Structural Engineering and Mechanics

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Machine learning surrogate model for reliability analysis of RC columns with reverse curvature

  • Arthur de C. Preuss (Graduate Program in Civil Engineering, Federal University of Rio Grande do Sul) ;
  • Herbert M. Gomes (Graduate Program in Civil Engineering, Federal University of Rio Grande do Sul)
  • Received : 2023.12.28
  • Accepted : 2024.09.05
  • Published : 2024.10.10
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Abstract

This work aims to present an analysis of the structural reliability of reinforced concrete (RC) columns designed according to the general method outlined in Eurocode 2 (EN 1992-1-1 2004). Probabilistic analyses are conducted by integrating the Monte Carlo method with metamodels (or surrogate models) generated using Kriging and some machine learning techniques. The study was developed based on an algorithm that verifies the columns subject to biaxial bending, considering the physical and geometric nonlinearities. Columns were analyzed assuming sign inversion of end bending moments (with reverse curvature), which portray the typical situations in conventional structures of RC buildings. The probabilistic results reveal that the typical RC columns in buildings designed according to the design procedures of the studied standard, whether they are located at the center, corner, or edge, exhibit reliability levels surpassing those deemed acceptable within the technical community. Furthermore, the integration of surrogate models proves beneficial by alleviating the computational burden associated with evaluations while preserving accuracy.

Keywords

Acknowledgement

The authors wish to thank CAPES and CNPq Brazilian councils for their support of this work.

References

  1. Alfano, G., Marmo, F. and Rosati, L. (2007), "An unconditionally convergent algorithm for the evaluation of the ultimate limit state of RC sections subject to axial force and biaxial bending", Int. J. Numer. Meth. Eng., 72(8), 924-963. https://doi.org/10.1002/nme.2033.
  2. Baji, H. (2014), "The effect of uncertainly in material properties and model error on the reliability of strength and ductility of reinforced concrete members", Ph.D. Dissertation, The University of Queensland, Brisbane, Australia.
  3. Baji, H., Ronagh, H.R. and Melchers, R.E. (2016), "Reliability of ductility requirements in concrete design codes", Struct. Saf., 62, 76-87. https://doi.org/10.1016/j.strusafe.2016.06.005.
  4. Bonet, J.L., Miguel, P.F., Fernandez-Prada, M.A. and Romero, M.L. (2001), "Efficient procedure for stress integration in concrete sections using a Gauss-Legendre quadrature", Proceedings of the 8th International Conference on the Application of Artificial Intelligence to Civil and Structural Engineering Computing, Stirling, Scotland, September.
  5. Charalampakis, A.E. and Koumousis, V.K. (2008), "Ultimate strength analysis of composite sections under biaxial bending and axial load", Adv. Eng. Softw., 39(11), 923-936. https://doi.org/10.1016/j.advengsoft.2008.01.007.
  6. Choi, B.S., Scanlon, A. and Johnson, P.A. (2004), "Monte Carlo simulation of immediate and time-dependent deflections of reinforced concrete beams and slabs", ACI Struct. J., 101(5), 633-641. https://doi.org/10.14359/13385.
  7. Collins, M.P. and Mitchell, D. (1991), Prestressed Concrete Structures, Prentice-Hall Inc., Englewood Cliffs, New Jersey, USA.
  8. Davidster, M.D. (1986), "Analysis of reinforced concrete columns of arbitrary geometry subjected to axial load and biaxial bending: A computer program for exact analysis", ACI Concrete Int.: Des. Constr., 8(7), 56-61.
  9. De Vivo, L. and Rosati, L. (1998), "Ultimate strength analysis of reinforced concrete sections subject to axial force and biaxial bending", Comput. Meth. Appl. Mech. Eng., 166(3-4), 261-287. https://doi.org/10.1016/S0045-7825(98)00091-7.
  10. Dobry, J., Wolfger, H. and Benko, V. (2022), "Reliability of slender concrete columns designed according to the eurocodes", Eng. Struct., 265, 114266. https://doi.org/10.1016/j.engstruct.2022.114266.
  11. Dundar, C. and Sahin, B. (1993), "Arbitrarily shaped reinforced concrete members subject to biaxial bending and axial load", Comput. Struct., 49(4), 643-662. https://doi.org/10.1016/0045-7949(93)90069-P.
  12. Ellingwood, B. and Galambos, T.V. (1982), "Probability-based criteria for structural design", Struct. Saf., 1(1), 15-26. https://doi.org/10.1016/0167-4730(82)90012-1.
  13. EN 1992-1-1 (2004), Eurocode 2, Design of Concrete Structures-Part 1-1: General Rules and Rules for Buildings, European Committee for Standardization, Brussels, Belgium.
  14. fib Model Code (2012), Model Code 2010, Final Draft, Bulletin 65, Vol. 1, Comite Euro-International du Beton, Lausanne, Switzerland.
  15. Forrester, A.I.J., Sobester, A. and Keane, A.J. (2008), Engineering Design via Surrogate Modelling: A Practical Guide, Jhon Wiley and Sons Ltd.
  16. Frangopol, D.M., Ide, Y., Spacone, E. and Iwaki, I. (1996), "A new look at reliability of reinforced concrete columns", Struct. Saf., 18(2-3), 126-150. https://doi.org/10.1016/0167-4730(96)00015-X.
  17. Gayton, N., Mohamed, A., Sorensen, J.D., Pendola, M. and Lemaire, M. (2004), "Calibration methods for reliability-based design codes", Struct. Saf., 26(1), 91-121. https://doi.org/10.1016/S0167-4730(03)00024-9.
  18. Guan, Z., Zhang, J. and Li, J. (2014), "A robust computational method for ultimate strength analysis of arbitrary reinforced concrete and composite sections subjected to axial force and biaxial bending", Adv. Struct Eng., 17(1), 83-96. https://doi.org/10.1260/1369-4332.17.1.83.
  19. Gulvanessian, H. and Holicky, M. (2005), "Eurocodes: Using reliability analysis to combine actions effects", Proc. Inst. Civil Eng.-Struct. Build., 158(4), 243-252. https://doi.org/10.1680/stbu.2005.158.4.243.
  20. Hong, H.P. and Zhou, W. (1999), "Reliability evaluation of RC columns", J. Struct. Eng., 125(7), 784-790. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:7(784).
  21. Jiang, Y., Peng, S., Beer, M., Wang, L. and Zhang, J. (2020), "Reliability evaluation of reinforced concrete columns designed by Eurocode for wind-dominated combination considering random loads eccentricity", Adv. Struct. Eng., 23(1), 146-159. https://doi.org/10.1177/1369433219866089.
  22. Kaymaz, I. (2005), "Application of kriging method to structural reliability problems", Struct. Saf., 27(2), 133-151. https://doi.org/10.1016/j.strusafe.2004.09.001.
  23. Kim, J. and Song, J. (2020), "Probability-adaptive Kriging in n-ball (PAK-Bn) for reliability analysis", Struct. Saf., 85, 101924. https://doi.org/10.1016/j.strusafe.2020.101924.
  24. Kim, J.H. and Lee, H.S. (2017), "Reliability assessment of reinforced concrete rectangular columns subjected to biaxial bending using the load contour method", Eng. Struct., 150, 636-645. https://doi.org/j.engstruct.2017.07.061.
  25. Kim, J.H., Lee, S.H., Paik, I. and Lee, H.S. (2015), "Reliability assessment of reinforced concrete columns based on the P-M interaction diagram using AFOSM", Struct. Saf., 51, 70-79. https://doi.org/j.strusafe.2015.03.003.
  26. Kim, J.K. and Lee, S.S. (2000), "The behavior of reinforced concrete columns subjected to axial force and biaxial bending", Eng. Struct., 22(11), 1518-1528. https://doi.org/10.1016/S0141-0296(99)00090-5.
  27. Kim, J.K. and Yang, J.K. (1995), "Buckling behaviour of slender high-strength concrete columns", Eng. Struct., 17(1), 39-51. https://doi.org/10.1016/0141-0296(95)91039-4.
  28. Leite, L., Bonet, J.L., Pallares, L., Miguel, P.F. and Fernandez-Prada, M.A. (2013), "Experimental research on high strength concrete slender columns subjected to compression and uniaxial bending with unequal eccentricities at the ends", Eng. Struct., 48, 220-232. https://doi.org/j.engstruct.2012.07.039.
  29. Mirza, S.A. and MacGregor, J.G. (1989), "Slenderness and strength reliability of reinforced concrete columns", ACI Struct. J., 86(4), 428-438. https://doi.org/10.14359/9229.
  30. Mirza, S.A. (1996), "Reliability-based design of reinforced concrete columns", Struct. Saf., 18(2-3), 179-194. https://doi.org/10.1016/0167-4730(96)00010-0.
  31. Nie, Z., Jiang, H. and Kara, L.B. (2019), "Stress field predicting in a cantilevered structures using convolutional neural networks", Proceedings of the ASME 2019 International Design Engineering Technical Conferences and 39th Computers and Information in Engineering Conference, California, United States of America, August.
  32. Pallares, L., Bonet, J.L., Miguel, P.F. and Fernandez-Prada, M.A. (2008), "Experimental research on high strength concrete slender columns subjected to compression and biaxial bending forced", Eng. Struct., 30(7), 1897-1894. https://doi.org/10.1016/j.engstruct.2007.12.005.
  33. Papanikolaou, V.K. (2012), "Analysis of arbitrary composite sections in biaxial bending and axial load", Comput. Struct., 98- 99, 33-54. https://doi.org/10.1016/j.compstruc.2012.02.004.
  34. Preuss, A. de C. (2023), "Analise probabilistica termoestrutural de pilares de concreto armado", M.Sc. Dissertation, Federal University of Rio Grande do Sul, Porto Alegre, Brazil.
  35. Preuss, A. de C.and Gomes, H.M. (2024), "Probability of failure of RC columns in fire situation", Rev. IBRACON Estrut. Mater., 17(1), e17102. https://doi.org/10.1590/S1983-41952024000100002.
  36. Ranganathan, R. (1998), Structural Reliability Analysis and Design, Jaico Publishing House, Mumbai, Maharashtra, India.
  37. Rasmussen, C.E. and Williams, C.K.I. (2005), Gaussian Processes for Machine Learning, MIT Press, Cambridge, Massachusetts, USA.
  38. Ribeiro, K. (2022), "Analise da confiabilidade de pilares muito esbeltos de concreto armado", D.Sc. Dissertation, Federal University of Santa Catarina, Florianopolis, Brazil.
  39. Ribeiro, K., Loriggio, D.D. and Real, M.D.V. (2021), "Reliability analysis of very slender columns subjected to creep", Lat. Am. J. Solid. Struct., 18(7), e401. https://doi.org/10.1590/1679-78256569.
  40. Ruiz, S.E. and Aguilar, J.C. (1994), "Reliability of short and slender reinforced-concrete columns", J. Struct. Eng., 120(6), 1850-1865. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:6(1850).
  41. Strauss, A., Hauser, M., Taubling, B., Ivankovic, A.M., Skokandic, D., Matos, J., ... & Orcesi, A. (2021), "Probabilistic and semi-probabilistic analysis of slender columns frequently used in structural engineering", Appl. Sci., 11(17), 8009. https://doi.org/10.3390/app11178009.
  42. Szerszen, M.M., Szwed, A. and Nowak, A.S. (2005), "Reliability analysis for eccentrically loaded columns", ACI Struct. J., 102(5), 676-688. https://doi.org/10.14359/14663.
  43. Wang, L. and Grandhi, R.V. (1996), "Safety index calculation using intervening variables for structural reliability analysis", Struct. Saf., 59(6), 1139-1148. https://doi.org/10.1016/0045-7949(96)00291-X.
  44. Wisniewski, D.F., Cruz, P.J.S., Henriques, A.A.R. and Simoes, R.A.D. (2012), "Probabilistic models for mechanical properties of concrete, reinforced steel and pre-stressing steel", Struct. Infrastr. Eng., 8(2), 111-123. https://doi.org/10.1080/15732470903363164.
  45. Xie, B., Peng, C. and Wang, Y. (2023), "Combined relevance vector machine technique and subset simulation importance sampling for structural reliability", Appl. Math. Model., 113, 129-143. https://doi.org/10.1016/j.apm.2022.09.010.
  46. Ye, D., Xu, Z. and Liu, Y. (2022), "Solution to the problem of bridge structure damage identification by a response surface method and an imperialist competitive algorithm", Sci. Rep., 12, 16495. https://doi.org/10.1038/s41598-022-17487-9.
  47. Yun, W. and Wang, Y. (2022), "An efficient Kriging model-based importance sampling method for estimating the failure probability-based parameter global sensitivity index with uncertain distribution parameters", Aerosp. Sci. Technol., 130, 107861. https://doi.org/10.1016/j.ast.2022.107861.
  48. Yun, W., Lu, Z. and Jiang, X. (2018), "An efficient reliability analysis method combining adaptative Kriging and modified importance sampling for small failure probability", Struct. Multidisc. Optim., 58, 1383-1393. https://doi.org/10.1007/s00158-018-1975-6.