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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
37
39
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.