Fractal dimension of concrete meso-structure based on X-ray computed tomography

A comprehensive understanding of the fractal properties of concrete meso-structure is important because it is associated with the complex and random mechanical behaviors of the concrete. The fractal dimensions of aggregates and cement are derived and discussed. An experimentation is devised using X-ray and computed tomography (CT) to determine the fractal dimensions of each component of the concrete meso-structure. The fractal dimension of the aggregates is constant and equal to three, whereas that of cement is a real number less than three. The definition for the fractal dimension of the concrete meso-structure was introduced based on these two observations. A comparison with the theoretical derivation indicates that the box-counting dimension of the concrete meso-structure is slightly greater than the theoretical value. Moreover, concrete with similar gradations have a similar fractal dimensions for the meso-structures.