# Shearing Characteristics of Mortar-Rock Binary Medium Interfaces with Different Roughness
## 2 Materials and Methods  
FLAC3D numerical simulation software is excellent for simulating stresses and strains in geotechnical materials under complex loads, but its modeling approach is complex. In this paper, a CAD-ANSYS combined modeling approach is used to establish the geometric model of the MRI. This means the 2D geometric surface domain of the model is created in CAD. The surface domain is then transferred to ANSYS to stretch and create a 3D geometric model. The model is meshed with tetrahedral cells. Finally, the node and cell data are converted into a numerical model that can be imported into FLAC3D by means of a self-programmed conversion program. Considering the complexity of the stresses and strains at the interface, the tetrahedral cells on both sides of the interface are set with small edge lengths to form a larger number of cells when meshing in ANSYS, which enable a more detailed analysis of the stresses and strains at the interface. However, if the whole model is meshed with small edge-length cells, it will lead to too many cells in the model and low computational efficiency. Therefore, on the premise that the number of cells at the interface is guaranteed, the number of cells is reduced by increasing the cell edge lengths near the edges of the model to improve computational efficiency. The mortar-rock binary media model used in this paper has a bonding effect between the two media. Therefore, an interlayer with a thickness of 0.001 m is placed between the two media. The interlayer parameters are the same as the mortar parameters. The contact between each set of units uses the contact force automatically generated by the software. We modeled the interface as an isosceles triangular sawtooth shape with different angles based on [PERSON]'s experimental study [34]. The \(\alpha\) is the base angle of the isosceles triangle. In this paper, we set the sawtooth angles to 8\({}^{\circ}\), 16\({}^{\circ}\), 23\({}^{\circ}\), 30\({}^{\circ}\), 36\({}^{\circ}\), and 45\({}^{\circ}\), as shown in Figure 1. The model diagrams of the samples of the BMI with various angles of the interface sawtooth are shown in the figure. We used a cube-shaped sample with a length, width, and height of 70 mm. The orange and blue units in the diagram represent the mortar and rock materials in the BMI, respectively. The numbers of the model units in Figure 1a-f are 14,354, 28,144, 29,042, 27,190, 26,863, and 26,143, respectively. We used the Mohr-Coulomb strain-softening model to analyze the stress-strain behavior of the rock mass, and in FLAC3D, the strain-softening model in the elastic stage is consistent with the Mohr-Coulomb model. They differ in their plasticity, and the material parameters decrease as deformation increases. For rocks, these parameters mainly include cohesion, internal friction angle, dilatancy angle, etc. In the Mohr-Coulomb model, these parameters are constant, and in the strain-softening model, the piecewise function can be customized, and the above parameter values will change with the change of strain value. Tables 1 and 2 show how these parameters relate to each other. The mechanical parameters of the rock and mortar are presented in Table 3, where \(E\) is the elastic modulus, \(\mu\) is Poisson's ratio, \(c\) is the cohesive force, \(\phi\) is the internal friction angle, \(\sigma_{\rm t}\) is the tensile strength, and \(d_{\rm n}\) is the dilatancy angle. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Plastic Strain** & **0** & **0.005** & **0.01** & **1** \\ \hline \(C/\)MPa & 3.12 & 0.64 & 0.48 & 0 \\ \hline \(\phi\) /\({}^{\circ}\) & 40 & 32 & 26 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mortar strain softening parameters.