## 2 A Brief Introduction of the Model Test
The maximum wave velocity \(v_{0}\) was defined as the wave velocity of the undamaged rock, so the initial damage variable \(D_{0}\) of the rock can be defined by the following equation, when the value of \(D_{0}\) is 0 and 1, respectively, indicating that the rocks are in an undamaged and fully damaged stage. \[D_{0}=1-(\frac{v_{1}}{v_{0}})^{2} \tag{3}\]  
where, \(v_{1}\) is the stress wave velocity under different static loads. Therefore, through Figure 4, the initial damage variable \(D_{0}\) variation curve of the rock under different biaxial static loads can be derived, as shown in Figure 5, while the initial damage value of the rock was considered to be 1 when the biaxial static load reached the biaxial compressive strength. Based on the five data samples in Figure 5, including four experimental data points and one data point that characterized the failure of the intact rock obtained by mechanical analysis, the fitting equation was obtained by the least square polynomial fitting as shown in Equation (4), and the adjusted R-square and residual sum of squares of the equation were 0.994 and 1.034 \(\times\) 10\({}^{-4}\), respectively. \[D_{0}=0.11253-0.18321\sigma_{b}+0.08918\sigma_{b}{}^{2}-0.00655\sigma_{b}{}^{3} \tag{4}\]  
The above equation is the initial damage evolution equation considering the compaction effect of the microcracks inside the rocks under different biaxial static loads. In addition, since the object studied in this section is the intact rock without macroscopic fractures, the initial damage evolution within the rocks can be assumed to be isotropic. Figure 1:0 Relationship between the stress wave velocity and the static load of the intact rock. Figure 1:1 Relationship between the initial damage variable and the static load of the intact rock. After the evolution equation of the initial damage variable \(D_{0}\) was determined, it was coupled with the internal Mohr-Coulomb elasto-plastic model in UDEC to establish the improved model considering the initial damage for the intact rock. Based on the Lemaite strain equivalence principle, the principal stress tensor \(\sigma_{i}\) and the effective principal stress tensor \(\widetilde{\sigma}_{i}\), the bulk modulus \(K\) and the initial damage bulk modulus \(\overline{K}\), the shear modulus \(G\), and the initial damage shear modulus \(\overline{G}\) should satisfy the following relationships:  
\[\left\{ \begin{array}{l}\widetilde{\sigma}_{i}=\sigma_{i}/(1-D_{0})\\ \overline{K}=(1-D_{0})K\\ \overline{G}=(1-D_{0})G\end{array} \right. \tag{5}\]  
After the bulk modulus \(\overline{K}\) and the shear modulus \(\overline{G}\) containing the initial damage factor \(D_{0}\) were obtained, the relationship between the stress increment \(\Delta\sigma_{i}\) and the strain increment \(\Delta\varepsilon_{i}\) in the Mohr-Coulomb elastic-plastic model of the rocks was given by:  
\[\Delta\sigma_{i}=\overline{\lambda}\delta_{i}\Delta\varepsilon_{i}+2\overline {G}\Delta\varepsilon_{i} \tag{6}\]  
where, \(\overline{\lambda}\) is the Lame constant of the damaged rock and \(\delta_{i}\) is the Kronecker symbol. Meanwhile, both the rock yield damage function and the plastic flow law within the Mohr-Coulomb elasto-plastic constitutive model were changed to functions based on the effective principal stress tensor \(\widetilde{\sigma}_{i}\), and the Mohr-Coulomb elasto-plastic constitutive model considering the initial damage was established.