## 5 Discussion  
### Direct Shearing of Concrete-Rock Joint with Different Asperity Roughness  
The direct shear test of concrete-rock joints with various roughness and regular triangular asperity was simulated using the 3D FDEM to investigate the effect of joint roughness on the shear failure process. Figures 13 and 14 compare the three concrete-rock joint models with the asperity angles of \(\alpha=10\) and 25 degrees in terms of the distributions of the maximum principal stress (PS1) and the macroscopic cracks. The case of \(\alpha=40\) degrees was already presented in Figure 11-VI. Similarly to Figure 10, the \(\tau_{\rm bulk}-d_{\rm s}\) curves for the three asperity angles \(\alpha=10\), 25, and 40 degrees in terms of \(\sigma_{\rm n}=2.0\) MPa are compared in Figure 15. As already explained using Figure 11-VI for the case of rougher asperity (\(\alpha=40\) degrees), the main fracture mechanism in overall shear resistance was joint asperity degradation, which was induced by tensile fracturing within the intact asperity. As can be seen from Figures 13 and 14 for the relatively smoother asperity (\(\alpha=10\) and 25 degrees), sliding was the main mechanism in the overall shear resistance. Since the smoother single asperity was more free from the bending moment, which more easily induced the tensile crack than the rough single asperity, the only factor of the shear resistance in the smooth asperity was the friction between the top (concrete) and bottom (rock) asperity. Figure 15a indicates that the relatively rougher asperity (\(\alpha=40\) degrees) shows clear shear softening behavior (transition from peak bulk shear stress to reduction) due to the joint asperity degradation. With the decrease of the asperity angle \(\alpha\), the shear softening behavior due to the joint asperity degradation became less obvious and in the case of \(\alpha=10\) degrees only showed constant \(\tau_{\rm bulk}\), i.e., a residual stress state immediately after the initial elastic behavior. Compared to the development of shear resistance between the simulation and experiment result in terms of the \(\tau_{\rm bulk}-d_{\rm s}\) curves as shown in Figure 15a,b, the overall development of shear resistance presents similar behaviors at each case of the \(\alpha\). However, the fluctuation of the \(\tau_{\rm bulk}\) is observed around the peak bulk  
Figure 12: A comparison of the resultant fracture pattern in the shear test with the rough concrete–rock joint in the case of an asperity angle of \(\alpha=40\) degrees: (**a**) numerical simulation and (**b**) experiment result. shear stress in the numerical simulation, while the \(\tau_{\rm bulk}\) shows the stress-drop after the peak bulk shear stress in the experiment. Figure 14: Simulation results in the shear test with a relatively smooth concrete–rock joint for the cases of asperity angles \(\alpha=25\) degrees. (**a**) Macroscopic crack, (**b**) maximum principal stress distribution (PS1). Figure 13: Simulation results in the shear test with a relatively smooth concrete–rock joint for the cases of asperity angles \(\alpha=10\) degrees. (**a**) Macroscopic crack, (**b**) maximum principal stress distribution (PS1). To interpret the obtained results more clearly, the FDEM simulation results for various values of \(\alpha\) (\(\alpha\) = 10, 25 and 40 degrees) and \(\sigma_{\rm n}\) (i.e., \(\sigma_{\rm n}\) = 1.0, 2.0 and 3.0 MPa) were fitted using a linear fitting line based on the M-C shear failure criteria as shown in Figure 16. To avoid confusion caused by notation between the microscopic cohesion and internal friction angle, which is summarized in Table 2, and the parameters of the M-C shear failure criteria, the M-C parameter is presented as the bulk cohesion (\(\rm c_{bulk}\)) and bulk internal friction angle (\(\rm\phi_{bulk}\)). In addition, the \(\rm c_{bulk}\) and \(\rm\phi_{bulk}\) reflect the overall shear resistance in the vicinity of the C-R joint, unlike the microscopic cohesion and internal friction angle represented in a single material.