poroMechanicalLaw

A composite law giving the total stress of a porous medium from the effective stress of a sub-law and a pore pressure. The runtime type is:

poroMechanicalLaw

User Guide

What it computes

This is a small-strain law: it implements the small-strain update only, so it and its sub-law are used with a linear geometry solid model, typically poroLinearGeometry. A nonlinear geometry solid model asks for the finite-strain update, and the run stops with an error.

The sub-law, given in the effectiveStressMechanicalLaw sub-dictionary, computes the effective stress, and the law returns

sigma = sigmaEff - b*(p + p0)*I

where b is the Biot coefficient, p the pore pressure and p0 a uniform reference pressure.

The effective stress is kept as persistent state. At the first evaluation of each integration point it is seeded from the total stress already standing there:

sigmaEff = sigma + b*(p + p0)*I

and that seeded value is handed to the sub-law as its incoming stress. After each evaluation sigmaEff holds what the sub-law returned. None of the current laws reads its incoming stress, so for them the seed does not change the answer; it is there for a sub-law whose response depends on the stress already standing.

The density and the bulk modulus are those of the sub-law. rho given on this law is passed down to the sub-law when its own dictionary has none, so it can be given once, on the outer dictionary.

Model options

biotCoeff and p0 are dimensioned scalars and are dimension-checked: biotCoeff must be dimensionless and p0 must have pressure dimensions. The effectiveStressMechanicalLaw sub-dictionary holds the sub-law's type and all of its entries. Any small-strain law can be used; the tutorials use linearElasticMohrCoulombPlastic and anisotropicBiotElastic.

Coupling inputs

The pore pressure is a required scalar input, named by pressureFieldName. The manager gathers it on every evaluation, at cells, faces and boundary faces alike, and takes it from the first of:

1. a volScalarField of that name registered by another model, such as the porePressure that poroLinearGeometry solves for;
2. the case directory given for it in inputCaseDirectories, or as <name>caseDirectory (e.g. porePressurecaseDirectory), read at the current time; see the framework README;
3. a file of that name in the current time directory, or failing that in 0.

If none exists the run stops with an error. The field is looked up on the solid mesh only.

State variables

The sub-law's state lives in a child state named effectiveStressMechanicalLaw.

Persistent state is written at each write time in two forms. For viewing, each variable is written as a volField named after the variable (sigmaEff, sigmaEffSeeded, and the sub-law's own, such as activeYield for linearElasticMohrCoulombPlastic), covering every material that declares it and zero elsewhere, and without dimensions; this is done for the cell-centred topology only, and a name another model has registered is skipped. For restart, the state is written as it is held, in files named <material>_<topology>_<variable>, e.g. soil_cellCentredIntegrationPointTopology_sigmaEff, with the sub-law's variables as <material>_<topology>_effectiveStressMechanicalLaw_<variable>. Only the restart files are read back.

Tangents

The pore pressure term does not depend on the strain, so the tangents are the sub-law's, unchanged: whichever of scalar, scalarDeviatoric, fourthOrder and fourthOrderFiniteDifference the sub-law supports.

Mixed displacement-pressure formulation

The law does not declare a volumetric split, whatever the sub-law: it returns the total stress only. A mixed displacement-pressure formulation therefore refuses to start with it, and so does hydrostatic stress smoothing (solvePressureEqn), wherever in the material's dictionary it is set.

Differences from the legacy law

• pressureFieldRegion is no longer read: the pore pressure is taken from the solid mesh, and can also come from a file in the time directory or from another case directory. Unused legacy entries are ignored rather than reported.
• p0 is a reference pressure added to p, as before, and still has no field form.
• biotCoeff and p0 are dimension-checked.
• The effective stress is persistent state, seeded per integration point and restarted with the rest of the state; the legacy law held separate sigmaEff and sigmaEfff fields.
• solvePressureEqn and pressureSmoothingScaleFactor inside the sub-law dictionary no longer smooth the sub-law's hydrostatic stress: the request is found by the solid model and refused. regionName is no longer read.
• The sub-law's tangent is passed through; the legacy law had none.

Example

From the stripFooting tutorial, with poroLinearGeometry:

planeStress     no;

mechanical
(
    soil
    {
        type            poroMechanicalLaw;
        rho             rho [1 -3 0 0 0 0 0] 7854;
        biotCoeff       biotCoeff [0 0 0 0 0 0 0] 1.0;

        effectiveStressMechanicalLaw
        {
            type            linearElasticMohrCoulombPlastic;
            E               E [ 1 -1 -2 0 0 0 0 ] 20e6;
            nu              nu [0 0 0 0 0 0 0] 0.3;
            frictionAngle   frictionAngle [0 0 0 0 0 0 0] 30;
            dilationAngle   dilationAngle [0 0 0 0 0 0 0] 0;
            cohesion        cohesion [1 -1 -2 0 0 0 0] 1e5;
        }
    }
);

Optional entries, with their defaults:

        p0                  p0 [1 -1 -2 0 0 0 0] 0;
        pressureFieldName   porePressure;

Tutorials

• solids/poroelasticity/stripFooting
• solids/poroelasticity/suctionCaission
• solids/poroelasticity/rodAndSeabed: with an anisotropicBiotElastic sub-law