Localised failure of geomaterials: how to extract localisation band behaviour from macro test data

The formulation and calibration of constitutive models for geomaterials require material behaviour from experiments under a wide range of triaxial loading conditions. However, failure of geomaterials usually involves localisation of deformation that leads to very strong inhomogeneous behaviour. Therefore, the experimentally measured macro (specimen) behaviour is a mix between very different responses inside and outside the localisation zone and thus should not be used as a true representation of the material responses. This paper proposes a theoretical framework that provides links between mechanical responses inside and outside the localisation band, alongside their contributions toward the overall behaviour of a specimen undergoing localised deformation. This meso–macro connection allows the quantification of behaviour inside the localisation band, which is the main source of material inelasticity, from experimentally measured specimen behaviour. Correlation between the thickness of the localisation band and its behaviour is shown, bounded by a unique stress–deformation relationship describing the behaviour of an idealised zero-thickness localisation band.