Radius of Arc when Total Shear Force on Slice is Available Calculator

Radius of Soil Section Formula:

\[ r = \frac{\Sigma W \times x}{\Sigma S} \]

Total Weight of Slice (ΣW):

Horizontal Distance (x):

Total Shear Force (ΣS):

Tolerance:

Radius of Soil Section (r):

1. What is Radius of Arc when Total Shear Force on Slice is Available?

Definition: This calculator determines the radius of the soil section arc based on the total weight of the slice, horizontal distance, and total shear force.

Purpose: It helps geotechnical engineers analyze soil stability and determine critical failure surfaces in slope stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{\Sigma W \times x}{\Sigma S} \]

Where:

\( r \) — Radius of soil section (meters)
\( \Sigma W \) — Total weight of slice (Newtons)
\( x \) — Horizontal distance from center of rotation (meters)
\( \Sigma S \) — Total shear force (Newtons)

Explanation: The radius is calculated by dividing the moment caused by the weight of the slice by the total shear force acting on the slice.

3. Importance of Radius Calculation

Details: Accurate radius determination is crucial for identifying potential failure surfaces and designing stable slopes in geotechnical engineering.

4. Using the Calculator

Tips: Enter the total weight of slice in Newtons, horizontal distance in meters, total shear force in Newtons, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for radius values?
A: Radius values vary widely depending on the slope geometry, but typically range from a few meters to several hundred meters.

Q2: Why include a tolerance percentage?
A: The tolerance accounts for measurement uncertainties and natural variability in soil properties.

Q3: How is the horizontal distance determined?
A: It's the perpendicular distance from the center of rotation to the vertical line passing through the centroid of the slice.

Q4: What affects the total shear force?
A: Shear force depends on soil properties, pore water pressure, and the geometry of the potential failure surface.

Q5: Can this be used for non-circular failure surfaces?
A: No, this formula specifically applies to circular failure surfaces in slope stability analysis.