# Study on Shear Mechanism of Bolted Jointed Rocks: Experiments and CZM-Based FEM Simulations
## 4 Numerical Simulation
### Analysis of Numerical Simulation Results  
#### 4.2.1 Verification of Numerical Simulation Results  
In order to verify the fidelity of this method applied to shear simulation of bolted joints, the experimental and simulation results are compared and analyzed from the macroscopic scale. Since there are many laboratory tests, here we only use S1-MG1, S2-MG1, and S3-MG1 to compare the results, as shown in Figure 14.  
The simulation results of specimen S1-MG1 show a good agreement with the experimental results. Specifically, the cracks appear near the joint with a relatively low degree of development. The damaged surface protuberances form a small fractured zone near the joint, and the S shaped bending of the bolt is consistent with the experiment. After shearing S2-MG1 bolted jointed rock, a part of the rock shows shear fracture far from loading side. Simulation results show that a large \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Bolted Mode**} \\ \cline{2-4}  & **MG1** & **MG2** & **MG3** \\ \hline Material & 1060 Aluminum alloy & 6063 Aluminum alloy & LY12 Aluminum alloy \\ Tensile strength \(\sigma_{\text{bo}}\) (MPa) & 95\(\sim\)125 & 250 & 410 \\ Equivalent strength \(\sigma_{\text{b1}}\) (MPa) & 22 & 42 & 72 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mechanical parameters of bolt. Figure 13: Numerical model for the shear experiment. (a) boundaries and (b) cohesive elements insertion. number of micro-cracks appeared along the joint surface. Although, the macro-cutting effect was not observed, it did show a large area of fractured zone, which was consistent with the experimental result. Last, the simulation results of S3-MG1 bolted jointed rock is also in good agreement with the experimental result. After shearing, the asperities on the joint surface are all sheared, and the joints are severely damaged. Similar to the earlier analyses, we compare the relationship between shear stress and shear displacement from the simulated result to the experimental result, as shown in Figure 15.  
Figure 14: Macro comparison of experiment and simulation results. (**a**) S1-MG1 Comparison of experimental and simulation results; (**b**) S2-MG1 Comparison of experimental and simulation results; (**c**) S3-MG1 Comparison of experimental and simulation results. Figure 15: Comparison of simulation and experimental results. (**a**) S1-MG1; (**b**) S2-MG1; (**c**) S3-MG1. We can see that, in general, the simulation results are in good agreement with the experimental results, which proves the fidelity of the simulation method. In addition, it can replicate the experimental shearing process fairly well, which allows for the investigation of the mechanical characteristics of bolted jointed rock. The data curves from numerical simulation is not smooth because the stress distribution on the jointed rock is not uniform during the shearing process. The failure of the surrounding cohesive elements causes the jumps in the outputted stress. The numerical simulation includes the strengthening stage, peak stage, softening stage, and residual strength stage, which is consistent with our experimental results and the literature, and to some extent proves the credibility of the simulation model. We believe this method can be used as a new research method to examine the shear failure mechanisms of bolted joints. According to the results of the numerical simulation, a quantitative analysis of the experimental results and numerical simulation results is performed, as listed in the Table 7. The mutual verification between numerical simulation and experiment shows that the test data are relatively correct, and the difference in peak shear strength between test and simulation results is about 11.5%, indicating that the experimental results and numerical simulation results are reasonably close. Because cohesive elements need to be pre-defined in the mesh, the crack can only propagate along the direction of the mesh.