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

# Cantilever sheet pile, 5 m excavation

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

- Asked in: 2076 Asoj, 3 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-5m-sand
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-5

## Question

An excavation of 5 m deep is to be carried out in sandy soil deposit having unit weight $= 22\ \text{kN/m}^3$ and angle of shearing resistance $= 33^\circ$. To support the soil, cantilever sheet pile walls are driven into the ground prior to excavation. Determine the depth of embedment needed for the sheet pile to retain the backfill. The water table is located below the base of the sheet pile.

## Short answer

Using the simplified moment method, theoretical embedment D = 3.98 m. With a 20% increase for safety, adopt D ≈ 4.8 m (total length ~9.8 m).

## Answer

**Data:** $H = 5$ m, $\gamma = 22$ kN/m$^3$, $\phi = 33^\circ$, no water above the pile tip. Cantilever sheet pile, simplified moment method (moments about the toe).

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

**Forces** (with $D$ = embedment below the dredge line, $\gamma$ same on both sides):
- Active force on the back: $P_a = \tfrac12K_a\gamma(H+D)^2$, acting at $(H+D)/3$ above the tip.
- Passive force in front: $P_p = \tfrac12K_p\gamma D^2$, acting at $D/3$ above the tip.

**Moment about the tip**
$$
\tfrac12K_a\gamma(H+D)^2\frac{H+D}{3} = \tfrac12K_p\gamma D^2\frac{D}{3}
\ \Rightarrow\ \frac{D}{H+D} = \left(\frac{K_a}{K_p}\right)^{1/3} = \left(\frac{0.2948}{3.3921}\right)^{1/3} = 0.4429
$$
$$
D = \frac{0.4429\times5}{1-0.4429} = 3.98\ \text{m}
$$

**Design depth:** since the method assumes full passive resistance and ignores the extra tip reaction, increase by 20%:
$$
D_{design} = 1.2\times3.98 = 4.77\ \text{m}
$$

**Answer: theoretical embedment $D = 3.98$ m; adopt $D \approx 4.8$ m** (total pile length about 9.8 m).

## Check yourself

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

1. What condition gives D?
   A. Moments of active and passive forces about the tip are equal
   B. Forces equal
   C. Anchor moment zero
   D. Active force zero
   Answer: A. Equating P_a (H+D)/3 to P_p D/3 gives the embedment. (Key point: Moment equation)

2. What is D/(H+D) here?
   A. 0.2948
   B. 0.4429
   C. 0.3333
   D. 0.5
   Answer: B. (0.2948/3.3921)^(1/3) = 0.4429. (Key point: Result of ratio)

3. What is theoretical D for H = 5 m?
   A. 2.21 m
   B. 5.0 m
   C. 3.98 m
   D. 4.77 m
   Answer: C. D = 0.4429x5/(1-0.4429) = 3.98 m. (Key point: Theoretical D)

4. Why is D increased by 20%?
   A. To reduce active pressure
   B. Method assumes full passive resistance and ignores tip reaction
   C. To account for the water table
   D. To reduce K_p
   Answer: B. The simplified method over-estimates passive support, so a 20% increase gives about 4.8 m. (Key point: Design increase)

## Related in Foundation Engineering

- [Cantilever sheet pile, 8 m excavation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acantilever-sheet-pile-8m-excavation) — 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
- [Anchor reduces cantilever sheet pile depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aanchor-reduces-embedment) — Foundation Engineering, chapter 5
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## Related in other subjects

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