Abstract
Consideration of parameter uncertainty in structural seismic performance has become an important issue in the last decade. A common means of including such uncertainties is through the reliability theory. Seismic reliability assessment is concerned with calculation of probability of exceeding a certain structural limit state against a ground motion intensity measure. However, an important factor which affects the reliability index is the selection of probability distributions for structural demand. Usually a lognormal distribution is assumed by researchers but recent studies show that such simple assumption may result in misleading reliability measures. In this study, a three parameter lognormal distribution is proposed to be used to describe seismic behavior at relatively high intensity measures. This distribution is unique as it considers the missing or collapse data and at the same time incorporates a location parameter to disregard the less likely displacements at high spectral accelerations in Incremental Dynamic Analysis (IDA). It was shown by means of the Shannon’s entropy that uncertainty of calculating the reliability index using the proposed distribution is minimum compared to other available methods and therefore it is recommended to be used for reliability assessment of collapse prevention limit state.
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References
Aslani, H. and Miranda, E. (2005). “Probability-based seismic response analysis.” Engineering Structures, Vol. 27, No. 8, pp. 1151–1163.
Baker, J. W. and Cornell, C. A. (2008). “Uncertainty propagation in probabilistic loss estimation.” Structural Safety, Vol. 30, No. 3, pp. 236–252.
Bojórquez, E., and Iervolino, I. (2011). “Spectral shape proxies and nonlinear structural response.” Soil Dynamics and Earthquake Engineering, Vol. 31, No. 7, pp. 996–1008, DOI: 10.1016/j.soildyn. 2011.03.006.
Bradley, B. A. and Lee, D. S. (2010). “Accuracy of approximate methods of uncertainty propagation in seismic loss estimation.” Structural Safety, Vol. 32, No. 1, pp. 13–24.
Buratti N. (2012). A comparison of the performances of various groundmotion intensity measures, The 15th World Conference on Earthquake Engineering, Lisbon, Portugal; 24-28 September.
Cho, H. N., Choi, H. H., Kim, J. H., and Choi, Y. M. (2004). “An experience of practical reliability-based safety assessment and capacity rating.” KSCE Journal of Civil Engineering, Vol.8, No. 1 /January 2004, pp. 65–73.
Cornell, C. A. and Krawinkler, H. (2000). “Progress and challenges in seismic performance assessment.” PEER Center News, Vol. 3, No. 2, http://peer.berkeley.edu/news/2000spring/performance.html.
Cornell, C.A., Jalayer, F., Hamburger, R. O., and Foutch, D. (2002). “The probabilistic basis for the 2000 SAC/FEMA steel moment frame guidelines.” Journal of Structural Engineering, Vol. 128, No. 4, pp. 526–533.
Decanini, L., Liberatore, L., and Mollaioli, F. (2003). “Characterization of displacement demand for elastic and inelastic SDOF systems.” Soil Dynamics and Earthquake Engineering, Vol. 23, No. 6, pp. 455–471.
Deierlein, G. G. (2004). Overview of a comprehensive framework for earthquake performance assessment, PEER 2004/05, International Workshop on Performance-Based Seismic Design Concepts and Implementation, ed. P. Fajfar and H. Krawinkler (Bled, Slovenia).
Bojórquez, E., Astorga, L., Reyes-Salazar, A., Terán-Gilmore, A., Velázquez, J., Bojórquez, J., and Rivera-Salas, L. (2015). “Prediction of hysteretic energy demands in steel frames under narrow-band motions using vector-valued IMs.” Steel and Composite Structures, Vol. 19, No. 3, pp. 697–711, DOI: 10.12989/scs.2015.19.3.697.
FEMA-355C (2000). State of the art report on systems performance of steel moment frames subjected to earthquake ground shaking, FEMA 355C/September 2000. Washington (DC): Building Seismic Safety Council.
Goda, K., Hong, H. P., and Lee, C. S. (2009). “Probabilistic characteristics of seismic ductility demand of SDOF systems with Bouc-Wen hysteretic behaviour.” Journal of Earthquake Engineering, Vol. 13, No. 5, pp. 600–622.
Goulet, C., Haselton, C., Mitrani-Reiser, J., Beck, J. L., Deierlein, G. G., Porter, K. A., and Stewart, J. P. (2007). “Evaluation of the seismic performance of a code-conforming reinforced concrete frame building: From seismic hazard to collapse safety and economic losses.” Earthquake Engineering and Structural Dynamics, Vol. 36, No. 13, pp. 1973–1997.
Gupta, A. and Krawinkler, H. (2000). “Behavior of ductile SMRFs at various seismic hazard levels.” ASCE Journal of Structural Engineering, Vol. 126, No. 1, pp. 98–107.
Ibarra, L. F. and Krawinkler, H. (2005). Global collapse of frame structures under seismic excitations, Report TR152, the John A. Blume Earthquake Engineering Center, Stanford University, Stanford, California.
Jalayer, F. and Cornell, C. A. (2009). “A’lternative non-linear demand estimation methods for probability-based seismic assessments.” Earthquake Engineering and Structural Dynamics, Vol. 38, pp. 951–972, DOI: 10.1002/eqe.876.
Kazantzi, A. K., Righiniotis, T. D., and Chryssanthopoulos, M. K. (2008). “Fragility and hazard analysis of a welded steel moment resisting frame.” Journal of Earthquake Engineering, Vol. 12, No. 4, pp. 596–615, 2008.
Kwon, O. S. and Elnashai A. (2006). “The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure.” Engineering Structures, Vol. 28, No. 2, pp. 2890303, 2006.
Marano, G. C., Greco, R., and Mezzina, M. (2008). “Stochastic approach for analytical fragility curves.” KSCE Journal of Civil Engineering, Vol. 12, Issue 5, pp. 305–312, DOI: 10.1007/s12205-008-0305-8.
Mazzoni, S., McKenna, F., Scott, M. H., and Fenves, G. L. (2007). OpenSees Command Language Manual, Pacific Earthquake Engineering Research Center. University of California, Berkeley.
Medina, R. A. and Krawinkler, H. (2005). “Evaluation of drift demands for the seismic performance assessment of frames.” Journal of Structural Engineering, ASCE, 2005, Vol. 131, No. 7, pp. 1003–1013.
Mitrani-Reiser, J. (2007). An ounce of prevention: probabilistic loss estimation for performance based earthquake engineering. PhD Thesis, California Institute of Technology, Pasadena, California.
Modica, A. and Stafford, P. (2014). “Vector fragility surfaces for reinforced concrete frames in Europe.” Bulletin of Earthquake Engineering, Vol. 12, No. 4, pp. 1725–1753, DOI: 10.1007/s10518-013-9571-z.
Porter, K. A. (2003). “An overview of PEER’s performance-based earthquake engineering methodology.” Proceedings of Ninth International Conference on Applications of Statistics and Probability in Civil Engineering, San Francisco, California.
Romão, X., Delgado, R., and Costa, A. (2012). “Statistical characterization of structural demand under earthquake loading. Part 1: robust estimation of the central value of the data.” Journal of Earthquake Engineering, Vol. 16, No. 5, pp. 686–718, DOI: 10.1080/13632469. 2012.669514.
Ruiz-Garcia, J. and Miranda, E. (2010). “Probabilistic estimation of residual drift demands for seismic assessment of multi-story framed buildings.” Engineering Structures, Vol. 32, No. 1, pp. 11–20, DOI: 10.1002/eqe.2288.
Sasani, M. and Der Kiureghian, A. (2001). “Seismic fragility of RC structural walls: Displacement approach.” Journal of Structural Engineering, Vol. 127, No. 2, pp. 219–228.
Shinozuka, M., Feng, M. Q., Lee, J., and Naganuma, T. (2000). “Statistical analysis of fragility curves.” Journal of Engineering Mechanics, Vol. 126, No. 12, pp. 1224–1231.
Shome, N. and Cornell, C. A. (1999). Probabilistic seismic demand analysis of nonlinear structures, Report RMS-35, Reliability of Marine Structures Program, Stanford University, Stanford, California.
Shome, N. and Cornell, C. A. (2000). Structural seismic demand analysis: Consideration of collapse, 8th ACSE Specialty Conference on Probabilistic Mechanics and Structural Reliability.
Stoica, M., Medina, R. M., and McCuen, R. H. (2007). “Improved probabilistic quantification of drift demands for seismic evaluation.” Structural Safety, Vol. 29, No. 2007, pp. 132–145, DOI: 10.1016/j.strusafe.2006.03.003.
Taghavi-Ardakan, S. (2006). Probabilistic seismic assessment of floor acceleration demands in multistory buildings, Ph.D. thesis, Stanford University, Stanford, California.
Telesca, L., Lovallo, M., Mohamed, A. E. A., ElGabry, M., El-hady S., AbouElenean, K. M., and ElBary, R. E. F. (2012). “Informational analysis of seismic sequences by applying the Fisher Information Measure and the Shannon entropy: An application to the 2004-2010 seismicity of Aswan area (Egypt).” Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 2012, pp. 2889–2897, DOI: 10.1016/j.physa.2011.12.047.
Vamvatsikos, D. and Fragiadakis, M. (2010). “Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty.” Earthquake Engineering and Structural Dynamics, Vol. 39, pp. 141–163, DOI: 10.1002/eqe.935.
Vamvatsikos, D., Aschheim, M. A., and Kazantzi, A. K. (2014). “Direct performance-based seismic design: Avant-garde and code-compatible approaches.” Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June-2 July 2014 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4.
Yazdani, A. and Eftekhari, S.-N. (2012). “Variance decomposition of the seismic response of structures.” Scientia Iranica, Vol. 19, Issue 1, February 2012, Pages 84–90, DOI: 10.1016/j.scient.2011.12.003.
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Yazdani, A., Salehi, H. & Shahidzadeh, M.S. A modified three-parameter lognormal distribution for seismic demand assessment considering collapse data. KSCE J Civ Eng 22, 204–212 (2018). https://doi.org/10.1007/s12205-017-1820-2
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DOI: https://doi.org/10.1007/s12205-017-1820-2