a b s t r a c tThe well-known Hvorslev (1951) formula was developed to estimate soil permeability using single-well slug tests and has been widely applied to determine riverbed hydraulic conductivity using in situ standpipe permeameter tests. Here, we further develop a general solution of the Hvorslev (1951) formula that accounts for flow in a bounded medium and assumes that the bottom of the river is a prescribed head boundary. The superposition of real and imaginary disk sources is used to obtain a semi-analytical expression of the total hydraulic resistance of the flow in and out of the pipe. As a result, we obtained a simple semi-analytical expression for the resistance, which represents a generalization of the Hvorslev (1951). The obtained expression is benchmarked against a finite-element numerical model of 2-D flow (in r-z coordinates) in an anisotropic medium. The results exhibit good agreement between the simulated and estimated riverbed hydraulic conductivity values. Furthermore, a set of simulations for layered, stochastically heterogeneous riverbed sediments was conducted and processed using the proposed expression to demonstrate the potential associated with measuring vertical heterogeneity in bottom sediments using a series of standpipe permeameter tests with different lengths of pipe inserted into the riverbed sediments.

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In addition to correct planning, pumping tests with partial penetrating wells, requires methods of processing and calculating parameters that are understandable not only to hydrogeologists, but also to geologists of related specialties. The data processing procedure should be brought to simple plotting and formulas. This requires an understanding of the validity and limitations in the use of the original expressions. Data analysis should begin with a meaningful diagnosis of pumping modes on experimental plots. Developed in the last decades, analytical solutions are applicable to homogeneous aquifers and include complex mathematical functions with complex arguments. Their use requires software. Without justification of the applicability of the chosen model, the mechanical computer "calculation" of pumping has serious drawbacks. The article presents methods for calculating hydraulic parameters from experimental pumping data that can be applied to nonhomogeneous conditions and take into account both degree of partial penetration and near-well destruction. The techniques use the known methods of a straight line on the graphs of combined and area tracing drawdown in semi-logarithmic coordinates, developed for fully penetrating wells. To do this, the well-known formulas introduce a correction ζΣ for degree of partial penetration, anisotropy, inertia of the wells, and other factors. The coordinate of the observation well r is replaced by the rated value rp = r•exp( ζΣ/2). It is impossible to calculate ζΣ except for the case of a homogeneous aquifer. Therefore, it is necessary to determine rp by selection, seeking to combine the experimental well curves on the combined tracking plot. The application of the method requires a realistic view of the accuracy of the field test in general and the procedure used in particular. The article is illustrated by plots and calculations of real field tests, the presentation is accompanied by an analysis of the causes of defectiveness of pumping data.