Three-dimensional behavior of a cylindrical underground structure under an oblique incidence of seismic wave was theoretically analyzed. The surrounding ground and the lining are taken as homogeneous, isotropic, and linear elastic mediums and the seismic wave is assumed as a plane harmonic shear wave. The solutions are obtained by means of the eigenfunction expansions method. Numerical results show that the circumferential strain is influenced by the ratio of the stiffness of ground mass relative to tunnel lining and is not influenced by the frequency of incident wave. On the other hand, the axial strain is influenced not only by the ratio of the stiffness of the ground mass relative to tunnel lining but also by the frequency. It is because the axial stiffness of the tunnel depends on the rate of change of the axial displacement. As a result of that, the axial strain becomes larger than the circumferential strain when the Young's modulus of the ground is one-tenth or less of that of the tunnel lining. Therefore, seismic design of the tunnel should be done not only for cross-sectional direction but also for axial direction when the tunnel is constructed in the weak rock.

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