## 6 Conclusions  
This paper takes the development pattern of the plastic zone of the surrounding rock in the floor of the working face under dynamic pressure as the research object. Based on theories such as elastic mechanics and Mohr-Coulomb, and by using methods of theoretical analysis and numerical simulation, a systematic study on the development pattern of the plastic zone of the surrounding rock in the floor of the working face under dynamic pressure has been carried out, and the following main conclusions are obtained:  
1. A mechanical model of the roadway under dynamic pressure of the floor was established, and the expression of the strength failure criterion \(f\) for the surrounding rock of the roadway was deduced. The change process of the maximum value of the Mohr-Coulomb discriminant \(f\) of the surrounding rock of the roadway and its included angle \(\beta\) with the horizontal axis under different horizontal and vertical distance conditions was analyzed. The results indicate the following:  
1. When the horizontal distance between the working face and the roadway is greater than 35 m, the roadway is less influenced by the mining activities of the working face, and the maximum development depth and the development pattern of the plastic zone of the surrounding rock of the roadway do not change significantly;
2. When the horizontal distance between the working face and the roadway is less than 35 m, the growth rate of the maximum value of the equation \(f\) increases  
Figure 21: The stage-by-stage instability of the anchor bolts in the “butterfly” plastic zone of the roadway. and is negatively correlated with the vertical distance. The growth rate range is 0.205-0.0295 MPa/m;
* The \(\beta\) value decreases linearly, and the decreasing rate range is 0.09-0.53\({}^{\circ}\)/m. At this point, the maximum development range of the plastic zone in the surrounding rock of the roadway increases, the butterfly leaf of the plastic zone deflects towards the working face, and the development shape gradually changes from a \"circular\" shape to a \"butterfly\" shape;
* The development law of the plastic zone in the surrounding rock of the roadway at different vertical distances (5-35 m) during the mining process of the working face was simulated by using FLAC\({}^{\rm 3D}\) software, and the simulation results were compared and analyzed with the analytical method. The analysis results indicate that the shaped characteristics of the plastic zone obtained by the analytical algorithm are highly consistent with those obtained by the numerical simulation method and are also consistent with the existing experimental results, demonstrating that the analytical algorithm has a certain degree of validity;
* The calculation results of the analytical method have certain deviations from those of the numerical simulation. As the vertical distance between the roadway and the working face gradually increases, the deviation between the calculation results of the analytical method and those of the numerical simulation becomes greater. When the vertical distances are 5 m, 12.5 m, 20.0 m, 27.5 m, and 35 m, respectively, the average deviations between the two are 19.4%, 35.1%, 49.5%, and 54.9%, respectively. According to the accuracy required for actual engineering, these issues can be disregarded;
* The comparative analysis of the simulation and theoretical calculation results reveals that the results obtained from the theoretical calculation and numerical simulation methods for the shaped characteristics of the plastic zone of the roadway's surrounding rock are highly consistent and are essentially in agreement with the existing research findings, demonstrating that this paper holds considerable theoretical value. A certain error exists between the theoretical calculation and the numerical simulation, and the error value increases with the increase in the vertical distance between the roadway and the working face. Conceptualization, Y.H., Q.M. and X.H. ; methodology, Y.H., Q.M. and X.H. ; software, Q.M. and Y.H. ; validation, Y.H.