Least-action variational continuum description of Darcian permeation of liquids and gases through stone materials

Watertightness of natural or artificial stone materials, like trap rock or concrete, is a basic property for assessing durability of the built heritage to weathering exposure. Fundamental research of the past century has shown that a reliable experimental determination of intrinsic permeability in stone materials can be achieved by uniaxial water-permeation tests under open-flow conditions, together with the opportunity of employing air permeation tests in place of water-tests to obtain important additional information on a given stone material. Correlations of practical relevance in such laboratory applications, among inlet pressure, outlet pressure and flow rate, stem all from solutions to the general continuum modelling problem of the permeation through a non-deformable homogeneous filter of an incompressible or compressible fluid under stationary uniaxial conditions. The present study addresses such class of mechanical problems on a theoretical variational basis to infer general correlations of practical relevance in permeability testing with a specific consideration of applications in which air-permeability testing combined with use of thinner filters makes the hypothesis of isothermal process in the permeating gas not straightforwardly applicable.