## 3 Calibration of the Combined Finite-Discrete Element Method by Modeling UCS and BTS  
An appropriate determination of the model parameters is essential for accurate simulation of the shearing process in the C-R joint using FDEM. In this section, the failure processes in the UCS and BTS tests, which are frequently performed for acquiring mechanical properties of rock-like materials (i.e., rocks and concrete) are simulated using the 3D FDEM. The numerical simulation results are compared with experimental data to calibrate input parameters in the 3D FDEM. Figure 4 shows the 3D FDEM models for UCS and BTS tests. The calibration works are performed for a granite specimen and concrete specimen with nominal UCS = 35 MPa (hereafter, 35 MPa-concrete). The UCS and BTS test models are discretized around 1.5 mm of the tetrahedral element where the element size is sufficient to exclude the mesh sensitivity effect for the specimen size [47]. The experimentally obtained physical and mechanical properties of the granite and concrete specimens are summarized in Table 1. The input elastic parameters for the 3D FDEM models for granite and concrete were taken from the values in Table 1. Considering the literature [47], the normal contact penalty (\(P_{n}\)) and cohesive penalty terms (\(P_{open}\), \(P_{tan}\), \(P_{overlap}\)) of the granite, concrete, and steel plates are assumed to be \(P_{n}=10E\), \(P_{open}=100E\), \(P_{tan}=100E\), and \(P_{overlap}=1000E\) where \(E\) indicates the Young's modulus of either rock (\(E_{\text{rock}}\)) or concrete (\(E_{\text{conc}}\)). The granite model or 35 MPa concrete model was placed between the top and bottom rigid loading plates with a slow velocity of 0.01 \(m/s\)[47] along with a critical damping scheme to approximately achieve a quasi-static loading condition [47; 48; 49; 50]. Figure 3: Tensile (**left**) and shear (**right**) softening curves in the ICZM. Figure 2: Types of finite elements (TET4 and CE6) in 3D finite-discrete element element method (FDEM) used in Y-HFDEM integrated development environment (IDE) code. Figures 5 and 6 shows the comparison of the FDEM simulation and experiment during the UCS tests of the granite and the concrete, respectively. Figures 5a and 6a present the plot of axial stress versus axial strain, and Figures 5b and 6b indicate the final fracture pattern between numerical simulation and experiment test. The FDEM simulation result of the UCS test shown in Figures 5 and 6 presents good agreement with the experiment result. Meanwhile, Figures 7 and 8 show the comparison of the FDEM simulation and experiment during the BTS test of granite. In Figures 7a and 8a, the plot of indirect tensile stress versus axial displacement is presented. Whereas in Figures 7b and 8b, the final fracture pattern between numerical simulation and experiment test is on display. The FDEM simulation results of the BTS test shown in Figures 7 and 8 are in agreement with the experiment results. Through the aforementioned calibration procedure of granite and 35 MPa concrete against the UCS and BTS tests, the calibrated input parameters for FDEM simulation of the direct shear test of the rough concrete-rock joint under shearing in the next section are summarized in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Value**} \\ \cline{3-4}  & & **35 MPa Concrete** & **Granite** \\ \hline Mass density & kg/m\({}^{3}\) & 2200 & 2700 \\ Young’s modulus & GPa & 30.0 & 46.0 \\ Poisson’s ratio & - & 0.20 & 0.21 \\ Tensile strength & MPa & 2.62 & 10.0 \\ Cohesion & MPa & 7.87 & 26.0 \\ Internal friction angle & Degrees & 35.0 & 58.1 \\ Uniaxial compressive & MPa & 35.0 & 202 \\ strength & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimentally obtained physical and mechanical properties of 35 MPa concrete and granite.