Safe Height from Toe to Top of Wedge Calculator

Safe Height Formula:

\[ H = \frac{4 \cdot c_m \cdot \sin(i) \cdot \cos(\phi_{mob})}{\gamma \cdot (1 - \cos(i - \phi_{mob}))} \]

Mobilized Cohesion (c_m):

Angle of Inclination (i):

Angle of Mobilized Friction (φ_mob):

Unit Weight of Soil (γ):

N/m³

Safety Factor (±5%):

Safe Height Range (H):

Minimum:

Maximum:

1. What is Safe Height from Toe to Top of Wedge?

Definition: This calculator determines the safe height of a soil wedge considering mobilized cohesion, friction, and unit weight of soil.

Purpose: It helps geotechnical engineers assess slope stability and prevent wedge failures in soil structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H = \frac{4 \cdot c_m \cdot \sin(i) \cdot \cos(\phi_{mob})}{\gamma \cdot (1 - \cos(i - \phi_{mob}))} \]

Where:

\( H \) — Safe height from toe to top of wedge (meters)
\( c_m \) — Mobilized cohesion in soil (Pascals)
\( i \) — Angle of inclination to horizontal (degrees)
\( \phi_{mob} \) — Angle of mobilized friction (degrees)
\( \gamma \) — Unit weight of soil (N/m³)

Explanation: The formula calculates the maximum stable height considering soil strength parameters and applies a safety factor.

3. Importance of Safe Height Calculation

Details: Proper calculation prevents slope failures, ensures structural stability, and helps in designing safe earthworks.

4. Using the Calculator

Tips: Enter all required parameters including a safety factor (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is mobilized cohesion?
A: It's the portion of soil cohesion actually resisting shear stress, typically less than total cohesion for safety.

Q2: How is angle of inclination measured?
A: It's the angle between the potential failure surface and the horizontal plane.

Q3: Why include a safety factor?
A: To account for uncertainties in soil parameters and environmental conditions.

Q4: What's a typical unit weight for soil?
A: Common values range from 16-22 kN/m³ (16000-22000 N/m³) for most soils.

Q5: When would I adjust the safety factor?
A: Increase for critical structures or uncertain conditions; decrease for temporary works with good data.