heydinger unsat hydraulic

8/3/2019 Heydinger Unsat Hydraulic

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Conductivity TestingConductivity Testing

ofofUnsaturated SoilsUnsaturated Soils

A Presentation to the

Case Western Reserve University

May 6, 2004

ByAndrew G. Heydinger

Department of Civil

Engineering


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Purpose of PresentationPurpose of Presentation

Present fundamental concepts

necessary for understanding

mechanics of unsaturated flow.

Discuss conductivity testing of

unsaturated soils.


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S

ome Fundamental ConceptsS

ome Fundamental Concepts


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Mechanics of UnsaturatedS

oilsMechanics of UnsaturatedS

oils Unsaturated soils are distinguished

from saturated soils by negativepore water pressures, soil suction,

that develop.

The negative pore pressures affect

soil properties and behavior.


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MatricS

uction DefinedMatricS

uction Defined

Component of the soil moisture

suction associated with thecapillary head.

Matric suction = (ua

- uw

)

ua = soil air pressure

uw = soil water suction pressure.


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Importance of MatricS

uctionImportance of MatricS

uction Soil matric suction is a primary

stress state variable used to

characterize unsaturated soil

behavior.

Relationships required to model

flow in unsaturated soils are given

as functions of pore water pressure

or matric suction.


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Mass Balance Equation forMass Balance Equation for

Water PhaseWater Phase Derived assuming homogeneous,

isotropic non-deforming medium and

incompressible, homogeneous fluid.

Volumetric water content depends

on pore water pressure, U(]).

tq x

x!

U


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Darcys LawDarcys Law A flow law relating the flow rate to

the driving potential is needed.

Flow depends on a coefficient,hydraulic conductivity ( ) , and

the total head gradient ( ).K

J! KqJ


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Hydraulic ConductivityHydraulic Conductivity

Hydraulic conductivity is the

coefficient obtained from a flow or

conductivity test.

Hydraulic conductivity depends on

medium and fluid properties. Hydraulic conductivity depends on

fluid pressure, K(]).


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Flow EquationFlow Equation

The two required functions are K(])

and U(]) where ] is the pressure head.

The functions can be given in terms ofpore water pressure, pressure head or

matric suction.

tzK

x

x

x

x!

]

]

]U]]

)()}()({


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SoilSoil--Water Retention FunctionWater Retention Function

After Mualem (1976)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400 500 600 700] = 0 ]

Us

U

BoundaryWetting

Boundary

Drying Curve

Drying and

Wetting

Scanning

Curves


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Conductivity FunctionConductivity Function

After Mualem (1976)

0.001

0.01

0.1

1

0 100 200 300 400 500 600 700]!]

Ks

K

Boundary

Wetting

Boundary

Drying Curve

Drying and

Wetting

Scanning

Curves


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Relative ConductivityRelative Conductivity

After Brooks and Corey (19

64)

K

KK

s

w

rw

!

0 20 40 60 80 100

Degree of Saturation, S (%)

Krw

or

Kra

AirWater

1

0.8

0.6

0.4

0.2

0


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Modeling With the FunctionsModeling With the Functions

Both functions exhibit hysteresis

during drying and wetting processes.

Mathematical expressions are used to

approximate the experimental curves,using the boundary drying or wetting

curve.


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van Genuchten (1980) Equationsvan Genuchten (1980) Equations

The curve fitting parameters, nand m, and other parameters are

obtained from the curves.

m

1)(

n

rs

r

E]

UUU]U

!

? A2m/15.0 11)( mees

SSKK !]


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Laboratory TestingLaboratory Testing


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Variation of Matric Suction inVariation of Matric Suction in

the Laboratorythe Laboratory To vary matric suction, both the

soil air and soil water pressures

are increased (axis translation

technique).

Matric suction is computed as thedifference between the two

pressures, always positive.


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High Air Entry Ceramic MaterialHigh Air Entry Ceramic Material

A ceramic material is used to

prevent flow of air from the soil.

Once the material is saturated, the

capillary pressure in the materialprevents air from flowing through

the material and out of the soil.


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Direct Measurement ofSoilDirect Measurement ofSoil

Moisture SuctionMoisture Suction Tensiometers. Directly measure

pore water pressures but are limited

to 90 centibars pressure.

Thermocouple Psychrometers.

Measure relative humidity of thesoil to compute the total suction,

to high suction values.


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Indirect Measurement ofSoilIndirect Measurement ofSoil

MoistureMoisture The physical properties of soil

minerals do not vary significantly,

but they differ significantly from

the properties of pure water.

Consequently, soil moisture contentor matric suction are correlated to

physical properties of soil.


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Indirect MeasurementS

ensorsIndirect MeasurementS

ensors

The types of sensors include:

o thermal conductivity sensors

o time domain reflectomety or

frequency domain sensors(dielectric properties)

o electrical resistivity sensors


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Measurement AccuracyMeasurement Accuracy

Sensor calibrations are nonlinear.

At low moisture contents, large

changes in matric suctions occur

with only small changes in watercontent, so the accuracy of the

sensors is reduced.


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Modified Triaxial CellModified Triaxial Cell Triaxial cells

were modifiedby adding two

ports and a

load cell inline with the

loading piston.


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Water Volume Change IndicatorWater Volume Change Indicator

Four burettes

and a gang ofzero volume

change valves

are used to

measure flow.


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Diffused Air Volume IndicatorDiffused Air Volume Indicator A burette is used

to collect andmeasure air

volume.

An exit tubemaintains constant

pressure.


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Steady State Conductivity TestSteady State Conductivity Test

Matric suction is varied and

steady state flow is induced tomeasure conductivity.

Soil air and water pressures and

outflow rates are measured. Tests are very difficult and time

consuming for fine grained soils.


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Instantaneous Profile TestInstantaneous Profile Test

Water or air is injected into the soil

at steady rates and water content or

pore water pressures are measured

at several locations at various times.

Water content and hydraulicconductivity calculations depend on

the test procedure and type of

measurements.


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SingleSingle--Step and MultiStep and Multi--StepStep

Outflow TestsOutflow Tests The soil air pressure is varied and

the water outflow or inflow ratesare measured.

The use of sensors is optional.

Hydraulic functions are computedusing an analytical or numerical

solution.


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GeoGeo--centrifuge Testingcentrifuge Testing Centrifuges are used for evaluating

petroleum yields from rock cores, for

measuring hydraulic properties of soils

and contaminant transport in soil.

Large and small-scale geo-centrifuges

are used.

Include sensors and different methods of

analysis to compute hydraulic properties.


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Laboratory Tests at theLaboratory Tests at the

University of ToledoUniversity of Toledo

Multi-step tests are conducted using

the modified triaxial apparatus.

Hydraulic conductivity is computed

from analytical solution that uses

soil diffusivity and that accounts for

the system impedance.


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Analytical Solution for DiffusivityAnalytical Solution for Diffusivity

The governing equation for1-D flow is

Hydraulic conductivity is computed from

x

x!

x

x

2

2

)(z

Dt

U]U

]

U]]

x

x! )()( DK


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Analysis ProcedureAnalysis Procedure

Normalized outflow is plotted versus anon-dimensional time factor.

Parameters are varied in the equation fortheoretical outflow until there is good

agreement between theoretical and

experimental curves.

Hydraulic conductivity is computed from

the diffusivity used in the calculation.


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Comparison of Measure andComparison of Measure and

Theoretical OutflowTheoretical Outflow

0.00100

0.01000

0.10000

1.00000

0.001 0.010 0.100 1.000 10.000

tau or t/tRP

Qt/Q0

(Q't/Qo)meas

(Qt/Qo)theo


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SoilSoil--Water Retention CurveWater Retention Curve

25

27

29

31

33

35

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0 50 100 150 200 250 300 350 400 450 500

Matric Suction, Ua - Uw (kPa)

VolumetricWaterContent(%

)

Pressure Plate Extractor Triaxial Apparatus

Modified Triaxial Test


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Hydraulic Conductivity FunctionHydraulic Conductivity Function

2.00E-10

1.20E-09

2.20E-09

3.20E-09

4.20E-09

5.20E-09

6.20E-09

7.20E-09

0 100 200 300 400 500

Matric Suction (kPa)

C

onductivity(c

m/sec)


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Inverse ModelingInverse Modeling

Numerical solutions that use finitedifference or finite element procedures

are used to back calculate the hydraulicfunctions using inverse modeling

techniques.

Parameters required for the curve fitting

equations are obtained using optimization

techniques.


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Vadose Zone ModelsVadose Zone Models

Program Description Developer Licenser Availability

VS2DHI FDM, fluid flow and

energy transport

USGS USGS Public domain

software

VS2DTI FDM, fluid flow and

solute transport

USGS USGS Public domain

software

TOUGH2 FDM, multi-phase

and energy transport

Lawrence Berkeley

National Lab. (DOE)

Energy Science and

Technology Center

License required

iTOUGH2 Inverse model for

TOUGH2

Lawrence Berkeley

National Lab. (DOE)

Energy Science and

Technology Center

License required

Hydrus-1D FEM, water and

solute transport

USSalinity Laboratory,

USDA

IGWMC Public domain

software

Hydrus-2D 1-D FEM, water USSalinity Laboratory,

USDA

IGWMC License required

STOMP FDM, multi-phaseand energy transport

Pacific Northwest NationalLab. (DOE)

Battelle Memorial Institute Research orCommercial

License

VADOSE FEM Geo-Slope, Inc. Geo-Slope, Inc. License required

SVFLUX FEM SoilVision, Inc. SoilVision, Inc. License required

Public domain

software

SUTRA FEM, water and

solute or energy

transport

USGS USGS


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Future WorkFuture Work


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Laboratory ProceduresLaboratory Procedures

Procedures for multi-step outflow

tests that do not require instrumentedsamples.

Measurement of system impedance.

Measurement of saturated/unsaturated

hydraulic conductivity.


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Data AnalysisData Analysis

Comparison of hydraulic functions

determined from analytical solutionwith known system impedance tonumerical modeling of multi-step

outflow tests using inverse modeling. Use of numerical modeling to investigate

hysteresis effects.


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Beyond the LaboratoryBeyond the Laboratory

Modeling flow in the vadose zone

using programs that couple heat andmoisture flow and contaminant transport.

Investigation of the movement ofboth liquid and vapor transport in the

vadose zone.

heydinger unsat hydraulic

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