Determining periodic representative volumes of concrete mixtures based on the fractal analysis

Sebsadji, Soumia Kheira; Chouicha, Kaddour

doi:10.1016/j.ijsolstr.2012.05.017

Cited by 39 publications

(19 citation statements)

References 27 publications

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“…Kim et al [38] showed that typical dense-graded Superpave asphalt concrete mixtures with a nominal maximum aggregate size of 19 mm could be characterized by their effective non-damaged properties with RVE size of 50 mm. Sebsadji and Chouicha [39] suggested that, for laboratory concrete testing, standard sample size should be at least 3.5 times the nominal maximum aggregate size in the case of ordinary concrete mixtures.…”

Section: Introductionmentioning

confidence: 99%

Representative volume element estimation for desorption isotherm of concrete with sliced samples

Rougelot

Burlion

et al. 2015

Cement and Concrete Research

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Section: Introductionmentioning

confidence: 99%

Representative volume element estimation for desorption isotherm of concrete with sliced samples

Rougelot

Burlion

et al. 2015

Cement and Concrete Research

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“…10 a is a parameter depending on some properties of concrete [3], the slope of the best-fitted line representing the relationship between C E and i  is the fractal dimension . DF One can achieve same results whatever the method of concrete composition (see [1,3,4]), that enables us to assume PSDs of real concrete mixtures as fractals, which allows identifying them by knowing two parameters, DF value and the total particle size range / . d D…”

Section: Introductionmentioning

confidence: 98%

“…Concrete mixtures can be considered as fractal objects because their corresponding solid particle size distributions (PSD), since they must be as close as possible to one of the ideal grading curves, they can be transformed to "grain number C E " vs "grain size i  " distributions, following a fractal power law of type 3,4]. To get a better understanding of this, we give an example.…”

Section: Introductionmentioning

confidence: 99%

Fractal dimension of concrete mix gradation: a quantitative parameter for some concrete properties

Sebsadji

Chouicha

2020

MATEC Web Conf.

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This study is based upon the fractal feature of ideal Particle Size Distributions (PSD) suggested by numerous concrete mix designs, i.e. ideal PSD can be shown to be equivalent to a power law distributions EC(ϕi) ∝ ϕi− DF, EC(ϕi) is the number of grains of size greater than ϕi, and DF is a nonwhole number called fractal dimension. This fact allows us to analyze the solid skeleton of a concrete mix (all solid components of the mixture) as a fractal structure, thus to determine some of physical properties of the concrete mixture. For DF ranging from 2.5 to 3, and based upon many parameters of the concrete mix (as the granular range, the volumetric fraction of solids in the concrete mixture…), analytical formulas have been proposed relating DF and some properties of the concrete in the solid state. The required properties are the coarse-to-fine aggregate ratio, the fineness modulus of the sand fraction, the average grain size and volume of the fine fraction in the concrete mix. The focus of this research is to develop formulas by which concrete properties can be predicted knowing the concrete mix gradation, i.e. the mix design method used.

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“…[22]), analytical approaches (e.g. [13,23]) and statistical-numerical methods (e.g. [24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

“…They have estimated the RVES by comparing the magnitude of the non-local term and the portion of the equation that relates ensemble average stresses and strains through a constant "overall" modulus tensor. Sebsadji and Chouicha [23] have proposed an analytical approach, using fractal analysis, to obtain the RVES for concrete mixtures. Kanit et al [24] have performed a statistical analysis of the numerical examples in order to quantify the RVES for two-phase three-dimensional Voronoii mosaic in the case of linear elasticity and thermal conductivity.…”

Section: Introductionmentioning

confidence: 99%

Determination of the size of the Representative Volume Element (RVE) for the simulation of heterogeneous polymers at finite strains

Mirkhalaf

Pires

Simões

2016

Finite Elements in Analysis and Design

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a b s t r a c tThe definition of the size of the Representative Volume Element (RVE) is extremely important for the mechanics and physics of heterogeneous materials since it should statistically represent the microstructure of the material. In the present contribution, a methodology based on statistical analysis and numerical experiments is proposed to determine the size of the RVE for heterogeneous amorphous polymers subjected to finite deformations. The approach is applied to Rubber Toughened Polystyrene (RT-PS) composed by a two phase random micro-structure. Different micro-structural samples with two different percentages of rubbery particles, namely 10% and 15%, inside the micro-structure are studied. Periodic boundary conditions (PBC) are enforced to the RVE due to their fast convergence to the theoretical/effective solution when the RVE size increases. The Finite Element Method (FEM) is used in combination with mathematical homogenization to obtain the macro-stress. Two criteria are proposed for the RVE size determination. The proposed statistical-numerical approach is general and easy to use, when compared to the previously proposed approaches, and covers other criteria available in the literature.

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Determining periodic representative volumes of concrete mixtures based on the fractal analysis

Cited by 39 publications

References 27 publications

Representative volume element estimation for desorption isotherm of concrete with sliced samples

Representative volume element estimation for desorption isotherm of concrete with sliced samples

Fractal dimension of concrete mix gradation: a quantitative parameter for some concrete properties

Determination of the size of the Representative Volume Element (RVE) for the simulation of heterogeneous polymers at finite strains

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