Soil Falling Head Permeability Calculator
Soil Mechanics & Hydrogeology: Compute hydraulic conductivity ($k$) from falling-head and constant-head permeameter tests with water temperature viscosity normalization ($k_{20}$).
Test Method & Specimen Geometry
Hydraulic Conductivity Results
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Soil Hydraulic Conductivity & Laboratory Permeameter Mechanics
Hydraulic conductivity ($k$) quantifies the ease with which water transmits through porous soil voids under a given hydraulic head gradient.
1. Falling-Head Permeameter Equation
In a falling head test, water flows from a small standpipe tube of area $a$ through a soil specimen of cross-sectional area $A$ and length $L$:
k_T = [ (a · L) / (A · Δt) ] · ln(h_1 / h_2)
2. Viscosity Temperature Correction ($k_{20}$)
Standardized to 20°C baseline via dynamic water viscosity ratios:
k_20 = k_T · ( μ_T / μ_20 ) v_seepage = ( k · i ) / n
Frequently Asked Questions
When is the falling-head test used versus the constant-head test?
The constant-head test (ASTM D2434) is utilized for coarse-grained cohesionless soils (clean sand, gravel) where permeability is high ($k > 10^{-2}$ cm/s) and water flows rapidly. The falling-head test is tailored for fine-grained soils (silts, fine sands, clays) with lower permeability ($k < 10^{-2}$ cm/s) where measuring small water volume discharge directly in a beaker would be inaccurate.
Why is temperature correction to 20°C (k20) required in permeability testing?
Water viscosity decreases significantly as temperature rises (dynamic viscosity at 30°C is ~20% lower than at 20°C). By Darcy's law, measured hydraulic conductivity $k_T$ varies inversely with water viscosity: $k_{20} = k_T \cdot (\mu_T / \mu_{20})$. Normalizing to 20°C standardizes permeability across summer and winter laboratory environments.
What is the difference between discharge velocity and seepage velocity?
Darcy discharge velocity $v = k \cdot i$ is a macroscopic superficial velocity calculated across the total cross-sectional area of the soil column. Actual water flow occurs only through interconnected pore channels. Seepage velocity $v_s = v / n$ (where $n$ is soil porosity) represents the actual true velocity of fluid particles through the soil matrix.