Multi-layer representation of continuous in-situ profiles in soil dynamics

In the dynamic analysis of soil-structure interaction, an issue of common concern is the influence of insitu modulus variation on the foundation response. In three-dimensional problems, one of the questions that remain to be clarified is the effects of continuous wave refractions and curvilinear rays of travel in the case of a smoothly heterogeneous soil medium. This paper summarizes the results for the dynamic response of a footing on a soil with a linear shear velocity profile via (i) an exact treatment, and (ii) an approximate representation in terms of a piecewise homogeneous multi-layered system. Both solutions are generated by a boundary element method which treats the unbounded contact tractions along the foundation edges rigorously. The spatial variation of the soil's stiffness in each case is achieved through the use of exact Green's functions. The comparison of the numerical predictions supplies physical insights as well as modeling hints for the discretized approach to the soil dynamics problem. Specific aspects of the problem such as the occurrence of local resonance peaks and the phenomenon of cutoff frequency are also examined.