Analysis on response of existing tunnels due to adjacent tunneling in multi-layered soils

A continuous elastic method for deformation responses of the existing tunnels in multi-layered soils caused by adjacent tunneling is presented based on the elastic layered half space soil model, whereas solutions only existed in homogeneous soils by the simplified method before. First, the initial functions of stress and displacement for single-layered soils are obtained by using the Laplace integral transformation. Analytical solutions are then obtained for multi-layered soils under vertical loads by means of the transferring matrix method, which is taken as basic solutions for the question. Second, the existing tunnel is regarded as the Euler-Bernoulli beam, and the continuous soil displacement can be calculated using the basic solutions of the elastic layered system. Composing free-soil settlements caused by the adjacent tunneling to the existing tunnel, the displacements and internal forces from the continuous elastic solution equation are obtained. Finally, the accuracy of the proposed method is verified by use of centrifuge model test data and the results from numerical methods, and the influences of the soil stratification on the tunnel response are also investigated. The proposed method provides a theoretical basis for the determination of rational protective measurements of the existing tunnels influenced by adjacent underground construction.