## 3 Meso Analysis of Mechanical Characteristics of Soil-Rock Mixture
### Meso-Structure Model Generation of Soil-Rock Mixture  
#### 3.1.1 Generation of Irregular Rock Block Model  
Geological survey results indicate that the rock blocks within the deposit slope are angular and exhibit uneven surfaces. Previous irregular rock block model generation methods have primarily relied on the mathematical and statistical results of the shape indices derived from the rock block morphology. While these methods facilitate the batch generation of rock blocks of varying sizes, they require a substantial amount of shape indices. However, it is important to note that collecting and processing image data for small-sized irregular rock blocks, as shown in Figure 3, presents considerable challenges, often resulting in shape indices with low accuracy. To address the particle size issue, this study employs shape fractal theory. It is posited that, as a natural geological product,  
Figure 7: Mechanical characteristics of soil-rock mixture with varying rock contents. the particle size distribution and surface distribution of soil-rock mixture exhibit distinct fractal characteristics, demonstrating self-similarity. Accordingly, rock blocks sized between 2-10 mm and 20-50 mm share the similar geometric morphologies based on the fractal theory, allowing the shape indices of the former to be determined by scaling the particle size of the latter. The rock blocks with a long axis ranging from 20 to 50 mm, collected from the deposit slope near the Taoyuan-Jinshajiang bridge site, were used as the generation template, as illustrated in Figure 8a. To accurately capture the geometric characteristics of the irregular blocks, a 3D handheld laser scanner (RS100S) was used to perform three-dimensional imaging and scanning of the rock blocks. The measurement accuracy of the 3D handheld laser scanner is between 0.005 mm and 0.015 mm, allowing for precise capture of the spatial point cloud on the outer surface of the rock blocks. The point cloud processing module and simplification function were then applied to obtain the accurate geometric shapes of the rock blocks with varying particle sizes. The three sides of the external cuboid of the irregular rock blocks correspond to the major axis, the central axis, and the minor axis, respectively, with the shape indices of the irregular rock blocks related to these three principal axes. The ratio of the central axis to the major axis is defined as the Elongation Index (\(EI\)), while the ratio of the minor axis to the central axis is referred as the Flatness Index (\(FI\)), as shown in Figure 8b. The calculation equations of \(EI\) and \(FI\) are expressed as follows:  
\[EI=b/a \tag{1}\]  
\[FI=c/b \tag{2}\]  
where \(a\) represents the major axis, \(b\) the central axis, and \(c\) the minor axis. The values of \(EI\) and \(FI\) range from 0 to 1. The closer the value is to 0, the flatter the shape of the rock block. Conversely, the closer the value is to 1, the more the rock block resembles a sphere. The base surfaces of the selected rock blocks are mainly convex polygons in order to improve calculation and modeling efficiency. The \(EI\) and \(FI\) values of rock blocks within the 20-50 mm size range were determined using digital image analysis. Given that the focus of the simulations in this paper is the mechanical characteristics of soil-rock mixture under two-dimensional plane conditions, the \(EI\) index was selected as the key parameter to represent the shape of the rock blocks. The probability distribution of the \(EI\) shape index is  
Figure 8: (**a**) Real rock blocks; (**b**) three-dimensional reconstruction; (**c**) distribution of EI of rock blocks; (**d**) base plane of irregular rock block models. illustrated in Figure 8c, showing that \(EI\) values range from 0.65 to 0.8, with a concentration around 0.7.