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Détail de l'auteur
Auteur Zdenek P. Bazant
Documents disponibles écrits par cet auteur
Affiner la rechercheAsymptotic Prediction of Energetic-Statistical Size Effect from Deterministic Finite-Element Solutions / Zdenek P. Bazant in Journal of engineering mechanics, Vol. 133 N°2 (Fevrier 2007)
in Journal of engineering mechanics > Vol. 133 N°2 (Fevrier 2007) . - 153-162 p.
Titre : Asymptotic Prediction of Energetic-Statistical Size Effect from Deterministic Finite-Element Solutions Titre original : Prévision Asymptotique d'Effet Statistique Energique de Taille des Solutions Déterministes d'Elément Finis Type de document : texte imprimé Auteurs : Zdenek P. Bazant, Auteur ; Arvid Naess, Editeur scientifique ; Novak, Drahomir ; Vorechovsky, Miroslav, Auteur Article en page(s) : 153-162 p. Note générale : Génie Mécanique Langues : Anglais (eng) Mots-clés : Size effects Stochastic models Simulation Damage Dams Dam safety Predictions Finite element method Modèles stochastiques Dommage Barrages Sûreté de barrage Prévisions Méthode d'élément fini Index. décimale : 620.1 Essais des matériaux. Défauts des matériaux. Protection des matériaux Résumé : An improved form of a recently derived energetic-statistical formula for size effect on the strength of quasibrittle structures failing at crack initiation is presented and exploited to perform stochastic structural analysis without the burden of stochastic nonlinear finite-element simulations. The characteristic length for the statistical term in this formula is deduced by considering the limiting case of the energetic part of size effect for a vanishing thickness of the boundary layer of cracking. A simple elastic analysis of stress field provides the large-size asymptotic deterministic strength, and also allows evaluating the Weibull probability integral which yields the mean strength according to the purely statistical Weibull theory. A deterministic plastic limit analysis of an elastic body with a through-crack imagined to be filled by a perfectly plastic “glue” is used to obtain the small-size asymptote of size effect. Deterministic nonlinear fracture simulations of several scaled structures with commercial code ATENA (based on the crack band model) suffice to calibrate the deterministic part of size effect. On this basis, one can calibrate the energetic-statistical size effect formula, giving the mean strength for any size of geometrically scaled structures. Stochastic two-dimensional nonlinear simulations of the failure of Malpasset Dam demonstrate good agreement with the calibrated formula and the need to consider in dam design both the deterministic and statistical aspects of size effect. The mean tolerable displacement of the abutment of this arch dam is shown to have been approximately one half of the value indicated by the classical deterministic local analysis based on material strength.
Une forme améliorée d'une formule statistique énergique récemment dérivée pour l'effet de taille sur la force des structures fragiles quasi échouant au déclenchement de fente est présentée et exploitée pour exécuter l'analyse structurale stochastique sans fardeau des simulations finies non linéaires stochastiques d'élément. La longueur caractéristique pour la limite statistique dans cette formule est déduite en considérant le cas de limitation de la partie énergique d'effet de taille pour une épaisseur de disparaition de la couche de frontière de fendre. Une analyse élastique simple de champ de contrainte fournit la force déterministe asymptotique de grande taille, et laisse également évaluer l'intégrale de probabilité de Weibull qui rapporte la force moyenne selon la théorie purement statistique de Weibull. Une analyse déterministe de limite de plasticité d'un corps élastique avec a par la fente a imaginé pour être remplie par une « colle » parfaitement en plastique est employée pour obtenir l'asymptote de petite taille de l'effet de taille. Les simulations non linéaires déterministes de rupture de plusieurs structures mesurées avec le code commercial ATENA (basé sur le modèle de bande de fente) suffisent pour calibrer la partie déterministe d'effet de taille. Sur cette base, on peut calibrer la formule statistique énergique d'effet de taille, donnant la force moyenne pour n'importe quelle taille des structures géométriquement mesurées. Les simulations non linéaires bidimensionnelles stochastiques de l'échec du barrage de Malpasset démontrent la bonne concordance avec la formule calibrée et la nécessité de considérer dans la conception de barrage les aspects déterministes et statistiques de l'effet de taille. Le déplacement tolérable moyen de la butée de ce barrage de voûte s'avère approximativement la moitié de la valeur indiquée par l'analyse locale déterministe classique basée sur la force matérielle.
DEWEY : 620.1 ISSN : 0733-9399 [article] Asymptotic Prediction of Energetic-Statistical Size Effect from Deterministic Finite-Element Solutions = Prévision Asymptotique d'Effet Statistique Energique de Taille des Solutions Déterministes d'Elément Finis [texte imprimé] / Zdenek P. Bazant, Auteur ; Arvid Naess, Editeur scientifique ; Novak, Drahomir ; Vorechovsky, Miroslav, Auteur . - 153-162 p.
Génie Mécanique
Langues : Anglais (eng)
in Journal of engineering mechanics > Vol. 133 N°2 (Fevrier 2007) . - 153-162 p.
Mots-clés : Size effects Stochastic models Simulation Damage Dams Dam safety Predictions Finite element method Modèles stochastiques Dommage Barrages Sûreté de barrage Prévisions Méthode d'élément fini Index. décimale : 620.1 Essais des matériaux. Défauts des matériaux. Protection des matériaux Résumé : An improved form of a recently derived energetic-statistical formula for size effect on the strength of quasibrittle structures failing at crack initiation is presented and exploited to perform stochastic structural analysis without the burden of stochastic nonlinear finite-element simulations. The characteristic length for the statistical term in this formula is deduced by considering the limiting case of the energetic part of size effect for a vanishing thickness of the boundary layer of cracking. A simple elastic analysis of stress field provides the large-size asymptotic deterministic strength, and also allows evaluating the Weibull probability integral which yields the mean strength according to the purely statistical Weibull theory. A deterministic plastic limit analysis of an elastic body with a through-crack imagined to be filled by a perfectly plastic “glue” is used to obtain the small-size asymptote of size effect. Deterministic nonlinear fracture simulations of several scaled structures with commercial code ATENA (based on the crack band model) suffice to calibrate the deterministic part of size effect. On this basis, one can calibrate the energetic-statistical size effect formula, giving the mean strength for any size of geometrically scaled structures. Stochastic two-dimensional nonlinear simulations of the failure of Malpasset Dam demonstrate good agreement with the calibrated formula and the need to consider in dam design both the deterministic and statistical aspects of size effect. The mean tolerable displacement of the abutment of this arch dam is shown to have been approximately one half of the value indicated by the classical deterministic local analysis based on material strength.
Une forme améliorée d'une formule statistique énergique récemment dérivée pour l'effet de taille sur la force des structures fragiles quasi échouant au déclenchement de fente est présentée et exploitée pour exécuter l'analyse structurale stochastique sans fardeau des simulations finies non linéaires stochastiques d'élément. La longueur caractéristique pour la limite statistique dans cette formule est déduite en considérant le cas de limitation de la partie énergique d'effet de taille pour une épaisseur de disparaition de la couche de frontière de fendre. Une analyse élastique simple de champ de contrainte fournit la force déterministe asymptotique de grande taille, et laisse également évaluer l'intégrale de probabilité de Weibull qui rapporte la force moyenne selon la théorie purement statistique de Weibull. Une analyse déterministe de limite de plasticité d'un corps élastique avec a par la fente a imaginé pour être remplie par une « colle » parfaitement en plastique est employée pour obtenir l'asymptote de petite taille de l'effet de taille. Les simulations non linéaires déterministes de rupture de plusieurs structures mesurées avec le code commercial ATENA (basé sur le modèle de bande de fente) suffisent pour calibrer la partie déterministe d'effet de taille. Sur cette base, on peut calibrer la formule statistique énergique d'effet de taille, donnant la force moyenne pour n'importe quelle taille des structures géométriquement mesurées. Les simulations non linéaires bidimensionnelles stochastiques de l'échec du barrage de Malpasset démontrent la bonne concordance avec la formule calibrée et la nécessité de considérer dans la conception de barrage les aspects déterministes et statistiques de l'effet de taille. Le déplacement tolérable moyen de la butée de ce barrage de voûte s'avère approximativement la moitié de la valeur indiquée par l'analyse locale déterministe classique basée sur la force matérielle.
DEWEY : 620.1 ISSN : 0733-9399 
in Journal of structural engineering > Vol. 137 N° 5 (Mai 2011) . - pp. 607-617
Titre : Can stirrups suppress size effect on shear strength of RC beams? Type de document : texte imprimé Auteurs : Yu, Qiang, Auteur ; Zdenek P. Bazant, Auteur Année de publication : 2011 Article en page(s) : pp. 607-617 Note générale : Génie Civil Langues : Anglais (eng) Mots-clés : Concrete design Size effect Shear reinforcement Failure probability RC beams Index. décimale : 624 Constructions du génie civil et du bâtiment. Infrastructures. Ouvrages en terres. Fondations. Tunnels. Ponts et charpentes Résumé : This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth d<1 m (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths d<0.5 m, 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are 10-6, 10-5, 10-4, and 10-3, whereas 10-6 is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth >1 m (39.4 in.), the size effect cannot be neglected.
DEWEY : 624.17 ISSN : 0733-9445 En ligne : http://ascelibrary.org/sto/resource/1/jsendh/v137/i5/p607_s1?isAuthorized=no [article] Can stirrups suppress size effect on shear strength of RC beams? [texte imprimé] / Yu, Qiang, Auteur ; Zdenek P. Bazant, Auteur . - 2011 . - pp. 607-617.
Génie Civil
Langues : Anglais (eng)
in Journal of structural engineering > Vol. 137 N° 5 (Mai 2011) . - pp. 607-617
Mots-clés : Concrete design Size effect Shear reinforcement Failure probability RC beams Index. décimale : 624 Constructions du génie civil et du bâtiment. Infrastructures. Ouvrages en terres. Fondations. Tunnels. Ponts et charpentes Résumé : This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth d<1 m (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths d<0.5 m, 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are 10-6, 10-5, 10-4, and 10-3, whereas 10-6 is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth >1 m (39.4 in.), the size effect cannot be neglected.
DEWEY : 624.17 ISSN : 0733-9445 En ligne : http://ascelibrary.org/sto/resource/1/jsendh/v137/i5/p607_s1?isAuthorized=no
in Journal of engineering mechanics > Vol. 138 N° 7 (Juillet 2012) . - pp.888–899.
Titre : Computation of probability distribution of strength of quasibrittle structures failing at macrocrack initiation Type de document : texte imprimé Auteurs : Jia-Liang Le, Auteur ; Jan Elias, Auteur ; Zdenek P. Bazant, Auteur Année de publication : 2012 Article en page(s) : pp.888–899. Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Finite weakest link model Strength statistics Representative volume element Structural safety Fracture Concrete structures Composites Résumé : Engineering structures must be designed for an extremely low failure probability, Pf<10−6. To determine the corresponding structural strength, a mechanics-based probability distribution model is required. Recent studies have shown that quasibrittle structures that fail at the macrocrack initiation from a single representative volume element (RVE) can be statistically modeled as a finite chain of RVEs. It has further been demonstrated that, based on atomistic fracture mechanics and a statistical multiscale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted at a point of the probability about 10−4 to 10−3. The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying gradually from the Gaussian distribution modified by a far-left Weibull tail applicable for small-size structures, to the Weibull distribution applicable for large-size structures. Compared with the classical Weibull strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution of the RVE strength makes the computation of the strength distribution of quasibrittle structures inevitably more complicated. This paper presents two methods to facilitate this computation: (1) for structures with a simple stress field, an approximate closed-form expression for the strength distribution based on the Taylor series expansion of the grafted Weibull-Gaussian distribution; and (2) for structures with a complex stress field, a random RVE placing method based on the centroidal Voronoi tessellation. Numerical examples including three-point and four-point bend beams, and a two-dimensional analysis of the ill-fated Malpasset dam, show that Method 1 agrees well with Method 2 as well as with the previously proposed nonlocal boundary method. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000396 [article] Computation of probability distribution of strength of quasibrittle structures failing at macrocrack initiation [texte imprimé] / Jia-Liang Le, Auteur ; Jan Elias, Auteur ; Zdenek P. Bazant, Auteur . - 2012 . - pp.888–899.
Mécanique appliquée
Langues : Anglais (eng)
in Journal of engineering mechanics > Vol. 138 N° 7 (Juillet 2012) . - pp.888–899.
Mots-clés : Finite weakest link model Strength statistics Representative volume element Structural safety Fracture Concrete structures Composites Résumé : Engineering structures must be designed for an extremely low failure probability, Pf<10−6. To determine the corresponding structural strength, a mechanics-based probability distribution model is required. Recent studies have shown that quasibrittle structures that fail at the macrocrack initiation from a single representative volume element (RVE) can be statistically modeled as a finite chain of RVEs. It has further been demonstrated that, based on atomistic fracture mechanics and a statistical multiscale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted at a point of the probability about 10−4 to 10−3. The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying gradually from the Gaussian distribution modified by a far-left Weibull tail applicable for small-size structures, to the Weibull distribution applicable for large-size structures. Compared with the classical Weibull strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution of the RVE strength makes the computation of the strength distribution of quasibrittle structures inevitably more complicated. This paper presents two methods to facilitate this computation: (1) for structures with a simple stress field, an approximate closed-form expression for the strength distribution based on the Taylor series expansion of the grafted Weibull-Gaussian distribution; and (2) for structures with a complex stress field, a random RVE placing method based on the centroidal Voronoi tessellation. Numerical examples including three-point and four-point bend beams, and a two-dimensional analysis of the ill-fated Malpasset dam, show that Method 1 agrees well with Method 2 as well as with the previously proposed nonlocal boundary method. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000396
in Cement and concrete research > Vol. 40 N° 2 (02 ex.) (Fevrier 2010) . - pp. 197-207
Titre : Identification of viscoelastic C-S-H behavior in mature cement paste by FFT-based homogenization method Type de document : texte imprimé Auteurs : Vít Smilauer, Auteur ; Zdenek P. Bazant, Auteur Année de publication : 2010 Article en page(s) : pp. 197-207 Note générale : Génie Civil Langues : Anglais (eng) Mots-clés : Micromechanics Creep Cement paste Microprestress Index. décimale : 691 Matériaux de construction. Pièces et parties composantes Résumé : A powerful and robust numerical homogenization method based on fast Fourier transform (FFT) is formulated to identify the viscoelastic behavior of calcium silicate hydrates (C-S-H) in hardened cement paste from its heterogeneous composition. The identification is contingent upon the linearity of the creep law. To characterize cement paste microstructure, the model developed by Bentz at the National Institute of Standards and Technology, which has the resolution of 1 μm, is adopted. Model B3 for concrete creep is adapted to characterize the creep of C-S-H in cement paste. It is found that the adaptation requires increasing the exponent of power law asymptote of creep compliance. This modification means that the rate of attenuation of creep with time is lower in C-S-H than in cement paste, and is explained by differences in stress redistribution. In cement paste, the stress is gradually transferred from the creeping C-S-H to the non-creeping components. The viscoelastic properties of C-S-H at the resolution of 1 μm were identified from creep experiments on cement pastes 2 and 30 years old, having the water–cement ratio of 0.5. The irreversible part of C-S-H creep, obtained from these old specimens at almost saturated state, is found to be negligible unless the specimens undergo drying and resaturation prior to the creep test.
DEWEY : 620.13 ISSN : 0008-8846 En ligne : http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TWG-4XP8T93-1&_user=6 [...] [article] Identification of viscoelastic C-S-H behavior in mature cement paste by FFT-based homogenization method [texte imprimé] / Vít Smilauer, Auteur ; Zdenek P. Bazant, Auteur . - 2010 . - pp. 197-207.
Génie Civil
Langues : Anglais (eng)
in Cement and concrete research > Vol. 40 N° 2 (02 ex.) (Fevrier 2010) . - pp. 197-207
Mots-clés : Micromechanics Creep Cement paste Microprestress Index. décimale : 691 Matériaux de construction. Pièces et parties composantes Résumé : A powerful and robust numerical homogenization method based on fast Fourier transform (FFT) is formulated to identify the viscoelastic behavior of calcium silicate hydrates (C-S-H) in hardened cement paste from its heterogeneous composition. The identification is contingent upon the linearity of the creep law. To characterize cement paste microstructure, the model developed by Bentz at the National Institute of Standards and Technology, which has the resolution of 1 μm, is adopted. Model B3 for concrete creep is adapted to characterize the creep of C-S-H in cement paste. It is found that the adaptation requires increasing the exponent of power law asymptote of creep compliance. This modification means that the rate of attenuation of creep with time is lower in C-S-H than in cement paste, and is explained by differences in stress redistribution. In cement paste, the stress is gradually transferred from the creeping C-S-H to the non-creeping components. The viscoelastic properties of C-S-H at the resolution of 1 μm were identified from creep experiments on cement pastes 2 and 30 years old, having the water–cement ratio of 0.5. The irreversible part of C-S-H creep, obtained from these old specimens at almost saturated state, is found to be negligible unless the specimens undergo drying and resaturation prior to the creep test.
DEWEY : 620.13 ISSN : 0008-8846 En ligne : http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TWG-4XP8T93-1&_user=6 [...]
in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.146–152.
Titre : Improved estimation of long - term relaxation function from compliance function of aging concrete Type de document : texte imprimé Auteurs : Zdenek P. Bazant, Auteur ; Mija H. Hubler, Auteur ; Milan Jirasek, Auteur Année de publication : 2013 Article en page(s) : pp.146–152. Note générale : Applied mechanics Langues : Anglais (eng) Mots-clés : Creep Concrete Stress relaxation Aging Creep analysis of structures Résumé : Based on asymptotic considerations, this paper develops an improved approximate formula for estimating the relaxation function from the given compliance function of concrete, which is considered as aging, linearly viscoelastic material. Compared with the formula developed in 1979 by Bažant and Kim, the new formula prevents any violation of the thermodynamic requirement of nonnegativeness of the relaxation function. It is significantly more accurate for long-time relaxation of concrete loaded at a young age, and, for this reason, it is particularly useful for compliance functions that correctly describe multidecade creep, which is the case for model B3 compliance function (a 1995 international RILEM recommendation) and not, for example, for the compliance functions of the American, European, Japanese, and Canadian standard recommendations, for which the benefit is smaller. The main application of the new formula is to evaluate the aging coefficient of the age-adjusted effective modulus method (AAEM) from the compliance function specified by the standard recommendation. The AAEM, developed in 1972 at Northwestern University and embodied in most standard design recommendations including those of the American Concrete Institute (ACI) and the Fédération internationale du béton (fib), provides an approximate estimate of the creep effects in structures according to the principle of superposition, which itself is a simplification neglecting nonlinear and diffusion effects. ISSN : 0733-9399 En ligne : //ascelibrary.org/doi/abs/10.1061/(ASCE)EM.1943-7889.0000339 [article] Improved estimation of long - term relaxation function from compliance function of aging concrete [texte imprimé] / Zdenek P. Bazant, Auteur ; Mija H. Hubler, Auteur ; Milan Jirasek, Auteur . - 2013 . - pp.146–152.
Applied mechanics
Langues : Anglais (eng)
in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.146–152.
Mots-clés : Creep Concrete Stress relaxation Aging Creep analysis of structures Résumé : Based on asymptotic considerations, this paper develops an improved approximate formula for estimating the relaxation function from the given compliance function of concrete, which is considered as aging, linearly viscoelastic material. Compared with the formula developed in 1979 by Bažant and Kim, the new formula prevents any violation of the thermodynamic requirement of nonnegativeness of the relaxation function. It is significantly more accurate for long-time relaxation of concrete loaded at a young age, and, for this reason, it is particularly useful for compliance functions that correctly describe multidecade creep, which is the case for model B3 compliance function (a 1995 international RILEM recommendation) and not, for example, for the compliance functions of the American, European, Japanese, and Canadian standard recommendations, for which the benefit is smaller. The main application of the new formula is to evaluate the aging coefficient of the age-adjusted effective modulus method (AAEM) from the compliance function specified by the standard recommendation. The AAEM, developed in 1972 at Northwestern University and embodied in most standard design recommendations including those of the American Concrete Institute (ACI) and the Fédération internationale du béton (fib), provides an approximate estimate of the creep effects in structures according to the principle of superposition, which itself is a simplification neglecting nonlinear and diffusion effects. ISSN : 0733-9399 En ligne : //ascelibrary.org/doi/abs/10.1061/(ASCE)EM.1943-7889.0000339
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