---
title: "Rankine versus Coulomb theory"
subject: "Foundation Engineering"
chapter: 3
key: "semester_5/foundation_engineering:rankine-vs-coulomb"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/rankine-vs-coulomb
site: BCT Engineering
---

# Rankine versus Coulomb theory

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

- Asked in: 2082 Bhadra, 2 marks; 2078 Bhadra, 4 marks; 2074 Chaitra, 2 marks (asked 3 times)
- Video: [Difference Between Rankine & Coulombs Earth Pressure Theory|Rankine vs. Coulomb|Foundation](https://www.youtube.com/watch?v=Ux_AYMHnVXw) — DIPAK  MANDAL
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/rankine-vs-coulomb
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

What are the differences between Rankine's and Coulomb's theories of lateral earth pressure (assumptions and four basic differences)?

## Short answer

Rankine assumes a smooth vertical wall, horizontal backfill, plastic equilibrium throughout the mass, and thrust parallel to the surface. Coulomb assumes a planar failure wedge, includes wall friction, allows inclined wall back and sloping backfill, and determines thrust from wedge force equilibrium.

## Answer

#### Assumptions
**Rankine's theory:**
- The soil is homogeneous, isotropic, semi-infinite and the wall back is **vertical and smooth** (no wall friction).
- The backfill surface is horizontal or a plane slope and the wall moves enough to reach the plastic state.
- Failure occurs by a state of plastic equilibrium in the whole soil mass; pressure acts parallel to the backfill slope.

**Coulomb's theory:**
- Soil is dry, homogeneous, isotropic and cohesionless.
- The failure surface is a **plane** through the heel of the wall; the failing wedge slides as a rigid body.
- Wall friction ($\delta$) acts on the back face; the wall back can be inclined and the backfill can slope.
- The resultant is found by wedge force equilibrium.

#### Four basic differences
| Point | Rankine | Coulomb |
|---|---|---|
| Approach | Stress state in soil mass (plastic equilibrium) | Force equilibrium of a sliding wedge |
| Wall friction | Neglected ($\delta = 0$) | Considered ($\delta \ne 0$) |
| Wall back / backfill | Vertical back, plane surface | Any inclined back and sloping backfill |
| Direction of thrust | Parallel to backfill surface | At angle $\delta$ to the normal to the wall |
| Failure surface | Planes through whole mass | Plane through the heel |
| Cohesion | Can include $c$ | Only cohesionless (basic form) |
| Result | Simple, slightly conservative for active | More accurate for active, less accurate for passive when $\delta > \phi/3$ |

## Check yourself

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

1. How do Rankine and Coulomb treat wall friction?
   A. Both consider it
   B. Rankine considers it, Coulomb neglects it
   C. Rankine neglects it (smooth wall), Coulomb considers it (delta)
   D. Both neglect it
   Answer: C. Rankine assumes a smooth vertical wall; Coulomb includes wall friction delta. (Key point: Wall friction)

2. What is the basic approach of Coulomb's theory?
   A. Stress state of plastic equilibrium in the whole mass
   B. Force equilibrium of a rigid sliding wedge
   C. Mohr circle at every point
   D. Finite element analysis
   Answer: B. Coulomb finds the resultant by force equilibrium of a wedge sliding on a plane through the heel. (Key point: Approach)

3. What is the direction of the thrust in Rankine's theory?
   A. At angle delta to the wall normal
   B. Perpendicular to the wall always
   C. Parallel to the backfill surface
   D. Vertical
   Answer: C. Rankine's pressure acts parallel to the backfill surface; Coulomb's acts at delta to the wall normal. (Key point: Thrust direction)

4. Which statement on cohesion is correct?
   A. Rankine can include c; Coulomb's basic form is only for cohesionless soil
   B. Coulomb can include c; Rankine cannot
   C. Neither can include c
   D. Both only for cohesive soil
   Answer: A. Rankine can include cohesion; the basic Coulomb theory is for dry cohesionless soil. (Key point: Soil type)

## Related in Foundation Engineering

- [Coulomb step ahead of Rankine](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acoulomb-step-ahead-rankine) — Foundation Engineering, chapter 3
- [Wall movement versus earth pressure plot](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-movement-pressure-plot) — Foundation Engineering, chapter 3
- [Earth pressure coefficients and types](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aearth-pressure-coefficients-types) — Foundation Engineering, chapter 3, asked 2×
- [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
- [Assumptions of conventional mat analysis](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-assumptions-conventional) — Foundation Engineering, chapter 7

## Related in other subjects

- [Limitations of Mohr-Coulomb theory](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amohr-coulomb-limitations) — Soil Mechanics, chapter 10
- [Design methods and basic assumptions](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Adesign-methods-assumptions) — Design of Steel and Timber Structure, chapter 2
- [Basic assumptions of working stress method](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Awsm-basic-assumptions) — Design of Steel and Timber Structure, chapter 2
- [Rankine efficiency and impulse versus reaction](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Arankine-efficiency-impulse-reaction) — Power Plant Equipment, chapter 7