Numerical values of shape factors for field permeability tests in unconfined aquifers

Field permeability tests are used to evaluate the local hydraulic conductivity. Their interpretation requires knowing the value of a shape factor, c. Regular values for shape factors were obtained for fully saturated conditions in an infinite material. However, many tests are performed in unconfined aquifers, with a bottom impervious boundary, and partly unsaturated seepage. This paper questions the applicability of the regular c values to field conditions. It presents numerical ways to model field permeability tests in unconfined aquifers and deduce the c value, under steady and transient states, with partly unsaturated seepage. Two series of monitoring wells were analyzed and compared; they have either a filter pack or not. The influences of four variables (radial distance of the external boundary, dimensions and positions of the water injection zone, and aquifer material type) on the numerical c values were studied. The results show that the boundary radial distance markedly affects the numerical c value. Therefore, practical approaches were proposed by reconciling the numerical and realistic test conditions, to determine the representative boundary radial distances for each type of test model. Additionally, the numerical values are compared with the theoretical values of Bouwer and Rice (Water Resour Res 12(3):423–428, 1976) and Hvorslev (Time-lag and soil permeability in ground water observations, U.S. Army Eng Waterw Exp Stn, Vicksburg, 1951).