Submerged Unit Weight given Shear Stress Component Calculator

Submerged Unit Weight Formula:

\[ \gamma' = \frac{\tau}{z \times \cos(i) \times \sin(i)} \]

Shear Stress for Submerged Slopes:

Depth of Prism:

Angle of Inclination:

rad

Tolerance:

Submerged Unit Weight (N/m³):

1. What is Submerged Unit Weight?

Definition: Submerged Unit Weight is the unit weight of soil observed underwater in a saturated condition.

Purpose: It's crucial for analyzing soil stability in underwater conditions, especially for slopes and foundations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma' = \frac{\tau}{z \times \cos(i) \times \sin(i)} \]

Where:

\( \gamma' \) — Submerged unit weight (N/m³)
\( \tau \) — Shear stress for submerged slopes (Pa)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (radians)

Explanation: The shear stress is divided by the product of depth and trigonometric functions of the inclination angle.

3. Importance of Submerged Unit Weight Calculation

Details: Accurate calculation helps in designing stable underwater structures and assessing slope stability in saturated conditions.

4. Using the Calculator

Tips: Enter shear stress in Pascals, depth in meters, angle in radians, and tolerance percentage. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for submerged unit weight?
A: For most soils, it ranges between 8-12 kN/m³ (8000-12000 N/m³).

Q2: Why is angle input in radians?
A: The trigonometric functions in the formula require angle in radians for accurate calculation.

Q3: What does the tolerance percentage represent?
A: It shows the acceptable range (±%) around the calculated value, accounting for measurement uncertainties.

Q4: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q5: When would I need to adjust the tolerance?
A: Increase tolerance for less precise measurements or more variable soil conditions.