Critical Slope Angle given Angle of Inclination Calculator

Critical Slope Angle Formula:

\[ \theta_{cr} = \frac{i + \phi_m}{2} \]

Critical Slope Angle:

Acceptable Range:

1. What is Critical Slope Angle?

Definition: The Critical Slope Angle in Soil Mechanics is the angle formed by the most dangerous plane where slope failure is most likely to occur.

Purpose: It helps geotechnical engineers assess slope stability and design safe earthworks.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta_{cr} = \frac{i + \phi_m}{2} \]

Where:

\( \theta_{cr} \) — Critical slope angle (degrees)
\( i \) — Angle of inclination to horizontal (degrees)
\( \phi_m \) — Angle of mobilized friction (degrees)

Explanation: The critical angle is the average of the inclination angle and the mobilized friction angle.

3. Importance of Critical Slope Angle

Details: Proper calculation prevents landslides, ensures structural stability, and helps in designing safe excavation slopes.

4. Using the Calculator

Tips: Enter the angle of inclination, mobilized friction angle, and tolerance percentage (default ±5%). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is angle of mobilized friction?
A: It's the slope angle at which an object starts sliding due to applied force, representing the soil's frictional resistance.

Q2: Why include a tolerance percentage?
A: The tolerance accounts for variations in soil properties and provides a safe range for practical applications.

Q3: What's a typical tolerance value?
A: ±5% is common, but this may vary based on project requirements and soil conditions.

Q4: How do I measure the angle of inclination?
A: It can be measured using inclinometers, clinometers, or through trigonometric calculations from survey data.

Q5: What factors affect the critical slope angle?
A: Soil type, moisture content, vegetation, and external loads all influence the critical angle.