## 1 Introduction
However, their model simplifies boulders as single spheres--an assumption that reveals a notable inconsistency between the idealized geometric representation and the actual morphological characteristics of gravel granules. [PERSON] et al. [28; 29] performed two-dimensional discrete element numerical simulations of triaxial and direct shear tests on an S-RM model obtained through digital image processing, comparing the mechanical properties and deformation characteristics of sand and S-RMs. This study models irregular particle morphologies numerically. However, its application remains limited to two-dimensional frameworks. [PERSON] et al. [30; 31] developed a two-dimensional discrete element model for the random microstructure of S-RMs by simplifying gravels into circles, triangles, and quadrilaterals, conducting numerical research on biaxial tests. Nevertheless, these models are still constrained by the limitations of two-dimensional simulation conditions. [PERSON] et al. [32] proposed a new random convex polygonal gravel model, which they used to establish a two-dimensional numerical model of S-RMs. This model was then used to study the influence of boundary conditions and consolidation state on the mechanical properties and deformation failure mechanism of biaxial specimens. Based on a two-dimensional discrete element model of S-RMs, [PERSON] et al. [30] analyzed the effect of factors such as gravel content, gravel shape, and stone coarseness on the shear strength and deformation characteristics of S-RMs. Nevertheless, the discrepancy in irregular shape characteristics between two-dimensional polygons and actual three-dimensional particles remains insufficiently addressed in current research. [PERSON] et al. [33] developed a three-dimensional discrete element model of triaxial tests of S-RMs, incorporating both irregularly shaped granules and sand mixtures containing spherical particles. The research successfully established an irregular particle configuration and performed comprehensive numerical analyses based on the proposed model. In summary, the aforementioned scholars have made notable contributions to mesoscopic-scale research on S-RMs through the application of the discrete element method. However, several limitations remain across various aspects of this field. Due to the relatively low complexity in constructing two-dimensional irregular-outline models, most existing studies focus on their numerical simulations [32; 34; 35]. However, these models are limited in accurately capturing the actual mesoscopic mechanical characteristics. Currently, systematic investigations into the stress states of S-RMs under three-dimensional conditions remain limited. Most existing studies [36; 37; 38; 39; 40; 41] employ rigid boundary conditions, which differ significantly from the rubber membrane boundaries commonly used in laboratory experiments. Moreover, although some studies [42] have incorporated the effects of particle breakage, the specimens employed are composed exclusively of gravel. As a result, these investigations do not adequately represent the unique mechanical behavior of S-RMs, which are inherently heterogeneous, multi-component geomaterials. Currently, the majority of research efforts focus on analyzing macroscopic mechanical properties. However, comprehensive investigations into the stress states of S-RMs under three-dimensional conditions remain limited, particularly at the microscale level. From a microscopic perspective, particles within S-RMs are interconnected through various types of contact forces, and the concept of complex systems is employed to describe the statistical characteristics of granular materials [43]. Microscale research aids in elucidating the origins of macroscopic responses [44], especially concerning factors such as the direction of contact forces [45], contact force transmission [46], and particle breakage [47]. It is particularly noteworthy that the contact force chain network constitutes a pervasive heterogeneous structure in the study of granular materials.