Depth of Prism given Submerged Unit Weight and Shear Stress Calculator

Depth of Prism Formula:

\[ z = \frac{\tau}{\gamma' \times \cos(i) \times \sin(i)} \]

Depth of Prism (m):

1. What is Depth of Prism given Submerged Unit Weight and Shear Stress?

Definition: This calculator determines the depth of a prism in soil mechanics based on submerged unit weight, shear stress, and angle of inclination.

Purpose: It helps geotechnical engineers analyze slope stability and soil behavior under submerged conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{\tau}{\gamma' \times \cos(i) \times \sin(i)} \]

Where:

\( z \) — Depth of prism (meters)
\( \tau \) — Shear stress for submerged slopes (%)
\( \gamma' \) — Submerged unit weight (%)
\( i \) — Angle of inclination to horizontal in soil (%)

Explanation: The shear stress is divided by the product of submerged unit weight and the trigonometric components of the angle of inclination.

3. Importance of Depth of Prism Calculation

Details: Accurate depth calculation is crucial for assessing slope stability, designing retaining structures, and preventing soil failures.

4. Using the Calculator

Tips: Enter the shear stress (%), submerged unit weight (%), and angle of inclination (%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle converted to radians?
A: The trigonometric functions in the formula require the angle in radians for accurate calculations.

Q2: What's a typical range for submerged unit weight?
A: Submerged unit weight typically ranges between 50-80% of the soil's dry unit weight.

Q3: How does angle of inclination affect the depth?
A: Steeper angles generally result in greater depth requirements for stability.

Q4: What units are used for the output?
A: The depth is calculated in meters (m).

Q5: Does this consider safety factors?
A: No, additional safety factors should be applied based on project requirements.