## 2 Materials and Methods  
### Traction Separation Criterion  
Generally, the cohesive element model follows the traction force separation criterion. This research developed the tangential and normal traction into a mixed-mode test to meet the model's accuracy. The mixed-mode traction separation criterion of the cohesive element is plotted in Figure 2, which mainly includes the elastic and the damage evolution. An elastic constitutive matrix, applied in the elastic stage, can be utilized to describe the nominal stresses to the nominal strains through the interface. When the external force on the cohesive element does not reach the initial damage stress, the cohesive element is at the elastic stage, and the corresponding stress and separation vectors can be expressed as follows:  
\[\mathrm{t}=\left\{ \begin{array}{l}\mathrm{t_{n}}\\ \mathrm{t_{s}}\\ \mathrm{t_{t}}\end{array} \right\}=\left[ \begin{array}{ccc}\mathrm{E_{nn}} &\mathrm{E_{ns}}&\mathrm{E_{nt}}\\ \mathrm{E_{sn}}&\mathrm{E_{ss}}&\mathrm{E_{st}}\\ \mathrm{E_{nt}}&\mathrm{E_{st}}&\mathrm{E_{tt}}\end{array} \right]\left\{ \begin{array}{l}\mathrm{\xi_{n}}\\ \mathrm{\xi_{s}}\\ \mathrm{\xi_{t}}\end{array} \right\}=\frac{1}{\mathrm{L}}\mathrm{\left[ \begin{array}{ccc}\mathrm{E_{nn}}&\mathrm{E_{ns}}&\mathrm{E_{nt}}\\ \mathrm{E_{ns}}&\mathrm{E_{ss}}&\mathrm{E_{st}}\\ \mathrm{E_{nt}}&\mathrm{E_{st}}&\mathrm{E_{tt}}\end{array} \right]\left\{ \begin{array}{l}\mathrm{\xi_{n}}\\ \mathrm{\delta_{s}}\\ \mathrm{\delta_{t}}\end{array} \right\}=\frac{1}{\mathrm{L}}\mathrm{K}\delta \tag{1}\]  
where \(\mathrm{t}\) is the nominal traction stress vector, it has three components, including the normal traction (\(\mathrm{t_{n}}\)) and two tangential tractions (\(\mathrm{t_{s}}\) and \(\mathrm{t_{t}}\)). \(\mathrm{\varepsilon_{n}}\), \(\mathrm{\varepsilon_{s}}\) and \(\mathrm{\varepsilon_{t}}\) are the three components of the nominal strain, and \(\mathrm{L}\) is the cohesive element's initial thickness. \(\mathrm{\delta_{n}}\), \(\mathrm{\delta_{s}}\) and \(\mathrm{\delta_{t}}\) are the corresponding displacement components for the three components, and \(\mathrm{K}\) is the stiffness matrix for the cohesive element. Generally, the stiffness of the cohesive element will decrease linearly after reaching the damage evolution. Scalar \(\mathrm{D}\) indicates the process of damage. The value of the damage in scalar \(\mathrm{D}\) is increased from 0 to 1. The function of the effective displacement (\(\mathrm{\delta_{m}}\)) is introduced to describe the damage evolution of the cohesive element, as follows:  
\[\mathrm{\delta_{m}}=\sqrt{\langle\mathrm{\delta_{n}}\rangle^{2}+\mathrm{ \delta_{s}^{2}}+\mathrm{\delta_{t}^{2}}} \tag{2}\]  
When \(\mathrm{\delta_{n}}\geq 0\) indicates tension, \(\mathrm{<\delta_{n}>}\) is equal to \(\mathrm{\delta_{n}}\). In addition, when \(\mathrm{\delta_{n}}\leq 0\) indicates compression, \(\mathrm{<\delta_{n}>}\) equals zero. Figure 1: Shear failure of rock masses on high slopes: (**a**) shear path of rock masses with holes (**b**) description of the hole location. Furthermore, the damage variable (D) evolves according to the following:  
\[\mathrm{D}=\frac{\delta_{\mathrm{mf}}(\delta_{\mathrm{mm}}-\delta_{\mathrm{mo}})}{ \delta_{\mathrm{mm}}(\delta_{\mathrm{mf}}-\delta_{\mathrm{mo}})} \tag{3}\]  
where \(\delta_{\mathrm{mf}}\) is the effective displacement when the tractions diminish, \(\delta_{\mathrm{mm}}\) is the maximum pure displacement during the loading process. \(\delta_{\mathrm{mo}}\) is the effective displacement when damage initiates. The normal stress components of the traction-separation model change as follows, due to the damage accumulation:  
\[\mathrm{t}_{\mathrm{n}}=\left\{ \begin{array}{ll}(1-\mathrm{D})\mathrm{t}_{ \mathrm{n}0},&\mathrm{t}_{\mathrm{n}0}\geq 0\\ \mathrm{t}_{\mathrm{n}0},&\mathrm{t}_{\mathrm{n}0}<0\end{array} \right.