Fractal Analysis of Defects in Concrete under Elevated Temperatures

This study aims to quantitatively analyze the fractal and multi-fractal characteristics of concrete at elevated temperatures. Based on the fractal geometry theory, fractal dimensions and the multi-fractal spectrum are used to characterize the fractal propaga-tion rules of defects in concrete. The results show that the fractal dimension D (box-counting method) can quantitatively describe the overall defect propagation inside concrete materials. Thus, the more diverse the defects, the larger the fractal dimension. More-over, the fractal dimension D ' (island method) does not exhibit considerable variations with different concrete loading types and temperatures. In addition, the multifractal spectrum can reflect the defect characteristics at different levels (local and global) while varying with the defect configurations. The capacity dimension D0 (f(alpha)max), the entropy dimension D1, the holder exponent of order zero alpha 0, and the signs and values ofL-R may reflect the range distri-bution, size distribution, the degree of mass concentration, and the heterogeneity of defects within concrete, respectively. Moreover, the relationship between the fractal dimension D and the thermal damage can be expressed by a quadratic function whose correla-tion coefficient exceeds 0.99897. Therefore, the thermal damage in concrete at elevated temperatures can be quantitatively described by the quadratic function using the fractal dimension D. This study provides theoretical and experimental bases for the fractal and multifractal characteristics, and the thermal damage evolution of concrete at elevated temperatures.