Comparison between Numerical and Analytical Analysis of the Dynamic Behavior of Circular Tunnels

Abstract

Dynamic behavior of underground structures is controlled by the strain field imposed by wave propagation and by the interaction between rock mass and structures. Shear and pressure waves propagating in the plane of the cross-section of the tunnel generate ground distortions, which tend to cause ovaling deformations of the lining. In this paper, the seismic response of a circular tunnel subjected respectively to shear waves and pressure waves will be analyzed both analytically and numerically at first, and then a complete 3D analysis will be given to show the overall effects on a tunnel induced by seismic events considering seismic inputs in three directions.

Analytical formulations of tunnel–soil–pile interaction under seismic excitations

“…Based on the first case, the spring stiffness is assumed to be independent of the wavelength. In this case, partial differentiates Equation ( 17) w.r.t the wavelength which is equated to be zero for obtaining the maximum wavelength of Equation (25). Also, the maximum wavelength is input in Equation ( 17) for getting the design shear force of Equation (26).…”

“…Also, experimental TSPI responses were closely varied to the three‐dimensional (3D) numerical analysis 4,5 . In addition, several authors evaluated the dynamic tunnel–soil interaction under seismic loading numerically and analytically 22–27 . In most recent studies, TSPI responses were evaluated numerically in liquefiable conditions considering the sand isotropic 2 and anisotropic 3 conditions.…”

“…4,5 In addition, several authors evaluated the dynamic tunnel-soil interaction under seismic loading numerically and analytically. [22][23][24][25][26][27] In most recent studies, TSPI responses were evaluated numerically in liquefiable conditions considering the sand isotropic 2 and anisotropic 3 conditions. However, the tunnel-soil interaction depended on the horizontal and vertical springs for P, SH, and SV waves, and the stiffnesses of these springs were related to Kelvin's and Flamant's problems.…”

Nonlinear anisotropic finite element analysis of liquefiable tunnel–sand–pile interaction under seismic excitation

“…However, both lateral and vertical deformations will occur in soil under seismic loading in numerical and analytical studies. The dynamic soil–structure interaction is affected by these deformation characteristics (Choudhury et al, 2018; Lakirouhani & Valioskooyi, 2017; Lu et al, 2018). Tunneling‐induced vertical and lateral movements of liquefiable sand are higher compared with the pure solid state of the soil.…”