## 4 Conclusions  
Utilizing flexible boundary loading conditions, this study conducted discrete element numerical simulations of triaxial drainage shear tests on irregularly shaped S-RMs with varying gravel contents and consolidation confining pressures. The irregularly shaped gravels were generated by CT scanning technology and pebble filling algorithms, aiming to more accurately replicate the geometric characteristics of natural geological materials. The study primarily focused on the comparative analysis of macroscopic mechanical behaviors of S-RM specimens during the loading process, particularly the macroscopic failure patterns, shear band evolution, and shear resistance capacity, as well as the microscopic contact force distribution, composition of the contact force chain skeleton, and evolution of fabric tensor characteristic quantities. The findings indicate that this integrated approach has made significant advancements in understanding the mechanical behavior of binary granular materials, extending beyond S-RMs:  
1. The strength of S-RMs is intricately correlated with the gravel content and consolidation state. The relationship between the shear strength of S-RMs and gravel content is  
Figure 13: The evolutionary trend of the anisotropic coefficient, \(\alpha^{\pi}\), in S-RMs. nonlinear, with a qualitative threshold identified in this study as 20% gravel content (this threshold may vary depending on parameter changes): when the gravel content reaches this threshold, the shear bearing capacity of the S-RM specimen decreases to its minimum value. Beyond this threshold, the shear strength of the specimens gradually increases; conversely, when the gravel content is below this threshold, the shear strength decreases. This indicates that insufficient addition of gravels to the sand does not significantly enhance the overall shear strength of the specimens. This conclusion not only applies to S-RMs but can also be extended to other binary granular materials. Additionally, the shear strength of S-RMs increases with increasing confining pressure, consistent with traditional understanding. 2. In discrete element numerical simulation, the selection of boundary conditions for triaxial experiments is of critical importance. When a flexible boundary composed of particles is employed, the S-RM specimens exhibit lateral expansion failure, forming asymmetric 'X'-shaped shear bands consistent with laboratory observations. Moreover, it is noteworthy that the failure pattern, size, and distribution of the shear bands are influenced not only by the gravel content but also significantly depend on the consolidation confining pressure. This observation intuitively underscores the unique characteristics of S-RMs as heterogeneous granular materials. 3. The macroscopic mechanical behavior of S-RMs has been investigated from the microscopic perspective of the contact force network. The contributions of three types of contact forces (\(f^{ss}\), \(f^{ss}\), and \(f^{SS}\)) to the critical shear strength were quantified at the microscale, and the evolution of strong and weak contacts within the contact force chain system was analyzed. This study integrated the analysis of the microscopic contact force chain distribution to reveal the mechanisms governing the transformation of the main skeleton of the contact force chain during the transitions between'single-phase' and'mixed-phase' states. Furthermore, the prominence of the main skeleton of the contact force chain significantly enhanced the shear resistance capacity of the specimens, and the higher shear strength further amplified these effects. In addition, observations in S-RMs with varying gravel contents revealed that the probability distribution of contact forces and the three-dimensional polar coordinate distribution of branch vectors indicated an increasing trend in the distribution of weak force chains and contact forces in non-loading directions as gravel content increased, thereby accentuating the primary structure of the contact force chain skeleton. 4.