Seepage within a soil medium can be shown by flow nets:

Groundwater 2a

In the figure above we show an seepage flow condition below a dam. The total head anywhere in the water body at the left of the dam is 14m and in the water body at the right side of the dam is 2m. To understand why, remember the formula for total head first:

Total Head = Elevation head + Velocity Head + Pressure Head

Now, we can immediately eliminate velocity head here, as the water on the left side and right side of the dam are static and not flowing. So we are left with:

Total Head = Elevation head + 0 + Pressure Head

Now, when we are at the surface of water on the left side for example, we have an elevation of 14 m, but a pressure is zero. So the total head is 14m there. If we start to move down , or elevation head will start do decrease, but then out pressure head will increase in the same amount. this will keep the total head constant at 14m. Why does pressure head increase same amount of elevation head drop? Because there is no medium to cause any drop in head there. We are simply moving up and down, left and right in same water body. We will also show this in the equation which we will give later under water resources engineering, but purposefully not giving it here yet, to underline it is important to know is that the head did not change as there is no medium to cause change.

Now that we understood the situation in the water body at the left of the dam (although we did not see the details of the equation yet), let’s start to follow the path of water towards the right of the dams as it flows.

We have seen that anywhere on the right of the dam, tota head is 14 m. The we reach to the bottom of the water on the right side. We still have 14 meter head. Now, as soon as we enter into the soil, we can immediately know that the total head will start to drop. Why? because on the right side of the dam, the total head of that water body is 2m. It means, there was a total drop of 14-2 = 12m head. Therefore, this head drop can only be caused by the soil under the dam. The soil under the dam hinders the flow of water and while doing it, it causes the total head of water to decrease.

So now we entered into the soil, right below the water body on the left side, and the total head started to drop. We know that in the end it dropped to 2 meters. But we do not know yet, in what part of that soil, it dropped to which value. We only know the end result *(Why is it important to know in what part of the soil the head dropped by, or became how much? Because if we know this, we can later find water forces accurately anywhere below the dam, which becomes important later when designing the dam or any sheet pile that we may insert below the dam and the forces that will act on it (which would actually cause us to draw a different flow net pattern).*

To make an accurate estimate of what happened to total head below the dam, we can start by thinking that the total head drop is 12, so we can divide this total drop to drops of equal intervals. So we draw imaginary lines, which are called equipotential lines, as seen in the figure above. Each equipotential line represents an equal drop in total head. Here for convenience, we drew 6 lines, each of which represents a drop of 12/6=2 meters. So for each equipotential line, we showed the total head on that line as TH, where it equally drops by 2 meters each time. So for example, on the equipotental line where we wrote TH=4, anywhere on the line will have a total head of 4 meters. In theory we could have drawn more or less lines. The more lines we draw, the more precise it would be, but the more difficult to draw a flow net.

Other than the potential drop, we also drew flow lines, which divides the total flow of water into channels of equal flow. So each channel between two flow lines is called a flow channel and each flow channel carries the same amount of flow. So in other words, in the figure above, the totla amount of flow would be 4q.

Drawing 6 equipotential lines and 3 flow lines were not totally by chance however, as there are a few things we must look at when we draw these. Firstly, we must draw the lines so that each area in the net would be as close as possible to a square shape. The also means, the lines should intersect each other as close as possible to 90 degrees. So for example we could not have drawn 12 equipotential lines and still 3 flow lines, as this time each area in the flow net would not be square.

For different conditions, the geometry of flow net changes but the rules we follow must remain the same. For example, we could insert a sheet pile wall below the dam, in order to further hinder the passage of water below the dam. In that case, our flow channels can not just continue as they were. The must go around the sheet piling, which would mean a much longer path through the soil, which would mean more total head loss, which would make the water level on the right less than 2 meters for example, which would be a good thing for our purpose, since the purpose of the dame is to prevent water flow in the first place. Of course since flow channels now go around the sheet pile, the shape of our flow net would be different but we would still follow the same rules when drawing it.

In the figure below, we give exactly the previous figure, to emphasize one thing only, to make sure it is clear. Let’s assume we inserted a tube (called a piezometer tube) down to the equipotential line with a total head of 4m as below. The water height will be as shown, which will climb to 2 meters above the 2 meter high water high water surface, for a total head of 4.

Groundwater 2b

In the next post of this series, we will discuss “Rock Mechanics”

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