GEO-SLOPE International Ltd, Calgary, Alberta, Canada
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Road Ditch Ponding during Rainfall
1
Introduction
This is a transient seepage example in which the objective is to determine, for an extreme rainfall event,
how deep water may pond in road side ditches. SEEP/W has a special feature that will let you create a
“surface region” on an existing geometry region. The surface region has some knowledge of its ground
surface profile and if a unit flux boundary condition is applied to the ground surface, SEEP/W can record
the infiltration, seepage face or runoff water, and depth of ponding in catchments or low points.
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Feature highlights
GeoStudio feature highlights include:
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Transient flow
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Surface region meshing with runoff and ponding
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Initial water table for starting a transient model
3
Geometry and boundary conditions
Elevation (m)
The image below shows a cross-section of a road with an asphalt driving surface. Either side of the road
has a drainage ditch to collect surface runoff. The image also shows an initial water table location which
is assumed to be located just beneath the base of the road embankment.
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Distance (m)
The finite element mesh for the cross-section is shown below. It is an unstructured mesh with a global
element size of approximately 1.0 meters. Also drawn on this image is the surface boundary condition, a
unit flux (q) hydraulic boundary condition with a value of 5.15 e-6 m/second. This would equate to 445
mm / day of rainfall. The model was set up to solve 12 time steps of 7200 seconds each for a total of one
day. Data was saved to file every second day. Adaptive time stepping was used with control parameters
of a minimum step of 500 seconds and maximum step of 3600 seconds.
SEEP/W Example File: Road Ditch Ponding during Rainfall (pdf) (gsz)
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If you look closer at the model you will see a thin region of elements just below the ground surface. This
is the special “surface region” created for the model. In this view, the details of the surface region mesh
have been intentionally hidden from view so that they don’t clutter the image. The second image below is
a close up view of the surface region detailed mesh in the vicinity of the asphalt and road shoulder contact
location.
You can see in this detailed view that there are many finite element divisions in close proximity at the
ground surface. This is intentional. It is quite common at the ground surface to have high wetting or
drying front hydraulic gradients which are better to deal with numerically if the mesh has a finer
discretization. In addition, if this model were also going to be used in a VADOSE/W analysis, the
detailed mesh in the surface region would enable plant transpiration as well as climate-soil coupling to be
considered.
The surface region mesh is created once the main soil cross-section is defined. When creating the surface
region it is necessary to specify how many “layers” will exist in the region. In this case, there is one layer
and it extends fully across the ground surface. Each layer can be assigned a thickness and then assigned a
material model using the Draw Surface Layer Material command. In this case, the asphalt model is
applied at the crest and it has very low conductivity as well as low storage potential. Finally, the Draw
Mesh Properties command can be used to select a layer an assign the number of element divisions within
that layer.
SEEP/W Example File: Road Ditch Ponding during Rainfall (pdf) (gsz)
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4
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Material properties
There are two material models in this example: the Till soil and the asphalt. The asphalt is not really a
soil but it can be assigned soil properties such that the desired performance is obtained. The asphalt can
be modeled using a Saturated Only soil model which requires a conductivity value and a coefficient of
compressibility (storage term). In this case, the conductivity is set to be 1e-14 m/s and the Mv is set to be
1e-8, which means there is basically no change in storage within the asphalt. The porosity of the asphalt
is set to be 0.01.
The property functions for the Till soil are shown below. The water content function was input and then
the hydraulic conductivity function estimated using the Van Genuchten approach. The Ksat of the Till is
set to be 1e-6 m/sec which is typical of a sandy clay soil.
Till Fill
Vol. Water Content (m³/m³)
0.4
0.3
0.2
0.1
0.01
0.1
1
10
100
1000
Matric Suction (kPa)
Till Fill
1.0e-06
X-Conductivity (m/sec)
1.0e-07
1.0e-08
1.0e-09
1.0e-10
1.0e-11
1.0e-12
0.01
0.1
1
10
100
1000
Matric Suction (kPa)
SEEP/W Example File: Road Ditch Ponding during Rainfall (pdf) (gsz)
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Discussion of results
Elevation (m)
The model was solved for a total elapsed time of 86400 seconds or one day. The computed pressure
contours along with the phreatic line shown below. Each contour color is a 20 kPa pressure difference.
You can see that the water table has rising into the embankment relative to its initial position and that if
you joined the ends of the water table lines in the ditches there would be surface water stored in the
ditches.
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Distance (m)
The following chart shows the development of the ditch ponds over time. This plot is Total Head so if
you compare the Total Head values with the elevations in the contour plot above you can see that the head
values also represent the elevation of the free water in the ditches.
Pond Elevations
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Head (m)
9
14400 sec
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28800 sec
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43200 sec
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57600 sec
5
72000 sec
86400 sec
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X (m)
The final image shows the cumulative water flow at all nodes along the ground surface. It shows that
there is no infiltration through the asphalt, and that the highest positive infiltration is on the top of the
slopes just off the end of the asphalt. This makes sense because the initial storage capability of the soil at
higher elevations above the initial water table is greatest so this is where the most demand is satisfied.
Lower down the slope, the soil will saturate sooner and turn from an infiltration location to a seepage face
SEEP/W Example File: Road Ditch Ponding during Rainfall (pdf) (gsz)
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location. In fact, in the ditches themselves, there is little to no infiltration in the first day and actually the
lower, sides of the ditches are seepage faces where water is leaving the slopes. This is water that has
infiltrated higher up and that is coming out lower down later on in the day.
Infiltration
Cumulative Water Flux (m³)
0.12
0.10
0.08
0.06
0.04
86400 sec
0.02
0.00
-0.02
-0.04
0
10
20
30
40
50
X (m)
In a transient analysis it is often useful to plot the water balance data. This image shows the cumulative
change in storage of water in the domain as well as the change in boundary flows. The difference
between the two is the computed error. In this case, most of the boundary flow is reported as change in
storage with a small error. The error can likely be reduced by using smaller time steps.
2.0
1.5
0.5
Water balance storage
change : Cumulative
Storage
0.0
Water balance boundary
flow s : Cumulative
Boundary Fluxes
(m³)
1.0
Water balance error :
Cumulative Water
Balance
-0.5
0
10000 20000 30000 40000 50000 60000 70000 80000 90000
Time (sec)
SEEP/W Example File: Road Ditch Ponding during Rainfall (pdf) (gsz)
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