## 3 Numerical Simulation of Compression Tests on Anchored Rock Mass
### Numerical Model Preparation and Acquisition Method of Bolt Stress  
The numerical model was developed according to the dimensions of rock mass as described above, and parameters were assigned to surrounding rocks. Afterward, a confining pressure of 1.0 MPa was applied to allow consolidation and equilibrium of the model. Then, corresponding parts of the model were regrouped according to the locations of the grout, bolt, bearing plate, and fracture, to which corresponding microscopic parameters were assigned. This was followed by re-equilibrium to generate the initial model needed for computation. The numerical model with a size of 300 mm \(\times\) 250 mm is shown in Figure 3, and the total number of particles was 35,000. To ensure the comparability of different computation schemes, the length of the bearing plate was set to 100 mm. In the computation, a displacement constraint was applied to the bottom of the model. To alleviate the end effect, the coefficient of friction between walls on the left and right sides and balls of surrounding rocks was set to 0. Horizontal speeds of 0.01 mm/s were used while opposite directions were applied to walls on both sides to compress surrounding rocks. In the model with fractures, balls at the location of fractures were directly deleted to simulate the prefabricated fractures. The horizontal stress on walls on both sides was monitored in the computation process. When the stress on the walls reached a peak and began to decrease, it meant that the anchorage system had failed. At that time, the computation was ended.  
To reveal the stress distribution along such bolts in the computation process, the function of measurement circles embedded in PFC was adopted to collect the axial (\(y\)-direction) stress on bolts (the measuring circle can calculate the resultant force of particles contained in the circle, the value of the axial stress of the bolt, which is equal to the resultant force of all the particles within the measuring circle in the \(y\)-direction divided by the area  
Figure 3: Initial numerical model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Micro-Properties** & **Soft Rock Mass** &
\begin{tabular}{c} **Relatively Hard** \\ **Rock Mass** \\ \end{tabular} & **Hard Rock Mass** & **Grout** & **Rockbolt** & **Plate** \\ \hline Density (kg/m\({}^{3}\)) & 2400 & 2700 & 3000 & 2500 & 7500 & 7500 \\ Elastic modulus (GPa) & 6.3 & 32.3 & 55.4 & 51.5 & 230 & 280 \\ Normal to shear stiffness ratio & 1.1 & 1.3 & 1.6 & 1.2 & 1.5 & 1.5 \\ Tensile strength (MPa) & 3.5 & 8.9 & 15.6 & 10.2 & 500 & 500 \\ Cohesion (MPa) & 10.9 & 29.4 & 38.1 & 32.8 & 300 & 500 \\ Friction coefficient (\({}^{\circ}\)) & 25 & 30 & 32 & 25 & 35 & 35 \\ \hline \end{tabular}
\end{table}
Table 3: Microscopic mechanical parameters of materials.  
of the measuring circle). Then, the anchorage force of bolts can be calculated according to the axial stress by Equation (1).  
\[F_{t}=\int_{0}^{l}\sigma_{y}\cdot\phi dl \tag{1}\]  
where \(\sigma_{y}\) is the average stress in the \(y\)-direction of measurement circles (Pa); \(F_{t}\) is the anchorage force of bolts (N); \(l\) denotes the anchorage length of bolts (m); \(\phi\) is the bolt diameter (m).