# Shearing Characteristics of Mortar-Rock Binary Medium Interfaces with Different Roughness
## 4 Discussion
The mortar and rock near the interface have a lot of damage, indicating that the binary medium interface with rough interface is under the action of large \(\sigma_{n}\). The shear failure mode is gnawing failure. Figure 11 shows the correlation of the shear strength and the normal stress of the BMI at various sawtooth angles. As shown, the shear strength of the BMIs increases with  
increasing \(\sigma_{n}\) and interfacial \(\alpha\). This is because the higher \(\sigma_{n}\) brings the two media closer together, enhancing the shear strength of the BMI. Different from most rock joints, the shear strength of the BMI with a \(\alpha\) of 8\({}^{\circ}\) does not change under the \(\sigma_{n}\) of 0.1 MPa, 0.5 MPa, and 1 MPa. This is because when the interface is relatively flat and the \(\sigma_{n}\) is low, the shear strength of the BMI is dependent on the bonding effect between the two media. Therefore, in this case of geotechnical engineering, increasing the strength of the BMI material and the roughness of the interface as much as possible can effectively improve the shear performance of the BMI. Taking the BMI material as an example, in this case, it is recommended to increase the roughness of the interface of the BMI and improve the bonding performance of the cement, for example by adding glass fiber, steel fiber, and using ultrafine cement. Based on the standard Mohr-Coulomb rock shear strength measurement, the shear strength parameters of the BMI at different \(\alpha\) are calculated: \(c\) and \(\phi\). The concrete findings are presented in Figure 12 and Table 6. From Table 6, the shear strength of the BMI at each sawtooth angle satisfies the Mohr-Coulomb criterion, and the fit coefficient is greater than 0.95, indicating the reliability of using the Mohr-Coulomb rock shear criterion to describe the correlation between the \(\tau\) of the BMI and the \(\alpha\). The mathematical relationship is shown in Formula (2). In the table, as the \(\alpha\) increases, the \(c\) and \(\phi\) of the mortar-rock BMI show an increasing trend. Figure 12a,b show the correlation between the interfacial adhesion angle and the \(\phi\) of the BMI and the sawtooth angle, respectively. Figure 12a indicates that the increase rate of the interfacial adhesion of the binary medium gradually increases as the sawtooth angle increases. Formula (3) is used to quantify the connection of the interface strength of the MRBM with the sawtooth angle. In the formula, \(c\) is the interface bonding force of the MRBM and the sawtooth angle. The correlation coefficient \(R^{2}\) is 0.98, more than 0.95, indicating that the fitting result is good and the fitting formula is reliable. From Figure 12b, as the \(\alpha\) becomes larger, the rate of increase in the \(\phi\) of the BMI first becomes larger and then smaller. To quantitatively express the relationship between the \(\phi\) of the binary interface and the \(\alpha\), the piecewise function is used to fit the data in Figure 12b. The result of the fitting is shown in Formula (4), and the fitting correlation coefficient, \(R^{2}=0.9866\), indicates that the fitting effect is favorable and the fitting formula is reliable. \[\tau_{\max}=c+\sigma_{n}\tan(\phi). \tag{2}\]  
Figure 11: Relationship between the shear strength and normal stress of the binary medium interface. where \(\tau_{max}\) is the interface shear strength of MRBM, \(\sigma_{n}\) is normal stress, \(c\) is binary medium interface cohesion, and \(\phi\) is the internal friction angle of BMI. \[c=a+b[\tan(\alpha)]^{d} \tag{3}\]  
where \(\alpha\) is the sawtooth angle and \(a\), \(b\), \(d\) are constants, \(a=1.199\), \(b=4.848\), \(d=1.43\). \[\phi=\left\{ \begin{array}{l}k+l\alpha,\alpha\leq\alpha_{i}\\ \phi_{i}+n(\alpha-\alpha_{i}),\alpha>\alpha_{i}.\end{array} \right. \tag{4}\]  
where \(\alpha_{i}\) is the critical sawtooth angle, \(\alpha_{i}=24.1752\), and \(k\), \(l\), \(n\) are constants, \(k=18.12\), \(l=0.7237\), \(n=0.1671\). Figure 12: Relationship between the shear strength parameters and sawtooth angle.