Analytical model for a circular lined tunnel embedded in the layered soil under seismic waves

Abstract

AbstractIn this study, based on the wave function expansion method and exact stiffness method (ESM), an analytical model for a circular lined tunnel embedded in the layered soil under seismic waves is established. For convenience, the wave field in the layered‐soil‐tunnel (LST) system is divided into three parts, that is, the free wave field and scattering wave field in the layered soil, as well as the transmitted wave field in the lining. The free wave field in the layered soil is determined by the ESM for the layered soil. The scattering wave field in the layered soil is further decomposed into three parts, namely, the principal and complementary wave fields in the soil layer with the tunnel (the tunnel layer) as well as the modified wave field occurring in the other soil layers. These scattering wave fields are represented by the corresponding principal, complementary, and modified wave functions, respectively. The principal wave functions associated with the direct cylindrical waves emanated from the tunnel are represented by the Hankel functions. The complementary and modified wave functions correspond to the additional responses of the tunnel layer and the other soil layers due to the direct cylindrical waves from the tunnel, and can be obtained by expanding direct cylindrical waves into plane waves together with the application of the ESM. The transmitted wave field in the lining is simply represented by two kinds of Bessel functions. With the aforementioned wave field representations, the boundary value problem for the LST system under seismic waves is formulated. Based on the proposed analytical model, some numerical results and corresponding analyses are presented. Presented numerical results indicate that the dynamic stress concentration factor (DSCF) associated with the stiffer tunnel layer is usually larger than that associated with the softer tunnel layer for the incidence of plane P waves with not very low frequencies, while the circumstance for the incidence of plane SV waves shows an opposite tendency.