Direct Integration Algorithms for Efficient Nonlinear Seismic Response of Reinforced Concrete Highway Bridges
Publication: Journal of Bridge Engineering
Volume 21, Issue 7
Abstract
Reinforced concrete (RC) highway bridges are essential lifeline structures, especially in California, which has numerous active faults at which earthquakes are common occurrences. Accurate seismic structural analysis is important to ensure their safety. The most suitable analytical simulation method for this purpose is nonlinear time-history analysis (NTHA). However, one of the main challenges for NTHA is related to the convergence of the numerical solution, which usually arises at high levels of nonlinearity. Inherent lack of high degrees of redundancy of the bridge systems and the need for their continuous functioning in the aftermath of an earthquake require accurate modeling and robust numerical solutions for the response investigation of these important structures. This paper presents solutions to the problems of convergence encountered in NTHA of RC highway bridges during the use of direct integration algorithms. The considered numerical integration algorithms include two that are explicit, namely, the Newmark and operator-splitting algorithms, and one that is implicit, namely, the TRBDF2 algorithm. Applicability of these integration algorithms, instead of the commonly used implicit Newmark, is explored for three representative RC highway bridges in California. Furthermore, the suitability of an adaptive switching among these integration algorithms during the NTHA is investigated. Finally, the efficacy of the solutions is demonstrated for a challenging performance-based earthquake engineering-related subject that involves a large number of NTHAs to identify the predominantly first-mode engineering demand parameters.
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Acknowledgments
This research was supported by Caltrans (Contract 65A0454) for the project “Guidelines for nonlinear seismic analysis of ordinary bridges.” The authors thank Caltrans for this support. Prof. Farzin Zareian, Univ. of California, Irvine, is acknowledged for providing the OpenSees models of the analyzed bridges.
References
Aviram A., Mackie K. R., and Stojadinović, B. (2008). “Guidelines for nonlinear analysis of bridge structures in California.” Rep. 2008/03, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Baker, J. W. (2011). “Conditional mean spectrum: Tool for ground motion selection.” J. Struct. Eng., 322–331.
Baker, J. W., Lin, T., Shahi, S. K., and Jayaram, N. (2011). “New ground motion selection procedures and selected motions for the PEER transportation research program.” 2011/03, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Bank, R. E., Coughran, W. M., Fichter, W., Grosse, E. H., Rose, D. J., and Smith, R. K. (1985). “Transient simulations of silicon devices and circuits.” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 4(4), 436–451.
Bathe, K. J. (2007). “Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme.” Comput. Struct., 85(7-8), 437–445.
Bathe, K. J., and Baig, M. M. I. (2005). “On a composite implicit time integration procedure for nonlinear dynamics” Comput. Struct., 83(31-32), 2513–2524.
Benzoti, G., Ohtaki, T., Pristley, M. J. N., and Seible, F. (1996). “Seismic performance of circular reinforced concrete columns under varying axial load.” Rep. 96/04, Division of Structural Engineering, Univ. of California, San Diego, CA.
Campbell, K. W., and Bozorgnia, Y. (2008). “NGA ground motion model for the geometric mean horizontal component of PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01 to 10s.” Earthquake Spectra, 24(1), 139–171.
Chopra, A. K. (2006). Dynamics of structures: Theory and applications to earthquake engineering, 3rd Ed., Pearson Prentice Hall, Upper Saddle River, NJ.
Combescure, D., and Pegon, P. (1997). “α-Operator splitting time integration technique for pseudodynamic testing error propagation analysis.” Soil Dyn. Earthquake Eng., 16(7-8), 427–443.
Günay, S., and Mosalam, K. M. (2013). “PEER performance-based earthquake engineering methodology, revisited.” J. Earthquake Eng., 17(6), 829–858.
Haselton, C. B., et al. (2009). “Evaluation of ground motion selection and modification methods: Predicting median interstory drift response of buildings.” Rep. 2009/01, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Hughes, T. J. R., Pister, K. S., and Taylor, R. L. (1979). “Implicit-explicit finite elements in nonlinear transient analysis.” Comput. Methods Appl. Mech. Eng., 17/18(Jan), 159–182.
Jayaram, N., Lin, T., and Baker, J. W. (2011). “A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance.” Earthquake Spectra, 27(3), 797–815.
Kappos, A. J., Gkatzogias, K. I., and Gidaris, I. G. (2013). “Extension of direct displacement-based design methodology for bridges to account for higher mode effects.” Earthquake Eng. Struct. Dyn., 42(4), 581–602.
Kaviani, P., Zareian, F., and Taciroglu, E. (2012). “Seismic behavior of reinforced concrete bridges with skew-angled seat-type abutments.” Eng. Struct., 45(Dec), 137–150.
Kaviani, P., Zareian, F., and Taciroglu, E. (2014). “Performance-based seismic assessment of skewed bridges.” Rep. 2014/01, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Liang, X., and Mosalam, K. M. (2015a). “Lyapunov stability and accuracy of direct integration algorithms in nonlinear dynamic problems and considering the strictly positive real lemma.” UCB/SEMM-2015/01 Technical Rep., Univ. of California, Berkeley, CA.
Liang, X., and Mosalam, K. M. (2015b). “Lyapunov stability and accuracy of direct integration algorithms applied to nonlinear dynamic problems.” J. Eng. Mech., in press.
Liang, X., Günay, S., and Mosalam, K. M. (2016). “ Seismic response of bridges considering different ground motion selection methods.” Chapter 12, Developments in international bridge engineering, A. Caner, P. Gülkan, K. Mahmoud, Eds., Vol. 9, Springer Tracts on Transportation and Traffic, Springer International, Cham, Switzerland, 147–154.
McKenna, F., Fenves, G. L., and Scott, M. H. (2000). “Open system for earthquake engineering simulation.” Univ. of California, Berkeley, CA, 〈http://opensees.berkeley.edu〉 (Sep. 15, 2015).
Nakashima, M., Kaminosono, T., Ishida, M., and Ando, K. (1990). “Integration technique for substructure pseudodynamic test,” Proc., 4th U.S. National Conf. on Earthquake Engineering, Vol. 12, Earthquake Engineering Research Institute, Oakland, CA, 515–524.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Eng. Mech., 85(3), 67–94.
PEER (Pacific Earthquake Engineering Research Center). (2011). PEER NGA Ground Motion Database. 〈http://peer.berkeley.edu/nga〉 (Sep. 15, 2015).
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© 2016 American Society of Civil Engineers.
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Received: Apr 24, 2015
Accepted: Nov 16, 2015
Published online: Feb 24, 2016
Published in print: Jul 1, 2016
Discussion open until: Jul 24, 2016
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