---
title: "Short note: Friction angle"
subject: "Engineering Geology I"
chapter: 6
key: "semester_3/engineering_geology_i:short-note-friction-angle"
source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/short-note-friction-angle
site: BCT Engineering
---

# Short note: Friction angle

Engineering Geology I · Chapter 6: Physical Geology

- Asked in: 2062 Baisakh (old course), 2 marks
- Video: [Simple Solution for Triaxial Tests | Use This Formula to Obtain Soil Cohesion and Friction Angle](https://www.youtube.com/watch?v=W1LIs7I8zSs) — 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_3/engineering_geology_i/short-note-friction-angle
- Whole chapter: https://www.bctengineer.com/md/semester_3/engineering_geology_i/chapter-6

## Question

Write a short note on friction angle.

## Short answer

Friction angle (φ) is the angle of shear resistance at which τ = σn tanφ for a cohesionless surface. It governs slope stability: a discontinuity dipping steeper than φ and daylighting can slide. Basic φb from smooth surfaces is 25–35°, and peak φ includes roughness.

## Answer

The **angle of friction ($\phi$)** is a measure of the shear strength due to friction on a surface or in a soil or rock. It is the angle whose tangent is the ratio of shear stress to normal stress at failure on a surface with no cohesion:

$$
\tau = \sigma_n \tan\phi \qquad \Rightarrow \qquad \phi = \tan^{-1}\left(\frac{\tau}{\sigma_n}\right)
$$

With cohesion $c$ the Mohr-Coulomb equation is $\tau = c + \sigma_n \tan\phi$.

- **Basic friction angle $\phi_b$:** from smooth, clean saw-cut rock surfaces (25 to 35 degrees).
- **Residual friction angle $\phi_r$:** after large displacement; lower than the peak value. Clay-filled joints can have $\phi_r$ of 10-20 degrees.
- **Peak friction angle:** includes roughness: $\phi_p = \phi_b + i$, where $i$ is the roughness angle.
- **Angle of repose:** the steepest angle of a loose heap that stays stable, about $\phi$ for dry granular material.

**Example:** $\tau = 140$ kPa at $\sigma_n = 200$ kPa gives $\phi = \tan^{-1}(0.7) = 35.0^\circ$.

A slope with a discontinuity dipping steeper than $\phi$ and daylighting in the face can slide.

## Check yourself

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

1. For a surface with no cohesion, the friction angle is:
   A. phi = tan(tau * sigma_n)
   B. phi = sigma_n / tau
   C. phi = sin^-1(tau + sigma_n)
   D. phi = tan^-1(tau / sigma_n)
   Answer: D. tau = sigma_n tan(phi) at failure. (Key point: Definition)

2. With cohesion, shear strength is:
   A. tau = c + sigma_n tan(phi)
   B. tau = c * sigma_n
   C. tau = c - sigma_n tan(phi)
   D. tau = sigma_n / tan(phi)
   Answer: A. Cohesion adds to the frictional term. (Key point: Mohr-Coulomb)

3. Residual friction angle compared with peak value is:
   A. Higher, since surfaces are rougher
   B. Lower, since it applies after large displacement
   C. Always equal
   D. Always zero
   Answer: B. Clay-filled joints may have residual phi of 10-20 degrees. (Key point: Residual vs peak)

4. With tau = 140 kPa at sigma_n = 200 kPa, phi equals:
   A. 45 degrees
   B. 20 degrees
   C. 35 degrees
   D. 55 degrees
   Answer: C. tan(phi) = 140/200 = 0.7, so phi = 35 degrees. (Key point: Example)

## Related in other subjects

- [Define limiting friction, angle of friction, coefficients](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alimiting-friction-angle-coefficient-definitions) — Applied Mechanics, chapter 5
- [Angle of friction; laws of static friction](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aangle-of-friction-laws-static-friction) — Applied Mechanics, chapter 5
- [Merchant circle and shear angle relation](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Amerchant-circle-force-relations-derivation) — Manufacturing and Production Processes, chapter 7