Effect of underground cavities on surface earthquakeground motion under SH wave propagation

A theoretical approach is presented to study the antiplane seismic response of underground structures, subjected to the incidence of both plane and cylindrical waves. The structure is assumed to be a circular inclusion embedded in a homogenous, isotropic and linear visco-elastic halfspace. The inclusion may consist either of a cavity, with or without a ring-shaped boundary, or it may be filled in with a linear-elastic material, without loss of generality. The analytical solution is obtained using expansions of wave functions in terms of Bessel and Hankel functions, relying on the technique of images and the use of Graf’s addition theorem to enforce the boundary conditions. The effects of underground cavities on surface earthquake ground motion are studied as a function of the size of the cavity, its embedment depth, the frequency content of the excitation, the incidence angle and the distance from the axis of symmetry of the cavity itself. A simple application of Rayleigh’s method allows us to verify that the ground surface response is dominated by the fundamental vibration mode of the portion of soil between the cavity and ground surface itself, in the frequency range of interest for engineering purposes. A simple relationship to estimate the fundamental natural frequency as a function of the embedment depth of the cavity is given. Finally, amplification factors on response spectra are obtained, to provide a practical insight into the effect of an underground cavity on surface ground motion during real earthquakes.