Angle of Internal Friction given Resisting Moment Calculator

Angle of Internal Friction Formula:

\[ \phi_i = \tan^{-1}\left(\frac{\frac{MR}{r} - (c_u \times L')}{\Sigma N}\right) \]

Resisting Moment:

N·m

Radius of Slip Circle:

Unit Cohesion:

Length of Slip Arc:

Sum of all Normal Component:

Tolerance:

Angle of Internal Friction (degrees):

Tolerance Range (±5%):

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 critical parameter in geotechnical engineering for analyzing slope stability, bearing capacity, and earth pressure calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi_i = \tan^{-1}\left(\frac{\frac{MR}{r} - (c_u \times L')}{\Sigma N}\right) \]

Where:

\( \phi_i \) — Angle of internal friction (degrees)
\( MR \) — Resisting moment (N·m)
\( r \) — Radius of slip circle (m)
\( c_u \) — Unit cohesion (Pa)
\( L' \) — Length of slip arc (m)
\( \Sigma N \) — Sum of all normal components (N)

Explanation: The formula calculates the angle by considering the balance between resisting forces (from friction and cohesion) and driving forces.

3. Importance of Angle of Internal Friction

Details: This parameter helps determine:

Slope stability and potential for landslides
Bearing capacity of foundations
Lateral earth pressure on retaining structures
Shear strength of soil under different loading conditions

4. Using the Calculator

Tips:

Enter all required parameters in consistent units
For purely frictional soils (sand), set cohesion to 0
For cohesive soils (clay), include both friction and cohesion
Default tolerance is ±5% but can be adjusted

5. Frequently Asked Questions (FAQ)

Q1: What's a typical range for φ in soils?
A: Sands: 28°-45°; Silts: 25°-35°; Clays: 10°-25° (can be 0° for pure soft clay).

Q2: How does cohesion affect the calculation?
A: Cohesion provides additional shear strength independent of normal stress.

Q3: What if I get a negative angle result?
A: Check your inputs - this suggests the resisting moment is insufficient for the given cohesion and normal forces.

Q4: Why include a tolerance range?
A: Soil properties are naturally variable - the range accounts for potential measurement and estimation uncertainties.

Q5: How is this different from the friction angle in direct shear tests?
A: This calculates the effective friction angle considering the entire failure surface, while direct shear gives the peak friction angle for a specific sample.