## 3 Experiment and Calibration  
In order to make the simulation results conform to the physical properties of rock materials, the rock was first tested under uniaxial compression, and then the micro-parameters calibrated according to the test results were used as the benchmark for further study. The rock material used in the test was sandy mudstone (Figure 1a), which was taken from \(-437.62\) m of buertai mine, Shandong mining area, Inner Mongolia, China. The main mineral compositions of rock materials were analyzed by D/max-2500 X-ray diffractometer in the School of materials science and engineering, Shandong University. The content of clay mineral was 34.8%, quartz was 51.9%, K-feldspar was 5.6%, and plagioclase was 7.7%. The rock was made into a standard rock sample with a height of 100 mm and a radius of 25 mm. The test loading rate was 1 mm/min. A cylindrical model with a height of 100 mm and a radius of 25 mm was constructed using PFC3D, and the damping coefficient used in the experiment was 0.7. Specimens were loaded using the top and bottom walls during uniaxial compression. A loading rate of 0.1 m/s was used in the simulation process to ensure the comparability and prevent interference of the loading rate on the results [26; 44] (Quasi-static modeling with PFC3D usually made usage of a high local damping coefficient to efficiently remove kinetic energy from the system. Therefore, typical quasi-static deformation could be performed at a much higher rate than in real experiments [26]. Because of the high damping coefficient used, the loading rate in PFC was different from that used in the actual test [42]. The loading rate of 0.1 m/s could meet the requirements of PFC3D uniaxial compression simulation). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**References**} & **Value Range of Bond** & **Influence Degree of** & \\  & **Normal-to-Shear** & **Bond Normal-to-Shear** & **Note** \\  & **Stiffness Ratio** & **Stiffness Ratio on UCS** & \\ \hline [PERSON], [PERSON] et al. [19] & 0.6–3.6 & Not significant & PFC3D \\ [PERSON], [PERSON] et al. [38] & 0–0.8 & Not considered & PFC3D \\ [PERSON], [PERSON] et al. [21] & 0.1–6 & Not considered & PFC2D \\ [PERSON], [PERSON] et al. [20] & 0.6–2 & Not significant & PFC2D \\ [PERSON], [PERSON] et al. [22] & 1–5 & Not significant & PFC2D \\ [PERSON], [PERSON] [18] & 0.5–10 & Not significant & PFC2D \\ [PERSON] et al. [43] & 1–100 & Not considered & PFC3D \\ \hline \hline \end{tabular}  
* Uniaxial compressive strength (UCS), three-dimensional particle flow code (PFC3D), two-dimensional particle flow code (PFC2D)  
\end{table} 
Table 1: Summary of the PFC study on the relationship between micro-parameters and UCS. The numerical simulation software was PFC3D5.0, purchased from Itasca Consulting Co., Ltd. (Wuhan, China). Based on the experimental data of sandy mudstone, a numerical model simulating sandy mudstone was established, and a set of micro-parameters to match the numerical results with the measured mechanical properties was determined. Calibrated micro-parameters were used to systematically explore the effects of \(\overline{\sigma}_{n}\), \(\overline{\tau}_{n}\), and \(\overline{k}^{*}\) in PFC3D on the macro-properties of rocks and the underpinning failure mechanisms by varying \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) and \(\overline{k}^{*}\). The micro parameters were adjusted by a trial-and-error method using the following specific steps: (1) According to the uniaxial compression test, the UCS, E, \(\upmu\) of sandy mudstone were obtained; (2) The numerical model was established by PFC3D software, and a group of micro-parameters was set up according to the experience, and the uniaxial compression test was simulated; (3) The UCS, E, and \(\upmu\) obtained from the experiment and simulation were compared; (4) The reasonable micro-parameters could be obtained by adjusting the micro-parameters until the simulation results were close enough to the experimental results.