Soufyane Benaboud
email: soufyane.benaboud@unilim.fr

Mokhfi Takarli
email: mokhfi.takarli@unilim.fr

Bertrand Pouteau
email: bertrand.pouteau@eurovia.com

Fatima Allou
email: fatima.allou@unilim.fr

Frédéric Dubois
email: frederic.dubois@unilim.fr

Pierre Hornych
email: pierre.hornych@univ-eiffel.fr

Mai Lan Nguyen
email: mai-lan.nguyen@univ-eiffel.fr

Fatigue Damage Monitoring and Analysis of Aged Asphalt Concrete Using Acoustic Emission Technique

Keywords: Asphalt Concrete (AC), Fatigue loading, Acoustic Emission (AE), Damage behavior, Failure Criteria

This paper presents an Acoustic Emission characterization of the damage behavior of asphalt concrete trapezoidal specimen subjected to bending fatigue loading. An experimental fatigue tests campaign is carried out on a damaged asphalt concrete extracted from an in-service highway pavement, built in 2001. Tests were performed in strain controlled mode with an amplitude of 175 µstrain, a loading frequency of 25 Hz, and at 10°C. Failure criteria based on modulus decrease are analysed to determine the fatigue lifespan. Acoustic emission measurements, as a non-destructive technique, are used to investigate the damage and failure processes in the specimen. A network of eight piezoelectric sensors was used to acquire the acoustic signals. Therefore, different fatigue stages are identified based on the temporal evolution of acoustic activity during the tests.

Hence, the event's spatial location is presented to show the crack path propagation. The results show that sensors located at the bottom of the specimen register more acoustic emission activity. The locations of acoustic events were in good agreement with the mechanical background calculations.

Introduction

This study is a part of the ANR-MOVEDVDC project (Modelling of Aging and Damage for the Assessment of Pavement Fatigue life) which aims to improve the design tools for in-service road pavements and to optimize their maintenance. In this context, understanding the cracking mechanisms of pavement materials in-service and monitoring the evolution of the damage and aging mechanisms are among the key factors to improve modelling of old pavements and calculation of their residfual design life.

The fatigue phenomenon is one of the main distress modes observed in the pavement under cyclic loadings (mechanical, thermal, and chemical). The fatigue life is defined as the number of cycles to failure which is the sum of the time necessary to nucleate the crack and the time to propagate it to failure. The fatigue life of AC depends on many factors such as mix composition [START_REF] Carswell | The Effect of Mixture Variables on the Fatigue Performance of Bituminous Materials[END_REF], loading control mode [START_REF] Tayebali | Fatigue Response of Asphalt-Aggregate Mixtures[END_REF], specimen geometry [START_REF] Boussabnia | Comparison of Fatigue Law Parameters obtained from Two-Point Bending and Tension-Compression Tests 20[END_REF], and size [START_REF] Bodin | Size effect regarding fatigue evaluation of asphalt mixtures: Laboratory cantilever bending tests[END_REF]. It is therefore quite complex to characterize AC in the laboratory using traditional fatigue tests. Many research works concerning the fatigue of AC may be found in the literature [START_REF] Baaj | Effect of Binder Characteristics on Fatigue of Asphalt Pavement Using an Intrinsic Damage Approach[END_REF][START_REF] Castro | Fatigue and Healing of Asphalt Mixtures: Discriminate Analysis of Fatigue Curves[END_REF][START_REF] De La Roche | Evaluation de l'endommagement par fatigue des enrobés bitumineux : Apport de la thermographie infrarouge[END_REF][START_REF] Mangiafico | Quantification of biasing effects during fatigue tests on asphalt mixes: nonlinearity, self-heating and thixotropy[END_REF][START_REF] Riahi | Quantification of self-heating and its effects under cyclic tests on a bituminous binder[END_REF] using homogeneous and nonhomogeneous tests [START_REF] Di Benedetto | Stiffness testing for bituminous mixtures[END_REF]. Accordingly, to predict fatigue life and analyze damage evolution, various approaches can be used. Based on the modulus evolution during the test, the AC lifespan can be defined by an arbitrary rate of loss of 50% and/or 30% of the initial stiffness [START_REF] Tapsoba | Analysis of Fatigue Test for Bituminous Mixtures[END_REF]. Other criteria that define fatigue life are based on the energy approach [START_REF] Ghuzlan | Fatigue damage analysis in asphalt concrete mixtures using the dissipated energy approach[END_REF][START_REF] Sun | Energy-Based Approach to Predict Fatigue Life of Asphalt Mixture Using Three-Point Bending Fatigue Test[END_REF].

As a Non-Destructive Technique (NDT), Acoustic Emission (AE) can be used to monitor the damage process in AC during fatigue tests [START_REF] Diakhaté | Acoustic Techniques for Fatigue Cracking Mechanisms Characterization in Hot Mix Asphalt (HMA)[END_REF][START_REF] Qiu | Assessment of Fatigue Damage in Asphalt Mixtures Using AE Approach[END_REF][START_REF] Ragni | Use of acoustic techniques to analyse interlayer shear-torque fatigue test in asphalt mixtures[END_REF]. AE is defined as a passive NDT method and designed to detect sounds caused by micro-damage within the material. Many research studies related with AE on bitumen and asphalt materials can be found in the literature, dealing with: determining embrittlement temperature and low temperature cracking (Behnia et al., 2016;[START_REF] Sinha | Acoustic emissions in asphalt subjected to thermal cycling at low temperature -NRC Publications Archive -Canada[END_REF], fracture process [START_REF] Jiao | Damage fracture characterization of pervious asphalt considering temperature effect based on acoustic emission parameters[END_REF], evaluating aging on AC [START_REF] Sun | Acoustic emission quantitative evaluation of rejuvenators to restore embrittlement temperatures to oxidized asphalt mixtures[END_REF], and investigating fatigue behavior [START_REF] Seo | Using Acoustic Emission to monitor fatigue damage and healing in Asphalt Concrete[END_REF].

Recently, the AE-based approach was used to assess the fracture damage process of a Pervious Asphalt (PA) under compression and splitting loading, applied on a cylindrical specimen [START_REF] Jiao | Damage fracture characterization of pervious asphalt considering temperature effect based on acoustic emission parameters[END_REF]. Tests were performed at different temperatures using one AE sensor with a frequency band ranging from 60 to 400 kHz.

Results showed that based on the AE parameters, different damage stages of the samples under compression and splitting can be defined. It was also found that the signal energy and the counts were the most sensitive parameters to reflect damage evolution and temperature effects. (Li et al., 2006), employed AE to characterize fracture behavior of AC at low temperature, studied using SCB (Semi-Circular Bending) tests. An AE localization method was used to track the crack path. It was found that the locations of AE events indicate that a process zone forms before the peak load, which eventually becomes the failure plane, and the movement of this process zone identifies propagation in the macroscale. Micro-cracks location was in good agreement with the crack path observed at the end of the test.

AE technique was used to evaluate the damage process leading to failure for asphalt pavement interlayers [START_REF] Ragni | Use of acoustic techniques to analyse interlayer shear-torque fatigue test in asphalt mixtures[END_REF]. The results issued from AE localization show that most AE events are located in the interlayer zone where the specimen is weaker and where the failure occurs. More, the AE events are concentrated in the outermost of the cross-section area of the specimen, where the shear stress is highest. This allows describing the crack path propagation which initiates on the perimeter and proceeds inwards.

The innovative feature of the study presented in this paper is the observation of fatigue in AC using the AE technique. This is performed in addition to the conventional 2PB fatigue tests on a trapezoidal specimen. Based on AE analysis new failure criteria are proposed and compared with the conventional mechanical criteria. Moreover, to describe the fatigue crack growth and understand the fracture mechanism of asphalt concretes, the 3D spatial distribution on the AE events was tracked.

AE Source Location Method

An AE source is the place at which a micro-crack is formed. The source location technique generally involves a network of AE sensors located at different points on the surface of the specimen. The AE location is based on the following assumption (1) sources are punctual (called event which is formed from a set of signals); (2) sources are temporally spaced apart from each other, so that the acoustic activity resulting from a source does not interfere with the acoustic activity of the next source; (3) wave propagation velocity is constant and (4) the material is supposed to be homogeneous and isotropic.

The spatial coordinates of AE sources were recovered from the arrival times of the primary waves. The principle of AE events localization is based on the relations between the arrival time t and the distance d related by the isotropic elastic wave velocity v of the material:

d v t  (1)
For the source localization, only geometrical arguments in 3D space are utilized.

If the position of the sensors is determined by coordinates ( , , ) i i i

x y z , and the source position is ( , , ) s s s

x y z , the distance from the source to the sensor i can be obtained from:

2 2 2 ( ) ( ) ( ) i i s i s i s d x x y y z z       (2)
Assuming that the wave propagation paths from the sources to the AE sensors are straight, the time differences from the source to the th i sensor (Time Difference Of Arrival (TDOA)) are expressed by: ()

i s i s t t d d v    (3)
Where s t is the time of event occurrence.

Therefore, the localization process is based on the measured arrival time of signals , i meas t

. Due to the lack of knowledge of the exact time when the source appeared, delays are considered relative to the first detected hit:

, , 1, i meas i meas meas t t t     .
Considering previous assumptions, the delays between sensors depend on the position of the source. Because of the nonlinear nature of the equations for the source coordinates, the location of events is thus determined by solving an error minimization problem between the data recorded via the sensors and an estimated event with a known position.

,exp

, 1 ()

N i i calc i tt       (4)
Where N is the number of sensors and consequently the number of equations for each AE event. The position of estimated events is determined by an iterative algorithm. The retained position corresponds to that of the estimated event for which the error criterion is minimum.

Materials and Methods

Material design

The tested asphalt mix was extracted from the traffic lane of the subbase layer of an inservice highway pavement, built in 2001. The mix was formulated with the aggregate gradation plotted in Figure 1. The Nominal Maximum Aggregate Size (NMAS) is 14 mm, the mix contains sand and filler and has a binder content of 4.6 percent by weight of aggregates (ppc). The binder used is pure bitumen, with a penetration grade of 35/50

(1/10 mm). MHz and a threshold of about 40 dB was also considered to remove background noise through the test. Therefore, a single AE hit is defined as an AE signal that exceeds the threshold level. It can be detected by several sensors and thus, the source that can be the physical origin of one or more AE events can be localized.

The acquisition parameters and the wave velocity were calibrated using the Pencil Lead Breaking (PLB) protocol.

Results and Discussion

Fatigue Failure Criteria

Fatigue life is usually a key parameter to describe the fatigue behavior of an asphalt mixture. In the literature, many different approaches exist to define the fatigue life, and thus to characterise the failure of asphalt materials.

In this paper, classical fatigue criteria are defined respectively as the number of cycles corresponding to a complex modulus decrease of 30% and 50% of its initial value (EN 12697-24, 2018). These criteria are based on an arbitrary relative decrease of complex modulus. However, they don't take into account several biasing effects appearing in phase I, and the effective initiation of damage. criterion, positioned at the end of the second phase and governed by fatigue phenomena, seems to be more relevant.

AE activity analysis

A large amount of literature is available on AE studies of construction materials under a variety of loading conditions [START_REF] Jiao | Damage fracture characterization of pervious asphalt considering temperature effect based on acoustic emission parameters[END_REF][START_REF] Lamy | Acoustic emission technique for fracture analysis in wood materials[END_REF][START_REF] Moradian | Hit-Based Acoustic Emission Monitoring of Rock Fractures: Challenges and Solutions[END_REF]. Several approaches have been adapted to analyze the various aspects of microcracking and fracture processes, for example :

(1) recording of events and expressing them in the form of event rate or cumulative events [START_REF] Diakhaté | Acoustic Techniques for Fatigue Cracking Mechanisms Characterization in Hot Mix Asphalt (HMA)[END_REF]Li et al., 2006);

(2) determination of source locations and study of individual events mechanisms (Li and Marasteanu, 2006);

(3) study of amplitude distributions [START_REF] Qiu | Assessment of Fatigue Damage in Asphalt Mixtures Using AE Approach[END_REF];

(4) investigation of the frequency characteristics associated with emission events [START_REF] Lu | Frequency characteristic analysis on acoustic emission of mortar using cement-based piezoelectric sensors[END_REF].

However, the most widely used and simplest approach to quantifying AE activity remains counting each signal that exceeds a set threshold (hits). The process of detecting and measuring an AE signal on a channel is referred to as "Hit" [START_REF] Rao | Pre-failure damage caused by micro-cracks in rock : A laboratory study using Acoustic Emission[END_REF].

The complex modulus decrease ratio is plotted in Figure 5 In order to identify the onset of the third stage, the Akaike Information Criterion (AIC) [START_REF] Kurz | Strategies for reliable automatic onset time picking of acoustic emissions and of ultrasound signals in concrete[END_REF][START_REF] Zhang | Automatic P-Wave Arrival Detection and Picking with Multiscale Wavelet Analysis for Single-Component Recordings[END_REF] is applied to the Non-Cumulative Hits Variation Rate (VR), i.e.:

( 1) ( )

hits VR Hits i Hits i    (5)
( 1)

Hits i  and ()

Hits i respectively refer to the numbers of hits at the 1 i  and i load cycles.

The AIC is based on the assumption that a time series (discrete signals) can be divided into locally stationary segments (each modelled as an autoregressive process).

The point at which the AIC is minimized (Figure 6) represents the optimal separation between the two time series (noise and signal). The AIC function minimum corresponds herein to the of the third phase characterized by irregular and more significant AE activity variation in the material (Figure 5). The AIC function can be computed using Equation 6.

        [ ] .log var [1,..., ] ( ).log var [ 1,..., ] AIC k k x k N k x k N     (6)

AE events location

Using the AE technique different source localization methods are available in the literature. The localization methods are broadly classified under five categories [START_REF] Sengupta | Structural damage localisation by acoustic emission technique: A state of the art review[END_REF], using : (1) analytical modelling; (2) signal processing; (3) artificial neural networks; (4) geometric methods, and (5) finite element analysis. The accuracy of the AE localization depends also on the algorithm for the resolution of the minimization problem [START_REF] Boniface | Evaluation of the acoustic emission 3D localisation accuracy for the mechanical damage monitoring in concrete[END_REF].

In this study, the source localization was performed by the geometric method based on the triangulation technique. In this technique, the correct picking of the waveform's Time Of Flight (TOF) strongly affects the accuracy of crack event location and source mechanism analysis [START_REF] Carpinteri | Reliable onset time determination and source location of acoustic emissions in concrete structures[END_REF][START_REF] Labuz | Identifying Failure through Locations of Acoustic Emission[END_REF]. Small variations in the wave velocity due to damage development can have a great effect on source localization [START_REF] Chouvion | Vibration analysis of beam structures with localized nonlinearities by a wave approach[END_REF]. It is also well-known that in anisotropic specimen, the acoustic energy does not always propagate in straight lines, which represents a source of error for the localization algorithm [START_REF] Kundu | A two-step hybrid technique for accurately localizing acoustic source in anisotropic structures without knowing their material properties[END_REF].

Moreover, in semi-infinite media, besides the volumetric waves (dilatational "P" and distortional "S") there are also Rayleigh and lateral (head) waves. Detection of different wave modes arrival times separately and evaluation of their velocities can significantly improve location accuracy. Nevertheless, detection and separation of different wave modes is computationally quite complex and inaccurate in the case of complex geometries. Despite the complexities of AE event localization, a simplified approach is used by considering a constant effective velocity obtained using the Automatic Sensor Test (AST) protocol [START_REF] Lamy | Acoustic emission technique for fracture analysis in wood materials[END_REF], by artificially generating short-duration and localized impulses, like the Breaking of a Pencil Lead (PLB), at known distances from sensors. The average effective AE wave velocity through the AC specimens was measured in direct transmission mode using an Automatic Sensor Testing procedure (AST) and equal to 3570 m/s at the initial state. [START_REF] Ragni | Use of acoustic techniques to analyse interlayer shear-torque fatigue test in asphalt mixtures[END_REF]) used a similar approach and performed a PLB protocol to calibrate the AE location in cylindrical asphalt specimen. A mean value of the standard deviation of 2.59 mm was obtained.

The simplified AE location process, without taking into account anisotropy and decrease of velocities during the fatigue test, allows an approximate localization of the damage and fracture zones, according to the theoretical estimated position.

Theoretically, for the cantilever homogeneous specimen used in the 2PB fatigue test, the crack initiates and propagates from a point located at approximately 1/3 of the height of the specimen. The literature review shows that for the 2PB fatigue test the bending moment is maximum in this zone [START_REF] Harvey | Four Point Bending[END_REF][START_REF] Maggiore | Evaluation of Stiffness and Fatigue Using 2 Point Bending and Indirect Tensile Fatigue Tests[END_REF].

Because of the inhomogeneity of asphalt concrete, deviations of the crack path from the point where the bending moment is maximum can be expected. ). 7 shows that most AE events occur in the bottom half of the specimen. The area with the maximum density of AE event is located near the theoretical zone with the maximum bending moment.

b) 30% f N c) FPT Bottom  d) 50% f N Figure
In Figure 8, we attempt to investigate the effect of the velocity decrease on the AE localization maps. From the initial velocity (3570 m/s), two levels of decrease of the velocity are evaluated : 16% (3000 m/s) and 30% (2500 m/s). Besides, the events are classified according to the amplitude of the AE signals. The results show that the zone of highest AE activity is not significantly affected. They also indicate that the AE signals of highest amplitudes are observed at the bottom of the specimen.

Comparison between mechanical and AE failure criteria

Figure 9 shows a summary of the fatigue lives determined according to the mechanical and acoustic criteria, for five replicate specimens tested in the same conditions.

Conclusion and Perspectives

The use of AE in characterizing the failure behavior of damaged asphalt concrete under mechanical fatigue loading was investigated. The fatigue failure process was analyzed and sequencing of the main stages was presented. The Acoustic Emission events location was studied considering different effective wave velocities. The damage initiation zone identified with AE localization and amplitude distribution agrees with theoretical calculations. The mechanical failure criteria based on modulus decrease were compared with the proposed acoustic criteria. Results show that the conventional 50% f N criterion should be revised to better characterize damaged asphalt mixtures. This criterion tends to overestimate the fatigue life.

Figure 1 .Figure 2

 12 Figure 1. Grading curve of the asphalt mix

  Figure 3. AE Sensors location

Figure 4 .

 4 Figure 4. Complex modulus decrease according to the number of cycles and indication of Nf50%, Nf30%For the presented specimen, the

Figure 5

 5 Figure 5. a) Non-Cumulative Hits evolution for the three sensor groups, b) AE-phases sequencing for bottom sensors group

FPTFigure 6 .

 6 Figure 6. Third phase (FPT) identification with the AIC criterion, for the average number of hits of the bottom sensors.

Figure 7

 7 Figure 7 presents an AE events source location during a fatigue test, considering

Figure 7 .

 7 Figure 7. AE events location corresponding to a) DIT Bottom  b)

Figure 8 .

 8 Figure 8. AE amplitudes for the events located with a wave velocity of (A) 3570 (B) 3000 (C) 2500 m/s, corresponding to the different failure criteria.

Figure 9 .

 9 Figure 9. Synthesis of the lifespan determined by acoustic and mechanical criteria

  more relevant and it can be considered as a failure propagation precursor. This paper is a result of an experimental study conducted on a damaged AC that can further be extended to field validation of the AE technique for the performance characterization of an undamaged AC. Additional research will be carried out to improve the localization accuracy by discriminating effectively AE source signals, for better monitoring of crack propagation. The relationship between AE activity and biasing phenomena such as heating should also be clarified. For that purpose, a new test program, with more test replicates and with temperature monitoring within the material is planned. The location method also needs to be enhanced, by a more accurate determination of the signal onset time and of the wave propagation velocity changes associated with damage effects.

Acknowledgment

This work was conducted as a part of the ANR-MOVEDVDC French national project (Modelling of Aging and Damage for the Assessment of Pavement Fatigue life). The National Research Agency is acknowledged for the financial support as well as the partners of the project for their valuable contributions.