Trajectories of loose sand samples in the Phase Space of Soil Mechanics

TL;DR

This paper investigates the behavior of loose sand samples in the soil mechanics phase space, revealing sigmoid-shaped trajectories and suggesting a singularity at the critical point, which enhances understanding of soil behavior under stress.

Contribution

It introduces the analysis of loose sand trajectories in the phase space, highlighting their sigmoid shape and the potential singularity at the critical state, which was not extensively reported before.

Findings

Loose sand trajectories are sigmoid-shaped in phase space.

A singularity at the critical point is suggested.

Trajectories depend on initial density and stress paths.

Abstract

In general, the evolution of soil submitted to simple stress-strain paths is characterised using the 3d phase space (v,p',q) i.e. (specific volume, mean intergranular pressure, deviatoric stress q. When uniaxial compressions is performed at constant lateral pressure p' or at constant mean pressure p', one finds that all trajectories end up at a line of attracting point called the critical-state line via the surface of Roscoe or of Hvorslev depending if the initial volume is the loosest possible one (at a given p') or densest. Trajectories of weakly dense samples are not often reported in this phase space. We find here that they shall present some sigmoid shape as it can be found from soil mechanics argument. This seems to indicate that Roscoe's surface shall exhibit a singularity at the critical point.