Critical Depth given Saturated Unit Weight Calculator

Critical Depth Formula:

\[ h_c = \frac{C}{(\gamma_{sat} \cdot \tan(i) \cdot \cos^2(i)) - (y_S \cdot \tan(\phi) \cdot \cos^2(i))} \]

Cohesion in Soil (kPa):

kPa

Saturated Unit Weight:

N/m³

Angle of Inclination:

Submerged Unit Weight:

kN/m³

Angle of Internal Friction:

Safety Factor:

Critical Depth (m):

With Safety Factor (m):

1. What is Critical Depth in Soil Mechanics?

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

Purpose: It helps determine the stability of slopes and the potential for failure in soil structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_c = \frac{C}{(\gamma_{sat} \cdot \tan(i) \cdot \cos^2(i)) - (y_S \cdot \tan(\phi) \cdot \cos^2(i))} \]

Where:

\( h_c \) — Critical depth (meters)
\( C \) — Cohesion in soil (kPa)
\( \gamma_{sat} \) — Saturated unit weight of soil (N/m³)
\( i \) — Angle of inclination to horizontal (degrees)
\( y_S \) — Submerged unit weight (kN/m³)
\( \phi \) — Angle of internal friction (degrees)

Explanation: The formula calculates the depth at which the driving forces equal the resisting forces in a slope.

3. Importance of Critical Depth Calculation

Details: Proper calculation helps prevent slope failures, ensures structural stability, and guides construction practices in geotechnical engineering.

4. Using the Calculator

Tips: Enter all required parameters including cohesion, unit weights, angles, and optional safety factor (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical safety factor for slope stability?
A: Common safety factors range from 1.3 to 1.5 (30-50%), but 5% is used here as a minimal adjustment factor.

Q2: How do I determine soil cohesion?
A: Cohesion is typically measured through laboratory tests like unconfined compression tests or field vane shear tests.

Q3: What's the difference between saturated and submerged unit weight?
A: Saturated unit weight includes water in the voids, while submerged unit weight is the effective weight under water.

Q4: Why do we need to convert angles to radians?
A: Trigonometric functions in programming languages typically use radians, so degree inputs must be converted.

Q5: What if I get a negative critical depth?
A: Negative values indicate an error in input parameters or an inherently unstable slope configuration.