Compression and Shear Tests

Three dry and three wet cylindrical matrix samples are uniaxially loaded to failure under strain-controlled mode (Hossain and Tarefder 2013; Hossain and Tarefder 2013a). Figure 4.2(a) shows the testing configuration of the matrix sample under compression. A loading rate of 1.27 mm/min (0.5 in/min) is used. Also three dry and three wet samples are compacted in a shear box and subjected to shear failure with a loading rate of 1.27 mm/min as shown in Figure 4.2(b). Average of three samples’ results from compression and shear tests are summarized in Table 4.1. Stiffness E-value is determined by measuring the slope of secant modulus. Secant modulus is defined as slope connecting origin to 50% of maximum strength of material (Santi et al. 2000). Several studies used and recommended secant modulus to calculate elastic modulus of asphalt concrete (Degrieck and Van Paepegem 2001; Voyiadjis and Allen 1996; Wang 2011). Ultimate strength of matrix obtained from compression and shear tests are also listed in Table 4.1

89

(Hossain and Tarefder 2013; Hossain and Tarefder 2013a). It can be seen that E-values of dry sample are higher than those of wet samples, which is expected. But there is an exception; E-value of wet sample under compression is found to be smaller than the E- value in shear. In a previous study, it has been observed that, aggregate surface roughness increases after moisture conditioning (Kasthurirangan Gopalakrishnan, Broj Birgisson, Peter Taylor 2011). This increased surface roughness might cause the material stiffer than the dry material. Unlike compressive test, the shear test is confined into shear box and might causes additional stiffness.

4.8 FEM Model Development

The FEM model is developed using ABAQUS/CAE 6.9-EF1, commercially available software. A two-dimensional idealization of a spherical aggregate surrounded by a layer of matrix material is considered. Obviously, it can be argued that the spherical aggregate is not a true representation of aggregate particles reside in an AC. Similar argument can be made on the size of the aggregate particle. Also other studies use spherical shape aggregate to predict moisture-induced damage (Kringos et al. 2008a; Kringos et al. 2008b). The fact is the shape and size of aggregate particle varies a lot in asphalt concrete. Therefore a study that would consider the effects of the size and shape on the outcomes, that is asphalt cohesion and adhesion, can itself be complex but doable. For simplicity, the model considered for this study is one quarter of a spherical coarse aggregate surrounded by a layer of matrix material, as shown in Figure 4.3. This suffices the purpose of this study. The radius of the aggregate is assumed to be 19.05 mm (0.75 in.) based on the nominal maximum size (25.4 mm or 1.0 in.) of the mix aggregate collect from the plant. Since matrix thickness varies in asphalt concrete, two thicknesses of

90

matrix layers (0.508 and 1.27 mm) are considered. The size of the selected fine aggregate is ranges from 1.19 mm to 0.074 mm. The thickness of matrix is chosen such that the fine aggregates itself have sufficiently coated with asphalt binder to make a homogeneous matrix material.

Though AC has been considered to be visco-elastic-plastic material, matrix is assumed to behave elastically following the behavior observed in other studies. It has been mentioned that AC behaves elastically at low temperature and visco-elastically at high temperature (Zhu et al. 2010). Also the stiffness of binder is close to stiffness of filler at lower temperature (Shashidhar and Shenoy 2002). In addition, the phase angle and rut factor for wet AC material is small comparing to dry AC material and wet AC material considered behaves elastically (Tarefder, Yousefi, et al. 2010). E-value of limestone aggregate is well established in literature, therefore laboratory tests are not conducted on aggregate. The E-value of aggregate used in this study is 48.26 GPa (7,000,000 psi) and the Poisson’s ratio is 0.20 (Roque et al. 2009).

The loading and the shape of the FEM model are symmetrical to the vertical axis. The model is restrained for vertical and horizontal movement at the bottom, but only horizontal movement is restrained on the sides. Four noded linear quadrilateral cohesive elements are used to define the matrix. Linear elements are used since quadratic elements are not available for assigning axi-symmetric cohesive element in ABAQUS. Three and four noded linear quadrilateral plane stress elements are used to define the aggregate. Combinations of both three and four noded elements are required due to the spherical shape of the aggregate. In ABAQUS, maximum stress criteria required maximum stress in both vertical and shear directions according to Eq. (4.2). Since the model is two-

91

dimensional, data from one shear direction is sufficient as per Eq. (4.3). The interface between matrix and aggregate is defined as cohesive interaction. The bottom of matrix surface and top of aggregate surface are selected to make an interface. FEM model should have interface interaction behavior while model consists of two different materials and in contact.

In the FEM model, instead of applying a load, a specified deformation is applied and stresses are calculated using Eq. (4.1) and used to determine damage according to the Eq. (4.3). Deformation magnitudes of 0.72 mm (0.0285 in.) and 1.45 mm (0.057 in.) are applied on the FEM model. The magnitude of the deformation is calculated based on a standard duel tandem wheel on a pavement. It has been observed that a dual tandem wheel of total 889.64 KN (200,000 lb) load produces a 1.45 mm (0.057 in.) deformation in a 203.02 mm (8 in.) thick AC. Therefore 1.45 mm value of the deformation is considered. Also, half of this 1.45 mm is considered. The selected deformation is the extreme deformation that a pavement can experience since the weight of the dual tandem is for the landing gear of an aircraft. Also an aggregate coated with matrix material located at the top surface of pavement might experiences that amount of deformation. This deformation is considered to observe the extreme scenario of damage in AC. The deformation load is applied on 10.16 mm (0.4 in.) length of matrix. Usually, Indirect tensile strength of asphalt concrete wheel is determined by subjecting an asphalt concrete sample diametrically though a 20.32 mm-25.4 mm (0.8-1.0 in.) loading strip. Since the model is axi-symmetric, deformation load is applied over 10.16 mm (0.4 in.) length.

Traffic load on the roadway pavement is dynamic and cyclic. The shape of the dynamic load varies and really depends on the tire foot-print and speed of the vehicle. For

92

example, dynamic modulus of asphalt concrete is determined using sinusoidal loading for using in the new mechanistic-empirical pavement design procedure. In this study the FEM is simulated using three deformations intensity shapes or patterns namely, triangle, sawtooth and rectangle (Hossain and Tarefder 2013b). In each case, only one cycle of dynamic deformation is applied. These three deformation patterns are shown in Figure 4.4. In this study the deformation intensity pattern used to see how damage initiates and progressed into matrix while the deformation applied with highest intensity for a very short time (i.e. triangular patter) or the deformation applied with highest intensity for the entire analysis period (i.e. rectangular patter) and in between of those two (i.e. sawtooth pattern).

The deformation is applied on the FEM model by following three load intensity patterns shown in Figure 4.4 and according to the function described in Table 4.2. According to Table 4.2, i stands for intensity magnitude and t stands for time in second. For an example, for triangular pattern, at t=0, 0.072 mm deformation multiply with intensity magnitude i=0, so total zero deformation is applied at t=0; then at t=0.05, 0.072 mm deformation multiply with intensity magnitude i=1.0, so total 0.072 mm deformation is applied at t=0.5; then at t=0.10, 0.072 mm deformation multiply with intensity magnitude i=0, so total zero deformation is applied at end of the cycle. If the time increment and corresponding magnitude in the cycle is needed for the ABAQUS solver then it calculated automatically by linear interpolation.

The analysis matrix is shown in Table 4.3. Total twenty-four FEM simulations are run according to Table 4.3.

93 4.9 Results and Discussions

The damage locations near the top surface of the matrix and/or in between the top surface and matrix-aggregate interface are named as cohesive damage. The damage locations at the bottom of matrix and/or near the matrix-aggregate interface are named as adhesive damage. The matrix layer with a thickness of 0.508 mm (0.02 in.) is termed as thin matrix and 1.27 mm (0.05 in.) is termed as thick matrix in the subsequent sections.