Height from Toe to Top of Wedge given Angle of Mobilized Friction Calculator

Height from Toe to Top of Wedge Formula:

\[ H = \frac{c_m}{0.5 \cdot \csc\left(\frac{i \cdot \pi}{180}\right) \cdot \sec\left(\frac{\phi_{mob} \cdot \pi}{180}\right) \cdot \sin\left(\frac{(i-\theta) \cdot \pi}{180}\right) \cdot \sin\left(\frac{(\theta_{slope}-\phi_{mob}) \cdot \pi}{180}\right) \cdot \gamma} \]

Mobilized Cohesion (c_m):

Angle of Inclination (i):

Angle of Mobilized Friction (φ_mob):

Slope Angle (θ):

Unit Weight of Soil (γ):

N/m³

Tolerance:

Height from Toe to Top of Wedge (H):

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

Definition: This calculation determines the vertical height of a potential failure wedge in soil mechanics, based on mobilized cohesion, friction angles, and soil properties.

Purpose: It helps geotechnical engineers assess slope stability and potential failure mechanisms in soil structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H = \frac{c_m}{0.5 \cdot \csc(i) \cdot \sec(\phi_{mob}) \cdot \sin(i-\theta) \cdot \sin(\theta_{slope}-\phi_{mob}) \cdot \gamma} \]

Where:

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

Explanation: The formula accounts for the balance between resisting forces (cohesion and friction) and driving forces (weight and slope angle) in a potential failure wedge.

3. Importance of Height Calculation

Details: Accurate height estimation is crucial for designing stable slopes, retaining walls, and other earth structures, preventing costly failures.

4. Using the Calculator

Tips: Enter all required parameters in appropriate units. The tolerance field (default ±5%) accounts for measurement uncertainties in soil properties.

5. Frequently Asked Questions (FAQ)

Q1: What is mobilized cohesion?
A: Mobilized cohesion is the portion of soil's total cohesion that is actually resisting shear stress at a given state of stress.

Q2: How do I determine the angle of mobilized friction?
A: This is typically determined through laboratory shear tests or back-calculation from observed failures.

Q3: Why include a tolerance range?
A: Soil properties are naturally variable; the tolerance accounts for this uncertainty in calculations.

Q4: What if I get a negative height?
A: Negative values indicate an error in input parameters or that the slope is inherently stable under given conditions.

Q5: How does unit weight affect the result?
A: Heavier soils (higher unit weight) generally result in smaller failure wedges for the same strength parameters.