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Unit Cohesion given Factor of Safety Calculator

Unit Cohesion Formula:

\[ c_u = \frac{fs \times W \times x'}{L' \times d_{radial}} \]

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1. What is Unit Cohesion given Factor of Safety?

Definition: This calculator determines the unit cohesion of soil based on the factor of safety and other geometric parameters.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ c_u = \frac{fs \times W \times x'}{L' \times d_{radial}} \]

Where:

  • \( c_u \) — Unit cohesion (Pascal)
  • \( fs \) — Factor of safety (±5%)
  • \( W \) — Weight of body (Newtons ±5%)
  • \( x' \) — Distance between LOA and COR (meters ±5%)
  • \( L' \) — Length of slip arc (meters ±5%)
  • \( d_{radial} \) — Radial distance (meters ±5%)

Explanation: The formula calculates the soil's shear strength by considering the equilibrium of forces acting on a potential slip surface.

3. Importance of Unit Cohesion Calculation

Details: Accurate unit cohesion values are critical for slope stability analysis, foundation design, and earth-retaining structures.

4. Using the Calculator

Tips: Enter all required parameters with their ±5% tolerance. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for factor of safety?
A: For slope stability, factors of safety typically range from 1.3 to 1.5, depending on project requirements.

Q2: How is the weight of body determined?
A: The weight is calculated from the soil mass within the potential failure zone, considering unit weight and volume.

Q3: What affects the unit cohesion value?
A: Soil type, moisture content, compaction, and stress history significantly influence cohesion values.

Q4: Why is ±5% tolerance important?
A: It accounts for measurement uncertainties and natural variability in soil properties.

Q5: How is radial distance measured?
A: It's the distance from the center of rotation to the point where cohesion is being evaluated along the slip surface.

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