NON-UNIQUENESS OF MICRO DEFORMATION OF ASPHALT CONCRETE

Transcription

1 Performance Testing and Evaluation of Bituminous Materials 483 NON-UNIQUENESS OF MICRO DEFORMATION OF ASPHALT CONCRETE L.B. Wang, Louisiana State University/Southern University, USA Ching S. Chang, University of Massachusetts at Amherst, USA Abstract: Asphalt concrete as a bonded granular material demonstrates duality in response to external load. At macro level, the material behaves like a continuum due to the binder. At micro level, loads are transmitted through particle contacts and stress concentrations become very complicated due to the involved packing pattern of aggregates and void distributions. To investigate this duality a set of tests on asphalt concrete under repeated load has been observed at both macro level and micro level. At macro level, the magnitude and the pattern of permanent deformation were measured. At micro level, strain localization zones and crack distributions were captured as digital images. Four cross sections from one specimen were measured and the measurements were compared. The comparisons show that with the same macro responses of permanent deformation, the strain localization pattern and crack distribution are very different. This phenomenon has important implications to constitutive modeling of asphalt concrete. Explanations of the phenomena by micromechanics are presented. 1. Introduction Asphalt concrete is a bonded granular material. And as such, its mechanical properties, including the permanent deformation under a repeated loading, are affected by the characteristics of the aggregate skeletons and the binder. Because of its granular skeleton, asphalt concrete demonstrates dilation or volumetric straining under shearing and stiffening under hydrostatic pressure. Because of the asphalt binder it demonstrates temperature and loading rate dependence. Traditionally an asphalt concrete is treated as a continuum by considering the macro responses of the material under the external loading without considering the responses of the aggregates and the binder at the micro scale. The behavior of asphalt concrete has been modeled in the past from as simple as a linear elastic material to as complex as a nonlinear viscoplastic material. The Superpave asphalt pavement design method [1] used a rather complex nonlinear viscoplastic model to describe the behavior of asphalt concrete to predict the permanent deformation of asphalt concrete under repeated traffic loading. However, it is believed that a study of the micro responses of asphalt concrete may lead to a better understanding of the mechanical properties of the material at the macro level. The term micro response used in this paper refers to the detailed deformation- displacement patterns of the aggregate and asphalt binder in an asphalt concrete. This paper presents an experimental study of the macro and the micro responses of an asphalt concrete specimen under repeated wheel loading. The experiment results showed that under the

2 484 6th RILEM Symposium PTEBM'03, Zurich, 2003 same repeated loading, the macro permanent deformation (rutting) of the asphalt concrete specimen at four different locations is nearly the same while the micro responses at these locations are significantly different. Explanations in terms of micromechanics are presented. 2. Experimental Observation A 125mm wide by 300 mm long by 75 mm thick asphalt concrete beam specimen was fabricated using the rolling compaction procedure [2]. The specimen was then cut into four sections and the cut surfaces were painted gray with 5mm x 5mm grids drawn on the surfaces. The four sections were put back together and were secured in a mold on four sides. The base of the specimen was supported on a rigid steel plate. The specimen was cured in a temperature conditioning chamber for twenty four hours at 60 C and the repeated loading was applied to the entire specimen in the same temperature conditioning chamber. The loaded wheel tester [3], which is capable of applying a controllable wheel load magnitude and contact pressure, was used in this experimental study, see Figure KN of wheel load and 690KN/M 2 contact pressure were used for the tests. The permanent deformations along the wheel path at each cut section were measured after 2000 loading cycles. The images of the cut surfaces were also acquired by an image acquisition system to study the micro deformation-displacement patterns under the repeated wheel load. 3. Experimental Results The maximum rut depths at the four cross sections were measured and are presented in Table 1. The rut-depths at these four sections are nearly the same. The images for the deformed grid patterns on the four cut surfaces after 2000 loading cycles are measured and shown in Figure 2A, 2B, 2C and 2D for the cut surfaces 1 to 4. It can be noticed from these images that the micro deformation-displacement patterns of these four cut surfaces are quite different. In figure 2A and 2B, microcracks beneath the hose were very dense and the deformation was very much localized; the zone with significant plastic deformation was restricted in a narrow stripe, which extended to a depth about half height of the specimen. In figure 2C, although the zone beneath the hose deforms similarly to these in Figure 2A and Figure 2B, the microcracks propagated to almost the whole depth of the specimen. In Figure 2D, there are fewer microcracks, however the lateral deformation is significant; the deformation patterns resemble the plastic flow of a continuum of Coulomb material [4].

3 Performance Testing and Evaluation of Bituminous Materials 485 Pressured Hose(100psi = 0.69MPa) 12in=305m m 3in=76m Cut Surfaces 5in=127m 100lb=445 5in=127m 3in=76mm Figure 1. Test Configuration (not to scale) Table 1 Measured Maximum Rut Depth after 2000 Cycles (mm) Section No Rut Depth (mm) Explanations The observed micro displacement responses could be explained by micromechanics. There have been significant developments in the area of micromechanics of granular materials in the last two decades. Two different approaches have been generally followed by researchers. One approach follows the routine of describing the particle contact and configuration [5, 6]; the other, the doublet mechanics[ 7, 8], assumes a Bravis Lattice as the microstructure and considers the doublet deformation and particle interaction by taking different orders of the deformation field expressed as a series of the coordinates. Both methods could explain the duality. Granik et al. [7] and Ferrari et al. [8] assumed a face centered cubic packing of spheres as the microstructure model of granular materials to solve the classical Flamant problem of a semiinfinite plate subjected to a point force normal to the boundary [9]. The model (see Figure 3) used by Granik and Ferrari shows that the macro stress distributions are the same as these of the Flamant solution based on the linear elastic continuum mode. See equations 1-a, 1-b, 1-c.

4 486 6th RILEM Symposium PTEBM'03, Zurich, 2003 a b c Plastic Zone, Slip Line d Figure 2. Non-uniqueness of Micro Deformation and Displacement Discontinuity x 2Px y [ ( x y ) ] (1-a) xy 2Pxy [ ( x y ) ] (1-b)

5 Performance Testing and Evaluation of Bituminous Materials y 2Py [ 3 ( x y ) ] (1-c) However the micro-stress of p1, p2 and p 3 in Figure 3, represented in equations 2-a, 2-b, 2-c are significantly different.( 0, / 2) p1 4Py ( x y)[ 3 ( x y ) ] (2-a) p2 4Py ( x y)[ 3 ( x y ) ] (2-b) p 2 2Py( y 3x )[ 3 ( x y ) ] (2-c) 3 where p1, p2 and p 3 are the micro-stresses along the directions of valences, where particles are in contact. These solutions show that the micro stress of granular materials could be in tension under the applied pressures at the boundary (positive indicates tension). However, the macrostresses are the same as those in a continuum (equations 1-a, 1-b, 1-c). This demonstrates the duality of bonded granular materials. It was also shown in [4], microstresses can be altered with microstructure(for example, in Figure 3) while the macro stresses remain to be the same as 1- a,1-b,1-c. In terms of the micromechanics approach followed by [5], when granular materials of different microstructures are subjected to the same uniform stress field, the forces between the particles are different and related to the microstructures. A formulation relating the macro stress to the forces between contacting particles for the simplest microstructures of 2D circles was presented in equation 3 by Emeriault et al. [10]. 2 RN ij nf i j nf j i P n d V ( ) ( ) (3) 0 where R-radius of circles in contact; N-number of contacts; V-representative volume n-contact normal direction; F-contact force; P(n)-contact normal distribution density. This equation also implies the duality, that is: given the same macro stress, the contacting forces are related to the fabric(contacting normal distribution etc.)

6 488 6th RILEM Symposium PTEBM'03, Zurich, 2003 P 3 P 2 P 1 5. Discussions Figure 3. Microstress Distribution of Granular Material in Half Space The experimental results presented in this paper indicate that the permanent deformations of the asphalt concrete beam specimen in the wheel path at different locations are nearly the same when subjected to the same loading conditions. However, the micro deformation-displacement patterns are quite different at different locations in the specimen. This implies that for a bonded granular material, such as an asphalt concrete, even the mass is not a continuum, its macro deformation properties could be described by continuum mechanics. This is because the permanent deformation is the sum of the micro deformations of the material within the zone influenced by the loading. As such, small localized irregularities may not have a dominating effect on the total deformation summed over the entire influenced zone. However crack initiation and propagation might not be well treated by continuum mechanics. This is because fatigue failure and rupture are initiated by a void, or micro cracks, imperfect interface and localized strains. Therefore, the material s microstructures and internal damages under loading should be used to achieve a better prediction of the fatigue properties of the material. This is demonstrated by the very large variance of fatigue life of asphalt concrete. To better evaluate fatigue life, material microstructures and internal damages should be quantified and included in predictive methods. Micromechanics could qualitatively interpret the observed phenomena. However, to make it a more useful predictive method, efforts in correlating the localized deformation pattern with micromechanics prediction are considered imperative.

7 Performance Testing and Evaluation of Bituminous Materials Conclusions The observations and the micromechanics interpretations could be summarized as follows: 1. Under the same macro deformation, micro deformation pattern is not unique. 2. Rutting and cracking are associated. Generally rutting and cracking were studied separately, however, from these test results, it is apparent that crack could be initiated and propagated at a relatively high temperature during rutting development. The study of rutting and cracking interaction could be an important research topic. 3. Although the micro deformation patterns are quite different, the macro permanent deformations show consistent magnitude and pattern. This implies even the mass is made of discrete aggregates, its deformation properties at macro level could be described by continuum mechanics. However crack initiation and opening might not be well treated by continuum mechanics. This is demonstrated by the very large variance of crack pattern in the asphalt concrete blocks. To better evaluate fatigue life, material microstructures and internal damages should be quantified and included in predictive methods. 7. References [1] Monismith, C.L. (1994). Permanent Deformation Response of Asphalt Aggregate Mixes, Strategic Highway Res. Program, National Research Council. SHRP-A-415 [2] Lai, J.S, and Shami, H., (1996). Development of a Rolling compaction Machine for Preparation of Asphalt Beam Samples, TRR No. 1492,pp [3] Collins, R., Shami, H., and Lai, J.S. (1996). Use of a Georgia Loaded Wheel Tester to Evaluate Rutting of Asphalt Concrete Samples, TRR No. 1545, pp [4] Hill, R. (1950), The Mathematical Theory of Plasticity, Clarendon Press, Oxford. [5] Chang, C. S. and Ma, L. (1991). A Micromechanical-Based Micropolar Theory for Deformation of Granular Solids. Int. J. Solids Structures, Vol. 28, No.1 pp [6] Christoffersen, J.; Mehrabadi, M.M. and Nemat-Nasser, S. (1981). A Micromechanical Description of Granular Material Behavior. Journal of Applied Mechanics, Vol.48, pp [7] Granik, V. T. and Ferrari, M. (1993), Microstructural Mechanics of Granular Media. Mechanics of Materials, Volume 15, pp [8] Ferrari, V. T.; Granik, A. and Nadeau, J. C. (Eds.) (1997). Advances in Doublet Mechanics. Springer. [9] Todhunter, I. and Pearson, K. (1960). A History of the Theory of Elasticity and Strength of Materials. Dover Publications, Inc., NY. [10]Emeriault, F. and Chang, C.S. (1997). Interparticle Forces and Displacement in Granular Materials. Computers and Geotechnics, Vol.20, No. ¾, pp