Inclined Length along Slope given Weight of Soil Prism Calculator

Inclined Length Formula:

\[ b = \frac{W}{\gamma \times z \times \cos(I)} \]

Weight of Prism:

Unit Weight of Soil:

kN/m³

Depth of Prism:

Angle of Inclination:

Tolerance:

Inclined Length (m):

1. What is Inclined Length along Slope?

Definition: The inclined length of a soil prism is the distance measured along the slope from the base to the top of the prism.

Purpose: This calculation is essential in slope stability analysis and earthwork calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{W}{\gamma \times z \times \cos(I)} \]

Where:

\( b \) — Inclined length along slope (meters)
\( W \) — Weight of soil prism (kg)
\( \gamma \) — Unit weight of soil (kN/m³)
\( z \) — Depth of prism (meters)
\( I \) — Angle of inclination (radians)

Explanation: The weight of the prism is divided by the product of unit weight, depth, and cosine of the inclination angle.

3. Importance of Inclined Length Calculation

Details: Accurate calculation of inclined length is crucial for slope stability analysis, retaining wall design, and earthwork calculations.

4. Using the Calculator

Tips: Enter the weight of prism in kg, unit weight of soil (default 18 kN/m³), depth of prism (default 3 m), angle of inclination in degrees (default 80°), and tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: Why do we use cosine of the angle?
A: The cosine function accounts for the horizontal component of the inclined length in relation to the slope.

Q2: What's a typical unit weight for soil?
A: Most soils range between 16-20 kN/m³, with 18 kN/m³ being a common average value.

Q3: How does the tolerance affect the result?
A: The tolerance provides a range (±%) around the calculated value to account for measurement uncertainties.

Q4: Can I use this for any slope angle?
A: Yes, but angles should be between 0° and 90° for meaningful results.

Q5: Why convert angle from degrees to radians?
A: The cosine function in most programming languages uses radians, so conversion is necessary when input is in degrees.