## 4 Numerical Simulations and Modeling Based on Visualization Techniques
### Realistic Aggregate Model  
Real shape modeling approximates the real aggregate shape by using different particles, which is especially needed in DE models [115]. Numerical models based on real aggregate models can save time and material, which is much better than the numerical models obtained by X-ray imaging techniques because numerical aggregate particles can be stored and reused to reconstruct the numerical model of the aggregate. Since the 3D structure of aggregates cannot be clearly visualized, [PERSON] [116] used a method for the automatic generation of spherical clusters to model the 3D shape of real aggregates. [PERSON] [117] built a realistic aggregate model based on laser scans of the aggregate surface from different angles. A 3D meshing of the aggregate particles was performed for finite element modeling, which was further investigated by creating a shape library. In many previous studies [118], non-overlapping circular clusters were utilized to represent the true shape of irregular aggregate particles, which indicates that the nature of the real aggregate model is using small circles or spheres to simulate the real shape of aggregate particles. An example of the randomly generated aggregate basic unit is shown in Figure 10. In the figure, the red extension line indicates the direction of the long axis of the irregular particle cluster clump. [PERSON] et al. [119] developed an algorithm for simulating the dense accumulation of large, spherical materials and investigated the way of particle filling and particle distribution by geometrical parameters and model variables. [PERSON] et al. [120] applied the concept of particle stacking simulation to develop a model of stable random dense stacking of particles with size distribution and studied the density and coordination number of fillers. Combined with nondestructive imaging and DEM simulation techniques, various parameters of the aggregate structure were optimally described. [PERSON] et al. [121] proposed a novel computer simulation of random stacking of variable-size particles in 3D space using DEM to model particle matrix stacking. [PERSON] et al. [122] used ellipsoidal and convex polyhedral particle random stacking models to study the effect of aggregate shape on the 3D diffusivity of mortar. The diffusivity of mortar was predicted by combining numerical fine view structure and dot matrix methods. The results show that aggregate shape has a significant effect on mortar diffusivity. [PERSON] et al. [123] utilized DEM to develop a novel system that can consider particle size, shape and filling method and proposed a numerical calculation method for dynamic motion calculation. The results showed a significant effect on filling density by particle shape. [PERSON] et al. [71] proposed a method for mixing image scanning with aggregate filling to randomly generated 2D digital asphalt concrete specimens for virtual testing and captured the detailed shape characteristics of the aggregates by calibrated high-resolution images. The differences between the simulated results and the measured values are discussed. [PERSON] et al. [124] proposed a practical modeling method for 2D arbitrarily shaped aggregates. An effective algorithm is proposed  
Figure 10: Basic unit and polygon particle clusters. for large-volume concrete with aggregate content up to 60-70%. The effect of aggregate shape on the mechanical properties of concrete was analyzed and explored. [PERSON] et al. [125] demonstrated in detail a convex extension method for constructing convex polygons and polyhedral represented by crushed coarse aggregates in two and three dimensions by building a fine-scale structural model of three-phase, fully graded concrete consisting of anisotropic high-content aggregates and cement slurry. [PERSON] et al.