## 3 Mechanical Analysis and Numerical Simulation of Roadway Wall Rock
### Wall Rock Support System and Its Mechanical Analysis  
After the rock mass is damaged, during the redistribution of internal stress, the rock mass around the roadway plays a major bearing role on the overlying strata and is the main bearer of the wall rock pressure [37]. The temporary support only bears 1-2% of the weight of the overlying strata. Applying the initial support force to the exposed roof in time can effectively prevent the roof falling trend, prevent the continuous expansion of the wall rock plastic circle, and reduce the damage degree of the roof rock mass. The temporary support and wall rock constitute the wall rock support system, and their interaction relationship is shown in Figure 1. The abscissa \(U\) in the figure represents the displacement of wall rock, and the ordinate \(P\) represents the support force of the temporary support. The original wall rock stress after roadway excavation is \(P_{m}\), and only a temporary support providing a support force equivalent to \(P_{m}\) can completely prevent the roof from sinking. If a small amount of displacement of the roof is allowed, the roof is supported at point \(A\). At this time, the displacement of the wall rock is \(U_{a}\), and the support force required by the temporary support equipment is reduced to \(P_{a}\), playing the role of self-bearing the wall rock. During the continuous sinking of the roof, the equipment working point is moved from point \(A\) to point \(B\) or point \(C\), and the support force required by the equipment is also reduced to \(P_{b}\) and \(P_{c}\). Therefore, in order to maximize the self-bearing effect of wall rock and reduce the support force required by the temporary support, it is required that the roadway support system have a certain strength and scalability, and the roof is allowed to have a certain displacement during the support process. The displacement U of the wall rock should be controlled within a reasonable range. When the displacement of the wall rock exceeds \(U_{c}\), the loose pressure of the roadway increases, causing the wall rock of the roadway to become loose and collapse, and the support force of the temporary support equipment also increases. Therefore, in order to maximize the use of the self-bearing function of the wall rock and ensure the stability of the wall rock, the displacement of the wall rock should be controlled within \(U_{c}\). The design of a temporary support should be based on meeting the maximum wall rock pressure of the roadway, and the solution of the wall rock pressure is a necessary step in support design. At present, the theories related to wall rock pressure mainly include the whole soil column theory, circular section elastoplastic theory, [PERSON]'s theory, PU's equilibrium arch theory, etc. Based on PU's equilibrium arch theory and [PERSON] theory, this paper adopted the method of comparing the two theoretical methods to solve the maximum wall rock pressure of the roadway and took a mining area as an example to carry out the mechanical calculation and analysis of the wall rock of the roadway. 1. Solution of wall rock pressure based on PU's equilibrium arch theory  
PU's equilibrium arch theory is a stress theory of wall rock that reflects the actual situation of roadway roof collapse proposed by [PERSON], and its calculation model is shown in Figure 2. According to this theory, the excavation of a roadway in a loose rock mass with a certain cohesion forms a natural equilibrium arch at its top. The wall rock pressure exerted on the temporary support is the self-weight of the rock mass inside the natural equilibrium arch. The rock mass inside the equilibrium arch cannot bear the tensile stress but can only bear the compressive stress [38]. A sliding surface with a certain angle to the vertical plane is formed on both sides of the roadway. Figure 1: Interaction between temporary support and wall rock.