Abstract
Lead rubber bearings (LRBs) have been widely used in seismic isolation systems for buildings and other structures to effectively mitigate the damaging effects of horizontal earthquake ground shaking. The horizontal flexibility of the LRBs, typically placed at the base of the structure, result in a concentration of displacements in the bearings while limiting deformations in the structure. Strong earthquake shaking can produce large displacement demands on the isolation system and are typically limited by a clearance or a moat around the perimeter of the structure. Recent research has evaluated the displacement capacity of isolated structures and the significant risk of failure from increased seismic demands on the isolators or from pounding to moat walls. This paper proposes a parallel nonlinear model to capture the complex behavior of LRBs at large strains in an effort to better predict isolator displacements and the potential for exceeding a limit state. The model captures strength degradation from lead core heating, stain hardening of the rubber, and unloading effects. Allowing the bearings to sustain large strains to induce hardening is explored as a means for reducing the impact velocity in the case that the clearance to the stop is exceeded. Numerical time history analyses are used to demonstrate the sensitivity of model selection for LRB especially when considering beyond design ground motions.
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Data Availability Statement
The following data, models, or code generated or used during the study are available from the corresponding author by request:
•
Generated code, and
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Calibrated models.
Acknowledgments
This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650112. Funding and experiment data for this project were provided by Korea Atomic Energy Research Institute (KAERI). The opinions, findings, and conclusions in this paper are those of the authors and do not necessarily reflect the views of those acknowledged here.
References
An, G., M. Kim, J.-W. Jung, G. Mosqueda, and J. F. Marquez. 2020. “Evaluation of clearance to stop requirements in a seismically isolated nuclear power plant.” Energies 13 (22): 6156. https://doi.org/10.3390/en13226156.
Aramaki, S., K. Uno, and K. Noyori. 2004. “Study of lead pillar damper for the earthquake resistance reinforcement of an established road bridge.” In Proc., 13th World Conf. on Earthquake Engineering. St. Louis, MO: Mira Digital Publishing.
Bouc, R. 1967. “Forced vibration of mechanical systems with hysteresis.” In Proc., 4th Conf. on Nonlinear Oscillations. Prague, Czech Republic: Academia.
CERF (Civil Engineering Research Foundation). 1998. Evaluation findings for Skellerup base isolation elastomeric bearings. Washington, DC: Civil Engineering Research Foundation.
Chandramohan, R., J. W. Baker, and G. G. Deierlein. 2016. “Quantifying the influence of ground motion duration on structural collapse capacity using spectrally equivalent records.” Earthquake Spectra 32 (2): 927–950. https://doi.org/10.1193/122813eqs298mr2.
Clark, P. W., I. D. Aiken, and J. M. Kelly. 1997. Experimental studies of the ultimate behavior of seismically-isolated structures. Berkeley, CA: Earthquake Engineering Research Center.
Dafalias, Y. F., and E. P. Popov. 1975. “A model of nonlinearly hardening materials for complex loading.” Acta Mech. 21 (3): 173–192. https://doi.org/10.1007/BF01181053.
Dall’Asta, A., and L. Ragni. 2008. “Nonlinear behavior of dynamic systems with high damping rubber devices.” Eng. Struct. 30 (12): 3610–3618. https://doi.org/10.1016/j.engstruct.2008.06.003.
Diani, J., B. Fayolle, and P. Gilormini. 2009. “A review on the Mullins effect.” Eur. Polym. J. 45 (3): 601–612. https://doi.org/10.1016/j.eurpolymj.2008.11.017.
Eem, S., and D. Hahm. 2019. “Large strain nonlinear model of lead rubber bearings for beyond design basis earthquakes.” Nucl. Eng. Technol. 51 (2): 600–606. https://doi.org/10.1016/j.net.2018.11.001.
Fenz, D. M., and M. C. Constantinou. 2008. “Spherical sliding isolation bearings with adaptive behavior: Theory.” Earthquake Eng. Struct. Dyn. 37 (2): 163–183. https://doi.org/10.1002/eqe.751.
Grant, D. N., G. L. Fenves, and A. S. Whittaker. 2004. “Bidirectional modelling of high-damping rubber bearings.” J. Earthquake Eng. 8 (1): 161–185. https://doi.org/10.1080/13632460409350524.
Hwang, J. S., J. D. Wu, T. C. Pan, and G. Yang. 2002. “A mathematical hysteretic model for elastomeric isolation bearings.” Earthquake Eng. Struct. Dyn. 31 (4): 771–789. https://doi.org/10.1002/eqe.120.
Ishida, K., H. Shiojiri, M. Iizuka, K. Mizukoshi, and K. Takabayashi. 1991. “Failure tests of laminated rubber bearings.” In Proc., 11th Int. Conf. on Structural Mechanics in Reactor Technology, 241–246. Tokyo: IASMiRT.
Ishii, K., and M. Kikuchi. 2019. “Improved numerical analysis for ultimate behavior of elastomeric seismic isolation bearings.” Earthquake Eng. Struct. Dyn. 48 (1): 65–77. https://doi.org/10.1002/eqe.3123.
Kalpakidis, I. V., and M. C. Constantinou. 2008. Effects of heating and load history on the behavior of lead-rubber bearings. Technical Rep. No. MCEER-08-0027. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research.
Kalpakidis, I. V., and M. C. Constantinou. 2009a. “Effects of heating on the behavior of lead-rubber bearings. I: Theory.” J. Struct. Eng. 135 (12): 1440–1449. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000072.
Kalpakidis, I. V., and M. C. Constantinou. 2009b. “Effects of heating on the behavior of lead-rubber bearings. II: Verification of theory.” J. Struct. Eng. 135 (12): 1450–1461. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000071.
Kikuchi, M., and I. D. Aiken. 1997. “An analytical hysteresis model for elastomeric seismic isolation bearings.” Earthquake Eng. Struct. Dyn. 26 (2): 215–231. https://doi.org/10.1002/(SICI)1096-9845(199702)26:2%3C215::AID-EQE640%3E3.0.CO;2-9.
Kikuchi, M., T. Nakamura, and I. D. Aiken. 2010. “Three-dimensional analysis for square seismic isolation bearings under large shear deformations and high axial loads.” Earthquake Eng. Struct. Dyn. 39 (13): 1513–1531. https://doi.org/10.1002/eqe.1042.
Kim, J., M. Kim, and I. Choi. 2017. “Experimental study on the bidirectional behavior of a lead-rubber bearing.” In Proc., 16th World Conf. on Earthquake Engineering (16WCEE). Santiago, Chile: Chilean Association on Seismology and Earthquake Engineering.
Kim, J. H., M. K. Kim, and I.-K. Choi. 2019. “Experimental study on seismic behavior of lead-rubber bearing considering bi-directional horizontal input motions.” Eng. Struct. 198 (Nov): 109529. https://doi.org/10.1016/j.engstruct.2019.109529.
Kitayama, S., and M. C. Constantinou. 2021. “Implications of strong earthquake ground motion duration on the response and testing of seismic isolation systems.” Earthquake Eng. Struct. Dyn. 50 (2): 290–308. https://doi.org/10.1002/eqe.3330.
Koh, C. G., and J. M. Kelly. 1988. “A simple mechanical model for elastomeric bearings used in base isolation.” Int. J. Mech. Sci. 30 (12): 933–943. https://doi.org/10.1016/0020-7403(88)90075-6.
Kumar, M., A. S. Whittaker, and M. C. Constantinou. 2014. “An advanced numerical model of elastomeric seismic isolation bearings.” Earthquake Eng. Struct. Dyn. 43 (13): 1955–1974. https://doi.org/10.1002/eqe.2431.
Kumar, M., A. S. Whittaker, and M. C. Constantinou. 2015. Seismic isolation of nuclear power plants using elastomeric bearings. Buffalo, NY: State Univ. of New York at Buffalo.
Lagarias, J. C., J. A. Reeds, M. H. Wright, and P. E. Wright. 1998. “Convergence properties of the Nelder–Mead simplex method in low dimensions.” SIAM J. Optim. 9 (1): 112–147. https://doi.org/10.1137/S1052623496303470.
Marquez, J. F., and G. Mosqueda. 2018. “Response of a seismically isolated structure with lead rubber bearings considering heating effects.” In Proc., 11th National Conf. in Earthquake Engineering. Oakland, CA: Earthquake Engineering Research Institute.
Masroor, A., and G. Mosqueda. 2013a. “Impact model for simulation of base isolated buildings impacting flexible moat walls.” Earthquake Eng. Struct. Dyn. 42 (3): 357–376. https://doi.org/10.1002/eqe.2210.
Masroor, A., and G. Mosqueda. 2013b. Seismic response of base isolated buildings considering pounding to moat walls. Buffalo, NY: State Univ. of New York at Buffalo.
McVitty, W. J., and M. C. Constantinou. 2015. Property modification factors for seismic isolators: Design guidance for buildings. Buffalo, NY: State Univ. of New York at Buffalo.
Mullins, L. 1969. “Softening of rubber by deformation.” Rubber Chem. Technol. 42 (1): 339–362. https://doi.org/10.5254/1.3539210.
Oliveto, N. D., A. A. Markou, and A. Athanasiou. 2019. “Modeling of high damping rubber bearings under bidirectional shear loading.” Soil Dyn. Earthquake Eng. 118 (Mar): 179–190. https://doi.org/10.1016/j.soildyn.2018.12.017.
Ryan, K. L., J. M. Kelly, and A. K. Chopra. 2005. “Nonlinear model for lead–rubber bearings including axial-load effects.” J. Eng. Mech. 131 (12): 1270–1278. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:12(1270).
Sanchez, J., A. Masroor, G. Mosqueda, and K. Ryan. 2013. “Static and dynamic stability of elastomeric bearings for seismic protection of structures.” J. Struct. Eng. 139 (7): 1149–1159. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000660.
Sarebanha, A., A. H. Schellenberg, M. J. Schoettler, G. Mosqueda, and S. A. Mahin. 2019. “Real-time hybrid simulation of seismically isolated structures with full-scale bearings and large computational models.” Comp. Model. Eng. Sci. 120 (3): 693–717. https://doi.org/10.32604/cmes.2019.04846.
Schellenberg, A., J. Baker, S. Mahin, and N. Sitar. 2014. Investigation of seismic isolation technology applied to the APR 1400 nuclear power plant-volume 2: Selection of ground motions. Berkeley, CA: Pacific Engineering Research Center, Univ. of California.
Tsai, C. S., T.-C. Chiang, B.-J. Chen, and S.-B. Lin. 2003. “An advanced analytical model for high damping rubber bearings.” Earthquake Eng. Struct. Dyn. 32 (9): 1373–1387. https://doi.org/10.1002/eqe.278.
Tyler, R. G., and W. H. Robinson. 1984. “High-strain tests on lead-rubber bearings for earthquake loadings.” Earthquake Eng. 17 (2): 90–105. https://doi.org/10.5459/bnzsee.17.2.90-105.
USNRC (US Nuclear Regulatory Commission). 2014. Design response spectra for seismic design of nuclear power plants. Rockville, MD: USNRC.
Vemuru, V. S. M., S. Nagarajaiah, and G. Mosqueda. 2016. “Coupled horizontal-vertical stability of bearings under dynamic loading.” Earthquake Eng. Struct. Dyn. 45 (6): 913–934. https://doi.org/10.1002/eqe.2691.
Warn, G. P., A. S. Whittaker, and M. C. Constantinou. 2007. “Vertical stiffness of elastomeric and lead–rubber seismic isolation bearings.” J. Struct. Eng. 133 (9): 1227–1236. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:9(1227).
Wen, Y. K. 1976. “Method for random vibration of hysteretic systems.” J. Eng. Mech. Div. 102 (2): 249–263. https://doi.org/10.1061/JMCEA3.0002106.
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Published In
Journal of Structural Engineering
Volume 147 • Issue 11 • November 2021
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© 2021 American Society of Civil Engineers.
History
Received: Jun 15, 2020
Accepted: Jun 9, 2021
Published online: Aug 25, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 25, 2022
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