## 1 Introduction
[17] developed a mechanical model to analyze the behavior of rock beams on roadways' floors subjected to dynamic pressure, quantified the displacement when each load acted independently, and proposed a control method of \"bottom crane + bottom corner anchor + floor anchor\" to control roadways under dynamic pressure. [PERSON] et al. [18] studied the deformation and failure mechanism of roadways under dynamic pressure in the entire process from excavation to working face mining, and they proposed a method of combining high pre-stress constant resistance support and roof-cutting technology (HPCR-RC). [PERSON] et al. [19] proposed a collaborative approach to control pressure relief during directional roof cutting in strong roadways subjected to dynamic pressure. They also developed a three-dimensional model testing system to compare the effectiveness of their method with the conventional approach. [PERSON] et al. [20] conducted a theoretical analysis on the radii and displacement deformations occurring in roadway plastic zones subjected to dynamic pressure, and they proposed a support system consisting of \"anchor + anchor cable + shotcrete + deep and shallow borehole grouting + invert\" to limit the roadway deformation. [PERSON] et al. [21,22] conducted an analysis on the damage characteristics of rocks surrounding roadways when subjected to deep dynamic pressure. They innovatively introduced a collaborative control technology involving external anchoring and internal unloading to effectively restrict significant deformations in the roadway. [PERSON] et al. [23] introduced a control strategy of \"slow production, long-short control\" for roadways under dynamic pressure affected by mining, and they designed a \"high-strength yield bolt (cable) + steel belt\" coupling support scheme. Although the above studies have produced certain scientific results, few scholars have analyzed the impact of the dynamic pressure coefficient on the plastic zone of the surrounding rock during the study of the mechanisms of changes. Moreover, most of the support improvement solutions for roadways under dynamic pressure are still active supports, and these support solutions can play a certain supporting role in dynamic pressure roadways. However, under the influence of multiple strong dynamic pressures, there is still a risk of the anchor bolt and anchor cable being sheared and broken, and there is a potential for localized instability of the rock adjacent to the roadway, which does not effectively address the issue of controlling the surrounding rock. Therefore, we have focused on investigating the influence coefficient of roadways when subjected to dynamic pressure. As a result, we have derived an implicit equation that describes the boundary of the plastic zone surrounding a roadway under dynamic pressure and with a nonuniform stress field. Additionally, our study has examined how the influence coefficient affects both the shape and extent of this plastic zone. Simultaneously, the effect of support resistance on the plastic zone of a roadway under dynamic pressure was analyzed, and based on this, a joint support scheme comprising an anchor cable and channel steel beam-CFST column combined bracket is proposed to achieve the protection of rocks surrounding roadways under dynamic pressure.