A comprehensive framework for assessing critical behavior of lead rubber bearings under Multiaxial-Loading: Numerical, theoretical, collapse probability, and seismic analysis

This study proposes a standardized and reusable finite element (FE)-based framework to evaluate the critical behavior of lead rubber bearings (LRBs) under multiaxial loading (bidirectional shear deformation and axial pressure) in comparison with biaxial loading (unidirectional shear and axial pressure). The objectives of this study are: 1) to develop an advanced ABAQUS-based FE model capable of capturing the critical response of LRBs under both biaxial- and multiaxial-loading; 2) to investigate the critical behavior of LRBs under multiaxial-loading paths, including circular, box, and figure-eight orbits with varying the first and second shape factors; 3) to derive empirical formulations for predicting the normalized critical load under biaxial- and multiaxial-loading; 4) to develop collapse probabilities of LRBs as functions of shear-strain; and 5) to assess the influence of LRBs' multiaxial behavior on the seismic response of a three-dimensional, four-story steel-building subjected to 88-ground-motions. The results demonstrate that the critical shear strain of LRBs under multiaxial loading is defined as the maximum of the X- and Y-direction values, ensuring consistent and meaningful comparisons across varying loading paths. The figure-eight loading orbit significantly reduces the critical deformation capacity of LRBs and increases the probability of collapse compared to biaxial loading. Furthermore, the multiaxial behavior of LRBs leads to increased deformation, acceleration, and base shear of steel-building by 22.0 %, 22.3 %, and 27.2 % in the X-direction, and by 29.0 %, 22.6 %, and 30.3 % in the Y-direction, respectively, relative to the biaxial behavior. The findings support performance-based design tools by enabling data-driven and modeling framework of LRBs under multiaxial-loading.