Depth of Prism for Cohesive Soil given Submerged Slope Calculator

Depth of Prism Formula:

\[ z = \frac{C_s}{(F_s - \frac{\tan(\phi)}{\tan(i)}) \times \gamma' \times \cos(i) \times \sin(i)} \]

Cohesion of Soil (Cs):

kPa

Factor of Safety (Fs):

Angle of Internal Friction (φ):

radians

Angle of Inclination (i):

radians

Submerged Unit Weight (γ'):

kN/m³

Depth of Prism (z): meters

1. What is Depth of Prism for Cohesive Soil?

Definition: This calculator determines the critical depth of a soil prism for cohesive soils on submerged slopes, considering soil properties and slope angle.

Purpose: It helps geotechnical engineers assess slope stability and potential failure depths in cohesive soils.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{C_s}{(F_s - \frac{\tan(\phi)}{\tan(i)}) \times \gamma' \times \cos(i) \times \sin(i)} \]

Where:

\( z \) — Depth of prism (meters)
\( C_s \) — Cohesion of soil (kPa)
\( F_s \) — Factor of safety
\( \phi \) — Angle of internal friction (radians)
\( i \) — Angle of inclination (radians)
\( \gamma' \) — Submerged unit weight (kN/m³)

Explanation: The formula calculates the critical depth where shear stress equals shear strength for a submerged cohesive slope.

3. Importance of Depth Calculation

Details: Proper depth estimation helps prevent slope failures, design retaining structures, and ensure construction safety in cohesive soils.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. The factor of safety typically includes ±5% margin.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical factor of safety for slopes?
A: Common values range from 1.3 to 1.5, with ±5% variation depending on project requirements.

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

Q3: Why use radians for angles?
A: The trigonometric functions in the formula require angle inputs in radians for accurate calculations.

Q4: What affects submerged unit weight?
A: It depends on soil particle density, water content, and degree of saturation.

Q5: When would this calculation be used?
A: For designing embankments, analyzing slope stability, or assessing landslide potential in cohesive soils.