## 1 Introduction
### Analysis of Influence Range of Expansion Body Section
In the initial loading stage, when the anchor rod is subjected to the pull-out load, the soil at the front end of the umbrella-shaped expansion head has not yet reached the compaction state (that is, in the elastic deformation stage). At this time, the uplift bearing capacity of the system is mainly provided by the interface friction resistance, so the ordinary anchor rod shows better uplift performance than the umbrella-shaped expansion head anchor rod. As the load continues to increase, the soil at the front end of the umbrella-shaped expansion head gradually enters the compaction state, and the soil stress field is redistributed, forming a significant confining pressure effect. At this stage, the pull-out mechanism of the umbrella-shaped enlarged head bolt changes from simple interface friction to a friction-confining pressure composite mode. The numerical simulation results show that the pull-out bearing capacity of the anchorage section of the umbrella-shaped enlarged head at this stage is 11.31644-20.38203% higher than that of the ordinary bolt. Through the comparative analysis of the full stress-strain curve, it is further revealed that there is a significant difference in the maximum uplift bearing capacity of the two anchoring systems. Among them, the umbrella-shaped expanded head anchor is 34.61538% higher than the ordinary anchor at the peak bearing capacity, that is, the overall anchoring efficiency is increased by about 35%. The results of this study not only confirm the significant improvement of the umbrella-shaped enlarged head structure on the pull-out resistance of the bolt system but also clarify the superiority of its working performance from the perspective of its mechanical mechanism, which provides a theoretical basis for the engineering application of the new anchorage system. Comparative Numerical Simulation Analysis of the Effect of Reinforcing Loose Circle in Expansive Body Section  
Using Abaqus CAE v2023 numerical analysis software, based on the field measurement of the loose circle range and the parameters obtained from the rock mechanics test, the difference between the expansion body section and the ordinary hollow grouting anchor in the fixation effect of the loose circle is simulated. In order to ensure the reliability of the experimental results, only the soil model is changed, and the constitutive model and the simulation process (except for the load form) are consistent with Section 5.1. The length of the expansion body section is consistent with the radius of the loose circle measured in the field. The bolt-soil coupling model is shown in Figure 18.  
Figure 12:0 Anchor–soil coupling model. Figures 19 and 20 show the stress distribution cloud map and displacement distribution cloud map of the soil (surrounding rock) during the extension of the expansive body section into the soil (surrounding rock). The stress cloud diagram clearly shows the stress concentration area and the distribution law of the soil around the expansive body section, especially the stress variation characteristics of the contact surface between the expansive body section and the soil. Figure 12:1 _Cont._  
Figure 12:2 The stress cloud diagram of the soil during the expansion body extending into the soil (top view) (the size of the soil model is 2 m \(\times\) 1.5 m \(\times\) 1.5 m). Figure 12:3 _Cont._  
Figure 21 further quantifies the influence of the expansive body section on the soil through the form of a curve, which is embodied in the relationship between the yield area of the soil and the time. The curve reveals the dynamic evolution process of soil yield area under the action of the expansive body section. The slope of the curve reflects the rate of soil yield development, and the overall trend of the curve shows the changing rule of soil yield area with time. Figures 22 and 23, respectively, show the stress distribution cloud map and the displacement distribution cloud map of the soil (surrounding rock) during the process of the ordinary anchor rod extending into the soil (surrounding rock).