Selection and application of a one-dimensional non-Darcy flow equation for two-dimensional flow through rockfill embankments

Abstract

Porous embankments comprised of relatively homogeneous coarse rockfill can be used to reduce the amount of spillage at downstream hydro dams or to control the outflow from stormwater detention basins. The stage-discharge rating curve is important in the design of such applications. In general, the coarseness of the material causes the flow to be non-Darcy; that is, characterized by a nonlinear relationship between bulk velocity and hydraulic gradient. Six one-dimensional (1D) non-Darcy flow equations, appearing in the literature, are presented. A limited comparison between computed and experimental results is then made on the basis of 1D packed-column tests performed in the hydraulics laboratory of the University of Ottawa. The question as to how such 1D closed-conduit equations might be used to estimate the quantity of flow through a porous embankment is then addressed, considering that the latter has a free surface and is a two-dimensional (2D) flow. The problem is successfully dealt with using the concept of "effective hydraulic gradient," a concept reminiscent of the method of sections used to analyze confined 2D seepage problems. A general equation is presented in which the effective hydraulic gradient is shown to be a function of two factors: (1) the shape of the embankment and (2) the upstream depth, relative to the height of the dam. The development and verification of the equation for the effective hydraulic gradient is described, together with its use in obtaining a rating curve for a hypothetical flowthrough dam composed of rock material 0.25 m in diameter. Key words : non-Darcy flow, flowthrough rockfill, effective hydraulic gradient, stage-discharge rating curve.