## 3 Parameter Calibration  
According to Section 2, the meso-scale parameters of the cement can be directly based on the mechanical parameters obtained in the experiments. For minerals, several literature and rock mineral monographs [39; 44; 45; 46] provide the basic mechanical parameters. The mechanical parameters of the three material components are summarized in Table 1. Regarding the meso-scale parameters for the six types of contacts, the contact parameters between the same components were first calibrated. In this paper, the numerical model is regarded as a virtual model containing only quartz or feldspar or cement. The contact parameters for cement-cement contact are equivalent to those of the homogeneous soft rock model. The calibration of the meso-scale contact parameters for the homogeneous model in its natural state are targeted at the average values of the mechanical parameters obtained  
Figure 4: Time-dependent GB-DEM model considering softening effect. from experiments. The uniaxial compression, Brazilian splitting, and biaxial compression numerical tests are then conducted. For quartz-quartz and feldspar-feldspar contact, only uniaxial compression numerical tests are conducted to calibrate the uniaxial compressive strength and elastic modulus. The meso-scale parameters of contact types between the same components after trial-and-error process are shown in Table 2, and the simulation results are shown in Figure 5 and Table 3. According to Figure 5a,b, the failure modes under uniaxial compression and Brazilian splitting conditions are primarily dominated by single-plane shear failure and splitting tensile failure, respectively, which are in good agreement with the failure modes under experimental conditions. Due to the inherent pores and fractures in the soft rock, it often undergoes a stage of pore and fracture compaction under loading conditions. Therefore, the initial slope of the axial stress-strain curve under experimental conditions is relatively small and gradually increases, which is different from the numerical simulation results. As shown in Table 3, except for the tensile strength with an error of \(-9.36\%\), which is relatively large, the simulation errors for the other parameters are at most \(2.78\%\), indicating that the meso-scale parameters of cement-cement contact are reasonable. Figure 5c shows that the axial peak stresses under different confining pressures are \(29.99\) MPa, \(35.5\) MPa, \(41.3\) MPa, \(53.6\) MPa, and \(80.9\) MPa, respectively. Compared to the experimental results, the simulation errors are \(2.81\%\), \(3.71\%\), \(-7.17\%\), \(3.45\%\), and \(0.52\%\), respectively. Except for the error at a confining pressure of \(2\) MPa, which is greater than \(5\%\), the rest of the errors are relatively small. Moreover, according to the simulation results of the virtual mineral model shown in Figure 5d, the uniaxial compressive strength and elastic modulus of quartz and feldspar are \(224\) MPa and \(80.2\) GPa, \(181\) MPa and \(56\) GPa, respectively, with errors of \(0.90\%\) and \(-0.99\%\), \(0.56\%\), and \(0.00\%\). \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}{*}{**Components**} & **Density** & **Elastic Modulus (kg/m3)** & **Poisson’s (GPa)** & **Uniaxial Ratio** & **Tensile Compression Strength (MPa)** & **Cohesion (MPa)** & **Friction Angle (\({}^{\circ}\))** \\ \hline Quartz & 2650 & 81 & 0.19 & 222 & 10–33.8 & \(\backslash\) & \(\backslash\) \\ Feldspar & 2600 & 56 & 0.27 & 180 & 36 & \(\backslash\) & \(\backslash\) \\ Cement & 2270 & 2.32 & 0.27 & 29.18 & 2.66 & 5.82 & 46.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic mechanical parameters of the material components.