---
title: "State Mohr-Coulomb failure criterion"
subject: "Soil Mechanics"
chapter: 10
key: "semester_4/soil_mechanics:mohr-coulomb-criterion-state"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/mohr-coulomb-criterion-state
site: BCT Engineering
---

# State Mohr-Coulomb failure criterion

Soil Mechanics · Chapter 10: Shear Strength of Soil

- Asked in: 2079 Asoj, 2 marks
- Video: [Mohr-Coulomb Failure Analysis of Triaxial Tests on Soil | How to Obtain Cohesion and Friction Angle](https://www.youtube.com/watch?v=N0ydpBr4NLM) — Soil Mechanics and Engineering Geology
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/mohr-coulomb-criterion-state
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-10

## Question

State Mohr-Coulomb's failure criterion.

## Short answer

The Mohr-Coulomb failure criterion states that soil fails when shear stress on a plane reaches τ_f = c + σ tan φ (effective stress: τ_f = c' + σ' tan φ'). The Mohr circle must not cross this line; failure occurs when it touches, on a plane inclined at 45°+φ/2 to major principal plane.

## Answer

**Mohr-Coulomb failure criterion:** a soil fails when the shear stress on any plane reaches the shear strength, which is a linear function of the normal stress on that plane:

$$
\tau_f = c + \sigma\tan\phi
$$

In terms of effective stress, $\tau_f = c' + \sigma'\tan\phi'$. Here $c$ is the cohesion intercept and $\phi$ is the angle of shearing resistance (internal friction).

- If the Mohr circle for a stress state lies wholly below the failure line, the soil is stable.
- If the circle touches the line, the soil is on the point of failure.
- A circle cannot extend above the line.

Failure occurs on a plane inclined at $45^\circ+\phi/2$ to the major principal plane.

## Check yourself

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

1. What does the Mohr-Coulomb criterion state?
   A. Shear strength is independent of normal stress
   B. Shear strength is proportional to the square of normal stress
   C. Shear strength is a linear function of normal stress: tau_f = c + sigma tan(phi)
   D. Shear strength equals cohesion only
   Answer: C. The strength increases linearly with normal stress at slope tan(phi), with intercept c. (Key point: Criterion)

2. What does a Mohr circle touching the failure line mean?
   A. The soil is perfectly stable
   B. The soil is on the point of failure
   C. The soil has already failed and cannot exist
   D. The soil has no friction
   Answer: B. Circles below the line are safe, tangent is failure, and circles cannot lie above the line. (Key point: Mohr circle position)

3. At what angle to the major principal plane is the failure plane?
   A. 45 - phi/2
   B. 45 + phi/2
   C. phi
   D. 90 + phi
   Answer: B. Failure occurs on a plane inclined at 45 + phi/2 to the major principal plane. (Key point: Failure plane)

## Related in Soil Mechanics

- [Derive Mohr-Coulomb principal stress relation](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amohr-coulomb-derive-principal-stresses) — Soil Mechanics, chapter 10, asked 4×
- [Limitations of Mohr-Coulomb theory](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amohr-coulomb-limitations) — Soil Mechanics, chapter 10
- [Principal stresses; Mohr circle at failure](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aprincipal-stresses-mohr-circle-friction) — Soil Mechanics, chapter 10