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Viscous and second gradient regularization techniques for the description of the behavior of geomaterials

Abstract : Geomaterials may exhibit timedependent behaviors as their microstructures evolve. This process may vary from a few minutes (sand) to several days or even years (soft soils). To describe this time-dependent behavior, viscoplastic models are commonly used. Other than providing an intrinsic description of the viscous behavior, rate-dependent constitutive laws are sometimes presented in the literature as a regularization technique. In this thesis, we study the possibility to use viscoplastic constitutive laws in transient problems to describe the time-dependent response of soft soils and strain localization. Analytical and numerical studies are presented and several conclusions are found based on the Hill’s criterion, the Rice’s criterion, a numerical perturbation algorithm and classical linear perturbation theory. It turns out that the use of viscoplastic models in transient problems is not able to regularize the problem. Viscoplastic models are then integrated in a higher order continuum, the second gradient model. Problems concerning the uniqueness, bifurcation and mesh dependency are examined and a classical linear perturbation analysis is presented. The combination of a second gradient model with viscoplastic laws makes possible both to regularize the problem and to take into account rate effects. Finally, the bearing capacity and progressive failure of a shallow foundation are analyzed in order to demonstrate the performance of the approach on a real case study.
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Huan Wang. Viscous and second gradient regularization techniques for the description of the behavior of geomaterials. Civil Engineering. École centrale de Nantes, 2019. English. ⟨NNT : 2019ECDN0063⟩. ⟨tel-02954012⟩

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