## 2 Model Development and Numerical Computation  
### Establishment of Irregular Gravel Specimens in the DEM  
Due to the highly intricate distribution and geometrical shapes of the gravels in S-RMs, as well as their extraordinary randomness, constructing a realistic three-dimensional microstructure for these materials presents considerable challenges. In numerical simulation, researchers typically develop stochastic microstructure models that adhere to statistical significance [50; 51]. For sand particles, spherical particles with minimal variation in diameter are commonly selected for numerical simulation [52]. Nevertheless, S-RMs are heterogeneous materials characterized by distinct gradation, and the particle size distribution and shape significantly influence their mechanical properties [2; 3]. Therefore, when constructing a three-dimensional discrete element model of S-RMs, it is crucial to accurately reflect the differences between sand particles and gravel granules. It is essential to clarify that throughout the subsequent sections of this research, \"S-RM\" is consistently utilized to denote the complete specimen. \"Gravel clump\" is specifically adopted to represent gravel granule clusters within the numerical model, while \"sand particle\" is systematically used to refer to individual sand particles.  
To date, the commonly employed technique for establishing the microstructure of gravels includes the random generation technique [32] and the computer scanning method [53]. The random generation technique involves stochastically generating irregular granules by using mathematical functions. The computer scanning method utilizes CT scanning technology to scan the gravels in specimens and reconstruct their three-dimensional geometric patterns. To accurately model gravel granules with realistic shapes, this study integrates3D scanning technology and pebble filling algorithms to establish a three-dimensional microstructure model of S-RMs.  
With the assistance of the irregular gravel model database provided by the MEGGS team at Tsinghua University, 50 three-dimensional models of 'artificial gravel granules' were generated, as illustrated in Figure 1. By leveraging the contour profiles from this database and incorporating realistic grading and grain size distributions of S-RMs, appropriate scaling of the gravel granules was conducted to generate a set of gravels with varying gravel contents. Subsequently, these scaled gravels were stochastically distributed within the constructed model domain to establish a three-dimensional random microstructure model of S-RMs.  
In large-scale triaxial tests, a grain size of 5 mm is commonly used as the demarcation point between sand and gravel [25]. The gravel clumps were sized between 2.5 mm and 5 mm, while the sand particles had an approximate diameter of 0.5 mm. Based on these established parameters, microstructural models of S-RMs with distinct structural characteristics were developed.  
PFC3d 6.0 is numerical software with considerable reliability for investigating the micro-mechanical behavior between granules. The model dimensions were set to 60 mm in height and 30 mm in diameter. To examine the influence of gravel content on the micro-mechanical behaviors of the specimen, the microstructural models were developed under three consolidation states (\(\sigma_{3}=300\) kPa, 500 kPa, and 1000 kPa) and seven categories of gravel content (GC = 10%, 20%, 30%, 45%, 55%, 70%, and 80%), as illustrated in Figure 2. The specific composition of the specimen, as detailed in Table 1, guarantees that the overall void ratio is maintained within an optimal range, thereby guaranteeing the accuracy and reliability of the simulation results. The gravel content is rigorously defined as the volumetric ratio of gravel to the total volume of the S-RMs. During the entire loading process, neither boulder particle clusters nor soil particles undergo any loss.