## 5 Applications and Outlook
### Mechanical Properties and Dimensional Effects of Aggregates
[180] investigated the effect of aggregate shape on the surface properties of hot-mix asphalt and evaluated the weaving and friction properties of asphalt mixtures. [PERSON] et al. [27] concluded that the mechanical properties of hot mix asphalt are influenced by the properties of aggregates and asphalt binder by studying the shape characteristics and texture of aggregate particles as an indicator of aggregate properties. [PERSON] [181] investigated the effect of coarse aggregate shape characteristics on the compaction and microstructural properties of asphalt mixtures using DEM simulations, and among the aggregate shape characteristics parameters, flatness, elongation, roundness and sphericity were statistically correlated with the initial density of the asphalt mixture as a compaction parameter. [PERSON] [4] investigated Polyurethane Polymer Concrete (PPC) and analyzed its mechanical properties. The effect of aggregate shape on the mechanical properties (strength, modulus of elasticity, damage behavior) of the new concrete was discussed by establishing a two-dimensional finite element model. [PERSON] et al. [177] investigated the effect of aggregate shape on the mechanical properties of concrete by designing and testing eight simple cementitious composites and found that the aggregate size significantly affected the fracture energy of crushed and spherical aggregates. [PERSON] et al. [182] investigated the effect of aggregate particle shape on the durability and performance of unbound aggregate bases used in road structures. [PERSON] [183] investigated the effect of aggregate particle size on shape parameters and discussed shape parameter measurements for coarse aggregate (CA) and fine aggregate (FA), and compared the shape parameters using statistical methods. [PERSON] [184] investigated the effect of aggregate shape parameters and gradation on Oklahoma's permeability of commonly used aggregate substrates. The study's results showed that an increase in the uniformity factor and the fines content led to a decrease in permeability. [PERSON] et al. [185] investigated the performance of concrete under high triaxial loading. They used a high-capacity triaxial press to study the shape and composition of coarse aggregates to analyze their effect on concrete. The inhomogeneous microstructural features are affected by the nonlinear mechanical response. [PERSON] [186] couples macroscopic and microscopic domains using the embedded unit cell (EUC) homogenization method. The EUC method considers standard periodic boundary conditions and specific boundary conditions around the cell boundary. This method is more accurate and efficient in terms of stress than direct numerical simulations. The particular boundary conditions around the UC are necessary to enforce acyclicity. The inclusions have different corresponding stress levels in different regions under different loads. [PERSON] [187] proposes a new method for the stochastic model building based on the periodic microstructure of aggregates. The models established when periodic boundary conditions are not considered are subject to certain stochastic errors. Most of the boundary conditions are reflected in the variance of the elastic modulus. It is worth noting that when the model size is very small, the boundary conditions cannot be neglected even  
Figure 16: The volume ratio of aggregates at different parts affected by: (**a**) angularity; (**b**) sphericity. more. The boundary effect and the size effect have significant effects on model accuracy; however, most studies do not consider them. Considering boundary effects when predicting aggregates' tensile or compressive strength can effectively reduce the errors introduced by the calculations. [PERSON] [188] generated a UC that takes into account periodic boundaries to characterize the periodic microstructure of aggregates by an efficient algorithm. The effect of the boundary conditions on the elastic modulus is investigated separately for different size models.