Angle of Internal Friction given Shear Strength of Cohesive Soil Calculator

Angle of Internal Friction Formula:

\[ \phi_c = \tan^{-1}\left(\frac{\tau_s - c_u}{\sigma_{Normal}}\right) \]

Angle of Internal Friction (φ): degrees

1. What is Angle of Internal Friction?

Definition: The angle of internal friction (φ) is a measure of the shear strength of soil due to friction between soil particles in cohesive soil.

Purpose: It's a critical parameter in geotechnical engineering for analyzing soil stability and designing foundations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi_c = \tan^{-1}\left(\frac{\tau_s - c_u}{\sigma_{Normal}}\right) \]

Where:

\( \phi_c \) — Angle of internal friction (degrees)
\( \tau_s \) — Shear strength (Pa)
\( c_u \) — Unit cohesion (Pa)
\( \sigma_{Normal} \) — Normal stress (Pa)

Explanation: The formula calculates the angle whose tangent is the ratio of (shear strength minus cohesion) to normal stress.

3. Importance of Angle of Internal Friction

Details: This parameter helps determine the shear strength of soil, which is crucial for slope stability analysis, retaining wall design, and foundation engineering.

4. Using the Calculator

Tips: Enter shear strength, unit cohesion, and normal stress in Pascals. All values must be ≥ 0. Results are accurate within ±5%.

5. Frequently Asked Questions (FAQ)

Q1: What is typical angle range for cohesive soils?
A: Typically 0° to 30°, with clay soils often having 0°-15° and silty soils 15°-30°.

Q2: How does cohesion affect the angle?
A: Higher cohesion generally results in a lower apparent angle of internal friction.

Q3: What if my normal stress is zero?
A: The calculation becomes undefined as division by zero is not possible.

Q4: How accurate is this calculation?
A: Results are theoretical and should be verified with laboratory tests (±5% accuracy).

Q5: Can I use different units?
A: The calculator uses Pascals (Pa), but you can convert from other units before input.