Chapter 8, Problem 8.1P

To determine

Draw the flow net and calculate the seepage loss per meter length of the sheet pile.

Answer to Problem 8.1P

The seepage loss per meter length of the sheet pile is $\underset{\_}{77.76\times {10}^{-2}{\text{m}}^{\text{3}}\text{/m/day}}$.

Explanation of Solution

Given information:

The hydraulic conductivity of the permeable soil layer k is $4\times {10}^{-4}\text{cm/sec}$.

The height of the water level $H_1$ is 6 m.

The height of the water level $H_2$ is 1.5 m.

The depth of permeable layer up to the end of sheet pile D is 3 m.

The depth of permeable layer $D_1$ is 6 m.

Calculation:

Draw the free body diagram of the flow net for the given values as in Figure (1).

Refer Figure 1.

Determine the head difference between the upstream and downstream using the relation.

$H=H_1-H_2$

Substitute 6 m for $H_1$ and 1.5 m for $H_2$.

$\begin{array}{c}H=6-1.5\\ =4.5\text{m}\end{array}$

Determine the seepage loss per meter length of the sheet pile using the relation.

$q=kH\frac{N_f}{N_d}$

Here, $N_f$ is the number of flow lines and $N_d$ is the number of potential drops.

Substitute $4\times {10}^{-4}\text{cm/sec}$ for k, 4.5 m for H, 4 for $N_f$, and 8 for $N_d$.

$\begin{array}{c}q=4\times {10}^{-4}\text{cm/sec}\times \frac{1\text{m}}{100\text{cm}}\times \frac{86,400\sec }{1\text{day}}\times 4.5\times \frac{4}{8}\\ =77.76\times {10}^{-2}{\text{m}}^{\text{3}}\text{/m/day}\end{array}$

Therefore, the seepage loss per meter length of the sheet pile is $\underset{\_}{77.76\times {10}^{-2}{\text{m}}^{\text{3}}\text{/m/day}}$.