# Study on Shear Mechanism of Bolted Jointed Rocks: Experiments and CZM-Based FEM Simulations
## 4 Numerical Simulation
### Model Establishment  
In order to obtain the accurate fracture damage parameters in shear numerical simulation of joints, we use the method of globally embedded cohesive elements to simulate uniaxial compression experiment, and calibrate the cohesive element parameters proposed by [PERSON] et al. [33] A numerical model of a cylinder with a height of 100 mm and a diameter of 50 mm is established, as shown in Figure 11. There are 68230 cohesive elements (COH3D6) and 35220 solid elements (C3D4) in the numerical simulation of cylinder, with a total of 103450 elements. The macroscopic physical and mechanical parameters, such as Young's modulus, Poisson's ratio, and cohesion, obtained in our experiments are used in the numerical model. Two types of elements are used in the model: Linear elastic solid element, and the cohesive element, which follows the traction-separation law. The results shown in Figure 12 are obtained by the trial and error method. From the figure, it can be seen that the numerical simulation results are in good agreement with the uniaxial compression experimental results, and the failure modes of both are splitting tensile failure (See Section 3.2 for details). It is, thus,  
Figure 10: Comparison of shear strength of three bolt materials under the same roughness. (a) S1-(MG1-MG3); (b) S2-(MG1-MG3); (c) S3-(MG1-MG3). proven that parameters can be used for shear experiment simulation, and the specific values of the calibrated meso-parameters are provided in Table 5 The version of ABAQUS used was 6.14. In the shear experiments, the bolts are made of aluminum alloy material. In order to simulate the failure behavior of the material during shearing, we have decided to use the continuum-based ductile metal damage model and shear damage model in the numerical simulation. The typical mechanical parameters of aluminum alloys, such as fracture strain, stress ratio, strain ratio, and failure displacement, are used in the work following the study of [PERSON] et al. (2016). In order to change the elongation and strength, the plastic criterion is redefined according to the characteristics of three different types of aluminum. The established model is a plane model. Because if we use the real material parameters of the bolt, it will lead to an increase in the contribution rate to the shear strength of the bolt, hence we reduce the yield strength of the material for the purpose of equivalent replacement. Since the diameter of the bolt is only 1/5 of the longitudinal length of the specimen, we reduced the yield strength of the bolt to 1/5 to make the model more suitable for the actual bolted, as listed in Table 6.  
Figure 11: Numerical model of the cylindrical specimen. (**a**) Solid element and (**b**) Cohesive elements insertion. Figure 12: Comparison of failure modes between simulated and experimental specimens. (**a**) Simulation result and (**b**) experimental results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Element Type**} & **Density kg/m\({}^{3}\)** & **Young’s** & **Stiffness** & **Poisson’s** & **Damage** & **Fracture Energy** \\  & **kg/m\({}^{3}\)** & **Modulus (GPa)** & **(GPa/m)** & **Ratio** & **Stress/MPa** & **(N/mm)** \\ \hline Cohesive element & 2350 & / & 17900 & 0.12 & 25.44 & 0.18 \\ Solid element & 2350 & 32.04 & / & / & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mechanical parameters used in the numerical simulation. In the pre-modelling process, we used the \"raster image\" function to import the Barton (JRC) joint surface image into CAD, and captured the shape of the joint surface with 100 points of equal spacing, then connected these 100 points into a line to redraw the JRC curve, and imported the JRC curve from CAD into ABAQUS for the modelling.