## 1 Introduction  
A soil-rock mixture (S-RM) consists of fine-grained soils, irregular gravels, and voids that exhibit variations in both size and spatial distribution, forming a granular medium characterized by extremely heterogeneous and nonlinear structural features [1, 2]. The presence of gravels endows S-RMs with distinctive mesoscopic structural characteristics, resulting in complex mechanical properties that are closely related to the shape, particle size distribution, and spatial arrangement of these blocks [3; 4; 5]. As a product of geological processes, S-RMs are widely distributed in natural environments [6], and their occurrence is frequently associated with catastrophic landslides [7]. The mechanical properties of S-RMs play a crucial role in determining the stability of geotechnical engineering structures. Consequently, the investigation of these properties constitutes a fundamental research focus with significant implications for enhancing engineering safety and reliability. A significant body of research has established a comprehensive framework for the mechanical properties of S-RMs, revealing that gravel content is the primary factor influencing their mechanical properties [8; 9]. [PERSON] et al. [10; 11] conducted triaxial tests on a physical model that incorporated multiple variables, including varying gravel contents and particle shape distributions. Their results indicated that cohesion decreases as the gravel content increases, while the internal friction angle and deformation modulus increase. Additionally, the distribution of gravels significantly affects the strength of S-RMs, particularly in terms of cohesion and the deformation modulus. Moreover, gravel content influences Poisson's ratio [12], compression strength [13], and the ultimate bearing capacity of pile ends [14]. Notably, even S-RMs with identical gravel contents can exhibit diverse mechanical behaviors [15]. Numerous researchers have investigated the impact of gravel size, shape, distribution, and other microstructural characteristics on the mechanical properties and mechanical behavior of S-RMs through extensive direct shear tests [1; 16; 17], in situ shear tests [18], laboratory large-scale triaxial tests [10; 19; 20], and numerical simulations [21; 22]. However, purely experimental methodologies prove insufficient for thoroughly elucidating the fundamental mechanical mechanisms governing S-RMs. S-RMs are heterogeneous and discontinuous granular materials [2] composed of irregular gravel and fine sand, which complicates the elucidation of their deformation patterns and failure mechanism when experimental research or traditional continuous-medium analysis methods are used. Moreover, it is nearly impossible to observe microstructural evolution in laboratory experiments. The discrete element method (DEM) offers a practical solution to these challenges. Numerous studies have demonstrated that the DEM is a practical approach for addressing discontinuity issues in granular materials [23], overcoming the limitation of assuming macro-level continuity in continuous-medium models. Starting from the contact forces between particles, the DEM identifies the constitutive relations at the contact points and constructs physical as well as mechanical models of these interactions. By establishing correlations between contact force, displacement, and velocity based on [PERSON]'s second law, the DEM enables numerical simulations of discontinuous particle behavior. The DEM provides a more reasonable approach to investigate the mechanical properties and micro-contact characteristics of S-RMs from the microscopic perspective and has been widely applied by researchers to simulate large-scale triaxial tests of S-RMs [24; 25]. Using a three-dimensional discrete element model, [PERSON] et al. [26; 27] conducted numerical simulations of large-scale direct shear tests on S-RMs with varying gravel content and shear strength.