Analytical solution of deformation of underlying shield tunnel caused by foundation pit excavation and dewatering

The foundation pit excavation and dewatering break the equilibrium stress field of the surrounding soil layer and negatively affect the underlying shield tunnel. The analytical solution of the longitudinal deformation of the underlying tunnel caused by foundation pit excavation and dewatering is proposed using a two-stage analysis method. In the first stage, Mindlin elastic solution and effective stress principle are used to calculate the additional stress caused by excavation and dewatering. In the second stage, the shield tunnel is treated as a Timoshenko beam resting on the Pasternak foundation to simulate the interaction between the tunnel and soil. The analytical solution of the longitudinal tunnel deformation is derived from the superposition method. By comparing with the monitoring data of engineering examples, the correctness of the proposed method is verified, and the influence of the excavation length, width, depth, tunnel burial depth, dropdown, and relative position of the foundation pit on the longitudinal displacement of the tunnel is further analyzed. The results show that with the increase of excavation length, width, and depth, the maximum uplift of the tunnel increases. The tunnel deformation decreases with the increase in tunnel burial depth. With the increase of the dropdown, the uplift decreases, and the settlement value increases. With the increased distance between the tunnel axis and the foundation pit center, there are a decreasing area of the uplift, an increasing area of the settlement, and a decreasing area of settlement.