Seismic risk analysis based on imprecise distribution and failure probability function under multidimensional limit state

Traditional probabilistic seismic risk analysis (PSRA) often adopts accurate probabilistic model to measure the uncertainties of structural response and capacity, which cannot evaluate the effect of the number of seismic waves on structural failure probability. A novel PSRA method based on imprecise distribution and failure probability function is proposed to solve the above problems. Multidimensional limit state function is adopted to measure the structural limit state. Based on lognormal distribution assumption, the means and standard deviations of engineering demand parameters (EDPs) and thresholds are all regarded as uncertain parameters, and the traditional PSRA formula is extended to the field of imprecise probability distribution. Interval estimation is used to evaluate the confidence interval and measure the uncertainties of the means and standard deviations at the given confidence level. Bayes formula method is adopted to solve the failure probability function and obtain the upper and lower bounds of vulnerability curve and mean annual failure probability. The results show that: The proposed method can measure the uncertainty of failure probability caused by the number of seismic waves through the width of vulnerability curve, which is very helpful to judge the reliability of estimated parameters. The wider width means the greater discreteness of structure response and the lower reliability of failure probability based on accurate parameters. With the increase of damage degree, the influence of the number of seismic waves on structural failure probability increases gradually.