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January 27, 2020 by

Soil Hydraulic Functions in Matlab

Water Retention Functions

The van Genuchten (1980) model is the most widely used water retention curve function:

\[\Theta = \left( 1 +(\alpha \psi)^n\right)^{-m}\]

where the effective saturation is defined as:

\[\Theta = \frac{(\theta - \theta_{r})}{ (\theta_{s} - \theta_{r})}\]

The hydraulic conductivity function is defined using Mualem Model.

The hydraulic capacity function.

The following function takes a scalr or vector of u as input: test

function [q,k,c] = Mualem_vanGenuchten(x,u,qr,por,a,n,ks)
mu = 0.5;
m  = 1-1/n;

UZ = u<0;

Q  = (1-UZ)*1   +   UZ .* ((1+(-a.*u).^n).^(-m));

q  = qr+(por-qr)*Q;
k  = ks*(Q.^mu).*(1-(1-Q.^(1/m)).^m).^2 ;
c  = (1-UZ)*0+ UZ.*(((por-qr)*n*m*a.*(-a.*u).^(n-1))./((1+(-a.*u).^n).^(m+1)));