Bayesian Updating of Fragilities with Application to RC Frames
Publication: Journal of Structural Engineering
Volume 124, Issue 8
Abstract
This paper presents a Bayesian statistical analysis method for updating earthquake ground motion versus damage relationships in the form of fragility curves and for estimating confidence bounds on these fragility curves. As building damage data from past earthquakes become increasingly available, these data need to be combined with analytical fragility curves to arrive at more robust fragility curves. The Bayesian method provides a technique for updating these relationships. The parameters of analytical fragility curves are used to estimate the prior distributions of damage in the Bayesian analysis. In an earlier paper, Singhal and Kiremidjian presented a general methodology for the development of analytical motion-damage relationships in terms of seismic fragility curves and damage probability matrices. Data on building damage are used to estimate the likelihood functions. The Bayesian method for fragility analysis is illustrated by using the damage data on reinforced concrete (RC) frame buildings from the January 17, 1994 Northridge, Calif. earthquake. The uncertainties in the fragility curves are represented by confidence bounds around the median fragility curves.
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References
1.
Anagnos, T., Rojahn, C., and Kiremidjian, A. S. (1995). “NCEER-ATC joint study on fragility of buildings.”NCEER-95-0003, Nat. Ctr. for Earthquake Engrg. Res., State Univ. of New York, at Buffalo.
2.
Ang, A. H.-S., and Tang, W. H. (1975). Probability concepts in engineering planning and design. Vol. I, John Wiley & Sons, New York, N.Y.
3.
ATC-13. (1985). “Earthquake damage evaluation data for California.” Appl. Technol. Council, Redwood City, Calif.
4.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and decision for civil engineers. McGraw-Hill Inc., New York, N.Y.
5.
De Leon, D., and Ang, A. H.-S. (1993). “A damage model for reinforced concrete buildings: Further study with the 1985 Mexico City earthquake.”Proc., 6th Int. Conf. on Struct. Safety and Reliability, Innsbruck, Austria, Vol. 3, 2081–2087.
6.
Der Kiureghian, A.(1989). “Measures of structural safety under imperfect states of knowledge.”J. Struct. Div., ASCE, 115(5), 1119–1140.
7.
Geyskens, P., Der Kiureghian, A., and Monteiro, P. (1993). “BUMP: Bayesian updating of model parameters.”Rep. No. UCB/SEMM-93/06, Struct. Engrg., Mech., and Mat. Program, Dept. of Civ. Engrg., Univ. of California at Berkeley.
8.
Kennedy, R. P., Cornell, C. A., Campbell, R. D., Kaplan, S., and Perla, H. F. (1980). “Probabilistic seismic safety study of an existing nuclear power plant.”Nuclear Engrg. and Design, 315–338.
9.
Kiremidjian, A. S.(1985). “Subjective probabilities for earthquake damage and loss.”Struct. Safety, Amsterdam, The Netherlands, 2, 309–317.
10.
OES. (1995). “The Northridge earthquake of January 17, 1994: Report of data collection and analysis, part A: Damage and inventory data.” Prepared by EQE Int., Inc., and the Geographic Information Sys. Group of the Governor's Ofc. of Emergency Services for the Governor's Ofc. of Emergency Services of the State of California.
11.
Park, Y.-J., and Ang, A. H.-S.(1985). “Mechanistic seismic damage model for reinforced concrete.”J. Struct. Engrg., ASCE, 111(4), 722–739.
12.
Park, Y.-J., Ang, A. H.-S., and Wen, Y. K. (1984). “Seismic damage analysis and damage-limiting design of RC buildings.”Struct. Res. Ser., Rep. No. UILU-ENG-84-2007, Univ. of Illinois at Urbana-Champaign, Urbana, Ill., Oct.
13.
Raiffa, H., and Schlaifer, R. (1961). “Applied statistical decision theory.” Div. of Res., Graduate School of Business and Admin., Harvard Univ., Cambridge, Mass.
14.
Singhal, A., and Kiremidjian, A. S.(1996). “Method for probabilistic evaluation of seismic structural damage.”J. Struct. Div., ASCE, 122(12), 1459–1467.
15.
Somerville, P. G., Graves, R. W., and Saikia, C. K. (1995). “Characterization of ground motions at the sites of subject buildings.” Rep. on Task 4 of the SAC Joint Venture Program for the Reduction of Earthquake Haz. in Steel Moment Frame Build.
16.
Whitman, R. V., Biggs, J. M., Brennan, J. III, Cornell, C. A., De Neufville, R., and Vanmarcke, E. H. (1974). “Methodology and pilot application—Seismic design decision analysis.”Rep. R74-15, Dept. of Civ. Engrg., Massachusetts Inst. of Technology, Cambridge, Mass.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 124 • Issue 8 • August 1998
Pages: 922 - 929
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Aug 1, 1998
Published in print: Aug 1998
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