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Permittivity equals normal hydraulic conductivity divided by thickness

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Permittivity Equation

Permittivity measures how easily water flows perpendicular to a geotextile fabric, in units of inverse seconds. It equals the normal hydraulic conductivity divided by the fabric thickness.

Ψ = Kₙ / t

Transmissivity Equation

Transmissivity measures how easily water flows within the plane of the geotextile fabric, in units of cm²/s. It equals the in-plane hydraulic conductivity multiplied by the fabric thickness.

θ = Kₚ × t

How It Works

Geotextiles are permeable fabrics used in civil engineering for filtration, drainage, separation, and reinforcement. Two key hydraulic properties govern how water moves through them: permittivity (Ψ = Kₙ / t) measures flow perpendicular to the fabric, while transmissivity (θ = Kₚ × t) measures flow within the plane of the fabric. Higher values mean better drainage.

Example Problem

A nonwoven geotextile is 0.3 cm thick with a normal hydraulic conductivity of 0.15 cm/s. What is its permittivity?

  1. Identify the knowns. Normal hydraulic conductivity Kₙ = 0.15 cm/s, fabric thickness t = 0.3 cm.
  2. Identify what we're solving for. We want the permittivity Ψ — the cross-plane flow capacity of the geotextile, in inverse seconds.
  3. Write the permittivity equation: Ψ = Kₙ / t. Note the centimeters cancel cleanly, leaving units of s⁻¹.
  4. Substitute the values: Ψ = 0.15 cm/s ÷ 0.3 cm.
  5. Simplify the arithmetic: 0.15 / 0.3 = 0.5, and the cm units cancel.
  6. **The permittivity is Ψ = 0.5 s⁻¹** — five times the AASHTO M288 minimum of 0.1 s⁻¹ for most subsurface drainage applications.

AASHTO M288 requires a minimum permittivity of 0.1 s⁻¹ for most subsurface drainage applications, so this fabric easily qualifies.

When to Use Each Variable

  • Solve for Permittivity — when you know the normal hydraulic conductivity and fabric thickness, e.g., verifying a geotextile meets AASHTO M288 requirements.
  • Solve for Normal Conductivity — when you know the permittivity and thickness, e.g., back-calculating conductivity from a lab permittivity test.
  • Solve for Thickness (Permittivity) — when you know the conductivity and permittivity, e.g., determining the fabric thickness from test data.
  • Solve for Transmissivity — when you know in-plane conductivity and thickness, e.g., evaluating a drainage layer's capacity to move water laterally.
  • Solve for In-Plane Conductivity — when you know transmissivity and thickness, e.g., extracting conductivity from a transmissivity test.
  • Solve for Thickness (Transmissivity) — when you know conductivity and transmissivity, e.g., verifying fabric thickness from hydraulic test results.

Key Concepts

Geotextile hydraulic properties govern how water interacts with the fabric. Permittivity (Ψ = Kn/t) measures cross-plane flow capacity and is critical for filtration applications. Transmissivity (θ = Kp × t) measures in-plane flow capacity and is critical for drainage layers. Both properties depend on fabric thickness, construction (woven vs. nonwoven), and the applied confining pressure.

Applications

  • Subsurface drainage: selecting fabrics for French drains, retaining wall drains, and pavement edge drains
  • Erosion control: using geotextiles as filters behind riprap and gabion walls to prevent soil piping
  • Landfill engineering: specifying drainage layers in leachate collection systems
  • Road construction: separating subgrade soil from aggregate base to prevent intermixing and maintain structural integrity

Common Mistakes

  • Confusing permittivity and transmissivity — permittivity is cross-plane flow (filtration), transmissivity is in-plane flow (drainage)
  • Ignoring confining pressure — permittivity and transmissivity decrease significantly under load as the fabric compresses
  • Using woven geotextile where nonwoven is needed — woven fabrics have lower permittivity and are better for separation, not filtration
  • Not matching the apparent opening size (AOS) to the soil — an oversized AOS allows soil migration and clogging

Frequently Asked Questions

What is the difference between geotextile permittivity and transmissivity?

Permittivity describes how easily water flows through the fabric (perpendicular to the surface), measured in s⁻¹. Transmissivity describes how easily water flows along the plane of the fabric, measured in cm²/s. Filtration applications rely on permittivity; drainage layers rely on transmissivity.

How do you select a geotextile for a retaining wall drain?

Match the geotextile’s permittivity and apparent opening size (AOS) to the surrounding soil. The permittivity should be at least 10 times the soil’s hydraulic conductivity to prevent clogging, and the AOS should retain at least 85% of the soil particles.

What is hydraulic conductivity in a geotextile?

Hydraulic conductivity (K) is the rate at which water moves through the fabric under a given head gradient, typically reported in cm/s. Normal conductivity (Kₙ) applies to cross-plane flow; in-plane conductivity (Kₚ) applies to flow along the fabric.

What minimum permittivity does AASHTO M288 require?

AASHTO M288 specifies minimum permittivity values of 0.5, 0.2, or 0.1 s⁻¹ depending on the percent of soil fines passing the #200 sieve (<15%, 15-50%, or >50% fines, respectively). Soils with more fines require higher flow capacity to prevent clogging.

Why does dividing K by thickness give a number with no length unit?

The units cancel cleanly. Hydraulic conductivity K has units of length/time (m/s); thickness t has units of length (m). K / t = (m/s) / m = 1/s, which is why permittivity is reported in s⁻¹. The reciprocal time tells you how quickly head dissipates through the fabric per unit head gradient.

Are woven and non-woven geotextiles interchangeable?

No. Non-woven (needle-punched or heat-bonded) geotextiles have high permittivity and porosity — ideal for filtration and drainage. Wovens have lower permittivity but higher tensile strength, so they specialize in separation, reinforcement, and stabilization roles. Pick the construction by function, not just by spec value.

How does confining pressure affect these values?

Heavy soil loads compress the fabric, reducing both thickness t and effective pore size. Permittivity typically drops 20–40% and transmissivity 30–60% under typical roadway or landfill confining pressures. Always check spec values are reported at the confining pressure your application will see, not at zero load.

When do I need a geocomposite instead of a single fabric layer?

When the required in-plane drainage capacity exceeds what a single fabric can deliver — typically transmissivity above about 10⁻⁵ m²/s, common for retaining-wall and landfill leachate-collection layers. A geocomposite pairs a geonet (high-flow drainage core) with one or two filter fabrics, multiplying transmissivity by 10–100× versus fabric alone.

Worked Examples

Highway Drainage

What's the permittivity of a non-woven separator with Kₙ = 0.05 cm/s and 3 mm thickness?

A DOT highway project specifies a non-woven needle-punched geotextile between the subgrade and the granular base. The spec sheet quotes a normal hydraulic conductivity of 5×10⁻² cm/s (= 5×10⁻⁴ m/s) and a nominal thickness of 3 mm. Compute the permittivity Ψ.

  • Kₙ = 0.05 cm/s = 5.0 × 10⁻⁴ m/s
  • t = 3 mm = 3.0 × 10⁻³ m
  • Ψ = Kₙ / t
  • Ψ = 5.0 × 10⁻⁴ / 3.0 × 10⁻³

Permittivity Ψ ≈ 0.167 s⁻¹

AASHTO M288 Class 2 separators for subgrade with 5–50% fines typically require Ψ ≥ 0.10 s⁻¹ — this fabric clears that minimum. Long-term clogging from migrating fines is handled in the durability spec, not by Ψ alone.

Retaining Wall Drainage

What's the transmissivity of a drainage geocomposite with Kₚ = 0.02 cm/s and 6 mm core?

Behind a 4-meter MSE retaining wall the contractor proposes a prefabricated drainage geocomposite with in-plane hydraulic conductivity Kₚ = 0.02 cm/s and a 6 mm flow-channel core. Find the transmissivity θ — the in-plane flow capacity per unit width.

  • Kₚ = 0.02 cm/s = 2.0 × 10⁻⁴ m/s
  • t = 6 mm = 6.0 × 10⁻³ m
  • θ = Kₚ × t
  • θ = 2.0 × 10⁻⁴ × 6.0 × 10⁻³

Transmissivity θ ≈ 1.2 × 10⁻⁶ m²/s

FHWA-NHI-10-024 calls for a minimum in-plane transmissivity of about 3 × 10⁻⁵ m²/s for retaining-wall drainage at moderate heights — this single fabric core falls well short, so a dedicated geonet-cored geocomposite would normally be specified instead.

Landfill Liner

How thick a fabric do you need for Ψ = 0.005 s⁻¹ at Kₙ = 1×10⁻³ cm/s?

A municipal landfill liner system specifies a non-woven filter geotextile with a target permittivity of 5 × 10⁻³ s⁻¹ to protect the leachate-collection layer. The fabric's measured normal hydraulic conductivity is 1 × 10⁻³ cm/s. Solve for the minimum thickness.

  • Kₙ = 1 × 10⁻³ cm/s = 1.0 × 10⁻⁵ m/s
  • Ψ = 5 × 10⁻³ s⁻¹
  • t = Kₙ / Ψ
  • t = 1.0 × 10⁻⁵ / 5.0 × 10⁻³

Thickness t ≈ 2.0 × 10⁻³ m = 2 mm

Most needle-punched non-woven liners ship at 3–6 mm thickness, so this requirement is easy to meet. Filter design also has to pass the soil-retention (AOS vs D₈₅), permeability ratio, and clogging-resistance criteria separately before the fabric is approved.

Geotextile Permittivity & Transmissivity Formulas

Two hydraulic properties characterize how water moves through a geotextile. Permittivity governs cross-plane flow (filtration); transmissivity governs in-plane flow (drainage). Both are derived from Darcy's law applied to the appropriate flow direction.

Ψ = Kn / tPermittivity (cross-plane flow)
θ = Kp × tTransmissivity (in-plane flow)

Where:

  • Ψ — permittivity, units of s⁻¹ (cross-plane flow capacity per unit head gradient)
  • Kn — normal hydraulic conductivity (m/s; cross-plane direction)
  • t — geotextile thickness under the applied confining pressure (m)
  • θ — transmissivity, units of m²/s (in-plane flow capacity per unit width)
  • Kp — in-plane hydraulic conductivity (m/s; flow parallel to the fabric)

Permittivity is reported in s⁻¹ because dividing conductivity (m/s) by thickness (m) leaves a reciprocal time. AASHTO M288 minimums range from 0.1 to 0.5 s⁻¹ depending on soil fines. Transmissivity sits in m²/s — a drainage geocomposite delivers 10⁻⁴ to 10⁻³ m²/s, two to four orders of magnitude above a single non-woven fabric.

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