Curve Length of Each Slice given Resisting Force from Coulomb's Equation Calculator

Curve Length Formula:

\[ \Delta L = \frac{F_r - (N \times \tan(\phi))}{c_u} \]

Resisting Force (F_r):

Normal Component of Force (N):

Angle of Internal Friction (φ):

rad

Unit Cohesion (c_u):

Tolerance:

Curve Length (ΔL):

1. What is Curve Length of Each Slice given Resisting Force from Coulomb's Equation?

Definition: This calculator determines the curve length of each slice in slope stability analysis using Coulomb's equation for resisting force.

Purpose: It helps geotechnical engineers analyze slope stability by calculating the length of potential failure surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Delta L = \frac{F_r - (N \times \tan(\phi))}{c_u} \]

Where:

\( \Delta L \) — Curve length of each slice (meters)
\( F_r \) — Resisting force (Newtons)
\( N \) — Normal component of force (Newtons)
\( \phi \) — Angle of internal friction (radians)
\( c_u \) — Unit cohesion (Pascals)

Explanation: The formula calculates the length of the failure surface segment that can be supported by the soil's shear strength.

3. Importance of Curve Length Calculation

Details: Accurate curve length calculation is crucial for determining slope stability and designing appropriate reinforcement measures.

4. Using the Calculator

Tips: Enter all required values in consistent units. The tolerance field (default ±5%) shows the acceptable range of values.

5. Frequently Asked Questions (FAQ)

Q1: What is the resisting force in slope stability analysis?
A: The resisting force is the shear strength of the soil that opposes the driving forces causing slope movement.

Q2: How do I convert degrees to radians for the angle input?
A: Multiply degrees by π/180 (approximately 0.0174533) to get radians.

Q3: What is unit cohesion in soils?
A: Unit cohesion is the shear strength attributable solely to cohesive forces between soil particles, independent of normal stress.

Q4: Why include a tolerance percentage?
A: The tolerance accounts for uncertainties in soil parameters and provides a practical range for engineering decisions.

Q5: Can this calculator be used for all soil types?
A: It's most applicable for cohesive soils where Coulomb's equation is valid. Different approaches may be needed for purely frictional soils.