Rectangular footing on soil with depth-degrading stiffness: Vertical and rocking impedances under conditional existence of surface waves

The response of rectangular rigid footings resting on an elastic soil of shear modulus decreasing monotonically with depth is studied. Such profiles are typically encountered after ground improvement. The propagation characteristics of SV/P surface waves are investigated, showing the appearance of cut-off frequencies above which surface waves do not exist. The semi-analytical method of the subdivision of the footing/soil contact area is then used for solving the boundary value problem, whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green׳s functions. Impedance functions are presented over a wide range of frequencies for typical values of the non-homogeneity parameters, the Poisson׳s ratio and the foundation geometry. The salient features that are associated with the non-homogeneity and the appearance of cut-off frequencies are elucidated.