Effects of Flexibility on Rocking Impedance of Deeply Embedded Foundation

Abstract

This paper presents a detailed investigation of the influence on the rocking impedance of flexible sidewalls in embedded foundations. The study focuses on vertical and cylindrical foundations embedded in a homogeneous elastic stratum. In order to anticipate the effects of the flexibility, closed-form formulae for rocking impedance are derived based on three-dimensional wave propagation theory and superposition of both the rocking and flexural movements on a single model by assuming complete bonding conditions between the soil and foundations. A function representing the effect of the flexibility is identified from the closed-form formulae, in terms of the height to radius ratio of the foundations and the ratio of the stiffnesses of the ground and foundations. The rocking impedance for a flexible sidewall differs from those evaluated under the assumption of a rigid sidewall. The applicable range of rocking impedance evaluated under the assumption of a rigid sidewall is assessed, and contours to assist in the estimation of the dynamic response of deeply embedded foundations are presented.