Analytical expressions of hydraulic conductivity intervals for steady flow to a single pumping well in an unconfined aquifer

Abstract

Results of pumping tests are normally uncertain due to insufficient exploration capability and complex hydrogeological conditions, which poses the question of how to calculate the range of hydraulic conductivity values if the factors affecting hydraulic conductivity fluctuate within this range. In this paper, the parameters affecting hydraulic conductivity were regarded as the range, or ‘interval’. From this perspective, three analytical expressions that can quickly calculate the hydraulic conductivity interval specifically for an unconfined aquifer with a single well were derived using the Dupuit–Forchheimer formula from three universal expressions. The relative errors for the three expressions were analysed by comparing them with the equal interval continuous sampling method (EICSM). The results indicated that on the premise that the absolute value of the relative error of the hydraulic conductivity extremum was controlled within 10%, the maximums and minimums should be calculated using Expression 2 (convex model formula) and Expression 3 (Taylor expansion formula), respectively. These expressions were considered as better choices because the allowable change rate could reach 20 and 10%. At the end of the research, an actual pumping test was introduced to verify the above deduction.