Depth of Prism given Upward Force Calculator

Depth of Prism Formula:

\[ z = \frac{\sigma_n - F_u}{\gamma_s \times (\cos(\frac{i \times \pi}{180}))^2} \]

Normal Stress (σ_n):

Upward Force (F_u):

Submerged Unit Weight (γ_s):

N/m³

Angle of Inclination (i):

Tolerance:

Depth of Prism (z):

1. What is Depth of Prism given Upward Force?

Definition: This calculator determines the depth of a soil prism considering normal stress, upward seepage force, submerged unit weight, and slope angle.

Purpose: It helps geotechnical engineers analyze slope stability and seepage conditions in soil mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{\sigma_n - F_u}{\gamma_s \times (\cos(\frac{i \times \pi}{180}))^2} \]

Where:

\( z \) — Depth of prism (meters)
\( \sigma_n \) — Normal stress in soil (Pascals)
\( F_u \) — Upward seepage force (Pascals)
\( \gamma_s \) — Submerged unit weight (N/m³)
\( i \) — Angle of inclination (degrees)

Explanation: The formula accounts for the balance between normal stress, upward seepage force, and the weight component along the slope.

3. Importance of Depth Calculation

Details: Accurate depth calculation is crucial for slope stability analysis, retaining wall design, and assessing seepage effects on soil structures.

4. Using the Calculator

Tips: Enter all required parameters including the tolerance percentage (±5% by default). The calculator provides both the exact value and tolerance range.

5. Frequently Asked Questions (FAQ)

Q1: What is typical submerged unit weight for soils?
A: Common values range from 8-12 kN/m³ (8000-12000 N/m³) for most soils, with 10 kN/m³ (10000 N/m³) as a typical default.

Q2: How does angle of inclination affect the result?
A: Steeper angles reduce the effective weight component, requiring greater depth for stability.

Q3: What's the purpose of the tolerance value?
A: The tolerance accounts for measurement uncertainties and material variability in field conditions.

Q4: Can this be used for vertical slopes?
A: Yes, set angle to 90° (cos(90°) becomes 0), though results may approach infinity as the denominator approaches zero.

Q5: What if upward force exceeds normal stress?
A: The result becomes negative, indicating potential for soil boiling or heaving failure.