Abstract: The cross-sectional ovalization of tunnels is often neglected in the analysis of longitudinal deformation in existing shield tunnels caused by the excavation of an overlying foundation pit. The authors propose a discontinuous deformation differential solution that accounts for the influence of cross-sectional ovalization. A two-stage analytical approach is adopted. First, the additional stresses due to excavation unloading are computed using a modified Mindlin solution. The existing tunnel is then modeled as a short Euler-Bernoulli beam on a Pasternak foundation. The rotational stiffness of tunnel joints is derived from a parametric expression considering cross-sectional ovalization. The proposed method is validated through two engineering case studies. Furthermore, the influence of joint stiffness and the number of longitudinal reinforcement rings on the tunnel′s longitudinal deformation is analyzed. The results show that: (1) The proposed solution aligns well with measured tunnel uplift, while ignoring cross-sectional ovalization underestimates uplift displacement and joint opening and overestimates joint dislocation. For large excavation areas, ovalization has a diminished effect on uplift displacement but still significantly affects joint deformation. (2) Increasing joint rotational stiffness reduces uplift displacement and joint opening but increases joint dislocation. Increasing shear stiffness reduces both uplift displacement and joint dislocation but increases joint opening. (3) Longitudinal reinforcement effectively mitigates tunnel uplift due to overcrossing excavation; however, the marginal benefit decreases as the number of reinforcement rings increases.

Key words: upper foundation pit excavation, shield tunnel, longitudinal deformation, longitudinal beam-spring model, ovalization of tunnel cross-section