Depth of Prism given Vertical Stress on Surface of Prism Calculator

Depth of Prism Formula:

\[ z = \frac{\sigma_{vertical}}{\gamma \times \cos(I)} \]

Vertical Stress at a Point:

Pascal

Unit Weight of Soil:

kN/m³

Angle of Inclination:

radians

Depth of Prism (z): meters

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

Purpose: It helps geotechnical engineers analyze stress distribution in inclined soil masses.

The calculator uses the formula:

\[ z = \frac{\sigma_{vertical}}{\gamma \times \cos(I)} \]

Where:

Explanation: The vertical stress is divided by the product of soil unit weight and cosine of inclination angle.

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

Tips: Enter vertical stress in Pascal, soil unit weight in kN/m³, and inclination angle in radians (±5%). All values must be > 0.

Q1: Why is the angle of inclination important?
A: The angle affects how vertical stress is distributed through the soil mass.

Q2: What's a typical unit weight for soil?
A: Common values range from 16-22 kN/m³ for most soils, depending on composition and moisture.

Q3: How accurate is this calculation?
A: Results are theoretical and may vary ±5% due to soil heterogeneity and measurement inaccuracies.

Q4: Can I use degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians by multiplying by π/180.

Q5: What if my angle is 0° (horizontal surface)?
A: At 0° inclination, cos(0)=1, simplifying to z = σ/γ.