models for permanent deformation for bituminous bound materials in flexible pavements

ISTU

SAMARIS – Presentation Draft Deliverable 11 – WP5 Meeting Roskilde, Denmark – 23/02/04 1

Institute for Road Construction and Maintenance – Vienna University of Technology

MODELS FOR PERMANENT DEFORMATION FOR BITUMINOUS BOUND MATERIALS IN FLEXIBLE

PAVEMENTS

Deliverable 11

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SURVEY PRESENTATION:

• Survey Models• Test Types• Required Laboratory Test Data• Further Steps• Discussion and Questions

Survey ModelsTest TypesRequired DataFurther Steps

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SURVEY MODELS

Routine Level Advanced Level

Francken / BRRC SHRP – Level II

SPDM / Shell Erkens / Delft

SHRP – Level I Maxwell model / ISTU

DBN / ENTPE


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SUMMARY TEST TYPES

• DSR Tests (Binder) Francken• Shear Tests (SST) SHRP• Uniaxial Creep Test Erkens• Uniaxial Dynamic Test SPDM• Triaxial Creep Test DBN• Triaxial Dynamic Test Francken, ISTU• Uniaxial Tension Test Erkens


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REQUIRED LABORATORY TESTS

LAB TEST

MODEL

Unia

xia

l Cre

ep T

est

Unia

xia

l Rep. Lo

ad T

est

Tria

xia

l Dynam

ic Test

Tria

xia

l Cre

ep T

est

Unia

xia

l Tensio

n T

est

RSST-C

H (S

ST)

FS-S

(SST)

Volu

metric T

est (S

ST)

Unia

xia

l Stra

in T

est (S

ST)

DSR

Tests

Francken / BRRC X X

SPDM / Shell X (X)

SHRP – Level I X X

SHRP – Level II X X X

ACRe / Delft X X

Maxwell model / ISTU X (X)

DBN / ENTPE X

... test performed at ISTU–Lab

... SHELL ... TRL

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FURTHER STEPS

Literature study (models)

Calibration of selected models

Validation of the selected models

Selection of potential models for validation

Data Lausann

e

Data Nantes

Data DART

Laboratory Test Data

Deliverable 11

Deliverable 28Survey ModelsTest TypesRequired DataFurther Steps

Selection of models for validation

?

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FURTHER STEPS


Activity of Partner Schedule Partner

Pre-selection of models for validation 23-02-2004 WP5

Designation of required laboratory test data 23-02-2004 WP5

Selection of historical data - Nantes Test Track until 07-2004 LCPC

Material transport and specimen preparation until 05-2004 ISTU

Laboratory Tests at ISTU from 05-2004 ISTU-Lab

Other laboratory tests (SHELL, TRL, DRI, LCPC) from 05-2004 all WPP

Analysis of test track data from 05-2004 ISTU

Calibration (FE-code implementation and simulations)

spring 2005 ISTU

Validation Summer 2005 ISTU

Deliverable 28 09-2005 ISTU

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Permanent Deformation Model by Francken/BRRC


• Basic principles:• Material model• Based on triaxial dynamic tests

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Francken / Basic principles:

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Francken / Basic principles:


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• Key equations:

25.0

31

25.0

31

1000*210002

f

N

Eff

N

EN

p

p

*log11,01135,11*log*log

10436,1

,**

1013,0

1010

1084,555,04 2

FeFR

V

VU

eUE

fTREE

U

B

A


p... plastic deformation

1... amplitude of vertical stress

3... lateral stress

Ep... plastic deformation modulus

N... number of load repetitions

f... load frequency

f()... coefficient, dependent on the void content

E*... complex elastic modulus

E∞... purely elastic or „glassy“ modulus

R*... reduced modulus

T... temperature

VA... aggregate content [Vol %]

VB... binder content [Vol %]

F*... reduced shear modulus (binder)

Francken / Key equations

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• Input parameters for the model: • Complex elastic modulus E*• Complex shear modulus G* of the binder • Aggregate content [vol. %]• Binder content [vol. %]


Francken / Input parameters

Triaxial test

DSR and vol. asphalt characteristics

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Rutting Prediction within the SHELL Pavement Design Method (SPDM)


• Basic principles:• Rutting prediction model• Multi layer theory (BISAR)• Based on the ratio of the stiffness of the asphaltic mix

and its bituminous binder• Uniaxial repeated load tests or RSST-CH for

determination of input parameters• SPDM-PC program for the calculation of rut depths

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• Key equations:


vbitvmix SqbS ,, logloglog

Smix,v Stiffness of the mix

Sbit,v Viscous component of the stiffness of the bituminous binder

b, q... Parameters, specific for a certain asphaltic mix, determined by creep tests0... Bitumen viscosity at the average paving temperature

Weq... ESALs

tw...Wheel loading time (traffic speed)

h... Rut depthk... Coefficient k=CmZ0, dynamic factor Cm= 1 by default

Z0... Configuration factor

0... Contact stress of the standard wheel

av,0...Average stress in the asphalt layer resulting from one standard wheel pass

h... Thickness of the asphalt layer

weqvbit tW

S

0

,

3

vmixShkh

,

0

0

0,0

avZ

SPDM / Key equations

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SPDM / Input parameters• Input parameters for the model:

•Traffic: axle loads, wheels per axle, axles per day and line, contact stress, rate of traffic growth per year, design period, loading time

•Climate: MMAT (Mean Monthly Air Temperature in °C)

•Material characteristics: penetration of the bitumen at 25°C, softening point of the bitumen, polymer modified bitumens: viscosities at two temperatures, mix composition (Vol.% bitumen, Vol.% aggregate), creep characteristics (parameters q and b)

•Structure: total thickness of asphalt layers, thickness of sub-base, Poisson’s ratio of asphalt layers, of the sub-base and of the subgrade, modulus of elasticity of the sub-base and the subgrade

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Rutting prediction model within the Strategic Highway Research Programme (SHRP) – Level I

• Basic principles:• Rutting prediction model• RSST-CH for determination of the input parameters• Traffic and climate assumptions included into model


50 °C @ 70 kPa

0.001

0.01

0.1

1 10 100 1,000 10,000RSST Belastungszyklen

WT 8-1

WT 8-3

WT 9-1

5%

RSST load cycles

Permanent shear deformation p

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Compare Nsupply with Ndemand

Select pavement structural section

Select trial mix

From simple shear test(s) at Tc select Nsupply for predetermined

allowable rut depth

Select multiplier M for Ndemand to reflect design reliability and

variabilities in Nsupply and Ndemand

Traffic, Environment

Nsupply < M ∙Ndemand

Mix

no

t sa

tisf

acto

ry

Mix satisfactory

Determine critical temperature Tc

Compute M ∙ Ndemand

Convert estimated traffic to Ndemand at Tc

Nsupply M ∙Ndemand

SHRP Level I / Basic principles

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SHRP Level I / Key equations

• Key equations:

SFTCFESALsNdemand

demandsupply NMN


Ndemand... applied traffic demand

TCF... temperature conversation factor (to be determined for specific climatic conditions)

SF... empirically determined shift factor (traffic wander, construction variability, differences between field and laboratory stress conditions, etc.)

Nsupply... estimated load repetitions to a limiting prescribed rut depth

M... reliability factor

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• Input parameters for the model: • ESALs• Temperature in form of a temperature equivalency factor• Chosen reliability

• Nsupply from RSST-CH for allowable rut depth


SHRP Level I / Input parameters

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• Basic principles: • Based on a rheological model (see figure)• FS-S, volumetric tests (SST) and uniaxial strain test (SST)

for the determination of the input parameters• FE analysis

Permanent deformation model within the Strategic Highway Research Programme (SHRP) – Level II

Maxwell model

Elastoplastic branch

...

E0

E1

En

1

n

P0


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Select pavement structural section

Select trial mix

Perform suite of tests to define mix parameters

for constitutive relationship

Estimate rut depth for Ndemand using FE solution

Compare rdcalc with

rdallow

TrafficEnvironment

rdcalc rdallowrdcalc rdallow

Mix

no

t sa

tisf

acto

ry

Mix satisfactory

Response model

SHRP Level II / Basic principles

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• Input parameters for the model:• Traffic and climate data see Level I• Parameters for the rheological model:

SHRP Level II / Input Parameters

Type of parameterName of parameter

Test

Nonlinear Elastic Parameters

C2, C4, C9Simple Shear Constant Height (Creep)

C1, C3, C6 and C7 Uniaxial Strain

C5 and C8 Volumetric

Viscoelastic Parameters

G*, , aTSimple Shear Constant Height (Frequency Sweep)

Plastic Parameters , y, Simple Shear Constant Height (Creep)H

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Asphalt Concrete Response model (ACRe) by Erkens / Delft• Basic principles:

• Material model• Based on Desai model (figure)• Uniaxial creep tests and uniaxial tension tests for the

determination of the input parameters• FE analysis


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ACRe / Key equations and input parameters

• Key equations:

0

3cos1

11

22

a

n

a

a

pRI

pRI

p

Jf

I1... first invariant of the stress tensor

p... isotropic stress

J2... second deviatoric stress invariant

J3... third deviatoric stress invariant

, , , n, R: model parameter

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Permanent Deformation Prediction Based on a Generalized Maxwell Model

• Basic principles:

• Rheological Material modelDecomposition of the Stress Tensor Pressure volume part of the material behavior is

assumed to be governed by a linear elastic model Deviatoric parts are assumed to satisfy a viscoelastic

model of a Generalized Maxwell Model

• Frequency sweep shear tests (FS-S) or dynamic triaxial testsat different frequencies and temperatures

• FE analysisSurvey ModelsTest TypesRequired DataFurther Steps

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Constitutive Equations

Deviatoric PartVolumetric Part

Stress Tensor

Representation

K0

Linear elastic model

G0G1 G2 Gn

1 2 n

Generalized Maxwell model

3

3 1 2

kk kkK

EK

0

2 d

t

ijij

ds t G t

/( ) ktk

k

G t G e

REPRESENTATION & CONSTITUTIVE EQUATIONS


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DATA FITTING MATERIAL MODELMATERIAL TESTING

PARAMETER

elastic: G0, G1, ... Gn

viscous: 1, 2, ... n

RESULTS G*()

()

G‘()

G“()

2 2

2 2( )1

kk

k k

G G

2

2 2( )1

kk

k k

G G

RELATIONSHIP(Tschoegl, 1988)

FS-S - TEST

G*

GENERALIZED MAXWELL MODEL

G0G1 G2 Gn

1 2 n



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28

xy

z PERSPECTIVE VIEW OF THE FE - MESH

REPRESENTATION OF A PAVEMENT IN A 3D FE - SYSTEM


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TIRE FOOTPRINT

VERTICAL CONTACT STRESS(FE – LOAD PATTERN)

Radial Tire - 56kN @ 690 kPa

VERTICAL CONTACT STRESS(TRANSPOSED SIM MEASUREMENT)

VRSPTA MEASUREMENT FE – LOAD INPUT

Permanent Deformation Prediction Based on a Generalized Maxwell ModelLOAD MODEL

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30

70 mm

140 mm

Pavement100.000 Load cycles

Normal stresses 22

SIMULATION RESULTS


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Permanent Deformation Model by Di Benedetto and Neifar (DBN) / ENTPE


• Basic principles:• Material model• Based on a generalized Kelvin-Voigt (KV) model• Calibration of the KV model by means of the Huet-Sayegh

model and a viscoplastic criterion by Di Benedetto• Triaxial creep tests for the determination of the input

parameters• Computer program EP1

V1

EP2

V2

EPN

VN

EP0VN+1

EP1 EP2 EPNE0

1(T) 2(T) N(T)

(a)

(b)

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DBN / Basic principles


(a) Huet-Sayegh model

Used for calibration in the small strain domain

(b) viscoplastic criterion by Di Benedetto

Used for model calibration in case of viscoplastic flow

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DBN / Key equations

• Key equations:

1

10

mod 11,*

n

j jj

el

TiEETiE

hk

SaySaySay

ii

EEEiE

1* ,0

0

s

sT

jj

TTC

TTCa

TT

2

1log

ni

i

SayModelSayModel EEEE1

2

1212

2

1111

ccp

0

ln

0

1

10

1

EE

EE

Say

n

j j

Say

Minimisation of:

E*model... complex elastic modulus of the DBN model

E*Say... complex elastic modulus of the Huet-Sayegh model

n... chosen number of KV bodies

... pulsation (=2f with frequency f)

i... complex number

T... temperature

... viscosity as function of the temperature

p... stress

c, c, ... functions of the temperature

0... 1%/min

aT… temperature translation factor

(a) (b)

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DBN / Input parameters

• Input parameters for the model:

• 3 constants for the WLF equation: C1, C2, TS

• 5 constants for the linear domain: k, h, , E∞Say, E0

Say

• 3 constants for plastic flow: C, , C

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DSRVisco-elastic behaviour

4 – 40 °C fatigue behaviour (SuperPave)

40 – 85 °C permanent deformation (SuperPave)


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36

MACHINE LAYOUT PICTURE

Simple Shear Tester


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RSST-CH

h = 0

perm. shear deformation

Haversine shear wave; typically 0,1sec on and 0,6sec off


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FS-S

s

h=0

Sinusoidal deformation wave, typically 10, 5, 2, 1, 0.5, 0.2, 0.1, 0.05, 0.02 and 0.01 Hz


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Uniaxial and Triaxial Tests

•Creep tests

The applied axial load is constant, so that specimen failure does not result from sudden load pulses. Most of these tests are run in compression states of stress.

•Repeated Load Tests

A block pulse waveform that is not symmetric is applied to the specimen. One load cycle contains a load period and a rest period.

•Dynamic/Cyclic Load Tests

Axial symmetric load curves are applied to the test specimen. Tests can be run in tension-compression as well as in compression only.Survey Models

Test TypesRequired DataFurther Steps

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0

600

0

time [sec]

loa

d c

urv

e f

orm

Creep test Repeated load test Dynamic load test

Test Types / Uniaxial and Triaxial Tests

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1,0 m (39.4 in.)

1,5

m

(59.1

in.)

3,1

m (1

22

.1 in

.)980 kg

-10 to +65 °C

(14 to 149 °F)

SERVO-HYDRAULIC TRIAXIAL TESTING MACHINE WBL0/050HH

Testing Equipment at ISTU Vienna

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42

Simulation of traffic load with

• constant cell pressure

• dynamic, sinusoidal axial load

• dynamic, oscillating cell pressure – phase displaced but of same frequency;

designed to prevent radial expansion completely or in part

PHASE LAG

CELL PRESSURE

AXIAL LOAD

AX

IAL

LOA

D

RA

DIA

L R

EA

CTIO

N


SERVO-HYDRAULIC TRIAXIAL TESTING MACHINE WBL0/050HH

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• stainless steel shell, up to 20 bar

• tension and compression – axial load

• compression resistant grommets

• installation volume measurement cell (for exact volume measuring) possible

• linear controlled LVDT’s for radial strains (inside)

• axial strain measuring with LVDT’s (inside/outside)

TRIAXIAL CELL



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Uniaxial Tension Test


Test specimen shape used by Erkens in her ACRe model

models for permanent deformation for bituminous bound materials in flexible pavements

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