Shape Factors for Permeability Tests in Boreholes and Piezometers

Several sets of values are available for the shape factor of the cylindrical injection zone used to perform a field permeability test. Depending on the selected value, the resulting difference for hydraulic conductivity may reach 40% for long intake zones, and more than 100% for short intake zones. The commonly used shape factor is that given by Hvorslev (1951). Seven other factors derived from numerical models are now available: they differ from Hvorslev's factor by up to 100%. Three possible reasons for the differences are examined. Reference is made to Laplace's equation and related mathematical results derived before 1945. Shape factor values obtained by numerical methods are shown to be more or less accurate solutions of particular cases when impervious or recharging boundaries exist close to the injection zone. Their influence upon the shape factor value can be calculated analytically, as shown in a detailed example. Analytical shape factor equations are given for a cylindrical injection zone with either a pervious or an impervious bottom. Based on the method of image wells, two other equations are established to correct the shape factors if draining (constant head) or impervious layers are known to be located close to the injection zone. These equations should be used for field permeability tests in boreholes or piezometers.