Effective Normal Stress given Submerged Unit Weight Calculator

Effective Normal Stress Formula:

\[ \sigma' = y_s \times z \times \cos^2(i) \]

Submerged Unit Weight (y_s):

kN/m³

Depth of Prism (z):

Inclination Angle (i):

Allowable Variation:

Effective Normal Stress (σ'):

1. What is Effective Normal Stress in Soil Mechanics?

Definition: Effective normal stress (σ') is the stress carried by the soil skeleton, calculated by considering submerged unit weight, depth, and slope angle.

Purpose: It's crucial for analyzing soil stability, bearing capacity, and slope stability in geotechnical engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma' = y_s \times z \times \cos^2(i) \]

Where:

\( \sigma' \) — Effective normal stress (kPa)
\( y_s \) — Submerged unit weight (kN/m³)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (°)

Explanation: The formula accounts for both the vertical stress due to submerged weight and the reduction due to slope angle.

3. Importance of Effective Normal Stress Calculation

Details: Proper calculation ensures accurate assessment of soil strength parameters, slope stability analysis, and foundation design.

4. Using the Calculator

Tips: Enter submerged unit weight, depth, inclination angle (0-90°), and allowable variation percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is submerged unit weight?
A: It's the unit weight of soil under water, accounting for buoyancy effects (typically 8-11 kN/m³ for soils).

Q2: Why use cos²(i) in the formula?
A: This accounts for the reduction in normal stress component as slope angle increases.

Q3: What's a typical variation percentage?
A: ±5% is common, but this depends on project requirements and soil variability.

Q4: How does depth affect the result?
A: Effective normal stress increases linearly with depth in homogeneous soil.

Q5: What if my slope angle is 0°?
A: At 0° (horizontal), cos²(0) = 1, so σ' = y_s × z (simple vertical stress).