(1. Research Center of Coastal and Urban Geotechnical Engineering，Zhejiang University，Hangzhou，Zhejiang 310058，China；2. Engineering Faculty，China University of Geosciences(Wuhan)，Wuhan，Hubei 430074，China；3. College of Civil，Construction and Environmental Engineering，Ningbo University，Ningbo，Zhejiang 315211，China；4. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education，Tongji University，Shanghai 200092，China；5. Hangzhou Qingchun Road Cross-river Tunnel Company Limited，Hangzhou，Zhejiang 310002，China)
Abstract：Pit excavation changes the ground stress state which affects the existing metro tunnels. An analytical method considering the shearing effect of tunnels was proposed to assess the longitudinal responses of tunnels induced by the adjacent excavation. The tunnel was assumed as a Timoshenko beam resting on the Winkler foundation. A two-stage approach was used to analyze the longitudinal deformation of the tunnel due to excavation. Firstly，equilibrium differential equations considering the effect of tunnel shearing were established based on the Timoshenko beam theory. Secondly，additional unloading pressure on the existing tunnel due to excavation was calculated using Mindlin′s elastic solution. Finally，the longitudinal deformation of the tunnel due to the unloading pressure was solved numerically using the finite difference method. The measured results from three well-documented published cases were selected to compare with the predicted results calculated with the proposed method as well as the Euler-Bernoulli beam method. Fairly good agreements are obtained between both two methods and the measurements. However，the Euler-Bernoulli method overestimates remarkably both the bending moment and shear force induced in the tunnel when compared to the results given by the proposed method. Because the proposed method is able to effectively model the shearing effect of the tunnel，the dislocation between the adjacent segmental linings subjected to the excavation can be further obtained by the proposed method.
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