Submerged Unit Weight given Normal Stress Component Calculator

Submerged Unit Weight Formula:

\[ \gamma' = \frac{\sigma_{Normal}}{z \times (\cos(i))^2} \]

Normal Stress (σ_Normal):

Depth of Prism (z):

Angle of Inclination (i):

rad

Tolerance:

Submerged Unit Weight (γ'):

1. What is Submerged Unit Weight?

Definition: Submerged unit weight (γ') is the effective unit weight of soil when it's submerged underwater in a saturated condition.

Purpose: It's crucial in geotechnical engineering for analyzing soil behavior under water, such as in foundations, retaining walls, and slope stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma' = \frac{\sigma_{Normal}}{z \times (\cos(i))^2} \]

Where:

\( \gamma' \) — Submerged unit weight (N/m³)
\( \sigma_{Normal} \) — Normal stress component (Pa)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (radians)

Explanation: The normal stress is divided by the product of depth and the squared cosine of inclination angle.

3. Importance of Submerged Unit Weight

Details: Accurate calculation of submerged unit weight is essential for:

Designing underwater foundations
Analyzing slope stability in saturated soils
Calculating effective stresses in soil mechanics
Determining bearing capacity of submerged soils

4. Using the Calculator

Tips:

Enter normal stress in Pascals (Pa)
Depth should be in meters (m)
Angle must be in radians (convert from degrees if needed)
Tolerance is set to ±5% by default but can be adjusted

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (≈0.01745). For example, 30° = 30 × π/180 ≈ 0.5236 radians.

Q2: What's a typical range for submerged unit weight?
A: Most soils range between 8-12 kN/m³ (8000-12000 N/m³) when submerged.

Q3: Why include a tolerance percentage?
A: Soil properties can vary, so the tolerance provides a practical range for engineering calculations.

Q4: When would the angle of inclination be zero?
A: For horizontal ground surfaces where the normal stress acts vertically downward.

Q5: How does water affect unit weight calculations?
A: Submerged unit weight is less than moist unit weight due to buoyancy effects.