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To assess the dynamic stiffness of shallow foundations, as an alternative to the existing rigorous approaches, it is convenient to idealize the soil as some semifinite truncated cones representing the infinite nature of the supporting soil. The one-dimensional wave equation for cones which is usually defined in frequency domain has been extended to be solved directly in the time domain. The recently streamlined strength of materials using cones has been developed in the time domain to calculate the response of shallow foundations on a layered half-space for translational degrees of freedom, while the wave pattern in the time domain is not studied for a rocking degree of freedom. The concept of echoes which converts the response of the footing on homogenous half-space to that of the footing on layered site is still applicable when the layered system excited by rocking moments. The echo constants are derived in the current research for rotational degrees of freedom in either the flexibility or stiffness formulation. In this paper, using the theory of cones, equations for direct analysis of soil-structure interaction in the time domain are obtained for the rocking degrees of freedom. The results, calculated exclusively in the familiar time domain, are in remarkable agreement with the results obtained in the frequency domain.

Rocking Response of Shallow Foundations in Time Domain Using Cone Model Theory