Saturated Unit Weight given Weighted and Mobilized Friction Angle Calculator

Saturated Unit Weight Formula:

\[ \gamma_{sat} = \frac{\gamma' \times \phi_m}{\phi_w} \]

Submerged Unit Weight (γ'):

N/m³

Angle of Mobilized Friction (φₘ):

rad

Weighted Friction Angle (φₙ):

rad

Tolerance:

Saturated Unit Weight (γₛₐₜ): N/m³

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 completely filled with water).

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma_{sat} = \frac{\gamma' \times \phi_m}{\phi_w} \]

Where:

\( \gamma_{sat} \) — Saturated Unit Weight (N/m³)
\( \gamma' \) — Submerged Unit Weight (N/m³)
\( \phi_m \) — Angle of Mobilized Friction (radians)
\( \phi_w \) — Weighted Friction Angle (radians)

Explanation: The formula relates the saturated unit weight to the submerged unit weight and the ratio of mobilized to weighted friction angles.

3. Importance of Saturated Unit Weight Calculation

Details: Accurate calculation is essential for designing foundations, retaining walls, and other structures where soil may become saturated with water.

4. Using the Calculator

Tips: Enter the submerged unit weight in N/m³, both angles in radians, and tolerance percentage (default ±5%). 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 when soil is underwater, while saturated unit weight includes pore water in the total weight.

Q2: Why use radians for angles?
A: Radians are the standard angular unit in most engineering calculations, especially when using trigonometric functions.

Q3: What's a typical tolerance percentage?
A: ±5% is common, but this may vary based on project requirements and material variability.

Q4: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q5: When would I need this calculation?
A: When analyzing slope stability, bearing capacity, or settlement of saturated soils.