Displacement of surrounding rock in a deep circular hole considering double moduli and strength-stiffness degradation

• Published in: Applied mathematics and mechanics Vol. 41; no. 12; pp. 1847 - 1860
• Main Authors: Zhao, Zenghui, Sun, Wei, Chen, Shaojie, Feng, Yuanhui, Wang, Weiming
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01-12-2020; College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590, Shandong Province, China; State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Qingdao 266590, Shandong Province, China%College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, Shandong Province, China
• Subjects: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; 74L10; strength-stiffness degradation; circular hole; deep rock; displacement solution; O344.3; double moduli
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-020-2665-9

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.