Weighted Friction Angle given Submerged Unit Weight Calculator

Weighted Friction Angle Formula:

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

Submerged Unit Weight (γ'):

N/m³

Internal Friction Angle (φ_iw):

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 engineers analyze soil stability by considering both submerged and saturated conditions of the soil.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \phi_w \) — Weighted Friction Angle (radians)
\( \gamma' \) — Submerged Unit Weight (N/m³)
\( \phi_{iw} \) — Internal Friction Angle (radians)
\( \gamma_{sat} \) — Saturated Unit Weight (N/m³)

Explanation: The formula calculates the effective friction angle by considering the ratio of submerged conditions to saturated conditions.

3. Importance of Weighted Friction Angle

Details: Proper calculation ensures accurate slope stability analysis, foundation design, and earth pressure calculations in geotechnical engineering.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for internal friction angle?
A: For soils, it typically ranges from 0.35 to 1.05 radians (20° to 60°), depending on soil type and density.

Q2: How does submerged unit weight differ from saturated unit weight?
A: Submerged unit weight considers buoyancy effects when soil is below water table, while saturated unit weight is the total weight when all voids are filled with water.

Q3: When would I adjust the tolerance percentage?
A: Adjust based on required precision - lower for critical structures, higher for preliminary estimates or when data quality is uncertain.

Q4: Can I use degrees instead of radians?
A: The calculator uses radians. Convert degrees to radians by multiplying by π/180 (approximately 0.0174533).

Q5: What's the practical significance of weighted friction angle?
A: It's crucial for designing stable slopes, retaining walls, and foundations in variable moisture conditions.