Unit Cohesion given Sum of Tangential Component Calculator

Unit Cohesion Formula:

\[ c_u = \frac{(FS \times F_t) - (\Sigma N \times \tan(\phi))}{L} \]

Factor of Safety (FS):

Sum of Tangential Components (Fₜ):

Sum of Normal Components (ΣN):

Angle of Internal Friction (φ):

Length of Slip Arc (L):

Unit Cohesion (cᵤ): Pa

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 slope stability and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ c_u = \frac{(FS \times F_t) - (\Sigma N \times \tan(\phi))}{L} \]

Where:

\( c_u \) — Unit cohesion (Pa)
\( FS \) — Factor of Safety
\( F_t \) — Sum of all tangential components (N)
\( \Sigma N \) — Sum of all normal components (N)
\( \phi \) — Angle of internal friction (°)
\( L \) — Length of slip arc (m)

Explanation: The formula calculates the cohesive strength of soil by considering the balance between driving and resisting forces along a potential failure surface.

3. Importance of Unit Cohesion Calculation

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

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. The ±5% indicates typical measurement uncertainty ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical Factor of Safety value?
A: For slope stability, FS typically ranges from 1.3 to 1.5, depending on project requirements.

Q2: How is the angle of internal friction determined?
A: It's determined through laboratory tests like direct shear or triaxial tests on soil samples.

Q3: What affects unit cohesion values?
A: Soil type, moisture content, density, and stress history significantly affect cohesion.

Q4: When would this calculation be used?
A: Primarily in slope stability analysis using methods like the Swedish Circle method.

Q5: What's the practical significance of the result?
A: It helps determine if a slope is stable or needs reinforcement to prevent failure.