A solution to transient seepage in unsaturated porous media

Num Anal Meth Geomechanics

Ehlers

2016

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SUMMARYThe complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi-static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one-dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non-dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated.

Section: Numerical Versus Analytical Resultsmentioning

confidence: 99%

One‐dimensional dynamics of saturated incompressible porous media: analytical solutions and influence of inertia terms

Num Anal Meth Geomechanics

Ehlers

2016

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“…Additionally, the intrinsic density variation is assumed to be very small and, hence, its gradient can be neglected. More comprehensive models can be found in other studies …”

Section: Porous Media Equationsmentioning

confidence: 99%

“…More comprehensive models can be found in other studies. 28,29,31 In the following, the order of the tensor is indicated by the number of underdots. For instance, ȧ , ä , ȧ̇̇, and ä̈are (different) tensors of first, second, third, and fourth order, respectively-Confusion is avoided because of the underdots.…”

Section: Porous Media Equationsmentioning

confidence: 99%

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FDM solutions to linear dynamics of porous media: Efficiency, stability, and parallel solution strategy

Numerical Meth Engineering

et al. 2017

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Summary This paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation. The method is named parallel‐lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations. As a result, the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved. The other advantage of the scheme is the fulfilment of the inf‐sup stability condition. The scheme is developed to solve porous media formulations derived from the theory of porous media. Both the u‐p and u‐v‐p formulations are considered (u: displacement of solid, p: pressure of liquid, and v: velocity of liquid). Several simulations are performed to demonstrate the capabilities of the method.

“…In some cases, Biot's theory can be equally applied [5][6][7][8][9]. While Biot's theory is derived from a more intuitive and phenomenological approach, the TPM [2,3] is more extensive and is consistently derived from continuous mechanics, thermodynamics, the theory of mixtures and the concept of volume fractions [10][11][12][13][14]. Biot's theory has, perhaps, the greatest acceptance in geophysics and geotechnical engineering [15]; however, for the case of materials with solids and liquids only (fully liquid saturation), the two theories are identical [16] as long as the following conditions are satisfied:…”

Section: Introductionmentioning

confidence: 99%

FDM and FEM solutions to linear dynamics of porous media: stabilised, monolithic and fractional schemes

Numerical Meth Engineering

2016

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SUMMARYA number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method, and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf-sup (Ladyženskaja-Babuška-Brezzi) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and finite element method algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so-called up and uvp formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes.