Inclined Length along Slope given Vertical Stress on Surface of Prism Calculator

Inclined Length Formula:

\[ b = \frac{W}{\sigma_z} \times 5 \]

Inclined Length (m):

1. What is Inclined Length along Slope given Vertical Stress?

Definition: This calculator determines the inclined length of a soil prism along a slope based on the prism's weight and vertical stress at a point.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{W}{\sigma_z} \times 5 \]

Where:

\( b \) — Inclined length of prism (meters)
\( W \) — Weight of prism (kilograms)
\( \sigma_z \) — Vertical stress at a point (MPa)

Explanation: The weight of the prism is divided by the vertical stress to get a base value, then multiplied by 5 to account for slope conditions.

3. Importance of Inclined Length Calculation

Details: Proper calculation of inclined length is crucial for slope stability analysis, retaining wall design, and foundation engineering.

4. Using the Calculator

Tips: Enter the weight of prism in kg and vertical stress in MPa. The calculation includes a ±5% tolerance factor.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 5x multiplier?
A: The multiplier accounts for typical slope conditions and provides a practical safety factor in calculations.

Q2: How do I determine the weight of the prism?
A: Calculate prism volume and multiply by soil unit weight (typically 16-20 kN/m³ for most soils).

Q3: What affects vertical stress in soil?
A: Depth below surface, soil density, water content, and any surface loads influence vertical stress.

Q4: Why is there a ±5% tolerance?
A: Soil properties are naturally variable, so calculations should account for this uncertainty.

Q5: Can this be used for rock slopes?
A: The formula is primarily for soil prisms. Rock slopes require different analysis methods.