Detailed Description

template<int DisplacementDim>
class MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >

Extended Permeability model based on Olivella&Alonso.

This property must be a medium property, it computes the permeability in dependence of the strain

The base model was proposed in [2] and it was further investigated in [31] . This extended Version features three orthotropic fracture planes.

The model takes the form of

\[ \mathbf{k} = k_\text{m} \mathbf{I} + \sum \limits_{i=1}^3 \frac{b_i}{a_i} \left( \frac{b_i^2}{12} - k_\text{m} \right) \left( \mathbf{I} - \mathbf{M}_i \right) \]

with

\[ \mathbf{M}_i = \vec{n}_i \otimes \vec{n}_i \]

and

\[ b_i = b_{i0} + \Delta b_i \\ \Delta b_i = a_i \langle \mathbf{\epsilon} : \mathbf{M}_i - \varepsilon_{0i} \rangle \]

where

\( k_\text{m} \)	permeability of undisturbed material
\( b_i \)	fracture aperture of each fracture plane
\( b_{i0} \)	initial aperture of each fracture plane
\( a_i \)	mean fracture distance of each fracture plane
\( \vec{n}_i \)	fracture normal vector of each fracture plane
\( \varepsilon_{i0} \)	threshold strain of each fracture plane

Definition at line 57 of file OrthotropicEmbeddedFracturePermeability.h.

#include <OrthotropicEmbeddedFracturePermeability.h>

Inheritance diagram for MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >:

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Collaboration diagram for MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >:

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Public Types
using	SymmetricTensor

Public Member Functions
	OrthotropicEmbeddedFracturePermeability (std::string name, std::vector< double > const &mean_fracture_distances, std::vector< double > const &threshold_strains, Eigen::Matrix< double, 3, 3 > const fracture_normals, ParameterLib::Parameter< double > const &intrinsic_permeability, ParameterLib::Parameter< double > const &fracture_rotation_xy, ParameterLib::Parameter< double > const &fracture_rotation_yz, double const jacobian_factor)

void	checkScale () const override

PropertyDataType	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override

PropertyDataType	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override

Public Member Functions inherited from MaterialPropertyLib::Property
virtual	~Property ()

virtual PropertyDataType	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

virtual PropertyDataType	value () const

virtual PropertyDataType	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	d2Value (VariableArray const &variable_array, Variable const variable1, Variable const variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
	Default implementation: 2nd derivative of any constant property is zero.

virtual void	setProperties (std::vector< std::unique_ptr< Phase > > const &phases)
	Default implementation:

void	setScale (std::variant< Medium , Phase , Component * > scale)

template<typename T >
T	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

template<typename T >
T	value () const

template<typename T >
T	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	d2Value (VariableArray const &variable_array, Variable const &variable1, Variable const &variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

Private Attributes
Medium *	_medium = nullptr

std::vector< double > const	_a

std::vector< double > const	_e0

Eigen::Matrix< double, 3, 3 > const	_n

ParameterLib::Parameter< double > const &	_k

ParameterLib::Parameter< double > const &	_phi_xy

ParameterLib::Parameter< double > const &	_phi_yz

double const	_jf

Additional Inherited Members
Protected Attributes inherited from MaterialPropertyLib::Property
std::string	name_

PropertyDataType	value_
	The single value of a property.

PropertyDataType	dvalue_

std::variant< Medium , Phase , Component * >	scale_

Member Typedef Documentation

◆ SymmetricTensor

template<int DisplacementDim>

using MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::SymmetricTensor

Initial value:

 Eigen::Matrix<
        double,
        MathLib::KelvinVector::kelvin_vector_dimensions(DisplacementDim), 1>

Definition at line 80 of file OrthotropicEmbeddedFracturePermeability.h.

Constructor & Destructor Documentation

◆ OrthotropicEmbeddedFracturePermeability()

template<int DisplacementDim>

MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::OrthotropicEmbeddedFracturePermeability	(	std::string	name,
		std::vector< double > const &	mean_fracture_distances,
		std::vector< double > const &	threshold_strains,
		Eigen::Matrix< double, 3, 3 > const	fracture_normals,
		ParameterLib::Parameter< double > const &	intrinsic_permeability,
		ParameterLib::Parameter< double > const &	fracture_rotation_xy,
		ParameterLib::Parameter< double > const &	fracture_rotation_yz,
		double const	jacobian_factor )

Definition at line 20 of file OrthotropicEmbeddedFracturePermeability.cpp.

    : _a(mean_fracture_distances),
      _e0(threshold_strains),
      _n(fracture_normals),
      _k(intrinsic_permeability),
      _phi_xy(fracture_rotation_xy),
      _phi_yz(fracture_rotation_yz),
      _jf(jacobian_factor)
{
    name_ = std::move(name);
}

References MaterialPropertyLib::name, and MaterialPropertyLib::Property::name_.

Member Function Documentation

◆ checkScale()

template<int DisplacementDim>

void MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::checkScale ( ) const

overridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 42 of file OrthotropicEmbeddedFracturePermeability.cpp.

{
    if (!std::holds_alternative<Medium*>(scale_))
    {
        OGS_FATAL(
            "The property 'OrthotropicEmbeddedFracturePermeability' is "
            "implemented on the 'media' scale only.");
    }
}

References OGS_FATAL.

◆ dValue()

template<int DisplacementDim>

PropertyDataType MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::dValue	(	VariableArray const &	variable_array,
		Variable const	variable,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property derivative value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

The default implementation of this method only returns the property value derivative without altering it.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 91 of file OrthotropicEmbeddedFracturePermeability.cpp.

{
    if (variable != Variable::mechanical_strain)
    {
        OGS_FATAL(
            "OrthotropicEmbeddedFracturePermeability::dValue is implemented "
            "for derivatives with respect to strain only.");
    }
 
    auto const eps = MathLib::KelvinVector::kelvinVectorToTensor(
        std::get<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
            variable_array.mechanical_strain));
    double const k = std::get<double>(fromVector(_k(t, pos)));
    double const _b0 = std::sqrt(12.0 * k);
 
    double const phi_xy = std::get<double>(fromVector(_phi_xy(t, pos)));
    double const phi_yz = std::get<double>(fromVector(_phi_yz(t, pos)));
    auto const rotMat_xy = Eigen::AngleAxisd(phi_xy, Eigen::Vector3d::UnitZ());
    auto const rotMat_yz = Eigen::AngleAxisd(phi_yz, Eigen::Vector3d::UnitX());
 
    MathLib::KelvinVector::KelvinMatrixType<DisplacementDim> result =
        MathLib::KelvinVector::KelvinMatrixType<DisplacementDim>::Zero();
 
    for (int i = 0; i < 3; i++)
    {
        Eigen::Vector3d const n_i = rotMat_yz * (rotMat_xy * _n.col(i));
        Eigen::Matrix3d const M = n_i * n_i.transpose();
        double const e_n = (eps * n_i).dot(n_i.transpose());
        double const H_de = (e_n > _e0[i]) ? 1.0 : 0.0;
        double const b_f = _b0 + H_de * _a[i] * (e_n - _e0[i]);
 
        result += H_de * (b_f * b_f / 4.0 - k) *
                  MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
                      Eigen::Matrix3d::Identity() - M) *
                  MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(M)
                      .transpose();
    }
    return Eigen::MatrixXd(_jf * result);
}

References MaterialPropertyLib::fromVector(), MathLib::KelvinVector::kelvinVectorToTensor(), MaterialPropertyLib::mechanical_strain, MaterialPropertyLib::VariableArray::mechanical_strain, and OGS_FATAL.

◆ value()

template<int DisplacementDim>

PropertyDataType MaterialPropertyLib::OrthotropicEmbeddedFracturePermeability< DisplacementDim >::value	(	VariableArray const &	variable_array,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 55 of file OrthotropicEmbeddedFracturePermeability.cpp.

{
    auto const eps = MathLib::KelvinVector::kelvinVectorToTensor(
        std::get<MathLib::KelvinVector::KelvinVectorType<DisplacementDim>>(
            variable_array.mechanical_strain));
    double const k = std::get<double>(fromVector(_k(t, pos)));
    double const _b0 = std::sqrt(12.0 * k);
 
    double const phi_xy = std::get<double>(fromVector(_phi_xy(t, pos)));
    double const phi_yz = std::get<double>(fromVector(_phi_yz(t, pos)));
    auto const rotMat_xy = Eigen::AngleAxisd(phi_xy, Eigen::Vector3d::UnitZ());
    auto const rotMat_yz = Eigen::AngleAxisd(phi_yz, Eigen::Vector3d::UnitX());
 
    Eigen::Matrix3d result = Eigen::Vector3d::Constant(k).asDiagonal();
 
    for (int i = 0; i < 3; i++)
    {
        Eigen::Vector3d const n_i = rotMat_yz * (rotMat_xy * _n.col(i));
        double const e_n = (eps * n_i).dot(n_i.transpose());
        double const H_de = (e_n > _e0[i]) ? 1.0 : 0.0;
        double const b_f = _b0 + H_de * _a[i] * (e_n - _e0[i]);
 
        // The H_de factor is only valid as long as _b0 equals
        // std::sqrt(12.0 * k), else it has to be dropped.
        result += H_de * (b_f / _a[i]) * ((b_f * b_f / 12.0) - k) *
                  (Eigen::Matrix3d::Identity() - n_i * n_i.transpose());
    }
 
    return result.template topLeftCorner<DisplacementDim, DisplacementDim>()
        .eval();
}