## 3 Model Validation and Analysis
### Parameter Determination of Equivalent Strain-Softening Model  
The rock mass volume \(V_{b}\) and structural plane condition factor \(J_{C}\) ranges are estimated according to Equations (1) and (2) in line with the on-site construction documentation, surveying, and mapping data. The calculation results are then substituted into Equation (3). The GSI value of the surrounding rock in this section is estimated to be between 58 and 63; thus, we take an average value of GSI = 60. A disturbance coefficient of rock mass \(D\) = 0 is taken according to the on-site excavation situation. The parameters in Equations (12)-(17) can be obtained by field observations. The uniaxial compressive strength of the intact rock  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Confining Pressure\(\sigma_{3}\)/MPa** & \(\sigma_{3}\) = 0 & \(\sigma_{3}\) = 1 & \(\sigma_{3}\) = 3 & \(\sigma_{3}\) = 7 \\ \hline Peak stress/MPa & 4.156 & 5.534 & 8.399 & 14.305 \\ Peak strain/\(10^{-2}\) & 0.875 & 1.289 & 2.068 & 3.882 \\ Residual stress/MPa & 0.709 & 1.787 & 3.812 & 8.051 \\ residual strain/\(10^{-2}\) & 1.668 & 4.148 & 6.134 & 10.115 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Compression test results for tuffaceous mudstone.  
Figure 6: Test specimens and experimental setup.  
Figure 7: Triaxial testing of tuffaceous mudstone under different confining pressures.  
mass is \(\sigma_{c}=4.156\) MPa < 100 MPa. The elastic modulus \(E\) can, therefore, be calculated according to the formula proposed by [PERSON] et al. (2016):  
\[E=\left(1-\frac{D}{2}\right)\sqrt{\frac{\sigma_{c}}{100}}\times 10^{\left[\left(GS 1-10\right)/40\right]} \tag{22}\]  
When a strain-softening model is solved using FLAC\({}^{\text{3D}}\) numerical software, the model softening parameter \(e^{ps}\) can be calculated by:  
\[e^{ps}=\frac{\sqrt{3}}{3}\sqrt{1+K_{\varphi}+K_{\psi}{}^{2}}\frac{\gamma^{p}}{ 1+K_{\psi}} \tag{23}\]  
The \(m_{i}\) value for the material parameters of different rocks can generally be evaluated using empirical tabular methods or according to:  
\[m_{i}=\sigma_{\text{c}i}/\left|\sigma_{t}\right| \tag{24}\]  
where \(\sigma_{t}\) is the uniaxial tensile strength of intact plutons. It is worth noting that the empirical tabular method heavily relies on practical engineering experience, which subjects the determination of the material parameters to some subjectivity and results in certain estimation errors. The \(m_{i}\) values can be evaluated using the theory of Equation (24), but are generally not easily calculated owing to the difficulty in obtaining the rock uniaxial tensile strength. [PERSON] et al. (2016, 2016) proposed that \(m_{i}\) be considered as an empirical fitting parameter and the construction of an \(m_{i}\) fitting formula on the basis of a large number of triaxial experiments. [PERSON] et al. (2016) proposed a negative exponential model for the relationship of \(m_{i}\) and the circumferential pressure, and fitted the model parameters using three-axis experimental data from multiple rocks to verify the rationality of the model. In this paper, the material parameter \(m_{i}\) of rock mass under different confining pressures is determined by the method presented in [PERSON] et al. (2016). The determination of \(m_{i}\) in combination with Equation (7) using the H-B constant \(m_{b}\) is listed in Table 2 and the model parameters are summarized in Table 3.