Simulation of the seepage face — Limitations of a one-dimensional approach

Potter, Scott T.; Gburek, William J.

doi:10.1016/0022-1694(86)90025-9

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…Intuitively, this collapse of the vertical dimension should be valid for systems that have much larger horizontal extent than vertical extent. For systems with a constant‐head profile at the downhill boundary, a Dupuit solution indeed performs better for a small ratio of depth to hillslope length [ Potter and Gburek , ]. For the system studied here, which features a no‐flow downhill boundary, this condition is necessary but not sufficient; Figures a–c show that the Dupuit solution fails even for small absolute values of d / L .…”

Section: Discussionmentioning

confidence: 99%

“…Although the validity of the Dupuit assumption has been extensively studied in regard to flow or water table prediction in a number of configurations [ Bear , ; Haitjema , ; Chenaf and Chapuis , ; Rushton and Youngs , ], it has been poorly studied in regard to seepage area prediction using models such as stated above. Potter and Gburek [] addressed this issue explicitly, comparing a Dupuit solution to the solution given by a variably saturated model in hillslope cross sections. However, although they examined a number of configurations, they restricted the analysis to a constant‐head profile at the downhill boundary, representing a stream.…”

Section: Introductionmentioning

confidence: 99%

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Is the Dupuit assumption suitable for predicting the groundwater seepage area in hillslopes?

Bresciani

Davy

Dreuzy

2014

Water Resources Research

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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 cutoff, the ratio of seepage length to hillslope length L S /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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Is the Dupuit assumption suitable for predicting the groundwater seepage area in hillslopes?

Bresciani

Davy

Dreuzy

2014

Water Resources Research

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“…A non-linear, unconfined aquifer that conforms to the Dupuit-Forchheimer assumptions (horizontal groundwater flow and discharge in proportion to saturated thickness) requires that either the effective length or width of the saturated thickness of the aquifer varies over time. In these cases, the change in water level will not be proportional to the de-watered volume as the aquifer drains, so discharge from the aquifer will not be a linear function of its storage (Potter and Gburek, 1986). For example, the change in water level for an aquifer with a triangular longitudinal section will be a decreasing function of its de-watered volume, and discharge will be weakly non-linear as the aquifer drains (Konrad, 2006a).…”

Section: State-space Baseflow Modelsmentioning

confidence: 99%