## 3 Results and Analyses
### Microscale Behaviors
#### 3.2.3 Contact Chain Skeleton Distributions of Contact Forces  
Leveraging the advantages of visualizing granular contacts through the DEM, Figure 10a illustrates the evolution of contact force chains during shearing processes in specimens with varying gravel proportions consolidated at a pressure level of 300 kPa--notably, the simulation results at consolidation pressures of 500 kPa and 1000 kPa exhibit consistent patterns. To provide a more comprehensive understanding of the role played by gravel in particle interaction, Equation (3), as detailed by [PERSON] [70], was employed to calculate the stress distribution within the contact network. The resulting percentage contributions are visually depicted in Figure 10b. In this figure, distinct colors represent specific types of contact forces: black indicates inter-clump contact forces between gravel clumps, green signifies contact forces between gravel and sand, and white denotes inter-sand particle contact forces. The thickness of the contact force chains reflects their relative magnitude after homogenization: robust contact forces are represented by thicker chains, whereas thinner chains indicate minor contact forces. The force chain distribution method [2] has become a widely adopted microscopic approach for elucidating the shear behavior of S-RMs. \[\frac{q}{p^{\prime}}=\xi_{gg}\sum\alpha^{gg}_{s}+\xi_{gs}\sum\alpha^{gs}_{s}+ \xi_{ss}\sum\alpha^{ss}_{s} \tag{3}\]  
where \(q\) is the deviatoric stress; \(p^{\prime}\) is the effective mean stress; \(\xi_{gg}\), \(\xi_{gs}\), and \(\xi_{ss}\) represent the weight parameters associated with three contact forces; and \(\alpha^{ss}_{s}\), \(\alpha^{ss}_{s}\), and \(\alpha^{ss}_{s}\) are the anisotropy coefficients of the three classifications of contact force. Upon a meticulous examination of Figure 10a, it is evident that the specimen has undergone complete consolidation, and the size and distribution of contact force chains between particles exhibit a relatively homogeneous nature, indicative of an isotropic state of consolidation. As axial strain increases, contact force chains in the specimen gradually accumulate from the loading direction (top-down) to form a predominant top-down contact force chain skeleton, aligning with the macroscopic loading path. When the gravel content in the S-RM is low (GC = 10%, 20%, and 30%), sand particles dominate the primary force chain subnetwork within the specimen, resulting in the mechanical properties of the S-RM being predominantly governed by these sand-sand (S-S) interactions. With an increase in gravel content (GC = 45% and 55%), the primary loading-bearing force chain shifts to being supported by contact forces between gravel clumps and sand particles (G-S). Consequently, the mechanical characteristics of S-RMs are significantly influenced by these G-S interactions. When the gravel content is high (GC = 70% and 80%), the dominant force chain skeleton is primarily provided by the interlocking forces between gravel clumps (G-G). Therefore, the mechanical properties of gravel become pivotal factors in determining the overall mechanical behavior of S-RMs. Based on the data presented in Figure 6, it is observed that when the gravel content is 20% (GC = 20%), the strength of the specimen is comparatively lower than that of S-RMs with GC = 10% and 30%. This discrepancy arises from variations in the composition of force chains within the main body skeleton owing to changes in gravel content. Specifically, at a gravel content of 10%, sand particles primarily bear the load and maintain a clear and well-defined main body skeleton structure. However, as the gravel content increases, alterations in force chain distribution lead to a less distinct main body skeleton, resulting in reduced shear strength. The contact stiffness, \(k_{ss}^{n}\), between gravel clumps and sand particles is greater than the contact stiffness, \(k_{ss}^{n}\), among sand particles.