## 1 Introduction
For this reason, the FDEM is expected to model the three-dimensionally complex asperity degradation and shear resistance process, and thus, this study employed the FDEM. FDEM has been applied to the investigation of the fracture process in the direct shearing of the R-R joints. For example, [PERSON] and [PERSON] [53] utilized 2D FDEM implemented in ELFEN software to investigate the process of the R-R joint degradation during direct shear tests with various joint roughness under different normal stress. Similarly, [PERSON] et al. [46] applied the 2D FDEM implemented in the Y-HFDEM IDE code to simulate the direct shearing process of rock with rough R-R joints under various dynamic loading and investigated the effect of different patterns of asperity roughness. They successfully simulated the development process of overall shear resistance including asperity sliding, asperity degradation, gauge formation, and gouge grinding. Furthermore, [PERSON] and [PERSON] [54] implemented the simulation of a direct shear test using the 2D FDEM implemented in Y-Geo code for a 2D profiled rock-rock joint in which the detailed joint topology was extracted from the 3D discontinuity surface data obtained from the micro-CT scanning system, and the simulation results of the direct shear test presented a good agreement with laboratory observations over the first 2-3 mm of shear displacement. According to these application examples, the FDEM has great capabilities for detailed investigations of complex fracture processes in the shear test of R-R joints. However, all the previous research using FDEM was limited to 2D problems and R-R joint problems. In addition, in the experience of the author, the heterogeneous fracturing was shown in a laboratory direct shear test of the concrete-rock joint specimen with uniform and rough tooth-saw-shaped asperity. Therefore, to achieve a better understanding of the development of resistance mechanisms in the C-R joints under shearing, 3D numerical simulation of the fracturing process of concrete and rock around the C-R joints is necessary, because the concrete and rock are fractured involving complex 3D processes. However, no previous research has been reported for the application of 3D FDEM to the investigation of the direct shear test of the rough C-R joint under shearing. In relation to the work summarized above, this paper aims to apply the 3D FDEM to investigate the detailed development of resistance mechanisms in a direct shear test of a rough C-R joint under shearing including asperity dilatation, asperity sliding, and asperity degradation behavior. The organization of this paper is as follows: Section 2 briefly introduced the 3D FDEM implemented in the Y-HFDEM integrated development environment (IDE) whose computational performance has been greatly improved by the introduction of parallel computation utilizing general-purpose-graphic-processing-unit (GPGPU). In Section 3, calibration of the input parameters for the 3D FDEM simulations in Section 4 was first conducted against the experimental results of the target rock and concrete through the uniaxial compressive strength (UCS) and Brazilian tensile strength (BTS) tests. Using calibrated input parameters, a direct shear test of the rough C-R joint was investigated in detail using 3D FDEM. Finally, the authors discuss the effect of the roughness of asperity as well as the effect of friction coefficient on friction resistance during direct shear development.