Dynamic rocking response of a rigid planar block on a nonlinear hysteretic Winkler foundation

A new design philosophy termed "rocking isolation" has been advocated in recent studies on soil-structure interaction (SSI) toward utilizing nonlinear foundation response for seismic protection of structures. Allowing structures to rock on their foundation enables nonlinearities arising from base uplifting and soil yielding to limit seismic actions on structures, contributing to resilient SSI systems with controllable residual deformation. The current work presents an improved Winkler-based rocking foundation model as an efficient practical tool to calculate the dynamic response of a rocking isolation system idealized as a rigid rectangular block rocking on a nonlinear hysteretic foundation allowing for base uplift. Compared with existing Winkler models where coupled shear-compressive soil behavior is usually ignored, improvements are made by using smooth biaxial hysteretic elements to describe the point-wise constitutive relation between tractions and displacements at the base. The foundation model is calibrated and validated against published experimental and numerical simulation data on clayey foundations. Analytical expressions are derived to estimate foundation rocking stiffness and failure envelope which describes the interaction between ultimate resultant forces developed on the foundation. The free-vibrational and seismic responses of a class of flexibly supported rigid rocking blocks are examined using the proposed model through nonlinear response-history analyses. It is found that sliding due to the coupled shear-compressive soil behavior tends to reduce free-vibrational rocking response of blocks with smaller slenderness ratios, while it may increase or decrease seismic overturning potential of blocks on heavily loaded foundations.