Background

The soil showed an initial water content of 0,20 cm³/cm³. At the beginning of the experiment a water head of 7,62 cm with a chloride content of 0,2 meq/l was infiltrated. After the chloride contenting water has seeped away another water head of 22,9 cm without tracer was infiltrated. After 17,5 hours the water has totally seeped away. With the help of the tensiometers and the sampling instruments it was possible to observe the spreading out of the moistened zone and the soluted chloride. After the observation the infiltration and the mass transport were calculated with the Finite Differences Method of HANKS & BOWERS (1962). The results of the simulation correlated in a high degree with the results of the experiment. Because of the comprehensible number of parameters the field experiment of WARRICK, BIGGAR et al. (1971) was used various times to validate different Finite Differences and Finite Element methods, i.e. von BRESLER (1973), UNGS et al. (1976), SEGOL (1977) and GUREGHIAN et al. (1979).
Van Genuchten has carried out a comparative study of numerous methods in the context of the "Third International Conference on Finite Elements in Water Resources" of the University of Mississippi in 1980. He directed his special attention to comparing the results of the Finite Differences and the Finite Elements methods. He compared the water content and the chloride concentration after 2 respectively 9 hours time of simulation.

Model construct:

Based on the calculations of VAN GENUCHTEN (1982) a validation of the modul SITRA of the program SPRING^® should be done. For this a vertical model with a single row of elements is created. The model consists of 202 nodes and 100 elements. Every element has a height [y] of 2 cm, a width [x] of 1 cm and a depth [z] of 1 m. So with 100 elements, the entire height is 2 m. The simulation period is 9 hours with time steps of t = 30 [s], the number of time steps is 1080.

The results are documented for each hour, but can only be compared with the data of WARRICK, BIGGAR et al. (1971) and VAN GENUCHTEN (1982) after 2 and 9 hours.

The model is based on the following:
• Saturation equation:
Sw = 1.52208 - 0.0718947 ln (-p) [kg / (m * s ²)]
-2892.38 for <p = <-1421.96
Sw = 1.52208 - 0.0718947 ln (-p) [kg / (m * s ²)]
for p <-2892.38
• Porosity: e = 0,38
• Dynamic viscosity: m = 1.0 10-3 [kg / m · s]
• Gravity: g = 9.81 [m / s ²]
• Permeability: k = 4.4558 10-13 [m²]
• relative K value: r = 1.235376 10-6 exp (13,604 Sw) [m / s]
• Density of water: r = 1000 [kg / m³]

Boundary conditions:
The upper model boundary is fully saturated during the whole simulation (Sw = 1, water content eSw = 0,38), the bottom is partly saturated with Sw = 0,526316 (e Sw = 0,20). The left and right side are impermeable. The concentration (K) of the solute amounts to 209,0 [meq/l] until the 168th minute of the simulation. Afterwards the concentration is reduced to 0,0 [meq/l] till the end of the simulation.

Initial conditions:
The initial saturation is calculated with the following formulas and is assigned to each element depending on its depth:
• Sw (x, t = 0) = 0.394737 + 0.219289 x [m]
for 0.0 <x = <0.60
• Sw (x, t = 0) = 0.526316 [m]
for 0.6 <x = <1.25
The initial concentration is 0 for the whole model.

Results

The following applications show the results of WARRICK (left), VAN GENUCHTEN (middle) and SPRING (right) for the water transfer:

3D animation of the water transfers from 0 to 9 hours

The following applications show the results of WARRICK (left), VAN GENUCHTEN (middle) and SPRING (right) fort he mass transport:

3D animation of the chemical transport of 1 to 9 hours

Based on the results shown above it is a successful validation of the modul SITRA as well for the water transfer as for the mass transport in the unsaturated zone.

Literature