Detailed Description

A strain dependent bimodal water retention model.

It is based on the van Genuchten model.

The equation is as follows

\[S_{e} = \left((e_{m}+a \Delta e) \left[\frac{1}{((\frac{p_{c}}{p_{b}})^{n}+1)}\right]^{m} + (e_{M} - a \Delta e) \left[\frac{1}{((\frac{p_{c}}{p_{{b,M}}})^{n} +1)}\right]^{n} \right) \frac{1}{e}\]

with effective saturation defined as \(S_{e}=\frac{S-S_r}{S_{max}-S_r}\), where \(S_r\) and \(S_{max}\) are the residual saturation and the maximum saturation, respectively. The exponent \(m \in (0,1)\) is the same as in the van Genuchten equation ( see SaturationVanGenuchten). In the original work another exponent \(n\) is used, but usually set to \(n = 1 / (1 - m)\), and also in this implementation. The pressure scaling parameter \(p_{b}\) is added by the user and is the scaling parameter of the micropores. The scaling parameter of the macropores can be calculated as follows \(p_{b,M} = p_{b} d_{diff}\) The total void ratio and the void ratio of the micropores are \(e_0\) and \(e_m\). Another scaling factor \(a\) scales the effect of the strain

The changing void ratio is calculated as \(\Delta e = -\frac{(1-e)\epsilon_{vol}}{e}\), with \(\epsilon_{vol}\) as the volumetric strain. The result is then clamped between the residual and maximum liquid saturations.

Definition at line 48 of file SaturationVanGenuchtenWithVolumetricStrain.h.

#include <SaturationVanGenuchtenWithVolumetricStrain.h>

Inheritance diagram for MaterialPropertyLib::SaturationVanGenuchtenWithVolumetricStrain:

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Collaboration diagram for MaterialPropertyLib::SaturationVanGenuchtenWithVolumetricStrain:

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Public Member Functions
	SaturationVanGenuchtenWithVolumetricStrain (std::string name, double const residual_liquid_saturation, double const residual_gas_saturation, double const exponent, double const p_b, double const e_0, double const e_m, double const a, double const d_diff)

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
double const	S_L_res_

double const	S_L_max_

double const	m_

double const	p_b_

double const	e_0_

double const	e_m_

double const	a_

double const	d_diff_

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_

Constructor & Destructor Documentation

◆ SaturationVanGenuchtenWithVolumetricStrain()

MaterialPropertyLib::SaturationVanGenuchtenWithVolumetricStrain::SaturationVanGenuchtenWithVolumetricStrain	(	std::string	name,
		double const	residual_liquid_saturation,
		double const	residual_gas_saturation,
		double const	exponent,
		double const	p_b,
		double const	e_0,
		double const	e_m,
		double const	a,
		double const	d_diff )

Definition at line 22 of file SaturationVanGenuchtenWithVolumetricStrain.cpp.

    : S_L_res_(residual_liquid_saturation),
      S_L_max_(1. - residual_gas_saturation),
      m_(exponent),
      p_b_(p_b),
      e_0_(e_0),
      e_m_(e_m),
      a_(a),
      d_diff_(d_diff)
{
    name_ = std::move(name);
 
    if (!(m_ > 0 && m_ < 1))
    {
        OGS_FATAL("The exponent value m = {:g}, is out of its range of (0, 1)",
                  m_);
    }
}

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

Member Function Documentation

◆ checkScale()

void MaterialPropertyLib::SaturationVanGenuchtenWithVolumetricStrain::checkScale ( ) const

inlineoverridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 62 of file SaturationVanGenuchtenWithVolumetricStrain.h.

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

References OGS_FATAL, and MaterialPropertyLib::Property::scale_.

◆ dValue()

PropertyDataType MaterialPropertyLib::SaturationVanGenuchtenWithVolumetricStrain::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 82 of file SaturationVanGenuchtenWithVolumetricStrain.cpp.

{
    if (variable != Variable::capillary_pressure)
    {
        OGS_FATAL(
            "SaturationVanGenuchtenWithVolumetricStrain::dValue is implemented "
            "for derivatives with respect to capillary pressure only.");
    }
    const double p_cap = variable_array.capillary_pressure;
 
    if (p_cap <= 0)
    {
        return 0.;
    }
 
    double const e_vol = variable_array.volumetric_strain;
 
    double const n = 1. / (1. - m_);
    double const d_e = -1 * (1 + e_0_) * e_vol / e_0_;
    double const p_b_M = p_b_ * (1 / d_diff_);
    double const p = p_cap / p_b_;
    double const p_to_n = std::pow(p, n);
    double const S_eff_mi = std::pow(p_to_n + 1., -m_);
    double const p_M = p_cap / p_b_M;
    double const p_to_n_M = std::pow(p_M, n);
    double const S_eff_M = std::pow(p_to_n_M + 1., -m_);
    double const S_eff =
        (e_m_ * S_eff_mi + ((e_0_ - e_m_ - (a_ * d_e)) * S_eff_M)) /
        (e_0_ - (a_ * d_e));
    double const S = S_eff * S_L_max_ - S_eff * S_L_res_ + S_L_res_;
 
    if (S < S_L_res_ || S > S_L_max_)
    {
        return 0.;
    }
 
    double const dS_eff_dp_cap =
        (-(e_m_)*n * m_ * p_to_n * std::pow(p_to_n + 1., -m_ - 1) -
         (e_0_ - e_m_ - (a_ * d_e)) * n * m_ * p_to_n_M *
             std::pow(p_to_n_M + 1., -m_ - 1)) /
        ((e_0_ - (a_ * d_e)) * p_cap);
    return dS_eff_dp_cap * (S_L_max_ - S_L_res_);
}

References a_, MaterialPropertyLib::capillary_pressure, MaterialPropertyLib::VariableArray::capillary_pressure, d_diff_, e_0_, e_m_, m_, OGS_FATAL, p_b_, S_L_max_, S_L_res_, and MaterialPropertyLib::VariableArray::volumetric_strain.

◆ value()

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

overridevirtual

Those methods override the base class implementations and actually compute and set the property values_ and dValues_.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 51 of file SaturationVanGenuchtenWithVolumetricStrain.cpp.

{
    const double p_cap = variable_array.capillary_pressure;
 
    if (p_cap <= 0)
    {
        return S_L_max_;
    }
 
    double const e_vol = variable_array.volumetric_strain;
 
    double const n = 1. / (1. - m_);
    double const d_e = -1 * (1 + e_0_) * e_vol / e_0_;
    double const p_b_M = p_b_ * (1 / d_diff_);
    double const p = p_cap / p_b_;
    double const p_to_n = std::pow(p, n);
    double const S_eff_mi = std::pow(p_to_n + 1., -m_);
    double const p_M = p_cap / p_b_M;
    double const p_to_n_M = std::pow(p_M, n);
    double const S_eff_M = std::pow(p_to_n_M + 1., -m_);
    double const S_eff =
        (e_m_ * S_eff_mi + ((e_0_ - e_m_ - (a_ * d_e)) * S_eff_M)) /
        (e_0_ - (a_ * d_e));
    double const S = S_eff * S_L_max_ - S_eff * S_L_res_ + S_L_res_;
 
    return std::clamp(S, S_L_res_, S_L_max_);
}