Radial Distance from Centre of Rotation given Mobilized Shear Resistance of Soil Calculator

Radial Distance Formula:

\[ d_{radial} = \frac{c_m}{\left(\frac{W \times x'}{L'}\right)} \]

Mobilized Shear Resistance of Soil:

Weight of Body in Newtons:

Distance between LOA and COR:

Length of Slip Arc:

Radial Distance (m):

1. What is Radial Distance from Centre of Rotation?

Definition: This calculator computes the radial distance from the center of rotation based on mobilized shear resistance of soil, body weight, distance between line of action and center, and slip arc length.

Purpose: It helps geotechnical engineers analyze soil stability and rotational failure mechanisms.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{radial} = \frac{c_m}{\left(\frac{W \times x'}{L'}\right)} \]

Where:

\( d_{radial} \) — Radial distance from center (meters)
\( c_m \) — Mobilized shear resistance of soil (Pascals)
\( W \) — Weight of body in Newtons
\( x' \) — Distance between LOA and COR (meters)
\( L' \) — Length of slip arc (meters)

Explanation: The formula balances the mobilized shear resistance against the rotational moment created by the body weight.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculation is crucial for assessing slope stability, foundation design, and earth retention structures.

4. Using the Calculator

Tips: Enter all required values with appropriate units. Note that distance and length inputs have ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is mobilized shear resistance of soil?
A: It's the shear strength of soil that is actually resisting movement, considering factors like friction and particle interlocking.

Q2: Why is there a ±5% tolerance on some inputs?
A: Field measurements of distances and lengths often have inherent variability, so the 5% accounts for this uncertainty.

Q3: What typical values should I expect for radial distance?
A: Values vary widely based on project scale, but typically range from 0.5m to 10m for most civil engineering applications.

Q4: How does slip arc length affect the calculation?
A: Longer slip arcs generally result in smaller radial distances, as the resisting moment is distributed over a greater length.

Q5: Can this calculator be used for rotational failure analysis?
A: Yes, it provides one component needed for analyzing potential rotational failures in soil masses.