Modelling creep in clay using the framework of hyper-viscoplasticity

Abstract

This paper addresses the derivation of creep models using the framework of hyperviscoplasticity. It demonstrates that the formulations widely used already can easily be obtained using the hyper-viscoplastic formalism. This means that existing formulations (i.e. of the flow potential) are thermodynamically sound. The key assumptions are that the free energy is only a function of elastic strains and that there is no dissipation under pure volumetric swelling (tension). The presented derivations, using the framework of hyperviscoplasticity, allows for further model development along the same lines, as presented here, with only minor modifications.

Tay creep: a multi-mechanism model for rate-dependent deformation of soils

“…Note that the projection centre that is used to define the image stress and quantify overstress can be assigned to locations other than the origin of stress space. Grimstad et al (2020) show that by assuming that the projection centre coincides with the centre of the consolidation surface, time-dependent swelling during creep following isotropic unloading can be replicated by overstress models. Similar consequences on the other hand can be achieved by augmenting the consolidation mechanism with an additional RSH mechanism that features kinematic hardening, as discussed in the following.…”

“…Appropriate characterization and modelling of these viscous behaviours have been shown to be critical for solving geotechnical engineering problems related to the long-term performance of infrastructure (Oldecop & Alonso, 2007;Karstunen & Yin, 2010;Kelly et al, 2018) and the prevention and mitigation of geohazards (Zhu & Randolph, 2011;Alonso et al, 2016). Accordingly, many rate-dependent constitutive models have been developed for soils (Adachi & Oka, 1982;di Prisco & Imposimato, 1996;Kutter & Sathialingam, 1992;Leoni et al, 2008;Yuan & Whittle, 2018;Borja et al, 2020;Wang et al, 2020;Grimstad et al, 2020Grimstad et al, , 2021, by means of overstress theory (Perzyna, 1963), isotache method (Suklje, 1957;Bjerrum, 1967), or based on thermodynamic principles (Houlsby & Puzrin, 2007) . These existing models have been found to be effective in replicating the observed viscous characteristics of soils under monotonic histories of stresses or strains.…”

Investigation of Development of the Earth Pressure Coefficient at Rest in Clay During Creep in the Framework of Hyper-Viscoplasticity

“…The notation used here follows closely the book of Houlsby and Puzrin (2006) with some minor exceptions. Grimstad et al (2020) used the force potential, z, given in Equation ( 1), to show that the conventional creep model based on the Modified Cam-Clay Model (Roscoe and Burland, 1968) can be derived within the hyper-viscoplastic formalism. They assumed that the free energy is only a function of elastic strains.…”

“…gives linear increase with strain rate, for clays, n would be slightly larger than 1 typically 163 around 1.04 (Grimstad et al, 2020)), vp v ε is the volumetric viscoplastic strain rate and vp q ε is the deviatoric viscoplastic strain rate, and M is the critical state stress ratio.…”