*3.1. Concrete Mesostructure*

Concrete is a multi-phase, strongly heterogeneous material and its mesostructure presents strong randomness characteristics. It consists of aggregates varying in diameter and shape, mortar mix, interface transition zones (ITZs) located between mortar and aggregates, cracks, and pores. All concrete components are randomly distributed within its volume. The major part of the concrete mixture is aggregate particles. They can be divided into two groups by size: Fine (≤4.75 mm) and coarse aggregate (>4.75 mm). The content of coarse aggregate in the concrete volume is usually equal to 40–50% and, thus, it largely determines the parameters of the concrete mixture, as well as its cost. The particle shape depends on the aggregate type. However, after other researchers [17,19,22] and for the sake of simplicity, in a later part of the paper, we assume that they are spherical.

The next component distinguished at the mesoscopic level is ITZs, which are the regions of the cement film covering the aggregate particles. As the first micro-cracks are induced at the interface, the ITZs are considered as the weak link in the concrete. Their negligible influence on guided wave propagation velocity was presented by Xu et al. [17] and, therefore, their existence is omitted in further investigations.

In this study, we consider a two-phase concrete model comprising mortar matrix and aggregate particles. In the following sections, the process of model generation is described step by step. The mesostructure of the concrete is generated using the Monte Carlo method, which allows for generation of random numbers with a specific distribution. The particles' diameters are chosen based on the a priori known grading curve, and particles' coordinates are generated by taking into account the certain restrictions related to the model dimensions.
