Saturated Unit Weight given Factor of Safety Calculator

Saturated Unit Weight Formula:

\[ \gamma_{sat} = \frac{\gamma' \cdot \tan(\phi \cdot \pi/180)}{FS \cdot \tan(i \cdot \pi/180)} \]

Submerged Unit Weight (γ'):

kN/m³

Angle of Internal Friction (φ):

Factor of Safety (FS):

Angle of Inclination (i):

Saturated Unit Weight (γ_sat): kN/m³

1. What is Saturated Unit Weight?

Definition: Saturated unit weight is the ratio of mass of saturated soil sample to total volume, including both solids and water-filled voids.

Purpose: It's a critical parameter in geotechnical engineering for slope stability analysis and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{sat} = \frac{\gamma' \cdot \tan(\phi \cdot \pi/180)}{FS \cdot \tan(i \cdot \pi/180)} \]

Where:

\( \gamma_{sat} \) — Saturated unit weight (kN/m³)
\( \gamma' \) — Submerged unit weight (kN/m³)
\( \phi \) — Angle of internal friction (°)
\( FS \) — Factor of Safety (dimensionless)
\( i \) — Angle of inclination to horizontal (°)

Explanation: The formula relates the saturated unit weight to the submerged unit weight, accounting for soil friction and slope stability.

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation is essential for designing stable slopes, retaining walls, and foundations in water-saturated conditions.

4. Using the Calculator

Tips: Enter submerged unit weight, friction angle (typically 25-40°), safety factor (default 1.5 ±5%), and inclination angle. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the typical range for submerged unit weight?
A: For most soils, γ' ranges from 8-12 kN/m³, depending on soil type and density.

Q2: Why is the safety factor shown with ±5%?
A: This accounts for typical uncertainty in safety factor determination in geotechnical engineering.

Q3: How does inclination angle affect the result?
A: Higher inclination angles generally require higher saturated unit weights for stability.

Q4: What if my friction angle is unknown?
A: Use typical values: 30-40° for sand, 20-30° for silt, 10-20° for clay.

Q5: Can this be used for unsaturated soils?
A: No, this formula specifically applies to saturated soil conditions.