Depth of Prism given Upward Force due to Seepage Water Calculator

Depth of Prism Formula:

\[ z = \frac{F_u}{\gamma_{water} \times (\cos(\frac{i \times \pi}{180}))^2} \]

Upward Force (F_u):

Unit Weight of Water (γ_water):

N/m³

Angle of Inclination (i):

Depth of Prism (z): m

1. What is Depth of Prism in Seepage Analysis?

Definition: The depth of prism refers to the vertical dimension of soil affected by upward seepage forces in geotechnical engineering.

Purpose: It helps determine the critical depth at which upward seepage forces might cause soil instability or piping.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ z = \frac{F_u}{\gamma_{water} \times (\cos(\frac{i \times \pi}{180}))^2} \]

Where:

\( z \) — Depth of prism (meters)
\( F_u \) — Upward force due to seepage (Pascals)
\( \gamma_{water} \) — Unit weight of water (N/m³, typically 9810)
\( i \) — Angle of inclination to horizontal (degrees)

Explanation: The upward seepage force is balanced against the weight of water and adjusted for the angle of inclination.

3. Importance of Depth of Prism Calculation

Details: Proper calculation helps prevent failures in retaining structures, dams, and excavations by identifying critical seepage conditions.

4. Using the Calculator

Tips: Enter the upward force in Pascals, unit weight of water (default 9810 N/m³), and angle of inclination in degrees (±5% accuracy).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical upward force value?
A: Values vary widely but typically range from 10,000 to 100,000 Pa depending on soil and water conditions.

Q2: Why is the angle important?
A: The angle affects how seepage forces are distributed; steeper angles increase the effective upward force.

Q3: What does ±5% mean for the angle?
A: This accounts for measurement uncertainty in field conditions.

Q4: How do I measure upward seepage force?
A: Use piezometers or pore pressure transducers in the field.

Q5: What if my calculated depth is negative?
A: Check your inputs - depth should always be positive. Negative values indicate input errors.