Length of Slip Arc Calculator by Tons of Concrete

Length of Slip Arc Formula:

\[ L' = \frac{2 \times \pi \times d_{radial} \times \delta \times \left(\frac{180}{\pi}\right)}{360} \]

Length of Slip Arc (m):

1. What is a Length of Slip Arc Calculator?

Definition: This calculator computes the length of an arc formed by a slip circle based on radial distance and arc angle.

Purpose: It helps geotechnical engineers and construction professionals analyze slope stability and potential failure surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L' = \frac{2 \times \pi \times d_{radial} \times \delta \times \left(\frac{180}{\pi}\right)}{360} \]

Where:

\( L' \) — Length of slip arc (meters)
\( d_{radial} \) — Radial distance (meters)
\( \delta \) — Arc angle (radians)
\( \pi \) — Pi constant (approximately 3.14159)

Explanation: The formula calculates arc length by converting the angle from radians to degrees and applying the standard arc length calculation.

3. Importance of Slip Arc Calculation

Details: Accurate slip arc length determination is crucial for slope stability analysis, landslide prediction, and designing appropriate stabilization measures.

4. Using the Calculator

Tips: Enter the radial distance in meters, arc angle in radians, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is radial distance in this context?
A: It's the distance from the center of rotation to the slip surface (radius of the slip circle).

Q2: Why is the angle in radians?
A: Radians are the standard angular measurement in mathematical calculations, though the formula converts to degrees internally.

Q3: What does the tolerance percentage represent?
A: It shows the acceptable variation range (±%) around the calculated value for engineering purposes.

Q4: How is this used in slope stability analysis?
A: The slip arc length helps determine potential failure surfaces and calculate safety factors against sliding.

Q5: Can I use degrees instead of radians?
A: The calculator requires radians, but you can convert degrees to radians by multiplying by π/180.