Conductivity TestingConductivity Testing of of Unsaturated Soils Unsaturated Soils

A Presentation to the Case Western Reserve University May 6, 2004

By Andrew G. Heydinger Department of Civil Engineering

2

Purpose of PresentationPurpose of Presentation

• Present fundamental concepts

necessary for understanding

mechanics of

unsaturated flow.• Discuss conductivity testing of

unsaturated soils.

3

Some Fundamental ConceptsSome Fundamental Concepts

4

Mechanics of Unsaturated SoilsMechanics of Unsaturated Soils

• Unsaturated soils are distinguished

from saturated soils by

negative pore water

pressures, soil suction, that

develop.• The negative pore pressures affect

soil properties and behavior.

5

Matric Suction DefinedMatric Suction Defined

• Component of the soil moisture suction associated with the capillary head.

• Matric suction = (ua - uw)

ua = soil air pressure

uw = soil water suction pressure.

6

Importance of Matric SuctionImportance of Matric Suction

• 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.

7

Mass Balance Equation for Mass 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, ().

tq

8

Darcy’s LawDarcy’s 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

Kq

9

Hydraulic Conductivity Hydraulic Conductivity

• Hydraulic conductivity is the coefficient obtained from a flow orconductivity test.

• Hydraulic conductivity depends on

medium and fluid properties.• Hydraulic conductivity depends on

fluid pressure, K().

10

Flow EquationFlow Equation

• The two required functions are K() and () where is the pressure

head.• The functions can be given in terms of

pore water pressure, pressure head or

matric suction.

tzK

)(

)}( )({

11

Soil-Water Retention FunctionSoil-Water 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

s

Boundary Wetting Curve

Boundary Drying Curve

Drying and Wetting Scanning Curves

12

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 Curve

Boundary Drying Curve

Drying and Wetting Scanning Curves

13

Relative ConductivityRelative Conductivity

After Brooks and Corey (1964)

KKK

s

wrw

0 20 40 60 80 100 Degree of Saturation, S (%)

Krw

or

Kra

Air Water

1

0.8

0.6

0.4

0.2

0

14

Modeling With the Functions Modeling 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.

15

van Genuchten (1980) Equationsvan Genuchten (1980) Equations

• The curve fitting parameters, n and m, and other parameters are obtained from the curves.

m 1

)(n

rsr

2 m /15.0 1 1 )( mees SSKK

16

Laboratory TestingLaboratory Testing

17

Variation of Matric Suction in Variation of Matric Suction in the Laboratory the Laboratory

• To vary matric suction, both the soil air and soil water pressures are increased (axis translation technique).

• Matric suction is computed as the difference between the two pressures, always positive.

18

High Air Entry Ceramic Material High 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 material prevents air from flowing

through the material and out of the soil.

19

Direct Measurement of Soil Direct Measurement of Soil Moisture Suction Moisture Suction

• Tensiometers. Directly measure pore water pressures but are

limited to 90 centibars pressure.

• Thermocouple Psychrometers. Measure relative humidity of the

soil to compute the total suction, to high suction values.

20

Indirect Measurement of Soil Indirect Measurement of Soil Moisture Moisture

• The physical properties of soil minerals do not vary

significantly, but they differ significantly from the properties of pure water.

• Consequently, soil moisture content or matric suction are correlated to

physical properties of soil.

21

Indirect Measurement Sensors Indirect Measurement Sensors

• The types of sensors include:

o thermal conductivity sensors

o time domain reflectomety or frequency domain sensors

(dielectric properties)

o electrical resistivity sensors

22

Measurement AccuracyMeasurement Accuracy

• Sensor calibrations are nonlinear.

• At low moisture contents, large changes in matric suctions occur

with only small changes in water content, so the accuracy of the sensors is reduced.

23

Modified Triaxial CellModified Triaxial Cell

• Triaxial cells were modified by adding two ports and a

load cell in line

with the loading piston.

24

Water Volume Change IndicatorWater Volume Change Indicator

• Four burettes and a gang of zero volume change valves

are used to measure

flow.

25

Diffused Air Volume IndicatorDiffused Air Volume Indicator

• A burette is used to collect

and measure air

volume.

• An exit tube maintains

constant pressure.

26

Steady State Conductivity Test Steady State Conductivity Test

• Matric suction is varied and steady state flow is induced to

measure conductivity.• Soil air and water pressures and

outflow rates are measured.• Tests are very difficult and time

consuming for fine grained soils.

27

Instantaneous Profile Test Instantaneous 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 hydraulic

conductivity calculations depend on the test procedure and type of

measurements.

28

Single-Step and Multi-Step Single-Step and Multi-Step Outflow Tests Outflow Tests

• The soil air pressure is varied and the water outflow or inflow

rates are measured.• The use of sensors is optional.• Hydraulic functions are computed

using an analytical or numerical solution.

29

Geo-centrifuge TestingGeo-centrifuge 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.

30

Laboratory Tests at the Laboratory 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.

31

Analytical Solution for Diffusivity Analytical Solution for Diffusivity

• The governing equation for 1-D flow is

• Hydraulic conductivity is computed from

2

2

)(z

Dt

)()( DK

32

Analysis ProcedureAnalysis Procedure

• Normalized outflow is plotted versus a non-dimensional time factor.

• Parameters are varied in the equation for theoretical outflow until there is good

agreement between theoretical and experimental curves.

• Hydraulic conductivity is computed from the diffusivity used in the calculation.

33

Comparison of Measure and Comparison of Measure and Theoretical Outflow Theoretical Outflow

0.00100

0.01000

0.10000

1.00000

0.001 0.010 0.100 1.000 10.000

tau or t/tRP

Qt/Q

0

(Q't/Qo)meas

(Qt/Qo)theo

34

Soil-Water Retention CurveSoil-Water 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)

Vol

um

etri

c W

ater

Con

ten

t (

%)

Pressure Plate Extractor Triaxial ApparatusModified Triaxial Test

35

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)

Co

nd

uc

tiv

ity

(c

m/s

ec)

36

Inverse ModelingInverse Modeling

• Numerical solutions that use finite difference or finite element

procedures are used to back calculate the hydraulic functions using inverse modeling techniques.

• Parameters required for the curve fitting equations are obtained using

optimization techniques.

37

Vadose Zone ModelsVadose Zone ModelsProgram Description Developer Licenser AvailabilityVS2DHI FDM, fluid flow and

energy transportUSGS 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

US Salinity Laboratory, USDA

IGWMC Public domain software

Hydrus-2D 1-D FEM, water US Salinity Laboratory, USDA

IGWMC License required

STOMP FDM, multi-phase and energy transport

Pacific Northwest National Lab. (DOE)

Battelle Memorial Institute Research or Commercial License

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

Public domain software

SUTRA FEM, water and solute or energy transport

USGS USGS

38

Future WorkFuture Work

39

Laboratory ProceduresLaboratory Procedures

• Procedures for multi-step outflow tests that do not require

instrumented samples.

• Measurement of system impedance.

• Measurement of saturated/unsaturated hydraulic conductivity.

40

Data AnalysisData Analysis

• Comparison of hydraulic functions determined from analytical

solution with known system impedance to numerical modeling of multi-step

outflow tests using inverse modeling.

• Use of numerical modeling to investigate hysteresis effects.

41

Beyond the LaboratoryBeyond the Laboratory

• Modeling flow in the vadose zone using programs that couple heat

and moisture flow and contaminant transport.

• Investigation of the movement of both liquid and vapor transport

in the vadose zone.