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This paper aims to introduce a simplified moment-rotation backbone model for exploring the nonlinear behavior of shallow foundations subjected to rocking. The model is developed based on parametric numerical investigations of rectangular footings on dense dry sand, taking advantage of a nonlinear macro-element model verified based on a set of experimental results. Empirical expressions are proposed for rocking stiffness degradation due to gravity loads and foundation rotation as a function of the factor of safety against vertical loads and aspect ratio of foundations. Similar to previous researches, the uplift reference rotation was introduced to explore a new closedform expression appropriate for normalizing the foundation response in a non-dimensional form. The proposed approach for stiffness degradation and nonlinear backbone model of rocking foundations aims to be simple, to minimize the dependence on the variable parameters, and to provide physically sound selections for engineering applications.

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