Coupled Sliding and Rocking of Embedded Foundations

Wide ranges of soil properties, foundation dimensions, and depths of embedment are considered, and typical results are presented for the maximum amplitudes of the sliding and rocking oscillations and the frequencies at which these maximum amplitudes occur. The natural frequencies of the system with and without radiation damping are dependent on the shear wave velocity and Poisson's ratio of the half-space material, the geometric proportions of the foundation, and the depth of embedment, and they increase substantially as the depth of embedment increases. The total peak amplitude of vibration for the coupled motion is expressed in terms of a linear function whose coefficients are dependent on Poisson's ratio, the foundation dimensions, and the depth of embedment depth, and graphical relationships are presented to facilitate the determination of these coefficients. The results obtained clearly illustrate that embedment of the foundation significantly decreases its total peak amplitude for a given exciting force.