Depth of Prism given Normal Stress and Saturated Unit Weight Calculator

Depth of Prism Formula:

\[ z = \frac{\sigma_n}{\gamma_{saturated} \times (\cos(\frac{i \times \pi}{180}))^2} \]

Normal Stress in Soil Mechanics:

Saturated Unit Weight of Soil:

Angle of Inclination to Horizontal in Soil:

Depth of Prism (m):

1. What is Depth of Prism given Normal Stress and Saturated Unit Weight?

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

Purpose: It helps geotechnical engineers and soil mechanics professionals analyze soil stability and stress distribution.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{\sigma_n}{\gamma_{saturated} \times (\cos(\frac{i \times \pi}{180}))^2} \]

Where:

\( z \) — Depth of prism (meters)
\( \sigma_n \) — Normal stress in soil mechanics (Pa)
\( \gamma_{saturated} \) — Saturated unit weight of soil (N/m³)
\( i \) — Angle of inclination to horizontal in soil (degrees)

Explanation: The normal stress is divided by the product of saturated unit weight and the square of cosine of the inclination angle (converted to radians).

3. Importance of Depth of Prism 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, saturated unit weight, and angle of inclination. All values must be > 0. The ±5% indicates the typical measurement tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is normal stress in soil mechanics?
A: Normal stress is the component of stress perpendicular to a plane, important for analyzing soil strength and deformation.

Q2: How do I determine saturated unit weight?
A: It's typically measured in laboratory tests on saturated soil samples, representing weight per unit volume.

Q3: Why does angle of inclination matter?
A: The angle affects how stress is distributed in sloping ground conditions.

Q4: What are typical values for saturated unit weight?
A: Common values range from 18-22 kN/m³ for most soils, but can vary significantly.

Q5: How accurate is this calculation?
A: Results are theoretical and should be verified with field measurements (±5% typical tolerance).