Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Abstract

Viscous dampers are widely used as passive energy dissipation devices for long-span cable-stayed bridges for mitigation of seismic load-induced vibrations. However, complicated finite element (FE) modeling, together with repetitive and computationally intensive nonlinear time-history analyses (NTHAs) are generally required in conventional design methods. To streamline the preliminary design process, this paper developed a simplified longitudinal double degree of freedom model (DDFM) for single and symmetric twin-tower cable-stayed bridges. Based on the proposed simplified longitudinal DDFM, the analytical equations for the relevant mass- and stiffness-related parameters and longitudinal natural frequencies of the structure were derived by using analytical and energy methods. Modeling of the relationship between the nonlinear viscous damper parameters and the equivalent damping ratio was achieved through the equivalent linearization method. Additionally, the analytical equations of longitudinal seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers were derived. Based on the developed simplified DDFM and suggested analytical equations, this paper proposed a simplified calculation framework to achieve a simplified design method of nonlinear viscous damper parameters. Moreover, the effectiveness and applicability of the developed simplified longitudinal DDFM and the proposed calculation framework were further validated through numerical analysis of a practical cable-stayed bridge. Finally, the results indicated the following. 1) For the obtained fundamental period and longitudinal stiffness, the differences between results of the simplified longitudinal DDFM and numerical analysis were only 2.05% and 1.5%, respectively. 2) Relative calculation errors of the longitudinal girder-end displacement and bending moment of the bottom tower section of the bridge obtained from the simplified longitudinal DDFM were limited to less than 25%. 3) The equivalent damping ratio of nonlinear viscous dampers and the applied loading frequency had significant effects on the longitudinal seismic responses of the bridge. Findings of this study may provide beneficial information for a design office to make a simplified preliminary design scheme to determine the appropriate nonlinear damper parameters and longitudinal seismic responses for long-span cable-stayed bridges.

Graphical abstract

Keywords

cable-stayed bridges / viscous dampers / simplified analytical model / equivalent damping ratio / seismic mitigation

References

[1] Cao X Y, Feng D C, Li Y. Assessment of various seismic fragility analysis approaches for structures excited by non-stationary stochastic ground motions. Mechanical Systems and Signal Processing, 2023, 186: 109838

[2] Cao X Y, Feng D C, Beer M. Consistent seismic hazard and fragility analysis considering combined capacity-demand uncertainties via probability density evolution method. Structural Safety, 2023, 103: 102330

[3] Li H H, Li L F, Wu W P, Xu L. Seismic fragility assessment framework for highway bridges based on an improved uniform design-response surface model methodology. Bulletin of Earthquake Engineering, 2020, 18(5): 2329–2353

[4] Li H H, Li L F, Zhou G J, Xu L. Effects of various modeling uncertainty parameters on the seismic response and seismic fragility estimates of the aging highway bridges. Bulletin of Earthquake Engineering, 2020, 18(14): 6337–6373

[5] Wen J N, Han Q, Xie Y Z, Du X L, Zhang J. Performance-based seismic design and optimization of damper devices for cable-stayed bridge. Engineering Structures, 2021, 237: 112043

[6] Wu W P, Li L F, Shao X D. Seismic assessment of medium-span concrete cable-stayed bridges using the component and system fragility functions. Journal of Bridge Engineering, 2016, 21(6): 04016027

[7] Li L F, Hu S C, Wang L H. Seismic fragility assessment of a multi-span cable-stayed bridge with tall piers. Bulletin of Earthquake Engineering, 2017, 15(9): 3727–3745

[8] Zhou L X, Wang X W, Ye A J. Shake table test on transverse steel damper seismic system for long span cable-stayed bridges. Engineering Structures, 2019, 179: 106–119

[9] Han Q, Wen J, Du X L, Zhong Z, Hao H. Nonlinear seismic response of a base isolated single pylon cable-stayed bridge. Engineering Structures, 2018, 175: 806–821

[10] Wesolowsky M J, Wilson J C. Seismic isolation of cable-stayed bridges for near-field ground motions. Earthquake Engineering and Structural Dynamics, 2003, 32(13): 2107–2126

[11] Xu L, Bi K M, Gao J F, Xu Y, Zhang C. Analysis on parameter optimization of dampers of long-span double-tower cable-stayed bridges. Journal of Earthquake Engineering, 2020, 16(9): 1286–1301

[12] Guo W, Li J Z, Guan Z G. Shake table test on a long-span cable-stayed bridge with viscous dampers considering wave passage effects. Journal of Bridge Engineering, 2021, 26(2): 04020118

[13] Chang K C, Mo Y L, Chen C C, Lai L C, Chou C C. Lessons learned from the damaged Chi-Lu cable-stayed bridge. Journal of Bridge Engineering, 2004, 9(4): 343–352

[14] Siringoringo D, Fujino Y, Namikawa K. Seismic response analyses of the Yokohama Bay cable-stayed bridge in the 2011 Great East Japan Earthquake. Journal of Bridge Engineering, 2014, 19(8): A4014006

[15] Li J Z, Peng T B, Xu Y. Damage investigation of girder bridges under the Wenchuan earthquake and corresponding seismic design recommendations. Earthquake Engineering and Engineering Vibration, 2008, 7(4): 337–344

[16] Camara A, Cristantielli R, Astiz M, Málaga-Chuquitaype C. Design of hysteretic dampers with optimal ductility for the transverse seismic control of cable-stayed bridges. Earthquake Engineering and Structural Dynamics, 2017, 46(11): 1811–1833

[17] Zhong J, Wan H P, Yuan W C, He M, Ren W X. Risk-informed sensitivity analysis and optimization of seismic mitigation strategy using Gaussian process surrogate model. Soil Dynamics and Earthquake Engineering, 2020, 138: 106284

[18] Pang Y T, He W, Zhong J. Risk-based design and optimization of shape memory alloy restrained sliding bearings for highway bridges under near-fault ground motions. Engineering Structures, 2021, 241: 112421

[19] Xiang N L, Goto Y, Obata M, Alam M S. Passive seismic unseating prevention strategies implemented in highway bridges: A state-of-the-art review. Engineering Structures, 2019, 194: 77–93

[20] Zhu J, Zhang W, Zheng K F, Li H G. Seismic design of a long-span cable-stayed bridge with fluid viscous dampers. Practice Periodical on Structural Design and Construction, 2016, 21(1): 04015006

[21] Lin Y Y, Chang K C, Chen C Y. Direct displacement-based design for seismic retrofit of existing buildings using nonlinear viscous dampers. Bulletin of Earthquake Engineering, 2008, 6(3): 535–552

[22] Ali H, Abdel-Ghaffar A M. Seismic energy dissipation for cable-stayed bridges using passive devices. Earthquake Engineering & Structural Dynamics, 1994, 23(8): 877–893

[23] Guan Z G, You H, Li J Z. Lateral isolation system of a long-span cable-stayed bridge with heavyweight concrete girder in a high seismic region. Journal of Bridge Engineering, 2017, 22(1): 04016104

[24] Xu Y, Tong C, Li J Z. Simplified calculation method for supplemental viscous dampers of cable-stayed bridges under near-fault ground motions. Journal of Earthquake Engineering, 2021, 25(1): 65–81

[25] Li X, Li J, Zhang X Y, Gao J F, Zhang C. Simplified analysis of cable-stayed bridges with longitudinal viscous dampers. Engineering, Construction, and Architectural Management, 2020, 27(8): 1993–2022

[26] Soneji B B, Jangid R S. Passive hybrid systems for earthquake protection of cable-stayed bridge. Engineering Structures, 2007, 29(1): 57–70

[27] Subhayan D, Wojtkiewicz S F, Johnson E A. Efficient optimal design and design-under-uncertainty of passive control devices with application to a cable-stayed bridge. Structural Control and Health Monitoring, 2017, 24(2): e1846

[28] Xu Y, Wang R L, Li J Z. Experimental verification of a cable-stayed bridge model using passive energy dissipation devices. Journal of Bridge Engineering, 2016, 21(12): 04016092

[29] Camara A, Ruiz-Teran A M, Stafford P J. Structural behaviour and design criteria of under-deck cable-stayed bridges subjected to seismic action. Earthquake Engineering and Structural Dynamics, 2012, 42(6): 891–912

[30] Shen X, Wang X W, Ye Q, Ye A J. Seismic performance of transverse steel damper seismic system for long span bridges. Engineering Structures, 2017, 141: 14–28

[31] Xu L, Zhang H, Gao J F, Zhang C. Longitudinal seismic responses of a cable-stayed bridge based on shaking table tests of a half-bridge scale model. Advances in Structural Engineering, 2019, 22(1): 81–93

[32] HuangY FXuYLiJ Z. Simplified parameter design method of viscous dampers for cable-stayed bridge under near-fault ground motions. China Civil Engineering Journal, 2016, 49(9): 72–77 (in Chinese)

[33] XuYHuangY FLiJ Z. Simplified calculation of longitudinal seismic response of cable-stayed bridges subjected to pulsed ground motions. Journal of South China University of Technology (Natural Science Edition), 2015, 43(2): 41–47 (in Chinese)

[34] ZhangW XKouW QChenYWangZ. Study on simplified calculation of first-order longitudinal vibration period for fixed hinge cable-stayed bridges. Journal of Hunan University (Natural Sciences), 2017, 44(3): 28–34 (in Chinese)

[35] ZhangW XKouW QChenYWangZ. Simplified calculation of first-order longitudinal natural vibration period of cable-stayed bridges based on energy method. China Journal of Highway and Transport, 2017, 30(7): 50–57 (in Chinese)

[36] SeleemahA AConstantinouM C. Investigation of Seismic Response of Buildings with Linear and Nonlinear Fluid Viscous Dampers. Buffalo: National Center for Earthquake Engineering Research (NCEER), 1997

[37] ASCE. Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Report FEMA-356. 2000

[38] LiW BLiuT LWangY. Compositions of time histories of acceleration and velocity and displacement of ground motion. Engineering Mechanics, 2020, 37(S1): 164–167 (in Chinese)

[39] Hwang J, Tseng Y. Design formulations for supplemental viscous dampers to highway bridges. Earthquake Engineering and Structural Dynamics, 2005, 34(13): 1627–1642

[40] ChopraA K. Dynamics of Structures: Theory and Applications to Earthquake Engineering. 3rd ed. Upper Saddle River, NJ: Prentice-Hall, Inc., 2007

[41] FuRFuR HAnshengF. Composition and amplitude-frequency characteristics of ground motion acceleration based on fast Fourier transform analysis. Acta Seismologica Sinica, 2014, 36(3): 417–424 (in Chinese)

[42] LiW HYangG WXuW. Design of steel truss girder cable-stayed bridge of 567-m main span of Huanggang Changjiang river rail-cum-road bridge. Bridge Construction, 2013, 43(2): 10–15 (in Chinese)

[43] LiuX HFengP CShaoX D. Key design technique for Haiwen sea-crossing bridge. Bridge Construction, 2020, 50(2): 73–79 (in Chinese)

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 51978257 and 52278176), and the authors gratefully acknowledge the financial support.

Competing interests

The authors declare that they have no competing interests.

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