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Saturated Unit Weight given Normal Stress Component Calculator

Saturated Unit Weight Formula:

\[ γ_{saturated} = \frac{σ_n}{z \times (\cos(\frac{i \times \pi}{180}))^2} \]

Pa
m
°
%

1. What is Saturated Unit Weight?

Definition: Saturated unit weight is the weight per unit volume of soil when all voids are filled with water.

Purpose: It's crucial in geotechnical engineering for analyzing soil stability, bearing capacity, and slope stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ γ_{saturated} = \frac{σ_n}{z \times (\cos(\frac{i \times \pi}{180}))^2} \]

Where:

  • \( γ_{saturated} \) — Saturated unit weight (N/m³)
  • \( σ_n \) — Normal stress (Pa)
  • \( z \) — Depth of prism (m)
  • \( i \) — Angle of inclination (degrees)

Explanation: The normal stress is divided by the depth multiplied by the square of cosine of the inclination angle (converted to radians).

3. Importance of Saturated Unit Weight

Details: Accurate calculation helps in designing stable foundations, retaining walls, and assessing slope stability in wet conditions.

4. Using the Calculator

Tips: Enter normal stress in Pascals, depth in meters, angle in degrees (0-90), and tolerance percentage. All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What is typical saturated unit weight range?
A: For common soils, it ranges from 18-22 kN/m³ (18000-22000 N/m³).

Q2: Why include tolerance percentage?
A: It accounts for measurement uncertainties and natural soil variability.

Q3: How does inclination angle affect the result?
A: Higher angles decrease the effective depth component, increasing calculated unit weight.

Q4: When would I need this calculation?
A: For slope stability analysis, retaining wall design, or foundation design in saturated soils.

Q5: What if my angle is 0°?
A: At 0° (horizontal), cos(0)=1, so the formula simplifies to γ = σn/z.

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