Issue 60

M. Vyhlídal et alii, Frattura ed Integrità Strutturale, 60 (2022) 13-29; DOI: 10.3221/IGF-ESIS.60.02

Figure 11: Microstructure of the granite–matrix interface characterized by SEM via the detection of secondary electrons (on the left) and backscattered electrons.

Figure 12: Microstructure of the marble–matrix interface characterized by SEM via the detection of secondary electrons (on the left) and backscattered electrons.

D ISCUSSION n this section, the correlations between components will be described and discussed. The Pearson’s correlation coefficient r xy , which is the covariance S XY of the two variables x and y divided by their standard deviation S XX , S YY respectively – see Eq. 8 [28], is applied to the data. In general, this correlation means a linear dependence between the variables x and y . The degree of correlation is expressed by a correlation coefficient, which can take values from  1 to +1. I



  )( x x y y x x y y   2 ) ( ( i i

)

S

XY





r

(8)



xy

2

(

)

S S

i

i

XX YY

The correlations will be divided according to their correlation coefficient value (dimensionless) into five groups – 0.00–0.30 weak, 0.31–0.70 moderate, 0.71–0.80 strong, 0.81–0.99 very strong and 1 for perfect – according to [29], [30], [31]. Negative correlations can be obtained by changing the sign to negative. Before making these detailed correlations, it should be emphasized that the mechanical fracture parameters of the rocks under study correspond very closely with their basic physical and mechanical properties. It is obvious that high bulk density, low porosity and corresponding high strength properties are reflected, for example, in high rock fracture toughness values. Regarding the correlation between the rock indirect tensile strength measured by the Brazilian test and the fracture toughness

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