Weighted Friction Angle given Mobilised Friction Angle Calculator

Weighted Friction Angle Formula:

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

Submerged Unit Weight (γ'):

N/m³

Angle of Mobilized Friction (φ_m):

radians

Saturated Unit Weight (γ_sat):

N/m³

Tolerance:

Weighted Friction Angle (φ_w):

1. What is Weighted Friction Angle?

Definition: Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.

Purpose: It helps in analyzing slope stability and foundation bearing capacity by considering the submerged and saturated conditions of soil.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the effective friction angle by considering the ratio of submerged unit weight to saturated unit weight, scaled by the mobilized friction angle.

3. Importance of Weighted Friction Angle

Details: Proper calculation ensures accurate stability analysis for slopes, retaining walls, and foundations in geotechnical engineering projects.

4. Using the Calculator

Tips: Enter the submerged unit weight, angle of mobilized friction, saturated unit weight, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for submerged unit weight?
A: For most soils, submerged unit weight ranges between 9-11 kN/m³ (9000-11000 N/m³).

Q2: How do I convert degrees to radians for the friction angle?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q3: Why include a tolerance percentage?
A: The tolerance accounts for measurement uncertainties and material variability in real-world conditions.

Q4: What's the difference between submerged and saturated unit weight?
A: Submerged weight considers buoyancy in water, while saturated weight is the total weight when all voids are water-filled.

Q5: When would I adjust the tolerance value?
A: Increase tolerance for highly variable materials or decrease for well-controlled laboratory conditions.