Unit Weight of Soil given Safe Height from Toe to Top of Wedge Calculator

Unit Weight of Soil Formula:

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

Mobilized Cohesion (c_m):

Angle of Inclination (i):

Angle of Mobilized Friction (φ_mob):

Height (H):

Tolerance:

Unit Weight of Soil (γ):

1. What is Unit Weight of Soil given Safe Height from Toe to Top of Wedge?

Definition: This calculator determines the unit weight of soil based on mobilized cohesion, angles of inclination and friction, and the height of the soil wedge.

Purpose: It helps geotechnical engineers assess soil stability and design safe slopes or retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the unit weight required to maintain equilibrium of a soil wedge considering its shear strength parameters.

3. Importance of Unit Weight Calculation

Details: Accurate unit weight determination is crucial for slope stability analysis, retaining wall design, and foundation engineering.

4. Using the Calculator

Tips: Enter all parameters in consistent units. The tolerance field (default ±5%) allows for uncertainty in input parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is mobilized cohesion?
A: Mobilized cohesion is the portion of soil's cohesive strength that is actually resisting shear stress under given conditions.

Q2: How do I determine the angle of mobilized friction?
A: This is typically determined through laboratory tests or estimated based on soil type and moisture content.

Q3: Why include a tolerance percentage?
A: Soil properties often vary, so the tolerance provides a realistic range of expected values.

Q4: What units should I use?
A: Use Pascals for cohesion, degrees for angles, and meters for height. The result is in N/m³.

Q5: When would this calculation be used?
A: For slope stability analysis, retaining wall design, or any situation where soil wedge failure might occur.