Submerged Unit Weight given Effective Normal Stress Calculator

Submerged Unit Weight Formula:

\[ y_S = \frac{\sigma'}{z \times \cos^2(i)} \]

Effective Normal Stress:

kN/m²

Depth of Prism:

Angle of Inclination:

Tolerance:

Submerged Unit Weight (kN/m³):

Tolerance Range (5%):

1. What is Submerged Unit Weight?

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

Purpose: This calculation is essential in geotechnical engineering for analyzing soil stability, especially for slopes and foundations below water tables.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ y_S = \frac{\sigma'}{z \times \cos^2(i)} \]

Where:

\( y_S \) — Submerged unit weight (kN/m³)
\( \sigma' \) — Effective normal stress (kN/m²)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The formula accounts for both the vertical stress distribution and the inclination angle of the soil mass.

3. Importance of Submerged Unit Weight

Details: Accurate calculation of submerged unit weight is crucial for slope stability analysis, retaining wall design, and foundation engineering in saturated soils.

4. Using the Calculator

Tips:

Enter effective normal stress in kN/m²
Enter depth of prism in meters
Angle of inclination should be between 0-90 degrees
Tolerance defaults to ±5% but can be adjusted

5. Frequently Asked Questions (FAQ)

Q1: What is typical submerged unit weight for soils?
A: Common values range from 8-11 kN/m³ for most saturated soils.

Q2: Why include a tolerance range?
A: Soil properties vary naturally; the tolerance accounts for this variability in real-world conditions.

Q3: How does angle of inclination affect the result?
A: Higher angles reduce the effective stress component normal to the plane, increasing the calculated submerged unit weight.

Q4: When would I use this calculation?
A: For underwater slope stability analysis, submerged retaining walls, or any structure interacting with saturated soils.

Q5: What if my angle is 0 degrees?
A: At 0° (horizontal), cos²(0)=1, simplifying the calculation to σ'/z.