Mobilized Friction Angle given Weighted Friction Angle Calculator

Mobilized Friction Angle Formula:

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

Saturated Unit Weight (γ_sat):

N/m³

Weighted Friction Angle (φ_w):

radians

Submerged Unit Weight (γ'):

N/m³

Tolerance:

Mobilized Friction Angle (φ_m):

1. What is Mobilized Friction Angle?

Definition: The mobilized friction angle is the slope angle at which an object starts sliding due to applied force, calculated based on saturated unit weight, weighted friction angle, and submerged unit weight.

Purpose: This calculation is crucial in geotechnical engineering for analyzing slope stability and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \phi_m \) — Mobilized friction angle (radians)
\( \gamma_{sat} \) — Saturated unit weight (N/m³)
\( \phi_w \) — Weighted friction angle (radians)
\( \gamma' \) — Submerged unit weight (N/m³)

Explanation: The formula calculates the effective friction angle considering the soil's saturated and submerged conditions.

3. Importance of Mobilized Friction Angle

Details: Accurate calculation helps prevent slope failures, ensures proper foundation design, and maintains structural stability in geotechnical projects.

4. Using the Calculator

Tips: Enter values for saturated unit weight, weighted friction angle, and submerged unit weight. The tolerance field (default ±5%) allows for practical range estimation.

5. Frequently Asked Questions (FAQ)

Q1: What's the typical range for weighted friction angle?
A: For most soils, φ_w ranges between 0.35 to 1.05 radians (20° to 60°), depending on soil type and conditions.

Q2: How does saturation affect the calculation?
A: Saturated conditions increase unit weight but reduce effective stress, impacting the mobilized friction angle.

Q3: When would I adjust the tolerance?
A: Increase tolerance for heterogeneous materials or when accounting for measurement uncertainties in field conditions.

Q4: Can I use degrees instead of radians?
A: The calculator uses radians, but you can convert degrees to radians (degrees × π/180) before input.

Q5: What's the practical significance of the tolerance range?
A: It provides a safety margin for design, accounting for material variability and measurement errors.