A Simplified 3D Theoretical Model for Calculating the Surface Settlement Induced by Tunnel Undercrossing Excavation

When calculating the surface settlement caused by tunnel excavation, the conventional stochastic medium theory is complicated by integration. Particularly for tunnel undercrossing excavation, it shows large errors in calculating the surface settlement. In this paper, the conventional 2D stochastic medium theory is simplified by means of a nonuniform convergence. Based on the Sagaseta formula, the ground loss along the tunnel excavation direction is derived, and the 2D model is extended to calculate the 3D surface settlement. Furthermore, the effect of the existing tunnel is considered by the equivalent layered method, and the simplified 3D model is proposed for calculating the surface settlement induced by tunnel undercrossing excavation. The simulated and measured data are compared with the predicted results of the theoretical model, and the characteristics of the 3D surface settlement are investigated. The results show that compared with the surface settlement in the non-undercrossing section, the surface settlement in the undercrossing section has a larger lateral range. However, the maximum settlement value is significantly reduced, and the surface settlement trough curve is characterized as "wider and shallower." The results of the proposed model are in better agreement with the simulated and measured data than those of the conventional stochastic medium theory and have higher correlation and broader applicability.