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Weight of Soil Prism given Saturated Unit Weight Calculator

Weight of Prism Formula:

\[ W_{prism} = \gamma_{saturated} \times z \times b \times \cos\left(\frac{i \times \pi}{180}\right) \]

N/m³
m
m
°
%

1. What is Weight of Soil Prism Calculator?

Definition: This calculator computes the weight of a soil prism based on saturated unit weight, prism dimensions, and inclination angle.

Purpose: It helps geotechnical engineers and soil mechanics professionals determine the weight of soil prisms for slope stability analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ W_{prism} = \gamma_{saturated} \times z \times b \times \cos\left(\frac{i \times \pi}{180}\right) \]

Where:

  • \( W_{prism} \) — Weight of soil prism (N)
  • \( \gamma_{saturated} \) — Saturated unit weight of soil (N/m³)
  • \( z \) — Depth of prism (m)
  • \( b \) — Inclined length of prism (m)
  • \( i \) — Angle of inclination to horizontal (°)

Explanation: The formula accounts for the vertical component of the prism's weight considering its inclination.

3. Importance of Weight Calculation

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

4. Using the Calculator

Tips: Enter all required dimensions and the angle of inclination. The tolerance field (default ±5%) provides a range for practical applications.

5. Frequently Asked Questions (FAQ)

Q1: What is saturated unit weight?
A: It's the weight per unit volume of soil when all voids are filled with water.

Q2: How does inclination affect the weight?
A: The cosine term accounts for the reduced vertical component of weight on inclined surfaces.

Q3: What's a typical saturated unit weight?
A: Common values range from 18-22 kN/m³ (18000-22000 N/m³) for most soils.

Q4: Why include a tolerance range?
A: Soil properties can vary, so ±5% provides a practical range for design purposes.

Q5: Can this be used for dry soils?
A: Yes, but use the dry unit weight instead of saturated unit weight.

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