Analytical Solution to the Problem of Lining Void in Deeply Buried Circular Tunnel

The excavation load is jointly borne by the surrounding rock and tightly-fitted lining, with different contact modes affecting the bearing effect. Therefore, this paper proposes a novel mechanical model of lining support to investigate the interaction between the lining and surrounding rock, particularly considering voids caused by tunnel excavation. By employing complex variable function method and optimization technique, it becomes possible to identify complete contact zones as well as void zones between the lining and surrounding rock, while also solving stress components at any point within them. Compared to other contact modes such as full contact, the proposed contact mode better reflects reality by avoiding occurrence of contact tensile stress during actual conditions. Subsequently, an analysis is conducted on how Young’s modulus of the lining, lateral pressure coefficient, and displacement release coefficient influence on voids. These research findings unveil the actual working mechanism behind lining support and provide a reliable theoretical foundation for preliminary design and void detection in lining support engineering.