Coefficient of Permeability Given Seepage Discharge in Earth Dam Calculator

Coefficient of Permeability Formula:

\[ k = \frac{Q_t}{i \times A_{cs} \times t} \]

Discharge from Dam:

m³/s

Hydraulic Gradient to Head Loss:

Cross-Sectional Area of Base:

m²

Time Taken to Travel:

Coefficient of Permeability (m/s):

1. What is Coefficient of Permeability?

Definition: The coefficient of permeability (k) describes how easily a liquid will move through soil or porous medium.

Purpose: It's crucial for analyzing seepage through earth dams, designing drainage systems, and groundwater studies.

2. How Does the Calculator Work?

The calculator uses Darcy's Law formula:

\[ k = \frac{Q_t}{i \times A_{cs} \times t} \]

Where:

\( k \) — Coefficient of permeability (m/s)
\( Q_t \) — Discharge from dam (m³/s)
\( i \) — Hydraulic gradient (dimensionless, ±5%)
\( A_{cs} \) — Cross-sectional area (m²)
\( t \) — Time taken (seconds)

Explanation: The discharge is divided by the product of hydraulic gradient, cross-sectional area, and time.

3. Importance of Permeability Calculation

Details: Accurate permeability values are essential for dam safety, preventing piping failures, and ensuring proper seepage control.

4. Using the Calculator

Tips: Enter discharge in m³/s, hydraulic gradient (±5%), cross-sectional area in m², and time in seconds. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a ±5% on hydraulic gradient?
A: Hydraulic gradient measurements typically have about 5% uncertainty due to measurement limitations.

Q2: What are typical permeability values?
A: Clay: 10⁻⁹ to 10⁻⁷ m/s, Sand: 10⁻⁵ to 10⁻³ m/s, Gravel: 10⁻³ to 10⁻¹ m/s.

Q3: How do I measure cross-sectional area?
A: Measure width and height of seepage flow path perpendicular to flow direction.

Q4: What affects permeability?
A: Soil type, porosity, fluid viscosity, and degree of saturation.

Q5: How accurate is this calculation?
A: Accuracy depends on input measurements, typically ±10% with good field data.