Analytical 3D transient elastodynamic fundamental solution of unsaturated soils

Ashayeri, Iman; Kamalian, Mohsen; Jafari, Mohammad Kazem; Gatmiri, Behrouz

doi:10.1002/nag.978

Cited by 13 publications

(4 citation statements)

References 41 publications

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“…In addition, Ashayeri et al . [] developed a closed‐form solution for the displacement of the soil skeleton, and liquid and gas pressures in unsaturated soils under Heaviside step loadings neglecting the effects of the dissipation of the shear wave in the medium. The aforementioned analytical methods, in general, came across with several constructive ideas, which may inspire some ongoing research seeking a precise solution for 1D consolidation for unsaturated geomaterials.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

Fatahi

Khabbaz

2013

Num Anal Meth Geomechanics

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SUMMARYThis paper introduces an exact analytical solution for governing flow equations for one-dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one-way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two-way drainage system where both soil ends allow free dissipation of pore-air and pore-water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first-order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated.

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Section: Introductionmentioning

confidence: 99%

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

Fatahi

Khabbaz

2013

Num Anal Meth Geomechanics

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“…The solution of an initial boundary‐value problem must accommodate governing conservation and constitutive laws, along with relevant boundary and initial conditions. Closed‐form analytical solutions are available for unsaturated flow in one dimension (Ashayeri et al, 2011; Shan et al, 2012; Wu et al, 2012). However, they are severely handicapped by numerous simplifying assumptions, making them unsuitable for general‐purpose problems.…”

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confidence: 99%

Finite Deformation and Fluid Flow in Unsaturated Soils with Random Heterogeneity

Song

Borja

2014

Vadose Zone Journal

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The first law of thermodynamics suggests an energy‐conjugate relationship among degree of saturation, suction stress, and density of an unsaturated porous material. Experimental evidence affirms that this constitutive relationship exists and that the water retention curves are dependent on the specific volume or density of the material. This constitutive feature must be incorporated into the mathematical formulation of boundary‐value problems involving finite deformation. We present a fully coupled hydromechanical formulation in the finite deformation range that incorporates the variation of degree of saturation with the Kirchhoff suction stress and the Jacobian determinant of the solid‐phase motion. A numerical simulation of solid deformation–fluid flow in unsaturated soil with randomly distributed density and degree of saturation demonstrates an intricate but well‐established coupling of the hydromechanical processes. As deformation localizes into a persistent shear band, we show that bifurcation of the hydromechanical response manifests itself not only in the form of a softening behavior but also through bifurcation of the state paths on the water‐retention surface.

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“…Analytical solutions were developed for the response of saturated and nearly saturated porous media under plane strain condition by Ulker and Rahman . An analytical transient 3D fundamental solution is presented in Ashayeri et al , . Gajo and Denzer provided the finite element implementation for dynamic analyses of saturated porous media at large strains with compressible solid and fluid constituents.…”

Section: Introductionmentioning

confidence: 99%

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

Cao

Sanavia

Schrefler

2016

Numerical Meth Engineering

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In this paper, the non-isothermal elasto-plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo-hydro-mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the Hybrid Mixture Theory. A computationally efficient reduced formulation of the macroscopic balance equations which neglects the relative acceleration of the fluids and the convective terms is adopted. The modified effective stress state is limited by the Drucker-Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non-linear set of equations is solved by the Newton method with a monolithic approach.Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. {\color{red}A numerical study of the regularization properties of the finite element model is shown and discussed.} A non-isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed

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Analytical 3D transient elastodynamic fundamental solution of unsaturated soils

Cited by 13 publications

References 41 publications

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

Finite Deformation and Fluid Flow in Unsaturated Soils with Random Heterogeneity

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

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