## 1 Introduction  
The deformation and deterioration of soil-rock mixtures (SRMs) are frequently encountered in most geotechnical disasters such as earthquake liquefaction, slope instability, and earth dam collapse [1]. As defined by [PERSON] [2], the threshold of soil and rock in a soil-rock mixture is 5% of the characteristic length. Therefore, understanding the behavior of soil-rock mixtures aids in the study of disaster early warnings such as landslides and debris flows. The first difficulty of studying the behavior of SRMs is to characterize the random geometry feature in different engineering practices. Due to differences in geological activity, the SRMs in different engineering practices have differences in their particle distributions, shapes, and placement angles. In most recent studies, the geometry features of SRMs have been characterized in two different ways. The first method is to use digital image processing (DIP) methods in SRM structures captured by a high-resolution camera (2D images) or X-ray CT (3D images). For example, [PERSON] et al. [3] used the DIP method in their captured images and reconstructed the mesostructures of SRMs. Based on the reconstructed mesostructures, [PERSON] simulated the mechanical behavior of the SRMs from a digital image by using the finite element method (FEM). Similar to [PERSON], [PERSON] et al. [4] used a DIP-based discrete element method (DEM) to analyze the heterogeneous geomaterials of SRMs. The second method of characterizing the geometry is to generate a random mesostructure of SRMs with similar statistic geometry parameters, such as gradation and fractal dimension. [PERSON] developed random generation algorithms for the mesostructures of both 2D [5] and 3D [6] SRMs. [PERSON]'s approach involves growing new tetrahedrons on a hexahedron base; therefore, it is suitable to generate angular rock particles. [PERSON] [7] et al. developed a different method that randomly picks vertices within a spherical domain to generate rock particles, which is efficient in producing rounded rock particles. [PERSON] [8] integrated [PERSON] and [PERSON]'s method and developed a new method that generates the mesostructures of SRMs using their gradation and particle shape proportion. The second challenge of investigating the behavior of SRMs is introducing the degradation process of large grains under compression or shear loadings. A considerable amount of the literature has revealed that the degradation process associated with loading-induced grain crushing affects the macroscopic mechanical behavior of SRMs [9; 10]. For example, [PERSON] et al. [11] performed an in situ direct shear test on the soil-rock mixtures in the three gorges reservoir area in China. The direct shear test showed that the grain breakage in SRMs has a significant influence on the shear strength of SRMs. Similar conclusions have been drawn by many other in situ or laboratory tests [12; 13; 14; 15]. To account for the degradation process of the large grains (or rock particles), several attempts have been made to develop a constitutive model of SRMs. For example, [PERSON] et al. [10] proposed an elastoplastic model for grain materials that takes into account grain breakage. [PERSON] et al. [9] developed a constitutive model for pyroclastic soil that considers the grain crushing process under loading of the large particles. [PERSON] et al. [16] developed a viscoelastic model for multi-layered coarse-grained soil that considers the interface-layer effect of SRMs. However, these constitutive models are all theoretic models based on the homogenization assumption and cannot be applied in the mesoscopic geometry models. Very few studies are available for considering the degradation process of large particles in a mesoscopic geometry simulation. Most of the studies that have been published so far about the mesoscale simulation of SRMs suffer from lacking consideration of grain crushing during the loading process. For example, [PERSON] et al.