DOI QR코드

DOI QR Code

Modelling reinforced concrete beams under mixed shear-tension failure with different continuous FE approaches

  • Marzec, Ireneusz (Department of Civil Engineering, Gdansk University of Technology) ;
  • Skarzynski, Lukasz (Department of Civil Engineering, Gdansk University of Technology) ;
  • Bobinski, Jerzy (Department of Civil Engineering, Gdansk University of Technology) ;
  • Tejchman, Jacek (Department of Civil Engineering, Gdansk University of Technology)
  • Received : 2012.02.17
  • Accepted : 2013.05.08
  • Published : 2013.11.25

Abstract

The paper presents quasi-static numerical simulations of the behaviour of short reinforced concrete beams without shear reinforcement under mixed shear-tension failure using the FEM and four various constitutive continuum models for concrete. First, an isotropic elasto-plastic model with a Drucker-Prager criterion defined in compression and with a Rankine criterion defined in tension was used. Next, an anisotropic smeared crack and isotropic damage model were applied. Finally, an elasto-plastic-damage model was used. To ensure mesh-independent FE results, to describe strain localization in concrete and to capture a deterministic size effect, all models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. Bond-slip between concrete and reinforcement was considered. The numerical results were directly compared with the corresponding laboratory tests performed by Walraven and Lehwalter (1994). The advantages and disadvantages of enhanced models to model the reinforced concrete behaviour were outlined.

Keywords

References

  1. Abaqus (2004), Theory Manual, Version 5.8, Hibbit, Karlsson & Sorensen Inc.
  2. Bazant, Z.P. and Bhat, P.D. (1976), "Endochronic theory of inelasticity and failure of concrete", ASCE J. Eng. Mech., 102(4), 701-722.
  3. Bazant, Z.P. and Ozbolt, J. (1990), "Non-local microplane model for fracture, damage and size effect in structures", ASCE J. Eng. Mech., 116(11), 2485-2505. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:11(2485)
  4. Bazant, Z. and Planas, J. (1998), Fracture and Size Effect in Concrete and Other Quasi-brittle Materials,CRC Press LLC.
  5. Bazant, Z.P. and Jirasek, M. (2002), "Numerical integral formulations of plasticity and damage: survey of progress", ASCE J. Eng. Mech., 128(11), 1119-1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)
  6. Bobinski, J. and Tejchman, J. (2004), "Numerical simulations of localization of deformation in quasibrittle materials within non-local softening plasticity", Comput. Concr., 1(4), 1-22. https://doi.org/10.12989/cac.2004.1.1.001
  7. Bobinski, J. and Tejchman, J. (2013), "A coupled continuous-discontinuous approach to concrete elements", Proceeding of the Int. Conf. Fracture Mechanics of Concrete and Concrete Structures FraMCoS-8, (Eds. van Mier, J.G.M., Ruiz, G., Andrade, C., Yu, R.C., Zhang, X.X.).
  8. Brinkgreve, R.B.J. (1994), "Geomaterial models and numerical analysis of softening", Ph.D. Thesis, Delft University of Technology, Delft.
  9. Carol, I. and Willam, K. (1996), "Spurious energy dissipation/generation in stiffness recovery models for elastic degradation and damage", Int. J. Solids Struct., 33(20-22), 2939-2957. https://doi.org/10.1016/0020-7683(95)00254-5
  10. Cervenka, J. and Papanikolaou, V.K. (2008), "Three dimensional combined fracture-plastic material model for concrete", Int. J. Plasticity, 24(12), 2192-2220. https://doi.org/10.1016/j.ijplas.2008.01.004
  11. Committe Euro-International du Beton (1991), "CEB-FIP model code 1990: design code", Bulletin d'inform., 213-224.
  12. de Borst, R. and Nauta, P. (1985), "Non-orthogonal cracks in a smeared finite element model", Eng. Comput., 2(1), 35-46. https://doi.org/10.1108/eb023599
  13. de Borst, R. (1986), "Non-linear analysis of frictional materials", Ph.D. Thesis, University of Delft, Delft.
  14. de Borst, R., Pamin, J. and Geers, M. (1999), "On coupled gradient-dependent plasticity and damage theories with a view to localization analysis", Eur. J. Mech. A/Solids, 18(6), 939-962. https://doi.org/10.1016/S0997-7538(99)00114-X
  15. de Vree, J.H.P., Brekelmans, W.A.M. and van Gils, M.A.J. (1995), "Comparison of non-local approaches in continuum damage mechanics", Comput. Struct., 55(4), 581-588. https://doi.org/10.1016/0045-7949(94)00501-S
  16. den Uijl, J.A. and Bigaj, A. (1996), "A bond model for ribbed bars based on concrete confinement", Heron, 41(3), 201-226.
  17. Dorr, K. (1980), "Ein Beitag zur Berechnung von Stahlbetonscheiben unter Berucksichtigung des Verbundverhaltens", Ph.D Thesis, Darmstadt University, Darmstadt , Germany.
  18. Dragon, A. and Mroz, Z. (1979), "A continuum model for plastic-brittle behaviour of rock and concrete", Int. J. Eng. Sci., 17(2), 121-137. https://doi.org/10.1016/0020-7225(79)90058-2
  19. Geers, M.G.D. (1997), "Experimental analysis and computational modeling of damage and fracture", Ph.D Thesis, Eindhoven University of Technology, Eindhoven, Netherland.
  20. Gitman, I.M., Askes, H. and Sluys, L.J. (2008), "Coupled-volume multi-scale modelling of quasi-brittle material", Eur. J. Mech. A/Solids, 27(3), 302-327. https://doi.org/10.1016/j.euromechsol.2007.10.004
  21. Haskett, M., Pehlers, D.J. and Mohamed Ali, M.S. (2008), "Local and global bond characteristics of steel reinforcing bars", Eng. Struct., 30(2), 376-383. https://doi.org/10.1016/j.engstruct.2007.04.007
  22. Haussler-Combe, U. and Prochtel, P. (2005), "Ein dreiaxiale stoffgesetz fur betone mit normalen und hoher festigkeit", Beton- Stahlbetonbau, 100(1), 56-62.
  23. Hordijk, D.A. (1991), "Local approach to fatigue of concrete", PhD Thesis, Delft University of Technology, Delft, Netherland.
  24. Hsieh, S.S., Ting, E.C. and Chen, W.F. (1982), "Plasticity-fracture model for concrete", Int. J. Solids Struct., 18(3), 181-187. https://doi.org/10.1016/0020-7683(82)90001-4
  25. Hughes, T.J.R. and Winget, J. (1980), "Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis", Int. J. Numer. Methods Eng., 15(12), 1862-1867. https://doi.org/10.1002/nme.1620151210
  26. Ibrahimbegovic, A., Markovic, D. and Gatuing, F. (2003), "Constitutive model of coupled damage-plasticity and its finite element implementation", Eur. J. Finite Elem., 12(4), 381-405.
  27. Jirasek, M. and Zimmermann, T. (1998), "Analysis of rotating crack model", ASCE J. Eng. Mech., 124(8), 842-851. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(842)
  28. Jirasek, M. (1999), "Comments on microplane theory", Mechanics of quasi-brittle materials and structures (Eds. Pijaudier-Cabot, G., Bittnar, Z. and Gerard, B.), Hermes Science Publications, 55-77.
  29. Jirasek, M. and Marfia, S. (2005), "Non-local damage model based on displacement averaging", Int. J. Numer. Methods Eng., 63(1), 77-102. https://doi.org/10.1002/nme.1262
  30. Lee, J. and Fenves, G.L. (1998), "Plastic-damage model for cyclic loading of concrete structures", ASCE J. Eng. Mech., 124(8), 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)
  31. Lorrain, M., Maurel, O. and Seffo, M. (1998), "Cracking behaviour of reinforced high-strength concrete tension ties", ACI Struct. J., 95(5), 626-635.
  32. Majewski, T., Bobi?ski, J. and Tejchman, J. (2008), "FE-analysis of failure behaviour of reinforced concrete columns under eccentric compression", Eng. Struct., 30(2), 300-317. https://doi.org/10.1016/j.engstruct.2007.03.024
  33. Mahnken, R. and Kuhl, E. (1999), "Parameter identification of gradient enhanced damage models", Eur. J. Mech. A/Solids, 18(5), 819-835. https://doi.org/10.1016/S0997-7538(99)00127-8
  34. Marzec, I., Bobi?ski, J. and Tejchman, J. (2007), "Simulations of crack spacing in reinforced concrete beams using elastic-plasticity and damage with non-local softening", Comput. Concrete, 4(5), 377-403. https://doi.org/10.12989/cac.2007.4.5.377
  35. Marzec, I. and Tejchman, J. (2012), "Enhanced coupled elasto-plastic-damage models to describe concrete behaviour in cyclic laboratory tests: Comparison and improvement", Arch. Mech., 64(3), 227-259.
  36. Mazars, J. (1986), "A description of micro- and macroscale damage of concrete structures", Eng. Fract. Mech., 25(5-6), 729-737. https://doi.org/10.1016/0013-7944(86)90036-6
  37. Menetrey, P. and Willam, K.J. (1995), "Triaxial failure criterion for concrete and its generalization", ACI Struct. J., 92(3), 311-318.
  38. Meschke, G. and Dumstorff, P. (2007), "Energy-based modeling of cohesive and cohesionless cracks via X-FEM", Comput. Meth. Appl. Mech. Eng., 196(21-24), 2338-2357. https://doi.org/10.1016/j.cma.2006.11.016
  39. Moonen, P., Carmeliet, J. and Sluys, L.J. (2008), "A continuous-discontinuous approach to simulate fracture processes", Philos. Mag., 88(28-29), 3281-3298. https://doi.org/10.1080/14786430802566398
  40. Oliver, J. and Linero, D.L. and Huespe, A.E. and Manzoli, O.L. (2008), "Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach", Comput. Meth. Appl. Mech. Eng., 197(5), 332-348. https://doi.org/10.1016/j.cma.2007.05.017
  41. Ooi, E.T. and Yang, Z.J. (2011), "Modelling crack propagation in reinforced concrete using a hybrid finite element-scaled boundary finite element method", Eng. Fract. Mech., 78(2), 252-273. https://doi.org/10.1016/j.engfracmech.2010.08.002
  42. Pamin, J. and de Borst, R. (1999), "Stiffness degradation in gradient-dependent coupled damage-plasticity", Arch. Mech., 51(3-4), 419-446.
  43. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M. and Geers, M.G.D. (1998), "Gradient enhanced damage modelling of concrete fracture", Mech. Cohes.-Frict. Mat., 3(4), 323-342. https://doi.org/10.1002/(SICI)1099-1484(1998100)3:4<323::AID-CFM51>3.0.CO;2-Z
  44. Pietruszczak, S., Jiang, J. and Mirza, F.A. (1988), "An elastoplastic constitutive model for concrete", Int. J. Solids Struct., 24(7), 705-722. https://doi.org/10.1016/0020-7683(88)90018-2
  45. Pijaudier-Cabot, G. and Bazant, Z.P. (1987), "Nonlocal damage theory", ASCE J. Eng. Mech., 113(10), 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  46. Rabczuk, T. and Zi, G. and Bordas, S. and Nguyen-Xuan, H. (2008), "A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures", Eng. Fract. Mech., 75(16), 4740-4758. https://doi.org/10.1016/j.engfracmech.2008.06.019
  47. Ragueneau, F., Borderie, Ch. and Mazars, J. (2000), "Damage model for concrete-like materials coupling cracking and friction", Int. J. Num. Anal. Meth. Geomech., 5(8), 607-625..
  48. Rots, J.G. and Blaauwendraad, J. (1989), "Crack models for concrete, discrete or smeared? Fixed, multi-directional or rotating?", Heron, 34(1), 1-59.
  49. Simo, K.C. and Ju, J.W. (1987), "Strain- and stress-based continuum damage models - I. Formulation", Int. J. Solids Struct., 23(7), 821-840. https://doi.org/10.1016/0020-7683(87)90083-7
  50. Simone, A. and Sluys, L.J. (2004), "The use of displacement discontinuities in a rate-dependent medium", Comput. Meth. Appl. Mech. Eng., 193(27-29), 3015-3033. https://doi.org/10.1016/j.cma.2003.08.006
  51. Skarzynski, L. and Tejchman, J. (2010), "Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending", Eur. J. Mech. A/Solids, 29(4), 746-760. https://doi.org/10.1016/j.euromechsol.2010.02.008
  52. Skarzynski, L., Syroka, E. and Tejchman, J. (2011), "Measurements and calculations of the width of the fracture process zones on the surface of notched concrete beams", Strain, 47(s1), 319-332. https://doi.org/10.1111/j.1475-1305.2008.00605.x
  53. Sluys, L.J. and de Borst, R. (1994), "Dispersive properties of gradient and rate-dependent media", Mech. Mater., 18(2), 131-149. https://doi.org/10.1016/0167-6636(94)00009-3
  54. Souza, R.A. (2010), Experimental and Numerical Analysis of Reinforced Concrete Corbels Strengthened with Fiber Reinforced Polymers, Computational Modelling of Concrete Structures, (Eds. N. Bicanic, R. de Borst, H. Mang, G. Meschke), Taylor and Francis Group, 711-718.
  55. Syroka, E., Bobi?ski, J. and Tejchman, J. (2011), "FE analysis of reinforced concrete corbels with enhanced continuum models", Finite Elem. Anal. Des., 47(9), 1066-1078. https://doi.org/10.1016/j.finel.2011.03.022
  56. Syroka-Korol, E. (2012), "Experimental and theoretical investigations of size effects in concrete and reinforced concrete beams", PhD Thesis, Gdask University of Technology, Gdask, Poland.
  57. Tejchman, J. and Bobi?ski, J. (2013), Continuous and Discontinuous Modeling of Fracture in Concrete Using FEM, Springer, (Eds. W. Wu and R. I. Borja), Berlin-Heidelberg, Germany.
  58. Walraven, J. and Lehwalter, N. (1994), "Size effects in short beams loaded in shear", ACI Struct. J., 91(5), 585-593.

Cited by

  1. Experimental Investigations of Fracture Process in Concrete by Means of X-ray Micro-computed Tomography vol.52, pp.1, 2016, https://doi.org/10.1111/str.12168
  2. Modelling of concrete fracture at aggregate level using FEM and DEM based on X-ray μCT images of internal structure vol.147, 2015, https://doi.org/10.1016/j.engfracmech.2015.08.010
  3. Investigation of bond-slip modeling methods used in FE analysis of RC members vol.56, pp.2, 2015, https://doi.org/10.12989/sem.2015.56.2.275
  4. Numerical analyses of novel prefabricated structural wall panels in residential buildings based on laboratory tests in scale 1:1 pp.2116-7214, 2018, https://doi.org/10.1080/19648189.2018.1474382
  5. Size effect in concrete beams under bending – influence of the boundary layer and the numerical description of cracks vol.262, pp.2261-236X, 2019, https://doi.org/10.1051/matecconf/201926210008
  6. Experiments and numerical analyses for composite RC-EPS slabs vol.20, pp.6, 2013, https://doi.org/10.12989/cac.2017.20.6.689
  7. A numerical-experimental evaluation of beams composed of a steel frame with welded and conventional stirrups vol.22, pp.1, 2013, https://doi.org/10.12989/cac.2018.22.1.027
  8. On Some Problems in Determining Tensile Parameters of Concrete Model from Size Effect Tests vol.26, pp.2, 2019, https://doi.org/10.2478/pomr-2019-0031