A prediction model for the thermal conductivity of rubber concrete based on fractal and Fourier morphological characterization

Traditional thermal conductivity prediction models lack a mathematical interface to translate the high-dimensional heterogeneous morphology of particles into thermal engineering variables, resulting in a significant logical disconnect between “morphological characterization” and “thermal performance prediction.” This has largely hindered the large-scale application of rubber concrete (RC) in the envelope structures of green, low-carbon buildings. This paper employs a combined approach of experimental research and theoretical modeling to systematically investigate the evolution mechanism of the thermal conductivity of rubber concrete. Through controlled-variable experiments, the macroscopic response patterns of thermal conductivity as a function of rubber volume fraction (0∼50 vol%) and particle size distribution were obtained under a full-factorial design. Based on this, the polar Fourier descriptor was introduced to perform a frequency-domain decomposition of the irregular rubber particle contours, extracting morphology feature parameters and establishing a morphology correction factor with clear physical significance. Furthermore, the topography correction factor, particle size distribution, and interfacial thermal resistance correction term were coupled and incorporated into the solid skeleton component of the Sierpinski fractal carpet model, resulting in a cross-scale fractal thermal conductivity prediction model capable of reflecting the synergistic mechanism of “rubber content–particle size–topography.” Results from two-factor analysis of variance indicate that both rubber volume content and particle size have highly significant effects on the thermal conductivity, with quantitative contribution rates of 77.94% and 19.67%, respectively. The calculated values from the multiscale model show excellent agreement with 25 sets of full-factor experimental data, with deviations below 5% in 80% of the sampled groups. The research further decodes the micro-scale mechanisms driving the “specific surface area effect” and the subsequent manifestation of thermal resistance accumulation. This model eliminates the underestimation error in heat flux curvature caused by morphological simplification and reveals, at the physical level, the regulatory mechanism by which microscopic topological structures govern macroscopic heat conduction behavior.

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