## 3 Parameter Calibration
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline \multirow{2}{*}{**Contact Types**} & **Normal Penalty** & **Tangential Penalty** & **Contact Tensile** & **Contact Cohesion** & **Contact Friction** \\  & **(\(\times\)10\({}^{3}\) GPa/m)** & **(\(\times\)10\({}^{3}\) GPa/m)** & **Strength (MPa)** & **(MPa)** & **Angle (\({}^{\circ}\))** \\ \hline Cement–cement & 14.5 & 5.8 & 3 & 8.1 & 10 \\ Quartz–quartz & 800 & 336 & 33 & 28 & 25 \\ Feldspar–feldspar & 350 & 140 & 36 & 24.5 & 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Contact parameters between the same components. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline \multirow{2}{*}{**Parameters**} & **Elastic Modulus (GPa)** & **Uniaxial Compression Strength (MPa)** & **Tensile Strength (MPa)** & **Cohesion (MPa)** & **Friction Angle (\({}^{\circ}\))** \\ \hline Experimental values & 2.32 & 29.18 & 2.66 & 5.82 & 46.57 \\ Simulation values & 2.36 & 29.99 & 2.41 & 5.75 & 46.85 \\ Error & 1.72\% & 2.78\% & \(-9.36\%\) & \(-1.20\%\) & 0.60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results and errors of mechanical parameters of the homogeneous model. For the contact parameters between different components, the average value of the contact parameters of two same components is taken in this paper, but the simulated uniaxial compressive strength and tensile strength are much higher than the mechanical parameters of silty mudstone under experimental conditions. Therefore, this paper simultaneously increases or decreases the same proportion factor for the contact parameters of the six contact types, and the calibrated contact parameters are shown in Table 4.  
Biaxial compression tests under various confining pressures and Brazilian splitting tests were simulated based on Table 4, with the results shown in Figure 6 and Table 5. The simulation results indicate that the failure modes simulated under uniaxial compression and Brazilian splitting conditions are highly consistent with those observed under experimental conditions. As can be seen from Figure 6c, the axial peak stresses under different confining pressures are 29.77 MPa, 35.91 MPa, 41.70 MPa, 53.46 MPa, and 79.56 MPa, respectively. The errors compared to the experimental results are 2.02%, 4.91%, \(-\)6.27%, 3.18%, and \(-\)1.14%, respectively. According to Table 5, the simulation error of elastic modulus is the  
Figure 5: Simulation results based on calibration parameters: (**a**) uniaxial compression simulation curve and failure mode; (**b**) Brazilian fracture simulation curve and failure model; (**c**) simulation error of the peak axial stresses under different confining pressures; and (**d**) stress–strain simulation curves of the quartz and feldspar models. largest, which is only \(-2.59\%\). The simulation errors for the other parameters are all less than \(2\%\). Therefore, the mechanical parameters in Table 4 are reasonable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Contact Types** & \begin{tabular}{c} **Normal Penalty** \\ **(\(\times 10^{3}\) GPa/m)** \\ \end{tabular} & \begin{tabular}{c} **Tangential Penalty** \\ **(\(\times 10^{3}\) GPa/m)** \\ \end{tabular} & \begin{tabular}{c} **Contact Tensile** \\ **Strength (MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Contact Cohesion** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Contact Friction** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} \\ \hline Quartz–quartz & 3.05 & 1.28 & 14.52 & 12.32 & 11.00 \\ Quartz–feldspar & 2.19 & 0.91 & 15.18 & 11.55 & 10.56 \\ Quartz–cement & 1.55 & 0.65 & 7.92 & 7.94 & 7.70 \\ Feldspar–feldspar & 1.34 & 0.53 & 15.84 & 10.78 & 10.12 \\ Feldspar–cement & 0.7 & 0.28 & 8.58 & 7.17 & 7.26 \\ Cement–cement & 0.06 & 0.02 & 1.32 & 3.56 & 4.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Finalized meso-scale contact parameters of the six contact types.