Table 1. Results determined by...

Table 1.

Results determined by regression analyses performed with multifractal scaling law

Samples	A	B	n	R	Remarks
Concrete* (90 days in water at 20°C)	692·53	81 380	4	0·902	$f_{c, d \to \infty} = \sqrt{A} = 26 \cdot 31 MPa$ ⁠, l_cr = 117·5, d_max = 19 mm, α = 6·18, w/c = 0·75 (Reference 2)

Concrete* (90 days at 20°C at 65% RH)	892·81	−44 556	4	0·979	$f_{c, d \to \infty} = \sqrt{A} = 29 \cdot 88 MPa$ ⁠, d_max = 19 mm, w/c = 0·75

Samples	A	B	n	R	Remarks
Concrete* (90 days in water at 20°C)	692·53	81 380	4	0·902	$f_{c, d \to \infty} = \sqrt{A} = 26 \cdot 31 MPa$ , l_cr = 117·5, d_max = 19 mm, α = 6·18, w/c = 0·75 (Reference 2)

Concrete* (90 days at 20°C at 65% RH)	892·81	−44 556	4	0·979	$f_{c, d \to \infty} = \sqrt{A} = 29 \cdot 88 MPa$ , d_max = 19 mm, w/c = 0·75

The crude experimental data were obtained from Soroka and Baum.3

The analytical expression of the multifractal scaling law (MFSL) can be written $σ_{c} = {(A + \frac{B}{d})}^{0 \cdot 5}$ (Reference 1)

A, B regression constants

d size of specimen

d_max maximum size of the coarse aggregate

f_c,d→∞ asymptotic value of compressive strength

l_cr microstructural characteristic size, $l_{cr} = \frac{B}{A} = α . d_{max}$

n number of specimens

R correlation coefficient

w/c water/cement ratio by weight

α the ratio $α = \frac{l_{cr}}{d_{max}}$

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