Factor of Safety for Cohesive Soil given Depth of Prism Calculator

Factor of Safety Formula:

\[ FS = \frac{C_s}{\gamma' \cdot z \cdot \cos(i) \cdot \sin(i)} + \frac{\tan(\phi)}{\tan(i)} \]

Cohesion of Soil (Cₛ):

kPa

Submerged Unit Weight (γ'):

kN/m³

Depth of Prism (z):

Angle of Inclination (i):

Angle of Internal Friction (φ):

Tolerance:

Factor of Safety (FS):

1. What is Factor of Safety for Cohesive Soil?

Definition: The Factor of Safety (FS) is a measure of how much the soil's strength exceeds the applied stresses, indicating slope stability.

Purpose: It helps geotechnical engineers assess the stability of slopes in cohesive soils and prevent failures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ FS = \frac{C_s}{\gamma' \cdot z \cdot \cos(i) \cdot \sin(i)} + \frac{\tan(\phi)}{\tan(i)} \]

Where:

\( FS \) — Factor of Safety
\( C_s \) — Cohesion of soil (kPa)
\( \gamma' \) — Submerged unit weight (kN/m³)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (°)
\( \phi \) — Angle of internal friction (°)

Explanation: The first term accounts for cohesive strength, while the second term represents frictional resistance.

3. Importance of Factor of Safety Calculation

Details: Proper FS calculation ensures slope stability, prevents landslides, and guides safe construction practices.

4. Using the Calculator

Tips: Enter all required parameters. The tolerance field (default ±5%) shows acceptable FS range based on measurement uncertainties.

5. Frequently Asked Questions (FAQ)

Q1: What is a good Factor of Safety value?
A: Typically 1.3-1.5 for temporary slopes, 1.5-2.0 for permanent slopes, depending on consequences of failure.

Q2: How does cohesion affect slope stability?
A: Higher cohesion increases stability (higher FS) as it provides shear resistance independent of normal stress.

Q3: Why is submerged unit weight used?
A: For slopes below water table, buoyancy reduces effective stresses, affecting stability calculations.

Q4: When would I adjust the tolerance?
A: Increase tolerance for higher uncertainty in input parameters or less critical applications.

Q5: How does inclination angle affect FS?
A: FS decreases as slope angle increases, with critical angle where FS=1 indicating imminent failure.