Cohesion given Factor of Safety for Cohesive Soil Calculator

Cohesion of Soil Formula:

\[ c = (fs - \frac{\tan(\phi)}{\tan(I)}) \times (\gamma \times z \times \cos(I) \times \sin(I)) \]

Factor of Safety:

Angle of Internal Friction (φ):

Angle of Inclination (I):

Unit Weight of Soil (γ):

N/m³

Depth of Prism (z):

Cohesion of Soil (c): Pa

1. What is Cohesion given Factor of Safety Calculator?

Definition: This calculator determines the cohesion of soil based on factor of safety, internal friction angle, inclination angle, unit weight, and depth.

Purpose: It helps geotechnical engineers assess soil stability for slope design and foundation engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ c = (fs - \frac{\tan(\phi)}{\tan(I)}) \times (\gamma \times z \times \cos(I) \times \sin(I)) \]

Where:

\( c \) — Cohesion of soil (Pascals)
\( fs \) — Factor of safety (dimensionless)
\( \phi \) — Angle of internal friction (degrees)
\( I \) — Angle of inclination (degrees)
\( \gamma \) — Unit weight of soil (N/m³)
\( z \) — Depth of prism (meters)

Explanation: The formula calculates the shear strength component from cohesion by accounting for the safety factor and geometric parameters.

3. Importance of Cohesion Calculation

Details: Accurate cohesion estimation is critical for slope stability analysis, retaining wall design, and foundation engineering.

4. Using the Calculator

Tips: Enter all required parameters. Angles should be in degrees (0-90°). Factor of safety typically ranges from 1.5 to 3.0 (±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for slopes?
A: For permanent slopes, 1.5 is common. Temporary slopes may use 1.3. Critical structures may require 2.0 or higher (±5%).

Q2: How do I determine the angle of internal friction?
A: This is typically measured through direct shear or triaxial tests in a geotechnical laboratory.

Q3: What if my soil has no cohesion (c = 0)?
A: This calculator is for cohesive soils. For cohesionless soils, different stability analysis methods are used.

Q4: Why do we need depth of prism?
A: Depth affects the normal stress on the potential failure plane, which influences the shear strength.

Q5: What units should I use?
A: Use degrees for angles, N/m³ for unit weight, meters for depth. Results are in Pascals (Pa).