Uncoupled multivariate power models for estimating performance-based seismic damage states of column curvature ductility

The assessment for the thresholds of different damage state plays a vital role in the performance-based seismic design of earthquake-resistant structures. Although fast evaluation for limit curvature of slight damage (DS1) is presented in specifications and literature, quantitative models for other damage states, i.e. moderate damage (DS2), extensive damage (DS3), and collapse damage (DS4) curvature are not clearly illustrated. Therefore, an uncoupled multivariate power model (UCMV-PM), i.e., multivariate logarithm linearity models is proposed to estimate the curvature ductility of four damage states of column sections by considering the effects of four factors (section dimensional (L): 1 to 3 m, volumetric percentage of the reinforcement (rho l): (0.01 to 0.03), transverse volumetric steel ratio(rho s): (0.01 to 0.03), axial compression ratio (Rac): 0.1 to 0.3). To obtain large sample data, a simplified parametric calculation procedure for moment-curvature (M-phi) curves and each damage state is proposed. Based on the efficient procedure, a sample space of 214 data with four factors and 21 levels is quickly established on a common desktop computer. Finally, verification, comparison, and application of UCMV-PM indicate its characteristics of high accuracy, strong practicability, and wide coverage.