Improved analytical solution for forecasting overlying excavation-induced tunnel response

Abstract

It is inevitable that deep excavation will induce free movement of the surrounding soil, which will further greatly influence the response of the underlying existing tunnel. Most theoretical studies are concerned with the mechanical equilibrium analysis of tunnel units, ignoring adopting the energy method to simulate tunnel-soil interaction, and further obtain the explicit solutions of tunnel response. On this basis, from the perspective of the energy relation, the existing tunnel’s deformation is simulated using the Rayleigh-Ritz method. Further, its potential energy equation is established based on Pasternak foundation. The minimum potential energy principle is selected to solve the variational tunneling energy solution, and then analytically solving for the overlying excavation-induced deformation on the existing tunnel. The proposed method’s rationality is tested against a series of finite element (FE) results as well as a field case study extracted from previous studies. Compared with the Winkler foundation model degraded from the suggested method, the corresponding results become closer to the measurement data. Additional parameter studies show that the soil elastic modulus, the excavation’s aspect ratio, and the tunnel axis depth are significant factors inducing the response of tunnel. Our proposed theoretical solution is beneficial to predicting the existing tunnels’ latent danger due to overlying excavation in related projects.