Angle of Inclination given Vertical Stress on Surface of Prism Calculator

Angle of Inclination Formula:

\[ I = \cos^{-1}\left(\frac{\sigma_{vertical}}{z \times \gamma}\right) \]

Angle of Inclination (radians):

Angle of Inclination (degrees):

1. What is Angle of Inclination given Vertical Stress?

Definition: This calculator determines the angle of inclination of a soil prism based on the vertical stress at a point, depth of the prism, and unit weight of the soil.

Purpose: It helps geotechnical engineers analyze slope stability and soil mechanics problems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ I = \cos^{-1}\left(\frac{\sigma_{vertical}}{z \times \gamma}\right) \]

Where:

\( I \) — Angle of inclination (radians)
\( \sigma_{vertical} \) — Vertical stress at a point (Pascal)
\( z \) — Depth of prism (meters)
\( \gamma \) — Unit weight of soil (N/m³)

Explanation: The inverse cosine function is applied to the ratio of vertical stress to the product of depth and unit weight.

3. Importance of Angle of Inclination Calculation

Details: Calculating this angle helps in understanding slope stability, potential for landslides, and designing proper retaining structures.

4. Using the Calculator

Tips: Enter the vertical stress in Pascals, depth in meters, and unit weight in N/m³. All values must be > 0. Results are shown in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the practical range for this angle?
A: Typically between 0° (horizontal) and 90° (vertical), but most natural slopes range between 15°-45°.

Q2: Why show results in both radians and degrees?
A: Radians are mathematically pure, while degrees are more intuitive for most users.

Q3: What does ±5% mean for inputs?
A: It indicates the acceptable measurement error range for each parameter.

Q4: How does soil type affect the results?
A: Different soils have different unit weights, which directly impacts the calculation.

Q5: When would this calculation be invalid?
A: When the ratio exceeds 1 (which is mathematically impossible for cosine), indicating incorrect input values.