Cohesion of Soil given Factor of Safety for Cohesive Soil Calculator

Cohesion of Soil Formula:

\[ c = (\zeta_{cs} \times fs) - (\sigma_n \times \tan(\phi)) \]

Shear Stress in Cohesive Soil:

kN/m²

Factor of Safety:

Normal Stress at a Point in Soil:

kN/m²

Angle of Internal Friction:

radians

Cohesion of Soil (kPa):

1. What is Cohesion of Soil given Factor of Safety?

Definition: This calculator determines the cohesion of soil based on shear stress, factor of safety, normal stress, and angle of internal friction.

Purpose: It helps geotechnical engineers evaluate the shear strength of cohesive soils for slope stability and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ c = (\zeta_{cs} \times fs) - (\sigma_n \times \tan(\phi)) \]

Where:

\( c \) — Cohesion of soil (kPa)
\( \zeta_{cs} \) — Shear stress in cohesive soil (kN/m²)
\( fs \) — Factor of safety (±5%)
\( \sigma_n \) — Normal stress at a point in soil (kN/m²)
\( \phi \) — Angle of internal friction (radians)

Explanation: The formula calculates soil cohesion by considering both the shear strength and frictional components of soil resistance.

3. Importance of Cohesion Calculation

Details: Accurate cohesion values are critical for designing stable earth structures, assessing slope stability, and preventing soil failures.

4. Using the Calculator

Tips: Enter shear stress (kN/m²), factor of safety (±5%), normal stress (kN/m²), and angle of internal friction (radians). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical cohesion for clay soils?
A: Clay soils typically have cohesion values ranging from 5-50 kPa, depending on moisture content and plasticity.

Q2: Why is factor of safety important?
A: The factor of safety accounts for uncertainties in material properties and loading conditions (±5% variation).

Q3: How do I measure angle of internal friction?
A: It's typically determined through direct shear tests or triaxial tests in a geotechnical laboratory.

Q4: Can this calculator be used for sandy soils?
A: For purely cohesionless soils (c=0), different formulas should be used that consider only frictional resistance.

Q5: What units should I use for the angle of internal friction?
A: The angle must be entered in radians (π radians = 180 degrees).