Stress–dilatancy relation for Mohr–Coulomb soils following a non-associated flow rule

Abstract

Rowe's stress–dilatancy relation for frictional (cohesionless) materials has been a cornerstone of soil mechanics. The original derivation of this relationship was based on incorrect energy minimisation considerations, but the relationship was proven later by De Josselin de Jong using friction laws, and has been confirmed by a large body of experimental results. In contrast, the validity of Rowe's stress–dilatancy relation for cohesive-frictional materials, which has also been used, although not as extensively, was never verified. This paper shows that Rowe's stress–dilatancy relation for Mohr–Coulomb soils (cohesive-frictional materials) is in fact incorrect. The paper also provides a correct stress–dilatancy relationship for non-associated Mohr–Coulomb soils that have both cohesive and frictional strength components. The derivation of the relationship for cohesive-frictional soils presented in this paper relies on use of the sawtooth model together with the application of the laws of friction.