Earthquake Engineering and Engineering Vibration

, Volume 17, Issue 4, pp 869–891 | Cite as

Seismic fragility of structures isolated by single concave sliding devices for different soil conditions

  • P. CastaldoEmail author
  • G. Amendola
  • M. Ripani


This study deals with the seismic fragility of elastic structural systems equipped with single concave sliding (friction pendulum system (FPS)) isolators considering different soil conditions. The behavior of these systems is analyzed by employing a two-degree-of-freedom model, whereas the FPS response is described by means of a velocity-dependent model. The uncertainty in the seismic inputs is taken into account by considering artificial seismic excitations modelled as timemodulated filtered Gaussian white noise random processes of different intensity within the power spectral density method. In particular, the filter parameters, which control the frequency content of the random excitations, are calibrated to describe stiff, medium and soft soil conditions. The sliding friction coefficient at large velocity is also considered as a random variable modelled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities of exceeding different limit states related to both the reinforced concrete (RC) superstructure and isolation level, defining the seismic fragility curves within an extensive parametric study carried out for different structural system properties and soil conditions. The abovementioned seismic fragility curves are useful to evaluate the seismic reliability of base-isolated elastic systems equipped with FPS and located in any site for any soil condition.


friction pendulum devices seismic isolation soil condition frequency content seismic fragility 


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  1. Almazàn JL and De la Llera JC (2003), “Physical Model for Dynamic Analysis of Structures with FPS Isolators,” Earthquake Engineering and Structural Dynamics, 32: 1157–1184.CrossRefGoogle Scholar
  2. Aoki Y, Ohashi Y, Fujitani H, Saito T, Kanda J, Emoto T and Kohno M (2000), “Target Seismic Performance levels in Structural Design for Buildings,” 12WCEE.Google Scholar
  3. Armouti NS (2003), “Response of Structures to Synthetic Earthquakes,” Emerging Technologies in Str. Eng. Proc. of the 9th Arab Str. Eng. Conf., Nov. 29 - Dec. 1, 2003, Abu Dhabi, UAE, 331–340.Google Scholar
  4. Aslani H and Miranda E (2005), “Probability-Based Seismic Response Analysis,” Engineering Structures, 27(8): 1151–1163.CrossRefGoogle Scholar
  5. Ayyub BM and McCuen RH (2002), Probability, statistics, and reliability for engineers, 2nd ed., NY: CRC Press.Google Scholar
  6. Barroso LR and Winterstein S (2002), “Probabilistic seismic demand analysis of controlled steel moment resisting frame structures,” Earth. Eng. and Str. Dynamics, 31(12): 2049–2066.CrossRefGoogle Scholar
  7. Bertero RD and Bertero VV (2002), “Performance-Based Seismic Engineering: the Need for a Reliable Conceptual Comprehensive Approach,” Earthquake Engineering and Structural Dynamics, 31: 627–652.CrossRefGoogle Scholar
  8. Building Seismic Safety Council (1997), NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, Provisions (FEMA 274), Washington, DC.Google Scholar
  9. Castaldo P, Mancini G and Palazzo B (2018a), “Seismic Reliability-Based Robustness Assessment of Three-Dimensional Reinforced Concrete Systems Equipped with Single-Concave Sliding Devices,” Engineering Structures, 163: 373–387.CrossRefGoogle Scholar
  10. Castaldo P, Palazzo B and Della Vecchia P (2015), “Seismic Reliability of Base-Isolated Structures with friction pendulum bearings,” Engineering Structures, 95: 80–93.CrossRefGoogle Scholar
  11. Castaldo P, Amendola G and Palazzo B (2017a), “Seismic Fragility and Reliability of Structures Isolated by Friction Pendulum Devices: Seismic Reliability-Based Design (SRBD),” Earthquake Engineering and Structural Dynamics, 46(3): 425–446, DOI: 10.1002/eqe.2798.CrossRefGoogle Scholar
  12. Castaldo P, Palazzo B and Ferrentino T (2017b), “Seismic Reliability-Based Ductility Demand Evaluation for Inelastic Base-Isolated Structures with Friction Pendulum Devices,” Earthquake Engineering and Structural Dynamics, 46(8): 1245–1266, DOI: 10.1002/eqe.2854.CrossRefGoogle Scholar
  13. Castaldo P, Palazzo B and Della Vecchia P, (2016), “Life-Cycle Cost and Seismic Reliability Analysis of 3D Systems Equipped with FPS for Different Isolation Degrees,” Engineering Structures, 125: 349–363, CrossRefGoogle Scholar
  14. Castaldo P and Ripani M (2016), “Optimal Design of Friction Pendulum System Properties for Isolated Structures Considering Different Soil Conditions,” Soil Dynamics and Earthquake Engineering, 90: 74–87, DOI: 10.1016/j.soildyn.2016.08.025.CrossRefGoogle Scholar
  15. Castaldo P, Ripani M and Lo Priore R (2018b), “Influence of Soil Conditions on the Optimal Sliding Friction Coefficient for Isolated Bridges,” Soil Dynamics and Earthquake Engineering, 111: 131–148.CrossRefGoogle Scholar
  16. Castaldo P and Tubaldi E (2015), “Influence of FPS Bearing Properties on the Seismic Performance of Base-Isolated Structures,” Earthquake Engineering and Structural Dynamics, 44(15): 2817–2836, DOI: 10.1002/eqe.2610.CrossRefGoogle Scholar
  17. Castaldo P and Tubaldi E (2018), “Influence of Ground Motion Characteristics on the Optimal Single Concave Sliding Bearing Properties for Base-Isolated Structures,” Soil Dynamics and Earthquake Engineering, 104: 346–364.CrossRefGoogle Scholar
  18. Celarec D and Dolšek M (2013), “The Impact of Modelling Uncertainties on the Seismic Performance Assessment of Reinforced Concrete Frame Buildings,” Engineering Structures, 52: 340–354.CrossRefGoogle Scholar
  19. CEN–European Committee for Standardization (2006), Eurocode 0: Basis of Structural Design. Final draft, Brussels.Google Scholar
  20. Chen J, Liu W, Peng Y and Li J (2007), “Stochastic Seismic Response and Reliability Analysis of Base-Isolated Structures,” J. Earthquake Eng., 11: 903–924.CrossRefGoogle Scholar
  21. Christopoulos C and Filiatrault A (2006), Principles of Passive Supplemental Damping and Seismic Isolation, IUSS Press: Pavia, Italy.Google Scholar
  22. Clough RW and Penzien J (1993), Dynamics of Structures, 2nd ed., McGraw-Hill, New York.Google Scholar
  23. Collins KR, Stojadinovic B (2000), “Limit States for Performance-Based Design,” 12WCEE.Google Scholar
  24. Constantinou MC, Mokha A and Reinhorn AM (1990), “Teflon Bearings in Base Isolation. II: Modeling,” J. Struct. Eng., 116(2): 455–474.CrossRefGoogle Scholar
  25. Cornell CA and Krawinkler H (2000), “Progress and Challenges in Seismic Performance Assessment,” PEER Center News, 4(1): 1–3.Google Scholar
  26. Dicleli M and Buddaram S (2006), “Effect of Isolator and Ground Motion Characteristics on the Performance of Seismic-Isolated Bridges,” Earthquake Eng. and Structural Dynamics, 35(2): 233–250.CrossRefGoogle Scholar
  27. Fan FG and Ahmadi G (1990), “Random Response Analysis of Frictional Base Isolation System,” J. Eng. Mech., 116(9): 1881–1901.CrossRefGoogle Scholar
  28. Hancock J and Bommer JJ (2006), “A State-of-Knowledge Review of the Influence of Strong-Motion Duration on Structural Damage,” Earthquake Spectra, 22(3): 827–845.CrossRefGoogle Scholar
  29. Hancock J and Bommer JJ (2007), “Using Spectral Matched Records to Explore the Influence of Strong-Motion Duration on Inelastic Structural Response,” Soil Dyn. and Eart. Eng., 27: 291–299.CrossRefGoogle Scholar
  30. Housner GW (1952), “Spectrum Intensities of Strong-Motion Earthquakes,” Proc. Symp. On Earthquake and Blast Effects Structures, Los Angeles.Google Scholar
  31. Jangid R (2008), “Stochastic Response of Bridges Seismically Isolated by Friction Pendulum System,” J. Bridge Eng., 13(4): 319–330.CrossRefGoogle Scholar
  32. Kanai K (1957), “Semiempirical Formula for the Seismic Characteristics of the Ground,” Bulletin of Earthquake Research Institute, 35: 309–325.Google Scholar
  33. Kelly JM (1997), Earthquake-Resistant Design with Rubber, 2nd ed., Berlin and New York: Springer-Verlag.CrossRefGoogle Scholar
  34. Kulkarni JA and Jangid RS (2003), “Effects of Superstructure Flexibility on the Response of Base-Isolated Structures,” Shock and Vibration, 26: 1–13.CrossRefGoogle Scholar
  35. Li C and Liu Y (2004), “Ground Motion Dominant Frequency Effect On The Design Of Multiple Tuned Mass Dampers,” Journal of Earthquake Engineering, 8(1): 89–105.Google Scholar
  36. Lin YK and Cai GQ (1995), Probabilistic Structural Dynamics—Advanced Theory and Applications, NY: McGraw-Hill.Google Scholar
  37. Luco N and Cornell CA (2007), “Structure-Specific Scalar Intensity Measures for Near-Source and Ordinary Earthquake Ground Motions,” Earthquake Spectra, 23(2): 357–392.CrossRefGoogle Scholar
  38. Math Works Inc. (1997), MATLAB-High Performance Numeric Computation and Visualization Software, User’s Guide. Natick: MA, USA.Google Scholar
  39. Mckey MD, Conover WJ and Beckman RJ (1979), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis from a Computer Code,” Technometrics, 21: 239–245.Google Scholar
  40. Mishra SK, Roy BK and Chakraborty S (2013), “Reliability-Based-Design-Optimization of Base Isolated Buildings Considering Stochastic System Parameters Subjected to Random Earthquakes,” Int J Mech Sci, 75: 123–133.CrossRefGoogle Scholar
  41. Mokha A, Constantinou MC and Reinhorn AM (1990), "Teflon Bearings in Base Isolation, I: Testing,” J. Struct. Eng., 116(2): 438–454.CrossRefGoogle Scholar
  42. NTC0 8-Norme Tecniche per le costruzioni (2008), Gazzetta Ufficiale del 04.02.08, DM 14.01.08, Ministero delle Infrastrutture.Google Scholar
  43. Palazzo B, Castaldo P and Della Vecchia P (2014), “Seismic Reliability Analysis of Base-Isolated Structures with Friction Pendulum System,” 2014 IEEE Workshop on Environmental, Energy and Structural Monitoring Systems Proceedings, Napoli, September 17–18.Google Scholar
  44. Palazzo B (1991), “Seismic Behavior of base-isolated Buildings,” Proc. International Meeting on earthquake Protection of Buildings, Ancona.Google Scholar
  45. Peng Y, Chen J and Li J (2014), “Nonlinear Response of Structures Subjected to Stochastic Excitations via Probability Density Evolution Method,” Adv. in Str. Eng., 17(6): 801–816.CrossRefGoogle Scholar
  46. Pinto P, Giannini R and Franchin P (2004), Seismic Reliability Analysis of Structures, Iuss Press.Google Scholar
  47. Porter KA (2003), “An overview of PEER’s Performance-Based Earthquake Engineering Methodology,” Proceedings of the 9th International Conference on Application of Statistics and Probability in Civil Engineering (ICASP9), San Francisco, California, 973–980.Google Scholar
  48. Ryan KL and Chopra AK (2004), “Estimation of Seismic Demands on Isolators Based on Nonlinear Analysis,” J. Struct. Eng., 130(3): 392–402.CrossRefGoogle Scholar
  49. Safak E and Frankel A (1996), “Effects of Ground Motion Characteristics on the Response of Base-Isolated Structures,” 11th World Conference on Earthquake Engineering (paper No. 1430).Google Scholar
  50. Saito T, Kanda J and Kani N (1998), “Seismic Reliability Estimate of Building Structures Designed According to the Current Japanese Design Code,” Proc. of the Struc. Eng. World Congress.Google Scholar
  51. Saritaş F and Hasgür Z (2014), “Dynamic Behavior of an Isolated Bridge Pier under Earthquake Effects for Different Soil layers and Support Conditions,” Digest, 1733–1756.Google Scholar
  52. SEAOC Vision 2000 Committee (1995), “Performance-Based Seismic Engineering,” Report prepared by Structural Engineers Association of California, Sacramento, CA.Google Scholar
  53. Shinozuka M and Sato Y (1967), “Simulation of Nonstationary Random Process,” J. Engrg. Mech. Div., 93(1): 11–40.Google Scholar
  54. Shinozuka M and Deodatis G (1991), “Simulation of Stochastic Processes by Spectral Representation,” Applied Mechanics Reviews, 44(4): 191–203.CrossRefGoogle Scholar
  55. Shome N, Cornell CA, Bazzurro P and Carballo JE (1998), “Earthquake, Records, and Nonlinear Responses,” Earthquake Spectra, 14(3): 469–500.CrossRefGoogle Scholar
  56. Su L, Ahmadi G and Tadjbakhsh IG (1989), “Comparative Study of Base Isolation Systems,” Journal of Engineering Mechanic, 115: 1976–1992.CrossRefGoogle Scholar
  57. Su L and Ahmadi G (1988), “Response of Frictional Base Isolation Systems to Horizontal–Vertical Random Earthquake Excitations,” Prob Eng Mech, 3(1): 12–21.CrossRefGoogle Scholar
  58. Tajimi H (1960), “A Statistical Method of Determining the Maximum Response of a Building Structure During an Earthquake,” Proc., 2nd World Conf. on Earthquake Eng., II: 781–798.Google Scholar
  59. Talaslidis DG, Manolis GD, Paraskevopoulos EA and Panagiotopoulos CG (2004), “Risk Analysis of Industrial Structures with Hazardous Materials under Seismic Input," 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1–6.Google Scholar
  60. Talal Awwad and Modar Donia (2016), “The Efficiency of Using a Seismic Base Isolation System for a 2D Concrete Frame Founded Upon Improved Soft Soil with Rigid Inclusions,” Earthquake Engineering and Engineering Vibration, 15(1): 49–60. Scholar
  61. Tsai CS, Hsueh CI and Su HC (2016), “Roles of Soil-Structure Interaction and Damping in Base-Isolated Structures Built on Numerous Soil Layers Overlying a Half-Space,” Earthquake Engineering and Engineering Vibration, 15(2): 387–400.CrossRefGoogle Scholar
  62. Vamvatsikos D and Cornell CA (2002), “Incremental dynamic analysis,” Earthquake Engineering and Structural Dynamics, 31(3): 491–514.CrossRefGoogle Scholar
  63. Zayas VA, Low SS and Mahin SA (1990), “A Simple Pendulum Technique for Achieving Seismic Isolation,” Earthquake Spectra, 6: 317–333.CrossRefGoogle Scholar
  64. Zou XK, Wang Q, Li G and Chan CM (2010), “Integrated Reliability-Based Seismic Drift Design Optimization of Base-Isolated Concrete Buildings,” J. Struct. Eng., 136: 1282–1295.CrossRefGoogle Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StructuralGeotechnical and Building Engineering (DISEG), Politecnico di TorinoTurinItaly
  2. 2.Department of Civil EngineeringUniversity of Salerno, Via GiovanniPaolo II (SA)Italy
  3. 3.Facultad de IngenieríaUniversidad de Buenos Aires. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Instituto de Tecnologías y Ciencias de la Ingeniería “Hilario Fernández Long” (INTECIN).Buenos AiresArgentina

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