Influence of foundation pit excavation on the horizontal deformation of adjacent shield tunnels considering non-limit earth pressure

Foundation pit excavation can induce significant horizontal deformation in adjacent shield tunnels, potentially threatening their structural and operational safety. However, the distribution of the excavation-induced additional stress field and the underlying tunnel-soil interaction mechanisms remain unclear. To improve the theoretical framework for predicting the horizontal deformation of adjacent tunnels during foundation pit excavation, this study proposes a two-stage approach to address the limitations of traditional computational theories such as incomplete consideration of factors like retaining structure displacement, non-limit soil pressure, and excavation depth. In the first stage, the Mindlin formula is used to calculate the total additional horizontal stress along the tunnel axis induced by unloading stresses at the pit wall and pit bottom. In the second stage, the tunnel is assumed to be an Euler beam on a Winkler elastic foundation model, and the corresponding differential equations are established. The weighted residual method is used to solve these equations and derive the analytical solution for the horizontal displacement of the tunnel. The research results indicate that the maximum horizontal displacement, bending moment, and shear force of the tunnel decrease with increasing subgrade coefficient and horizontal distance between the tunnel and the excavation pit, while increasing with greater excavation depth. The maximum horizontal displacement and bending moment of the tunnel occur at the center of the tunnel axis, while the maximum shear force occurs near the two ends along the long side of the excavation pit. When non-limit soil pressure is considered, the calculated tunnel horizontal displacement at the same location better aligns with actual engineering behavior, whereas neglecting it yields overly conservative results. The proposed method provides a useful theoretical reference value for evaluating tunnel deformation induced by foundation pit excavation in actual engineering projects.