On the fundamental nature of the state parameter

Abstract

The state parameter ψ is widely used for soil characterisation and as a controlling parameter in modern constitutive understanding of soil, but there remains a perception that the control of soil strength by ψ is merely that of a correlation. This perception possibly stems from ψ having been introduced from ‘principles’ of critical state theory rather than derived, which is now rectified. It is shown that the control of limiting dilatancy by the state parameter (and thus soil strength through stress–dilatancy) is a formal mathematical consequence of Casagrande's canonical characterisation linking void ratio to soil constitutive behaviour. This formal consequence is independent of soil type, being applicable across the spectrum from clays to sands. Three dimensionless and familiar soil properties are involved in addition to those characterising the critical state locus: M_tc, N and X. The framework is kinematic, with no constitutive model: it is a constraint on models. Example data are shown for sands, silts and clays to illustrate the independence of the theory from geological descriptors.