A thermodynamic approach to modelling pre- and post-localisation behaviour of partially saturated soils for failure analysis using the Smoothed Particle Hydrodynamics

Abstract

Geotechnical failures usually involve changes in the state of partially saturated soils under different loading and saturation regimes resulting in significant differences in its nonlinear responses observed in experiments. The macro inelastic behaviour of partially saturated soils is intrinsically linked to the coupled mechanical and hydraulic dissipations governed by the interaction between frictional sliding, grain rearrangement and ruptures of liquid bridges and their redistributions at the grain contacts. This nature of the grain scale interaction leads to strong coupling between plastic strains and irrecoverable degree of saturation as two key internal variables in thermodynamics-based continuum modelling of partially saturated soils. This thesis focuses on the development of a new generic thermo-mechanical approach reflecting these underlying mechanisms in modelling the coupled hydro-mechanical behaviour of unsaturated soils. A generic form of dissipation potential is developed in this study to capture the interdependence of thermodynamic forces, internal variables and their rates. The proposed dissipation potential allows the derivation of constitutive models possessing a unique yield surface dependent on both stress and suction, and two evolutions rules for irrecoverable saturation and plastic strain, both of which share the same “plastic” multiplier. This feature automatically guarantees simultaneous activation and evolution of both hydraulic and mechanical yielding responses, reflecting the inseparable nature of grain-scale hydro-mechanical interactions and their effects on macro behaviour. It makes the current approach distinct from other thermodynamics-based approaches where multiple yield functions are usually needed as a consequence of adding more internal variables and a decoupling of dissipative stresses from all the rates of internal variables. The potential of the proposed generic approach is elucidated through a specific constitutive model for partially saturated soils. Two explicitly defined free energy and dissipation potentials are used for the formulation of a thermodynamically consistent critical state model encapsulating a path-dependent water retention curve. The model is able to naturally capture the interdependence between wetting-drying and loading-unloading paths without having to use a separate Soil Water Characteristic Curve (SWCC) for inelastic behaviour, as usually found in existing unsaturated soil models. The benefit of this approach is the reduction in the number of parameters and the identification and calibration of all parameters based on standard tests. Extensive analyses of coupled hydro-mechanical dissipation characteristics and experimental validation show the capabilities of the model and the advantages of the proposed thermodynamics-based approach. Hydro-mechanical coupling is also a crucial element in modelling localised failures in the form of shear banding and size effects commonly observed in partially saturated soils, given the dependence of the onset and orientation of localisation bands on material properties and different hydromechanical conditions. Deformation and saturation in such cases are inhomogeneous, with irreversible behaviours taking place inside the shear band, while the zone outside it usually undergoes reversible processes, invalidating the classical homogenous assumption implicitly adopted in all existing continuum models for partially saturated soils. This characteristic, along with properties of the mesoscale shear band (inclination, thickness) and specimen size, is essentially incorporated into a thermodynamics-based approach for localised behaviour of partially saturated soils. In this double-scale approach, enrichment terms for both kinematics and degree of saturation are used to take into account strong variations of strain and saturation degree outside and inside the shear band. The proposed formulation automatically leads to a size-dependent constitutive structure capable of describing the transition correctly from diffuse to localised stages of deformation. A bifurcation criterion taking into account a wide range of loading-unloading and wetting-drying paths is used to determine the onset of localisation and orientation of the localisation band. The promising features of the proposed double-scale formulation are illustrated using a model based on critical state soil mechanics and data in suction-controlled triaxial tests. The developed generic thermodynamics-based approach and models are used in a mixed formulation for flow through partially saturated porous media. The governing equations are implemented in a numerical code based on the Smoothed Particle Hydrodynamics (SPH) for the solutions of Boundary Value Problems involving partially saturated porous media. The adoption of the above-proposed thermodynamics-based model allows a better reflection of the intrinsic behavioural mechanisms of partially saturated soils at the constitutive level, where the inseparable relationship between plasticity and hydraulic irreversibility is captured. This distinguishes the current approach from other existing SPH studies for flow through partially saturated porous media. The performance of the SPH approach is investigated through a range of numerical examples of Boundary Value Problems under various loading and saturation conditions.