Horizontal displacement of an adjacent metro station induced by foundation pit excavation with structural interaction effects

• Established quantitative coupling among pit support displacement, station displacement, and finite soil pressure. • Developed a theoretical model for displacement considering pit-station dynamic interaction. • Proposed a calculation expression for ultimate displacement of finite soil lateral pressure. • Validated model applicability via numerical simulation and literature comparison. • Analyzed key parameters’ influence on station displacement using the theoretical model. Aiming at the problem of predicting the displacement impact on an existing metro station adjacent to the new foundation pit, this paper establishes a quantitative coupling relationship among the support displacement of the foundation pit, the metro station displacement, and the lateral earth pressure by equating the finite width soil (abbreviated as finite soil) between the foundation pit and the station to horizontally independent soil springs. A trigonometric function model is employed to describe the displacement-dependent lateral earth pressure, and the hyperbolic tangent function is introduced to achieve a smooth transition between ultimate and non-ultimate lateral earth pressure states. Based on Euler – Bernoulli beam theory, a closed-form solution framework is constructed, leading to the development of a theoretical model for displacement response that considers the dynamic structural interaction effects between the new foundation pit and the existing metro station. This model overcomes the limitation of the traditional two-stage analysis method, which neglects the bidirectional interactions between structures. Model validation shows the theoretical maximum horizontal displacement ( δ max ) of the station under various conditions aligns closely with simulated values, with a maximum difference of 8.30 mm. Under actual conditions, the deviation between theoretical calculations and literature data for δ max is only 1.11 mm. Theoretical solutions for lateral earth pressure also match literature data well under both finite and infinite soil conditions. Parameter analysis indicates that increasing the finite soil width can effectively mitigate the impact on the metro station. A greater station cover depth facilitates a transition of the lateral earth pressure from the active state of finite soil to the passive state of infinite soil, ultimately driving δ max toward zero. Furthermore, an increase in the soil-structure friction angle enhances horizontal friction at the station boundary, leading to a monotonic decrease in δ max .