Effective Angle of Internal Friction given Weighted Friction Angle Calculator

Formula:

\[ \phi' = \frac{\phi_{IF}}{\left(\frac{\gamma'}{f_s \times \gamma_{sat}}\right)} \]

Weighted Friction Angle (φ_IF):

rad

Submerged Unit Weight (γ'):

N/m³

Factor of Safety (f_s):

Saturated Unit Weight (γ_sat):

N/m³

Effective Angle of Internal Friction (φ'):

1. What is Effective Angle of Internal Friction?

Definition: The effective angle of internal friction (φ') is the shear strength of soil due to friction between soil particles when subjected to effective stress.

Purpose: It's a critical parameter in geotechnical engineering for analyzing soil stability, slope stability, and foundation design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi' = \frac{\phi_{IF}}{\left(\frac{\gamma'}{f_s \times \gamma_{sat}}\right)} \]

Where:

φ' — Effective angle of internal friction (radians)
φ_IF — Weighted friction angle for internal friction (radians)
γ' — Submerged unit weight (N/m³)
f_s — Factor of safety (±5%)
γ_sat — Saturated unit weight (N/m³)

Explanation: The formula relates the weighted friction angle to the effective angle considering soil weight conditions and safety factors.

3. Importance of Calculation

Details: Accurate calculation of φ' is essential for designing stable earth structures, assessing landslide risks, and ensuring safe foundation designs.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for φ'?
A: For most soils, φ' ranges between 25° to 45° (0.436 to 0.785 radians), with sands at the higher end and clays at the lower end.

Q2: Why is the factor of safety important?
A: The factor of safety accounts for uncertainties in soil properties and loading conditions (±5% variation).

Q3: How do I determine submerged unit weight?
A: γ' = γ_sat - γ_w, where γ_w is unit weight of water (9.81 kN/m³).

Q4: When would I need this calculation?
A: For slope stability analysis, retaining wall design, and any geotechnical application where soil shear strength is important.

Q5: How accurate is this calculation?
A: Results are theoretical and should be verified with laboratory tests like direct shear or triaxial tests.