Vertical Stress on Surface of Prism given Unit Weight of Soil Calculator

Vertical Stress Formula:

\[ \sigma_z = z \times \gamma \times \cos(\theta) \]

Depth of Prism (z):

Unit Weight of Soil (γ):

kN/m³

Angle of Inclination (θ):

Tolerance:

Vertical Stress (σ_z):

1. What is Vertical Stress on Surface of Prism?

Definition: This calculator determines the vertical stress at a point beneath the surface of a soil prism, considering the unit weight of soil and angle of inclination.

Purpose: It helps geotechnical engineers and construction professionals analyze stress distribution in soil structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_z = z \times \gamma \times \cos(\theta) \]

Where:

\( \sigma_z \) — Vertical stress at a point (kPa)
\( z \) — Depth of prism (m)
\( \gamma \) — Unit weight of soil (kN/m³)
\( \theta \) — Angle of inclination (degrees)

Explanation: The vertical stress increases with depth and unit weight, but decreases as the angle of inclination increases.

3. Importance of Vertical Stress Calculation

Details: Accurate stress calculation is crucial for foundation design, slope stability analysis, and earth pressure calculations.

4. Using the Calculator

Tips: Enter the depth in meters, unit weight in kN/m³ (default 18), angle in degrees (default 80), and tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical unit weight for soil?
A: Common values range from 16-20 kN/m³ for most soils, with clay typically around 18 kN/m³.

Q2: Why include angle of inclination?
A: The angle affects how much of the weight acts vertically versus horizontally.

Q3: What does the tolerance percentage mean?
A: It shows the acceptable range of variation (±5% by default) for engineering calculations.

Q4: How does depth affect vertical stress?
A: Stress increases linearly with depth in homogeneous soil.

Q5: When would I use 0° inclination?
A: For perfectly horizontal surfaces where all weight acts vertically.