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# Stress Function of Rock Surrounding the Circular Roadway with Uniform and Local Support by Natural BEM

Dan Ma1,2, Xianbiao Mao1, Xiexing Miao1, Shaojie Liu1

1 State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221008, China
2 Tel: +86-516-83885995. Fax: +86-516-83885058. Email: madan518@126.com

Computer Modeling in Engineering & Sciences 2011, 74(3&4), 233-246. https://doi.org/10.3970/cmes.2011.074.233

## Abstract

Rock surrounding the circular roadway with uniform and local support is one of the most common phenomenons in roadway support engineering, which needs to be studied thoroughly at the theoretical level. The existing literatures on stress field function of rock surrounding the 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 support has not been provided. Based on the mechanical models of uniform support and local support, the methods of the complex variable function and the complex Fourier series, using the boundary integral equations which is obtained by the natural boundary reduction, this paper obtains the rock surrounding's Airy stress functions of the circular roadway with the whole equilibrium uniform support and the non-equilibrium partial local support respectively, as well as the analytical and numerical solutions to the each stress field functions. We also analyze the rules of different distribution for the two stress fields varying with the lateral pressure coefficient and the support angle by comparison. The results of calculation show that, with the increasing of the lateral pressure coefficient and the support angle of the circular roadway with local support, the peak value of the compressive stress declines, thus the stability of the overlaying strata is improved.

## Keywords

Ma, D., Mao, X., Miao, X., Liu, S. (2011). Stress Function of Rock Surrounding the Circular Roadway with Uniform and Local Support by Natural BEM. CMES-Computer Modeling in Engineering & Sciences, 74(3&4), 233–246.

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