Simplest deformation models of a fluid-saturated poroelastic medium

Bocharov, Oleg; Rudyak, V. Ya.; Seryakov, Alexander

doi:10.1134/s1062739114020057

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…The most famous representatives of this approach are analytical macroscopic models of poroelasticity whose theoretical basis was first discussed by Biot [14,15]. They were further developed by taking into account a range of scales in real materials, damage accumulation, dilatancy and their influence on the skeleton elastic properties and pore fluid pressure [16][17][18][19][20][21][22]. The computational methods based on a discrete representation of the medium are widely used to describe media where fracture on different scales is a factor determining a mechanical response.…”

Section: Brief Description Of the Hybrid Cellular Automaton Methodsmentioning

confidence: 99%

Theoretical Study of Physico-mechanical Response of Permeable Fluid-Saturated Materials Under Complex Loading Based on the Hybrid Cellular Automaton Method

Dimaki

Shilko

2020

Springer Tracts in Mechanical Engineering

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We give a brief description of the results obtained by Prof. Sergey G. Psakhie and his colleagues in the field of theoretical studies of mechanical response, including fracture, of permeable fluid-saturated materials. Such materials represent complex systems of interacting solid and liquid phases. Mechanical response of such a medium is determined by processes taking place in each phase as well as their interaction. This raised a need of developing a new theoretical approach of simulation of such media—the method of hybrid cellular automaton that allowed describing stress-strain fields in solid skeleton, transfer of a fluid in crack-pore volume and influence of fluid pressure on the stress state of the solid phase. The new method allowed theoretical estimation of strength of liquid-filled permeable geomaterials under complex loading conditions. Governing parameters controlling strength of samples under uniaxial loading and shear in confined conditions were identified.

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Section: Brief Description Of the Hybrid Cellular Automaton Methodsmentioning

confidence: 99%

Theoretical Study of Physico-mechanical Response of Permeable Fluid-Saturated Materials Under Complex Loading Based on the Hybrid Cellular Automaton Method

Dimaki

Shilko

2020

Springer Tracts in Mechanical Engineering

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“…Besides, the mapping is continuous in the domain C 0,0 (Q). Moreover, the mapping U is a completely continuous mapping: any continuous function is transformed to a function from the class C α,α/2 (Q) satisfying the inequality (9). Consequently, all conditions of the Schauder fixed-point theorem are satisfied for our mapping U .…”

Section: Lemma 3 Let ϕ and S Be The Classical Solution Of The Problementioning

confidence: 98%

Model isothermal internal erosion of soil

Papin

Sibin

2016

J. Phys.: Conf. Ser.

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Abstract. The process of internal erosion in a three-phase saturated soil is studied. The problem is described by the equations of mass conservation, Darcy's law and the equation of capillary pressure. The original system of equations is reduced to a system of two equations for porosity and water saturation. In general, the equation of water saturation is degenerate. The degenerate problem in a one-dimensional domain and one special case of the problem in a two-dimensional domain are solved numerically using a finite-difference method. Existence and uniqueness of a classical solution of a nondegenerate problem is proved. IntroductionVarious models of internal erosion are used for describing applied problems of the formation of cavities under dam reservoir, the destruction of the wellbore walls as a result of soil erosion, the suffusion craters formation on surface topography. Evaluation of suffusion removal is also a relevant problem in many environmental works. Advanced models of internal erosion are based on approaches of mechanics of multiphase media [1,2,3,4]. These models are intended to describe more detailed picture of the movement of water and fluidized solid particles mixture in soil. Precisely, the determination of a velocity field, porosity, water saturation and pressure of each phase.These models include phase transition and use filtration approximation. The basic equations are mass conservation law for each phase and Darcy's law for moving phases. This system of equations is similar in structure to the system of Masket-Leverett equations of two-phase filtration for immiscible fluids; for detailed mathematical theory description see [5,6]. We did not find any study related to the justification problem of the system of equations with porosity to be determined, except a few special cases [7,8].The key points of the problem are the degeneracy of the equations of the obtained solution (relative phase permeability coefficients k 0i can be equal to 0 if saturation of the ith phase s i ≤ 0 in the equation (2)) and the unknown porosity of soil. The problem in this formulation is very difficult to study analyticaly, especially it is necessary to justify the physical principles of maximum for the porosity and the water saturation (0This approach is also used in the study of two-phase filtration, dissociation of hydrates in natural layers with iced parts, heat and mass transfer in freezing or melting soil. Formulation of the problemWe consider a mathematical model of internal erosion of soil in a finite domain Q ⊂ R n (where Q and n will be specified further). Saturated soil is a three-phase porous medium [1] consisting of water (i = 1, the first phase), fluidized solid particles (i = 2, the second phase) and solid

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“…The model was not justified. This was done later in [11], [12], where particular solutions were derived. O.B.…”

Section: Introductionmentioning

confidence: 99%

On the existence of global solution of the system of equations of liquid movement in porous medium

Tokareva

Papin²

2021

E3S Web Conf.

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The initial-boundary value problem for the system of one-dimensional isothermal motion of viscous liquid in deformable viscous porous medium is considered. Local theorem of existence and uniqueness of problem is proved in case of compressible liquid. In case of incompressible liquid the theorem of global solvability in time is proved in Holder classes. A feature of the model of fluid filtration in a porous medium considered in this paper is the inclusion of the mobility of the solid skeleton and its poroelastiс properties. The transition from Euler variables to Lagrangian variables is used in the proof of the theorems.

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Simplest deformation models of a fluid-saturated poroelastic medium

Cited by 10 publications

References 6 publications

Theoretical Study of Physico-mechanical Response of Permeable Fluid-Saturated Materials Under Complex Loading Based on the Hybrid Cellular Automaton Method

Theoretical Study of Physico-mechanical Response of Permeable Fluid-Saturated Materials Under Complex Loading Based on the Hybrid Cellular Automaton Method

Model isothermal internal erosion of soil

On the existence of global solution of the system of equations of liquid movement in porous medium

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