## 1 Introduction  
The complexity of coal mining conditions in China is on the rise, and the proportion of mining in close-range coal seams is gradually expanding [1]. In tandem, roadway damage under the influence of dynamic pressure is becoming prominent. Frequent damage phenomena, such as roadway tunnels' roofs breaking and falling, anchor bolts and cables shearing and detaching, and shoulder corners of the roadways severely squeezing and deforming, require regular repairs and maintenance. This has seriously affected the daily use of roadways and personnel safety, and the situation has gradually attracted the attention of experts and scholars [2, 3]. Many experts have analyzed and summarized the phenomena of damage to roadways due to the impact of dynamic pressure, revealing the damage mechanisms at work through theoretical derivation and numerical simulation [4, 5]. [PERSON] et al. [6] believe that the underlying factor behind significant deformation in deep roadways subjected to dynamic pressure is attributed to the development of precarious plastic regions. The main factor leading to the shift of the plastic zone from a stable state to an unstable one is attributed to external influences, including tectonic stress and mining activities. [PERSON] et al. [7] found that the stability of the surrounding rock and the large loose circle is often compromised under current support conditions, leading to significant deformation in the rock adjacent to roadways when subjected to dynamic pressure. According to the limit analysis theory, a roadway soft rock failure model was developed by [PERSON] et al. [8], and they analyzed the fracture evolution process of surrounding rocks subjected to various mining stresses. [PERSON] et al. [9] developed a model to analyze the structure of the overlying rock and stress distribution in coal pillars within a goat roadway subjected to dynamic pressure. They also proposed theoretical criteria for assessing the stability of both the \"arch beam\" structure and coal pillars in goaf entry roadways subjected to dynamic pressure. [PERSON] et al. [10] established models of F-shaped roof structures with long and short arms for various mining stages in the initial working area, and they presented stress calculation approaches for the surrounding rock on the gob side of a roadway. [PERSON] et al. [11] investigated the mechanism of structural evolution in goaf roof roadways when subjected to dynamic pressure, computed the roof pressure for the short arm beam dynamic pressure model, formulated a calculation formula for identifying roof fractures, and derived a criterion for determining roof fracture occurrence. [PERSON] et al. [12] employed numerical simulation techniques to examine the instability properties of coal roadways with composite roofs. They uncovered the progressive evolution patterns of fractures, as well as the modes of instability and failure in roadways surrounding rock subjected to multiple dynamic pressures. In addition, the selection of roadway support under dynamic pressure is intricately intertwined with roadway section shape and surrounding rock condition, which must be met for specific geological and mining conditions [13], and dynamic loads contribute to the use of a support that is not only more durable but yielding [14]. Some scholars have improved the support technology of dynamic pressure roadways and proposed targeted support schemes. [PERSON] et al. [15] observed that the effectiveness of U-shaped steel supports in mitigating deformation and damage to roadways under dynamic pressure was limited. [PERSON] et al. [16] studied the stress field in a side coal roadway of a goaf under the influence of mining, and they suggested a support scheme that combines \"anchor cable + grouting + single pillar\". [PERSON] et al.