Sum of All Tangential Component given Factor of Safety of Earth Dam Calculator

Formula Used:

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

Effective Cohesion (c'):

Length of Slip Arc (L'):

Sum of all Normal Component (ΣN):

Total Pore Pressure (ΣU):

Effective Angle of Internal Friction (φ'):

Factor of Safety (fs):

Sum of all Tangential Component (ΣT):

1. What is Sum of All Tangential Component in Earth Dam Stability?

Definition: This calculation determines the total tangential (shear) forces acting along a potential slip surface in an earth dam, considering the factor of safety.

Purpose: It helps geotechnical engineers assess the stability of earth dams against sliding failure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula combines the cohesive strength and frictional resistance along the slip surface, divided by the safety factor.

3. Importance of Tangential Component Calculation

Details: Accurate calculation ensures dam stability against sliding, preventing catastrophic failures and ensuring long-term structural integrity.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is effective cohesion (c')?
A: It's the soil's shear strength due to particle bonding, independent of normal stress.

Q2: How is the slip arc length determined?
A: Through stability analysis, typically using methods like Bishop's or Janbu's.

Q3: Why subtract pore pressure (ΣU)?
A: Pore pressure reduces effective stress, which affects frictional resistance.

Q4: What's a typical factor of safety (fs)?
A: Usually 1.3-1.5 for earth dams, depending on risk and regulations.

Q5: How accurate are these calculations?
A: Results are typically within ±5% of actual values, assuming accurate input parameters.