Normal Stress Component given Submerged Unit Weight and Depth of Prism Calculator

Normal Stress Formula:

\[ \sigma_n = F_u + (\gamma_s \times z \times \cos^2(i)) \]

Upward Force in Seepage Analysis:

Submerged Unit Weight:

N/m³

Depth of Prism:

Angle of Inclination:

Normal Stress (Pa):

Definition: Normal stress is the stress component that acts perpendicular to the plane of interest in soil mechanics.

Purpose: It helps geotechnical engineers analyze soil stability, particularly in slope stability and foundation design.

The calculator uses the formula:

\[ \sigma_n = F_u + (\gamma_s \times z \times \cos^2(i)) \]

Where:

Explanation: The formula accounts for both the upward seepage force and the vertical component of the submerged soil weight.

Details: Accurate normal stress calculation is crucial for determining soil shear strength and assessing slope stability.

Tips: Enter upward force, submerged unit weight (default 5000 N/m³), depth of prism (default 3 m), and angle of inclination (default 64° ±5%).

Q1: What is the typical range for submerged unit weight?
A: For most soils, it ranges from 8-12 kN/m³ (8000-12000 N/m³).

Q2: Why is angle of inclination important?
A: It affects how much of the soil weight contributes to normal stress versus shear stress.

Q3: How does seepage affect normal stress?
A: Upward seepage forces reduce effective normal stress, potentially leading to instability.

Q4: What if my angle exceeds 90°?
A: The calculator limits input to 0-90° as these are physically meaningful values.

Q5: How precise should my angle measurement be?
A: The ±5% tolerance accounts for typical field measurement inaccuracies.