Products: ABAQUS/Standard ABAQUS/CAE
is the relationship between the volumetric flow rate per unit area of a particular wetting liquid through a porous medium and the gradient of the effective fluid pressure;
must be specified for a wetting liquid in ABAQUS/Standard for an effective stress/wetting liquid diffusion analysis (see Coupled pore fluid diffusion and stress analysis, Section 6.7.1);
is defined, in general, by Forchheimer's law, which accounts for changes in permeability as a function of fluid flow velocity; and
can be isotropic, orthotropic, or fully anisotropic and can be given as a function of void ratio, saturation, temperature, and field variables.
According to Forchheimer's law, high flow velocities have the effect of reducing the effective permeability and, therefore, “choking” pore fluid flow. As the fluid flow velocity reduces, Forchheimer's law approximates the well-known Darcy's law. Darcy's law can, therefore, be used directly in ABAQUS/Standard by omitting the velocity-dependent term in Forchheimer's law.
Forchheimer's law is written as
is the volumetric flow rate of wetting liquid per unit area of the porous medium (the effective velocity of the wetting liquid);
is the fluid saturation ( for a fully saturated medium, for a completely dry medium);
is the porosity of the porous medium;
is the void ratio;
is the wetting fluid volume in the medium;
is the void volume in the medium;
is the volume of grains of solid material in the medium;
is the volume of trapped wetting liquid in the medium;
is the total volume of the medium;
is the fluid velocity;
is a “velocity coefficient,” which may be dependent on the void ratio of the material;
is the dependence of permeability on saturation of the wetting liquid such that at ;
is the density of the fluid;
is the specific weight of the wetting liquid;
is the magnitude of the gravitational acceleration;
is the permeability of the fully saturated medium, which can be a function of void ratio (e, common in soil consolidation problems), temperature (), and/or field variables ();
is the wetting liquid pore pressure;
is position; and
is the gravitational acceleration.
Permeability can be defined in different ways by different authors; caution should, therefore, be used to ensure that the specified input data are consistent with the definitions used in ABAQUS/Standard.
Permeability in ABAQUS/Standard is defined as
Some authors refer to the definition of permeability used in ABAQUS/Standard, (units of ), as the “hydraulic conductivity” of the porous medium and define the permeability as
Permeability can be isotropic, orthotropic, or fully anisotropic. For non-isotropic permeability a local orientation (see Orientations, Section 2.2.5) must be used to specify the material directions.
For isotropic permeability define one value of the fully saturated permeability at each value of the void ratio.
|Input File Usage:|
Property module: material editor: OtherPore FluidPermeability: Type: Isotropic
For orthotropic permeability define three values of the fully saturated permeability (, , and ) at each value of the void ratio.
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Property module: material editor: OtherPore FluidPermeability: Type: Orthotropic
For fully anisotropic permeability define six values of the fully saturated permeability (, , , , , and ) at each value of the void ratio.
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Property module: material editor: OtherPore FluidPermeability: Type: Anisotropic
ABAQUS/Standard assumes that by default, meaning that Darcy's law is used. If Forchheimer's law is required (), must be defined in tabular form.
Property module: material editor: OtherPore FluidPermeability: SuboptionsVelocity Dependence
You can define the dependence of permeability, , on saturation, s, by specifying . ABAQUS/Standard assumes by default that for ; for . The tabular definition of must specify for .
Property module: material editor: OtherPore FluidPermeability: SuboptionsSaturation Dependence
The specific weight of the fluid, , must be specified correctly even if the analysis does not consider the weight of the wetting liquid (i.e., if excess pore fluid pressure is calculated).
Property module: material editor: OtherPore FluidPermeability: Specific weight of wetting liquid:
Permeability can be used only in elements that allow for pore pressure (see Choosing the appropriate element for an analysis type, Section 21.1.3).