THE CORRELATION BETWEEN THE FRACTAL DIMENSION AND INTERNAL FRICTION ANGLE OF DIFFERENT GRANULAR MATERIALS

U. GORI  and M. MARI

ABSTRACT : This study aims to verify if there is a relationship between the fractal dimension (Dtot) and the internal friction angle (j) of sandy materials while also considering the mineralogical composition of these materials. Geotechnical and morphometric tests were therefore carried out on both natural and artificial samples, which differ markedly from one another in terms of shape and roundness, yet all the samples fell within the granulometric band ranging from 177 to 710 mm. A linear relationship was found between the internal friction angle and fractal dimension that can be expressed by the equation: j = 237.89 Dtot - 218.2. In addition, a relationship was also found between the internal friction angle and the textural fractal dimension (D1), as well as the structural fractal dimension (D2) of the analysed samples. In the first case, the two parameters are linked by the linear equation j = 399.47 D1 - 381.28; in the second case, the general relationship that links the friction angle and structural fractal dimension is j = 109.83 D2 - 89.362, but if the carbonatic samples are excluded, D2 shows a stronger correlation with the value of the internal friction angle using a parabolic function: j = 2114.9 D22 - 4387.3 D2 + 2300.3 . In fact, the carbonatic samples were found under the regression line in all the cases considered, and therefore a graph was only plotted for the siliceous or mixed samples.

Key Words: fractal dimension; grain shape; granular materials; internal friction angle (IGC: D03/D06)