Total Length of Slip Circle given Resisting Moment Calculator

Length of Slip Arc Formula:

\[ L' = \frac{\left(\frac{MR}{r}\right) - \left(\Sigma N \times \tan(\phi_i)\right)}{c_u} \]

Resisting Moment (MR):

kN·m

Radius of Slip Circle (r):

Sum of all Normal Components (ΣN):

Angle of Internal Friction (φ):

Unit Cohesion (c_u):

Tolerance:

Length of Slip Arc (L'): m

1. What is Length of Slip Arc?

Definition: The length of the slip arc is the curved distance along which potential failure may occur in a soil mass, calculated based on resisting moments and soil properties.

Purpose: This calculation is crucial in slope stability analysis to determine the critical failure surface in soil mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L' = \frac{\left(\frac{MR}{r}\right) - \left(\Sigma N \times \tan(\phi_i)\right)}{c_u} \]

Where:

\( L' \) — Length of slip arc (meters)
\( MR \) — Resisting moment (kN·m)
\( r \) — Radius of slip circle (meters)
\( \Sigma N \) — Sum of all normal components (Newtons)
\( \phi_i \) — Angle of internal friction (degrees)
\( c_u \) — Unit cohesion (Pascals)

Explanation: The formula calculates the arc length where shear resistance balances the driving forces along a potential failure surface.

3. Importance of Slip Arc Calculation

Details: Accurate calculation helps engineers design stable slopes, retaining structures, and foundations by identifying potential failure surfaces.

4. Using the Calculator

Tips: Enter all required parameters including resisting moment, radius, normal components, friction angle, and cohesion. The tolerance field (default ±5%) provides a range estimate.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for angle of internal friction?
A: For soils, φ typically ranges from 0° (pure clay) to 45° (dense gravel).

Q2: How is resisting moment determined?
A: Resisting moment is calculated from soil shear strength along the potential failure surface.

Q3: Why include a tolerance percentage?
A: The tolerance accounts for uncertainties in soil parameters and calculation assumptions.

Q4: What if I get a negative result?
A: Negative values indicate calculation error - check your input parameters for validity.

Q5: How does unit cohesion affect the result?
A: Higher cohesion values result in shorter calculated slip arcs, indicating more stable conditions.