Abstract
Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes.
Highlights
For the Reinforced Concrete (RC) moment frame (Figure 9a–c), considering the pre-code drift limits, all five cases are resulting in similar fragility estimates
Where T ∗ is the downtime and t is the required downtime level, P( T ∗ > t DS = dsi ) is the conditional probability of exceeding a required downtime level, Nds is the number of damage states, and λ( I M > im) is the seismic hazard expressed as a probability of exceeding an Intensity Measure (IM) level in fifty years
This method mostly uses linear regression which assumes that the: median relationship between seismic response and intensity is linear in a log-log space; standard deviation is constant across different intensity levels; and distribution of response residuals follows a Gaussian distribution
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The degree to which the individual/compounded assumptions of linear regression affect the different damage states for a variety of mid-rise buildings (which make up a bulk of the building stock) has not been explored The impacts these assumptions have on the seismic risk of buildings assessed through the Performance-Based Earthquake Engineering framework (PBEE) [17]. This paper employs Gaussian kernel techniques to systematically alleviate the linear regression assumptions and explore the impacts on fragility and risk. Gaussian kernel techniques provide a form-free and data-driven means to capture the median variation of structural response, prediction standard deviation, and distribution of residuals as a function of the IM.
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