Title: Fractal Analysis of Defects in Concrete under Elevated Temperatures

Author(s): Jiarong Shen, Qianjun Xu, Mingyi Liu

Publication: Materials Journal

Volume: 119

Issue: 6

Appears on pages(s): 19-33

Keywords: concrete; fractal; multifractal; defects; thermal damage; elevated temperature

DOI: 10.14359/51737183

Date: 11/1/2022

Abstract:
This study aims to quantitatively analyze the fractal and multifractal characteristics of concrete at elevated temperatures. Based on the fractal geometry theory, fractal dimensions and multi-fractal spectrum are used to characterize the fractal propagation 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 this fractal dimension. Moreover, 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(α)max), the entropy dimension, D1, the holder exponent of order zero, α0, and the signs and values of L–R may reflect the range distribution, 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 correlation 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.