Influence of Viscous Coupling in Propagation of Elastic Waves in Saturated Soil

Abstract

The interactions between the solid and fluid phases of saturated porous media are due to inertial, viscous, and mechanical coupling. In particular, viscous coupling plays a key role because it makes wave propagation dispersive. The effects of viscous coupling on harmonic problems were described in detail by Biot, but the implications in transient problems have not been fully analyzed. Therefore, a detailed analysis is carried out on the effects of viscous coupling on the mechanics of transient wave propagation, by considering the propagation of simple shaped driving pulses (a step pulse, a single sine, and a single triangle), for both constant and frequency-dependent viscous coupling. Particular attention is paid to the interpretation of dynamic soil test measurements, because of their importance in the current practice of soil investigation, both in laboratory and in situ. Results show that it is possible to identify two extreme kinds of transient behavior: in the first, the porous medium behaves as a two-phase medium in which the velocity of propagation corresponds to null viscous coupling; in the second, the behavior corresponds to a one-phase medium with velocity of propagation corresponding to infinite viscous coupling. There is a gradual transition between these two extreme behaviors, but it extends for quite a narrow range of values of travel length and of the coefficient of permeability for a given frequency content of the driving pulse. Such conclusions are very useful in the interpretation of dynamic measurements and should enhance the comprehension of the mechanics of dispersive wave propagation in saturated porous media.