Unit Weight of Soil given Critical Depth for Cohesive Soil Calculator

Unit Weight of Soil Formula:

\[ \gamma = \frac{c}{h_c \times (\tan(I) - \tan(\phi)) \times \cos^2(I)} \]

Cohesion of Soil (c):

kPa

Critical Depth (h_c):

Angle of Inclination (I):

Angle of Internal Friction (φ):

Calculation Uncertainty:

Unit Weight of Soil (γ):

1. What is Unit Weight of Soil given Critical Depth?

Definition: This calculator determines the unit weight of soil based on cohesion, critical depth, and angles of inclination and internal friction.

Purpose: It helps geotechnical engineers analyze slope stability and bearing capacity of cohesive soils.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma = \frac{c}{h_c \times (\tan(I) - \tan(\phi)) \times \cos^2(I)} \]

Where:

\( \gamma \) — Unit weight of soil (kN/m³)
\( c \) — Cohesion of soil (kPa)
\( h_c \) — Critical depth (m)
\( I \) — Angle of inclination (°)
\( \phi \) — Angle of internal friction (°)

Explanation: The formula relates soil cohesion to its unit weight considering slope geometry and shear resistance.

3. Importance of Unit Weight Calculation

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

4. Using the Calculator

Tips: Enter cohesion in kPa, depth in meters, and angles in degrees. The uncertainty field (default ±5%) accounts for calculation variability.

5. Frequently Asked Questions (FAQ)

Q1: What is critical depth in soil mechanics?
A: Critical depth is the soil depth where net pressure equals zero, important for slope stability and bearing capacity calculations.

Q2: How does angle of inclination affect the result?
A: Steeper angles increase the denominator, resulting in lower calculated unit weight for the same cohesion.

Q3: What's a typical cohesion value for clay?
A: Soft clay might have 5-25 kPa, while stiff clay can have 50-200 kPa cohesion.

Q4: Why include uncertainty percentage?
A: Soil properties are naturally variable, so ±5% provides a realistic range for design purposes.

Q5: When would this calculation be invalid?
A: When tan(I) ≤ tan(φ), which would make the denominator zero or negative (physically impossible condition).