Length of Slip Arc given Factor of Safety Calculator ±5%

Length of Slip Arc Formula:

\[ Ls' = \frac{fs}{\left(\frac{c_u \times d_{radial}}{W \times x'}\right)} \]

Factor of Safety:

Unit Cohesion:

Radial Distance:

Weight of Body:

Distance between LOA and COR:

Length of Slip Arc (m):

1. What is Length of Slip Arc given Factor of Safety?

Definition: This calculator determines the length of the potential slip arc in slope stability analysis considering a specified factor of safety.

Purpose: It helps geotechnical engineers assess slope stability and potential failure surfaces in soil mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Ls' = \frac{fs}{\left(\frac{c_u \times d_{radial}}{W \times x'}\right)} \]

Where:

\( Ls' \) — Length of slip arc with factor of safety (meters)
\( fs \) — Factor of safety (%)
\( c_u \) — Unit cohesion (%)
\( d_{radial} \) — Radial distance (%)
\( W \) — Weight of body in Newtons (%)
\( x' \) — Distance between LOA and COR (%)

Explanation: The formula calculates the critical slip arc length that would maintain the specified factor of safety against slope failure.

3. Importance of Slip Arc Calculation

Details: Accurate slip arc determination is crucial for designing stable slopes, retaining structures, and preventing landslides.

4. Using the Calculator

Tips: Enter all values as percentages. The calculator accounts for ±5% variation in input parameters.

5. Frequently Asked Questions (FAQ)

Q1: Why are all inputs in percentages?
A: Percentage inputs allow for standardized comparison and account for the ±5% measurement tolerance.

Q2: What is a typical factor of safety for slopes?
A: Common FOS values range from 1.3 to 1.5, with higher values for critical structures.

Q3: How does unit cohesion affect the slip arc?
A: Higher cohesion values typically result in shorter critical slip arcs as the soil is more resistant to failure.

Q4: What if my radial distance is unknown?
A: Estimate based on slope geometry or use our Slope Geometry Calculator tool.

Q5: Does this include seismic factors?
A: No, for seismic zones, additional dynamic analysis is required beyond this static calculation.