Saturated Unit Weight given Weighted and Effective Friction Angle Calculator

Saturated Unit Weight Formula:

\[ γ_{sat} = \frac{γ' \times φ'}{φ_{IF} \times fs} \]

Submerged Unit Weight (γ'):

N/m³

Effective Angle of Internal Friction (φ'):

rad

Weighted Friction Angle (φ_IF):

rad

Factor of Safety (fs):

Saturated Unit Weight (γ_sat):

1. What is Saturated Unit Weight?

Definition: Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water (all soil pores are filled with water).

Purpose: It's crucial for geotechnical engineering calculations involving soil stability, bearing capacity, and slope stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ γ_{sat} = \frac{γ' \times φ'}{φ_{IF} \times fs} \]

Where:

\( γ_{sat} \) — Saturated Unit Weight (N/m³)
\( γ' \) — Submerged Unit Weight (N/m³)
\( φ' \) — Effective Angle of Internal Friction (radians)
\( φ_{IF} \) — Weighted Friction Angle for Internal Friction (radians)
\( fs \) — Factor of Safety (dimensionless, typically ±5%)

Explanation: The formula calculates the saturated unit weight considering the submerged conditions, friction angles, and safety factor.

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation is essential for designing foundations, retaining walls, and other geotechnical structures where soil is likely to be saturated.

4. Using the Calculator

Tips: Enter the submerged unit weight in N/m³, friction angles in radians, and safety factor (consider ±5% variation). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between submerged and saturated unit weight?
A: Submerged unit weight considers buoyancy effects, while saturated unit weight includes the weight of both soil particles and pore water.

Q2: Why is the safety factor expressed as ±5%?
A: The ±5% accounts for typical variations in field conditions and material properties.

Q3: How do I convert degrees to radians for the friction angles?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q4: What's a typical value for the factor of safety?
A: Common values range from 1.5 to 3.0 depending on the application and risk level.

Q5: When would I need this calculation?
A: For designing structures in wet conditions, analyzing slope stability after rainfall, or calculating earth pressures on retaining walls.