Mobilized Cohesion given Angle of Mobilized Friction Calculator

Mobilized Cohesion Formula:

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

Angle of Inclination to Horizontal:

Angle of Mobilized Friction:

Slope Angle:

Unit Weight of Soil:

N/m³

Height from Toe to Top:

Mobilized Cohesion (Pa):

1. What is Mobilized Cohesion?

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

Purpose: It helps geotechnical engineers analyze slope stability and determine the safety factor against failure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( c_m \) — Mobilized cohesion (Pa)
\( i \) — Angle of inclination to horizontal (°)
\( \phi_{mob} \) — Angle of mobilized friction (°)
\( \theta_{slope} \) — Slope angle (°)
\( \gamma \) — Unit weight of soil (N/m³)
\( H \) — Height from toe to top of wedge (m)

Explanation: The formula calculates the cohesion required to maintain equilibrium in a soil wedge considering various angles and soil properties.

3. Importance of Mobilized Cohesion Calculation

Details: Accurate calculation helps in designing stable slopes, retaining walls, and other earth structures by determining the safety factor against shear failure.

4. Using the Calculator

Tips: Enter all angles in degrees, unit weight in N/m³, and height in meters. The ±5% indicates the typical measurement tolerance for these parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for mobilized friction angle?
A: It typically ranges between 10° to 30° for most soils, but can vary based on soil type and conditions.

Q2: Why is the height from toe to top important?
A: It determines the size of the potential failure wedge and directly affects the mobilized cohesion calculation.

Q3: How does unit weight affect the result?
A: Heavier soils (higher unit weight) generally require more cohesion to maintain stability.

Q4: What does the ±5% tolerance mean?
A: It indicates that the input values may have up to 5% measurement error, which should be considered in your analysis.

Q5: Can this be used for all soil types?
A: This is primarily for cohesive-frictional soils. Pure clays or sands may require different approaches.