Amplification and Increased Duration of Earthquake Motion on Uneven Stress-Free Ground

by A. Wirgin & J.-P. Groby arXiv.org E-print Archive, 22 Sep 2006 When a flat stress-free surface separating air from a isotropic, homogeneous or horizontally-layered, solid substratum is solicited by a shear horizontal plane body wave incident in the substratum, the response in the substratum is a single specularly-reflected body wave. When the stress-free condition, equivalent to vanishing surface impedance, is relaxed by the introduction of a spatially-constant, non-vanishing surface impedance, the response in the substratum is again a single reflected body wave whose amplitude is less than the one in the situation of a stress-free ground. When the stress-free condition is relaxed by the introduction of a spatially-modulated surface impedance, which simulates the action of an uneven ground, the frequency-domain response takes the form of a spectrum of plane body waves and surface waves and resonances are produced at the frequencies of which one or several surface wave amplitudes can become large. It is shown, that at resonance, the amplitude of one, or of several, components of the motion on the surface can be amplified with respect to the situation in which the surface impedance is either constant or vanishes. Also, when the solicitation is pulse-like, the integrated time history of the square of surface displacement and of the square of velocity can be larger, and the duration of the signal can be considerably longer, for a spatially-modulated impedance surface than for a constant, or vanishing, impedance surface. Read more