A fractional viscoplastic model to predict the time-dependent displacement of deeply buried tunnels in swelling rock

Abstract

This study focused on tunneling under challenging conditions, particularly with regard to the stress distribution and deformation in the humidity stress field. The swelling phenomenon during tunneling was treated as a quasi–humidity–mechanics coupled process, where the humidity diffusion and stress dilatancy were considered together to obtain the stress and deformation fields for tunnels crossing formations with high swelling potential. A solution to the nonstationary process of humidity transfer was derived according to Fick’s second law. First, the humidity distribution was obtained from the surrounding rock mass to determine the stress field. Then, a modified fractional viscoplastic model was developed to describe the whole creep process of soft rock swelling, as well as the damage and swelling deformation due to water immersion. Next, closed-form analytical solutions were derived for the displacement in the viscoplastic region, with more focus on the tunnel wall, based on a non-associated flow rule. The sensitivity of time-independent parameters was also analyzed. The solution was found to reasonably represent the tunnel convergence versus time when compared with the numerical simulation and monitoring data from the Nabetachiyama Tunnel.