Revisiting the existence of an effective stress for wet granular soils with micromechanics

Summary The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3‐phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization [Duriez et al. J Mech Phys Solids 99 (2017): 495‐511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small‐scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.

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“…However, a more elaborate demonstration of this argument is beyond the scope of the present study. ()…”

Section: Dimensionless Groupsmentioning

confidence: 99%

“…Furthermore, this finding complicates the extension of Terzaghi‐effective stress‐based approaches to such unsaturated cases, let alone the existence of an effective stress in 3‐phase media. ()…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of stress transmission in wet granular materials

Pouragha

Wan

Duriez

et al. 2018

Num Anal Meth Geomechanics

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“…where C(V s ) is the cumulative probability of the solid volume within the cell being smaller than V s . The limits of the integrals can now be identified using the bounds given by Equation 4:…”

Section: Deriving Pvd From Psdmentioning

confidence: 99%

“…Relevant to this issue is the degree of saturation that appears as an essential term in Bishop's expression for effective stress,() or relative distributions of the phases and related interfaces in modern micromechanical incarnations of Bishop's equation. ()…”

Section: Introductionmentioning

confidence: 99%

“…Relevant to this issue is the degree of saturation that appears as an essential term in Bishop's expression for effective stress, 1,2 or relative distributions of the phases and related interfaces in modern micromechanical incarnations of Bishop's equation. [3][4][5][6][7] The underlying hydraulic process depicted by the SWCC can be envisaged by considering a fully saturated soil undergoing drying (drainage) as the matric suction (or suction for short) due to the pressure difference between air and water pressures increases and the water is gradually squeezed out of water-saturated pores. The suction at which a water-saturated pore is invaded by air is often referred to as the pore entry pressure, which is controlled by capillary effects, and as such, the smaller the pore size, the larger the pore entry pressure.…”

Section: Introductionmentioning

confidence: 99%

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A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

Wan

Pouragha

Eghbalian

et al. 2019

Num Anal Meth Geomechanics

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Summary The paper offers an analytical determination of the hydraulic properties of an unsaturated soil with reference to its retention curve, which describes the relationship between the volumetric water content and capillarity through matric suction. The analysis combines a particulate approach focused on the physics at the pore scale, including microstructural aspects, with a probabilistic approach where the void space and grain size are considered as random variables. In the end, the soil water characteristic curve of an unsaturated granular medium along a drying path can be derived analytically based on the sole information of particle size distribution. The analysis hinges on the tessellation of a wet granular system into an assemblage of tetrahedral unit cells revealing a pore network upon which capillary physics are computed with respect to pore throat invasion by a non‐wetting fluid with evolving pendular capillary bridges. The crux of the paper is to pass from particle size probability distribution to a matching void space distribution to eventually reveal key information such as void cell and solid volume statistics. Making reasonable statistically based assumptions to render calculations tractable, the water retention curve can be readily constructed. Model predictions compare quite favourably with experimental data available for actual soils, especially in the high saturation range. Having a sound scientific basis, the model can be made amenable to address a variety of soils with a wider range of particle sizes.

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Micromechanical formulation of first‐ and second‐order works in unsaturated granular media

Eghbalian

Pouragha

Wan

2023

Num Anal Meth Geomechanics

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The current work provides a micromechanical formulation of the first-and second-order works for unsaturated granular media. For this purpose, a Representative Elementary Volume (REV) of a triphasic medium is considered, which consists of a collection of particles with the pore space in between them occupied by wetting and non-wetting fluids. By assigning a kinematics to the REV at the micro-scale, the first-and second-order works of internal forces associated with the solid phase, fluids, and the interfaces between them are derived. The formulations are presented in the most general case considering large deformations within both Eulerian and Lagrangian formalisms, while the special case of infinitesimal deformation and rotation is also investigated. With respect to classical formulations, the obtained expressions for the first-and second-order works include additional contributions related to the deformation of the interface of the two fluids, and in case of the first-order work, the change in geometry of the intersection line of the three phases. Next, we consider a special case of pendular regime at low wetting saturation, where the wetting fluid appears as a set of isolated liquid bridges formed between particle pairs. Such condition has been previously simulated via Discrete Element Method (DEM) numerical framework where the distributed capillary forces are replaced with a resultant capillary force that is added as a new contact force. We show here that using the resultant capillary force, the generated first-and second-order works in the REV are generally different from the ones produced by the distributed capillary forces, unless under special conditions.

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Revisiting the existence of an effective stress for wet granular soils with micromechanics

Cited by 21 publications

References 46 publications

Statistical analysis of stress transmission in wet granular materials

Statistical analysis of stress transmission in wet granular materials

A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

Micromechanical formulation of first‐ and second‐order works in unsaturated granular media

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