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Numerical modeling of the tension stiffening in reinforced concrete members via discontinuum models

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Abstract

This study presents a numerical investigation on the fracture mechanism of tension stiffening phenomenon in reinforced concrete members. A novel approach using the discrete element method (DEM) is proposed, where three-dimensional randomly generated distinct polyhedral blocks are used, representing concrete and one-dimensional truss elements are utilized, representing steel reinforcements. Thus, an explicit representation of reinforced concrete members is achieved, and the mechanical behavior of the system is solved by integrating the equations of motion for each block using the central difference algorithm. The inter-block interactions are taken into consideration at each contact point with springs and cohesive frictional elements. Once the applied modeling strategy is validated, based on previously published experimental findings, a sensitivity analysis is performed for bond stiffness, cohesion strength, and the number of truss elements. Hence, valuable inferences are made regarding discontinuum analysis of reinforced concrete members, including concrete–steel interaction and their macro behavior. The results demonstrate that the proposed phenomenological modeling strategy successfully captures the concrete–steel interaction and provides an accurate estimation of the macro behavior.

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References

  1. Massicotte B, Elwi AE, MacGregor JG (1990) Tension stiffening model for planar reinforced concrete members. J Struct Eng 116:3039–3058

    Article  Google Scholar 

  2. Ožbolt J, Lettow S, Kožar I (2002) Discrete bond element for 3D finite element analysis of reinforced concrete structures. In: Proceedings of 3rd International Symposium Bond Concr. Res. to Stand, pp 1–11

  3. Wu HQ, Gilbert RI (2009) Modeling short-term tension stiffening in reinforced concrete prisms using a continuum-based finite element model. Eng Struct 31:2380–2391. https://doi.org/10.1016/j.engstruct.2009.05.012

    Article  Google Scholar 

  4. Lowes LN, Moehle JP, Govindjee S (2004) Concrete-steel bond model for use in finite element modeling of reinforced concrete structures. ACI Struct J 101:501–511. https://doi.org/10.14359/13336

    Article  Google Scholar 

  5. Stramandinoli RSB, La Rovere HL (2008) An efficient tension-stiffening model for nonlinear analysis of reinforced concrete members. Eng Struct 30:2069–2080. https://doi.org/10.1016/j.engstruct.2007.12.022

    Article  Google Scholar 

  6. Michou A, Hilaire A, Benboudjema F et al (2015) Reinforcement-concrete bond behavior: experimentation in drying conditions and meso-scale modeling. Eng Struct 101:570–582. https://doi.org/10.1016/j.engstruct.2015.07.028

    Article  Google Scholar 

  7. Slobbe AT, Hendriks MAN, Rots JG (2012) Sequentially linear analysis of shear critical reinforced concrete beams without shear reinforcement. Finite Elem Anal Des 50:108–124. https://doi.org/10.1016/j.finel.2011.09.002

    Article  Google Scholar 

  8. Vecchio FJ, Shim W (2004) Experimental and analytical reexamination of classic concrete beam tests. J Struct Eng 130:460–469. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(460)

    Article  Google Scholar 

  9. Grassl P, Johansson M, Leppänen J (2018) On the numerical modelling of bond for the failure analysis of reinforced concrete. Eng Fract Mech 189:13–26. https://doi.org/10.1016/j.engfracmech.2017.10.008

    Article  Google Scholar 

  10. Murcia-Delso J, Benson Shing P (2015) Bond-slip model for detailed finite-element analysis of reinforced concrete structures. J Struct Eng (United States) 141:1–10. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001070

    Article  Google Scholar 

  11. Jendele L, Cervenka J (2006) Finite element modelling of reinforcement with bond. Comput Struct 84:1780–1791. https://doi.org/10.1016/j.compstruc.2006.04.010

    Article  Google Scholar 

  12. Yu RC, Saucedo L, Ruiz G (2011) Finite-element study of the diagonal-tension failure in reinforced concrete beams. Int J Fract 169:169–182. https://doi.org/10.1007/s10704-011-9592-z

    Article  MATH  Google Scholar 

  13. Lorig LJ, Cundall PA (1989) Modeling of reinforced concrete using the distinct element method. In: Shah SP, Swartz SE (eds) Fracture of concrete and rock. Springer, New York, pp 276–287

    Chapter  Google Scholar 

  14. Živaljić N, Nikolić Ž, Smoljanović H (2014) Computational aspects of the combined finite-discrete element method in modelling of plane reinforced concrete structures. Eng Fract Mech 131:362–389. https://doi.org/10.1016/j.engfracmech.2014.10.017

    Article  Google Scholar 

  15. Munjiza A, Smoljanović H, Živaljić N et al (2019) Structural applications of the combined finite–discrete element method. Comput Part Mech. https://doi.org/10.1007/s40571-019-00286-5

    Article  Google Scholar 

  16. Kawai T (1978) New discrete models and their application to seismic response analysis of structures. Nucl Eng Des 48:207–229. https://doi.org/10.1016/0029-5493(78)90217-0

    Article  Google Scholar 

  17. Bolander JE, Le BD (1999) Modeling crack development in reinforced concrete structures under service loading. Constr Build Mater 13:23–31

    Article  Google Scholar 

  18. Aydin BB, Tuncay K, Binici B (2018) Overlapping Lattice Modeling for concrete fracture simulations using sequentially linear analysis. Struct Concr 19:568–581. https://doi.org/10.1002/suco.201600196

    Article  Google Scholar 

  19. Aydin BB, Tuncay K, Binici B (2019) Simulation of reinforced concrete member response using lattice model. J Struct Eng 145:04019091. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002381

    Article  Google Scholar 

  20. De Borst R, Nauta P (1985) Non-orthogonal cracks in a smeared finite element model. Eng Comput 2:35–46. https://doi.org/10.1108/eb023599

    Article  Google Scholar 

  21. Bernardi P, Ferretti D, Michelini E, Sirico A (2016) Evaluation of crack width in RC ties through a numerical “range” model. Procedia Struct Integr 2:2780–2787. https://doi.org/10.1016/j.prostr.2016.06.347

    Article  Google Scholar 

  22. Rots JG, Belletti B, Invernizzi S (2008) Robust modeling of RC structures with an “event-by-event” strategy. Eng Fract Mech 75:590–614. https://doi.org/10.1016/j.engfracmech.2007.03.027

    Article  Google Scholar 

  23. Ensink SWH, Graaf AV Van De, Slobbe AT, et al (2012) Modelling of bond behaviour by means of sequentially linear analysis and concrete-to-steel interface elements. In: Proceedings of the fourth international symposium” bond in concrete 2012: bond, anchorage, detailing”. Brescia, pp 161–167

  24. Gijsbers FBJ, Hehemann AA (1977) Some tensile tests on reinforced concrete. Rijswijk

  25. Walraven JC (1984) The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement. University of Technology, Department of Civil Engineering

  26. Cundall PA (1971) A computer model for simulating progressive, large-scale movements in blocky rock systems. In: The international symposium on rock mechanics. Nancy, pp 47–65

  27. Itasca Consulting Group Inc. (2013) 3DEC three dimensional distinct element code

  28. Pulatsu B, Erdogmus E, Lourenço PB et al (2020) Discontinuum analysis of the fracture mechanism in masonry prisms and wallettes via discrete element method. Meccanica 55:505–523. https://doi.org/10.1007/s11012-020-01133-1

    Article  MathSciNet  Google Scholar 

  29. Pulatsu B, Erdogmus E, Lourenço PB, Quey R (2019) Simulation of uniaxial tensile behavior of quasi-brittle materials using softening contact models in DEM. Int J Fract 217:105–125. https://doi.org/10.1007/s10704-019-00373-x

    Article  Google Scholar 

  30. Pulatsu B, Kim S, Erdogmus E, Lourenço PB (2020) Advanced analysis of masonry retaining walls using mixed discrete-continuum approach. Proc Inst Civ Eng—Geotech Eng. https://doi.org/10.1680/jgeen.19.00225

    Article  Google Scholar 

  31. Quey R, Dawson PR, Barbe F (2011) Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing. Comput Methods Appl Mech Eng 200:1729–1745. https://doi.org/10.1016/j.cma.2011.01.002

    Article  MATH  Google Scholar 

  32. Quey R (2014) Neper Reference Manual 3.5.1

  33. Quey R, Renversade L (2018) Optimal polyhedral description of 3D polycrystals: method and application to statistical and synchrotron X-ray diffraction data. Comput Methods Appl Mech Eng 330:308–333. https://doi.org/10.1016/j.cma.2017.10.029

    Article  MathSciNet  MATH  Google Scholar 

  34. Quey R, Villani A, Maurice C (2018) Nearly uniform sampling of crystal orientations. J Appl Crystallogr 51:1162–1173. https://doi.org/10.1107/S1600576718009019

    Article  Google Scholar 

  35. Lemos JV (2012) Explicit codes in geomechanics—FLAC, UDEC and PFC. In: Ribeiro e Sousa L, Vargas E Jr, Fernandes MM, Azevedo R (eds) Innovative numerical modelling in geomechanics. CRC Press, Boca Raton, pp 299–315

    Google Scholar 

  36. Cundall PA (1987) Distinct element models of rock and soil structure. In: Brown ET (ed) Analytical and computational methods in engineering rock mechanics. George Allen Unwin, London, pp 129–163

    Google Scholar 

  37. Cundall PA (1988) Formulation of a three-dimensional distinct element model—part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech 25:107–116

    Article  Google Scholar 

  38. Itasca (2004) 3DEC universial discrete element code theory and background. Minneapolis

  39. Lemos J (2008) Block modelling of rock masses. Concepts and application to dam foundations. Rev Eur Génie Civ 12:915–949. https://doi.org/10.3166/ejece.12.915-949

    Article  Google Scholar 

  40. Oñate E, Zárate F, Miquel J et al (2015) A local constitutive model for the discrete element method. Application to geomaterials and concrete. Comput Part Mech 2:139–160. https://doi.org/10.1007/s40571-015-0044-9

    Article  Google Scholar 

  41. Kazerani T, Zhao J (2010) Micromechanical parameters in bonded particle method for modelling of brittle material failure. Int J Numer Anal Methods Geomech 34:1877–1895. https://doi.org/10.1002/nag.884

    Article  MATH  Google Scholar 

  42. Bui TT, Limam A (2012) Masonry walls under membrane or bending loading cases: experiments and discrete element analysis. In: Topping BHV (ed) Proceedings of the eleventh international conference on computational structures technology. Stirlingshire

  43. Pulatsu B, Erdogmus E, Bretas EM, Lourenço PB (2019) In-plane static response of dry-joint masonry arch-pier structures. In: AEI 2019. American Society of Civil Engineers, Reston, VA, pp 240–248

  44. Bui T-T, Limam A, Sarhosis V (2019) Failure analysis of masonry wall panels subjected to in-plane and out-of-plane loading using the discrete element method. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2018.1552897

    Article  Google Scholar 

  45. Yankelevsky DZ, Reinhardt HW (1989) Uniaxial behavior of concrete in cyclic tension. J Struct Eng 115:166–182. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:1(166)

    Article  Google Scholar 

  46. Van Mier JGM, Man H-K (2009) Some notes on microcracking, softening, localization, and size effects. Int J Damage Mech 18:283–309. https://doi.org/10.1177/1056789508097545

    Article  Google Scholar 

  47. Vervuurt A, Van Mier JGM (1994) Experimental and numerical analysis of boundary effects in uniaxial tensile tests. WIT Trans Eng Sci 4:1–10

    Google Scholar 

  48. Azevedo NM, Lemos JV, Almeida JR (2010) A discrete particle model for reinforced concrete fracture analysis. Struct Eng Mech 36:343–361. https://doi.org/10.12989/sem.2010.36.3.343

    Article  Google Scholar 

  49. Pulatsu B, Bretas EM, Lourenço PB (2016) Discrete element modeling of masonry structures: Validation and application. Earthq Struct 11:563–582. https://doi.org/10.12989/eas.2016.11.4.563

    Article  Google Scholar 

  50. Godio M, Stefanou I, Sab K (2018) Effects of the dilatancy of joints and of the size of the building blocks on the mechanical behavior of masonry structures. Meccanica 53:1629–1643. https://doi.org/10.1007/s11012-017-0688-z

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Nebraska-Lincoln, Lincoln, USA

    Bora Pulatsu & Ece Erdogmus

  2. ISISE, University of Minho, Braga, Portugal

    Paulo B. Lourenço

  3. LNEC, Lisbon, Portugal

    José V. Lemos

  4. Middle East Technical University, Ankara, Turkey

    Kagan Tuncay

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  1. Bora Pulatsu
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Correspondence to Bora Pulatsu.

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Pulatsu, B., Erdogmus, E., Lourenço, P.B. et al. Numerical modeling of the tension stiffening in reinforced concrete members via discontinuum models. Comp. Part. Mech. 8, 423–436 (2021). https://doi.org/10.1007/s40571-020-00342-5

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