Laboratory Characterization of Reinforced Crushed Limestone under Monotonic and Cyclic Loading

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Laboratory Characterization of Reinforced CrushedLimestone under Monotonic and Cyclic Loading

Munir Nazzal1; Murad Abu-Farsakh2; and Louay Mohammad3

Abstract: A series of triaxial compression tests and cyclic triaxial tests were conducted on unreinforced and geogrid reinforced crushedlimestone samples to investigate the effects of the geogrid type, location, and number of layers on the strength, stiffness, and cyclicdeformability of these samples. Five different types of geogrids were used. For each geogrid type, four different reinforcement arrange-ments were investigated. Comprehensive statistical analyses were conducted on the collected triaxial test data. The results of theseanalyses indicated that the geogrid inclusion within crushed limestone samples increased significantly their elastic modulus and ultimateshear strength, while it reduced their permanent deformation; thus, the geogrid is expected to enhance the performance of base coursematerial in the field and reduce its deformation. The results also showed that stiffer geogrids exhibited greater improvement. Moreover,samples reinforced with two geogrid layers placed at the upper and lower third of the sample height always had the highest improvement,while the lowest improvement was observed for samples with a single geogrid layer placed at the sample’s midheight. Finally, the resultsdemonstrated that the geogrid did not have a significant effect on the resilient behavior of the crushed limestone samples.

DOI: 10.1061/�ASCE�0899-1561�2007�19:9�772�

CE Database subject headings: Limestone; Geogrids; Deformation; Statistics; Cyclic loads.

Introduction

Over the last 2 decades, geosynthetics have been used as rein-forcement in flexible pavements, bridge abutments, and manyother engineering applications. Three main geosynthetic familiesof products were used as a reinforcement: geogrids, geotextiles,and synthetic fibers. The most commonly used type of geo-synthetics for reinforcement of flexible pavement systems isgeogrids. Geogrids are extruded sheets of polyethylene or poly-propylene with apertures that interlock with soil particles in aregular pattern producing a stronger composite mass. They arecommercially available at different types �sizes and shapes�, andtensile properties.

Many studies have been conducted to characterize the behav-ior of geosynthetic reinforced pavement structures in large-scalemodel experiments �Haas et al. 1988; Barksdale et al. 1989;Miura et al. 1990; Webster 1993; Al-Qadi et al. 1994; Collin et al.1996; Berg et al. 2000; Cancelli and Montanelli 1996; Al-Qadiet al. 1997; and Perkins 2002�, and investigate their benefits.These studies showed that geosynthetic reinforcements were

1Graduate Research Assistant, Dept. of Civil and EnvironmentalEngineering, Louisiana State Univ., Baton Rouge, LA 70808.

2Research Assistant Professor, Louisiana Transportation ResearchCenter, Louisiana State Univ., Baton Rouge, LA 70808 �correspondingauthor�. E-mail: [email protected]

3Associate Professor, Dept. of Civil and Environmental Engineering,Louisiana Transportation Research Center, Louisiana State Univ., BatonRouge, LA 70808.

Note. Associate Editor: Houssam A. Toutanji. Discussion open untilFebruary 1, 2008. Separate discussions must be submitted for individualpapers. To extend the closing date by one month, a written request mustbe filed with the ASCE Managing Editor. The manuscript for this paperwas submitted for review and possible publication on November 30,2005; approved on March 7, 2006. This paper is part of the Journal ofMaterials in Civil Engineering, Vol. 19, No. 9, September 1, 2007.
©ASCE, ISSN 0899-1561/2007/9-772–783/$25.00.
772 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING © ASCE / SEPTE

J. Mater. Civ. Eng. 200

able to mechanically improve the overall strength and stability ofreinforced pavement structures and reduce the accumulated per-manent deformation. To better understand the reinforcementmechanisms acting in a large-scale reinforced soil and pavementstructures, studies were conducted to evaluate such mechanismsat small-scale laboratory controlled conditions. These studieshave investigated the effect of geosynthetics on the strength andstiffness behavior of reinforced material under monotonic andcyclic loading.

Gray and Al-Refeai �1986� conducted triaxial compressiontests on dry reinforced sand using five different types of geotex-tile. The test results demonstrated that the use of reinforcementincreased the peak strength, axial strain at failure, and, in mostcases, reduced postpeak loss of strength. However, at a very lowstrain �less than 1% axial strain�, reinforcement resulted in a lossof compressive stiffness. The failure envelope of the reinforcedsand showed a clear failure with respect to the confining pressure.After the point of break, the failure envelope for the reinforcedsand paralleled the unreinforced sand envelope.

Ashmawy and Bourdeau �1997, 1998� conducted monotonicand cyclic triaxial tests on geotextile-reinforced silt and sandsamples with a 71 mm diameter and 170 mm height. The resultsof these studies showed that the presence of geosynthetics signifi-cantly improved the strength of the tested samples. In addition,the geosynthetic layer tended to reduce the accumulated plasticstrains under cyclic loading. Ashmawy and Bourdeau �1997� alsoinvestigated the effects of reinforcement layer spacing and rein-forcement material properties on the achieved improvement.Their results showed that the amount of improvement dependedon the spacing of the geotextile layers, and to a lesser extent, onthe geotextile and interface properties.

Moghaddas-Nejad and Small �2003� conducted drained cyclictriaxial compression tests on two granular materials �sand and finegravel� reinforced by geogrids. The geogrid layer was placed at
the midheight of that sample which was 200 mm in diameter and
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400 mm in length. The results of their study indicated that thegeogrid reinforcement can significantly reduce the permanent de-formation of the triaxial specimen. However, their results showedthat the geogrid did not have considerable influence on the resil-ient modulus of the tested materials.

Perkins et al. �2004� conducted cyclic triaxial tests on geosyn-thetic reinforced samples to evaluate the effects of the reinforce-ment on the permanent and resilient deformation of a base courseaggregate material. Two sample sizes were investigated, namely;samples with 150 mm diameter and 300 mm height, and sampleswith 300 mm diameter and 600 mm height. For reinforced speci-mens, a single layer of reinforcement was placed at the sample’smidheight. Four different types of reinforcement were used in thetests �two geogrids, one geotextile, and one geocomposite�. Theirresults supported the previous work reported by Moghaddas-Nejad and Small �2003�, where it showed that the reinforcement

Table 1. Physical and Mechanical Properties of Geogrids

Geogrid

Tensile stiffness at�strain %�a

Aperturedimension

Flexuralstiffnessb

MD�kN/m�

CMD�kN/m�

MD�mm�

CMD�mm� �g cm�

BX-1500 580 �2%� 690 �2%� 25 30.5 2,000

1,200 �5%� 1370 �5%�

BX-1200 410 �2%� 650 �2%� 25 33 750

810 �5%� 1340 �5%�

BX-6200 380 �2%� 510 �2%� 33 33 250

720 �5%� 1000 �5%�

BX-1100 280 �2%� 450 �2%� 25 33 750

580 �5%� 920 �5%�

BX-6100 250 �2%� 380 �2%� 33 33 250

550 �5%� 720 �5%�aMeasured in accordance with ASTM standard method for determiningtensile properties of geogrids ASTM D6637 �Tensar Earth TechnologiesInc. 2003�.bMeasured in accordance with ASTM standard test method fordetermining stiffness of nonwoven fabrics using the cantilever test ASTM

Fig. 1. Particle size distribution of tested crushed limestone material

D-5732-95 �Tensar Earth Technologies Inc. 2003�.

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does not have an effect on the resilient modulus properties ofunbound aggregates, but showed appreciable reduction in the per-manent deformation properties of unbound aggregate as seen inthe cyclic permanent deformation tests. Perkins et al. �2004� alsoindicated that the relatively poor repeatability seen in the perma-nent deformation tests made it difficult to distinguish betweentests with different reinforcement products. In addition, the rein-forcement did not have an appreciable effect on the permanentdeformation until a mobilized friction angle of approximately 30°was reached. Finally, their results showed that the effect of thesample size on the physical properties was insignificant.

Objectives and Scope

The objective of this study was to evaluate the influence of thegeogrid type, location, and number of layers on the strength prop-erties as well as permanent and resilient behavior of crushed lime-stone samples under monotonic and cyclic loading.

To achieve this, drained triaxial compression tests, resilientmodulus tests, and permanent deformation tests were conductedon unreinforced and geogrid reinforced samples. Five types ofgeogrids with different stiffness properties were used. For eachtype, four different arrangements were investigated. These ar-rangements included varying the location and the number of geo-grid layers. Statistical analyses were carried out on the test resultsto study the effects of the different variables.

Testing Program

Materials Properties

Crushed LimestoneThe tested material was taken from a selected crushed limestonesample used in the construction of base course layers in Louisi-

Fig. 2. MTS triaxial testing machine

ana. Fig. 1 shows the grain size distribution for the tested crushed

ERIALS IN CIVIL ENGINEERING © ASCE / SEPTEMBER 2007 / 773

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limestone material. The material has a maximum size of 19 mm,and a D10 and D60 sizes of 0.18 and 6 mm, respectively, giving ita uniformity coefficient of 30. In addition, it is classified as A-1-aand GW-GC according to the American Association of StateHighway and Transportation �AASHTO� classification system,and the Unified Soil Classification System �USCS�, respectively.The tested crushed limestone material has a maximum dry unitweight of 17.2 kN/m3 and an optimum moisture content of 7.0%,as measured by the standard Proctor test. Finally, the materialhas an internal friction angle of 48° and a specific gravity valueof 2.72.

GeogridThe reinforcement material used in this study included five dif-ferent types of biaxial geogrids, namely, BX-6100, BX-1100,BX-6200, BX-1200, and BX-1500. Where BX-6100 representsthe lowest stiffness geogrid and BX-1500 represents the stiffestgeogrid. These geogrids are typically used to reinforce a base

Fig. 3. Preparation and testing of crushed limestone sample

Fig. 4. Reinforcement arran



course layer in pavement structures. The physical and mechanicalproperties of these products as reported by the manufacturer arepresented in Table 1 �Tensar Earth Technologies Inc. 2005�. TypeI, II, III, IV, and V will be used thereafter to refer to BX-6100,BX-1100, BX-6200, BX-1200, and BX-1500, respectively.

Testing Setup

All triaxial tests were performed using the Material Testing Sys-tem �MTS� 810 machine with a closed loop, and a servo hydraulicloading system. The applied load was measured using a load cellinstalled inside the triaxial cell. This type of setup reduces theequipment compliance errors as well as the alignment errors. Thecapacity of the load cell used was ±22.25 kN �±5,000 lbf�. Theaxial displacement measurements were made using two linearlyvariable differential transducers �LVDT� placed between the topplaten and base of the cell to reduce the amount of extraneousaxial deformation measured compared to external LVDTs. Airwas used as the confining fluid to the specimens. Fig. 2 depicts apicture of the testing setup used in this study.

Sample Size

Dimensions of the sample tested in the triaxial experiment arebased on the maximum particle size of its material. TheAASHTO-T307 recommends that for untreated granular base ma-terial, the tested sample should have a diameter greater than fivetimes the maximum particle size of that material. In addition, theNCHRP Project 1-28A recommends the use of samples with150 mm diameter and 300 mm height for a base material with amaximum particle size greater than 19 mm �NCHRP 2004a�.Since the crushed limestone material used in this study had amaximum particle size of 19.0 mm, all samples were preparedwith 150 mm diameter and 300 mm height.

Sample Preparation

AASHTO-T307 recommends that a split mold be used for com-paction of granular materials. Therefore, all samples were pre-pared using a split mold with an inner diameter of 150 mm and aheight of 350 mm. The material was first oven dried at the pre-specified temperature and then mixed with water at the optimummoisture content. The achieved water contents were within ±0.5%of the target value. The material was then placed within the splitmold and compacted using a vibratory compaction device to

ts investigated in this study
gemen
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achieve the maximum dry density measured by the standard Proc-tor test. To achieve a uniform compaction throughout the thick-ness, samples were compacted in six 50 mm layers. Each layerwas compacted until the required density was obtained; thiswas done by measuring the distance from the top of the moldto the top of the compacted layer. The smooth surface on topof the layer was lightly scratched to achieve good bonding withthe next layer. The achieved dry densities of the preparedsamples were within ±1% of the target value. Samples wereenclosed in two latex membranes with a thickness of 0.3 mm.

Fig. 5. Drained triax

Fig. 3 illustrates the preparation procedure of crushed limestone

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samples. For reinforced samples, the geogrid was placed horizon-tally between layers at the desired locations. Four differentarrangements of reinforcement were investigated in this study;namely, single layer placed at the sample midheight �middle ar-rangement�, single layer placed at the upper one-third of thesample height �upper one-third arrangement�, single layer placedat the lower one-third of the sample height �lower one-thirdarrangement�, and two layers placed at one- and two-thirds ofthe sample height �double arrangement�. A sketch describing thefour reinforcement arrangements investigated in this study is

pression test results
ial com
shown in Fig. 4.


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Triaxial Compression Tests

Drained triaxial compression tests were conducted on both unre-inforced and reinforced samples. The tests were conducted with astrain rate less than 10% strain per hour. This rate was chosen toensure that no excess pore water will develop during testing. Ineach test, the sample was loaded to a strain level of 1%, unloaded,and then reloaded to failure. Drained triaxial compression testswere first performed on unreinforced samples at three different

Fig. 6. Improvement Factors: �a� IM-Es1%; �b� IM-Es2%; and �c�IM-USS

confining pressures �21, 48, and 69 kPa� to obtain the strength



properties of the crushed limestone. They were then performed at21 kPa confinement pressure on samples reinforced with each ofthe five geogrid types investigated in this study. For each geogridtype, the four reinforcement arrangements shown in Fig. 4 wereinvestigated. Three replicate samples were tested for each case toensure repeatability, for a total of 69 triaxial compression tests.

Cyclic Triaxial Tests

Resilient Modulus TestsCyclic triaxial tests were performed in accordance withAASHTO-T307 standard method for determining the resilientmodulus of base course material �AASHTO 2003�. In thismethod, a series of steps consisting of different levels of cyclicdeviatoric stress are followed such that the resilient modulus ismeasured at varying normal and shear stress levels. The cyclicloading consists of repeated cycles of a haversine shaped loadpulse. These load pulses have a 0.1 s load duration and 0.9 s restperiod. Cyclic triaxial tests were conducted on unreinforcedsamples, and samples reinforced with each of the five geogridtypes used in this study. Three different arrangements were inves-tigated for each reinforcement type �middle, upper one-third, anddouble arrangement�. Three replicate samples were tested foreach case to ensure repeatability. A total of 48 resilient modulustests were conducted.

Permanent Deformation TestsCyclic triaxial tests were performed to determine the permanentand resilient behavior of unreinforced and reinforced crushedlimestone samples at a different number of load cycles. The testsconsisted of applying 10,000 load cycles at a constant confiningpressure �21 kPa� and peak cyclic stress. Each cycle consisted ofthe same load pulse used in resilient modulus tests. All sampleswere conditioned before the test by applying 1,000 repetitions ofa specified cyclic deviatoric stress. The condition step removesmost irregularities on the top and bottom surfaces of the testsample and also suppresses most of the initial stage of permanentdeformation. This procedure is similar to those followed in pre-vious studies �Heath 2002; and Mohammad et al. 2005�.

Since the purpose of these tests was to model the behavior ofcrushed limestone base material under the vehicle-inducedstresses in a pavement structure, a finite-element analysis wasconducted using the ABAQUS software package on a pavementsection to determine the stress levels within the base course layer.The analyzed pavement section consisted of a 75 mm asphaltconcrete �AC� layer, a 250 mm base course layer, and a subgradelayer. Two main elastoplastic models were used in the finite-element analyses. The AC layer was modeled using an elastic-perfectly plastic model, while the base course and subgrade layerswere modeled using the Drucker–Prager model with isotropichardening. The finite-element analysis included subjecting thepavement section to an idealized vehicle load of 80 kN singleaxle wheel with a total load on each wheel of 40 kN. The wheelload was simulated by applying a 550 kPa contact pressure on acircular area with a radius of 150 mm at the surface. The appliedload had a haversine-shaped wave form, which is similar tothat applied in permanent deformation tests. For further detailsabout the finite-element analysis one can refer to Nazzal et al.�2006�. Based on the results of the finite-element analysis, thepeak cyclic deviatoric stress was selected to be 230 kPa, while acontact stress of 27 kPa was used. The cyclic permanent defor-
mation tests were conducted on unreinforced samples and
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samples reinforced with geogrid Types II, IV, and V. As in theresilient modulus test, three different arrangements were investi-gated for each geogrid type, and three replicate samples weretested for each case. A total of 30 permanent deformation testswere conducted.

Test Results

Triaxial Compression Test Results

The results of the triaxial compression tests conducted on un-reinforced samples showed that the crushed limestone used inthis study had a friction angle of 48°. Figs. 5�a–e� present thestress-strain curve obtained from the triaxial compression testsconducted on unreinforced samples and samples reinforced withgeogrid Types I–V. It is clear that the inclusion of geogrid rein-forcement layer/s improved the strength and stiffness of thecrushed limestone material substantially. This improvement wasmore pronounced at strain levels greater than 1%. To quantita-tively evaluate the improvement achieved due to the reinforce-ment under monotonic loading, three response parameters wereobtained from each triaxial test, namely, the secant elastic moduliat 1% strain level �Es1%�, the secant elastic moduli at 2% strainlevel �Es2%�, and the ultimate shear strength �USS�. These re-sponse parameters were chosen to assess the reinforcement influ-ence on the behavior of the tested material at different strainlevels. Improvement factors IM-Es1%, IM-Es2%, and IM-USS

Fig. 7. Resilient modulus va

were then determined using the following equation:

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IM =parameter from reinforced sample

parameter from unreinforced sample�1�

Figs. 6�a–c� present the average improvement factor and thestandard deviation values for each reinforced case. The figures

different deviatoric stresses

Fig. 8. Improvement factor of resilient modulus values at selectedstress state

lues at


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show that the improvement in all three parameters depended onthe type, location, and number of geogrid layers. It can be seenclearly that the improvement increased by increasing the geogridstiffness. In addition, the double arrangement had the maximumimprovement. This will be discussed in detail later in the “Statis-tical Analysis” sections. The figures also show that the improve-ment was more appreciable in the Es2% and USS than those inEs1%, and the maximum improvement was detected in the USS;the IM-Es1% ranged from 0.95 to 1.82, the IM-Es2% ranged from0.99 to 2.32, and IM-USS ranged from 1.163 to 2.42.

Resilient Modulus Test Results

To determine the resilient modulus parameters of unreinforcedand reinforced samples, the resilient modulus was first calculatedas the cyclic axial stress divided by the resilient �recoverable�strain for the last ten cycles of each step in a test. A regressionanalysis was then carried out to fit each test data to the general-ized constitutive model �Eq. �2�� that was adopted by the newmechanistic-empirical design guide �NCHRP 2004b�

MR = pak1� �

pa�k2� �oct

pa+ 1�k3

�2�

In Eq. �2�, MR=resilient modulus; pa=atmospheric pressure�101.3 kPa�; �=bulk stress which equals �1+2�3; �oct

=octahedral shear stress which equals �2/3 ��1−�3�; �1 and �3

=major and minor principle stresses, respectively; and k1, k2, and

Fig. 9. Permane

k3=material properties.



Based on the parameters determined in the regression analy-ses, the resilient modulus was calculated for the different unrein-forced and reinforced cases at a confining stress of 21 kPa, andthree deviatoric stresses: 80 kPa, 160, and 250 kPa. Fig. 7 pre-sents the results of this calculation. It can be noticed that theresilient modulus values increased by increasing the deviatoricstress. A slight improvement in resilient modulus was detectedonly for samples reinforced with two layers of geogrid Type V athigh deviatoric stresses.

The resilient modulus was also calculated at the stress stateapplied in the permanent deformation tests for the different unre-inforced and reinforced samples. An improvement factor �IM-Mr�was then determined using Eq. �1�. Fig. 8 presents the averageimprovement factor and the standard deviation values for all re-inforced cases. It can be noticed that only samples reinforced withtwo geogrid layers had a slight improvement in the resilientmodulus values calculated at the selected stress state. However,no conclusion can be drawn since this improvement lies withinthe margin of error of the calculated values. This will be investi-gated later in the statistical analysis section.

Permanent Deformation Test Results

In each permanent deformation test, the permanent and resilientstrains were determined for each load cycle. The curves of theaverage permanent strain value versus number of load cyclesfor unreinforced samples and samples reinforced with geogrid

ormation curves
nt def
Types II, IV, and V are shown in Figs. 9�a–c�, respectively. It

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can be seen that the geogrid reinforcement resulted in a reduc-tion in the permanent strain. This reduction was more pronouncedat a greater number of load cycles, hence at higher strain levels.Figs. 10�a–c� present the average resilient strain curves for unre-inforced samples and samples reinforced with geogrid Types II,IV, and V, respectively. The resilient strain had a similar trendin both reinforced and unreinforced samples, such that it de-creased with increasing the number of load cycles until reaching

Fig. 10. Resilie

sections.

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an asymptote at about 1,000 load cycles and then maintaining thesame magnitude for the rest of the test. Figs. 10�a–c� demonstratethat the geogrids did not have a significant effect on the resilientbehavior of the crushed limestone samples.

Based on the results of the permanent deformation tests, thereduction in the permanent strain at 10,000 load cycles �RPS10,000�due to geogrid reinforcement was determined as follows:

rmation curves

RPS10,000�%� =permanent strain without geogrid-permanent strain with geogrid

permanent strain without geogrid� 100% �3�

The average �RPS10,000� and the standard deviation values forthe reinforced cases investigated are presented in Fig. 11. Theinclusion of the geogrid reinforcement resulted in a reductionof the permanent strain up to 65%. Similar to the triaxial com-pression test results, the geogrid improvement in permanent de-formation test depended on the geogrid type, location, and thenumber of reinforcement layers, such that stiffer geogrids ex-hibited a higher reduction in permanent strains than the ones withthe least stiffness, as can be seen for Type V geogrids comparedto Type II geogrids. The figure also shows that the upper one-third location had better improvement than the middle location,while the maximum improvement was observed when using twogeogrid layers. A more detailed analysis is presented in the next

Statistical Analyses

ANOVA and Post-ANOVA Analyses

An analysis of variance �ANOVA� was conducted using statisticalanalysis software �SAS� to detect the effects of geogrid type andarrangement on the degree of improvement in the response pa-rameter obtained from the drained triaxial compression tests,resilient modulus tests, and permanent deformation tests. TheANOVA analyses were performed using a “MIXED” procedureavailable in SAS. The linear model used in these analyses was acompletely randomized factorial design �geogrid arrangements�geogrid types�, as shown in Eq. �4�. The dependent variablesused in the analyses included: the IM-Es1%, IM-Es2%, IM-USS,

nt defo

IM-Mr, and RPD10,000


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Yijk = � + �1i + �2j + �1�2ij + �ijk �4�

In Eq. �4�, �=overall mean; �1i=effect of geogrid arrange-ment; �2j =effect of geogrid type; �1�2ij =effect of the interactionbetween the geogrid arrangement and type; �ijk=random samplingvariation for observation k, at any location case and stiffness levelij; and Yijk=dependent variable.

The results of the ANOVA showed that, at a 95% confidencelevel, the geogrid type and arrangement had significant effect onthe IM-Es1%, IM-Es2%, IM-USS, and RPD10,000, but not on theIM-Mr. The geogrid type had a more significant effect onIM-Es1% than the geogrid arrangement, while the geogrid arrange-ment affected more significantly the IM-Es2%, IM-USS, andRPD10,000 values, as indicated by the F value. The interactioneffect of the geogrid type-geogrid arrangement ��1�2ij� had sig-nificant effects only on the IM-Es2%, and IM-USS. The signifi-cance of interaction indicates that the behaviors of the two maineffects �geogrid type and arrangement� are inconsistent, whichmeans that they do not increase and decrease by the same rate.

Based on the result of the ANOVA analyses, post-ANOVAleast square means �LSM� analyses were conducted to comparethe effects of all different geogrid types and arrangements on theIM-Es1%, IM-Es2%, IM-USS, and RPD10,000. Tukey adjustmentwas used in this analysis since it provides tests for all pairwisecomparisons at a good balance of the Type I and Type II errorswhen compared to other adjustments available �SAS Institute Inc.2004�. Saxton’s macro was implemented to convert the results inthe MIXED procedure to letter groupings. The results of thisgrouping are presented in Tables 2 and 3. In these tables thegroups are listed in descending order from the best improvementto the worst, and groups with the same letter next to them are notsignificantly different.

Table 2 shows the grouping of the geogrid type effect onIMEs1%, IM-Es2%, IM-USS, and RPD10,000. The maximum andminimum improvement was achieved when using geogrid TypesV and I, respectively. These two geogrid types have the highestand the lowest stiffness, respectively. The effects of geogridTypes III and IV on IM-Es1% were not statistically different from

Fig. 11. Reduction in permanent deformation

each other. However, the effect of geogrid Type III on IM-Es2%



and IM-USS was significantly different from geogrid Type IV butnot from geogrid Type II. Table 3 presents the grouping of theeffect of geogrid arrangement on the IM-Es1%, IM-Es2%, IM-USS,and RPD10,000 improvement factors. The highest benefit wasachieved when the double arrangement was used, while the low-est benefit was observed for the middle arrangement. In addition,the upper and lower one-third arrangement effects on IM-USSwere not statistically different from each other.

The previous ANOVA results showed that neither the geogridtype nor the geogrid arrangement had a significant effect onthe IM-Mr, therefore it was necessary to find out if the geogridinclusion had any influence on the resilient modulus of crushedlimestone samples. This was done by conducting ANOVA andpost-ANOVA-LSM analyses with a single factor completely ran-domized design with 17 effect levels �16 reinforced cases and one

Table 2. Grouping of Geogrid Type Effect

Dependentvariable

Geogridtype Estimate

Standarderror

Lettergroup

IM-Es1%V 1.7413 0.01978 A

III 1.5705 0.01978 B

IV 1.5681 0.01978 B

II 1.2658 0.01978 C

I 1.1817 0.01978 D

IM-Es2%V 1.9013 0.01532 A

IV 1.6640 0.01532 B

III 1.5888 0.01532 C

II 1.5526 0.01532 C

I 1.2847 0.01532 D

IM-USS V 1.9215 0.01438 A

IV 1.7038 0.01438 B

III 1.5810 0.01438 C

II 1.5682 0.01438 C

I 1.4986 0.01438 D

RPS10,000 V 46.4478 0.9186 A

IV 38.0944 0.9186 B

II 31.3244 0.9186 C

Table 3. Grouping of Geogrid Arrangement Effect

Dependentvariable

Geogridarrangement Estimate

Standarderror

Lettergroup

IM-Es1%Double 1.6049 0.01769 A

Upper one 1.4993 0.01769 B

Lower one 1.4286 0.01769 C

Middle 1.3291 0.01769 D

IM-Es2%Double 1.9187 0.01371 A

Upper one 1.6378 0.01371 B

Lower one 1.5813 0.01371 C

Middle 1.2554 0.01371 D

IM-USS Double 2.0358 0.01286 A

Upper one 1.6633 0.01286 B

Lower one 1.6302 0.01286 B

Middle 1.2892 0.01286 C

RPS10,000 Double 53.9144 0.9186 A

Upper one 32.5367 0.9186 B

Middle 29.4156 0.9186 C

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unreinforced case�, and then comparing the LSM of the rein-forced samples to those of the unreinforced sample. Duntte’sadjustment was used in this analysis, since it is usually used tocompare a control effect to all other effects �SAS Institute Inc.2004�. The results of this analysis showed that at a 95% confi-dence level only the resilient modulus values of samples rein-forced with double layers of geogrid Type V were higher thanthose of unreinforced samples. This suggests that the reinforce-ment did not have much effect on the resilient behavior ofcrushed limestone, which confirms the results of the permanentdeformation tests. This result is consistent with the recent worksreported by Moghaddas-Nejad and Small �2003� and Perkins etal. �2004�, where similar test results were reported on differentgranular materials �silica sand and aggregates� reinforced with asingle and double layers of geogrid.

Multisource Regression Analysis

Regression analyses were conducted on the triaxial compressionand permanent deformation test results to develop regressionmodels to evaluate the IM-Es1%, IM-Es2%, IM-USS, and RPD10 000

as a function of the geogrid stiffness and geogrid arrangement.Since the geogrid arrangement is not a quantitative variable, amultisource regression analysis �also called analysis of covariance�ANCOVA�� had to be used. As the name implies, multisourceregression analysis is a regression analysis that includes class orindicator independent variables as well as quantitative indepen-dent variables. Indicator variables are variables that can have avalue of 0 or 1. In this analysis the geogrid arrangement was usedas an indicator independent variable, while the equivalent geogridstiffness modulus was used as a quantitative independent variable.

In multisource regression analysis, a regression model is firstdeveloped for one arrangement �which is called control arrange-ment� selected randomly by the SAS program �the selected ar-rangement in this analysis was the upper one-third arrangement�.Regression models are then developed for the other arrangements.If the intercept of the regression model of an arrangement is notwithin the 95% confidence limits �CL� of the intercept of thecontrol case model, the intercept in the general model is adjustedby adding indicator variables corresponding to this arrangement.In addition, if the slope of the regression line of an arrangement isnot within the 95% CL of the slope of the control case model, theslope in the general model is adjusted by adding an interactionvariable consisting of the quantitative variable multiplied by anindicator variable corresponding to this arrangement. The generallinear model for this analysis was in the following form

Y = �0 + �1X1 + �2X2 + �3X3 + �4X4 + �5X1X2 + �6X1X3 + �7X1X4

�5�

In Eq. �5�, X1=quantitative variable representing the geogridmodulus at 2% strain normalized to the modulus at 2% strainfor Type I geogrid; X2= indicator variable that represents themiddle arrangement; X3= indicator variable that represents thelower one-third arrangement �not used in the RPD10000 model�;X4ª indicator variable that represents the double arrangement;X1X2, X1X3, and X1X4= interactions of each of the indicator vari-ables and normalized geogrid modulus; and Y =dependent vari-able, which represents the improvement in each of the responseparameters �IM-Es1%, IM-Es2%, IM-USS, and RPD10,000�.

The results of the multisource regression analyses for pre-
dicting IM-Es1%, IM-Es2%, IM-USS, and RPD10000 based on the
JOURNAL OF MAT


geogrid stiffness modulus and geogrid arrangement as indepen-dent variables, yielded the general regression models shown inEqs. �6�–�9�, respectively

IM-Es1% = 0.969 + 0.355*X1 − 0.329*X2 �6�

IM-Es2% = 1.068 + 0.382*X1 − 0.375*X2 + 0.100*X4 �7�

IM-USS = 1.182 + 0.322*X1 − 0.375*X2 + 0.239*X4 �8�

RPD10,000 = 6.44 + 15.23*X1 + 18.991*X4 �9�

The results of the analysis showed that the slope of the regres-sion lines of all reinforcement arrangements were within the 95%confidence limits of the slope of the regression line for the controlarrangement. Thus no adjustment was applied to the slope in thegeneral models. The results of the regression analysis for predic-tion of IM-Es1%, IM-Es1%, and IM-USS values indicated that theintercept of the regression models representing the middle ar-rangement was not within the 95% confidence limit of the inter-cept of models representing the control arrangement. Therefore,an indicator variable �X2� was applied to the intercept for themiddle arrangement in IM-Es2%, IM-Es1%, and IM-USS generalmodels, as seen in Eqs. �6�–�8�. The coefficient of the X2 variablewas negative, which indicates that the predicted improvement val-ues for the middle arrangement will be less than those for theupper one-third arrangement. Finally, the results showed that theintercept of the regression lines for predicting the IMEs2%, IM-USS, and RPD10,000 for the double reinforcement arrangementwas higher than the upper 95% confidence limit of the interceptfor the control arrangement regression line. Therefore, when pre-dicting the IM-Es2%, IM-USS, and RPD10,000 values for the doublereinforcement arrangement, an increase in the intercept of thegeneral models was employed by adding the X4 indicator variable�Eqs. �7�–�9��.

Discussion of Results

The preceding results indicated that the presence of geogrid rein-forcement resulted in an increase in the strength and stiffnessparameters obtained under monotonic loading and a reduction inthe permanent deformation accumulating under cyclic loading.The improvement in the response parameters under monotonicloading can be attributed to the increase in the lateral confinementdue to the presence of geogrid reinforcement. This can be ex-plained as follows: as the sample is loaded, tensile lateral strainsare created in the crushed limestone aggregate sample. The place-ment of a geogrid layer or layers within the sample allows thedevelopment of shear interaction and interlocking between theaggregate and the geogrid. Shear stress is transmitted from theaggregate to the geogrid, which places the geogrid in tension. Therelatively high stiffness of the geogrid acts to retard the develop-ment of lateral tensile strains in the material adjacent to the geo-grid, and thus results in an increase in the confinement.

Under cyclic loading conditions, other mechanisms such asdynamic interlock can also occur. The dynamic interlock mecha-nism was identified by McGown et al. �1990�. In modeling thismechanism, the geogrid is assumed to have a nonlinear visco-elasto-plastic stress-strain behavior. Thus, when the geogrid isloaded the induced tensile strain consists of a recoverable elasticcomponent, a time-dependent recoverable viscous component,and a nonrecoverable plastic component. Upon unloading, soil
particles are locked into the geogrid apertures, which prevent the

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complete recovery of the elastic and viscous components ofstrain, hence locking in stresses within the reinforcement. As aresult, the lateral confinement in the surrounding material is en-hanced and its mechanical performance is improved.

Clearly, the stiffer the geogrid, the more improvement isachieved. The reason for this is that stiffer geogrids have highertensile modulus, which allows for the development of most oftheir strength at a relatively smaller deformation when comparedto weaker geogrids. The results also indicated that the geogridbenefit is more pronounced at a higher strain level. This can beinterpreted by the fact that the higher the strain level is, thegreater the mobilization of the geogrid reinforcement strength.Finally, samples reinforced with two geogrid layers had the bestperformance. This can be attributed to the larger restraint offeredby the two reinforcement layers, making the sample behave as ashort sample.

Conclusions

A series of monotonic and cyclic triaxial tests were conducted onunreinforced and geogrid reinforced crushed limestone samples toevaluate the effects of geogrid location, number of layers, andstiffness on the strength properties and stress-strain response pa-rameters of reinforced samples. Three response parameters wereselected from monotonic triaxial test results as criterion to evalu-ate the benefits of geogrid reinforcement. The cyclic triaxial testsincluded determining the permanent strain and resilient modulusvalues. Based on the results of this study the following conclusioncan be drawn:1. The inclusion of geogrid reinforcement layer/s significantly

improves the compressive strength and stiffness and reducesthe permanent deformation of crushed limestone material.Consequently, it is expected that the use of a geogrid willresult in improving the performance of this material in thefield.

2. The geogrid improvement was more pronounced at higherstrain levels, as indicated by the triaxial compression testsand permanent deformation tests.

3. The improvement in the strength and stiffness response pa-rameters of crushed limestone was found to be a function ofthe geogrid location, type, and number of layers. This resultcan be used and verified in future studies that investigate thebenefits of using the geogrid reinforcement in field pavementsections.

4. At a certain geogrid location, stiffer geogrids exhibitedgreater benefits. For a specific geogrid type, the highest im-provement was achieved when using two geogrid layersplaced at the upper and lower third of the sample height,while the lowest improvement was found for samples rein-forced with a single geogrid layer placed at the midheight.

5. The results of the cyclic triaxial tests showed that the geogridreinforcement did not have a significant effect on the resilientbehavior of crushed limestone samples.

6. The multisource regression analyses showed that theIM-Es2%, IM-Es2%, IM-USS, and RPD10 000 factors can bepredicted for all geogrid locations using a general model con-sisting of the geogrid stiffness modulus as a quantitative vari-able, and the geogrid arrangement as an indicator variable.

Acknowledgments

This research project is funded by the Louisiana Transportation
Research Center �LTRC Project No. 05-5GT� and Louisiana De-


partment of Transportation and Development �State Project No.736-99-1312�. The writers gratefully acknowledge the help andadvice of Zhongjie Zhang, Pavement and Geotechnical Adminis-trator at LTRC.

References

AASHTO. �2003�. “Standard method of test for determining the resilientmodulus of soils and aggregate materials.” AASHTO T307–99, Wash-ington, D.C.

Al-Qadi, I. L., Brandon, T. L., and Bhutta, S. A. �1997�. “Geosyntheticsstabilized flexible pavements.” Proc., Geosynthetics’ 97, Vol. 2, LongBeach, Calif., 647–661.

Al-Qadi, I. L., Brandon, T. L., Valentine, R. J., Lacina, B. A., and Smith,T. E. �1994�. “Laboratory evaluation of geosynthetic reinforced pave-ment sections.” Transportation Research Record. 1188, TransportationResearch Board, Washington, D.C., 25–31.

Ashmawy, A. K., and Bourrdeau, P. L. �1997�. “Testing and analysis ofgeotextile-reinforced soil under cyclic loading.” Proc., Geosynthetics’97, Long Beach, CA, Vol. 2, 663–674.

Ashmawy, A. K., and Bourrdeau, P. L. �1998�. “Effect of geotextile re-inforcement on the stress strain and volumetric response of sand.”Proc., 6th Int. Conf. on Geosynthetics, Vol. 2, Atlanta, 1079–1082.

Barksdale, R. D., Brown, S. F., and Chan, F. �1989�. “Potential benefits ofgeosynthetics in flexible pavement systems.” National CooperativeHighway Research Program Rep. No. 315, Transportation ResearchBoard, National Research Council, Washington, D.C.

Berg, R. R., Christopher, B. R., and Perkins, S. W. �2000�. “Geosyntheticreinforcement of the aggregate base course of flexible pavement struc-tures.” GMA White Paper II, Geosynthetic Material Association,Roseville, Minn.

Cancelli, A., and Montanelli, F. �1996�. “In-ground test for geosyntheticreinforced flexible paved roads.” Proc., Geosynthetics ’99, Vol. 2,Boston, 863–878.

Collin, J. G., Kinney, T. C., and Fu, X. �1996�. “Full scale highway loadtest of flexible pavement systems with geogrid reinforced basecourses.” Geosynthet. Int., 3�4�, 537–549.

Gray, D. H., and Al-Refeai, T. �1986�. “Behavior of fabric- vs. fiber-reinforced sand.” J. Geotech. Engrg., 112�8�, 804–820.

Haas, R., Walls, J., and Carroll, R. G. �1988�. “Geogrid reinforcement ofgranular bases in flexible pavements.” Transp. Res. Rec., 1188,19–27.

Heath, A. C. �2002�. “Modeling unsaturated granular pavement materialsusing bounding surface plasticity.” Ph.D. thesis, Univ. of California atBerkeley, Berkeley, Calif.

McGown, A., Yeo, K. C., and Yogarajah, I. �1990�. “Identification of adynamic interlock mechanism. Performance of reinforced soil struc-tures.” Proc., Int. Reinforced Soil Conf., Glasgow, U.K., 377–379.

Miura, N., Sakai, A., Taesiri, Y., Yamanouchi, T., and Yasuhara, K.�1990�. “Polymer grid reinforced pavement on soft clay grounds.”Geotext. Geomembr., 9�1�, 99–123.

Moghaddas-Nejad, F. , and Small, J.C. �2003�. “Resilient and permanentcharacteristics of reinforced granular materials by repeated load tri-axial tests.” Geotech. Test. J., 26�2�, 152–166.

Mohammad, L. N., Herath, A., Rasoulian, M., and Zhongjie, Z. �2005�.“Laboratory evaluation of untreated and treated pavement base mate-rials from a repeated load permanent deformation test.” Transporta-tion Research Record, in press.

National Cooperative Highway Research Program �NCHRP�. �2004a�.“Laboratory determination of resilient modulus for flexible pavementdesign.” NCHRP research results digest for NCHRP 1–28A project,Washington, D.C.

National Cooperative Highway Research Program �NCHRP�. �2004b�.“Guide for mechanistic-empirical design of new and rehabilitatedpavement structures.” NCHRP Final Rep. for NCHRP 1-37A Project,
Washington, D.C., �www.NCHRP 1-37A Designdesignguide.com�
MBER 2007

7.19:772-783.

Dow

nloa

ded

from

asc

elib

rary

.org

by

LO

UIS

IAN

A S

TA

TE

UN

IV o

n 08

/01/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

�July 20, 2005�.Nazzal, M. D., Abu-Farsakh, M., and Mohammad, L. �2006� “Numerical

analyses of geogrid reinforced flexible pavements.” Proc., GeoCon-gress Conf., Atlanta.

Perkins, S. W. �2002�. “Evaluation of geosynthetic reinforced flexiblepavement systems using two pavement test facilities.” Rep. No.FHWA/MT-02–008/20040, Department of Transportation, FederalHighway Administration, Washington, D.C.

Perkins, S. W., et al. �2004�. “Development of design methods for geo-
synthetic reinforced flexible pavements.” Rep. Prepared for the U. S.
JOURNAL OF MAT


Department of Transportation, No. FHWA/DTFH61–01-X-00068,Federal Highway Administration, Washington D.C., 263.

SAS Institute Inc. �2004�. “SAS OnlineDoc® 9.1.2.” Cary, N.C.Tensar Earth Technologies, Inc. �2005�. �www.tensarcorp.com/

uploadedFiles/SPECTRA_MPDS_BX_8.05.pdf� �July 20, 2005�.Webster, S. L. �1993�. “Geogrid reinforced base courses for flexible

pavements for light aircraft, test section construction, behaviorunder traffic, laboratory tests, and design criteria.” Technical Rep. No.GL-93–6, U.S. Army Corps of Engineers, Waterways Experiment
Station, Vicksburg, Miss.

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Documents

Laboratory Characterization of Reinforced Crushed Limestone under Monotonic and Cyclic Loading