7th RILEM International Conference on Cracking in Pavements || Top-Down and Bottom-Up Fatigue Cracking of Bituminous Pavements Subjected to Tangential Moving Loads

A. Scarpas et al. (Eds.), 7th RILEM International Conference on Cracking in Pavements, pp. 675–685. © RILEM 2012

Top-Down and Bottom-Up Fatigue Cracking of Bituminous Pavements Subjected to Tangential Moving Loads

Zoa Ambassa1,2, Fatima Allou1, Christophe Petit1, and Robert Medjo Eko2

1 Groupe d’Étude des Matériaux Hétérogènes – Equipe Génie Civil et Durabilité, Université de Limoges, boulevard Jacques Derche, 19300 Egletons, France 2 University of Yaoundé I, P.O. 812 Yaoundé, Republic of Cameroon

Abstract. A model allowing for the determination of bituminous pavement degradation on traffic circle is presented. The development work has relied on the viscoelastic modeling of bituminous pavements subjected to multiple-axle traffic loads, using the following variables: pavement structure, load speed (or frequency), load configuration, and bituminous materials temperature. The method derived has successfully simulated the phenomenon under investigation. Results obtained indicate that the design concept based on bending fatigue in bituminous layers is not sufficient to realistically predict the degradation of a bituminous pavement structure. The phenomenon of shear at bituminous interface must also be taken into account, as revealed by the simulation results for the degradation of two pavement structures from the French design code [10] (i.e. flexible pavement and thick asphalt pavement).

1 Introduction

Trucks driving over pavements across the world feature multiple axle configurations, ranging from a single axle up to 8 axles [1-2]. Motor vehicles with such configurations also cause pavement degradations, the extent of which has yet to be sufficiently assessed. To date, the relative intensity of multiple-axle loads has been determined through the application of Miner’s law. From a material mechanics standpoint, the fatigue life expectancy of a bituminous layer is evaluated in the laboratory using a two-point flexural strength test (NF EN 12697-24), consisting of inserting into the small base of a trapezoid a tube embedded in its larger base. With this position, the set-up emits a continuous sinusoidal signal that helps determine the number of load cycles before failure occurs [3]. It is observed that the load signal shape affects the fatigue life expectancy of asphalt pavements [1-5].

Pavement structure materials are made to be subjected upon every truck crossing to both fast and short loadings. The accumulation of damage generated in these materials, which is reflected in a loss of stiffness, leads to fatigue cracking. The

676 Z. Ambassa et al.

objective of this paper is to develop a model which will allow determining the pavement degradations which occur on traffic circle. The work performed has been based on the following variables: type of pavement structure, load speed (or frequency), load configuration, and bituminous material temperature. Various moving loads configurations (single, dual standard (130-kN), tandem and tridem-axle loads) will be considered. The effects of tire loading on pavement degradation on traffic circle will be assessed by taking into account not only the vertical component, but also the centrifugal strengths (transverse component) and the effect of braking (longitudinal component). The viscoelastic law of the Generalized Kelvin-Voigt model, which has been incorporated into the Cast3M FE code [6], will be used to estimate the mechanical behavior of bituminous layers.

2 Bituminous Materials Behavior

The pavement structure is composed of two identical viscoelastic bituminous layers (BB: asphalt concrete and GB: asphalt gravel). Their complex modulus was measured in the LCPC Laboratory [7]. The complex modulus responses of the mixes measured in the laboratory were first replicated using the 2S2P1D model, which is a generalization of the Huet-Sayegh model [8]. In reference to the 2S2P1D model, the Kelvin-Voigt body values were fixed. Table 1 lists the Kelvin-Voigt parameters used for bituminous materials (BB and GB) [9].

Table 1. The Generalized Kelvin-Voigt model parameters at 20° and 30°C.

n ° Ei (MP a) i(20°C) (MP a.s ) i(30°C) (MP a .s ) Ei (MP a) i(20°C) (MP a.s ) i(30°C) (MP a.s )

33500 310001 1479000 9,15E-06 5,34E-07 1522500 1,04E-05 8,95E-072 1397400 8,65E-05 5,04E-06 1438500 9,79E-05 8,46E-063 1091400 6,76E-04 3,94E-05 1123500 7,65E-04 6,61E-054 705840 4,37E-03 2,55E-04 726600 4,95E-03 4,27E-045 433500 2,68E-02 1,57E-03 446250 3,04E-02 2,62E-036 265200 1,64E-01 9,57E-03 273000 1,86E-01 1,61E-027 159120 9,85E-01 5,74E-02 163800 1,12E+00 9,63E-028 90576 5,61E+00 3,27E-01 93240 6,35E+00 5,48E-019 46716 2,89E+01 1,69E+00 48090 3,27E+01 2,83E+0010 20196 1,25E+02 7,29E+00 20790 1,42E+02 1,22E+0111 7007 4,34E+02 2,53E+01 7214 4,91E+02 4,24E+0112 1999 1,24E+03 7,22E+01 2058 1,40E+03 1,21E+0213 495 3,06E+03 1,79E+02 509 3,47E+03 2,99E+0214 99 6,12E+03 3,57E+02 102 6,93E+03 5,98E+0215 22 1,33E+04 7,77E+02 22 1,51E+04 1,30E+0316 216 1,34E+06 7,81E+04 223 1,52E+06 1,31E+0517 733 4,54E+07 2,65E+06 755 5,14E+07 4,44E+0618 19278 1,19E+10 6,96E+08 19845 1,35E+10 1,17E+0919 504900 3,13E+12 1,82E+11 519750 3,54E+12 3,06E+11

BB GB

3 The Pavement Model Considered for the Present Analysis

The French design code for pavement structures [10-11] proposes a set of sizes (materials and layers thicknesses) for pavement structures. This set is based on the

Top-Down and Bottom-Up Fatigue Cracking of Bituminous Pavements Subjected 677

class of trucks traffic (TCi), the class of pavement foundation performance (PFi) and the road category. The mechanics associated with the material properties and layer thicknesses of the selected pavement structures are demonstrated in Figure 1.

E=300 MPa

E=120 MPa

6 cm8 cm20 cm

300 cm

E= 50 MPa

6 cm8 cm8 cm

300 cm

Flexible Pavement

1. Surface course of asphalt concrete2. Base layer of asphalt gravel3. Unbound granular materials4. Pavement foundation

Thick asphalt Pavement

1. Surface course of asphalt concrete2. Base layer of asphalt gravel3. Base layer of asphalt gravel4. Pavement foundation

Fig. 1. The selected Asphalt pavements samples

3.1 Model Geometry and Mesh

Different types of loads can be considered in a pavement design. These are related to single, dual, tandem or tridem-axle loads. To take into account the effects of different configurations of loading, the French design method consists of modeling single or dual loads effects on an elastic pavement. The vertical contact stresses in this study equal 662 kPa (for the single, dual standard and tridem axle) and 535 kPa (for the tandem axle), centrifugal stress is 472 kPa and braking stress is 347 kPa.

O

Z

L

T

vertical strengths

Fig. 2. The 3D FE model geometry for a dual standard

Effects of moving tire loading were estimated on traffic circle by taking into account not only the vertical component, but also the transverse component and the effect of braking (longitudinal component). The structures were modeled in 3D


by means of the Cast3M FE code [6]. The FE mesh employed and the modeled pavement geometry are both shown in Figure 2 (for a thick asphalt pavement). The eight-node hexahedral “brick” elements were used for the FE analysis. When using the dual axle configuration at 42 km/h in the thick asphalt pavement structure, the mesh contains 90,752 elements and a total of 98,338 nodes. The interfaces between pavement layers were assumed to be perfectly bonded.

3.2 Moving Load Analysis and Boundary Conditions

The considered pavement section was composed of homogeneous and isotropic elastic material layers (pavement foundation and unbound granular materials) as well as bituminous layers with linear viscoelastic behavior. The Generalized Kelvin-Voigt model was implemented for this purpose (its parameters were listed in Table 1). For each layer, Poisson’s ratio of 0.35 has been used. A mechanical calculation of this pavement structure has been performed in using small strains under a moving load at constant speed, over same time period as the OL axis (longitudinal axis) (Fig. 2). The pavement response due to a moving tire load has been estimated at 42 km/hr. The load duration depends on both the vehicle speed S and length l of the tire contact area. It is reasonable to assume that the load exerts practically no effect when it is located a distance of 6l from the point under consideration. In this paper, the tire contact pressure is uniformly distributed over a rectangular surface area 270*184 mm2, with the inter-axle distance equal to 1.35 m for multi-axle configurations. The vertical, transverse and longitudinal displacements of the bottom plane of the model (Fig. 2) are fixed. The nodes of both sides of the L-Z plane, which transversely limit the model, are constrained relative to the T axis (transverse axis), and the movements of both transverse T-Z planes are constrained with respect to the L axis (longitudinal axis).

4 Pavement Response and Damage Analysis

In this section, the effects of loading a moving tire on the pavement will be discussed. These results have been derived from the simulation run on Cast3M [6]. The numerical calculation resulting from the simulation of single, dual, and multiple-axle loading conditions will then be given. For the elastic calculus, viscoelastic effects due to asphalt materials are taken into account only through an equivalent elastic modulus, which is determined from complex modulus test. The values of frequency of request are computed from the signals of longitudinal strain at the bottom of the Bituminous Gravel (GB) in the single wheel path. The period T is measured between both peaks in contraction of the longitudinal signal [12] (see figure 3). The frequency determined by this method is equal to 8 Hz [9]. It corresponds to a vehicle speed of 42 km/h at a reference temperature. This frequency was determined in the thick asphalt pavement at a depth of 22 cm from


the surface of pavement. The equivalent elastic modulus obtained for the reference temperatures (20 and 30 °C) and a frequency of 8 Hz are the followings:

- BB at a frequency of 8 Hz: E=6000 MPa at 20 °C; E=1300 MPa at 30 °C. - GB at a frequency of 8 Hz: E=6000 MPa at 20 °C; E=2000 MPa at 30 °C.

-100

-50

0

50

100

150

200

250

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

Horiz

onta

l mic

rost

rain

s

Time (s)

Thick asphalt pavement

εt,L (S=42km/h--T=30°C)

εt,T (S=42km/h--T=30°C)

T=0,12s

Fig. 3. Frequency measured between both peaks in contraction of the longitudinal signal at the bottom of the GB layer

4.1 Numerical Calculation Results

Figure 4 presents the horizontal strain signals at the bottom of the GB3 layer for tridem axle configuration. These results are simultaneously obtained thanks to a viscoelastic and elastic calculus on Cast3M. The signals of the viscoelastic calculus are expressed according to the speed (S) and to the temperature (T) whereas those of the equivalent elastic calculus are expressed according to the frequency (f) and the temperature. Furthermore, the slowing in the recovery of transverse strain cannot be predicted by the elastic model. This delay is ascribable to viscoelasticity, as illustrated by the experimental results, which clearly indicate that bituminous material viscoelasticity needs to be taken into account in order to generate a more realistic simulation of strains produced by loads moving at low speed on flexible pavements.

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

Hor

izon

tal m

icro

stra

ins

Time (s)

Thick asphalt pavementεt,L (S=42km/h - T=30°C)

εt,T (S=42km/h - T=30°C)

εt,L (F=8Hz-T=30°C)

εt,T (F=8Hz-T=30°C)

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

Hor

izon

tal m

icro

stra

ins

Time (s)

Thick asphalt pavementεt,L (S=42km/h - T=30°C)

εt,T (S=42km/h - T=30°C)

εt,L (S=42km/h - T=20°C)

εt,T (S=42km/h - T=20°C)

a) b)

Fig. 4. Computed longitudinal (εt,L) and transverse (εt,T) strains at the bottom of the GB layer (for a thick asphalt pavement) for the tridem axle configuration


The main modifications brought about by the viscoelastic modeling with respect to the elastic modeling (Fig. 4-a) are the following: the maximal amplitudes of transverse strain signals are higher than the longitudinal (thick asphalt pavement), the viscoelastic signals are dissymmetrical, the amplitudes of maximum strain obtained by the viscoelastic modeling are obtained after the middle of the load crosses the point of measure, this occurs as later as temperature is increased. Along the length direction, the area of strain distribution increases as the temperature drops (Fig. 4-b). The loading time gradually decreases as the number of axles rises. Figure 5 displays computed longitudinal shear stresses of the BB/GB interface layer for the tridem axle configuration. The latest fatigue test studies bituminous material behavior in either bending or tension-compression. At the present time, the design concept based solely on bending fatigue is insufficient to realistically predict the fatigue life expectancy of a pavement structure; the phenomenon of shear at the BB/GB interface must also be taken into account. At this interface, the maximum shear stress develops in the bituminous pavement structure [13]. To date, identifying the fatigue behavior of pavement structures by the bending of bituminous layers has been preferred, as well as by the shear at the BB/GB interface. These two approaches complement each other in deriving a global prediction of the fatigue life expectancy of pavement structures.

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

Shea

r str

ess

at B

B/G

B in

terf

ace

(MPa

)

Time (s)


σ,LZ (S=42km/h--T=30°C)

σ,LZ (F=8Hz-T=30°C)

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

Shea

r str

ess

at B

B/G

B nt

erfa

ce (

MPa

)

Times (s)


σ,LZ (S=42km/h--T=30°C)

σ,LZ (V42km/h--T=20°C)

Fig. 5. Computed longitudinal (τLZ) shear stresses at the BB/GB interface (thick asphalt pavement) for the tridem axle configuration

The results presented in this section reveal that both the quantification and qualification of the strains and shear stress signal depend on the loading history experienced by the pavement structure. The developed method indicates that the intrinsic magnitudes helping to characterize strains and shear stress signals are not neccessarily constant, but instead functions of the following main parameters:

- pavement structure (material behavior, thickness and stiffness of pavement layers, temperature, type of interface between layers, etc.);

- load configuration (intensity, type of wheels, axles, etc.); - load speed (or frequency).


It would be possible to list all these parameters affecting the bituminous behavior of a pavement structure, but it would not be realistic to separate them should the goal be to improve the knowledge of the structural behavior since take place between these various parameters.

4.2 Damage Analysis

Characterizing the bituminous pavement damage caused by multiple-axle loads requires both the quantification and summation of pavement responses. The Load Equivalent Factor (LEF) is defined as the damage of an axle group relative to the damage of a dual standard axle (130-kN). In this paper, the LEF has been calculated according to the strain area mathod. This method has been devoloped by Chatti and Hajek [1-2,14] (Equat. 1 and 2).

.

tan .. .

0

0

ni

Axle j

s dard axle s ni

t

j

t

s

DamageLEF

Damage

dt

dt

ε

ε= =

(1) 0

0

ni

ni

t

j

t

s

LEF

dt

dtτ

τ

τ=

(2)

ƐS,j is the horizontal strain acting upon the dual standard axle s (respectively axle j); t is the time, if this strain is expressed in the time domain, or the distance, if the strain is expressed in the space domain; τs,j is the shear stress at the BB/GB interface subjected to the dual standard axle s (respectively axle j); and ni is the integration method exponent (n=1 in this paper).

Table 2 presents the LEF of loading of a moving tire on the bituminous pavement structure on traffic circle. It is determined by using the relationship 1 and 2.

Table 2. The LEF on the GB3 layer and LEFτ at the BB/GB interface

Axle Single Dual standand (130 kN) Tandem Tridem

LEF 0.86 1.00 1.61 2.36

LEFτ 0.85 1.00 1.32 1.80

4.3 Towards a Proposition of a New Fatigue Law of Multi-axle Configurations

The current law, which verifies the fatigue of bituminous layers in bending, as defined by the relationship in (Equat. 3), does not strictly allow taking into account all parameters influencing pavement structure behavior, as presented in the Section 4.1.

( ) ( )log .logf tN a bε= + (3)


A new fatigue law has therefore been adopted. Such a law overcomes the gaps in the current fatigue law for multi-axle configurations; it uses both the LEF (Equat. 1) and strain amplitude as inputs. For these special configuration, the critical strain will represent the maximum peak in tension. The expression of this new fatigue law is given by the relationship (4). Similarly, a new fatigue law to identify cracking occurring at the interface is given by the relationship (5).

1

1.

bt

fNLEF a

ε − =

(4)

1

max.

1.

b

f iNLEF aτ

τ − =

(5)

4.4 Predictions of Pavement Lives

The French design method [10] uses the following fatigue criterion on bituminous layer:

( ) ( )( )

0,5

6 6

1010 ,25 . . . .

10

b

ft c r s

eq

NE CC Hz k k k

E Tε ε

° = °

(6)

Similar to the fatigue cracking model, the interface fatigue model can be written as follows [15-17]:

( )( )

1.697 0,223

.6 6

10.

20 10f is

s

NK C

K Cτ τ

− − ° = °

(7)

with: 6

6

(10 ) : 0,36 ; 104 /

(20 ) : 0,13 ; 57 /s

s

C MPa K MPa mm

C MPa K MPa mm

ττ

° = = ° = =

The damage is computed as the inverse of the fatigue life expectancy as shown in equation 8.

1

f

DN

= (8)

Tables 3, 4 and 5 present the results of fatigue life and damage on pavement structure analyzed.

Table 3. Fatigue life and damage of the GB layer in the thick asphalt pavement

Axle configuration Temperature 20°C Temperature 30°C Temperature 20°C Temperature 30°C

Viscoelastic calculus (vehicle speed:42km/h) Elastic calculus (Frequecy: 8Hz) Nf (1/Nf) Nf (1/Nf) Nf (1/Nf) Nf (1/Nf)

Single 2.06E+5 4.85E-6 8.61E+4 1.16E-5 5.34E+4 1.87E-5 5.56E+4 1.80E-5 Dual standand (130kN) 2.65E+4 3.78E-5 1.56E+4 6.42E-5 1.31E+4 7.65E-5 3.60E+3 2.78E-4

Tandem 2.25E+4 4.44E-5 8.15E+3 1.23E-4 4.28E+4 2.34E-5 9.00E+3 1.11E-4 Tridem 1.65E+4 6.07E-5 6.84E+3 1.46E-4 1.08E+5 9.25E-6 1.80E+4 5.55E-5


Table 4. Fatigue life and damage of the GB layer in the flexible pavement

Axle configuration Temperature 20°C Temperature 30°C Temperature 20°C Temperature 30°C

Viscoelastic calculus (vehicle speed:42km/h) Elastic calculus (Frequecy: 8Hz) Nf (1/Nf) Nf (1/Nf) Nf (1/Nf) Nf (1/Nf)



Table 5. Fatigue life and damage at the BB/GB interface in the bituminous pavement structures

Axle configuration Viscoelastic: 42km/h Elastic: 8Hz Viscoelastic: 42km/h Elastic: 8Hz

Thick asphalt pavement (temperature 20°C) Flexible pavement (temperature 20°C) Nf (1/Nf) Nf (1/Nf) Nf (1/Nf) Nf (1/Nf)



Figure 6 clearly shows the level of global damage of the pavement structures on

traffic circle. For the thick asphalt pavement structure, the mode of main damage is the “bottom-up cracking” type; whereas the “top-down cracking” damage is the type displayed for the flexible pavement. To date, identifying the fatigue behavior of pavement structures by the bending of bituminous layers has been preferred, as well as by the shear at the BB/GB interface. These two approaches complement each other in deriving a global prediction of the fatigue life expectancy of pavement structures.

0,0E+00 2,0E-05 4,0E-05 6,0E-05 8,0E-05

Single

Dual standard

Tandem

Tridem

Pavement damage (structure VRNS2 : BB/GB/GB) on the Gyrating crossroads

bottom of GB3 layer (S=42km/h, T=20°C)

Interface BB/GB3 (S=42km/h, T=20°C)

0,0E+00 2,0E-05 4,0E-05 6,0E-05 8,0E-05

Single

Dual standard

Tandem

Tridem

Pavement damage (structure VRNS26 : BB/GB/GNT) on the Gyrating crossroads

bottom of GB3 layer (S=42km/h, T=20 °C)

Interface BB/GB3 (S=42km/h, T=20°C)

Pavement damage (thick asphalt pavement) Pavement damage (flexible pavement)

Fig. 6. Pavement damage

5 Conclusion

The objective of this paper was to develop a model allowing the determination of damage of bituminous pavement on traffic circle. The parameters input to simulate the above fatigue were: pavement structure, load speed (or frequency), load configuration, and bituminous material temperature. The method developed in this paper has successfully replicated the observed phenomenon. This paper has also shown that the design concept based solely on the bending fatigue of asphalt layers may not be sufficient to predict damage. Moreover, shear fatigue phenomena at the


BB/GB interface must be taken into account. These two approaches complement each other for a global prediction of the fatigue life expectancy of the bituminous pavement structures.

References

[1] Chatti, K., Salama, H.K.: Evaluation of fatigue and rut damage prediction methods for asphalt concrete pavements subjected to multiple axle loads. International Journal of Pavement Engineering 12(1), 25–36 (2011)

[2] Chatti, K., Manik, A., Salama, H.K., Chadi, M., Lee, S.: Effect of Michigan multi-axle trucks on pavement distress, Final Report MDOT, p. 312 (2009)

[3] Homsi, F.: Endommagement des chaussées bitumineuses sous chargements multi-essieux, Ph.D. Thesis in french, Ecole Centrale de Nantes, France, p. 203 (2011)

[4] Kogo, K., Himeno, K.: The effect of different waveforms and rest period in cyclic loading on the fatigue behavior of the asphalt mixture. In: Al Qadi, Scarpas, Loizos (eds.) Pavement Cracking (2008)

[5] Bodin, D., Merbouh, M., Balay, J.-M., Breysse, D., Moriceau, L.: Experimental study of the waveform shape effect on asphalt mixes fatigue. In: Proceeding of the 7th International RILEM Symposium on Advanced Testing and Characterization of Bituminous Materials (ATCBM 2009), Rhodes, May 26-28, vol. 2, pp. 725–734 (2009)

[6] Cast3M, Cast3M is a research FEM environment; its development is sponsored by the French Atomic Energy Commission (2010), http://www-cast3m.cea.fr/cast3m

[7] LCPC, Vérification du comportement mécanique des matériaux du manège (2003) [8] Olard, F., Di Benedetto, H.: General “2S2P1D” Model and Relation Between the

Linear Viscoelastic Behaviours of Bituminous Binders and Mixes. Road Materials and Pavement Design 4(2), 185–224 (2003)

[9] Zoa, A., Allou, F., Petit, C., Medjo, R.: Modélisation viscoélastique de l’endommagement des chaussées bitumineuses sous chargement multi-essieux. In: Actes des 29e Rencontres Universitaires de Génie Civil, Tlemcen, Algérie, Mai 29-31, vol. 3, pp. 120–129 (2011)

[10] LCPC–SETRA, Conception et dimensionnement des structures de chaussée, Guide technique, Paris (1994)

[11] LCPC-SETRA, Catalogue des structures types de chaussées neuves, Ministère de l’équipement, des transports et du logement (1998)

[12] Domec, V.: Endommagement par fatigue des enrobés bitumineux en condition de trafic simulé et de température, Ph.D. Thesis in french, Université de Bordeaux 1, France,p. 277 (2005)

[13] Zoa, A., Allou, F., Petit, C., Medjo, R.: Importance de la modélisation des interfaces dans la conception rationnelle des chaussées. In: Actes des 28e Rencontres Universitaires de Génie Civil, La bourboule, France, Juin 02-04, pp. 1112–1121 (2010)

[14] Hajek, J.J., Agarwal, A.C.: Influence of Axle Group Spacing on Pavement Damage. Transportation Research Record (1286), 138–149 (1990)

[15] Diakhaté, M.: Fatigue et comportement des couches d’accrochages dans les structures de chaussée, Ph.D. Thesis in french, Université de limoges, France, p. 241(2007)


[16] Petit, C., Diakhaté, M., Millien, A., Phelipot-Mardelé, A., Pouteau, B.: Pavement Design for Curved Road Sections - Fatigue Performances of Interfaces and Longitudinal top-down Cracking in Multilayered Pavements. Road Materials and Pavement Design 10(3), 609–624 (2009)

[17] Diakhaté, M., Millien, A., Petit, C., Phelipot-Mardelé, A., Pouteau, B.: Experimental investigation of tack coat fatigue performance: Towards an improved lifetime assessment of pavement structure interfaces. Construction and Building Materials 25, 1123–1133 (2011)

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7th RILEM International Conference on Cracking in Pavements || Top-Down and Bottom-Up Fatigue Cracking of Bituminous Pavements Subjected to Tangential Moving Loads