# 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 Strength Parameters  
To investigate the influence of bonded conditions on the strength parameters of the binary interfaces, the relationship between the shear strengths under different bonded conditions is firstly analyzed, and then cohesion and friction coefficients are obtained by fitting. The shear strengths of binary interfaces with various bonded degrees under different normal stresses are shown in Figure 3. Obviously, the shear strength of the binary interface shows a good linear relationship with the normal stress, which conforms to the Mohr-Coulomb criterion. This also provides further evidence of the validity of the simulation results. Beyond that, it can be seen that the bonded degree has a significant influence on the shear strength of the binary interface; the higher the bonded degree, the greater the shear strength. For a more intuitive observation of the influence of the bonded degree on the shear strength of the binary media, the strength factor \(\theta\) is established to characterize the relationship between the shear strength of the partially bonded binary interfaces and the fully bonded as well as the unbonded binary interfaces. The strength factor \(\theta\) is the approximation representation of the shear strength of partially bonded binary interfaces to that of the fully bonded binary interfaces, which can be calculated by Equation (1). \[\theta=\left(\tau_{p}-\tau_{u}\right)/\left(\tau_{b}-\tau_{u}\right) \tag{1}\]  
where \(\tau_{p}\) is the partially bonded binary interface shear strength; \(\tau_{u}\) is the unbonded binary interface shear strength; \(\tau_{b}\) is the fully bonded binary interface shear strength. The strength factor of the unbonded binary interface is 0, and the strength factor of fully bonded binary interface is 1. According to the definition of strength factor, the values of strength factor for different bonded conditions are obtained and further analyzed (as shown in Figure 4). As the bonded degree increases from 0% to 25%, the shear strength increases significantly, and the \(\theta\) also greatly rises, with a slope greater than 1. Meanwhile, the increase in shear strength is relatively small when the bonded degree increases from 25% to 50% and 75%, and the rise in \(\theta\) slows down, with slopes of less than 1. Additionally, the increase in shear strength is greater when the bonded degree is increased from 75% to 100%, and \(\theta\) also rises significantly with a slope greater than 1. Therefore, it can be noted that the change rate of the strength factor is greater than 1, and the variation of the shear strength of the binary interface is significant when the bonded state is transformed among unbonded, partially bonded and fully bonded. While in the partially bonded state, the change in bonded degree has a relatively small effect on the shear strength. This may be attributed to the specificity of the bonded state of the interface. Relative to unbonded interfaces, partially bonded interfaces allow for a substantial increase in shear resistance due to the high cohesion that the bonded portion can provide. Compared to fully bonded interfaces, partially bonded interfaces have a substantially lower shear resistance for a certain percentage of the non-bonded region since it corresponds to a large fracture and cannot provide cohesion. Based on the nature of the curves, the strength parameters of the interfaces are derived, which are shown in Table 4. The cohesion of binary interfaces is 0 MPa in the unbonded state and up to 4.25 MPa in the fully bonded state, while the cohesion of partially bonded interfaces ranges from 1.56 MPa to 2.25 MPa. The increase in cohesion is very significant during the transition process from an unbonded state to a partially bonded state (25%), as well as during the transition from a highly bonded state (75%) to a fully bonded state. It  
Figure 3: Shear strength of binary interfaces for different bonded conditions. is evident that the influence of the bonded state on cohesion is considerable.