A generalized variable-head borehole permeameter analysis for saturated, unsaturated, rigid or deformable porous media

Abstract

The variable-head borehole permeameter (VHBP) method is a long-standing international standard for in-situ measurement of field-saturated hydraulic conductivity, KFS, in natural and engineered porous media. Its applicability is restricted, however, because traditional VHBP theory does not apply for unsaturated or deformable porous media, and because precise knowledge of the boundary condition on the interface of the borehole outlet (screen) is required for accurate KFS determination. This study extends the traditional VHBP theory to include saturated, unsaturated, rigid and deformable porous media, and also clarifies the boundary condition at the screen interface. Using a recent VHBP analysis developed for rigid, unsaturated porous media, it is shown (via flow conservation and the total increment theorem) that change in porous medium water content, ∆θ, can be extended to include change in porosity (deformation) as well as change in degree of saturation. It is also shown that the appropriate boundary condition on the borehole screen is antecedent pore water pressure head, Ha, for saturated porous media, but effective wetting front pressure head, ψf (or sorptive number, α*), for unsaturated porous media. The KFS, ∆θ, Ha, and ψf (or α*) parameters can be determined using numerical optimization (e.g. “Solver” in the Excel spreadsheet) to curve-fit the extended VHBP analysis directly to borehole head versus time measurements; however, fitting to the velocity graph (borehole head plotted against change in head with time) is generally less problematic. In a cursory assessment of the extended VHBP analysis, KFS was determined with ≤7% error, ∆θ with ≤15% error, Ha with ≤1.4% error, and ψf with ≤0.5% error, which is more than sufficient accuracy for most applications. It was concluded that the VHBP method was successfully extended for application to saturated, unsaturated, rigid and deformable porous media.