Bilinear log n - log p relation and critical power-law grain size distribution of crushable aggregates under compression and shear

Abstract

In order to investigate the relation between the bulk plastic compression behavior and the evolution of grain size distribution (GSD) due to grain crushing under high-pressure compression and shear, we performed three types of loading experiments; single grain crushing (SGC) test, one-dimensional compression (ODC) test and rotary shear (RS) tests. The materials used are an angular mountain silica sand and a round river silica sand. The major findings are summarized as follows: (1) The SGC tests reveal that the Weibull model is successfully applied with the modulus m=2 for single grain crushing stress. (2) In the ODC tests, the relation between the applied pressure, p, and the resulting porosity, n, fits better on a bi-linear model in a log n - log p plot than in the classical e-log p plot, where e is the void ratio. (3) Both in the ODC and the RS tests, the GSD converges into a power-law (fractal) distribution with the exponent (fractal dimension) of about -2.5, which is close to the one for Apollonian sphere packing, -2.47 (Borkovec et al., 1994). (4) The proposed recursive pore filling model successfully describes the log n - log p relation in the ODC test and log n - log relation, where is the shear strain, in the RS test in a consistent manner.