Dupuit Equation for Steady-State Flow to a Trench in an Unconfined Aquifer (With Recharge)

Application: Geotechnics

  • Format: Online Tool Tool Tip
  • Fee for Use: Free Tool Tip
  • Enrollment: Not Required Tool Tip

Summary

An interactive hydrogeology tool for analysis of steady-state flow (with recharge) to a trench in an unconfined aquifer, based on the Dupuit equation ... with hydrogeology unit conversions.

Notes on Dupuit Equation for Steady-State Flow to a Trench in an Unconfined Aquifer (with Recharge)

  • Select the required output, then set the other parameters to the required values.
  • The Dupuit equation for horizontal flow can also be applied to flow to a river, but caution should be used when interpreting results as riverbed permeabilities can vary significantly from the surrounding aquifer material.
  • The Dupuit equation for horizontal flow only applies if the water table in the aquifer and trench is constant.

For equations, assumptions and references see equations.

Tool Parameters

Values displayed with a may be changed ... click on a value to display an entry form ... or use the arrows right of a value to select from a list.

Tool Behaviour

This tool exhibits spreadsheet-like behaviour ... change a value and related values are re-calculated automatically.

Dupuit Equation for Steady-State Flow to a Trench in an Unconfined Aquifer1

1Dupuit, J., Etudes theoriques et pratiques sur le mouvement des eaux dans les canaux decouverts et a travers les terrains permeables, 2eme edition; Dunot, Paris, 1863.

Variable Recharge:


where:
Q = discharge per unit thickness (m2/d)
K = hydraulic conductivity of aquifer (m/d)
h2, h1 = steady-state heads measured along flow path (m)
L = distance between steady-state head measurements (m)
R = net recharge (-ve for net evapotranspiration) (m/d)

Assumptions2:

  1. The aquifer is unconfined.
  2. The aquifer has an infinite areal extent.
  3. The trench is of infinite length (into the page).
  4. The aquifer is homogeneous, isotropic and of uniform thickness over the area influenced by the trench.
  5. Prior to trench dewatering, the water table is horizontal over the area influenced by the trench.
  6. The trench penetrates the entire saturated thickness of the aquifer.
  7. The flow to the trench is at steady-state.
  8. The velocity of flow is proportional to the tangent of the hydraulic gradient instead of the sine as it is in reality.1
  9. The flow is horizontal and uniform everywhere in a vertical section through the trench (cross-sectional flow).1

References:

1Dupuit, J., Etudes theoriques et pratiques sur le mouvement des eaux dans les canaux decouverts et a travers les terrains permeables, 2eme edition; Dunot, Paris, 1863.

2Kruseman, G.P. and N.A. de Ridder, Analysis and Evaluation of Pumping Test Data (Second Edition), Publication 47; International Institute for Land Reclamation and Improvement, Wageningen, 1994.

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