Sensitivity analysis of the plastic hinge region in the wall pier of reinforced concrete bridges

  • Babaei, Ali (Civil Engineering Department, Semnan Branch, Islamic Azad University) ;
  • Mortezaei, Alireza (Seismic Geotechnical and High Performance Concrete Research Centre, Civil Engineering Department, Semnan Branch, Islamic Azad University) ;
  • Salehian, Hamidreza (Seismic Geotechnical and High Performance Concrete Research Centre, Civil Engineering Department, Semnan Branch, Islamic Azad University)
  • Received : 2019.05.10
  • Accepted : 2019.08.03
  • Published : 2019.12.25


As the bridges are an integral part of the transportation network, their function as one of the most important vital arteries during an earthquake is fundamental. In a design point of view, the bridges piers, and in particular the wall piers, are considered as effective structural elements in the seismic response of bridge structures due to their cantilever performance. Owing to reduced seismic load during design procedure, the response of these structural components should be ductile. This ductile behavior has a direct and decisive correlation to the development of plastic hinge region at the base of the wall pier. Several international seismic design codes and guidelines have suggested special detailing to assure ductile response in this region. In this paper, the parameters which affect the length of plastic hinge region in the reinforced concrete bridge with wall piers were examined and the sensitivity of these parameters was evaluated on the length of the plastic hinge region. Sensitivity analysis was accomplished by independently variable parameters with one standard deviation away from their means. For this aim, the Monte Carlo simulation, tornado diagram analysis, and first order second moment method were used to determine the uncertainties associated with analysis parameters. The results showed that, among the considered design variables, the aspect ratio of the pier wall (length to width ratio) and axial load level were the most important design parameters in the plastic hinge region, while the yield strength of transverse reinforcements had the least effect on determining the length of this region.


  1. AASHTO (2011), Guide Specifications for LRFD Seismic Bridge Design, American Association of State Highway and Transportation Officials, Washington, D.C., USA.
  2. ACI Committee 318 (2014), Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14), American Concrete Institute; Farmington Hills, Michigan, USA.
  3. Alembagheri, M. and Seyedkazemi, M. (2015), "Seismic performance sensitivity and uncertainty analysis of gravity dams", Earthq. Eng. Struct. Dynam., 44(1), 41-58.
  4. Alim, H. (2014), "Reliability based seismic performance analysis of retrofitted concrete bridge bent", M.Sc. Disseration, Chittagong University of Engineering and Technology (CUET), Chittagong, Bangladesh.
  5. Aslani, H., Cabrera, C. and Rahnama, M. (2012), "Analysis of the sources of uncertainty for portfolio-level earthquake loss estimation", Earthq. Eng. Struct. Dynam., 41(11), 1549-1568.
  6. Baker, J.W. and Cornell, C.A. (2008), "Uncertainty propagation in probabilistic seismic loss estimation", Struct. Safety, 30(3), 236-252.
  7. Baynes, L.C. (2005), "An evaluation of free field liquefaction analysis using OpenSees", M.Sc. Dissertation, University of Washington, Seattle, USA.
  8. Caltrans (2013), Seismic Design Criteria 1.7., California Department of Transportation; Sacramento, CA, USA.
  9. Canadian Standard Association (2004), Design of Concrete Structures, CAN/CSA-A23.3-04, Mississauga, Ontario, Canada.
  10. Celarec, D. and Dolsek, M. (2013), "The impact of modelling uncertainties on the seismic performance assessment of reinforced concrete frame buildings", Eng. Struct., 52, 340-354.
  11. Celik, O.C. and Ellingwood, B.R. (2010), "Seismic fragilities for nonductile reinforced concrete frames - Role of aleatoric and epistemic uncertainties", Struct. Safety, 32(1), 1-12.
  12. CEN (2004), Eurocode 8: Design of Structures for Earthquake Resistance. Part 1: General Rules, Seismic Actions and Rules for Buildings, EN 1198-1, European Committee for Standardization; Belgium.
  13. CEN (2005), Eurocode 8: design provisions of structures for earthquake resistance. Part 2: Bridges. EN 1998-2. European Committee for Standardization; Belgium.
  14. Crozet, V., Politopoulos, I., Yang, M., Martinez, J.M. and Erlicher, S. (2018), "Sensitivity analysis of pounding between adjacent structures", Earthq. Eng. Struct. Dynam., 47(1), 219-235.
  15. Eldin, M.N. and Kim, J. (2016), "Sensitivity analysis on seismic life-cycle cost of a fixed-steel offshore platform structure", Ocean Eng., 121, 323-340.
  16. Ellingwood, B., Galambos, T.V., MacGregor, J.G. and Cornell, C.A. (1980), Development of a Probability Based Load Criterion for American National Standard A58-Building Code Requirement for Minimum Design Loads in Buildings and Other Structures, National Bureau of Standards, Dept. of Commerce, Washington, D.C., USA.
  17. Ghaderi Bafti, F., Mortezaei, A. and Kheyroddin, A. (2019), "The length of plastic hinge area in the flanged reinforced concrete shear walls subjected to earthquake ground motions", Struct. Eng. Mech., 69(6), 651-665.
  18. Lee, T.H. and Mosalam, K.M. (2004), "Probabilistic fiber element modeling of reinforced concrete structures", Comput. Struct., 82, 2285-2299.
  19. Lee, T.H. and Mosalam, K.M. (2005), "Seismic demand sensitivity of reinforced concrete shear-wall building using FOSM method", Earthq. Eng. Struct. Dynam., 34(14), 1719-1736.
  20. Lee, T.H. and Mosalam, K.M. (2006), "Probabilistic Seismic Evaluation of Reinforced Concrete Structural Components and Systems", University of California, Berkeley, CA, USA.
  21. Management and Planning Organization (2005), Road Safety Manual: Safety at Bridge and Tunnel, No: 267, Office of Deputy for Technical Affairs, Technical, Criteria Codification and Earthquake Risk Reduction Affairs Bureau, Tehran, Iran.
  22. Ministry of Roads and Transportation (2008), Road and Railway Bridges Seismic Resistant Design Code, NO: 463, Office of Deputy for Strategic Supervision Bureau of Technical Execution System, Ministry of Roads and Transportation, Tehran, Iran.
  23. Mirza, S.A. and MacGregor, J.G. (1979), "Variability in dimensions of reinforced concrete members", J. Struct. Division, 105(ST4), 751-766.
  24. Mirza, S.A. and MacGregor, J.G. (1979), "Variability of mechanical properties of reinforcing bars", J. Struct. Division, 105(ST5), 921-937.
  25. Mortezaei, A. (2015), "Effect of frequency content of near-fault ground motions on seismic performance of reinforced concrete bridge piers", J. Transport. Infrastruct. Eng., 1(3), 93-109.
  26. Mortezaei, A. and Ronagh, H.R. (2012), "Plastic hinge length of FRP strengthened reinforced concrete columns subjected to both far-fault and near-fault ground motions", Scientia Iranica, 19, 1365-1378.
  27. Murat, O. (2015), "Field Reconnaissance of the October 23, 2011, Van, Turkey Earthquake: Lessons from Structural Damages", J. Performance Construct. Facilities, 29(5),
  28. Na, U.J., Chaudhuri, S.R. and Shinozuka, M. (2008), "Probabilistic assessment for seismic performance of port structures", Soil Dynam. Earthq. Eng., 28(2),147-158.
  29. NZS 3101 (2006), The Design of Concrete Structures. Concrete Structures Standard, Part 1: Code of practice, Wellington, New Zealand Standard, New Zealand.
  30. Padgett, J.E. and DesRoches, R. (2007), "Sensitivity of seismic response and fragility to parameter uncertainty", J. Struct. Eng., 133(12), 1710-1718.
  31. Porter, K.A., Beck, J.L. and Shaikhutdinov, R.V. (2002), "Investigation of sensitivity of building loss estimates to major uncertain variables for the Van Nuys test bed", Pacific Earthquake Engineering Research Center, University of California, Berkeley, USA.
  32. Rota, M., Penna, A. and Magenes, G. (2010), "A methodology for deriving analytical fragility curves for masonry buildings based on stochastic nonlinear analyses", Eng. Struct., 32(5), 1312-1323.
  33. Seo, J. (2013), "Statistical determination of significant curved Igirder bridge seismic response parameters", Earthq. Eng. Eng. Vib., 12(2), 251-260.
  34. Seo, J. and Linzell, D.G. (2013), "Nonlinear seismic response and parametric examination of horizontally curved steel bridges using 3D computational models", J. Bridge Eng., 18(3), 220-231.
  35. Seo, M.S., Kim, H.S., Truong, G.T. and Choi, K.K. (2017), "Seismic behaviors of thin slender structural walls reinforced with amorphous metallic fibers", Eng. Struct., 152, 102-115.
  36. Sung, Y. C., Chang, D. W., Cheng, M. Y., Chang, T. L. and Liu, K. Y. (2009), "Enhancing the structural longevity of the bridges with insufficient seismic capacity by retrofitting", Structural Longevity, 1(1), 1-16.
  37. Vamvatsikos, D. and Fragiadakis, M. (2010), "Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty", Earthq. Eng. Struct. Dynam, 39(2), 141-163.
  38. Zona, A., Ragni, L. and Dall'Asta, A. (2012), "Sensitivity-based study of the influence of brace over-strength distributions on the seismic response of steel frames with BRBs", Eng. Struct., 37, 179-192.