Empirical models for the nonlinear rocking response of shallow foundations

This paper aims to introduce simple empirical models to describe the nonlinear behavior of shallow foundations under rocking vibration. The model is developed based on parametric numerical investigations of rectangular surface footings on homogenous dense dry sand, taking advantage of a nonlinear macro-element model verified based on a set of experimental results. The proposed empirical expressions include the moment-rotation backbone curve, stiffness degradation and equivalent damping ratio as well as the correlation of the foundation settlements with cumulated rotations. These expressions are provided mainly as a function of the rotation, static factor of safety and aspect ratio of foundation. Similar to previous researches, the uplift reference rotation was introduced as a normalization parameter for the new closed-form expressions to be expressed in a non-dimensional form, whenever possible. The proposed approach aimed to be simple, in order to minimize the dependence on the variable parameters, and to provide physically sound selections for engineering applications.