Angle of Internal Friction given Shear Strength of Soil Calculator

Angle of Internal Friction Formula:

\[ \Phi_i = \arctan\left(\frac{\tau_s}{\sigma} \times \tan(I)\right) \]

Angle of Internal Friction (Φᵢ):

1. What is Angle of Internal Friction?

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

Purpose: It helps geotechnical engineers determine the stability of soil slopes and design foundations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Phi_i = \arctan\left(\frac{\tau_s}{\sigma} \times \tan(I)\right) \]

Where:

\( \Phi_i \) — Angle of internal friction (degrees)
\( \tau_s \) — Shear strength (Pa)
\( \sigma \) — Shear stress (Pa)
\( I \) — Angle of inclination (degrees)

Explanation: The formula calculates the angle of internal friction based on the ratio of shear strength to shear stress and the angle of inclination.

3. Importance of Angle of Internal Friction

Details: This parameter is crucial for analyzing slope stability, bearing capacity of foundations, and designing retaining structures.

4. Using the Calculator

Tips: Enter the shear strength, shear stress, and angle of inclination. All values must be > 0. Results are accurate within ±5%.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for angle of internal friction?
A: For soils, it typically ranges from 25° to 45°, with sands at the higher end and clays at the lower end.

Q2: Why do we need to consider ±5% tolerance?
A: Soil properties are naturally variable, and test results typically have this range of uncertainty.

Q3: How is this different from cohesion?
A: Internal friction relates to particle interlocking, while cohesion relates to chemical bonds between particles.

Q4: What units should I use for input?
A: Use consistent units (Pa for stresses, degrees for angles). The calculator handles the conversions.

Q5: How does water content affect the results?
A: Increased water content generally reduces the angle of internal friction, especially in fine-grained soils.