Resilient Modulus Model

2009 TRB Annual Meeting Workshop2009 TRB Annual Meeting WorkshopEnvironmental Effects in the MEEnvironmental Effects in the ME--PDGPDG

January 11, 2009January 11, 2009

Dragos Andrei, Ph.D., P.E.Dragos Andrei, Ph.D., P.E.

1999

Stress Dependent MR ModelA harmonized resilient modulus test A harmonized resilient modulus test method was developed at the University of method was developed at the University of Maryland, under NCHRP project 1Maryland, under NCHRP project 1--28A28A30 30 MMRR tests were performed on 6 materials tests were performed on 6 materials from different sources: FHWAfrom different sources: FHWA--ALF, ALF, MnRoad, USACEMnRoad, USACE--CRREL.CRREL.Data was analyzed with 14 models Data was analyzed with 14 models including the classical including the classical ““kk11--kk22””models, the models, the ““UniversalUniversal”” model and the model and the ““SHRPSHRP--SuperpaveSuperpave”” MMRR modelmodel

“Universal” MR Model

Applicable to both coarseApplicable to both coarse--grained and grained and finefine--grained materialsgrained materialsIncludes both the volumetric and shear Includes both the volumetric and shear components of stresscomponents of stressNormalization by Normalization by ppaa makes makes kkii parameters parameters dimensionlessdimensionless

32

1

k

a

oct

k

aaR pp

pkM ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⋅=

τθ

Variations of the “Universal” Model

Use semiUse semi--log instead of loglog instead of log--log formlog formReplace Replace θθ with (with (θθ –– 33kk66) or ) or σσ33

Replace Replace ττoctoct/p/paa with (with (ττoctoct/p/paa + 1) or + 1) or ((σσcyccyc/p/paa+1)+1)Replace Replace ττoctoct/p/paa with (with (ττoctoct/p/paa + + kk77), where ), where kk77>1>1

32

76

13

k

a

oct

k

aaR k

ppkpkM ⎟⎟

⎠

⎞⎜⎜⎝

⎛+⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⋅⋅=

τθ

Key Findings of the 1-28A Study

Models including both Models including both θθ and and ττoctoct were were clearly superior to the classical clearly superior to the classical kk11--kk22modelsmodelsLogLog--log models were more accurate than log models were more accurate than the corresponding semithe corresponding semi--log modelslog modelsModels using Models using θθ and and ττoctoct were generally were generally more accurate than those using more accurate than those using σσ33 and and σσcyccyc

The higher the number of The higher the number of kkii parameters parameters ––the better the goodness of fitthe better the goodness of fit

Model Selection for Implementation in ME-PDG

Goodness of fitGoodness of fitComputational stabilityComputational stabilityImplementable in the general framework of Implementable in the general framework of the MEthe ME--PDGPDG

32

11

k

a

oct

k

aaR pp

pkM ⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⋅=

τθ

2000

MR - Moisture Effects

Literature review performed at Arizona Literature review performed at Arizona State University in an effort to quantify the State University in an effort to quantify the effect of changes in moisture and density effect of changes in moisture and density on on MMRR

Data retrieved from published papers:Data retrieved from published papers:Li and Selig, Drumm et al, Jin et al, Jones Li and Selig, Drumm et al, Jin et al, Jones and Witczak, Rada and Witczak, Santha, and Witczak, Rada and Witczak, Santha, CRREL, Muhanna et al.CRREL, Muhanna et al.

Key Findings of ASU StudyMMRR reduces with increased moisture; the reduces with increased moisture; the reduction in modulus is greater for fine reduction in modulus is greater for fine grained materialsgrained materialsRegardless of the model used, a linear Regardless of the model used, a linear relationship is observed when plotting: relationship is observed when plotting: log(log(MMRR)) versus moistureversus moistureSome researchers used Some researchers used SS while others while others preferred preferred wwThe compactive energy (standard or The compactive energy (standard or modified) was not always specifiedmodified) was not always specified

Analysis

Use approach from Li and Selig paper to Use approach from Li and Selig paper to normalize normalize MMRR, , ww and and SS with respect to with respect to values at optimum and to plot values at optimum and to plot changechange in in MMRR versus versus changechange in moisturein moistureUse the literature models to create Use the literature models to create MMRR--moisture data pointsmoisture data pointsDivide materials into:Divide materials into:

CoarseCoarse--Grained and FineGrained and Fine--GrainedGrained

Use sigmoid model form to fit the Use sigmoid model form to fit the ““datadata””

MR - Moisture Model for Coarse-Grained Materials

0

0.5

1

1.5

2

2.5

-70 -60 -50 -40 -30 -20 -10 0 10 20 30(S - Sopt)%

MR/M

Rop

t

Literature Data

Predicted

MR - Moisture Model for Fine-Grained Materials

0.0

0.5

1.0

1.5

2.0

2.5

-70 -60 -50 -40 -30 -20 -10 0 10 20 30(S - Sopt)%

MR/M

Rop

t

Literature Data

Predicted

MR – Moisture Model

MMRR = Resilient Modulus at = Resilient Modulus at SSMMRoptRopt = Resilient modulus at = Resilient modulus at SSoptopt

a, b, ka, b, kmm = Regression parameters= Regression parametersββ = ln= lnee ((--bb//aa) from condition of (0,1) intercept) from condition of (0,1) intercept

( )( )Ropt

SSkEXPaba

R MM optm ⋅= −⋅++−

+β110

MOISTURE ADJUSTMENT FACTOR (FU )

MR = FU *MRopt

a, b, km Values for ME-PDG

CoarseCoarse--Grained:Grained:aa = = --0.31230.3123bb = 0.3 (maximum = 0.3 (maximum MMRR/M/MRoptRopt ratio of 2)ratio of 2)kkmm = 6.8157= 6.8157

FineFine--Grained:Grained:aa = = --0.59340.5934bb = 0.4 (maximum = 0.4 (maximum MMRR/M/MRoptRopt ratio of 2.5)ratio of 2.5)kkmm = 6.1324= 6.1324

MRopt Estimates in the ME-PDG

Several options available:Several options available:USCS ClassificationUSCS ClassificationAASHTO ClassificationAASHTO ClassificationCBRCBRRR--ValueValueAASHTO Structural Layer CoefficientAASHTO Structural Layer CoefficientGradation and Atterberg LimitsGradation and Atterberg Limits

( )( )32

110 11

k

a

oct

k

aa

SSkEXPaba

R pppkM optm

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⋅⋅= −⋅++

−+ τθβ

Combined Effects of Moisture and Stress in ME-PDG

This form was implemented in the METhis form was implemented in the ME--PDG PDG for for ““unfrozenunfrozen”” unbound materialsunbound materialsCalibration/validation of the model with Calibration/validation of the model with laboratory test data was desiredlaboratory test data was desired

MOISTURE ADJUSTMENT FACTOR (FU )

STRESS DEPENDENTMR MODEL

Moisture Variation in Unbound Pavement Layers

Compaction Compaction –– optimum moisture contentoptimum moisture contentWith time With time –– equilibrium moisture contentequilibrium moisture contentSeasonal Seasonal –– variations around equilibriumvariations around equilibriumFreezing Freezing –– soil becomes very stiffsoil becomes very stiffThawing Thawing –– temporary softening below temporary softening below equilibrium stiffnessequilibrium stiffness

FU

?

Freeze-Thaw Effects: Freezing

From Literature:From Literature:MMRR = 2,500,000 psi for non= 2,500,000 psi for non--plastic materialsplastic materialsMMRR = 1,000,000 psi for plastic materials= 1,000,000 psi for plastic materials

Model Form:Model Form:MMRR = = FFFF**MMRoptRopt

FFFF = Adjustment factor for frozen materials= Adjustment factor for frozen materials

2001

Freeze-Thaw Effects: Thawing

Modulus Reduction FactorModulus Reduction Factor0.40 0.40 …… 0.85 as a function of plasticity index and 0.85 as a function of plasticity index and % fines (% fines (wPIwPI))

Recovery PeriodRecovery Period90 90 …… 150 days as a function of 150 days as a function of wPIwPI

Model Form:Model Form:MMRR = = FFRR**MMRoptRopt

FFRR = Adjustment factor for thawing = Adjustment factor for thawing (recovering) materials(recovering) materials

ExampleMinnesota

0.1

1

10

100

08/23/96 12/01/96 03/11/97 06/19/97 09/27/97

Time

Fenv

TROPTIMUM

EQUILIBRIUM

FROZEN

EQUILIBRIUM

RECOVERY

From NODE to LAYER …Time (days)

Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 141 AC23 F F F F F F F F F F F F F F F F F R F R F R F R F R F R BASE4 F F F F F F F F F F F F F F F F F R F R F R F R F R F R

5 F F F F F F F F F F F F F F F R F R F R F R F R F R F R

6 F F F F F F F F F F F F F F F R F R F R F R F R F R F R

7 F F F F F F F F F F F F F F F R F R F R F R F R F R F R8 F F F F F F F F F F F F F F F R F R F R F R F R F R F R

9 F F F F F F F F F F F F F F F R F R F R F R F R F R F R SUBBASE10 F F F F F F F F F F F F F F F R F R F R F R F R F R F R

11 F F F F F F F F F F F F F R F R F R F R F R F R F R F R

12 F F F F F R F R F R F R F R F R F R F R F R F R F R F R

13 F F F R F R F R F R F R F R F R F R F R F R F R F R F R

14 F R F R F R F R F R F R F R F R F R F R F R F U F U F U

15 F R F R F R F R F R F R F R F R F R F R F U F U F U F U16 F R F R F R F R F R F R F R F R F U F U F U F U F U F U

17 F R F R F R F R F R F U F U F U F U F U F U F U F U F U SUBGRADE18 F R F R F U F U F U F U F U F U F U F U F U F U F U F U

19 F U F U F U F U F U F U F U F U F U F U F U F U F U F U

20 F U F U F U F U F U F U F U F U F U F U F U F U F U F U21 F U F U F U F U F U F U F U F U F U F U F U F U F U F U LEGEND:22 F U F U F U F U F U F U F U F U F U F U F U F U F U F U FROZEN23 F U F U F U F U F U F U F U F U F U F U F U F U F U F U RECOVERING24 F U F U F U F U F U F U F U F U F U F U F U F U F U F U UNFROZEN

SPRING ANALOGY

Fenv = Layer Adjustment Factor

hhnodenode = Length between mid= Length between mid--point nodespoint nodeshhtotaltotal = Total height of the considered layer/sublayer= Total height of the considered layer/sublayertttotaltotal = The desired time period (either a two= The desired time period (either a two--week period or a week period or a month period) month period) FFnode,tnode,t = Adjustment factor at a given node and time increment = Adjustment factor at a given node and time increment which could be Fwhich could be FF F , F, FR R , or F, or FUU

Principle: Find Fenv corresponding to an equivalent (composite) modulus that produces the same average displacement over the total thickness of the layer/sublayer for the considered analysis period (1 month or 2 weeks).

∑ ∑= =

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=totalt

t

n

node timenode

node

totaltotalenv

Fh

htF

1 1 ,

Fenv Calculation Example

MMR (layer, analysis period)R (layer, analysis period) = = FFenvenv**MMRoptRopt

All calculations done in EICM !All calculations done in EICM !

Time (days)Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 14

3 50 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 BASE4 50 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 F env = 1.455 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.76 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.77 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.78 50 50 50 50 50 50 50 0.7 0.7 0.7 0.7 0.7 0.7 0.7

9 75 75 75 75 75 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 SUBBASE10 75 75 75 75 75 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 F env = 0.9211 75 75 75 75 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.712 75 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.713 75 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 LEGEND:14 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 1 1 FROZEN15 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 1 1 1 RECOVERING16 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 1 1 1 1 1 UNFROZEN

ADOT MR -Moisture Lab Study

Arizona DOT MaterialsArizona DOT Materials4 base materials4 base materials4 subgrade soils4 subgrade soils

Each material tested at:Each material tested at:3 moisture contents (optimum, soaked and dried)3 moisture contents (optimum, soaked and dried)2 compactive efforts (standard and modified)2 compactive efforts (standard and modified)2 replicates (minimum)2 replicates (minimum)

Total: 96 tests performed using the Total: 96 tests performed using the NCHRP 1NCHRP 1--28A test protocol28A test protocol

2002

Key Findings

Density strongly affects the Density strongly affects the MMRR--SSrelationship and should be added as a relationship and should be added as a predictor to the model based on predictor to the model based on SSWhen gravimetric moisture content was When gravimetric moisture content was used instead, the effect of density was used instead, the effect of density was greatly minimizedgreatly minimizedMR MR –– Moisture models including stress Moisture models including stress dependency (like the one in the MEdependency (like the one in the ME--PDG) PDG) were successfully used to fit the measured were successfully used to fit the measured lab test datalab test data

Phoenix Valley Subgrade (A-2-4, SC), Hot Conditions

1,000

10,000

100,000

1,000,000

0.0 20.0 40.0 60.0 80.0 100.0Degree of Saturation (%)

Res

ilien

t Mod

ulus

(psi

)

Standard Measured

Standard Sigmoid

Modified Measured

Modified Sigmoid

Effect of Density (Compactive Energy)

Using Moisture ContentPhoenix Valley Subgrade (A-2-4, SC), Hot Conditions

1,000

10,000

100,000

1,000,000

0 2 4 6 8 10 12 14 16 18Moisture Content (%)

Res

ilient

Mod

ulus

(psi

)

Standard

Modified

Predicted

PVSG (A-2-4, SC) - MR(w-w opt , θ, τoct) Model

n =142, Se/Sy =0.15, R2 = 0.98

1,000

10,000

100,000

1,000,000

1,000 10,000 100,000 1,000,000

Measured Resilient Modulus (psi)

MR Predicted

Line of Equality

Goodness of Fit – Phoenix Valley Subgrade

GMAB2 (A-1-a, GW) - MR(w-w opt , θ, τoct) Model

n = 254, R2 = 0.90, Se/Sy = 0.32

1,000

10,000

100,000

1,000,000

1,000 10,000 100,000 1,000,000

Measured Resilient Modulus (psi)

MR Predicted

Line of Equality

Goodness of Fit – Gray Mountain Base

Fu for ADOT Base MaterialsGrey Mountain Base (A-1-a, GW)

0.1

1

10

100

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2wi - wopt (%)

MR/M

Rop

t

Fu for ADOT A-2/SC Subgrade Soils

All A-2 Subgrades, M R - Moisture Model

n = 36, R2 = 0.96, Se/Sy = 0.20

0.1

1

10

100

-12 -10 -8 -6 -4 -2 0 2 4 6wi - wopt (%)

PVSG (A-2-4), PI=9.9, p200=21.6

FCSG (A-2-6), PI=17.2, p200=31.5

SCSG (A-2-4), PI=12.1, p200=25

Predicted

ADOT Database of MR Model Parameters

Material ID AASHTO USCS a b k w β k 1 k 2 k 3 w opt std

%

Phoenix Valley Subgrade A-2-4 SC 0.24 41.88 67.255 0.974 467 0.358 -0.686 11.3

Yuma Area Subgrade A-1-a GP 1.00 94.01 82.757 8.714 1,468 0.838 -0.888 11.0

Flagstaff Area Subgrade A-2-6 SC 0.31 10.93 74.489 0.722 634 0.187 -0.855 19.0

Sun City Subgrade A-2-6 SC 0.13 19.22 53.166 0.360 747 0.224 -0.104 11.3

Grey Mountain Base A-1-a GW 0.00 2096.40 2.559 -0.539 1,423 0.758 -0.288 6.7

Salt River Base A-1-a SP 0.59 2096.41 22.401 2.666 1,170 0.919 -0.572 6.9

Globe Area Base A-1-a SP-SM 0.68 2096.44 35.787 2.981 1,032 0.830 -0.307 6.7

Precott Area Base A-1-a SP-SM 1.00 2096.45 144.223 8.711 1,092 0.784 -0.236 6.3

ADOT A-1-a AB2 Base Materials A-1-a SP-SM 0.60 2096.65 24.221 2.721 1,075 0.841 -0.305 6.7

ADOT A-2 Subgrade Materials A-2 SC 0.22 21.79 58.965 0.699 - - - -

Final Remarks

Moisture, density and state of stress all Moisture, density and state of stress all affect affect MMRR and should be included in a Mand should be included in a M--E E predictive methodologypredictive methodologyChanges in moisture will trigger Changes in moisture will trigger significant changes in significant changes in MMRR, especially for , especially for finefine--grained materialsgrained materialsCoarseCoarse--grained materials are especially grained materials are especially affected by changes in the state of stress affected by changes in the state of stress

Final Remarks (Cont’d)

The MRThe MR--Moisture material models Moisture material models implemented in the MEimplemented in the ME--PDG were verified PDG were verified through a limited laboratory testing study through a limited laboratory testing study performed at ASUperformed at ASUAgencies could engage in similar studies Agencies could engage in similar studies to develop a database of material to develop a database of material properties for typical unbound pavement properties for typical unbound pavement materials used on highway construction materials used on highway construction projects.projects.