%0 Journal Article
%T Is the Dupuit assumption suitable for predicting the groundwater seepage area in hillslopes?
%+ GĂ©osciences Rennes (GR)
%A Bresciani, Etienne
%A Davy, Philippe
%A de Dreuzy, Jean-Raynald
%< avec comitĂ© de lecture
%Z PL03279
%@ 0043-1397
%J Water Resources Research
%I American Geophysical Union
%V 50
%N 3
%P 2394-2406
%8 2014
%D 2014
%R 10.1002/2013WR014284
%Z Sciences of the Universe [physics]/Earth SciencesJournal articles
%X 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/LS. For d/LS<0.2, the relative difference between the two solutions is quite small (<14% for the wide range of parameter values tested), whereas for d/LS>0.2, it increases dramatically. In practice, this criterion can be used to test the validity of Dupuit solutions. When d/LS increases beyond that cutoff, the ratio of seepage length to hillslope length LS/L given by the full-depth solution tends toward a nonzero 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, nonhorizontal impervious base and variable-slope topography is discussed.
%G English
%2 https://insu.hal.science/insu-00979585/document
%2 https://insu.hal.science/insu-00979585/file/bresciani.pdf
%L insu-00979585
%U https://insu.hal.science/insu-00979585
%~ INSU
%~ UNIV-RENNES1
%~ UR2-HB
%~ CNRS
%~ GR
%~ OSUR
%~ UR1-HAL
%~ UR1-SDLM
%~ UR1-SDLMJONCH
%~ GR-DIMENV
%~ UNIV-RENNES2
%~ TEST-UNIV-RENNES
%~ TEST-UR-CSS
%~ UNIV-RENNES
%~ INRAE
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%~ GR-ET