A compatible uniaxial Bouc–Wen model for accurate estimation of residual deformation of seismically isolated structures

Abstract

Bouc–Wen (BW) model is commonly used to model lead rubber bearings (LRBs) in seismically isolated buildings. However, the original BW model violates the Drucker’s or Ilyushin’s postulate of plasticity by displaying the displacement drift, force relaxation, and non-closure of hysteretic loops. These deficiencies can significantly impact the seismic performance of the isolated structures, leading to unrealistic evaluation of residual deformation concentrated in the isolation layer. To address these issues, a step-by-step amendment algorithm is proposed to develop a compatible uniaxial BW (CBW) model that conforms to the basic physical rules. The proposed algorithm involves adding a reinforcement factor to the short-path reloading branches, defining reversal and reloading points to identify reloading behavior. Furthermore, it develops an adaptive limit to distinguish between the short-path and full-path reloading branches. The proposed algorithm was validated using various short unloading–reloading scenarios. Subsequently, a simplified single degree of freedom (SDOF) model representing a seismically isolated building was defined. Incremental dynamic analysis was performed to evaluate the seismic responses of the isolated building designed with the original BW, CBW, and bilinear models. Results indicate that although the peak displacement and seismic force of the isolation layer induced by the three models produce small deviations, considerable errors in residual displacement are observed. Compared with the original BW model, the bilinear model produces unrealistic sharp yielding transition and overestimates the residual displacement. However, it can reduce displacement drift and force relaxation. By contrast, the proposed CBW with the improved algorithm can effectively correct the defects of the original BW and bilinear models. The CBW model can be used to accurately estimate the residual deformation of the seismically isolated buildings.