Local Second Gradient Models and Damage Mechanics: 1D Post-Localization Studies in Concrete Specimens

The drilling of galleries induces damage propagation in the surrounding medium and creates, around them, the Excavation Damaged Zone, EDZ. The prediction of the extension and fracture structure of this zone remains a major issue especially in the context of underground nuclear waste storage. Experimental studies on geomaterials indicate that localised deformation in shear band mode usually appears prior to fractures. Thus, the excavation damaged zone can be modelled by considering the development of shear strain localisation bands. In the classical finite element framework, strain localisation suffers of a mesh-dependency problem. Therefore, an enhanced model with a regularisation method is required to correctly model the strain localisation behaviour. Among the existing methods, we choose the coupled local second gradient model. We extend it to unsaturated conditions and we include the solid grain compressibility. Furthermore, air ventilation inside underground galleries engenders a rock-atmosphere interaction that could influence the damaged zone. This interaction has to be investigated in order to predict the damaged zone behaviour. Finally, a hydro-mechanical modelling of a gallery excavation in claystone is presented and leads to a fairly good representation of the EDZ. The main objectives of this study are to model the fractures by considering shear strain localisation bands and to investigate if an isotropic model accurately reproduces the in situ measurements. The numerical results provide information about the damaged zone extension, structure and behaviour that are in very good agreement with in situ measurements and observations. For instance, the strain localisation bands develop in chevron pat-B. Pardoen * · S. Levasseur · F. Collin Université de Liège, Département ArGEnCo, Chemin des Chevreuils 1, 4000 Liège, Belgium Tel.: +32-4-3662033 E-mail: b.pardoen@ulg.ac.be * FRIA, F.R.S.-FNRS scholarship holder tern during the excavation and rock desaturation is observed close to the gallery due to air ventilation.

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“…The internal length scale relevant for the shear band width is related to this parameter (Chambon et al 1998;Kotronis et al 2007). In Eq.…”

Section: Second Gradient Mechanical Lawmentioning

confidence: 99%

Using Local Second Gradient Model and Shear Strain Localisation to Model the Excavation Damaged Zone in Unsaturated Claystone

2014

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“…It consists of an isotropic linear relationship deduced from Mindlin (1965) that gives the 290 Jaumann double stress rateΣ ijk as a function of the micro second gradient ratė h ijk . It depends on only one constitutive elastic parameter D that represents the physical microstructure and that is related to the internal length scale relevant for the shear band width (Chambon et al, 1998;Kotronis In order to obtain a local second gradient continuum medium, the microkinematic gradient is equal to the macrodeformation gradient υ ij = F ij , leading to :…”

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confidence: 99%

Shear banding modelling in cross-anisotropic rocks

Pardoen

Seyedi²,

Collin

2015

International Journal of Solids and Structures

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Sedimentary geomaterials such as rocks frequently exhibit cross-anisotropic properties and their behaviour depends on the direction of loading with respect to their microstructure. As far as material rupture is concerned, localised deformation in shear band mode appears generally before cracks and material failure. cavation fractured zone that develops around a gallery is strongly influenced by the material anisotropy.

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“…This was soon followed with several applications for plane strain shear banding 20 , 21 , 22 , 23 mostly in soils, using constitutive models based on plasticity. Similar approaches were also recently used in the framework of damage mechanics combined with homogenization techniques by 24 , 25 , see also 26 , 27 , 28 and 29 for application in concrete structures.…”

Section: Introductionmentioning

confidence: 94%

Using a penalty term to deal with spurious oscillations in second gradient finite elements

Soufflet

Jouan

Kotronis

et al. 2018

International Journal of Damage Mechanics

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It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three points reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to one, occurring often in mode I crack propagation problems, is finally discussed.

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Local Second Gradient Models and Damage Mechanics: 1D Post-Localization Studies in Concrete Specimens

Cited by 24 publications

References 35 publications

Using Local Second Gradient Model and Shear Strain Localisation to Model the Excavation Damaged Zone in Unsaturated Claystone

Using Local Second Gradient Model and Shear Strain Localisation to Model the Excavation Damaged Zone in Unsaturated Claystone

Shear banding modelling in cross-anisotropic rocks

Using a penalty term to deal with spurious oscillations in second gradient finite elements

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