Fractal behavior of particle-size distribution during particle crushing of quartz sand and gravel

The particle breakage of granular soil under loading alters the particle-size distribution (PSD) and further affects its mechanical properties. The experimental evidence shows that any initial distribution of soil particles will tend to be fractal with the development of particle breakage. In order to reveal the transformation mechanism of fractal PSD of soil, a series of confined compression tests on a quartz sand and gravel are conducted to investigate the evolution of PSD and the behavior of particle breakage under even larger compressive stress. The fractal behavior of PSD is studied during particle crushing based on a fractal model and the measured PSD data. It is found that a fractal distribution of granular soil is caused by the growth of particle breakage, which is related to the amount of particle breakage and characterized by the increase of the values of fractal dimension. Despite the different initial distributions and particle sizes of the quartz sand and gravel, the measured PSD data that the values of fractal dimension exceed to 2.2 are shown to be strictly self-similar. Therefore the value of 2.2 can be considered as the lower limit of the fractal dimension of a fractal distribution. The Hardin’s relative breakage is larger than the Einav’s relative breakage in the same breakage state, but the rule of two indexes in response to the stress and volumetric strain is consistent. Once the PSD becomes fractal during particle crushing, the ratio of volumetric strain to relative breakage remains constant and is not much affected by either the uniformity of the initial distribution or the initial particle size. This constant ratio is a useful index for the identification of a fractal distribution, and implies that the relative breakage may be estimated from the measured volumetric strain in a test if the PSD is fractal, without having to terminate the test to analyze the particle size.