Factor of Safety with respect to Shear Strength given Weighted Friction Angle Calculator

Factor of Safety Formula:

\[ fs = \frac{\gamma' \times \phi'}{\phi_{IF} \times \gamma_{sat}} \]

Submerged Unit Weight (γ'):

N/m³

Effective Angle of Internal Friction (φ'):

rad

Weighted Friction Angle (φ_IF):

rad

Saturated Unit Weight (γ_sat):

N/m³

Tolerance:

Factor of Safety (fs):

1. What is Factor of Safety with respect to Shear Strength?

Definition: This calculator determines the factor of safety for shear strength based on submerged unit weight, effective angle of internal friction, weighted friction angle, and saturated unit weight.

Purpose: It helps geotechnical engineers assess the stability of soil structures by comparing the available shear strength to the required shear strength.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ fs = \frac{\gamma' \times \phi'}{\phi_{IF} \times \gamma_{sat}} \]

Where:

\( fs \) — Factor of Safety
\( \gamma' \) — Submerged Unit Weight (N/m³)
\( \phi' \) — Effective Angle of Internal Friction (rad)
\( \phi_{IF} \) — Weighted Friction Angle for Internal Friction (rad)
\( \gamma_{sat} \) — Saturated Unit Weight (N/m³)

Explanation: The formula compares the shear strength contribution from submerged conditions to the shear strength under saturated conditions.

3. Importance of Factor of Safety Calculation

Details: Proper calculation ensures structural stability, prevents slope failures, and helps in designing safe geotechnical structures.

4. Using the Calculator

Tips: Enter all required parameters in appropriate units. The tolerance field (default ±5%) allows you to see the acceptable range for the factor of safety.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable factor of safety?
A: For most geotechnical applications, a factor of safety between 1.3 and 1.5 is typically acceptable, but this depends on project requirements.

Q2: How do I determine the weighted friction angle?
A: The weighted friction angle is determined through laboratory tests or empirical correlations based on soil composition and conditions.

Q3: What does a factor of safety less than 1 indicate?
A: A value less than 1 indicates that the structure is unstable and likely to fail under the current loading conditions.

Q4: How does water content affect the calculation?
A: Water content significantly affects both submerged and saturated unit weights, which directly impact the factor of safety.

Q5: When should I adjust the tolerance percentage?
A: Adjust tolerance based on project specifications, material variability, and desired confidence levels in the results.