Angle of Shearing Resistance Corresponding to Local Shear Failure Calculator

Formula:

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

Angle of Shearing Resistance (φ): %

Tolerance Range: %

1. What is Angle of Shearing Resistance?

Definition: The Angle of Shearing Resistance (φ) is a component of the shear strength of soils, which is frictional material composed of individual particles.

Purpose: This calculator determines the angle of shearing resistance corresponding to local shear failure based on the mobilized friction angle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \phi \) — Angle of Shearing Resistance (degrees)
\( \phi_m \) — Angle of Mobilized Friction (degrees)

Explanation: The formula relates the mobilized friction angle to the shearing resistance angle through a trigonometric relationship.

3. Importance of Angle Calculation

Details: Proper calculation of the shearing resistance angle is crucial for analyzing soil stability and designing foundations, slopes, and retaining structures.

4. Using the Calculator

Tips: Enter the mobilized friction angle in percentage and the tolerance (default ±5%). The calculator will provide the angle of shearing resistance and its tolerance range.

5. Frequently Asked Questions (FAQ)

Q1: What is local shear failure?
A: Local shear failure occurs when only a portion of the soil mass reaches failure while the rest remains stable.

Q2: Why is tolerance important?
A: Tolerance accounts for variations in soil properties and measurement uncertainties.

Q3: What's a typical mobilized friction angle?
A: Values typically range from 20% to 40%, depending on soil type and conditions.

Q4: How does this relate to factor of safety?
A: The mobilized friction angle is often the actual friction angle divided by the factor of safety.

Q5: Can I use this for all soil types?
A: This formula is most applicable for granular soils; cohesive soils require additional parameters.