Publication Date:
2014-03-11
Description:
Many physically-based hydrological/hydrogeological models used for predicting groundwater seepage areas, including topography-based index models such as TOPMODEL, rely on the Dupuit assumption. To ensure the sound use of these simplified models, knowledge of the conditions under which they provide a reasonable approximation is critical. In this study, a Dupuit solution for the seepage length in hillslope cross-sections is tested against a full-depth solution of saturated groundwater flow. In homogeneous hillslopes with horizontal impervious base and constant-slope topography, the comparison reveals that the validity of the Dupuit solution depends not only on the ratio of depth to hillslope length d/L (as might be expected), but also on the ratio of hydraulic conductivity to recharge K/R and on the topographic slope s . The validity of the Dupuit solution is shown to be in fact a unique function of another ratio, the ratio of depth to seepage length d/L S . For d/L S 〈 0.2, the relative difference between the two solutions is quite small (〈 14% for the wide range of parameter values tested), whereas for d/L S 〉 0.2, it increases dramatically. In practice, this criterion can be used to test the validity of Dupuit solutions. When d/L S increases beyond that cut-off, the ratio of seepage length to hillslope length L S /L given by the full-depth solution tends towards a non-zero asymptotic value. This asymptotic value is shown to be controlled by (and in many cases equal to) the parameter R/sK . Generalization of the findings to cases featuring heterogeneity, non-horizontal impervious base and variable-slope topography is discussed.
Print ISSN:
0043-1397
Electronic ISSN:
1944-7973
Topics:
Architecture, Civil Engineering, Surveying
,
Geography
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