Unit Cohesion given Resisting Force from Coulomb's Equation Calculator

Unit Cohesion Formula:

\[ c_u = \frac{F_r - (N \times \tan(\phi))}{\Delta L} \]

Resisting Force (Fr):

Normal Component of Force (N):

Angle of Internal Friction (φ):

Curve Length (ΔL):

Unit Cohesion (cu):

1. What is Unit Cohesion?

Definition: Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles.

Purpose: It helps geotechnical engineers analyze soil stability and design appropriate foundations or retaining structures.

2. How Does the Calculator Work?

The calculator uses Coulomb's equation:

\[ c_u = \frac{F_r - (N \times \tan(\phi))}{\Delta L} \]

Where:

\( c_u \) — Unit Cohesion (Pascals)
\( F_r \) — Resisting Force (Newtons)
\( N \) — Normal Component of Force (Newtons)
\( \phi \) — Angle of Internal Friction (degrees)
\( \Delta L \) — Curve Length (meters)

Explanation: The formula calculates the cohesive strength by accounting for both frictional and cohesive components of shear resistance.

3. Importance of Unit Cohesion Calculation

Details: Accurate cohesion values are critical for slope stability analysis, earth pressure calculations, and foundation design.

4. Using the Calculator

Tips: Enter all required values with ±5% tolerance. The angle of internal friction should be in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for unit cohesion?
A: Cohesion values vary widely: 0-10 kPa for loose sands, 10-50 kPa for stiff clays, and up to 200 kPa for very stiff clays.

Q2: Why is the angle converted from degrees to radians?
A: The trigonometric functions in programming languages typically use radians, so conversion is necessary for accurate calculations.

Q3: How does normal force affect cohesion?
A: Higher normal forces increase the frictional component of shear strength, reducing the apparent cohesion needed for stability.

Q4: What if my curve length is very small?
A: Very small curve lengths can lead to unrealistically high cohesion values. Double-check your measurements.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise, but remember field conditions may vary by ±5% or more due to soil heterogeneity.