On Jaky constant of oedometers, Rowe's relation and incremental modeling

TL;DR

This paper combines incremental modeling and Rowe's relation to analyze oedometer tests, revealing that the stress ratio approaches an asymptotic value consistent with the Jaky constant, depending solely on the friction angle.

Contribution

It introduces a combined approach linking incremental modeling and Rowe's relation to derive the Jaky constant from first principles.

Findings

The stress ratio B converges to an asymptotic value ko.

The asymptotic ko depends only on the friction angle.

The derived ko aligns well with experimental Jaky constant.

Abstract

It is recalled that stress-strain incremental modelling is a common feature of most theoretical description of the mechanical behaviour of granular material. An other commonly accepted characteristics of the mechanical behaviour of granular material is the Rowe's relation which links the dilatancy K to the ratio B of vertical to lateral stress during a test at constant lateral stress, i.e. B=(1+M)(1+K). We combine these two features and extract an incremental pseudo-Poisson coefficient which varies with the stress ratio . We solve the oedometric-test case, starting from isotropic sample and stress, for which the vertical stress is increased continuously. It is found that the stress ratio B evolves towards an asymptotic value ko which depends on the friction angle only. It is shown that this asymptotic value ko compares well with the experimental fit known as the Jaky constant.