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The Biot model of interpenetrating continua and its role in geomechanics
Published in J.-F. Thimus, Y. Abousleiman, A.H.-D. Cheng, O. Coussy, E. Detournay, Poromechanics, 2020
One more physical nonlinearity can be considered in the poromechanics to account for plastic dilatant flow after failure of the matrix. This problem is important for a sand production, see discussion by Geilikman & Dusseault (1997).
Poroplasticity
Published in William G. Pariseau, Notes on Geoplasticity, 2019
Example problems of surface and underground excavation in wet rock demonstrate practical application where laboratory measurements and field observations were made by the author and students in cooperative research studies with mining companies and government agencies. In this regard, poromechanics applied to rock encounter a major challenge in accounting for effects of joints. In these studies and finite element models, equivalent properties serve the purpose. Practical results allow for quantifying the role of water on excavation stability under site-specific conditions. Of necessity, much detail is relegated to references. The literature concerning poromechanics is vast, and no attempt was made to do a formal review of the subject. Only the few references of direct relevance were used here.
Measuring stiffness of soils in situ
Published in Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto, Computer Methods and Recent Advances in Geomechanics, 2014
Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto
Peters, G.P., & Smith, D.W. 1998. One-dimensional contaminant transport through a consolidating soil: Application to contaminant transport through a geocomposite liner Biot conference on poromechanics. Louvain, Belgium. 481-486. Rotterdam: Balkema.
Coupled hydro-chemo-mechanical model for fault activation under reactive fluid injection
Published in European Journal of Environmental and Civil Engineering, 2023
H. Tounsi, A. Pouya, J. Rohmer
When combining the continuity equation of the fluid phase with Darcy’s law in the poromechanics framework (Pouya, 2015), the following equation can be obtained: where where is the ratio between the intrinsic permeability coefficient k and the dynamic viscosity of the fluid phase p is the sum of the hydrostatic and the injection pressure, is the volumetric component of the linearized strain tensor and is the storage coefficient of the porous matrix. The latter is function of the saturation degree considered as a function of pore pressure p, the porosity the initial porosity the isothermal compressibility coefficient of the fluid phase the Biot coefficient b and the bulk modulus of solid particles The source term r translates the hydro-mechanical coupling.
Shear banding in unsaturated geomaterials through a strong nonlocal hydromechanical model
Published in European Journal of Environmental and Civil Engineering, 2022
This section presents a strong nonlocal hydromechanical model cast in the framework of state-based peridynamics through the recently proposed hydromechanical correspondence principle (Song & Silling, 2019). State-based peridynamics is a nonlocal reformulation of classical continuum mechanics in terms of integro-differential equations. In this formulation, it is assumed that the porous media are composed of material points that interact with each other in a nonlocal region called the ‘horizon’. Passive atmospheric pressure is assumed for the pore air pressure in the mathematical formulation, as usually adopted in geotechnical engineering (Zienkiewicz et al., 1999). Thus, each material point has four degrees of freedom, e.g. three for displacement and one for pore water pressure. In line with the classic poromechanics, solid skeleton is described by Lagrangian coordinate system, and pore water is described by the relative Eulerian coordinate system with respect to the solid skeleton. Next, we first introduce the governing equations for the coupled hydromechanical process. Then we introduce the non-local constitutive laws for the solid skeleton and fluid flow through the hydromechanical correspondence principle.
Fractal nonlocal thermoelasticity of thin elastic nanobeam with apparent negative thermal conductivity
Published in Journal of Thermal Stresses, 2022
Rami Ahmad El-Nabulsi, Waranont Anukool
The role of fractal geometry in several fields of sciences and engineering including disordered thermal phenomena, heat transport phenomena in porous media, and thermophysical problems in biology and chemical physics are well-known [1]. Various studies were done in these directions, e.g. fractal thermophysical description of nano-suspensions [2], fractal geometric description of real soil structure [3] and soil porosity [4], thermal fractal analysis of powders [5], fractal approach in the kinetics of solid-gas reactions and decompositions [6,7], fractal analysis of thermal conductivity of bidispersed porous media [8], fractal description of macroporous metal foams [9], etc. In elasticity and thermoelasticity, fractals were used to model rubber-like, super-elasticity of polymers [10], mechanics of elastic materials [11,12], formulations of gradient linear and nonlinear elasticity [13,14] and study of a notched heterogeneous material [15]. Besides, fractals were used in the study of cracks in micropolar elastic solids [16], thermo-poromechanics of fractal media [17], micropolar continuum mechanics of fractal media [18] among others [19–31]. Since thermoelasticity and conductivity are correlated in particular through the nonlocal thermoelasticity beam theory (NTBT) formulated by Eringen in his nonlocal approach to small scales structures problems, it will be motivating to explore the impacts of fractals on NTBT which is an approach used to model structures showing nano-size effects. In NTBT, the tiny length scales are taken into account by introducing a characteristic length scale such as the length of the C-C bond into the constitutive relationship.