Applications of unsteady Darcy and non-Darcy free-surface flow through porous media

Laminar flow through porous media is governed by Darcy's Law. If the flow regime is beyond the laminar, a non-Darcy flow expression must be used. Three applications of unsteady flow through porous media were considered in this study. One, governed by Darcy's Law, concerns the time-to-failure of flood barriers. This problem was restricted to cases wherein the river stage increases slowly, but still causes a surge-like water level increase to move toward the barrier. The resulting proximity of the water table may cause it to fail in sliding, due to a reduction in basal effective stress. Although calculations of a geotechnical nature were not included in the considerations, summarizing graphs are presented which may assist in assessing the time-to-failure, based on having a water table very close to the base of the barrier. Two other unsteady applications were also investigated: so-called 'flow-through' rockfill dams, and 'rock drain' deposits at mine sites. Due to the very coarse material present, non-Darcy flow expressions were used in both cases. Flow-through rockfill dams are sometimes used to attenuate flood hydrographs by providing temporary storage. Rock drains are long deposits of coarse waste rock that are generated at open-pit coal mines. In both cases, the intention of the proposed research was to obtain the water surface profile for the unsteady flood wave that travels through the rockfill. The Dupuit assumptions were invoked. Unsteady translatory waves in porous media move more slowly than waves in open-channels. Criteria already exist to help decide a priori whether an unsteady wave in an open channel will be kinematic, diffusive, or fully dynamic, but not, apparently, for unsteady free-surface flows through porous media. Numerical methods appropriate to each of these wave types were tested through comparison of simulated waves with a limited number of experimentally-generated unsteady waves. Using the guidance of dimensionless numbers first proposed by others for assessing the dynamicity of translatory waves in ordinary open channels, criteria are presented which may be used to decide which of these numerical methods is probably best suited to the problem.;The effects of seepage forces in and on the downstream toe of rockfill dams and drains (where the Dupuit assumptions break down) were also investigated. When a sudden flood enters the pool at the upstream end of a rockfill dam (or drain), an unsteady translatory wave is initiated. It travels the length of the deposit and when it emerges from the downstream face it may generate high exit gradients. The associated seepage forces can destabilize large particles residing on or near the downstream toe, initiating a type of slope failure known as 'unravelling'. Various numerical models were successfully developed to simulate unsteady Darcy and non-Darcy water surface profiles through porous media. These models were fundamentally based on Darcy's, Wilkins' and Stephenson's relationships. The potential for unravelling failure was studied using a small viewing-channel having a dense nest of piezometers attached to the toes of various model rock drains, from which exit gradients could be inferred. Non-Darcy pore-pressure modelling outcomes, obtained via flow-net and finite difference methods, are successfully shown to be valid by comparing these outcomes against experimentally-observed data. The expression of Hansen et al. (2005) was further investigated with respect to the factor of safety for individual particles on the face of a rock drain toe.