Computational modelling of heterogeneity of asphalt mixtures...Daniel Castillo. 31.05.2018....

Daniel Castillo31.05.2018Transport Research Finland 2018

Computational modelling of heterogeneity of asphalt mixtures

AC Heterogeneity

• AC: Mixture and compaction of bitumen, aggregates and air voids. Heavily used in construction of road infrastructure, enduring traffic loadings and environmental conditions.

• Differences among AC constitutive phases’ response to mechanical and environmental solicitations.

• AC is a heterogeneous material, and this heterogeneity may induce variability in the response.

Aggregates Air voids

Fine Aggregate Matrix (FAM)

Initial considerations

“Macro” approaches

A random field is a n-dimensional vector of random values that exhibit spatial correlation.

Correlated random field, isotropic.

Uncorrelated random normal numbers.

3.02-3.23

Three dimensional random field, isotropic

CASTILLO & CARO (2014). “Effects of air voids variability on the thermo-mechanical response of asphalt mixtures”

AC Heterogeneity – “Macro”Random fields

AC Heterogeneity – “Macro”Methodology

Mas

adet

al.

(200

9)

0

500

1000

1500

2000

0 20 40 60

E(t)

[MPa

]

Time [s]

AV 4%

AV 7%

AV 10%

Field of horizontal strains (εh)

-3.08

3.18

εh ×10-4

Random field of Air Voids

4.43

10.07

AV [%]

Calculated Linear Viscoelastic properties

6200

11,900

Eo [MPa]

Air VoidsLVEStrain (εh)

CASTILLO & CARO (2014). “Probabilistic modeling of air void variability of asphalt mixtures in flexible pavements”

AC Heterogeneity – “Macro”

Air Void content 5.9 %

AV 6.6 %

Average AV content 6.45 %

AV 7.4 %

AV 6.68 %

AV 7.06 %

AV 7.44 %

AC layer 1

AC layer 2

AC layer N

AC layer 3

AV 8.3 %

Computational applications

AV [%]1.3 14.88.1 11.44.7


1.0E-04

1.2E-04

1.4E-04

1.6E-04

1.8E-04

98 100 102 104 106 108 110

εh

x [cm]

Bottom row

x

Homogeneous layers

AC Heterogeneity – “Macro”Computational applications


1.0E-04

1.2E-04

1.4E-04

1.6E-04

1.8E-04

98 100 102 104 106 108 110

εh

x [cm]

Bottom row

x

Heterogeneous layers


Response dispersion increases (approx. x8)




Heterogeneous FE model of the pavement structure

Eo [GPa]

20.7

45.9

33.3

39.6

27.0

Area of moving load application

× N

x

y

z

Heterogeneity in the asphalt material (3D RF)


CASTILLO & AL-QADI (2018). “Importance of Heterogeneity in Asphalt Pavement Modeling”

AC Heterogeneity – “Macro”Computational applications

AC layer – Top view

x

y

z

×

7.83 μεCV 5.6%

CASTILLO & AL-QADI (2018). “Importance of Heterogeneity in Asphalt Pavement Modeling”

AC layer – Bottom view

×

x

y

z

std(E11) [με]0.00 9.003.17 6.080.25

7.83 μεCV 6.58%

“Micro” approaches

AV content

Aggregate fraction

AC Heterogeneity – “Micro”Random generator of microstructure (MG)

CASTILLO, CARO, DARABI & MASAD (2015). “Studying the effect of microstructural properties on the mechanical degradation of asphalt mixtures”

MG

2D specimen shape

Gradation Random 2D asphalt concrete microstructure



Random 2D asphalt concrete microstructure


t = 150 s t = 225 s t = 300 s

Pavement Analysis using Nonlinear Damage Approach

DAMAGE DENSITY, Φ0.00 2.531.26 1.890.62


28.11 mm²

0

10

20

30

40

50

60

70

80

100 150 200 250 300

Dam

aged

FAM

are

a [m

m²]

Time [s]

NMAS 12.5 mm4% Air voids

43.00 mm²

0

10

20

30

40

50

60

70

80

100 150 200 250 300

Dam

aged

FAM

are

a [m

m²]

Time [s]


31.89 mm²

0

10

20

30

40

50

60

70

80

100 150 200 250 300

Dam

aged

FAM

are

a [m

m²]

Time [s]


48.50 mm²

0

10

20

30

40

50

60

70

80

100 150 200 250 300

Dam

aged

FAM

are

a [m

m²]

Time [s]


x100specimens

x100specimens

x100specimens

x100specimens



x100

x100

Materials in nature are heterogeneous. Artificial materials, even more! We need to study and include this heterogeneity as an intrinsic part of our computational models.

In summary…What did we do?We considered AC heterogeneity implicitly/explicitly into our computational models.

Why did we do it?Heterogeneity has an important, measurable effect on the variability of material response. This is particularly true for a material as highly heterogeneous as asphalt concrete. Uncertainty data on mechanical properties/response is traditionally scarce.

What can we do with it?• Several applications come to mind. In the previous modelling studies we just generated hundreds (!) of specimens, at

random, with a degree of ‘control’ over properties that only a computer can provide. This can be seen as an alternative to complement the laboratory work, which requires resources (effort, time and materials – money). Also, traditional as well as non-traditional materials and mechanical properties can be tested (RAP, aged materials, aggregate shapes). Some sources call this “virtual laboratory”.

• Apart from the previous modelling studies, it is possible to apply the tools when developing specifications, and for quality control.

• We can estimate new data on uncertainty in response, which is difficult or sometimes impossible to obtain in the laboratory or the field.

• The tools provide a framework for approaching the modelling of heterogeneity to any existing/new materials; they have applicability to a variety of infrastructure and building materials.

Bogotá

Urbana-Champaign

Prof. ImadAl-Qadi, PhD

Prof. Silvia Caro, PhD

College StationDoha

Prof. EyadMasad, PhD

Modelling HeterogeneityCurrent work

Homogeneous plate, 20 GPa

E [GPa]

12.2

26.5

19.3

22.9

15.7

NON-LOCAL EQUIVALENT STRAIN [×10-3]

0.0

8.0

4.0

6.0

2.0Heterogeneous

plate

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Computational modelling of heterogeneity of asphalt mixtures...Daniel Castillo. 31.05.2018....

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