# Numerical Simulation and Engineering Application of Temporary Stress Field in Coal Mine Roadway
###### Abstract
The support structure actively alters the stress state of the surrounding rock to maintain stability, with the stress field being a core issue reflecting the stability and failure of the rock and the interaction between the rock and the support [42; 43]. Using simulation software, scholars have analyzed the stress fields of rock bolts under different geological conditions based on coal mine geology [44; 45; 46; 47; 48]. As an elongated rod, the support stress field generated by a rock bolt within the surrounding rock far exceeds its own dimensions, and the related parameters of the rock bolt affect the distribution characteristics of the stress field [49; 50; 51; 52; 53; 54]. Therefore, the stress field of temporary support will not be confined to the supported location alone. The related parameters of support are crucial in determining equipment selection, cutting parameters, and control parameters. Scholars have analyzed the relationships between tunnel parameters, rock characteristics, unsupported span, support force, support location, and the stress-strain behavior of the surrounding rock [55; 56; 57; 58; 59; 60]. Among these factors, temporary support force and maximum unsupported span are the most critical factors in ensuring rock stability and improving tunneling efficiency. However, there has been limited research on the effects of temporary support on the surrounding rock in unsupported areas, particularly regarding the main parameters of temporary support, including temporary support length, temporary support force, and maximum unsupported distance, and their impacts on the stress-strain behavior of the surrounding rock in unsupported areas. This lack of clarity hinders the ability to ensure the stability of the surrounding rock in unsupported areas and to determine a reasonable unsupported span, which is a key limitation in enhancing tunneling efficiency. In this work, a stress distribution model for temporary support was developed to clarify the distribution characteristics of support forces within the surrounding rock. The impact of temporary support force, support length, and unsupported distance on the stress-strain behavior of the tunnel roof was further investigated through simulated tunnel excavation and support experiments. The model assumes that the temporary support applies a normal, uniform force on a semi-infinite plane. By performing two integrations, the distribution law of the temporary support force within the tunnel was derived. The difference in stress between unsupported areas with and without temporary support reveals that temporary support creates a stress field in the unsupported area. Analysis of this stress differential demonstrates that temporary support induces a beneficial stress field in these areas. Based on the linear relationship between the optimal support force and unsupported distance, the necessary optimal temporary support force for the unsupported area was calculated from this distance. The evolution of roof stress-strain with varying unsupported distances indicates that roof strain increases minimally when the unsupported distance is less than 3 m, as the attenuation of temporary support stress is minimal in this range. Finally, the correlation between unsupported distance, temporary support length, and roof stress-strain behavior was explored, identifying a distinct inflection point 18 m from the tunnel face. Beyond this distance, roof stress increased significantly, while it remained relatively stable up to this point.