## 1 Introduction
### Analysis of Influence Range of Expansion Body Section
With a slurry stopper at the tail of the conventional anchorage section, it can effectively prevent the leakage of the grouting fluid and accelerate the formation of the grouting body. The overall bolt adopts a hollow design. In the conventional support, after the grouting is injected from the tail of the bolt, the grouting fluid is transmitted to the umbrella-shaped expansion head of the bolt head through the entire bolt and then flows out from the slurry outlet of the umbrella-shaped expansion head. Under the action of the slurry stopper, the area between the entire anchorage section and the soil can be filled quickly and effectively. The free section at the end of the bolt is an unfixed section, which can absorb the variable situation energy of the soil or rock mass and play a role in buffering and regulating. Consistent with the theoretical calculation results in Section 3, the umbrella-shaped enlarged-head anchorage section is the key bearing member in the bolt system, and its structural composition is shown in Figure 9. The structure is composed of multiple functional components, including a grouting liquid outlet, upper chassis, umbrella claw, support rod, lower chassis, expansion ring, sleeve, and internal movable steel cable. At the initial stage of bolt installation, the umbrella-shaped expansion head is in a closed state. At this time, the support rod remains contracted, and the umbrella claw is closely attached to the bolt body to ensure smooth entry into the borehole. When the bolt reaches the predetermined depth, the sleeve is driven down by the movable steel cable at the tail of the traction and then the supporting-rod umbrella hinge mechanism is activated to expand the umbrella claw and embed it into the surrounding soil. Subsequently, the pre-tightening force is applied by tightening the pallet nut. When the anchor is subjected to external tension, the umbrella claw will further penetrate the soil, thereby significantly improving the overall uplift bearing capacity of the anchor system. This unique mechanical structure design not only ensures the convenience of the installation process but also optimizes the anchoring performance. Figure 8: Hollow grouting expansion structure diagram of umbrella-shaped expansion head. As one of the key research objects of this study, the expansion body section of the hollow grouting anchor with the umbrella-shaped expansion head with an expansion pipe plays an important role in improving the overall uplift resistance of the anchor. The spatial positioning of the expansion body section is between the slurry stopper and the pad, and its detailed structural composition is shown in \[\sigma_{n}=\frac{F_{n}}{A_{s}}=\frac{P_{0}tan\theta_{c}}{\pi\frac{(D_{c}+D_{0} )}{2}R_{d}} \tag{34}\]0 The section is composed of multiple precision components, including an expansion ring, an expansion sleeve, a flat washer, a spring washer, a sleeve nut, a gasket, and a gasket nut. In practical engineering applications, the installation of each component follows a specific order: first the slurry stopper and its limit ring are installed, then the expansion ring is installed, followed by the expansion sleeve, flat washer, spring washer, sleeve nut, gasket, and finally the gasket nut. In order to monitor the stress state of the bolt in real time, a bolt dynamometer can be installed between the plate and the plate nut, so as to realize the accurate measurement of the working load. \[\sigma_{n}=\frac{F_{n}}{A_{s}}=\frac{P_{0}tan\theta_{c}}{\pi\frac{(D_{c}+D_{0} )}{2}R_{d}} \tag{34}\]1 Expansive body segment structure diagram. \[\sigma_{n}=\frac{F_{n}}{A_{s}}=\frac{P_{0}tan\theta_{c}}{\pi\frac{(D_{c}+D_{0} )}{2}R_{d}} \tag{34}\]2 Umbrella enlarged-head segment structure diagram.