Depth of Prism given Effective Normal Stress Calculator

Depth of Prism Formula:

\[ z = \frac{\sigma'}{(\gamma_{saturated} - \gamma_{water}) \times \cos^2(i)} \]

Effective Normal Stress:

Saturated Unit Weight of Soil:

N/m³

Unit Weight of Water:

N/m³

Angle of Inclination:

degrees

Depth of Prism (m):

Definition: This calculator determines the depth of a soil prism based on effective normal stress, soil properties, and inclination angle.

Purpose: It helps geotechnical engineers and soil mechanics professionals analyze soil stability on slopes.

The calculator uses the formula:

\[ z = \frac{\sigma'}{(\gamma_{saturated} - \gamma_{water}) \times \cos^2(i)} \]

Where:

Explanation: The effective stress is divided by the submerged unit weight and adjusted for slope angle.

Details: Accurate depth calculation is crucial for slope stability analysis, retaining wall design, and foundation engineering.

Tips: Enter effective normal stress, saturated unit weight (default 9810 N/m³ for water), and inclination angle. All values must be ≥ 0.

Q1: What is effective normal stress?
A: It's the stress carried by the soil skeleton, calculated as total stress minus pore water pressure.

Q2: Why use submerged unit weight?
A: Submerged weight (saturated - water) accounts for buoyancy effects below the water table.

Q3: How does angle affect the result?
A: Higher angles reduce the normal component of weight, requiring greater depth for the same stress.

Q4: What are typical values for saturated soil?
A: Typically 18-22 kN/m³ (18000-22000 N/m³), but varies with soil type.

Q5: When would this calculation be used?
A: For analyzing potential failure planes in slopes or behind retaining structures.