Probabilistic seismic assessment of RC box-girder highway bridges with unequal-height piers subjected to earthquake-induced pounding

  • Hossein Rezaei
  • Seyyed Amirhossein Moayyedi
  • Robert JankowskiEmail author
Original Research


This paper uses the probabilistic seismic assessment to study the effects of pounding and irregularity on the seismic behavior of typical concrete box-girder bridges with four levels of altitudinal irregularity. To extend the results for all bridges in the same class, uncertainty related to the earthquake, structural geometries, and materials are considered. Pounding is likely to take place in two cases: the first one concerns the seat-type abutments, and the second is at the in-span hinge of multi-frame bridges. Accordingly, the present study is an attempt to investigate the behavior of irregular bridges considering the effects of pounding in both cases. In the first case, the effects of changes in the gap size on engineering demand parameters (EDPs) were investigated. Then, correlations between earthquake parameters and the pounding force were evaluated. Furthermore, the pounding force exerted on the abutment was compared for different bridge irregularity levels. In the second part of the paper, the effects of pounding of adjacent bridge segments in the decks of non-continuous bridges were studied for equivalent Two-Degree-of-Freedom structures, for which the probability of non-occurrence was estimated. In the end, the relationship between structural or seismic parameters and the pounding force was evaluated in case of pounding. The results of the study show that the gap size between the abutment and the deck has the highest effect on the abutment passive deformation, pounding force, and base shear. Also, the substructure irregularity of bridges reduces the correlation between the gap size and the EDPs, except for the column ductility. Moreover, decreasing the ratio of periods of the adjacent frames diminishes the effect of the type of the earthquake but increases the probability of pounding.


Irregular bridge Nonlinear time history analysis Structural pounding Seismic excitation Gap size Intensity measure 



  1. Abbasi M, Zakeri B, Amiri GG (2015) Probabilistic seismic assessment of multiframe concrete box-girder bridges with unequal-height piers. J Perform Constr Facil 30(2):04015016CrossRefGoogle Scholar
  2. American Association of State Highway and Transportation Officials (AASHTO) (1998) LRFD bridge design specifications. Washington, DCGoogle Scholar
  3. Amjadian M, Agrawal AK (2016) Rigid-body motion of horizontally curved bridges subjected to earthquake-induced pounding. J Bridge Eng 21(12):04016090CrossRefGoogle Scholar
  4. Amjadian M, Kalantari A, Agrawal AK (2018) Analytical study of the coupled motions of decks in skew bridges with the deck–abutment collision. J Vib Control 24(7):1300–1321CrossRefGoogle Scholar
  5. Applied Technology Council, & Structural Engineers Association of California (1978) Tentative provisions for the development of seismic regulations for buildings: a cooperative effort with the design professions, building code interests, and the research community. vol 510, Department of Commerce, National Bureau of StandardsGoogle Scholar
  6. Arias A (1970) A measure of earthquake intensity: seismic design for nuclear power plants. Massachusetts Institute of Technology, CambridgeGoogle Scholar
  7. Ayyub BM, Lai KL (1989) Structural reliability assessment using Latin hypercube sampling. In: Proceedings of the 5th international conference on structural safety and reliability (ICOSSAR’89), Part II. ASCE, San FranciscoGoogle Scholar
  8. Baker JW, Cornell CA (2005) A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthq Eng Struct Dyn 34(10):1193–1217CrossRefGoogle Scholar
  9. Baker JW, Lin T, Shahi SK, Jayaram N (2011) New ground motion selection procedures and selected motions for the PEER transportation research program. Pacific Earthquake Engineering Research Center, University of California, Berkeley, Berkeley, CA, PEER Report, (2011/3)Google Scholar
  10. Bi K, Hao H, Chouw N (2010) Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding. Earthq Eng Struct Dyn 39(3):303–323Google Scholar
  11. Buckle I (1994) The Northridge, California earthquake of January 11, 1994: performance of highway bridges. Tech Rep. NCEER-94-0068. National Center for Earthquake Engineering ResearchGoogle Scholar
  12. Buckle I, Hube M, Chen G, Yen WH, Arias J (2012) Structural performance of bridges in the offshore Maule earthquake of 27 February 2010. Earthq Spectra 28(S1):S533–S552CrossRefGoogle Scholar
  13. Celik OC, Ellingwood BR (2010) Seismic fragilities for non-ductile reinforced concrete frames—role of aleatoric and epistemic uncertainties. Struct Saf 32(1):1–12CrossRefGoogle Scholar
  14. Chang GA, Mander JB (1994) Seismic energy based fatigue damage analysis of bridge columns. Part 1—Evaluation of seismic capacity. NCEER Technical Rep N NCEER-94-0006. State Univ of New York, Buffalo, NYGoogle Scholar
  15. Chase JG, Boyer F, Rodgers GW, Labrosse G, MacRae GA (2015) Linear and nonlinear seismic structural impact response spectral analyses. Adv Struct Eng 18(4):555–569CrossRefGoogle Scholar
  16. Chau KT, Wei XX (2001) Pounding of structures modelled as non-linear impacts of two oscillators. Earthq Eng Struct Dyn 30(5):633–651CrossRefGoogle Scholar
  17. Chau KT, Wei XX, Guo X, Shen CY (2003) Experimental and theoretical simulations of seismic poundings between two adjacent structures. Earthq Eng Struct Dyn 32(4):537–554CrossRefGoogle Scholar
  18. Chen D, Zhao CM, Dockray GJ, Varro A, Van Hoek A, Sinclair NF, Koh TJ (2000) Glycine-extended gastrin synergizes with gastrin 17 to stimulate acid secretion in gastrin-deficient mice. Gastroenterology 119(3):756–765CrossRefGoogle Scholar
  19. Choi E (2002) Seismic analysis and retrofit of mid-America bridges. Doctoral dissertation, School of Civil and Environmental Engineering, Georgia Institute of TechnologyGoogle Scholar
  20. Chouw N, Hao H (2008a) Significance of SSI and non-uniform near-fault ground motions in bridge response II: effect on response with modular expansion joint. Eng Struct 30(1):154–162CrossRefGoogle Scholar
  21. Chouw N, Hao H (2008b) Significance of SSI and nonuniform near-fault ground motions in bridge response I: effect on response with conventional expansion joint. Eng Struct 30(1):141–153CrossRefGoogle Scholar
  22. Chouw N, Hao H (2012) Pounding damage to buildings and bridges in the 22 February 2011 Christchurch earthquake. Int J Prot Struct 3(2):123–139CrossRefGoogle Scholar
  23. DesRoches R, Muthukumar S (2002) Effect of pounding and restrainers on seismic response of multiple-frame bridges. J Struct Eng 128(7):860–869CrossRefGoogle Scholar
  24. Dimitrakopoulos EG (2011) Seismic response analysis of skew bridges with pounding deck–abutment joints. Eng Struct 33(3):813–826CrossRefGoogle Scholar
  25. Dimitrakopoulos EG (2013) Nonsmooth analysis of the impact between successive skew bridge-segments. Nonlinear Dyn 74(4):911–928CrossRefGoogle Scholar
  26. Dimitrakopoulos E, Makris N, Kappos AJ (2009) Dimensional analysis of the earthquake-induced pounding between adjacent structures. Earthq Eng Struct Dyn 38(7):867–886CrossRefGoogle Scholar
  27. Dutta A (1999) On energy based seismic analysis and design of highway bridges. Doctoral dissertation, State University of New York at BuffaloGoogle Scholar
  28. EERI (1995) EERI: Northridge Earthquake of January 17, 1994—Reconnaissance Report. EERI Report 95–03, vol 1. Earthquake Engineering Research Institute, OaklandGoogle Scholar
  29. Electrical Power Research Institute (EPRI) (1988) A criterion for determining exceedance of the operating basis earthquake. EPRI NP-5930. Palo Alto, CAGoogle Scholar
  30. Ellingwood B, Hwang H (1985) Probabilistic descriptions of resistance of safety-related structures in nuclear plants. Nuclear Eng Des 88(2):169–178CrossRefGoogle Scholar
  31. Fajfar P, Vidic T, Fischinger M (1990) A measure of earthquake motion capacity to damage medium-period structures. Soil Dyn Earthq Eng 9(5):236–242CrossRefGoogle Scholar
  32. Fang JQ, Li QS, Jeary AP, Liu DK (1999) Damping of tall buildings: its evaluation and probabilistic characteristics. Struct Des Tall Build 8(2):145–153CrossRefGoogle Scholar
  33. Federal Emergency Management Agency (FEMA) (1994) NEHRP Recommended provisions for the development of seismic regulations for new buildingsGoogle Scholar
  34. Filippou FC, Popov EP, Bertero VV (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Report no. UCB/EERC-83/19, Earthquake Engineering research Center, USAGoogle Scholar
  35. Housner GW (1970) Strong ground motion. Earthq Eng 75:91Google Scholar
  36. Huo Y, Zhang J (2012) Effects of pounding and skewness on seismic responses of typical multispan highway bridges using the fragility function method. J Bridge Eng 18(6):499–515CrossRefGoogle Scholar
  37. Jankowski R (2005) Impact force spectrum for damage assessment of earthquake-induced structural pounding. Key Eng Mater 293–294:711–718CrossRefGoogle Scholar
  38. Jankowski R (2006) Pounding force response spectrum under earthquake excitation. Eng Struct 28(8):1149–1161CrossRefGoogle Scholar
  39. Jankowski R (2015) Pounding between superstructure segments in multi-supported elevated bridge with three-span continuous deck under 3D non-uniform earthquake excitation. J Earthq Tsunami 9(4):1550012CrossRefGoogle Scholar
  40. Jankowski R (2017) Damage-involved structural pounding in bridges under seismic excitation. Key Eng Mater 754:309–312CrossRefGoogle Scholar
  41. Jankowski R, Mahmoud S (2015) Earthquake-induced structural pounding. Springer, Cham, SwitzerlandCrossRefGoogle Scholar
  42. Jankowski R, Walukiewicz H (1997) Modeling of two-dimensional random fields. Probab Eng Mech 12(2):115–121CrossRefGoogle Scholar
  43. Jankowski R, Wilde K (2000) A simple method of conditional random field simulation of ground motions for long structures. Eng Struct 22(5):552–561CrossRefGoogle Scholar
  44. Jankowski R, Wilde K, Fujino Y (2000) Reduction of pounding effects in elevated bridges during earthquakes. Earthq Eng Struct Dyn 29(2):195–212CrossRefGoogle Scholar
  45. Kawashima K, Unjoh S, Hoshikuma J-I, Kosa K (2011) Damage of bridges due to the 2010 Maule, Chile, earthquake. J Earthq Eng 15(7):1036–1068CrossRefGoogle Scholar
  46. Kim SH, Shinozuka M (2003) Effects of seismically induced pounding at expansion joints of concrete bridges. J Eng Mech 129(11):1225–1234CrossRefGoogle Scholar
  47. Kosa K, Tazaki K, Yamaguchi E (2002) Mechanism of damage to Shiwei Bridge caused by 1999 Chi–Chi earthquake. Struct Eng Earthq Eng 19(2):221s–226sCrossRefGoogle Scholar
  48. Kramer SL (1996) Geotechnical earthquake engineering. Prentice Hall, Upper Saddle River, p 569Google Scholar
  49. Kun C, Jiang L, Chouw N (2017) Influence of pounding and skew angle on seismic response of bridges. Eng Struct 148:890–906CrossRefGoogle Scholar
  50. Lin N (2002) Social capital: a theory of social structure and action, vol 19. Cambridge University Press, CambridgeGoogle Scholar
  51. Mackie K, Stojadinović B (2003) Seismic demands for performance-based design of bridges. Pacific Earthquake Engineering Research Center, BerkeleyGoogle Scholar
  52. Mahmoud S, Chen X, Jankowski R (2008) Structural pounding models with Hertz spring and nonlinear damper. J Appl Sci 8(10):1850–1858CrossRefGoogle Scholar
  53. Mandal A, Pal SC (2015) Achieving agility through BRIDGE process model: an approach to integrate the agile and disciplined software development. Innov Syst Softw Eng 11(1):1–7CrossRefGoogle Scholar
  54. Mander JB, Kim DK, Chen SS, Premus GJ (1996) Response of steel bridge bearings to reversed cyclic loading. Technical Rep. No. NCEER 96-0014, US National Center for Earthquake Engineering Research (NCEER)Google Scholar
  55. McKenna F (2011) OpenSees: a framework for earthquake engineering simulation. Comput Sci Eng 13(4):58–66CrossRefGoogle Scholar
  56. Megally SH, Garg M, Seible F, Dowell RK (2001) Seismic performance of precast segmental bridge superstructures. SSRP, 24Google Scholar
  57. Megally SH, Silva PF, Seible F (2002) Seismic response of sacrificial exterior keys in bridge abutments. Report no. SSRP–2001/23. Department of Structural Engineering, University of California, San Diego, La Jolla, CAGoogle Scholar
  58. Menegotto M, Pinto P (1973) Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometryand non-elastic behavior of elements under combined normal force and bending. In: Proceedings. IABSE sympoium on resistance and ultimate deformability of structures acted on by well-defined repeated loadsGoogle Scholar
  59. Muthukumar S, DesRoches R (2006) A Hertz contact model with non-linear damping for pounding simulation. Earthq Eng Struct Dyn 35(7):811–828CrossRefGoogle Scholar
  60. NBI (National Bridge Inventory) (2010) National bridge inventory data. U.S. Dept. of Transportation, Federal Highway Administration, WashingtonGoogle Scholar
  61. Nielson BG (2005) Analytical fragility curves for highway bridges in moderate seismic zones. Doctoral dissertation, Georgia Institute of TechnologyGoogle Scholar
  62. Otsuka H, Unjoh S, Terayama T, Hoshikuma J, Kosa K (1996) Damage to highway bridges by the 1995 Hyogoken Nanbu earthquake and the retrofit of highway bridges in Japan. In: Proceedings of the 3rd US Japan workshop on seismic retrofit of bridgeGoogle Scholar
  63. Padgett JE (2007) Seismic vulnerability assessment of retrofitted bridges using probabilistic methods. Doctoral dissertation, Georgia Institute of TechnologyGoogle Scholar
  64. Pahlavan H, Zakeri B, Amiri GG, Shaianfar M (2015) Probabilistic vulnerability assessment of horizontally curved multiframe RC box-girder highway bridges. J Perform Constr Facil 30(3):04015038CrossRefGoogle Scholar
  65. Park YJ, Ang AHS, Wen YK (1985) Seismic damage analysis of reinforced concrete buildings. J Struct Eng 111(4):740–757CrossRefGoogle Scholar
  66. Priestley MN, Seible F, Calvi GM, Calvi GM (1996) Seismic design and retrofit of bridges. Wiley, HobokenCrossRefGoogle Scholar
  67. Raheem SEA (2014) Mitigation measures for earthquake induced pounding effects on seismic performance of adjacent buildings. Bull Earthq Eng 12(4):1705–1724CrossRefGoogle Scholar
  68. Ramanathan KN (2012) Next generation seismic fragility curves for California bridges incorporating the evolution in seismic design philosophy. Doctoral dissertation, Georgia Institute of TechnologyGoogle Scholar
  69. Rathje EM, Faraj F, Russell S, Bray JD (2004) Empirical relationships for frequency content parameters of earthquake ground motions. Earthq Spectra 20(1):119–144CrossRefGoogle Scholar
  70. Riddell R, Garcia JE (2001) Hysteretic energy spectrum and damage control. Earthq Eng Struct Dyn 30(12):1791–1816CrossRefGoogle Scholar
  71. Ruangrassamee A, Kawashima K (2001) Relative displacement response spectra with pounding effect. Earthq Eng Struct Dyn 30(10):1511–1538CrossRefGoogle Scholar
  72. Shamsabadi A, Kapuskar M (2010) Nonlinear soil–abutment–foundation–structure interaction analysis of skewed bridges subjected to near-field ground motions. Transp Res Record J Transp Res Board 2202:192–205CrossRefGoogle Scholar
  73. Shamsabadi A, Yan L (2008) Closed-formed force-displacement backbone curves for bridge abutment backfill systems. In: Proc. geotechnical earthquake engineering and soil dynamic IV congress. ASCE, Reston, VAGoogle Scholar
  74. Shantz T, Roblee C (2011) Estimates of foundation springs, piles capacities and uncertainties for typical Caltrans bridges. [email] (Personal communication with Ramanathan K., DesRoches R., Padgett J. Dukes J. and Turner L., 25 March)Google Scholar
  75. Shimazaki K, Sozen M (1984) Seismic drift of reinforced concrete structures Res. Rep. Hazama-Gumi Ltd., Tokyo (in Japanese) Google Scholar
  76. Singh RP, Bhoi S, Sahoo AK (2002) Changes observed in land and ocean after Gujarat earthquake of 26 January 2001 using IRS data. Int J Remote Sens 23(16):3123–3128CrossRefGoogle Scholar
  77. Smith W (2005) The challenge of earthquake risk assessment. Seismol Res Lett 76(4):415–416CrossRefGoogle Scholar
  78. Tothong P, Luco N (2007) Probabilistic seismic demand analysis using advanced ground motion intensity measures. Earthq Eng Struct Dyn 36(13):1837–1860CrossRefGoogle Scholar
  79. Vamvatsikos D, Cornell CA (2005) Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information. Earthq Eng Struct Dyn 34(13):1573–1600CrossRefGoogle Scholar
  80. Von Thun JL (1988) Earthquake ground motions for design and analysis of dams. In: Earthquake engineering and soil dynamics II-recent advances in ground-motion evaluationGoogle Scholar
  81. Wang TL, Li QN (2011) Research on pounding response at expansion joint in the linear bridge and the curved bridge under earthquake. Adv Mater Res 255:2303–2307CrossRefGoogle Scholar
  82. Wang LX, Chau KT, Wei XX (2009) Numerical simulations of nonlinear seismic torsional pounding between two single-story structures. Adv Struct Eng 12(1):87–101CrossRefGoogle Scholar
  83. Won JH, Mha HS, Kim SH (2015) Effects of the earthquake-induced pounding upon pier motions in the multi-span simply supported steel girder bridge. Eng Struct 93:1–12CrossRefGoogle Scholar
  84. Yashinsky M, Oviedo R, Ashford SA, Fargier-Gabaldon L, Hube M (2010) Performance of highway and railway structures during the February 27, 2010 Maule Chile earthquake. EERI/PEER, FHWA Bridge Team ReportGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Earthquake Engineering, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Structural Engineering Research CenterInternational Institute of Earthquake Engineering and Seismology (IIEES)TehranIran
  3. 3.Faculty of Civil and Environmental EngineeringGdansk University of TechnologyGdanskPoland

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