Infiltration in Homogeneous Sands and a Mechanistic Model of Unstable Flow

Abstract

One‐dimensional infiltration experiments were conducted to study the mechanics of unstable flow in homogeneous soils under non‐ponding infiltration. A mechanistic model is presented which explains soil water pressure gradients that are characteristic of stable and unstable flow in homogeneous soils and is based on a dynamic soil water entry pressure, the Darcy‐Buckingham flux equation, and hysteretic moisture retention functions. Infiltration experiments were conducted with five sand samples under applied fluxes of 2, 5, 20, and 50% of their saturated hydraulic conductivity. Soil water pressures were measured at fixed depths following passage of the wetting front. A trend of decreasing soil water pressure over time following passage of the wetting front is not predicted by Richards' equation and produces unstable flow. Under air‐dry initial soil water conditions, soil water pressures were unstable for all fluxes in the three coarser sands. In the two finer sands, unstable flow occurred at infiltration rates of 20 and 50% of their respective saturated hydraulic conductivities but stable flow occurred at lower fluxes. Soil water pressure measured just behind the wetting front was found to be an increasing function of applied flux and average grain size of the media for infiltration with air‐dry initial soil water content. Additional tests showed that systems that produced unstable flow under air‐dry initial soil water contents exhibited stable flow during infiltration with initial soil water contents that were greater than air dry.

Unexpected water content profiles under flux‐limited one‐dimensional downward infiltration in initially dry granular media

“…The occurrence of a drainage process, such as a q-bump profile, is known or expected to occur in fingers emerging during infiltration in a horizontally extended column [Glass et al, 1989;Baker and Hillel, 1988;Selker et al, 1992b;Cho and de Rooij, 1999;Kawamoto and Miyazaki, 1999]. However, our experiment, along with the experiment by Geiger and Durnford [2000] where water pressure is measured, showed that it is not a special phenomenon restricted to finger columns that are surrounded by dry media in a two-or three-dimensional flow field, but are a more common phenomenon seen even in one-dimensional infiltration. The saturated wetting front advance is a physical property of the dry granular medium having a narrow particle size distribution, which is not conditioned by any special boundary condition.…”

“…If a drainage process is to occur, the water content right behind the wetting front needs to be almost saturated, and it decreases upward until a value is reached such that the hydraulic conductivity equals the applied water flux. Such water content profiles with q-bumps (or nonmonotonic profiles) at the wetting front are expected based on studies on finger structures [Glass et al, 1989;Selker et al, 1992bSelker et al, , 1992c and especially from pressure histories measured during 1-D infiltration into a material that exhibits fingering [Geiger and Durnford, 2000]. However, such profiles are not expected from the general theory of water flow in unsaturated porous media that is based on equation (1).…”

“…The water pressure in the fingers falls after the finger tip passes [Kawamoto and Miyazaki, 1999]. Geiger and Durnford [2000] showed that even in 1-D infiltration with a lower flux than the saturated hydraulic conductivity, the water pressure decreases after the wetting front has passed. These observations indicate an upward negative pressure (drainage profile) behind the wetting front.…”

Velocity‐dependent capillary pressure in theory for variably‐saturated liquid infiltration into porous media

“…In Richards' theory, the pressure head y is assumed to be in equilibrium and to depend on q, y = y eq (q) (neglecting capillary hysteresis). [7] We are inspired by a model for dynamic capillary pressure at a wetting front that Hsu and Hilpert [2011] recently incorporated into the GA model for water infiltration and that is supported by various Darcy-scale infiltration experiments [Weitz et al, 1987;Geiger and Durnford, 2000;DiCarlo, 2004;Annaka and Hanayama, 2005]:…”

“…[17] To arrive at a parameterization for the nonequilibrium capillary pressure given by equation (4), we built on a parameterization of dynamic capillary pressure at an infiltration front that was recently developed [Hsu and Hilpert, 2011] based on an analysis of water-infiltration experiments into dry porous media [Geiger and Durnford, 2000]:…”