improving mechanistic-empirical models for predicting hma ... · improving mechanistic-empirical...

Improving MechanisticImproving Mechanistic--Empirical Models Empirical Models for Predicting HMA Ruttingfor Predicting HMA Rutting

Charles SchwartzCharles SchwartzUniversity of MarylandUniversity of Maryland

Pavement Performance Prediction Symposium 2006, Laramie WY

NCHRP 9-30A

“Calibration of Rutting Models for HMA Structural and Mix Design “

• PI: Harold Von Quintus/Applied Research Associates

• Co-PIs:Charles Schwartz/University of MarylandRamon Bonaquist/Advanced Asphalt Technologies

• Other subcontractors:Burns Denton Cooley, Inc.North Carolina State University

Primary Project Objectives

“Recommend revisions to the HMA rut depth prediction model in the M-E PDG developed in NCHRP Project 1-37A”

Enhancements to existing HMA rutting model

Investigation of alternative models

Evaluation via calibration and validation against field sections using measuredmaterial properties

Secondary Project Objectives

• Compile laboratory-measured material property values for select full-scale pavement sections

• Develop a database tailored to calibration and validation of M-E distress prediction models

• Support the continuing advance toward more fully mechanistic performance prediction models

Motivation for Project

• Perceived deficiencies in current M-E model for HMA rutting:

Inadequate measured (“level 1”) material properties for LTPP calibration sectionsNo layer properties related to permanent deformation resistance of mixtureCounterintuitive variations of permanent deformations with depthNo robust basis for apportioning measured surface rutting to various layers

00.20.40.60.8

11.21.41.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Measured Rut Depth, inches

Pred

icte

d R

ut D

epth

(In

put L

evel

3),

inch

es

NCAT WesTrack Line of EqualityMnRoads FHWA-ALF

00.20.40.60.8

11.21.41.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Pred

icte

d R

ut D

epth

(In

put L

evel

3),

inch

es

NCAT WesTrack Line of EqualityMnRoads FHWA-ALF

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Pred

icte

d R

ut D

epth

(Inp

ut

Leve

l 1),

inch

es

NCAT WesTrack FHWA-ALF Line of Equality MnRoads

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Pred

icte

d R

ut D

epth

(Inp

ut

Leve

l 1),

inch

es

NCAT WesTrack FHWA-ALF Line of Equality MnRoads

Level 3 E* Inputs

Level 1 E* Inputs

NCHRP 9-30(001)

Phase I: Workshop—Objectives

• Identify alternate rut models for evaluation

• Develop guidance on two key issues:Maximum allowable prediction errorDesign criterion/limit for HMA rutting

• Identify problem statements for future workShort term (HMA structural, mix design; performance based specifications)Long term (more mechanistic approaches)

23 participants over 2 days

Phase II: Database Design Review

Major Data Areas• General project information• Pavement structure• Traffic• Climate• Material properties• Performance (load-related cracking,

transverse cracking, rutting, roughness)

M-E_DPM Database

M-E_DPM vs. LTPP

• Simpler table structuresNo need to track complex pavement histories, e.g.

• More emphasis on material propertiesHighly flexible, extensible definition of material property data fields

• LTPP data imported as appropriate for GPS/SPS sections

TrafficPerformance

• Focus: model calibration/validation

+ links to test data files

Current Database Population

1941

96

SPSGPSTest Tracks

1941

96

SPSGPSTest Tracks

291 sections total

SPS Sections

47

85

30

17 9 6SPS-1SPS-5SPS-6SPS-9JSPS-9NSPS-9O

47

85

30

17 9 6SPS-1SPS-5SPS-6SPS-9JSPS-9NSPS-9O

ALF/Test Tracks

12

11

9

922

4

9

20 MnRoadNCATALF (1/2)LA ALFWesTrackNevadaMS I55CAL/APT

12

11

9

922

4

9

20 MnRoadNCATALF (1/2)LA ALFWesTrackNevadaMS I55CAL/APT

Phase III: Execute Experimental Plan

• Final experiment matrix

• Field investigations/sample collection

• Laboratory testingPart A (intensive testing of few sections)Part B (routine testing of all sections)

• Database population

• Model calibration/validation/evaluationModel refinement/enhancement

Experimental Plan Matrix

Identified Sections

Models Considered

• “Mostly” empiricalWorld BankBaladi

• Other Mechanistic-EmpiricalPermanent axial strain models

LeahyAsphalt InstituteVESYSVerstraetenUzan

Permanent shear strain modelsWestrack

• Enhanced NCHRP 1-37ANCHRP 1-40A+NCHRP 1-40B

Models to be Evaluated

• Current model (NCHRP 1-37A)New calibrations from NCHRP 1-40D

• Westrack

• NCHRP 1-40BModified RLPD characteristics based on volumetrics, gradation

• Enhanced NCHRP 1-37A

Westrack M-E based on γp

γp = permanent shear strain at a depth of 2 inches below the surface τ = mechanistically-determined elastic shear stress at z = 2 inγe = mechanistically-determined elastic shear strain at z = 2 ina, b, c = material constants, obtained from SST-CH

ce

bp Nae γγ τ=

Time-hardening principle:

[ ],1 1 1c

p a Nγ = Δ1

, 1,

c

cp t

p t t tt

a Na

γγ −

⎡ ⎤⎛ ⎞⎢ ⎥= + Δ⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥⎣ ⎦

teb

t aea ,γτ=

γe,t = elastic shear strain for the tth period of loadingγp,t = permanent shear strain for the tth periodΔNt = number of load applications during the tth period

RD = Kγp,t

NCHRP 1-40B Enhancements

( )31 21 10 rr rp kk k

r

k T Nεε

=

Adjustment of permanent deformation constants based on HMA volumetric properties

Constant kr1:3 0.5213 1.0057

1 1log 1.5093 10 3.4488r r a beffk K V V−⎡ ⎤= × × × × −⎣ ⎦

Kr1 = intercept coefficient (see Figure A.1)

Depth function

Material Properties

NCHRP 1-40B (cont’d)

22.22.42.62.8

33.23.43.63.8

4

30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84

Voids Filled with Asphalt, %

Log

Kr1

Coe

ffici

ent

Fine Gradation Coarse Gradation

22.22.42.62.8

33.23.43.63.8

4

30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84

Voids Filled with Asphalt, %

Log

Kr1

Coe

ffici

ent

Fine Gradation Coarse Gradation

Figure A.1


Constant kr2: 0.25 1.25

2( ) ( )

1.5606 a br index index

a design b opt

V Pk F CV P⎛ ⎞ ⎛ ⎞

= ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Va(design) = design air voidsPb = asphalt content by weightPb(opt) = design asphalt content by weightFindex = fine aggregate angularity index (Table A.2)Cindex = coarse aggregate angularity index (Table A.3)


Table A.2. Fine aggregate angularity index used to adjust permanent deformation parameters, FIndex.

Fine Aggregate Angularity Gradation – External to restricted zone. < 45 > 45

Dense Grading – External to Restricted Zone 1.00 0.90 Dense Grading – Through Restricted Zone 1.05 1.0

Table A.3. Coarse aggregate angularity index used to adjust permanent deformation parameters, CIndex.

Percent Crushed Material with Two Faces Type of Gradation 0 25 50 75 100 Well Graded 1.1 1.05 1.0 1.0 0.9 Gap Graded 1.2 1.1 1.05 1.0 0.9


3 3( )

0.4791 br r

b opt

Pk KP

= × ×Constant kr3:

Kr3 = slope coefficient:

fine-graded mixtures with GI<20 → Kr3=0.40coarse-graded mixtures with 20<GI<40 → Kr3=0.70

with GI>40 → Kr3=0.80

GI = gradation index = #50

(0.45)3/8

i ii

P P=

−∑


00.20.40.60.8

11.21.41.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Measured Rut Depth, in.

Pre

dict

ed R

ut D

epth

, in.

APT, Full-Scale Truck Loading Line of EqualityAPT, Simulated Truck Loading Roadway, Mixed Truck Traffic

00.20.40.60.8

11.21.41.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Measured Rut Depth, in.

Pre

dict

ed R

ut D

epth

, in.

APT, Full-Scale Truck Loading Line of EqualityAPT, Simulated Truck Loading Roadway, Mixed Truck Traffic

ALF Comparisons: Lane 10

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000ESALs

Rut

ting

(in)

MeasuredLeahyNCHRP 1-37AWestrackVerstraetenVESYSNCHRP 1-40B

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000ESALs

Rut

ting

(in)


Westrack Comparisons: Section 4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06

ESALs

Rut

ting

(in)


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06

ESALs

Rut

ting

(in)


ALF Comparisons

Lane 5 Lane 9 Lane 10 Lane 11 Lane 12 AverageLeahy 5 5 6 5 6 5.41-37A 3 3 3 3 3 3.0Westrack 6 6 4 6 5 5.4Verstraeten 4 4 5 4 4 4.2VESYS 1 2 1 1 2 1.41-40B 2 1 2 2 1 1.6

Ranking (only sections with complete sets of data)

Data sources:• Westrack: SST RSCH tests from NCHRP 9-19 + AAPT calibration procedure• Leahy, Option A: Mixture summaries from NCHRP 9-19 reports• VESYS: Confined RLPD tests from NCHRP 9-19 reports

Westrack Comparisons

Ranking (only sections with complete sets of data)

Section 4 Section 15 Section 23 Section 24 AverageLeahy 5 5 2 1 3.31-37A 4 3 5 5 4.3Westrack 1 2 4 2 2.3Verstraeten 6 4 6 6 5.5VESYS 2 6 3 4 3.81-40B 3 1 1 3 2.0

Data sources:• Leahy, Option A: Mixture summaries from NCHRP 9-19 reports• Westrack: Calibration parameters from Westrack report• VESYS: Confined RLPD tests from NCHRP 9-19 reports

Enhanced NCHRP 1-37A

• Material-dependent RLPD propertiesTreat as layer property rather than global parameters

• Additional stress terms/influencesConfining stressDeviatoric stress

• More rational depth factorLook to mechanistic models for guidance?

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Predicted HMA Rut Depth, in.

Resi

dual

Err

or (P

redi

cted

M

inus

Mea

sure

d), i

n.

NCAT WesTrack MnRoads

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9


Resi

dual

Err

or (P

redi

cted

M

inus

Mea

sure

d), i

n.

NCAT WesTrack MnRoads

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Resi

dual

Err

or (P

redi

cted

M

inus

Mea

sure

d), i

n.

WesTrack NCAT MnRoads

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Resi

dual

Err

or (P

redi

cted

M

inus

Mea

sure

d), i

n.

WesTrack NCAT MnRoads

“Level 3” RLPDProperties

“Level 2” RLPDProperties(NCHRP 1-40B)

Stress Effects on Material Response

0.0001

0.001

0.01

0.1

0.010 0.100 1.000 10.000 100.000 1000.000

Cumulative Deviatoric Load Time (sec)

Cum

. Dev

iato

ric V

isco

plas

tic S

trai

n 1525 kPa Unconfined Replicates1500 kPa 250 kPa Confined Replicates1480 kPa 500 kPa Confined Replicates

Depth Factor

0

1

2

3

4

5

6

7

8

9

10

-0.02 0 0.02 0.04 0.06

Vertical Plastic StrainD

epth

(in)

k1=f(z)k1=constant

0

1

2

3

4

5

6

7

8

9

10

-0.02 0 0.02 0.04 0.06

Vertical Plastic StrainD

epth

(in)

k1=f(z)k1=constant

10” AC layer

Before Adjustment

After Adjustment

Field Evaluation Activities

• Compile existing data:TrafficClimateVisual distressPerformance (rutting)FWD

• Collect new data:TrenchesCoresMaterial samples

Trenches are Essential

• Measured rutting is total rutting at surface

• M-E models predict rutting in individual layersHMAUnbound base/subbaseSubgrade

• Trench data provide rational basis for apportioning total surface rutting to layers

Material Property Tests

• For all sections:Uniaxial dynamic modulusTriaxial repeated load permanent deformationShear dynamic modulusRepeated load constant height shear

• For selected sections:Triaxial RLPD at additional stress statesAdvanced material characterization (e.g., NCHRP 9-19 test suite):

Triaxial constant strain rate to failure (compression, tension)Triaxial creep and recovery (compression)Others?

Project Timeline

• Project Panel meeting on July 27

• Phase III commences August/September

• Two year duration for Phase III

m-E M-E M-e

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