A new method for the interpretation of the constant-head well permeameter

A novel semi-analytical solution for the interpretation of the constant-head permeameter test is introduced, which accounts for the correct mixed-type boundary condition at the wellbore, unlike all published analytical solutions. Capillarity can also be accounted for. The simplifications are that flow from the bottom of the borehole is neglected (therefore the solution is applicable to slender boreholes, where the ponding depth is at least 10 times the radius) and capillarity can be modeled with a quasi-linear approach. The Green's function approach leads to an integral equation, the solution of which does not show significant ill-posedness. Two sub-cases are presented: the first neglects capillary effects (the all-saturated approximation) and the second (general solution) takes them into account. The all-saturated solution is successfully tested against finite element simulations. The corresponding values of the borehole shape factor C are slightly larger than the ones obtained with approximate analytical solutions from the literature. When capillarity is accounted for, C changes of a factor of 10 when the dimensionless sorptive number A goes from typical values for fine soils to typical values for coarse soils (about two orders of magnitude of variation for A). This range shifts to lower values of A as the dimensionless borehole depth increases. Consequently, the all-saturated solution is a good approximation of the soil behavior for boreholes with large ponding depth, and coarse soils. The proposed semi-analytical solution is fast to compute and thus it is possible to use it in an automated optimization technique to fit field data and estimate the field-saturated hydraulic conductivity and the sorptive number; this would not be feasible using a numerical solution.