Journal of Vibration and Sound

Journal of Vibration and Sound

Seismic Analysis of Cable-Stayed Bridges in the Frequency Domain Using Nonlinear Dynamic Analysis: Effects of Sequential Cable Failure

Document Type : research article

Authors
Mahdi Yazdani 1
Davood Farahani 2
1 Department of civil engineering, Arak university
2 Faculty of Civil Engineering, Arak University
Abstract
Practical experience from bridge construction has shown that partial failures—such as cable ruptures in cable-stayed bridges, which are critical and costly—are almost inevitable during construction and even throughout service life. Considering that many of these bridges are located in seismically active regions and must remain operational after earthquakes, this study investigates the influence of sequential cable failures on the seismic capacity of cable-stayed bridges in the frequency domain. The Bill Emerson Memorial Bridge was selected as a case study and modeled in OpenSees. After validation, scenarios of defective cable ruptures were considered, and the structure was subjected to nonlinear dynamic analyses under different intensities of the Superstition Hills earthquake. Dynamic responses—including deck displacement, velocity, and acceleration at mid-span in all three directions and pylon-top displacement, velocity, and acceleration in longitudinal and transverse directions—were recorded. Fourier Transform analysis was then applied to extract frequency-domain responses, and critical spectral peaks were identified using power spectral density analysis and compared with the fundamental frequencies of the bridge. The results indicate that rupture of two cables does not diminish the seismic capacity of the bridge; however, rupture of three cables leads to reductions, accompanied by frequency-content shifts that generate spectral peaks close to the structural natural frequencies. Transfer-function analysis showed that the deck response in the transverse direction exhibits higher sensitivity than in other directions due to its wider effective bandwidth. This finding suggests that provisions related to the control and design of deck torsional stiffness should be addressed with precision in current standards.
Keywords
Progressive collapse
Cable-stayed bridge
Frequency domain analysis
Power spectral density (PSD)
Transfer function
Subjects
[1] Homaei, F., and Yazdani M. "Seismic Fragility, Loss, and Resiliency of Old Railway Masonry Arch Bridges under near-Field Ground Motion." Sustainable and Resilient Infrastructure  (2025): 1-28.
]2[ کشته‏گر، ب.، حلبیان، ا. و هاشم الحسینی، ح. "بررسی لرزه‏ای رفتار غیر خطی پل‏های کابلی ایستای دهانه بزرگ"، چهارمین کنگره ملی مهندسی عمران، 1387.
]3[ توکلی، ح.  و مرادی، م. "ارزیابی حساسیت پاسخ یک پل کابلی دارای جداساز لرزه‌ای تحت زلزلۀ نزدیک به گسل نسبت به تغییرات مصالح"، نشریه مهندسی عمران امیرکبیر، 1399، شماره 12، دوره 52، صفحه 3145-3160.
[4] Efthymiou, Eleftheria-Anthi. "The Effect of Multi-Angle Spatially Variable Ground Motions on the Seismic Behaviour of Cable-Stayed Bridges." City, University of London, 2019.
[5] Hyppolito, Henrique Franzener. "Effect of Cable Damage on the Structural Behaviour of a Cable-Stayed Bridge", 2020, Master's Thesis, Universidade do Porto.
]6[ اسماعیل­نیا عمران، م. و حسینی کرانی، ع. "ارزیابی عملکرد جداساز غلطکی درون قفس بر رفتار خرابی پیش­رونده پل­های کابلی (مطالعه موردی پل کابلی بیل امرسون)"، نشریه مهندسی عمران امیرکبیر، 1400، شماره 2، دوره 53، صفحه 639-658.
]7[ فتح­الله­زاده قیصری، ا. "بررسی خرابی پیش‏رونده در پل‏های کابلی ناشی از خرابی کابل نگهدارنده"، 1394، پایان­نامه کارشناسی ارشد، دانشگاه صنعتی نوشیروانی بابل.
[8] Wolff, Maren, and Uwe Starossek. "Cable Loss and Progressive Collapse in Cable-Stayed Bridges." Bridge structures 5, no. 1 (2009): 17-28.
[9] Kao, Chin-Sheng, and Chang-Huan Kou. "The Influence of Broken Cables on the Structural  Behavior of Long-Span Cable-Stayed Bridges." Journal of Marine Science and Technology 18, no. 9 (2010): 3.
[10] Mozos, CM, and AC Aparicio. "Parametric Study on the Dynamic Response of Cable Stayed Bridges to the Sudden Failure of a Stay, Part II: Bending Moment Acting on the Pylons and Stress on the Stays." Engineering Structures 32, no. 10 ( 2010): 3301- 12.
[11] Samali, Bijan, Yukari Aoki, Ali Saleh, and Hamid Valipour. "Effect of Loading Pattern and Deck Configuration on the Progressive Collapse Response of Cable-Stayed Bridges." Australian Journal of Structural Engineering 16, no. 1 (2015): 17-34.
[12] Das, R, AD Pandey, MJ Mahesh, P Saini, and S Anvesh. "Progressive Collapse of a Cable Stayed Bridge." Procedia Engineering 144 (2016): 132-39.
]13[ فراهانی، د. و یزدانی، م. "بررسی تاثیر گسیختگی کابل‏های متوالی بر ظرفیت لرزه‏ای پل‏های کابلی خودایستا"، سیزدهمین کنگرۀ بین‏المللی مهندسی عمران، 1402.
]14 [ یزدانی، م.  و معرفت، م ص. "بررسی اثر رفتار دینامیکی بار قطار بر پاسخ پل‏های قوسی بتنی غیر مسلح در حوزۀ فرکانس"، نشریه علمی ترویجی صوت و ارتعاش، 1393، شماره 6، سال 3، صفحه 47-56.
[15] Caracoglia, L. & Jones, N. P. "Time domain vs. frequency domain characterization of aeroelastic forces for bridge deck sections."  Journal of Wind Engineering and Industrial Aerodynamics, 91, no. 3 (2003): 371-402.‏
[16] Ettouney, M., Hapij, A., & Gajer, R. "Frequency-domain analysis of long-span bridges subjected to nonuniform seismic motions." Journal of Bridge Engineering, 6, no. 6 (2001): 577-586.‏
 
[17] Furukawa, A. & Kawamatsu, Y. "Earthquake Damage Assessment for RC Piers By Time-Frequency Analysis Considering Entire Bridge." GEOMATE Journal, 25 no. 111 (2023): 1-8.‏
 
[18] Wei, K., Zhang, J. & Qin, S. "Experimental and numerical assessment into frequency domain dynamic response of deep water rigid-frame bridge." Journal of Earthquake Engineering, 26 no. 1 (2022): 307-330.‏
 
[19] Chen, Genda, Dongming Yan, Wenjian Wang, Man Zheng, Louis Ge, and Frank Liu. "Assessment of the Bill Emerson Memorial Cable-Stayed Bridge Based on Seismic Instrumentation Data." (2007).
[20] Dyke, Shirley J, Juan Martin Caicedo, Gursoy Turan, Lawrence A Bergman, and Steven Hague. "Phase I Benchmark Control Problem for Seismic Response of Cable-Stayed Bridges." Journal of Structural Engineering 129, no. 7 (2003): 857-72.
]21 [حسینی، م. و کنارنگی، ه. "کاربرد نرم افزار OpenSees در مدل­سازی و تحلیل سازه­ها"، تهران: نشر آزاده، 1392.
[22] Zhu, LD, HF Xiang, and You Lin Xu. "Triple-Girder Model for Modal Analysis of Cable-Stayed Bridges with Warping Effect." Engineering structures 22, no. 10 (2000): 1313-23.
[23] Ren, Wei-Xin, and Makoto Obata. "Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges." Journal of Bridge Engineering 4, no. 3 (1999): 194-203.
[24] FEMA, P. "Quantification of building seismic performance factors", Washington, DC, (2009).
[25] Farahmand-Tabar, Salar, and Majid Barghian. "Seismic Assessment of a Cable-Stayed Arch Bridge under Three-Component Orthotropic Earthquake Excitation." Advances in Structural Engineering 24, no. 2 (2021): 42-227.
[26] Domaneschi, Marco, and Luca Martinelli. "Performance Comparison of Passive Control Schemes for the Numerically Improved Asce Cable-Stayed Bridge Model." Earthquakes and Structures 3, no. 2 (2012): 181-201.
[27] Chopra, Anil K. Dynamics of Structures. Pearson Education India, 2007.
[28] McKenna, Frank, G. L. Fenves, and M. H. Scott. "OpenSees: open system for earthquake engineering simulation. Pacific Earthquake Engineering Research Center." University of California, Berkeley, CA, USA. http://opensees. berkeley. edu 11 (2004).
]29 [پهلوان، ح.، میرزا گلتبار روشن، ع. و ناصری، ع. "تحلیل منحنی‏های شکنندگی پل‏ها در معرض زلزله‏های حوزه نزدیک و دور از گسل (مطالعه موردی پل بیل امرسون)"، نشریه مهندسی سازه و ساخت، 1400، شماره 5، دوره 8، صفحه 148- 162.