Vulnerability Functions of Buildings based on Damage Survey Data of Earthquakes after the 1995 Kobe Earthquake

Abstract

After an earthquake, early damage estimation of damaged buildings is important for Business Continuity Plan (BCP). In this paper, Bayesian inference for damage probabilities using real time monitoring data is proposed. The authors developed the structural monitoring system for evaluating structural failure levels by measuring relative story displacement. This system can obtain failure data of monitored buildings just after an earthquake. Damage of non-monitored buildings and exposed area against earthquake can be estimated by analyses of the monitored data. Bayesian inference which can estimate uncertain phenomenon (posterior distribution) from prior distribution and likelihood function is applied to the damage estimation of structures. In this paper, posterior distribution is included in a posterior fragility curve of a structure due to new earthquake, prior distribution is included in a prior fragility curve obtained by damage investigations due to historical earthquakes and a likelihood function is generated by the damage probability based on real time monitoring data. Parametric studies were conducted to understand the characteristics of Bayesian inference model for the estimation. The characteristics of the prior fragility curve are a distribution form which is determined by mean and standard deviation of normal distribution, and a distribution of probabilities which is assumed by Beta distribution. The variation can be evaluated by pre-investigation hypothetical sample which expresses the uncertainty of probability based on Beta distribution. The parameters for likelihood functions are the number of targeted total buildings and the ratio of the monitored data to the total buildings. The likelihood functions are generated by monitored damage data in an actual earthquake and by Monte Carlo method considering the variation (uncertainties) of probability in a simulation at every seismic intensity. The parametric studies clarify that the number of monitored buildings largely influence the posterior fragility curve. The more the number increases, the higher the certainty increases and the smaller the region of 95%HDR (Highest Density Region) of Beta distribution. Application example is conducted using damage data due to historical earthquakes [1]. The paper showed the numbers of damaged buildings for every damage level and at every measured seismic intensity. Referring these data, it was investigated how the ratio of the monitored buildings to the total buildings influence to the estimation of the posterior fragility curve. Lack and differences of the number of monitored data at every seismic intensity influence to the certainty of maximum likelihood damage level distribution. Through these studies, the applicability and consideration for uncertainty of damage probability of the proposed method are shown.