Predicting the Displacement of a Circular Tunnel in an Elastic Medium Exhibiting Time-Dependent Swelling Behavior

This paper is aimed at developing an analytical solution for predicting the time-dependent swelling displacement of a circular tunnel. The unlined tunnel is assumed to be infinitely long with a uniform cross-section satisfying plane-strain conditions subjected to uniform far-field stress. Also, the gravity effect on the mechanical behavior of the tunnel is neglected. The material is considered to be isotropic, homogenous, and elastic with time-dependent swelling behavior. The swelling behavior is represented by an extended form of Grob’s law. This study assumes that the tunnel is excavated instantaneously, and elastic displacement occurs before the surrounding rock’s swelling begins. The proposed analytical solution is compared with the results obtained from numerical modeling, which proved close similarity (within 1% accuracy). Additionally, a parametric analysis was performed to investigate the effect of different parameters on the swelling displacement around the circular tunnel. Obtained results showed that the maximum swelling pressure controls both the magnitude of swelling displacement and the swelling extent around the tunnel. Moreover, the results show that a 10 percent increase in the maximum swelling pressure causes a 12.9 percent increase in the swelling radial displacement. In comparison, a 10 percent increase in either the swelling coefficient or the tunnel radius could only cause about a 10 percent increase in the final radial displacement.