Factor of Safety with respect to Shear Strength Calculator

Factor of Safety Formula:

\[ FS = \left(\frac{\gamma'}{\gamma_{sat}}\right) \times \left(\frac{\tan(\phi)}{\tan(\phi_{IF})}\right) \]

Submerged Unit Weight (γ'):

kN/m³

Saturated Unit Weight (γ_sat):

kN/m³

Angle of Internal Friction (φ):

Weighted Friction Angle (φ_IF):

Safety Margin:

Factor of Safety (FS):

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

Definition: This calculator determines the factor of safety against shear failure in soils, considering submerged and saturated unit weights, internal friction angles, and a safety margin.

Purpose: It helps geotechnical engineers assess slope stability and foundation safety by comparing available shear strength to required shear strength.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ FS = \left(\frac{\gamma'}{\gamma_{sat}}\right) \times \left(\frac{\tan(\phi)}{\tan(\phi_{IF})}\right) \]

Where:

\( FS \) — Factor of Safety
\( \gamma' \) — Submerged unit weight (kN/m³)
\( \gamma_{sat} \) — Saturated unit weight (kN/m³)
\( \phi \) — Angle of internal friction (°)
\( \phi_{IF} \) — Weighted friction angle (°)

Explanation: The ratio of unit weights multiplied by the ratio of tangent functions provides the safety factor against shear failure.

3. Importance of Factor of Safety Calculation

Details: Proper FS calculation prevents slope failures, ensures foundation stability, and helps design safe earth structures.

4. Using the Calculator

Tips: Enter all required parameters. The safety margin (default ±5%) allows for conservative design. FS > 1 indicates stable conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable Factor of Safety?
A: For slopes, FS ≥ 1.3-1.5 is typically required. For foundations, FS ≥ 2.5-3.0 is common.

Q2: How do I determine submerged and saturated unit weights?
A: These are obtained from laboratory tests on soil samples or from geotechnical investigation reports.

Q3: What's the purpose of the safety margin?
A: The margin accounts for uncertainties in material properties, loading conditions, and analysis methods.

Q4: Can I use this for cohesive soils?
A: This formula is primarily for granular soils. Cohesive soils require additional cohesion parameters.

Q5: What if I get FS < 1?
A: This indicates potential instability. Consider soil improvement, slope flattening, or structural reinforcement.