## 3 Results and Analyses
### Microscale Behaviors
#### 3.2.1 Probability Distributions of Contact Force  
In this study, the distribution of contact forces under varying gravel contents is compared using a normalized approach. Specifically, the average contact force, \(f_{0}^{n}\), within the specimen particles is determined using Equation (2). Subsequently, the contact forces between all granules in the specimen are normalized relative to this mean intuitive assessment. [PERSON] et al. [46] classified contact forces into two categories: strong and weak contact forces [68], based on the average contact force, \(f_{0}^{n}\), within the granule system. By analyzing the distribution of strong and weak contact forces in S-RM samples with different gravel contents, this research aims to investigate the skeleton force chain system from a microscopic perspective.  
\[f_{0}^{n}=\frac{\sum f_{n}^{ss}+\sum f_{n}^{gs}+\sum f_{n}^{gs}}{N_{ss}+N_{gs}+ N_{gs}} \tag{2}\]  
where \(f_{n}^{ss},f_{n}^{gs}\), and \(f_{n}^{gs}\) denote the magnitudes of three distinct contact forces, while \(N_{ss}\), \(N_{gs}\), and \(N_{gs}\) represent their corresponding frequencies.  
The evolution of the contact force distribution in an S-RM specimen during the loading process is illustrated in Figure 8 under a consolidation pressure of \(\sigma_{3}\) = 300 kPa. Upon isotropic consolidation, the normal contact forces within the system exhibit a Gaussian  
Figure 7: Particle rotation cloud diagrams of S-RMs with varying gravel contents under different axial strains.  
distribution, which remains unaffected by variations in gravel content. The distribution of the normal contact forces is primarily concentrated around the average contact force, \(f_{0}^{n}\), with the highest density observed near this value. The yellow line in the figure represents the average contact force, \(f_{0}^{n}\). During the loading phase, a significant alteration in the distribution of contact force density is observed: when the gravel content is less than 30%, the density of weak force chains is relatively low. According to Figure 9a, it is observed that the current state of the force chain skeleton in S-RMs is primarily constituted by the contact forces between sand particles. Due to the relatively low stiffness of these contact forces, the overall distribution of force chains remains relatively uniform. When sand particles predominate as the main component of the force chain skeleton, there are fewer weak force chains and a higher proportion of strong force chains (Figure 8a, P = 0.044; Figure 8b, P = 0.043; and Figure 8c, P = 0.042). As the gravel content increases, the integrity of the contact force chain begins to change significantly. Compared with the consolidated state, the number of strong chains decreases markedly (Figure 8d, \(P_{0}\) = 0.05, P = 0.034; Figure 8e, \(P_{0}\) = 0.045, P = 0.030). Specifically, when the gravel content exceeds 70%, the number of weak force chains increases sharply (Figure 8f, P = 0.020; Figure 8g, P = 0.010). In contrast to Figure 10a, in this scenario, gravel clumps form the dominant force chain skeleton through contact forces, resulting in high stiffness but limited quantity, leading to a significant increase in weak contact density. When comparing S-RM specimens with different gravel contents, the distribution probability of contact forces between sand and gravel exhibits similar patterns during the loading process and isotropic consolidation. Although the distribution pattern of strong chains shows a consistent trend, the distribution probability of weak chains varies. Therefore, by calculating the interval of the probability density function values of weak force chains, the primary components of the force chains in samples with different gravel contents can be distinguished.