Simple Techniques for Estimating Simple Techniques for Estimating the Shear Strength and the Coefficient of Permeability the Shear Strength and the Coefficient of Permeability

of Unsaturated Soilsof Unsaturated Soils

ByBySai K. VanapalliSai K. Vanapalli

Lakehead University, Thunder BayLakehead University, Thunder BayCanadaCanada

Unsaturated Soil Engineering: Applications in PavementsUnsaturated Soil Engineering: Applications in Pavements

Maplewood, Minnesota: 55th th August, 2002August, 2002

Today’s PresentationToday’s Presentation

EstablishEstablish: Need for unsaturated soil mechanics : Need for unsaturated soil mechanics in pavement designsin pavement designs

TheoryTheory: Simple extensions of classical soil : Simple extensions of classical soil mechanicsmechanics

Simple Techniques/Procedures for Interpreting Simple Techniques/Procedures for Interpreting the Engineering Behavior of Unsaturated Soilsthe Engineering Behavior of Unsaturated Soils: : Using conventional soil mechanics lab facilitiesUsing conventional soil mechanics lab facilities

Pavement Design ProceduresPavement Design Procedures●● Present /conventional proceduresPresent /conventional procedures: Experience and : Experience and

andand Empirical proceduresEmpirical procedures

●● Rational procedureRational procedure: Take into account of the influence : Take into account of the influence of wetof wet--dry and freezedry and freeze--thaw cycles thaw cycles (Use principles of (Use principles of unsaturated soil mechanics)unsaturated soil mechanics)

●● Rational ApproachRational Approach: Use stress state variable approach : Use stress state variable approach (Two stress state variables: Net normal stress, ((Two stress state variables: Net normal stress, (σσ –– uuaa) ) and matric suction, (and matric suction, (uuaa –– uuww))))

●● Key engineering propertiesKey engineering properties: Shear strength and the : Shear strength and the Coefficient of permeabilityCoefficient of permeability

Unsaturated Soils TestingUnsaturated Soils TestingShear Strength of Shear Strength of Unsaturated SoilsUnsaturated Soils

Coefficient of Permeability Coefficient of Permeability of Unsaturated Soilsof Unsaturated Soils

UnsaturatedUnsaturated Soils TestingSoils Testing

Need extensive laboratory facilitiesNeed extensive laboratory facilities

Time consuming and expensiveTime consuming and expensive

Need simple techniquesNeed simple techniques: for practical applications : for practical applications such as the design of pavementssuch as the design of pavements

FocusFocus: Estimating the shear strength and the : Estimating the shear strength and the coefficient of permeability of unsaturated soilscoefficient of permeability of unsaturated soils

Key informationKey information: Soil: Soil--Water Characteristic Curve Water Characteristic Curve (SWCC)(SWCC)

Soil-Water Characteristic Curve (SWCC)A useful tool in the interpretation of USM

Degree of saturation

(%)

Soil suction (kPa)

100

80

60

20

01 10 100 1000 10000 100000 1000000

Residual air content

Capillarysaturation

zoneAir entry

value

Desaturationzone

Wetting curve (Adsorption)Drying curve (Desorption)

Residual conditions

Measurement of the SWCCMeasurement of the SWCC

Tempe Cell/ Pressure plateTempe Cell/ Pressure plate(liquid phase flow)(liquid phase flow)

Osmotic DesiccatorsOsmotic Desiccators(Vapor phase flow)(Vapor phase flow)

Small Small -- Scale Scale Beckman Beckman Centrifuge Centrifuge

J6 J6 –– HCHC(Simple and fast technique (Simple and fast technique

for SWCC measurement)for SWCC measurement)

Saturated Soil Specimens and Saturated Soil Specimens and Saturated Ceramic Cylinders in the Saturated Ceramic Cylinders in the

Specimen HoldersSpecimen Holders

Soil Specimen Holders Soil Specimen Holders Ready to CentrifugeReady to Centrifuge

Indian Head Till Test ResultsIndian Head Till Test ResultsG

ravi

met

ric w

ater

co

nten

t, %

0

8

16

1 10 100 1000Matric suction (kPa)

Centrifuge curveTempe cell curve

Centrifuge test, ρd = 1.77 Mg/m3, w = 19.2%Tempe cell test, ρd = 1.77 Mg/m3, w = 19%

24

Time Required to Obtain a SWCCTime Required to Obtain a SWCC

Test methodused

Silt Regina ClayIndian Head Till

Centrifuge time (days) 0.5 1 2

Tempe celltime (days) 14 42 112

Pore Water DistributionPore Water DistributionShear strength and Volume Change: Related to the interphase contact area controlling stress transfer

Coefficient of permeability : Related to the continuity and tortuosity of liquid phase

SS = 100= 100 1 > S > S1 > S > Srr S = SS = Srr

Shear Strength of Shear Strength of Unsaturated SoilsUnsaturated Soils

Relationship Between SWCC and Relationship Between SWCC and Shear Strength versus Matric SuctionShear Strength versus Matric Suction

φ′ clayey silt

φ′ sand

SandClayey silt

c′

Water contentw (%)

Shear strength

τ

Commencement of desaturation

Matric suction (kPa)

Matric suction (kPa)

Unsaturated Soils Shear Strength Unsaturated Soils Shear Strength Prediction Prediction (Vanapalli et al. 1996)(Vanapalli et al. 1996)

( ) ( )[ ] ( ) φψφστ tantan wa

κan uuuc −Θ+−+= ′′ ′

where: Θ(ψ) = θ(ψ)/θsθ(ψ) = volumetric water content at any suction

κ= fitting parameter to account for non-linearity between area and volume representation of the amount of water contributing to the shear strength

0

250

500

750

1000

0 2500 5000 7500 10000 12500 15000

Soil Suction, kPa

Shea

r Str

engt

h, k

Pa

Red silty clay(σ - ua) = 120 kPa

Comparison between Predicted and Comparison between Predicted and Measured Shear StrengthsMeasured Shear Strengths(Vanapalli and Fredlund, 2000)(Vanapalli and Fredlund, 2000)

Relationship between Relationship between κ κ vs Ivs Ipp(Vanapalli and Fredlund, 2000)(Vanapalli and Fredlund, 2000)

0

1

2

3

4

0 10 20 30 40

Plasticity Index, Ip

Fitti

ngpa

ram

eter

, κ

• Useful relationship to estimate the fitting parameter value, κ

PrePre--shearshear andand PostPost--shearshear SWCC data SWCC data fromfromthethe Triaxial Triaxial ShearShear Test Test ResultsResults on Dhanauri on Dhanauri clayclay specimensspecimens ((derivedderived fromfrom SatijaSatija 1978)1978)

40

60

80

100

1 10 100 1000 10000

Matric suction, (ua -uw), kPa

Deg

ree

of S

atur

atio

n, S

, (%

)

Pre-Shear SWCC

Post-Shear SWCC

Measured and Predicted Shear Strength of Measured and Predicted Shear Strength of Dhanauri clay for Low Suction Range (Using Dhanauri clay for Low Suction Range (Using Pre and PostPre and Post--shear SWCC)shear SWCC)

0

100

200

0 100 200 300 400 500

Matric Suction (ua-uw), kPa

Shea

r Str

engt

h du

e to

Suc

tion,

kP

a

Predicted from post-shear SWCC

Predicted from pre-shear SWCC

Measured and Predicted Shear Strength Measured and Predicted Shear Strength of Dhanauri clay for High Suction Range of Dhanauri clay for High Suction Range (Using Pre and Post(Using Pre and Post--shear SWCC)shear SWCC)

0

200

400

0 500 1000 1500

Matric suction (ua - uw), kPa

Shea

r Str

engt

h du

e to

Suc

tion,

kP

a

Predicted from post-shear SWCC

Predicted from pre-shear SWCC

Simple Test ProceduresSimple Test Procedures

Conventional test proceduresConventional test procedures: Unconfined : Unconfined compression test and Direct shear testscompression test and Direct shear tests

Estimate of soil suction from simple tests?Estimate of soil suction from simple tests?Based on indirection estimation: Based on indirection estimation:

–– Determine the degree of saturation (from Determine the degree of saturation (from volumevolume--mass properties)mass properties)

–– Use SWCC information and estimate suction Use SWCC information and estimate suction for corresponding degree of saturationfor corresponding degree of saturation

Estimation of Suction from the SWCCEstimation of Suction from the SWCC

0

20

40

60

80

100

0.01 1 100 10000 1000000Suction, Ψ (kPa)

Deg

ree

of S

atur

atio

n, S

(%)

Shear Strength Interpretation from Shear Strength Interpretation from Unconfined Compression Test ResultsUnconfined Compression Test Results

(53(53rdrdCanadian Canadian GeotechGeotech Conf: Vanapalli et al. 2000)Conf: Vanapalli et al. 2000)Specimen preparation for a Specimen preparation for a silt specimen (silt specimen (IIpp = 8)= 8)

–– statically compacted statically compacted saturated specimens saturated specimens prepared using prepared using constant volume constant volume moldsmolds

–– air dried for varying air dried for varying time intervals so that time intervals so that fully saturated to fully fully saturated to fully dry samples would be dry samples would be testedtested

–– suctions estimated suctions estimated from SWCCfrom SWCC

Unconfined Compression TestUnconfined Compression TestTestingTesting

–– Quickly loaded at a Quickly loaded at a strain rate of approx. strain rate of approx. 1.2 mm/min1.2 mm/min

–– stress readings taken stress readings taken at every 0.2 mm at every 0.2 mm interval travelinterval travel

AssumptionsAssumptions–– Suction in the Suction in the

specimen does not specimen does not change during change during loadingloading

–– Interpretation based Interpretation based on initial suction on initial suction values in the values in the specimensspecimens

Predicted and Measured Unconfined Predicted and Measured Unconfined Compressive Strengths (Silt)Compressive Strengths (Silt)

1

10

100

1000

10000

0.1 1 10 100 1000 10000 100000

Soil suction, kPa

Unc

onfin

ed

com

pres

sive

str

engt

h, k

Pa

Shear strength prediction using fitting parameter, κ =

1.8

*Symbols are experimental results

Determination of Shear Strength of Determination of Shear Strength of Compacted Till Using Conventional Compacted Till Using Conventional Direct Shear Apparatus (Vanapalli & Lane Direct Shear Apparatus (Vanapalli & Lane 2002)2002)

Shear strength of Indian Shear strength of Indian Head tillHead till

–– Three different compaction Three different compaction water contentswater contents

–– Provide comparisons Provide comparisons between CDST and MDSTbetween CDST and MDST

AssumptionAssumption

–– Suction in the specimen Suction in the specimen does not change during does not change during loadingloading

Compacted Soil Specimen Extraction Compacted Soil Specimen Extraction from Constant Volume Mouldfrom Constant Volume Mould

Soil Specimen Saturation ProcedureSoil Specimen Saturation Procedure

Soil Specimen & CutterSoil Specimen & Cutter

Comparison between Shear Strength Test Results Using MDST and CDST (Vanapalli & Lane 2002)

0

25

50

75

100

125

150

0 100 200 300 400 500Matric Suction (kPa)

Shea

r Stre

ngth

Con

tribu

tion

due

to S

uctio

n (k

Pa)

Modified Direct Shear Test Results Best-Fit Curve

Coefficient of Permeability of Coefficient of Permeability of Unsaturated SoilsUnsaturated Soils

Relationship Between the Relationship Between the SWCC and Coefficient of PermeabilitySWCC and Coefficient of Permeability

Permeability functions

Clayey silt

Sand

1 10 100 1000

1 10 100 1000

Matric suction (kPa)

Matric suction (kPa)

10

20

3040

50

0

Watercontentw (%)

10-10

10-9

10-8

10-7

10-6

10-5

Coefficient of permeability

kw (m/s)

Sand

Clayey silt

Predicting the Unsaturated Predicting the Unsaturated Coefficient of Permeability of SoilsCoefficient of Permeability of Soils

Several procedures available in the literatureSeveral procedures available in the literature

Key informationKey information: SWCC and : SWCC and kksatsat

Several parameters influence the SWCC and the Several parameters influence the SWCC and the kkunsatunsat ::-- applied stressapplied stress-- compaction energy compaction energy -- soil structure (function of initial soil structure (function of initial

compaction water content) compaction water content) (important (important particularly in fineparticularly in fine--grained soils)grained soils)

Normalization Technique for Normalization Technique for Estimating the Coefficient of Estimating the Coefficient of Permeability of Unsaturated SoilsPermeability of Unsaturated Soils

Time consuming and expensive to measure Time consuming and expensive to measure SWCC taking into account the influence of SWCC taking into account the influence of parameters such as the stress state and soil parameters such as the stress state and soil structurestructure

Useful to the practicing engineers if a simple Useful to the practicing engineers if a simple technique can be proposed.technique can be proposed.

Relative or the normalized coefficient of permeability, krel = kunsat/ksat

Comparison of krel and S for a Typical Sand and Clay Loam

0.11.0 Degree of Saturation1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

krel

Sand

Clay Loam

Experimentaldata points

0.11.0 (Degree of Saturation)1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00k r

el

Sandγ = 0.70Clay Loamγ = 1.40

γ

krel versus S Using Different γ Values

• Unique trend line for both the soils: Sand and Clay Loam throughthe use of different fitting parameter, γ values

krel versus Sγ for Columbia Sandy Loam

0.11.0

(Degree of Saturation)

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

k rel

PredictedExperimental

γ

Columbia Sandy LoamBrooks & Corey, 1964

Ip = 5%

krel versus Sγ for Touchet Silt Loam

0.11.0(Degree of Saturation)

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

krel

PredictedExperimental

γ

Touchet Silt LoamBrooks & Corey, 1964

Ip = 6%*

krel versus Sγ for Yolo Light Clay

0.11.0

(Degree of Saturation)

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

krel

PredictedExperimental

γ

Yolo Light ClayMoore, 1939

Influence of Stress State on the krel versus Sγ Relationship (Silt)

0.11.0(Degree of Saturation)

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

k rel

0 kPa

25 kPa

50 kPa

100 kPa

200 kPa

γ

SiltHuang, 1994

Ip = 5.6%

kkrelrel versus versus SSγγ for soils (Using Brooks & for soils (Using Brooks & Corey 1964 Results)Corey 1964 Results)

0.11.0Adjusted Degree of Saturation, Sγ

Rel

ativ

e Pe

rmea

bilit

y, k

rel

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00Touchet Silt Loam (0.85)Fragmented Mixture (0.75)Volcanic Sand (0.70)Fine Sand (0.60)Normalizing Function

kkrelrel versus versus SSγγ wetting & drying for wetting & drying for London Clay (London Clay (CroneyCroney & Coleman, & Coleman, 1954)1954)

0.11.0Adjusted Degree of Saturation, Sγ

Rel

ativ

e Pe

rmea

bilit

y, k

rel

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00Drying (1.55)

Wetting (1.90)

NormalizingFunction

The Relationship Between the krel versus Sγ

0.11.0(Degree of Saturation)γ

1.E-071.E-061.E-051.E-041.E-031.E-021.E-011.E+00

k rel

where:krel = kunsat/ksat

γ9.7Skrel ≈

Relationship between Fitting Relationship between Fitting Parameter Parameter γγ and Plasticity Index, and Plasticity Index, IIpp

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0% 10% 20% 30% 40% 50% 60%

Plasticity Index, Ip (%)

Fitti

ng P

aram

eter

, γ

Estimation of Unsaturated Estimation of Unsaturated Coefficient of PermeabilityCoefficient of Permeability

• The coefficient of permeability can be estimated using the simple function.

• Required information: Saturated coefficient of permeability, ksat, Water content, w or the degree of saturation, S, and and the plasticity index, Ip.

• More studies are in progress to test the validity and the limitations of the proposed simple function.

γ9.7Skrel ≈

SummarySummary• SWCC can be used as a tool to propose simple

estimation techniques for interpreting the engineering behavior of unsaturated soils.

• SWCC can be measured using centrifuge techniquesreliably in a relatively shorter period of time compared to conventional procedures.

• The engineering properties of unsaturated of soils can be estimated using simple techniques with the aid of conventional experimental results.

• These studies are useful to extend the principles of unsaturated soils into engineering practice such as the design of pavements

Thank you,

☺Sai VanapalliSai Vanapalli

August 5, 2002August 5, 2002