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

Abstract

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.

Strain localization in the standard triaxial tests of granular materials: Insights into meso‐ and macro‐scale behaviours

“…Researchers often assumed a purely elastic behaviour for materials outside the shear band. 28,62 However, this assumption appears to be too strong for granular behaviour. Figure 16B demonstrates that both outside ME and outside MS undergo plastic deformation.…”

“…An example of such a data interpretation method from the standard triaxial experiment can be found in the recent work proposed by. 28…”

Enriching constitutive models with meso-scale behaviour: a thermodynamics-based formulation and examples

“…This is of course a simplification of a much more complex BVP so that localised failure can be tackled in a simplest possible but physically meaningful way at the constitutive level. The benefits include (i) physically meaningful correlation between behaviour and failure mode in constitutive modelling that helps minimise the use of fitting parameters [Le et al, 2018[Le et al, , 2019[Le et al, , 2017, (ii) good balance between computational efficiency and accuracy of the prediction [Nguyen et al, 2017, Nguyen et al, 2016b, and (iii) explicit links between meso-scale behaviour of the localisation band and macro (specimen) behaviour that are useful for the determination of behaviour inside the localisation band from standard triaxial tests [Le et al, 2022]. The readers can refer to our papers on the use of this two-scale approach in FEM, MPM and SPH applications [Bui and Nguyen, 2021, Le et al, 2018, 2016b, Tran et al, 2019.…”

“…This meso scale behaviour should be used for the calibration of model parameters. Details on this approach to analysing experimental data involving localised failure has been elaborated and illustrated in [Le et al, 2022]. This analysis of experimental data should be coupled with calibration procedures to obtain a good match between experiment and modelling in both pre-and post-localisation stages, including the onset and orientation of localisation band.…”

“…In this sense, it is essential to make sure the descriptions of constitutive behaviour are physically meaningful and correct first, before any attempts to improve the performance of the models to reproduce experimental results. This has been our focus over the last 10 years on bridging behaviour across a few scales in constitutive modelling and applications in geomechanics [Bui and Nguyen, 2021, Le et al, 2022, 2017, Nguyen et al, 2012, 2016a,b, Tran et al, 2019. It has been shown in these papers that adding meso scale behaviour of a localisation band in constitutive modelling of geomatetrials is not only an essential way to describe correctly post-localisation behaviour but also a good approach to incorporate behaviour at a scale lower than meso scale [Le et al, 2019].…”