Angle of Internal Friction given Effective Normal Stress Calculator

Angle of Internal Friction Formula:

\[ \Phi_i = \arctan\left(\frac{F_s \times \zeta_{soil}}{\sigma_{effn}}\right) \]

Angle of Internal Friction:

1. What is Angle of Internal Friction?

Definition: The Angle of Internal Friction (Φ) is a measure of the shear strength of soil due to friction between soil particles.

Purpose: It's a key parameter in geotechnical engineering used to analyze soil stability and bearing capacity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Phi_i = \arctan\left(\frac{F_s \times \zeta_{soil}}{\sigma_{effn}}\right) \]

Where:

\( \Phi_i \) — Angle of internal friction (radians or degrees)
\( F_s \) — Factor of safety (dimensionless)
\( \zeta_{soil} \) — Shear stress of soil (MPa)
\( \sigma_{effn} \) — Effective normal stress (MPa)

Explanation: The formula calculates the angle whose tangent is the ratio of the product of safety factor and shear stress to the effective normal stress.

3. Importance in Geotechnical Engineering

Details: This angle is crucial for designing foundations, retaining walls, and slope stability analysis.

4. Using the Calculator

Tips: Enter the factor of safety, shear stress (MPa), and effective normal stress (MPa). All values must be > 0. Results are shown in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for angle of internal friction?
A: For soils, it typically ranges from 0° (pure clay) to 45° (dense gravel).

Q2: Why do we need the factor of safety?
A: The factor of safety accounts for uncertainties in material properties and loading conditions.

Q3: What affects the angle of internal friction?
A: Soil type, density, moisture content, and particle shape all influence this angle.

Q4: How accurate is this calculation?
A: The calculation has ±5% accuracy, but field testing provides more reliable results.

Q5: What's the difference between total and effective normal stress?
A: Effective stress accounts for pore water pressure, which reduces the stress between soil particles.