---
title: "Anchored sheet pile, free earth, with anchor pull"
subject: "Foundation Engineering"
chapter: 5
key: "semester_5/foundation_engineering:anchored-sheet-pile-embedment"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/anchored-sheet-pile-embedment
site: BCT Engineering
---

# Anchored sheet pile, free earth, with anchor pull

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

- Asked in: 2081 Baisakh, 3+1 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/anchored-sheet-pile-embedment
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-5

## Question

Determine the depth of embedment of the free earth support anchored sheet pile shown in figure below. Also, find the tensile force (T) per meter acting on the anchor. Assume necessary conditions. [Figure: anchored sheet pile with 8.0 m height above dredge level, anchor (tie rod) T about 2.5 m below top; soil above water level $\gamma = 16\ \text{kN/m}^3$, $\phi = 35^\circ$ for about 3.0 m; below that $\gamma_{sat} = 19\ \text{kN/m}^3$, $\phi = 35^\circ$. Dimensions as read from the scan.]

## Short answer

Using free earth support method, moment equilibrium about the anchor gives embedment depth D = 2.57 m. The anchor force T = 77.3 kN/m. Increase embedment by 30% to 3.3 m for design.

## Answer

**Data and assumptions (figure values as read):** height above dredge level $H = 8.0$ m; anchor (tie rod) at 2.5 m below the top; soil above the water table: $\gamma = 16$ kN/m$^3$, $\phi = 35^\circ$ for the top 3.0 m; below: $\gamma_{sat} = 19$ kN/m$^3$, $\phi = 35^\circ$. Water level is taken the same on both sides (no net water pressure), so $\gamma' = 19 - 9.81 = 9.19$ kN/m$^3$ is used below the water table. Free earth support method, passive resistance with $FS = 1$ for the theoretical depth.

$$
K_a = \tan^2(45^\circ-17.5^\circ) = 0.2710,\qquad K_p = \tan^2(45^\circ+17.5^\circ) = 3.6902
$$

**Active pressure** (back, depth $z$): $p_a = K_a\sigma_v'$
- $z = 3$ m: $\sigma_v' = 48$, $p_a = 13.01$ kN/m$^2$.
- $z = 8$ m (dredge): $\sigma_v' = 48 + 9.19\times5 = 93.95$, $p_a = 25.46$ kN/m$^2$.
- Below the dredge line: the effective stress increases by $\gamma'$ per metre.

**Passive pressure** (front): $p_p = K_p\gamma' y = 33.91\,y$ kN/m$^2$, $y$ measured below the dredge line.

**Moment about the anchor** (level 2.5 m): for a trial embedment $D$,
$$
\sum M_{active} = \int_0^{8+D} p_a\,(z-2.5)\,dz,\qquad \sum M_{passive} = \int_0^{D} p_p\,(8 + y - 2.5)\,dy
$$
Equating and solving by trial and error:
$$
D = 2.57\ \text{m}
$$
At this depth: active force $P_a = 189.3$ kN/m, passive force $P_p = 112.0$ kN/m.

**Design embedment:** increase by 30% (free earth support): $D_{design} = 1.3\times2.57 = 3.3$ m.

**Tension in the anchor** from horizontal equilibrium:
$$
T = P_a - P_p = 189.3 - 112.0 = 77.3\ \text{kN/m}
$$

**Answer: depth of embedment $D \approx 2.57$ m (adopt about 3.3 m); anchor force $T \approx 77$ kN per metre run.**

## Check yourself

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

1. Where are moments taken for the free earth support pile?
   A. About the dredge line
   B. About the pile tip
   C. About the anchor level
   D. About the water table
   Answer: C. Moments about the anchor eliminate T and give D. (Key point: Method used)

2. What water assumption is used?
   A. Water only on the back
   B. Water level same on both sides, so gamma' = 9.19 used below the water table
   C. Dry soil throughout
   D. Full seepage
   Answer: B. No net water pressure, with submerged unit weight 19 - 9.81 = 9.19 kN/m^3. (Key point: Water pressure assumption)

3. How is the anchor force found?
   A. T = P_p
   B. T = P_a + P_p
   C. T = P_a - P_p, about 77 kN/m
   D. T = 0.3 P_a
   Answer: C. Horizontal equilibrium gives 189.3 - 112.0 = 77.3 kN/m. (Key point: Tie rod force)

4. What is the embedment from analysis and the adopted value?
   A. 3.3 m theoretical, 2.57 m adopted
   B. 2.57 m theoretical, about 3.3 m adopted (30% increase)
   C. 8 m
   D. 2.57 m, no increase
   Answer: B. Trial and error gives D = 2.57 m; increased by 30% to about 3.3 m. (Key point: Design embedment)

## Related in Foundation Engineering

- [Anchored sheet pile, free earth procedure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aanchored-sheet-pile-free-earth-procedure) — 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
- [Free earth versus fixed earth support](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afree-vs-fixed-earth-support) — Foundation Engineering, chapter 5
- [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
- [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
- [Sheet pile and deflected shapes](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asheet-pile-deflected-shapes) — Foundation Engineering, chapter 5

## Related in other subjects

- [Sheet pile seepage quantity numerical](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-seepage-quantity-numerical) — Soil Mechanics, chapter 7
- [Force method: frame with hinged support](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aforce-method-frame-30knm-50kn-hinged) — Theory of Structures II, chapter 2