Dynamics of Rectangular Footings by Finite Elements

A finite element solution in three dimensions for rectangular footings resting on soil medium has been presented for the vertical mode of vibration. Soil medium has been idealized as an elastic half space. Both linear and nonlinear, as well as depth dependent, soil properties have been considered for analysis. For discretizing into a finite number of elements, the semi-infinite elastic medium is idealized as a bounded region by adopting appropriate boundary conditions. A simple hexadedron isoparametric element with eight nodes (ZIB8) has been taken as basic element. Experimental and analytical studies indicate that the nature of contact pressures at the footing-soil interface changes with the magnitudes of operational frequencies, thus all probable contact pressures have been incorporated in the analysis. Effects of embedment, static surcharge, nonhomogeneity, and nonlinear stress-strain characteristics are shown. Influences of the aforementioned factors on the resonant frequencies have been reported. Results are compared with the existing solutions and presented graphically.