# Study on elastic-plastic displacement response spectra of base-isolated structures and its influencing factors

## TL;DR

This study develops a formula to predict displacement in base-isolated structures during earthquakes, improving seismic design safety.

## Contribution

A practical formula for elastic-plastic displacement spectra of base-isolated structures is proposed, considering soil and earthquake factors.

## Key findings

- A two-degree-of-freedom system model with Bouc-Wen damping accurately calculates displacement response spectra.
- A formula was developed to estimate isolation layer displacement for base-isolated structures with natural vibration periods up to 10 seconds.
- The formula effectively predicts displacement under various site conditions and earthquake types.

## Abstract

In seismic design, the acceleration response spectrum method is used to calculate the bearing capacity of structures to ensure their safety. However, under intense earthquake action, insufficient deformation capacity of structures is the main cause of their failure. For base-isolated structures, the failure is caused by the displacement of the isolation layer exceeding the limit value. To derive practical elastic-plastic displacement spectra for base-isolated structures and incorporate them into seismic design, this paper categorizes 1217 strong motion records, with peak accelerations exceeding 10 gal, into nine groups based on soil conditions and earthquake type. To make the obtained displacement response spectra more accurate, this paper establishes the motion equation of a two-degree-of-freedom system model, using non-proportional damping and the Bouc-Wen model to describe the damping and mechanical characteristics of the isolation layer, the elastic-plastic displacement response spectrum is calculated using numerical methods. Accordingly, a practical formula for the elastic-plastic displacement spectra of base-isolated structures is established by analyzing the factors influencing (soil conditions, earthquake type, parameters in Bouc-wen model) the spectra. Herein, the elasto-plastic displacement response spectrum for base-isolated structures was established, and a formula for calculating the displacement of the isolation layer in base-isolated structures with natural vibration periods within 10 seconds was provided, along with the design peak ground displacement under different conditions. Based on the elastic-plastic analysis of two distinct base-isolated structures, results demonstrate that the current formula is an effective and rapid predictor for estimating the displacement of the isolation layer in base-isolated structures considering various site conditions.