Steady-state underflow in gravel river beds

Abstract

Because gravel size is normally larger than soil particles, seepage through gravel layers is often assumed to be nonlinear and described by Forchheimer's equation. This study of underflow in gravel-bed rivers comprises: (i) the calculation of quantities concerning the underflow problems, (ii) the determination of gravel hydrogeologic properties. These are important in predicting underflow quantities and directions for water resource calculations and for fish habitat.

Two equations were derived for calculating the flowrate of nonuniform nonlinear underflow through gravel layers resting on an inclined impervious floor; one is less accurate but much simpler than the other. These two equations and the conventional linear seepage equation were compared using data from four groups of experiments on underflow through relatively uniform clean gravels in a tilting flume. The flowrates from the two equations are very close together and to the experimental results, but those from the conventional equation are not close when Reynolds' numbers are greater than 50.

A finite difference method was also derived for solving the problems of steady-state nonlinear seepage through inhomogeneous gravel, with complex boundary conditions such as are common in river bed situations. This method was tested with data from experiments on underflow (i) through gravel mounds under five different conditions in the laboratory, (ii) through gravel bars under two conditions in the field. The tests show that the method can predict the stream lines and flowrates with accuracy.

Tortuosity (a gravel property for relating flux velocity to pore velocity) of relatively uniform gravels (mean diameters = 4.29, 5.56, 9.69 mm) was determined accurately in two situations; flow through gravel in a vertical cylinder and in a sloping flume. The average tortuosity found is 1.0.

Two semi-empirical formulae, one for estimating the linear hydraulic resistivity a and the other for the nonlinear resistivity b from gravel porosity and mean diameter, were obtained by rederiving Forchheimer's equation and performing permeameter tests on five sets each of closely- and widely-graded gravels. These formulae were tested with available data from various sources and found preferable to the past formulae.

The empirical conventional standpipe method, the most suitable field method for measuring permeability K of stream gravel layers, was improved by applying the finite difference theory of axisymmetrical nonlinear groundwater flow. The improved method, therefore, can overcome many restrictions of the conventional one, and can obtain also the hydraulic resistivities, a and b.