Unit Weight of Soil given Angle of Mobilized Friction Calculator

Unit Weight of Soil Formula:

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

Mobilized Cohesion (c_m):

Angle of Inclination (i):

Angle of Mobilized Friction (φ_mob):

Slope Angle (θ_slope):

Height (H):

Tolerance:

Unit Weight of Soil (γ):

Tolerance Range (±5%):

1. What is Unit Weight of Soil given Angle of Mobilized Friction?

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

Purpose: It helps geotechnical engineers analyze slope stability and soil mechanics problems where the angle of mobilized friction is a key parameter.

2. How Does the Calculator Work?

The calculator uses the formula:

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

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 (°)
\( \theta_{slope} \) — Slope angle (°)
\( H \) — Height from toe to top of wedge (m)

Explanation: The formula accounts for the trigonometric relationships between the various angles and the mobilized shear strength of the soil.

3. Importance of Unit Weight Calculation

Details: Accurate unit weight determination is crucial for slope stability analysis, foundation design, and earth pressure calculations.

4. Using the Calculator

Tips:

Enter all angles in degrees
Mobilized cohesion should be in Pascals (Pa)
Height should be in meters (m)
Tolerance is set to ±5% by default but can be adjusted

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 does angle of mobilized friction affect the result?
A: Higher mobilized friction angles typically result in lower calculated unit weights, as more shear resistance comes from friction rather than cohesion.

Q3: What is the typical range for unit weight of soils?
A: Most soils range from 16-22 kN/m³ (16,000-22,000 N/m³), but organic soils can be lighter and dense gravels heavier.

Q4: Why include a tolerance range?
A: Soil properties are naturally variable; the tolerance range accounts for this uncertainty in calculations.

Q5: How do I determine mobilized friction angle?
A: It's typically a fraction (often 0.5-0.8) of the soil's peak friction angle, depending on safety requirements.