Total Shear Force on Slice given Radius of Arc Calculator

Total Shear Force Formula:

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

Total Weight of Slice (ΣW):

Horizontal Distance (x):

Radius of Soil Section (r):

Tolerance:

Total Shear Force (ΣS): N

1. What is Total Shear Force on Slice?

Definition: This calculator determines the total shear force acting on a soil slice in slope stability analysis, considering the weight of the slice, its horizontal distance from the center of rotation, and the radius of the failure arc.

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

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The shear force is calculated by multiplying the slice weight by its moment arm (distance from center) and dividing by the failure surface radius.

3. Importance of Shear Force Calculation

Details: Accurate shear force calculation is critical for determining the factor of safety against slope failure and designing appropriate stabilization measures.

4. Using the Calculator

Tips: Enter the slice weight in Newtons, horizontal distance in meters, radius in meters, and tolerance percentage (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical tolerance used in slope stability analysis?
A: A ±5% tolerance is commonly used to account for variations in soil properties and measurement uncertainties.

Q2: How do I determine the radius of the failure arc?
A: The radius is typically determined through geotechnical investigation and analysis of potential failure surfaces.

Q3: What units should I use for input values?
A: Use Newtons for weight, meters for distances, and percentage for tolerance.

Q4: Can this calculator be used for rock slopes?
A: The basic principle applies, but rock mechanics may require additional considerations for discontinuities and rock strength.

Q5: How does slice weight affect the shear force?
A: Shear force increases proportionally with slice weight, making heavier slices more critical for stability.