Analysis of the Seismic Fragility of Rocking Bridges Based on SMA Ring Springs and ECC Material

Abstract

To achieve a graded seismic protection objective, namely, no damage under minor earthquakes, repairable damage under moderate earthquakes, and replaceable damage under major earthquakes, a novel rocking bridge system based on shape memory alloy (SMA) ring springs is proposed in this study. A constitutive model of the SMA ring springs is first developed and implemented in open-source finite element software OpenSees. An iterative design procedure for rocking piers is subsequently proposed, in which the slip ratio is adopted as an optimization index for the geometric configuration of the rocking piers. A typical bridge is then selected as a case study example. Finite element models of both a conventional bridge and an engineered cementitious composite (ECC) rocking bridge are subsequently established in OpenSees, and the seismic fragility of the two bridge systems is analyzed. The results indicate that the self-locking mechanism of the SMA ring springs effectively controls the rocking amplitude of the piers, thereby ensuring safe and reliable performance. Compared with conventional bridges, rocking bridges exhibit superior seismic performance and lower seismic fragility.

Keywords

seismic response / SMA ring springs / ECC rocking piers / fragility analysis

Conflict of Interest Statement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Funding

The authors extended their sincere gratitude for the Shandong Hi-Speed Co., Ltd. (SDEYH-2020-04), the Qinghai Provincial Science and Technology Department project (2024-QY-202), and the scientific research project of the Guizhou Provincial Highway Bureau, the Natural Science Foundation of Shanghai (Grant No. 24ZR1472500) from Science and Technology Commission of Shanghai Municipality, Supported by Science and Technology Projects of Xizang Autonomous Region, China (Grant No. XZ202601ZY0251).

References

[1] Ministry of Transport of the People's Republic of China. JTJ 004-89 Specifications of Earthquake Resistant Design for Highway Engineering. China Communications Press: Beijing, 1989. (in Chinese)

[2] American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Design Specifications, 3rd ed.; American Association of State Highway and Transportation Officials: Washington DC, 2005.

[3] Zhuang, W.; Liu, Z.; Jiang, J. Earthquake-induced Damage Analysis of Highway Bridges In Wenchuan Earthquake and Countermeasures. Chinese Journal of Rock Mechanics and Engineering 2009, 28, doi:10.3321/j.issn:1000-6915.2009.07.011. (in Chinese)

[4] Ministry of Transport of the People's Republic of China. JTG/T B02-01-2008 Specifications for Seismic Design of Highway Bridges. China Communications Press: Beijing, 2008. (in Chinese)

[5] American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Design Specifications, 6th ed.; American Association of State Highway and Transportation Officials: Washington DC, 2012.

[6] Kawashima, K.; MacRae, G.A.; Hoshikuma, J.; Nagaya, K. Residual displacement response spectrum. Journal of Structural Engineering-Asce 1998, 124, 523-530, doi:10.1061/(Asce)0733-9445(1998)124:5(523).

[7] Federal Emergency Management Agency. Seismic performance assessment of buildings, Volume 1 - Methodology; FEMA P-58-1; U.S. Department of Homeland Security: 2018.

[8] Japan Road Association. Design specifications of highway bridges, Part V Seismic Design. Japan Road Association: 2012.

[9] Hieber, D.G.; Wacker, J.M.; Eberhard, M.O.; Stanton, J.F. Precast concrete pier systems for rapid construction of bridges in seismic regions; WA-RD 611.1; University of Washington:Washington DC, 2005.

[10] Mander, J.B.; Cheng, C.T. Seismic resistance of bridge piers based on damage avoidance design; NCEER-97-0014; University at Buffalo: 1997.

[11] Pang, J.B.; Steuck, K.P.; Cohagen, L.; Eberhard, M.O.; Stanton, J.F. Rapidly constructible large-bar precast bridge-bent connection; WA-RD 684.2; University of Washington:Washington DC, 2008.

[12] Nguyen, W.; Trono, W.; Panagiotou, M.; Ostertag, C.P. Seismic response of a hybrid fiber-reinforced concrete bridge column detailed for accelerated bridge construction PEER 2014/19; University of California, Berkeley: 2014.

[13] Cheng, C.T. Shaking table tests of a self-centering designed bridge substructure. Engineering Structures 2008, 30, 3426-3433, doi:10.1016/j.engstruct.2008.05.017.

[14] Palermo, A.; Pampanin, S.; Marriott, D. Design, modeling, and experimental response of seismic resistant bridge piers with posttensioned dissipating connections. Journal of Structural Engineering 2007, 133, 1648-1661, doi:10.1061/(Asce)0733-9445(2007)133:11(1648).

[15] Pollino, M.; Bruneau, M. Seismic retrofit of bridge steel truss piers using a controlled rocking approach. Journal of Bridge Engineering 2007, 12, 600-610, doi:10.1061/(Asce)1084-0702(2007)12:5(600).

[16] Kam, W.Y.; Pampanin, S.; Palermo, A.; Carr, A.J. Self‐centering structural systems with combination of hysteretic and viscous energy dissipations. Earthquake Engineering & Structural Dynamics 2010, 39, 1083-1108, doi:10.1002/eqe.983.

[17] Palermo, A.; Pampanin, S.; Calvi, G.M. Concept and development of hybrid solutions for seismic resistant bridge systems. Journal of Earthquake Engineering 2005, 9, 899-921, doi:10.1142/S1363246905002328.

[18] Tilby, C. South Rangitikei Railway Bridge Construction. Transactions of the New Zealand Institution of Engineers Incorporated: Civil Engineering Section 1981, 8, 33-48.

[19] Han, Q.; Jia, Z.; He, W.; et al. Seismic Design Method and Its Engineering Application of Self-centering Double-column Rocking Bridge. China Journal of Highway and Transport 2017, 30, 169-177, doi:10.3969/j.issn.1001-7372.2017.12.018. (in Chinese)

[20] DesRoches, R.; Delemont, M. Seismic retrofit of simply supported bridges using shape memory alloys. Engineering Structures 2002, 24, 325-332, doi:10.1016/S0141-0296(01)00098-0.

[21] Varela, S.; Saiidi, M. A bridge column with superelastic NiTi SMA and replaceable rubber hinge for earthquake damage mitigation. Smart Materials and Structures 2016, 25, doi:10.1088/0964-1726/25/7/075012.

[22] Ge, J.P.; Saiidi, M.S.; Varela, S. Computational studies on the seismic response of the State Route 99 bridge in Seattle with SMA/ECC plastic hinges. Frontiers of Structural and Civil Engineering 2019, 13, 149-164, doi:10.1007/s11709-018-0482-6.

[23] Fang, C.; Yam, M.C.H.; Ma, H.; Chung, K.F. Tests on superelastic Ni-Ti SMA bars under cyclic tension and direct-shear: towards practical recentring connections. Materials and Structures 2013, 48, 1013-1030, doi:10.1617/s11527-013-0212-4.

[24] Qiu, C.X.; Fang, C.; Liang, D.; Du, X.L.; Yam, M.C.H. Behavior and application of self-centering dampers equipped with buckling-restrained SMA bars. Smart Materials and Structures 2020, 29, doi:10.1088/1361-665X/ab6883.

[25] Zouatine, M.; Helm, L.; Sadegh-Azar, H. Seismic performance and design of an innovative structure with controlled rocking shear wall using ring springs. Soil Dynamics and Earthquake Engineering 2024, 185, doi:10.1016/j.soildyn.2024.108911.

[26] Engelke, C.F.; Helm, L.; Sadegh-Azar, H. Experimental study on the displacement- and frequency-dependency of ring springs under dynamic loads. Structures 2026, 85, doi:10.1016/j.istruc.2026.111181.

[27] Wang, W.; Fang, C.; Zhao, Y.S.; Sause, R.; Hu, S.L.; Ricles, J. Self-centering friction spring dampers for seismic resilience. Earthquake Engineering & Structural Dynamics 2019, 48, 1045-1065, doi:10.1002/eqe.3174.

[28] Menegotto, M.; Pinto, P.E. Method for analysis of cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending. In Proceedings of the Proceedings of IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads, Lisbon, 1973.

[29] Zhang, N.; Gu, Q.; Dong, Y.; Qian, J.; Zheng, Y. Seismic performance of bridges with ECC-reinforced piers. Soil Dynamics and Earthquake Engineering 2021, 146, doi:10.1016/j.soildyn.2021.106753.

[30] Mackie, K.R.; Stojadinović B. Fragility basis for California highway overpass bridge seismic decision making; 2005/02; Pacific Earthquake Engineering Research Center, University of California, Berkeley: 2005.

[31] Padgett, J.E.; Nielson, B.G.; DesRoches, R. Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios. Earthquake Engineering & Structural Dynamics 2007, 37, 711-725, doi:10.1002/eqe.782.

[32] Federal Emergency Management Agency. Multi-hazard loss estimation methodology earthquake model: Technical manual; U.S. Department of Homeland Security: Washington, D.C, 2003.

[33] Nielson, B.G.; DesRoches, R. Seismic fragility methodology for highway bridges using a component level approach. Earthquake Engineering & Structural Dynamics 2007, 36, 823-839, doi:10.1002/eqe.655.

[34] Song, J.; Kang, W.H. System reliability and sensitivity under statistical dependence by matrix-based system reliability method. Structural Safety 2009, 31, 148-156, doi:10.1016/j.strusafe.2008.06.012.

[35] Kim, S.H.; Mha, H.S.; Lee, S.W. Effects of bearing damage upon seismic behaviors of a multi-span girder bridge. Engineering Structures 2006, 28, 1071-1080, doi:10.1016/j.engstruct.2005.11.015.