Angle of Internal Friction given Factor of Safety for Cohesive Soil Calculator

Angle of Internal Friction Formula:

\[ \phi_i = \arctan\left(\frac{(\tau_{Shearstress} \times fs) - c_u}{\sigma_{Normal}}\right) \]

Shear Stress for Factor of Safety:

Factor of Safety:

Unit Cohesion:

Normal Stress:

Angle of Internal Friction (degrees):

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:

\[ \phi_i = \arctan\left(\frac{(\tau_{Shearstress} \times fs) - c_u}{\sigma_{Normal}}\right) \]

Where:

\( \phi_i \) — Angle of internal friction (degrees)
\( \tau_{Shearstress} \) — Shear stress for factor of safety (±5%)
\( fs \) — Factor of safety (±5%)
\( c_u \) — Unit cohesion (±5%)
\( \sigma_{Normal} \) — Normal stress (±5%)

Explanation: The formula calculates the angle whose tangent is the ratio of (shear stress times safety factor minus cohesion) to normal stress.

3. Importance of Angle of Internal Friction

Details: This parameter is crucial for designing foundations, retaining walls, and slopes, as it directly affects soil strength.

4. Using the Calculator

Tips: Enter all required values with appropriate units. The calculator accounts for ±5% variation in input parameters.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the ±5% variation important?
A: Soil properties can vary naturally, so this accounts for measurement uncertainty.

Q3: What if I get a negative result?
A: Negative values indicate the cohesion exceeds the shear strength, which may suggest an error in inputs.

Q4: How does factor of safety affect the result?
A: Higher safety factors will generally result in higher calculated friction angles.

Q5: What units should I use?
A: Use consistent units (all in Pa or all in kPa) for accurate results.