Estimating Volume Loss for Shield-Driven Tunnels Based on the Principle of Minimum Total Potential Energy

Volume loss is an important method to estimate ground movement during tunnelling. However, volume loss is usually estimated by empirical methods, especially for volume loss at the tunnel face, which is a three-dimensional problem. Based on the principle of minimum total potential energy, we proposed a semi-analytical method to predict the volume loss at the tunnel face and ground surface. The proposed method provides a more direct way of estimating volume loss at the tunnel face from an energy point of view. Moreover, a new deformation mechanism was designed to describe the ground movement before the tunnel face. Based on the proposed method, we investigated the influence of the support pressure, tunnel diameter, and tunnel depth on the volume loss at the tunnel face, and other parameters related to surface subsidence. The volume loss at the tunnel face decreased with the increase in the support pressure ratio and the slurry weight. The volume loss at ground surface was generally smaller than the volume loss at the tunnel face due to the soil compression during ground movement. The bigger the tunnel diameter, the bigger the volume loss at the tunnel face. However, the volume loss at ground surface may not increase with the increase in tunnel depth, because of the soil arching effect. Moreover, the deeper the tunnel, the more obvious the influence of the support pressure ratio on volume loss. Similarly, the bigger the tunnel diameter, the more obvious the influence of the slurry weight on the volume loss.