A 6 ft diameter, 2000 ft long sewer drain pipe is to be installed 24 ft below the ground surface as shown in Figure 8.6. To build this pipe, a long trench must be excavated below the groundwater table as shown. Steel sheet piles (heavy, corrugated sheets of steel) will be installed to keep the

Question

A 6 ft diameter, 2000 ft long sewer drain pipe is to be installed 24 ft below the ground surface as shown in Figure 8.6. To build this pipe, a long trench must be excavated below the groundwater table as shown. Steel sheet piles (heavy, corrugated sheets of steel) will be installed to keep the sides from collapsing, and the trench will be dewatered with pumps. After the pipeline is installed, the pumps will be removed, the trench will be backfilled, and the sheet piles will be removed.

The dewatering pumps will be placed at 100 ft intervals along the trench. Assuming the sheet piles are perfectly watertight (probably not a good assumption!), draw a flow net and compute the $Q$ for each pump.

The dewatering pumps will be placed at 100 ft intervals along the trench. Assuming the sheet piles are perfectly watertight (probably not a good assumption!), draw a flow net and compute the [latex]Q[/latex] for each pump.

Accepted Answer

1. The cross-section is symmetrical about a vertical axis through the center of the trench, so we will draw a flow net for the left half only, then double the computed [latex]Q[/latex].
2. The hydraulic conductivity in the clean sand strata is 1000 times higher than in the sandy silt, so the groundwater will move laterally into the sand much more easily than it will seep through the sandy silt. Therefore, the only significant head losses will be through the sandy silt, and we only need to draw the flow net through this strata.
3. The resulting flow net, developed by the converging trial-and-error method described above, is shown on the right side of Figure 8.6. We chose to use [latex]N_{F}= 4[/latex] and [latex]a/b = 1[/latex], and counted [latex]N_{D} = 12.6[/latex] from the finished flow net. The uppermost equipotential drop is not a full "square," so it only counts as 0.6.
4. The flow rate per pump is then:

[latex]Q=2kL\Delta h\frac{N_{F}}{N_{D}} \frac{b}{a} =2\left(2 imes 10^{-6} ft/s ight) \left(100ft ight) \left(20ft ight) \left\lgroup\frac{4}{12.6} ight group \left(1 ight) =2.5 imes 10^{-3}ft^{3}/s imes 449 gal/min per ft^{3}/s[/latex] = 1.1 gal/min per pump

5. According to Equation 7.1 [latex]Q= u A[/latex], the velocity is greatest when the area is small, so the groundwater velocity will be greatest when the flow tube is narrow. In this cross-section, the narrowest spot is near the tip of the sheet pile. Because the velocity here is high, there will be much more friction between the flowing water and the soil, so the hydraulic gradient also will be high. Thus, the equipotential lines also are close together in this area.

Question 8.1: A 6 ft diameter, 2000 ft long sewer drain pipe is to be inst...

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