Theoretical Analysis of Energy Distribution Characteristics in Deeply Buried Circular Tunnels with a Revealed Cave

Abstract

This study aims to analyze the distribution characteristics of energy in deeply buried circular tunnels with a revealed cave. Analytical solutions for the stress and elastic strain energies in these tunnels are derived using the complex variable method and compared with numerical solutions obtained from finite element simulations. Subsequently, a parametric study investigates the effects of the cave’s orientation, shape, and protrusion on the distribution of elastic strain energy. Finally, the influence of the revealed cave on the stability of the surrounding rock is analyzed using the evaluation index based on energy theory. The conclusions are as follows: the presence of the cave causes elastic strain energy to accumulate in the surrounding rock near the middle of the cave. The smaller the angle between the cave direction and the minimum principal stress, the more severe the energy accumulation near the cave. As the cave’s protrusion increases and the b/a ratio of its shape decreases, energy accumulation near the cave becomes more severe. The presence of the cave increases the tendency for tunnel failure. The middle of the cave is susceptible to damage due to the accumulation of strain energy, while the intersection of the cave and the tunnel is more prone to damage because tensile stresses lower the energy threshold for surrounding rock failure. The study indicates that the middle of the cave and the junction between the cave and the tunnel are key areas requiring safety protection during construction.