Yhd-12.3105 Subsurface Hydrology

1. Yhd-12.3105 SubsurfaceHydrology UnsaturatedFlow 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. SoilMoistureProfile – FromGroundwaterlevel to soilsurface • Recallsomedefinitions • Groundwaterlevel is defined to bethatlevel where soil water pressure is atmospheric • Below the groundwaterlevel the soil is saturatedwithwater and above the groundwaterlevel the soil is unsaturated • Immediatelyabove the groundwaterlevelthere is a capillaryfringethat is (amost) fullysaturated

3. UnsaturatedZone • Wateroriginatingfromprecipitationorirrigationinfiltratesthrough the soilsurface and percolatesthrough the unsaturatedzone • Thisformsrecharge to an aquifer • Harmfulsubstancesmovewithwater • In unsaturatedzone the waterpressure is negative • Water is retained in soilbycapillaryforces, whichare a combination of cohesive and adhesiveforces Does the percolatingwater in the figureaboveenter the subsurfacedrain? Why / whynot?

4. Soil sample Porous plate Tensiometer Water hc • Negative waterpressure in soil is measuredusing a tensiometer 1. Howcanyouread the pressurehead in the soilsampleusing the tensiometershown in the figure? 2. The porousplateneeds to beairtight. Why? 3. Whydoes the waterentering the soilsampledoesnotsignificantlyaffect the measurement?

5. WaterRetentionCurve • A graphthatshows the relationshipbetweensoilwaterpressurehead and moisturecontent of soil is called the waterretentioncurve • In the waterretentioncurve the soilwaterpressurehead is typicallyexpressed as a pFvalue • pFvalue is the 10-based logarithm of the absolutevalue of the pressureheadexpressed in centimeters of watercolumnheight • As pressureheadvaluesrangeacross a largescaletaking a logarithmlead s to a garphthat is easier to interpret Pressurehead is – 100 cm. What is the correspondingpFvalue? Pressurehead is – 100 cm => pFvalue is 2

6. WaterRetentionCurve III ha II qres I I: Porosity II: Air-entrypressureheadha III: Residualmoisturecontentqres

7. Clay Sand WaterRetentionCurve • Itwillnotbe a greatsurprisethatdifferentsoilshavewaterretentioncurves of differentshape Whichone of the shownwaterretentioncurves is for a claysoil and whichone for a sandsoil? Why?

8. WaterFlow in UnsaturatedZone • Whatare the differences to saturated (groundwater) flow? • Hydraulicconductivity is a function of the moisturecontent of soil • Whenmoisturecontentdecreaseslargesoilporesareemptiedfirst, whichleadsboth in reducedcross-sectionalarea of flow and increasedtortuosity of the flowpaths => hydraulicconductivitydrops • The air-filled pore space is a function of the moisturecontent of soil • Recall the largedifference (severalorders of magnitude) in the storativity of confined and unconfinedaquifers • Recallthatmoisturecontent and pressureheadarerelated via the waterretentioncurve • Hydraulicconductivity and the air-filled pore spacecanalsobeexpressed as a function of pressurehead

9. Darcy’sLaw in UnsaturatedZone • As presentedearlier the hydraulicheadH is the sum of pressureheadh and gravityheadz • In the unsaturatedflow the interestoften is to studypercolation to groundwater, solet us firstwriteDarcy’slaw in one dimension and in verticaldirection Here the direction of the z-axis is points downward – hence the negative sign.

10. Darcy’sLaw in UnsaturatedZone: 3D Why is the -1 present in the equation of qzmissingfrom the equations for qx and qy?

11. UnsaturatedHydraulicConductivity Coarsegravel Relationship between the pressure head and the hydraulic conductivity for different soil types Finesand Peat Clay Hydraulicconductivity Pressurehead

12. UnsaturatedHydraulicConductivity • The water retention curve (pF curve) and the unsaturated hydraulic conductivity can be described with the following equations originally proposed by M.Th. van Genuchten and Y. Mualem Where  is the soil moisture (cm3/cm3), R is the residual water content of soil (cm3/cm3), S is the saturated water content of soil (cm3/cm3), S is the saturation of soil (cm3/cm3), h is the pressure head (cm), and ha is the air entry pressure head. Symbols , , and  refer to the parameters of the van Genuchten model, and  = 1 – 1/. K is the unsaturated hydraulic conductivity, KS is the saturated hydraulic conductivity (cm/h), and KR is the relative conductivity of unsaturated soil (KR = K / KS).

13. Reminder: TransientGroundwaterFlow in 3D Specificstorativity S0 volume of wateradded to storage, per unitvolume and per unitrise in hydraulichead

14. Flow in UnsaturatedZone: Richards’ Equation Specific moisture capacity: Differential water capacity: Volume of water released from (or added to) storage per unit decrease (or increase) of pressure head C [1/m]

15. DifferentialWaterCapacity The definition was: Volume of water released from (or added to) storage per unit decrease (or increase) of pressure head Differential water capacity: C [1/m] From the definition above it follows: ,where qis the volumetric moisture content So:

16. DifferentialWaterCapacity Pressure head h Moisture content q Dq Dh

17. NumericalSolution – RichardsEquation • Let us discretize the Richardsequation in 2D for a longitudialsection: x (i) Sink / source z (j)

18. x (i) NumericalSolution – RichardsEquation Dx z (j) Dz

19. NumericalSolution – RichardsEquation

20. NumericalSolution – RichardsEquation • Approximating the differentialwatercapacityC • Estimateusing the Van Genuchtenequation the moisturecontentthatcorresponds to the pressurehead at the desiredtime and location • Perturbate the pressureheadwith a smalldisplacement of Dh • Compute the moisturecontent at h + Dh • NowyoucanestimateCusing the differencemethod as Recallthat . HowwouldyouapproximateC?