Critical Depth given Stability Number for Cohesive Soil Calculator

Critical Depth Formula:

\[ h_{cs} = \frac{c}{\gamma \times S_n} \]

Critical Depth (m):

1. What is Critical Depth for Stability Number?

Definition: The Critical Depth for Stability Number is the depth within a soil mass where the Stability Number reaches a critical value for slope stability analysis.

Purpose: It helps geotechnical engineers assess the stability of slopes in cohesive soils and determine safe excavation depths.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{cs} = \frac{c}{\gamma \times S_n} \]

Where:

\( h_{cs} \) — Critical depth (meters)
\( c \) — Cohesion of soil (kPa)
\( \gamma \) — Unit weight of soil (kN/m³)
\( S_n \) — Stability Number (dimensionless, ±5%)

Explanation: The formula calculates the depth at which the resisting forces (cohesion) balance the driving forces (weight and stability number) for slope stability.

3. Importance of Critical Depth Calculation

Details: Proper calculation helps prevent slope failures, ensures safe construction practices, and aids in designing stable earth structures.

4. Using the Calculator

Tips: Enter the soil cohesion in kPa, unit weight in kN/m³, and stability number (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for stability numbers?
A: Stability numbers typically range from 0.1 to 0.3 for most cohesive soils, but can vary based on soil conditions.

Q2: How does cohesion affect critical depth?
A: Higher cohesion values result in greater critical depths, indicating more stable slopes.

Q3: Why is there a ±5% on the stability number?
A: This accounts for variability in soil conditions and measurement uncertainties.

Q4: Can this be used for non-cohesive soils?
A: No, this formula is specifically for cohesive soils where cohesion is significant.

Q5: How is unit weight determined?
A: Through laboratory tests on soil samples or from standard tables based on soil classification.