Angle of Internal Friction given Angle of Inclination and Slope Angle Calculator

Angle of Internal Friction Formula:

\[ \phi_i = \tan^{-1}\left(\left(F_s - \frac{c}{\frac{1}{2}\gamma H \left(\frac{\sin((\theta_i - \theta_{slope})\frac{\pi}{180})}{\sin(\theta_i\frac{\pi}{180})}\right) \sin(\theta_{slope}\frac{\pi}{180})}\right) \times \tan(\theta_{slope}\frac{\pi}{180})\right) \]

Factor of Safety:

Cohesion of Soil:

Unit Weight of Soil:

N/m³

Height of Wedge:

Angle of Inclination:

Slope Angle:

Angle of Internal Friction:

1. What is Angle of Internal Friction?

Definition: The angle of internal friction is a measure of the shear strength of soil due to friction between soil particles.

Purpose: It's crucial for analyzing slope stability and designing earth structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi_i = \tan^{-1}\left(\left(F_s - \frac{c}{\frac{1}{2}\gamma H \left(\frac{\sin((\theta_i - \theta_{slope}))}{\sin(\theta_i)}\right) \sin(\theta_{slope})}\right) \times \tan(\theta_{slope})\right) \]

Where:

\( \phi_i \) — Angle of internal friction (degrees)
\( F_s \) — Factor of safety
\( c \) — Cohesion of soil (Pa)
\( \gamma \) — Unit weight of soil (N/m³)
\( H \) — Height of soil wedge (m)
\( \theta_i \) — Angle of inclination (degrees)
\( \theta_{slope} \) — Slope angle (degrees)

3. Importance of This Calculation

Details: Accurate determination of internal friction angle is essential for safe slope design and preventing landslides.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for typical conditions. All angles must be between 0° and 90°.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety?
A: For slopes, Fs typically ranges from 1.3 to 1.5. Higher values (2.0+) are used for critical structures.

Q2: How does cohesion affect the result?
A: Higher cohesion values generally allow for steeper stable slopes or lower friction angles.

Q3: What's the ±5% significance?
A: It indicates the expected accuracy range for input parameters in typical field conditions.

Q4: How do I measure angle of inclination?
A: It's the angle between the potential failure plane and horizontal, often determined through site surveys.

Q5: What if my result is negative?
A: Check your inputs - negative values suggest impossible conditions (Fs too low or cohesion too high).