Normal Stress Component given Saturated Unit Weight Calculator

Normal Stress Formula:

\[ \sigma_n = \gamma_{sat} \times z \times \cos^2(i) \]

Normal Stress (kPa):

1. What is Normal Stress Component given Saturated Unit Weight?

Definition: This calculator computes the normal stress component acting on a soil prism when given the saturated unit weight of soil, depth, and angle of inclination.

Purpose: It helps geotechnical engineers and soil mechanics professionals analyze stress distribution in inclined soil layers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_n = \gamma_{sat} \times z \times \cos^2(i) \]

Where:

\( \sigma_n \) — Normal stress component (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 accounts for the vertical component of stress acting normal to an inclined plane in saturated soil conditions.

3. Importance of Normal Stress Calculation

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

4. Using the Calculator

Tips: Enter the saturated unit weight (typically 18-22 kN/m³ for soils), depth of interest, and inclination angle (0-90°). All values include ±5% tolerance.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is angle of inclination important?
A: The angle affects how much of the total stress acts normal to the plane of interest.

Q3: What's a typical saturated unit weight for clay?
A: Clay soils typically range from 18-20 kN/m³ when saturated.

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

Q5: What does the ±5% tolerance mean?
A: It accounts for typical variations in soil properties and measurement accuracy.