Depth of Prism given Submerged Unit Weight Calculator

Depth of Prism Formula:

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

Normal Stress:

Submerged Unit Weight:

N/m³

Angle of Inclination:

Tolerance:

Depth of Prism (z):

1. What is Depth of Prism given Submerged Unit Weight?

Definition: This calculator determines the depth of a soil prism based on normal stress, submerged unit weight, and angle of inclination.

Purpose: It helps geotechnical engineers analyze slope stability and soil mechanics problems.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( z \) — Depth of prism (meters)
\( \sigma_{Normal} \) — Normal stress (Pascals)
\( \gamma' \) — Submerged unit weight (N/m³)
\( i \) — Angle of inclination (degrees)

Explanation: The normal stress is divided by the product of submerged unit weight and the square of cosine of the inclination angle.

3. Importance of Depth Calculation

Details: Accurate depth calculation is crucial for slope stability analysis, retaining wall design, and foundation engineering.

4. Using the Calculator

Tips: Enter normal stress in Pascals, submerged unit weight in N/m³, angle in degrees, and tolerance percentage. All values except angle must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is submerged unit weight?
A: It's the effective unit weight of soil when submerged in water, accounting for buoyancy effects.

Q2: Why is angle of inclination important?
A: The angle affects how stress is distributed in the soil mass, influencing the depth calculation.

Q3: What does the tolerance percentage represent?
A: It shows the acceptable range (±value) around the calculated depth to account for uncertainties.

Q4: Typical values for submerged unit weight?
A: For most soils, it ranges between 8-12 kN/m³ (8000-12000 N/m³).

Q5: When would this calculation be used?
A: Primarily in slope stability analysis, embankment design, and other geotechnical applications.