---
title: "Stability checks of retaining walls"
subject: "Foundation Engineering"
chapter: 3
key: "semester_5/foundation_engineering:stability-checks-retaining-wall"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/stability-checks-retaining-wall
site: BCT Engineering
---

# Stability checks of retaining walls

Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls

- Asked in: 2075 Chaitra, 3 marks; 2075 Asoj, 2 marks (asked 2 times)
- Video: [4.14 Example 1: Stability check - overturning and sliding](https://www.youtube.com/watch?v=9mD5ag4gEcM) — Eng-aim
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/stability-checks-retaining-wall
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

Describe the methods (mathematical procedures) of stability check of a retaining wall.

## Short answer

Check overturning: FS = resisting moment / overturning moment ≥ 2. Sliding: FS = (V tanδb + ca B + Pp) / H ≥ 1.5. Bearing capacity: find eccentricity e ≤ B/6; qmax = (V/B)(1+6e/B) ≤ qa, qmin ≥ 0. Also check deep-seated slope stability (FS ≥ 1.5) and structural design.

## Answer

A retaining wall is checked for the following modes; $\sum V$ = total vertical load, $\sum H$ = total horizontal thrust.

#### 1. Overturning about the toe
$$
FS_{ot} = \frac{\sum M_R}{\sum M_O} \ge 2 \ (1.5 \text{ minimum in some codes})
$$
$M_R$ = resisting moment of wall weight, soil above heel, and passive pressure (if reliable); $M_O$ = overturning moment of lateral thrust about the toe.

#### 2. Sliding along the base
$$
FS_{s} = \frac{\sum V\tan\delta_b + c_a B + P_p}{\sum H} \ge 1.5
$$
$\delta_b$ = friction angle between base and soil (about $\tfrac23\phi$), $c_a$ = adhesion. A shear key is added if $FS$ is low.

#### 3. Bearing capacity and base pressure
Eccentricity $e = B/2 - \bar{x}$, with $\bar{x} = (\sum M_R - \sum M_O)/\sum V$; need $e \le B/6$ (no tension).
$$
q_{max,min} = \frac{\sum V}{B}\left(1 \pm \frac{6e}{B}\right)
$$
Check $q_{max} \le q_a$ (i.e. $FS = q_u/q_{max} \ge 3$) and $q_{min} \ge 0$.

#### 4. Overall (deep-seated) slope stability
Check circular slip surfaces below and around the wall (Fellenius or Bishop method), $FS \ge 1.5$.

#### 5. Settlement and structural checks
Estimate settlement of the base and check bending and shear of stem, heel and toe in RC walls.

## Check yourself

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

1. Factor of safety against overturning is:
   A. Sum of resisting moments / sum of overturning moments about the toe, at least 2
   B. Sum V tan(delta)/sum H, at least 1.5
   C. qu/qmax, at least 3
   D. Sum of overturning moments / sum of resisting moments
   Answer: A. FS_ot = sum M_R / sum M_O about the toe, normally at least 2. (Key point: Overturning FS)

2. In the sliding check, the resisting force comes from:
   A. Overturning moment
   B. Base friction (sum V tan delta_b), adhesion and passive pressure if reliable
   C. Only the active thrust
   D. Eccentricity of load
   Answer: B. FS_s = (sum V tan delta_b + c_a B + Pp)/sum H, at least 1.5. (Key point: Sliding)

3. To avoid tension at the base, the eccentricity e must satisfy:
   A. e <= B/2
   B. e <= B/3
   C. e <= B/6
   D. e >= B/6
   Answer: C. The resultant must lie in the middle third: e <= B/6, so q_min >= 0. (Key point: No-tension condition)

4. Overall (deep-seated) stability is checked using:
   A. Circular slip surfaces (Fellenius or Bishop), FS at least 1.5
   B. Rankine formula
   C. Culmann curve
   D. Eccentricity
   Answer: A. Circular slip surfaces below and around the wall are checked with FS >= 1.5. (Key point: Overall stability)

## Related in Foundation Engineering

- [Guidelines and design considerations, retaining walls](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aretaining-wall-guidelines) — Foundation Engineering, chapter 3
- [Proportioning of retaining walls](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aproportioning-retaining-walls) — Foundation Engineering, chapter 3, asked 3×
- [Stability of gravity wall, two layers](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astability-gravity-wall-two-layer) — Foundation Engineering, chapter 3
- [Stability of wall with surcharge 25 kN/m²](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astability-retaining-wall-q25) — Foundation Engineering, chapter 3
- [Stability of cantilever wall, q = 50 kPa](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astability-cantilever-wall-q50) — Foundation Engineering, chapter 3
- [Stability of cantilever wall, 8.6 m](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astability-cantilever-wall-8-6m) — Foundation Engineering, chapter 3

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