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Summary: Fingered infiltration of a wetting fluid through a porous network is a widely studied subject in the field of fluid mechanics. However, the effect of this heterogeneous percolation on the response of granular materials, in particular fine‐grained soils, is a poorly investigated and badly understood topic which deserves deep analysis, considering, among others, possible applications in soil remediation and underground energy storage. This paper presents a first application of a new formulation of unsaturated poromechanics based on a phase field approach that allows to characterize on the one hand the occurrence of fingering hydraulic instabilities and on the other one to capture their effects on the irreversible, and possible unstable, deformation of the solid skeleton. The envisaged application concerns the behavior of fine‐grained soils whose dilatant/contractant behavior is more and more attracting the interest of the scientific community both in the fields of experimental research and numerical modeling. [ABSTRACT FROM AUTHOR]

This paper focuses on the influence of sample preparation on the multi scale structure of sand-clay mixtures. Three different protocols to mix silica and kaolinite were tested in the laboratory to identify the one providing the most homogeneous microstructure. From the macroscopic to the microscopic scales, optical observation, 3D X-ray tomography, 2D scanning electron microscopy (SEM) and 2D environmental scanning electron microscopy (ESEM) were carried out on wet and dry samples. This paper provides a first insight on the mechanisms of sand clay mixing from the cm to μm scale. Preliminary results demonstrate that the microstructures of the samples prepared by the three procedures have similar macroporosities based on imaging techniques. However, the preparation which consists in mixing the sand firstly, followed by water and clay provides a more homogeneous microstructure with silica grains well-surrounded by an oriented clay layering, probably due to a geometrical effect. Understanding the formation of the oriented clay layering brings microstructural features that will help to better explain the grain displacements and rotations during direct shear tests, the behaviour at the pile sand-clay soil interfaces and to formulate sand clay microstructure models.

In this contribution a new model for partially saturated porous media is presented, within the framework of gradient poromechanics, based on a phase field approach. While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of the surface tension between the wetting and the non-wetting fluid, occupying the pore space, is stated considering a regularized phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. This approach provides similar results as those of the model based on the concept of specific interfacial area. The dependence of the free energy on the gradient of the saturation also implies that Darcy law must be extended to become a fourth order partial differential equation.

This paper aims to investigate the hydro-mechanical behaviour of a loosely compacted embankment during an inundation event. This study is based on the results of a centrifuge test carried out on a small-scale embankment model made of an artificially compacted clay–sand mixture. The wetting-induced displacements are analyzed and interpreted by means of a constitutive model adapted to unsaturated conditions. The numerical predictions are presented in terms of time evolutions of settlements, as well as, spatial distributions of vertical displacements. These profiles are compared to those experimentally observed in order to validate the predictive capabilities of the model on a boundary value problem. Moreover, the stress paths followed by elementary soil elements located at different depths are analyzed to emphasize the stress and strain variations due to capillary rise.

The mixing order of silica sand, clay (kaolinite), and water controls the microstructure of resulting artificial soil samples. Most homogeneous microstructures can be achieved by applying the mixing order "sand-water-clay." The following methods were used to validate this statement: (1) optical observation, (2) X-ray tomography, (3) scanning electron microscopy, and (4) Mercury intrusion porosimetry. For all samples, clays are mainly organized in a homogeneous matrix but are also dispersed heterogeneously in micrometer-sized layers surrounding sand particles, particularly where sand grains show a greater roughness. At water contents ≥1.5 w L , the microstructures are visually similar from the mm to μm scale whatever mixing order is used. However, for water contents lower than 1.5 w L , the mixing order controls the distribution of the clay particles. This paper proposes a motivated choice of a preparation protocol of artificial clayey materials to be used in laboratory experiments. It might contribute to better understanding and modeling grain movements and arrangements in artificial muds, used for instance in underground mining, foundation settlement, hydraulic containment, road construction, soil stabilization, and in natural soils in the occurrence of soil liquefaction, industrial brick manufacturing, and in studying shear processes in tectonic fault zones. [ABSTRACT FROM AUTHOR]

Granular soils subjected to seepage flow may suffer suffusion, ie, a selective internal erosion. Extending the classical approach of poromechanics, we deduce a new form of the Clausius‐Duhem inequality accounting for dissipation due to suffusion, and we deduce restrictions on the constitutive laws of the soil. We suggest (a) a possible coupling between the seepage forces and the suffusion kinetics and (b) an extension of an existing elastoplastic model for the skeleton mechanical behaviour. Numerical integrations of the elastoplastic model are carried out under drained axisymmetric triaxial and oedometric conditions. As a result, we prove that the extended model is able to qualitatively reproduce the suffusion induced strains and the strength reduction experimentally observed. Predictions on the oedometric behaviour of suffusive soils are also provided. [ABSTRACT FROM AUTHOR]

Biphasic flow propagating through a granular medium can be established as an unstable infiltration and can be precursors of nonnegligible deformations. Capturing such infiltration through the lens of a high‐resolution camera, full‐field strain maps are determined via digital image correlation (DIC). However, this image analysis technique is based on the fundamental assumption of grey level conservation between the reference and deformed images. In this paper, DIC algorithm is recalled, and suitable controlling parameters are introduced to improve the accuracy of the output displacement fields and to remove the grey level variations induced by an air‐water flow percolating through a Fontainebleau sand. In addition, an in‐depth investigation on the full‐field volumetric strain maps is conducted in order to extract the hidden relationship between the front propagation and the strains evolution. [ABSTRACT FROM AUTHOR]

Flows involving immiscible displacement of one fluid by another in a porous media are known to destabilize and form fluid fingering. When the non-wetting fluid is a highly mobile gas (air) and the wetting fluid is an in-compressible liquid (water) the classical macroscopic theory is unable to describe the fingered flow. In Part I of this study we have introduced a model that interprets the mixture of wetting and non-wetting fluids within the pore space as a single saturating non-uniform pore fluid characterized by a phase field parameter, which is considered to be the saturation degree of the wetting fluid. In the current study we present a linear stability analysis of its solutions which describe both imbibition and drainage. The analysis sheds light on the sensitivity of the flow stability on injection flux, imposed pressure gradient and initial saturation degree. Two-dimensional numerical simulation results are as well presented which verify the stability analysis and reveal the rich structure of the fluid fingering realized by this model. While these results are found to be in qualitative agreement with experimental observations, they also warrant further experimentation to explore the additional features predicted by the model. • Linear stability analysis of a phase field model for partially saturated porous media. • Conditional growth of imposed transverse and longitudinal perturbations. • Two-dimensional simulations depicting fingered flow both in imbibition and drainage. [ABSTRACT FROM AUTHOR]

A model describing immiscible fluid–fluid displacements in partially saturated porous media is presented. This is based on a phase field approach that interprets the mixture of wetting (liquid water) and non-wetting (air) fluids within the pore space as a single saturating non-uniform pore fluid characterized by a phase field parameter, which is considered to be the saturation degree of the wetting fluid. While the standard retention curve provides for the retention properties of the pore walls, a Cahn–Hilliard like double-well energy is employed to describe the possible co-existence of the immiscible fluid phases. An enhanced description of the macroscopic surface tension between the fluid phases is obtained naturally within the phase field framework due to a regularization that depends on the spatial gradient of the water content. A generalized Darcy's law is used to describe dissipation due to fluid flow driven by the gradient of a generalized chemical potential. Thus, in the context of soil hydrology this model is interpreted as an extension to the classical Richards equation governing the spatio-temporal evolution of the phase field parameter. Employing a convex–concave flux function it is shown, using one-dimensional analysis, that both imbibition and drainage fronts can be modeled in this phase field framework. The non-monotonicities observed in the resolved solutions are explained using a combination of asymptotic matching techniques and dynamical systems analysis. • Phase field model of partially saturated porous media. • Fourth-order extended Richards equation for drainage and imbibition processes. • TW-solutions describing the propagation of drainage and imbibition fronts. • Analysis of the shock structure of the TW-solutions. [ABSTRACT FROM AUTHOR]

A fluid-filled cylindrical cavern of circular cross section in a homogeneous infinite fluid-saturated polycristalline (salt) formation subjected to isotropic stress is set under internal pressure that differs from the confining pressure. The fluid in the cavern and in the mixture is treated as ideal and the solid as elastic. The state of stress that is established as a consequence of an outside pressure and a cavern pressure serves as the reference state. Perturbing the cavern pressure induces small changes in the solid and fluid densities and in the solid displacements. We compute these and other fields as functions of the radial distance from the cavern center and show that, depending on the relative stress levels, the (salt) formation experiences either a dilatation or a compaction that is highly concentrated in a thin boundary layer near the cavern wall and tapers off as one moves away from it. The amount of dilatation/compaction of the cylindrical wall and the thickness of the boundary layer grow with an increase in the difference between the referential confining pressure and the pressure in the cavern. [ABSTRACT FROM AUTHOR]

We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase. [ABSTRACT FROM AUTHOR]

The appearance of the fluid-rich phase in saturated porous media under the effect of an external pressure is investigated. For this purpose we introduce a two field second gradient model allowing the complete description of the phenomenon. We study the coexistence profile between poor and rich fluid phases and we show that for a suitable choice of the parameters nonmonotonic interfaces show up at coexistence.