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Vol. 9  No. 5

EVALUATING GROUNDWATER MOUNDING WITH A NUMERICAL MODEL

&
HYDRUS

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EVALUATING GROUNDWATER MOUNDING WITH A NUMERICAL MODEL

In a previous newsletter we presented a calculator for determining the maximum groundwater mounding under a rectangular recharge area. This calculator uses the analytical solution presented by Hantush (1967) to evaluate the maximum groundwater mounding. While this analytical solution gives an excellent initial estimation, it is often necessary to evaluate the impact of constant recharge on the groundwater system in more detail.  One way to do this is the use of a numerical model. In this newsletter we will describe the basics of using one such model, HYDRUS, to evaluate groundwater mounding. We will also describe some key differences between the Hantush evaluation and the results from HYDRUS.

Setting Up the Simulation

The example given in the groundwater mounding calculator will be demonstrated using HYDRUS here.  The example given is in three-dimensions, however for computational ease we will simplify the problem from 3D to 2D for the numerical simulation. This can be done by assuming the recharge area is now circular, with the same contributing area as our rectangular problem (original area is 3m x 4m = 12m2, converting this to a circular area using A =ğr2, the area has a radius of 1.94m). As we are still infiltrating the same amount of water this will have no impact on the maximum groundwater mounding depth. With a circular recharge area we can evaluate this problem as a 2D axisymmetrical problem (see Domain Information).

Aside from the contributing area, the other key parameters in our example are:

  • 1000 L/d infiltration (converts to 0.08 m/d)

  • infiltration time of 2 days

  • hydraulic conductivity of 0.087 m/d

  • initial saturated thickness of 2m

The following section will describe where these parameters are assigned within HYDRUS.

Domain Information

The size of the domain is the region that the model will produce a solution for, and the discretization of this domain determines how much detail will be presented.  The solution is evaluated at each point in the grid, therefore a finer discretization allows for more detail in the solution. The size of the entire domain, and the discretization in HYDRUS are entered in two different windows. In the following window, Geometry Information, the domain orientation and size are selected.  Here you can see the 2D axisymmetrical orientation of our problem:

The depth of the domain has been set to 7 m (5 m to the water table; not a parameter required by the Hantush example), and the entire radius has been set to 10 m.  The size of the recharge area will be assigned later.

The discretization of this domain is done within the FE mesh section of HYDRUS, in the Rectangular Domain Discretization window.  Here the domain is discretized in both the X- and Z-directions.

 

Assigning Material Properties

Properties such as hydraulic conductivity and  the unsaturated flow parameters are outlined in the Flow and Transport Parameters section of HYDRUS, within the Water Flow folder, under Soil-Hydraulic Parameters:

In this section you outline the variety of materials that are present within your domain.  Assigning these properties to sections of the domain occur in a separate window, as described later. In the example we are demonstrating here, there is only one material property.

There are other sections within HYDRUS that describe more advanced material properties.  These include the anisotropic ratios and unsaturated zone solution method, amongst others.

Assigning Boundary Conditions

The only boundary condition of concern is the recharge boundary along 1.94 m along the top of our domain. The recharge flux value can be entered in the Flow and Transport Parameters, in the Variable Boundary Conditions window.

These conditions can then be assigned to specific nodes within the Boundary Conditions section.  By clicking on Variable Flux 1 on the right hand list, you can then click on each node that you would like to assign this boundary condition to.  In addition, no flux boundaries are assigned to the remainder of the boundary.

Assigning Initial Conditions

Initial conditions are required so that HYDRUS has a start point from which to run. The initial pressure head in this simulation is a water table located at 2 m above our base (the location of the aquitard). Within the Domain Properties section, in the Default Domain Properties window, the initial conditions can be assigned at the top layer (-5 m) and at the base (2 m), and then by clicking 'Linear Interpolation of Pressure Heads between the first and last layer', the initial conditions will be distributed between all layers such that the water table (pressure head of 0 m) is located 2 m above the base.

Duration of the Simulation

You also need to tell the program how long you would like it to run for. HYDRUS uses a variable time stepping routine, which means that the size of the time steps varies with the stability of the system; when the hydraulic head is changing rapidly the time steps are smaller, when it stable the time steps get bigger.  In this window you not only assign your initial and final simulation time, but also maximum and minimum time steps allowed during the run.

In this example the end time selected is 100 days. This allows for a 2 day infiltration period, and 98 more days for the infiltrated water to move towards the water table.

Desired Output Information

The program is run to get results, and simulation times and quantity of information desired must be specified. The number of output times can be increased by increasing the count, and assigning the times to each count.

Results

The results of the HYDRUS simulation outlined above for pressure head, at time 100 days is:

It can be seen that the infiltrated water has not even reached the water table, and thus has not had a chance to raise the water table.  Obviously a significant difference from the Hantush analytical solution.

By applying the recharge as a constant source for 150 days (reaching essentially steady state), the water table is raised by approximately 1 m.

 

Differences Between the Hantush Calculator and HYDRUS

There are many differences between using an analytical solution and a numerical model.  In our case, there are a few key differences between the Groundwater Mounding Calculator given in this website, and the results from a properly set-up numerical simulation of HYDRUS. The following are two of the key differences:

Inclusion of Unsaturated Zone

The Hantush analytical solution does not include any consideration of the depth, saturation, etc. of the unsaturated zone between the surface and the water table.  In a numerical solution such as one from HYDRUS the unsaturated zone is taken into account, and the time required to infiltrate through this zone, in addition to the distribution of water throughout it would be considered.

Description of Entire Domain

The Hantush analytical solution given in the online calculator gives the maximum groundwater mounding, which is assumed to be below the center of the infiltration zone.  The results from a numerical solution, such as HYDRUS, would provide the user with information about the depth of the water table throughout the entire domain, in addition to saturation, velocity, and other key parameters.

The use of the groundwater mounding calculator available online at GroundwaterSoftware.com is an excellent initial estimate of the reaction of a water table to infiltration.  However, for a more detailed analysis, the use of a numerical model, such as HYDRUS would be required.


References

 

Hantush, M.S. (1967). Growth and Decay of Groundwater-Mounds in Response to Uniform Percolation. Water Resources Research, vol. 3 num. 1, pp 227-234.

 

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HYDRUS

Hydrus is capable of simulating a wide variety of scenarios. These include:

Two-Dimensional HYDRUS Examples Distributed With the Model

Direct HYDRUS Examples

  • Column infiltration test
  • Water flow and solute Transport in a field soil profile under grass - seasonal simulation
  • Two-dimension unidirectional solute transport - comparison with analytical solution
  • One-dimensional solute transport with nitrification chain - comparison with analytical solution
  • One-dimensional solute transport with nonlinear cation adsorption - Data from Selim et al. (1987)
  • One-dimensional solute transport with non-equilibrium cation adsorption
  • Axisymetrical three-dimensional water and solute infiltration test
  • One-dimensional water flow with multiple hysteretic loops, data from Lenhard et al. (1991)
  • Water flow and solute transport from furrow to a drain
  • Three wetland examples

Inverse HYDRUS Examples

  • Parameter estimation from a cone penetrometer experiment (Gribb et al., 1987) Parameter estimation from a tension disc infiltrometer experiment (Simunek et al., 1998)

Three-Dimensional HYDRUS Examples Distributed with the Model

Direct HYDRUS Examples

  • Column infiltration test
  • Water flow and solute Transport in a field soil profile under grass - seasonal simulation
  • Three-dimension unidirectional solute transport - comparison with analytical solution
  • One-dimensional solute transport with nitrification chain - comparison with analytical solution
  • One-dimensional solute transport with nonlinear cation adsorption - Data from Selim et al. (1987)
  • One-dimensional solute transport with non-equilibrium cation adsorption
  • One-dimensional solute transport with first-order attachment
  • One-dimensional water flow with multiple hysteretic loops, data from Lenhard et al. (1991)
  • Three-dimensional contaminant transport from a waste disposal site
  • Three-dimensional flow and transport through a dike with a seepage face and root water uptake

Other Existing HYDRUS Applications

Agricultural HYDRUS Applications

  • Irrigation management
  • Drip irrigation design
  • Sprinkler irrigation design
  • Tile drainage design - flow to a drainage system
  • Crop grow models, i.e., cotton model
  • Salinization and reclamation processes, salt leaching
  • Movement of pesticides; nonpoint source pollution
  • Seasonal simulation of water flow and plant response

Non-Agricultural HYDRUS Applications

  • Deep percolation beneath final closure cap designs for radioactive waste management sites at the Nevada test site
  • Flow around nuclear subsidence craters at the Nevada test site
  • Capillary barrier at the Texas low-level radioactive waste disposal site
  • Evaluation of approximate analytical analysis of capillary barriers
  • Landfill covers with and without vegetation
  • Risk analysis of contaminant plume from landfills
  • Seepage of wastewater from land treatment systems
  • Tunnel design - flow around buried objects
  • Highway design - road construction - seepage
  • Stochastic theory - solute transport in heterogeneous media
  • Lake basin recharge analysis
  • Interaction between groundwater aquifers and streams
  • Environmental impact of the drawdown of shallow water tables
  • Analysis of cone permeameter and tension infiltrometer experiments

For more info click here:  HYDRUS
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