## 6 Conclusions  
The analysis and research on the hollow grouting anchor with an umbrella-shaped expansion head with an expansion pipe is divided into two categories: umbrella-shaped expansion head research and expansion body section research. After theoretical analysis, mechanical performance analysis, experimental analysis, and numerical analysis, the following conclusions can be obtained:  
1. Through the systematic theoretical analysis of the support mechanism and stress form of the umbrella-shaped enlarged head section and the expansive body section, the mechanical behavior and mechanism of the two are discussed in depth. The research clarified the working mode of the hollow grouting anchor with an umbrella-shaped expansion head with an expansion pipe, including its anchoring process in soil (surrounding rock), load transfer path, and deformation coordination characteristics. At the same time, the theoretical analysis also reveals the working ability of the anchor, including its uplift bearing capacity, shear resistance, and reinforcement effect on the surrounding soil. 2. Through the analysis of the mechanical properties of the system, the formula for calculating the maximum drawing force of the umbrella-shaped expansion head is studied and clarified. The formula comprehensively considers the geometric parameters, material properties, and mechanical properties of the soil (surrounding rock) of the umbrella-shaped expansion head, and can accurately predict its ultimate bearing capacity under drawing load. At the same time, the study also quantifies the influence range of the expansion body section on the fixation of the loose circle and analyzes the expansion effect of the expansion body section in the soil and its reinforcement effect on the surrounding loose area. The results show that the expansion body section can effectively restrain the expansion of the loose circle and significantly improve the overall support performance of the bolt by improving the stress distribution state of the soil. 3. On the basis of theoretical analysis, mechanical performance analysis, and experimental analysis, the system optimization design of the umbrella-shaped enlarged-head hollow grouting bolt with an expansion pipe is carried out. The theoretical analysis clarifies the load transfer mechanism and support mechanism of the anchor rod. The mechanical performance analysis determines the calculation formula of the maximum pull-out force of the umbrella-shaped expansion head and the fixed range of the expansion body section compared to the loose circle. The experimental analysis verifies the mechanical behavior and reinforcement effect of the anchor rod under actual working conditions. Based on the above research, the optimization design is mainly aimed at adjusting the structural parameters of the anchor rod (such as the geometric size of the umbrella head, and the length and diameter of the expansion body section) and the material properties (such as the strength of the grouting material and the expansion rate of the expansion pipe) to improve its overall support performance and engineering applicability. 4. Recommendations for engineering application parameters: In order to realize the efficient application of the optimized umbrella-shaped expansion, hollow grouting anchor system in practical engineering, the following design and construction parameters are recommended. The length of the anchor should be flexibly adjusted according to the geological conditions. In the clay layer, a shorter length of 2.0-2.5 m is preferred to take advantage of its high shear resistance, while in the broken rock mass it needs to be extended to 2.8-3.0 m to ensure that the anchorage depth exceeds the loose zone; it is recommended to adopt a staggered arrangement mode of 0.8-1.5 m for anchor spacing, and the specific value needs to be dynamically adjusted in combination withgeotechnical strength.