The Correlation Between the Fractal Dimension and Internal Friction Angle of Different Granular Materials

This study aims to verify whether there is a relationship between the fractal dimension (Dtot) and the internal friction angle (φ) 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 differed markedly from one another in terms of shape and roundness and yet all the samples fell within the granulometric band ranging from 177 to 710 μm. A linear relationship was found between the internal friction angle and fractal dimension that can be expressed by the equation: φ =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 φ = 399.47 D1 – 381.28; in the second case, the general relationship that links the friction angle and structural fractal dimension is φ = 109.83 D2 −89.362.