## 2 The Mechanical Principle of the Interfacial Bond between the Rock Bolt and the Grouting Body  
It is generally believed that the bond-slip is divided into three stages according to the failure process of tensile test. These stages are the elastic stage, the plastic slip stage, and the residual shear stage [5]. Under the action of axial tensile force, when shear stress on the surface between the rock bolt and the grouting body is smaller than the shear strength on the interface, the tensile force at this time is less than the ultimate tensile force under an elastic state. Under a complete elastic state, there is no relative displacement between interfaces. When the tensile force increases continuously, once the shear stress on the surface between the rock bolt and the grouting body is greater than the shear strength on the interface, the extrusion plastic zone will develop in the front of the deformation plane. The extrusion plastic zone will expand continuously and form a squeezing wedge accumulation and a new extrusion slip surface. When the extrusion slip surface is crushed, the interface will slip and come into the plastic flow state. With a further increase in tensile force, shear stress decreases significantly and transverse fracture and failure happen on the anchorage body. Finally, the anchorage body is then separated from the hole wall and enters the residual shear stage [18]. Shear stress on the interface of the anchorage body increases with the increase in tensile force. The variations are shown in Figure 1.  
Considering shear strength between the rock bolt and grouting body and supposing that the anchorage body material conforms to [PERSON]'s law, along the direction of the rock bolt length, a micro rock bolt segment whose length is \(dz\) is taken at the place where the distance from the pull end is \(z\), as shown in Figure 2. On the supposition that axial displacement \(u_{(z)}\) is produced under the action of axial force \(P_{(z)}\), according to the static equilibrium relationship and the principle of the load transfer method, it can be concluded that the shear displacement of \(z\) at any position on the interface between the anchorage body and the rock bolt equals the value of the axial displacement of the rock bolt under the action of tensile force (this does not consider the deformation of the rock bolt itself) [5].  
When the calculated position of \(z\) on the interface between the rock bolt and the grouting body is at the position of \(j\) on the strain gauge, combined with Equation (1) and based on the variation in strain value of the strain gauge at each point, which is arranged along the axial direction of the rock bolt, Equation (2) can be obtained. Equation (2) is used to calculate the axial force at point \(j\). According  
Figure 1: Shear stress variation law along with the tensile force: (**a**) elastic stage; (**b**) plastic slip stage; (**c**) residual shear stage.  
Figure 2: Schematic diagram of the interaction between rock bolts and the grouting body.  
to the strain value of two adjacent points and Equation (3), the average value of shear stress on the interface between the rock bolt and the grouting body of two adjacent points can be obtained [19].  
\[\epsilon_{(z)}=\frac{du_{(z)}}{dz}=-\frac{P_{(z)}}{AE} \tag{1}\]  
\[P_{(l)}=\epsilon_{(j)}EA \tag{2}\]  
\[\tau_{(i)}=\frac{[\epsilon_{(j)}+\epsilon_{(j+1)}]EA}{\pi d\Delta z} \tag{3}\]  
where \(P_{(j)}\) is the calculated value of the axial force at the point \(j\); \(\tau_{(i)}\) is the average value of shear stress between point \(j\) and point \(j+1\). \(\epsilon_{(j)}\) and \(\epsilon_{(j+1)}\) are the strain values measured by the strain gauge at the point \(j\) and point \(j+1\); \(E\) is the elastic modulus of the rock bolt. \(A\) and \(d\) are the cross-sectional area and diameter of the rock bolt rod, respectively; \(\Delta z\) is the distance between adjacent strain gauges.