Skip to main content
Log in

Parametric Identification and Sensitivity Analysis Combined with a Damage Model for Reinforced Concrete Structures

  • Research Article-Civil Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The present work proposes a methodology to analyze the identification of constitutive model parameters for concrete. This procedure is an important step to develop reliable constitutive models for materials with complex mechanical behavior, as concrete. A parametric sensitivity analysis has been developed using a damage model applied to concrete performing numerical analyses in uniaxial states and plain concrete plate. To solve the identification problem, an inverse optimization technique based on bio-inspired computational algorithm has been applied. To validate the inverse problem results, reinforced concrete beams found in the literature have been used. Thus, a comparison between experimental results and the ones obtained from the proposed technique has been made observing an adherence index about 95%. Finally, it is possible to note that the proposed methodology is robust and efficient concerning to the automatization of the parametric identification problem discussed on this paper when compared to traditional techniques used in Structural Engineering in the context of damage constitutive models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Liu, T.; Zhang, X.; He, N.; Jia, G.: Numerical Material Model for Composite Laminates in High-Velocity Impact Simulation. Lat. Am. J. Solids Struct. 14, 1912–1931 (2017). https://doi.org/10.1590/1679-78253750

    Article  Google Scholar 

  2. Sirois, F.; Grilli, F.: Potential and limits of numerical modelling for supporting the development of HTS devices. Supercond. Sci. Technol. 28, 043002 (2015). https://doi.org/10.1088/0953-2048/28/4/043002

    Article  Google Scholar 

  3. Steinhauser, M.; Hiermaier, S.: A review of computational methods in materials science: examples from shock-wave and polymer physics. IJMS 10, 5135–5216 (2009). https://doi.org/10.3390/ijms10125135

    Article  Google Scholar 

  4. Vlcek, L.; Vasudevan, R.K.; Jesse, S.; Kalinin, S.V.: Consistent integration of experimental and ab initio data into effective physical models. J. Chem. Theory Comput. 13, 5179–5194 (2017). https://doi.org/10.1021/acs.jctc.7b00114

    Article  Google Scholar 

  5. Khalfallah, A.; Bel Hadj Salah, H.; Dogui, A.: Anisotropic parameter identification using inhomogeneous tensile test. Eur. J. Mech. A/Solids 21, 927–942 (2002). https://doi.org/10.1016/S0997-7538(02)01246-9

    Article  MATH  Google Scholar 

  6. Barabasz, B.; Gajda-Zagórska, E.; Migórski, S.; Paszyński, M.; Schaefer, R.; Smołka, M.: A hybrid algorithm for solving inverse problems in elasticity. Int. J. Appl. Math. Comput. Sci. 24, 865–886 (2014). https://doi.org/10.2478/amcs-2014-0064

    Article  MathSciNet  MATH  Google Scholar 

  7. Murray-Smith, D.J.: The inverse simulation approach: a focused review of methods and applications. Math. Comput. Simul. 53, 239–247 (2000). https://doi.org/10.1016/S0378-4754(00)00210-X

    Article  Google Scholar 

  8. Wardeh, M.A.; Toutanji, H.A.: Parameter estimation of an anisotropic damage model for concrete using genetic algorithms. Int. J. Damage Mech. 26, 801–825 (2017). https://doi.org/10.1177/1056789515622803

    Article  Google Scholar 

  9. Rechenmacher, A.L.; Medina-Cetina, Z.: Calibration of soil constitutive models with spatially varying parameters. J. Geotech. Geoenviron. Eng. 133, 1567–1576 (2007). https://doi.org/10.1061/(ASCE)1090-0241(2007)133:12(1567)

    Article  Google Scholar 

  10. Zagho, M.; Hussein, E.; Elzatahry, A.: Recent overviews in functional polymer composites for biomedical applications. Polymers 10, 739 (2018). https://doi.org/10.3390/polym10070739

    Article  Google Scholar 

  11. Brünig, M.; Michalski, A.: Numerical analysis of damage and failure behavior of concrete. Int. J. Damage Mech 29, 570–590 (2020). https://doi.org/10.1177/1056789519866005

    Article  Google Scholar 

  12. Marie, I.; Mahdi, M.: Numerical simulation of concrete mix structure and detection of its elastic stiffness. J. Comput. Eng. Phys. Model. (2018). https://doi.org/10.22115/cepm.2018.54011

    Article  Google Scholar 

  13. Ožbolt, J.; Sharma, A.: Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads. Int. J. Impact Eng. 38, 940–950 (2011). https://doi.org/10.1016/j.ijimpeng.2011.08.003

    Article  Google Scholar 

  14. Jin, L.; Zhang, S.; Li, D.; Xu, H.; Du, X.; Li, Z.: A combined experimental and numerical analysis on the seismic behavior of short reinforced concrete columns with different structural sizes and axial compression ratios. Int. J. Damage Mech. 27, 1416–1447 (2018). https://doi.org/10.1177/1056789517735679

    Article  Google Scholar 

  15. Grassl, P.; Jirásek, M.: Damage-plastic model for concrete failure. Int. J. Solids Struct. 43, 7166–7196 (2006). https://doi.org/10.1016/j.ijsolstr.2006.06.032

    Article  MATH  Google Scholar 

  16. Peng, Y.; Chu, H.; Pu, J.: Numerical simulation of recycled concrete using convex aggregate model and base force element method. Adv. Mater. Sci. Eng. 2016, 1–10 (2016). https://doi.org/10.1155/2016/5075109

    Article  Google Scholar 

  17. Holzapfel, G.A.; Fereidoonnezhad, B.: Modeling of damage in soft biological tissues. In: Biomechanics of living organs, pp. 101–123. Elsevier (2017). https://doi.org/10.1016/B978-0-12-804009-6.00005-5

    Chapter  Google Scholar 

  18. Ozbolt, J.; Ananiev, S.: Scalar damage model for concrete without explicit evolution law. ArXiv:07042663 [Cond-Mat] (2007)

  19. Pereira Junior, W.M.; Araújo, D.L.; Pituba, J.J.C.: Numerical analysis of steel-fiber-reinforced concrete beams using damage mechanics. Rev. IBRACON Estrut. Mater. 9, 153–191 (2016). https://doi.org/10.1590/S1983-41952016000200002

    Article  Google Scholar 

  20. Sawangikar, M.M.S.; Burande, D.C.S.; Burande, D.B.C.: Irreversible thermodynamics: a review. 02, 7 (2016)

  21. Alastrué, V.; Rodríguez, J.F.; Calvo, B.; Doblaré, M.: Structural damage models for fibrous biological soft tissues. Int. J. Solids Struct. 44, 5894–5911 (2007). https://doi.org/10.1016/j.ijsolstr.2007.02.004

    Article  MATH  Google Scholar 

  22. Malcher, L.; Mamiya, E.N.: An improved damage evolution law based on continuum damage mechanics and its dependence on both stress triaxiality and the third invariant. Int. J. Plast. 56, 232–261 (2014). https://doi.org/10.1016/j.ijplas.2014.01.002

    Article  Google Scholar 

  23. Li, W.: Damage models for soft tissues: a survey. J. Med. Biol. Eng. 36, 285–307 (2016). https://doi.org/10.1007/s40846-016-0132-1

    Article  Google Scholar 

  24. Bai, Q.; Mohamed, M.; Shi, Z.; Lin, J.; Dean, T.: Application of a continuum damage mechanics (CDM)-based model for predicting formability of warm formed aluminium alloy. Int. J. Adv. Manuf. Technol. 88, 3437–3446 (2017). https://doi.org/10.1007/s00170-016-8853-4

    Article  Google Scholar 

  25. Williams, K.V.; Vaziri, R.: Application of a damage mechanics model for predicting the impact response of composite materials. Comput. Struct. 79, 997–1011 (2001). https://doi.org/10.1016/S0045-7949(00)00200-5

    Article  Google Scholar 

  26. Cipollina, A.; Flórez, L.J.: Modelos simplificados de daño en pórticos de concreto armado. Revista Internacional de Métodos Numéricos Para Cálculo y Diseño En Ingeniería 11, 3–22 (1995)

    Google Scholar 

  27. Comi, C.: A non-local model with tension and compression damage mechanisms. Eur. J. Mech. A. Solids 20, 1–22 (2001). https://doi.org/10.1016/S0997-7538(00)01111-6

    Article  MATH  Google Scholar 

  28. Comi, C.; Perego, U.: Fracture energy based bi-dissipative damage model for concrete. Int. J. Solids Struct. 38, 6427–6454 (2001). https://doi.org/10.1016/S0020-7683(01)00066-X

    Article  MATH  Google Scholar 

  29. Juárez-Luna, G.; Méndez-Martínez, H.; Ruiz-Sandoval, M.E.: An isotropic damage model to simulate collapse in reinforced concrete elements. Lat. Am. J. Solids Struct. 11, 2444–2459 (2014). https://doi.org/10.1590/S1679-78252014001300007

    Article  Google Scholar 

  30. Wang, Z.; Jin, X.; Jin, N.; Shah, A.A.; Li, B.: Damage based constitutive model for predicting the performance degradation of concrete. Lat. Am. J. Solids Struct. 11, 907–924 (2014). https://doi.org/10.1590/S1679-78252014000600001

    Article  Google Scholar 

  31. Pituba, J.J.C.; Pereira Júnior, W.M.: A bi-dissipative damage model for concrete. Rev. IBRACON Estrut. Mater. 8, 49–65 (2015). https://doi.org/10.1590/S1983-41952015000100006

    Article  Google Scholar 

  32. Pituba, J.J.C.; Fernandes, G.R.: Anisotropic damage model for concrete. J. Eng. Mech. 137, 610–624 (2011). https://doi.org/10.1061/(ASCE)EM.1943-7889.0000260

    Article  Google Scholar 

  33. Pituba, J.J.C.; Lacerda, M.M.S.: Simplified damage models applied in the numerical analysis of reinforced concrete structures. Rev IBRACON Estrut. Mater. 5, 26–37 (2012). https://doi.org/10.1590/S1983-41952012000100004

    Article  Google Scholar 

  34. Cicekli, U.; Voyiadjis, G.Z.; Abu Al-Rub, R.K.: A plasticity and anisotropic damage model for plain concrete. Int. J. Plast 23, 1874–1900 (2007). https://doi.org/10.1016/j.ijplas.2007.03.006

    Article  MATH  Google Scholar 

  35. Zhou, F.; Cheng, G.: A coupled plastic damage model for concrete considering the effect of damage on plastic flow. Math. Probl. Eng. 2015, 1–13 (2015). https://doi.org/10.1155/2015/867979

    Article  Google Scholar 

  36. Mazars, J.; Hamon, F.; Grange, S.: A new 3D damage model for concrete under monotonic, cyclic and dynamic loadings. Mater. Struct. 48, 3779–3793 (2015). https://doi.org/10.1617/s11527-014-0439-8

    Article  Google Scholar 

  37. Omidi, O.; Lotfi, V.: Finite element analysis of concrete structures using plasticdamage model in 3-D implementation. 8, 17 (2010)

  38. Pituba, J.J.C.; Neto, E.A.S.: Modeling of unilateral effect in brittle materials by a mesoscopic scale approach. Comput. Concr. 15, 735–758 (2015). https://doi.org/10.12989/CAC.2015.15.5.735

    Article  Google Scholar 

  39. Pituba, J.J.C.: A damage model formulation: unilateral effect and RC structures analysis. Comput. Concr. 15, 709–733 (2015). https://doi.org/10.12989/CAC.2015.15.5.709

    Article  Google Scholar 

  40. Nghia Nguyen, T.; Le, T.C.; Kathir, S.; Abdel, W.M.: A novel approach to the complete stress strain curve for plastically damaged concrete under monotonic and cyclic loads. Comput. Concr. 28, 39–53 (2021). https://doi.org/10.12989/CAC.2021.28.1.039

    Article  Google Scholar 

  41. Krejčí, T.; Koudelka, T.; Bernardo, V.; Šejnoha, M.: Effective elastic and fracture properties of regular and irregular masonry from nonlinear homogenization. Comput. Struct. 254, 106580 (2021). https://doi.org/10.1016/j.compstruc.2021.106580

    Article  Google Scholar 

  42. Fichant, S.; La Borderie, C.; Pijaudier-Cabot, G.: A comparative study of isotropic and anisotropic descriptions of damage in concrete structures. Stud. Appl. Mech. 46, 259–274 (1998). https://doi.org/10.1016/S0922-5382(98)80046-9

    Article  Google Scholar 

  43. Arslan, A.; Gümüş, M.: A simple and robust approach for 2D-simulation of reinforced concrete member. Structures 32, 1701–1716 (2021). https://doi.org/10.1016/j.istruc.2021.03.050

    Article  Google Scholar 

  44. Amorim, D.L.N.D.F.; Proença, S.P.B.; Flórez-López, J.: Simplified modeling of cracking in concrete: application in tunnel linings. Eng. Struct. 70, 23–35 (2014). https://doi.org/10.1016/j.engstruct.2014.03.031

    Article  Google Scholar 

  45. Mazars, J.; Pijaudier-Cabot, G.: Continuum damage theory—application to concrete. J. Eng. Mech. 115, 345–365 (1989). https://doi.org/10.1061/(ASCE)0733-9399(1989)115:2(345)

    Article  Google Scholar 

  46. Wang, Y.; Zhang, B.; Li, B.; Li, C.: A strain-based fatigue damage model for naturally fractured marble subjected to freeze-thaw and uniaxial cyclic loads. Int. . Damage Mech. (2021). https://doi.org/10.1177/10567895211021629

    Article  Google Scholar 

  47. Guo, Y.; Liu, G.; Liu, H.; Huang, Y.: Creep damage model considering unilateral effect based on bimodulus theory. Int. J. Damage Mech. (2021). https://doi.org/10.1177/10567895211017319

    Article  Google Scholar 

  48. Junior, W.M.P.; Borges, R.A.; Araújo, D.L.; Pituba, J.J.C.: A proposal to use the inverse problem for determining parameters in a constitutive model for concrete. Soft Comput 25, 8797–8815 (2021). https://doi.org/10.1007/s00500-021-05745-x

    Article  Google Scholar 

  49. Kang, F.; Li, J.; Xu, Q.: Structural inverse analysis by hybrid simplex artificial bee colony algorithms. Comput. Struct. 87, 861–870 (2009). https://doi.org/10.1016/j.compstruc.2009.03.001

    Article  Google Scholar 

  50. Sun, H.; Luş, H.; Betti, R.: Identification of structural models using a modified artificial bee colony algorithm. Comput. Struct. 116, 59–74 (2013). https://doi.org/10.1016/j.compstruc.2012.10.017

    Article  Google Scholar 

  51. Morio, J.: Global and local sensitivity analysis methods for a physical system. Eur. J. Phys. 32, 1577–1583 (2011). https://doi.org/10.1088/0143-0807/32/6/011

    Article  Google Scholar 

  52. Link, K.G.; Stobb, M.T.; Di Paola, J.; Neeves, K.B.; Fogelson, A.L.; Sindi, S.S., et al.: A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow. PLoS ONE 13, e0200917 (2018). https://doi.org/10.1371/journal.pone.0200917

    Article  Google Scholar 

  53. Razavi, S.; Gupta, H.V.: What do we mean by sensitivity analysis? The need for comprehensive characterization of “global” sensitivity in earth and environmental systems models: a critical look at sensitivity analysis. Water Resour. Res. 51, 3070–3092 (2015). https://doi.org/10.1002/2014WR016527

    Article  Google Scholar 

  54. Felmlee, M.A.; Krzyzanski, W.; Morse, B.L.; Morris, M.E.: Use of a local sensitivity analysis to inform study design based on a mechanistic toxicokinetic model for γ-hydroxybutyric acid. AAPS J. 13, 240–254 (2011). https://doi.org/10.1208/s12248-011-9264-y

    Article  Google Scholar 

  55. Dong, Z.; Xie, L.; Yang, Y.; Bridgwater, A.V.; Cai, J.: local sensitivity analysis of kinetic models for cellulose pyrolysis. Waste Biomass Valor. 10, 975–984 (2019). https://doi.org/10.1007/s12649-017-0097-5

    Article  Google Scholar 

  56. Czitrom, V.: One-factor-at-a-time versus designed experiments. Am. Stat. 53, 126–131 (1999). https://doi.org/10.1080/00031305.1999.10474445

    Article  Google Scholar 

  57. Saltelli, A.: Sensitivity analysis: could better methods be used? J. Geophys. Res. 104, 3789–3793 (1999). https://doi.org/10.1029/1998JD100042

    Article  Google Scholar 

  58. Mazars J. Application de la mecanique de l’endommagement au comportement non lineaire et a la rupture du beton de structure. Universite Pierre et Marie Curie: Laboratoire de Mecanique et Technologie (1984)

  59. Gelim, J.-C.; Ghouati, O.: An inverse method for material parameters estimation in the inelastic range. Comput. Mech. 16, 143–150 (1995)

    Article  MATH  Google Scholar 

  60. Viola, E.; Bocchini, P.: Non-destructive parametric system identification and damage detection in truss structures by static tests. Struct. Infrastruct. Eng. 9, 384–402 (2013). https://doi.org/10.1080/15732479.2011.560164

    Article  Google Scholar 

  61. Andersson, D.C.; Lindskog, P.; Larsson, P.-L.: Inverse modeling applied for material characterization of powder materials. J. Test Eval. 43, 20130266 (2015). https://doi.org/10.1520/JTE20130266

    Article  Google Scholar 

  62. Meraghni, F.; Chemisky, Y.; Piotrowski, B.; Echchorfi, R.; Bourgeois, N.; Patoor, E.: Parameter identification of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix. Eur. J. Mech. A. Solids 45, 226–237 (2014). https://doi.org/10.1016/j.euromechsol.2013.12.010

    Article  Google Scholar 

  63. Karaboga D. An idea based on Honey bee swarm for numerical optimization n.d.:10

  64. Karaboga, D.; Basturk, B.: Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In: Melin, P.; Castillo, O.; Aguilar, L.T.; Kacprzyk, J.; Pedrycz, W. (Eds.) Foundations of fuzzy logic and soft computing, pp. 789–798. Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-72950-1_77

    Chapter  MATH  Google Scholar 

  65. Bacanin, N.; Tuba, M.: Artificial bee colony (ABC) algorithm for constrained optimization improved with genetic operators. Stud. Inform. ControlI (2012). https://doi.org/10.24846/v21i2y201203

    Article  Google Scholar 

  66. Xu, Y.; Fan, P.; Yuan, L.: A simple and efficient artificial bee colony algorithm. Math. Probl. Eng. 2013, 1–9 (2013). https://doi.org/10.1155/2013/526315

    Article  Google Scholar 

  67. Alkayem, N.F.; Cao, M.; Ragulskis, M.: Damage localization in irregular shape structures using intelligent FE model updating approach with a new hybrid objective function and social swarm algorithm. Appl. Soft Comput. 83, 105604 (2019). https://doi.org/10.1016/j.asoc.2019.105604

    Article  Google Scholar 

  68. Taetragool, U.; Shah, P.H.; Halls, V.A.; Zheng, J.Q.; Batra, R.C.: Stacking sequence optimization for maximizing the first failure initiation load followed by progressive failure analysis until the ultimate load. Compos. Struct. 180, 1007–1021 (2017). https://doi.org/10.1016/j.compstruct.2017.08.023

    Article  Google Scholar 

  69. Álvares M da S. Estudo de um modelo de dano para o concreto: formulação, identificação paramétrica e aplicação com o emprego do método dos elementos finitos. text. Universidade de São Paulo (1993)

  70. Fédération Internationale du Béton. Model Code 2010, final draft. Lausanne: FIB (2012)

  71. Fernandes, G.R.; Crozariol, L.H.R.; Furtado, A.S.; Santos, M.C.: A 2D boundary element formulation to model the constitutive behavior of heterogeneous microstructures considering dissipative phenomena. Eng. Anal. Boundary Elem. 99, 1–22 (2019). https://doi.org/10.1016/j.enganabound.2018.10.018

    Article  MathSciNet  MATH  Google Scholar 

  72. Fernandes, G.R.; Marques Silva, M.J.; Vieira, J.F.; Pituba, J.J.C.: A 2D RVE formulation by the boundary element method considering phase debonding. Eng. Anal. Boundary Elem. 104, 259–276 (2019). https://doi.org/10.1016/j.enganabound.2019.03.018

    Article  MathSciNet  MATH  Google Scholar 

  73. Yuuki, R.; Cao, G.: Shape optimization for stress concentration problems in orthotropic materials by using Boundary Element method. Boundary Element Methods (1990). https://doi.org/10.1016/B978-0-08-040200-0.50036-4

    Article  Google Scholar 

  74. Fernandes, G.R.; Pituba, J.J.C.; de Souza Neto, E.A.: Multi-scale modelling for bending analysis of heterogeneous plates by coupling BEM and FEM. Eng. Anal. Boundary Elem. 51, 1–13 (2015). https://doi.org/10.1016/j.enganabound.2014.10.005

    Article  MathSciNet  MATH  Google Scholar 

  75. Mehta, P.K.; Monteiro, P.J.M.: Concrete: microstructure, properties, and materials, 4th edn. McGraw-Hill Education, New York (2014)

    Google Scholar 

  76. Rodrigues, E.A.; Manzoli, O.L.; Bitencourt, L.A.G., Jr.; dos Prazeres, P.G.C.; Bittencourt, T.N.: Failure behavior modeling of slender reinforced concrete columns subjected to eccentric load. Lat. Am. J. Solids Struct. 12, 520–541 (2015). https://doi.org/10.1590/1679-78251224

    Article  Google Scholar 

  77. de Melo, G.L.; Fernandes, A.L.T.: Evaluation of empirical methods to estimate reference evapotranspiration in Uberaba, State of Minas Gerais. Brazil. Eng Agríc 32, 875–888 (2012). https://doi.org/10.1590/S0100-69162012000500007

    Article  Google Scholar 

  78. Perin, V.; Sentelhas, P.C.; Dias, H.B.; Santos, E.A.: Sugarcane irrigation potential in Northwestern São Paulo, Brazil, by integrating Agrometeorological and GIS tools. Agric. Water Manag. 220, 50–58 (2019). https://doi.org/10.1016/j.agwat.2019.04.012

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank CNPq (National Council for Scientific and Technological Development) and FAPEG (Goiás Research Foundation) for the financial support (FAPEG: 2017.10.267000.513, FAPEG: 201710267000521, CNPQ: 304281/2018-2, CNPQ: 439126/2018-5).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W. M. Pereira Junior.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare. All co-authors have seen and agree with the contents of the manuscript, and there is no financial interest to report. We certify that the submission is original work and is not under review at any other publication.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pereira Junior, W.M., Borges, R.A., Araújo, D.L. et al. Parametric Identification and Sensitivity Analysis Combined with a Damage Model for Reinforced Concrete Structures. Arab J Sci Eng 48, 4751–4767 (2023). https://doi.org/10.1007/s13369-022-07132-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-022-07132-6

Keywords

Navigation