Inverse-form modelling for initial seismic retrofit design

The concept of performance-based seismic design (PBSD) has been explored by researchers for over a decade and the implementation stage is at the cusp of beginning. One important aspect of this early implementation stage is to examine existing analysis and design concepts that can serve as linkages to help improve and speed up implementation by integrating directly into the PBSD philosophy. To date, structural reliability has served as the cornerstone for load and resistance factor design (LRFD) code calibration and to some extent it could provide for some level of PBSD code calibration. This paper presents a summary of the results of a numerical study to examine the application of the inverse first order reliability method (I-FORM) for preliminary design of a base isolation system within the context of PBSD. In other words, it is given that a target structural reliability level is required for a particular structure, how does one select the properties (i.e., design) of the base isolation system to ensure the desired reliability level to all possible earthquakes? This is accomplished herein by decoupling the earthquake demand from the structural concept using a method known as the environmental contour procedure which is essentially I-FORM. The earthquake is described in terms of magnitude, site-to-source distance, and an uncertainty parameter that lumps both aleatory and epistemic uncertainties using readily available earthquake data. A ground motion attenuation function provides the link between the earthquake demand description and the structural concept in the form of spectral acceleration as a function of natural period. An illustrative example for a hypothetical building located in Los Angeles, CA having a fundamental period of vibration of 0.4 s prior to retrofit is presented. In this example, the stiffness of a laminated rubber bearing isolation system is the design variable of interest