Submerged Unit Weight given Factor of Safety Calculator

Submerged Unit Weight Formula:

\[ yS = \frac{Fs}{\left(\frac{\tan\left(\frac{\Phi_i \times \pi}{180}\right)}{\gamma_{saturated} \times \tan\left(\frac{i \times \pi}{180}\right)}\right)} \]

Factor of Safety (Fs):

Angle of Internal Friction (Φi):

Saturated Unit Weight (γ):

N/m³

Inclination Angle (i):

Submerged Unit Weight (yS):

1. What is Submerged Unit Weight given Factor of Safety?

Definition: This calculator determines the submerged unit weight of soil based on the factor of safety, internal friction angle, saturated unit weight, and inclination angle.

Purpose: It helps geotechnical engineers assess soil stability and safety factors in slope stability analysis and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ yS = \frac{Fs}{\left(\frac{\tan\left(\frac{\Phi_i \times \pi}{180}\right)}{\gamma_{saturated} \times \tan\left(\frac{i \times \pi}{180}\right)}\right)} \]

Where:

\( yS \) — Submerged unit weight (N/m³)
\( Fs \) — Factor of safety (typically 2.8)
\( \Phi_i \) — Angle of internal friction (°)
\( \gamma_{saturated} \) — Saturated unit weight (N/m³)
\( i \) — Angle of inclination to horizontal (°)

Explanation: The formula calculates the submerged unit weight considering the safety factor and soil's mechanical properties.

3. Importance of Submerged Unit Weight Calculation

Details: Accurate calculation is crucial for slope stability analysis, retaining wall design, and foundation engineering in saturated soil conditions.

4. Using the Calculator

Tips: Enter the factor of safety (default 2.8), internal friction angle (default 82.86°), saturated unit weight (default 11890 N/m³), and inclination angle (default 64°). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety value?
A: Common values range from 1.5 to 3.0, with 2.8 being typical for many geotechnical applications.

Q2: How do I determine the angle of internal friction?
A: This is typically measured through laboratory tests like direct shear or triaxial tests.

Q3: What's the difference between submerged and saturated unit weight?
A: Submerged unit weight considers buoyancy effects when soil is below water table.

Q4: Why is the inclination angle important?
A: It accounts for the slope angle which significantly affects stability calculations.

Q5: Can I use this for quick field estimates?
A: Yes, but for critical projects, always verify with detailed geotechnical analysis.