Hyper-Viscoplastic Modelling of Clay Behaviour

Abstract

The modified cam clay (MCC) model, deduced from the unified and comprehensive behavioural framework of critical state soil mechanics (CSSM), revolutionised the understanding of the mechanical behaviour of soil, particularly clay. Although it was originally energy-based, the MCC model could not stand against the critiques of modern thermodynamics. The laws of thermodynamics (widely considered to be true) summarise the properties of energy and the feasibility of its transformation from one form to another. Constitutive models with no thermodynamic validity cannot confidently be utilised as there is no guarantee against false generation/loss of energy. Soon after its presentation, the MCC model was given a thermodynamic description known today as hyperplasticity. The hyperplastic description lifted the unnecessary normality rule and led to a family of MCC-type models with versatile yield criteria and inelastic flow directions.

In addition to the normality restriction, which results in extreme dilatancy for over-consolidated clays, the original MCC model suffers from several limitations. Perhaps, as pointed out by its founders, the most profound one can be the lack of the concept of time. In developing the MCC model, it is assumed that the state of the material does not spontaneously change with the march of time. Numerous attempts with the overwhelming use of the overstress viscoplastic theory as the vogue approach have been undertaken, but the thermodynamic consistency of most of them is under question. Moreover, no attempts with the hyperplasticty approach have rigorously addressed the issue of time-independency.

This doctoral research contributes to understanding the thermodynamically-based hyperplasticity framework and its application in the constitutive modelling of soil, particularly the viscous behaviour of clay with an orientation toward the CSSM and the isotache viscosity. In this regard, hyperplasticity formalism is laid out after providing a review of the viscous behaviour of clay with a focus on the development of the isotache concept. Next, the MCC model is integrated with the concept of time, resulting in a classical critical state hyper-viscoplastic model with similarities to the soft soil creep model. The profound impact of Ziegler’s orthogonality condition, the backbone of the hyperplasticty approach, on the critical state envelope is realised, paving the way for generalising the developed classical hyper-viscoplastic model with isotache viscosity. It is demonstrated that the typical MCC plastic-free energy could not be considered for a rate-dependent system with a single internal variable. Otherwise, by imposing Ziegler’s orthogonality condition, the uniqueness of the critical state envelope, which is the useful paradigm of critical state soil mechanics, is lost under different loading rates. A versatile force potential or dissipation rate function is constructed that provides adjustability of the location of the critical state (Spacing Ratio) while securing a unique critical state friction envelope as the useful paradigm of the CSSM to have a unified description of the mechanical behaviour of soil. Non-associated inelastic flow as an essential property of particulate frictional materials is adopted via accommodating an effective pressure-dependent shear dissipative mechanism. This later distinction lifts the unnecessarily restrictive condition of normality invoked in the original overstress and consistency viscoplasticity theories. Moreover, different frictional criteria of Drucker-Prager, Mohr-Coulomb, and Matsuoka-Nakai have been considered, and their features in terms of friction mobilisation and inelastic flow direction are explored. By realising the homothetic functioning of isotache viscosity, an emphasis has been put on the delicate practice of the effective stress ratio tensor (the deviatoric stress tensor normalised by the effective pressure) as an essential state variable of frictional material to achieve all the features mentioned previously such as adjustability of the spacing ratio and non-associativity of inelastic flow with different frictional criteria while securing the uniqueness of critical state envelope. Lastly, the efficacy of the proposed hyper-viscoplastic constitutive model is evaluated by simulating sets of triaxial and true triaxial tests conducted on the Hong Kong Marine Deposit (HKMD) and the Fujinomori clay.