A semi-analytical generalized Hvorslev formula for estimating riverbed hydraulic conductivity with an open-ended standpipe permeameter

•Develops a generalized Hvorslev formula for interpreting falling head slug tests.•Obtains an semi-analytical expression of total hydraulic resistance of flow.•Provides an alternative method to quantify sediment heterogeneity. The 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.