# Numerical Analysis for Shear Behavior of Binary Interfaces under Different Bonded Conditions
## 3 Shear Mechanical Behavior under Different Bonded Conditions
### Influence of Bonded Conditions on Crack Development  
For a better understanding, the change in crack number in the shear process is analyzed first, and then the influence on the damage pattern is investigated in conjunction with the distribution of the fractured region. According to Figures 3-6, the following conclusions can be obtained. (1) Binary interfaces in an unbonded state have almost no cracks generated during the shear process, which owes to the fact that unbonded interfaces are completely straight and penetrating, and the rock blocks on both sides are not significantly damaged during shearing. However, since the interface is not spatially \"absolutely straight\", a small number of cracks can occur locally during the shearing process. This mainly occurs during the stress rise period before the peak and corresponds to a displacement interval of 0-1 mm. (2) For bonded binary interfaces, cracks develop significantly during shear, which can be divided into three stages. The number of cracks hardly grows in the first stage, which indicates that the elastic deformation of the binary interfaces in this stage is able to resist the shear stress generated by the shear movement well. However, it is insufficient near the peak, and cracks begin to develop. The number of cracks rises sharply in the second stage, and the development of cracks further reduces the bearing capacity of the interfaces, leading to more cracks, which corresponds to the displacement interval of 1-4 mm. The growth rate of cracks in the third stage slows down substantially relative to the second stage because the bonded part of the binary interfaces has been damaged at this time, the shear failure surface has been formed, and the shear behavior in this stage is dominated by sliding, which produces fewer cracks. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Shear Strength**} & \multicolumn{5}{c}{**Bonded Conditions of Binary Interfaces**} \\ \cline{2-6}  & **0\%** & **25\%** & **50\%** & **75\%** & **100\%** \\ \hline Cohesion/MPa & 0 & 1.56 & 1.69 & 2.25 & 4.25 \\ Friction coefficient & 0.53 & 0.66 & 0.69 & 0.69 & 0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fitted values of shear strength parameters. Figure 4: Variation of strength factor with bonded ratio. Figure 5: Strength parameters of binary interfaces under different bonded conditions. Figure 6: Crack development in binary interfaces under different bonded states. (**a**) Unbonded binary interfaces; (**b**) 25% bonded binary interfaces; (**c**) 50% bonded binary interfaces; (**d**) 75% bonded binary interfaces; (**e**) 100% bonded binary interfaces. The number of cracks is strongly related to the bonded condition of interfaces. As can be seen in Figures 3-6, more cracks appear in the shear process of the binary interfaces with larger bonded degrees, which is due to the fact that the cracks mainly occur in the bonded region. From the slope of the curve, the greater the bonded degree, the greater the crack growth rate and the more complex the crack growth. At a lower bonded degree, the slope of the curve in the stress drop section changes little, indicating stable crack development. Meanwhile, in the case of a larger bonded degree, such as 75% and 100% bonded interfaces, the crack growth rate is extremely fast at the initial stage of the stress drop section and slows down significantly at the later stage. In the shear residual stage, the rate of crack development has slowed down to a great extent, but it is still increasing. In terms of the curve slope, the binary interface with a greater bonded degree has a faster crack growth rate in the residual phase, as well as for normal stress. This also indicates that the greater the bonded degree, the greater the roughness of the failure surface. The region of crack development is influenced by the variability of the rock blocks on both sides of the interface.