Depth of Prism given Factor of Safety for Cohesive Soil Calculator

Depth of Prism Formula:

\[ z = \frac{c_u}{(FS - (\frac{\tan(\phi_i)}{\tan(I)})) \times \gamma \times \cos(I) \times \sin(I)} \]

Unit Cohesion (c_u):

kPa

Factor of Safety (FS):

Angle of Internal Friction (φ_i):

Angle of Inclination (I):

Unit Weight of Soil (γ):

kN/m³

Depth of Prism (z): m

1. What is Depth of Prism given Factor of Safety?

Definition: This calculator determines the maximum stable depth of a soil prism considering cohesion, internal friction, slope angle, and safety factor.

Purpose: It helps geotechnical engineers assess slope stability and design safe earth structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{c_u}{(FS - (\frac{\tan(\phi_i)}{\tan(I)})) \times \gamma \times \cos(I) \times \sin(I)} \]

Where:

\( z \) — Depth of prism (meters)
\( c_u \) — Unit cohesion (kPa)
\( FS \) — Factor of Safety (dimensionless)
\( \phi_i \) — Angle of internal friction (degrees)
\( I \) — Angle of inclination (degrees)
\( \gamma \) — Unit weight of soil (kN/m³)

Explanation: The formula balances shear strength against driving forces, adjusted by safety factor.

3. Importance of Depth Calculation

Details: Proper depth estimation prevents slope failures, ensures structural stability, and optimizes material usage.

4. Using the Calculator

Tips: Enter all parameters with appropriate units. Angles in degrees will be converted to radians. Default values represent typical conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical Factor of Safety for slopes?
A: Common FS values range from 1.3 to 1.5 for temporary slopes, and 1.5 to 2.0 for permanent slopes.

Q2: How does cohesion affect prism depth?
A: Higher cohesion allows greater stable depths, while low cohesion soils require shallower slopes.

Q3: What if I get negative or infinite results?
A: This indicates unstable conditions - the denominator becomes zero or negative when FS ≤ tan(φ)/tan(I).

Q4: How accurate is this calculation?
A: It's a simplified model. For critical projects, perform detailed slope stability analysis.

Q5: Can I use this for vertical cuts?
A: No, this formula is for inclined slopes. Vertical cuts require different analysis methods.