The Forchheimer Approach for Soil Air Permeability Measurement

Abstract

Core Ideas We developed an apparatus with automatic registration of flow (Q) and pressure (ΔP). A curvilinear Q–ΔP relation was found for seven of eight soil samples tested. Ignoring non‐linear pressure loss gave permeability errors up to 65% at ΔP=100 Pa. We suggest an index for pore tortuosity based on the non‐linear Q–ΔP relation. Air permeability affects a range of soil functions and is useful in the quantification of soil pore characteristics. Measurements of air flow used to quantify air permeability are mostly performed at a fixed pressure difference, assuming a linear relation between flow and pressure. However, evidence exists that nonlinear pressure losses may occur even at low pressure gradients. We constructed an apparatus that allows automatic measurement of air flow at a range of pressures. The new methodology was applied to eight soil samples deriving from a loamy, Stagnic luvisol. Three artificial cores were also tested: a solid cylinder of plastic with drilled, vertical holes; a cylinder of autoclaved aerated concrete (AAC), and an AAC cylinder with drilled holes. The historical Forchheimer approach, including a polynomial regression of flow–pressure data, was applied to derive the true Darcian flow based on the coefficient to the linear part of the relation. Flow‐pressure data appeared to be curvilinear for all test specimens, except for one of the soil samples. The results showed up to 65% errors in estimates of air permeability if the nonlinear pressure losses were ignored when applying a pressure difference as low as 100 Pa. Our results strongly suggest use of the Forchheimer approach based on measurements of flow and pressure difference at a range of air pressures. We suggest an index for soil pore tortuosity, which appears to reflect the pore characteristics of the artificial samples tested. More studies are needed to evaluate the applicability of the index for soil samples.