Uncertainty in Water Surface Profile of Buried Stream Flowing under Coarse Material

Non-Darcy flow occurs when a hydraulic gradient is set up across a matrix of coarse porous media, resulting in turbulence in the void spaces. Buried streams that are formed at open-pit coal mines in mountainous areas (due to the disposal of large quantities of waste rock in valley terrain) are good examples of this phenomenon. An overview of the sources of uncertainty associated with non-Darcy water surface profile computations is presented. Numerical and experimental examples are used to illustrate how the mathematical developments presented in this paper can be used to quantify some of the inherent uncertainties. A model buried stream built as part of this study was used to test these mathematical developments. The performance of an equation for optimizing cross-section spacing is described. Uncertainty equations developed using first-order uncertainty analysis is applied to a rectangular stream. A procedure for quantifying the probable error in the computed depth of flow is illustrated herein by applying a simplified form of the total uncertainty equation to a model buried stream. Based on these results, guidance is provided for the uncertainty analysis of water surface profiles for field-scale buried streams.