactionmoisture contents.

Compaction degree, 𝑘, defined as the ratio of dry densityof the field compaction to laboratory maximum dry density,is a key parameter for ensuring the proper performance ofa subgrade and is also an important factor influencing thedevelopment of permanent deformations [23–25]. Barksdale[23] observed an increase of permanent axial strain of about185% when the granular material was compacted at 95%instead of 100% of maximum compaction density. However,the effect of density on 𝐸𝑑 and PPS of fine grained soils suchas lateritic soil has not been clearly observed.

The primary objective of this study is to address thevariations of 𝐸𝑑, PPS, and critical dynamic stress (𝜎𝑑𝑐) withpostcompaction moisture contents and compaction densityfor compacted lateritic soil. Specimens are compacted atOMC and three degrees of compaction (90%, 93%, and 96%)and then subjected to wetted or dried procedures and sixlevels of moisture contents (OMC, OMC ± 3%, OMC ± 6%,and OMC + 9%) are selected for repeated load triaxial tests.An empirical relationship between 𝐸𝑑 and applied cyclicdeviator stress (𝜎𝑑) is developed that incorporates density andmoisture variations. Furthermore, based on the shakedownconcept, the envelope curves of 𝜎𝑑𝑐 moisture of lateritic soilwith different compaction degrees are presented.

2. Materials and Specimen Preparation

2.1. Materials. Residual lateritic soil sampled from JiangxiProvince, frequently encountered subgrade soil in the con-struction of highways in southern China, was selected fortesting in this study. Specific gravity, Atterberg limits, wetsieve and hydrometer analysis, and compaction characteris-tics were performed on the tested soil. A summary of the testresults is presented in Table 1. The liquid limit and plasticityindex of the soil are 45% and 20, respectively.The silt contentand clay content are 28.9% and 55.2%, respectively. This soilwas classified as A-7-5 according to AASHTO classificationmethod and as CL as per unified soil classification system(USCS). The results of MDD and OMC obtained fromthe standard Proctor compaction test are used to establishcompaction conditions for the repeated load triaxial tests.

Table 1: Properties of tested soil.

Property Lateritic soilSpecific gravity 2.70Liquid limit (LL, %) 45Plasticity index (PI) 20Sand (>0.075mm, %) 15.9Silt (0.005mm to 0.075mm, %) 28.9Clay (<0.005mm, %) 55.2AASHTO classification A-7-5USCS classification CLMaximum dry density, MDD (kN/m3) 17.8Optimum moisture content, OMC (%) 18.0

2.2. Specimen Preparation. Prior to specimen preparation,bulk soil samples were subjected to air drying. The drysoil was first processed through a 2.00mm sieve and thenthoroughly mixed with the desired amount of deaired waterto achieve the optimum moisture content, and the wet soilmixture was left in an airtight container overnight to achievehomogenous moisture conditions.

Three degrees of compaction (90%, 93%, and 96%)were selected to prepare specimens for triaxial tests. Thecylindrical specimenswith 50mm in diameter and 100mm inheightwere compacted in a rigid splitmold and in three layersof equal weight using a Proctor hammer. After compaction,the cylindrical specimen was extracted from the split moldand the initial weight, height, and diameter were measured.

In order to simulate different stages of the in-servicesubgrade exposure to seasonal environmental conditions, thespecimens firstly compacted at optimum moisture contentwere then subjected to drying or wetting procedures. Thisprocess of varying moisture contents under the same ini-tial condition was followed to minimize fabric effects onthe subsequent test results. This is because the change incompaction moisture content affects the soil structure [6].Six levels of moisture contents, dry side (OMC − 3% andOMC − 6%), optimum (OMC), and wet side (OMC + 3%,OMC+6%, andOMC+9%),were selected to address variationof postcompaction moisture content. The selected range ofmoisture content deviating fromOMC is generally consistentwith results from field monitoring research undertaken byThang et al. [3] and Taamneh and Liang [26].

Air-drying, carried out inside a temperature controlledlaboratory to ensure constant condition, was employed asthe drying procedure to achieve different moisture contentslower than OMC. Specimens were subjected to drying proce-dure, while the specimen mass was continuously measured.As soon as the specimen reached the target mass (and hencetarget water content), it was wrapped in a cling film for threedays, which is sufficient to achieve uniformity distribution ofmoisture in the specimens.

The procedure used to increase the water content ofsample was a more laborious system compared to the dryingprocedure. According to the procedure developed byMendes[27], the wetting process was performed by using minifog-gers. After wetting to achieve the target water content, the

Advances in Materials Science and Engineering 3

Table 2: Parameters for 𝐸𝑑 and PPS test.

Compactiondegree, 𝑘

Moisture content,𝑤

Confiningpressure, 𝜎𝑐 (kPa)

Static deviatorstress, 𝜎𝑠 (kPa)

Dynamic deviator load (N)

Multistage loadingsequence for 𝐸𝑑

Single-stageloading sequence

for PPS90%93%96%

12%, 15%, 18%,21%, 24%, 27% 60 30

15, 30, 45, 60, 75,90, 105, 120, 135,

15090, 120, 150, 180

specimens were also wrapped in a cling film for three days toassure homogenization of the water content within the soil.Mendes [27] verified that this method can wet the sampleshomogeneously and uniformly.

3. Test Methods and Procedures

A DDS-70 cyclic triaxial test apparatus with electromagneticcontrol system was used to perform 𝐸𝑑 and PPS testson the specimens. Two externally mounted linear variabledifferential transducers (LVDTs), directly connected to thedata acquisition system, were used to measure the axialdisplacements of the soil sample. The maximum scale strokefor these two LVDTs is ±10mm, with a resolution accuracy of0.001mm.

The 𝐸𝑑 and PPS tests were conducted in accordancewith the SL237-032 [28] test methods. To simulate the slowdrainage relative to the traffic loading duration, the tests werecarried out under undrained conditions. Compressed air wasused to apply confining pressure to the specimens. The effectof confining pressure on 𝐸𝑑 and PPS properties was ignoredin this study and a constant confining pressure of 60 kPa wasapplied to represent the in situ effective consolidation pres-sures. Moreover, to stimulate the nonisotropic consolidationstate due to the pavement loading, an initial static deviatorstress of 30 kPawas applied to the specimen.A semisinusoidalwave load with a frequency of 1Hz with no rest period wasapplied to represent the loading conditions experienced by apavement layer under vehicular loading.

It should be pointed out that only the cyclic load isallowed to be input in the DDS-70 test system, and themagnitude of obtained cyclic stress depends on the stiffnessof test specimen. The greater stiffness results in larger cyclicstress. That is, the same magnitude of cyclic load applied todifferent specimens would result in different magnitudes ofcyclic stress. According to the SL237-032, multistage loadingmethod was adopted for 𝐸𝑑 test, and ten dynamic deviatorloads of 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150Nwere applied in sequence for each specimen, as presented inTable 2. For each sequence, 10 load cycles were applied andthe cyclic stress and the vertical displacement were measuredand used to determine the elastic modulus. For the PPS test,single-stage loading method was adopted, and four differentdeviator loads of 90, 120, 150, and 180N were applied. Eachspecimen for PPS test was subjected to a prescribed deviatoricload level controlled by an internal load cell for 5000 cycles.

4. Results and Discussion

4.1. Dynamic Elastic Modulus. The dynamic elastic modulusis defined as the ratio of cyclic deviator stress to elasticstrain. Figure 1 presents the relationship between dynamicelastic modulus and deviator stress at various moisturecontents for specimens compacted at 90%, 93%, and 96% ofMDD, respectively. The dynamic elastic modulus decreasesnonlinearly with an increase in the cyclic deviator stress. Thesignificant effect of change in the postcompaction moisturecontent on the dynamic elastic modulus is also evident asshown in the figure. For tested specimens with differentdegrees of compaction, an increase in the moisture contentthat corresponded to decrease of matric suction resulted inconsiderable reduction in the dynamic elastic modulus. Thisbehavior could be attributed to the fact that an increase inmoisture content lubricates the grains and weakens the soilfabric, which in turn leads to an increased vulnerability todeformation, as shown in Figure 2.The elastic strain increaseswith an increase in the moisture content under the samedeviator stress.

It is further observed that the dynamic elastic modulusexhibits a higher sensitivity to the moisture contents at lowerdeviator stress level. That is, at lower deviator stress level,the dynamic elastic modulus of the specimen decreases ata higher rate as the moisture content increases from 12%to 27%, compared to that at higher deviator stress level. Inaddition, the typical stress-strain curves shown in Figure 2 atdifferent moisture contents exhibit obvious nonlinear behav-ior, which can usually be characterized by the hyperbolicmodel [29], as shown in

𝜎𝑑 =𝜀𝑑

1/𝐸𝑑0 + 𝜀𝑑/𝜎𝑑𝑦

, (1)

where 𝐸𝑑0 is the initial elastic modulus (tangent of thehyperbolic curve at the origin) and 𝜎𝑑𝑦 is the ultimatedeviator stress (2 times the limit shear strength of specimen).The values of 1/𝐸𝑑0 and 1/𝜎𝑑𝑦 can be obtained from theintercept and the slope of the measured 1/𝐸𝑑-𝜀𝑑 linear curve.

It is stated that the values of 𝐸𝑑0 and 𝜎𝑑𝑦 depend on theinitial state of sample such as the applied confining stress,moisture content, and dry density, and 𝐸𝑑0, 𝜎𝑑𝑦 can be usedas useful index for normalizing the relationships betweenmodulus and strain for soils with various moisture contentsand compaction degrees. Figure 3 presents the relationshipbetween the normalized elastic modulus 𝐸𝑑/𝐸𝑑0 and thenormalized elastic strain 𝜀𝑒/𝜀𝑟 for all the tested specimens,


w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

0

50

100

150

200

250El

astic

mod

ulus

,Ed

(MPa

)

20 40 60 80 1000Cyclic deviator stress, 𝜎d (kPa)

(a)

20 40 60 80 10000

50

100

150

200

250

300

350

400

Elas

tic m

odul

us,E

d(M

Pa)

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

Cyclic deviator stress, 𝜎d (kPa)

(b)

0

100

200

300

400

500

Elas

tic m

odul

us,E

d(M

Pa)

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

20 40 60 80 1000Cyclic deviator stress, 𝜎d (kPa)

(c)

Figure 1: Variation of dynamic elastic modulus with deviator stress at various moisture contents for different degrees of compaction: (a)𝑘 = 90%; (b) 𝑘 = 93%; (c) 𝑘 = 96%.

where 𝜀𝑟 = 𝜎𝑑𝑦/𝐸𝑑0 was defined as the reference strain[29]. Interestingly, a unique relationship between 𝐸𝑑/𝐸𝑑0and (𝜎𝑑/𝐸𝑑)/(𝜎𝑑𝑦/𝐸𝑑0) is obtained, within a large range ofmoisture contents (12–27%) and various compaction degrees(90–96%). A regression analysis gives the following simpleequation with a correlation coefficient 𝑅2 of 0.99:

𝐸𝑑

𝐸𝑑0

= 0.48 [(𝜎𝑑/𝐸𝑑)

(𝜎𝑑𝑦/𝐸𝑑0)

]

−0.678

. (2)

Figure 4 illustrates the variation of normalized initialelastic modulus 𝐸𝑑0/(Pa × 10

3) with moisture content and

degree of compaction, and Figure 5 shows the trend ofnormalized ultimate deviator stress 𝜎𝑑𝑦/Pa with moisturecontent and degree of compaction. As can be seen, both𝐸𝑑0/(Pa × 10

3) and 𝜎𝑑𝑦/Pa decrease with an increase of

moisture content and increase with an increase of degreeof compaction. Furthermore, with the moisture contentincreasing, the magnitude of changes in 𝐸𝑑0/(Pa × 10

3)

and 𝜎𝑑𝑦/Pa decreases. Based on the described properties of

𝐸𝑑0/(Pa × 103) and 𝜎𝑑𝑦/Pa, the following regression-based

empirical models for 𝐸𝑑0 and 𝜎𝑑𝑦 behavior of compactedsubgrade are proposed:

𝐸𝑑0/ (Pa × 103) = 𝛼1𝑤

𝛼2𝑘𝛼3 ,

𝜎𝑑𝑦/Pa = 𝛽1𝑤𝛽2𝑘𝛽3 ,

(3)

where Pa is the standard atmospheric pressure,𝑤 is moisturecontent, 𝑘 is degree of compaction, and 𝛼1, 𝛼2, and 𝛼3 and 𝛽1,𝛽2, and 𝛽3 are regression parameters.

The regression parameters for the model presented in(3) were determined by least square curve fitting on themeasured 𝐸𝑑0 and 𝜎𝑑𝑦. The test data points obtained fromsix moisture contents and three degrees of compaction wereused for this statistical analysis. The solver function inMicrosoft Excel was used for the proposedmodel parametersoptimization which was set up to minimize the sum of thesquared errors between the measured value and the valuepredicted by the model. The coefficient of determination𝑅2 was also calculated to evaluate the goodness of model


0

20

40

60

80

100

0.0 0.2 0.4 0.6 0.8 1.0

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

Elastic strain, 𝜀e (%)

Cycli

c dev

iato

r stre

ss,𝜎

d(k

Pa)

(a)

0

20

40

60

80

100

0.0 0.2 0.4 0.6 0.8

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%


Cycli

c dev

iato

r stre

ss,𝜎

d(k

Pa)

(b)

0

20

40

60

80

100

0.0 0.2 0.4 0.6 0.8 1.0

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%


Cycli

c dev

iato

r stre

ss,𝜎

d(k

Pa)

(c)

Figure 2: Relationship between deviator stress and elastic strain at variousmoisture contents for different degrees of compaction: (a) 𝑘 = 90%;(b) 𝑘 = 93%; (c) 𝑘 = 96%.

fitting at all the compaction degrees. Figure 4 presents therelationships between measured data and predicted resultusing the model with the parameters determined from theoptimization procedure, and the calibrated parameters of themodels and the 𝑅2 values are also presented in the figure. Itis seen that the coefficients of determination for 𝐸𝑑0/(Pa ×103) and 𝜎𝑑𝑦/Pa curves are 0.99 and 1.00, respectively, which

indicate that the proposed models accurately capture thetrends ofmeasured𝐸𝑑0/(Pa×10

3) and𝜎𝑑𝑦/Pa versusmoisture

contents at various degrees of compaction.Combining (2) and (3), an empirical relationship between

dynamic elastic modulus 𝐸𝑑 and cyclic deviator stress 𝜎𝑑 isdeveloped that incorporates density and moisture contentvariations. That is, the elastic modulus 𝐸𝑑 of subgrade at in-service state with different moisture contents and degrees ofcompaction can be predicted as the applied cyclic deviatorstress and confining stress are available.

4.2. Plastic Permanent Deformation. A series of cyclic loadtests were performed at different moisture content levels with

varying degrees of compaction and at different deviator stresslevels. As an example, at a constant cyclic deviator load of150N, the measured accumulated permanent strains as afunction of number of load applications for a predeterminedrange of moisture contents are presented in Figure 5. Thisfigure shows a considerable influence of moisture contenton the permanent strain response of the compacted lat-eritic soil. The permanent strain increases as the moisturecontent increases and the increase is more pronounced athigh moisture content. With increasing in moisture content,the type of permanent strain response to cyclic loadingchanges from stable state to unstable state. That is, at lowmoisture content, the specimen exhibits a long-term steadystate with no further accumulation of permanent strain andentirely resilient response, while at high moisture contentthe specimens have achieved progressive failure or collapsestate after a finite number of load cycles. Furthermore, resultsin Figure 5 show that a higher degree of compaction yieldsa lower accumulated permanent strain and a more stableresponse; that is, the failure or collapse state achieved in


10 100

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

Fitted curve:

0.1𝜀e/𝜀r or (𝜎d/Ed)/(𝜎dy/Ed0)

y = 0.48x−0.678

k = 90% k = 93% k = 96%

0.0

0.2

0.4

0.6

0.8

1.0

Ed

/Ed0

1

R2 = 0.99

Figure 3: Correlation of 𝐸𝑑/𝐸𝑑0 with (𝜎𝑑/𝐸𝑑)/(𝜎𝑑𝑦/𝐸𝑑0).

0

2

4

6

8

5 10 15 20 25 30

0.133

𝜎c = 60kPaEd0/(

Pa×10

3)

k = 96%, predictedk = 93%, predictedk = 90%, predicted

k = 96%, measuredk = 93%, measuredk = 90%, measured

Moisture content, w (%)

𝛼1 𝛼2 𝛼3 R2

−2.0 8.40 0.99

(a)

0.5

0.7

0.9

1.1

1.3

5 10 15 20 25 30

0.448

𝜎c = 60kPa

k = 96%, predictedk = 93%, predictedk = 90%, predicted

k = 96%, measuredk = 93%, measuredk = 90%, measured

Moisture content, w (%)

𝛽1 𝛽2 𝛽3 R2

−0.514 3.0 1.00

𝜎dy

/Pa

(b)

Figure 4: Comparison of lab-measured results and model-predicted values versus moisture content for various degrees of compaction: (a)𝐸𝑑0/(Pa × 10

3); (b) 𝜎𝑑𝑦/Pa.

the specimens compacted at 90% and 93% of MDD is notobserved in the specimens with 96% of MDD.

Figure 6 shows the variation of permanent strain after5000 cycles with cyclic deviator stress for different moisturecontents and degrees of compaction. It is observed that thehigher cyclic deviator stress results in the higher permanentstrain at the samemoisture content. As increasing inmoisturecontent, especially increases from 18% (OMC), the accumu-lation of permanent strain exhibits more sensitivity to thecyclic deviator stress, and higher magnitudes of change inpermanent strain are observed for specimens with highermoisture content. Quite similar trends are observed for

specimens with three different degrees of compaction. Thisis due to a decrease in soil matric suction with an increaseof moisture content, thus reducing the effective stress, whichin turn decreases the resistance to withstand accumulation ofpermanent deformation.

Figure 7 shows the associated permanent strain rateversus accumulative permanent strain from a series of cyclictests with combination of various moisture contents anddeviator stress. For example, the test condition with moisturecontent of 12% and the deviator stress of 45 kPa is expressed as12%–45 in the legend. It is observed that the permanent strainrate decreases rapidly for the cases with lowmoisture content


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 1000 2000 3000 4000 5000 6000

Plasticstable

Plastic creep

Incrementalcollapse

Perm

anen

t str

ain,

𝜀 p(%

)

Number of load cycles, N

w = 27%w = 24%w = 21%

w = 18%

w = 15%

w = 12%

(a)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 1000 2000 3000 4000 5000 6000

Incrementalcollapse

Plastic creep

Plasticstable

Perm

anen

t str

ain,

𝜀 p(%

)


w = 27%w = 24%w = 21%

w = 18%

w = 15%

w = 12%

(b)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 1000 2000 3000 4000 5000 6000

Plasticcreep

Plasticstable

Perm

anen

t str

ain,

𝜀 p(%

)


w = 27%w = 24%w = 21%

w = 18%

w = 15%

w = 12%

(c)

Figure 5: Permanent strain under a cyclic deviator load of 150N for various moisture contents and different degrees of compaction: (a)𝑘 = 90%; (b) 𝑘 = 93%; (c) 𝑘 = 96%.

and low deviator stress. In contrast, for the cases with highmoisture content and high deviator stress, the permanentstrain rate decreases very slowly or keeps constant, whichcauses progressive accumulation of permanent strain andmay eventually lead to unstable or failure state. Furthermore,both permanent strain rate and permanent strain decreasewith the increase of degree of compaction under an identicalcondition, and more curves of permanent strain responsewith stable state are observed for the case with high degreeof compaction.

The evolution of permanent strain of fine grained sub-grade soils with load cycles is complex and dependent onthe stress level, moisture content, and degree of compaction.The shakedown concept, firstly introduced in pavementengineering by Sharp and Booker [30], is used to characterizethe permanent deformation behavior of compacted lateriticsoil under cyclic loading. According to Werkmeister et al.[31], the concept maintains that the materials response under

repeated loading can be classified into four different cate-gories: elastic shakedown, plastic shakedown, plastic creep,and incremental collapse:

(1) Elastic shakedown, where the applied cyclic stressis sufficiently small compared to the strength of thematerial and the material response is purely elastic.

(2) Plastic shakedown, where the cumulative permanentstrain rate decreases rapidly until it reaches a stateof equilibrium and the material gradually achieves along-term steady state response.

(3) Plastic creep shakedown, where the permanent strainrate is decreasing and slowly accumulative perma-nent strain is observed; however, the material plasticresponse neither ceases nor leads to a sudden collapse.

(4) Incremental collapse, where the applied cyclic stressis relatively large to cause the material to reach and


20 40 60 80 100

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

Cyclic deviator stress, 𝜎d (kPa)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0Pe

rman

ent s

trai

n,𝜀 p

,500

0(%

)

(a)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

Perm

anen

t str

ain,

𝜀 p,5

000

(%)

40 60 80 10020Cyclic deviator stress, 𝜎d (kPa)

(b)

w = 27%

w = 24%

w = 21%

w = 18%

w = 15%

w = 12%

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Perm

anen

t str

ain,

𝜀 p,5

000

(%)

40 60 80 10020Cyclic deviator stress, 𝜎d (kPa)

(c)

Figure 6: Relationships between permanent strain after 5000 cycles and cyclic deviator stress for different moisture contents and degrees ofcompaction: (a) 𝑘 = 90%; (b) 𝑘 = 93%; (c) 𝑘 = 96%.

exceed the yield stress and the accumulated plasticstrains then increase rapidly with failure occurring ina small number of load cycles.

Based on the above-stated definitions of different defor-mation stages and the shapes or slopes of the measuredpermanent strain curves, three states of permanent strainaccumulation, plastic stable, plastic creep, and incrementalcollapse, are observed and labeled in Figures 5 and 7. All testspecimens experience some permanent strain; thus none ofresults shows behavior in the elastic shakedown range.

By considering the shakedown concept, the classifica-tion assumes the existence of certain limiting values whichdefine the stress states at which the type of permanentstrain response changes. In particular, for design purposes,this implies that the maximum cyclic stress level, which isassociated with a resilient response after slight plastic strain

accumulates in the initial cycles, should be determined andsubsequently not be exceeded, if uncontrolled permanentdeformations are to be prevented.Themaximum cyclic stressis defined as the critical dynamic stress 𝜎𝑑𝑐, below whichpermanent deformations are small and shaken down andabove which repeated applications of a load cause largepermanent deformations attributed to unstable state.

The critical dynamic stress distinguishing stable fromunstable state is the key design parameter and can beestimated from themaximum stress in the plastic shakedownstage. Figure 8 presents the estimated critical dynamic stressas a function of moisture content for various degrees ofcompaction. It can be clearly seen that the critical dynamicstress decreases with an increase in moisture content, andthe magnitude of decrease in 𝜎𝑑𝑐 is higher at the wet sideof OMC than that at dry side of OMC. With increase of


0.01

1

Plastic creepPlasticstable

Perm

anen

t str

ain

rate

(10−2/lo

ad cy

cle)

0 1 2 3 4 5 6 7 8Permanent strain, 𝜀p (%)

Incremental collapse

1E − 3

1E − 4

1E − 5

1E − 6

0.1

12%–4518%–4024%–3812%–60

24%–5018%–55

12%–7518%–6824%–6212%–8818%–8224%–75

15%–4221%–4027%–3615%–5721%–5227%–48

15%–7021%–6527%–6015%–8521%–7827%–72

(a)

1

Plastic creep

Plasticstable

Perm

anen

t str

ain

rate

(10−2/lo

ad cy

cle)



1E − 3

1E − 4

1E − 5

1E − 6

0.01

0.1

12%–4818%–4224%–3812%–65

24%–5318%–58

12%–7818%–7224%–6812%–9018%–8524%–80

15%–4521%–4027%–3615%–6221%–5527%–50

15%–7521%–7027%–6215%–8821%–8227%–75

(b)

1

Plastic creep

Plastic


Perm

anen

t str

ain

rate

(10−2/lo

ad cy

cle)


1E − 3

1E − 4

1E − 5

1E − 6

0.01

0.1

stable

12%–5018%–4524%–4012%–65

24%–5518%–60

12%–8018%–7524%–7012%–9518%–8724%–80

15%–4821%–4227%–3815%–6221%–5827%–50

15%–7721%–7227%–6515%–9021%–8527%–75

(c)

Figure 7: Relationship between permanent strain rate (log scale) and permanent strain under combination of various moisture contents anddeviator stress values for different degrees of compaction: (a) 𝑘 = 90%; (b) 𝑘 = 93%; (c) 𝑘 = 96%.

degree of compaction the critical dynamic stress increases,and higher magnitude of increase in 𝜎𝑑𝑐 is observed as thedegree of compaction changes from 90% to 93% compared tothat of the case with changing from 93% to 96%. Moreover,the presented envelope curves of 𝜎𝑑𝑐 moisture for differentcompaction degrees can provide reference for the pavement

design, for assuring that the compacted subgrade soils shouldpreferably not undergo cyclic stress level higher than the crit-ical dynamic stress, in which condition the permanent strainaccumulation would terminate after a sufficient number ofloading cycles and onlyminor permanent deformationwouldtake place.


20

40

60

80

100

9 12 15 18 21 24 27 30Moisture content, w (%)

Criti

cal d

ynam

ic st

ress

,𝜎dc

(kPa

)

k = 96%

k = 93%

k = 90%

Figure 8: Critical dynamic stress versus moisture content forvarious degrees of compaction.

5. Conclusions

Both elastic (resilient) deformation and plastic permanentdeformation behavior of compacted lateritic soil were inves-tigated using a series of repeated loading tests. The tests wereconducted at different moisture contents with varying drydensities and at different cyclic stress levels to simulate theseasonal environmental and traffic conditions in reality. Thefollowing conclusions are drawn in view of the results:

(1) The elastic stiffness (𝐸𝑑) decreases with increasedmoisture content and cyclic deviator stress (𝜎𝑑) andincreases with increased degree of compaction. Anempirical relationship between dynamic elastic mod-ulus 𝐸𝑑 and applied cyclic stress 𝜎𝑑 is developedthat incorporates variations of density and postcom-paction moisture content.

(2) The plastic permanent strain decreases due to dry-ing and increases due to wetting. With increasingin moisture content, the type of permanent strainaccumulation response changes from plastic stable(shakedown) to plastic creep and eventually to incre-mental collapse.

(3) With an increase in moisture content, the highermagnitude of decrease in critical dynamic stress 𝜎𝑑𝑐is observed at the wet side of OMC compared tothe corresponding changes at dry side of OMC.Moreover, the envelope curves of 𝜎𝑑𝑐 moisture fordifferent degrees of compaction are presented, whichmay be useful for improving the pavement designto incorporate the postcompaction moisture contentvariation due to seasonal environmental effect.

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

Theauthors acknowledge theNational Natural Science Foun-dation of China (51208517, U1134207, and 51478054), Projectfunded by China Postdoctoral Science Foundation (no.2013M530360), and State Engineering Laboratory ofHighwayMaintenance Technology, Changsha University of Science &Technology (kfj150103). The authors are also grateful to Mr.Tianqi Qiu at Tsinghua University and Mr. Xiangtian Yangat Tongji University for their help in the repeated loadingtriaxial tests.

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