B Lossouarn
email: boris.lssouarn@cnam.fr

G Kerschen

J.-F De Ü

J.-F Deü

VIBRATION MITIGATION OF MULTIPLE NONLINEAR RESONANCES THROUGH AN ANALOGOUS PIEZOELECTRIC NETWORK

Keywords: Vibration damping, Piezoelectric coupling, Broadband control, Nonlinear resonances

The objective of this works is to investigate the interest of analogous piezoelectric networks for vibration mitigation of multiple nonlinear resonances. An electrical network providing a similar dynamics as the considered structure is first designed according to linear considerations. Then, a nonlinear electrical component is added to the network to ensure both a spatial analogy and a principle of similarity regarding the mathematical form of the mechanical nonlinearity. Once the electrical network and the mechanical structure are coupled through an array of piezoelectric elements, it is shown that such an analogous coupling offers strong benefits for vibration mitigation over a broad frequency range and a broad range of excitation amplitudes.

INTRODUCTION

Tuned vibration absorbers [START_REF] Hartog | Mechanical Vibrations McGraw-Hill[END_REF][START_REF] Hagood | Damping of structural vibrations with piezoelectric materials and passive electrical networks[END_REF] usually provide effective solutions for passive vibration mitigation. However, mechanical nonlinearities generate a detuning that seriously affects damping performance. A solution to this issue consists in the introduction of an additional nonlinearity in the absorber [START_REF] Habib | A principle of similarity for nonlinear vibration absorbers[END_REF]. The interest of nonlinear piezoelectric shunts has already been proven for vibration mitigation of single nonlinear resonances [START_REF] Soltani | The nonlinear piezoelectric tuned vibration absorber[END_REF][START_REF] Lossouarn | A fully passive nonlinear piezoelectric vibration absorber[END_REF]. The concept was then extended to the design of a nonlinear and multi-branch piezoelectric shunt [START_REF] Raze | A multimodal nonlinear piezoelectric vibration absorber[END_REF]. The present work addresses the development of a multimodal and fully passive piezoelectric analogous network that mitigates several resonances of a nonlinear structure.

An electrical network can be assembled to reproduce the dynamics of a cantilever beam in the linear regime of motion. In this case, several electrical resonances are simultaneously tuned to the mechanical resonances, thus providing the equivalent of a multimodal vibration absorber from electromechanical coupling through an array of piezoelectric patches [START_REF] Andreaus | Piezoelectric passive distributed controllers for beam flexural vibrations[END_REF][START_REF] Lossouarn | Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network[END_REF]. This allows broadband vibration mitigation at low forcing amplitudes. Yet, higher amplitudes still lead to a serious detuning of the absorber when considering nonlinear structures.

By extending a principle of similarity to spatial considerations, a nonlinear component is placed in the electrical network in order to mimic the dynamics of the mechanical structure. The electromechanical analogy is thus ensured beyond the linear regime. In this work, the use of a nonlinear capacitor generates an autonomous adjustment of the electrical resonances for a wide range of excitation amplitudes. The interest of this method is investigated numerically and experimentally by focusing on structural vibrations over a broad frequency range that covers the first three modes of a beam with localized cubic nonlinearity.

SINGLE MODE DAMPING WITH A PIEZOELECTRIC TUNED VIBRATION ABSORBER

For linear and nonlinear resonances

The resonant piezoelectric shunt, also called piezoelectric tuned vibration absorber, is commonly used to reduce the vibration amplitude of a single linear resonance. It is made of a piezoelectric transducer of capacitance C at zero strain connected to an inductor and a resistor whose values are typically obtained from

L = 1 Cω 2 O and R = 3 2 k c Cω O , where k c = ω 2 O -ω 2 S ω 2 S . (1)
The angular frequencies ω S and ω O corresponds to the resonances in short-and open-circuit, respectively. This formulation highlights a coupling factor k c , which is usually considered for the positioning of the piezoelectric elements. Indeed, since k c is directly related to damping performance [START_REF] Thomas | Performance of piezoelectric shunts for vibration reduction[END_REF], maximizing the coupling factor implies minimizing vibration amplitude for an adequate tuning of the electrical circuit. As seen in Eq. ( 1), part of the tuning procedure is to ensure that the electrical resonance at angular frequency 1/ √ LC matches the open-circuit natural frequency. As a consequence, it is clear that a mechanical nonlinearity altering the angular frequency ω O would deteriorate the tuning of the piezoelectric shunt and thus the damping performance.

A solution to overcome the influence of mechanical nonlinearities on piezoelectric tuned vibration absorbers is to introduce nonlinearities in the electric shunt itself. Following a principle of similarity, the added nonlinearity should possess the same mathematical form as the one in the mechanical system. For example, if a nonlinear force is modeled by a cubic function of the displacement u,

f NL = K NL u 3 , (2)
it has been shown that the required additional voltage in the shunt is also a cubic function of the electric charge q [4, 5]:

v NL = 1 C NL q 3 with 1 C NL = 2 L m 2 K NL , (3)
where m corresponds to the modal mass of the mechanical structure. This theoretical nonlinear capacitance in series with the inductor would ensure an adequate tuning of the resonant shunt by maintaining an equal-peak condition over a broader range of excitation amplitudes [START_REF] Soltani | The nonlinear piezoelectric tuned vibration absorber[END_REF]. While the nonlinear voltage in Eq. ( 3) could be synthesized with a numerical controller, find a passive electrical component able to satisfy this purely nonlinear condition is not obvious [START_REF] Gluskin | The use of non-linear capacitors[END_REF]. In order to circumvent this limitation, it has been proposed to rather introduce the nonlinearity in the inductor [START_REF] Lossouarn | A fully passive nonlinear piezoelectric vibration absorber[END_REF]. Indeed, a one-term harmonic balance approximation shows that Eq. ( 3) is close to

v NL = L 1 -α q2 q with α = 6 LK NL m 2 ω 4 O . (4)
While no passive inductors seems to be able to precisely satisfy this nonlinear relation, the next experimental section still shows that it is possible to benefit from saturation of magnetic circuits to approximate the required nonlinearity. or with an optimal linear shunt (-).

Experimental validation of the principle of similarity

The experimental setup is based on a cantilever beam involving a cubic nonlinearity. As shown in Fig. 1, a thin lamina is clamped at the left end of the beam, which generates the hardening nonlinearity. The structure is covered with an array of piezoelectric patches in order to mitigate vibration with a piezoelectric tuned vibration absorber. The passive inductor in Fig. 2(a) is realized by winding copper wire around a magnetic circuit in ferrite material. When connected to the piezoelectric patches, Fig. 2(b) demonstrates that the passive inductor allows a strong reduction of the vibration amplitude at low excitation levels. However, Fig. 3(a) shows that an increasing forcing amplitude leads to a complete detuning of the resonant shunt because of the mechanical nonlinearity.

As mentioned previously, a solution to overcome this effect is to introduce in the absorber a nonlinearity similar to that of the primary structure. Here, the electrical circuit is made of an inductor whose inductance value depends on the current flowing through it. An approximation of the nonlinear relation in Eq. ( 4) is obtained by choosing a magnetic circuit that provides an adequate magnetic saturation.

F = 0.2 N (-), F = 0.4 N (--), F = 0.6 N (-• -) and F = 0.8 N (• • • ) -(a)
linear shunt, (b) nonlinear piezoelectric tuned vibration absorber [START_REF] Lossouarn | A fully passive nonlinear piezoelectric vibration absorber[END_REF].

Restraining the analysis to the first harmonic, a decrease of the equivalent inductance value leads to an increasing electrical resonance frequency that follows the increase of the mechanical natural frequency due to the cubic stiffness. As shown in Fig. 3(b) this solution is able to maintain vibration mitigation performance compared to a case involving a linear shunt.

MULTIMODAL DAMPING WITH AN ANALOGOUS PIEZOELECTRIC NETWORK

Broadband damping in the linear regime

The extension of resonant piezoelectric shunts to multimodal structures consists in designing a multiresonant circuit whose electrical natural frequencies are sufficiently close to the mechanical resonances to be controlled. With a single piezoelectric transducer, the most direct approach is the so-called multibranch shunt [START_REF] Raze | A Simplified Current Blocking Piezoelectric Shunt Circuit for Multimodal Vibration Mitigation[END_REF][START_REF] Wu | Method for multiple mode piezoelectric shunting with single PZT transducer for vibration control[END_REF] made of inductors and capacitors organized with just as many branches as the target mechanical resonances. The main limitation is that this solution does not optimize the coupling factor k c for all the considered modes. The first reason concerns the addition of external capacitors in the shunt which decreases electromechanical coupling [START_REF] Fleming | Reducing the inductance requirements of piezoelectric shunt damping systems[END_REF]. The second reason is related to the positioning of the single piezoelectric patch that is generally not optimal for different mode shapes.

Another solution for multimodal damping is based on analogous piezoelectric coupling. This requires several piezoelectric transducers that are interconnected with electrical components so as to build a multiresonant network with modal properties similar to that of the considered structure. The analogy is no more restrained to the natural frequencies as with the multi-branch shunts because similar mode shapes are also ensured. The design of the electrical analogue of a beam has been fully described in Ref. [START_REF] Lossouarn | Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network[END_REF]. The first step consists in discretizing the bending wave differential equation from a finite difference approximation. Then, a direct electromechanical analogy is applied to find the unit cell of the electrical network. The complete network is built by reproducing this unit cell along one direction, taking into account that the number of unit cells per wavelength has to be sufficiently large to approximate the continuous mechanical medium. For the case of a beam, the electrical unit cell is made of an inductance L representing the analogue of a point mass, a capacitance C that represents the inverse of a bending stiffness and a transformer of ratio â that is analogous to a mechanical lever of length a.

A beam electrical analogue involving 10 unit cells is represented in Fig. 4. In order to approximate the mode shapes of a cantilever beam, we need to ensure analogous boundary conditions. This is realized by short-circuiting one end of the network (equivalent to zero force and moment), while leaving open the other end (equivalent to zero displacement and angle). Another critical condition is the tuning of the dispersion relation in the electrical waveguide. From the discrete model, it can be shown that the electrical parameters need to satisfy 1 â2

1 L C = 1 a 2 K θ m , (5)
where K θ is the bending stiffness of the mechanical unit cell, m is its mass and a its length [START_REF] Lossouarn | Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network[END_REF]. Considering the practical example described in the last section, one wants to couple a clamped beam to its analogous electrical network with an array of piezoelectric patches. Thanks to the inherent capacitance C of the piezoelectric patches, there is no need for external capacitors for the analogue of the bending stiffness. Only transformers and inductors satisfying Eq. ( 5) are required for the analogue of a clamped beam. In the present case, however, one has to take into account the clamping through the thin lamina. In the linear regime, the lamina can be modeled by a linear spring of stiffness K end . So, its analogue is a capacitor to be placed at the end of the electrical network, as shown in Fig. 5. Considering the nondimensionalized equations in the two domains when no coupling occurs, one can find a relation between the end capacitance and its analogous linear stiffness:

C end = K θ K end â2 a 2 C . (6)
A last step consists in introducing appropriate damping in the electrical network. Coming back to Eq. ( 1), remark that the optimal electrical quality factor at

ω O is Q = Lω O /R = 2/3/k c .
A similar damping ratio can be obtained with a resistance R L in series with the inductance L or a resistance R C in series with the capacitance C when

R L = 3 2 k c ω O L or R C = 3 2 k c ω O C . ( 7
)
The dependence on ω O in those equations shows that using a resistance R L that is optimal for the first mode of the structure would be too low for the next modes leading to an underdamped case. On the other hand an optimal resistance R C for the first mode would lead to overdamped highest modes. In the present case focusing on the first three modes of the beam which are fully separated, it is decided to benefit from both damping configurations by tuning R L for the first mode and R C for the third mode. This requires the computation of individual coupling factors for each modes by comparing natural frequencies when L = 0 and when this inductance tends to infinity. In the end, both resistances are reduced by 10% to be closer to the optimal damping because R C still has a slight influence on the damping of the first mode. The resulting linear frequency response functions of the beam are represented in Fig. 6 with and without coupling. One can see the simultaneous vibration mitigation of the first three modes of the beam through the equivalent of a multimodal tuned mass damper. Note that damping of the second mode is not optimized (underdamped) because the considered tuning of two electrical quality factors on L and C only allows optimal damping at two specific frequencies around the first and third modes. A last remark concerns the third mode which does not ensure an equal peak condition. This is directly due to the fact that the discrete network only involve 10 unit cells inducing a slight mismatch between the mechanical and electrical resonances.

Damping of multiple nonlinear resonances

Although analogous piezoelectric coupling provides broadband damping in the linear regime, higher vibration amplitudes still lead to the undesired behavior illustrated in Fig. 3(a) if only linear electrical components are considered. The next objective is thus to find the adequate nonlinearity to be introduced in the electrical network. Here, contrary to the previous experimental validation involving a nonlinear inductor [START_REF] Lossouarn | A fully passive nonlinear piezoelectric vibration absorber[END_REF], a nonlinear capacitor is incorporated at the end of the electrical network to ensure a strict analogy with the nonlinear stiffness at the end of the beam. This actually combines the principle of similarity used for nonlinear control [START_REF] Habib | A principle of similarity for nonlinear vibration absorbers[END_REF] and the spatial analogy used for multimodal damping [START_REF] Lossouarn | Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network[END_REF].

Still, it remains the question of the numerical value for the nonlinear capacitance. Focusing on Eq. ( 3), it can be remarked that the nonlinear capacitance depends on the ratio of the inductance L over the modal mass m, which can be seen as a mass ratio between the absorber and the main structure. Using a single mode piezoelectric shunt L/m = 1/CK where K is the open-circuited modal stiffness, which depends on the considered mode. However, considering two modal systems with similar mode shapes, all modal mass ratio L/m becomes equal to the same local mass ratio L /m , which does not depend on the mode of interest anymore. This is a critical point because Eq. ( 3) then leads to a tuning of the capacitance nonlinearity at the end of the network that does not depend on frequency: With the proposed nonlinear capacitor, the analogy is not only valid in the linear regime but also in the nonlinear regime. Damping performance is thus maintained over an extended range of forcing amplitudes. This is first observed in Fig. 7 which compares frequency responses with and without nonlinear capacitance. The results are obtained from a harmonic balance with three harmonics and a forcing amplitude equal to 0.8 N. This level of excitation does not induce a significant nonlinearity for the second and third modes but the first mode is seriously affected. In Fig. 8, the excitation amplitude is set independently for all three modes so as to provoke the merging of the right local maximum with a detached resonance curve when no nonlinearity is introduced in the electrical network. The addition of the nonlinear capacitance in Eq. ( 8) significantly reduces the vibration amplitude of all the considered modes. While we are close to an equal peak condition for mode 1, the responses for modes 2 and 3 are further from the linear case. Those differences are definitely due to the lack of damping for mode 2 and to the imprecise linear tuning for mode 3.

1 C NL = 2 L m 2 K NL . ( 8
)

Development of the multi-resonant network

Starting with the linear case, assembling the previously described electrical network requires 9 inductors, 10 transformers and one capacitor as shown in Fig. 5. The magnetic components are specifically designed for this application. In order to first validate the electrical dynamics alone, the piezoelectric patches are replaced by ceramic capacitors. Then, an impedance meter is placed at the end of the network in order to measure the frequency response function of the current over the voltage that actually corresponds to the end admittance of the circuit.

Figure 10 shows the good agreement between the experimental results and the numerical simulations computed from the discrete set of equations that describe the electrical circuit. Note that the resistance of copper wire in the inductors and transformers has been added to the model because of its strong influence on the electrical quality factor. Even so, one can easily detect the three resonances corresponding to the first three modes of the electrical network. The distributions of the electrical current are then plotted at frequencies corresponding to those three maxima of admittance. As represented in Fig. 11, the electrical distributions are similar to mode shapes of a clamped beam which definitely validate the topology of the analogous network.

While those results validate the analogue of a beam that is clamped at one end, one has to remember that we also need to take into account the weak clamping through the thin lamina at the other end. As it can be modeled by a capacitor in the electrical domain, the influence of such a passive component at the end of the electrical network is investigated. The experimental admittance around the first resonance is plotted in Fig. 12(a) for various end capacitors. We note that a capacitance equal to 266 µF places the electrical resonance around the first natural frequency of the beam, which is consistent with Eq. ( 6). While the considered end capacitor ensures modal coupling at low excitation level, it should also offer a nonlinear contribution in order to ensure a similarity with the nonlinear lamina. This contribution has to satisfy Eq. ( 3) whose first-harmonic approximation is

V NL = 3 4C NL Q 3
, where V NL is the amplitude of the nonlinear voltage contribution and Q is the amplitude of the electric Supposing that the component that provides this nonlinear voltage is in with a linear capacitor C end , the equivalent variable capacitance is defined as

C end NL (Q) = 1 1 C end + 3Q 2 4C NL . ( 9
)
The variation of this capacitance as a function of the electrical charge is plotted in Fig. 12(b). This provides the objective function when looking for an appropriate nonlinear capacitor. Some multilayered ceramic capacitors offer saturation at relatively low voltage levels leading to a decrease of the equivalent capacitance. Unfortunately, up to now, no passive component has been found to correctly approximate the prescribed nonlinear function. Investigations are in progress to define if a non-passive numerical impedance is required or if a fully passive component can still be found.

First experimental results on multimodal damping of the nonlinear beam

The electrical network in Fig. 9 is coupled with the nonlinear beam through the array of piezoelectric patches. The full setup is seen in Fig. 13 that also shows the electromechanical shaker and the impedance head used for drive-point measurement at the end of the beam. The experimental and numerical frequency response functions appear in Fig. 14. First, the experimental response with short-circuited patches clearly shows the first and second modes of the beam but the third mode comes after two unpredicted resonances. Those extra resonances are finally related to the mounting system and this point will be corrected in the next version of the setup. In any case, multimodal damping is clear for the first three modes of the beam, which also validates the numerical model.

Concerning the tuning of the electrical network, note that it is slightly underdamped for modes 2 and 3 but it is overdamped for the first mode. This excessive damping is clearly observed on the first response in Fig. 15 that does not offer the local minimum normally observed with optimized tuned vibration absorbers. This shows a limit of the present analogous network whose copper losses in the magnetic components are not optimal for a broad frequency range. A new design of the electrical circuit will address this issue by providing optimal damping for the first mode and external resistors will be used to slightly lower the electrical quality factor at higher frequencies. Another limitation of the present network is the lack of an adequate nonlinear capacitor. Consequently, the effect of the mechanical nonlinearity on the tuning of the piezoelectric vibration absorber is observed in Fig. 15. Increasing the forcing amplitude moves the mechanical resonance to higher frequency without similar adjustment of the corresponding electrical resonance. This results in an increase of the vibration amplitude similar to what has been observed in Fig. 3(a) for single mode control with optimized damping. The next step thus consists in finding an adequate nonlinear capacitor and place it in an optimally damped electrical network so as to retrieve similar results as in Fig. 3(b).

CONCLUSIONS

This work aims to show that the principle of nonlinear similarity can be extended to multimodal damping with piezoelectric networks. To this end, an analogous electrical circuit is proposed in order to reproduce the dynamics of the considered structure. A multimodal coupling offers vibration mitigation over a wide frequency range. For higher forcing amplitudes, however, a mechanical nonlinearity leads to a serious increase of the vibration amplitude. A nonlinear capacitor is thus placed in the electrical network at an analogous position. Numerical results show that using an electrical nonlinearity similar to the mechanical one can lead to a substantial gain in terms of damping performance around several modes of the mechanical structure. This definitely proves that broadband damping of a nonlinear structure can be achieved with a fully passive vibration absorber. Experiments will be conducted to obtain further results with an improved analogous electrical network.

Figure 1 :

 1 Figure 1: Beam covered with an array of piezoelectric patches; half of the patches are connected to a single resonant shunt for vibration damping of the first mode [5].

Figure 2 :

 2 Figure 2: Piezoelectric tuned vibration absorber -(a) physical inductor, (a) experimental frequency response function around the first mechanical resonance, with short circuit (• • • ), with open circuit (• • • ) or with an optimal linear shunt (-).

Figure 3 :

 3 Figure 3: Experimental frequency response functions for various forcing amplitudes, F = 0.2 N (-), F = 0.4 N (--), F = 0.6 N (-• -) and F = 0.8 N (• • • ) -(a) linear shunt, (b) nonlinear piezoelectric tuned vibration absorber [5].

Figure 4 :

 4 Figure 4: Electrical analogue of a cantilever beam.

Figure 5 :

 5 Figure 5: Beam coupled to its electrical analogue through an array of piezoelectric patches.

Figure 6 :

 6 Figure 6: Simulated frequency response function of the beam with short-circuited patches (• • • ) and with the analogous electrical network (-).

Figure 7 :

 7 Figure 7: Simulated frequency response function of the nonlinear beam for F = 0.8 N without nonlinear capacitance (• • • ) and with nonlinear capacitance (-).

Figure 8 :

 8 Figure 8: Simulated frequency responses for the first three modes -(a) mode 1 for F = 0.8 N, (b) mode 2 for F = 80 N, (c) mode 3 for F = 1800 N.

B

  . Lossouarn, G. Kerschen and J.-F. Deü

Figure 9 :

 9 Figure 9: Electrical analogue of the cantilever beam with passive inductors, transformers and capacitors.

Figure 10 :

 10 Figure 10: Experimental (-) and simulated (--) frequency response functions of the electrical network.

Figure 11 :Figure 12 :

 1112 Figure 11: Experimental distributions of the electrical current -(a) mode 1 , (b) mode 2, (c) mode 3.

BFigure 13 :Figure 14 :

 1314 Figure 13: Experimental setup involving the beam coupled to its analogous electrical network.

3 Figure 15 :

 315 Figure 15: Experimental frequency response functions around the first mode for various forcing amplitudes, F = 0.05 N (-), F = 0.1 N (--), F = 0.2 N (-• -) and F = 0.4 N (• • • ).


Mariia Nesterova

Franziska Schmidt

Christian Soize

Estimation of Remaining Life of the Orthotropic Deck of a Bridge Exposed to Extreme Traffic and Wind Actions

Design rules in normative documents provide additional capacity to structures by using safety coefficients and considering the worst cases of loads that in most cases never occur during the life of a structure. This extra capacity allows not only to stay on a safe side during the design operational period of structures but also to re-estimate and to extend their possible operational life. One of the most appropriate ways to estimate the remaining life of an existing structure is the extrapolation of monitored actions or load effects in critical details. The main objective of the current study is the assessment of the reliability of the steel orthotropic deck of a viaduct at the end of its design life based on limited data for traffic and static wind actions. The object of study is the Millau viaduct, a cable-stayed bridge located in Southern France, which is exposed to both, heavy traffic loads and wind loading among other actions. Monitoring data used for traffic are provided from the bridge weigh-in-motion system and include six months of data for the more loaded side of the bridge. Wind velocity and directions for the same period are taken from the structural health monitoring system of the viaduct and the nearest weather station. The methodology is based on fitting the generalized Pareto distribution to extreme stresses induced by traffic actions and by wind in order to obtain return levels at the end of the 120 years design live. Reliability indexes for the most critical part of the deck are calculated for both types of load effects separately and for their combination. Moreover, the comparison between models based on data from monitoring and on European standard models is shown.

INTRODUCTION

In a case of suspension or cable-stayed bridges, one of the main live loads to consider is the wind. European bridges are designed against wind according to European Norms (EN) [START_REF]1-4: Eurocode 1: Actions on structures -Part 1-4: General actions -Wind actions[END_REF], however, there are no rules how to reassess actual wind load to a bridge __________________ Mariia Nesterova, Franziska Schmidt, Experimentation et modelisation for civil and urban engineering (EMGCU), Materials and Structures department (MAST), IFSTTAR, Marne-la-Vallé, 77420, Email: mariia.nesterova@ifsttar.fr; Internet: https://www.emgcu.ifsttar.fr Christian Soize, Université Paris-Est, MSME UMR 8208, UPEM, Marne-la-Vallée, 77420, France Inter-net: http://msme.u-pem.fr Steps to be taken to access reliability based on data from monitoring in order to update the reliability of its parts (i.e. deck) based on structural health monitoring (SHM). Another question is how to assess load effects in the deck if only limited data from monitoring of wind and traffic actions are available and how to combine these actions together. A recent study [START_REF] Arena | Aeroelastic behavior of long-span suspension bridges under arbitrary wind profiles[END_REF] of the aeroelastic behavior of long-span suspension bridges under wind actions shows that the effects caused by wind may negatively influence the reliability of a bridge. Another work [START_REF] Zhang | Fatigue life estimation of existing bridges under vehicle and non-stationary hurricane wind[END_REF] on a combination of wind and traffic loads takes vehicles as mass points and shows that forces from higher wind velocities do not always cause a shorter life but induce large stresses in the structure if combined with heavy vehicles. In the current work, only static wind loads [START_REF] Davenport | The generalization and simplification of wind loads and implications for computational methods[END_REF] are studied that simplifies the calculation process and makes it possible to achieve results based on available weather data. Wind velocities from SHM system are used in a computational model (CM) to assess stresses in the deck caused by the wind, see Figure 1, I. Stresses due to traffic actions are obtained from a finite element model (FEM) using data from monitoring by bridge Weigh-in-Motion (BWIM) system, see Figure 1, II.

In development of European standards for traffic actions, such as background works on EN [START_REF] Jacob | Methods for the prediction of extreme vehicular loads and load effects on bridges[END_REF], some approaches of the extreme values theory (EVT) are used for forecasting of return levels of actions [START_REF] Coles | An Introduction to Statistical Modeling of Extreme Values[END_REF]. EVT has been successfully used to envision the forthcoming situation of bridges [START_REF] Treacy | Monitoring of traffic action local effects in highway bridge deck slabs and the influence of measurement duration on extreme value estimates[END_REF][START_REF] Zhou | Statistical analysis of traffic loads and their effects on bridges[END_REF] based on the long-term monitoring of traffic actions. One of the most efficient approaches of EVT to be used in wind engineering [START_REF] Agarwal | Simulation of offshore wind turbine response for longterm extreme load prediction[END_REF] is the Peaks Over Threshold (POT) method, that has proven to work well also for precipitation predictions with non-stationary data [START_REF] Roth | Projections of precipitation extremes based on a regional, non-stationary peaks-over-threshold approach[END_REF] or for electricity demand estimation with a time-varying threshold [START_REF] Sigauke | Modelling non-stationary time series using a peaks over threshold distribution with time varying covariates and threshold[END_REF]. Here, it is used for load effects caused by heavy vehicles and for wind velocities to be used in the reliability analysis.

A correct choice of a reliability method depends on the structure, input data, initial conditions, and computational sources [START_REF] Morio | A survey of rare event simulation methods for static input-output models[END_REF]. As the frequently used method in bridge engineering, the first order reliability method (FORM) is used [START_REF] Klüppelberg | Risk -A Multidisciplinary Introduction[END_REF]. A work on the reliability of bridges [START_REF] Ghasemi | Target reliability for bridges with consideration of ultimate limit state[END_REF] concludes that not only fatigue but also extreme values have to be studied in the reliability analysis of bridges. Therefore, the ultimate limit state is considered here. The current study results in comparison of predicted reliability indexes β at several return periods p, Figure 1, for three possible cases: traffic actions (I), wind actions (II), and combination of both (I+II).

THE MILLAU VIADUCT

Millau viaduct is a cable-stayed bridge with a steel orthotropic deck and it consists of 8 spans with a total length of 2460 m, see Figure 2. The object of this study is the deck between second and third spans accounting for wind actions on pile P2 with its pylon.

The data on traffic actions were provided from BWIM system that was located in the middle of the first span of the viaduct. It includes axle weights [kN] and spacing [m], vehicle speed [m/s], axles configuration, pavement temperature. Recordings were made between October 2016 and June 2017 with a total of 180 days of recorded traffic. Wind velocities at different heights (bottom of the pile P2, deck, top of the pylon P2) were collected by the bridge management system and a nearest national weather station with a following correlation [START_REF] Nesterova | Probabilistic analysis of the effect of the combination of traffic and wind actions on a cable-stayed bridge[END_REF]. The available period of weather data is taken for the operational period of the bridge from the end of the year 2004 until the end of 2017 (13 years). Traffic and wind loads are independent in this case as recorded wind velocities do not cross the value of 39 m/s, that would lead to a closure of the viaduct for traffic.

For the current study, the critical detail is chosen to be a welded connection between a longitudinal stiffener and the plate of the orthotropic deck that is located right under a truck wheel assuming a vehicle is passing in the middle of the slow lane, Figure 3.

METHODOLOGY

A basic limit state function G(a) = 0, eq. ( 1), is defined by comparison of material resistance R and stress S(a) derived from structural monitoring data for a load effect a. The values of reliability index β (2) and probability of failure P f are found using FORM.

G(a) = R -S(a) (1)
β = -Φ -1 (P f ) = -Φ -1 G(a)≤0 q(a)da , (2)
where q(a) is the probability density function of the load effect a and Φ(a) is the cummulative distribution function (CDF) of the standardized Normal distribution:

Φ(a) = 1 √ 2π a -∞ e -a 2 /2 da (3)
Limit state functions use return values of load effects estimated for different return periods with the Peaks Over Threshold (POT) approach [START_REF] Coles | An Introduction to Statistical Modeling of Extreme Values[END_REF]. The method is based on fitting values of a load effect, that cross a chosen threshold, to generalized Pareto distribution (GPD) [START_REF] Pickands | Statistical Inference Using Extreme Order Statistics[END_REF].

Return levels of load effects

Let X be the sequence of n random variables x representing values of a load effect. Let Y be the sequence of m random variables y representing exceedance of a threshold u and defined by Y = X -u ≥ 0, for every threshold excess x ∈ X so that x > u. Then,

H(y; ξ; σ; u) = 1 -[1 + ξ( y σ )] -1/ξ , ξ = 0 1 -exp(-y σ ), ξ = 0 (4)
where σ > 0 and ξ are shape and scale parameters of GPD H. The value of threshold u is estimated using the graphical method [START_REF] Nesterova | Probabilistic analysis of the effect of the combination of traffic and wind actions on a cable-stayed bridge[END_REF]. Values of load effects are assumed to be identically distributed and statistically independent. The value of the p-observation return level S return (p) for the probability P [X ≤ x|x > u] with the probability of exceedance (PE) ζ u = P {x > u}, is a quantile that exceeds once every p observations:

S return = S u + σ ξ [(pζ) -ξ -1], ξ = 0 S u + σlog(pζ), ξ = 0 (5)
Limit state functions for traffic and wind load effects

In the case of traffic actions, axle loads are obtained from the BWIM system installed in the bridge. The value of stress in the critical detail from each passing axle is obtained from detailed FEM of the part of the deck, Figure 3. The model takes into account the self-weight of the bridge deck with its asphalt layer, axle configuration of trucks and amplitudes of axle loads. The model is calibrated with the data from strain gauges (using signals from strain gauges recorded during the proof load test). Therefore, the limit state function (LSF) G t for traffic is:

G t = R -S t (u t , σ t , ξ t , ζ t ) = R - u t + σt ξt [(pζ t ) -ξt -1], ξ t = 0 u t + σ t log(pζ t ), ξ t = 0 (6)
where u t is a threshold for maximum values of stress from each passing vehicle, ζ t ∼ B (0.013, 0.0003) is the amount of load effects, that exceed the threshold, over a total amount of monitored trucks, σ t ∼ L (9.5, 0.31) and ξ t ∼ N (0, 0.05) are parameters of a fitted GPD (4), B, L and N stand for Binomial, Log-normal and Normal distributions.

In the case of wind actions, values of stress depend on the wind pressure P = 0.5ρv 2 A ref that is a function of the wind velocity v [m/s]. Hourly maximum values of v are obtained from SHM together with the air temperature to evaluate the air density ρ. The pressure is applied to the computational model of the studied part of the viaduct in order to asses values of stresses in the considered detail. The computational model is built in Matlab software and it considers the geometry of the viaduct A ref , the vertical variation of the wind pressure and the stiffness of the deck. For the return values of stresses induced by the wind, LSF G w for wind load effects is:

G w = R -S G - u w + σw ξw [(pζ w ) -ξw -1], ξ w = 0 u w + σ w log(pζ w ), ξ w = 0 (7)
where S G is the stress induced by the self weight of the structure, u w is a threshold for stresses calculated from hourly wind velocities (for the period of 13 years), ζ w ∼ B (0.002, 2.2 × 10 -4 ) is the amount of extreme events (velocities that exceed the threshold) over a total amount of hours (24×180 days), σ w ∼ L (22.17, 4.4) and ξ w ∼ N (0.1, 0.16) are parameters of the fitted GPD, (4). The LSF G C for the combination of loads for the case when ξ t = 0 and ξ w = 0:

G C = R -(u t + σ t ξ t [(pζ t ) -ξt -1] + u w + σ w ξ w [(pζ w ) -ξw -1]) (8)
The summary of random variables for each LSF, ( 6), ( 7) and ( 8), based on described approaches is given in Table I.

RESULTS OF RELIABILITY ANALYSIS

Three failure modes are observed in the current study: 1. extreme traffic load on one side of the deck (T), 2. extreme static wind load normal to the deck (W), 3. unfavorable combination of traffic and the wind. It is important to note that the combination of both actions is conditioned by the wind speed, that does not cross the value of 140m/s that causes the closure of the bridge for traffic (W+T).

The results of reliability analysis are listed in Table II. It presents values of the reliability index β and the probability of failure P f for three different return periods: one year, 50 years (in order to compare with EN return values), 120 years (the end of the design operational life of the viaduct). For the value of 50 years, it provides a comparison between reliability indexes derived from monitoring data with those from design load models. The last column shows reliability levels required by EN [START_REF]EN 1990: Eurocode: Basis of structural design[END_REF].

CONCLUDING REMARKS

The result of the current study shows the reliability of a welded connection between the plate and a longitudinal stiffener of the steel orthotropic deck of the Millau viaduct. Three load cases were observed: static wind, heavy vehicles and their combination.

The evaluation of the detail after one year from monitoring shows that the reliability index is high in all cases. It is so because the probability of occurrence of strong winds or heavy trucks with a highly overweighted axle is low. For the 50 years return period, design load model for traffic gives a low probability of failure, however, in reality, the presence of several heavy vehicles on the deck negatively affect the reliability index. It shows the importance of structural monitoring with following updating of design load models during the operational life of a structure.

Another conclusion is that static wind actions alone do not affect much the deck, however, if combined with traffic, they contribute significantly into its reliability. So, both types of action, traffic and climatic, should be considered in the reliability analysis of an orthotropic deck.

The probability of failure due to the combination of traffic and wind loads from monitored actions is lower than the value obtained with the design load models. It confirms that the design standards stay on the safe side. It is found that the reliability index at the end of the design life of the viaduct (120 years) is high enough. However, results for the case of fatigue should be taken into consideration in order to make further conclusions on the reliability of welded details of the orthotropic deck of the viaduct.

FORMFigure 1 .

 1 Figure 1. Steps to be taken to access reliability based on data from monitoring

Figure 2 .

 2 Figure 2. Millau viaduct, position of SHM and BWIM systems.

Figure 3 .

 3 Figure 3. Finite element model of the part of the deck.

TABLE I

 I

	. RANDOM VARIABLES FOR THE RELIABILITY ANALYSIS
	Case	Random variable	Distribution Mean CoV
	resistance steel strength R, MPa Log-normal	400	0.05
	self-weight	stress S G , MPa	constant	2.5	0
	traffic	threshold	u t	constant	27	0
		shape	ξ t	Normal	0	-
		scale	σ t	Log-normal	9.5	0.03
		PE	ζ t	Binomial	0.013 0.02
	wind	threshold	u w	constant	152	0
		shape	ξ w	Normal	22.17 0.2
		scale	σ w	Log-normal	0.1	1.58
		PE	ζ w	Binomial	0.002 0.02

TABLE II

 II × 10 -10 10 -18 ≈ 0 10 -7 7.2 × 10 -5 120 β 21.7 11.4 4.5 years P f ≈ 0 10 -30 2.0 × 10 -6 -

			. RESULTS OF THE RELIABILITY ANALYSIS
	return		Monitoring + EVT	Design models, [1, 18]	EN [17]
	period	W	T	W+T	W	T	W+T	value
	1	β 21.9 21.8	9.9		-		4.7
	year	P f ≈ 0	≈ 0	10 -23		-	1.3 × 10 -6
	50	β 21.8 14.4	6.2	8.9	24.3	5.3	3.8
	years P f ≈ 0	≈ 0	3.3

ACKNOWLEDGEMENTS

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 676139. The grant is gratefully acknowledged.

The BWIM measurements for the Millau viaduct were obtained with the help from


François Toutlemonde
email: francois.toutlemonde@ifsttar.fr

Sébastien Bernadi

Yves Brugeaud
email: yvesbrugeaudyb@betonweb.fr

Alain Simon
email: alain.simon@eiffage.com

Sébastien Bernardi
email: sebastien.bernardi@lafargeholcim.com

Twenty years-long French experience in UHPFRC application

Keywords: UHPFRC, Application, Standards, Execution, Specification, Design

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

-Strength and compactness improvement of cement materials by intense reduction of the water to binder ratio, which was made more and more possible and efficient with R&D advances in superplasticizers and mineral additions; -Use of steel fibers to provide post-cracking tensile capacity and pseudo-ductility (Fig. 1), which was made possible thanks to more than two decades of conceptual and exploratory development of conventional fiber-reinforced concrete, and really efficient as compared to it due to the high quality of the matrix and the possibility to incorporate high amounts of fibers; -Reduction of natural imperfections due to aggregate in limiting their size and selecting very high quality materials in an optimized grading, which took benefit of aggregate packing models having being developed in the late 80s.

Figure 1: Evidence of ductility, test for approval of UHPFRC beams in view of their application in the renovation of thermal exchange devices in Cattenom plant cooling tower [START_REF] Birelli | UHPFRC development: Review of a determining application[END_REF] This concept combination has enabled to produce several industrially controlled patented materials [START_REF] Dutalloir | BSI: A new, very high performance concrete. Initial industrial application[END_REF] markedly overpassing the highest (very) high-performance concrete available at that time, with 150 MPa-characteristic compressive strength at least, and possibly dispensing with the traditional use of secondary reinforcement due to material non-brittleness and with thick cover in aggressive environment due to much reduced transfer coefficients. This allowed dispensing with keeping systematic continuity with traditional reinforced concrete design provisions. Moreover, mixing, placement, thermal treatment and formwork technology could be kept understood in the continuity of emerging self-compacting concrete.

UHPFRC is indebted to some pioneers in this concept combination: Pierre Richard †, Marcel Cheyrezy, Gérard Birelli, Thierry Thibaux and Gilles Chanvillard †. These people were convinced that it could open the way to new horizons for cement materials. They promoted this combination as an answer to badly answered demands, in order to:

-Reduce local brittleness governed by defects; -Promote industrial control in constructions processes and products; -Optimize the use of cement in a high added value material; -Initiate a trend « less is beautiful » in concrete architecture.

A tens of years later, in parallel with a growing demand for outstandingly slender and attractive architectonic elements, the use of organic and stainless steel fibres in UHPFRC-type materials was developed, the range of mixes was extended addressing the fire-resistance demand and the possibly lower strength requirements, and ribbed plates or shells with passive reinforcement in the stiffeners tended to appear as structurally efficient. Growing interest and economic significance of this development in building components turned out evident from the first international symposium strictly dedicated to UHPFRC applications, organized in Marseille (France) in 2009 [START_REF]Designing and Building with UHPFRC: State of the Art and Development[END_REF].

Five years later, and particularly for the Standardization process intended to ease UHPFRC ordering, clarification of the UHPFRC-type materials designation had become necessary given the ongoing development of these materials, and the request for precise classification associated to the degree of validation for available background in view of structural design, and effective field experience of implementation and durability. The designation established by the recently published French Standard [START_REF]French Standard 'NF P 18-470, Concrete -Ultra-high performance fibre-reinforced concretes -Specifications, performance, production and conformity[END_REF] is displayed in Table 1. Although this designation is not universally accepted for the moment, it has been adopted as a reference in the French Standard and is used for common understanding in this paper. UHPFRC (as covered by the NF P18-470 Standard [START_REF]French Standard 'NF P 18-470, Concrete -Ultra-high performance fibre-reinforced concretes -Specifications, performance, production and conformity[END_REF]) is thus associated to non-brittleness and compressive strength higher than 130 MPa (which is also related to durability characteristics). Non-brittleness threshold is considered a key issue for possibly dispensing with secondary reinforcement and acceptability by building authorities even for non-strictly structural components. Characterization of the post-cracking UHPFRC capacity (contribution to take tensile forces and provide structural non-brittleness), which turns out for design at least as significant as the (often non-directly critical) compressive strength, (Fig. 2) has thus deserved standing R&D efforts for the justification of the tests and data analysis procedures [START_REF] Baby | UHPFRC tensile behavior characterization: inverse analysis of four-point bending test results[END_REF]. And therefore the 'UHPFRC' designation of non-brittle materials differs from 'UHPC'. 2: Typical four point-bending characterization on prisms and results [START_REF] Guénet | Modeling Ultra-high Performance Fibre-Reinforced Concrete behaviour using micromechanics: accounting for fibre orientation effect at the structural scale[END_REF] UHPFRC as covered by NF P18-470 [START_REF]French Standard 'NF P 18-470, Concrete -Ultra-high performance fibre-reinforced concretes -Specifications, performance, production and conformity[END_REF] Concerning UHPFRC types designation, type A fiber-reinforcement is related to clear physical differences from metallic fibers e.g. when exposed to high temperatures. The strength limiting values equal to 130 and 150 MPa may appear as somehow conventional thresholds, they are however related to present accepted experience and they determine the accepted design methods. Type S-UHPFRC correspond to the materials first developed and used, for which structural design provisions have been validated, and thus correspond to the scope of the NF P18-710 Standard [START_REF]French Standard 'NF P 18-710, National addition to Eurocode 2 -Design of concrete structures: specific rules for Ultra-High Performance Fibre-Reinforced Concretes (UHPFRC)[END_REF] associated to UHPFRC structural design. Changing the limiting values would require collecting and documenting significant additional background.

It should be mentioned that this technical designation may differ from the commercial (ranges) designation of UHPFRC-type materials.

UHPFRC HISTORICAL DEVELOPMENT IN FRANCE

Since implementation of innovative building solutions highly depends on the capacity to convince owners and authorities, regional and national issues and experience are worth being considered although worldwide scientific and technical exchange on UHPFRC technology have been existing for more than 15 years.

2.1

Genesis Since the first major UHPFRC applications in France concerned a number of prestressed beams for the renovation of the heat exchange zone in a cooling tower of Cattenom nuclear power plant (NPP) (Fig. 3), and an innovative competition for typical bridge crossing over 2 x 2 lanes-highway, implemented at Bourg-lès-Valence in South-Eastern France (Fig. 4), the owners (Power Company and State Highways) and the associated technical authorities requested an extensive documentation on UHPFRC structural behaviour to be collected, supporting the computation files that had to gain contradictory validation. At the same time, companion prospective efforts towards nuclear applications additionally helped demonstrating outstanding strength and resistance to transfer, so that durability and lightness of prestressed members have appeared as main advantages to be searched in structural applications. As a conclusion of this initial implementation period, the first worldwide recommendations for production, characterization of UHPFRC and structural design using these materials, were published in France in 2002 [START_REF] Resplendino | Ultra high performance fibre-reinforced concrete[END_REF]. Drafting of these recommendations had taken full benefit of the owners and contractors involvement in these pioneer applications, with high level of technical supervision and results of R&D efforts. Additional favourable conditions have ncluded the fact that several industrially available materials had been developed, and that stakeholders were convinced of their common interest in scientific advance and development of relevant UHPFRC implementation to face durability and building performance challenges.

Exploration

Based on a limited number of well-characterized UHPFRC mixes, and considering that fresh UHPFRC technology could be understood in the continuity of that of emerging selfcompacting concrete, efforts could be focused from 2002 to 2012 on exploring structurally efficient applications, relying on the AFGC Recommendations [START_REF] Resplendino | Ultra high performance fibre-reinforced concrete[END_REF] design principles for prestressed / post-tensioned beams and boxes and non-reinforced thin elements. Application to footbridges as Seon Yu Footbridge (Fig. 5) and Passerelle des Anges (Fig. 6) led to lightness / slenderness records [START_REF] Mazzacane | The Passerelle des Anges footbridge[END_REF]. Effective realization of these projects motivated consistent research efforts to ensure controlled quality of the material produced and placed. Figure 7: ITE® beams. Left) Just handled after precasting for Buthaumont Bridge [START_REF] Hajar | Buthaumont Bridge on the Orne river in Boncourt[END_REF]. Center) Being installed at Pinel Bridge, allowing safe deck completion from above [START_REF] Hajar | ITE® beams, a costeffective enduring alternative to filler-beam decks[END_REF].

Right) After completion, deck from below: Pont de la République in Montpellier [START_REF] Ricciotti | La République Bridge in Montpellier[END_REF] For road bridges, optimized shapes, like ITE® beams [START_REF] Hajar | ITE® beams, a costeffective enduring alternative to filler-beam decks[END_REF], first applied for Pinel bridge in 2006 (Fig. 7), were demonstrated as favourable for valuable implementation, while costefficiency also relied on indirect material savings or lightness benefits for the method of execution. Study of alternative shapes such as post-tensioned box-girders [START_REF] Hajar | Construction of an ultra-high performance fibre-reinforced concrete thin shell structure over the Millau viaduct toll gates[END_REF][START_REF] Delauzun | Construction of the PS34 UHPFRC bridge[END_REF] or ribbed slabs [START_REF] Tavakoli | UHPFRC waffle deck concept for a bridge at Livron-Loriol[END_REF] turned out technically attractive and led to significant progress in validation of extensive design provisions, yet being scarcely applied due to lack of high-volume application opportunities which would have resulted in cost-effectiveness.

Besides valuable application in structural components, exploration of UHPFRC by architects helped develop attractive façade and roofing components, thanks to new aesthetic possibilities associated to durable mineral surface quality, lightness and possible complex shapes and semi-transparency, with typical examples of Villa Navarra [START_REF] Ricciotti | The Enrico Navarra Gallery[END_REF] roofing ribbed plates (Fig. 8) and "Les enfants du Paradis" net panels (Fig. 9) in 2007. For such nonstructural elements the range of mixes was extended significantly. Plain thin UHPFRC plates or ribbed plates with passive reinforcement in the stiffeners proved structurally efficient. Association of UHPFRC with glass panels, developed for the Jean Bouin Stadium renovation [START_REF] Mazzacane | Roofing of the Jean Bouin Stadium in UHPFRC[END_REF] has given a new impulse to semi-transparent roofing components (Fig. 10). Growing interest and economic significance of this development in building applications allowed UHPFRC produced volumes to take off in France from the 2010s, although technically optimized applications like light prestressed bridges (as in Malaysia), or joint fills between precast beams or deck slabs (as in North American projects of "accelerated bridge (re)construction") did not find their market here.

Demonstration

The year 2013, associated to the second international symposium on UHPFRC applications organized in Marseille [START_REF] Toutlemonde | UHPFRC 2013[END_REF] and to the publication of the revised edition of AFGC Recommendations [START_REF] Resplendino | Ultra high performance fibre-reinforced concrete. Recommendations[END_REF], has constituted a significant milestone for UHPFRC in France. Revision of the AFGC recommendations had been motivated by consistency with the format of Eurocode enforced as the reference for structural design, and by taking into account the scientific advances in UHPFRC engineering and gained experience in UHPFRC design and realizations. As a key example of fine-tuned prestressed UHPFRC structural design, these revised recommendations have been applied for the design of the 'Ring of Memory' (Fig. 11) at Notre-Dame de Lorette First World War Memorial [START_REF] Prost | Memorial of Notre-Dame de Lorette[END_REF][START_REF] Bouhours | The international Memorial of Notre-Dame de Lorette: detailed design and realization[END_REF].

Two major projects associated to highly visible urban renovation projects, the MuCEM [START_REF] Gazon | Museum of European and Mediterranean Civilizations (MuCEM): the owner's ambition[END_REF][START_REF] Ricciotti | Museum of European and Mediterranean Civilizations (MuCEM): high UHPFRC content structure design[END_REF][START_REF] Rivillon | Museum of European and Mediterranean Civilizations (MuCEM): experimentation and modeling of straight and Y-shaped UHPFRC prestressed columns under the action of an off-centered vertical load[END_REF][START_REF] Mazzacane | MuCEM: the builder's perspective[END_REF] in Marseille (Fig. 12) and the Jean Bouin Stadium [START_REF] Mazzacane | Roofing of the Jean Bouin Stadium in UHPFRC[END_REF] in Paris (Fig. 13), had been completed the same year, constituting significant industrial achievements for the delivery of high numbers of UHPFRC precast components, and a decisive involvement of designers, checkers and authorities for safety verification of all innovative details. Their completion led to widened awareness of technical and architectural capabilities of UHPFRC among professional (architects, engineers) and for the public, including clients of constructions. As a sign of international recognition of these achievements, the MuCEM was designated by the ACI Excellence in Concrete Construction Award Committee 1 st prize in 2015 in the category Low Rise Building and Excellence Award; the Jean Bouin Stadium was awarded the 1 st prize in the category Decorative Concrete in 2015, and the Ring of Memory won the 1 st prize in the category Infrastructure in 2016.

Technical acceptance of the design, industrial processes and details associated to these projects, as well as previous satisfactory French 15 years-experience of building components and bridges made of UHPFRC, has made it possible to launch the standardization process in France on the basis of the technical consensus expressed in AFGC Recommendations [START_REF] Resplendino | Ultra high performance fibre-reinforced concrete. Recommendations[END_REF]. Availability of standards was mostly deemed to help acceptability of UHPFRC structures and buildings incorporating UHPFRC by insurance companies.

STANDARDS FOR UHPFRC: ARCHITECTURE AND MAIN IDEAS

Complying with the architecture of existing French standards which derives from that of European standards, three documents [START_REF] Toutlemonde | Product and Design Standards for UHPFRC in France[END_REF] have been elaborated (Fig. 14): the NF P18-470 standard for UHPFRC as a construction product [START_REF]French Standard 'NF P 18-470, Concrete -Ultra-high performance fibre-reinforced concretes -Specifications, performance, production and conformity[END_REF], published in 2016, which substitutes to the standard valid for ordinary structural concrete (NF EN 206/CN [START_REF]French Standard 'NF EN 206/CN, Concrete -Specification, performance, production and conformity-National addition to NF EN 206[END_REF]) and includes as annexes test protocols or adaptations of standards and test results analysis when applied to UHPFRC; the NF P18-710 standard for the design of UHPFRC structures [START_REF]French Standard 'NF P 18-710, National addition to Eurocode 2 -Design of concrete structures: specific rules for Ultra-High Performance Fibre-Reinforced Concretes (UHPFRC)[END_REF], published in 2016, which stands as a national addition to Eurocode 2; and the NF P18-451 standard for the execution of UHPFRC structures [START_REF]French Standard 'NF P 18-451, Execution of concrete structures -Specific rules for UHPFRC[END_REF], to be published by end of 2018, which provides complements, precisions or amendments to the execution standard NF EN 13670/CN [START_REF]French Standard 'NF EN 13670/CN:2013, Execution of concrete structures -National addition to NF EN 13670:2013[END_REF]. Moreover, the revision of EN 13369 (common rules for precast concrete products) will comprise, when published as a French standard [START_REF]French Standard 'NF EN 13369, Common rules for precast products[END_REF], a reference to these three UHPFRC "basic standards" in the National Foreword, to cover the case of UHPFRC precast products. The NF P18-470 and NF P18-451 standards cover UHPFRC with a characteristic compressive strength equal to or greater than 150 MPa and comprising metallic fibers (these UHPFRC mixes are designated « BFUP-S »), since they were addressed by the AFGC Recommendations since 2002 [START_REF] Resplendino | Ultra high performance fibre-reinforced concrete[END_REF][START_REF] Resplendino | Ultra high performance fibre-reinforced concrete. Recommendations[END_REF]. Design of structures to be made with these materials is covered by NF P18-710 Standard. However, NF P18-470 and NF P18-451 also cover UHPFRC materials where the non-brittleness is achieved through the use of other types of fibers (designated "type A UHPFRC") as well as UHPFRC mixes with a lower characteristic strength, yet above 130 MPa, whatever the type of fibers contributing to non-brittleness (See Table 1). For the moment however, due to lack of documentation of feedback and experience in real applications, structural design using UHPFRC with non-metallic fibers and/or with a compressive strength lower than 150 MPa has been considered as non-traditional, thus out of the scope of the NF P18-710 Standard, and thus requires dedicated technical approval.

Architecture of French standards for UHPFRC

Consistently with effective feedback of implemented materials in technically and economically efficient projects, the scope of these standards is also separated from present standards (NF EN 1992-1-1 [START_REF]French Standard 'NF EN 1992-1-1, Eurocode 2: Design of Concrete structures -Part 1-1: General rules and rules for buildings[END_REF] and NF EN 206/CN [START_REF]French Standard 'NF EN 206/CN, Concrete -Specification, performance, production and conformity-National addition to NF EN 206[END_REF], which cover concrete with a maximum compressive strength class of C90/105 and C100/115, respectively). Moreover, while these standards are compatible with fib Model Code 2010 [START_REF]fib Model Code for concrete structures 2010[END_REF] principles concerning fiber-reinforced concrete ( § 5.6.1), they give specifically adjusted provisions based on experience of materials associated to a high enough fiber ratio to ensure a minimal ductility.

3.1

Material specification and control Namely, the required 'non-brittleness', i.e. the UHPFRC hardening behavior under pure bending that shall be effective, is one remarkable performance of these materials besides compressive strength. NF P18-470 provides explicitly the Equation (1) to be verified: Where: wlim = 0,3 mm fctm,el is the average value of the elasticity limit under tension, in MPa σ(w) is the characteristic post-cracking strength as a function of the crack opening w, in MPa. The method for obtaining this function from inverse analysis of bending tests on prisms or thin plates is detailed in Annexes D and E of NF P18-470 Standard.

The UHPFRC designation also implies that the material fulfils the following requirements: nominal upper size of aggregates lower or equal to 10 mm; density comprised between 2200 kg/m 3 and 2800 kg/m 3 ; characteristic value of the elasticity limit under tension at 28 days fctk,el higher or equal to 6,0 MPa; water porosity at 90 days ≤ 9,0 %; coefficient of apparent diffusion of chloride ions at 90 days ≤ 0,5 10 -12 m²/s; and apparent gas permeability at 90 days ≤ 9 10 -19 m².

Moreover, classes are defined in the NF P18-470 Standard to make UHPFRC specification easier. They mostly concern compressive strength, tensile constitutive law, workability, the type of thermal treatment possibly applied, and improved potential durability characteristics. The compressive strength class is determined referring to the characteristic strength measured at 28 days on cylinders with nominal dimensions 110 mm in diameter / 220 mm in height. The class associated to the tensile behavior of a UHPFRC mix (namely T1: strain softening under direct tension, T2: limited strain hardening or T3: significant strain hardening) is obtained by comparing the elasticity limit fct,el with the post-cracking strength fctf, both for the average response curve and for the characteristic curve. It is determined considering an a priori fixed value of the Kglobal orientation factor which is applied to the post-cracking phase to account for the placement effect of the UHPFRC material in the structure, the postulated value of this factor being 1,25. This orientation factor is consistent with the definition given in fib Model Code 2010 [START_REF]fib Model Code for concrete structures 2010[END_REF] for any type of fiber-reinforced concrete ( § 5.6.7). Conformity to the specified class can thus be evaluated for the material, whatever its structural application.

Workability of UHPFRC should be preferably specified using a target value. In absence of such a value, it can be specified using consistence classes. The classes corresponding to improved potential durability are worth being specified in case of a particularly severe exposure (e.g. tidal or splash zone at seashore, or exposure to severe freeze-thaw cycles with de-icing salts) or particularly long design service life (over 100 years). Finally, using an RM class adapted to the intensity of the abrasion risk associated to the more or less loaded hydraulic flow should allow dispensing with the sacrificial cover which appears as the default provision for prevention of wear in the design standard NF P18-710.

The NF P18-470 standard gives those requirements that conforming UHPFRC have to meet. These requirements concern constituents, mix-proportions, properties of UHPFRC at the fresh state and properties of hardened UHPFRC. Except specified otherwise for a given project, properties of hardened UHPFRC shall be measured at 28 days when UHPFRC production does not include a post-setting thermal treatment, otherwise they shall be measured after completion of this thermal treatment. Some requirements apply to all UHPFRC while some of them are optional, depending on requested characteristics for a given project. The NF P18-470 standard defines a concept of 'identity card', document which, where relevant, gives for each property, the performance value met from effective production experience by a given UHPFRC mix. Placing fresh UHPFRC, curing and possible thermal treatments application belong to operations covered by standards related to the execution of structures, though having a critical influence on the performance to be met by UHPFRC as a material. Therefore NF P18-470 includes the target requirements associated to these processes and associated control (procedure, control parameters, acceptability criteria).

NF P18-470 defines the different steps of evaluation and acceptance of UHPFRC supply as well as the part which is responsible for declaring conformity to given requirements. UHPFRC is deemed a 'design concrete', i.e. for which required properties are specified. Meeting these requirements by choosing a given UHPFRC material derives from experience documented in the material identity card, or is validated by the results of the design study. The design study is carried out by the producer of UHPFRC or under his responsibility. It consists in verifying that the UHPFRC mix allows meeting the project requirements, taking into account possible deviations in the manufacturing process (thus it includes batches according to the nominal recipe, and liquid / solid deviations). When the identity card exists, the UHPFRC producer may use it to prove that all or part of the specifications are met. When it does not exist or in case of missing information, the design study must include tests associated to the determination of required characteristics that were not previously investigated.

Verifying that the required properties are effectively met in the production conditions of the specific project is the aim of the suitability test (trial production). This suitability test should be carried out by the producer of UHPFRC so that the specifier can validate the choice of the proposed UHPFRC mix, taking into account the effective production, transport, placing, curing and possible treatment processes specified in the execution procedures. This trial testing should also comprise the production of a prototype element, carried out under the responsibility of the user of UHPFRC; this step is required for validating all the execution procedures, especially those associated to placing, curing and thermal treatment, by demonstrating that the specified performances (noticeably K-factors) are met (Fig. 15).

Figure 15: K-factors identification from prisms sawn from prototype elements [START_REF] Mazzacane | MuCEM: the builder's perspective[END_REF][START_REF] Delplace | Precast thin UHPFRC curved shells in a waste water treatment plant[END_REF] Evaluation of the conformity of UHPFRC to NF P18-470 is thus split in several steps: a) Evaluation of conformity of the pre-mix, when the considered UHPFRC is produced using this pre-mix of constituents (evaluation applies to a potential conformity to the UHPFRC identity card); b) Initial evaluation of conformity of the UHPFRC by acceptance of the design study, which where relevant includes the results given in the UHPFRC identity card (evaluation applies to the conformity to the specification, without taking into account all specific aspects of the production process); c) Initial evaluation of conformity of the UHPFRC by acceptance of the suitability test based on the trial production of the prototype element (evaluation applies to the full conformity to the specification, taking full account of the UHPFRC recipe and mixing, transport, placing and possible treatment processes); d) Evaluation of conformity of the UHPFRC during the production process based on the results of internal inspection testing along with the UHPFRC production at the fresh state; e) Evaluation of conformity of the UHPFRC during the production process based on the results of internal inspection testing along with UHPFRC placing, possible treatments applied, and with specified required characteristics at the hardened state.

Conformity of UHPFRC to NF P18-470 is established only when conformity at each of these steps has been established, should property transfers have taken place or not.

3.2

Structural design As a complement to Eurocode 2 [START_REF]French Standard 'NF EN 1992-1-1, Eurocode 2: Design of Concrete structures -Part 1-1: General rules and rules for buildings[END_REF], the NF P18-710 Standard focuses on provisions specific to UHPFRC, and indicates direct applicability or non-relevance of other clauses. The major difference with ordinary concrete, consisting in effectively using the tensile contribution of the UHPFRC material, is thus emphasized. This tensile contribution may be described with different admissible degrees of approximation. It is used for ultimate limit state (ULS) verifications, namely in bending, shear and torsion, and also for serviceability limit state verifications especially for crack control. For the final design justification, the material characteristics determined during the suitability tests and trial prototype production, as well as the effective set of orientation factors, have to be used to calibrate the design curve for tensile UHPFRC contribution, which is indeed a specific feature of UHPFRC structural design process. Since the tensile contribution of UHPFRC is used, and may often result in dispensing with conventional secondary reinforcement, a partial material factor γcf for UHPFRC under tension has been defined and calibrated based on present experience of characteristics measured on effective industrial production of UHPFRC.

Another main specific issue concerns non-brittleness. The minimum reinforcement ratio conditions of Eurocode 2 Section 9 are replaced by two verifications: first, the minimum material ductility characterized by Equation (1); secondly, for cross-sections which are not under full compression, a 20 % margin has to be demonstrated between the resisting bending moment, taking into account the contribution of cracked UHPFRC under tension, and the elastic bending moment (corresponding to the limit of linearity of the material constitutive behavior). When this latter condition is verified with the only contribution of UHPFRC, no conventional reinforcement for non-brittleness is required.

Improved UHPFRC properties have a direct influence on reinforced UHPFRC structural design and detailing, resulting in reduced anchor lengths of reinforcing bars and cover thicknesses, for which the condition associated to correct placement may become more critical than bar corrosion prevention (in general, the cover thickness has to exceed 1,5 times the fiber length).

For UHPFRC, the different useful design characteristics (Young's modulus, tensile characteristics, creep and shrinkage values…) cannot be estimated a priori as functions of the sole compressive strength. For preliminary design, an informative set of parameters range is provided in Annex T of NF P18-710 [START_REF]French Standard 'NF P 18-710, National addition to Eurocode 2 -Design of concrete structures: specific rules for Ultra-High Performance Fibre-Reinforced Concretes (UHPFRC)[END_REF]. And when available, identity cards of UHPFRC mixes can be useful to provide guidance for the first verifications. But for the final design justification, parameter determination based on trial production values is mandatory.

Although quite short in length, the normative annex R corresponding to fire design is critical for the safe implementation of UHPFRC, e.g. in buildings or tunnels. The principles of fire design in Eurocode 2 are kept, except the use of simplified tabulated methods. Determination of material properties at high temperature is to be carried out following NF P18-470 provisions, which combine values deriving from standard curves and values to be explicitly determined experimentally, for which the testing protocol is given. Moreover, the control of thermal instability (spalling), which is generally achieved with a sufficient polypropylene fiber content, is not a material intrinsic property and has to be demonstrated experimentally with sufficient representativeness in terms of specimen geometry, fire scenario and loading conditions.

The (also short) normative annex U related to seismic verification is also a key reference for UHPFRC application in fulfilment with national regulations for prevention of seismic risks. First, material partial factors associated to seismic verifications are given. Moreover, it is admitted that elements be justified if their behavior keeps elastic, assuming non-cracked members inertia and a damping factor equal to 2 %, and the effects of seismic actions being lower than resisting ULS moment / axial force. When a ductility demand is to be satisfied, an experimental demonstration is required. For this demonstration, the representative component shall be submitted to at least five cycles up to the ultimate demanded displacement, and the corresponding decrease in bearing capacity shall not exceed 20 % of the maximum load.

Execution

The most recently elaborated NF P18-451 Standard [START_REF]French Standard 'NF P 18-451, Execution of concrete structures -Specific rules for UHPFRC[END_REF] follows the same outline as the NF EN 13670/CN standard [START_REF]French Standard 'NF EN 13670/CN:2013, Execution of concrete structures -National addition to NF EN 13670:2013[END_REF], so that specific rules for UHPFRC are emphasized. The scope of the standard covers UHPFRC conforming to NF P 18-470 whatever its production conditions, which can be either cast in a place different from the final construction site to produce (structural or non-structural) precast elements, cast in place to produce structural or non-structural members, or cast in place as a joint-fill, coating or repair material along existing members. According to this standard for the execution of the UHPFRC structure or elements, the quality management refers to execution class 2 at least, which implies mandatory inspection -not only self-control -of all important casting steps (Fig. 16).

Figure 16: Inspection of UHPFRC placement in a critical zone of post-tensioning anchorage, requiring a window in the formwork and control before prestressing application [START_REF] Mimram | Roofing of Montpellier -South of France TGV Station[END_REF].

As a specific feature of the documentation, the execution specification shall comprise: a detailed UHPFRC mixing protocol; a detailed concreting programme; procedures for the management of early age transient steps, form removal, handling of precast elements; and a procedure for placing and adjustment of precast elements, where relevant.

Concerning falsework and formwork, specific care is requested due to UHPFRC characteristics at the fresh state, during setting and at early age. Tightness and rigidity of the forms shall be ensured. Formworks geometry and surface should promote the UHPFRC flow and avoid fibers blockage (e.g. sharp edges should be avoided). Early age thermal and autogenous deformations shall be anticipated for reaching the requested geometry (e.g. owing to active control of falsework and formworks geometry, using matched joints, etc.). Restraints at early age due to formworks should be avoided (e.g. with appropriate moulds rigidity and/or optimized form removal time). Significance of the formed surfaces and high slenderness of the members make the control of the facings aspect critical. Care is thus requested on the choice of appropriate solutions for the material of the formwork skin, the form release agent, air vents to release entrapped air, etc. (Fig. 17). The control of inserts location requires specific provisions in thin and frequently unreinforced members. Testing the resistance of anchors may be requested.

Since following a documented mixing protocol is part of the conformity of UHPFRC to the NF EN 18-470 Standard, the choice of the appropriate mixer (capacity, precision of dosage, device for fibers introduction) is a sensitive step. Also storage conditions of the constituents are to be mentioned in the protocol. The concreting programme, to be validated from the suitability test and especially from trial application in concreting the scale one mock-up, shall include: transport, placing and compaction methods (avoid dropping, segregation, cold joints, give indications in case of injection), and for this the tools to be used, the maximum placing duration, the management of flows and layers of fresh UHPFRC, the control tests during this phase, the methods of joint treatment, and the treatment of existing surfaces if UHPFRC is cast against such ones so that a composite structure is realized. It shall also give the finishing provisions, describe the curing method, the thermal treatments if any, the provisions in case of hot weather / cold weather / unexpected casting interruption, the methodology of cooling management if any (prevention of thermal cracking), and the indications concerning form removal (especially aiming to prevention of restraints).

Figure 17: Typical form solutions for UHPFRC elements. Left) supple material for the mould of a net panel with numerous inclusions [START_REF] Bouhours | Architectonic UHPFRC elements in BSI®[END_REF]. Right) Match-casting of thin walled segments to be assembled by post-tension [START_REF] Bouhours | The international Memorial of Notre-Dame de Lorette: detailed design and realization[END_REF].

Figure 18: Typical handling operations of large and thin UHPFRC elements [START_REF] Delplace | Precast thin UHPFRC curved shells in a waste water treatment plant[END_REF][START_REF] Mazzacane | Roofing of the Jean Bouin Stadium in UHPFRC[END_REF][START_REF] Mimram | Roofing of Montpellier -South of France TGV Station[END_REF].

A specific section of the NF P18-451 standard addresses execution of structures with precast concrete elements. It is confirmed that jointing using UHPFRC is considered as (UHPFRC) concreting. In case of assembling precast UHPPFRC elements whatever the method, experience motivates to take special care due to frequent slenderness, deformability and thus possible risk of instability of the elements during handling (Fig. 18). In the case of thin precast UHPFRC members, the risks of mismatch and unexpected loads due to connection are to be prevented with specific provisions related to geometrical (position) control. Given the sensitivity to the quality of execution, and the associated safety issues, the use of glue for jointing UHPFRC elements shall be validated by (type) testing.

The section of the standard dedicated to geometrical tolerances distinguishes class 1 « normal » values, which however comprise reduced tolerances as compared to NF EN 13670 for thin members (less than 50 or 75 mm), and class 2 « reduced » values, which correspond to smaller deviations taken into account for instability verification, mainly for columns, according to the design standard (NF P 18-710) [START_REF]French Standard 'NF P 18-710, National addition to Eurocode 2 -Design of concrete structures: specific rules for Ultra-High Performance Fibre-Reinforced Concretes (UHPFRC)[END_REF]. In any case, stricter tolerance values may be requested for functional requirements (especially for thin or slender members).

4.

PRESENT AND PROMISING FIELDS OF APPLICATION

Civil structures and bridges

As stated in the context of the third international symposium dedicated to UHPFRC organized in France [START_REF] Toutlemonde | Designing and Building with UHPFRC: New large-scale implementations, recent technical advances, experience and standards[END_REF], worldwide recognition especially within ACI Excellence in Concrete Construction Awards program has been gained for outstanding UHPFRC projects. Noticeably enough, due to optimization in conceptual design, UHPFRC has made possible competitive solutions not only for tailor-made signature projects (Fig. 19), but also for typical bridge situations exemplified by the Buthaumont Bridge [START_REF] Hajar | Buthaumont Bridge on the Orne river in Boncourt[END_REF] or the footbridge at Le Cannet des Maures [START_REF] Pastor | UHPFRC footbridge in Le Cannet des Maures[END_REF]. Cost-efficiency of UHPFRC bridges generally also comes from the indirect advantages of a light / slender deck, in case of difficult soil conditions, in association with quicker / cheaper erection methods, or due to lower access embankments with reduced earth works. Such benefits are effectively taken in Malaysia in the context of important new infrastructure needs [START_REF] Voo | Malaysia, taking ultra-high performance concrete bridges to new dimensions[END_REF]. They also motivated the development of light prefabricated bridge solutions to be exported to sites with limited possibilities of local resources and workmanship [START_REF] Brugeaud | Express bridge deck and light duty bridge[END_REF]. While the market of new road bridges may keep limited in France and Western Europe, efficient UHPFRC solutions for (urban) rail bridges may still deserve valuable exploration [START_REF] Montens | An innovative approach of using UHPC or metro viaducts[END_REF]. In this context, compliance with UHPFRC standards is a key condition for acceptability by the clients and the supervisors, and for a sound competition with alternative solutions.

Figure 19 : La République Bridge in Montpellier [START_REF] Ricciotti | La République Bridge in Montpellier[END_REF] Beside new bridges which may require a rather expensive case-by-case approach, optimized series of applications in civil engineering structures and facilities could become an increasing field of UHPFRC usage, especially in relation to the generally high durability-demand. Examples already exist with the industrial buildings at Achères water treatment plant (Fig. 20), or the noise barriers of metro viaducts in Rennes. Opportunities might be found in the field of renewable energies and urban networks. In addition to materials and design standards, documentation of effective UHPFRC field durability and sustainability appears as a key for development of this prospective market.

4.2

Building components From 2010 the driving field of UHPFRC application in France has concerned ultra-thin, often highly transparent and architecturally appealing cladding and roofing panels, for buildings as "La Mantilla" residence or ITER headquarters (Fig. 21) as well as for large public infrastructure projects as the new Montpellier high speed railway station (Fig. 22). While answering versatile aesthetical demands, such UHPFRC 'secondary elements' of the buildings have gained acceptable cost-efficiency due to their lightness, thus reduced costs for transport, installation and fixation to the main frame of the structure and reduced applied loads on it. Their economical acceptability, promoted when the number of components is high (Fig. 23), has also imposed clever formwork and moulding solutions to allow variations with minimal adaptations of the industrial tools. While the NF P18-451 Standard gives general indications based on the gained industrial experience in this domain, detailed precasters' skills beyond the standard are clearly associated to the success of such UHPFRC applications, as a result of the material sensitivity to its placing process and early-age treatment and restraints. Left) Façade elements of La Marseillaise high rise building [START_REF] Brault | La Marseillaise Tower[END_REF]. Right) Roofing palm-shaped shells of Montpellier new railway station [START_REF] Mimram | Roofing of Montpellier -South of France TGV Station[END_REF].

4.3

Repair With the iconic examples of Chillon viaducts [START_REF] Brühwiler | Strengthening of existing structures using R-UHPFRC: principles and conceptual design[END_REF] and Hammersmith Flyover [START_REF] Cousin | Hammersmith Flyover: a complete innovative renovation[END_REF] (Fig. 24) and progressively also in France especially for maintenance of ancient [START_REF] Jaffrelo | New UHPFRC deck slab for the Grand Pont in Thouaré-sur-Loire (France). How to extend the life of a 19 th century metallic structure bridge?[END_REF] and/or fatiguesensitive [START_REF] Hajar | Innovative solution for strengthening orthotropic decks using UHPFRC: the Illzach bridge[END_REF] steel bridges, bridge deck repair or protection using UHPFRC has deserved increasing interest. Repair solutions, for buildings also, are increasingly considering UHPFRC.

Figure 24: UHPFRC applied for rejuvenation of prestressed concrete viaducts [START_REF] Brühwiler | Strengthening of existing structures using R-UHPFRC: principles and conceptual design[END_REF][START_REF] Cousin | Hammersmith Flyover: a complete innovative renovation[END_REF]. Left) UHPFRC overlay. Right) Small UHPFRC anchor blocks for additional post-tension Key technical advantages are associated to the possible low intrusiveness of the repair intervention, associated to the limited required material amount with respect to the high bearing capacity. Fire resistance, adaptability to complex geometrical shapes, possible implementation underwater may also be comparative advantages with respect to alternative repair solutions. UHPFRC allow e.g. low overlay or deck slabs thicknesses (Fig. 25) reducing incidence on the supports and foundations. Added mass of anchoring blocks for additional post-tensioning can similarly be very limited [START_REF] Cousin | Hammersmith Flyover: a complete innovative renovation[END_REF]. High stiffness, low creep, intrinsic durability and wear resistance of the UHPFRC applied will result in a long expected lifespan for the repaired structure. Even water-tightness may be achieved, provided adequate design, mix and execution provisions are taken.

Figure 25: Thin slabs for redecking the Grand Pont in Thouaré-sur-Loire [START_REF] Jaffrelo | New UHPFRC deck slab for the Grand Pont in Thouaré-sur-Loire (France). How to extend the life of a 19 th century metallic structure bridge?[END_REF] or the Illzach orthotropic deck [START_REF] Hajar | Innovative solution for strengthening orthotropic decks using UHPFRC: the Illzach bridge[END_REF].

Versatility of the UHPFRC application for repair should thus result in cost-efficiency despite a possibly still high unitary material cost. This however requires a combined optimization of the UHPFRC material, design and execution of the repair operation. Especially important are the methods of execution: How to connect precast elements to the existing structures, what is the geometrical tolerance, how durable is the fixation? Should the UHPFRC be placed by gravity pouring, injected, spread with a finisher? With which consequences on water tightness and fibre orientation / homogeneous distribution?

The combined design-mix-methods optimization may result in reduced time for jobsite operations (which saves money and risks), taking possible advantage of precasting, and/or adaptable fresh UHPFRC rheology then rapid hardening if cast on site. In addition to bridge strengthening, protection of marine structures, seismic retrofitting and external thermal insulation of buildings with UHPFRC-born façades probably constitute promising fields of application. Recently published French standards on UHPFRC are intended to ease the acceptance of UHPFRC in the repair projects and their implementation. However, the effective possibility to combine optimization of design, mix and methods may require an adapted contract and delay organization.

PROSPECTS AND FURTHER NEEDS OF EFFORTS

Availability of UHPFRC Standards in France [START_REF]French Standard 'NF P 18-470, Concrete -Ultra-high performance fibre-reinforced concretes -Specifications, performance, production and conformity[END_REF][START_REF]French Standard 'NF P 18-710, National addition to Eurocode 2 -Design of concrete structures: specific rules for Ultra-High Performance Fibre-Reinforced Concretes (UHPFRC)[END_REF][START_REF]French Standard 'NF P 18-451, Execution of concrete structures -Specific rules for UHPFRC[END_REF][START_REF]French Standard 'NF EN 13369, Common rules for precast products[END_REF] has opened new conditions for easier acceptance of UHPFRC projects and solutions referring to a technical shared background and reference for contracts. However, consolidation and dissemination of design skills, and engineering and industrial know-how is a key condition for further development of UHPFRC applications. Several architects, designers, checkers, engineering offices, and precasting plants, although quite few, have developed such a UHPFRC expertise. Education associated to the standards dissemination should strengthen these capabilities. Especially from the new NF P18-451 on execution, it can be expected an easier specification of works using UHPFRC, clarification of the critical tasks in UHPFRC works execution, inspection and supervision, clarification of "UHPFRC know how" for the precast industry and for contractors, and anticipation of execution issues, resulting in more reliable costs and delays prevision.

Further research and development efforts should address advanced UHPFRC modelling, seismic design with UHPFRC, development of typical "UHPFRC solutions", and nonconventional placement process optimization including 3D printing and -with a more immediate promising prospect -sprayed UHPFRC (especially for steel culverts repair [START_REF] Huynh | Innovative rehabilitation technology for corrugated metal pipe culverts using wet-mix sprayed UHPFRC[END_REF]) which could widen the scope of cost-efficient UHPFRC implementation. Moreover, dissemination of information related to satisfactory durability and field implementation, and improved laboratory characterization of UHPFRC durability characteristics, still deserve efforts for convincing possible owners and supervisors especially for technically demanding applications.

Finally, given the significance of relevant applications of type-A and type-Z UHPFRCs, extension with possible adaptation of the NF P 18-710 Standard to these materials should be undertaken at short term.

Figure 3 :Figure 4 :

 34 Figure 3: UHPFRC beams for thermal exchange devices in Cattenom NPP cooling tower [3]

Figure 5 :

 5 Figure 5: Pi-shaped cross-section of the UHPFRC arch Seonyu footbridge in Seoul.

Figure 6 :

 6 Figure 6: Passerelle des Anges, post-tensioned braced lateral beams, 1/38 slenderness[START_REF] Mazzacane | The Passerelle des Anges footbridge[END_REF]

Figure 8 :

 8 Figure 8: Thin UHPFRC roofing panels at Villa Navarra [17].

Figure 9 :

 9 Figure 9: First UHPFRC net panels Figure 10: Roofing panels of Jean Bouin Stadium [18]

Figure 11 :

 11 Figure 11: The Ring of Memory, curved UHPFRC post-tensioned structure [21-22].

Figure 12 :

 12 Figure 12: the MuCEM in Marseille [23-26]: 330 UHPFRC post-tensioned columns, 380 net cladding and roofing UHPFRC panels, two UHPFRC footbridges.

Figure 13 :

 13 Figure 13: Jean Bouin Stadium [18]. 10,700 m² roofing panels, 1811 façade net panels.

Figure 20 :

 20 Figure20: UHPFRC roofing elements for Achères water treatment plant[START_REF] Delplace | Precast thin UHPFRC curved shells in a waste water treatment plant[END_REF]

Figure 21 :

 21 Figure 21: UHPFRC building components. Left) balustrade elements in Montpellier [36]. Right) Cladding elements for ITER Headquarters in Cadarache

Figure 23 :

 23 Figure 23: Variations in replication of UHPFRC precast building components.Left) Façade elements of La Marseillaise high rise building[START_REF] Brault | La Marseillaise Tower[END_REF]. Right) Roofing palm-shaped shells of Montpellier new railway station[START_REF] Mimram | Roofing of Montpellier -South of France TGV Station[END_REF].

Table 1 :

 1 UHPFRC-type materials designation (in italics, French acronyms)

	fck (MPa)	non-brittle	non-brittle	Possibly
		metallic fibres	other fibres	brittle
	150 to 250	UHPFRC -BFUP		UHPC
		type S	UHPFRC -BFUP
	130 to less	UHPFRC -BFUP	Type A
	than 150	Type Z
	less than 130	VHPFRC	VHPC
	Figure

New in 2018 Published 2016 Published 2016

						Case by case
	Compatible with European Standards for Concrete	NF P 18-710 national addition to Eurocode 2	Design of non technical approvals
		Design Standard: Design of UHPFRC structures (UHPFRC with steel fibres) (related to EN 1992)	structural UHPFRC elements
		NF P 18-470 self-supporting standard substitute	Note: Design of UHPFRC
	Revision of NF EN 13369	to EN 206 (similar outline)			structures made of UHPFRC with non-metallic
	Common rules for precast products	Norme Produit « BFUP pour structures » Premix Product Standard: UHPFRC Type A or Z: UHPFRC for non structural or sur site Type S: UHPFRC for structures Malaxage conformity) (specification, performance, production and	T S T E	fibres shall be dealt with as non-traditional
		BPE On-site prefabrication Préfabrication architectonic elements foraine Premix	Mixed on site	S
	Revision of specific standards	No Premix	Prefabrication in a precasting plant	Ready-mix	Annexes to NF P 18-470
	Special rules for precast products	Execution Standard: NF P 18-451 national addition to NF EN 13670/CN	New in 2018
		applicable to execution of UHPFRC structures and non-
			structural or architectonic UHPFRC elements

Figure 14: Architecture of the French Standards related to UHPFRC.

ACKNOWLEDGEMENTS

The authors are pleased to acknowledge Jacques Resplendino's efforts in the elaboration of first worldwide Recommendations on UHPFRC [9], in their recent revision [20] and in promotion of UHPFRC development with co-organization of three major conferences in France on UHPFRC application in 2009, 2013 and 2017 [4,19,37]. They are also indebted to Michel Delort's contribution to UHPFRC Standardization [5,27].