Perpetual Pavement Design

Southeast Pavement Managementand Design Conference

June 21, 2005Savannah, Georgia

Goal of Perpetual Pavement Design

• Design the structure such that there are no deep structural distresses– Bottom up fatigue cracking– Structural rutting

• All distresses can be quickly remedied from surface

• Result in a structure with ‘Perpetual’ or ‘Long Life’

Surface Distresses Only

Top Down Cracking

Non-Structural Rutting

How do you compute pavement response?• Flexible pavements consist of multiple layers• Using physical principles, we can calculate

stresses beneath loads

Pa

zr

t

H1, E1, µ1

H2, E2, µ2

En, µn

Linear Elastic System Assumptions

• Many constitutive models available• Linear Elastic Most Common• Assumptions

– Homogeneity– Finite thickness– Infinite in horizontal direction– Isotropic– Full friction between layers– No surface shear forces

Two-Layer Systems• Analytical solution derived by Burmister (1940’s)• Importance of stiffness ratio (E1/E2)

Vertical Stress, σz/p

1.0

E 1/E 2=

1.0

E1/E2=100

0.70.10.0

Layer 1

Layer 2

Dep

th, z

/a

Two Layer System – Shear Stress

Horizontal Shear Stress, τrz/p1.00.0

E 1/E

2=1.

0E1/E2=

50 Layer 1

Layer 2

Dep

th, z

/a

Two-Layer System – Tensile Stresses

σx

Dep

th, z

Tension Compression

Layer 1

Layer 2

Three Layer Systems• Much more complicated system!• Initially solved for a limited set of parameters due to

computational limitations– µ = 0.5

• Limited number of locations

Pa

H1, E1, µ1 σz1σr1

H2, E2, µ2 σz2σr2

σr3

En, µn

Materials

1 2

BeforeLoading

3

AfterLoading -

Same Sizeas BeforeLoading

DuringLoading

Figure 1. How an Elastic Material Behaves.

D

∆D/2σ∆l

l

εl = ∆l/l E = σ/ε

εt = ∆D/D µ = εl/εt

Figure 1. Definitions of E and µ.

Dynamic Modulus Test

Witczak Equation for E*log . . . ( ) . .

.. . . . ( ) .

( . ` . log( ) . log( ))

E V

VV V e

a

beff

beff af

= − + − − −

−+

⎛

⎝⎜

⎞

⎠⎟ +

− + − ++ − − −

1249937 0 29232 0 001767 0 002841 0 058097

08022083871977 0 0021 0 003958 0 000017 0 005470

1

200 2002

4

4 38 382

340 6033 3 0 313351 0 393532

ρ ρ ρ

ρ ρ ρ ρη

• bitumen viscosity (dynamic shear rheometer)

• loading frequency• air voids• effective bitumen content

• cum. % retained on 19-mm sieve

• cum. % retained on 9.5-mm sieve

• cum. % retained on 4.76-mm sieve

• % passing the 0.075-mm sieve

HMA Modulus Versus

Temperature

10

100

1000

10000

0 20 40 60 80 100 120

Temperature, F

Mod

ulus

, 100

0 ps

i

Soil Modulus Testing

Dynamic Cone Penetration

Rod

Reference

Mass

Effect of Moisture Content

1

10

100

0 5 10 15 20

Moisture Content, %

Mod

ulus

, ksi

FWD Testing

Backcalculation

PavementStructure

Def

lect

ion

Deflection SensorsLoad

E = f(Load, Pressure, Deflection, Distance)

Traffic

AASHO Road Test

Trucks

Single Tire Dual Tire

Tandem Tridem

Layer 1HMA

E1

Layer 2Granular Base

E2

Layer 2Layer 2Granular BaseGranular Base

EE22

Layer 3Subgrade Soil

E3

Tire has a total load P, spread over a circulararea with a radius of a, resulting in a contactpressure of p.

PavementReactions

Deflection (δ)

Tensile Strain (εt)

Compressive Strain (Compressive Strain (εεvv))

Nohorizontalboundary, assumelayersextendinfinitely.

h1

h2

No bottom boundary, assume soil goes on infinitely.

Figure 2. Layered Elastic Model Representation of a Pavement.

0

100

200

300

400

20 30 40 50 60Wheel Load, kN

Tran

sver

seSt

rain

, µε

Test Section 21

LayeredElasticResults

Mn/ROADMeasurements

Figure 4. A Comparison of Measured Strains and Computed Strainsat Mn/ROAD. (After Timm et al., 1998, Development of Mechanistic-Empirical Pavement Design, Transportation Research Record No. 1629, Transportation Research Board, Washington, DC.)

Layer 1HMA

E1h1 Tensile Strain (εt)

Thickness vs. Tensile StrainH

MA

Ten

sile

St ra

in

HMA Thickness

Modulus vs. Tensile Strain

Layer 1HMA

E1h1 Tensile Strain (εt)

HM

A T

ens i

le S

t rain

HMA Modulus

HMA Thickness

Sub

grad

e C

omp r

ess i

v e S

tr ain

E1

E2EE22

E3

h1

h2

Compressive Strain (Compressive Strain (εεvv))

Thickness vs. Compressive Strain

Traditional M-E Design

Log N

Log ε

Perpetual Pavement Design

No Damage Accumulation

Log N

Log ε

ThresholdStrain

Normal Fatigue Testing Results VersusEndurance Limit Testing

0

200

400

600

800

1000

1200

1000 100000 10000000 1.1E+08

Number of Loads to Failure

Stra

in, (

10E

-06)

Endurance Limit

Normal Range forFatigue Testing

0

200

400

600

800

1000

1200

1000 100000 10000000 1.1E+08

Number of Loads to Failure

Stra

in, (

10E

-06)

Endurance Limit

0

200

400

600

800

1000

1200

1000 100000 10000000 1.1E+08

Number of Loads to Failure

Stra

in, (

10E

-06)

Endurance Limit

Normal Range forFatigue Testing

εt

εv

Transfer Functions

Miner’s Hypothesis

• Provides the ability to sum damage for a specific distress type

•• D = D = ΣΣ nnii/N/Ni i ≤≤ 1.01.0where ni = actual number of loads

during condition iNi = allowable number of loads

during condition i

0

200

400

600

800

1000

1200

1000 100000 10000000 1.1E+08

Number of Loads to Failure

Stra

in, (

10E

-06)

Endurance Limit

Normal Range forFatigue Testing

0

200

400

600

800

1000

1200

1000 100000 10000000 1.1E+08

Number of Loads to Failure

Stra

in, (

10E

-06)

Endurance Limit

0

200

400

600

800

1000

1200

1000 100000 10000000 1.1E+08

Number of Loads to Failure

Stra

in, (

10E

-06)

Endurance Limit

Region of DamageAccumulation

NoDamageAccumulation

Probabilistic Design – Monte Carlo Simulation

Thickness

f

Material Properties

f

Axle Weight

f

MonteCarlo

RandomSampling

MechanisticModel

Pavement Response

f % Below Threshold

% Above Threshold

% Below Threshold

• Design should have high % below threshold

f

Pavement Response

% Below Threshold

How much ‘damage’ does this

area correspond to?

‘Damage Computation’• For responses exceeding threshold, compute N

using transfer function– User defined

• Calculate damage accumulation rate– Damage / MESAL

f

Pavement Response

% Below Threshold

DamageMESAL

Estimated Long Life

• Convert damage rate into an estimated life– Use traffic volume and growth– Calculate when damage = 0.1

• Use for Low Vol. Roads (t ~30 yrs.)

10 - 20/wk 3 - 5/wk 10 - 20/wk

Low Volume Traffic

PerRoad 2.4• Sponsored by APA• Developed at Auburn University / NCAT• M-E Perpetual Pavement Design and Analysis Tool• Help File is the Users Manual• Press F1 at Any Time for Help File

Perpetual Pavement DesignGoal of Perpetual Pavement DesignSurface Distresses OnlyHow do you compute pavement response?Two-Layer SystemsTwo Layer System – Shear StressTwo-Layer System – Tensile StressesThree Layer SystemsMaterialsDynamic Modulus TestWitczak Equation for E*HMA Modulus VersusTemperatureSoil Modulus TestingDynamic Cone PenetrationEffect of Moisture ContentFWD TestingBackcalculationTraditional M-E DesignPerpetual Pavement DesignMiner’s HypothesisProbabilistic Design – Monte Carlo Simulation% Below Threshold‘Damage Computation’Estimated Long LifePerRoad 2.4