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

# Coulomb step ahead of Rankine

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

- Asked in: 2080 Baisakh, 2 marks
- Video: [How to Calculate Coulomb Earth Pressure: Step-by-Step Retaining Wall Example](https://www.youtube.com/watch?v=GWCe0ZIY7HI) — Soil Mechanics and Engineering Geology
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/coulomb-step-ahead-rankine
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

How is Coulomb's theory a step ahead of Rankine's theory for calculating earth pressure? Justify your answer in reference to the limitations of Rankine's theory.

## Short answer

Coulomb’s theory includes wall friction δ, adhesion, and allows inclined backfill and wall, giving a more realistic thrust direction. Rankine assumes a smooth vertical wall, horizontal or uniformly sloping backfill, and thrust parallel to the surface. Coulomb thus removes Rankine’s limitations for rough, inclined walls and irregular ground.

## Answer

Rankine's theory is limited because it assumes a **smooth, vertical wall back** (no wall friction), a **horizontal or uniformly sloping** backfill, and a thrust parallel to the backfill surface. It cannot deal with an inclined wall back, a broken ground surface or a rough wall, and its fixed thrust direction does not match the real direction on a rough wall.

Coulomb's wedge theory removes these limits:
- It includes **wall friction** ($\delta$) and wall **adhesion**, so the result is more realistic for rough concrete or masonry walls.
- It allows an **inclined wall back** and a **sloping backfill**.
- The thrust direction (at $\delta$ to the normal to the wall) is obtained, and loads such as surcharge and line loads can be included through the wedge weight (and the Culmann graphical method).
- It handles irregular ground surfaces.

Hence Coulomb's theory is more general and gives a more accurate active thrust, so it is a step ahead of Rankine's.

## Check yourself

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

1. Which is a limitation of Rankine's theory?
   A. Cannot consider a smooth wall
   B. Assumes a smooth vertical wall back, so cannot handle a rough or inclined wall
   C. Cannot handle horizontal backfill
   D. Requires wall friction
   Answer: B. Rankine assumes a smooth, vertical wall and thrust parallel to the surface. (Key point: Rankine limitation)

2. Coulomb's theory improves on Rankine by:
   A. Ignoring wall friction
   B. Including wall friction, inclined wall back, sloping backfill and giving thrust direction
   C. Only handling cohesive soil
   D. Using Mohr circles
   Answer: B. Coulomb includes delta, inclined backs, sloping and irregular surfaces and thrust direction. (Key point: Coulomb improvement)

3. How can surcharges and line loads be included in Coulomb's approach?
   A. Through the wedge weight (and Culmann method)
   B. They cannot be included
   C. By changing phi
   D. By ignoring the wedge
   Answer: A. The loads are added into the wedge weight. (Key point: Loads in wedge)

## Related in Foundation Engineering

- [Rankine versus Coulomb theory](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Arankine-vs-coulomb) — Foundation Engineering, chapter 3, asked 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×
- [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

## 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
- [Theory of filtration and its limitations](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Atheory-of-filtration) — Water Supply Engineering, chapter 6, asked 2×
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- [Applications and limitations of hydrograph theory](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahydrograph-theory-applications-limits) — Engineering Hydrology, chapter 5