The Resilient Modulus TestThe Resilient Modulus TestProf. Lynne H. Irwin, DirectorProf. Lynne H. Irwin, DirectorCornell Local Roads ProgramCornell Local Roads Program

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ObjectivesObjectivesReview materials behavior principlesReview materials behavior principlesOverview of AASHTO T 307 Overview of AASHTO T 307 repeatedrepeated--load triaxial test procedure load triaxial test procedure and related issuesand related issuesBrief overview of new FHWA study of Brief overview of new FHWA study of lab versus field properties of lab versus field properties of pavement materialspavement materialsDiscuss how the two projects can Discuss how the two projects can complement each othercomplement each other

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A little quiz A little quiz How many agencies present How many agencies present occasionally or routinely perform the occasionally or routinely perform the laboratory repeatedlaboratory repeated--load triaxial testload triaxial test Occasionally?Occasionally? Routinely?Routinely?

How many people here personally How many people here personally run the test?run the test? How long have you been doing so?How long have you been doing so?

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Materials BehaviorMaterials Behavior

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A couple of definitionsA couple of definitionsStressStress

Stress = Load / AreaStress = Load / Area

StrainStrainStrain = Strain = Deformation / Original lengthDeformation / Original length

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StressStress--strain curvestrain curve

StrainStrain

S

t

r

e

s

s

S

t

r

e

s

s

TangentTangent ChordChord

~ 10% strain in foundation ~ 10% strain in foundation geotechnicsgeotechnics

~ 0.1% strain in pavement ~ 0.1% strain in pavement geotechnicsgeotechnics

Types of materials responsesTypes of materials responsesElasticElastic

ElastoElasto--PlasticPlastic

ViscousViscous

ViscoVisco--elasticelastic

Load Released

Load Applied

D

e

f

o

r

m

a

t

i

o

n

Time

UnrecoverableUnrecoverable

RecoverableRecoverableYield Point

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ElasticElastic stressstress--strain behaviorstrain behavior

StrainStrain

S

t

r

e

s

s

S

t

r

e

s

s

Strain is fully recoveredStrain is fully recovered

>>>>

LoadingLoading

UnloadingUnloading

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Linear Linear elasticelastic behaviorbehavior

StrainStrain

S

t

r

e

s

s

S

t

r

e

s

s

Strain is fully recoveredStrain is fully recovered

>>>>

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Hooke's lawHooke's lawStress is Stress is linearlylinearlyproportional to proportional to strainstrainE is Young's E is Young's modulus of modulus of elasticityelasticityMMrr is the resilient is the resilient modulusmodulus MMrr is often interchanged is often interchanged

with Ewith E

zz E =S

t

r

e

s

s

S

t

r

e

s

s

StrainStrain

E or ME or Mrr

1010

"Resilient" behavior is like "Resilient" behavior is like elastic behavior except there elastic behavior except there is a is a tinytiny amount of amount of permanent strain remaining permanent strain remaining after each load cycle. after each load cycle.

Hence the term resilient Hence the term resilient modulus, as opposed to modulus, as opposed to elastic modulus.elastic modulus.

1111

Poisson's ratioPoisson's ratioWhen a material is When a material is compressed it expands compressed it expands laterallylaterally is Poisson's ratio (is Poisson's ratio ( is is also usedalso used) ) The strains are of The strains are of opposite sign, so a opposite sign, so a negative is inserted to negative is inserted to keep keep a positive a positive numbernumber = 0.50 for an = 0.50 for an incompressible material incompressible material (no volume change)(no volume change)

zx - =z

x

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Nonlinear Nonlinear elasticelastic behaviorbehavior

Strain is fully recoveredStrain is fully recovered StrainStrain

S

t

r

e

s

s

S

t

r

e

s

s

>>>>

MMrr

MMrr

MMrr is a function of stress levelis a function of stress level

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The triaxial test cellThe triaxial test cellEncloses the test specimenEncloses the test specimenPermits loading the specimenPermits loading the specimenProvides for measurement of Provides for measurement of specimen responsespecimen response

1414

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Key elements of the triaxial cellKey elements of the triaxial cellJacketed cylindrical test specimen with Jacketed cylindrical test specimen with top/bottom end caps (platens)top/bottom end caps (platens)Cell wall and support rodsCell wall and support rodsAbility to apply and measure the cell Ability to apply and measure the cell pressurepressureAbility to apply and measure the axial loadAbility to apply and measure the axial loadAbility to measure the specimen response Ability to measure the specimen response to load (deformation to load (deformation -- axially and radially)axially and radially)Ability to saturate specimen and measure Ability to saturate specimen and measure internal pressureinternal pressure

XXYY

ZZ

33

33

11Principal stressesPrincipal stresses

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The Resilient Modulus TestThe Resilient Modulus TestAASHTO T 307AASHTO T 307

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AASHTO T 307 materials typesAASHTO T 307 materials typesType 1 (coarseType 1 (coarse--grained)grained) Unbound bases, subbases and subgradesUnbound bases, subbases and subgrades

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Repeated cyclic loadingRepeated cyclic loadingA sequence of pressures are usedA sequence of pressures are usedBase/subbase materialsBase/subbase materials 33--66--9; 59; 5--1010--15; 1015; 10--2020--30 psi30 psi Sequence varies with cell pressureSequence varies with cell pressure

Subgrade materialsSubgrade materials 22--44--66--88--10 psi10 psi Same sequence for all cell pressuresSame sequence for all cell pressures

0.1 second pulse duration, 0.9 to 3.0 0.1 second pulse duration, 0.9 to 3.0 sec rest periodsec rest period

2020

Test procedureTest procedure500 to 1000 cycles conditioning at 500 to 1000 cycles conditioning at start of test (first sequence)start of test (first sequence)100 cycles at each subsequent stress 100 cycles at each subsequent stress level level Measure and record specimen Measure and record specimen response for the last four cycles of response for the last four cycles of each sequenceeach sequenceTerminate test if >5% permanent Terminate test if >5% permanent strain occursstrain occurs

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Permanent Deformation

(Recoverable Deformation)

2222

Resilient modulusResilient modulusCyclic stress = Cyclic stress = Repeated Load / Specimen AreaRepeated Load / Specimen Area

Recoverable strain =Recoverable strain =Total Vertical Deformation / initial Total Vertical Deformation / initial

Gage LengthGage Length

2323

Resilient modulusResilient modulus

strain eRecoverablstressCyclic Mr =

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Issues in T 307Issues in T 307Double plunger compaction methodDouble plunger compaction methodInitial confining stress ratio effectInitial confining stress ratio effectConstitutive modelsConstitutive modelsPulse duration too fastPulse duration too fastProcedure needs a good editProcedure needs a good edit

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Double plunger methodDouble plunger method(Annex 3)(Annex 3)

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Double plunger methodDouble plunger method

2727

Density gradient (Annex 5)Density gradient (Annex 5)

2828

Double plunger methodDouble plunger method

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Double plunger methodDouble plunger method

3030

Kneading compactor method Kneading compactor method (Annex 4)(Annex 4)

3131

Initial confining stress ratio effectInitial confining stress ratio effectConfining stress ratio =Confining stress ratio =

kkcc = = 11 / / 33Stress condition before cyclic loadingStress condition before cyclic loading

In AASHTO T 307In AASHTO T 307kkcc = 1.05 to 1.1= 1.05 to 1.1Under a pavement Under a pavement 0.2 < k0.2 < kcc < 2.0< 2.0Research has shown Research has shown that Mthat Mrr (k(kcc))--0.70.7

11

33

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StressStress--dependent materialsdependent materialsFor many years we have believedFor many years we have believedE = kE = k11 Stress Stress kk22which is a logwhich is a log--log modellog model[ Log E = log k[ Log E = log k11 + k+ k22 Log Stress ]Log Stress ]

Log kLog k11

kk22

Log ELog E

Log StressLog Stress

3333

Typical stress parametersTypical stress parameters

31321 2 Stress Bulk +=++=:

31d Stress Deviator =:

213

232

221oct )()()(3

1

:Stress Shear Octahedral

++=

3 Stress Confining =:

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ProblemProblemPavement under load is in bending, Pavement under load is in bending, thus stresses can be positive thus stresses can be positive (compression) or negative (tension)(compression) or negative (tension)Bulk stress is often negative at Bulk stress is often negative at bottom of upper layers (surface and bottom of upper layers (surface and base courses)base courses)

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Tensile zones in Tensile zones in pavement layerspavement layers

Tensile zones

Surface

Base

Subgrade

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SolutionSolutionUse a semiUse a semi--log modellog model

E = kE = k11 exp(kexp(k22 * Stress)* Stress)

[ Log E = log k[ Log E = log k11 + k+ k2 2 * Stress]* Stress]

Log kLog k11

kk22

Log ELog E

StressStress

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Comparison of modelsComparison of models

050

100150200250300350400

-50 50 150 250 350

Bulk Stress, kPa

M

o

d

u

l

u

s

,

M

P

a

Log-log Model Semi-log Model Test Data

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Comparison of modelsComparison of modelsResults of regression with the data:Results of regression with the data:

0.96)r model, log-(log

4181E2

0.779

==

0.95)r model, log-(semi

) 00567.0-(exp8.214E2 =

=

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Load pulse durationLoad pulse duration0.1 second pulse originally selected for 0.1 second pulse originally selected for asphalt surface layer testingasphalt surface layer testing Flexural fatigue testFlexural fatigue test Simulates vehicle moving about 30 mphSimulates vehicle moving about 30 mph

Stress and strain from moving wheel is Stress and strain from moving wheel is more broadly distributed at the depth of more broadly distributed at the depth of base/subbase and subgradebase/subbase and subgrade0.2 sec (base course) to 0.25 sec 0.2 sec (base course) to 0.25 sec ((subgradesubgrade) pulse duration would be more ) pulse duration would be more realisticrealistic

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Relationships Between Relationships Between LaboratoryLaboratory--Measured and Measured and FieldField--Derived Properties of Derived Properties of

Pavement LayersPavement LayersDTFH61DTFH61--0808--RR--0003200032

4141

Research teamsResearch teamsMichigan State UniversityMichigan State University Dr. Dr. KarimKarim ChattiChatti Dr. M. Dr. M. EminEmin KutayKutay, P.E., P.E. Asphalt concrete characterizationAsphalt concrete characterization

Cornell UniversityCornell University Dr. Lynne H. Irwin, P.E.Dr. Lynne H. Irwin, P.E. Dr. David P. Orr, P.E.Dr. David P. Orr, P.E. Unbound materials characterizationUnbound materials characterization

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ObjectivesObjectivesDevelop a fundamental understanding of Develop a fundamental understanding of the factors underlying observed the factors underlying observed differences between laboratorydifferences between laboratory--measured measured and fieldand field--derived properties of pavement derived properties of pavement layerslayersDevelop improved methods and/or Develop improved methods and/or relationships that will allow both to be relationships that will allow both to be used interchangeably for design and used interchangeably for design and performing analysesperforming analyses

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GoalGoalThis project will be considered This project will be considered successful if it yields either successful if it yields either relationships enabling the relationships enabling the interchangeable use of laboratoryinterchangeable use of laboratory--resilient modulus test data and resilient modulus test data and backcalculated values, or a clear backcalculated values, or a clear explanation of why it was not explanation of why it was not possible to derive such relationshipspossible to derive such relationships

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OutputsOutputsThe expected outputs from this The expected outputs from this research may take one of two research may take one of two posssibleposssible forms. (1) Develop forms. (1) Develop meaningful relationships between meaningful relationships between laboratorylaboratory--measured and fieldmeasured and field--derived properties of pavement derived properties of pavement materials, based upon the materials, based upon the fundamental materials properties fundamental materials properties that are that are obtanedobtaned from each from each approach. Or ... approach. Or ...

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OutputsOutputs(2) If meaningful relationships (2) If meaningful relationships cannot be developed, conduct further cannot be developed, conduct further investigation as needed to explain investigation as needed to explain reasons underlying the discrepancies reasons underlying the discrepancies between laboratory and field moduli, between laboratory and field moduli, and provide a clear explanation of and provide a clear explanation of the reasons that relationships could the reasons that relationships could not be derivednot be derived