Depth of Prism given Vertical Stress and Saturated Unit Weight Calculator

Depth of Prism Formula:

\[ z = \frac{\sigma_{zkp}}{\gamma_{saturated} \times \cos\left(\frac{i \times \pi}{180}\right)} \]

Vertical Stress at a Point:

kPa

Saturated Unit Weight of Soil:

kN/m³

Angle of Inclination:

degrees

Depth of Prism (m):

1. What is Depth of Prism Calculator?

Definition: This calculator computes the depth of prism based on vertical stress, saturated unit weight of soil, and angle of inclination.

Purpose: It helps geotechnical engineers and construction professionals determine the depth of soil prism under given stress conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{\sigma_{zkp}}{\gamma_{saturated} \times \cos\left(\frac{i \times \pi}{180}\right)} \]

Where:

\( z \) — Depth of prism (meters)
\( \sigma_{zkp} \) — Vertical stress at a point (kPa)
\( \gamma_{saturated} \) — Saturated unit weight of soil (kN/m³)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The vertical stress is divided by the product of saturated unit weight 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 vertical stress in kPa, saturated unit weight (default 11.89 kN/m³), and angle of inclination (default 64°). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for saturated unit weight?
A: For most soils, it ranges between 18-22 kN/m³, but can vary based on soil type and moisture content.

Q2: Why is angle of inclination important?
A: It affects the component of weight acting vertically, which influences the stress distribution.

Q3: What does ±5% tolerance mean?
A: It indicates the acceptable measurement or estimation error range for input parameters.

Q4: Can this be used for unsaturated soils?
A: No, this formula specifically applies to saturated soil conditions.

Q5: How is vertical stress typically measured?
A: Through pressure sensors or calculated from overburden weight and applied loads.