Wave Propagation in Partially Saturated Soils

Abstract

In this article we will survey some of the methodology that has been developed in order to study the problem of wave propagation in soils or sediments; specifically, we are interested in the behavior of explosion induced shock waves propagating in partially saturated soils or sediments. Because waves in soils may be induced by many type of sources (e.g., earthquakes, machinery, explosions) the topic at hand has a long history and occupies a central position in the broad subject of soil dynamics; these different sources of propagating waves in soils must often be treated in different ways. In particular for determining the plastic deformations of a soil, or partially saturated sediment, which are caused by an explosive detonation, it is not possible to use the rheological model employed in investigating the processes of soil compaction caused by impact or vibration; this is well understood in the literature as being explained by the fact that the dynamic pressures and the velocities of deformation associated with an explosive detonation are many times greater than during an impact or vibration. Thus, the rheological features of the sediment in the zone of plastic deformations are different with an explosion as opposed to a small dynamic disturbance. In addition, it was established, some time ago, that there is an appreciable difference, in terms of the response to loadings generated by explosive detonations, between soils saturated and not saturated with water; in the latter type of soil, or sediment, plastic deformations predominate under loading while the elastic deformations are small and are observed only when the load is removed. In saturated sediments, however, it is mainly elastic deformations which are originated even under very high pressures. These conclusions form the basis for the use of a “plastic gas” medium in modeling the behavior of a partially saturated sediment near the source of an explosive detonation in the sediment; such models, which were studied quite early in the Russian literature (e.g., Refs. 1-5), have been brought into a satisfactory analytical state (Refs. 6-9) with respect to studying the dynamic compacting of a partially saturated soil or sediment in the neighborhood of a concentrated explosive source. The “plastic gas” models refer, in particular, to a medium which, upon being loaded, changes its density according to a definite law, but is such that when the load is removed (i.e., when there is a marked reduction in pressure) it retains the density obtained upon loading. If one has an interest primarily in the compaction of a partially saturated sediment in the immediate neighborhood of an explosive detonation, which is caused by the generation of a shock wave induced by that detonation, be it either spherical, cylindrical, or plane, then the appropriate approach would appear to be the one discussed in Sec. 2, which is based on the use of a plastic gas continuum model.