equivalent loading asphalt layer pavement …...1 equivalent loading frequencies to simulate asphalt...

1

Equivalent Loading Frequencies to Simulate Asphalt Layer Pavement Responses Under

Dynamic Traffic Loading

Elie Y. Hajj, Ph.D.Alvaro Ulloa, Ph.D. Candidate

Peter E. Sebaaly, Ph.D. Raj V. Siddharthan, Ph.D.

University of Nevada Reno

Asphalt Mixture & Construction ETGPhoenix, ArizonaMarch 18, 2011

Introduction

• Dynamic response of AC pavements under moving load is a key component for accurate prediction of flexible a key component for accurate prediction of flexible pavement performance.

• Reliable determination of pavement responses to moving load is essential for a successful mechanistic design procedure.

• Time and temperature dependency of asphalt must be considered in the mechanistic analysis response model.

2

Linear Elastic Analysis

AASHTO MEPDG Approach

HMA

Tire Foot Print(Dual Spacing)/2-4

-2

0

2

4

6

0 2 4 6 8 10 12

h

Transverse Distance, inch

t2, T2

t3, T3

t4, T4

t T

|E*|2

|E*|3

|E*|4

|E*|

Static Tire

t5, T5|E*|5

t1, T1|E*|1

Base

Subgrade

6

8

10

12

14

16

18

Dep

th, i

nct6, T6|E*|6

-4-3-2-101234

0 50 100 150

Shift

Fac

tor,

log(

aT)

Temperature, F

• Vertical stress distribution used to estimate traffic-induced loading time.

AASHTO MEPDG

g– Axle load configuration, Vehicle speed & Pavement structure

3

Literature Review

• Dongre, R. N., Myers, L. A., and D’Angelo, J. A., “Conversion of Testing Frequency to Loading Time: Impact on Performance Predictions Obtained from the Mechanistic Empirical Pavement Design Guide” Presented at 85th Annualthe Mechanistic–Empirical Pavement Design Guide , Presented at 85th Annual Meeting of the Transportation Research Board, Washington, D.C., 2006.

• Al‐Qadi, I. L., W. Xie, and Elseifi, M. A., “Frequency Determination from Vehicular Loading Time Pulse to Predict Appropriate Complex Modulus in MEPDG”, Journal of the Association of Asphalt Paving Technologists, Vol. 77, 2008, pp. 739‐772.

• Katicha, S., Flintsch, G.W., Loulizi, A., and Wang L. “Conversion of Testing F t L di Ti A li d t M h i ti E i i l P t D iFrequency to Loading Time Applied to Mechanistic‐Empirical Pavement Design Guide,” Transportation Research Record No. 2087, TRB, Washington D.C., 2008, pp. 99‐109.

• …

Appropriate Representative Elastic ModulusB. S. Underwood and Y. R. Kim

• “Determination of the Appropriate Representative Elastic Modulus for Asphalt Concrete,” IJPE, Vol. 10, Iss. 2, 2009, pp. 77‐86for Asphalt Concrete, IJPE, Vol. 10, Iss. 2, 2009, pp. 77 86

– Evaluated several approximation methods for calculation of stresses & strains in linear viscoelastic materials.

– MEPDG method is biased towards overestimating the appropriate stiffness by up to a 31% error.

– Representative modulus to use for LEA is average ofd i d l f l 1/ d dynamic modulus at a frequency equal to 1/tp and

relaxation modulus evaluated at a time equal to ½ tp.

– Proposed Method resulted in 2 ‐ 6% error

4

•Investigate the existence of one or more predominant frequencies (f ) associated with the

Research Objective

predominant frequencies (fp) associated with the AC layer that controls the dynamic response of pavements.

•AC Critical Reponses :p– Longitudinal & transverse tensile strains

– Vertical compressive strains

Viscoelastic vs. Pseudo Analysis

Viscoelastic Pseudo‐staticPseudo‐dynamic

HMA

CAB

SG

|E*| = f(freq) & = f(freq) HMA

CAB

SG

|E*| fp =? fp = 0HMA

CAB

SG

|E*|fp =?, fp = ?

VelocityVelocity

Pavement responses

SG

Pavement responses

SG

Pavement responses

SG

5

Pavement Analysis3D-Move Analysis Software

Freeware Download at:http://www.arc.unr.edu/Software.html

1. 3D-Move vs. ViscoRoute (2010)– ViscoRoute (IFFSTAR – LCPC): moving circular loaded areas with

Pavement Analysis3D-Move Analysis Software - Validation

uniform contact pressure, viscoelastic material properties

A380 Pavement

Reference:Chabot, A., Chupin, O., Deloffre, L., and Duhamel, D., “Viscoroute 2.0: a tool for the simulation of moving load effects on asphalt pavement,” Road Materials and Pavement Design an International Journal, Volume 11/2,

Experimental Program for aircrafts.

Comparison between elastic computations, ViscoRoute1.0 simulationsand transversal strain measurements at the bottom of bituminous layers for a 4-

wheels moving load

2010, pp. 227-250.

Loft A., "Evaluation de Viscoroute-v1 pour l’étude de quelques chaussées souples", Msc.Dissertation, Dresden University of Technology specialityUrban and Road construction,2005.

6

250

300

mic

ron

s

20ºC 3D-Move

20ºC ViscoRoute

10ºC 3D Move

HMA thickness = 3.9"3D-Move vs. ViscoRouteVehicle speed = 6 to 70 mph


0

50

100

150

200

0 10 20 30 40 50 60 70

Tra

nsv

erse

str

ain

yy

, m

Vehicle speed, mph

10ºC 3D-Move

10ºC ViscoRoute

0ºC 3D-Move

0ºC ViscoRoute

-10ºC 3D-Move

-10ºC ViscoRoute

-20ºC 3D-Move

-20ºC ViscoRoute

250

300

ron

s

20ºC 3D-Move

20ºC ViscoRouteHMA thickness = 7.9”

Pavement temperature = -20ºC to 20ºC

0

50

100

150

200

0 10 20 30 40 50 60 70

Tra

nsv

erse

str

ain

yy

, mic

r

Vehicle speed, mph

10ºC 3D-Move

10ºC ViscoRoute

0ºC 3D-Move

0ºC ViscoRoute

-10ºC 3D-Move

-10ºC ViscoRoute

-20ºC 3D-Move

-20ºC ViscoRoute

ViscoRoute Test Results Refer to:Chabot, A., Chupin, O., Deloffre, L., and Duhamel, D., “Viscoroute 2.0: a tool for the simulation of moving load effects on asphalt pavement,” Road Materials and Pavement Design an International Journal, Volume 11/2, 2010, pp. 227-250.

2. SD Heavy Off-Road Vehicle Field Sections (2000)


7

3. PennState University Test Track (1999)


4. MnRoad (1997)


8

Database of pavement responses

Structures 1 & 2 pavement analyses

Structure 1 Structure 2 Structure 3 Structure 4

completed

Pavement Responses Locations

4 inch HMA layer 8 inch HMA layer

XXX

X

X

X

XX

X

X

X

X

0.5”

0.5”

1.0”

1.0”

1.0”

0.5”

0.5”

1.0”

1.0”

1 0”

0.25”0.5”0.75”

1.5”

2.5”

3.5”

0.25”0.5”0.75”

1.5”

2.5”

3.5”

XXX

X

X

X

XXX

X

X

X

XXX

X

X

X

XXX

X

X

X

XX

X

X

X

X

XX

X

X

X

X

XX

X

X

X

X

XX

X

X

X

X

AX

X

X

X

1.0

4.0”

4.0”

6.0”

8.0”

Data analysis completed for responses at center line of the load

XXX X

X

X

X

X

X

X

X

X

X

X

X

X

9

Proposed approach to determine fp

• Example: Bottom of the 4-inch HMA layer:

‐200

‐100

0

100

200

Norm

al Strains, m

icrons

εxx

t= 0.03 secCompression

Pavement temperature = 70FVehicle speed = 40 mph

t= 0.05 sec

‐400

‐300

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40

Time, sec

εyyTension

Proposed approach to determine fp

• FFT amplitudes of the normal strains of the 4-inch HMA

15

20

25

30

35

40

45

50

FFT am

pltitude

εxx

εyy

fp = Predominant frequency

fp= 14.4 Hz


0

5

10

0 20 40 60 80 100Frequency, Hz

fp= 12.8 Hz

10

fp for the 4-inch HMA layerCase Study Depth (in)

Predominant frequency, (Hz)

xx yy zz zz

fp fpseudo fp fpseudo fp fpseudo fp fpseudo

Case 1: 70ºF and 40 mph

0.25 14.4

14.4

12.8

14.4

14.4

14.4

14.4

14.4

0.5 14.4 12.8 14.4 14.40.75 14.4 12.8 14.4 14.41.5 14.4 12.8 14.4 14.42.5 14.4 12.8 14.4 14.43 5 14 4 12 8 14 4 14 43.5 14.4 12.8 14.4 14.44 14.4 12.8 14.4 14.4


0.25 14.4

14.4

14.4

14.4

14.4

30.4

14.4

14.4

0.5 14.4 12.8 30.4 14.40.75 14.4 14.4 30.4 14.41.5 12.8 14.4 30.4 14.42.5 30.4

30.414.4 14.4

14.414.4

3.5 30.4 14.4 14.4 14.44 28.8 14.4 14.4 14.4


0.25 21.6

21.6

19.4

21.6

21.6

21.6

21.6

21.6

0.5 21.6 19.4 21.6 21.60.75 21.6 19.4 19.4 21.61.5 21.6 16.8 21.6 21.62.5 21.6 21.6 21.6 21.63.5 21.6 19.4 21.6 21.64 21.6 19.4 21.6 21.6

0.25 21.6

21.6

21.6 43.3

43.3

21.60.5 21.6 19.2 43.3 21.6

0.75 21.6 19.2 43.3 21.6Case 4: 104ºF

and 60 mph21.6 21.61.5 21.6 21.6 43.3 21.6

2.5 43.343.3

21.6 21.621.6

21.63.5 43.3 21.6 21.6 21.64 43.3 21.6 21.6 21.6


0.25 3.6

7.6

3.2

3.6

3.6

7.6

3.6

3.6

0.5 3.6 3.2 3.6 3.60.75 3.6 3.2 3.6 3.61.5 3.2 3.2 7.6 3.62.5 7.6 3.6 7.6 3.63.5 4 3.6 3.6

3.63.6

4 4 3.6 3.6 3.6


0.25 7.67.6

3.2

3.6

7.67.6

3.6

3.6

0.5 7.6 3.2 7.6 3.60.75 7.6 3.2 7.6 3.61.5 11.2

11.2

3.6 3.6

3.6

3.62.5 11.2 3.6 3.6 3.63.5 11.2 3.6 3.6 3.64 11.2 3.6 3.6 3.6

Case 4 Predominant FrequenciesTemp = 104F, V = 60 mph, Tensile Strain xx

600Compression

400

‐200

0

200

400

ongitudinal Strain, exx microns

εxx top

t= 0.02 sec

t= 0.01 sec

‐600

‐400

0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25

Lo

Time, sec

εxx bottomTension

11

Case 4 Predominant FrequenciesTemp = 104F, V = 60 mph, Tensile Strain xx

100

120

εxx top

20

40

60

80

FFT am

plitude εxx bottom

fp= 21.6 Hz

fp= 24 Hz fp= 43.3 Hz

0

0 20 40 60 80 100

Frequency, Hz

Pseudo-Dynamic Analysis

Viscoelastic Pseudo‐dynamic

HMA

CAB

SG

|E*| = f(freq) & = f(freq) HMA

CAB

SG

fp =21.6 Hz |E*|fp , fp

VelocityVelocity

fp =43.3 Hz |E*|fp , fp

= 60 mph = 60 mph

Pavement responses

SG

Pavement responses

SG

12

Case 4 Pseudo-Dynamic AnalysisTemp = 104F, V = 60 mph, Tensile Strain xx

0 100 200 300 400 500 600 700

Maximum tensile strain XX, microns

0.0

1.0

2.0

3 0

Depth, in

3D‐Move Viscoelastic

fpseudo = 21.6 Hz

fpseudo = 21.6/43.3 Hz

3.0

4.0 10%

20%

fp for the 8-inch HMA layerCase Study

Depth* (in)

Predominant frequency, (Hz)

xx yy zz zz

fp fpseudo fp fpseudo fp fpseudo fp fpseudo


0.25 12.8

12.8

16

12.8

30.4

30.4

14.4

14.4

0.5 12.8 11.2 30.4 14.40.75 12.8 9.6 30.4 14.41.5 12.8 14.4 30.4 14.42.5 12.8 14.4 30.4 14.43.5 30.4

30 414.4 14.4

12 814.4

6 30 4 12 8 12 8 14 430.4 12.86 30.4 12.8 12.8 14.48 14.4 12.8 12.8 14.4


0.25 14.4

14.4

12.8

14.4

30.4

30.4

14.4

14.4

0.5 14.4 12.8 30.4 14.40.75 14.4 11.2 30.4 14.41.5 12.8 12.8 30.4 14.42.5 30.4

30.4

12.8 14.4

14.4

14.43.5 30.4 12.8 14.4 14.46 30.4 12.8 14.4 14.48 30.4 12.8 14.4 14.4


0.25 19.2

19.2

19.2

19.2

19.2

45.7

21.6

21.6

0.5 19.2 16.8 40.8 21.60.75 19.2 16.8 45.7 21.61.5 19.2 19.2 45.7 21.62.5 19.2 19.2 43.2 21.63.5 45.7

45.721.6 21.6

19.221.6

6 45.7 19.2 19.2 21.68 45.7 19.2 19.2 21.6

C 10 104ºF

0.25 21.621.6

19.2 45.745.7

21.60.5 21.6 19.2 45.7 21.6

0.75 19.2 16.8 45.7 21.61 5 45 7 21 6 21 6 21 6Case 10: 104ºF

and 60 mph21.6 21.6

1.5 45.7

45.7

21.6 21.6

21.6

21.62.5 45.7 21.6 21.6 21.63.5 43.3 21.6 21.6 21.66 43.3 21.6 21.6 21.68 43.3 19.2 21.6 21.6


0.25 3.6

3.6

3.2

3.6

7.6

7.6

3.6

3.6

0.5 3.6 3.2 7.6 3.60.75 3.6 3.2 7.6 3.61.5 3.6 3.6 7.6 3.62.5 3.6 3.6 7.6 3.63.5 7.6

7.63.6 7.6

3.63.6

6 3.6 3.2 3.6 3.68 3.6 3.2 3.6 3.2


0.25 3.6

11.2

3.2

3.6

7.67.6

3.6

3.6

0.5 3.6 3.2 7.6 3.60.75 3.2 3.6 7.6 3.61.5 11.2 3.6 3.6

3.6

3.62.5 11.2 3.6 3.6 3.63.5 11.2 3.6 3.6 3.66 4 3.2 3.6 3.68 3.6 3.2 3.6 3.2

13

Viscoelastic vs. Pseudo-Dynamic analysis

400

500, m

icro

ns 4-inch HMA layer - 70ºF - 40 mph

400

500

, mic

rons 4-inch HMA layer - 70ºF - 60 mph

400

500

mic


4-inch HMA layer

0

100

200

300

0 100 200 300 400 500

Com

pute

d ps

eudo

str

ains

,

3D-Move viscoelastic strains, microns

εxx

εyy

εzz

+10%

-10%

400

500

rain

s, m

icro


800

1000

1200

rain

s, m

icro


0

100

200

300

0 100 200 300 400 500

Com

pute

d ps

eudo

str

ains

,


εxx

εyy

εzz

+10%

-10%

0

100

200

300

400

0 100 200 300 400 500

Com

pute

d ps

eudo

str

ains

, m


εxx

εyy

εzz

+10% -10%

800

1000

1200

rain

s, m

icro


0

100

200

300

0 100 200 300 400 500

Com

pute

d ps

eudo

str


εxx

εyy

εzz

+10%

-10%

0

200

400

600

0 200 400 600 800 1000 1200

Com

pute

d ps

eudo

str


εxx

εyy

εzz

+10%

-10%

0

200

400

600

0 200 400 600 800 1000 1200

Com

pute

d ps

eudo

str


εxx

εyy

εzz

+10%

-10%

Viscoelastic vs. Pseudo-Dynamic analysis

8-inch HMA layer200

mic


200

mic


200

mic


0

50

100

150

0 50 100 150 200

Com

pute

d ps

eudo

str

ains

, m


εxx

εyy

εzz

+10%

-10%

600

750

900

stra

ins,

mic


0

50

100

150

0 50 100 150 200

Com

pute

d ps

eudo

str

ains

, m


εxx

εyy

εzz

+10%

-10%

600

750

900

o st

rain

s, m

icro


0

50

100

150

0 50 100 150 200

Com

pute

d ps

eudo

str

ains

, m


εxx

εyy

εzz

+10%

-10%

450

600

750

900

do s

trai

ns, m

icro


εxx

0

150

300

450

0 150 300 450 600 750 900

Com

pute

d ps

eudo

s


εxx

εyy

εzz

+10%

-10%

0

150

300

450

0 150 300 450 600 750 900

Com

pute

d ps

eud


εxx

εyy

εzz

+10%

-10%

0

150

300

450

0 150 300 450 600 750 900

Com

pute

d ps

eud


εxx

εyy

εzz

+10%

-10%

14

Pseudo-Static Analysis

• Pseudo-Static:Vehicle speed = 0– Vehicle speed = 0

– Linear Elastic Analysis (LEA)– Use fp to select |E*|fp

– Damping fp = 0

• Also Compare pavement responses following– MEPDG approach (f = 1/t)– Modified MEPDG (f = 1/(2t))– Ferry (f = 1/(2t))

Pavement responses comparison

0.0

0.5

1.0

0 100 200 300 400 500 600


Pavement temperature = 70ºFVehicle speed = 40 mph

0.0

0.5

1.0

0 100 200 300 400 500 600

Maximum tensile strain yy, microns


P t

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn= 14.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat= 14.4 Hz

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn = 14.4 Hz

MEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)

Ferry (fi=1/2tipi) fpseudo stat = 14.4 Hz

0 0

0 100 200 300 400 500 600

Maximum vertical strain zz, microns

Pavement temperature = 70 F4‐inch HMA layer40 mph

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn = 14.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo dyn = 14.4 Hz


15


0.0

0.5

1.0

0 100 200 300 400 500 600 700



0.0

0.5

1.0

0 100 200 300 400 500 600 700



P t

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn = 14.4/30.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat = 14.4/30.4 Hz

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn = 14.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat = 14.4 Hz

0 0

0 200 400 600 800 1000 1200 1400



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dep

th, i

n

3D-Move Viscoelastic fpseudo stat= 30.4/14.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat= 30.4/14.4 Hz



0.0

1.0

2.0

0 50 100 150 200 250 300



0.0

1.0

2.0

0 50 100 150 200 250 300



2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn=12.8/30.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo st=12.8/30.4 Hz

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn = 12.8 Hz

MEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)

Ferry (fi=1/2tipi) fpseudo st = 12.8 Hz

0 0

-100 0 100 200 300


P t0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn = 30.4/12.8 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo st = 30.4/12.8 Hz



16


0.0

1.0

2.0

0 100 200 300 400 500 600 700


0.0

1.0

2.0

0 100 200 300 400 500 600 700


P t

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn=14.4/30.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat=14.4/30.4 Hz


2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn= 14.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat= 14.4 Hz


0 0

0 200 400 600 800 1000 1200 1400



0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Dep

th, i

n

3D-Move Viscoelastic fpseudo dyn= 30.4/14.4 HzMEPDG (fi=1/ti) Modified MEPDG (fi=1/2ti)Ferry (fi=1/2tipi) fpseudo stat= 30.4/14.4 Hz



Pavement temperature = 70 F4‐inch HMA layer

17





18



Overall Findings

• Use of one single set of fp cannot be assigned to the AC layer to study all responses. layer to study all responses.

• Pavement responses can be successfully predicted (within ±10%) by Pseudo-Dynamic equivalent approach.

• MEPDG approach derives in comparable pavement responses only when asphalt layer is stiff and there are no multiple fp within the asphalt layer.

19

Additional needed work…

• Investigate influence of axle load, response location and axle configuration on faxle configuration on fp.

• Investigate influence of CTB on fp.

• Evaluate different time-frequency conversions.

• Other!

…Feedback…

Acknowledgment

– This work is part of the overall effort in the Asphalt Research Consortium (ARC) work element E2d Research Consortium (ARC) work element E2d. (www.arc.unr.edu)

– FHWA support gratefully acknowledged.

f f– Contents reflect the views of the authors and do not necessarily reflect the official views & policies of FHWA.

equivalent loading asphalt layer pavement …...1 equivalent loading frequencies to simulate asphalt...

Documents