Decision-making of alternative pylon shapes of a benchmark cable-stayed bridge using seismic risk assessment

  • Received : 2014.12.15
  • Accepted : 2016.09.24
  • Published : 2016.10.25


One of the main applications of seismic risk assessment is that an specific design could be selected for a bridge from different alternatives by considering damage losses alongside primary construction costs. Therefore, in this paper, the focus is on selecting the shape of pylon, which is a changeable component in the design of a cable-stayed bridge, as a double criterion decision-making problem. Different shapes of pylons include H, A, Y, and diamond shape, and the two criterion are construction costs and probable earthquake losses. In this research, decision-making is performed by using developed seismic risk assessment process as a powerful method. Considering the existing uncertainties in seismic risk assessment process, the combined incremental dynamic analysis (IDA) and uniform design (UD) based fragility assessment method is proposed, in which the UD method is utilized to provide the logical capacity models of the structure, and the IDA method is employed to give the probabilistic seismic demand model of structure. Using the aforementioned models and by defining damage states, the fragility curves of the bridge system are obtained for the different pylon shapes usage. Finally, by combining the fragility curves with damage losses and implementing the proposed cost-loss-benefit (CLB) method, the seismic risk assessment process is developed with financial-comparative approach. Thus, the optimal shape of the pylon can be determined using double criterion decision-making. The final results of decision-making study indicate that the optimal pylon shapes for the studied span of cable-stayed bridge are, respectively, H shape, diamond shape, Y shape, and A shape.


  1. Agrawal, A.K., Ghosn, M., Alampalli, S. and Pan, Y (2012), "Seismic fragility of retrofitted multispan continuous steel bridges in New York", J. Bridge Eng., 17(4), 562-575.
  2. Aviram, A., Mackie, K. and Stojadinovic, B. (2008), "Guidelines for nonlinear analysis of bridge structures in California (Techincal Report)", Pacific Earthquake Engineering Research Center(PEER), University of California, Berkeley.
  3. Barnawi, W. and Dyke, S. (2014), "Seismic fragility relationships of a cable-stayed bridge equipped with response modification systems", J. Bridge Eng. 19(SPECIAL ISSUE: Recent Advances in Seismic Design, Analysis, and Protection of Highway Bridges), A4013003.
  4. Bhagwat, M., Sasmal, S., Novák, B. and Upadhyay, A. (2009), "Dynamic performance evaluation of straight and curved cable-stayed bridges", Bridge Struct.: Assess., Des. Constr., 5(2-3), 87-95.
  5. Bhagwat, M., Sasmal, S., Novak, B. and Upadhyay, A. (2011), "Investigations on seismic response of two span cable-stayed bridges", Earthq. Struct., 2(4), 337-356.
  6. Caltrans, S.D.C. (2004), Caltrans Seismic Design Criteria version 1.3, California Department of Transportation, Sacramento, California.
  7. Calvi, G.M., Sullivan, T.J. and Villani, A. (2010), "Conceptual seismic design of cable-stayed bridges", J. Earthq. Eng., 14(8), 1139-1171.
  8. Casciati, F., Cimellaro, G.P. and Domaneschi, M. (2008), "Seismic reliability of a cable-stayed bridge retrofitted with hysteretic devices", Comput. Struct., 86(17), 1769-1781.
  9. Chang, K.C., Mo, Y.L., Chen, C.C., Lai, L.C. and Chou, C.C. (2004), "Lessons learned from the damaged Chi-Lu cable-stayed bridge", J. Bridge Eng., 9(4), 343-352.
  10. Deco, A. and Frangopol, D.M. (2011), "Risk assessment of highway bridges under multiple hazards", J. Risk Res., 14(9), 1057-1089.
  11. Domaneschi, M. (2010), "Feasible control solutions of the ASCE benchmark cable‐stayed bridge", Struct. Control Hlth. Monit., 17(6), 675-693.
  12. Domaneschi, M. and Martinelli, L. (2012), "Performance comparison of passive control schemes for the numerically improved ASCE cable-stayed bridge model", Earthq. Struct., 3(2), 181-201.
  13. Domaneschi, M. and Martinelli, L. (2013), "Extending the benchmark cable-stayed bridge for transverse response under seismic loading", J. Bridge Eng., 19(3), 04013003.
  14. Fang, K.T., Lin, D.K., Winker, P. and Zhang, Y. (2000), "Uniform design: theory and application", Technometrics, 42(3), 237-248.
  15. Fangfang, G., Youliang, D., Jianyong, S., Wanheng, L. and Aiqun, L. (2014), "Passive control system for seismic protection of a multi-tower cable-stayed bridge", Earthq. Struct., 6(5), 495-514.
  16. Farquhar, D.J. (2008), Cable-stayed bridges. ICE Manual of Bridge Engineering (2nd edition), Institution of Civil Engineers, London, UK.
  17. Ferguson, T.S. (1967), Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York, USA.
  18. Gholipour, Y., Bozorgnia, Y., Rahnamaa, M. and Berberian, M. (2008), "Probabilistic seismic hazard analysis, phase I-Greater Tehran Regions (Technical Report)", College of Engineering, University of Tehran.
  19. Jara, J.M., Galvan, A., Jara, M. and Olmos, B. (2013a), "Procedure for determining the seismic vulnerability of an irregular isolated bridge", Struct. Infrastruct. Eng., 9(6), 516-528.
  20. Jara, J.M., Villanueva, D., Jara, M. and Olmos, B.A. (2013b), "Isolation parameters for improving the seismic performance of irregular bridges", Bull. Earthq. Eng., 11(2), 663-686.
  21. Jara, J.M., Lopez, M.G., Jara, M. and Olmos, B.A. (2014), "Rotation and damage index demands for RC medium-length span bridges", Eng. Struct., 74, 205-217.
  22. Kawashima, K., Unjoh, S. and Tunomoto, M. (1993), "Estimation of damping ratio of cable‐stayed bridges for seismic design", J. Struct. Eng., 119(4), 1015-1031.
  23. Khan, R.A., Datta, T.K. and Ahmad, S. (2006), "Seismic risk analysis of modified fan type cable stayed bridges", Eng. Struct., 28(9), 1275-1285.
  24. Khan, R.A. and Datta, T.K. (2010), "Probabilistic risk assessment of fan type cable-stayed bridges against earthquake forces", J. Vib. Control, 16(6), 779-799.
  25. Kim, D., Yi, J.H., Seo, H.Y. and Chang, C. (2008), "Earthquake risk assessment of seismically isolated extradosed bridges with lead rubber bearings", Struct. Eng. Mech., 29(6), 689-707.
  26. Li, H., Liu, J. and Ou, J. (2009), "Investigation of seismic damage of cable-stayed bridges with different connection configuration", J. Earthq. Tsunami, 3(03), 227-247.
  27. Mackie, K.R. and Stojadinovic, B. (2005), "Fragility basis for California highway overpass bridge seismic decision making (Techincal Report)", Pacific Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley.
  28. Makris, N. and Zhang, J. (2002), "Structural characterization and seismic response analysis of a highway overcrossing equipped with elastomeric bearings and fluid dampers: A case study (Techincal Report)", Pacific Earthquake Engineering Research Center, PEER, University of California, Berkeley.
  29. Mander, J.B., Dhakal, R.P., Mashiko, N. and Solberg, K.M. (2007), "Incremental dynamic analysis applied to seismic financial risk assessment of bridges", Eng. Struct., 29(10), 2662-2672.
  30. Mander, J.B., Priestley, M.J.N. and Park, R. (1988), "Theoretical stress-strain model for confined concrete", J. Struct. Eng., 114(8), 1804-1826.
  31. Mander, J.B., Sircar, J. and Damnjanovic, I. (2012), "Direct loss model for seismically damaged structures", Earthq. Eng. Struct. Dyn., 41(3), 571-586.
  32. Muntasir Billah, A.H.M. and Shahria Alam, M. (2014), "Performance-based prioritisation for seismic retrofitting of reinforced concrete bridge bent", Struct. Infrastruct. Eng., 10(8), 929-949.
  33. Nazmy, A.S. and Abdel-Ghaffar, A.M. (1990), "Three-dimensional nonlinear static analysis of cable-stayed bridges", Comput. Struct., 34(2), 257-271.
  34. Nielson, B.G. and DesRoches, R. (2007), "Seismic fragility methodology for highway bridges using a component level approach", Earthq. Eng. Struct. Dyn., 36(6), 823-839.
  35. Olmos, B.A., Jara, J.M. and Jara, M. (2012), "Influence of some relevant parameters in the seismic vulnerability of RC bridges", Earthq. Struct., 3(3-4), 365-381.
  36. Pacific Earthquake Engineering Research Center (PEER). (2008), "Users manual for the PEER ground motion database web application", University of California, Berkeley.
  37. Padgett, J.E., Dennemann, K. and Ghosh, J. (2010), "Risk-based seismic life-cycle cost-benefit (LCC-B) analysis for bridge retrofit assessment", Struct. Safety, 32(3), 165-173.
  38. Pang, Y., Wu, X., Shen, G. and Yuan, W. (2013), "Seismic fragility analysis of cable-stayed bridges considering different sources of uncertainties", J. Bridge Eng., 19(4), 04013015.
  39. Raheem, S.E.A. and Hayashikawa, T. (2013), "Energy dissipation system for earthquake protection of cablestayed bridge towers", Earthq. Struct., 5(6), 657-678.
  40. Ren, W.X. and Obata, M. (1999), "Elastic-plastic seismic behavior of long span cable-stayed bridges", J. Bridge Eng., 3(194), 194-203.
  41. Ross, S.M. (2009), Introduction to Probability and Statistics for Engineers and Scientists, Academic Press, New York, USA.
  42. SAP2000 (2005), "Linear and nonlinear static and dynamic analysis and design of three-dimensional structures: basic analysis reference manual", Computers and Structures Inc., CSI, Berkeley, California.
  43. Sasmal, S., Ramanjaneyulu, K. and Lakshmanan, N. (2007), "Priority ranking towards condition assessment of existing reinforced concrete bridges", Struct. Infrastruct. Eng., 3(1), 75-89.
  44. Seismosoft. (2013), SeismoMatch v2.1-A computer program for spectrum matching of earthquake records, available from
  45. Shah, S.G., Desai, J.A. and Solanki, C.H. (2010), "Effect of pylon shape on seismic response of cable-stayed bridge with soil structure interaction", Int. J. Civ. Struct. Eng., 1(3), 667-682.
  46. Shinozuka, M., Kim, S.H., Kushiyama, S. and Yi, J.H. (2002), "Fragility curves of concrete bridges retrofitted by column jacketing", Earthq. Eng. Eng. Vib., 1(2), 195-205.
  47. Solberg, K.M., Dhakal, R.P., Mander, J.B. and Bradley, B.A. (2008), "Computational and rapid expected annual loss estimation methodologies for structures", Earthq. Eng. Struct. Dyn., 37 (1), 81-101.
  48. Svensson, H. (2013), Cable-Stayed Bridges: 40 Years of Experience Worldwide, John Wiley & Sons. New York, USA.
  49. Tang, M.C. (1992), "Guidelines for the design of cable-stayed bridges", American Society of Civil Engineers (ASCE), New York.
  50. Tesfamariam, S., and Goda, K. (Eds.). (2013), Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems, Woodhead Publishing Series in Civil and Structural Engineering, Cambridge, UK.
  51. Vamvatsikos, D. and Cornell, C.A. (2002), "Incremental dynamic analysis", Earthq. Eng. Struct. Dyn., 31(3), 491-514.
  52. Yi, J.H., Kim, S.H. and Kushiyama, S. (2007), "PDF interpolation technique for seismic fragility analysis of bridges", Eng. Struct., 29(7), 1312-1322.
  53. Wang, B. and Yuan, W. (2009), "Risk- and performance-based seismic analysis for long-span cable-stayed bridges", TCLEE 2009: Lifeline Earthquake Engineering in a Multihazard Environment, Oakland, California, USA, June 28-July 1.