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

## TL;DR

This study investigates how grain crushing under compression and shear affects grain size distribution, revealing a power-law relation and proposing a recursive pore filling model to describe the observed behaviors.

## Contribution

It introduces a bi-linear log n - log p relation and demonstrates that grain size distribution converges to a fractal pattern with a specific exponent, supported by experimental data.

## Key findings

- Weibull model with modulus m=2 fits single grain crushing stress.
- Bi-linear log n - log p relation better describes porosity-pressure data.
- GSD converges to a power-law distribution with exponent ~-2.5.

## 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.

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Source: https://tomesphere.com/paper/1706.00910