Depth of Prism given Saturated Unit Weight Calculator

Depth of Prism Formula:

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

Weight of Prism:

Saturated Unit Weight:

N/m³

Inclined Length:

Angle of Inclination:

Depth of Prism (m):

1. What is Depth of Prism given Saturated Unit Weight?

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

Purpose: It helps geotechnical engineers and soil mechanics professionals analyze slope stability and soil behavior under different conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( z \) — Depth of prism (meters)
\( W_{prism} \) — Weight of prism (Newtons)
\( \gamma_{sat} \) — Saturated unit weight (N/m³)
\( b \) — Inclined length of prism (meters)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The weight is divided by the product of saturated unit weight, length, and cosine of the angle (converted to radians).

3. Importance of Depth Calculation

Details: Accurate depth calculation is crucial for slope stability analysis, retaining wall design, and understanding soil behavior under saturated conditions.

4. Using the Calculator

Tips: Enter the prism weight in Newtons, saturated unit weight (default 32.24 N/m³), inclined length (default 0.019 m), and angle (default 1.117°). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the angle of inclination?
A: The angle affects the component of weight acting normal to the potential failure plane, crucial for stability calculations.

Q2: Why use saturated unit weight?
A: Saturated conditions represent worst-case scenarios for many slope stability problems when pore water pressure is highest.

Q3: What does the ±5% represent?
A: It indicates the acceptable margin of error for input values in typical engineering calculations.

Q4: How do I measure the weight of a soil prism?
A: Typically calculated from soil density and prism dimensions, or measured in laboratory tests.

Q5: When would I need this calculation?
A: For slope stability analysis, landslide prediction, and designing earth-retaining structures.