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Soil Permeability / Darcy's Law Calculator

Q: What is Darcy's Law?

Darcy's Law states that the flow rate through a porous medium is proportional to the hydraulic conductivity, cross-sectional area, and hydraulic gradient: Q = k × i × A.

Q: What is the difference between constant head and falling head tests?

Constant head is used for high-permeability soils (sands, gravels). Falling head is used for low-permeability soils (silts, clays). Constant head maintains a steady head difference while falling head measures head drop over time.

Q: What are typical hydraulic conductivity values?

Gravel: 10⁻²–10⁰ m/s, Sand: 10⁻⁵–10⁻² m/s, Silt: 10⁻⁹–10⁻⁵ m/s, Clay: <10⁻⁹ m/s.

Q: Why is temperature correction needed?

Water viscosity changes with temperature. The standard reference temperature is 20°C. Correction adjusts measured k to the equivalent value at 20°C for consistent reporting.

Q: What is the difference between discharge and seepage velocity?

Discharge velocity (v = ki) is the flow per unit area of the entire cross-section. Seepage velocity (vs = v/n) is the actual velocity through pore spaces, always faster than discharge velocity.

Q: What is hydraulic gradient?

Hydraulic gradient i = Δh/L is the head loss per unit length of flow path. It represents the driving force for flow through soil.

Q: What is a typical porosity for soils?

Sand: 0.25–0.50, Silt: 0.35–0.50, Clay: 0.40–0.70. Higher porosity means more void space for flow.

Q: What standards govern permeability testing?

ASTM D2434 (constant head), ASTM D5084 (falling head), IS 2720 Part 17. These specify test apparatus and procedures.

Calculate flow rate, hydraulic gradient, discharge velocity, and seepage velocity using Darcy's Law. Supports constant head and falling head permeability tests with temperature correction.

Soil Mechanics Geotechnical engineers, hydrogeologists, lab technicians Commercial Intent: HIGH

Engineering Formulas

Darcy's Law

Q = k × i × A
i = Δh / L

Q: Flow rate (m³/s)

k: Hydraulic conductivity (m/s)

i: Hydraulic gradient

A: Cross-sectional area (m²)

Δh: Head difference (m)

L: Flow path length (m)

Constant Head Permeability

k = (Q × L) / (A × Δh × t)

Q: Collected flow volume (m³)

t: Time (s)

Falling Head Permeability

k = (a × L) / (A × t) × ln(h₁/h₂)

a: Standpipe area (m²)

h₁: Initial head (m)

h₂: Final head (m)

Discharge & Seepage Velocity

v = k × i
vs = v / n

v: Discharge velocity (m/s)

v_s: Seepage velocity (m/s)

n: Porosity

Worked Example

Constant Head Test on Sand

testType: constant-headsoilType: sandk: 0.001A: 0.01L: 0.3deltaH: 0.5t: 60temperature: 20porosity: 0.3

Gradient

i = 0.5 / 0.3 = 1.6667

Flow Rate

Q = 0.001 × 1.6667 × 0.01 = 1.667 × 10⁻⁵ m³/s

Disch. Vel.

v = 0.001 × 1.6667 = 1.667 × 10⁻³ m/s

Seep. Vel.

vs = 0.001667 / 0.3 = 5.556 × 10⁻³ m/s

Result: Q = 1.667 × 10⁻⁵ m³/s, i = 1.667, v = 1.667 × 10⁻³ m/s, vs = 5.556 × 10⁻³ m/s (Medium permeability — sand)

Engineering Notes

Darcy's Law assumes laminar flow — valid for most groundwater flow except near wells or in coarse gravel.

Field permeability can be 10–1000× higher than lab values due to macro-pores and fissures.

For clay liners in landfills, k < 10⁻⁹ m/s is typically required.

Permeability anisotropy (kₕ ≠ kᵥ) is common in layered soils.

Perform falling head tests on low-permeability soils — constant head is inaccurate for k < 10⁻⁵ m/s.

Assumptions

• Soil is saturated and homogeneous

• Laminar flow (Darcy's law valid)

• Steady-state conditions assumed

• No chemical or thermal effects on permeability

• Temperature correction uses standard viscosity model

Common Mistakes

✕ Using Darcy's Law for very fine-grained soils where flow may not be laminar

✕ Forgetting temperature correction for non-standard temperatures

✕ Confusing discharge velocity with seepage velocity

✕ Using wrong cross-sectional area for falling head tests

✕ Not accounting for macro-pores and fissures in field permeability

Frequently Asked Questions

What is Darcy's Law?

Darcy's Law states that the flow rate through a porous medium is proportional to the hydraulic conductivity, cross-sectional area, and hydraulic gradient: Q = k × i × A.

What is the difference between constant head and falling head tests?

Constant head is used for high-permeability soils (sands, gravels). Falling head is used for low-permeability soils (silts, clays). Constant head maintains a steady head difference while falling head measures head drop over time.

What are typical hydraulic conductivity values?

Gravel: 10⁻²–10⁰ m/s, Sand: 10⁻⁵–10⁻² m/s, Silt: 10⁻⁹–10⁻⁵ m/s, Clay: <10⁻⁹ m/s.

Why is temperature correction needed?

Water viscosity changes with temperature. The standard reference temperature is 20°C. Correction adjusts measured k to the equivalent value at 20°C for consistent reporting.

What is the difference between discharge and seepage velocity?

Discharge velocity (v = ki) is the flow per unit area of the entire cross-section. Seepage velocity (vs = v/n) is the actual velocity through pore spaces, always faster than discharge velocity.

What is hydraulic gradient?

Hydraulic gradient i = Δh/L is the head loss per unit length of flow path. It represents the driving force for flow through soil.

What is a typical porosity for soils?

Sand: 0.25–0.50, Silt: 0.35–0.50, Clay: 0.40–0.70. Higher porosity means more void space for flow.

What standards govern permeability testing?

ASTM D2434 (constant head), ASTM D5084 (falling head), IS 2720 Part 17. These specify test apparatus and procedures.

References & Standards

ASTM D2434ASTM D5084IS 2720 Part 17BS 1377-5

ASTM D2434

Standard Test Method for Permeability of Granular Soils (Constant Head)

ASTM D5084

Standard Test Methods for Measurement of Hydraulic Conductivity of Saturated Porous Materials

IS 2720 Part 17

Methods of Test for Soils: Permeability

BS 1377-5

Methods of Test for Soils: Permeability Tests

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