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Register a new userA Conceptual Approach to Two-Scale Constitutive Modelling For Hydro-Mechanical Coupling
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Large scale modelling of fluid flow coupled with solid failure in geothermal reservoirs or hydrocarbon extraction from reservoir rocks usually involves behaviours at two scales: lower scale of the inelastic localization zone, and larger scale of the bulk continuum where elastic behaviour can be reasonably assumed. The hydraulic conductivities corresponding to the mechanical properties at these two scales are different. In the bulk elastic host rock, the hydraulic conductivity does not vary much with the deformation, while it significantly changes in the lower scale of the localization zone due to inelastic deformation. Increase of permeability due to fracture and/or dilation, or reduction of permeability due to material compaction can take place inside this zone. The challenge is to predict the evolution of hydraulic conductivities coupled with the mechanical behaviour of the material in all stages of the deformation process. In the early stage of diffuse deformation, the permeability of the material can be reasonably assumed to be homogenous over the whole Representative Volume Element (RVE) However, localized failure results in distinctly different conductivities in different parts of the RVE. This paper establishes a general framework and corresponding field equations to describe the hydro-mechanical coupling in both diffuse and localized stages of deformation in rocks. In particular, embedding the lower scale hydro-mechanical behaviour of the localization zone inside an elastic bulk, together with their corresponding effective sizes, helps effectively deal with scaling issues in large-scale modelling. Preliminary results are presented which demonstrate the promising features of this new approach.
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Desiccation cracking in clayey soils occurs when they lose moisture, leading to an increase in their compressibility and hydraulic conductivity and hence significant reduction of soil strength. The prediction of desiccation cracking in soils is challenging due to the lack of insights into the complex coupled hydro-mechanical process at the grain scale. In this paper, a new hybrid discrete-continuum numerical framework, capable of capturing hydro-mechanical behaviour of soil at both grain and macro scales, is proposed for predicting desiccation cracking in clayey soil. In this framework, a soil layer is represented by an assembly of DEM particles, each occupies an equivalent continuum space and carries physical properties governing unsaturated flow. These particles move freely in the computational space following the discrete element method (DEM), while their contact network and the continuum mixture theory are used to model the unsaturated flow. The dependence of particle-to-particle contact behaviour on water content is represented by a cohesive-frictional contact model, whose material properties are governed by the water content. In parallel with the theoretical development is a series of experiments on 3D soil desiccation cracking to determine essential properties and provide data for the validation of mechanical and physical behaviour. Very good agreement in both physical behaviour (e.g. evolution of water content) and mechanical behaviour (e.g. occurrence and development of cracks, and distribution of compressive and tensile strains) demonstrates that the proposed framework is capable of capturing the hydro-mechanical behaviour of soil during desiccation. The capability of the proposed framework facilitates numerical experiments for insights into the hydro-mechanical behaviour of unsaturated soils that have not been possible before.
Many textbooks dealing with surface tension favor the thermodynamic approach (minimization of some thermodynamic potential such as free energy) over the mechanical approach (balance of forces) to describe capillary phenomena, stating that the latter is flawed and misleading. Yet, mechanical approach is more intuitive for students than free energy minimization, and does not require any knowledge of thermodynamics. In this paper we show that capillary phenomena can be unmistakably described using the mechanical approach, as long as the system on which the forces act is properly defined. After reminding the microscopic origin of a tangential tensile force at the interface, we derive the Young-Dupr{e} equation, emphasizing that this relation should be interpreted as an interface condition at the contact line, rather than a force balance equation. This correct interpretation avoids misidentification of capillary forces acting on a given system. Moreover, we show that a reliable method to correctly identify the acting forces is to define a control volume that does not embed any contact line on its surface. Finally, as an illustration of this method, we apply the mechanical approach in a variety of ways on a classic example: the derivation of the equilibrium height of capillary rise (Jurins law).
Charged colloidal dispersions make up the basis of a broad range of industrial and commercial products, from paints to coatings and additives in cosmetics. During drying, an initially liquid dispersion of such particles is slowly concentrated into a solid, displaying a range of mechanical instabilities in response to highly variable internal pressures. Here we summarise the current appreciation of this process by pairing an advection-diffusion model of particle motion with a Poisson-Boltzmann cell model of inter-particle interactions, to predict the concentration gradients around a drying colloidal film. We then test these predictions with osmotic compression experiments on colloidal silica, and small-angle x-ray scattering experiments on silica dispersions drying in Hele-Shaw cells. Finally, we use the details of the microscopic physics at play in these dispersions to explore how two macroscopic mechanical instabilities -- shear-banding and fracture -- can be controlled.
We develop a framework for constitutive modeling of unsaturated soils that has the embedded elements of lower scale grain to grain contacts. Continuum models developed from this framework will possess two different phases idealizing the solid grains and their interactions. As a consequence, two different constitutive relationships, corresponding to the grain to grain contact and bulk behavior, co-exist in a constitutive model and govern the response of the model. To be specific, grain to grain sliding under dry or wet condition is idealized and appears as a simple contact law embedded in a continuum framework. There is no need to define plastic strain, as this quantity naturally emerges at the continuum scale as the consequence of frictional sliding at the lower scale. In addition, the effective stress can be naturally worked out from the grain to grain contact law embedded in the model without being subjected to any interpretation. This, in our opinion, is a closer representation of unsaturated soil behavior, compared to existing continuum approaches that map everything onto a single stress-strain relationship. In this paper, the framework is presented in its simplest form that takes into account sliding on a single orientation. Grain to grain contact law with capillary effects is used for the demonstration of the concept, and the technical details behind it. Generalization of the framework for better representation of unsaturated soil behavior will also be sketched out.
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