Sufficiency assessments of ground motion intensity measures employing kullback-leibler theory (applied for typical south pars offshore platforms)

Document Type : Research


1 PhD Candidate, Department of Civil Engineering, University of Qom, Qom, Iran.

2 Assistant Professor, Department of Civil Engineering, University of Qom, Qom, Iran.


The potential ingrained uncertainty in ground motion records may significantly influence the structural seismic risk assessment in performance-based earthquake engineering (PBEE). One of the basic components of the socio-economic method of PBEE design is probabilistic seismic demand model (PSDM).  The level of uncertainty in PSDM, depends greatly on the selected seismic intensity measure (IM), while these models are traditionally conditioned on a single IM. Among various terms utilized in optimal IM selection, this study particularly aims to bring the “sufficiency” assessment procedures into focus. However, the IM efficiency evaluations have also been considered. The sufficiency of IM is gauged by the extent to which the residual demand measure values are statistically independent of ground motion magnitude (Mw) and distance (R), regressing of IM. The objective of this study is to introduce a recently emerged quantitative procedure by employing relative sufficiency measure (RSM) on the basis of Kullback‐Leibler divergence concepts to indicate the superiority of one IM relative to another in the representation of ground motion uncertainty. Besides, the traditional methods of sufficiency evaluation are also discussed. To this end, a three-dimensional finite element model of typical South Pars fixed pile-founded offshore platforms has been built. Several IM candidates are classified and compared in terms of the expected difference in the information they provide for predicting a wide range of structural response parameters. It can be deduced that the most informative of the fourteen considered IMs are among velocity-related ones. The results also demonstrate the absolute necessity of the RSM in optimal IM ranking.


1. Cornell, CA., Krawinkler, H., (2000), Progress and challenges in seismic performance assessment, PEER Cent News 3(2)
2. Moehle, JP., Deierlein, GG., (2004), A framework methodology for performance-based earthquake engineering, In: Proceedings of the 13th world conference on earthquake engineering, Vancouver, Canada.
3. Shome, N., (1999), Probabilistic seismic demand analysis of nonlinear structures, Dissertation, Stanford University, Stanford, CA
4. Shome, N., Cornell, CA., (1999), Probabilistic seismic demand analysis of nonlinear structures, RMS Program, Stanford University, Report No. RMS35. Accessed 2 June 2014
5. Luco, N., Cornell, CA., (2007), Structure-specific scalar intensity measures for near-source and ordinary earthquake ground motions, Earthq Spectra Vol. 23 p.357-392. http://doi:10.1193/1.2723158 [DOI:10.1193/1.2723158]
6. Mackie, K., Stojadinović, B., (2003), Seismic demands for performance-based design of bridges, PEER 312
7. Bradley, BA., Cubrinovski, M., Dhakal, RP., MacRae, GA., (2009), Intensity measures for the seismic response of pile foundations, Soil Dyn Earthq Eng 29:1046-1058. https://doi:10.1016/j.soildyn.2008.12.002 [DOI:10.1016/j.soildyn.2008.12.002]
8. Housner, GW., (1959), Behavior of structures during earthquakes, J Eng Mech Div Vol. 85 p.109-130 [DOI:10.1061/JMCEA3.0000102]
9. Shafieezadeh, A., (2011), Seismic vulnerability assessment of wharf structures, Dissertation, Georgia Institute of Technology, Atlanta, GA.
10. Amirabadi, R., Bargi, Kh., Dolatshahi, M., Heidary Torkamani, H., Maccullough, N., (2014), Determination of optimal probabilistic seismic demand models for pile-supported wharves, Structure and Infrastructure Eng: Maintenance, Management, Life-Cycle Design and Performance 10:9. https://1119-1145, DOI: 10.1080/15732479.2013.793723 [DOI:10.1080/15732479.2013.793723]
11. Ebrahimian, H., Jalayer, F., Lucchini, A., Mollaioli, F., Manfredi, G., (2015), Preliminary ranking of alternative scalar and vector intensity measures of ground shaking, Bull Earthq Eng., https://doi:10.1007/s10518-015-9755-9 [DOI:10.1007/s10518-015-9755-9]
12. Wang, X., Shafieezadeh, A., Ye, A., (2017), Optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefied and laterally spreading ground, Bull Earthquake Eng., [DOI:10.1007/s10518-017-0199-2]
13. Kullback, S., Leibler, RA., (1951), On information and sufficiency, Ann Math Stat 22(1):79-86 [DOI:10.1214/aoms/1177729694]
14. Jalayer, F., Beck, J., Zareian, F. (2012), Analyzing the sufficiency of alternative scalar and vector intensity measures of ground shaking based on information theory, J Eng Mech. Vol.138(3) p.307-316. [DOI:10.1061/(ASCE)EM.1943-7889.0000327]
15. Jalayer, F., and Beck, J. L., (2006), Using information theory concepts to compare alternative intensity measures for representing ground motion uncertainty, Proc., 8th U. S. National Conf. Earthquake Engineering, Paper ID: 974, Curran Associates, New York.
16. Shannon, C. E., (1948a), A mathematical theory of communication, Bell Syst. Tech. J., Vol. 27(3), p. 379-423. [DOI:10.1002/j.1538-7305.1948.tb01338.x]
17. Shannon, C. E., (1948b), A mathematical theory of communication. Bell Syst. Tech. J., Vol. 27(4), p. 623-656. [DOI:10.1002/j.1538-7305.1948.tb00917.x]
18. Cover, T. M., and Thomas, J. A., (1991), Elements of information theory, Wiley, NY [DOI:10.1002/0471200611]
19. Jafari, A., and Dezvareh R. (2021), Determination of collapse prevention (CP) of offshore wind turbine with jacket platform. Iranian Journal of Marine Science and Technology Vol. 24(96): 35-43.
20. Dezvareh, R. (2019), Application of Soft Computing in the Design and Optimization of Tuned Liquid Column-Gas Damper for Use in Offshore Wind Turbines. International Journal of Coastal and Offshore Engineering, Vol. 2(4), p. 47-57. [DOI:10.29252/ijcoe.2.4.47]
21. Cornell, CA., Jalayer, F., Hamburger, RO., Foutch, DA., (2002), Probabilistic basis for 2000 SAC/FEMA steel moment frame guidelines, J Struct Eng Vol. 128(4) p. 526-533. https://doi:10. 1061/(ASCE)0733-9445 [DOI:10.1061/(ASCE)0733-9445(2002)128:4(526)]
22. Fisher, RA., (1925), Statistical Methods for Research Workers, Edinburgh, UK: Oliver and Boyd
23. Tang, WH., Ang, A., (2007), Probability concepts in engineering: Emphasis on applications to civil and environmental engineering, 2nd edn. Wiley, Hoboken, ISBN: 978-0-471-72064-5
24. Altman, N., Krzywinski, M., (2016), Points of significance: p values and the search for significance, Nat Methods 14:3-4. https://doi:10.1038/nmeth.4120 [DOI:10.1038/nmeth.4120]
25. Matlock, H., (1970), Correlations for Design of Laterally Loaded Piles in Soft Clay, Second Annual Offshore Technology Conference, Houston, Col. Vol. 1(1204) p.557 - 594 [DOI:10.4043/1204-MS]
26. Reese, LC., Cox, WR., (1975), Field testing and analysis of laterally loaded piles in stiff clay, Offshore technology conference, OTC 2312 [DOI:10.4043/2312-MS]
27. O'Neill, MW., Murchinson, JM., (1983), An Evaluation of p-y Relationships in Sands, A Report to the American Petroleum Institute.
28. American Petroleum Institute, (2000), Recommended practice for planning, designing and constructing fixed offshore platforms, API Recommended Practice 2A (RP-2A). 21st ed. American Petroleum Institute, Washington, D. C
29. Sap 2000, (2005), structural Analysis Program, Analysis Reference Manual. Computers and structures, Inc., Berkeley, California, USA
30. American Petroleum Institute, (2008), Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design, API recommended practice (RP-2A-WSD), 21st Edition, Errata and Supplement
31. Rathje, EM., Kottke, RA., Trent, WL, (2010), Influence of input motion and site property variabilities on seismic site response analysis, J Geotech Geoenviron Eng ASCE, Vol. 136(4) ISSN 1090-0241/2010/4-607-619 [DOI:10.1061/(ASCE)GT.1943-5606.0000255]
32. Hashash, Y., Groholski, D., Phillips, C., Park, D., Musgrove, M., (2012), DEEPSOIL 5.1. User Manual and Tutorial.
33. Shome, N., Cornell, C.A., Bazzurro, P., & Caraballo, J.E., (1998), Earthquakes, records, and nonlinear responses. Earthquake Spectra, 14(3), 467-500. [DOI:10.1193/1.1586011]
34. Foutch, D.A., Yu, C.Y., & Wen, Y.K., (1992), Reliability of steel frame buildings under seismic load, 10th World Conference on Earthq. Eng., Rotterdam, Netherlands.
35. Pacific earthquake engineering research center., (2006), PEER NGA Database. Berkeley: University of California, [].
36. NEHRP., (2001), NEHRP recommended provisions for seismic regulations for new buildings and other structures, Washington, DC, USA: Building Seismic Safety Council.
37. Cornell, C. A., and Luco, N., (1999), The Effects of Connection Fractures on Steel Moment Resisting Frame Seismic Demand and Safety, A Report on SAC Phase II Task 5.4.6, Report No. SAC/BD-99/03, SAC Joint Venture, Sacramento, California.
38. Ji, J., Elnashai, A.S., Kuchma, D.A., (2007), Seismic fragility assessment for reinforced concrete high-rise buildings - Report 07-14, Mid-America Earthquake Center, University of Illinois at Urbana-Champaign.
39. Pejović, J and Jancović, S., (2015), Dependence of high-rise buildings response on the earthquake Intensity. GRADEVINAR; Vol. 67(8), p. 749-759.
40. Asgarian, B., Aghakouchak, A.A., Alanjari, P., and Assareh, M. A., (2008), Incremental Dynamic Analysis of Jacket Type Offshore Platforms Considering Soil-Pile Interaction, 14th World Conference on Earthq Eng. Beijing China.
41. El-Din, M. N., & Kim, J., (2014), Seismic performance evaluation and retrofit of fixed jacket offshore platform structures, J Perform Constr Fac. Article ID04014099. [DOI:10.1061/(ASCE)CF.1943-5509.0000576]
42. Mollaioli F, Lucchini A, Cheng Y, Monti G (2013) Intensity measures for the seismic response prediction of base-isolated buildings. Bull Earthq Eng 11(5):1841-1866. http://doi: 10.1007/s10518-013-9431-x [DOI:10.1007/s10518-013-9431-x]