ASSESSMENT AND EVALUATION OF FRACTAL DIMENSION OF CONCRETE FRACTURE SURFACE DIGITIZED IMAGES

Recently, a new non-destructive technique was introduced and tested by the authors [1,2] for the evaluation of fractal dimension of fractured concrete specimens. The objectives of this paper are to expand and elaborate on the advantages of the technique, to provide a basic understanding of fractal geometry and to discuss the potential application of fractal geometry to fracture in cementitious materials. This may eventually lead to a better understanding of the fracture mechanics properties of such materials. Through this technique and the utilization of an Image Analyzer System, the fracture surface was photographed and stored as an image. Different methods of fractal analysis, e.g. modified slit island technique (SIT) and two-dimensional Fourier spectral analyses (2D FFT) were employed. Fractured concrete specimens with a maximum aggregate size of 37.5 mm and a projected fracture area of 367.5 mm long and 125 mm wide were used in the study. Results of the analysis suggest that concrete fracture surface exhibit fractal characteristics over the scales considered. A scaling relation between toughness at different length scales holds only over a limited range of wave lengths. The mean fractal dimension for the modified slit island technique is D=2.21 and the mean stochastic fractal dimension for two-dimensional Fourier spectral analyses is D=2.59. Also, the digitized fracture surface images were found to mimic the actual fracture surfaces.