Angle of Internal Friction given Factor of Safety Calculator

Angle of Internal Friction Formula:

\[ \phi = \arctan\left(\frac{F \cdot \gamma_{sat} \cdot \tan(\phi_{IF})}{\gamma'}\right) \]

Factor of Safety (F):

Saturated Unit Weight (γ_sat):

N/m³

Weighted Friction Angle (φ_IF):

rad

Submerged Unit Weight (γ'):

N/m³

Angle of Internal Friction (φ):

1. What is Angle of Internal Friction?

Definition: The Angle of Internal Friction (φ) is a measure of the shear strength of soils and other granular materials.

Purpose: It's crucial for analyzing slope stability, bearing capacity, and earth pressure calculations in geotechnical engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi = \arctan\left(\frac{F \cdot \gamma_{sat} \cdot \tan(\phi_{IF})}{\gamma'}\right) \]

Where:

\( \phi \) — Angle of internal friction (radians or degrees)
\( F \) — Factor of Safety
\( \gamma_{sat} \) — Saturated unit weight (N/m³)
\( \phi_{IF} \) — Weighted friction angle (radians)
\( \gamma' \) — Submerged unit weight (N/m³)

3. Importance of Angle of Internal Friction

Details: This parameter is fundamental for designing foundations, retaining walls, and assessing slope stability in soil mechanics.

4. Using the Calculator

Tips: Enter all required parameters. The calculator provides results in both radians and degrees. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for φ in soils?
A: For sands: 28°-45°; for silts: 25°-35°; for clays: 0°-25° (depending on consolidation).

Q2: Why use both radians and degrees?
A: Radians are mathematically convenient, while degrees are more intuitive for engineering applications.

Q3: What does ±5% mean?
A: It indicates the typical measurement or estimation uncertainty for these parameters.

Q4: How does factor of safety affect the result?
A: Higher safety factors result in higher calculated friction angles, indicating more conservative designs.

Q5: When would I need this calculation?
A: When designing earth structures, analyzing slope stability, or assessing bearing capacity of foundations.