Skip to main content
SpringerLink
Log in

Steady state groundwater seepage in sloping unconfined aquifers

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

This paper reviews analytical solutions for steady state seepage of groundwater in an ideal sloping unconfined aquifer, recharged by an effective infiltration, when the unsaturated seepage is neglected. Available solutions are examined and compared. Their robustness is assessed with a finite element code, which solves the complete equations for saturated and unsaturated flow, thus making none of the simplifying assumptions of the theoretical solutions. An example is provided for a sloping aquifer on the north shore of the Saint-Lawrence River.

Résumé

L’article fait la revue des solutions analytiques pour l’écoulement souterrain permanent dans un aquifère incliné à nappe libre, rechargé par infiltration efficace, quand l’écoulement non saturé est négligé. Les solutions disponibles sont examinées et comparées. Leur robustesse est évaluée à l’aide d’un code d’éléments fins, qui résout les équations complètes des écoulements saturé et non saturé, et qui donc ne fait aucune des hypothèses simplificatrices des solutions théoriques. Un exemple est fourni pour un aquifère incliné sur la rive nord du Saint-Laurent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Aubertin M, Bussière B, Aachib M, Chapuis RP (1996) Une modélisation numérique des écoulements non saturés dans les couvertures multicouches en sols. Hydrogéologie 96(1):3–13

    Google Scholar 

  • Aubertin M, Cifuentes E, Apithy S, Bussière B, Chapuis RP, Molson JW (2010) Analysis of water diversion along inclined covers with capillary barrier effects. Can Geotech J 46(x), (in print)

  • Bear J (1972) Dynamics of fluids in porous media. Elsevier, New York

    Google Scholar 

  • Beven K (1981) Kinematic subsurface stormflow. Water Res Res 17:1419–1424

    Article  Google Scholar 

  • Boussinesq J (1877) Essai sur la théorie des eaux courantes. Mémoire, Académie des sciences, Inst. Fra. 23(1):252–260

    Google Scholar 

  • Brutsaert W (1994) The unit response of groundwater outflow from a hillslope. Water Res Res 30:2759–2763

    Article  Google Scholar 

  • Brutsaert W (1995) The unit response of groundwater outflow from a hillslope: Reply. Water Res Res 31:2379–2380

    Article  Google Scholar 

  • Bussière B, Aubertin M, Chapuis RP (2003) The behavior of inclined covers used as oxygen barriers. Can Geotech J 40(3):512–525

    Article  Google Scholar 

  • Chapman T (1995) Comment on “The unit response of groundwater outflow from a hillslope” by W Brutsaert. Water Res Res 31:2377–2378

    Article  Google Scholar 

  • Chapuis RP (1995) Controlling the quality of groundwater parameters: some examples. Can Geotech J 32:172–177

    Article  Google Scholar 

  • Chapuis RP (1998a) Overdamped slug tests in monitoring wells: review of interpretation methods with mathematical, physical and numerical analysis of storativity influence. Can Geotech J 35:697–719

    Article  Google Scholar 

  • Chapuis RP (1998b) Poor borehole sampling and consequences for permeability evaluation. Proc 8th Congress IAEG, Vancouver, Balkema 4:417–423

    Google Scholar 

  • Chapuis RP (1999) Borehole variable-head permeability tests in compacted clay liners and covers. Can Geotech J 36(1):39–51

    Article  Google Scholar 

  • Chapuis RP (2002a) Solution analytique de l’écoulement en régime permanent dans un aquifère incliné à nappe libre, et comparaison de cette solution avec des solutions numériques plus complètes, Rapport Tech EPM-RT-02-03, août 2002, École Polytechnique, Montréal, URL:http://www.polymtl.ca/biblio/epmrt/rapports/rt2003-03.pdf

  • Chapuis RP (2002b) The 2000 R.M. Hardy Lecture: full-scale hydraulic performance of soil-bentonite and compacted clay liners. Can Geotech J 39(2):417–439

    Article  Google Scholar 

  • Chapuis RP (2005) Numerical modelling of rising-head permeability tests in monitoring wells after lowering the water level down to the screen. Can Geotech J 42:705–715

    Article  Google Scholar 

  • Chapuis RP (2006) Interpreting variable-head tests performed in open holes or monitoring wells with several screens. Geotech Test J 29(6):467–473

    Google Scholar 

  • Chapuis RP (2009a) Variable head permeability tests in monitoring wells: comparing the shape factor defined by Bouwer and Rice (1976) to the shape factor given by Hvorslev (1951). Geotech News 27(1):41–43

    Google Scholar 

  • Chapuis RP (2009b) Numerical modeling of reservoirs or pipes in groundwater seepage. Comput Geotech 36:895–901

    Article  Google Scholar 

  • Chapuis RP, Aubertin M (2001) Evaluation of saturated and unsaturated seepage through dikes in steady state conditions. Can Geotech J 38:1321–1328

    Article  Google Scholar 

  • Chapuis RP, Chenaf D (2002) Slug tests in a confined aquifer: experimental results in a large soil tank and numerical modeling. Can Geotech J 39:14–21

    Article  Google Scholar 

  • Chapuis RP, Chenaf D (2003a) Effects of monitoring and pumping well pipe capacities on pumping tests in confined aquifers. Can Geotech J 40(6):1093–1103

    Article  Google Scholar 

  • Chapuis RP, Chenaf D (2003b) Variable-head field permeability tests in driven casings: physical and numerical modeling. Geotech Testing J 26:245–256

    Google Scholar 

  • Chapuis RP, Chesnaux R (2006) Travel time to a well pumping an unconfined aquifer without recharge. Ground Water 44:600–603

    Article  Google Scholar 

  • Chapuis RP, Dénes A (2009) Écoulement saturé et non saturé de l’eau souterraine vers des drains en aquifère à nappe libre. Can Geotech J 45:1210–1223

    Article  Google Scholar 

  • Chapuis RP, Chenaf D, Bussière B, Aubertin M, Crespo R (2001) A user’s approach to assess numerical codes for saturated and unsaturated seepage conditions. Can Geotech J 38:1113–1126

    Article  Google Scholar 

  • Chapuis RP, Chenaf D, Acevedo N, Marcotte D, Chouteau M (2005) Unusual drawdown curves for a pumping test in an unconfined aquifer at Lachenaie, Quebec: Field data and numerical modeling. Can Geotech J 42:1133–1144

    Article  Google Scholar 

  • Chapuis RP, Bélanger C, Chenaf D (2006) Pumping test in a confined aquifer under tidal influence. Ground Water 44:300–305

    Article  Google Scholar 

  • Chapuis RP, Dallaire V, Marcotte M, Chouteau M (2007a) Falling-head permeability tests using monitoring wells in unconfined aquifers. Geotech Testing J 30:104–112

    Google Scholar 

  • Chapuis RP, Masse I, Madinier B, Aubertin M (2007b) A long column test for determining unsaturated properties of coarse material. Geotech Test J 30:83–89

    Google Scholar 

  • Chenaf D, Chapuis RP (1998) Étude numérique du pompage en régime permanent dans un aquifère à nappe libre. In: Proc 51st Can Geotech Conf, Edmonton 523–528

  • Chenaf D, Chapuis RP (2007) Seepage face height, water table position, and well efficiency for steady state. Ground Water 45:167–177

    Article  Google Scholar 

  • Chesnaux R, Chapuis RP (2007) Detecting and quantifying leakage through defective borehole seals: A new methodology and laboratory verification. Geotech Test 30:17–24

    Google Scholar 

  • Chesnaux R, Molson J, Chapuis RP (2005) An analytical solution for groundwater transit time through an unconfined recharged aquifer. Ground Water 43:511–517

    Article  Google Scholar 

  • Chesnaux R, Chapuis RP, Molson JW (2006) A new method to characterize hydraulic short-circuits in defective borehole seals. Ground Water 44:676–681

    Google Scholar 

  • Dunne T, Black R (1970) Partial area contributions to storm runoff in a small New England watershed. Water Res Res 6:1296–1311

    Article  Google Scholar 

  • Dupuit J (1857) Mémoire sur le mouvement des eaux dans les terrains perméables. Mémoire déposé en 1857, Comptes Rendus des séances de l’Acad des Sciences, Paris, tome LII, séance du 3 juin 1861

  • Dupuit J (1863) Études théoriques et pratiques sur le mouvement des eaux dans les canaux découverts et à travers les terrains perméables, 2e éd. Dunod Paris chap 7:229–293

    Google Scholar 

  • Etcheverry D, Perrochet P (2000) Direct simulation of groundwater transit-time distributions using the reservoir theory. Hydrogeol J 8:200–208

    Article  Google Scholar 

  • Freeze RA (1972a) Role of subsurface flow in generating surface runoff: 1. Base flow contributions to channel flow. Water Res Res 8:609–623

    Article  Google Scholar 

  • Freeze RA (1972b) Role of subsurface flow in generating surface runoff: 2. Upstream source areas. Water Res Res 8:1272–1283

    Article  Google Scholar 

  • Geo-Slope (2003) Seep/W for finite element seepage analysis. User’s Guide. Geo-Slope International, Calgary, Alberta

    Google Scholar 

  • Kamke E (1944) Differential Gleichungen. Lösungsmethoden und Lösungen, 3rd edn. Chelsea, New York, p 329

    Google Scholar 

  • Kao C, Bouarfa S, Zimmer D (2001) Steady state analysis of unsaturated flow above a shallow water-table aquifer drained by ditches. J Hydrol 250:122–133

    Article  Google Scholar 

  • Kirkby M (1988) Hillslope runoff processes and models. J Hydrol 100:315–339

    Article  Google Scholar 

  • Koussis AD (1992) A linear conceptual subsurface storm model. Water Res Res 28:1047–1052

    Article  Google Scholar 

  • Koussis AD, Lien L (1982) Linear theory of subsurface storm flow. Water Res Res 18:1738–1740

    Article  Google Scholar 

  • Loáiciga HA (2005) Steady state phreatic surfaces in sloping aquifers. Water Res Res 41:W08402. doi:10.1029/2004WR003861

    Article  Google Scholar 

  • Pavlovsky NN (1956) Motion of Groundwater, Collected Works. Academy of Sciences, Moscow-Leningrad

    Google Scholar 

  • Polubarinova-Kochina PY (1962) Theory of groundwater movement. Translated from Russian by JMR de Wiest. Princeton University Press, Princeton, New Jersey

    Google Scholar 

  • Richards LA (1931) Capillary conduction of liquids through porous medium. Physics 1:318–333

    Article  Google Scholar 

  • Rupp DE, Selker JS (2006) On the use of the Boussinesq equation for interpreting recession hydrographs from sloping aquifers. Water Res Res 42:W12421. doi:10.1029/2006WR005080

    Article  Google Scholar 

  • Schoeller H (1962) Les eaux souterraines : hydrologie dynamique et chimique, exploitation et évaluation des ressources. Masson, Paris

    Google Scholar 

  • Strack ODL (1989) Groundwater mechanics. Prentice-Hall, Englewoods Cliffs

    Google Scholar 

  • Verhoest NFC, Troch PA (2000) Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer. Water Res Res 36:793–800

    Article  Google Scholar 

Download references

Acknowledgments

These studies were subsidized by the Natural Sciences and Engineering Council of Canada. The author thanks John Molson and Richard Darling for reading and commenting on the manuscript.

Author information

Authors and Affiliations

  1. Department of Civil, Geological and Mining Engineering, Ecole Polytechnique, PO Box 6079, Sta. CV, Montreal, QC, H3C 3A7, Canada

    Robert P. Chapuis

Authors
  1. Robert P. Chapuis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert P. Chapuis.

Appendix

Appendix

Figures 12 and 13 are provided as complements to Figs. 9 and 11.

Fig. 12
figure 12

Complement to Fig. 9: numerical results for the Darcy velocity (second example), below the water table, along equipotential lines starting from the substratum at x = 100, 200, 400, 600, 800 and 1,000 m. It confirms that the Darcy velocity may be assumed constant along each equipotential

Full size image
Fig. 13
figure 13

Complement to Fig. 11: to illustrate the dampening capacity of the unconfined aquifer, we have considered a 50 mm rain during 1 h. There is no runoff. Before and after the rain, the mean annual effective infiltration was considered. The figure below shows that the response of the water table at x = 500 m (middle of the slope) is strongly delayed and dampened

Full size image

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chapuis, R.P. Steady state groundwater seepage in sloping unconfined aquifers. Bull Eng Geol Environ 70, 89–99 (2011). https://doi.org/10.1007/s10064-010-0282-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10064-010-0282-2

Keywords

Mots clés

Search

Navigation