Dynamics and Seismic Performance of Bridges with Rocking Piers of Nonconventional Configuration
Publication: Journal of Bridge Engineering
Volume 29, Issue 6
Abstract
The present study focuses on the seismic response of bridges with rocking piers of nonconventional shape, combining the inherent benefits of rocking isolation and accelerated bridge construction. The governing equations of motion of bridge structures with different configurations of piers are derived, including the basic kinematics of the rocking motion, the equation of motion during rocking, as well as the intrinsic energy dissipation mechanisms of impact at the rocking interfaces and on the abutment backwalls. This analytical framework is based on dimensionless parameters that are related to the shape of the piers, and it is shown that the reduction of mass that is achieved with the nonconventional pier configurations leads to: (1) lower restoring effects compared to conventional piers that are rectangular in elevation; and (2) higher rocking stability based on rocking principles. The efficiency of the proposed pier configurations in a bridge with rocking pier isolation is examined for different levels of seismic action, also including earthquakes much stronger than the design earthquake in the area. It is demonstrated that the proposed nonconventional pier configurations can improve the seismic performance of rocking bridges, and at the same time bring benefits related to economic and sustainability aspects associated with a reduction in the use of construction materials.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Agalianos, A., A. Psychari, M. F. Vassiliou, B. Stojadinovic, and I. Anastasopoulos. 2017. “Comparative assessment of two rocking isolation techniques for a motorway overpass bridge.” Front. Built Environ. 3 (47): 1–19.
Andisheh, K., R. Liu, A. Palermo, and A. Scott. 2018. “Cyclic behavior of corroded fuse-type dissipaters for posttensioned rocking bridges.” J. Bridge Eng. 23 (4): 04018008. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001197.
Athanassiadou, C. J., G. G. Penelis, and A. J. Kappos. 1994. “Seismic response of adjacent buildings with similar or different dynamic characteristics.” Earthquake Spectra 10: 293–317. https://doi.org/10.1193/1.1585775.
Bachmann, J. A., M. F. Vassiliou, and B. Stojadinovic. 2019a. “Rolling and rocking of rigid uplifting structures.” Earthquake Eng. Struct. Dyn. 48: 1556–1574. https://doi.org/10.1002/eqe.3213.
Bachmann, J. A., M. F. Vassiliou, M. Broccardo, and B. Stojadinovic. 2019b. “Modelling of rocking structures: Are our models good enough?” In Proc., 2nd Int. Conf. on Natural Hazards & Infrastructure. Athens, Greece: Innovation Center on Natural Hazards and Infrastructure.
CEN (Comité Européen de Normalisation). 2004a. Design of concrete structures–Part 1-1: General rules and rules for buildings. Eurocode 2 (EN1992-1-1). Brussels, Belgium: CEN.
CEN (Comité Européen de Normalisation). 2004b. Design of structures for earthquake resistance–Part 1: General rules, seismic actions and rules for buildings. Eurocode 8 (EN1998-1). Brussels, Belgium: CEN.
Cheng, C.-T. 2007. “Energy dissipation in rocking bridge piers under free vibration tests.” Earthquake Eng. Struct. Dyn. 36: 503–518. https://doi.org/10.1002/eqe.640.
Cheng, C.-T. 2008. “Shaking table tests of a self-centering designed bridge substructure.” Eng. Struct. 30: 3426–3433. https://doi.org/10.1016/j.engstruct.2008.05.017.
Cheng, C.-T., and F.-L. Chen. 2014. “Seismic performance of a rocking bridge pier substructure with frictional hinge dampers.” Smart Struct. Syst. 14 (4): 501–516. https://doi.org/10.12989/sss.2014.14.4.501.
Di Egidio, A., and A. Contento. 2009. “Base isolation of slide-rocking non-symmetric rigid blocks under impulsive and seismic excitations.” Eng. Struct. 31: 2723–2734. https://doi.org/10.1016/j.engstruct.2009.06.021.
Dimitrakopoulos, E. G., and M. J. DeJong. 2012. “Overturning of retrofitted rocking structures under pulse-type excitations.” J. Eng. Mech. 138: 963–972. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000410.
Dimitrakopoulos, E. G., and A. I. Giouvanidis. 2015. “Seismic response analysis of the planar rocking frame.” J. Eng. Mech. 141 (7): 04015003. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000939.
Doolen, T. L., B. Tang, A. Saeedi, and S. Emani. 2011. “To ABC or NOT?” Public Roads 75 (3).
ElGawady, M. A., and H. M. Dawood. 2012. “Analysis of segmental piers consisted of concrete filled FRP tubes.” Eng. Struct. 38: 142–152. https://doi.org/10.1016/j.engstruct.2012.01.001.
Gkatzogias, K. I. 2017. “Performance-based seismic design of concrete bridges for deformation control through advanced analysis tools and control devices.” Ph.D. thesis, School of Science and Technology, Univ. of London.
Housner, G. W. 1963. “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am. 53 (2): 403–417. https://doi.org/10.1785/BSSA0530020403.
Jankowski, R. 2007. “Theoretical and experimental assessment of parameters for the non-linear viscoelastic model of structural pounding.” J. Theor. Appl. Mech. 45 (4): 931–942.
Kalliontzis, D., S. Sritharan, and A. Schultz. 2016. “Improved coefficient of restitution estimation for free rocking members.” J. Struct. Eng. 142 (12). https://doi.org/10.1061/(ASCE)ST.1943-541X.0001598.
Kappos, A. J., P. Potikas, and A. G. Sextos. 2007. “Seismic assessment of an overpass bridge accounting for non-linear material and soil response and varying boundary conditions.” In Proc., ECCOMAS Thematic Conf., on Computational Methods in Structural Dynamics and Earthquake Engineering. Lisbon, Portugal: European Congress on Computational Methods in Applied Sciences and Engineering.
Leitner, E. J., and H. Hao. 2016. “Three-dimensional finite element modelling of rocking bridge piers under cyclic loading and exploration of options for increased energy dissipation.” Eng. Struct. 118: 74–88. https://doi.org/10.1016/j.engstruct.2016.03.042.
Makris, N., and M. F. Vassiliou. 2013. “Planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam.” Earthquake Eng. Struct. Dyn. 42: 431–449. https://doi.org/10.1002/eqe.2222.
Makris, N., and M. F. Vassiliou. 2014. “Are some top-heavy structures more stable?” J. Struct. Eng. 140 (5): 06014001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000933.
Mantawy, I. M., T. Thonstad, D. H. Sanders, J. F. Stanton, and M. O. Eberhard. 2016. “Seismic performance of precast, pretensioned, and cast-in-place bridges: Shake table test comparison.” J. Bridge Eng. 21 (10): 04016071. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000934.
Mathey, C., C. Feau, I. Politopoulos, D. Clair, L. Baillet, and M. Fogli. 2016. “Behavior of rigid blocks with geometrical defects under seismic motion: An experimental and numerical study.” Earthquake Eng. Struct. Dyn. 45: 2455–2474. https://doi.org/10.1002/eqe.2773.
MATLAB. 2016. Version 9.1.0.441655 (R2016). Natick, MA: The MathWorks Incorporation.
Muthukumar, S., and R. DesRoches. 2006. “A Hertz contact model with non-linear damping for pounding simulation.” Earthquake Eng. Struct. Dyn. 35: 811–828. https://doi.org/10.1002/eqe.557.
Mylonakis, G., S. Nikolaou, and G. Gazetas. 2006. “Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations.” Soil Dyn. Earthquake Eng. 26: 824–853. https://doi.org/10.1016/j.soildyn.2005.12.005.
Ou, Y.-C., M. Chiewanichakorn, A. J. Aref, and G. C. Lee. 2007. “Seismic performance of segmental precast unbonded posttensioned concrete bridge columns.” J. Struct. Eng. 133 (11): 1636–1647. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:11(1636).
Palermo, A., S. Pampanin, and G. M. Calvi. 2004. “Use of “controlled rocking” in the seismic design of bridges.” In Proc., 13th World Conf., on Earthquake Engineering. Tokyo, Japan: International Associations of Earthquake Engineering (IAAEE).
Ricker, N. 1943. “Further developments in the wavelet theory of seismogram structure.” Bull. Seismol. Soc. Am. 33: 197–228. https://doi.org/10.1785/BSSA0330030197.
Ricker, N. 1944. “Wavelet functions and their polynomials.” Geophysics 9: 314–323. https://doi.org/10.1190/1.1445082.
Roh, H., and A. M. Reinhorn. 2010. “Modeling and seismic response of structures with concrete rocking columns and viscous dampers.” Eng. Struct. 32: 2096–2107. https://doi.org/10.1016/j.engstruct.2010.03.013.
Sakai, J., and S. A. Mahin. 2004. “Mitigation of residual displacements of circular reinforced concrete bridge columns.” In Proc., 13th World Conf., on Earthquake Engineering. Tokyo, Japan: International Associations of Earthquake Engineering (IAAEE).
Sideris, P. 2015. “Nonlinear quasi-static analysis of hybrid sliding-rocking bridge columns subjected to lateral loading.” Eng. Struct. 101: 125–137. https://doi.org/10.1016/j.engstruct.2015.06.053.
Thiers-Moggia, R., and C. Málaga-Chuquitaype. 2019. “Seismic protection of rocking structures with inerters.” Earthquake Eng. Struct. Dyn. 48: 528–547. https://doi.org/10.1002/eqe.3147.
Thomaidis, I. M. 2020. “Analytical and numerical investigation of the seismic behaviour of bridges with rocking piers.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of London.
Thomaidis, I. M., A. Camara, and A. J. Kappos. 2022. “Dynamics and seismic performance of asymmetric rocking bridges.” J. Eng. Mech. 148 (3): 04022003. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002074.
Thomaidis, I. M., A. J. Kappos, and A. Camara. 2018. “Simulating the rocking response of rigid bodies using general-purpose finite element software.” In Proc., 16th European Conf., on Earthquake Engineering. Istanbul, Turkey: European Association for Earthquake Engineering.
Thomaidis, I. M., A. J. Kappos, and A. Camara. 2020a. “Dynamics and seismic performance of rocking bridges accounting for the abutment-backfill contribution.” Earthquake Eng. Struct. Dyn. 49 (12): 1161–1179. https://doi.org/10.1002/eqe.3283.
Thomaidis, I. M., A. J. Kappos, and A. Camara. 2020b. “Rocking vs Conventional seismic isolation: Comparative assessment of asymmetric bridges in a design context.” In Proc., 17th World Conf., on Earthquake Engineering. Tokyo, Japan: International Associations of Earthquake Engineering (IAAEE).
Thonstad, T., I. M. Mantawy, J. F. Stanton, M. O. Eberhard, and D. H. Sanders. 2016. “Shaking table performance of a new bridge system with pretensioned rocking columns.” J. Bridge Eng. 21 (4): 04015079. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000867.
Tucker, C., and L. Ibarra. 2016. “Effects of partial-design-strength concrete on the seismic performance of concrete-filled tube columns in accelerated bridge construction.” J. Bridge Eng. 21 (6): 04016023. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000812.
Vassiliou, M. F., and N. Makris. 2012. “Analysis of the rocking response of rigid blocks standing free on a seismically isolated base.” Earthquake Eng. Struct. Dyn. 41: 177–196. https://doi.org/10.1002/eqe.1124.
Zhang, J., Z. Guan, L. Liang, and X. Ling. 2018. “Experimental study on longitudinal joints with accelerated construction features in precast multibox girder bridges.” J. Bridge Eng. 23 (1): 04017116. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001172.
Zhang, J., and N. Makris. 2001. “Rocking response of free-standing blocks under cycloidal pulses.” J. Eng. Mech. 127 (5): 473–483. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(473).
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 29 • Issue 6 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Feb 10, 2023
Accepted: Dec 24, 2023
Published online: Mar 19, 2024
Published in print: Jun 1, 2024
Discussion open until: Aug 19, 2024
ASCE Technical Topics:
- Base isolation
- Bridge abutments
- Bridge components
- Bridge engineering
- Construction engineering
- Construction industry
- Construction management
- Continuum mechanics
- Dynamics (solid mechanics)
- Earthquake engineering
- Engineering fundamentals
- Engineering mechanics
- Equations of motion
- Geotechnical engineering
- Hydraulic engineering
- Hydraulic structures
- Infrastructure construction
- Piers
- Ports and harbors
- Seismic design
- Seismic effects
- Seismic tests
- Solid mechanics
- Structural engineering
- Tests (by type)
- Water and water resources
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.