Saturated Unit Weight given Effective Normal Stress Calculator

Saturated Unit Weight Formula:

\[ \gamma_{saturated} = \gamma_{water} + \left( \frac{\sigma'}{z \times \cos^2(i)} \right) \]

Unit Weight of Water:

N/m³

Effective Normal Stress:

Depth of Prism:

Angle of Inclination:

Saturated Unit Weight (N/m³):

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

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

Purpose: It helps geotechnical engineers determine the weight of saturated soil under specific stress conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{saturated} = \gamma_{water} + \left( \frac{\sigma'}{z \times \cos^2(i)} \right) \]

Where:

\( \gamma_{saturated} \) — Saturated unit weight of soil (N/m³)
\( \gamma_{water} \) — Unit weight of water (N/m³)
\( \sigma' \) — Effective normal stress (Pa)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The formula accounts for both the weight of water and the stress distribution through the soil at an inclined angle.

3. Importance of Saturated Unit Weight Calculation

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

4. Using the Calculator

Tips: Enter the unit weight of water (default 9810 N/m³), effective normal stress, depth of prism, and angle of inclination (±5%). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical unit weight of water?
A: The unit weight of water is typically 9810 N/m³ (9.81 kN/m³) at standard conditions.

Q2: How does angle of inclination affect the result?
A: Higher angles increase the cos²(i) term in the denominator, reducing the stress component's contribution.

Q3: What's the range for angle of inclination?
A: The angle should be between 0° (horizontal) and 90° (vertical), with ±5% tolerance.

Q4: How do I determine effective normal stress?
A: Effective stress is total stress minus pore water pressure, typically measured in field tests.

Q5: Why is depth of prism important?
A: Depth affects how stress is distributed through the soil column.