Material models in flow analysis

The steady state flow analysis is driven by Darcy’s law specifying the relationship between the flow velocity and the gradient of hydraulic head. The current version of the program assumes constant values of coefficients of permeability independent of pore pressure.

The program also requires specifying the initial void ratio e₀ for the determination of current porosity n and subsequently the actual velocity of water flowing through pores only v_s=v/n, where v is the average flow velocity through the whole seepage area.

By introducing the relative coefficient of permeability K_r the program allows for tracking the transition zone between fully saturated (S=1, K_r=1) and unsaturated (K_r => 0) region of the soil body. As an example we may consider the problem of unconfined flow. The process of tracking the transition zone is governed by one of the two models of transition zone determining the evolution of relative coefficient of permeability K_r as a function of pore pressure, see figures.

(a) Log-linear model [1],  (b) Van Genuchten model [2]

Log-linear model

The Log-linear transition zone model described e.g. in [1] is defined by the following parameters:

pmin	-	minimum value of pore-pressure in fully saturated region [kPa]
PTZ	-	transition zone width [m]
R	-	reduction parameter,  a sufficiently large number R=100-1000 [-]

Van Genuchten model

In this case the value of relative coefficient of permeability K_r is given by:

where δ, n ,m=1-1/n are model parameters. Their values can be obtained from laboratory measurements of retention curves approximated by:

where:	Ssat	-	Degree of saturation of fully saturated soil, default setting Ssat=1
	Sirr	-	Irreducible degree of saturation, default setting Sirr=0

Literature:

Details can be found in [2].

[1] D.M. Potts, L. Zdravkoviè, Finite element analysis in geotechnical engineering – theory, Thomas Telford, London, 1999.

[2] M. Th. Van Genuchten, A closed formulation for predicting the hydraulic conductivity of unsaturated soils, Journal Soil Science Society of America 44 (1988), 239-259.