Analytical Solution of a Circular Opening considering Nonuniform Pressure and Its Engineering Application

Peng Wu,Liang Chen,Wei Zhang,Xianbiao Mao,Yanlong Chen,Zhushan Shao

doi:10.1155/2020/8828917

Peng Wu, Liang Chen + Show 4 more

Open Access

https://doi.org/10.1155/2020/8828917

Copy DOI

Abstract

Based on the Mohr–Coulomb criterion, a new analytical solution of a circular opening under nonuniform pressure was presented, which considered rock dilatancy effect and elastic-brittle-plastic failure characteristics. In the plastic zone, the attenuation of Young’s modulus was considered using a radius-dependent model (RDM), and solution of the radius and radial displacement of plastic zone was obtained. The results show that many factors have important impact on the response of the surrounding rock, including lateral pressure coefficient, dilation coefficient, buried depth, and Young’s modulus attenuation. Under nonuniform pressure condition, the distribution of plastic zone and deformation around the opening show obvious nonuniform characteristic: with the increasing of lateral pressure coefficient, the range of plastic zone and deformation decrease gradually at side, while they increase at roof and floor, and the location of the maximum value of support and surrounding rock response curve transfers from side to roof. Based on the analytical results and engineering practice, an optimization method of support design was proposed for the circular opening under nonuniform pressure.

Highlights

It is important to predict the distribution of stress and deformation accurately for a deep circular opening, which is the basis for evaluating the stability of surrounding rock and reliability of support design in deep mining and other underground engineering
Many efforts have been paid on this topic, based on the linear Mohr–Coulomb (M-C) criterion or nonlinear Hoek–Brown (H-B) criterion, considering ideal elastic-plastic model (EPM), elastic-brittle-plastic model (EBM), or strain-softening model [1,2,3,4,5,6,7,8,9,10,11]
Some theoretical analysis and numerical simulation results indicate that the lateral pressure coefficient has a remarkable influence on the stress state of surrounding rock [17,18,19]. erefore, the research results without considering the effect of lateral pressure coefficient are inconsistent with the engineering conditions

Summary

Introduction

It is important to predict the distribution of stress and deformation accurately for a deep circular opening, which is the basis for evaluating the stability of surrounding rock and reliability of support design in deep mining and other underground engineering. A mechanical model for circular opening with nonuniform confining pressure is first proposed. As for Young’s modulus, at present, there are two methods to define the attenuation process for the postpeak rock. Based on the proposed mechanical model, the closedform solutions of stress, deformation, and radius of plastic zone of the surrounding rock in circle opening with nonuniform confining pressure was obtained. En, according to the engineering practices in different geological conditions, a support design method was proposed considering nonuniform stress state Based on the proposed mechanical model, the closedform solutions of stress, deformation, and radius of plastic zone of the surrounding rock in circle opening with nonuniform confining pressure was obtained. e influence of the lateral pressure coefficient, dilation coefficient, and Young’ modulus attenuation on the response of the surrounding rock was studied. en, according to the engineering practices in different geological conditions, a support design method was proposed considering nonuniform stress state

Fundamental Assumptions

Solution of Stress and Deformation of Plastic Zone

Analytical Results

Support Design for Opening under Nonuniform Pressure