Prediction of Ground Settlement Due to Excavation of a Quasi-Rectangular Shield Tunnel Based on Stochastic Medium Theory

In this study, a method for calculating the ground loss-induced ground settlement during quasi-rectangular shield (QRS) tunnelling was investigated. Based on stochastic medium theory, an equation for calculating QRS tunnelling-induced transverse ground settlement was derived. A tunnelling face convergence mode coefficient, α, was introduced to make the derived equation applicable to various tunnelling face convergence modes. A modified equation for calculating the longitudinal variation in the ground loss ratio (ε) was proposed to calculate ε for any arbitrary cross-section in the tunnelling direction. On this basis, the proposed equation was longitudinally expanded, and an equation for calculating the three-dimensional (3D) ground settlement was obtained. A simplified model for additional grouting pressure was established, and the influence of additional grouting pressure on surface deformation was analysed. In addition, the proposed method was used to calculate the QRS tunnelling-induced ground settlement, and the results were compared with actual measurements. It is found that the predicted ground settlement obtained using the proposed method matches the actual measurements relatively well and reflects the 3D variations in the ground settlement. As α increases, the maximum ground settlement increases and the width of the ground settlement trough decreases, whereas the positions of the inflection points of the settlement curve remain unchanged. The horizontal distance between the inflection points is approximately twice the width of the tunnel.