The Japanese Geotechnical Society

Soils and Foundations

Soils and Foundations 2014;54(2):94–108

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Anisotropy in compressive strength and elastic stiffnessof normal and polymer-modified asphalts

Warat Kongkitkuln, Noppadon Musika1, Chaloemchai Tongnuapad1,Pornkasem Jongpradist2, Sompote Youwai3

Department of Civil Engineering, Faculty of Engineering, King Mongkut's University of Technology Thonburi, 126 Pracha Uthit Road, Bang Mod, Thung Khru,Bangkok 10140, Thailand

Received 10 July 2012; received in revised form 4 September 2013; accepted 1 October 2013Available online 21 March 2014

Abstract

Anisotropy in the compressive strength and the elastic stiffness of normal hot-mix asphalt (HMA) and polymer-modified asphalt (PMA) wereinvestigated experimentally. Two types of prismatic specimen with planes of compaction either normal to or parallel to the applied axialcompression were used. Both axial and lateral principal strains were measured locally. Continuous monotonic loadings at a constant strain ratewere axially applied to investigate the anisotropy in the compressive strength. Very small strain–amplitude cyclic stresses were also applied bymeans of another load-controlled apparatus to investigate the anisotropy in the elastic stiffness. The followings were found: (i) compressivestrengths of both HMA and PMA are anisotropic in that the values for the vertical direction were significantly larger than those of horizontaldirection; (ii) the small strain stiffness of both HMA and PMA are anisotropic with the vertical elastic Young's modulus being greater than thehorizontal elastic Young's modulus; (iii) the elastic Young's modulus is stress level dependent, exhibiting a hypo-elastic behaviour; and (iv) theelastic Young's modulus becomes greater with the applications of the normal and the polymer-modified asphalt cement binders.& 2014 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

Keywords: Anisotropy; Asphalt; Compressive strength; Elasticity; Local strain; Unconfined compression; IGC: D06/M03

0.1016/j.sandf.2014.02.0024 The Japanese Geotechnical Society. Production and hosting by

g author. Tel.: þ66 2 470 9304; fax: þ66 2 427 9063.sses: warat.kon@kmutt.ac.th (W. Kongkitkul),hotmail.com (N. Musika),

com (C. Tongnuapad),mutt.ac.th (P. Jongpradist),utt.ac.th (S. Youwai).70 9155; fax: þ66 2 427 9063.70 9305; fax: þ66 2 427 9063.70 9308; fax: þ66 2 427 9063.der responsibility of The Japanese Geotechnical Society.

1. Introduction

Asphalt, a mixture of asphalt cement and aggregate com-pacted to a designated density, has long been widely used as aflexible pavement layer in road construction. Its popularitymay be due to its good-performance, ease of construction andbecause its smooth top surface allows for good riding quality.Recently, the application of asphalt has been extended fromthe field of pavement engineering to the field of geotechnicalengineering; that is, it has been used as the impermeablesealing core of earth and embankment dams (e.g., ICOLD,1992; Hoeg et al., 2007; Feizi-Khankandi et al., 2008). Fromthis perspective, it is apparent that more realistic considerationsof the properties of asphalt have become necessary. However,

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W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 95

most of the laboratory experiments and analytical models forasphalt are presently based on the assumption that it exhibitsisotropic material properties. Most known models are based onthe linear elastic or linear visco-elastic theory in which asphaltis assumed to be homogenous and isotropic (e.g., Huang,2004). With this assumption, the deformational behaviourspredicted by the models may not be realistic. In pavementdesign, for example, the isotropic analysis may lead to anunderestimation of both the shear and tensile stresses that arerelated to permanent deformation and fatigue cracking assess-ment (e.g., Chen et al., 2011).

In the field of geotechnical engineering, a number of studies onthe anisotropy of strength and deformation properties of variousunbound geomaterials (i.e., sands and gravels) have been widelyperformed (e.g., Jiang et al., 1997; Hoque and Tatsuoka, 1998;Tatsuoka et al., 1999). Moreover, the mechanical behaviours ofmany bound materials, such as natural clay (Graham and Houlsby,1983; Piriyakul and Haegeman, 2009), kaolin clay (Anantanasakulet al., 2012), cement-mixed gravel (Kongsukprasert et al., 2007),soft sedimentary rock (Fu et al., 2012) and asphalt (Masad et al.,2002) are known to be anisotropic. Also, it has been realised thatthe anisotropy of asphalt is influenced by the specimen prepara-tions and test conditions. Its anisotropic behaviour is furtherinfluenced by the magnitude of the stresses and strains inducedin the specimen and the loading rate applied to the specimen (e.g.,Wang et al., 2004). In addition, in reality, the direction of the majorprincipal stress generated at an element of the pavement by thetraffic load rotates from the approaching moment to the departingmoment of the wheel load (e.g., Inam et al., 2012). However, veryfew laboratory research studies (e.g., Masad et al., 2002; Mamlouket al., 2002; Motola and Uzan, 2006; Liang et al., 2006) have beenperformed with the aim of understanding the anisotropic propertiesof asphalt in detail, though this is necessary for further realisticmodelling. In pavement design, for example, the anisotropicproperties can be implemented in order to adjust or fine-tune thematerial characterisation models before calibration testing begins.This might lead to a significant reduction in testing requirements ifisotropic conditions for the selected test parameters are identified(Mamlouk et al., 2002).

In recent years, polymer-modified asphalt has been gainingpopularity in road construction. This may be due to its better per-formances including resistance to permanent deformation, ruttingand cracking, and its high stiffness, among other qualities (e.g.,Zhao et al., 2008; Yildirim, 2007). Since its major constituentmaterial is also an aggregate, it is likely that the mechanical pro-perties of polymer-modified asphalt are also anisotropic. However,little is known with regard to the characterisation and modelling ofthe anisotropic properties of polymer-modified asphalt. In particu-lar, to the best of the authors' knowledge, it seems that there is onlyvery limited research studies specially performed to understand notonly the anisotropic behaviours of both asphalt types individuallybut also the comparisons among them.

In view of the above, in the present study, a series ofunconventional unconfined compression tests were performedon the normal asphalt specimens and the polymer-modifiedasphalt specimens compacted to different densities to studytheir effects. The compaction directions were designed such

that the direction of the applied axial load in the tests waseither perpendicular to or parallel to the compaction plane tostudy the anisotropic properties. As mention earlier, amongdifferent models assumed for the modelling of asphalt, elasticstiffness, which expresses the recoverable deformation uponload release, is always basically incorporated. In this study,therefore, the effects of different asphalt types and differentdensities on the anisotropic elastic properties were investi-gated. Summarising the above, the unconventional unconfinedcompression tests performed in this study included: (i) con-tinuous monotonic loading tests to investigate the compressivestrengths and (ii) small-amplitude cyclic loading tests toinvestigate the elastic properties.

2. Anisotropic elasticity

Most of the geomaterials deposited naturally or artificially orcompacted vertically, exhibit cross-anisotropic deformationproperties, which are symmetrical about the vertical axis. Asasphalt is constituted from the aggregate mixed with theasphalt cement (AC) binder and then compacted vertically, itis very likely that it also exhibits cross-anisotropic deformationproperties. Cross-anisotropy requires only six elastic para-meters for the characterisation of soil properties (Hoque andTatsuoka, 1998). Under triaxial stress states when the hor-izontal principal stress is the same, the incremental relationshipbetween stresses and strains (Hooke's law) is

δεh

δεh

δεv

264

375 ¼

1=Eh �νhh=Eh �νvh=Ev

�νhh=Eh 1=Eh �νvh=Ev

�νhv=Eh �νhv=Eh 1=Ev

264

375

δshδshδsv

264

375 ð1Þ

where Ev and Eh are the vertical and horizontal elastic Young'smoduli; νvh, νhh and νhv are the elastic Poisson's ratios. Theseelastic parameters were determined from multiple small-strainamplitude unload and reload cycles (cyclic loading, CL) with asingle axial strain amplitude in the order of 0.001%. In thisstrain range, deformation moduli are negligibly influenced bystress–strain histories within the ranges of stress change smallenough to maintain the initial fabric, the type of loading(monotonic or cyclic), wave form during cyclic loading andthe rate of shearing (dynamic or static) (Tatsuoka and Kohata,1995; Jamiolkowski et al., 1991). In other words, the applica-tion of such small-strain amplitude unload and reload cycles isnon-destructive.Based on the above-mentioned tests, a hypo-elasticity model

with inherent and stress system-induced anisotropy has beendeveloped (Tatsuoka et al., 1999):

Ev ¼ ðEvÞ0svs0

� �mv

; independent of sh ð2Þ

Eh ¼ ðEhÞ0shs0

� �mh

; independent of sv ð3Þ

where Ev and Eh are the elastic Young's moduli respectivelyfor the vertical and horizontal directions; s0 is the referencestress value (e.g., 1 kPa as used in this study or any others);

Table 1Properties of asphalt cement (AC) and polymer-modified asphalt cement (PM-AC) used in this study.

Properties AC PM-AC

Min. Max. Min. Max.

Penetration at 25 1C, 100 g, 5 s 0.1 mm 60 70 60 70Flash point (Cleveland open cup) 1C 232 – 220 –

Ductility, 5 cm/minAC at 25 1C cm 100 –

PM-AC at 13 1C cm 55 –

Solubility in Trichloroethylene per cent 99.0 – 99.0 –

Thin-film oven test, 3.2 mm, 163 1C 5 hLoss on heating per cent – 0.8 – 0.5Penetration of residue at 25 1C per cent of original 54 – 70 –

Ductility of residue at 25 1C, 5 cm/minAC at 25 1C cm 50 –

PM-AC at 13 1C cm 40 –

Loss on heating, 163 1C, 5 h per cent – 0.8 – 0.5

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–10896

ðEvÞ0 and ðEhÞ0 are the values of Ev and Eh respectively whensv¼s0 and sh¼s0; and, mv and mh are constants, expressingthe dependencies of Ev and Eh on the respective vertical andhorizontal stresses. The s0 in Eqs. (2) and (3) was implemen-ted so that the units of ðEvÞ0 and Ev and ðEhÞ0 and Eh are thesame. When mv=mh=m, this means that the dependencies ofEv and Eh on the respective stresses are qualitatively the samefor both directions. In this case, the vertical and horizontalelastic moduli could be related as

Ev

Eh¼ ðEvÞ0

ðEhÞ0svsh

� �m

ð4Þ

Eq. (4) means that, when ma1.0, the ratio of Ev=Eh increasesin a non-linear manner with the ratio sv=sh.

3. Test materials and test methods

3.1. Test materials

Asphalt cement (AC) type AC 60/70 in the penetrationgrade or PG 70-10 in the performance grade was used in thepreparations of the normal asphalt. For preparations ofpolymer-modified asphalt, a type of polymer modified asphaltcement (PM-AC), which is produced by mixing styrenebutadiene styrene (SBS) with normal asphalt cement (AC)type AC 60/70, was used. These AC and PM-AC weremanufactured to meet the specifications by the Departmentof Highways, Thailand (i.e., DH-SP. 401/2531 and DH-SP.408/2536, respectively) and provided from the respectivemanufacturers in liquid form stored in sealed containers. Theproperties of the AC and PM-AC used in this study are listedfor comparison purposes in Table 1, following the specifica-tions given by the Department of Highways, Thailand.

The aggregate used was a limestone widely used in typicalpavement construction in Thailand. It was cleaned by washingwith tap water and then sieved to classify the sizes. Then,the classified aggregates of different sizes were brought formixing to obtain the grain size distribution designated by theDH-S. 408/2532. The resultant aggregate had the following

properties: a maximum particle size (Dmax) of 12.50 mm, amean particle size (D50) of 2.55 mm, a coefficient of uni-formity (Uc) of 25, and a specific gravity (Gs) of 2.63. In thisstudy, all the test specimens, both for the normal asphalt andthe polymer-modified asphalt, were prepared from the sameaggregate.

3.2. Specimen preparations

In this study, all specimens were prepared by hot-mixingbetween the respective asphalt cement types and the aggregate.Preparations started with heating the aggregate in the oven forabout 2 h at 140 1C and 180 1C for the normal and thepolymer-modified asphalts, respectively. For preparations ofthe normal asphalt specimens, the AC was heated up by a gasstove to a controlled temperature of 140 1C; then, both the ACand the aggregate were mixed together on a tray heated by astove (Kongkitkul et al., 2010). The PM-AC was heated byhot-oil filled in a double-layer container to 180 1C (Kongkitkulet al., 2012a), as recommended by the manufacturer. Thismethod was used to avoid damage to the SBS (polymer resinadded to AC), which would result in the loss of the quality ofdeveloped strength and stiffness. Then, similar to the normalasphalt specimens, the aggregate was mixed together with thePM-AC on a tray heated by stove. The asphalt cement contentof 5% by the weight of the aggregate was used, both for thenormal and the polymer-modified asphalts.Then, the compaction process was started, with the same

process used for both the normal and the polymer-modifiedasphalts. The details are as follows. There were two types ofmoulds used this study (Fig. 1): (i) a vertical mould and (ii) ahorizontal mould. The dimensions of these two mould types arealso given in Fig. 1. These two mould types were prepared sothat, when performing the unconfined compression tests, thedirection of the major principal stress (s1) is perpendicular to orparallel to the planes of compaction when subjected to verticaland horizontal compactions, respectively (Fig. 2). After havingcompleted the assembly of the moulds as shown in Fig. 1, therespective hot mixtures were then poured into them. By carefully

Fig. 1. Mould types used to prepare HMA and PMA specimens in this study: (a) vertical mould and (b) horizontal mould.

Fig. 2. Directions of compression (s1) relative to the planes of compaction: (a) vertical compaction and (b) horizontal compaction.

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 97

and manually performing the compaction into five equivalentlayers for both the vertical and horizontal moulds (Fig. 2), thecompaction energy can be thoroughly applied when forming aspecimen to achieve different target densities (Table 2). Thetypical density value of asphalt pavement compacted in the fieldis around 2.35–2.40 g/cm3. In this study, to investigate the effectsof various densities, the values of 1.90 g/cm3, 2.15 g/cm3 and2.37 g/cm3 were selected for both the normal hot-mix asphalt(HMA) specimens and the polymer-modified asphalt (PMA)specimens. The corresponding air void contents for these threedifferent densities are 22.8%, 12.7% and 3.8%, respectively.During compaction procedure, after the compaction of each layer,the obtained density was checked to ensure that the obtained finaldensity of the entire specimen was almost the same as the target

value. This inspection was performed on every specimen in thisstudy. Note that the values of 1.90 g/cm3 and 2.15 g/cm3 arearound 80% and 90% of the value of 2.37 g/cm3. Then, thespecimens were cured in the mould for 16 h. The elapsed timebetween the starts of compactions of the two consecutive layerswas less than 45 min so as to avoid discontinuity between layers.Then, the HMA specimens and the PMA specimens wereobtained. In this study, the density and air void content of eachspecimen were controlled by averaging values for the entirespecimen. Further study is necessary to evaluate the uniformityof air void content distribution inside the specimens prepared bythe compaction procedures used in this study and its effects onthe anisotropy of compressive strength and elastic stiffness. Thisissue is beyond the scope of the study.

Table 2Test programme for investigations of anisotropy in the compressive strength and elastic stiffness of the normal hot-mix asphalt (HMA) used in this study.

Densities(g/cm3)

Directionsofcompaction

Testnames

Loadingschemes

Stress level (kPa) SLperiod(min)

ΔsduringCL (kPa)

1.90 Vertical H-VSM-01 (a) – – –

H-VSM-02H-VSM-03H-VSC-01 (b) 8.9, 17.8 and 26.7 180 2.7H-VSC-02H-VSC-03 (b) 10.2, 20.4 and 30.6 360 4.4

Horizontal H-HSM-01 (a) – – –

H-HSM-02H-HSM-03H-HSC-01 (b) 8.9, 17.8 and 26.7 180 2.7H-HSC-02H-HSC-03

2.15 Vertical H-VMM-01 (a) – – –

H-VMM-02H-VMM-03H-VMC-01 (b) 21.3, 42.7, 64.0, 85.3,

106.7, 128.0 and 149.3180 10.7

H-VMC-02H-VMC-03

Horizontal H-HMM-01 (a) – – –

H-HMM-02H-HMM-03H-HMC-01 (b) 17.8, 35.6, 53.3, 71.1, 88.9

and 106.7180 8.9

H-HMC-02H-HMC-03

2.37 Vertical H-VLM-01 (a) – – –

H-VLM-02H-VLM-03H-VLC-01 (b) 32.9, 68.4, 103.9, 139.5,

175.1, 210.6, 246.2,281.7, 317.3, 352.9, 388.4and 424.0

30 8.9H-VLC-02

H-VLC-03 (b) 45.8, 95.6, 145.4, 195.1,244.9, 294.7, 344.5,394.3 and 444.0

180 10.7H-VLC-04

Horizontal H-HLM-01 (a) – – –

H-HLM-02H-HLM-03H-HLC-01 (b) 35.6, 71.1, 106.7, 142.2, 177.8,

213.3 and 248.9180 10.7

H-HLC-02H-HLC-03

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–10898

3.3. Test apparatuses and measuring devices

There were two types of compression apparatuses used toperform unconfined compression tests in this study: apparatus Aand apparatus B (Fig. 3). Apparatus A, which is a displacement-controlled type, was used to perform continuous monotonicloading (ML) at a constant strain rate to evaluate the compres-sive strengths and secant moduli (explained later) of thespecimens tested. Apparatus B, which is a load-controlled type,was used to perform small-amplitude cyclic loading (CL) teststo determine the equivalent elastic Young's modulus.

To avoid any bedding errors that may develop at contactsbetween the specimen top end and the cap and between thespecimen bottom end and the pedestal which are associated with

unexpected gaps and irregularities of specimen ends, both the topand bottom specimen ends were smoothened by adhering themwith a thin layer of gypsum paste (Fig. 4). Then, the specimen wasplaced on the triaxial cell pedestal and the top cap was moveddown so that it was placed on the top specimen end. Then, handcompression was applied and the piston was locked until the topand bottom gypsum paste layers had been set. Subsequently, thespecimen was removed from the triaxial cell and stored before itwas tested. This technique ensured that the top and bottomspecimen ends were in good contact with the pedestal and thecap when compression was applied (Abdelrahman et al., 2008).Before the placement of the specimen on the triaxial cell forthe test, the top cap and pedestal were lubricated by smearingwith a 50-μm thick high-vacuum silicone grease (HIVAC-G

Fig. 4. Diagram showing preparations of the top and bottom specimen endsbefore application of compression.

Fig. 3. Compression apparatuses used to perform unconfined compression tests in this study: (a) displacement-controlled type (apparatus A) and (b) load-controlledtype (apparatus B).

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 99

manufactured by Shin-Etsu Chemical Co., Ltd) and then a 0.3-mmthick latex rubber sheet was attached (see Fig. 4) (Tatsuoka andHaibara, 1985).

A load cell was used to measure the axial load and a LVDTto externally measure the axial deformation. To evaluate thepre-peak stiffness of relatively stiff geomaterials, it is neces-sary to employ sensitive and accurate local strain measurementin the laboratory stress–strain tests. Several methods have beenproposed to locally and sensitively measure the axial strainsfree from the large effects of bedding error at the specimenends (e.g., Jardine et al., 1984; Burland, 1989; Tatsuoka et al.,1999; Clayton, 2011). In this study, in order to make preciselocal measurements of the axial and lateral deformations, a pair

of local deformation transducers (LDTs; Goto et al., 1991) andthree clip gauges were installed directly on the specimenperiphery (Fig. 5). These local strain measurement techniqueswere also used in the triaxial compression tests on sand andgravel (e.g., Maqbool et al., 2011), and cement-mixed gravellysoil (e.g., Kongsukprasert and Tatsuoka, 2007; Taheri et al.,2012).

3.4. Loading schemes

For each combination of density and direction of compac-tion, the following two loading schemes were employed:

(a)

continuous ML by apparatus A at a constant axial strainrate of 0.03%/min until the end of test; and

(b)

ML at a constant axial stress rate of 1.778 kPa/min forHMA specimens or 3.556 kPa/min for PMA specimens byapparatus B until a prescribed stress level was reached,followed by a stage of sustained loading (SL) and then 10cycles of unload/reload with a small amplitude and a restartof the ML to the next prescribed stress level.

Tables 2 and 3 summarise the test programs respectively for theHMA and PMA specimens tested in the present study. Theprefixes of “H-” and “P-” in front of test names stand for HMAand PMA, respectively. For others, similar suffixes were used forthe same density and the compaction direction for both HMA andPMA specimens. In summary, for loading scheme (a), threespecimens were used for each combination of density and com-paction direction (e.g., H-VSM-01, H-VSM-02 and H-VSM-03and P-VSM-01, P-VSM-02 and P-VSM-03 respectively for HMAand PMA specimens vertically compacted to the density of 1.90 g/cm3). For loading scheme (b), the stress level at which smallunload/reload cycles (CLs) were performed, the duration of SLprior to the CLs and the double stress amplitude of CLs (Δs) were

Fig. 5. Installations of local deformation measuring devices including a pair of LDTs and three clip gages: (a) installation configurations and (b) photo of aspecimen being tested.

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108100

designated as tabulated in Tables 2 and 3 to ensure the following:(i) the SL was long enough to allow the behaviour during theCLs to be significantly elastic; (ii) the CL amplitude was smallenough for specimens to behave elastically while large enough toallow for linear fitting to obtain the elastic Young's modulus(explained later); and (iii) the stress levels at which the CLs wereperformed were varied so as to determine the elastic Young'smodulus values for various stress levels. The combinations ofthese three points of considerations depended on the compressivestrengths and stiffnesses of specimens prepared at differentdensities and compaction directions which were investigated inadvance by loading scheme (a). All the tests in this study wereperformed at 25 1C in a temperature-controlled room at thegeotechnical engineering laboratory, the King Mongkut's Uni-versity of Technology Thonburi.

4. Test results and discussions

4.1. Compressive strengths and secant stiffnesses

Fig. 6a and b compare the stress–strain relations followingloading scheme (a) by apparatus A for the vertically andhorizontally compacted HMA specimens, respectively. Similarly,Fig. 7a and b compares those for vertically and horizontallycompacted PMA specimens, respectively. It is worth noting thatthe strain values along the abscissa of these figures wereexternally measured by the LVDT. In these figures, as thestress–strain relations for either the three HMA specimens or thethree PMA specimens prepared at the same density andcompaction direction (Tables 2 and 3) were slightly different,the respective average relations were shown. In order to comparethe stiffnesses among different specimens, the vertical andhorizontal secant moduli (Ev;50 and Eh;50), defined as the slopesof the lines passing to the origins of stress–strain relations and the

data points along the stress–strain relations at which the verticaland horizontal stresses were half the respective compressivestrengths (sv; max and sh; max), were selected as the representa-tives. In Fig. 8a, the compressive strengths (sv; max and sh; max) ofthe vertically and horizontally compacted HMA and PMAspecimens are compared for different densities. In Fig. 8b, thesecant moduli (Ev;50 and Eh;50) among the HMA and PMAspecimens vertically and horizontally compacted to differentdensities are compared in a similar manner to Fig. 8a. Thefollowing trends of behaviour may be seen from Figs. 6–8:

(1)

For the respective directions of compaction, the compres-sive strength (sv; max or sh; max) and the secant modulus(Ev;50 or Eh;50) increased with density, indicating asignificant effect on compaction.

(2)

For the respective densities and types of asphalt, the valueof sv; max was higher than the respective sh; max value whilethe strain value at which sv; max was exhibited was lessthan the respective value at which sh; max was exhibited. Asa result, Ev;50 was also higher than the respective Eh;50.This clearly indicates anisotropic behaviours on the com-pressive strength and stiffness of both HMA and PMA.

(3)

For the respective directions of compaction and densities,PMA exhibited higher compressive strength and a highersecant modulus than those of HMA. As the aggregate used inthe preparations of both HMA and PMA specimens was thesame, this observation showed the effects of binder type on theimprovements of strength and stiffness characteristics ofasphalt.

Findings (1) and (2) showed that the strength and stiffnessbehaviours of both HMA and PMA are not only density-dependent but also anisotropic by being dependent on the

Table 3Test programme for investigations of anisotropy in the compressive strength and elastic stiffness of the polymer-modified asphalt (PMA) used in this study.

Densities(g/cm3)

Directionsofcompaction

Test names Loadingschemes

Stress level (kPa) SLperiod(min)

Δs duringCL (kPa)

1.90 Vertical P-VSM-01 (a) - - -P-VSM-02P-VSM-03P-VSC-01 (b) 26.0, 52.0 and 79.0 180 11.0P-VSC-02P-VSC-03 (b) 17.0, 35.0 and 52.0 180 7.0

Horizontal P-HSM-01 (a) – – –

P-HSM-02P-HSM-03P-HSC-01 (b) 15.5, 32.0 and 48.0 180 6.0P-HSC-02P-HSC-03 (b) 24.0, 40.0 and 56.0 180 7.0

2.15 Vertical P-VMM-01 (a) – – –

P-VMM-02P-VMM-03P-VMC-01 (b) 48, 97, 146, 196, 254 and 295.5 180 12.0P-VMC-02P-VMC-03 (b) 73.0, 122.0, 172.0, 221.0

and 272.0180 12.0

Horizontal P-HMM-01 (a) – – –

P-HMM-02P-HMM-03P-HMC-01 (b) 28.0, 56.0, 85.0, 114.0, 143.0

and 173.0180 12.0

P-HMC-02P-HMC-03 (b) 42.0, 70.5, 99.0, 128.0, 157.0

and 186.0180 12.0

2.37 Vertical P-VLM-01 (a) – – –

P-VLM-02P-VLM-03P-VLC-01 (b) 86.5, 174.0, 261.0, 349.0, 437.0,

525.0 and 615.0180 26.0

P-VLC-02 120P-VLC-03 (b) 130.0, 217.0, 304.0, 391.0, 479.0,

567.0 and 656.0180 26.0

P-VLC-04Horizontal P-HLM-01 (a) – – –

P-HLM-02P-HLM-03P-HLC-01 (b) 70.0, 140.0, 212.0, 284.0,

358.0 and 433.0180 18.0

P-HLC-03P-HLC-02 (b) 105.0, 175.0, 246.0, 317.0,

389.0 and 462.0180 18.0

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 101

direction of the applied major principal stress (s1) relative tothe plane of compaction. It is likely that these anisotropicbehaviours may be due to one or a combination of thefollowing:

(1)

During compaction, because the aggregate particles werearranged in the form of layers, when they were compressedin the same direction as they were formed, they would bestronger than in other directions. That is, the specimenshad more experience to be loaded in the same direction asthat when they were compacted than in other directions.

(2)

When specimens were axially compressed, the jointsinevitably formed between the layers by compaction werecompressed or expanded when they are respectively normal

to or parallel to the direction of compression (Fig. 2). Also,when the joints were compressed, the behaviour of the entirespecimen was more united, while, it was more segmentedwhen expanded. Similar discussions in this respect werealso found for the behaviours of cement-mixed gravellysoils (i.e., Kongsukprasert et al., 2007).

4.2. Determination of equivalent elastic Young's modulus

Fig. 9a shows the stress–strain relation obtained following theloading scheme (b) by apparatus B, performed on the HMAspecimen vertically compacted to a density of 2.37 g/cm3 (i.e.,H-VLC-03, Table 2). Fig. 9b shows a zoomed-up portion ofFig. 9a. Similarly, Fig. 10a and b shows the test result of the PMA

Fig. 6. Effects of compaction density on the stress–strain behaviours of HMA:(a) vertically compacted specimens and (b) horizontally compacted specimens(εv and εh were measured by LVDT).

Fig. 7. Effects of compaction density on the stress–strain behaviours of PMA:(a) vertically compacted specimens and (b) horizontally compacted specimens(εv and εh were measured by LVDT).

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108102

specimen vertically compacted to a density of 2.37 g/cm3 (i.e.,P-VLC-01, Table 3). Following the technique that has been widelyused to reliably determine the elastic property by triaxial tests onunbound geomaterials (e.g., Shibuya et al., 1992; Tatsuoka et al.,1994; Hoque and Tatsuoka, 1998) and cement-mixed gravel (e.g.,Kongsukprasert and Tatsuoka, 2007) and one of polymer geogridsby tensile loading tests (e.g., Hirakawa et al., 2003; Kongkitkulet al., 2012b), respective sets of 10 small unload/reload cycles wereapplied after sustained loading (SL). It was expected that thestress–strain behaviour during cyclic loading (CL) would beessentially elastic when this method was used. The followingtrends of behaviours may be seen from Figs. 9 and 10:

(1)

The creep strain during the SL and prior to the smallunload/reload cycles were significant. They resulted inconsiderably less deformation due to the viscous propertiesduring the subsequent cyclic loadings.

(2)

The behaviour during the small unload/reload cycles washighly linear–elastic, as was clear from the following: (i) thestress–strain loops generated during the respective unload/reload cycles were very small and exhibited negligible energy

dissipation and (ii) the residual strain developed by therespective unload/reload cycles was very small. These beha-viours also showed that small unload/reload cycles applied tothe specimen were non-destructive.

Fig. 11a shows the small unload/reload loop nos. 6–10 at astress level of 217 kPa for the PMA specimen verticallycompacted to a density of 2.37 g/cm3 (P-VLC-03, Table 3).It can be seen that the unload stress–strain branches exhibithighly linear elasticity for a large range of stress incrementsrelative to the whole stress amplitude (i.e., 26 kPa, Table 3).Thus, it is relevant to evaluate the equivalent elastic Young'smodulus (Eeq) from a linear relation fitted to respectiveportions of the unload stress–strain branches presented inFig. 11a. Although the data scatters to some extent, as canbe seen in this figure, the Eeq values can be defined ratherconfidently. The value of Eeq is rather constant during theseunload branches from loop nos. 6 to 10 at the respective CLstages. This indicates that the deformation during these unloadstress–strain branches is essentially elastic.

Fig. 8. Comparisons for: (a) compressive strengths and (b) secant moduli,among HMA and PMA specimens compacted vertically and horizontally.

Fig. 9. Vertical stress–vertical strain relation obtained following loadingscheme (b) on a HMA specimen vertically compacted to ρ¼2.37 g/cm3 (H-VLC-03): (a) whole relationship and (b) zoom-up during SL and CL (εv weremeasured by LDTs).

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 103

However, the range of stress increments for which theunload stress–strain branches exhibited highly linear elasticitydecreases as the stress level increases. This is because theresidual strains that developed during the unload/reload cyclesat high stress levels are not negligible, as can be seen fromFigs. 9a and 10a. In addition, upon the start of unloading, therewas an occasional delay in the recovered strain. For example,the unload stress–strain branches from loop nos. 6 to 10 at thestress level of 175.1 kPa from HMA specimen verticallycompacted to a density of 2.37 g/cm3 (H-VLC-01, Table 2)are shown in Fig. 11b. It may be seen that the unload stress–strain branches exhibit highly linear elasticity for a relativesmaller stress range when compared to the whole stressamplitude (i.e., 8.9 kPa, Table 2). In these cases, it is thereforenecessary to find a portion exhibiting essentially elastic(i.e., rate-independent and reversible) behaviour from thewhole stress–strain behaviour during respective unload/reloadcycles.

Fig. 11b also shows data typical of cases in which thestress–strain behaviour is highly linear and reversible only fora smaller range of stress increment near the bottom end of the

stress–strain loop. When only these bottom stress range weretaken into account (e.g., Fig. 11b), the behaviours can bedeemed to be essentially reversible (therefore elastic). A linearrelation was fitted to the bottom range of the respective unloadstress–strain branches presented in Fig. 11b to obtain theequivalent elastic Young's modulus (Eeq). Although the datascatters to some extent, as seen in Fig. 11b, values of Eeq canbe defined rather confidently as they are rather constant duringthese unload/reload cycle loops.The Eeq values of HMA and PMA compacted to different

densities and compaction directions (i.e., for both the verticaland horizontal directions as Ev;eq and Eh;eq, respectively) at thestress levels listed in Tables 2 and 3 (other than thosepresented in Fig. 11a and b) were determined in the mannerindicated in Fig. 11a and b.

4.3. Comparisons of equivalent elastic Young's modulus

Among the five measured values of Eeq at respective CLstages (i.e., loop nos. 6–10) at different stress levels (as shownin Fig. 11a and b), the lowest and the highest values were

Fig. 10. Vertical stress–vertical strain relation obtained following loadingscheme (b) on a PMA specimen vertically compacted to ρ¼2.37 g/cm3 (P-VLC-01): (a) whole relationship and (b) zoom-up during SL and CL (εvweremeasured by LDTs).

Fig. 11. Linear fittings to the unload branches of the small-amplitude CL loopsnos. 6–10 for determining the equivalent elastic Young's modulus (Eeq) whenlinear elastic behaviour exhibited for: (a) a large range of stress and (b) asmaller stress range.

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108104

excluded and the average Eeq was determined from theremaining three. Fig. 12a and b shows the relations betweenthe Eeq values and the stress for HMA specimens compacted todifferent densities in the vertical and horizontal directions,respectively. Similarly, Fig. 13a and b shows the relations forthe PMA specimens. In these figures, it is clear that the Eeq

value increased significantly with an increase in the stress inthe respective direction of compaction. These trends indicatethat the HMA and PMA have specific hypo-elastic properties(i.e., Eqs. (2) and (3)). With respect to their hypo-elasticproperties, the trend that the elastic Young's modulus ofgeomaterial increases with increasing major principal stresswhen the elastic modulus is defined has also been obser-ved in triaxial tests of many types of unbound geomaterial(e.g., Shibuya et al., 1992; Tatsuoka et al., 1994; Hoque andTatsuoka, 1998). In addition, under different constant ambienttemperatures, the elastic stiffness of polymer geogrids alsoincreases significantly with an increase in the load level (e.g.,Kongkitkul et al., 2012b).

In order to correct for the effects of different densities andtherefore void ratios, the void ratio function proposed by

Hardin and Richart (1963) shown in Eq. (5) was used fornormalisation of the Eeq values in this study.

f ðeÞ ¼ ð2:17�eÞ21þe

ð5Þ

where e is void ratio. Fig. 14a compares the relationshipsbetween the normalised equivalent elastic Young's modulus(Eeq=f ðeÞ) and the respective stresses for HMA vertically andhorizontally compacted to different densities. Similarly,Fig. 14b shows such a comparison for the PMA. From thesefigures, it is clear that the tendencies of increasing Eeq=f ðeÞvalues with the stress, for respective HMA and PMA speci-mens compacted either vertically or horizontally to differentdensities, collapsed in the same manner.From the test results shown in Figs. 12–14, it seems that the

elastic Young's modulus, defined for the major principal strainincrement (dε1) in a particular direction (as employed in thepresent study), is a function of the normal stress in thedirection of dε1 (Stokoe et al., 1991; Lo Presti and O'Neill,

00101

100

1000

3000

70800

ρ = 1.90 g/cm3:Ev,eq = 44.897 x (σv/σ0)

0.559Equ

ival

ent v

ertic

al e

last

ic

You

ng's

mod

ulus

, Ev,

eq (M

Pa)

Vertical stress, σv (kPa)

Remark: σ0 = 1 kPa

ρ = 2.37 g/cm3:Ev,eq =194.287 x (σv/σ0)

0.359

HMA (vertically compacted)

ρ = 2.15 g/cm3:Ev,eq = 34.396 x (σv/σ0)

0.693

3

00101

100

1000

Remark: σ0 = 1 kPa

ρ = 1.90 g/cm3:Eh,eq = 49.829 x (σh/σ0)

0.479

ρ = 2.15 g/cm3:Eh,eq = 51.387 x (σh/σ0)

0.572

ρ = 2.37 g/cm3:Eh,eq =180.075 x (σh/σ0)

0.330

HMA (horizontally compacted)

Equ

ival

ent h

oriz

onta

l ela

stic

Y

oung

's m

odul

us, E

h,eq

(MP

a)

Horizontal stress, σh (kPa)

3000

703 800

Fig. 12. Relations between equivalent elastic Young's modulus and stress ofHMA compacted to different densities: (a) Ev,eq–sv for the vertical directionand (b) Eh,eq–sh for the horizontal direction.

000100101

100

1000

Remark: σ0 = 1 kPa

PMA (vertically compacted)ρ = 2.37 g/cm3:Ev,eq = 285.329 x (σv/σ0)

0.339

ρ = 2.15 g/cm3:Ev,eq = 63.797 x (σv/σ0)

0.596

ρ = 1.90 g/cm3:Ev,eq = 39.307 x (σv/σ0)

0.622

Equ

ival

ent v

ertic

al e

last

ic

You

ng's

mod

ulus

, Ev,

eq (M

Pa)

Vertical stress, σv (kPa)

5000

606

000100101

100

1000

PMA (horizontally compacted)

Remark: σ0 = 1 kPa

ρ = 1.90 g/cm3:Eh,eq = 23.868 x (σh/σ0)

0.814

ρ = 2.15 g/cm3:Eh,eq = 41.767 x (σh/σ0)

0.679

ρ = 2.37 g/cm3:Eh,eq =270.508 x (σh/σ0)

0.295

Equ

ival

ent h

oriz

onta

l ela

stic

Y

oung

's m

odul

us, E

h,eq

(MP

a)

Horizontal stress, σh (kPa)

5000

60

6

Fig. 13. Relations between equivalent elastic Young's modulus and stress ofPMA compacted to different densities: (a) Ev,eq–sv for the vertical directionand (b) Eh,eq–sh for the horizontal direction.

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 105

1991; Hoque and Tatsuoka, 1998). This characteristic ofelastic moduli is also found with intact hard rock cores(King, 1970; Wu et al., 1991). By modifying Eqs. (2) and(3) to account for the void ratio function, the mathematicalexpressions become

Ev ¼ ðEvÞ0f ðeÞsvs0

� �mv

; independent of sh ð6Þ

Eh ¼ ðEhÞ0f ðeÞshs0

� �mh

; independent of sv ð7Þ

In Fig. 14a and b, Eqs. (6) and (7) were respectively best-fittedto the test data.

The values of mv and mh for different directions ofcompaction and different types of asphalt are also similar.This implies that the dependencies of the elastic Young'smodulus on stress are similar. A larger mv or mh value means alarger dependency of Ev;eq or Eh;eq on the respective sv and sh.From Fig. 14a and b, the values of Ev;eq for respective types ofasphalt are always greater than Eh;eq in a board sense. When

sv¼sh¼s0, the ratios of Ev;eq to Eh;eq are 1.037 and 1.044 forHMA and PMA, respectively. These non-unity values clearlyshow the anisotropy of elastic Young's modulus characteristicsof both HMA and PMA tested.In Fig. 15a and b the relations between the normalised

elastic Young's modulus (Eeq=f ðeÞ) and the stress between theHMA and PMA in the present study are compared with theunbound Hime gravel reported by Hoque and Tatsuoka (1998)for vertical and horizontal directions, respectively. A compar-ison with the unbound gravel indicates the effects of the binderon the developed elastic Young's modulus. However, in thepresent study, since no confining pressure was used, theunconfined compression tests were not able to be performedon the aggregate used in the preparations of HMA and PMAspecimens. The Hime gravel used in the study done by Hoqueand Tatsuoka (1998) had D50¼1.73 mm, Uc¼1.33 andGs¼2.65. It was herein assumed that the tendencies for (i)anisotropy and (ii) the stress level dependency of the elasticYoung's modulus of Hime gravel reported by Hoque andTatsuoka (1998) are not much different from the aggregateused in the present study. In fact, in their study, similaranisotropic and stress level dependent elastic Young's modulus

00101

100

1000

Remark: σ0 = 1 kPa30

800

Horizontally compacted:Eh,eq/f(e)= 27.597 x (σh/σ0)

0.462

Nor

mal

ised

equ

ival

ent v

ertic

al o

r hor

izon

tal e

last

ic

You

ng's

mod

ulus

, Ev,

eq/f(

e) o

r Eh,

eq/f(

e) (M

Pa)

Vertical or horizontal stress, σv or σh (kPa)

Vertically compacted:Ev,eq/f(e)= 28.617 x (σv/σ0)

0.492

HMA

3

000100101

100

1000

6

2000

PMA

Remark: σ0 = 1 kPa

Nor

mal

ised

equ

ival

ent v

ertic

al o

r hor

izon

tal e

last

ic

You

ng's

mod

ulus

, Ev,

eq/f(

e) o

r Eh,

eq/f(

e) (M

Pa)

Vertical or horizontal stress, σv or σh (kPa)

Vertically compacted:Ev,eq/f(e)= 45.697 x (σv/σ0)

0.445

Horizontally compacted:Eh,eq/f(e)= 43.757 x (σh/σ0)

0.431

50

Fig. 14. Relations between the equivalent elastic Young's modulus normalisedby the void ratio function and the respective stress for the vertical and thehorizontal directions: (a) HMA and (b) PMA.

00101

100

1000

30Remark: σ0 = 1 kPaN

orm

alis

ed e

quiv

alen

t ver

tical

ela

stic

Y

oung

's m

odul

us, E

v,eq

/f(e)

(MP

a)

Vertical stress, σv (kPa)

Vertically compacted

PMA (this study)

HMA (this study)

Hime gravel(Hoque & Tatsuoka, 1998)

8003

00101

100

1000

Horizontally compacted

Remark: σ0 = 1 kPa

Nor

mal

ised

equ

ival

ent h

oriz

onta

l ela

stic

Y

oung

's m

odul

us, E

h,eq

/f(e)

(MP

a)

Horizontal stress, σh (kPa)

PMA (this study)

HMA (this study)

Hime gravel(Hoque & Tatsuoka, 1998)

303 800

Fig. 15. Comparisons among the elastic Young's moduli of HMA and PMA inthis study and the unbound Hime gravel reported by Hoque and Tatsuoka(1998) for: (a) the vertical direction and (b) the horizontal direction.

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108106

behaviours were noted for Toyoura sand, SLB sand, andTicino sand as well as the Hime gravel reproduced in Fig. 15aand b. From Fig. 15a and b, the following may be noted:

(1)

Both the anisotropic and stress level dependent elastic Young'smodulus behaviours of the HMA and PMA used in this studyand the Hime gravel used by Hoque and Tatsuoka (1998) forrespective directions are remarkably similar.

(2)

For each respective direction, the elastic Young's modulusof PMA is greater than that of the HMA at the same valueof stress. In fact, the only difference between the HMA andPMA was the binder type. This shows the effects of usingbetter binding material on the developed elastic Young'smodulus which may be derived from better interlockingbetween the aggregate particles.

(3)

For each respective direction, the elastic Young's moduli ofboth HMA and PMA were greater than that of Hime gravelat the same value of stress. This shows the effect usingbinder which results in the adhesion at the particle contactson the developed elastic Young's modulus.

5. Conclusions

The following conclusions may be derived from the testresults presented in this study:

(1)

The compressive strengths of PMA were greater than thoseof HMA, indicating that the binder type had an effect onthe developed compressive strengths.

(2)

The compressive strengths of both the HMA and PMAcompacted vertically were significantly greater than thosecompacted horizontally, indicating anisotropy in the com-pressive strengths of both HMA and PMA.

(3)

The small strain stiffness of both the HMA and PMAtested were anisotropic with the vertical elastic Young'smodulus greater than the horizontal elastic Young's mod-ulus at the same stress level.

(4)

The elastic Young's moduli of both the HMA and PMAtested were a function of the normal stress in the directionof the major principal strain increment, similar to that ofmany unbound geomaterials found in the literature.

W. Kongkitkul et al. / Soils and Foundations 54 (2014) 94–108 107

(5)

At the same stress level and when the direction ofcompaction was the same, the elastic Young's modulusof PMA was greater than that of HMA, showing the effectsof binder type on the developed elastic Young's modulus.When compared the elastic Young's moduli of HMA andPMA with the one of unbound Hime gravel reported in theliterature, the effects of binder at the particle contacts wererevealed.

Acknowledgements

The authors would like to sincerely acknowledge Prof.Fumio Tatsuoka, in the Department of Civil Engineering atthe Tokyo University of Science for his advice and commentson the test results presented in this study. Financial supportfrom King Mongkut's University of Technology Thonburi(KMUTT) via the National Research University (NRU) projectand from the National Research Council of Thailand (NRCT)are gratefully acknowledged. The normal asphalt cement andthe polymer-modified asphalt cement used in this study wereprovided from the Shell Co. of Thailand Ltd. and the TipcoAsphalt Public Company Limited, Thailand, respectively.

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