Mobilized Cohesion given Safe Height from Toe to Top of Wedge Calculator

Mobilized Cohesion Formula:

\[ C_{mob} = \frac{H}{4 \cdot \sin(\theta_i) \cdot \cos(\phi_{mob})} \cdot \frac{1}{\gamma_w \cdot (1 - \cos(\theta_i - \phi_{mob}))} \]

Height from Toe to Top (H):

Angle of Inclination (θi):

Angle of Mobilized Friction (φmob):

Unit Weight of Water (γw):

kN/m³

Tolerance:

Mobilized Cohesion (Cmob):

1. What is Mobilized Cohesion?

Definition: Mobilized cohesion is the amount of cohesive strength in soil that is actually resisting shear stress at a given state of stress.

Purpose: This calculator determines the mobilized cohesion based on the safe height of a soil wedge, inclination angles, and water unit weight.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{mob} = \frac{H}{4 \cdot \sin(\theta_i) \cdot \cos(\phi_{mob})} \cdot \frac{1}{\gamma_w \cdot (1 - \cos(\theta_i - \phi_{mob}))} \]

Where:

\( C_{mob} \) — Mobilized cohesion (kPa)
\( H \) — Height from toe to top of wedge (m)
\( \theta_i \) — Angle of inclination (°)
\( \phi_{mob} \) — Angle of mobilized friction (°)
\( \gamma_w \) — Unit weight of water (kN/m³)

3. Importance of Mobilized Cohesion Calculation

Details: Calculating mobilized cohesion helps in slope stability analysis and determining the safety factor against slope failure.

4. Using the Calculator

Tips:

Enter height in meters
Angles should be in degrees
Default unit weight of water is 9.81 kN/m³
Tolerance is ±5% by default (adjustable)

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for mobilized cohesion?
A: Values typically range from 0 kPa (for cohesionless soils) to over 100 kPa for highly cohesive clays.

Q2: How does angle of inclination affect the result?
A: Steeper angles generally require higher cohesion values to maintain stability.

Q3: Why include a tolerance percentage?
A: Soil properties are naturally variable, so results should be considered with an appropriate safety margin.

Q4: What if my angle of mobilized friction is zero?
A: This would represent a purely cohesive soil with no frictional strength.

Q5: How accurate is this calculation?
A: It provides a theoretical estimate; actual field conditions may vary.