SVFlux - Automatic Mesh Refinement Applied to Reservoir Draw-Down

How does automatic mesh refinement benefit the calculation of pore-water pressures in a reservoir draw-down scenario? The following example identifies errors which may occur using a fixed mesh approach.

One particularly interesting class of seepage modeling problems is the calculation of pore-water pressures in earth dams next to reservoirs.  The function of the earth dam is primarily to dissipate the energy of the head created by the reservoir water level.  However, a number of additional design and operational issues may be examined with a seepage model.   These design issues include:

1. Calculations of head loss.
2. Calculation of maximum exit gradient.
3. Pore-water pressure build up due to rapid draw-down

In this article we wish to concentrate on the third application:  pore-water pressure build-up due to rapid draw-down.  In this scenario a numerical model is set up to evaluate the initial pore-water pressures of an earth dam experiencing rapid draw-down of the reservoir.  Excessive pore-water pressures in the earth dam in this scenario can lead to upstream slope failures.

It is commendable that the practicing geotechinical consultant has become aware of the need to apply numerical models to this type of problem.  The correct calculation of pore-ware pressures in this particular application can lead to significant numerical challenges as shown in the following example.

In this case let’s take the example of a typical earth dam.

Figure 1 - Geomtery of a typical earth dam experiencing reservoir draw-down

In this scenario the earth dam upstream face contains an outer layer of sand overlaying a silty clay material, which is designed to create head-loss through the dam.  The reservoir level will be lowered from an elevation of 54m to 36m over the course of 10 days.   It is the desire that the seepage model then tell us the pore-water pressures in the earth dam during this draw-down period.

Such draw-down models are often run with fixed mesh finite element software.  However, it can be seen that if a fixed mesh is used in the current model the results are governed by instability. The instability is created by the sharp changes in head occuring as a result of the rapid draw-down.

Figure 2 – Results obtained by fixing the finite element mesh demonstrating numerical instability.

The automatic mesh refinement in the SVFLUX software package was then used to examine the model.  It can be seen from the following animation that the requirement is that the mesh be refined significantly in order to provide a reasonable solution to the model within acceptable error limits.

Figure 3 – Animation of the mesh refinement and resulting correct pore-water pressures.

The resulting final pore-water pressures may then be seen in Figure 3.  It can be observed in the abrupt but smooth pore-water pressure contours that appropriate values have been calculated.

Automatic mesh refinement is a critical part of the calculations of pore-water pressures in a rapid draw-down scenario. The likely primary source of numerical difficulties with this type of scenario is lack of proper mesh resolution.