Weighted Friction Angle given Effective Angle of Internal Friction Calculator

Weighted Friction Angle Formula:

\[ \phi_{IF} = \frac{\gamma' \times \phi'}{fs \times \gamma_{sat}} \]

Submerged Unit Weight (γ'):

N/m³

Effective Angle of Internal Friction (φ'):

rad

Factor of Safety (fs):

Saturated Unit Weight (γ_sat):

N/m³

Weighted Friction Angle (φ_IF): rad

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 engineers determine the combined frictional resistance of different soil layers or materials in a slope or foundation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi_{IF} = \frac{\gamma' \times \phi'}{fs \times \gamma_{sat}} \]

Where:

\( \phi_{IF} \) — Weighted Friction Angle (radians)
\( \gamma' \) — Submerged Unit Weight (N/m³)
\( \phi' \) — Effective Angle of Internal Friction (radians)
\( fs \) — Factor of Safety (±5%)
\( \gamma_{sat} \) — Saturated Unit Weight (N/m³)

Explanation: The formula calculates the effective friction angle considering the submerged and saturated conditions of the soil with an appropriate safety factor.

3. Importance of Weighted Friction Angle

Details: Proper calculation ensures accurate slope stability analysis, foundation design, and earth retaining structure design.

4. Using the Calculator

Tips: Enter the submerged unit weight (default 31 N/m³), effective angle (default 0.174 rad), factor of safety (default 2.8 ±5%), and saturated unit weight (default 9.98 N/m³). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the factor of safety important?
A: The factor of safety accounts for uncertainties in material properties and loading conditions, ensuring stability under various conditions.

Q2: What's a typical value for effective angle of internal friction?
A: It varies by soil type: 0.17-0.35 rad (10-20°) for sands, 0.26-0.52 rad (15-30°) for gravels, and lower for clays.

Q3: How does submerged vs saturated unit weight differ?
A: Submerged weight is the effective weight under water (buoyant weight), while saturated weight is the total weight when all voids are water-filled.

Q4: When would I need to calculate weighted friction angle?
A: When analyzing layered soils, composite materials, or when different zones have varying frictional properties.

Q5: What does the ±5% on factor of safety mean?
A: It indicates the acceptable variation range for the safety factor in calculations.