## 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  
By studying the phenomena and laws of particle breakage, it is evident that particle breakage, density, and confining pressure significantly influence the strength characteristics of soil-rock mixtures. The linear Mohr-Coulomb strength criterion is commonly used for stability analysis. When dealing with soil-rock mixtures, it is important to consider cohesion when determining the internal friction angle. The Mohr-Coulomb strength criterion is employed to determine the cohesion in a linear manner. Soil materials typically fail through shear failure, and [PERSON] suggested the following equation for shear strength:  
\[\tau_{f}=c+\sigma\tan\varphi \tag{14}\]  
where \(\tau_{f}\) represents the shear strength, \(\sigma\) represents the normal stress, \(c\) represents the cohesion, and \(\varphi\) represents the internal friction angle. According to the data in Table 4, the Mohr circle and strength envelope under different dry densities are drawn. The internal friction angle estimates for large particles or rockfill made of weak minerals or weathered rocks clearly show a nonlinear strength envelope. When analyzing the stability of a waste slag rockfill dam, it is important to consider the nonlinear characteristics of the strength envelope of the soil-rock mixture under high confining pressure [34]. Assuming that the cohesion of the same dry density is constant, the internal friction angle is calculated using the nonlinear equation of the strength envelope. The nonlinear equation of the strength envelope [35; 36] is as follows:  
\[\tau_{f}=c+\sigma\tan(\varphi_{0}-\Delta\varphi lg\frac{\sigma_{3}}{\rho_{a}}) \tag{15}\]  
where \(\varphi\) represents the angle of internal friction when the continuous cohesion is extended in reverse to the point where the axis intersects the Mohr circle. represents the angle of internal friction under a pressure of one atmosphere. \(\Delta\varphi\) is a nonlinear parameter that signifies the reduction in \(\varphi\) over a logarithmic period as \(\varphi_{3}\) increases. \(p_{a}\) represents the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{\(\rho_{4}\)} & \multicolumn{3}{c}{\((\sigma_{1}-\sigma_{3})_{f}\)**kPa**} \\  & **g/cm\({}^{3}\)** & **100** & **200** & **400** & **800** \\ \hline
1 & 1.76 & 473.2 & 770.1 & 1350.8 & 2311.8 \\
2 & 1.82 & 548.8 & 906.5 & 1520.8 & 2610.8 \\
3 & 2.00 & 805.2 & 1085.6 & 1782.2 & 3083.1 \\
4 & 2.15 & 812.7 & 1150.3 & 1832.9 & 3196.0 \\
5 & 2.30 & 978.7 & 1383.9 & 2095.6 & 3587.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Peak shear stress and shear strength index under different dry densities. Figure 14: Relationship curve between the breakage index and failure dilatancy rate. atmospheric pressure, with a value of 101.3 kPa, which has the same unit as \(\sigma_{3}\). The values for \(\varphi\), \(\varphi_{0}\), \(\Delta\varphi\) and \(c\) can be found in Table 5. At the same time, draw the Mohr circle and strength envelope of the sample with dry density of 1.82 g/cm\({}^{3}\), as shown in Figure 15.  
Figure 16 displays the relationship curves between the confining pressure \(\sigma_{3}\) and internal friction angle \(\varphi\) at different densities, based on the data in Table 5. At a constant confining pressure \(\sigma_{3}\), increasing the dry density results in a greater internal friction angle \(\varphi\), more pronounced interparticle occlusion, and greater shear strength. The internal friction angle of the soil-rock mixture mostly originates from the sliding friction of particle surfaces and the occlusion friction between particles. As the confining pressure \(\sigma_{3}\) increases in this process, the binding force also increases, making it harder for particles to move across, leading to more severe particle breakage and increased particle breakage. As the bite force between particles diminishes, the internal friction angle \(\varphi\) and shear strength also decrease.