Filling Pond Head vs Volume Functions

Transcription

1 Introduction Filling Pond Head vs Volume Functions The objective of this illustration is show how to model the filling of a pond where the water is seeping into the pond from the soil. The head in the pond is not known, and depends on the volume of water seeping out of the soil. A special head boundary function can be used in this case. Feature Highlights Transient boundary conditions Rising water level in a river Seepage through a levee into a pond Head vs Volume boundary function Geometry and boundary conditions The geometry of this example is over-simplified so that the key points are clearly illustrated. Figure represents a river or lake on the left, separated by a levee from a channel on the right. The channel shape is very angular, because it is easy to compute the volume of air above the ground surface. This volume has the potential to be filled with water if it leaks out of the levee as a negative flux boundary flow. Figure Geometry SEEP/W Example File: Filing pond H vs V functions.doc (pdf) (gsz) Page of

2 Rising river Time (day) Figure Increase in water level over time Filling Pond (H vs V) - - Volume (m³) Figure Head vs Volume function In this example, the function in Figure is applied to the sides and base of the river or lake. It represents an increase in water level over time. The function in Figure is the unique Head vs Volume function that relates how deep the water in the channel or pond will become as a function of how much volume of water flows out of all the edges to which this boundary condition is applied. Looking at the geometry in Figure, you can see that there are two volume areas of the channel. The lowest elevation would have a volume of cubic meters; while the volume above that would be cubic meters. The total volume of the air is cubic meters. Knowing this, we can make the Head vs Volume function shown in Figure. We can say that if cubic meters of water (volume) passed all the boundary edges, the Total Head would sit at m. If the total volume flow out of the edges is cubic meters, then the Total Head must be m. The model is set up with a water table as an initial condition, so the only analysis in the file is the transient filling of the reservoir, which we assume takes days. The model is run to simulate days total. A summary of boundary conditions and initial conditions is shown in Figure below. SEEP/W Example File: Filing pond H vs V functions.doc (pdf) (gsz) Page of

3 River with rising Head vs time function Pond with seepage from levee The head in this pond depends on the volume of water seeping out of the soil. A Head vs Volume function boundary condition can set the head based on the volume flow of water into the pond. - - Volume Flow Out of soil (m) The volume of this pond is cubic meters. If the volume flow into the pond is zero, the Head is m. When the flow into the pond (and out of the soil) is, the pond is full and the Head is m. Figure Summary of boundary conditions and initial conditions Material properties For transient simulations, both a hydraulic conductivity function and a volumetric water content function will be required, and are shown in Figure. The shape and value of these are not really that important to the purpose of this example, but they are required in the model, as there will both saturated and unsaturated flow. Embankment Embankment.. Vol. Water Content (m³/m³).... X-Conductivity (m/day) Matric Suction (kpa) Matric Suction (kpa) Figure Hydraulic conductivity function and a volumetric water content function Discussion of results The water table and infiltration flow after day is shown in Figure below. Figure is the same data, but at the end of the analysis. SEEP/W Example File: Filing pond H vs V functions.doc (pdf) (gsz) Page of

4 Figure Water table and infiltration flow after day SEEP/W Example File: Filing pond H vs V functions.doc (pdf) (gsz) Page of

5 Figure Water table and infiltration flow at end of analysis A movie of the entire process can be viewed by clicking the following link: filling pond_h vs v functions.avi. This link will work as long as the movie file and this *.PDF file remain in the same folder. We can now use the Draw Graph feature to consider the applied and computed heads, as well as the total volume of flow leaving the river and entering the pond on the right. The first graph shows both the river head the computed pond head. The river head is from a result point at the bottom of the river, and we can confirm that it matches the input boundary function. The second series in the graph shows that the computed pond head is about. after days. River Elevation : Node (, ) Pond filling elevation : Node (, ) Time (day) SEEP/W Example File: Filing pond H vs V functions.doc (pdf) (gsz) Page of

6 We can back calculate from the applied H vs V function that if the head is., then about cubic meters of water must have passed into the channel. The next two images confirm this. The first image shows the location of all model edges used to cumulate all nodal flow. The second is a plot of the sum of each nodal flow as plotted versus the time. Seepage from soil into pond Cumulative Water Flux (m³) Time (day) NOTE: This type of boundary function is somewhat sensitive to the time step size, because the applied head at the next time step depends on the computed flow from the last time step. For this reason, it is a good idea to use even time stepping and not too large time steps. SEEP/W Example File: Filing pond H vs V functions.doc (pdf) (gsz) Page of