Analytical and numerical modelling of underground structures in seismic conditions

Waves propagating in the plane of the cross-section of a tunnel during seismic shaking generate ground distortions which tend to cause ovaling deformations of the lining. The resulting change in shape of the tunnel cross-section generates circumferential strains in the lining which can cause cracking and/or crushing of concrete and reduction of its carrying load capacity. In this paper, different closed form solutions for the analysis of the tunnel response are considered on the basis of the theory that the stress increment due to seismic loading can be assessed through a correct estimation of free-field deformations. Numerical analyses, in both two and three dimensional conditions, with the Finite Element Method, are performed and the comparison with analytical solutions is carried out. The uncoupled seismic response of a circular tunnel is analyzed both analytically and numerically, to investigate the seismic response of tunnels subjected only to shear or pressure waves. Then, a complete three dimensional analysis is performed to evaluate the overall response of the tunnel and the stresses induced in the lining by seismic loading. The results obtained by numerical modelling, in both two and three dimensional conditions, agree well with most of the analytical results, as long as seismic loading is applied in one direction only. When consideration is given to the three dimensional model with both horizontal and vertical motion, the numerical results agree with the analytical results based on a combination of the corresponding analytical solutions.