---
title: "Cantilever sheet pile, 8 m excavation"
subject: "Foundation Engineering"
chapter: 5
key: "semester_5/foundation_engineering:cantilever-sheet-pile-8m-excavation"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/cantilever-sheet-pile-8m-excavation
site: BCT Engineering
---

# Cantilever sheet pile, 8 m excavation

Foundation Engineering · Chapter 5: Flexible Retaining Structures and Coffer Dams

- Asked in: 2082 Bhadra, 4 marks
- Video: [Design of Cantilever sheet pile wall](https://www.youtube.com/watch?v=vLQYlU09LRw) — Civil Engineering 4 free
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/cantilever-sheet-pile-8m-excavation
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-5

## Question

Find the depth of embedment for the cantilever sheet pile supporting 8 m deep excavation in cohesionless soil. Take $\gamma_{sat} = 20\ \text{kN/m}^3$, $\gamma = 20\ \text{kN/m}^3$, $\phi = 33^\circ$ and water table at 6.5 m from the ground surface.

## Short answer

By balancing active and passive earth pressure moments about the pile tip, theoretical embedment below the 8 m excavation is 9.1 m. Applying a 20% safety increase yields a design depth of 10.9 m (total pile length ~19 m).

## Answer

**Data and assumptions:** excavation depth $H = 8$ m (dredge level); $\gamma = \gamma_{sat} = 20$ kN/m$^3$, $\phi = 33^\circ$; water table at 6.5 m below ground, taken at the same level on both sides (the excavation is flooded to the water table, no seepage and no net water pressure), so effective stresses with $\gamma' = 20 - 9.81 = 10.19$ kN/m$^3$ are used below the water table. Moments are taken about the pile tip (simplified cantilever method).

**Coefficients**
$$
K_a = \tan^2(45^\circ - 16.5^\circ) = 0.2948,\qquad K_p = \tan^2(45^\circ + 16.5^\circ) = 3.3921
$$

**Pressures**
- Active (back), depth $z$: $p_a = K_a\sigma_v'$; at 6.5 m $= 38.32$ kN/m$^2$; below 6.5 m the effective stress increases with $\gamma'$.
- Passive (front), depth $y$ below the dredge line: $p_p = K_p\gamma' y = 34.57\,y$ kN/m$^2$.

**Moment equilibrium about the tip:** for a trial embedment $D$,
$$
M_{active}(D) = \int_0^{8+D} p_a\,(8+D-z)\,dz,\qquad M_{passive}(D) = \tfrac16K_p\gamma' D^3
$$
Setting $M_{active} = M_{passive}$ and solving by trial and error:
$$
D = 9.10\ \text{m}:\quad M_{active} = 4338,\quad M_{passive} = 4338\ \text{kN m/m}
$$
(Active force 699 kN/m, passive force 1430 kN/m at this depth.)

**Design depth:** increase by 20% for safety (practice 20-40%):
$$
D_{design} = 1.2\times9.10 = 10.9\ \text{m}
$$

**Answer: theoretical embedment $D \approx 9.1$ m (below the 8 m dredge level); provide $\approx 11$ m, i.e. a total pile length of about 19 m.** For comparison, without the water table, $D = 6.4$ m.

## Check yourself

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

1. Why is gamma' = 10.19 kN/m^3 used below the water table?
   A. Water level is the same on both sides, so only buoyant weight matters with no net water pressure
   B. Soil is dry there
   C. Water is removed
   D. To increase passive pressure
   Answer: A. With equal water level both sides, net water pressure cancels and effective stress uses gamma' = 20 - 9.81. (Key point: Effective unit weight)

2. What are K_a and K_p for phi = 33 degrees?
   A. 0.33 and 3.0
   B. 0.2948 and 3.3921
   C. 3.39 and 0.295
   D. 0.5 and 2.0
   Answer: B. K_a = tan^2(28.5) = 0.2948, K_p = tan^2(61.5) = 3.3921. (Key point: Coefficients)

3. How is the theoretical embedment found?
   A. Vertical equilibrium
   B. Moments about the anchor
   C. Moments about the tip, equating active and passive moments by trial and error
   D. Direct formula without trials
   Answer: C. The simplified cantilever method equates moments about the pile tip for trial D. (Key point: Method)

4. What is the final design embedment?
   A. 9.10 m, unchanged
   B. 11 m, about 1.2 x 9.10
   C. 6.4 m
   D. 15 m
   Answer: B. D is increased by 20% for safety: 1.2 x 9.10 = 10.9, about 11 m. (Key point: Design depth)

## Related in Foundation Engineering

- [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
- [Anchor reduces cantilever sheet pile depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aanchor-reduces-embedment) — Foundation Engineering, chapter 5
- [Cantilever sheet pile, simplified method](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acantilever-sheet-pile-backfill-3m) — Foundation Engineering, chapter 5
- [Anchored sheet pile, free earth, with anchor pull](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aanchored-sheet-pile-embedment) — Foundation Engineering, chapter 5
- [Sheet pile and deflected shapes](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asheet-pile-deflected-shapes) — Foundation Engineering, chapter 5
- [Active pressure, sloping backfill and water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-sheet-pipe-sloping-backfill) — Foundation Engineering, chapter 3

## Related in other subjects

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