Abstract: Current theoretical studies on deformation induced by excavation of foundation pits in soft soils in adjacent small curvature radius tunnels generally consider the foundation as a linear elastic body, which does not take the influence of the rheological property of soil body into account. Meanwhile, the deformation characteristics of curved tunnels are less analyzed, thus it is not possible to accurately predict the impact of foundation pit excavation on the deformation of existing tunnels with small curvature radius under the time effect. Firstly, a mechanical model of deformation induced by excavation of a soft soil pit with fractional order Merchant viscoelasticity adjacent to a small curvature radius tunnel is developed. The Laplace domain parameters of the fractional order viscoelastic soil are further derived according to the Laplace time-domain variability properties. Secondly, the additional stress field on the adjacent existing small curvature radius tunnels is solved based on foundation pit unloading and Mindlin stress solution theory. The time domain solutions for radial and vertical deformation of the existing small curvature radius tunnels are then derived by finite difference method and Laplace positive and inverse transformations based on Pasternak foundation and Timoshenko beam theory. Finally, the engineering measured data and three-dimensional numerical simulation results are compared with the analytical solution to verify relatively accuracy.