Critical Depth given Submerged Unit Weight Calculator

Critical Depth Formula:

\[ h_c = \frac{C_s \cdot \sec^2(i)}{\gamma' \cdot (\tan(i) - \tan(\phi))} \]

Cohesion of Soil:

kPa

Angle of Inclination:

rad

Submerged Unit Weight:

N/m³

Angle of Internal Friction:

rad

Safety Factor:

Critical Depth (m):

With Safety Factor (m):

1. What is Critical Depth?

Definition: Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge in soil mechanics.

Purpose: It helps geotechnical engineers determine the stability of slopes and embankments.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_c = \frac{C_s \cdot \sec^2(i)}{\gamma' \cdot (\tan(i) - \tan(\phi))} \]

Where:

\( h_c \) — Critical Depth (m)
\( C_s \) — Cohesion of Soil (kPa)
\( i \) — Angle of Inclination to Horizontal (rad)
\( \gamma' \) — Submerged Unit Weight (N/m³)
\( \phi \) — Angle of Internal Friction (rad)

Explanation: The formula calculates the depth at which a slope becomes unstable considering soil properties and geometry.

3. Importance of Critical Depth Calculation

Details: Proper calculation ensures slope stability, prevents landslides, and helps in safe construction planning.

4. Using the Calculator

Tips: Enter all required parameters in their respective units. The safety factor defaults to 5% but can be adjusted.

5. Frequently Asked Questions (FAQ)

Q1: Why is the safety factor important?
A: It provides a margin of safety to account for uncertainties in soil properties and loading conditions.

Q2: What are typical values for cohesion?
A: Cohesion varies widely: 0-10 kPa for loose sand, 10-100 kPa for clay, and higher for cemented soils.

Q3: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.01745).

Q4: What if tan(i) - tan(φ) is negative?
A: This indicates an unstable condition where the slope angle exceeds the friction angle.

Q5: When would I adjust the safety factor?
A: Increase for critical structures or uncertain soil conditions; decrease for temporary works with good data.