Factor of Safety given Stability Number Calculator

Factor of Safety Formula:

\[ F_c = \frac{c}{S_n \times \gamma \times H_{Mobilised}} \]

Cohesion of Soil:

kPa

Stability Number:

Unit Weight of Soil:

kN/m³

Mobilized Cohesion Depth:

Factor of Safety:

1. What is Factor of Safety with respect to Cohesion?

Definition: The Factor of Safety with respect to Cohesion is the ratio of material's shear strength to applied shear stress, ensuring stability against sliding.

Purpose: It helps geotechnical engineers assess slope stability and design safe earth structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_c = \frac{c}{S_n \times \gamma \times H_{Mobilised}} \]

Where:

\( F_c \) — Factor of Safety with respect to Cohesion
\( c \) — Cohesion of Soil (kPa)
\( S_n \) — Stability Number (±5%)
\( \gamma \) — Unit Weight of Soil (kN/m³ ±5%)
\( H_{Mobilised} \) — Depth at Mobilized Cohesion (m ±5%)

Explanation: The cohesion is divided by the product of stability number, unit weight, and mobilized depth to determine the safety factor.

3. Importance of Factor of Safety Calculation

Details: Proper calculation ensures slope stability, prevents landslides, and maintains structural integrity of earthworks.

4. Using the Calculator

Tips: Enter the cohesion value, stability number (typically 2-3), unit weight (typically 15-20 kN/m³), and mobilized depth. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical Stability Number range?
A: Stability numbers typically range between 2.0 and 3.0 for most soil conditions, with ±5% variation.

Q2: How accurate are these calculations?
A: Results are theoretical estimates with ±5% accuracy; field tests should verify critical applications.

Q3: What's a safe Factor of Safety value?
A: Typically 1.5 or higher is considered safe, but requirements vary by project and regulations.

Q4: Why include ±5% in inputs?
A: This accounts for natural variability in soil properties and measurement uncertainties.

Q5: How does mobilized depth affect the result?
A: Deeper mobilization depths generally decrease the factor of safety, indicating potential instability.