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Yhd-12.3105 Soil and Groundwater Hydrology

Yhd-12.3105 Soil and Groundwater Hydrology. Steady-state flow. Teemu Kokkonen. Email : firstname.surname@aalto.fi Tel. 09-470 23838 Room : 272 (Tietotie 1 E). Water Engineering Department of Civil and Environmental Engineering Aalto University School of Engineering.

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Yhd-12.3105 Soil and Groundwater Hydrology

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  1. Yhd-12.3105 Soil and GroundwaterHydrology

    Steady-stateflow Teemu Kokkonen Email: firstname.surname@aalto.fi Tel. 09-470 23838 Room: 272 (Tietotie 1 E) Water Engineering Department of Civil and Environmental Engineering Aalto UniversitySchool of Engineering

  2. Aquifertypes

    Aquifer Latin: aqua(water) + ferre(bear, carry) An underground bed or layer of permeable rock, sediment, or soil that yields water Confined aquifer Between two impermeable layers Groundwater is under pressure and will rise in a borehole above the confining layer Unconfined aquifer (phreaticaquifer) Groundwater table forms the upper boundary

  3. AquiferTypes

  4. SomeTerms

    Saturated zone (vadose zone) Pore space fully saturated with water Groundwater level (water table) Is defined as the surface where the water pressure is equal to the atmospheric pressure In groundwater studies the atmospheric pressure is typically used as the reference point and assigned with the value of zero Capillary fringe Saturated (or almost saturated) layer just above the grounwater level Unsaturated zone Both water and air are present in the pore space

  5. Hydraulisia johtavuuksia

  6. Equation for Groundwater Flow Steady state 1D

    When the waterlevel in the containerdoesnotchangeit is in steady-state The influx and outfluxmustthenbeequal to eachother Inflow per unittime Qi = 2 l s-1 Inflow per unittime and unitarea (influx) qi = 2 l s-1 / 0.4 m2 = 0.5 cm s-1 Outflow per unittimeQo = 2 l/s Outflow per unittime and unitarea (outflux) qo = 0.5 cm s-1

  7. Equation for Groundwater Flow Steady state 1D

    Darcy’s law Conservation of momentum Continuity equation Conservation of mass In steady state conditions the amount of stored water does not change The outgoing flux must equal the incoming flux

  8. Equation for Groundwater Flow Steady state 1D

    Conservation of mass Inserting Darcy’s law to describe the flux q yields: Under the assumption of homogeneity: Laplace equation in 1D

  9. Equation for Groundwater Flow Steady state 3D

    The groundwater equation just derived in one dimension is easy to generalise to three dimensions Analogous analysis to the previous slide yields for the homogeneous 3D case:

  10. Equation for Groundwater Flow Steady state 2D

    Typicallythicknes of aquifers is relativelysmallcompared to theirarealextent, whichjustifies the assumption of essentiallyhorizontalflow

  11. Exchange of Water: SinkorSource

    An aquifer can receive (source) or loose (sink) water in interaction with the world beyond its domain Source: recharge from precipitation, injection wells Sink: pumping wells In the groundwater equation added or removed water is described using a sink / source term

  12. Equation for Groundwater Flow Steady state 2D, Sink / Source

    Explain in yourown words what waterbalancecomponents the circledterms in the aboveequationrepresent. Usethen the valuesgivenbelow to computetheirvaluesassumingthat the derivativesareconstantwithin the rectangularcontrolvolume. Givealsounits to the quantitieslistedbelow. qx(x) = 9 ? qx(x+Dx) = 6 ? qy(y) = 2 ? qy(y+Dy) = 5 ? Dx = 3 ? Dy = 2 ? b = 2 ? R = -1 ?

  13. Equation for Groundwater Flow Steady state 2D, Sink / Source

  14. Equation for Groundwater Flow Steady state 2D, Sink / Source

    Howdoes the equationchangeif the aquifer is homogeneous? Howdoes the equationchangeif the aquifer is isotropic? DefiningtransmissivityT to be the product of hydraulicconductivityK and the thickness of the waterconductinglayerbyields:

  15. Equation for Groundwater Flow Steady state 2D, Sink / Source

    Does R vary in space? When? Does T vary in space? When?

  16. BoundaryConditions

    Governingequation for groundwaterflow Describeshow the waterfluxdepends on the gradient of the hydraulichead (Darcy’slaw) Requires the mass to beconserved To represent a particularaquiferboundaryconditionsneed to bedefined Boundaryconditionsdescribehow the studiedaquiferinteractswith the regionssurrounding the aquifer

  17. BoundaryConditions

    Two main categories Constant head (fixed head, prescribed head) Dirichlet condition Water bodies (lakes, rivers) Constant flux Neumann condition Impermeable boundary is a common special case (clay, rock, artificial liners...)

  18. NumericalSolutionSteady-state 1D

    Homogeneousaquifer Let us derive a numericalapproximation for the steady-state 1D groundwaterflowequation. Step 1. Howwouldyouapproximate the spatialderivativebetweennodesi and i+1? Step 2. Howwouldyouapproximate the spatialderivativebetweennodesi-1 and i? Step 3. Howwouldyouapproximate the 2nd spatialderivativearoundnodei? Dx Dx

  19. NumericalSolutionSteady-state 1D

    Geometricaverage Heterogeneousaquifer Let us againderive a numericalapproximation for the steady-state 1D groundwaterflowequation. How to compute and ? Dx Dx

  20. NumericalSolution2D Steady-stateFlow, Sink/sourceTerm

    i j
  21. Hydraulichead to becomputedfrom the groundwaterflowequation.

    BoundaryConditionsNumericalSolution

    Hydraulichead set to a fixedvaluerepresenting the level of the lake. Hydraulicheadvalue is ”mirrorred” across the no-flowboundary. Lake H = 10 m I II Clay (almostimpermeable) Hydraulicgradientacrossthislinebecomeszero => no flow HII = HI
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