Dynamic Response of the Shield Tunnel with the Staggered-Jointed Lining to Elastic Waves
摘要
The staggered-jointed lining is now widely used as the lining for the shield-driven tunnel due to its advantages over the straight-jointed lining. However, due to its complex layout, the analytical method for the shield-driven tunnel with the staggered-jointed lining under external loadings still lacks in the literature. In this study, an analytical method for the staggered-jointed tunnel surrounded by the linearly elastic soil under harmonic seismic waves is developed. To develop the analytical method, the lining of the staggered-jointed tunnel is simplified as the periodic equivalent continuous shell (PECS) lining first, and accordingly the staggered-jointed lining and surrounding soil can be treated as a periodic system, referred to as the periodic soil–tunnel system (PSTS) subsequently. Then, with the periodicity of the PSTS, the representation for the scattered waves in the soil is developed using the wave function expansion method. Further, using the Fourier space equations of motion for the PECS lining and wave field representation for the soil as well as the continuity condition at the soil–lining interface, the coupled equations for the PECS lining and surrounding soil are deduced. The lining displacement and wavefunction coefficients of the soil due to the incident seismic waves can be determined by solving the coupled equations. The proposed analytical method for the PSTS is validated by comparing results obtained by the proposed method with those due to three analytical solutions. With the proposed analytical method for the staggered-jointed tunnel, some results for the dynamic response of the staggered-jointed tunnel to seismic waves are presented.