## 4 Results and Discussions  
### Damage Characteristics under Different Confining Pressures  
The crack initiation threshold (\(\sigma_{\text{ci}}\)), the crack damage threshold (\(\sigma_{\text{cd}}\)), the damage degree (\(D\)), and the tensile and shear crack ratio are used to investigate the damage characteristics of soft rock under different confining pressures and water immersion durations. Based on previous studies [47; 48; 49], this paper defines the stress corresponding to the first occurrence of tensile cracks as the crack initiation threshold, and the inflection point of the shear crack curve where it significantly increases as the crack damage threshold. The damage degree refers to the ratio of the length of broken contact elements to the total length of contact elements. The proportion of tensile (shear) cracks is the ratio of the number of tensile (shear) crack elements to the total number of contact elements. The number of cracks and the crack types are both identified and recorded using the built-in FISH language in UDEC software. Since the failure modes of heterogeneous models with different water immersion time are relatively similar, the influence of confining pressure on the damage and failure characteristics is investigated by taking the heterogeneous model in the natural state as an example. Figure 7 shows the relationship curves between stress, the number of tensile and shear cracks, damage degree, and strain of heterogeneous models under different confining pressures. The results indicate that the heterogeneous models first generate tensile cracks at the initial stage of loading, with the transverse strain linearly decreasing and the volumetric strain linearly increasing, indicating some degree of damage in the rock during the early stage of loading. Moreover, the relationship curves between the number of tensile and shear cracks and the damage degree with strain fluctuate significantly due to the significant divergence in mechanical properties between different components. As loading continues, the shear crack curves will all exhibit a clear increase in slope, the number of tensile cracks continues to increase, and the rock also exhibits characteristics of nonlinear deformation. As the confining pressure continues to increase, the relationship curves between the deviatoric stress and axial strain, transverse strain, and volumetric strain become more prominent in the post-peak stage, indicating that the greater the confining pressure, the greater the inhibiting effect on the failure of rock specimen. At the approach to the peak strength, the shear crack curves gradually tend to stabilize. Although the tensile cracks continue to increase, the rate of increase slightly slows down, indicating that the main tensile and shear cracks are generated before the strength. The failure mode under low confining pressure conditions (0 MPa and 1 MPa) is mainly characterized by \"X-type conjugate shear failure\". As the confining pressure continues to increase, the main failure mode is single-plane shear failure, with local features observable as \"X-type conjugate shear failure\". According to the fitting results shown in Figure 8, the crack initiation threshold, crack damage threshold, and damage degree all show a linear increase trend with the confining pressure. The tensile and shear crack ratio also have linear positive correlation with confining pressure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & **Elastic Modulus** & **Uniaxial Compression** & **Tensile Strength** & **Cohesion** & **Friction** \\  & **(GPa)** & **Strength (MPa)** & **(MPa)** & **(MPa)** & **Angle (\({}^{\circ}\))** \\ \hline Experimental values & 2.32 & 29.18 & 2.66 & 5.82 & 46.57 \\ Simulation values & 2.26 & 29.65 & 2.66 & 5.91 & 46.26 \\ Error & \(-2.59\%\) & \(1.61\%\) & \(0\%\) & \(1.55\%\) & \(-0.67\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results and errors of mechanical parameters of the heterogeneous model.