Strength of Materials

, Volume 50, Issue 5, pp 711–723 | Cite as

XFEM Simulation of Pore-Induced Fracture of a Heterogeneous Concrete Beam in Three-Point Bending

  • C. C. Zhang
  • X. H. Yang
  • H. Gao

The extended finite element method with the linear softening law is employed to simulate poreinduced crack initiation and propagation in heterogeneous plain concrete beams in three-point bending. A series of numerical simulations was performed and experimentally validated. The crack was found to always initiate at the beam bottom in the point nearest to the pore, propagating through it. When the pore has a larger offset from the beam midspan, the beam displays higher fracture resistance and energy dissipation spent for fracture. With an increase in a distance from the beam bottom, the ultimate load also increases, but the energy dissipation slightly varies. The pore sizes have a little effect on the fracture resistance of the concrete beam.


heterogeneous plain concrete beam three-point bending extended finite element method pore-induced fracture 



This work is supported by the National Basic Research Program of China (973 Program: 2011CB013800).


  1. 1.
    B. Goszczyñska, “Analysis of the process of crack initiation and evolution in concrete with acoustic emission testing,” Arch. Civ. Mech. Eng., 14, No. 1, 134–143 (2014).CrossRefGoogle Scholar
  2. 2.
    K. Ohno, K. Uji, A. Ueno, and M. Ohtsu, “Fracture process zone in notched concrete beam under three-point bending by acoustic emission,” Constr. Build. Mater., 67, 139–145 (2014).CrossRefGoogle Scholar
  3. 3.
    A. Ghosh and P. Chaudhuri, “Computational modeling of fracture in concrete using a meshfree meso-macro-multiscale method,” Comp. Mater. Sci., 69, 204–215 (2013).CrossRefGoogle Scholar
  4. 4.
    B. Rehder, K. Banh, and N. Neithalath, “Fracture behavior of pervious concretes: The effects of pore structure and fibers,” Eng. Fract. Mech., 118, 1–16 (2014).CrossRefGoogle Scholar
  5. 5.
    Y. Labadi and N. E. Hannachi, “Numerical simulation of brittle damage in concrete specimens,” Strength Mater., 37, No. 3, 268–281 (2005).CrossRefGoogle Scholar
  6. 6.
    H. Haeri, “Simulating the crack propagation mechanism of pre-cracked concrete specimens under shear loading conditions,” Strength Mater., 47, No. 4, 618–632 (2015).CrossRefGoogle Scholar
  7. 7.
    K. Ohno and M. Ohtsu, “Crack classification in concrete based on acoustic emission,” Constr. Build. Mater., 24, No. 12, 2339–2346 (2010).CrossRefGoogle Scholar
  8. 8.
    Z. Yang, W. Ren, M. Mostafavi, et al., “Characterisation of 3D fracture evolution in concrete using in-situ X-ray computed tomography testing and digital volume correlation,” in: Proc. of the 8th Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures (2013), pp. 1–7.Google Scholar
  9. 9.
    C. Baþyiðit, B. Çomak, Þ. Kýlýnçarslan and I. Serkan Üncü, “Assessment of concrete compressive strength by image processing technique,” Constr. Build. Mater., 37, 526–532 (2012).CrossRefGoogle Scholar
  10. 10.
    A. P. Jivkov, D. L. Engelberg, R. Stein, and M. Petkovski, “Pore space and brittle damage evolution in concrete,” Eng. Fract. Mech., 110, 378–395 (2013).CrossRefGoogle Scholar
  11. 11.
    W. Ren, Z. Yang, R. Sharma, et al., “Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete,” Eng. Fract. Mech., 133, 24–39 (2015).CrossRefGoogle Scholar
  12. 12.
    Z. J. Yang, X. T. Su, J. F. Chen, and G. H. Liu, “Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials,” Int. J. Solids Struct., 46, No. 17, 3222–3234 (2009).CrossRefGoogle Scholar
  13. 13.
    J. P. B. Leite, V. Slowik, and H. Mihashi, “Computer simulation of fracture processes of concrete using mesolevel models of lattice structures,” Cement Concrete Res., 34, No. 6, 1025–1033 (2004).CrossRefGoogle Scholar
  14. 14.
    C. M. López, I. Carol, and A. Aguado, “Meso-structural study of concrete fracture using interface elements. II: compression, biaxial and Brazilian test,” Mater. Struct., 41, No. 3, 601–620 (2008).CrossRefGoogle Scholar
  15. 15.
    A. Yin, X. Yang, G. Zeng, and H. Gao, “Fracture simulation of pre-cracked heterogeneous asphalt mixture beam with movable three-point bending load,” Constr. Build. Mater., 65, 232–242 (2014).CrossRefGoogle Scholar
  16. 16.
    G. Fu and W. Dekelbab, “3-D random packing of polydisperse particles and concrete aggregate grading,” Powder Technol., 133, Nos. 1–3, 147–155 (2003).CrossRefGoogle Scholar
  17. 17.
    A. Yin, X. Yang, S. Yang, and W. Jiang, “Multiscale fracture simulation of three-point bending asphalt mixture beam considering material heterogeneity,” Eng. Fract Mech., 78, No. 12, 2414–2428 (2011).CrossRefGoogle Scholar
  18. 18.
    S. F. Yang, X. H. Yang, A. Y. Yin and W. Jiang, “Three-dimensional numerical evaluation of influence factors of mechanical properties of asphalt mixture,” J. Mech., 28, No. 3, 569–578 (2012).CrossRefGoogle Scholar
  19. 19.
    A. Yin, X. Yang, C. Zhang, et al., “Three-dimensional heterogeneous fracture simulation of asphalt mixture under uniaxial tension with cohesive crack model,” Constr. Build. Mater., 76, 103–117 (2015).CrossRefGoogle Scholar
  20. 20.
    C. Zhang, X. Yang, H. Gao, and H. Zhu, “Heterogeneous fracture simulation of three-point bending plain-concrete beam with double notches,” Acta Mech. Solida Sin., 29, No. 3, 232–244 (2016).CrossRefGoogle Scholar
  21. 21.
    J. D. Clayton and J. Knap, “Phase field modeling of directional fracture in anisotropic polycrystals,” Comp. Mater. Sci., 98, 158–169 (2015).CrossRefGoogle Scholar
  22. 22.
    J. D. Clayton and J. Knap, “Phase field modeling and simulation of coupled fracture and twinning in single crystals and polycrystals,” Comput. Method. Appl. M., 312, 447–467 (2016).CrossRefGoogle Scholar
  23. 23.
    C. Miehe, F. Welschinger and M. Hofacker, “Thermodynamically consistent phase- field models of fracture: Variational principles and multi-field FE implementations,” Int. J. Numer. Meth. Eng., 83, No. 10, 1273–1311 (2010).CrossRefGoogle Scholar
  24. 24.
    M. J. Borden, C. V. Verhoosel, M. A. Scott, et al., “A phase-field description of dynamic brittle fracture,” Comput. Method. Appl. M., 217–220, 77–95 (2012).CrossRefGoogle Scholar
  25. 25.
    T. Belytschko and T. Black, “Elastic crack growth in finite elements with minimal remeshing,” Int. J. Numer. Meth. Eng., 45, No. 5, 601–620 (1999).CrossRefGoogle Scholar
  26. 26.
    I. M. Lancaster, H. A. Khalid, and I. A. Kougioumtzoglou, “Extended FEM modelling of crack propagation using the semi-circular bending test,” Constr. Build. Mater., 48, 270–277 (2013).CrossRefGoogle Scholar
  27. 27.
    G. L. Golewski, P. Golewski, and T. Sadowski, “Numerical modelling crack propagation under Mode II fracture in plain concretes containing siliceous fly-ash additive using XFEM method,” Comp. Mater. Sci., 62, 75–78 (2012).CrossRefGoogle Scholar
  28. 28.
    N. Kenny and Q. Dai, “Investigation of fracture behavior of heterogeneous infrastructure materials with extended-finite-element method and image analysis,” J. Mater. Civil. Eng., 23, No. 12, 1662–1671 (2011).CrossRefGoogle Scholar
  29. 29.
    H. Wang, C. Zhang, L. Yang, and Z. You, “Study on the rubber-modified asphalt mixtures’ cracking propagation using the extended finite element method,” Constr. Build. Mater., 47, 223–230 (2013).CrossRefGoogle Scholar
  30. 30.
    E. Piotrowska, Y. Malecot, and Y. Ke, “Experimental investigation of the effect of coarse aggregate shape and composition on concrete triaxial behavior,” Mech. Mater., 79, 45–57 (2014).CrossRefGoogle Scholar
  31. 31.
    X. F. Wang, Z. J. Yang, J. R. Yates, et al., “Monte Carlo simulations of mesoscale fracture modelling of concrete with random aggregates and pores,” Constr. Build. Mater., 75, 35–45 (2015).CrossRefGoogle Scholar
  32. 32.
    I. V. Singh, B. K. Mishra, S. Bhattacharya, and R. U. Patil, “The numerical simulation of fatigue crack growth using extended finite element method,” Int. J. Fatigue, 36, No. 1, 109–119 (2012).CrossRefGoogle Scholar
  33. 33.
    S. Kumar, I. V. Singh, B. K. Mishra, and T. Rabczuk, “Modeling and simulation of kinked cracks by virtual node XFEM,” Comput. Method. Appl. M., 283, 1425–1466 (2015).CrossRefGoogle Scholar
  34. 34.
    N. Moes, J. Dolbow, and T. Belytschko, “A finite element method for crack growth without remeshing,” Int. J. Numer. Meth. Eng., 46, No. 1, 131–150 (1999).CrossRefGoogle Scholar
  35. 35.
    M. Duflot, “A study of the representation of cracks with level sets,” Int. J. Numer. Meth. Eng., 70, No. 11, 1261–1302 (2007).CrossRefGoogle Scholar
  36. 36.
    M. Mungule and B. K. Raghuprasad, “Meso-scale studies in fracture of concrete: A numerical simulation,” Comput. Struct., 89, Nos. 11–12, 912–920 (2011).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • C. C. Zhang
    • 1
  • X. H. Yang
    • 1
    • 2
  • H. Gao
    • 1
  1. 1.School of Civil Engineering and MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory of Engineering Structural Analysis and Safety AssessmentWuhanChina

Personalised recommendations