mechanistic-empirical pavement design guide: a … materials services, llc sensitivity analysis four...

Mechanistic-Empirical Pavement Design Guide: A User’s

Perspective

Brian D. Prowell, Ph.D., P.E.

ADVANCED MATERIALSSERVICES, LLC

Empirical Approach

• Based on results of experiments or experience

• Scientific basis not established

• AASHTO 86/93 an empirical design method

• Refer to AASHO Road Test


Typical Loop Layout--AASHO Road TestLoop 5 Single Axles 22.4 kips, Tandems 40 kips

Loop 6 Single Axles 30.0 kips, Tandems 48 kips


AASHTO Flexible Design Method

• Empirical Method based on AASHO Road Test

• Design Inputs (Example):– Delta psi = 1.2 (4.2 – 3.0)– Reliability = 90%– Standard Deviation = 0.45– Effective Resilient Modulus = 6177 psi– Design Traffic = 5.7 million ESALs


Empirical ApproachAASHTO Flexible Pavement

Performance Equation

Solve for SN using nomograph or bisection method


Empirical ApproachAASHTO Flexible Pavement

Performance Equation

log10 W18 = (ZR) (S0) + (9.36)(log (SN + 1)) - 0.20 +{log10[ΔPSI/(4.2-1.5)]/[0.40 + 1.094/(SN + 1)5.19 } + (2.32) (log10MR) - 8.07

Solve for SN using nomograph or bisection method


AASHTO 93 Pavement Design GuideExample Design Section

7.5 in HMA

12.5 in SP B

6.0 in SP C

SN

2.9

1.0

1.5

Required S

N =

5.4

Total = 5.4

a3 = 0.149, d3= 0.8

a2 = 0.138, d2= 1.2

a1 = 0.39


Mechanistic-Empirical

• Mechanistic: Determine stresses, strains, or deflections at critical locations in a pavement structure.

• Empirical: Relates stresses, strains, or deflections to pavement performance. Often referred to as Transfer Functions.


Important Advantages• Relate material properties to design

• More accurate portrayal of traffic effects and changes in axle loading

• Effects of construction variability and traffic variability can be accounted for

• Pavement layers can be engineered for expected distresses


Pavement Design Addresses Two Primary Distresses: Fatigue and Rutting

HMA

Base

Subgrade



RepeatedBending

HMA

Base

Subgrade



RepeatedBending

Leads toFatigue Cracking

HMA

Base

Subgrade



RepeatedBending


RepeatedDeformation

HMA

Base

Subgrade



RepeatedBending


RepeatedDeformation

Leads toRutting

HMA

Base

Subgrade

ADVANCED MATERIALSSERVICES, LLCPriest and Timm, 2006

Mechanistic-Empirical Pavement Design


M-E design process requires

•Material properties of each layer (Ei, µi)

•Thickness of each layer (hi) and load (P, a)


Hierarchical Input Levels

• Level 1– Advanced materials testing (E*, MR)

• Level 2– Available test procedures (like CBR) with

correlation equations

• Level 3– Default values


Traffic

• Traffic Volume – AADTT

• Directional and lane distributions

• Growth factor• Speed

• Vehicle Classification and axle-distribution– Level I – site specific load

spectra– Level III – default

distributions by road class

M-E PDG Traffic Inputs


MEASURED PAVEMENT RESPONSE


Climate


Enhanced Integrated Climatic Model

• Weather station or location• Heat capacity, thermal conductivity,

depth of water table• Output

– Calculates every 6 minutes for design life; up to 7 layers. Temperatures collected into 5 “bins” for analysis

– Correction factors to adjust the optimum modulus of unbound layers (moisture and freeze/thaw based)


Example Temperature Histogram – NCAT Test Track


Material Properties


Unbound Layers• Level I – Resilient modulus using stress

dependent FEM. Not calibrated at this time!

• Level II – Resilient Modulus based on correlations with empirical tests– Can use other M-E program to determine

“average” stress dependent modulus (better approach)


Correlations


Using Resilient Modulus DataMaterial k1 k2 k3 R2

Granite Base 716.28 0.8468 -0.4632 0.93Subgrade 1878.97 0.4067 -0.7897 0.42

where:Mr = resilient modulus,pa = atmospheric pressure (14.696 psi),θ = bulk stress = σ1+σ2+σ3 = σ1+2σx,y,σ1 = major principal stress = σz + po,σ3 = minor principal stress/confining pressure = σx,y + ko (po)σz = vertical stress from wheel load(s) calculated using layered-elastic theory,σx,y = horizontal stress from wheel load(s) calculated using layered-elastic theory,po = at-rest vertical pressure from overburden of paving layers above unbound layer or subgrade,ko = at-rest earth pressure coefficient,τoct = octahedral shear stress = 1/3((σ1-σ2)2+(σ1-σ3)2+(σ2-σ3)2)1/2, andk1, k2, k3 = regression coefficients.


Asphalt Inputs• Binder Properties

• Volumetric Properties

• Dynamic Modulus– Levels II and III use Witzak Equation to

predict from gradation, binder and volumetric properties

– Level I test or use Hirsch model

• Low Temperature IDT


Test Samples for SPT Tests

150 mm tall by 100 mm diameter, cored from SGC


Dynamic Modulus

φ/ω

σ,ε

Time, t

εoσo

εosin(ωt-φ)

σosin(ωt)


Faster Traffic orLower Temperatures

Slower Traffic orHigher Temperatures


Structural Modeling AC Pavements• Multi-layer elastic solution

– Main engine: JULEA

• 2-D Finite element analysis– For special loading conditions,– Non-linear unbound material characterization


How well does it work?


Evaluated Using Performance of Structural Sections from 2003


Observed Cracking in Field


Observed Cracking in FieldSection Failure Date Cracking, % of

Total Lane Area

Cracking, % of Wheel Path

AreaN1 6/14/2004 20.2 58.3

N2 7/19/2004 19.5 56.3

N8 8/15/2005 18.5 53.5

Failure defined as 20% cracking in total lane area,For MEPDG, damage (D) = 100% for 50% crackingOf wheel path, For N6 D = 0.7 at end of loading


MEPDG Cracking N1


MEPDG N2 and N6


Using Endurance Limit for Pavement Design

Perpetual Pavements


Definition of the Endurance Limit

HMA Fatigue Endurance Limit – A level of strain below which there is no cumulative damage over an indefinite number of load cycles.

From NCHRP 9-44 HMA Endurance Limit Workshop, August 2007


Practical Definition of the Endurance Limit

• Nunn defined long-life pavement as those that last 40 years without structural strengthening


Practical Definition of the Endurance Limit

• 500 million load repetitions is approximate maximum in 40 years

• Assume shift factor of 10 recommended by SHRP

• Endurance Limit is that laboratory strain that provides for 50 million cycles to failure


Regions of Fatigue Behavior

DeBenedetto, 1996


Regions of Fatigue Behavior

DeBenedetto, 1996

50% Initial Stiffness


BeamFatigue


AASHTO T321 - Beam Fatigue Test Results

ß1 = shift factor Between lab and field


Transfer Function Coefficients from Beam Fatigue TestingMix K1 K2 R2 Endurance

Limit, msPG 67-22 7.19E-15 5.78 0.99 151

PG 67-22 Opt.+ 4.42E-09 4.11 0.98 158

PG 76-22 4.66E-12 5.05 0.92 146

All 19.0 mm NMAS mix with same aggregate,Opt.+ has additional 0.7% asphalt


Fatigue Shift Factor• Laboratory fatigue tests underestimate

field fatigue life, e.g. number of repetitions to some level of cracking

• Shift factor accounts for difference– Ranges from 10 to 100– SHRP recommended 10 – used in NCHRP

9-38

• Accounts for factors such as healing,

PG 67-22 at Optimum


Mix Beam FatigueBeam Fatigue Beam Fatigue Round RobinBeam Fatigue Round RobinMix

Predicted 95% Lower Confidence

Limit

Predicted 95% Lower Confidence

Limit

PG 58-22 107 82 NA NAPG 64-22 89 75 NA NAPG 67-22 172 151 182 130PG 67-22 Opt. + 184 158 176 141PG 76-22 220 146 195 148PG 76-22 Opt. + 303 200 NA NA

Summary of Predicted E-L


Sensitivity AnalysisFour Analyses:

1. Comparison of conventional and perpetual pavement thickness for 2003 NCAT Test Track structural sections and loading conditions

2. Evaluate sensitivity of perpetual pavement thickness for NCAT Test Track traffic

3. Repeat 1. using MEPDG’s Truck Traffic Classification No. 1 for principal arterials

4. Repeat 2. using MEPDG’s Truck Traffic Classification No. 1 for principal arterials


Used in original Test Track design

Value calculated using the multi-variable, non-linear stress sensitivity model for unbound layers

10.6% cracking vs. 0% cracking of total lane area

Test Track Traffic

Required Thickness MEPDG Traffic

Perpetual Pavement Thickness M-E PDG Traffic


Summary• Mechanistic-empirical design programs

require more inputs than 93 AASHTO– Some are readily available, some are not

• Nationally calibrated fatigue models appear to do a good job at predicting cracking; rutting overestimated

• M-E PDG and PerRoad can both be used for perpetual designs; M-E PDG more conservative


Questions?Contact Information:

Brian Prowell

Advanced Material Services, LLC2515 E. Glenn Ave., Suite 107

Auburn, AL 36830

mechanistic-empirical pavement design guide: a … materials services, llc sensitivity analysis four...

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