Natural Boundary Element Method for Stress Field in Rock Surrounding a Roadway with Weak Local Support

摘要

Weak local support is a very common phenomenon in roadway support engineering. It is a problem that needs to be studied thoroughly at the theoretical level. So far, the literature on stress field theory of rock surrounding a roadway is largely restricted to analytical solutions of stress for roadways with a uniform support or no support at all. The corresponding stress solution under conditions of local or weak local support has not been provided. Based on a mechanical model of weak local support at the boundary of a circular roadway and the boundary element method on boundary value problems of bi-harmonic equations of a circular exterior domain, the boundary integration formula of an Airy stress function is deduced for roadways with weak local support. Using the boundary surface force of the roadway to calculate the boundary stress function and its normal derivative and substituting them into an integration formula, we derived a concrete expression of the stress function under various levels of support resistance. Furthermore, we have provided the rules of the distribution of stress and strain in the rock surrounding a roadway with different areas of weak support and support resistance. From the integration formula, the solutions for analytical stress can be directly obtained for the rock surrounding a roadway with uniform support or without any support at all. The solutions are exactly the same as those given in the literature.