Depth of Prism given Submerged Unit Weight and Effective Normal Stress Calculator

Depth of Prism Formula:

\[ z = \frac{\sigma'}{\gamma_s \times (\cos(\frac{i \times \pi}{180}))^2} \]

Effective Normal Stress (σ'):

kN/m²

Submerged Unit Weight (γₛ):

kN/m³

Angle of Inclination (i):

Tolerance:

Depth of Prism (z): m

1. What is Depth of Prism in Soil Mechanics?

Definition: The depth of prism refers to the vertical distance of soil being analyzed, particularly in slope stability calculations.

Purpose: It helps geotechnical engineers determine the critical depth for slope stability analysis and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{\sigma'}{\gamma_s \times (\cos(\frac{i \times \pi}{180}))^2} \]

Where:

\( z \) — Depth of prism (meters)
\( \sigma' \) — Effective normal stress (kN/m²)
\( \gamma_s \) — Submerged unit weight (kN/m³)
\( i \) — Angle of inclination to horizontal (degrees)

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

3. Importance of Depth of Prism Calculation

Details: Accurate calculation ensures proper slope stability analysis, helps prevent landslides, and is crucial for safe foundation design in inclined terrains.

4. Using the Calculator

Tips:

Enter effective normal stress in kN/m²
Enter submerged unit weight in kN/m³
Enter angle of inclination in degrees (0° for horizontal)
Set tolerance percentage (default ±5%)

5. Frequently Asked Questions (FAQ)

Q1: What is effective normal stress?
A: It's the stress carried by the soil skeleton, calculated as total stress minus pore water pressure.

Q2: Why use submerged unit weight?
A: Submerged unit weight accounts for buoyancy effects when soil is below the water table.

Q3: What does the angle of inclination represent?
A: It's the angle between the potential failure plane and horizontal surface.

Q4: Why include a tolerance percentage?
A: Soil properties can vary, so tolerance provides a practical range for engineering decisions.

Q5: When would this calculation be used?
A: Primarily in slope stability analysis, retaining wall design, and foundation engineering on inclined surfaces.