New Hyperstatic Reaction Method for Design of Subrectangular Tunnel Under Quasi-Static Loading in Full-Slip Condition

In seismic tunnel lining design, most existing studies have focused on circular and box-type tunnels, while the response of subrectangular tunnel linings under seismic loading, especially in imperfect soil-lining conditions, remains underexplored. The present paper aims to address this gap by investigating the behavior of subrectangular tunnel lining subjected to seismic loadings in full-slip condition using a novel calculation approach based on the hyperstatic reaction method (HRM). The innovation of this study is the introduction of a new quasi-static loading scheme to characterize the soil-lining interaction for subrectangular tunnels. New relationships between loading parameters, soil Young's modulus, tunnel lining thickness, tunnel dimension, and maximum horizontal acceleration are established through the back analysis of HRM and finite difference method (FDM) calculations. These relationships are then verified by considering different input parameters affecting subrectangular tunnel behavior under full-slip conditions. Numerical results indicate that the maximum incremental internal forces computed by the new HRM model are in excellent agreement with those from FDM. Meanwhile, the computational efficiency of HRM is far better than FDM due to 1D meshing and simpler boundary conditions. Therefore, the new HRM model offers an effective alternative to FDM for the preliminary design of the subrectangular tunnels subjected to seismic loading in full-slip conditions.