ABSTRACT
Often in the dynamic analysis of shallow footings, length to radius ratio ≤ 2.0, the footing is assumed to be perfectly rigid. In the literature, there is no evidence on the effect of footing-soil stiffness ratio on the dynamic response of shallow foundations. To study this aspect, a continuum-based analysis for axial dynamics of shallow footings floating in a soil stratum is developed. In the analysis, the soil displacement field because of the axial load is expressed as a product of separable functions and the footing is described as a one-dimensional bar. The Extended Hamilton′s Principle is applied to obtain the differential equations of the footing and soil, which are solved analytically in an iterative algorithm. The analysis is verified with an existing formulation in the literature. It is further employed to obtain the dynamic response of shallow foundations for several values of footing-soil stiffness ratios.
