## 3 Engineering Geological Model
### Parameter Calibration  
The micro-parameters in PFC differ from the macro-mechanical parameters of materials. Consequently, it is common and essential to adjust the micro-parameters of various groups in the numerical model until the modeled macro-mechanical properties (such as the compressible strength, tensile strength, shear strength, and elastic modulus, etc.) are consistent with the results from the laboratory tests. The shear strength parameters of mudstone and brown shale were obtained from the field investigation data (as shown in Table 1). To get similar macro-shear strength parameters, biaxial compression tests and direct shear tests were conducted in this study. Under a confining pressure of 0, 5, or 10 MPa, a set of biaxial compression tests was carried out to obtain the stress-strain curves. Then, a Mohr-Coulomb failure envelope was depicted to calculate the relevant strength and deformation parameters [35; 40; 41; 42]. If the obtained macro-parameters (cohesion, internal friction angle, and Yong's modulus in this study) were similar to the field investigation data, the micro-parameters of PBM were considered to be available. The SJM parameters come from shear tests of a fractured specimen. The strength and stiffness of the LM were lower than that of the bond in the two sides of the bedding plane in this study. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Strength Parameters**} & \multicolumn{5}{c}{**Rock Type**} \\ \cline{2-6}  & \multicolumn{2}{c}{**Mudstone**} & \multicolumn{2}{c}{**Brown Shale**} \\ \cline{2-6}  & **Field Investigation Data** & **PFC 2D** & **Field Investigation Data** & **PFC 2D** \\ \hline \(\rho\) (kg/m\({}^{3}\)) & 2300 & 2300 & 2100 & 2100 \\ \(c\) (0.1 MPa) & 1.50 & 1.62 & 3 & 2.96 \\ \(\varphi\) (\({}^{\circ}\)) & 30.0 & 30.0 & 17.0 & 16.2 \\ \(E\) (GPa) & 3 & 2.85 & 3 & 2.93 \\ \hline \hline \end{tabular} Note: \(\rho\) is density, \(c\) is cohesion, \(\varphi\) is frictional angle, and \(E\) is Yong’s modulus. \(c\) and \(\varphi\) are calculated by \(\tau=c+\sigma_{n}lung\), which is an envelope line of Mohr’s circle according to the biaxial tests. \(E\) is the ratio of the 50% uniaxial compression strength and the 50% axial strain, which is from the uniaxial compression test.  
\end{table} 
Table 1: Strength parameters from the field investigation data and PFC 2D. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Rock Type**} & \multicolumn{2}{c}{**Particle Parameters**} & \multicolumn{5}{c}{**Parallel Bond Parameters**} \\ \cline{2-9}  & \(R\) **(m)** & \(E_{c}\) **(GPa)** & \(K_{n}\)/\(K_{s}\)** & \(\frac{-}{E_{c}\) **(GPa)**} & \(\frac{-}{K_{n}}\)/\(K_{s}\)** & **Normal Strength (MPa)** & **Shear Strength** (MPa)** & **\(\mu\)** \\ \hline Mudstone & 0.1-0.15 & 0.064 & 1.0 & 0.064 & 1.0 & 3.86 & 1.56 & 0.20 \\ Brown shale & 0.12-0.18 & 0.048 & 1.4 & 0.048 & 1.4 & 1.66 & 1.22 & 0.25 \\ \hline \hline \end{tabular} Note: There is no direct functional relationship between the micro- and macro-parameters. Thus, the micro-parameters cannot be obtained from the equations in PFC. \(R\) is particle size, \(E_{c}\) is the particle contact module, \(K_{n}\) and \(K_{s}\) are the normal stiffness and tangential stiffness of the particle, respectively. \(\overline{E}_{c}\) is the parallel bond module, \(\overline{K}_{n}\) and \(\overline{K}_{s}\) are the normal stiffness and tangential stiffness of the parallel bond, respectively, and \(\mu\) is the friction coefficient of the parallel bond.  
\end{table} 
Table 2: Calibrated micro-mechanical properties of the PBM.