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Comptes Rendus. Physique
Fracture and permeability of concrete and rocks
Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 507-525.

Part of the special issue: Prizes of the French Academy of Sciences 2019 (continued)

Continuum Damage Mechanics provides a framework for the description of the mechanical response of concrete and rocks which encompasses distributed micro-cracking, macro-crack initiation, and then its propagation. In order to achieve a consistent setting, an internal length needs to be introduced to circumvent the difficulties inherent to strain softening and to avoid failure without dissipation of energy. Upon inserting this internal length, structural size effect is captured too. This paper reviews some the progresses achieved by the author since the introduction of the nonlocal damage model in 1987. Among them, the early proposals exhibited a proper description of the inception of failure but a poor one for complete failure since it is not straightforward to model a discrete cracking with a continuum approach. Candidate solutions, e.g. by considering a variable internal length are outlined. Then, the coupled effects between material damage and material permeability are considered. Is is recalled that the permeability of the material should be indexed on the damage growth in the regime of distributed cracking. Upon macro-cracking, there is a change of regime and it is the crack opening that controls the fluid flow in the cracked material. Both regimes may be captured with a continuum damage approach, however.

La mécanique de l’endommagement fournit un cadre qui permet de décrire l’ensemble du processus de rupture d’un matériau quasi-fragile sollicité par un chargement mécanique, à savoir une micro fissuration distribuée tout d’abord, puis l’amorçage et la propagation d’une macro-fissure. Une longueur interne doit être introduite afin d’obtenir une énergie dissipée non nulle à la rupture. Cette longueur interne induit un effet de taille cohérent lui aussi avec les données expérimentales. Cet article passe en revue quelques-uns des progrès réalisés par l’auteur depuis l’introduction du modèle d’endommagement non local en 1987. Parmi ceux-ci, les premiers modèles permettaient de bien décrire l’amorçage de la rupture mais moins bien la rupture complète, qui est une chose peu naturelle dans le contexte d’une description continue d’un solide. Des solutions possibles à ce problème, par exemple en faisant varier la longueur interne, sont évoquées. Puis, les effets couplés entre l’endommagement et la perméabilité d’un matériau sont abordés. La perméabilité du matériau doit être indexée sur la croissance des dommages dans le régime de fissuration distribuée. Lors de la macro-fissuration, il y a un changement de régime et c’est l’ouverture de fissure qui contrôle l’écoulement du fluide dans le matériau fissuré. Cependant, ces deux régimes peuvent être décrits avec un formalisme unique basée, au plan mécanique, sur la mécanique de l’endommagement.

Published online:
DOI: 10.5802/crphys.38
Keywords: Damage, Cracking, Permeability, Size effect, Strain softening, Strain localisation, Internal length
Gilles Pijaudier-Cabot 1, 2

1 Institut Universitaire de France, France
2 Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, Total, LFCR, Anglet, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Gilles Pijaudier-Cabot. Fracture and permeability of concrete and rocks. Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 507-525. doi : 10.5802/crphys.38. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.38/

[1] G. R. Irwin Analysis of stresses and strains near the end of a crack traversing a plate, Trans. ASME, J. Appl. Mech., Volume 24 (1957), pp. 361-364

[2] J. F. Knott Fundamentals of Fracture Mechanics, Butterworth and Co., Delft, the Netherlands, 1973

[3] A. A. Griffith The theory of rupture, Proc. 1st Int. Conf. of Applied Mech., 1924, pp. 55-63

[4] K. Haidar; G. Pijaudier-Cabot; J. F. Dube; A. Loukili Correlation between internal length, fracture process zone and size effect in mortar and model materials, Mater. Struct., Volume 38 (2005), pp. 201-210

[5] G. I. Barenblatt The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., Volume 7 (1962), pp. 55-129

[6] D.S. Dugdale Yielding of steel sheets containing slits, J. Mech. Phys. Solids, Volume 8 (1960), pp. 100-108

[7] A. Hillerborg; M. Modeer; P. E. Petersson Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement Concr. Res., Volume 6 (1976), pp. 773-782

[8] J. Mazars; G. Pijaudier-Cabot Continuum damage theory—application to concrete, J. Eng. Mech ASCE, Volume 115 (1989), pp. 345-365

[9] G. Pijaudier-Cabot; Z. P. Bažant Nonlocal damage theory, J. Eng. Mech. ASCE, Volume 113 (1987), pp. 1512-1533

[10] Z. P. Bažant; G. Pijaudier-Cabot Nonlocal continuum damage, localization instability and convergence, Trans. ASME, J. Appl. Mech., Volume 55 (1988), pp. 287-294

[11] J. Lemaitre; J. L. Chaboche Mécanique des matériaux solides, Dunod, Paris, France, 1985

[12] D. Krajcinovic; J. G. M. Van Mier Damage and Fracture of Disordered Materials, CISM Courses and Lectures No. 410, Springer Verlag, Wien, Austria, 2000

[13] A. Delaplace; G. Pijaudier-Cabot; S. Roux Progressive damage in discrete models and consequences on continuum modeling, J. Mech. Phys. Solids, Volume 44 (1996), pp. 99-136

[14] J. Hadamard Leçons sur la propagation des ondes et les équations de l’hydrodynamique, Hermann, Paris, France, 1903

[15] Z. P. Bažant Instability, ductility and size effect in strain-softening concrete, J. Eng. Mech. ASCE, Volume 102 (1976), pp. 331-344

[16] Z. P. Bažant; G. Pijaudier-Cabot Measurement of the characteristic length of nonlocal continuum, J. Eng. Mech. ASCE, Volume 115 (1989), pp. 755-767

[17] Z. P. Bažant; J. Planas Fracture and Size Effect in Concrete and Other Quasi-brittle Materials, CRC Press, London, UK, 1998

[18] Z. P. Bažant; P. A. Pfeiffer Determination of fracture energy from size effect and brittleness number, ACI Mater. J. (1987), pp. 463-480

[19] D. Grégoire; L. Rojas-Solano; G. Pijaudier-Cabot Failure and size effect for notched and unnotched concrete beams, Int. J. Numer. Anal. Methods Geomech., Volume 37 (2013), pp. 1434-1452

[20] C. Le Bellego; J. F. Dube; G. Pijaudier-Cabot; B. Gérard Calibration of nonlocal damage model from size effect tests, Eur. J. Mech. A, Volume 22 (2003), pp. 33-46

[21] C. Giry; F. Dufour; J. Mazars Stress-based nonlocal damage model, Int. J. Solids Struct., Volume 48 (2011), pp. 3431-3443

[22] L. Rojas Solano; D. Grégoire; G. Pijaudier-Cabot Interaction based nonlocal damage model for failure in quasi-brittle materials, Mech. Res. Commun., Volume 54 (2013), pp. 56-62

[23] A. Simone; H. Askes; L. J. Sluys Incorrect initiation and propagation of failure in non-local and gradient-enhanced media, Int. J. Solids Struct., Volume 41 (2004), pp. 351-363

[24] A. Krayani; G. Pijaudier-Cabot; F. Dufour Boundary effect on weight function in nonlocal damage model, Eng. Fract. Mech., Volume 76 (2009), pp. 2217-2231

[25] Z. P. Bažant; M. Jirasek Nonlocal integral formulations of plasticity and damage: survey of recent progress, J. Eng. Mech. ASCE, Volume 128 (2002), pp. 1119-1149

[26] R. H. J. Peerlings; R. de Borst; W. A. M. Brekelmans; J. H. P. de Vree Gradient enhanced damage for quasibrittle materials, Int. J. Numer. Methods Eng., Volume 39 (1996), pp. 3391-3403

[27] G. Pijaudier-Cabot; N. Burlion Damage and localisation in elastic materials with voids, Mech. Cohesive Frict. Mater., Volume 1 (1996), pp. 129-144

[28] S. C. Cowin; J. W. Nunziato Linear elastic materials with voids, J. Elast., Volume 13 (1983), pp. 125-147

[29] S. C. Cowin; M. A. Goodman A variational principle for granular materials, Z. Angew. Math. Mech., Volume 56 (1976), pp. 281-286

[30] M. Fremond; B. Nedjar Endommagement et principe des puissances virtuelles, C. R. Acad. Sci., Paris II (1993), pp. 857-864

[31] N. Provatas; K. Elder Phase-field Methods in Material Science and Engineering, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010

[32] A. Karma; D. A. Kessler; H. Levine Phase-field model for mode III dynamic fracture, Phys. Rev. Lett., Volume 87 (2001), 045501

[33] C. Miehe; M. Hofacker; F. Welshinger A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator split, Comput. Methods Appl. Mech. Eng., Volume 199 (2010), pp. 2765-2778

[34] B. Bourdin; G. Francfort; J. J. Marigo The Variational Approach to Fracture, Springer, New York, USA, 2008

[35] C. V. Verhoosel; R. de Borst A phase-field model for cohesive fracture, Int. J. Numer. Methods Eng., Volume 96 (2013), pp. 43-62

[36] D. C. Feng; J. Y. Wu Phase-field regularised cohesive zone model and size effect of concrete, Eng. Fract. Mech., Volume 197 (2018), pp. 66-79

[37] G. Pijaudier-Cabot; C. La Borderie; T. Rees; W. Chen; O. Maurel; F. Rey-Betbeder; A. de Ferron Electrohydraulic Fracturing of Rocks, ISTE-Wiley, London, UK, 2016

[38] L. Jason; G. Pijaudier-Cabot; S. Ghavamian; A. Huerta Hydraulic behaviour of a representative structural volume for containment buildings, Nucl. Eng. Des., Volume 237 (2007), pp. 1259-1274

[39] G. Chatzigeorgiou; V. Picandet; A. Khelidj; G. Pijaudier-Cabot Coupling between progressive damage and permeability of concrete: analysis with a discrete model, Int. J. Numer. Anal. Methods Geomech., Volume 29 (2005), pp. 1005-1018

[40] Z. P. Bažant; B. H. Oh Crack band theory for fracture of concrete, Mater. Struct., Volume 16 (1983), pp. 155-177

[41] V. Lefort; O. Nouailletas; D. Grégoire; G. Pijaudier-Cabot Lattice modelling of hydraulic fracture: theoretical validation and interactions with cohesive joints, Eng. Fract. Mech., Volume 235 (2020), 107178

[42] F. Dufour; G. Pijaudier-Cabot; M. Choinska; A. Huerta Extraction of crack opening from a continuous approach using regularised damage models, Comput. Concr., Volume 5 (2008), pp. 375-388

[43] G. Pijaudier-Cabot; F. Dufour; M. Choinska Permeability due to the increase of damage in concrete: from diffuse to localised damage distributions, J. Eng. Mech. ASCE, Volume 135 (2009), pp. 1022-1028

[44] D. Grégoire; L. Rojas Solano; G. Pijaudier-Cabot Continuum to discrete transition in nonlocal damage models, Int. J. Multiscale Comp. Eng., Volume 10 (2012), pp. 567-580

[45] G. Pijaudier-Cabot; D. Grégoire A review of nonlocal continuum damage: modelling of failure?, Netw. Heterog. Media, Volume 9 (2014), pp. 575-597

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