---
title: "Sheet pile seepage quantity numerical"
subject: "Soil Mechanics"
chapter: 7
key: "semester_4/soil_mechanics:sheet-pile-seepage-quantity-numerical"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/sheet-pile-seepage-quantity-numerical
site: BCT Engineering
---

# Sheet pile seepage quantity numerical

Soil Mechanics · Chapter 7: Seepage through Soils

- Asked in: 2078 Poush, 4 marks
- Video: [Flow-Net - Solved Numerical - Soil Mechanics - Geotechnical Engineering](https://www.youtube.com/watch?v=bw7GzGwiOeY) — Vital Vibes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/sheet-pile-seepage-quantity-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-7

## Question

A deposit of cohesionless soil with a permeability of $4 \times 10^{-2}$ cm/s has a depth of 10 m with an impervious ledge below. A sheet pile wall is driven into this deposit to a depth of 7 m. The wall extends above the surface of the soil and a 3 m depth of water acts on one side. Sketch the flow net and determine the seepage quantity per metre length of the wall.

## Short answer

For sheet pile with k=4×10⁻⁴ m/s, H=3 m, penetration ratio 0.7, flow net gives Nf=3, Nd=8. Seepage q = kH(Nf/Nd) = 4.5×10⁻⁴ m³/s per m (≈39 m³/day per m).

## Answer

#### Given

$k = 4\times10^{-2}$ cm/s $= 4\times10^{-4}$ m/s. Permeable layer depth $T = 10$ m, sheet pile penetration $s = 7$ m (so $s/T = 0.7$), net head $H = 3$ m.

#### Flow net

```text
  H=3m ▽       |P|
  ~~~~~~~~~~~~~|P|~~~~~~ (downstream ground)
   ground      |P|   7 m
   3 flow channels, 8 equipotential drops
   ______________|__|________
   ======== impervious, 10 m deep ========
```

Draw the flow net with the pile tip 3 m above the impervious layer. Sketching it gives about

- $N_f = 3$ flow channels
- $N_d = 8$ equipotential drops

#### Seepage quantity

$$
q = k\,H\,\frac{N_f}{N_d} = 4\times10^{-4} \times 3 \times \frac{3}{8} = 4.5\times10^{-4}\ \text{m}^3/\text{s per m}
$$

$$
q = 4.5\times10^{-4} \times 86400 = 38.9\ \text{m}^3/\text{day per metre length}
$$

A check with the exact solution for a single sheet pile of penetration ratio $s/T = 0.7$ gives $q/(kH) = 0.371$, i.e. $q = 4.45\times10^{-4}$ m³/s per m, so the flow net values agree.

**Answer: $q \approx 4.5\times10^{-4}$ m³/s per metre length ($\approx 39$ m³/day per m).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is k = 4 x 10^-2 cm/s in m/s?
   A. 4 x 10^-4
   B. 4 x 10^-3
   C. 4 x 10^-5
   D. 4 x 10^-1
   Answer: A. cm/s to m/s divides by 100, giving 4 x 10^-4 m/s. (Key point: Unit conversion)

2. What net head H is used?
   A. 10 m
   B. 7 m
   C. 3 m
   D. 4 m
   Answer: C. The water depth of 3 m on one side is the head loss. (Key point: Net head)

3. From the sketched flow net, which counts are used?
   A. N_f = 8, N_d = 3
   B. N_f = 3, N_d = 8
   C. N_f = 7, N_d = 10
   D. N_f = 3, N_d = 3
   Answer: B. The net has 3 flow channels and 8 equipotential drops. (Key point: Flow net counts)

4. What is q = k H N_f/N_d?
   A. 4.5 x 10^-4 m3/s per m
   B. 1.2 x 10^-3 m3/s per m
   C. 4.5 x 10^-2 m3/s per m
   D. 1.6 x 10^-4 m3/s per m
   Answer: A. 4e-4 x 3 x 3/8 = 4.5e-4 m3/s per m. (Key point: Result)

## Related in Soil Mechanics

- [Impervious dam seepage discharge](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aimpervious-dam-seepage-discharge-numerical) — Soil Mechanics, chapter 7
- [Earth dam with filter, seepage quantity](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aearth-dam-horizontal-filter-seepage) — Soil Mechanics, chapter 7
- [Infinite slope, cohesionless, steady seepage](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Ainfinite-slope-cohesionless-seepage) — Soil Mechanics, chapter 11
- [Flow net under sheet pile, discharge](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-flow-net-steps-discharge) — Soil Mechanics, chapter 7
- [Sheet pile flow net; graded filter](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-flow-net-graded-filter) — Soil Mechanics, chapter 7
- [Average permeability of layered soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Alayered-soil-average-permeability) — Soil Mechanics, chapter 6

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- [Cantilever sheet pile, 5 m excavation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acantilever-sheet-pile-5m-sand) — Foundation Engineering, chapter 5
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