Abstract
The problem of cavity stability widely exists in deep underground engineering and energy exploitation. First, the stress field of the surrounding rock under the uniform stress field is deduced based on a post-peak strength drop model considering the rock’s characteristics of constant modulus and double moduli. Then, the orthogonal non-associative flow rule is used to establish the displacement of the surrounding rock under constant modulus and double moduli, respectively, considering the stiffness degradation and dilatancy effects in the plastic region and assuming that the elastic strain in the plastic region satisfies the elastic constitutive relationship. Finally, the evolution of the displacement in the surrounding rock is analyzed under the effects of the double moduli characteristics, the strength drop, the stiffness degradation, and the dilatancy. The results show that the displacement solutions of the surrounding rock under constant modulus and double moduli have a unified expression. The coefficients of the expression are related to the stress field of the original rock, the elastic constant of the surrounding rock, the strength parameters, and the dilatancy angle. The strength drop, the stiffness degradation, and the dilatancy effects all have effects on the displacement. The effects can be characterized by quantitative relationships.
Highlights
Circular holes are widely involved in deep underground energy exploitation, nuclear waste storage, and underground space development, such as circular chambers in mines, water conveyance tunnels, mine borehole pressure relief, oil and gas development, and columnar holes in coalbed methane mining[1,2,3,4,5]
The tensile and compressive elastic modulus ratio is defined as E = E+/E−, the ratio of Poisson’s ratios is defined as μ = μ+/μ−, and the residual strength coefficient in the plastic strength drop zone is defined as λc = cr/c and λφ = φr/φ
A unified analytical solution for the displacement of the surrounding rock is obtained for the problem of circular holes in deep underground engineering, considering different characteristics of the tensile and compressive elastic moduli of the surrounding rock, the strength-stiffness degradation, and the dilatancy behavior in the plastic zone
Summary
Circular holes are widely involved in deep underground energy exploitation, nuclear waste storage, and underground space development, such as circular chambers in mines, water conveyance tunnels, mine borehole pressure relief, oil and gas development, and columnar holes in coalbed methane mining[1,2,3,4,5]. Based on the Hoek-Brown failure criterion, Brown et al.[6] analyzed the theoretical solutions for the stress and displacement of circular holes in two models, i.e., elasticplastic and elastic-brittle-plastic. In many reports, the analytical solutions of the stress and displacement of a circular hole were obtained considering the initial damage caused by blasting loads[14,15,16,17]. Researchers have established analytical solutions for various circular holes based on different working conditions using different constitutive models. In these solutions, the displacement in the plastic zone was developed based on the following three assumptions. Displacement of surrounding rock in a deep circular hole considering double moduli
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