# Study on Shear Mechanism of Bolted Jointed Rocks: Experiments and CZM-Based FEM Simulations
## 4 Numerical Simulation
### Analysis of Numerical Simulation Results
#### 4.2.2 Failure Mechanisms of Bolted Rock  
Understanding the stress in the bolt is of significance to evaluating the bolting effect and preventing the failure of bolted system. In addition, the use of high strength and low elongation bolt can cause a large range of rock fragmentation, which is another significant reason to explore the causes of this phenomenon for engineering construction. Therefore, we will analyze the S1-MG1 simulation results in detail in the following paragraphs. During the shearing process of bolted joint surface, the shear stress is larger on the joint surface and smaller at two ends, hence, the joint surface is prone to shear failure. As the shear displacement  
Figure 17: Comparison the results of different mesh (**a**) Crack evolution (fine mesh); (**b**) Crack evolution (coarse mesh); (**c**) Shear strength comparison. increases, the shear stress tends to increase gradually. It can be seen that, in most cases, the failure of the bolt occurs near the joint, and is mainly shear failure. This type of failure mainly concentrates on the joint surface, which is not the real cause for the rock fracture. Figure 18 shows the shear stress as a function of distance from the joint for bolt S1-MG1 under 2-6 mm shear displacement conditions. Normal stress distribution in Figure 19 illustrates that the stress of the bolt is not uniform during the shearing process. Specifically, the upper right side (near the loading side) and the lower left side (far from the loading side) are mainly subjected to tensile stress, while the opposite two sides are mainly subjected to compressive stress. In addition, it is proved that the same stress exists at the position where the bolt contacts the rock. Figure 20 shows the axial stress of bolt as a function of distance from the joint under 2-6 mm shear displacement conditions. In order to further explore the tensile stress of rock under three different bolted modes, the axial stress of rock under three different bolted modes with shear displacement of 2 mm is obtained. It is found that the tensile stress of jointed rock increases with increasing bolt strength, as shown in Figure 21.  
Figure 19: Normal stress contour of the jointed rock. Figure 18: Shear stress of bolt (S1-MG1) as a function of distance from the joint. It is well-known that the material properties of bolt and the surrounding rock are very different, and the rock has the typical characteristics of bearing compressive stress, but not tensile stress. Therefore, deformation mismatch is very easy to occur in the process of shearing. When shear dilatancy occurs, the bolt with higher elongation can be deformed greatly, so the bolt and the surrounding rock can be deformed cooperatively, which can effectively reduce the normal stress between the bolt and the surrounding rock. However, when the elongation of the bolt is low, the deformation of the bolt is small, and the stiffness of the bolt is far greater than that of the rock, and because of the strong bonding between the bolt and the surrounding rock, the contact position of the bolt and the surrounding rock will form a larger tensile stress. This leads to the initiation of the crack from the contact position and gradually propagating to the top of the rock. This also explains the phenomenon that all cracks pass through the bolt hole in the experiments. Figure 21: Comparison of axial stress of three bolted modes with 2 mm shear displacement. Figure 20: Axial stress of bolt under different shear displacements. In order to further confirm the above observation, we take S1-(MG1-MG3) as examples to show the shear deformation characteristics of different bolted joints, as shown in Figure 22, where D stands for the shear displacement. As can be seen from Figure 22, the bolted jointed rock with 25% elongation has the largest deformation in the shearing process due to the high elongation of the bolt. The rock and the bolt are cooperatively deformed during the shear process, which is beneficial to the bolted support.