Simulation based improved seismic fragility analysis of structures

  • Ghosh, Shyamal (Department of Civil Engineering, Indian Institute of Engineering Science and Technology) ;
  • Chakraborty, Subrata (Department of Civil Engineering, Indian Institute of Engineering Science and Technology)
  • Received : 2017.01.14
  • Accepted : 2017.05.26
  • Published : 2017.05.25


The Monte Carlo Simulation (MCS) based seismic fragility analysis (SFA) approach allows defining more realistic relationship between failure probability and seismic intensity. However, the approach requires simulating large number of nonlinear dynamic analyses of structure for reliable estimate of fragility. It makes the approach computationally challenging. The response surface method (RSM) based metamodeling approach which replaces computationally involve complex mechanical model of a structure is found to be a viable alternative in this regard. An adaptive moving least squares method (MLSM) based RSM in the MCS framework is explored in the present study for efficient SFA of existing structures. In doing so, the repetition of seismic intensity for complete generation of fragility curve is avoided by including this as one of the predictors in the response estimate model. The proposed procedure is elucidated by considering a non-linear SDOF system and an existing reinforced concrete frame considered to be located in the Guwahati City of the Northeast region of India. The fragility results are obtained by the usual least squares based and the proposed MLSM based RSM and compared with that of obtained by the direct MCS technique to study the effectiveness of the proposed approach.


Grant : Seismic vulnerability assessment of existing building to North Eastern Region

Supported by : DST, Govt. of India


  1. Atkinson, G.M. and Boore, D.M. (1998), "Evaluation of models for earthquake source spectra in eastern north America", Bull. Seismol. Soc. Am., 88(4), 917-934.
  2. Balasubramanian S.R., Balaji Rao, K., Meher Prasad, A., Goswami, R. and Anoop, M.B. (2014), "A methodology for development of seismic fragility curves for URBM buildings", Earthq. Struct., 6(6), 611-625.
  3. Boore, D.M. and Boatwright, J. (1984), "Average body wave radiation coefficients", Bull. Seismol. Soc. Am., 74(5), 1615-1621.
  4. Boore, D.M. (1996), "SMSIM-Fortran programs for simulating ground motions from earthquakes: Version 1.0", U.S. Geological Survey.-Open-File Report, 96-80-A: 1-73.
  5. Boore, D.M. (2003), "Simulation of ground motion using the stochastic method", Pure Appl. Geophys., 160, 635-676.
  6. Brune, J. (1970), "Tectonic stress and the spectra of seismic shear waves from earthquakes", J. Geophys. Res., 75(26), 4997-5009.
  7. Buratti, N., Ferracuti, B. and Savoia, M. (2010), "Response Surface with random factors for seismic fragility of reinforced concrete frames", Struct. Saf., 32(1), 42-51.
  8. Calvi, G.M., Pinho, R., Magenes, G., Bommer, J.J., Restrepo-Velez, L.F. and Crowley, H. (2006), "Development of seismic vulnerability assessment methodologies over the past 30 years", J. Earthq. Technol., 43(3), 75-104.
  9. Chandler, A.K., Lam, N.T.K. and Tsang, H.H. (2006), "Nearsurface attenuation modelling based on rock shear-wave velocity profile", Soil Dyn. Earthq. Eng., 26(11), 1004-1014.
  10. Dymiotis, C., Kappos, A.J. and Chryssanthopoulos, M.K. (1999), "Seismic reliability assessment of RC frames with uncertain drift and member capacity", J. Struct. Eng., ASCE, 125(9), 1038-1047.
  11. Eads, L., Miranda, E., Krawinkler, H. and Lignos, D.G. (2013), "An efficient method for estimating the collapse risk of structures in seismic regions", Earthq. Eng. Struct. D., 42(1), 25-41.
  12. Esra, M.G. and Nazli, D. (2014), "Seismic fragility analysis of conventional and viscoelastically damped moment resisting frames", Earthq. Struct., 7(3), 295-315.
  13. Fang, K.T. (1980), "Experimental design by uniform distribution", Acta Mathematice Applicatae Sinica, 3, 363-372.
  14. FEMA 350, (2000), Recommended seismic criteria for new steel moment frame building, Washington.
  15. Fragiadakis, M., Vamvatsikos, D., Karlaftis, M.G., Lagaros, N.D. and Papadrakakis, M. (2015), "Seismic assessment of structures and lifelines", J. Sound Vib., 334, 29-56.
  16. Franchin, P., Lupoi, A. and Pinto, P.E. (2003), "Seismic fragility of reinforced concrete structures using a response surface approach", J. Earthq. Eng., 7(Sp. Issue 1), 45-77.
  17. Gasparini, D.A. and Vanmarcke, E.H. (1976), "SIMQKE, a program for artificial motion generation, user‟s manual and documentation", Publication R76-4, MIT Press, Cambridge, Massachusetts.
  18. Goswami, S., Ghosh, S. and Chakraborty, S. (2016), "Reliability Analysis of structures by iterative improved response surface method", Struct. Saf., 60, 56-66.
  19. Gerard, J.O. and Timothy, J.S. (2016), "Fragility functions for eccentrically braced steel frame structures", Earthq. Struct., 10(2), 367-378.
  20. IS 1893. (2002), Criteria for Earthquake Resistant Design of Structures, Part 1: General Provisions and Buildings (Fifth Revision).
  21. Kang, S.C., Koh, H.M. and Choo, J.F. (2010), "An efficient response surface method using moving least squares approximation for structural reliability analysis", Prob. Eng. Mech., 25(4), 365-371.
  22. Kaul, M.K. (1978), "Stochastic characterization of earthquakes through their response spectrum", Earthq. Eng. Struct. D., 6, 497-509.
  23. Kazantzi, A.K., Righiniotis, T.D. and Chryssanthopoulos, M.K. (2008), "Fragility and hazard analysis of a welded steel moment resisting frame", J. Earthq. Eng., 12(4), 596-615.
  24. Kim, C., Wang, S. and Choi, K.K. (2005), "Efficient response surface modeling by using moving least-squares method and sensitivity", AIAA J., 43(1), 2404-2411.
  25. Konno, K. and Ohmachi, T. (1998), "Ground-motion characteristics estimated from spectral ratio between horizontal and vertical components of microtremor", Bull. Seismol. Soc. Am., 88(1), 228-241.
  26. Kwon, O.S. and Elnashai, A.S. (2006), "The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure", Eng. Struct., 28(2), 289-303.
  27. Lin, D.K.J. and Tu, W. (1995), "Dual Response Surface Optimization", J. Quality Technol., 21(1), 34-39.
  28. Lu, D., Yu, X., Jia, M. and Wang, G. (2014), "Seismic risk assessment for a reinforced concrete frame designed according to Chinese codes", Struct. Infrastruct. Eng., 10(10), 1295-1310.
  29. Mandal, T.K., Ghosh, S. and Pujari, N.N. (2016), "Seismic fragility analysis of a typical Indian PHWR containment: comparison of fragility models", Struct. Saf., 58, 11-19.
  30. Mander, J.B., Priestley, M.J.N. and Park, R. (1988), "Theoretical stress-strain model for confined concrete", J. Struct. Eng., ASCE, 114(8), 1804-1826.
  31. Mann, N.R., Schafer, R.E. and Singpurwalla, N.D. (1974), Methods for statistical analysis of reliability and life data, John Wiley & Sons, Inc., New York., NY.
  32. Marano, G.C., Greco, R. and Mezzina, M. (2008), "Stochastic approach for analytical fragility curves", KSCE J. Civ. Eng., 12(5), 305-312.
  33. Moller, O., Ricardo, O.F., Rubinstein, M. and Quiroz, L. (2009), "Seismic structural reliability using different nonlinear dynamic response surface approximations", Struct. Saf., 31(5), 432-442.
  34. Mitra, S., Priestley, K., Bhattacharyya, A.K. and Gaur, V.K. (2005), "Crustal structure and earthquake focal depths beneath northeastern India and Southern Tibet", Geophys. J. Int., 160(1), 227-248.
  35. Minas, D.S. and Chatzi, E.N. (2015), "Metamodeling of nonlinear structural systems with parametric uncertainty subject to stochastic dynamic excitation", Earthq. Struct., 8(4), 915-934.
  36. Nicholas, K., Sohaib, A., Kypros, P., Kyriacos, N. and Christis, C. (2014), "A probabilistic analytical seismic vulnerability assessment framework for substandard structures in developing countries", Earthq. Struct., 6(6), 665-687.
  37. Park, J. and Towashiraporn, P. (2014), "Rapid seismic damage assessment of railway bridges using the response-surface statistical model", Struct. Saf., 47, 1-12.
  38. Raghukanth, S.T.G. and Somala, S.N. (2009), "Modeling of strong-motion data in northeastern india: q, stress drop, and site amplification", Bull. Seismol. Soc. Am., 99(2A), 705-725.
  39. Saha, S.K., Matsagar, V. and Chakraborty, S. (2016), "Uncertainty quantification and seismic fragility of base-isolated liquid storage tanks using response surface models", Prob. Eng. Mech., 43, 20-35.
  40. Saragoni, G.R. and Hart, G.C. (1974), "Simulation of artificial earthquakes", Earthq. Eng. Struct. D., 2(3), 249-268.
  41. Simpson, T.W., Peplinski, J.D., Koch, P.N. and Allen, J.K. (2001), "Metamodels for computer-based engineering design: survey and recommendations", Eng. Computers, 17(2), 129-150.
  42. Singh, S.K., Ordaz, M., Dattatrayam, R.S. and Gupta, H.K. (1999), "A spectral analysis of the 21 May 1997, Jabalpur, India, earthquake (Mw 5:8) and estimation of ground motion from future earthquakes in the Indian shield region", Bull. Seismol. Soc. Am., 89(6), 1620-1630.
  43. Taflanidis, A.A. and Cheung, S.H. (2012), "Stochastic sampling using moving least squares response surface approximations", Prob. Eng. Mech., 28, 216-224.
  44. Towashiraporn, P. (2004), "Building seismic fragility using response surface metamodel", Ph.D. Thesis, Georgia Inst. of Tech.
  45. Unnikrishnan, U., Prasad, A.M. and Rao, B.N. (2013), "Development of fragility curves using high-dimensional model representation", Earthq. Eng. Struct. D., 42(3), 419-430.
  46. Zeinab, B. and Masoud, S. (2016), "Ground motion selection and scaling for seismic design of RC frames against collapse", Earthq. Struct., 11(3), 445-459.