## 6 Conclusions  
In this study, a GPGPU-parallelized FDEM was applied to model the shear failure process of a rough concrete-rock joint in direct shear tests under constant normal loading conditions. Before simulating the direct shear test, the combined finite-discrete element method was calibrated by simulating the concrete and rock fracture process in the UCS and BTS tests and was compared with the experimental results. Then, the direct shear test of the concrete-rock joint was modeled using the combined finite-discrete element method to investigate the shear resistance process of a concrete-rock joint. We focused on the asperity dilatation, sliding, and degradation in terms of various asperity roughness under different constant normal loading (CNL) conditions. The effect of the joint roughness and friction coefficient between the concrete and rock interface on the behavior of the shear resistance was also discussed. In this study, the following conclusions can be drawn:  
1. The GPGPU-parallelized FDEM reproduced the asperity dilatation, sliding, and degradation on the direct shear test of the concrete-rock joint with rough saw-tooth triangular asperity. Compared with laboratory observation, the simulation result presented a good agreement on the bulk shear stress-horizontal displacement curve before the regime of residual shear resistance. However, the laboratory test results presented a continuous decrease of bulk shear stress unlike the numerical simulation result, which showed constant residual stress after shear softening. In this study, we concluded that the additional damages found in the experiment results induced a continuous stress drop and presented different behaviors in the numerical simulation in the regime of the constant residual stress statement. 2. The roughness of asperities in the concrete-rock joint affects the overall joint shear resistance, where the main fracture mechanism is asperity sliding in the smooth asperity and asperity degradation in the rough asperity. The smoother single asperity is freer from the bending moment, which was easy to induce in the tensile crack in concrete asperity base, than the rough single asperity. The only factor of the shear resistance in the smooth asperity is the friction between the concrete and rock joint interface. The effect of the increment of asperity roughness affects the shear strength increment and causes the asperity degradation, which presents the shear softening behavior after the peak bulk shear stress, while the smooth asperity roughness presents the residual stress statement immediately after the initial elastic behavior. In addition, when the direct shear test results are presented as Mohr-Coulomb criterion, the bulk internal friction angle was clearly increased with an increasing asperity angle. In this study, the effect of asperity roughness on the bulk internal friction angle follows the [PERSON]'s theoretical model. 3. The friction coefficient is an important parameter for simulating the direct shearing of the concrete-rock joint. Especially, the friction coefficient was more effective on the internal friction angle in terms of the smooth joint than the rough joint. The asperity degradation was the main mechanism in the rough joint, the concrete asperity base was fractured, and the friction was applied at the macroscopic crack surface in the concrete asperity base. Thus, the internal friction angle in the vicinity of the rough concrete-rock joint may be independent of the friction coefficient between the rock and concrete. However, in the smooth joint, the main mechanism of shear resistance was sliding without fracturing, and the different friction coefficient was directly reflected to the friction force as well as the internal friction angle. Conceptualization, Y.K., M.C. and S.C.; methodology, G.M., D.F., S.O., Y.K., H.L., M.C. and S.C.; investigation, G.M., D.F., S.O. and S.C.; writing--original draft preparation, G.M., D.F. and S.C.; writing--review and editing, G.M., D.F., H.L.