Constitutive laws

The mass transport equation is based on the constitutive laws for the capacity $ c$ and the hydraulic conductivity $ k$.

The capacity $ c$ is defined as


where $ \theta$ is the volumetric water content ( with the volume of water, and the total volume) which is calculated by a modified version of van Genuchten’s retention model. Note that the presence of a crack in an element does not influence the capacity in the present model.

The volumetric water content is


where and are the residual and saturated water contents corresponding to effective saturation values of and , respectively.

The effective degree of saturation is defined as


where is an additional model parameter and is the air-entry value of capillary pressure which separates saturated ( ) from unsaturated states ( ). It is intuitive that the smaller the pore size of the mate- rial, the larger the value of will be.

The relative conductivity is a function of the effective degree of saturation and is defined as


If , we have : the equation reduces to the expression of the relative conductivity of the original van Genuchten model.

The model parameters are summarized

Table 61: Material for unsaturated flow in lattice models - summary.
Description Material for fluid transport in lattice models
Record Format latticetransmat num(in) # d(rn) # k(rn) # vis(rn) # contype(in) # thetas(rn) # thetar(rn) # paev(rn) # m(rn) # a(rn) # thetam(rn) # [ ctor(rn) #]
Parameters - num material model number
  - d fluid mass density
  - k permeability ()
  - vis dynamic viscosity ()
  - contype unsaturated flow allowed when contype=1
  - thetas saturated water content
  - thetar residual water content
  - paev air-entry value of capillary pressure
  - m van Genuchten parameter
  - a van Genuchten parameter
  - thetam additional model parameter for the modified version of van Genuchten’s retention model
  - ctor coefficient of tortuosity ( )
Supported modes 2dMassLatticeTransport

Borek Patzak