Quasi-static mechanics of granular materials

TL;DR

This textbook provides a comprehensive analysis of the quasi-static rheology of granular materials, covering theoretical models, typical tests, and behaviors like dilatancy and liquefaction, with a focus on macroscopic and micro-macro relationships.

Contribution

It introduces an isotropic incremental model with a stress-dependent pseudo Poisson coefficient that aligns well with experimental data, simplifying the understanding of granular behavior.

Findings

Good agreement of the model with experimental trends

Description of cyclic behaviors and liquefaction mechanisms

Prediction of the v-log(p) law for critical state

Abstract

This textbook in French describes the rheology of granular materials in the quasi static regime at a macroscopic scale. It starts defining cohesion, friction and the Coulomb approach, from the large-strain range. Then it focuses on the range of small and intermediate deformation when the medium can dilate if it is dense; different specific typical tests (oedometric, constant pressure, constant volume) are defined, the behaviours they lead are carefully described and their dependences upon initial density recalled. Roles of friction and dilatancy are exemplified and their link with the deviatoric stress too. "Natural" "phase space" is defined, which is (specific volume, mean pressure, axial or deviatoric stress). Then the "critical" state, the "characteristic" state and the Rowe's law of dilatancy are defined, and the previous behaviours analysed in term of plastic deformation, showing that these behaviours obey a specific rule of dissipation. An isotropic incremental modelling is then proposed and studied, with a pseudo Poisson coefficient that evolves with the stress ratio. It shows a good agreement with experimental trends, while the theory keeps simple, which describes in particular the isochoric compression and the oedometric compression correctly. Cyclic behaviours are then described, and their link with soil liquefaction, with a peculiar attention to the role of stress ratio. Basic concepts on micro-macro passage are given, starting with a theoretical approach leading to an exponential distribution of forces ; then it proposes a theory for the compaction of the medium with pressure, that predicts the v-log(p) law for the critical state.