Base Isolation Benefits of 3‐D Rocking and Uplift. I: Theory

Abstract

Block objects, standing on a shaking foundation, tend to rock and may uplift. Rocking of buildings in earthquakes is of particular interest because human lives and high costs are at stake. Most previous studies on rocking are limited to two‐dimensional motion for simplicity. In this paper, a new model is studied, which includes the three‐dimensional rocking, rolling, and uplift of a rigid cylinder when subjected to ground motion. The cylinder rests on a Winkler foundation of independent springs and dashpots. To simulate uplift, the springs and dashpots separate from the base of the cylinder when the springs are about to be in tension. The governing equations of this system are derived exactly using the Lagrange equation. Then numerical integration is employed to obtain the motion of any point within the structure, and simple beam theory is used to calculate the 3‐D state of stresses within the cylinder. Computer simulations show that 3‐D motion is significant under earthquake‐like excitations. Near‐2‐D rocking also occurs and produces very high spikes in accelerations and internal stresses. Moreover, restricting uplift can introduce high stresses and accelerations inside the structure.