Effective Cohesion given Factor of Safety of Earth Dam Calculator

Effective Cohesion Formula:

\[ c' = \frac{(fs \times \Sigma T) - ((\Sigma N - \Sigma U) \times \tan(\frac{\phi' \times \pi}{180}))}{L'} \]

Factor of Safety (fs):

Sum of Tangential Components (ΣT):

Sum of Normal Components (ΣN):

Total Pore Pressure (ΣU):

Effective Angle of Internal Friction (φ'):

Length of Slip Arc (L'):

Effective Cohesion (c'): Pa

1. What is Effective Cohesion in Earth Dam Safety?

Definition: Effective cohesion is the shear strength of soil that results from the bonding between particles when subjected to effective stress.

Purpose: This calculator determines the effective cohesion needed to maintain a specified factor of safety for an earth dam's slope stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ c' = \frac{(fs \times \Sigma T) - ((\Sigma N - \Sigma U) \times \tan(\frac{\phi' \times \pi}{180}))}{L'} \]

Where:

\( c' \) — Effective cohesion (Pa)
\( fs \) — Factor of safety
\( \Sigma T \) — Sum of tangential components (N)
\( \Sigma N \) — Sum of normal components (N)
\( \Sigma U \) — Total pore pressure (N)
\( \phi' \) — Effective angle of internal friction (°)
\( L' \) — Length of slip arc (m)

Explanation: The formula calculates the required soil cohesion to achieve the specified safety factor considering all forces acting on the potential slip surface.

3. Importance of Effective Cohesion Calculation

Details: Accurate cohesion calculation is critical for dam safety, preventing slope failures, and ensuring long-term structural integrity.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. The ±5% indicates typical measurement uncertainties. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for earth dams?
A: Common factors range from 1.3 to 1.5, with higher values for critical structures.

Q2: How is the slip arc length determined?
A: It's typically identified through slope stability analysis as the most critical failure surface.

Q3: Why include pore pressure in calculations?
A: Pore pressure reduces effective stress, significantly impacting slope stability.

Q4: What affects the effective angle of internal friction?
A: Soil type, density, and moisture content primarily influence this parameter.

Q5: How accurate are these calculations?
A: Results are theoretical estimates; field tests provide more accurate cohesion values.