Inclined Length along Slope given Volume Per Unit Length of Prism Calculator

Formula:

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

Volume per unit length of prism (V_l):

m²

Depth of Prism (z):

Angle of Inclination (I):

rad

Tolerance:

Inclined Length (b): m

1. What is Inclined Length along Slope?

Definition: The inclined length of a prism is the distance measured along the slope, accounting for both horizontal and vertical components.

Purpose: This calculation is essential in geotechnical engineering and slope stability analysis to determine the true length of failure surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( b \) — Inclined length along slope (meters)
\( V_l \) — Volume per unit length of prism (square meters)
\( z \) — Depth of prism (meters)
\( I \) — Angle of inclination (radians)

Explanation: The formula accounts for the geometric relationship between the prism dimensions and the slope angle.

3. Importance of Inclined Length Calculation

Details: Accurate calculation of inclined length is crucial for slope stability analysis, earthwork calculations, and construction planning on inclined surfaces.

4. Using the Calculator

Tips:

Enter volume per unit length in m²
Enter depth in meters
Enter angle in radians (convert from degrees if needed)
Set tolerance percentage (default ±5%)

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (≈0.0174533). Many calculators have a degree-to-radian function.

Q2: What is volume per unit length?
A: It's the cross-sectional area of the prism (volume divided by length in the third dimension).

Q3: Why include a tolerance percentage?
A: Engineering calculations often require safety factors or account for material variability.

Q4: What's a typical angle of inclination?
A: Natural slopes typically range from 20° to 45° (0.35 to 0.79 radians).

Q5: How does depth affect the inclined length?
A: Greater depth generally results in shorter inclined length for a given volume per unit length.