Harmonic Rocking of Rigid Block on Flexible Foundation

Abstract

A study of the rocking response of a rigid block resting on a foundation of independent springs and dashpots is made. To simulate the lack of appreciable tension strength in soil foundations, uplifting of the block base from the foundation is allowed when the springs are in tension. Two piecewise equations of motion are derived, and they are also coupled and nonlinear. Due to uplifting the system behaves as a softening system. An approximate analytical solution combining static condensation and the method of averaging is used to predict the rocking amplitude when the foundation moves horizontally due to a harmonic acceleration. The analysis shows that relatively large rocking amplitudes, compared to the model with perfect bonding, can occur at excitation frequencies below the natural rocking frequency. Further, an approximate method for predicting the maximum tilt-angle under horizontal earthquake excitation by relying on the linear seismic response spectra is developed. The predicted results are found in reasonable agreement with data obtained from numerical integration of the exact equations of motion.