## 3 Test Scheme and Result Analysis
In the formula, \(b\) is the radius of the anchor rod body, and \(\tau\) is the anchorage force between the anchor rod and the surrounding rock. When the anchoring length along \((z_{0},z_{0}+L)\) in the anchoring section is \(L\), the vertical stress generated by the shear stress load at the interface of the anchor body at any internal point \((x,y,z)\) is  
\[\sigma_{\rm z}=\frac{kdf}{8(1-\mu)} \tag{1}\]  
where \(\mu\) is the Poisson's ratio of the surrounding rock, \(f\) is the parameter relating to coordinate location, \(d\) is the diameter of anchoring bolt, and \(k\) is the Shear stiffness of interaction interface between bolt and surrounding rock. According to the research on the interfacial shear stiffness of the bolt [19; 20], the interfacial shear stiffness of the bolt can be determined by the following formula:  
\[k=\frac{G_{\rm g}G_{\rm m}}{[G_{m}\ln(r_{g}/r_{b})+G_{g}\ln(R/r_{g})]r_{b}} \tag{2}\]  
where \(G_{g}\) and \(G_{m}\) represent the shear modulus of anchoring cartridge and surrounding rock, \(r_{b}\) is the radius of the anchor rod, \(r_{g}\) is the radius of the anchor body, and \(R\) is the radius of the influence of the anchor rod. It can be seen from the formula that the higher the shear modulus of anchoring cartridge and surrounding rock is, the larger the shear stiffness is. According to the above two formulas, the vertical stress generated by the anchoring force in the surrounding rock is affected by the shear stiffness of the anchoring interface. Due to the high shear stiffness (high shear modulus) of the hard rock, the stress values of its anchoring force acting on each point in the surrounding rock are higher than those in the soft rock. Figure 5: Stress distribution of surrounding rock near the structural plane. The prestress field of lengthening anchor bolt support is shown in Figure 6. The comparison of Figures 3 and 6 yields the change of surrounding rock stress near the bolt body along the bolt axis (shown in Figure 7). In the front area of bolt action (Y = 0\(\sim\)1050 mm), the overall stress size and change trend of the two are basically consistent. In the middle and rear parts of the bolt action (Y > 1050 mm), the stress distribution of the end anchorage and the lengthening anchorage is obviously different. The surrounding rock of the lengthening anchorage is basically in the range of tensile stress in the middle and rear parts of the bolt, and the tensile stress increases first and then decreases slowly along the bolt body. The surrounding rock of the end anchorage shows a high compressive stress effect in the middle of the bolt and is only tensioned at the rear part of anchoring bolt, but the peak value of the tensile stress zone is higher than that of the lengthening anchorage and decreases rapidly along the bolt body. Figure 6: Prestress field of lengthening anchor bolt support. Figure 7: Stress distribution of surrounding rock around the bolt along the axis of anchor bolt. The stress diffusion of surrounding rock at the hard rock side and the soft rock side of the soft-hard interface is analyzed. Figure 8 shows the variation law of stress near the structural plane along its diffusion radius. The stress properties of surrounding rock near the structural plane of end anchorage and lengthening anchorage are different. In the case of end anchorage, both the hard rock side and the soft rock side of the structural plane are subject to compressive stress; the compressive stress gradually decreases along the stress diffusion direction (X direction), and the surrounding rock pressure on the hard rock side is generally higher than that on the soft rock side. In the case of lengthening anchorage, both sides of the structural plane are subject to tensile stress, the tensile stress gradually decreases along the stress diffusion direction (X direction), and the tensile stress value of the soft rock side of the structural plane is higher than that of the hard rock side.