Anisotropy in compressive strength and elastic stiffness of normal and polymer-modified asphalts

Soils and Foundations 2014;54(2):94–108 The Japanese Geotechnical Society

Soils and Foundations www.sciencedirect.com journal homepage: www.elsevier.com/locate/sandf

Anisotropy in compressive strength and elastic stiffness of 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 2013 Available 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) were investigated experimentally. Two types of prismatic specimen with planes of compaction either normal to or parallel to the applied axial compression were used. Both axial and lateral principal strains were measured locally. Continuous monotonic loadings at a constant strain rate were axially applied to investigate the anisotropy in the compressive strength. Very small strain–amplitude cyclic stresses were also applied by means of another load-controlled apparatus to investigate the anisotropy in the elastic stiffness. The followings were found: (i) compressive strengths of both HMA and PMA are anisotropic in that the values for the vertical direction were significantly larger than those of horizontal direction; (ii) the small strain stiffness of both HMA and PMA are anisotropic with the vertical elastic Young's modulus being greater than the horizontal elastic Young's modulus; (iii) the elastic Young's modulus is stress level dependent, exhibiting a hypo-elastic behaviour; and (iv) the elastic 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

1. Introduction n

Corresponding author. Tel.: þ66 2 470 9304; fax: þ 66 2 427 9063. E-mail addresses: [email protected] (W. Kongkitkul), [email protected] (N. Musika), [email protected] (C. Tongnuapad), [email protected] (P. Jongpradist), [email protected] (S. Youwai). 1 Tel.: þ66 2 470 9155; fax: þ 66 2 427 9063. 2 Tel.: þ66 2 470 9305; fax: þ 66 2 427 9063. 3 Tel.: þ66 2 470 9308; fax: þ 66 2 427 9063. Peer review under responsibility of The Japanese Geotechnical Society.

Asphalt, a mixture of asphalt cement and aggregate compacted to a designated density, has long been widely used as a flexible pavement layer in road construction. Its popularity may be due to its good-performance, ease of construction and because its smooth top surface allows for good riding quality. Recently, the application of asphalt has been extended from the field of pavement engineering to the field of geotechnical engineering; that is, it has been used as the impermeable sealing core of earth and embankment dams (e.g., ICOLD, 1992; Hoeg et al., 2007; Feizi-Khankandi et al., 2008). From this perspective, it is apparent that more realistic considerations of the properties of asphalt have become necessary. However,

http://dx.doi.org/10.1016/j.sandf.2014.02.002 0038-0806 & 2014 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

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

most of the laboratory experiments and analytical models for asphalt are presently based on the assumption that it exhibits isotropic material properties. Most known models are based on the linear elastic or linear visco-elastic theory in which asphalt is assumed to be homogenous and isotropic (e.g., Huang, 2004). With this assumption, the deformational behaviours predicted by the models may not be realistic. In pavement design, for example, the isotropic analysis may lead to an underestimation of both the shear and tensile stresses that are related to permanent deformation and fatigue cracking assessment (e.g., Chen et al., 2011). In the field of geotechnical engineering, a number of studies on the anisotropy of strength and deformation properties of various unbound geomaterials (i.e., sands and gravels) have been widely performed (e.g., Jiang et al., 1997; Hoque and Tatsuoka, 1998; Tatsuoka et al., 1999). Moreover, the mechanical behaviours of many bound materials, such as natural clay (Graham and Houlsby, 1983; Piriyakul and Haegeman, 2009), kaolin clay (Anantanasakul et 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 that the anisotropy of asphalt is influenced by the specimen preparations and test conditions. Its anisotropic behaviour is further influenced by the magnitude of the stresses and strains induced in the specimen and the loading rate applied to the specimen (e.g., Wang et al., 2004). In addition, in reality, the direction of the major principal stress generated at an element of the pavement by the traffic load rotates from the approaching moment to the departing moment of the wheel load (e.g., Inam et al., 2012). However, very few laboratory research studies (e.g., Masad et al., 2002; Mamlouk et al., 2002; Motola and Uzan, 2006; Liang et al., 2006) have been performed with the aim of understanding the anisotropic properties of asphalt in detail, though this is necessary for further realistic modelling. In pavement design, for example, the anisotropic properties can be implemented in order to adjust or fine-tune the material characterisation models before calibration testing begins. This might lead to a significant reduction in testing requirements if isotropic conditions for the selected test parameters are identified (Mamlouk et al., 2002). In recent years, polymer-modified asphalt has been gaining popularity in road construction. This may be due to its better performances including resistance to permanent deformation, rutting and cracking, and its high stiffness, among other qualities (e.g., Zhao et al., 2008; Yildirim, 2007). Since its major constituent material is also an aggregate, it is likely that the mechanical properties of polymer-modified asphalt are also anisotropic. However, little is known with regard to the characterisation and modelling of the anisotropic properties of polymer-modified asphalt. In particular, to the best of the authors' knowledge, it seems that there is only very limited research studies specially performed to understand not only the anisotropic behaviours of both asphalt types individually but also the comparisons among them. In view of the above, in the present study, a series of unconventional unconfined compression tests were performed on the normal asphalt specimens and the polymer-modified asphalt specimens compacted to different densities to study their effects. The compaction directions were designed such

95

that the direction of the applied axial load in the tests was either perpendicular to or parallel to the compaction plane to study the anisotropic properties. As mention earlier, among different models assumed for the modelling of asphalt, elastic stiffness, which expresses the recoverable deformation upon load release, is always basically incorporated. In this study, therefore, the effects of different asphalt types and different densities on the anisotropic elastic properties were investigated. Summarising the above, the unconventional unconfined compression tests performed in this study included: (i) continuous monotonic loading tests to investigate the compressive strengths and (ii) small-amplitude cyclic loading tests to investigate the elastic properties. 2. Anisotropic elasticity Most of the geomaterials deposited naturally or artificially or compacted vertically, exhibit cross-anisotropic deformation properties, which are symmetrical about the vertical axis. As asphalt is constituted from the aggregate mixed with the asphalt cement (AC) binder and then compacted vertically, it is very likely that it also exhibits cross-anisotropic deformation properties. Cross-anisotropy requires only six elastic parameters for the characterisation of soil properties (Hoque and Tatsuoka, 1998). Under triaxial stress states when the horizontal principal stress is the same, the incremental relationship between stresses and strains (Hooke's law) is 2 3 2 32 3 1=E h  νhh =Eh  νvh =E v δεh δsh 6 δε 7 6  ν =E 6 7 1=E h  νvh =E v 7 ð1Þ hh h 4 h5¼4 54 δsh 5  νhv =E h  νhv =E h 1=E v δεv δsv where E v and E h are the vertical and horizontal elastic Young's moduli; νvh , νhh and νhv are the elastic Poisson's ratios. These elastic parameters were determined from multiple small-strain amplitude unload and reload cycles (cyclic loading, CL) with a single axial strain amplitude in the order of 0.001%. In this strain range, deformation moduli are negligibly influenced by stress–strain histories within the ranges of stress change small enough to maintain the initial fabric, the type of loading (monotonic or cyclic), wave form during cyclic loading and the rate of shearing (dynamic or static) (Tatsuoka and Kohata, 1995; Jamiolkowski et al., 1991). In other words, the application of such small-strain amplitude unload and reload cycles is non-destructive. Based on the above-mentioned tests, a hypo-elasticity model with inherent and stress system-induced anisotropy has been developed (Tatsuoka et al., 1999):  mv sv Ev ¼ ðEv Þ0 ; independent of sh ð2Þ s0  mh sh Eh ¼ ðE h Þ0 ; independent of sv ð3Þ s0 where Ev and Eh are the elastic Young's moduli respectively for the vertical and horizontal directions; s0 is the reference stress value (e.g., 1 kPa as used in this study or any others);

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

Penetration at 25 1C, 100 g, 5 s Flash point (Cleveland open cup) Ductility, 5 cm/min AC at 25 1C PM-AC at 13 1C Solubility in Trichloroethylene Thin-film oven test, 3.2 mm, 163 1C 5 h Loss on heating Penetration of residue at 25 1C Ductility of residue at 25 1C, 5 cm/min AC at 25 1C PM-AC at 13 1C Loss on heating, 163 1C, 5 h

AC

PM-AC

Min.

Max.

Min.

Max.

0.1 mm 1C

60 232

70 –

60 220

70 –

cm cm per cent

100

–

99.0

–

55 99.0

– –

per cent per cent of original

– 54

0.8 –

– 70

0.5 –

cm cm per cent

50

–

–

0.8

40 –

– 0.5

ðEv Þ0 and ðE h Þ0 are the values of E v and Eh respectively when sv ¼ s0 and sh ¼ s0 ; and, mv and mh are constants, expressing the dependencies of E v and E h on the respective vertical and horizontal stresses. The s0 in Eqs. (2) and (3) was implemented so that the units of ðEv Þ0 and E v and ðE h Þ0 and E h are the same. When mv =mh =m, this means that the dependencies of E v and E h on the respective stresses are qualitatively the same for both directions. In this case, the vertical and horizontal elastic moduli could be related as   Ev ðEv Þ0 sv m ¼ ð4Þ E h ðEh Þ0 sh Eq. (4) means that, when m a 1.0, the ratio of E v =E h increases in 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 penetration grade or PG 70-10 in the performance grade was used in the preparations of the normal asphalt. For preparations of polymer-modified asphalt, a type of polymer modified asphalt cement (PM-AC), which is produced by mixing styrene butadiene styrene (SBS) with normal asphalt cement (AC) type AC 60/70, was used. These AC and PM-AC were manufactured to meet the specifications by the Department of Highways, Thailand (i.e., DH-SP. 401/2531 and DH-SP. 408/2536, respectively) and provided from the respective manufacturers in liquid form stored in sealed containers. The properties of the AC and PM-AC used in this study are listed for comparison purposes in Table 1, following the specifications given by the Department of Highways, Thailand. The aggregate used was a limestone widely used in typical pavement construction in Thailand. It was cleaned by washing with tap water and then sieved to classify the sizes. Then, the classified aggregates of different sizes were brought for mixing to obtain the grain size distribution designated by the DH-S. 408/2532. The resultant aggregate had the following

properties: a maximum particle size (Dmax ) of 12.50 mm, a mean particle size (D50 ) of 2.55 mm, a coefficient of uniformity (U c ) of 25, and a specific gravity (Gs ) of 2.63. In this study, all the test specimens, both for the normal asphalt and the polymer-modified asphalt, were prepared from the same aggregate. 3.2. Specimen preparations In this study, all specimens were prepared by hot-mixing between the respective asphalt cement types and the aggregate. Preparations started with heating the aggregate in the oven for about 2 h at 140 1C and 180 1C for the normal and the polymer-modified asphalts, respectively. For preparations of the normal asphalt specimens, the AC was heated up by a gas stove to a controlled temperature of 140 1C; then, both the AC and the aggregate were mixed together on a tray heated by a stove (Kongkitkul et al., 2010). The PM-AC was heated by hot-oil filled in a double-layer container to 180 1C (Kongkitkul et al., 2012a), as recommended by the manufacturer. This method was used to avoid damage to the SBS (polymer resin added to AC), which would result in the loss of the quality of developed strength and stiffness. Then, similar to the normal asphalt specimens, the aggregate was mixed together with the PM-AC on a tray heated by stove. The asphalt cement content of 5% by the weight of the aggregate was used, both for the normal and the polymer-modified asphalts. Then, the compaction process was started, with the same process used for both the normal and the polymer-modified asphalts. The details are as follows. There were two types of moulds used this study (Fig. 1): (i) a vertical mould and (ii) a horizontal mould. The dimensions of these two mould types are also given in Fig. 1. These two mould types were prepared so that, when performing the unconfined compression tests, the direction of the major principal stress (s1 ) is perpendicular to or parallel to the planes of compaction when subjected to vertical and horizontal compactions, respectively (Fig. 2). After having completed the assembly of the moulds as shown in Fig. 1, the respective hot mixtures were then poured into them. By carefully

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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.

and manually performing the compaction into five equivalent layers for both the vertical and horizontal moulds (Fig. 2), the compaction energy can be thoroughly applied when forming a specimen to achieve different target densities (Table 2). The typical density value of asphalt pavement compacted in the field is around 2.35–2.40 g/cm3. In this study, to investigate the effects of various densities, the values of 1.90 g/cm3, 2.15 g/cm3 and 2.37 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 three different 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 final density of the entire specimen was almost the same as the target

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

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Table 2 Test 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)

Directions of compaction

Test names

Loading schemes

Stress level (kPa)

SL period (min)

Δs during CL (kPa)

1.90

Vertical

H-VSM-01 H-VSM-02 H-VSM-03 H-VSC-01 H-VSC-02 H-VSC-03 H-HSM-01 H-HSM-02 H-HSM-03 H-HSC-01 H-HSC-02 H-HSC-03

(a)

–

–

–

(b)

8.9, 17.8 and 26.7

180

2.7

(b) (a)

10.2, 20.4 and 30.6 –

360 –

4.4 –

(b)

8.9, 17.8 and 26.7

180

2.7

H-VMM-01 H-VMM-02 H-VMM-03 H-VMC-01 H-VMC-02 H-VMC-03 H-HMM-01 H-HMM-02 H-HMM-03 H-HMC-01 H-HMC-02 H-HMC-03

(a)

–

–

–

(b)

21.3, 42.7, 64.0, 85.3, 106.7, 128.0 and 149.3

180

10.7

(a)

–

–

–

(b)

17.8, 35.6, 53.3, 71.1, 88.9 and 106.7

180

8.9

H-VLM-01 H-VLM-02 H-VLM-03 H-VLC-01 H-VLC-02

(a)

–

–

–

(b)

30

8.9

H-VLC-03 H-VLC-04

(b)

180

10.7

H-HLM-01 H-HLM-02 H-HLM-03 H-HLC-01 H-HLC-02 H-HLC-03

(a)

32.9, 68.4, 103.9, 139.5, 175.1, 210.6, 246.2, 281.7, 317.3, 352.9, 388.4 and 424.0 45.8, 95.6, 145.4, 195.1, 244.9, 294.7, 344.5, 394.3 and 444.0 –

–

–

180

10.7

Horizontal

2.15

Vertical

Horizontal

2.37

Vertical

Horizontal

(b)

3.3. Test apparatuses and measuring devices There were two types of compression apparatuses used to perform unconfined compression tests in this study: apparatus A and apparatus B (Fig. 3). Apparatus A, which is a displacementcontrolled type, was used to perform continuous monotonic loading (ML) at a constant strain rate to evaluate the compressive strengths and secant moduli (explained later) of the specimens tested. Apparatus B, which is a load-controlled type, was used to perform small-amplitude cyclic loading (CL) tests to determine the equivalent elastic Young's modulus. To avoid any bedding errors that may develop at contacts between the specimen top end and the cap and between the specimen bottom end and the pedestal which are associated with

35.6, 71.1, 106.7, 142.2, 177.8, 213.3 and 248.9

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

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99

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

of local deformation transducers (LDTs; Goto et al., 1991) and three clip gauges were installed directly on the specimen periphery (Fig. 5). These local strain measurement techniques were also used in the triaxial compression tests on sand and gravel (e.g., Maqbool et al., 2011), and cement-mixed gravelly soil (e.g., Kongsukprasert and Tatsuoka, 2007; Taheri et al., 2012). 3.4. Loading schemes For each combination of density and direction of compaction, the following two loading schemes were employed:

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

manufactured by Shin-Etsu Chemical Co., Ltd) and then a 0.3-mm thick latex rubber sheet was attached (see Fig. 4) (Tatsuoka and Haibara, 1985). A load cell was used to measure the axial load and a LVDT to externally measure the axial deformation. To evaluate the pre-peak stiffness of relatively stiff geomaterials, it is necessary to employ sensitive and accurate local strain measurement in the laboratory stress–strain tests. Several methods have been proposed to locally and sensitively measure the axial strains free from the large effects of bedding error at the specimen ends (e.g., Jardine et al., 1984; Burland, 1989; Tatsuoka et al., 1999; Clayton, 2011). In this study, in order to make precise local measurements of the axial and lateral deformations, a pair

(a) continuous ML by apparatus A at a constant axial strain rate of 0.03%/min until the end of test; and (b) ML at a constant axial stress rate of 1.778 kPa/min for HMA specimens or 3.556 kPa/min for PMA specimens by apparatus B until a prescribed stress level was reached, followed by a stage of sustained loading (SL) and then 10 cycles of unload/reload with a small amplitude and a restart of the ML to the next prescribed stress level.

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

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

designated as tabulated in Tables 2 and 3 to ensure the following: (i) the SL was long enough to allow the behaviour during the CLs to be significantly elastic; (ii) the CL amplitude was small enough for specimens to behave elastically while large enough to allow for linear fitting to obtain the elastic Young's modulus (explained later); and (iii) the stress levels at which the CLs were performed were varied so as to determine the elastic Young's modulus values for various stress levels. The combinations of these three points of considerations depended on the compressive strengths and stiffnesses of specimens prepared at different densities and compaction directions which were investigated in advance by loading scheme (a). All the tests in this study were performed at 25 1C in a temperature-controlled room at the geotechnical engineering laboratory, the King Mongkut's University of Technology Thonburi. 4. Test results and discussions 4.1. Compressive strengths and secant stiffnesses Fig. 6a and b compare the stress–strain relations following loading scheme (a) by apparatus A for the vertically and horizontally compacted HMA specimens, respectively. Similarly, Fig. 7a and b compares those for vertically and horizontally compacted PMA specimens, respectively. It is worth noting that the strain values along the abscissa of these figures were externally measured by the LVDT. In these figures, as the stress–strain relations for either the three HMA specimens or the three PMA specimens prepared at the same density and compaction direction (Tables 2 and 3) were slightly different, the respective average relations were shown. In order to compare the stiffnesses among different specimens, the vertical and horizontal secant moduli (E v;50 and Eh;50 ), defined as the slopes of the lines passing to the origins of stress–strain relations and the

data points along the stress–strain relations at which the vertical and horizontal stresses were half the respective compressive strengths (sv; max and sh; max ), were selected as the representatives. In Fig. 8a, the compressive strengths (sv; max and sh; max ) of the vertically and horizontally compacted HMA and PMA specimens are compared for different densities. In Fig. 8b, the secant moduli (E v;50 and E h;50 ) among the HMA and PMA specimens vertically and horizontally compacted to different densities are compared in a similar manner to Fig. 8a. The following trends of behaviour may be seen from Figs. 6–8: (1) For the respective directions of compaction, the compressive strength (sv; max or sh; max ) and the secant modulus (Ev;50 or Eh;50 ) increased with density, indicating a significant effect on compaction. (2) For the respective densities and types of asphalt, the value of sv; max was higher than the respective sh; max value while the strain value at which sv; max was exhibited was less than the respective value at which sh; max was exhibited. As a result, E v;50 was also higher than the respective E h;50 . This clearly indicates anisotropic behaviours on the compressive strength and stiffness of both HMA and PMA. (3) For the respective directions of compaction and densities, PMA exhibited higher compressive strength and a higher secant modulus than those of HMA. As the aggregate used in the preparations of both HMA and PMA specimens was the same, this observation showed the effects of binder type on the improvements of strength and stiffness characteristics of asphalt.

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

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101

Table 3 Test 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)

Directions of compaction

Test names

Loading schemes

Stress level (kPa)

SL period (min)

Δs during CL (kPa)

1.90

Vertical

P-VSM-01 P-VSM-02 P-VSM-03 P-VSC-01 P-VSC-02 P-VSC-03 P-HSM-01 P-HSM-02 P-HSM-03 P-HSC-01 P-HSC-02 P-HSC-03

(a)

-

-

-

(b)

26.0, 52.0 and 79.0

180

11.0

(b) (a)

17.0, 35.0 and 52.0 –

180 –

7.0 –

(b)

15.5, 32.0 and 48.0

180

6.0

(b)

24.0, 40.0 and 56.0

180

7.0

P-VMM-01 P-VMM-02 P-VMM-03 P-VMC-01 P-VMC-02 P-VMC-03

(a)

–

–

–

(b)

48, 97, 146, 196, 254 and 295.5

180

12.0

(b)

180

12.0

P-HMM-01 P-HMM-02 P-HMM-03 P-HMC-01 P-HMC-02 P-HMC-03

(a)

73.0, 122.0, 172.0, 221.0 and 272.0 –

–

–

28.0, 56.0, 85.0, 114.0, 143.0 and 173.0 42.0, 70.5, 99.0, 128.0, 157.0 and 186.0

180

12.0

180

12.0

P-VLM-01 P-VLM-02 P-VLM-03 P-VLC-01 P-VLC-02 P-VLC-03 P-VLC-04 P-HLM-01 P-HLM-02 P-HLM-03 P-HLC-01 P-HLC-03 P-HLC-02

(a)

–

–

–

(b)

86.5, 174.0, 261.0, 349.0, 437.0, 525.0 and 615.0 130.0, 217.0, 304.0, 391.0, 479.0, 567.0 and 656.0 –

180 120 180

26.0

–

–

70.0, 140.0, 212.0, 284.0, 358.0 and 433.0 105.0, 175.0, 246.0, 317.0, 389.0 and 462.0

180

18.0

180

18.0

Horizontal

2.15

Vertical

Horizontal

2.37

Vertical

Horizontal

(b) (b)

(b) (a)

(b) (b)

direction of the applied major principal stress (s1 ) relative to the plane of compaction. It is likely that these anisotropic behaviours may be due to one or a combination of the following: (1) During compaction, because the aggregate particles were arranged in the form of layers, when they were compressed in the same direction as they were formed, they would be stronger than in other directions. That is, the specimens had more experience to be loaded in the same direction as that when they were compacted than in other directions. (2) When specimens were axially compressed, the joints inevitably formed between the layers by compaction were compressed or expanded when they are respectively normal

26.0

to or parallel to the direction of compression (Fig. 2). Also, when the joints were compressed, the behaviour of the entire specimen was more united, while, it was more segmented when expanded. Similar discussions in this respect were also found for the behaviours of cement-mixed gravelly soils (i.e., Kongsukprasert et al., 2007). 4.2. Determination of equivalent elastic Young's modulus Fig. 9a shows the stress–strain relation obtained following the loading scheme (b) by apparatus B, performed on the HMA specimen vertically compacted to a density of 2.37 g/cm3 (i.e., H-VLC-03, Table 2). Fig. 9b shows a zoomed-up portion of Fig. 9a. Similarly, Fig. 10a and b shows the test result of the PMA

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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).

specimen vertically compacted to a density of 2.37 g/cm3 (i.e., P-VLC-01, Table 3). Following the technique that has been widely used to reliably determine the elastic property by triaxial tests on unbound 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 geogrids by tensile loading tests (e.g., Hirakawa et al., 2003; Kongkitkul et al., 2012b), respective sets of 10 small unload/reload cycles were applied after sustained loading (SL). It was expected that the stress–strain behaviour during cyclic loading (CL) would be essentially elastic when this method was used. The following trends of behaviours may be seen from Figs. 9 and 10:

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

(1) The creep strain during the SL and prior to the small unload/reload cycles were significant. They resulted in considerably less deformation due to the viscous properties during the subsequent cyclic loadings. (2) The behaviour during the small unload/reload cycles was highly linear–elastic, as was clear from the following: (i) the stress–strain loops generated during the respective unload/ reload cycles were very small and exhibited negligible energy

Fig. 11a shows the small unload/reload loop nos. 6–10 at a stress level of 217 kPa for the PMA specimen vertically compacted to a density of 2.37 g/cm3 (P-VLC-03, Table 3). It can be seen that the unload stress–strain branches exhibit highly linear elasticity for a large range of stress increments relative to the whole stress amplitude (i.e., 26 kPa, Table 3). Thus, it is relevant to evaluate the equivalent elastic Young's modulus (E eq ) from a linear relation fitted to respective portions of the unload stress–strain branches presented in Fig. 11a. Although the data scatters to some extent, as can be seen in this figure, the Eeq values can be defined rather confidently. The value of Eeq is rather constant during these unload branches from loop nos. 6 to 10 at the respective CL stages. This indicates that the deformation during these unload stress–strain branches is essentially elastic.

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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 loading scheme (b) on a HMA specimen vertically compacted to ρ¼2.37 g/cm3 (HVLC-03): (a) whole relationship and (b) zoom-up during SL and CL (εv were measured by LDTs).

However, the range of stress increments for which the unload stress–strain branches exhibited highly linear elasticity decreases as the stress level increases. This is because the residual strains that developed during the unload/reload cycles at high stress levels are not negligible, as can be seen from Figs. 9a and 10a. In addition, upon the start of unloading, there was an occasional delay in the recovered strain. For example, the unload stress–strain branches from loop nos. 6 to 10 at the stress level of 175.1 kPa from HMA specimen vertically compacted 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 relative smaller stress range when compared to the whole stress amplitude (i.e., 8.9 kPa, Table 2). In these cases, it is therefore necessary to find a portion exhibiting essentially elastic (i.e., rate-independent and reversible) behaviour from the whole stress–strain behaviour during respective unload/reload cycles. Fig. 11b also shows data typical of cases in which the stress–strain behaviour is highly linear and reversible only for a smaller range of stress increment near the bottom end of the

stress–strain loop. When only these bottom stress range were taken into account (e.g., Fig. 11b), the behaviours can be deemed to be essentially reversible (therefore elastic). A linear relation was fitted to the bottom range of the respective unload stress–strain branches presented in Fig. 11b to obtain the equivalent elastic Young's modulus (E eq ). Although the data scatters to some extent, as seen in Fig. 11b, values of E eq can be defined rather confidently as they are rather constant during these unload/reload cycle loops. The E eq values of HMA and PMA compacted to different densities and compaction directions (i.e., for both the vertical and horizontal directions as E v;eq and Eh;eq , respectively) at the stress levels listed in Tables 2 and 3 (other than those presented in Fig. 11a and b) were determined in the manner indicated in Fig. 11a and b. 4.3. Comparisons of equivalent elastic Young's modulus Among the five measured values of Eeq at respective CL stages (i.e., loop nos. 6–10) at different stress levels (as shown in Fig. 11a and b), the lowest and the highest values were

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Fig. 10. Vertical stress–vertical strain relation obtained following loading scheme (b) on a PMA specimen vertically compacted to ρ¼2.37 g/cm3 (PVLC-01): (a) whole relationship and (b) zoom-up during SL and CL (εv were measured by LDTs).

excluded and the average Eeq was determined from the remaining three. Fig. 12a and b shows the relations between the E eq values and the stress for HMA specimens compacted to different densities in the vertical and horizontal directions, respectively. Similarly, Fig. 13a and b shows the relations for the PMA specimens. In these figures, it is clear that the E eq value increased significantly with an increase in the stress in the respective direction of compaction. These trends indicate that the HMA and PMA have specific hypo-elastic properties (i.e., Eqs. (2) and (3)). With respect to their hypo-elastic properties, the trend that the elastic Young's modulus of geomaterial increases with increasing major principal stress when the elastic modulus is defined has also been observed in triaxial tests of many types of unbound geomaterial (e.g., Shibuya et al., 1992; Tatsuoka et al., 1994; Hoque and Tatsuoka, 1998). In addition, under different constant ambient temperatures, the elastic stiffness of polymer geogrids also increases significantly with an increase in the load level (e.g., Kongkitkul et al., 2012b). In order to correct for the effects of different densities and therefore void ratios, the void ratio function proposed by

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

Hardin and Richart (1963) shown in Eq. (5) was used for normalisation of the E eq values in this study. f ðeÞ ¼

ð2:17  eÞ2 1þe

ð5Þ

where e is void ratio. Fig. 14a compares the relationships between the normalised equivalent elastic Young's modulus (E eq =f ðeÞ) and the respective stresses for HMA vertically and horizontally compacted to different densities. Similarly, Fig. 14b shows such a comparison for the PMA. From these figures, it is clear that the tendencies of increasing Eeq =f ðeÞ values with the stress, for respective HMA and PMA specimens compacted either vertically or horizontally to different densities, 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 strain increment (dε1 ) in a particular direction (as employed in the present study), is a function of the normal stress in the direction of dε1 (Stokoe et al., 1991; Lo Presti and O'Neill,

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

5000

3000

PMA (vertically compacted) Equivalent vertical elastic Young's modulus, Ev,eq (MPa)

Equivalent vertical elastic Young's modulus, Ev,eq (MPa)

HMA (vertically compacted) 3

ρ = 2.37 g/cm :

Ev,eq =194.287 x (σv/σ0)

1000

0.359

3

ρ = 2.15 g/cm :

Ev,eq = 34.396 x (σv/σ0)

0.693

3

ρ = 1.90 g/cm :

Ev,eq = 44.897 x (σv/σ0) 100 70

0.559

1000 3

ρ = 2.15 g/cm : 0.596 Ev,eq = 63.797 x (σv/σ0) 3

ρ = 1.90 g/cm :

Ev,eq = 39.307 x (σv/σ0) 100

Remark: σ0 = 1 kPa 3

3

ρ = 2.37 g/cm : 0.339 Ev,eq = 285.329 x (σv/σ0)

10

800

100

Remark: σ0 = 1 kPa 6

10

100

10 0 0

Vertical stress, σv (kPa)

5000

3000

PMA (horizontally compacted) Equivalent horizontal elastic Young's modulus, Eh,eq (MPa)

HMA (horizontally compacted) Equivalent horizontal elastic Young's modulus, Eh,eq (MPa)

0.622

60

Vertical stress, σv (kPa)

3

ρ = 2.37 g/cm :

1000

Eh,eq =180.075 x (σh/σ0)

0.330

3

ρ = 2.15 g/cm :

Eh,eq = 51.387 x (σh/σ0)

0.572

3

ρ = 1.90 g/cm :

Eh,eq = 49.829 x (σh/σ0) 100 70

105

0.479

3

ρ = 2.37 g/cm : 0.295 Eh,eq =270.508 x (σh/σ0) 1000 3

ρ = 2.15 g/cm : 0.679 Eh,eq = 41.767 x (σh/σ0) 3

ρ = 1.90 g/cm :

Eh,eq = 23.868 x (σh/σ0) 100

Remark: σ0 = 1 kPa

0.814

Remark: σ0 = 1 kPa

60

3

10

100

800 6

Horizontal stress, σh (kPa)

100

1000

Horizontal stress, σh (kPa)

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

1991; Hoque and Tatsuoka, 1998). This characteristic of elastic 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 mathematical expressions become  mv sv ; independent of sh s0

ð6Þ

 mh sh E h ¼ ðE h Þ0 f ðeÞ ; independent of sv s0

ð7Þ

E v ¼ ðE v Þ0 f ðeÞ

10

In Fig. 14a and b, Eqs. (6) and (7) were respectively best-fitted to the test data. The values of mv and mh for different directions of compaction and different types of asphalt are also similar. This implies that the dependencies of the elastic Young's modulus on stress are similar. A larger mv or mh value means a larger dependency of Ev;eq or E h;eq on the respective sv and sh . From Fig. 14a and b, the values of E v;eq for respective types of asphalt are always greater than E h;eq in a board sense. When

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

sv ¼ sh ¼ s0 , the ratios of E v;eq to E h;eq are 1.037 and 1.044 for HMA and PMA, respectively. These non-unity values clearly show the anisotropy of elastic Young's modulus characteristics of 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 the HMA and PMA in the present study are compared with the unbound Hime gravel reported by Hoque and Tatsuoka (1998) for vertical and horizontal directions, respectively. A comparison with the unbound gravel indicates the effects of the binder on the developed elastic Young's modulus. However, in the present study, since no confining pressure was used, the unconfined compression tests were not able to be performed on the aggregate used in the preparations of HMA and PMA specimens. The Hime gravel used in the study done by Hoque and Tatsuoka (1998) had D50 ¼ 1.73 mm, U c ¼ 1.33 and Gs ¼ 2.65. It was herein assumed that the tendencies for (i) anisotropy and (ii) the stress level dependency of the elastic Young's modulus of Hime gravel reported by Hoque and Tatsuoka (1998) are not much different from the aggregate used in the present study. In fact, in their study, similar anisotropic and stress level dependent elastic Young's modulus

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

Normalised equivalent vertical elastic Young's modulus, Ev,eq/f(e) (MPa)

1000 1000

HMA Vertically compacted: 0.492 Ev,eq/f(e)= 28.617 x (σv/σ0)

100

Horizontally compacted: 0.462 Eh,eq/f(e)= 27.597 x (σh/σ0) Remark: σ0 = 1 kPa

30 3

Vertically compacted

PMA (this study)

10

100

Hime gravel (Hoque & Tatsuoka, 1998)

100

HMA (this study) Remark: σ0 = 1 kPa 30

3

10

800

Vertical or horizontal stress, σv or σh (kPa)

2000

PMA 1000

Vertically compacted: 0.445 Ev,eq/f(e)= 45.697 x (σv/σ0)

Horizontally compacted: 0.431 Eh,eq/f(e)= 43.757 x (σh/σ0)

100

Remark: σ0 = 1 kPa

1000

Horizontally compacted

PMA (this study)

100

Hime gravel (Hoque & Tatsuoka, 1998) HMA (this study) Remark: σ0 = 1 kPa

30

3

10

100

1 000

Vertical or horizontal stress, σv or σh (kPa)

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

behaviours were noted for Toyoura sand, SLB sand, and Ticino sand as well as the Hime gravel reproduced in Fig. 15a and b. From Fig. 15a and b, the following may be noted: (1) Both the anisotropic and stress level dependent elastic Young's modulus behaviours of the HMA and PMA used in this study and the Hime gravel used by Hoque and Tatsuoka (1998) for respective directions are remarkably similar. (2) For each respective direction, the elastic Young's modulus of PMA is greater than that of the HMA at the same value of stress. In fact, the only difference between the HMA and PMA was the binder type. This shows the effects of using better binding material on the developed elastic Young's modulus which may be derived from better interlocking between the aggregate particles. (3) For each respective direction, the elastic Young's moduli of both HMA and PMA were greater than that of Hime gravel at the same value of stress. This shows the effect using binder which results in the adhesion at the particle contacts on the developed elastic Young's modulus.

10

100

800

Horizontal stress, σh (kPa)

50 6

800

100

Vertical stress, σv (kPa)

Normalised equivalent horizontal elastic Young's modulus, Eh,eq/f(e) (MPa)

Normalised equivalent vertical or horizontal elastic Young's modulus, Ev,eq/f(e) or Eh,eq/f(e) (MPa)

Normalised equivalent vertical or horizontal elastic Young's modulus, Ev,eq/f(e) or Eh,eq/f(e) (MPa)

106

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

5. Conclusions The following conclusions may be derived from the test results presented in this study: (1) The compressive strengths of PMA were greater than those of HMA, indicating that the binder type had an effect on the developed compressive strengths. (2) The compressive strengths of both the HMA and PMA compacted vertically were significantly greater than those compacted horizontally, indicating anisotropy in the compressive strengths of both HMA and PMA. (3) The small strain stiffness of both the HMA and PMA tested were anisotropic with the vertical elastic Young's modulus greater than the horizontal elastic Young's modulus at the same stress level. (4) The elastic Young's moduli of both the HMA and PMA tested were a function of the normal stress in the direction of the major principal strain increment, similar to that of many unbound geomaterials found in the literature.

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(5) At the same stress level and when the direction of compaction was the same, the elastic Young's modulus of PMA was greater than that of HMA, showing the effects of binder type on the developed elastic Young's modulus. When compared the elastic Young's moduli of HMA and PMA with the one of unbound Hime gravel reported in the literature, the effects of binder at the particle contacts were revealed.

Acknowledgements The authors would like to sincerely acknowledge Prof. Fumio Tatsuoka, in the Department of Civil Engineering at the Tokyo University of Science for his advice and comments on the test results presented in this study. Financial support from King Mongkut's University of Technology Thonburi (KMUTT) via the National Research University (NRU) project and from the National Research Council of Thailand (NRCT) are gratefully acknowledged. The normal asphalt cement and the polymer-modified asphalt cement used in this study were provided from the Shell Co. of Thailand Ltd. and the Tipco Asphalt Public Company Limited, Thailand, respectively. References Abdelrahman, G.E., Kawabe, S., Tsukamoto, Y., Tatsuoka, F., 2008. Smallstrain stress-strain properties of expanded polystyrene geofoam. Soils Found. 48 (1), 61–71. Anantanasakul, P., Yamamuro, J.A., Lade, P.V., 2012. Three-dimensional drained behaviour of normally consolidated anisotropic kaolin clay. Soils Found. 52 (1), 146–159. Burland, J.B., 1989. Small is beautiful – the stiffness of soils at small strains. Can. Geotechn. J. 26, 499–516. Chen, J., Pan, T., Huang, X., 2011. Numerical investigation into the stiffness anisotropy of asphalt concrete from a microstructure perspective. Constr. Build. Mater. 25 (7), 3059–3065. Clayton, C.R.I., 2011. Stiffness at small strain: research and practice. Géotechnique 61 (1), 5–37. DH-S. 408/2532. Asphalt Concrete or Hot-Mix Asphalt, Department of Highways, Thailand. DH-SP. 401/2531. Specification for Asphalt Cement, Department of Highways, Thailand. DH-SP. 408/2536. Specification for Polymer Modified Asphalt Cement for Asphalt Concrete (Asphalt Concrete or Hot-mix Asphalt), Department of Highways, Thailand. Feizi-Khankandi, S., Mirghasemi, A.A., Ghalandarzadeh, A., Hoeg, K., 2008. Cyclic triaxial tests on asphalt concrete as a water barrier for embankment dams. Soils Found. 48 (3), 319–332. Fu, Y., Iwata, M., Ding, W., Zhang, F., Yashima, A., 2012. An elasto plastic model for soft sedimentary rock considering inherent anisotropy and confining-stress dependency. Soils Found. 52 (4), 575–589. Goto, S., Tatsuoka, F., Shibuya, S., Kim, Y.-S., Sato, T., 1991. A simple gauge for local strain measurements in the laboratory. Soils Found. 31 (1), 169–180. Graham, J., Houlsby, G.T., 1983. Anisotropic elasticity of a natural clay. Géotechnique 33 (2), 165–180. Hardin, B.O., Richart, F.E., 1963. Elastic wave velocities in granular soils. J. Soil Mech. Found. Div., ASCE 89 (SM1), 33–65. Hirakawa, D., Kongkitkul, W., Tatsuoka, F., Uchimura, T., 2003. Timedependent stress–strain behaviour due to viscous properties of geogrid reinforcement. Geosynth. Int. 10 (6), 176–199.

107

Hoeg, K., Valstad, T., Kjaernsli, B., Ruud, A.M., 2007. Asphalt core embankment dams: recent case studies and researches. J. Hydropower Dams 13 (5), 112–119. Hoque, E., Tatsuoka, F., 1998. Anisotropy in elastic deformation of granular materials. Soils Found. 38 (1), 163–179. Huang, Y.H., 2004. Pavement Analysis and Design, 2nd ed. Prentice Hall, Pearson. ICOLD, 1992. Bituminous Cores for Earth and Rock-fill Dams, Bulletin 84, International Commission on Large-Dam. Inam, A., Ishikawa, T., Miura, S., 2012. Effect of principal stress axis rotation on cyclic plastic deformation characteristics of unsaturated base course material. Soils Found. 52 (3), 465–480. Jamiolkowski, M.B., Leroueil, S., Lo Presti, D.C.F., 1991. Design Parameters from Theory to Practice, Theme Lecture, Geo-Coast '91, Yokohama, pp. 877–917. Jardine, R.J., Symes, M.J., Burland, J.B., 1984. The measurement of soil stiffness in triaxial apparatus. Géotechnique 34 (3), 323–340. Jiang, G.L., Tatsuoka, F., Flora, A., Koseki, J., 1997. Inherent and stress stateinduced anisotropy in very small strain stiffness of a sandy gravel. Géotechnique 47 (3), 509–521. King, M.S., 1970. Static and dynamic elastic moduli of rocks under pressure, Rock-Mechanics: Theory and Practice. In: Proceedings of the 11th Symposium on Rock Mechanics, Berkeley, California, AIME: NY, Somerton, W.H. (Ed.), pp. 329–351. Kongkitkul, W., Issaro, P., Jongpradist, P., Youwai, S., 2010. Deformation characteristics of asphaltic concrete in uniaxial compression, ASCE Geotechnical Special Publication No. 203 (Paving Materials and Pavement Analysis), Proceedings of Sessions of GeoShanghai 2010, Shanghai, 3–5 June 2010, Baoshan Huang, Erol Tutumluer, Imad L. Al-Qadi, Jorge Prozzi and Xiang Shu (Eds.), Reston, VA: ASCE/Geo Institute, pp. 66–74. Kongkitkul, W., Tongnuapad, C., Jongpradist, P., Youwai, S., 2012a. Anisotropy in the strength and elastic properties of polymer-modified asphalt. In: Proceedings of the International Conference on Highway Engineering 2012, Bangkok, Thailand, 18–20 April 2012, vol. 2, pp. 493–498. Kongkitkul, W., Tabsombut, W., Jaturapitakkul, C., Tatsuoka, F., 2012b. Effects of temperature on the rupture strength and elastic stiffness of geogrids. Geosynth. Int. 19 (2), 106–123. Kongsukprasert, L., Tatsuoka, F., 2007. Small strain stiffness and non-linear stress–strain behaviour of cement-mixed gravelly soil. Soils Found. 47 (2), 375–394. Kongsukprasert, L., Sano, Y., Tatsuoka, F., 2007. Compaction-induced anisotropy in the strength and deformation characteristics of cement-mixed gravelly soils. In: Soil Stress–Strain Behavior: Measurement, Modeling and Analysis, Geotechnical Symposium in Roma, March 16–17, 2006, pp. 479–490. Liang, R.Y., Abu Alfoul, B.A., Khasawneh, M., 2006. Laboratory investigation of anisotropic behavior of HMA. In: Proceedings of the 2006 International Conference on Perpetual Pavement, 2006, 14 pp. Lo Presti, D.C.F., O'Neill, D.A., 1991. Laboratory investigation of small strain modulus anisotropy in sands. In: Proceedings of the First International Symposium on Calibration Chamber Testing (ISOCCTI), Potsdam, NY, USA, 28–29 June, 1991, Elsevier, Huang, A.B. (Ed.), vol. 2, pp. 213–224. Mamlouk, M.S., Witczak, M.W., Kaloush, K.E., Ho, Y.-S., 2002. Effect of anisotropy on compressive and tensile properties of asphalt mixtures. J. Test. Eval. 30 (5), 432–438 (ASTM). Maqbool, S., Kuwano, R., Koseki, J., 2011. Improvement and application of a p-wave measurement systems for laboratory specimens of sand and gravel. Soils Found. 51 (1), 41–52. Masad, E., Tashman, L., Somedavan, N., Little, D., 2002. Micromechanicsbased analysis of stiffness anisotropy in asphalt mixtures. J. Mater. Civil Eng. 14 (5), 374–383 (ASCE). Motola, Y., Uzan, J., 2006. Anisotropy of field-compacted asphalt concrete material. J. Test. Eval. 35 (1), 1–3 (ASTM). Piriyakul, K., Haegeman, W., 2009. Stiffness anisotropy of boom clay. In: Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering, 5–9 October 2009, Alexandria, Egypt, vol. 1, pp. 167–171.

108

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

Shibuya, S., Tatsuoka, F., Teachavorasinskun, S., Kong, X.-J., Abe, F., Kim, Y.-S., Park, C.-S., 1992. Elastic deformation properties of geomaterials. Soils Found. 32 (3), 26–46. Stokoe, K.H. II, Lee, J.N.K., Lee, S.H.H., 1991. Characterization of soil in calibration chamber with seismic waves. In: Proceedings of the First International Symposium on Calibration Chamber Testing (ISOCCTI), Potsdam, NY, USA, 28–29 June, 1991, Elsevier, Huang, A.B. (Ed.), vol. 2, pp. 363–376. Taheri, A., Sasaki, Y., Tatsuoka, F., Watanabe, K., 2012. Strength and deformation characteristics of cement-mixed gravelly soil in multiple-step triaxial compression. Soils Found. 52 (1), 126–145. Tatsuoka, F., Haibara, O., 1985. Shear resistance between sand and smooth or lubricated surfaces. Soils Found. 25 (1), 89–98. Tatsuoka, F., Sato, T., Park, C.-S., Kim, Y.-S., Mukabi, J.N., Kohata, Y., 1994. Measurements of elastic properties of geomaterials in laboratory compression tests. Geotech. Test. J., GTJODJ 17 (1), 80–94. Tatsuoka, F., Kohata, Y., 1995. Stiffness of hard soils and soft soils in engineering applications, Keynote Lecture. In: Proceedings of International Symposium on Pre-Failure Deformation of Geomaterials, Balkema, vol. 2, pp. 947–1063.

Tatsuoka, F., Jardine, R.J., Lo Presti, D.C.F., Di Benedetto, H., Kodaka, T., 1999. Characterising the pre-failure deformation properties of geomaterials, Theme Lecture for the Plenary Session No.1. In: Proceeding of the 14th International Conference on Soil Mechanics and Foundation Engineerings, Hamburg, September 1997, vol. 4, pp. 2129–2164. Wang, L.B., Hoyos, L.R., Wang, J., Voyiadjis, G., Abadie, C., 2004. Anisotropic properties of asphalt concrete: characterization and implementation in pavement design and analysis. In: The 83rd Transportation Research Board Annual Meeting. Wu, B., King, M.S., Hudson, J.A., 1991. Stress-induced ultrasonic wave velocity anisotropy. Int. J. Rock Mech. Min. Sci. Geomech. 28 (1), 101–107. Yildirim, Y., 2007. Polymer modified asphalt binders. Constr. Build. Mater. 21, 66–72. Zhao, L., Zhao, Y., Fan, Y., Liu, Z., 2008. Study on road application performance of asphalt concrete reinforced by fiber and modified asphalt. In: Proceedings of 8th International Conference of Chinese Logistics and Transportation Professionals, ASCE.