Minimizing Superstructure Twist in Irregular Bridges through Optimization of Structural Parameters
Publication: Journal of Bridge Engineering
Volume 28, Issue 7
Abstract
Uneven distribution of mass, stiffness, and strength over the length of a bridge can produce rigid body rotation of the superstructure, or “twisting,” during an earthquake. Twisting response modes lead to the concentration or amplification of damage in the bridge substructure and, as such, are undesirable. AASHTO recommends a balanced stiffness approach to limiting bridge irregularities and provides possible modification techniques for bridges that do not satisfy the recommendations. However, there is a lack of research documenting the implementation details and benefits of these modification techniques on the performance of irregular bridges. This study investigated the effectiveness of three techniques to reduce the twisting response modes for geometrically irregular bridges during earthquakes: adjusting the effective heights of the bridge columns, modifying column end fixity conditions, and redistributing the superstructure mass profile. First, analytical equations were derived to estimate the values of parameters needed to achieve a balanced stiffness using each technique for any arbitrary bridge. Next, a finite-element model of an irregular, reinforced concrete, quarter-scale bridge previously tested on a shake table was validated against available experimental data. This model was used in conjunction with a metaheuristic optimization algorithm to determine the optimal values of the parameters such that the superstructure rotation was minimized for the experimental ground motions. Then, a parametric study was performed using a suite of hazard-consistent and spectrally matched ground motions to investigate the sensitivity of the optimization results to the number and spectral characteristics of the ground motions. The parametric study showed that reducing the effective heights of the columns by stiffening the lower portion of the columns was the most effective method to reduce the twisting response of the bridge and that three ground motions with different spectral shapes were the most computationally efficient subset when performing the optimization methodology.
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Data Availability Statement
Some data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request. These include the numerical models of the base and modified bridges, the experimental data used in validating the numerical model, and the optimization script used in this study.
This research was supported by the Department of Civil & Environmental Engineering at the University of Washington. The authors acknowledge the University of Washington’s ecosystem of high-performance computing clusters, HYAK, for providing computational resources that contributed to the results reported in this study.
References
AASHTO. 2014. AASHTO guide specifications for LRFD seismic bridge design (2nd edition) with 2012, 2014 and 2015 interim revisions. Washington, DC: AASHTO.
Adanur, S., A. C. Altunışık, H. B. Başağa, K. Soyluk, and A. A. Dumanoğlu. 2017. “Wave-passage effect on the seismic response of suspension bridges considering local soil conditions.” Int. J. Steel Struct. 17 (2): 501–513. https://doi.org/10.1007/s13296-017-6010-z.
Akbari, R., and S. Maalek. 2010. “Adequacy of the seismic analysis methods for single-column-bent viaducts considering regularity and higher modes effects.” J. Vib. Control 16 (6): 827–852. https://doi.org/10.1177/1077546309103422.
Alam, M. 2016. “Particle swarm optimization: Algorithm and its codes in MATLAB.” Int. J. Electr. Power Energy Syst. 81: 153–164.
Almazán, J. L., and J. C. de la Llera. 2009. “Torsional balance as new design criterion for asymmetric structures with energy dissipation devices.” Earthquake Eng. Struct. Dyn. 38 (12): 1421–1440. https://doi.org/10.1002/eqe.909.
Amjadian, M., and A. K. Agrawal. 2017. “Torsional response of horizontally curved bridges subjected to earthquake-induced pounding.” In Proc., 16th World Conf. on Earthquake Engineering. Tokyo, Japan: International Association for Earthquake Engineering (IAEE).
Anagnostopoulos, S., M. Kyrkos, and K. Stathopoulos. 2015. “Earthquake induced torsion in buildings: Critical review and state of the art.” Earthquakes Struct. 8: 305–377. https://doi.org/10.12989/eas.2015.8.2.305.
Araújo, M., M. Marques, and R. Delgado. 2014. “Multidirectional pushover analysis for seismic assessment of irregular-in-plan bridges.” Eng. Struct. 79: 375–389. https://doi.org/10.1016/j.engstruct.2014.08.032.
Baker, J. W. 2011. “Conditional mean spectrum: Tool for ground-motion selection.” J. Struct. Eng. 137 (3): 322–331. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000215.
Berry, M. P., and M. O. Eberhard. 2003. Performance modeling strategies for modern reinforced concrete bridge columns. Berkeley, CA: Pacific Earthquake Engineering Research Center.
Calvi, G. M., A. S. Elnashai, and A. Pavese. 1994. “Influence of regularity on the seismic response of RC bridges.” In Proc., 2nd Int. Workshop on Seismic Design and Retrofitting of RC Bridges, 80–89. Wellington, New Zealand: Earthquake Commission of New Zealand (EQC).
Calvi, G. M., and A. Pavese. 1997. “Conceptual design of isolation systems for bridge structures.” J. Earthquake Eng. 1 (1): 193–218.
CREW (Cascadia Region Earthquake Workgroup). 2009. Cascadia shallow earthquakes. Olympia, WA: CREW.
Coello, C. A., A. D. Christiansen, and F. S. Hernández. 1997. “A simple genetic algorithm for the design of reinforced concrete beams.” Eng. Comput. 13 (4): 185–196. https://doi.org/10.1007/BF01200046.
Comité Européen de Normalisation (CEN). 1994. “Eurocode 8 – Design Provisions for earthquake resistance of structures – Bridges.” ENV 1998-2:1994. Brussels, Belgium: Comité Européen de Normalisation.
Dang, Y., G. Zhao, H. Tian, and G. Li. 2021. “Two-stage optimization method for the bearing layout of isolated structure.” Adv. Civ. Eng. 2021: e4895176. https://doi.org/10.1155/2021/4895176.
Dolati, A., T. Taghikhany, M. Khanmohammadi, and A. Rahai. 2015. “Scenario-based seismic performance assessment of regular and irregular highway bridges under near-fault ground motions.” Earthquakes Struct. 8 (3): 573–589. https://doi.org/10.12989/EAS.2015.8.3.573.
Engelbrecht, A. P. 2007. Computational intelligence: An introduction. Hoboken, NJ: Wiley.
Goel, R. K., and A. K. Chopra. 1990. “Inelastic seismic response of one-storey, asymmetric-plan systems: Effects of stiffness and strength distribution.” Earthquake Eng. Struct. Dyn. 19 (7): 949–970. https://doi.org/10.1002/eqe.4290190703.
Isakovic, T., and M. Fischinger. 2000. “Regularity indices for bridge structures.” In Proc., 12th World Conf. on Earthquake Engineering. Paper 1725. Tokyo, Japan: International Association for Earthquake Engineering (IAEE).
Jamian, J. J., M. N. Abdullah, H. Mokhlis, M. W. Mustafa, and A. H. A. Bakar. 2014. “Global particle swarm optimization for high dimension numerical functions analysis.” J. Appl. Math. 2014: e329193. https://doi.org/10.1155/2014/329193.
Johnson, N., R. T. Ranf, M. S. Saiidi, D. Sanders, and M. Eberhard. 2008. “Seismic testing of a two-span reinforced concrete bridge.” J. Bridge Eng. 13 (2): 173–182. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:2(173).
Kaviani, P., F. Zareian, and E. Taciroglu. 2012. “Seismic behavior of reinforced concrete bridges with skew-angled seat-type abutments.” Eng. Struct. 45: 137–150. https://doi.org/10.1016/j.engstruct.2012.06.013.
Kennedy, J., and R. Eberhart. 1995. “Particle swarm optimization.” In Vol. 4 of Proc., IEEE Int. Conf. on Neural Networks, 1942–1948. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE).
Kohrangi, M., R. Bento, and M. Lopes. 2015. “Seismic performance of irregular bridges—Comparison of different nonlinear static procedures.” Struct. Infrastruct. Eng. 11 (12): 1632–1650. https://doi.org/10.1080/15732479.2014.983938.
Liang, J., K. Qin, P. Suganthan, and B. Subramanian. 2006. “Comprehensive learning particle swarm optimiser for global optimisation of multimodal functions.” IEEE Trans. Evol. Comput. 10: 281–295. https://doi.org/10.1109/TEVC.2005.857610.
Maalek, S., R. Akbari, and M. Maheri. 2009. “The effect of higher modes on the regularity of single-column-bent highway viaducts.” Bridge Struct. Assess. Des. Constr. 5: 29–43. https://doi.org/10.1080/15732480902775573.
Marafi, N. A., A. J. Makdisi, J. W. Berman, and M. O. Eberhard. 2020. “Design strategies to achieve target collapse risks for reinforced concrete wall buildings in sedimentary basins.” Earthquake Spectra 36 (3): 1038–1073. https://doi.org/10.1177/8755293019899965.
Marini, F., and B. Walczak. 2015. “Particle swarm optimization (PSO). A tutorial.” Chemom. Intell. Lab. Syst. 149: 153–165. https://doi.org/10.1016/j.chemolab.2015.08.020.
Martinez, F. J., F. González-Vidosa, A. Hospitaler, and V. Yepes. 2010. “Heuristic optimization of RC bridge piers with rectangular hollow sections.” Comput. Struct. 88 (5): 375–386. https://doi.org/10.1016/j.compstruc.2009.11.009.
Martinez-Martin, F. J., F. González-Vidosa, A. Hospitaler, and V. Yepes. 2012. “Multi-objective optimization design of bridge piers with hybrid heuristic algorithms.” J. Zhejiang Univ. Sci. 13 (6): 420–432. https://doi.org/10.1631/jzus.a1100304.
Mitropoulou, C. C., I. A. Naziris, N. A. Kallioras, and N. D. Lagaros. 2022. “Optimized strengthening based on concrete jacketing for minimum eccentricity.” Front. Built Environ. 8: 147–170. https://doi.org/10.3389/fbuil.2022.856380.
Paya, I., V. Yepes, F. González-Vidosa, and A. Hospitaler. 2008. “Multiobjective optimization of concrete frames by simulated annealing.” Comput.-Aided Civ. Infrastruct. Eng. 23 (8): 596–610. https://doi.org/10.1111/j.1467-8667.2008.00561.x.
Paya-Zaforteza, I., V. Yepes, A. Hospitaler, and F. González-Vidosa. 2009. “CO2-optimization of reinforced concrete frames by simulated annealing.” Eng. Struct. 31 (7): 1501–1508. https://doi.org/10.1016/j.engstruct.2009.02.034.
Piotrowski, A. P., J. J. Napiorkowski, and A. E. Piotrowska. 2020. “Population size in particle swarm optimization.” Swarm Evol. Comput. 58: 100718.
Priestley, M. J. N., F. Seible, and G. M. Calvi. 1996. Seismic design and retrofit of bridges. New York: Wiley.
Ranf, R. T. 2007. “Model selection for performance-based earthquake engineering of bridges.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of Washington.
Sajed, M., and P. Tehrani. 2020. “Effects of column and superstructure irregularity on the seismic response of four-span RC bridges.” Structures 28: 1400–1412. https://doi.org/10.1016/j.istruc.2020.09.057.
Sengupta, S., S. Basak, and R. A. Peters. 2019. “Particle swarm optimization: A survey of historical and recent developments with hybridization perspectives.” Mach. Learn. Knowl. Extr. 1 (1): 157–191. https://doi.org/10.3390/make1010010.
Thonstad, T., M. O. Eberhard, and J. F. Stanton. 2021. “Design of prestressed, jointed columns for enhanced seismic performance.” Structures 33: 1007–1019. https://doi.org/10.1016/j.istruc.2021.01.105.
United States Geological Survey. 2017. National seismic hazard mapping project. Washington, DC: USGS.
Zhu, M., F. McKenna, and M. H. Scott. 2018. “OpenSeesPy: Python library for the OpenSees finite element framework.” SoftwareX 7: 6–11. https://doi.org/10.1016/j.softx.2017.10.009.
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Published In
Journal of Bridge Engineering
Volume 28 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Sep 8, 2022
Accepted: Mar 6, 2023
Published online: Apr 25, 2023
Published in print: Jul 1, 2023
Discussion open until: Sep 25, 2023
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