## Dewatering Example Model Overview

Review this model, download it, and play with it to learn how to apply AnAqSim to dewatering problems.

This is a model of a complex dewatering system that includes a partially-penetrating circular sheet pile barrier, three shallow wells pumping inside the barrier, and a shallow recharge trench outside the barrier, where the discharge of the wells is put back into the aquifer. The aquifer is unconfined and sandy, with about 120 ft of saturated thickness. The system will allow excavation 10 ft below the ambient water table within the barrier to install a tank.

The figure at right shows a map of the system elements. The sheet pile wall is 63 ft in diameter and it penetrates 30 ft below the water table. The pumping wells are screened in the upper 20 ft of saturated thickness and are 6 inches in diameter. The recharge trench introduces water into the uppermost part of the saturated zone and is 116 ft long.

The upper 30 ft of saturated thickness in the aquifer is more conductive (20 ft/d) than the lower 90 ft (6 ft/day), so the barrier cuts off flow in the more conductive part. The model is set up just to model drawdowns – all initial heads are zero (water table) and deviations from zero are simulated.

Near the system, there are 7 layers, with thinner layers near the bottom of the barrier where there are important vertical flows (see below). Far away from the system, there is only one layer, with an interdomain boundary linking the 7 layers within to the single layer without. At the interdomain boundary, the total normal components of discharge are matched over intervals and heads are matched at points. The topmost layers (1) are unconfined and layers 2-7 are confined (fixed transmissivity).

The entire modeled region is bounded on the outside of the single-level area by a constant head boundary with h=0; this boundary is far enough away that the system induces no significant head changes near it.

The 7-layer region is small compared to the single-layer region.

Vertical leakage and storage fluxes are simulated using spatially-variable area sinks (SVAS), which model a smooth distribution of areal extraction (leakage + storage fluxes, L/T) in a domain, getting the extraction rate essentially perfectly at basis points and approximately in between basis points. AnAqSim can automatically distribute basis points as a regular hexagonal array of points within a domain and within polygons, and these can be nested within each other. This allows you to create and adjust the distribution and density of basis points with minimal input and effort. Basis points are shown as green “+” symbols in the plots and the SVAS polygons are shown in light blue.

Here is a close-up of special well basis point spacing, with higher basis point density near the well according to a logarithmic function.

## Modeling Goals

This hypothetical model aims to give guidance on questions that are typical for dewatering system design:

- What initial pumping rates for the wells will allow the water table inside the sheet pile barrier to be drawn down at least 10 ft within a period of 3 to 4 days?
- Once the desired drawdown is achieved by pumping at the initial rates, what schedule of reduced pumping rates will be needed to keep the heads drawn down at least 10 ft for a construction period of 7 days?
- What are the predicted heads at the well screens during pumping?
- What amount of mounding will occur at the recharge trench, assuming it injects all the water extracted at the pumping wells?

## Model Results

After building and adjusting the model, it was found that initial pumping rates of 1000 ft^{3}/d (5.2 gpm) at each of the three wells will get heads within the barrier down at least 10 ft in the top layer after 3.5 days of pumping. The model had two time periods, the first one 3.5 days long for the initial fixed-discharge pumping. During a second 7-day period, the discharge-specified wells were replaced with head-specified wells, so AnAqSim could determine the discharges needed to maintain the heads at required levels. This figure shows contours of heads and velocity vectors in level 1 (water table) at the end of period 1. A heavy blue line (many contours) occurs at the barrier, where heads jump from near 0 on the outside to about -10.5 ft on the inside. The location “x” is where head is highest within the barrier.

This figure shows heads and velocity vectors in level 4, just below the bottom of the barrier. At this level, flow converges towards the dewatering system, and rises upward to the pumping wells above.

This figure shows the evolution of head profiles running N-S through the recharge trench and the dewatering system in layer 1. The heads (water table elevations) in level 1 draw down more than 10.5 ft inside the barrier along this profile, which passes near one of the wells.

In level 4, there is no jump in head at the barrier since it is below the barrier, and the maximum drawdown under the center of the dewatering system is about 5.1 ft. In both profiles, the head patterns stabilize in the second period when the wells become head-specified.

A plot of head hydrographs at point X (see contour plot of level 1 heads above for location), which had the highest head inside the barrier (-10.3 ft) after 3.5 days of pumping. Deeper levels see smaller head changes. During the second period, heads remained essentially steady at all levels at point X.

This plot shows the discharges of one of the head-specified wells during the second period. These second period discharges ranged from 600 to 640 ft^{3}/d per well, considerably lower than the initial rate of 1000 ft^{3}/d. The head-specified wells were shut off in the first period. Discharge-specified wells at the same locations were pumping at the initial rate during the first period and shut off during the second period.

Heads at one well screen during the simulation are shown here. Heads rebounded some in the second period as discharges were reduced compared to the first period. The other wells are similar.

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Hydrographs for a location at the center of the recharge trench are shown here. The highest head increase occurs in level 1 at the end of the first period (h=1.34 ft), and head at this point is less than 0.9 ft by the end of the simulation because the system discharge goes from 3000 ft^{3}/d in the first period to 1900 ft^{3}/d in the second period.

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## Summary

With AnAqSim, it was fairly quick work to get insight into all the key design questions regarding anticipated discharges and heads. The entire modeling effort took about 4 hours to complete, from constructing the model through adjustments and creating outputs. Most of the modeling was done with a coarser model (3300 equations, 5 time steps), which took about 2 minutes to solve on an i5 computer. The final model used for the plots here had finer basis point spacing and more time steps (6600 equations, 10 time steps) and took about 12 minutes to solve. To alter the basis point spacing and number of time steps takes seconds, so it is easy to adjust the resolution of a model. Once a model is solved, the solution can be saved to disk and reloaded in seconds. To download the input files, right-click on the following links and select “Save link as…”.