Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

For the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations,a longitudinal integral response deformation method classified as a practical approach is proposed in this paper.The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well.When applying the proposed method,the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads.Then,the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation.Afterwards,the critical longitudinal seismic responses of the tunnel are obtained.The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing,determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-of-plane and in-plane waves.The results show that the proposed method has a clear concept with high accuracy and simple progress.Meanwhile,this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure.Therefore,the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.

Longitudinal mechanical response of tunnels under active normal faulting

This paper aims to clarify the mechanism of the longitudinal response of a tunnel under normal faulting via a comprehensive analysis of available experimental data and numerical simulations.Four 1 g condition model tests were reviewed and reanalysed to highlight the key characteristics of the tunnel response under normal faulting:S-shaped deformation and inverted S-shaped bending strain distribution in the longitudinal direction;the main affected zone of faulting is approximately six times the tunnel diameter to the fault plane.A threedimensional finite element model was also established and verified,followed by a sensitivity analysis of key parameters,including the fault dislocation,dip angle,tunnel rigidity and relative stiffness between the hanging wall and footwall.All results reveal that the longitudinal mechanical response under normal faulting is dominated by a combination of bending,tension,and shearing.Bending and shearing are induced by the large unbalanced rock pressure at the vault in the hanging wall and the inverted arch in the footwall;the value of unbalanced rock pressure is directly proportional to the dislocation but negatively correlated with the dip angle.Although the main part of the tunnel stays in tension,axial compressive strain exists around the fault plane when the dip angle is greater than 70 °,which may be related to the ovaling effect of the tunnel.Such an ovaling effect is caused by the compression at the cross-section of the tunnel and may lead to more complicated internal strain.