Lama Elias-Birembaux

Iulian Rosu
email: rosu@lma.cnrs-mrs.fr

Frederic Lebon
email: lebon@lma.cnrs-mrs.fr

Thermo-mechanical modelling of the aircraft tyre cornering

Keywords: aircraft tyre, Finite Element Method, thermo-mechanical modelling

Some numerical models are proposed for simulate the aircraft tyre behaviour on the ground in critical situations. Fully coupled thermo-mechanical analysis procedures taking into account finite deformation, dynamics and frictional contact are studied. The proposed models are compared with experimental data such as contact area, lateral and longitudinal stiffnesses, surface temperature evolution due to friction, self-alignment torque, and lateral friction coefficients. A good agreement is observed at low speed (less than 70 km/h). Thus, the model is extrapolated to high speeds and seems able to predict results in cases for which it is not possible to obtain realistic experimental data.

Introduction

Landing and take-off operations are the most critical phases of an aircraft flight. Indeed, the high speed, the violent impact when the aircraft touches the ground, the need of braking efficiently, the ground irregularities, the climatic conditions (crosswind, contaminations, etc.) as well as other parameters can make these ground manoeuvres very complex.

Knowing at each time the forces in the contact patch allows controlling the behaviour at the tire/ground interface. For aeronautical applications, the experiments realized on real tire, at moderated speeds (less than 70 km/h), help to analyse the tire/ground behaviour in this reduced field. However, numerical models based of Finite Element method are fundamental methods to predict the tyre behaviour at higher speed, taking into account the high non-linearities related Machine Dynamics Research 2013, Vol. 37, N° 1 pp. 29-36 to materials, and coupled phenomena (contact with friction, thermal-mechanical couplings, and internal dissipation).

Modelling of tire aircraft by Finite Element Methods

In this study, finite element analyses were performed in several steps. In the first step, the tyre was modeled under inflation pressure using an axisymmetric 2-D model. A 3-D model was then developed for performing static vertical loading simulations. To study the lateral, torsional and longitudinal stiffnesses of tire, a quasi-static analysis was performed after the static analysis. Recently a fully coupled thermo-mechanical 3-D model was also realized to predict the tire behaviour during landing and taking-off operations: an improved geometry description was introduced, materials behaviours were identified, experimental determination of rubber properties was validated, and Mooney-Rivlin model was used to characterize the hyper-elasticity of rubber. The visco-elasticity properties of rubber were also taken into account.

Static simulation

Cross section mesh

In previous papers [START_REF] Kongo Kondé | Thermomechanical analysis of an aircraft tore cornering using coupled ale and lagrangian formulations[END_REF][START_REF] Kongo Kondé | On the modelling of aircraft tire[END_REF], some simulations are presented and analyzed in detail. The main defect of these simulations is the rather low number of elements constituting the mesh. In this part a new refined mesh was realized for the 2-D Element Finite model of tire (Fig. 3, second part). This operation was necessary to analyze the mesh sensibility, thus the number of elements was increased in the contact area, and a higher number for circumferential elements was used for the 3-D modelling. Total run time for a complete static analysis with this refined cross section mesh is still little expensive for industrial applications. This new strategy will be adopted in all our future analyses, both for static and dynamic simulations.

Contact area

In this study, the inflation analysis of the axisymmetric new model was followed by a 3-D quasi-static analysis of a vertically loaded tyre. Simulations were performed under static vertical loads Fz ranging from 0.125 to 0.75 % of f 0 . The inflation pressure p 0 was equal to 17.2 bars and the static friction coefficient µ was equal to 0.65. f 0 stands for a reference value of the vertical load. The (Fig. 4) shows the numerical evolution of the contact area with regard to the vertical loading in comparison with the experimental results. As we can see in (Fig. 5), a good agreement is observed between numerical and experimental data; footprints were measured in the case of a grooved tire.

Dynamic simulations

When we study tire yawed rolling, it is relevant to well estimate the Self Aligning Torque and the ratio, lateral force/ normal force. They respectively express the ability of a tyre to turn back to its steering direction when it is no longer steered and the lateral grip potential of the rubber/ground couple. Indeed, the ratio µ Y (between the lateral force and the vertical one) defines the equilibrium which exists between steering lock action and the trajectory of the vehicle. During µ Y upward phase, there is equilibrium; more the pilot turns the wheel, more β increases. It corresponds to pseudo-sliding in the contact patch up to β max (usually around β=4 to 7° for automobile pneumatics, around 15 to 25° for aircraft).

In this study, mechanical and fully coupled thermo-mechanical analyses are developed to predict the friction ratio µ y and the self-aligning torque M z . A classical rolling (CR) method based on a Lagrangian formulation was studied, thus from an observer point of view, the tyre mesh (51circumferential elements) is rotating and moving forward. A variable friction coefficient µ (P,T) depending on pressure and temperature was used in the thermo-mechanical model, real viscosity parameters were also introduced in this model. Concerning the mechanical model, a fixed friction coefficient  0 was adopted. These simulations (for both models) require two numerical steps, an acceleration step from zero to a given velocity and a rolling cornering step at a constant given velocity and a given slip angle.

Experimental vs Numerical simulations

Self aligning torque/ lateral friction coefficient

Mechanical and thermo-mechanical analyses were investigated; these studies concerned a grooved aircraft tire. Fig. 6 shows the evolution of the self aligning torque M z versus the slip angle. In order to show the influence of the temperature on the lateral friction coefficient µ y and on the self-aligning torque M z , purely mechanical, and thermo-mechanical models were performed under the same loading conditions and for the same slip angles. Results were compared with experimental data. In the case of the pure mechanical simulation without any temperature dependence, we can observe that the lateral coefficient µ y (Fig. 7) reaches a plateau equal to µ 0 with respect to the Coulomb's friction low. β max , the angle for which the self-aligning torque is maximum, seems to be in good agreement with experimental data. The self-aligning torque M z increases up to β max at which the full grip potential is reached. The self-aligning torque M z decreases when β> β max , and tends to negative values.

In the case of a thermo-mechanical approach, the dependence of the lateral friction coefficient on the temperature (Fig. 7) resulted in a decrease in µ y beyond the β max value. The self-aligning torque M z (Fig. 6) falls quickly toward null values. Cornering rolling is obtained by imposing longitudinal and lateral velocities (related to a slip angle β). Figure 8 shows the temperature distribution at the tyre tread. After a few seconds of rolling in cornering, an increase of the temperature occurs on tire tread and especially on groove sides; a warming zone is observed on the entire contact zone. However a slight diffusion of temperature is observed after a short period of rolling. We note also the role of a thermal barrier presented by the reinforced zones. Recently different experimental and numerical tests were performed; their purpose was to verify the behaviour of rubber during cornering rolling. These studies confirmed the necessity of taking into account the frictional heating of rubber and also the heating produced by energy dissipation (viscoelasticity properties). Fig. 9 shows a rolling cornering case of an aircraft tyre at a low velocity and for a small slip angle; a good agreement seems to be obtained between the thermomechanical model and experimental data.

Conclusion

In this paper, we have proposed some numerical models to simulate the aircraft tyre behaviour in cornering. Fully coupled thermo-mechanical analysis procedures taking into account finite deformation were studied. The proposed models have been compared with experimental data such as contact area, lateral and longitudinal stiffnesses, surface temperature evolution due to friction, selfalignment torque, and lateral friction coefficients. A good agreement was observed at low speeds (less than 70 km/h) and the model seems to be able to predict results at high speeds, in which case it is not possible to obtain realistic experimental data.

In the future, we intend to improve the models introducing more complex constitutive equations coupling thermo-mechanical effects, particularly taking into account viscosity, internal dissipation, etc. Other kind of experimental devices will be proposed in order to confirm the validity's domain of our models in various critical situations.

  Fig.1. 2-D tire structure: (a) real cross-section of tire (b) 2-D axisymmetric FE model

Fig. 2

 2 Fig.2.3-D fully coupled thermo-mechanical model

Fig. 3 .

 3 Fig.3. Comparison between old (Kongo et al. 2012) and new refined cross mesh for 2-D FEM model. At left side: cross section mesh before and after refinement. At right side: cross treads stress before and after refinement.

Fig. 4 .

 4 Fig.4. Evolution of contact area in the case of a grooved tire

Fig. 6 .

 6 Fig.6. Comparison between experimental data, mechanical and thermo-mechanical modelsSelf aligning torque M z , Under given loading conditions (vertical load, pressure and velocity)

Fig. 8 .

 8 Fig.8. Temperature gradient for a cornering simulation at given velocity and slip angle


Odile Abraham
email: odile.abraham@ifsttar.fr

Yuxiang Zhang

Xavier Chapeleau

Olivier Durand

Vincent Tournat

Monitoring of a Large Cracked Concrete Sample with Non-Linear Mixing of Ultrasonic Coda Waves

Keywords: Ultrasonic, Coda Wave Interferometry, Non linear acoustics, crack, concrete

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The ultrasonic non destructive testing of concrete structures is often performed with sources having a frequency content well below 150 kHz. This is due to the fact that wavelengths are chosen larger than the aggregate sizes, which are currently as large as 2 cm, in order to avoid rapid attenuation of signal amplitude. In the contrary monitoring methods using coda waves aim to take advantage of the heterogeneity of the material to reach a high precision . The general idea is to take advantage of the long travel paths of the incoherent waves resulting from multiple reflections at the aggregates' interfaces. A small change in the propagation medium is more easily detectable by travel time comparison if the travel path is long [START_REF] Snieder | Coda wave interferometry and the equilibration of energy in elastic media[END_REF][START_REF] Snieder | The theory of coda wave interferometry[END_REF]. Coda Wave Interferometry (CWI) can monitor changes in propagation velocities with a high precision (10 -3 % in relative). Several promising experiments have been carried out in the laboratory [START_REF] Larose | Monitoring stress related velocity variation in concrete with a 2 x 10 5 relative resolution using diffuse ultrasound[END_REF][START_REF] Payan | Determination of third order elastic constants in a complex solid applying coda wave interferometry[END_REF][START_REF] Schurr | Damage detection in concrete using coda wave interferometry[END_REF][START_REF] Zhang | Study of stress-induced velocity variation in concrete under direct tensile force and monitoring of the damage level by using thermally-compensated Coda Wave Interferometry[END_REF], but few in situ [START_REF] Larose | Observation of multiple scattering of khz vibrations in a concrete structure and application to monitoring weak changes[END_REF][START_REF] Zhang | Following stress level modification of real size concrete structure with coda wave interferometry (cwi)[END_REF], Stahler et al., 2011]. This is due to the fact that many biases can impinge on the reproducibility of the measurements such as ambient temperature [START_REF] Zhang | Following stress level modification of real size concrete structure with coda wave interferometry (cwi)[END_REF], Zhang et al., 2013] which is common to all application fields [START_REF] Mazzeranghi | Methodology for minimizing effects of temperature in monitoring with the acousto-ultrasonic technique[END_REF], Lu & Micheals, 2006]. Compensation of biases coming from fluctuations of the ambient temperature can be achieved in the laboratory with a reference sample that duplicates the sample under test [Zhang et al., 2013]. Unfortunately it is often not possible to duplicate the structure under study especially for large in situ concrete structures. Here, we use reference signals, recorded in an area of the structure free of load, to compensate the environmental bias. In order to increase the sensitivity of the CWI to the presence of cracks, and to design a new non destructive methods to detect the presence of cracks, non-linear mixing of the coda wave via frequency-swept pump waves (NLMCODA) measurements were carried out as depicted in Zhang (2013) in glass. In [START_REF] Donskoy | Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[END_REF][START_REF] Zaitsev | On the ultimate sensitivity of nonlinear-modulation method of crack detection[END_REF][START_REF] Van Den Abeele | Micro-damage diagnostics using nonlinear elastic wave spectroscopy (news)[END_REF] it is shown that probing a medium with a low-amplitude ultrasonic wave (called the probe wave), at the same time that a large-amplitude wave at lower frequency is exciting the medium, leads to modulation of the probe wave in the presence of faults such as cracks. To apply non-linear acoustics to detect cracks in concrete several challenges have to be tackled among which: 1/ the non linearity when the material is damaged shall be distinguishable from that of the sound material 2/ the detection of a crack should be possible even when closed by pre-stressing.

PRESENTATION OF THE CONCRETE STRUCTURE AND LOADING

A concrete specimen (Fig. 1) has been designed in order to create tensile cracks in a pre-stressed section while, approximately one meter away, a zone remains free of stress (surface C). Thermocouples, fibre optics and strain gauges are located in the pre-stressed section to compare and discuss results. The specimen has a complex structure; three surfaces are coloured for explanation in Figure 1. The surface A (50 cm x 160 cm) has a 3 cm thick slot in view of creating a crack in the structure at mid-height. The crack is initiated by tightening a screw that crosses the specimen at its top, perpendicularly to surface B. The top of the slot is put into compression and a crack is created in the zone where traction is the highest (initiation of the crack on face B at the height of the slot bottom end). The screw is tighten step by step to reach 100 % of the roughly estimated traction strength (3 Mpa): 50 %, 85 %, 90 %, 95 %, 100 %, 110 %, 130 %. The concrete rupture occurred at 130 % of the estimated traction strength. The specimen was monitored by CWI during the whole experiment that lasted 3 days. The increase of the load from 0 % to 130 % was done in 8 hours. After the largest load corresponding to the apparition of a crack (loading step 130 %), the screw was loosen to close the crack thanks to the pre-stressing cables.

© Vigouroux Pays de la Loire

Coda wave interferometry

The principle of CWI is to compare two signals (ui(t) and up(t)) recorded before and after a perturbation of the propagation medium to determine the variation of the propagation velocity [START_REF] Snieder | Coda wave interferometry and the equilibration of energy in elastic media[END_REF][START_REF] Snieder | The theory of coda wave interferometry[END_REF]. In this paper the stretching method is used [START_REF] Hadziioannou | Stability of monitoring weak changes in multiply scattering media with ambient noise correlation: Laboratory experiments[END_REF]. The reference signal ui(t) is stretched/compressed by a factor αi and compared to the perturbed signal up(t) by computing the correlation coefficient CC(αi) :

(1) Among all the value of αi, the one that maximizes CC is noted α and is equal to the relative modification of the velocity v: α = ∆v/v. The associated decorrelation coefficient Kd = 1-CC(α) (from 0 % to 100 %) gives an indication about the decorrelation between the two signals ui(t) and up(t).

Non-linear mixing via frequency-swept pump waves

At each loading steps (0 %, 50 %, 85 %, 90 %, 95 %, 100 %, 110 %, 130 % and 0 % of estimated traction strength) NLMCODA measurements are performed. It consists in measuring by Coda Wave Interferometry the variation of α as a function of pump wave amplitude. The pump wave excitation voltage, that governs the pump wave amplitude, varies from 0 mV to 1300 mV back to 0 mV in twelve voltage steps (0 mV 100 mV 400 mV 700 mV 1000 mV 1300 mV 1300 mV 1300 mV 0 mV 0 mV 0 mV 0 mV 0 mV).

Experimental set-up

The probe wave generated is a chirp from 200 kHz to 800 kHz with a duration of 200 µs (Fig. 3). Two pairs of CWI source and receiver are located in the crack zone area (surface B) and in a reference zone (fare from loading) in surface C top right corner (Figure 1). The pump wave is another chirp from 20Hz to 2kHz with a duration of 1 s generated by a vibration equipment located on surface B (Fig. 2). More than 15 structure resonances frequencies are excited.

Both chirp signals are asynchronous. Signals of both pairs of coda wave receivers are recorded simultaneously. Figure 4 shows one probe signal. Fiber optic measurements where carried out before and after NLCODA measurements to control the apparition of the crack.

RESULTS

Bias compensation

To illustrate the methodology to compensate temperature effect on coda wave signal, we focus on one loading step (fig. 5) during which the air temperature varies as depicted in red in figure 6 and in blue inside the concrete. The variation of α as a function of time during one loading step is given in figure 7 for both coda receivers (respectively αref in the reference zone and αtest in the load zone). In the reference zone, the influence of temperature is clearly visible on αref, the same trend is observed in the load zone αtest somehow masking the load effect. Figure 9 : αcorr = αtestαref. The temperature effect is removed. To remove the thermal bias on the CWI measurements, the difference between the two signals is carried out to give αcorr = αtestαref. The variation of velocity during loading is more easily explainable. The acousto-elastic effect is clearly visible (diminution of velocity with traction), the permanent decrease of velocity after traction can be explained by the kaiser effect and finally the stabilisation to the new velocity that takes several minutes can be explained by slow dynamics [TenCate 2000, Larose 2009]. In the following the correction of temperature will be applied to all the coda wave signals.

Crack detection

Figure 7 presents preliminary results obtained with NLMCODA. αcorr and Kd are presented as a function of pump amplitude levels (10 measurements per level are performed leading to 130 values) for 4 load levels: 0 %, 95 %, 130 %, 0 %. After the load level 130 %, the structure is cracked. Before loading (first load level at 0 %) we can see that concrete shows a non-linear behaviour (Fig. 7a): the velocity is sensitive to the level of the pump. Before cracking of the structure (for instance at load level 95 %, fig. 7b) the non-linear behaviour remains very similar. At the load level 130 % (Fig. 7c) a crack is present (the crack is open because the load is kept constant); the influence of the pump wave amplitude on αcorr and Kd is clearly increased from previous state, especially for Kd. The fact that αcorr and Kd do not come back to zero when the pump amplitude is shut down is due to the fact that the temperature effect has been compensated but not the relaxation of the concrete. Very interestingly, once the load level is cancelled (equal to 0 %) the sensitivity of αcorr and Kd stays of the same order of grandeur. This means that NLMCODA can detect a closed crack under compression.

CONCLUSION

In this first experiment carried out on a metric size concrete specimen we have shown that we can compensate the temperature bias by using a reference signal recorded in a zone that undergoes only environmental perturbations. This is very promising result for the use of coda wave interferometry on in situ concrete structures. In addition by using non-linear mixing of the coda wave via frequency-swept pump waves we have shown that a cracked zone has a signature that is clearly different from sound concrete (even if the material is non-linear when sound) and that this detection is possible when the crack is closed by a pre-stressing.

Figure 1 :

 1 Figure 1 : concrete specimen dimensions Figure 2 : coda wave set-up

Figure 3 :

 3 Figure 3 : probe signal source example: a chirp of 200 µs with frequency between 200 kHz and 800 kHz.

Figure 4 :

 4 Figure 4 : Modulus of the Fourier transform of a signal recorded near the vibrating loawfrequency vibrator.

Figure 5 :Figure 6 :Figure 8 :

 568 Figure 5 : measured load level (% of estimated traction strength)

Figure 7 :

 7 Figure 7: α and Kd as a function of pump amplitude for 4 load levels (a-0 %, b-95 %, c-130 %, d-0 %)

July 8-11, 2014. La Cité, Nantes, France Copyright © Inria (2014)

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENT

This research has been supported by the ECND-PdL (Loire Valley cluster for Non-Destructive Evaluation and Control), which is financed by the Loire Valley Regional government (France). Our thanks extend to Ivan Gueguen, Alain Grosseau and Jean-philippe Gourdon from Ifsttar (France) and to Jean-Paul Balayssac from LMDC (France) for their assistances during the tests and its preparation.


Yuxiang Zhang
email: yuxiang.zhang@ujf-grenoble.fr

Eric Larose

Thomas Planes

Gautier Moreau

Claude Rospars

IMAGING OF EARLY-STAGE CRACKING ON REAL-SIZE CONCRETE STRUCTURE FROM 4-POINTS BENDING TEST

Keywords: LOCADIFF, Imaging, real-size concrete, cracking, 4-point bending

. By mapping the intensity of modification on localized microstructure, the new technique is able to detect perturbations at multiple locations.

Here we present the application of this new technique on a real-size 15 tons concrete structure for imaging early-stage cracking procedure issued from four point bending load, as part of the CEOS.fr project. Experimental results show that this technique can not only locate cracks that appeared simultaneously at multiple locations, but also detect them and observe their developments since an early-stage.

INTRODUCTION

Being non-destructive, non-hazardous and naturally sensitive to elastic properties, ultrasonic waves are advantageous for characterizing material's mechanical properties or damage detection [START_REF] Planès | A review of ultrasonic Coda Wave Interferometry in concrete[END_REF]. By letting ultrasounds interact with defects (which are, in general, discontinuities representing high impedance contrast on surface) and analyzing thereby produced echo, traditional ultrasonic nondestructive testing (NDT) methods (e.g. impact echo or pulse echo) are capable of detecting, locating or even imaging defects in a homogeneous medium [START_REF] Wiggenhauser | Advanced ndt methods for the assessment of concrete structures[END_REF]. However, their capacity is restrained when the propagation medium is heterogeneous.

The propagation of elastic waves in a heterogeneous medium is complex and highly depends on their frequencies [START_REF] Planès | A review of ultrasonic Coda Wave Interferometry in concrete[END_REF]. In the case of ultrasounds in concrete, the multiply scattering effect occurs due to random distributed scatters (aggregates) and leads to a noise-like appearance of recorded signal. In general, one can either use the part of the signal that formed only by coherent waves, or decrease frequency to avoid such multiple scattering effects. However, from one hand, the use of coherent waves requests a smaller propagation distance [START_REF] Larose | Locating a small change in a multiple scattering environment[END_REF] which makes global inspection impossible when the structure has large dimensions. On the other hand, lowering frequency makes propagation medium less heterogeneous to ultrasounds and easier for them to propagate. Nevertheless, the consequential increase of wavelength will degrade the spatial resolution and detection sensitivity. Such dilemma confines the application scope of traditional ultrasonic NDT methods on concrete [START_REF] Larose | Locating a small change in a multiple scattering environment[END_REF]. Meanwhile, being the mostly used civil engineering material, the NDT technique of concrete has been always in large demand.

Despite its noise-like appearance, record of multiply scattered waves (a.k.a. coda waves) contains detailed information about propagation medium and is highly sensitive to time-lapse perturbation. Based on such features, a technique called coda wave interferometry (CWI) has been developed by Poupinet [6] and Snieder [START_REF] Snieder | Coda wave interferometry for estimating nonlinear behavior in seismic velocity[END_REF], and considered as a promising NDT technique on concrete. Efforts have been made from different angles to use CWI analysis for damage detection of concrete [START_REF] Stähler | Monitoring stress changes in a concrete bridge with coda wave interferometry[END_REF][START_REF] Schurr | Damage detection in concrete using coda wave interferometry[END_REF][START_REF] Zhang | Study of stress-induced velocity variation in concrete under direct tensile force and monitoring of the damage level by using thermally-compensated coda wave interferometry[END_REF]. A new imaging technique for heterogeneous medium has been recently reported its application using multiply scattered seismic waves [START_REF] Obermann | Imaging pre-and co-eruptive structural changes of a volcano with ambient seismic noise[END_REF]. In this manuscript, we present its application for crackimaging on a massive concrete structure using ultrasonic waves. This technique is based on method called LOCADIFF. Different from previously reported method [START_REF] Rossetto | Locating a weak change using diffuse waves: Theoretical approach and inversion procedure[END_REF], which allows locating the presence of one defect in heterogeneous medium, here we aim at imaging defects appearing simultaneously at different locations and at monitoring their evolutions. After a brief introduction of CWI analysis and the LOCADIFF imaging technique, an experimental study performed on a realsize concrete beam will be reported. Experimental results are then compared to acoustic emission results for discussion.

METHOD

For the sake of robustness and better precision, CWI analyses are performed using the "stretching method" [START_REF] Sens-Schönfelder | Lunar noise correlation, imaging and monitoring[END_REF][START_REF] Hadziioannou | Stability of Monitoring Weak Changes in Multiply Scattering Media with Ambient Noise Correlation: Laboratory Experiments[END_REF]. This method simulates a variation in propagation velocity by dilating/compressing the signal on a given ratio α i . The stretched signal is then compared to a reference signal by evaluating their correlation coefficient within a given time-window [𝑡1, 𝑡2].

CC(α

i ) = h p [t(1+α i )]⋅ h i [t]dt t1 t 2 ∫ h 2 p [t(1+α i )]dt ⋅ h 2 i [t]dt t1 t 2 ∫ t1 t 2 ∫ . ( 1
)
Amount all possible value of α i , the one that maximizes 𝐶𝐶 𝛼 = 𝑀𝐴𝑋 𝐶𝐶 𝛼 𝑖 is considered as the apparent relative variation of propagation velocity as α = Δ v v

. The remnant de-correlation coefficient Kd can be calculated:

Kd = 1-CC(α) . (2)
This parameter quantifies the level of perturbation in the waveforms, which can be the result of a localized modification of microstructure in the propagation medium. According to Larose et al. [START_REF] Rossetto | Locating a weak change using diffuse waves: Theoretical approach and inversion procedure[END_REF], Kd caused by the presence of an extra diffuser (a crack in our case) observed by a given sourcereceiver pair (S-R) at a propagation time 𝑡 could be theoretically predicted as:

Kd S-R (r D , t) = c 0 2 ⋅σ ⋅ K S-R (r R , t) (3)
using sensitivity Kernel introduced by Pacheco and Snieder [START_REF] Hadziioannou | Stability of Monitoring Weak Changes in Multiply Scattering Media with Ambient Noise Correlation: Laboratory Experiments[END_REF]:

) , , ( ) , , ( ) , , ( ) , ( 0 t r r g du u r r g u t r r g t r K R S t R D D S R R S ∫ ⋅ - = - . (4)
g(r i , r j , t) is the probability function for the ultrasounds transfer from location r i to r j after a propagation time t, and can be estimated experimentally from the acoustic intensity. Note that 𝑟 ! , 𝑟 !, 𝑐 ! refer to the source location, receiver location and the propagation velocity; the extra diffuser is characterized by its location r S and its effective cross-section σ. The sensitivity kernel K S-R (r R , t) can be understood as the spatial distribution of ultrasounds time-spent at location 𝑟 ! (in relative) as a function of arrival time t. By reforming Equation 3 into a matrix form, one can obtain the following relation: By solving the related inverse problem one can image the modifications in the propagation medium's microstructure (model m) that occurred between two records. In order to do so, we used the minimum square method for linear problem proposed by Tarantola and Valette [START_REF] Tarantola | Generalized nonlinear inverse problems solved using the least squares criterion[END_REF]:

d = Gm .
m = m 0 + C m G t (GC m G t + C d ) -1 (d obs -Gm 0 ) , (6)
where C m is the covariance matrix of model, C d is the covariance matrix of the model and m 0 is the initial model which is filled with zeros in our case [START_REF] Planes | Imaging local changes in heterogeneous media with diffuse waves[END_REF].

EXPERIMENTAL PROCEDURE

A real-size reinforced concrete beam (6.1m × 1.6m × 0.8m) weighting 15 tons is the specimen at test. This beam is part of an experimental program on massive beams and thick walls of the French research project CEOS.fr on the behavior of cracking on massive elements, creep and shrinkage (c.f. references [START_REF] Demilecamps | Reliable shrinkage and crack design: CEOS.fr French national research program[END_REF][START_REF] Rospars | CEOS.fr experimental program and reference specimen tests results[END_REF] for details). Having its both ends firmly tied on the ground and the forces applied upward at two symmetric locations along Y-axis by actuators (c.f. Figure 1), the beam is subjected to 4-points bending load. By placing two PVC pipes into the specimen during the cast of concrete, two cylindrical cavities that passing through the beam are formed in order to be representative of inclusion of pre-stressed cable duct. For the loading procedure, applied force increases step-by-step with an increment of ~150kN to a maximum level of ~2500 kN. With this increase of loading level, we observe that cracks start to appear on the surface at the end of loading step 4 (loading level of 600 kN) and concrete beam reached its ultimate strength and failed at the end of the test. Since this manuscript mainly focuses on damages at early stage, only results obtained from the first four loading steps will be shown and discussed in Section 4.

For ultrasonic measurement, 20 identical ultrasonic transducers are glued on the upper surface of the beam. As illustrated in figure 1, 20 transducers are ranged approximately into 3 rows (along Yaxis): the 8 in the middle serve as emitters while the other 12 serve as receivers. The transducers are not perfectly aligned deliberately to avoid symmetries. Given the loading condition and for symmetry reasons, we assume that the produced cracks are transversal along X-axis, and that they develop in depth along the Z-axis and/or open along the Y-axis. Therefore, the primary objective of damage-imaging is locating cracks' position along Y-axis and Z-axis. During the experiment, an acoustic emission measurement has been performed and its results will be compared to that of LOCADIFF.

For each acquisition, a chirp signal (frequency increases from 50 kHz to 200 kHz) is amplified and sent to concrete using one of the emitters. Simultaneously, every receiver starts to pick up a 5-mslong signal. At the end of each loading step, 50 acquisitions are performed continuously (repetition frequency of 25 Hz) using each and every emitter.

EXPERIMENTAL RESULT

Table 1 contains physical parameters that are necessary to perform CWI analysis and LOCADIFF imaging calculation. Their values are obtained experimentally from the specimen used in our experiment. Except for 𝑐 ! , the propagation velocity of coda waves, whose value is estimated under assumption of energy equipartition between longitudinal waves and shear waves [START_REF] Snieder | Coda wave interferometry and the equilibration of energy in elastic media[END_REF]. We perform CWI analysis by comparing a signal-to-test (a signal recorded by a given sourcereceiver pair at a loading step from 1 to 4) to a corresponding reference signal (a signal recorded at loading step 0 using a same source-receiver pair) within six different time-windows, and six Kd are derived accordingly. The beginning of the first time-window is set to 400μs such that the propagation time is much longer than the transport mean free time t * . The width of the time-window is set to 500μs so it contains enough information (several oscillations) to ensure the quality of analysis. We obtained 576 Kd values for each loading steps (96 source-receiver pairs × 6 timewindows), but considered only the reliable ones, i.e. average signal to noise ratio within the timewindow > 20 dB, and with a physical significance (i.e. the center time of corresponding time-window > the arrival time of ballistic waves). These values formed the experimental data 𝑑 !"# used for solving inverse problem (Equation ( 6)).

The propagation medium (concrete beam) is meshed by cubic voxels (mesh length is set to 𝑙 * ), the positions of which are referred by the coordinates of their center locations (𝑥, 𝑦, 𝑧). For each sourcereceiver pair, six sensitivity kernels 𝐾 𝑡 𝑆!𝑅 𝑥, 𝑦, 𝑧 = 𝐾 𝑆!𝑅 𝑥, 𝑦, 𝑧, 𝑡 are calculated for 6 timewindows used in CWI analysis where t refers to their center times. In corresponding to each element of 𝑑 𝑜𝑏𝑠 , a sensitivity kernel 𝐾 𝑡 𝑆!𝑅 𝑥, 𝑦, 𝑧 calculated under the same condition (i.e. same sourcereceivers pair and same time-window) is used to form G matrix.

By solving the inverse problem as described (c.f. Section 2), we obtain a 3D matrix 𝑚(𝑥, 𝑦, 𝑧) for each loading step. It maps the modification in propagation medium-compared to its initial status (loading step 0) -with a density of changes σ (m 2 /m 3 ) within each voxel. The higher the value of 𝑚(𝑥, 𝑦, 𝑧)is, the more important the modification of microstructure at location (𝑥, 𝑦, 𝑧). In the case of our experiment, modification is majorly caused by cracking or development of cracks. As cracks are assumed transversal along X-axis (c.f. Section 3), and for the sake of clarity in illustration, only 𝑚(𝑦, 𝑧)-the average values of 𝑚(𝑥, 𝑦, 𝑧) along x dimension -are displayed in figure 2 for each loading step.

Step 1

Step 2

Step 3

Step 4 The four images at the left of figure 2 are illustrating 𝑚 𝑦, 𝑧 obtained at each loading step. The locations of PVC pipes and applied forces are also illustrated. By putting four images in a fixed color scale, we observe that the modifications are initiated as early as loading step 2 and become more and more important. Theoretical prediction of Kd is calculated using obtained the output model 𝑚(𝑥, 𝑦, 𝑧) (Equation 5). For demonstrating the quality of the inversion analysis, comparisons between theoretical and experimentally Kd are illustrated in the images at the right side of figure 2. As two values fit rather well each other in all four images, we believe that the inverse problem has been correctly solved.

From the illustration of 𝑚(𝑥, 𝑦, 𝑧) for loading step 4, we observe that microstructure modifications (red in color map) show high concentration at two locations: horizontally (on Y-axis) centered at the locations of the PVC pipes and near the upper surface. This result coincides with the expectation that: 1) under 4-points bending load, the upper part of the beam between actuators is under traction and is subject to cracking; and 2) the presence of PVC pipes might favor the cracks initiation. The acoustic emission measurement confirms these ultrasonic results too: according to the acoustic emission measurement: 1) during loading step 4, a large number of acoustic emission event have been captured which indicating the creation of crack(s); 2) these events are located horizontally (on Y-axis) around the level of two PVC pipes.

Knowing that the observation of acoustic emission event is the capture of energy in form of elastic waves released by the opening of cracks, and that there is nearly no noticeable event observed before, it can be conclude that most micro-cracks occurred during loading step 4. However, ultrasonic results show modification of microstructure since loading step 2. And such modification continues and shows a concentration around the left PVC pipe at loading step 3. Cracking on surface appeared really 2 steps latter and the position is not corresponding exactly to the PVC pipe position. To understand this difference in observation between the two techniques, author would like to propose two possible explanations: 1) cracks (or micro-cracks) are indeed created during loading step 3, though their released-energy are not strong enough to be capture by acoustic emission measurement; or 2) crack is not created before loading step 4, and the modification of microstructure observed by ultrasonic method at the end of loading step 3 are caused by localized deformations. Either explanation indicates that with LOCADIFF imaging technique, the detection of damages might be archived at a very early-stage (i.e. when cracks are about to form or damages are only micro-cracks that too small to be detected by other method, e.g. acoustic emission).

CONCLUSION & PERSPECTIVES

In this manuscript, we presented the application of a newly developed imaging technique on a realsize concrete structure for cracks' imaging. A concrete beam is subject to a 4-point bending load for the creation of cracks. By analyzing multiply scattered ultrasonic waves recorded using 8 emitters and 12 receivers with CWI analysis and LOCADIFF imaging technique, the localized microstructure modification are mapped with density of 𝜎. At the end of loading step 4, cracks appeared with applied force reaches 600 kN. LOCADIFF imaging results show concentration of microstructure modification around the position of two pre-casted cavities. Acoustic emission measurement also confirms the formation of cracks around these locations during loading step 4. Thus, influence of the pipes only occurs during the formation of micro-cracking at core, before occurrence of the first crack on surface. Therefore, we conclude that this imaging technique is able to detect first micro-damage at early stage and to locate them even damages appear simultaneously at multiple places.

Considering the mechanism of LOCADIFF imaging technique, two further research directions at NDT purposes are conceivable:

• The location of possible damaged before the actual creation of cracks, especially of damages caused by locally concentrated stress. Due to acoustoelastic effect of concrete, localized concentration in stress cause localized variation of propagation velocity, which can be detected by CWI analysis and located by LOCADIFF imaging technique; • The imaging of macro cracks. By connecting scattering cross-section to real dimension of the scatterers, one can not only locate a crack but also estimate its shape, direction and even its dimensions.

6

( 5 )

 5 In this expression d represents experimental Kd values obtained from experimental signals recorded at two different moments; G = σ ⋅ c 0 ⋅ K S-R (r R , t) ; and m is the spatial distribution model of density of σ that we are looking for.

  By source-correlating the 50 averaged signals recorded by a same source-receiver pair (i.e. a same receiver and a same emitter) a total number of 96 signals (8 emitters × 12 receivers) are obtained with a significantly good signal to noise ratio. These signals are referred to as coda signals in further analyses.

Figure 1 :

 1 Figure 1: Three view drawing of the experimental set-up: a concrete beam in dimensions of 1.6m ×6.1m ×0.8m is subject to a 4-points bending load with 12 receivers and 8 emitters are glued on the upper surface of the specimen for ultrasonic measurements (CEOS.fr database).

Figure 2 :

 2 Figure 2: Schematic representation of inversion analysis results. For each loading step, the left image is the 2D illustration of 𝑚(𝑦, 𝑧) which indicates the average density of effective cross-section 𝜎 (m²/m 3 ) by the right image is the comparison between theoretical prediction value of Kd and the experimental values.

Table 1 :

 1 List of physical parameters for CWI analysis and LOCADIFF.

	Parameter	Notation	Value
	Propagation velocity of coda (m/s)	𝑐 !	~2500
	Diffusion constant (m²/s) Transport mean free path (m) Transport mean free time (μs)	𝐷 𝑙 * = 3𝐷/𝑐 ! 𝑡	140 0.16

* = 𝑙 * /𝑐 ! ~60

ACKNOWLEDGEMENTS

The investigation and results reported herein are partly supported by the French National Program CEOS.fr (Study and design of specific structures in relation to cracking and shrinkage) sponsored by the French Ministry in charge of sustainable development (MEDDE-DRI).


Benoit Hilloulin
email: benoit.hilloulin@ec-nantes.fr

Yuxiang Zhang

Odile Abraham

Frédéric Grondin

Ahmed Loukili

Olivier Durand

Vincent Tournat

Closed Crack Detection in Concrete with Coda Wave Non-Linear Modulation

Keywords: Coda Wave Interferometry, Concrete, Cracks, Health monitoring

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Concrete is very sensitive to crack formation. Cracks are generally taken into consideration into design codes recommendations but they influence the durability of structures. Closed cracks in reinforced concrete, which are defined as cracks whose lips are in contact, are generally invisible at naked eye (with a width of some dozen of micrometers) and endanger the durability of structures as they accelerate the penetration of aggressive substances. In order to optimize structural health management, non-destructive techniques have been extensively studied and, among them, ultrasonic methods offer the advantage to provide information related to the elastic properties including part of the medium which is not directly accessible from its surface. However, up to now, linear ultrasonic methods can only detect large opened cracks [START_REF] Hévin | Characterization of surface cracks with rayleigh waves: a numerical model[END_REF][START_REF] Kee | Surface wave transmission measurements across distributed surfacebreaking cracks using air-coupled sensors[END_REF]. Studies have been recently led to develop nonlinear ultrasonic methods to increase the sensitivity to damage and showed good sensitivity to notches or partially opened cracks [START_REF] Peter | Fatigue damage assessment by nonlinear ultrasonic materials characterization[END_REF][START_REF] Sathishk | Ultrasound diffusion for crack depth determination in concrete[END_REF][START_REF] Deroo | Damage detection in concrete using diffuse ultrasound measurements[END_REF][START_REF] Quiviger | Effect of the presence and size of a real macro-crack on diffuse ultrasound in concrete[END_REF]. However, the detection of small closed cracks in concrete remains a great challenge for NDT techniques. In this study, we present a novel nondestructive technique with the aim to detect closed cracks into concrete.

Coda Wave Interferometry (CWI) which relies on the analysis of the last part of the signal after multiple scattering due to heterogeneities is a very sensitive method. CWI has been successfully adapted to concrete, which is a highly heterogeneous medium, to determine nonlinear elastic properties [START_REF] Payan | Determination of third order elastic constants in a complex solid applying coda wave interferometry[END_REF] or detect and locate a small defect (hole of some millimeters) [START_REF] Schurr | Damage detection in concrete using coda wave interferometry[END_REF]. With the control of the thermal bias, CWI can monitor propagation velocities with a high precision (10 -5 in relative terms) [START_REF] Zhang | Validation of a thermal bias control technique for coda wave interferometry (cwi)[END_REF].

Besides, acoustic nonlinear modulation amplifies the signature of a defect with the use of an acoustic load provided by a pump source. The sample is submitted to a low amplitude ultrasonic wave (known as probe wave) and a large amplitude wave at a lower frequency (known as pump wave). If the sample contains nonlinearity caused by, e.g. the presence of cracks or, more generally, contact-type defects, the probe wave will be modulated because of the variation of local and surrounding effective elasticity (elastic modulus or acoustic dissipation) due to the pump excitation [START_REF] Donskoy | Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[END_REF][START_REF] Zaitsev | Novel nonlinearmodulation acoustic technique for crack detection[END_REF][START_REF] Yu | On the ultimate sensitivity of nonlinear-modulation method of crack detection[END_REF][START_REF] Yu | Elastic-wave modulation approach to crack detection: Comparison of conventional modulation and higher-order interactions[END_REF][START_REF] Zhang | Nonlinear mixing of ultrasonic coda waves with lower frequency-swept pump waves for a global detection of defects in multiple scattering media[END_REF].

In this paper, we present a NDT technique combining the use of diffuse ultrasounds within nonlinear modulation method to detect closed cracks in an initially nonlinear material (concrete).

PHYSICAL BACKGROUND AND METHODOLOGY

1.1 CWI analysis by stretching Two methods can be applied for the estimation of the variation of velocity: Doublet and Stretching. Under the assumption of a constant variation of velocity, Stretching provides more stable and accurate results [START_REF] Hadziioannou | Stability of monitoring weak changes in multiply scattering media with ambient noise correlation: Laboratory experiments[END_REF], hence, an opportunity to increase the sensitivity of detection. For this reason, Stretching has been chosen to carry out the CWI analysis of this study. This method assumes that a decrease (resp increase) in propagation velocity δ v i must be simulated by means of stretching (resp compressing) the time axis t of a reference signal h 0 [t] with a given dilatation rate τ i = δ v i /v 0 . In order to quantify the similarity between the stretched reference signal h 0 [t(1 + τ i )] and the test signal h 1 [t] within a chosen time interval [t 1 ,t 2 ], cross-correlation coefficient CC can be calculated according to Equation (1) :

CC (t 1 ,t 2 ) (h 0 ,h 1 ) (τ i ) = t 2 t 1 h 0 [t(1 + τ i )] . h 1 [t] dt t 2 t 1 h 2 0 [t(1 + τ i )] dt . t 2 t 1 h 2 1 [t] dt (1)
Following a grid search to maximize the cross-correlation coefficient as a function of τ i , the relative variation of velocity α = (v 1v 0 )/v 0 = δ v/v 0 can be derived, where v 1 is the estimated perturbed propagation velocity. Besides, the cross-correlation coefficient CC(α) and the decorrelation coefficient Kd = 1 -CC(α) (from 0% to 100%) give an indication about the decorrelation between the unperturbed and the perturbed signals.

Nonlinear mixing via frequency-swept pump waves

In order to minimize this pump frequency dependence on the extracted and Kd, frequency-swept pump waves are used as recommended by [START_REF] Zhang | Nonlinear mixing of ultrasonic coda waves with lower frequency-swept pump waves for a global detection of defects in multiple scattering media[END_REF] instead of searching for close resonance frequencies. With frequency-swept pump waves, several modes of the specimen can be excited. Excitation occurs over a relatively wide band (in our case, 10 -50 kHz which corresponds to around 20 modes numerically determined and observed experimentally). Hence, one can consider that the samples can be excited homogeneously in space and the results would not be affected by the presences of localized vibration nodes, thereby making it possible to conduct a global inspection. In the following, experiments are carried out to show that this principle can be extended to closed crack detection in mortar.

EXPERIMENT DESIGN

Specimen preparation

Mortar samples with dimensions of 7 cm x 7 cm x 28 cm were prepared with a water to cement ratio of 0.35. Mortar mixtures consisted of 1350 g sand (0/2 sand), 450 g Portland cement (CEM II), 155 g water and 8 g superplasticizer (ChrysoFluid Optima 206). After 1 day curing in sealed conditions in an air-conditioned room with a temperature of 20 • C, the specimens were demoulded and further cured in sealed conditions wrapped in aluminium foil.After 1 week, a notch with a depth of 1.5 cm and a width of 5 mm was created at the centre of the beam in order to initiate the crack. The specimens were placed again in the same curing conditions until the creation of the cracks.

Two weeks after casting, two of the three specimens were cracked using crack mouth opening displacement (CMOD) controlled three-point-bending test. In order to study the influence of the crack width on CWI measurements, specimens B and C were cracked with different CMOD values after unloading. CMOD values and crack geometrical details after unloading are summarized in Table 1 and explicated in Figure 1.

CWI set-up

To achieve CWI measurements, three piezoelectric transducers were glued on each specimen: two transducers with a working frequency range between 200 and 800 kHz were glued to the specimen around the notch for the probe wave excitation and detection, and one piezoelectric ceramic generating the larger-amplitude pump acoustic wave at lower frequencies typically in the range of 10 -50 kHz was glued at a side of each specimen (Figure 2). The excitation signal for the probe source was a chirp with frequency varying linearly from 200 kHz to 800 kHz. The formation of coda wave is mainly due to the multiply reflected by the boundaries of the specimen. Synchronously, a 4-ms-long received signal is recorded by probe receiver using a 5-MHz sampling frequency and 16-bit amplitude dynamics. In order to improve the signalto-noise ratio, an average of 256 successive acquisitions is set as one coda record, and 10 successive records are saved.

A pump signal with a lower frequency (10 -50 kHz) is sent to the specimen to induce nonlinear acoustic modulation. The pump signals fed to transducer are amplified by a R Bruël & Kjaer type-2713 power amplifier up to 100 V RMS. During the test, the pump signal amplitude is manually altered through the power amplifier gain. The pump signal is linearly swept in frequency from 10 to 50 kHz in 11 ms, and swept signals are continuously generated. In order to distribute the effect of the swept pump waves on the coda waves, pump and probe signals are generated in an asynchronous manner.

A late time-window between t1 = 0. calculation reliably and 2) these signals should be formed by waves that underwent a sufficient number of scattering events. Figure 3 represents one recorded signal with the time-window used for the CWI analysis.

EXPERIMENTAL RESULTS AND DISCUSSION

the pump wave amplitude increased from 0 to 60 dB, signals recorded from an uncracked specimen are almost identical (Figure 4 a-b), while those from cracked specimens show a small phase shift and waveform distortion, which is only visible in a late time-window (Figure 4 c-d). Thus, this finding indicates that nonlinear modulation has taken place due to the presence of a crack in the specimen and emphasizes the benefit of analysing the coda part of the signals.

The velocity variations induced by the pump excitation output from CWI measurements allow the detection of a crack. Indeed, for the cracked specimens, when the pump amplitude is increased from 0 dB to 60 dB, the propagation velocity decreases by up to 0.025% as illustrated in Figure 5 while a smaller velocity variation can be observed on uncracked specimens when the pump amplitude is increased. A thermal bias correction as depicted in Figure 5 b) is implemented numerically by subtracting the results for alpha of the specimen which was not excited by its pump emitter to the two other samples. Thus, a clear distinction can thus be made between cracked and uncracked specimens when the pump amplitude exceeds 50 dB. The wave-form of the cracked specimen is changed when the pump amplitude increases as illustrated by the variation of the decorrelation coefficient Kd. CWI analysis results also allow to discriminate the specimen C with the larger crack from the specimen B with a smaller crack. When the pump amplitude is decreased back to 0 dB after an excitation to 60 dB, both α and Kd return to values very close to the initial values obtained at the beginning of the test.

A linear fit for the evolution of corrected propagation velocity as a function of pump amplitude agrees well with the CWI data (Figure 6) as proposed by [START_REF] Zhang | Nonlinear mixing of ultrasonic coda waves with lower frequency-swept pump waves for a global detection of defects in multiple scattering media[END_REF]. This linear fit allows a clear distinction between cracked and uncracked specimen. For the decorrelation coefficient Kd, a quadratic increase with pump amplitude is found.

CONCLUSION

In this study, an implementation of a novel NDT method combining the use of Coda Wave Interferometry (CWI) with a nonlinear acoustic modulation process has been proposed following the original method developed by [START_REF] Zhang | Nonlinear mixing of ultrasonic coda waves with lower frequency-swept pump waves for a global detection of defects in multiple scattering media[END_REF]. This method shows the capabilities of global detection of very small defects in concrete using coda signals that potentially originate from multiple scattering or reverberating media. The main idea is to utilize wide-frequency band signals, for both the probing coda signals (200 -800 kHz frequency sweeps) and pump wave (10 -50 kHz frequency sweeps), which acts to modulate the medium properties encountered by the probe (coda) wave. Originally developed to detect large nonlinear defects in a linear medium, the method can be successfully applied to detect small and nonlinear defects as cracks in an otherwise nonlinear medium such as concrete and mortar. The pump wave amplitude influences the detected coda signal and the method observables show good sensitivity to the presence of defects. The changes in velocity variations and decorrelation coefficient vs pump amplitude allow to discriminate cracked mortar from uncracked mortar. The method is reproducible and can provide an easy way to differentiate damaged and sound concrete. Several applications of this technique could be developed in the field of civil engineering. For example, the detection of small cracks causing leakage could be realised without the need of percolating fluid. Moreover, it could be possible that a mechanical information about microscopic damage could be obtained from this very sensitive method.

Table 1 :Figure 1 :

 11 Figure 1 : Schematic diagram of three-point-bending test and crack geometrical properties measurement.

  3 ms and t2 = 0.5 ms is used to performed CWI analysis. To choose such a time-window one needs to ensure: 1) it contains enough signals to performed Stretching

Figure 2 :

 2 Figure 2 : Schematic diagram of three-point-bending test and crack geometrical properties measurement.

Figure 3

 3 Figure 3 coda signals recorded and time-window used for CWI

Figure 4 :

 4 Figure 4 : Temporal coda signals recorded and time-window used for CWI analysis: a), b) an uncracked specimen (A), c) and d) for a cracked specimen (C) with two different pump wave amplitudes Apump (0 dB and 60 dB). a) and c) are close-ups of the coda signals during an early time interval (20-s wide); and b) and d) are close-ups of the coda signals during a late time interval (20-s).

Figure 5 :

 5 Figure 5 : Results of CWI analysis of probe coda waves mixed with pump waves for the first series: a) Velocity variation a vs. step number; b) Corrected velocity variation vs step; c) Excitation amplitude of the pump waves at each step of the test; and d) Decorrelation coefficient a vs. step number. Specimen name with 'coda' indicates a specimen which is not excited by the pump waves and which is used for temperature compensation of the following two specimens in the legend. Thus, the three groups of three specimens of the legend correspond to three experiments for three activated pump configurations.

Figure 6 :

 6 Figure 6 : Pump amplitude dependence of CWI measurements: a) Corrected velocity variation α vs. normalized pump amplitude and b) Remnant correlation coefficient Kd vs. normalized pump amplitude. Both the linear and quadratic fits are proposed. Standard deviations are indicated.

7th European Workshop on Structural Health Monitoring July 8-11, 2014. La Cité, Nantes, France Copyright © Inria (2014)

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENTS

Financial support from the GIS LIRGeC, Rgion Pays de la Loire (France), for this study is gratefully acknowledged.


Andrés Belisario-Briceño

Sabeha Zedek

Thierry Camps

Raoul François

Christophe Escriba

Jean-Yves Fourniols

SHM BASED ON MODAL ANALYSIS: ACCELEROMETER AND PIEZOELECTRIC TRANSDUCERS INSTRUMENTATION FOR CIVIL ENGINEERING IN HETEROGENEOUS STRUCTURES

Keywords: SHM, Piezoelectric, Modal Analysis, Heterogeneous Structures

This paper presents a strategy for the detection of mechanical damage of a reinforced concrete beam strengthened by Carbon Fiber Reinforced Polymers (CFRP) sheets (TFC ©) based on the joint use of piezoelectric sensors and conventional accelerometers. The beam is subjected to repeat impacts that may represent the action of vehicles on a roadway joint of a bridge, at different levels of damage induce by bending of the reinforced concrete beam. The results show that piezoelectric sensors provide a much wide response those accelerometers allowing a study in the high frequency range (above 2 kHz). The spectral response appears largely affected by mechanical damage on the beam and suggests a possible use for SHM in Civil Engineering structures.

INTRODUCTION

One way to address the understanding and modeling of large complex systems is to develop a distributed instrumentation based on multiphysic sensors, combining low energy versatile computing architecture to diagnose weaknesses of the observed system. We focus for several years on methods and technologies able to analysis vibrations propagation in heterogeneous materials. In this article we demonstrate how distributed instrumentation onto surface can benefit on the vibrations induced by road traffic on a civil engineering work to diagnose, by a frequency signature variation, identifying structural changes in the structure synonym of potential defects.

Owed to the growth of traffic on the bridges and environmental attacks such as deicing salt, progressive damage could occur and lead to premature end of service life. We offer a case study where a concrete member is subjected to mechanical damage due to over-loading in flexure. The structure studied and characterized is a reinforced concrete beam strengthened with Carbon Fiber Reinforced Polymer (CFRP). To perform a wide-band spectrum analysis, we compare sensor response provided by a silicon accelerometer and piezoceramic transducer.

Such an approach with large-scale frequency response is worth of interest for successful prognosis damage detection. The experiment's principle is compare efficiency and complementarity of piezoelectric and accelerometer frequency response. The methodology presented in the final paper demonstrates as beam's harmonics frequency changes before and after mechanical stresspressure and impulsive shocks.

EXPERIMENTAL BENCH

The beam tested is a reinforced concrete element with dimensions of 150 x 280 x 3000 mm. As reinforcement two high bond (ribbed) rebars with 12 mm diameter were embedded (cover depth 20 mm) and the beam is strengthened by a carbon sheet (TFC©) on tension surface. The beam is subjected to 4-point bending and instrumented with two ends and mid range Fig. -1.

Such an approach with large-scale frequency response is worth of interest for successful prognosis damage detection. The experiment's principle is compare efficiency and complementarity of piezoelectric and accelerometer frequency response. The methodology presented in the final paper demonstrates as beam's harmonics longitudinal frequency changes before and after mechanical damage.

Figure -1: Test setup 4-point bending bench and instrumentation

Loading consists of a bearing of 20kN above cracking level and a loading of 30 kN after yielding of tension reinforcement followed by a total unloading of the beam Fig. -2. The impacts made on the end of the beam are obtained by a jackhammer with a slightly curved cylindrical tool steel to avoid damaging the concrete and impacting the beam at a rate of about 24 strokes per second.

Figure -2: load versus deflection and levels of measurement

The acquisition system comprises a measurement three-node zone with an accelerometer (XYZ) and a piezoelectric transducer -PZT-. These sensors are robust and low cost which can allow installation on large structures such as bridges. The use of accelerometers in three directions of the beam will verify the accuracy of information delivered by the PZT sensors Fig. -3.

Figure -3: Detail of the instrumentation architecture of measurement

The piezoelectric transducer is used for acoustic emission detection. The piezoelectric material we chosed in PbZrTiO 3 alloy, graded PZT-5A. This sensor has an excellent electromechanical coupling with |D31| = 175 pC/N. The associated charge amplifier with the PZT was designed to eliminate the low frequency waves, under 100 Hz, and it provides a steady gain up to 20 kHz and a total gain of 220 dB V/C. An 8 th order low pass filter limits the bandwidth of the system to 20 kHz with a rapid cutoff. Lastly, the accelerometer is based on the MMA7361. As specified in its data-sheet, the accelerometer is limited to 1.6 kHz with a double 1 st order filter. It features a selectable sensitivity of 1.5G or 6G and a bandwidth of 1.6 kHz on three axes.

ANALYSIS OF EXPERIMENTAL RESULTS

The In addition, we also find that the PZT sensors are used to obtain a high response, (rate>1kHz), which is not the case of accelerometers. This is the last show a reduced bandwidth (~2kHz), but also and especially a limited signal to noise ratio 40dB which does not allow them to measure vibration in more than two decades. For its part, the PZT sensor is not limited by its frequency response and allows measurements over a dynamic signal than four decades. This is valuable for signal analysis beyond the kilohertz or the signal amplitude is attenuated rapidly, from 3 to 4 order of magnitudes. Thus, we clearly see the presence of vibrations up to about 10kHz (50µS).

In the figure below -Figure 4.b -, we can see that the difference between the spectra of the piezoelectric sensor and accelerometer. We can perceive as the rich spectrum of the PZT contains more information beyond the 2 kHz, as a perspective for the progress of this research work this will be the area of interest for data exploitation. To analyse the behavior of the beam, it will be based on the excitation imposed by the jackhammer and simplify the spectrum by discretizing frequency. For example, we cover the spectrum after damage to 30 kN After an acquisition time of 5 seconds with sampling at 50 kHz, there are 250,000 points. The first two seconds, corresponding to the transitional regime are removed, and reduces the acquisition to three seconds in regime-established, 150000 pts. This score is very high and in the perspective of achieving an autonomous system and compact, it's necessary in our pre-treatment drastically reduce these numbers point to a few hundred points.

To analysing the waveform, we used the Discrete Fourier Transform -DFTof the time signal gives a spectrum ranging from 10 to 20 kHz, with high resolution -0.33 Hz-and it is still ready to treat 60,000 pts. Instead of full spectrum, we prefer the discrete spectrum is limited to keep the points in the spectrum corresponding to multiples of the excitation rate impact -24.17 Hz, this decimated FFT consists of only 827 points in accordance with our expectations -Fig. 5.band -Fig.

-6 for the PZT-. Although this seems coarse spectrum envelope, it's still relevant to the degradation of quantization.

Figure -6: Spectral profile of PZT and Harmonics at Stimuli's frequency

To better visualize the change in spectral response, the relationship between the track amplitude spectrum before and after damage due to the load (30kN) beyond the bearing steels plasticity tensioned. This amplitude ratio gives information about the irreversible damage suffered by the beam. In the below images we can note the spectral changes in two frequency bands. We divided the frequency into two groups, low -0 Hz @ 2 kHz-and high for -2 kHz @ 15kHz. This visual method Fig.

-7 will allow us to look at changes in spectral level of the initial state of the structure. We can quantify several methods for treating the mechanical phenomena of the signal from structure. One of the easiest to implement analyses is to find how the are responses to frequency change in amplitude and own frequencies. We noted how the spectral change of the signal recovered after damage is shifted in frequency. The spectral profile in high frequency is shifted in frequency and magnitude.

It is thus possible propose a method of monitoring the work in relation to a certain definition of the level of damage. And setting a threshold can control the level of damage and launch control when this threshold is reached. In practice, it may be more appropriate to define the damage threshold compared to an area rather than level. A possible solution in our analysis is triggered some value amplitude value as we saw previously demonstrated the frequency-displacements and the voltage gain after the degradation of the health of structure.

It remains to quantify the level of mechanical damage measured by the amplitude ratio. Furthermore the frequency domain where the threshold is exceeded likely to learn about the size and nature of the damage. This will be a series of tests at different load levels and type of irreversible damage on reinforced concrete elements and then be quantified by approaches based on learning by neural networks

We are interested to develop an autonomous and intelligent system for the calculation and estimation points for the signal dynamics with the help of software acquisition of data and signal processing.

CONCLUSIONS AND PERSPECTIVES

The analysis of the spectral response of a reinforced concrete beam requested by longitudinal vibrations that can simulate the traffic on the bridge deck shows that its spectral response is sensitive to irreversible mechanical damage undergone by the beam. A first analysis based on the difference in amplitude of the harmonic response of the request indicates that it is possible to quantify damage by spectral analysis. It remains of course to progress on the meaning and classification of damage by correlating the spectral evolution to mechanical damage.

In addition, Fig. -9 shows spectral responses of beam for a range from 0 Hz to 2 kHz (9.a) and from 2kHz to 15kHz (9.b) before and after degradation. For the first range, spectrum are quite similar and the second one spectrum are distinctly separate (appearance of new resonances) and we believe that it is in this range it will be investigated to extract a spectral fingerprint of the degradation. To achieve this we must have, by changing the first floor "charge amplifier" integrate a high pass filter to (FC ~ 2kHz), and thus reduce the amplitude of low frequency high amplitude signals (longitudinal mode)! This will amplify particular advantage before the A/D conversion and the time signals will also reduce acquisition time to 0.3 seconds while maintaining good accuracy.

  Fig. -4 shows the response of sensors. The accelerometer incorporates the vibrations along the axes X and Y, Fig. -4.a. The PZT is omnidirectional in the plane longitudinal and transverse, Fig. -4.b.

Figure - 4 :

 4 Figure -4: Comparison of spectral profiles accelerometers X and Y with the PZT

Fig. - 5

 5 by restricting the analysis to 2 kHz. The discretized signal is studied in the frequency of stimuli beyond 2kHz as show in Figure5b. According to a mathematical approximation a script we find the spectral signal profile.

Fig. 5 Figure - 5 :

 55 Fig. 5.a Fig. 5.b Figure -5: (a) Signals Accelerometers Raw and peaks excitation rate (b) Discrete Peaks and Spectral Profile

Figure - 7 :

 7 Figure -7: Spectral Profile before damage and Spectral Harmonics after damage

Figure - 8 :

 8 Figure -8: Evolution of the amplitude spectrum before and after damage by a load 30kN

Figure - 9 :

 9 Figure -9: Evolution of the spectra measured by the PZT in the range 1kHZ to 20kHz damage before and after a loading 30kNw

July 8-11, 2014. La Cité, Nantes, France Copyright © Inria (2014)

EWSHM 2014 -Nantes, France


Philippe Guéguen
email: philippe.gueguen@ujf-grenoble.fr

Matthieu Valla

Béatrice Augère

Didier Goular

Analysis of Reinforced Concrete Buildings Using Multipath Lidar

Keywords: Lidar, modal analysis, earthquake engineering

This paper compares the modal analysis of reinforced-concrete buildings obtained using sensitive velocimeters and coherent LIDAR. Ambient vibrations are recorded by these two systems and processing using operative modal analysis method for getting building frequency and mode shapes. Real-scale trials applied to five buildings located at Grenoble (France) are presented. The efficiency and reliability of the Lidar is discussed and the modal parameters measured by Lidar at a range of 200m and by insitu velocimeters are compared. The results are in good agreement and allow us to conclude on the ability of the coherent Lidar to assess modal parameters of existing buildings at long range and without any retroreflectors placed on the structures. The results open new perspectives for remotely testing buildings, without getting inside, facilitating dynamic analysis of buildings for earthquake engineering applications.

INTRODUCTION

Since the design seismic forces in structures are frequency and damping dependent, these two parameters are the subject of particular attention in many research activities, to fix numerical [START_REF] Ventura | Dynamic characteristics of a base isolated building from ambient vibration measurement and low level earthquake shaking[END_REF][START_REF] Volant | Seismic evaluation of existing nuclear facil-ity using ambient vibration test to characterize dynamic behavior of the structure and microtremor measurements to characterize the soil: a case study[END_REF][START_REF] Michel | Full Scale Dynamic response of a RC building under weak seismic motions using earthquake recordings, ambient vibrations and modelling[END_REF] or analytical models [START_REF] Perrault | Reducing the uncertainties of the fragility curves using experimental testing in existing buildings: the case of the BRD Tower of Buccarest (Romania)[END_REF] or to provide empirical relationships between the main characteristics (height, design, etc.) of buildings and their period of vibration found in seismic regulation documents [START_REF] Goel | Period formulas for concrete shear wall buildings[END_REF][START_REF] Chopra | Building period formulas for estimating seismic displacements[END_REF][START_REF] Oliveira | Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques[END_REF][START_REF] Gallipoli | Empirical estimate of fundamental frequencies and damping for Italian buildings[END_REF][START_REF] Michel | Comparison between seismic vulnerability models and experimental dynamic properties of existing buildings in France[END_REF]. Clinton and Heaton [START_REF] Clinton | Potential advantages of a strong-motion Vvlocity meter over a strongmotion accelerometer[END_REF] related the evolution of the performance of building instrumentation for earthquake engineering activities since the 1960's and the beginning of the building permanent instrumentation program in US [START_REF] Housner | Interaction of buildings and ground during an earthquake[END_REF][START_REF] Jennings | Vibration and soil-structure interaction tests of a nine-story reinforced concrete building[END_REF][START_REF] Blume | Highrise building characteristics and responses determined from nuclear seismology[END_REF][START_REF] Crouse | Soil-structure interaction during the San Fernando earthquake[END_REF][START_REF] Luco | On the apparent change in dynamic behavior of a nine-story reinforced concrete building[END_REF] and Japan [START_REF] Satake | Evaluation of vibration properties of high-rise steel buildings using data of vibration tests and earthquake observations[END_REF]. With the low sensitivity of the new seismic and accelerometric sensors, ambient vibrations (AV)-based methods for modal analysis have been commonly used to monitor structures in earthquake engineering communities providing an effective tool for short-and/or long-term monitoring of structural health.

In addition, a significant amount of research has been conducted over the last two decades on non-destructive damage evaluation (NDE) based on changes in the dynamic modal responses of a structure. The basic idea is that modification of a system's stiffness, mass or energy dissipation characteristics may alter its dynamic response [START_REF] Doebling | Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review[END_REF][START_REF] Farrar | An introduction to structural health monitoring[END_REF]. For example, a comparison of initial and final values of frequency, damping and mode shape after extreme events provides information on the post-earthquake integrity of structures [START_REF] Dunand | Utilisation du bruit de fond pour l'analyse des dommages des bâtiments de Boumerdes suite au séisme du 21 mai 2003[END_REF][START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF][START_REF] Nayeri | A novel approach for the structural identification and monitoring of a full-scale 17-story building based on ambient vibration measurements[END_REF][START_REF] Vidal | Changes in dynamic characteristics of Lorca RC buildings from pre-and post-earthquake ambient vibration data[END_REF]. Analysis of the damage related to variations of the fundamental frequency of the buildings is common practice in earthquake engineering since, as supported by Farrar et al. [START_REF] Farrar | Vibration-based structural damage identification[END_REF], frequency is probably the modal parameter that is most sensitive to change, particularly because the loss of stiffness directly impacts the frequency values [START_REF] Dunand | Utilisation du bruit de fond pour l'analyse des dommages des bâtiments de Boumerdes suite au séisme du 21 mai 2003[END_REF][START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF][START_REF] Celebi | Dynamic characteristics of five tall buildings during strong and low-amplitude motions[END_REF][START_REF] Ivanovic | Ambient vibration tests of a seven-story reinforced concrete building in Van Nuys, California, damaged by the 1994 Northridge earthquake[END_REF][START_REF] Michel | Time-frequency analysis of small frequency variations in civil engineering structures under weak and strong motions using a reassignment method[END_REF]. Moreover, damage detection methods are also based on mode shape analysis, such as the mode flexibility method [START_REF] Pandey | Damage detection in structures using changes in flexibility[END_REF], the curvature flexibility method [START_REF] Zhang | The damage indices for constructed facilities[END_REF] and the mode shape curvature method [START_REF] Pandey | Damage detection from changes in curvature mode shapes[END_REF].

Few applications are available in practice, in spite of the fact that the estimation of damage severity makes a significant contribution to the action of decision-makers in emergency situations after extreme events. One of the reasons to explain this observation is that in general, the testing is performed by putting sensors in the structures, a delicate and dangerous activity in the event of seismic crises because of repeated aftershocks and of large number of buildings to be tested. The main objective of this paper is to test a remote assessment of modal parameters (frequencies and mode shapes) of existing buildings, having as objective the health monitoring. After presenting the multipath Lidar instrument used here, and the building tested, we compare the modal parameters assessment provided by Lidar and classic velocimeters deployed in the structures.

THE LIDAR

The system developed for this study is a triple all-fiber Lidar vibrometer [START_REF] Cariou | Performance of an erbium Laser vibration sensor[END_REF] working at 1.55µm, using polarization-maintaining fibers (Fig. 1A). In figure 1B, the backscattered wave is mixed with a portion of the signal called the local oscillator (LO). On the photodetector, the interference between the two optical waves yields a current, called the heterodyne current, whose frequency is given by the difference between the frequencies of the two optical waves. During Lidar operation, the frequency of the signal backscattered by the target building surface suffers a Doppler frequency shift which is proportional to the difference in velocity between the Lidar system and the target building surface in the direction of the Lidar line-of-sight. The frequency of the heterodyne current is thus equal to the Doppler frequency shift. These currents are then sent to the analog signal processing module, where the backscattered signals are filtered and downshifted in base band. The digitized signals are then processed in real time for in-situ spectral visualization and stored for furthermore detailed analysis.

As we are aiming at static but vibrating targets, the overall Doppler frequency shift due to target velocity is null and the carrier frequency of the heterodyne signal is centered on the frequency of the acoustic-optic modulator (AOM, Fig. 1B) frequency. In monostatic architecture, parasitic signal exists that creates crosstalk phenomena, i.e. a fraction of the power emitted by the Lidar is accidently redirected into the reception. The parasitic signal from the back-reflection of the emitted beam on the output lens is also centered on the AOM frequency shift, preventing the frequency separation of the useful signal. All paths are bistatic (separate transmitting and receiving lenses) in order to avoid being blinded by parasitic signal due to the redirection of a fraction of power emitted by the Lidar into the reception (crosstalk phenomena).

The two first sensor heads are mounted on an automated turret (Fig. 1A), which allows a series of points to be addressed on the target building. The third sensor head is used as a time synchronization reference, sighting a fixed reference point on the target building and providing a synchronization reference for vibrations measured successively by the mobile sensor heads. The building vibration velocity is determined using the autocorrelation between one complex sample and its first neighbor. The result is accumulated over a number of complex samples. The phase of the computed autocorrelation gives the instantaneous frequency of the signal, which is proportional to vibration velocity. The output (i.e. vibration velocity) of the digital signal processing is computed every 5 ms, resulting in a vibration sampling frequency of 200 Hz. This sampling frequency is chosen in order to avoid parasitic vibrations (presence of electric motors, machine, lifts…), which appear up to 80 Hz, whereas building frequencies remain below 20 Hz. These vibrations are usually observed during experimental works conducted in structures resulting from the operating of the buildings (presence of electric motors, machines, lifts…). The reference beam, kept fixed during all the experiment, gives the time reference and the synchronization is made with the mobile beams as well as the amplitude normalization.

DESCRIPTION OF THE EXPERIMENT

Grenoble (France) is a dynamic city that increased in population during the late 60s. Many high-rise buildings were built at that time. In the framework of this study, five such buildings have been tested. 2) with a Cityshark II [START_REF] Chatelain | Ambient vibration recording for singlestation, array and building studies made simple: CityShark II[END_REF] and 6 velocimeters Lennartz 3D 5s. We used the Frequency Domain Decomposition method (FDD) [START_REF] Brincker | Modal identification of output only systems using frequency domain decomposition[END_REF] to analyse the modes of the structure. A reference site was kept at the top of the building and several sets of recordings (at 200Hz) were done moving velocimeters along the height of the building. The two first modes are 0.66, 2.69Hz and 0.85, 3.25Hz in the T and L directions, respectively [START_REF] Mikael | Long-term frequency and damping wandering in buildings analysed using the Random Decrement Technique (RDT)[END_REF]. For Belledonne and Chartreuse, the modal frequencies were computed using the Fast Fourier Transform (FFT) applied to the top recording done during the Lidar experiment (Fig. 3). Even if the three buildings are perfectly similar in term of design, shape and height, some variations were observed due to the presence of differences in design or due to the high sensitivity of frequency to changes confirmed recently by Mikael et al. [START_REF] Mikael | Long-term frequency and damping wandering in buildings analysed using the Random Decrement Technique (RDT)[END_REF]. Furthermore, a torsion mode [START_REF] Mikael | Long-term frequency and damping wandering in buildings analysed using the Random Decrement Technique (RDT)[END_REF] was also observed at 0.99Hz. We followed the same process in December 2002 in one of the two ARPEJ towers, 15-story RCbuildings in the campus. For ten years, ARPEJ2 has been used as a test bed for training activities and instrument tests. Mode shapes and modal frequencies were obtained for this building [START_REF] Gueguen | Seismic vulnerability of structures[END_REF]. The two first modes were found at 1.17, 4.57 Hz and 1.32, 5.03 Hz in the T and L directions, respectively (Fig. 3). A torsion mode, corresponding to 1.37 Hz, was also detected on the Fourier spectra. The stability of the modes shapes over ten years allows us to assume a very stable and robust method for extracting the dynamic characteristics of existing buildings.

The Lidar experiment has followed the same process as for AV recording. One sight was kept at the top of the building as the reference and the other two sights were moved down from floor to the bottom of the building. The Lidar was positioned on a support resting on the ground, located to allow direct sight of the full height of the building. The distance of sight for the ARPEJ buildings was around 100 m and for the Ile Verte buildings the distance was close to 300 m. After signal processing of the raw Lidar data, each file corresponded to 10 minutes of recordings with a sampling rate of 200 Hz. Gueguen et al. [START_REF] Guéguen | Comparison of velocimeter and coherent lidar measurements for building frequency assessment[END_REF] have confirmed the Lidar records the frequencies of the target and of the support. For that reason, the Lidar support was designed to be stiff enough with respect to the classic range of building frequencies to avoid interferences. After data conversion, FDD was applied and the modal analysis was performed. The major advantage of the Lidar designed for this experiment is the have a perfect synchronization of recordings without requiring a specific reflector placed on the surface of the structure. Nevertheless, the longer sight distances introduce more noise, reducing the signal-to-noise ratio due to beam divergence of the optical wave and affecting the performance of the Lidar system. This could be resolved by increasing the performance of the Lidar but it introduces contrains on complying with the restrictive eye safety regulation.

RESULTS

Fast Fourier Transform is computed at the top of the building using velocimeters and Lidar systems (Fig. 3). The Lidar detects the modal frequencies of the buildings, including longitudinal and transverse direction but also the torsion mode. Below 2 Hz, i.e. close to the fundamental frequencies of the tested buildings, the signal-to-noise ratios (SNR) are comparable, because the building vibration is large enough to be detected. At high frequency, we observed that the noise level of the Lidar is higher that for the velocimeter, as already suggested by Gueguen et al. [START_REF] Guéguen | Comparison of velocimeter and coherent lidar measurements for building frequency assessment[END_REF]. This low SNR introduces some drawbacks for the clear analysis of the second frequencies, visible in the 2-5 Hz range. For the Ile Verte towers, the SNR at high frequency is worse than for the ARPEJ buildings, due to the distance of sight between the Lidar and the building. Moreover, the Lidar measures velocity along a single direction of sight. By consequent, the frequencies detected are directly influenced by the azimuth of the sight with respect to the main direction of vibration of the buildings. This is clearer for the Ile Verte buildings for which the differences in azimuth of the sight for the three buildings tested were greater, i.e. 11°, 45° and 70° for the Chartreuse, Montblanc and Belledonne towers, respectively. For Chartreuse, the sight was close to the perpendicular axis of the building and we detected only the T direction of vibration and the torsion mode (Fig. 3). For the Belledonne tower, all three modes were recorded, with amplitude variations compared to the velocimeter results. For Montblanc, corresponding to 45° of sight azimuth, the three modes were perfectly recorded by the Lidar. This is the main drawback of the Lidar measurement technique: recording the vibration along a single direction of sight means that the modal analysis can be biased. Nevertheless, in the case of remote monitoring, we observed that the frequency values are reliable and representative of the dynamic response state of the buildings let us assume the efficiency of the Lidar for detecting the frequency variations related to changes or damages.

The singular value decompositions of the velocimeter and Lidar data for the ARPEJ2 and Montblanc towers are displayed figure 4. The same singular value decomposition is observed for both buildings whatever the equipment used. Due to the SNR, the two horizontal modes in the T and L direction are well detected, as well as the torsion mode clearly observed here. This detection is not dependent on the single sight of the Lidar along one direction. It is particularly interesting to point out the presence of parasite frequencies at 4 and 10Hz for the ARPEJ2 building, seen with both systems and certainly produced by a permanent internal source of vibration (e.g., lift or air conditioning). In both cases, 15 Hz is observed on the LIDAR, corresponding to the vibration of the Lidar support, as also reported by Gueguen et al. [START_REF] Guéguen | Comparison of velocimeter and coherent lidar measurements for building frequency assessment[END_REF]. At high frequency, for the higher modes, the Lidar system is noisier, resulting in low resolution of the second singular value. This is clearer for the Montblanc tower, due to the increase in noise with the distance of sight (280 m for Montblanc and 120 m for ARPEJ2). In this case, the 3 Hz second mode cannot be analysed. Since the singular values (frequencies) and singular vectors (mode shapes) were detected, it is possible to draw the 3D shapes of the modes, by associating with each sensor the 3D deformation of the building. This is displayed Fig. 5 for the Montblanc and ARPEJ2 buildings. In order to improve shape visualisation, we considered each floor to be stiff and undeformable, that corresponds to associate at each point of the floor the motion recorded by the sensor or the Lidar. According to the velocimeter, the Montblanc mode shapes are clearly related to bending modes in the L direction, corresponding to frequencies 0.85Hz. Because of the 3C of ambient vibrations recorded with the velocimeters, the full motion of the building can be reconstructed by modal analysis. For the Lidar, only one direction of sight is available. We therefore observe (Fig. 5) the coupling of the mode shapes of the two horizontal directions of the structure, as well as the vertical direction. The angle of deflection is related to the azimuth of the sight with respect to the building. This means that mode shape reconstruction is not possible unless we record vibrations in the direction of the perpendicular modes, even if the singular values and vectors are detected perfectly by the Frequency Domain Decomposition. Moreover, the Lidar sights from the ground level and the vertical motion are also present in the coupling mode shapes defined by FDD. Nevertheless, this drawbacks does not reduce the major advantage of the Lidar equipement, i.e. performing remotely dynamic characteristic assessments of existing buildings, from one site without entering the building and considerably reducing the time (and therefore cost) of the experiments. For information, we assessed the three Ile Verte towers in 6 hours, which is approximately the same as the time required using the velocimeter.

CONCLUSIONS

The large-scale instrumentation and monitoring of existing buildings is of more than academic interest. Testing buildings provides information on safety by evaluating the variation of their elastic properties, often related to damage. In view of the number of buildings that must be tested after an extreme event, the development of remote systems, such as the Lidar, may be the key to improving the operability and efficiency of decisions. The assessment of changes between the physical properties of structures before and after earthquakes can help classify buildings as being suitable for immediate occupancy, requiring further and additional analysis or for demolition. Moreover, the long-term monitoring of buildings is also critical for decision makers and local authorities in order to check the effects of ageing and to assess the remaining life span of their structures.

In this paper, we have reported on the development and field trial of a 3-path Lidar vibrometer for this purpose. We have showed that application-related constraints are fulfilled: low velocity noise, real-time signal processing, compactness and laser safety. Autonomous and operability of the equipment was demonstrated during a vibration measurement campaign at long distance of sight. A good fit was observed between the modal frequency and mode shape values detected by Lidar and classical velocimeter. Despite a higher level of noise for the Lidar than for the velocimeter, most of the existing buildings could be monitored using this remote sensing method for large urban areas. The drawback related to the single direction of sight can be compensated by the efficiency of remote assessment fo frequency and mode shapes, giving a fast and accurate assessment of the structural health. Shorter experiment times and reliability of measurements lead us to imagine broad application on the scale of a city, allowing long-distance and repetitive scanning of structures.

Figure 1 :

 1 Figure 1: Description of the Lidar. A) Scheme of principle; B) Electronical and optical description of the Lidar

Figure 2

 2 Figure 2 Description of the Buildings (left: Arpej buildings; right: Ile Verte towers)

Figure 3

 3 Figure 3 Fourier transforms of ambient vibrations recorded at the buildings top (left: Ile Verte; right: ARPEJ) with velocimeters (CS) and Lidar.

Figure 4

 4 Figure 4 Singular value decomposition of ambient vibrations recored by Lidar and velocimeter (CS) for the MontBlanc (left) and the ARPEJ2 (right) towers.

Figure 5

 5 Figure 5 Shapes of the first (A) and second (B) mode using velocimeter (left) and Lidar (right) systems for the Mont-Blanc Tower

ACKNOWLEDGMENTS

This work was supported by the French Research National Agency (ANR) under the RiskNat program (project URBASIS n°ANR-09-RISK-009).