Factor of Safety for Cohesive Soil given Cohesion Calculator

Factor of Safety Formula:

\[ FS = \frac{c}{\gamma \cdot z \cdot \cos(I) \cdot \sin(I)} + \frac{\tan(\phi)}{\tan(I)} \]

Unit Cohesion (c):

Unit Weight of Soil (γ):

N/m³

Depth of Prism (z):

Angle of Inclination (I):

Angle of Internal Friction (φ):

Safety Margin:

Factor of Safety (FS):

FS with 5% Safety Margin:

1. What is Factor of Safety for Cohesive Soil?

Definition: The Factor of Safety (FS) is a measure of how much stronger a slope is than it needs to be to resist failure. For cohesive soils, it considers both soil cohesion and internal friction.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ FS = \frac{c}{\gamma \cdot z \cdot \cos(I) \cdot \sin(I)} + \frac{\tan(\phi)}{\tan(I)} \]

Where:

\( FS \) — Factor of Safety
\( c \) — Unit cohesion (Pa)
\( \gamma \) — Unit weight of soil (N/m³)
\( z \) — Depth of prism (m)
\( I \) — Angle of inclination (°)
\( \phi \) — Angle of internal friction (°)

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

3. Importance of Factor of Safety Calculation

Details: Proper FS calculation prevents slope failures, ensures structural stability, and helps meet engineering safety standards.

4. Using the Calculator

Tips: Enter all required parameters. The safety margin (default 5%) accounts for uncertainties. A FS ≥ 1.5 is typically considered safe.

5. Frequently Asked Questions (FAQ)

Q1: What is a good Factor of Safety value?
A: Typically 1.5-2.0 for slopes, but depends on project requirements and consequences of failure.

Q2: How does cohesion affect stability?
A: Higher cohesion increases stability, allowing steeper slopes to be stable.

Q3: What's the purpose of the safety margin?
A: It provides additional conservatism to account for material variability and uncertainties.

Q4: How do I measure soil cohesion?
A: Through laboratory tests like unconfined compression or triaxial tests.

Q5: What if I get FS < 1?
A: The slope is unstable and requires redesign (flattening, reinforcement, or drainage).