Infiltration and Air Pressure Build-up

Transcription

1 1 Introduction Infiltration and Air Pressure Build-up This air flow example illustrates how the build-up of air pressure in advance of a wetting front can inhibit water movement. The example is based on the work of Touma and Vauclin (1986), as presented in a Ph.D. dissertation by Philip Binning (P. Binning, Modeling unsaturated zone flow and contaminant transport in the air and water phases, PhD thesis, Princeton University, 1994). In this example, water infiltration rates of 8.3 cm/hr and 16.6 cm/hr are applied to a 1 meter box, which is initially at atmospheric air pressure. The box is closed except at the surface, so air will be displaced by infiltrating water. 2 Feature highlights GeoStudio feature highlights include: Air pressure review boundary condition in AIR/W Surface mesh and water ponding in SEEP/W Verification with published examples. 3 Geometry and boundary conditions 2 1 Figure 3-1 Model regions (1 - main soil, 2 - surface layer) The above figure shows the modeled domain with the applied surface water flow boundary condition applied. The geometry is defined using two types of regions. Region 1 is the main soil region, and region 2 is a special surface layer region. The surface layers have special attributes in GeoStudio. In the case AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 1 of 8

2 of SEEP/W and AIR/W, a water flux applied to a surface layer has the ability to build up a positive pressure on the ground surface. A water flux that does not infiltrate into a regular soil region will only result in a pressure of zero, which is typical of a seepage face. There are two analyses in this example file, and both are transient and do not refer to another file for their initial conditions. You can see in the image above, a watertable (blue dashed line) is drawn at the base of the model. This means it is assumed the water pressure is zero at this location and decreases hydrostatically above that location. So, at the top of the model, the initial pressure will be -1m or -10 kpa. The initial air pressure is assumed to be zero throughout the box, and this is indicated by setting the air activation pressure to zero in the air material property. The activation pressure is only applied the first time a new soil region becomes active, which in this case, is the actual analysis. The boundary conditions applied in the two transient models are a water flow rate of 16.6 cm/ hr and 8.3 cm/hr respectively. The air boundary condition in both cases is an air pressure review boundary condition. When this boundary condition is set up, you must enter an air entry value (or bubbling pressure), which is a maximum air pressure the soil will increase to under saturated infiltration, before the air will break through the saturated water and be released to the atmosphere. The model will start out with atmospheric air pressure at the surface, but if the difference between computed air and water pressure (Ua Uw) becomes zero, this is an indication that the ground surface has saturated. At this point, air becomes trapped and starts to resist water infiltration. Water will build up a positive pressure on the ground surface and air will build up pressure within the soil up to the user-specified bubbling pressure. 4 Material properties The material properties used in this example are those reported by Binning (1994) in his summary of the Touma and Vauclin (1986) experiments. The material model used is a fully saturated / unsaturated model with hydraulic and air material functions, as illustrated below. This analysis is not coupled with TEMP/W, so there are no thermal properties to specify, and a TEMP/W license is not required. AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 2 of 8

3 touma e-04 e-05 X-Conductivity (m/sec) e-06 e-07 e-08 e-09 e Matric Suction (kpa) 0.35 touma 0.30 Vol. Water Content (m³/m³) Matric Suction (kpa) AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 3 of 8

4 touma e-02 e-03 Air X-Conductivity (m/sec) e-04 e-05 e-06 e-07 Degree of Saturation 5 Discussion of results This discussion will compare the results of the two analyses one with a lower infiltration rate, and one with a higher infiltration rate. A discussion of the key mechanisms observed is also included. Analysis with 8.3 cm/hr infiltration The applied infiltration for the ond experiment in this analysis is a constant rate of 8.3 cm/hr which equates to 1.15e-6 m/sec. At this infiltration rate, the air does not become trapped and positive water pressures do not build up on the ground surface. The air and water pressures over time are illustrated below. Surface Pw vs time Surface Pa vs time Pore-Water Pressure (kpa) Air Pressure (kpa) AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 4 of 8

5 The water is infiltrating into the soil, and as a result, is wetting it up. The next two images show the corresponding water and air pressure profiles over time. Water Pressure Air Pressure Pore-Water Pressure (kpa) Air Pressure (kpa) The difference between air and water pressure (Ua Uw) is termed matric suction, and at a value of zero, is the point the soil is fully saturated. The matric suction profile is given below, and it can be seen that the matric pressure at the base is increasing over time as a positive number. This means that the soil is actually de-saturating at its base while wetting up above. The water content profile is shown adjacent to the matric pressure profile. Matric pressure Water content Matric Suction (kpa) Vol. Water Content (m³/m³) Analysis with 16.3 cm/hr infiltration In this analysis, the applied water flux is now great enough to cause saturation and trapping of air. The surface water and air pressures over time are shown below. These exhibit a different pattern than with the lower water flow rate. You can see that the water pressure approaches zero while the air pressure remains atmospheric. At the point the water pressure reaches zero, the air pressures start to build up. The air pressure increases rapidly and then less rapidly until it approaches 1.4 kpa the bubbling pressure for this soil. At this point, the air pressure remains constant under the constant infiltration. AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 5 of 8

6 Surface Pw vs time Surface Pa vs time Pore-Water Pressure (kpa) Air Pressure (kpa) -2 What is happening to the infiltration during this process? Consider the water and air flow across the ground surface, as shown below. The water initially infiltrates at the applied rate until air pressures start to build up and inhibit flow. The air flow balances the water flow until the ground surface saturates, and then air flow is shut off until the air pressures in the soil exceed the bubbling pressure. Surface Qw vs time Surface Qa vs time Water Flux (m³/sec) Air Flux (kg/sec) The water and air pressure profiles over time are shown below. You can see that for the water pressure, there is a zone of positive pressure that progresses deeper into the soil. This positive pressure does not necessarily mean a saturated wetting front, however. Recall that the degree of saturation is a function of matric pressure, not just water pressure. AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 6 of 8

7 Water Pressure Air Pressure Pore-Water Pressure (kpa) Air Pressure (kpa) The matric pressure and water content functions are shown below. You can see clearly in this image that there are no negative matric pressures (a negative matric pressure indicates a saturated soil) and that the water contents are near saturation at the surface, but are decreasing quite rapidly over time at the base of the sample. The water contents are reducing because the air pressures are increasing and forcing out the water. Matric pressure Water content Matric Suction (kpa) Vol. Water Content (m³/m³) 5.2 Comparison with Binning data As a final image, consider the superposition of water and air pressures as shown below in the AIR/W and Binning images. In these images, the water pressures are the negative values on the left and the air pressures are the positive values on the right. Material property data used to generate results shown in this image differ slightly from those used above. Slight differences in three functions can yield different results, as infiltration and air pressure response is a highly coupled process. To be honest, when the example was re-formulated using the current release version of GeoStudio, I did not want to spend half a day re-calibrating the material properties to exactly match those of Binning. The following figure was based on earlier modeling, while all above images are included in the example folder shipped with AIR/W. You can see below that there is good agreement between AIR/W and Binning. AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 7 of 8

8 Air and Water Pressure vs time water 0 w ater 10 min w ater 30 min w ater 60 min w ater 90 min Air 10 min Air 30 min Air 60 min Air 90 min Elevation (m) Pressure (kpa) 0 Figure 5-1 AIR/W results for 8.3 cm/hr case Figure 5-2 Results for 8.3 cm/hr case as presented by Binning (1994) AIR/W Example File: Infiltration and air pressure build up.doc (pdf) (gsz) Page 8 of 8