Analytic Expressions of Hydraulic Conductivity Intervals for Steady Flow to the Single Pumping Well in Unconfined Aquifer

Results of pumping test are normally uncertain due to insufficient exploration capability and complex hydrogeological conditions, which poses a question as to how to calculate the range of hydraulic conductivity, if the factors affecting the hydraulic conductivity fluctuate within a range. In this paper, the parameters affecting the hydraulic conductivity were regarded as a range, which is called intervals. From this perspective, three analytical expressions which could quickly calculate the intervals of hydraulic conductivity specifically for unconfined aquifer with single well were derived through Dupuit-Forchheimer formula from three universal expressions. The relative errors of the three expressions were analyzed by comparing them with that of 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 by Expression 2 (convex model formula) and Expression 3 (Taylor expansion formula) respectively. They 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.