Random-fractal-method-based generation of meso-model for concrete aggregates

• Fractal iteration is useful for modeling particulate materials.
• The meso-model can be generated by using fractal iteration.
• Randomly convex quadrilateral (2D space) and hexahedral shapes (3D space) define the meso-model.
• The fractal effect limited dimension, below which the fractal effect does not exist, was defined.
• A coefficient was defined for the probability of an aggregate occurring in the idealized location.

Concrete is widely applied in various industries as a composite material, and the relationship between the structure and properties of concrete has been a topic of common interest. An understanding of the composite mechanical behavior of concrete is useful for concrete mix design and damage prediction. This prompted the proposal of an analysis based on the mesoscopic approach for modeling the behavior of concrete. The quality of the finite element analysis that is used to analyze the concrete meso-model depends on the shape, spatial distribution, and orientation of the simulated aggregates. This paper describes a versatile method for simulating the meso-model of concrete aggregates with the result of the sieving test affirmed, based on the formulation of three principal hypotheses. As the aggregates in concrete resemble those generated by random fractal iteration, the particular model is assumed to be random convex quadrilateral in 2D space, and random convex hexahedral in 3D space, and several parameters influencing the modeling result are defined and devised. Prior to generating the meso-model, an idealized model is mathematically defined, with reference to the fractal method, in which several property parameters of the mix conditions of the graded aggregates are explicitly described by mathematical expressions. Based on a comparison between the numerical and experimental tests performed on the concrete under uniaxial compression, it is validated that the random fractal method could basically be used to generate the meso-model of concrete aggregates. Several modifications and prospects expected from future work are discussed.

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