Mobilised Angle of Shearing Resistance Corresponding to Local Shear Failure Calculator

Formula:

\[ \phi_m = \tan^{-1}\left(\frac{2}{3} \times \tan(\phi)\right) \]

Mobilised Angle (φ_m): °

Tolerance Range:

1. What is Mobilised Angle of Shearing Resistance?

Definition: The mobilised angle of shearing resistance (φ_m) is the effective friction angle at which soil begins to fail under shear stress, accounting for partial mobilization of shear strength.

Purpose: This calculation is crucial in geotechnical engineering to determine the safety factor against shear failure in soils.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi_m = \tan^{-1}\left(\frac{2}{3} \times \tan(\phi)\right) \]

Where:

\( \phi_m \) — Mobilised angle of shearing resistance (degrees)
\( \phi \) — Angle of shearing resistance (degrees)
The 2/3 factor represents the partial mobilization of shear strength

Explanation: The formula calculates the reduced friction angle that would be mobilized at failure, considering not all shear strength is utilized.

3. Importance in Geotechnical Engineering

Details: This calculation helps determine the safety factor against slope failures, bearing capacity of foundations, and stability of retaining structures.

4. Using the Calculator

Tips: Enter the angle of shearing resistance (φ) in degrees and the desired tolerance percentage (default ±5%). The calculator provides the mobilised angle and its tolerance range.

5. Frequently Asked Questions (FAQ)

Q1: Why is the mobilised angle smaller than the peak angle?
A: The mobilised angle represents partial failure where not all shear strength is utilized, while the peak angle represents complete failure.

Q2: What's a typical angle of shearing resistance for soils?
A: It varies: 30-40° for sandy soils, 20-30° for silty soils, and 10-20° for clayey soils.

Q3: When would I adjust the tolerance percentage?
A: Adjust based on required precision - higher for critical structures, lower for preliminary estimates.

Q4: How does this relate to factor of safety?
A: The 2/3 factor represents a safety factor of about 1.5 against complete shear failure.

Q5: Can this be used for all soil types?
A: Primarily for granular soils; cohesive soils require additional cohesion parameters.