Probabilistic Study on the Relationship Between the Residual Deformation and the Accumulated Plastic Deformation By An Earthquake


Abstract eng:
The residual deformation after an earthquake could be an index of structural damage to a building, if the relationship between the residual deformation (d r ) and the accumulated (total) plastic deformation (d t ), were obtained. For this purpose, in this paper, the probabilistic relationship between residual deformation and accumulated plastic deformation of a perfectly elastic-plastic single-degree-of-freedom oscillator is discussed. In the previous study, the author showed that the conditional probability of the residual deformation (d r ) given the number of plastic excursions (n) and the accumulated plastic deformation (d t ) is almost a normal distribution with an average of zero and a standard deviation of d t over the square root of n. Using this finding, the probability density function (PDF) of the residual deformation (d r ) can be formulated with the joint PDF of n and d t . Moreover, if one can assume that n and d t were statistically independent, it could be represented with each PDFs of d t and d t . Inversely, in this paper, the conditional PDF of d t given d r was derived, which would make it possible to estimate accumulated structural damage (i.e., d t ) to a building from the observed residual deformation (i.e., d r ) after an earthquake. In order to validate the derived equations of the conditional PDF of d t given d r , dynamic response analysis using a large number of pseudo ground motions simulated by the inverse Fourier transform. The analysis result showed that each PDF of the number of plastic excursion (n) and the accumulated plastic deformation (d t ) can be approximated by the gamma distribution. From these approximated PDF for n and d t and the derived equations, with the assumption that n and d t are statistically independent, the conditional PDF of d t given d r was calculated and compared to the histogram of d r calculated from the analysis result. The estimated PDF succeeded to capture the tendency that larger d t would be estimated when larger d r was observed, which was seen in the analytical results. The estimated mean and standard deviation of d t given d r also showed a reasonable agreement with the analytical results. From the above discussion, it can be concluded that, it is impossible to estimate d t (i.e. structural damage) only from d r , however, if the prior distributions of d t and n is known, it would be possible to improve the estimation accuracy of d t using the proposed equations and the observed d r .

Conference Title:
Conference Title:
16th World Conference on Earthquake Engineering
Conference Venue:
Santiago (CL)
Conference Dates:
2017-01-09 / 2017-01-13
Rights:
Text je chráněný podle autorského zákona č. 121/2000 Sb.



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 Record created 2017-01-18, last modified 2017-01-18


Original version of the author's contribution as presented on USB, paper 603.:
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