Unit Weight of Soil given Weight of Soil Prism Calculator

Unit Weight of Soil Formula:

\[ \gamma = \frac{W}{z \times b \times \cos(I)} \]

Weight of Prism:

Depth of Prism:

Inclined Length:

Angle of Inclination:

Tolerance:

Unit Weight of Soil (kN/m³):

Acceptable Range (±5%):

1. What is Unit Weight of Soil?

Definition: Unit weight of soil mass is the ratio of the total weight of soil to the total volume of soil.

Purpose: It's a fundamental property in geotechnical engineering used in slope stability analysis, foundation design, and earth pressure calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma = \frac{W}{z \times b \times \cos(I)} \]

Where:

\( \gamma \) — Unit weight of soil (kN/m³)
\( W \) — Weight of prism (kg)
\( z \) — Depth of prism (m)
\( b \) — Inclined length of prism (m)
\( I \) — Angle of inclination (radians)

Explanation: The weight of the soil prism is divided by the product of its dimensions and the cosine of the inclination angle.

3. Importance of Unit Weight Calculation

Details: Accurate unit weight determination is crucial for stability analysis of slopes, retaining wall design, and settlement calculations.

4. Using the Calculator

Tips: Enter the weight of prism in kg, dimensions in meters, angle in degrees, and tolerance percentage (default ±5%). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle converted to radians?
A: The cosine function in mathematical calculations typically uses radians, not degrees.

Q2: What's a typical unit weight for common soils?
A: Clay: 16-22 kN/m³, Sand: 18-21 kN/m³, Gravel: 19-22 kN/m³, but varies with moisture content.

Q3: When would I adjust the tolerance?
A: For critical projects where tighter control is needed, you might reduce the tolerance to ±2%.

Q4: How do I measure the weight of a soil prism?
A: Excavate a known volume of soil and weigh it, ensuring minimal disturbance to the natural state.

Q5: Does this include pore water effects?
A: No, this calculates total unit weight. For saturated soils, buoyant unit weight calculations are different.