## 3 Results and Analyses
### Microscale Behaviors
#### 3.2.4 Analysis of Fabric Tensor in Contact Force Chain Skeletons  
Under the influence of a continuous load, particles within the particulate-medium material system undergo translational or rotational adjustments to achieve overall stabilization of the specimen. During this process, the granule arrangement within the specimen exhibits various configurations in response to loading effects, resulting in diverse microstructures. Laboratory test data from numerous scholars have indicated that granular soil exhibits significant anisotropy in its mechanical behavior upon reaching the critical state [67,68]. Additionally, studies by other researchers [69] have shown that granular materials display distinct anisotropic structures when in the same consolidation state during the critical state. Given the multiphase nature of S-RMs and their substantial research significance, this study selects the average coordination number (\(CN\)) and the anisotropy coefficient (\(a^{\prime}\)) to investigate the intrinsic relationship between the fabric characteristics and the main contact force chain skeleton of S-RM specimens at the critical state. The average coordination number, \(CN\):  
The variation in the average coordination number (\(CN\)) of S-RM specimens under different gravel contents and confining conditions (\(\sigma_{3}\) = 300 kPa, 500 kPa, and 1000 kPa) during shearing is illustrated in Figure 11. This study identifies three local contact modes  
Figure 10: (**a**) Evolution of contact force chain in a soil–rock mixture specimen under 300 kPa consolidation condition. (**b**) Influence of gravel features on shearing behavior evaluated by contact behavior. between gravel clumps and sand particles: the contact between gravel clumps (\(f^{SS}\)), the contact between gravel clumps and sand particles (\(f^{SS}\)), and the contact between sand particles (\(f^{ss}\)). The average coordination numbers, \(CN_{gg}\), \(CN_{gs}\), and \(CN_{ss}\), for these partial contact forces can be calculated using Formula (4), provided by [PERSON] (2017):  
\[CN=CN_{gg}+CN_{gs}+CN_{ss} \tag{4}\]  
\[CN_{gg}=2N_{gg}/N_{g} \tag{4a}\] \[CN_{gs}=2N_{gs}/\left(N_{g}+N_{s}\right)\] (4b) \[CN_{ss}=2N_{ss}/N_{s} \tag{4c}\]  
where \(N_{g}\) and \(N_{s}\) are the numbers of gravel clumps and sand particles, respectively. The average coordination number remains relatively constant under similar consolidation pressures during compaction. However, varying states of consolidation pressure result in distinct differences in the particle structure of S-RMs, indicating a more tightly packed arrangement under higher confining pressure. During the shear process, the average coordination number of the S-RM samples rapidly decreases within a small strain range before stabilizing. This trend is closely associated with an increase in gravel content and is independent of the initial consolidation state. Moreover, the increase in gravel content is associated with a decrease in the stable average coordination number of the specimen. This can be attributed to the agglomeration of larger particle clumps, leading to a reduction in fine particles (such as sand particles) within the void structure and subsequently diminishing the number of inter-particle contacts formed in localized areas inside the specimen. Detailed observations from Figure 11a-c show that the S-RMs with sand as the primary particle framework (GC = 10%, 20%, 30%) rapidly achieve mechanical stability within a limited strain range (\(\varepsilon\leq 2\%\)), demonstrating consistent stability values. As gravel content increases, the primary load-bearing framework shifts to contact forces generated within the gravel clumps and sand particles (GC = 45%, 55%). Consequently, the time required for the average coordination number to stabilize increases (\(\varepsilon\approx 12\%\)), while characteristic \(CN\) values remain consistent in this stabilized condition.