STOCHASTIC-ANALYSIS OF STEADY-STATE UNSATURATED FLOW IN HETEROGENEOUSMEDIA - COMPARISON OF THE BROOKS-COREY AND GARDNER-RUSSO MODELS

Existing stochastic models of unsaturated flow and transport are usual ly developed using the simple Gardner-Russo constitutive relationship though it is generally accepted that the more complex van Genuchten an d Brooks-Corey relationships may perform better in describing experime ntal data. In this paper, we develop first-order stochastic models for gravity-dominated flow in second-order stationary media with both the Brooks-Corey and the Gardner-Russo constitutive relationships. These models also account for the spatial variability in effective water con tent, while the spatial variability is generally neglected in most exi sting stochastic models. Analytical solutions are obtained for the cas e of one-dimensional gravity-dominated flow. On the basis of the solut ions, we illustrate the differences between results from these two con stitutive models through some one-dimensional examples. It is found th at the impacts of the constitutive models on the statistical moments o f suction head, effective water content, unsaturated hydraulic conduct ivity, and velocity depend on the saturation ranges. For example, the mean head and the mean effective water content for the Brooks-Corey mo del differ in a great manner with their counterparts for the Gardner-R usso model near the dry and wet limits while the differences are small at the intermediate range of saturation. This finding is confirmed wi th some two-dimensional examples. It:is also found that the Brook-Core y model has certain advantages over the Gardner-Russo model in analyzi ng unsaturated flow in heterogeneous media. For example, the stochasti c model developed based on the Brooks-Corey function requires the coef ficient of variation of head and soil parameter ''alpha(BC)'' to be sm all (much less than 1), whereas that based on the Gardner-Russo functi on assumes the one-point cross covariance of head and alpha(GR) to be small (much less than 1). Illustrative examples reveal that the latter condition may be violated because the one-point covariance is found t o increase rapidly to beyond unity as the soil becomes dry, whereas th e former may be readily satisfied.