Upstream Boundary Conditions for Seepage Modeling
A feature of SVFlux™
December 1, 2011
It is often necessary to model the cases of rapid drawdown or rapid filling of earth dams and embankments. These scenarios create unique boundary condition requirements for which special boundary conditions have been implemented in SVFlux™. Often the focus in this type of numerical modeling is on the downstream side of the earth dam. What is often neglected is the proper formulation for the upstream side of the earth dam. This was particularly apparent in a recent analysis performed by a client of ours.
Consider the case where there is a rapid drawdown scenario. This scenario may be represented with a standard Dirichlet (head) boundary condition where the reservoir elevations are entered in the software as a data table. This type of boundary condition is simple to evaluate numerically and generally runs fast. The downside of this type of representation is that, as the water table lowers, increasingly high soil suctions are forced on the upper portions of the boundary. This can be considered unrealistic in some scenarios.
In order to overcome the limitations of a standard head boundary condition, SVFlux™ implements two variations of an upstream boundary condition which allow for more rigorous numerical modeling of the scenarios. SVFlux™ is currently the only commercially software available to implement both of these scenarios.
Upstream Head Flow Boundary Conditions
The Head Flow boundary condition is designed to divide the upstream boundary condition into two segments; i) below the reservoir level, and ii) above the reservoir level. Below the reservoir level, the water is allowed to flow freely in or out of the model, depending upon if the model is under rapid filling or rapid drawdown conditions. Above the reservoir elevation, the boundary is treated as a "no flow" boundary condition. It is possible in this boundary condition that the phreatic surface may approach and touch the boundary during rapid drawdown scenarios. The description of the Head Flow boundary condition is shown in the following figure:
Figure 1: Description of the Head Flow boundary condition
Upstream Head Review Boundary Conditions
When a rapid drawdown scenario is considered in a numerical model, there are three potential zones which must be considered separately. These zones are illustrated in the figure shown below. The Head Review boundary condition in SVFlux™ is designed to handle all three of these conditions. Specifically, water is allowed to flow into or out of the model (depending on the difference in pressures) below the reservoir elevation. Between the phreatic line exit point and the reservoir elevation, water may exit the model if pore-water pressures approach zero. Above the phreatic line are unsaturated conditions which allow "no flow" conditions.
Figure 2: Three zones of potential consideration on the upstream side of a rapid drawdown scenario with the Head Review boundary condition
The combination of these two types of boundary conditions make SVFlux™ the most comprehensive software currently available for the analysis of rapid drawdown scenarios. It is also possible to couple SVFlux™ with our SVSlope® limit equilibrium software to calculate the factory safety of such rapid drawdown scenarios.