Unit Weight of Soil given Vertical Stress on Surface of Prism Calculator

Unit Weight of Soil Formula:

\[ \gamma = \frac{\sigma_{vertical}}{z \times \cos(I)} \]

Vertical Stress at Point (σ):

Depth of Prism (z):

Angle of Inclination (I):

Unit Weight of Soil (γ):

kN/m³

1. What is Unit Weight of Soil given Vertical Stress?

Definition: This calculator determines the unit weight of soil based on vertical stress at a point, depth of prism, and angle of inclination.

Purpose: It helps geotechnical engineers and construction professionals analyze soil properties for foundation design and slope stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma = \frac{\sigma_{vertical}}{z \times \cos(I)} \]

Where:

\( \gamma \) — Unit weight of soil (kN/m³)
\( \sigma_{vertical} \) — Vertical stress at point (Pa)
\( z \) — Depth of prism (m)
\( I \) — Angle of inclination (degrees)

Explanation: The vertical stress is divided by the product of depth and cosine of inclination angle to determine the soil's unit weight.

3. Importance of Unit Weight Calculation

Details: Accurate unit weight estimation is crucial for calculating earth pressures, bearing capacity, and settlement analysis.

4. Using the Calculator

Tips: Enter vertical stress in pascals, depth in meters, and inclination angle in degrees (0-90°). The angle input has ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is typical unit weight for common soils?
A: Sand: 18-21 kN/m³, Clay: 16-20 kN/m³, Gravel: 19-22 kN/m³, Organic soil: 10-15 kN/m³.

Q2: Why does angle of inclination affect unit weight?
A: The cosine component accounts for the reduced vertical stress component on inclined surfaces.

Q3: How to measure vertical stress in field?
A: Use pressure cells or estimate from overburden pressure (γ × depth).

Q4: What if my angle is exactly 90 degrees?
A: The formula becomes invalid (division by zero) as cos(90°) = 0.

Q5: How accurate is this calculation?
A: It provides theoretical value; actual unit weight depends on soil composition, moisture, and compaction.