Depth of Prism given Weight of Soil Prism Calculator

Depth of Prism Formula:

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

Weight of Prism:

Unit Weight of Soil:

kN/m³

Inclined Length:

Angle of Inclination:

Tolerance:

Depth of Prism (z):

1. What is Depth of Prism given Weight of Soil Prism?

Definition: This calculator determines the depth of a soil prism based on its weight, unit weight of soil, inclined length, and angle of inclination.

Purpose: It helps geotechnical engineers and construction professionals analyze soil stability and design proper retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( z \) — Depth of Prism (meters)
\( W \) — Weight of Prism (kg)
\( \gamma \) — Unit Weight of Soil (kN/m³)
\( b \) — Inclined Length (meters)
\( I \) — Angle of Inclination (radians)

Explanation: The weight of the prism is divided by the product of unit weight, inclined length, and cosine of the inclination angle.

3. Importance of Depth Calculation

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

4. Using the Calculator

Tips: Enter the weight in kg, unit weight (default 18 kN/m³), inclined length (default 10 m), angle in degrees (default 80°), and tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is a soil prism?
A: A soil prism is a theoretical section of soil used in stability analysis, typically with a unit width.

Q2: Why is angle converted to radians?
A: The cosine function in the formula requires the angle in radians for accurate calculation.

Q3: What's a typical unit weight for soil?
A: Most soils range from 16-20 kN/m³, with 18 kN/m³ being a common average value.

Q4: How does tolerance affect the result?
A: The tolerance provides a range (±%) around the calculated depth to account for measurement uncertainties.

Q5: When would I adjust the tolerance?
A: Increase tolerance for less precise measurements or highly variable soil conditions.