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Length of Slip Circle given Factor of Safety of Earth Dam Calculator

Length of Slip Arc Formula:

\[ L' = \frac{(fs \times \Sigma T) - ((\Sigma N - \Sigma U) \times \tan(\phi'))}{c'} \]

N
N
N
rad
Pa

1. What is Length of Slip Circle?

Definition: The length of the slip circle arc is a critical parameter in slope stability analysis of earth dams, representing the potential failure surface.

Purpose: It helps geotechnical engineers assess the stability of earth dams and slopes by analyzing potential circular failure surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L' = \frac{(fs \times \Sigma T) - ((\Sigma N - \Sigma U) \times \tan(\phi'))}{c'} \]

Where:

  • \( L' \) — Length of slip arc (meters)
  • \( fs \) — Factor of Safety
  • \( \Sigma T \) — Sum of all tangential components (N)
  • \( \Sigma N \) — Sum of all normal components (N)
  • \( \Sigma U \) — Total pore pressure (N)
  • \( \phi' \) — Effective angle of internal friction (radians)
  • \( c' \) — Effective cohesion (Pa)

Explanation: The formula calculates the length of the potential failure arc based on the balance between driving forces and resisting forces in the slope.

3. Importance of Slip Circle Analysis

Details: Proper calculation ensures dam safety, prevents catastrophic failures, and helps in designing appropriate stabilization measures.

4. Using the Calculator

Tips: Enter all required parameters with ±5% accuracy. Ensure all values are positive except pore pressure which can be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for earth dams?
A: Typically 1.3-1.5 for temporary structures and 1.5-2.0 for permanent dams.

Q2: How is pore pressure measured?
A: Through piezometers installed in the dam body and foundation.

Q3: What affects the effective angle of internal friction?
A: Soil type, density, moisture content, and stress history.

Q4: How is effective cohesion determined?
A: Through laboratory tests like direct shear or triaxial tests on soil samples.

Q5: What if my calculation returns a negative length?
A: Check your inputs - this usually indicates an error in parameter values or unrealistic conditions.

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