A simple stress-dilatancy equation for sand

TL;DR

This paper introduces a novel fractional-order stress-dilatancy equation for sand that captures the soil's response with minimal parameters, improving constitutive modeling accuracy.

Contribution

A new fractional-order stress-dilatancy equation is analytically derived, requiring only the fractional order parameter, and validated within an existing constitutive model.

Findings

The model accurately simulates stress-dilatancy behavior of different sands.

The fractional order influences the phase transformation and state-dependent stress ratios.

Good agreement observed between simulations and experimental data.

Abstract

The stress-dilatancy relation is of critical importance for constitutive modelling of sand. A new fractional-order stress-dilatancy equation is analytically developed in this study, based on stress-fractional operators. An apparent linear response of the stress-dilatancy behaviour of soil after sufficient shearing is obtained. As the fractional order varies, the derived stress-dilatancy curve and the associated phase transformation state stress ratio shift. But, unlike existing researches, no other specific parameters, except the fractional order, concerning such shift and the state-dependence are required. The developed stress-dilatancy equation is then incorporated into an existing constitutive model for validation. Test results of different sands are simulated and compared, where a good model performance is observed.