Angle of Inclination given Vertical Stress and Saturated Unit Weight Calculator

Angle of Inclination Formula:

\[ i = \cos^{-1}\left(\frac{\sigma_z}{\gamma \times z}\right) \]

Vertical Stress at Point:

Unit Weight of Soil:

N/m³

Depth of Prism:

Tolerance:

Angle of Inclination (radians):

Angle of Inclination (degrees):

Tolerance Range (±5%):

1. What is Angle of Inclination given Vertical Stress and Saturated Unit Weight?

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

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ i = \cos^{-1}\left(\frac{\sigma_z}{\gamma \times z}\right) \]

Where:

\( i \) — Angle of inclination (radians)
\( \sigma_z \) — Vertical stress at point (Pa)
\( \gamma \) — Unit weight of soil (N/m³)
\( z \) — Depth of prism (m)

Explanation: The inverse cosine function calculates the angle whose cosine equals the ratio of vertical stress to the product of unit weight and depth.

3. Importance of Angle of Inclination Calculation

Details: Proper calculation helps in assessing slope stability, designing retaining structures, and preventing soil failures.

4. Using the Calculator

Tips: Enter vertical stress in Pascals, unit weight in N/m³ (default 18000), depth in meters (default 3), and tolerance percentage (default ±5%). All values must be > 0 except tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical unit weight for saturated soil?
A: Saturated unit weight typically ranges from 18,000 to 22,000 N/m³ depending on soil type.

Q2: How does vertical stress affect the angle?
A: Higher vertical stress results in a smaller angle of inclination, indicating more stable conditions.

Q3: What does the tolerance percentage represent?
A: It shows the acceptable range (±%) around the calculated angle for practical applications.

Q4: When would the angle be 0 degrees?
A: When vertical stress equals γ×z, meaning the surface is perfectly horizontal.

Q5: What's the maximum possible angle?
A: Theoretically 90° when vertical stress is zero, but practically much less due to soil properties.