## 3 Rock Mass Model Based on Digital Image Recognition
### Numerical Analysis of the Anisotropic Mechanical Properties  
Anisotropic mechanical behaviours of jointed rock mass are key influencers for the deformation and failure of rock engineering, and have been paid attention in recent years [36; 37; 38; 39; 40]. RDFN models with different rotation angles and the same size were established to evaluate the anisotropy of rough-jointed rock mass under biaxial compression. Firstly, a square area rock mass with a fixed pixel size was selected based on the fixed centre point of the original model. Thereafter, the selected regional rock mass was rotated to seven different angles (\(\theta\) = 0\({}^{\circ}\), 30\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), 150\({}^{\circ}\), 180\({}^{\circ}\)), with interception at the same size to establish the models (as shown in Figures 6 and 7). According to the specimens, we could examine the spatial variation of deformation and strength of the jointed rocks. Finally, the digital images compiled by MATLAB converted these models into PFC models (as shown in Figure 8) for the compression test to study the differences in mechanical properties between models in different directions. The information of the intact rock elements and joint elements is listed in Table 5. As is shown in Figure 6, the wall elements, which could provide numerical boundary conditions around the joint model in the PFC code, are set up to monitor both the stress and displacement. The confining pressure is monitored by controlling the servo pressure in both the x and y directions, whose value was initially set as 1 MPa. According to the preload, the confining pressure is first applied to the particle model. The preload is controlled by changing the magnitude of the servo stress in the x-direction and y-direction. Thereafter, the servo in the y-axis direction is set to turn off while the servo in the x-axis direction is turned on and the y-axis direction is constantly being loaded. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Micro-Parameters** & **Numerical Value** \\ \hline \multirow{6}{*}{Particle properties} & Ratio of particles, & 1.7 \\  & \(R\)max/\(R\)min & 2700 \\  & Particle density (kg/m\({}^{3}\)) & 2700 \\  & Static elastic modulus between particles (Pa) & 6.0e9 \\  & Particle method/Tangential stiffness ratio & 0.45 \\  & Coefficient of friction & 0.7 \\ \hline \multirow{6}{*}{Parallel connection properties} & Modulus of elasticity (GPa) & 5.4 \\  & Normal/Tangential stiffness ratio & 0.45 \\ \cline{1-1}  & Normal strength/Standard deviation (MPa) & 4.5/0.6 \\ \cline{1-1}  & Shear strength/Standard deviation (MPa) & 5.0/0.7 \\ \cline{1-1}  & Parallel bond radius multiplier & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Micro-mechanical parameters of the particle model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Total Number** & **Rock Unit** & **Joint Unit** & **Ratio of Joint Units** \\ \hline PFC model & 22,500 & 19,477 & 3023 & 13.43\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PFC model particle information. Figure 6: The schematic of RDFN models under varied directions for anisotropic test. Figure 7: Joint model taken by rotation at different angles. The following monitoring is carried out during loading: (1) the change in the distance between the walls is used as the benchmark for compression displacement to monitor the change in the distance between the upper and lower walls. According to the displacement obtained by the distance change, the instantaneous strain of the rock mass in the biaxial compression test was calculated based on the displacement obtained from the distance change. Thereafter, the detailed information file of the stress and strain change for each step is exported. (2) The reaction forces on the upper and lower walls are monitored and the average value of the reaction forces is used as the instantaneous normal stress of biaxial compression.