## 4 Numerical Simulations and Modeling Based on Visualization Techniques
### Idealized Aggregate Model  
The self-defined aggregate models can be divided into idealized aggregate models, ordinary angular aggregate models, and special angular aggregate models. This chapter focuses on and summarizes the self-defined digital aggregate models. The previous article describes in detail the application of X-ray CT-based imaging technology. The digital aggregate modeling approach based on aggregate properties is shown in Figure 9.  
Existing research tends to combine aggregate accumulations with computer computing to deal with the complex problems arising from the accumulation of large numbers of particles by modeling the dense accumulation of particle assemblies and developing algorithms. [PERSON] [105] used the discrete element method to simulate the creep flexibility tests of ideal HMA mixtures. A total of 102 digital specimens of ideal asphalt mixtures were constructed by two user-defined models, and both the DE model and the FE model are capable of building ideal models. [PERSON] [106] developed a finite element model of an aggregate consisting of multiple randomly distributed irregular aggregates and cement mortar, which was also used to calculate the effect of large-size recycled coarse aggregate on the strength of recycled aggregate concrete. [PERSON] [107] proposed an isotropic damage model for quasi-brittle materials and demonstrated its performance in the anal  
Figure 8: Categories of idealized model and modelling methods for aggregate. Figure 9: Digital aggregate modeling approach based on aggregate properties. ysis of crack extension in concrete. A benchmark test of a mixed-mode fracture was also performed to demonstrate the performance of the proposed damage model. A simple and reliable two-dimensional finite element (FE) model was defined by [PERSON] [108]. The comparison between numerical analysis results and experimental data was also used to highlight the reliability of the finite element model and analytical model. Structural indicators of asphalt mixtures determine the mixture's non-uniform nature, which significantly impacts the micromechanical response of the mixture. Virtual modeling based on real aggregates aims to simulate the microstructure of the mixture using computer image processing techniques to extract real aggregates using CT [109; 110] or laser scanning equipment. However, [PERSON] et al. [87] proposed a virtual design method for mixture microstructure based on the structural indicators of a digital library of real aggregates, and the microstructure of the virtual mixture was obtained by compaction simulation with DEM software. The microstructure of the virtual mix was obtained by determining the location orientation according to the distribution of the selected aggregates, and the indirect tensile test was simulated numerically to obtain the different mechanical properties of the specimens. [PERSON] et al. [111] proposed a user-defined material model in DEM based on a random polygon algorithm for simulating the dynamic modulus test of asphalt mixes by creating polygon particles to represent the shape and size of aggregates. Meanwhile, [PERSON] et al. [112] developed a 3D visualization simulation technique for random particle generation without the use of the X-ray CT technique and used a 3D discrete cell model to visualize and simulate the microscopic properties of asphalt concrete under mechanical loading. Most researchers used digital imaging techniques to prepare the required samples. However, this method was laboratory dependent and required the preparation and scanning of real asphalt mixtures to obtain digital samples [113], and expensive equipment, labor consumption, and time costs were limitations, which made it difficult to obtain a large number of numerical samples of different grading types, aggregate shapes, angles, and void ratios. Instead, the aggregate stochastic generation model is a method that is independent of the laboratory.