Study of the Fractal and Multifractal Scaling Intervening in the Description of Fracture Experimental Data Reported by the Classical Work: Nature 308, 721–722(1984)

Table 1

Main features of the fractal: log𝐴=𝑐₀+𝑐₁log𝑃 and multifractal (parabolic): log𝐴=𝑐_𝑜+𝑐₁log𝑃+𝑐₂(log𝑃)² scalings of the parameters 𝐴, 𝑃 of the slit islands of fracture surfaces reported by Figure  1 [29].

The type of the log𝐴=𝑓(log𝑃) correlation (scaling)	Regression line; (fractal scaling)	Parabolic correlation; (multifractal scaling)
𝑐0	−1.776	−1.5686
𝑐1	1.6265 (average slope)	+2.39074
𝑐2	0	−0.16965
Correlation coefficient	0.9655	0.9792
Average relative error (%) for all 41 studied slit islands	7.540%	7.346%
Average relative error for the 6 extreme (first 3 and last 3) representative points of Figure  1 [24, 25]	10.134%	8.733%
Apparent fracture surface fractal dimension: 𝐷𝑀=1+slope	2.6265	2.4487 ⋯ 3.0514
Fracture surface fractal dimension according to our considerations (this work): 𝐷𝑠=1+2/slope	2.23	1.975 ⋯ 2.380