A Surrogate Modeling Approach for Rocking-Flexure Interaction

Abstract

Uplift of a structure is a seismic isolation technique: it works as a structural fuse limiting the maximum base moment (rocking foundation) or base shear (rocking podium) transferred to the foundation. To use uplifting in seismic design, the interaction between rocking and flexure must be understood well. Ideally, surrogate models to predict the seismic response of such systems should be also available to facilitate design. This paper presents the equations of motion of a building mounted on a rocking foundation and on a rocking podium in modal coordinates, then surrogate models are developed by applying component mode synthesis. Analytical equations for calculating the uplifted frequency and modal shapes are derived and used to compare how uplift affects both systems.In the following, it is shown that the overturning moment in both systems is dominated by the first mode, therefore a surrogate model with two degrees of freedom (2DOF surrogate), namely the rocking angle and the first mode coordinate, is considered adequate to represent the entire system. Finally, a hundred different buildings, with varying periods, aspect ratios and number of stories, are generated and the maximum dynamic response of the complete system is compared to the 2DOF surrogate ones, the coefficient of determination between all the responses is greater than 0.81 for all cases, thus the 2DOF surrogate is considered adequate to represent the response of the full model.