# Synthetic Microstructure Generation and Multiscale Analysis of Asphalt Concrete
## 1 Introduction  
Asphalt pavement layers constitute the group of upper layers of the flexible asphalt pavement structure. Their main role is to transfer the load coming from the moving vehicles to the lower layers and the subgrade. A traditional asphalt mixture used for these layers is asphalt concrete (AC). It comprises two main constituents: the aggregate particles made of the crushed stone (inclusions) and the bituminous agent (matrix), in which they are embedded. In fact, the matrix comprises not only the binder itself, but also a filler (a very fine fraction of the aggregate) and air voids constituting a mastic. A number of special additives improving AC performance can be also used. An extensive overview research in this important field can be found, e.g., in [1]. The impact of such additives and the external loads (understood as an action of mechanical load, thermal load, moisture etc.) is examined manifold: via theoretical formulations, laboratory experiments, and numerical modeling. All of them used together can give a deep insight into the understanding of novel materials performance. Our paper is devoted to the latter of these pillars.  
A development of the material models for the mastic/binder is a very active field of science. Inelastic analyses of AC can be found, e.g., in [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. For the sake of brevity, we restrict ourselves in this paper only to the linear elastic computations, since we focus in this paper on the syntheticmicrostructure generation and the multiscale computations. The proposed framework can be easily extended to analysis of non elastic materials. In our previous paper [15], we applied successfully the MsFEM to the viscoelasticity problem. The overall analysis with the comparison of the obtained numerical results with the laboratory ones (validation) is one of our future research goals but is beyond the scope of this paper.  
In numerical analyses, the AC grading curves should be incorporated into the synthetic microstructure modeling algorithms to reflect its real morphology. Due to the resources limitations, one accounts only for the part of the prescribed curve, e.g., in [16], the value of 2 mm was used as a threshold. In Figure 1, one can observe an exemplary grading curve (red solid line) that can be used for the modeling purposes. Setting the threshold value for the minimum grain size to be considered in the analysis is specific to the type of AC used and the computational resources. For instance, using the value of 2 mm in the case of the mixture presented in Figure 1 would exclude nearly a half of the grains from the analysis.  
In our paper, we present a methodology of AC microstructure generation accounting for the prescribed grading curve. We combine and modify certain known concepts in order to speed up the process.  
Another issue addressed in this paper is the multiscale analysis of AC. The multiscale finite element method is used for this purpose. It enables for a large reduction of the degrees of freedom (and the CPU time) used in direct numerical analysis with the overkill mesh. Both of the components used together can be very beneficial in the case of the tests performed on novel asphalt mixtures. They can reduce the costs of the whole design process substituting some of the laboratory experiments, giving the opportunity to test the developed constitutive models and speeding up the numerical analysis itself.