Vertical Stress on Prism given Saturated Unit Weight Calculator

Vertical Stress Formula:

\[ \sigma_{z} = (\gamma_{sat} \times z \times \cos(\frac{i \times \pi}{180})) \]

Saturated Unit Weight of Soil:

kN/m³

Depth of Prism:

Angle of Inclination:

Tolerance:

Vertical Stress (kPa):

Acceptable Range (5% tolerance):

1. What is Vertical Stress on Prism?

Definition: This calculator determines the vertical stress at a point in soil given the saturated unit weight, depth, and angle of inclination.

Purpose: It helps geotechnical engineers analyze stress distribution in soil for foundation design and slope stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{z} = (\gamma_{sat} \times z \times \cos(\frac{i \times \pi}{180})) \]

Where:

\( \sigma_{z} \) — Vertical stress at a point (kPa)
\( \gamma_{sat} \) — Saturated unit weight of soil (kN/m³)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The formula calculates the vertical component of stress considering the weight of saturated soil and the inclination angle.

3. Importance of Vertical Stress Calculation

Details: Accurate stress calculation is crucial for foundation design, slope stability analysis, and settlement predictions in geotechnical engineering.

4. Using the Calculator

Tips: Enter the saturated unit weight, depth, angle of inclination (0° for horizontal), and optional tolerance percentage. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is saturated unit weight?
A: It's the weight per unit volume of soil when all voids are filled with water.

Q2: Why include angle of inclination?
A: The angle affects the vertical component of stress - steeper angles reduce the vertical stress component.

Q3: What's the purpose of the tolerance field?
A: It calculates an acceptable range (±%) around the calculated value for practical engineering applications.

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

Q5: When would angle be 0 degrees?
A: For perfectly horizontal ground surfaces where the stress is purely vertical.