Synthesizing Ensembles of Spatially Correlated Accelerograms

Manish Shrikhande

Lect., Dept. of Earthquake Engrg., Univ. of Roorkee, Roorkee 247667, India.

Vinay K. Gupta

Assoc. Prof., Dept. of Civ. Engrg., Indian Inst. of Technol., Kanpur 208016, India.

A new approach has been proposed for the simulation of ensembles of spatially correlated accelerograms from an equivalent stationary random field model of the design earthquake motion. This is based on the method of stochastic decomposition and the use of a stationary coherency model. Realistic temporal variations in amplitudes and frequency composition have been introduced into the simulated motions by using the phase and duration spectra of recorded earthquake motions. The simulated motions are consistent with the design spectrum in the mean sense. The proposed method has been illustrated by synthesizing accelerograms with widely different characteristics at four stations spaced 100 m apart.  

References

  1. Bendat, J. S., and Piersol, A. G. (1986). Random data. John Wiley & Sons, Inc., New York, N.Y.
  2. Berrah, M., and Kausel, E.(1992). "Response spectrum analysis of structures subjected to spatially varying motions."Earthquake Engrg. and Struct. Dyn., 21, 461–470.
  3. Boissières, H.-P., and Vanmarcke, E. H.(1995). "Estimation of lags for a seismograph array: Wave propagation and composite correlation."Soil Dyn. and Earthquake Engrg., 14, 5–22.
  4. Deodatis, G.(1996). "Simulation of ergodic multivariate stochastic processes."J. Engrg. Mech., ASCE, 122, 778-787.
  5. Der Kiureghian, A.(1996). "A coherency model for spatially varying ground motions."Earthquake Engrg. and Struct. Dyn., 25, 99–111.
  6. Der Kiureghian, A., and Neuenhofer, A.(1992). "Response spectrum method for the multi-support seismic excitation."Earthquake Engrg. and Struct. Dyn., 21, 713–740.
  7. Gupta, I. D., and Joshi, R. G. (1993). "On synthesizing response spectrum compatible accelerograms."Eur. Earthquake Engrg., Bologna, Italy, VII(2), 25–33.
  8. Hao, H., Oliviera, C. S., and Penzien, J.(1989). "Multiple-station ground motion processing and simulation based on SMART-1 array data."Nuclear Engrg. and Des., 111, 293–310.
  9. Harichandran, R. S.(1991). "Estimating the spatial variation of earthquake ground motion from dense array recordings."Struct. Safety, Amsterdam, The Netherlands, 10, 219–233.
  10. Harichandran, R. S., and Vanmarcke, E. H.(1986). "Stochastic variation of earthquake ground motion in space and time."J. Engrg. Mech., ASCE, 112, 154–174.
  11. Harichandran, R. S., and Wang, W.(1990). "Response of indeterminate two-span beam to spatially varying seismic excitation."Earthquake Engrg. and Struct. Dyn., 19, 173–187.
  12. Heredia-Zavoni, E., and Vanmarcke, E. H.(1994). "Seismic random vibration analysis of multisupport structural systems."J. Engrg. Mech., ASCE, 120, 1107–1128.
  13. Hindy, A., and Novak, M.(1980). "Response of pipelines to random ground motions."J. Engrg. Mech.. Div., ASCE, 106, 339–360.
  14. Iyengar, R. N., and Rao, P. N.(1979). "Generation of spectrum compatible accelerograms."Earthquake Engrg. and Struct. Dyn., 7, 253–263.
  15. Jenkins, G. M., and Watts, D. G. (1968). Spectral analysis and its applications. Holden-Day, Oakland, Calif.
  16. Kaul, M. K.(1978). "Stochastic characterization of earthquakes through their response spectrum."Earthquake Engrg. and Struct. Dyn., 6, 497–509.
  17. Lee, V. W.(1990). "Surface strains associated with strong earthquake shaking."Struct. Engrg./Earthquake Engrg., JSCE, Tokyo, Japan, 7, 187–194.
  18. Lee, V. W., and Trifunac, M. D.(1985). "Torsional accelerograms."Soil Dyn. and Earthquake Engrg., 4, 132–139.
  19. Lee, V. W., and Trifunac, M. D.(1987). "Rocking strong earthquake accelerograms."Soil Dyn. and Earthquake Engrg., 6, 75–89.
  20. Lee, V. W., and Trifunac, M. D. (1989). "A note on filtering strong motion accelerograms to produce response spectra of specified shape and amplitude."Eur. Earthquake Engrg., Bologna, Italy, III(2), 38–45.
  21. Lee, V. W., Trifunac, M. D., Todorovska, M. I., and Novikova, E. I. (1995). "Empirical equations describing attenuations of peaks of strong motion in terms of magnitude, distance, path effects and site conditions."Rep. No. 95-02, Dept. of Civ. Engrg., Univ. of Southern California, Los Angeles, Calif.
  22. Li, Y., and Kareem, A.(1991). "Simulation of multivariate nonstationary random processes by FFT."J. Engrg. Mech., ASCE, 117, 1037–1058.
  23. Nigam, N. C.(1982). "Phase properties of a class of random processes."Earthquake Engrg. and Struct. Dyn., 10, 711–717.
  24. Novikova, E. I., and Trifunac, M. D.(1994). "Duration of strong ground motion in terms of earthquake magnitude, epicentral distance, site conditions and site geometry."Earthquake Engrg. and Struct. Dyn., 23, 1023–1043.
  25. O'Connor, J. M., and Ellingwood, B. R.(1987). "Reliability of nonlinear structures with seismic loading."J. Struct. Engrg., ASCE, 113, 1011–1028.
  26. Ohsaki, Y.(1979). "On the significance of the phase content in earthquake ground motions."Earthquake Engrg. and Struct. Dyn., 7, 427–439.
  27. Preumont, A.(1980). "A method for the generation of artificial earthquake accelerograms."Nuclear Engrg. and Des., 59, 357–368.
  28. Preumont, A.(1984). "The generation of spectrum compatible accelerograms for the design of nuclear power plants."Earthquake Engrg. and Struct. Dyn., 12, 481–497.
  29. Priestley, M. B. (1981). Spectral analysis and time series. Academic Press, Inc., London, U.K.
  30. Ramadan, O., and Novak, M.(1993). "Simulation of spatially incoherent random ground motions."J. Engrg. Mech., ASCE, 119, 997–1016.
  31. Ramadan, O., and Novak, M.(1994). "Simulation of multidimensional, anisotropic ground motions."J. Engrg. Mech., ASCE, 120, 1773–1785.
  32. Shinozuka, M.(1971). "Simulation of multivariate and multidimensional random processes."J. Acoust. Soc. Amer., 49, 357–367.
  33. Shinozuka, M. (1987). "Stochastic fields and their digital simulation."Stochastic methods in structural dynamics, G. I. Schüeller and M. Shinozuka, eds., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 93–133.
  34. Shinozuka, M., and Deodatis, G.(1988). "Stochastic process models for earthquake ground motion."J. Prob. Eng. Mech., 3, 114–123.
  35. Shrikhande, M., and Gupta, V. K. (1996). "On generating ensemble of design spectrum compatible accelerograms."Eur. Earthquake Engrg., Bologna, Italy, X(3), 49–56.
  36. Smith, S. W., Ehrenberg, J. E., and Hernandez, E. N.(1982). "Analysis of the El Centro differential array for 1979 Imperial Valley earthquake."Bull. Seismological Soc. Am., 72, 237–258.
  37. Sundararajan, C.(1980). "An iterative method for the generation of seismic power spectral density functions."Nuclear Engrg. and Des., 61, 13–23.
  38. Tatsuoka, M. M. (1971). Multivariate analysis. John Wiley & Sons, Inc., New York, N.Y.
  39. Trifunac, M. D.(1971). "A method for synthesizing realistic strong ground motion."Bull. Seismological Soc. Am., 61, 1739–1753.
  40. Trifunac, M. D.(1990). "Curvograms of strong ground motions."J. Engrg. Mech., ASCE, 116, 1426–1432.
  41. Trifunac, M. D., and Westermo, B. D.(1982). "Duration of strong earthquake shaking."Soil Dyn. and Earthquake Engrg., 2, 117–121.
  42. Unruh, J. F., and Kana, D. D.(1981). "An iterative procedure for the generation of consistent power/response spectrum."Nuclear Engrg. and Des., 66, 427–435.
  43. Vanmarcke, E. H. (1976). "Structural response to earthquakes."Seismic risk and engineering decisions, C. Lomnitz and E. Rosenblueth, eds., Elsevier Science Publishers BV, Amsterdam, The Netherlands, 287–337.
  44. Wong, H. L., and Trifunac, M. D.(1979). "Generation of artificial strong motion accelerograms."Earthquake Engrg. and Struct. Dyn., 7, 509–527.
  45. Zerva, A.(1990). "Response of multi-span beams to spatially incoherent ground motions."Earthquake Engrg. and Struct. Dyn., 19, 819–832.
  46. Zerva, A.(1992). "Seismic ground motion simulations from a class of spatial variability models."Earthquake Engrg. and Struct. Dyn., 21, 351–361.
  47. Zerva, A., Ang, A.H.-S., and Wen, Y. K.(1988). "Lifeline response to spatially varying ground motions."Earthquake Engrg. and Struct. Dyn., 16, 361–379.
  48. Zerva, A., and Shinozuka, M.(1991). "Stochastic differential ground motion."Struct. Safety, Amsterdam, The Netherlands, 10, 129–143.