# pavement design— where are we?

TRANSCRIPT

Pavement Design—Where are We??

State-of-Practice State-of-the-Art

Actual Current

Practice??

Empirical Mechanistic-Empirical

Mechanistic

InputsStructure Materials Traffic Climate

To account for Reliability,both mean and standard deviations inputs are required

Selection of Trial Design

Structural Responses (σ, ε, δ)

Performance PredictionDistresses Smoothness

Performance VerificationFailure criteria

Design

ReliabilityDesign

Requirements

Satisfied? No

Yes

Final Design

Rev

ise

tria

l des

ign

LOAD RELATED - Rutting

•• Vertical DisplacementsVertical Displacements

•• Lateral DisplacementsLateral Displacements

Rutting -Permanent deformation in

all layers.

Wide versus narrow rut depths.Wide versus narrow rut depths.

Rutting

• Vertical and/or horizontal permanent

deformation of one or more layers in

the pavement system.

Rutting Mechanisms

• Densification – Vertical movements

– Compression – �

– Consolidation –

• Shear deformation – Lateral movements

Rutting Mechanisms

• Potential Primary Causes:

– Plastic movement of HMA in hot weather

– Inadequate compaction of HMA during

construction

• Potential Secondary Causes:

– Plastic movement in other layers

– Inadequate compaction in other layers

Plastic movement - Depression in the Wheel

Path with Humps in Either Side

Consolidation/Densification -Depression in the

Wheel Path Without Any Humps

Mechanical Deformation - Subsidence or

Densification in the Unbound Base or Subgrade

and Accompanied by a Cracking Pattern

Permanent or Plastic Deformations

Stress Under Repeated Loads

Re c

ov

e ra

bl e

an

d P

las t

i c S

tra

ins

εεεεr

εεεεp

Rutting Models

• Subgrade compressive strain models:determine the cover requirements to protect the subgrade or embankment soil.

• Permanent deformation/strain models:these models accumulate all permanent strain values to estimate the total rutting at the surface of the pavement structure.

Subgrade Strain Models

• Austroad

• Asphalt Institute

• Shell

• Transport and Road Research Lab (TRRL)

• Belgian Road Research Center (BRRC)

( ) 2

1

f

Vf fN−

= ε

?76.017*10-15

AUSTROADS (New)

?7.141.66*10-15

AUSTROADS (Old)

10 (0.4)4.353.05 x 10-9

Belgian Road Research Center

10 (0.4)3.956.18 x 10-8

Laboratory C (85% Reliability)

U.K. Transport and Road Research

41.05 x 10-7

95% Reliability

13 (0.5)41.94 x 10-7

85% Reliability

46.15 x 10-7

50% Reliability

Shell (revised 1985)

13 (0.5)4.4771.365 x 10-9

Asphalt Institute

Allowable Rut

Depth, mm (in)f2

f1

Organization

Material Properties Dictate The

Maximum Allowable Permanent

Deformation

Per

man

ent

Str

ain

(in

/in)

Loading Cycles

N FN (Flow Number)

Primary

Secondary

Tertiary

Per

man

ent

Str

ain

(in

/in)

Loading Cycles

N FN (Flow Number)

Per

man

ent

Str

ain

(in

/in)

Loading Cycles

N FN (Flow Number)

Primary

Secondary

Tertiary

∆V=0Shear Failure

Comparison between different

compressive strain models

100

1000

10000

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Ver

tica

l C

om

pres

siv

e S

tra

in (

µµ µµεε εε)

Number of Load Repetitions to Failure

AUSTROADS (New)

TRRL (Rutf =10 m

m)

A.I. (Rutf =13 m

m)

SHELL (Rutf =13 m

m)

Old

Subgrade Strain Models

• Based on:

– Specific design conditions

– Material properties

– Environmental conditions

• Limitations

– Can't accurately be extended beyond inference space

– Models suggest that allowable rut depth will not be

exceeded if εv is limited

– Assume that all permanent deformations occur in the subgrade.

v

Permanent Deformations in all

Pavement Layers

0* =−−= t

b ppSaF

)(*3

1321 σσσ ++=p

31 σσ −=S

where:

a,b = material parameters that are independent of plastic deformation.

pt= the hardening parameter that represents the hydrostatic tensile

strength of the material.

σ1, σ2,and σ3 = major, intermediate and minor principal stresses,

respectively.

X-Section of FEM

.

.

FIGURE 5 Cross Section of the Finite Element Model

.

10 Elements each (2000-X)/10 mmBoundary Conditions

.

Plane of Symmetry

1250 mm

X

8 E

lem

ents

eac

h 1

12.5

mm

8 e

lem

ents

eac

h 7

5 m

m

Longitudinal Section in the FEM

FIGURE 4 Elevation View of the Finite Element Model

3000 mm

Subgrade LayerPl

ane

of S

ymm

etry

Unbound Base Course

.8 E

lem

ents

eac

h 7

5 m

m8

Ele

me n

ts e

ach 1

12.5

mm

2000-XX

Drucker-Prager Model

Hydrostatic or spherical axis

σ1=σ2=σ3

σ1

σ2

σ3

Deviatoric Plane

π-Plane or deviatoric plane at σ1+σ2+σ3=0

Yie

ld S

urfa

ce

Permanent Vertical Strain& Rutting Calculations

0

200

400

600

800

1000

1200

1400

1600

0 100 200 300 400 500 600

Depth (mm)

Pri

ncip

al P

erm

an

en

t S

train

(M

icro

str

ain

)

P= 50kN, q= 750 kPa

P=40 kN, q=750 kPa

P=40 kN, q=650 kPaBase course Subgrade Layer

Interface betw een base course and subgrade

37% Rutting 63% Rutting

Permanent Deformation

Prediction Models

• Considers permanent deformation of each layer individually

• General form of models:

• Deformation (rutting) is calculated:

∑=

=n

i

iip hRuttingTotal1

*)(ε

( )LogNbaLog p +=ε

Ohio State Model

• Permanent Strain Accumulation Model (rutting rate)

• "A" and "m" are constants based on material type and stress state

= A (N)εεεε

N

p -m= A (N)

εεεε

N

p -m

Typical values of A and m in the Ohio State model (Barenberg and Thompson, 1990).

Moisture

Unconfined Strength, kPa

(psi)

Repeated Deviator Stress,

kPa (psi) m A x 10

-4

Optimum 159 (23) 34 (5) 69 (10) 103 (15)

0.86 0.86 0.86

12.4 18.2 43.7

Optimum + 4% 90 (13) 34 (5) 69 (10) 103 (15)

0.83 0.83 0.83

17.0 42.5 138.0

Asphalt Institute Model

( ) ( )Log Log N Log T

Log Log V Log P

Log Vv

p

d be

ε

σ

= − + +

+ − +

+

14 97 0 408 6865

1107 0117 1908

0 971

. . * . * ( )

. * ( ) . * ( ) . * ( )

. * ( )

εp = Permanent strain (axial).N = Number of load repetitions to failure.

T = Temperature, oF.

σd = Deviator stress, psi.V = Viscosity at 21 oC (70oF), Ps x 106.

Pbe = Percent by volume of effective bitument.

Vv = Percent volume of air voids.

Allen and Dean Model

( )[ ] ( )[ ] ( )[ ]3

3

2

21 NLogCNLogCNLogCCLog op +++=ε

εp = Permanent strain (axial).

N = Number of stress or wheel load repetitions.

C0-3 = Regression coefficients that are factors of the

temperature and the deviator stress, as shown in Table below.

Coefficient HMA Dense-Graded Aggregate Base

Subgrade

Co - 0.000663 T2 + 0.1521 T - 13.304 + (1.46 - 0.00572 T) * log �1

- 4.41 + (0.173 + 0.003 w) * �1 - (0.00075 + 0.0029 w) * �3

- 6.5 + 0.38w - 1.1 (log �3) + 1.86 (log �1)

C1 0.63974 0.72 10(-1.1 + 0.1 w)

C2 - 0.10392 - 0.142 + 0.092 (log w) 0.018 w

C3 0.00938 0.0066 - 0.004 (log w). 0.007 - 0.001 w

where, T = Temperature, °F. σ1 = Deviator stress, lbf/in2.

w = Moisture content, percent. σ1 = Deviator stress, lbf/in2. σ3 = Confining pressure, lbf/in2

Fatigue Criteria

( ) ( ) 32

1

KK

tf EKN ε=

N R

N M R

f

f r

= =

= =

− −

− − −

2 35 10 0 996

6 64 10 0 995

13 4 719 2

11 4 514 0 5116 2

. * * .

. * * * .

.

. .

ε

ε

University of Canterbury Fatigue Models for AC-10

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000

Measured Repetitions

Pre

dic

ted

Re

pe

titio

ns

996.0R

*10*35.2N

2

719.413

f

=

ε= −−

HMA, AC10

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000

Measured Repetitions

Pre

dic

ted R

epetitions

995.0R

M**10*64.6N

2

5116.0

r

5144.411

f

=

ε=−−−

HMA, AC10

Lab ModelResilient Modulus-0.5116-4.51446.64*10-11ε

Lab Model0-4.7192.35*10-13ε

Canterbury

20Dynamic Modulus0-5.128.86x10-14ε

Ontario

---0-4.764.92x10-14ε

Belgian

---0-4.321.66x10-10ε

TRRL

45Flexure Modulus-0.854-3.2911.219x1016ε

10Flexure Modulus-0.854-3.2918.851x1015ε

Lab, Crack InitiationFlexure Modulus-0.854-3.2916.601x1014ε

PDMAP

20Dynamic Modulus-2.363-5.6710.0685ε

Shell

Percent Asphalt by

Volume

50Percent Air Voids-0.854-3.2910.0796ε

Dynamic Modulus

Asphalt

Institute

HMA

Modulus

Exponent, K3

Response

Exponent, K2

Coefficient, K1

Definition of Failure, %

Cracking

Other Parameters in

Equation

Fatigue Constants

Response

Parameter

Fatigue

Equation

Fatigue Criteria

0.0001

0.001

100 1000 10000 100000 1000000 10000000

Number of Load Repetitions

Str

ain

Le

ve

l (m

m/m

m)

AUSTROADS

TRRL

PDM

AP

UC-Model

BRRC