Submerged Unit Weight given Factor of Safety with respect to Shear Strength Calculator

Submerged Unit Weight Formula:

\[ \gamma' = \frac{\tan\left(\frac{\phi_w \times \pi}{180}\right)}{\left(\frac{1}{\gamma_{sat}}\right) \times \left(\frac{\tan\left(\frac{\Phi_i \times \pi}{180}\right)}{fs}\right)} \]

Weighted Friction Angle:

Saturated Unit Weight:

kN/m³

Angle of Internal Friction:

Factor of Safety:

Submerged Unit Weight (kN/m³):

1. What is Submerged Unit Weight?

Definition: Submerged Unit Weight is the effective weight of soil per unit volume when submerged in water, accounting for buoyancy effects.

Purpose: It's crucial for analyzing soil stability in water-saturated conditions, such as in foundations below water tables or underwater structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma' = \frac{\tan\left(\frac{\phi_w \times \pi}{180}\right)}{\left(\frac{1}{\gamma_{sat}}\right) \times \left(\frac{\tan\left(\frac{\Phi_i \times \pi}{180}\right)}{fs}\right)} \]

Where:

\( \gamma' \) — Submerged unit weight (kN/m³)
\( \phi_w \) — Weighted friction angle (°)
\( \gamma_{sat} \) — Saturated unit weight (kN/m³)
\( \Phi_i \) — Angle of internal friction (°)
\( fs \) — Factor of safety (±5%)

Explanation: The formula relates the submerged weight to the saturated weight through trigonometric functions of friction angles, with a safety factor adjustment.

3. Importance of Submerged Unit Weight Calculation

Details: Accurate calculation is essential for designing stable foundations, retaining walls, and slopes in water-bearing soils.

4. Using the Calculator

Tips: Enter all angles in degrees. The factor of safety includes a ±5% margin. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the factor of safety expressed as ±5%?
A: The 5% margin accounts for typical variations in soil properties and measurement uncertainties.

Q2: What's a typical range for saturated unit weight?
A: Most soils range from 18-22 kN/m³ when saturated, depending on particle density and void ratio.

Q3: How does submerged weight differ from saturated weight?
A: Submerged weight is less due to buoyancy - it's the saturated weight minus unit weight of water (9.81 kN/m³).

Q4: When would I need this calculation?
A: Essential for any geotechnical analysis involving water-saturated soils, like dam design or underwater construction.

Q5: How accurate is this calculation?
A: Accuracy depends on input precision. The ±5% safety factor helps account for typical variations.