## 3 Large-Scale Triaxial Test on the Shear Failure Characteristics of a Soil-Rock Mixture
### Analyzing the Impact of the Breakage Index \(B_{C}\) on the Strength Characteristics
At the same time, increasing the dry density results in a higher nonlinear parameter \(\Delta\varphi\) and leads to a greater nonlinear shear strength of the sample. \begin{table}
\begin{tabular}{c c c c c c} \hline \(\rho_{d}\) **(g/cm\({}^{3}\))** & \(\sigma_{3}\) **(kPa)** & \(\varphi\) & \(\varphi_{0}\) & \(\Delta\varphi\) & \(c\)**/kPa** \\ \hline  & 100 & 36.63 & & & \\  & 200 & 36.33 & & & \\
1.76 & 400 & 36.00 & & & \\  & 800 & 35.01 & & & \\  & 100 & 38.55 & & & \\  & 200 & 38.10 & & & \\
1.82 & 400 & 37.66 & & & \\  & 800 & 36.46 & & & \\  & 100 & 40.86 & & & \\
2.00 & 200 & 39.42 & 40.60 & 2.46 & 109 \\  & 400 & 39.30 & & & \\  & 800 & 38.43 & & & \\  & 100 & 41.45 & & & \\
2.15 & 200 & 40.51 & & & \\  & 400 & 39.72 & 41.34 & 2.71 & 112 \\  & 800 & 39.20 & & & \\  & 100 & 43.85 & & & \\
2.30 & 200 & 43.09 & & & \\  & 400 & 41.66 & 43.76 & 3.14 & 127 \\  & 800 & 41.11 & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Shear strength parameters of samples with different dry densities. Figure 15: Mohr circle and strength envelope diagram of sample with dry density of 1.82 g/cm\({}^{3}\). The analysis presented in Figure 16 demonstrates that as the confining pressure increases, particle breakage intensifies, resulting in a slower reduction in the internal friction angle \(\varphi\). Overall, the internal friction angle exhibits a nonlinear trend. This is because with a further increase in the confining pressure, particle breakage or deformation occurs, leading to changes in the surface shape and structure of some particles. Consequently, the magnitude and distribution of the friction force also change. The contact region between soil particles tends to become saturated, and further increasing the confining pressure has little effect on the soil. Therefore, particle breakage is a significant contributing factor to the nonlinear trend of the internal friction angle. Figure 17 displays the correlation between the breakage index \(B_{C}\), fractal dimension \(D\), and internal friction angle \(\varphi\) at various dry densities. Figure 17a illustrates a clear correlation between the particle breakage and internal friction angle \(\varphi\). At the same dry density, with increasing breakage index \(B_{C}\), the internal friction angle \(\varphi\) gradually decreases, and the internal friction angle \(\varphi\) exhibits a nonlinear trend, which is consistent with the conclusion of the above relationship curve between the confining pressure \(\sigma_{3}\) and the internal friction angle \(\varphi\). For fractal dimension \(D\), the larger the fractal dimension \(D\), the higher the degree of breakage [15]. As can be seen from Figure 17b, with the increase in fractal dimension d, the internal friction angle also shows a decreasing trend. Comparing the two relationship curves shows that the decreasing trend of the internal friction angle \(\varphi\) is similar under different dry densities in both panels of Figure 17a,b, indicating the rationality of using the improved breakage index \(B_{C}\) to analyze the strength characteristics. Figure 16: Relationships between the confining pressure \(\sigma_{3}\) and internal friction angle \(\varphi\). Figure 17: Relationship between the internal friction angle and the particle breakage index. (**a**) Relationship curve between the breakage index and internal friction angle. (**b**) Relationship curve between the fractal dimension and the internal friction angle.