Scattering of Harmonic Waves by a Circular Cavity in a Porous Medium: Complex Functions Theory Approach

Gatmiri, Behrouz; Eslami, Hashem

doi:10.1061/(asce)1532-3641(2007)7:5(371)

Cited by 35 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Íåñìîòðÿ íà îòìå÷åííûå äîñòîèíñòâà ÌÃÝ, âîçìîaeíîñòü ìîäåëèðîâàíèÿ ïîðîóïðóãîé äèíàìèêè ñ åãî ïîìîùüþ ãëàâíûì îáðàçîì îïðåäåëÿåòñÿ íàëè÷èåì ñîîòâåòñòâóþùèõ ãðàíè÷íîèíòåãðàëüíûõ óðàâíåíèé (ÃÈÓ) è ôóíäàìåíòàëüíûõ ðåøåíèé. Ôóíäàìåíòàëüíûå ðåøåíèÿ è ÃÈÓ äèíàìè÷åñêîé òåîðèè ïîðîóïðóãîñòè ïîëó÷åíû â ñòàòüÿõ [19][20][21][22]; â [23][24][25][26] ðåàëèçîâàíû ðàçëè÷íûå âàðèàíòû ãðàíè÷íî-ýëåìåíòíûõ ñõåì äëÿ ðåøåíèÿ çàäà÷ ïîðîäèíàìèêè è ïðåäñòàâëåíû ðåçóëüòàòû ÷èñëåííûõ ýêñïåðèìåíòîâ. Ðåçóëüòàòû ãðàíè÷íî-ýëåìåíòíîãî ìîäåëèðîâàíèÿ äèíàìèêè ïîðîóïðóãèõ ïîëóïðîñòðàíñòâ ïðèâåäåíû â ïóáëèêàöèÿõ [27][28][29][30][31].…”

Section: ââåäåíèåunclassified

Bem Analysis of Wave Propagation in Poroviscoelastic Layered Halfspace and Halfspace With Cavity

Ipatov

2020

PSP

View full text Add to dashboard Cite

The paper is dedicated to the wave propagation a porous-viscoelastic material. As a mathematical model of a fully saturated poroelastic medium, we consider the Biot model with four basic functions – pore pressure and skeleton movements. The Biot model is supplemented by the principle of elastic and viscoelastic reaction correspondence. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is spplied to describe the viscoelastic properties of a skeleton. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. To solve boundary integral equations, the boundary element method is performed. Quadrangular eight-node biquadratic elements are used for boundary element discretization. Numerical integration is carried out according to Gaussian quadrature formulas using algorithms for lowering the order and eliminating features. To obtain a solution in explicit time, numerical inversion of the Laplace transform is applied based on the Durbin algorithm with a variable frequency step. This study is a development of the existing boundary-element technique for solving problems on layered porous-elastic half-spaces. This will allow you to take into account the heterogeneity of the soil in depth. The problem of the action of a vertical force in the form of the Heaviside function on the surface of a layered porous-elastic half-space and a half-space with a cavity is considered. Variants of a homogeneous and heterogeneous half-space are considered. Under the model of heterogeneity we understand the piecewise homogeneous solid. The responses of the boundary displacements on the surface of the half-space are presented. The effect of the viscoelastic material model parameter on the dynamic response of displacements is demonstrated. It is established that the viscosity parameters have a significant effect on the nature of the distribution of parameters of wave processes.

show abstract

Section: ââåäåíèåunclassified

Bem Analysis of Wave Propagation in Poroviscoelastic Layered Halfspace and Halfspace With Cavity

Ipatov

2020

PSP

View full text Add to dashboard Cite

show abstract

“…,). Then the results were compared with the results of isotropic problem (the results of Mei et al [3], Gatmiri and Eslami [4]). When the problem reduces to the isotropic case, again three values and one value are found but they are changed to the isotropic results as 1 (the same as 1 of P1 wave in the isotopic case), 2 ∼ = 0 (extremely small), 3 (the same as 2 of P2 in the isotopic case) and (the same as of SV wave in the isotopic case).…”

Section: Verificationmentioning

confidence: 99%

“…In the previous researches, the isotropic condition was considered for porous media. For this case, it can be mentioned as the works by Mei et al [3] using a boundary layer approximation, and Gatmiri and Eslami [4] using complex variables method. Also Gatmiri [5] proposed a finite element (FE) solution for the problem concerning to the harmonic wave loading in quasi-static condition.…”

Section: Introductionmentioning

confidence: 99%

Two formulations for dynamic response of a cylindrical cavity in cross‐anisotropic porous media

Eslami

Gatmiri

2009

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

SUMMARYTwo formulations for calculating dynamic response of a cylindrical cavity in cross-anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u-w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations.

show abstract

“…The comprehensive state-of-the-art review by Gatmiri and Kamalian (2002), Gatmiri and Nguyen (2005), Seyrafian et al (2006) and Gatmiri and Eslami (2007) provides clearly presented information on the dynamic fundamental solution applied to the soil and the porous media.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional transient thermo-hydro-mechanical fundamental solutions of multiphase porous media in frequency and time domains

Gatmiri

Maghoul

Duhamel

2010

International Journal of Solids and Structures

View full text Add to dashboard Cite

International audienceIn this paper, the closed form two-dimensional fundamental solutions for a non-isothermal unsaturated deformable porous medium have been derived for a symmetric polar domain in both Laplace transform and time domains. The governing differential equations of the non-isothermal unsaturated soil consist of equilibrium, moisture, air and heat transfer equations including the suction effect, temperature effect and dissolved air in water. The derived fundamental solution has been verified mathematically by comparison with the previously presented corresponding fundamental solutions in three limiting cases including the steady-state thermo-hydro-mechanical, steady-state hydro-mechanical and elastostatic fundamental solutions. Also these 2D kernel functions are tested in comparison with a finite element method (FEM

show abstract

Scattering of Harmonic Waves by a Circular Cavity in a Porous Medium: Complex Functions Theory Approach

Cited by 35 publications

References 12 publications

Bem Analysis of Wave Propagation in Poroviscoelastic Layered Halfspace and Halfspace With Cavity

Bem Analysis of Wave Propagation in Poroviscoelastic Layered Halfspace and Halfspace With Cavity

Two formulations for dynamic response of a cylindrical cavity in cross‐anisotropic porous media

Two-dimensional transient thermo-hydro-mechanical fundamental solutions of multiphase porous media in frequency and time domains

Contact Info

Product

Resources

About