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Angle of Internal Friction given Shear Strength of Cohesionless Soil Calculator

Angle of Internal Friction Formula:

\[ \phi = \tan^{-1}\left(\frac{\tau_s}{\sigma_{nm}}\right) \]

MPa
MPa

1. What is Angle of Internal Friction?

Definition: The angle of internal friction is a measure of the shear strength of soils due to friction between particles.

Purpose: It's a key parameter in soil mechanics used to analyze slope stability, bearing capacity, and earth pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi = \tan^{-1}\left(\frac{\tau_s}{\sigma_{nm}}\right) \]

Where:

  • \( \phi \) — Angle of internal friction (degrees)
  • \( \tau_s \) — Shear strength (MPa)
  • \( \sigma_{nm} \) — Normal stress (MPa)

Explanation: The angle is calculated as the arctangent of the ratio of shear strength to normal stress.

3. Importance in Geotechnical Engineering

Details: This parameter is crucial for designing foundations, retaining walls, and assessing slope stability in cohesionless soils.

4. Using the Calculator

Tips: Enter the shear strength and normal stress values in MPa. The ±5% indicates typical measurement accuracy.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical range for φ in cohesionless soils?
A: For sands: 28°-45°; for gravels: 35°-50°; higher values indicate more angular particles.

Q2: Why is this only for cohesionless soils?
A: Cohesive soils have additional shear strength from cohesion, requiring a different formula (Mohr-Coulomb).

Q3: How is shear strength determined experimentally?
A: Typically through direct shear tests or triaxial tests in a geotechnical laboratory.

Q4: What affects the angle of internal friction?
A: Particle shape, size distribution, density, and mineral composition all influence φ.

Q5: How accurate is this calculation?
A: The ±5% reflects typical measurement accuracy; actual field conditions may vary further.

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