J.-L Bantignies

J.-L Sauvajol

A Rahmani

E Flahaut

Infrared-active phonons in carbon nanotubes

Keywords: number͑s͒: 78, 67, Ch, 78, 30, Na

The aim of the present paper is to identify the main infrared vibrational features of carbon nanotubes. In this goal, infrared experiments have been performed on different well-characterized single-walled carbon nanotubes ͑SWCNTs͒ and double-walled carbon nanotubes ͑DWCNTs͒ as well as graphite and carbon aerogel. The comparison between the experimental spectra measured on these different samples allows us to identify the infrared-active modes of carbon nanotubes. In SWCNTs, the tangential modes are located around 1590 cm -1 and the radial mode around 860 cm -1 . This latter mode vanishes in the infrared spectrum of DWCNTs. Finally, in the infrared spectra of all the carbon nanotubes investigated, a band around 1200 cm -1 is evidenced and assigned to the D-band ͑disorder-induced band͒.

I. INTRODUCTION

Since the discovery of carbon nanotubes, 1 much attention has been devoted to the investigation of their vibrational properties, experimentally as well as theoretically. Resonant Raman scattering technique has been shown to provide a powerful tool for studying the phonon dynamic of singlewalled carbon nanotubes ͑SWCNTs͒. 2,[START_REF] Reich | Carbon Nanotubes. Basic Concepts and Physical Properties ͑Wiley-VCH[END_REF] By contrast, the infrared-active modes of SWCNTs are very difficult to detect. Indeed, SWCNTs do not support a static dipole moment and the infrared ͑ir͒ activity is related to a dynamic dipole moment that is weak. Nevertheless, infrared spectroscopy has shown significant promise for the study of SWCNT chemistry. [START_REF] Kim | [END_REF] Obviously, the use of ir spectroscopy to study the SWCNT chemistry implies the knowledge of the ir intrinsic vibrational modes of SWCNTs. The aim of the present investigation is to identify the intrinsic infrared features of carbon nanotubes.

Only few experiments have been devoted to the measurement of the infrared-active vibrational modes of SWCNTs. [5][6][7][8][9] Most of the observations and conclusions of these previous studies are sometimes opposite. For instance, two modes located around 873 and 1597 cm -1 have been reported in Ref. 6. These modes are upshifted with respect to the A 2u ͑868 cm -1 ͒ and E 1u ͑1590 cm -1 ͒ ir-active modes of graphite. 6,10 By contrast, in other investigations performed on functionalized SWCNTs 7 or industrially produced SWCNTs, 8 both ir-bands are downshifted by comparison to the related infrared-active modes in graphite. In Ref. 8, these bands are located around 820 and 1535 cm -1 , respectively. Very recently, an ir investigation was performed on thin films of SWCNT bundles. The sample used in this latter experiment was purifed ͑from successive oxydation processes͒ and vacuum annealed at 1400 °C. [START_REF] Kim | [END_REF] The resulting sample was ultrasonicated in 2-propanol and several drops of the solution were deposited from solution onto ZnSe substrates for the ir experiments. By contrast with all the previous studies, a larger number of lines was observed in this latter investigation. The sharp lines in the ir spectra of these purified and annealed SWCNTs were assigned to one-and two-phonons modes. 9 Especially, eight distinct groups of lines located between 680 and 1600 cm -1 were assigned to first order ir modes belonging along A 2 and E 1 symmetry ͑see Table 1 in Ref. 9͒. In summary, a large disagreement is found in the literature concerning the assignment of the ir-active modes of SWCNTs. On the other hand, the infrared-active phonon modes of SWCNTs have been calculated from different methods: zone folding model, [11][12][13] tight binding approach, 14 force constant model, [15][16][17][18] and ab initio calculations. 19 Concerning the diameter dependence of the ir active modes these predictions are sometimes opposite.

The main aim of the present paper is to identify unambiguously the ir features of carbon nanotubes. In this goal, infrared experiments have been performed on different wellcharacterized single-walled ͑SWCNTs͒ and double-walled ͑DWCNTs͒ carbon nanotubes.

II. EXPERIMENT

Infrared experiments have been performed on graphite ͑sample 1͒, SWCNTs ͑samples 2-6͒, carbon aerogel ͑sample 7͒, and DWCNTs ͑sample 8͒. The SWCNT samples were prepared by the electric arc method 20 and laser ablation. 21 These samples were first characterized by x-ray diffraction. We have selected parts of the different samples that showed a strong intensity of the ͑10͒ Bragg peak. In consequence, these parts contain a large amount of bundles ͑samples 2-5͒. 22 The main difference between the selected samples is the size of the bundles. Typically, the average number of tubes in a bundle is around 20 tubes in the SWCNT samples prepared by the electric arc method and above 50 tubes for the SWCNT samples prepared by laser ablation. On the other hand, we have also selected a part of a SWCNT sample prepared by the electric arc method that showed no ͑10͒ Bragg peak in its x-ray diffraction pattern ͑sample 6͒. By contrast with the other SWCNT samples ͑samples 2-4͒, x-ray diffraction has also revealed that this latter sample contained a significant amount of amorphous carbon. In all the samples, the tube diameters were estimated from the position of their radial breathing modes measured by Raman spectroscopy. The diameter distribution is centered around 1.4 nm ͑distribution width of about 0.2 nm͒. A DWCNT sample was prepared by the method described in Ref. 23. Transmission electronic microscopy ͑TEM͒ observations showed that DWCNTs are clean ͑no amorphous deposit͒ and generally isolated, or gathered into small-diameter bundles. 24 The outer ͑inner͒ diameters range from about 1.3 to 1.6 nm ͑from about 0.7 to 1 nm͒. 25 Carbon aerogels were prepared from the sol-gel polymerization of resorcinol with formaldehyde followed by CO 2 supercritical drying and carbonization ͑the method is described in Ref. 26͒. X-ray diffraction experiments have revealed the amorphous carbon character of this sample.

After outgassing and annealing all the samples at 230 °C for 24 h under dynamical vacuum, they were gently mixed with potassium bromide ͑KBr͒ and then pressed into pellets for infrared experiments.

Fourier transform infrared ͑FTIR͒ experiments was carried out on a Bruker IFS 113V spectrometer equipped with a N2-cooled MCT ͑mercury-cadnium telluride͒ detector. Transmission ir spectra were recorded in the 400-4000 cm -1 range. The spectral resolution was 2 cm -1 and 64 scans were coadded for each spectrum.

III. RESULTS

The 450-4000 cm -1 wave-number range of the ir transmission spectra measured on carbon aerogel ͑amorphous car-bon͒, a SWCNT sample, and graphite are compared in Fig. 1. As expected, the intensities of the ir absorption bands are weak. Only small features centered around 860 and 1590 cm -1 are evidenced in graphite and SWCNTs. An additional component around 1190 cm -1 is observed in all the SWCNT samples ͑Fig. 2͒. It is the most intense band of the ir spectrum. No band in the stretching mode range of C v O ͑between 1600 and 1800 cm -1 ͒, CH ͑2800-3000 cm -1 ͒, and OH ͑3000-3600 cm -1 ͒ groups was observed. Consequently, our SWCNT samples are free of usual functionalization. In carbon aerogel, bands around 880 cm -1 , 1590 cm -1 , and a very broad and complex feature centered around 1250 cm -1 are found.

In this paper, we focus on the identification of the main infrared modes of SWCNTs. In Fig. 2͑a͒ ͑curves 2-6͒ the 800-900 cm -1 wave-number range of the ir spectra measured on five SWCNT samples are displayed. They are com-pared to the ir spectrum of graphite ͓Fig. 2͑a͒, curve 1͔ and carbon aerogel ͓Fig. 2͑a͒, curve 7͔. In graphite, the weak ͑0.02% transmittance͒ and narrow band centered at 868 cm -1 was assigned to the A 2u out-of-plane vibration mode. 10 For all the SWCNT samples under consideration ͑samples 2-6͒, an ir band is systematically observed around 860 cm -1 . This band is assigned to the ir-active radial mode as predicted from calculations. 19 With respect to the position of the A 2u mode in graphite centered at 868 cm -1 , this band shows a downshift of 8 cm -1 in SWCNTs. Such a component is totally absent in the ir spectrum of the carbon aerogel in which a band at 880 cm -1 is observed ͓Fig. 2͑a͒, curve 7͔. Such a band was previously observed in amorphous carbon 27 confirming that carbon aerogel is an amorphous carbon sample as also revealed by x-ray diffraction ͑see the experimental section͒. A 880 cm -1 band is also found in the ir spectrum of the sample 6 ͓Fig. 2͑a͒, curve 6͔ in agreement with the large amount of amorphous carbon present in this SWCNT sample ͑see the experimental section͒. Finally, in the SWCNT samples ͑samples 2-5͒ that show a clear bundle organization, the 880 cm -1 band is totally absent. Concerning the dependence of these radial modes with the tube diameters, in agreement with our results, ab initio calculations predict an upshift of the frequency of this mode with the diameter. The ir-active radial mode at 860 cm -1 does not show any significant sample dependence. Because the SWCNT samples under investigation mainly differ by the size of the bundles, we conclude, in agreement with recent calculations, 16 that the position of this infrared active mode does not significantly depend on the bundle size.

The wave-number range 900-1300 cm -1 is shown in Fig. 2͑b͒. A broadband located around 1190 cm -1 is found in the ir spectrum of all the SWCNT samples ͓Fig. 2͑b͒, curves 2-6͔. This well-defined band is the most intense ir feature of the spectrum ͑Fig. 1͒. We come back on its attribution in the following. A very broad feature is observed around 1250 cm -1 in carbon aerogel ͓Fig. 2͑b͒, curve 7͔. In sample 6, other weak features ͑0.3% to 0.4 % transmittance͒ are found around 1045 and 1090 cm -1 ͓Fig. 2͑b͒, curve 6͔. Because these bands are also measured in carbon aerogel ͓Fig. 2͑b͒, curve 7͔, they clearly originate from the ir response of the part of amorphous carbon present in sample 6. Additional weak lines ͑0.2% transmittance͒ are also observed around 1127, 1168 and 1188 cm -1 in carbon aerogel ͓Fig. 2͑b͔͒.

In the region of the tangential modes, the ir spectra of samples 2-5 show a broad band located around 1587 cm -1 ͓Fig. 2͑c͒, curves 2-6͔. In graphite, the E 1u in-plane vibration mode is located close of this same wave number ͓Fig. 2͑c͒, curve 1͔. In sample 6, this band is slightly downshifted to around 1582 cm -1 ͓Fig. 2͑c͒, curve 6͔. Finally, in carbon aerogel, a band is also observed around 1587 cm -1 ͓Fig. 2͑c͒, curve 7͔. This band displays a larger broadening than in graphite and SWCNTs. These results show that the position of the tangential mode does not significantly depend on the curvature of the graphene sheet and on the long range order. With regards to the large differencies between the structural parameters of the SWCNT samples investigated ͑bundles of different sizes͒, we conclude that the position of this band is not sensitive to the packing of the carbon nanotubes, in agreement with recent calculations. 16 With regards to the large width of this band and its nonsymmetric profile, a precise measurement of the position of this peak is not easy. In consequence, the wave number of this mode cannot be used as an efficient experimental tool to characterize the structure of SWCNT samples. Concerning the dependence of these tangential modes with the tube diameters, ab initio calculations predict an upshift of the frequency of this mode with the diameter. For diameter larger than 1.4 nm, the position of this band was more or less constant and close to that of graphene. 19 These latter predictions are in complete agreement with our data ͑see Table I͒.

In Fig. 3 are compared the ir spectra measured on SWCNT and DWCNT samples. The most important result is that the radial ir-mode located around 860 cm -1 in the SWCNT samples is silent in the DWCNT sample ͓Fig. 3͑a͔͒. In the region of the tangential modes, a well-defined band located at 1580 cm -1 ͓Fig. 3͑c͔͒ is observed. The position of this band is located near those observed in the different carbon materials ͑graphite, SWCNT, and carbon aerogel͒. This observation agrees with our previous conclusion about the slight sensitivity of this mode to the structural organization of carbon nanotubes. Finally, a well-defined band at 1190 cm -1 is also found in the ir spectrum of this wellcharacterized DWCNT sample ͓Fig. 2͑b͔͒

IV. DISCUSSION

These results question the assignments of the ir features of a SWCNT previously proposed. [6][7][8] Clearly, our data and the ab initio calculations are opposite to the results of Kulh- W avenum ber (cm -1 )

Transmittance (%) (a) (b) (c)
FIG. 3. Comparison between the transmittance ir spectra measured on a DWCNT sample ͑top͒ and a SWCNT sample ͑bottom͒. ͑a͒ The radial mode range, ͑b͒ the 900-1300 cm -1 range, and ͑c͒ the TM range. The spectra have been shifted for clarity. mann et al. who assign the ir-active radial mode to the experimental line located around 874 cm -1 and the tangential modes to the line located at 1600 cm -1 . Both lines are upshifted with respect to the A 2u mode and E 1u infrared-active modes in graphite centered at 868 and 1590 cm -1 , respectively. In other investigations, 7,8 significant downshifts of the ir-active radial mode ͑lines located around 820 and 840 cm -1 ͒ and tangential modes ͑lines around 1535, 1555, and 1564 cm -17 ͒ are found. The experimental downshift of radial and tangential modes when the diameter increases 8 is opposite to the predictions of the ab initio calculations. 19 It must be emphasized that these latter investigations have been performed on purified samples. Because functionalization of the tubes usually occurs under purification treatments, a part of the shift can be mainly assigned to the effect of the functionalization on the vibrational modes ͑extrinsic effects͒ and consequently they do not reflect the intrinsic phonon dynamics of SWCNTs.

Clearly, the radial ir-active mode observed around 860 cm -1 in a SWCNT is not observed in a DWCNT. The possible balancing between the dynamic dipole moments on the inner and outer nanotubes can lead to the vanishing of the collective radial mode of both layers in a DWCNT. Ab initio calculations of the ir spectrum of a DWCNT in the framework of the density functional theory are in progress to confirm this assumption.

The observation of a component around a 1190 cm -1 in all the carbon nanotube samples investigated suggests that this band is an infrared feature of carbon nanotubes. An iractive mode is predicted in this frequency range ͑more precisely, in the 1200-1250 cm -1 range in most of the model-izations͒. However, its intensity is expected to be weak with regards to the intensity of the main infrared modes in SWCNTs. 16 On the other hand, in the Raman spectrum of the same SWCNT samples, a D-band is observed. In Raman scattering, the D-band is activated by the presence of defects which lower the crystalline symmetry of the quasi-infinite lattice. As expected in the framework of a double-resonance process, 28,29 the position of this band is excitation dependent. With regards to the linear dependence of the position of the D-band with the laser energy ͑E Laser ͒, 30 its position is predicted around 1200 cm -1 at E Laser = 0. In consequence, considering the symmetry-breaking in SWCNTs containing structural defects, such a D-band can be active in the ir spectrum, and its frequency is expected around 1200 cm -1 . On the basis of this information, we assign the 1190 cm -1 feature observed in all the carbon nanotubes as resulting from the overlap between a weak ir-active mode of a SWCNT and a strong contribution of the D-band.

Finally, the observation of few ir-active modes in the range 600-1800 cm -1 is in complete disagreement with the great number of weak and sharp ir modes reported in the most recent ir investigation ͑Figs. 1 and 2 and Table 1 in Ref. 9͒. It must be emphasized that to prepare the films used in this latter experiment, successive oxydation processes, vacuum annealing, and an ultrasonication process were performed. 9 Clearly, our ir spectra measured on different well-characterized samples, with no chemical and sonication treatments, are opposite to these observations. Some of the lines attributed to first order ir modes in Ref. 9 could be assigned to defect modes created by the successive treatments. Especially, because the sample was ultrasonicated after the purification treatment and before the ir experiments, it is possible that a significant amount of short tubes was obtained during this latter operation leading to the observation of a great number of lines as predicted by recent calculations. 16

V. CONCLUSION

In conclusion, the experimental infrared spectra measured on well-characterized different samples allow us to identify unambiguously the ir fingerprints of a SWCNT. The radial mode and tangential modes are unambiguously identified around 860 and 1587 cm -1 , respectively. With regards to the radial displacements of the carbon atoms involved in the radial mode located around 860 cm -1 in a SWCNT, its frequency is sensitive on the curvature of the tubes and on the interaction between tubes as revealed by its nonactivity in a DWCNT. Comparisons with previous investigations suggest that the frequencies of both modes depend on extrinsic effects ͑for instance, the functionalization of the nanotube͒, which affect the dynamics of the phonon. In all the carbon nanotubes, a band located around 1200 cm -1 is evidenced. It mainly origins from the contribution of the D-band to the ir spectrum of SWCNTs with defects.

19

 19

1 FIG. 1 .FIG. 2 .

 112 FIG.1. The transmittance ir spectra of carbon aerogel ͑top͒, SWCNT sample ͑middle͒, and graphite ͑bottom͒. The spectra have been shifted for clarity.

TABLE I .

 I ir frequencies for our data and those given in the literature; w, m, b, and s stand for weak, middle, broad, and strong intensity, respectively.

	Expt.
	͑cm -1 ͒	Attribution			References Material
	682 ͑w͒		1st order A 2			9		Purified SWCNT
	806 ͑w͒		1st order A 2			9
	854 ͑w͒		1st order E 1			9
	820 ͑w͒							7,8		Purified SWCNT
	840 ͑w͒							7,8		Purified SWCNT
	860 ͑w͒		radial mode		This work	SWCNT
	868 ͑w͒			A 2u				6,19		Graphite
	873 ͑w͒							6		SWCNT
	880 ͑w͒		1st order A 2			9		Purified SWCNT
	1045							This work Amorphous carbon
	1090							This work Amorphous carbon
	1127							This work Amorphous carbon
	1168							This work Amorphous carbon
	1188							This work Amorphous carbon
	1190 ͑b,s͒			D-band		This work	SWCNT
	1250 ͑b,s͒						This work Amorphous carbon
	1262			1st order A 2			9		Purified SWCNT
	1369			1st order A 2			9		Purified SWCNT
	1535								8		Purified SWCNT
	1541			1st order A 2			9		Purified SWCNT
	1555								8		Purified SWCNT
	1564			1st order E 1			7,9		Purified SWCNT
	1580							This work	DWCNT
	1582 ͑m͒ Tangential mode This work
	1585			1st order E 1			9		Purified SWCNT
	1587 ͑m͒ Tangential mode This work	SWCNT
	1587 ͑m͒						This work Amorphous carbon
	1590 ͑m͒			E 1u				6,19		Graphite
	1597 ͑m͒							6		SWCNT
	800	820	840	860	880	900	900	1000	1100	1200	1300	1500 1520 1540 1560 1580 1600 1620
								W avenum ber (cm -1 )		W avenum ber (cm -1 )

ACKNOWLEDGMENT

This work was supported by a CNRS-France/CNRST-Morocco agreement.


François Soleilhet

Farid Benboudjema

Fabrice Gatuingt

Xavier Jourdain

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF DRYING EFFETS ON CONCRETE'S MECHANICAL PROPERTIES

Introduction

Concrete is one of the major construction materials due to its resistance and easy use. Its use in numerous applications leads to different stakes. Currently, one of the major concerns for concrete structure is the long-term behaviour and durability of the construction. Multiple kind of solicitations combined with concrete heterogeneous mixture make it difficult to be fully defined. The purpose of this present work is to deal with the effects of drying process on tension mechanical properties of concrete.

Conventionally, when mechanical properties of concrete are characterized, internal stresses are assumed to be equal to zero and drying phenomenon are not taken into account. However, differential drying between the surface and the core of the structure can induce significant micro cracking. In some particular cases, this phenomenon could be important.

The impact of drying and micro cracking on mechanical properties is not well studied whereas it seems to have a significant impact on the mechanical properties. Regarding Young's Modulus most authors report a decrease of 4 to 30 % as concrete dries [9-14]. Conversely, there is no consensus regarding the compressive and tensile strengths so far: concerning compressive strength, some authors report an increase [10,11,13,14] Relatively few evaluations comparing each of the methods to determine concrete's mechanical properties available today have been made. Firstly, this communication presents the effect of drying, on constant relative humidity, following each methods of characterisation: flexural test, splitting test, compressive test and direct tensile test. Secondly, the results will be compared to numerical simulations.

Experimental program 2.1 Material data

The concrete considered in this study, is the one used in the VerCors project's framework. It is based on ordinary Portland cement (CEM I) and its water to cement ratio is equal to 0.62. In addition, a plasticizer is used for a better workability.

Its characteristic parameters are: an average compressive strength at 28 days equals to 40.75 MPa on 16x32 cylinder, a tensile strength equals to 3.5 MPa (using splitting test) and an Young modulus equals to 32.2 MPa.

Experimental campaign

For the purpose of this present work, each specimen is made with the same concrete mixture in order to reduce the impact of concrete variability and manufactured in mould. Prismatic samples (7x7x28) are casted into a steel mould, compressive and splitting samples (11x22) are made in a carton mould, and flexural (10x10x84) and direct tensile ones are poured in reusable formwork specifically built for that purpose. After this production, samples are stored in water during 28 days. At the end of the curing period, half of the samples is placed into a humidity-and temperature-controlled room, where they are exposed to drying conditions until they reach a percentage of mass loss above 40 with respect to the maximum one. The other half of the samples remains in water until the tests of all the samples are carried out.

Experimental tests

For each test, three samples of each specimen are used in order to obtain mean values.

Drying test

Isothermal drying test is performed to quantify the drying of every specimen. After the curing period, drying samples are put into a climatic chamber with an average relative humidity and temperature of 34% ± 13% and 25°C ± 1°C respectively (Figure 1). The water in excess on the sample surface is removed with a wet cloth then each sample is weighed in open air using the same weighing device. At the beginning, samples are weighed every hour and then daily.

It was not possible to weigh flexural samples (about 20 kilograms) because they are too heavy for the weighting device (15 kg ± 0.1 g).

As the study is made on multiple methods of characterisation, the drying is performed under a unique relative humidity. (1)

Where S l , P c , , K, k rl and µ l are, respectively, the saturation degree, the capillary pressure, the porosity, the intrinsic permeability, the relative permeability and the viscosity of the liquid water.

It is shown [START_REF] Bažant | Effect of cracking on drying permeability and diffusivity of concrete[END_REF][START_REF] Hansen | Creep of concrete: the influence of variations in the humidity of ambient atmosphere[END_REF] that this equation is sufficient for an accurate prediction of the drying of ordinary and high-performance concretes at 20°C with a relative humidity greater than 50%.

The capillary pressure and the relative permeability are related to the degree of saturation through van Genuchten's relation [START_REF] Lassabatère | Sur le couplage entre séchage du béton et contrainte appliqué[END_REF]:

(

Where and are materials parameters.

Drying shrinkage modelling

There are different ways to model drying shrinkage. Some of these are based on pore mechanic problem. The development of this kind of modelling could be easily found in [Biot] or [Thierry]. Others models are based on phenomenological observations. Indeed, following experimental results, [START_REF] Goltermann | Mechanical predictions of concrete deterioration -Part 2: classification of crack patterns[END_REF][START_REF] Baroghel-Bouny | Characterization and identification of equilibrium and transfer moisture properties for ordinary and highperformance cementitious materials[END_REF] found a proportional relation between water content variation and drying shrinkage rate:

Where is a hydrous compressibility factor and is the unit matrix.

It is possible to find alternative approach but in this present work this modelling was chosen.

Mechanical modelling

This study, based on 3D modelling and meshing of all samples, uses a non-explicit modelling of concrete cracking by the way of damage theory. The variable D, a scalar damage variable ranging from 0 to 1, is considered in the stress-strain relation:

(5) Where , , , are respectively stress, elastic stiffness and elastic components.

The evolution of the damage relies on an equivalent strain criterion, calculated from the equivalent strain introduced by [Ref Mazars]. It was shown [Feenstra] that the evolution of damage in tension could be taken as exponentially decreasing: [START_REF] Bažant | Effect of cracking on drying permeability and diffusivity of concrete[END_REF] Where

, with the tensile strength and the Young modulus, and a parameter controlling the softening behaviour of the concrete.

Softening behaviour of concrete may lead to non-unity of solutions and mesh dependency. Energetic regularization prevents these difficulties [Hillerborg]. Regularization is based on the parameter , which is a function of the size of finite element h, tensile strength , fracture energy and a parameter for the initiation of the damage .

Finally, a random field on the tensile strength generated by the Turning Band Method [Matheron] is used. The parameters are: -The coefficient of variation equals to 10 per cent; -The correlation length taken as three times the size of the biggest aggregate.

Conclusion and perspectives

Below are examples of references to a conference contribution [START_REF] Laustsen | CT measurements of SAP voids in concrete[END_REF], a journal paper [START_REF] Jensen | Water-entrained cement-based materials. I. Principles and theoretical background[END_REF], a standard test method [START_REF] Astm C457 | Standard test method for microscopical determination of parameters of the air-void system in hardened concrete[END_REF], and a thesis [START_REF] Laustsen | Engineered air-entrainment of concrete[END_REF], respectively.

Figure 1 :samples in the climatic chamber 2 . 3 . 2

 1232 Figure 1 : Drying samples in the climatic chamber 2.3.2 Splitting and Compressive tests

  while others

	International RILEM Conference on Materials, Systems and Structures in Civil Engineering
	Conference segment on Service life of cement-based materials and structures
	22-24 August 2016, Technical University of Denmark, Lyngby, Denmark
	report a decrease [9, 15-17]. Concerning tensile strength, a slight increase was found in a
	splitting test [17] while an initial decrease followed by a progressive increase up to zero
	percent relative humidity was observed in bending [12,16,18]. A decrease followed by an
	increase was also measured in direct tensile tests [18,19].

Table 1 :

 1 Concrete composition.

	Compound	Nature	Quantity	Unit
	Cement	CEM I 52,5 R	320	kg/m 3
	Sand		830	kg/m 3
	Aggregate (4-11mm)	Calcareous	445	kg/m 3
	Aggregate (8-16mm)	Calcareous	550	kg/m 3
	Water		197.6	kg/m 3
	Plasticizer	SIKAPLAST Techno 80	2.75	kg/m 3

  International RILEM Conference on Materials, Systems and Structures in Civil Engineering Conference segment on Service life of cement-based materials and structures 22-24 August 2016, Technical University of Denmark, Lyngby, Denmark

Splitting test is the first made. The settings of this test are presented in Figure 2. It is performed under strength-controlled conditions with a rate of 1.94 kN.s -1 until failure. Special attention is paid to limit loading eccentricity.

Figure 2 : Settings of the splitting test

Regarding the compressive test, samples are firstly planed to obtain a good flatness and to avoid press fitting and eccentricity. The test is then performed under strength-controlled conditions with a rate of 5 kN.s -1 . A cage strain, composed of three LVDT, is placed on the sample to measure strain. At the beginning of the test, to calculate the Young's modulus of the sample, three unloading and reloading are accomplished up to 30 percent of tensile strength. Finally, the test is conducted to completion, until the failure of the sample.

Flexural strength test

[A finir. Je ne connais pas encore bien la procédure. Je fais les essais demain avec Xavier] The drying of cement-based materials is a complex phenomenon. Several, more-or-less coupled, mechanisms are involved: permeation, diffusion, adsorption-desorption and condensation-evaporation. Drying can be analysed through the resolution of liquid water,


Didier Fraix-Burnet
email: didier.fraix-burnet@obs.ujf-grenoble.fr

Mauro D'onofrio

Paola Marziani

Didier Fraix

Phylogenetic Analyses of Quasars and Galaxies

Keywords:

Phylogenetic approaches have proven to be useful in astrophysics. We have recently published a Maximum Parsimony (or cladistics) analysis on two samples of 215 and 85 low-z quasars (z < 0.7) which offer a satisfactory coverage of the Eigenvector 1-derived main sequence. Cladistics is not only able to group sources radiating at higher Eddington ratios, to separate radio-quiet (RQ) and radio-loud (RL) quasars and properly distinguishes core-dominated and lobe-dominated quasars, but it suggests a black hole mass threshold for powerful radio emission as already proposed elsewhere. An interesting interpretation from this work is that the phylogeny of quasars may be represented by the ontogeny of their central black hole, i.e. the increase of the black hole mass. However these exciting results are based on a small sample of low-z quasars, so that the work must be extended. We are here faced with two difficulties. The first one is the current lack of a larger sample with similar observables. The second one is the prohibitive computation time to perform a cladistic analysis on more that about one thousand objects. We show in this paper an experimental strategy on about 1500 galaxies to get around this difficulty. Even if it not related to the quasar study, it is interesting by itself and opens new pathways to generalize the quasar findings.

These tools try to establish the relationships between the species by minimizing the total evolutionary cost depicted on a phylogenetic tree. The most general and the simplest to implement technique is Maximum Parsimony, also known as cladistics, and is based on the parameters, and not on distances between the objects. The trees that result from cladistic analysis should not be interpreted as genealogic trees: here, as the trees do not indicate ancestor or descendant objects, each quasar supposedly represents a species (i.e., a class). In this phylogenetic sense, the trees can be rooted according to a parameter that may have an evolutionary meaning.

Figure 1. The cladistics tree of 85 quasars. The tree representation is unrooted, but the low black hole masses (MBH) are at the top. We identify ten groups corresponding to bunches of branches and colored as in Fig. 2. The colored ellipsoidal regions indicates well known categories of quasars and encompass several of our groups.

The phylogenetic tools are devised to take the evolution of object populations into account. They do not rely on similarities, derived from the computation of distances, but on the fact that diversity is gained through evolution and speciation. For instance, similarity techniques (like most statistical clustering and classification or phenetic tools) tend to find hyperspheres in the parameter space, while phylogenetic tools are able to detect evolutionary paths as can be shown on stellar evolutionary tracks (Fraix-Burnet, 2016). Many applications have been published on many kinds of astrophysical objects [START_REF] Fraix-Burnet | The environment of formation as a second parameter for globular cluster classification[END_REF][START_REF] Fraix-Burnet | The environment of formation as a second parameter for globular cluster classification[END_REF][START_REF] Fraix-Burnet | A six-parameter space to describe galaxy diversification[END_REF][START_REF] Cardone | Hints for families of grbs improving the hubble diagram[END_REF][START_REF] Fraix-Burnet | Stellar populations in ω centauri: a multivariate analysis[END_REF][START_REF] Jofre | Cosmic phylogeny: reconstructing the chemical history of the solar neighbourhood with an evolutionary tree[END_REF][START_REF] Holt | Cladistical analysis of the Jovian and Saturnian satellite systems[END_REF].

Phylogenetic approaches represent the relationships using trees or networks, the first ones being simpler to read. From these evolutionary schemes, it is possible to gather objects into groups that supposedly share the same common ancestor species (monophyletic groups). These groups appear as sub-structures (i.e. bunches of branches) in the tree, their exact number depending on the desired level of details in their physical interpretation.

In this paper, we summarize an exciting cladistic analysis of low-z quasars and illustrate a possible approach to extend such study on much larger samples.

A CLADISTIC ANALYSIS OF A LOW-Z QUASAR SAMPLE

This analysis is published in [START_REF] Fraix-Burnet | The phylogeny of quasars and the ontogeny of their central black holes[END_REF]. Two samples of low-redshift (z≤ 0.7) quasars are used: one with 215 objects presented by [START_REF] Marziani | An optical spectroscopic atlas of low-redshift active galactic nuclei[END_REF], and another one made of 85 quasars cross-matched with [START_REF] Sulentic | C iv 1549 as an eigenvector 1 parameter for active galactic nuclei[END_REF] have measurements of the CIV line. These two samples are modest in size but have good quality measurements of emission lines (H β , FeII, [OIII], CIV...). For the cladistic analysis, the 215 and 85 object samples have respectively seven and eleven parameters. With such relatively small samples, the cladistic analysis is relatively easy, and allows for extensive test of its reliability through kinds of bootstrap approaches. The most parsimonious tree in Fig. 1 shows the 85 quasars at the leaves (ends of the branches). Bunches of branches that appear to depart from the main trunk are coloured to define groups of quasars that hypothetically may share similar evolutionary histories.

To understand and interpret this tree, it is necessary to look at the properties of the groups, for instance using boxplots (Fig. 2). The tree (Fig. 1) is arbitrarily presented with the group having the lowest black hole mass is at the top. The groups on the boxplots are then ordered from the top of the tree to the bottom.

It is striking to note that the black hole mass increases nearly regularly towards the bottom of the tree. Since the black hole mass (MBH) can only grow as a function of quasar evolution and cosmic time, the ontogeny of black holes is represented by their monotonic increase in mass. Considering that MBH provides a sort of arrow of time of nuclear activity, a phylogenetic interpretation of the tree becomes possible if the cladistic tree is rooted on black hole mass.

Considering other properties, the cladistic tree is thus consistent with the more massive radio-quiet Population B sources (disk dominated, lower Eddingon ratio) at low-z appearing as a more evolved counterpart of Population A (wind dominated sources, higher Eddington ratio) to which the local Narrow-Line Seyfert 1s belong.

The core-dominated and lobe-dominated Radio Loud (RL) sources are in two distinct groups at the bottom of the tree, indicating they are monophyletic groups. Quite interestingly, these powerful RL sources appear in our low-z sample only above a mass threshold.

In conclusion, the quasar sample studied in [START_REF] Fraix-Burnet | The phylogeny of quasars and the ontogeny of their central black holes[END_REF] contains a population of massive quasars which are more evolved and a population of less-massive quasars that are radiating at a higher L/Ledd. While L/Ledd remains the physical factor governing E1 [START_REF] Marziani | Searching for the physical drivers of the eigenvector 1 correlation space[END_REF][START_REF] Sulentic | The case for two quasar populations[END_REF][START_REF] Sulentic | Quasars in the 4d eigenvector 1 context: a stroll down memory lane[END_REF], high-MBH quasars may have resembled low-MBH quasars in an earlier stage of their evolution.

The cladistic analysis is thus able to recover well-known classes of quasars, but more importantly brings a unique insight on their phylogeny. However, this picture is only valid for the low-z sample studied, and no generalization to the entire quasar population is possible. But the results are sufficiently exciting to justify extensions of this work to other samples. Two directions are foreseen, both requiring higher-z quasar populations, to better depict the quasar evolution. Firstly, it would be interesting to study a sample within a constrained redshift range at another epoch of the Universe to check whether the evolution of the properties of quasars is similar. Secondly, the relationships between quasar populations in a larger redshift range would give a clearer picture of the global evolution of the black hole mass and the different properties like the radio loudness or the disk/wind dichotomy.

Unfortunately, data are either not existing or of insufficient quality which requires dedicated surveys with large-collecting area telescopes to match the luminosity range of low-z quasars that remain almost unobserved at intermediate-to-high redshift [START_REF] Sulentic | Gtc spectra of z 2.3 quasars: comparison with local luminosity analogs[END_REF]. In addition, the cladistic technique is very demanding in computing resources. Basically, all possible trees made of the objects must be built to select the most parsimonious one in terms of evolutionary complexity. There are heuristic tricks to avoid this thorough quest, but still a cladistic analysis is practically not feasible with more than about a thousand objects.

Another approach is required. Since we do not have a big quasar sample, we present in the following a tentative strategy on a different sample made of galaxies, as an example of potential applications of cladistics to large samples of sources.

A CLADISTIC ANALYSIS OF LOW-L ELGS IN CLUSTER

SAMPLE

The WINGS survey [START_REF] Fasano | Wings: a wide-field nearby galaxy-cluster survey. i. optical imaging[END_REF] is an imaging and spectroscopic study of the brightest X-ray clusters at redshift 0.04 < z < 0.07 selected from the ROSAT all sky survey. The sample for this analysis has 1494 galaxies belonging to several clusters, and eleven parameters have been used for the cladistic analysis itself: B-V, logRe, surface brightness, Hβ, D4000, Mass, Sersic index n (measures the degree Figure 3. The cladistics tree of 300 pre-clusters of the WINGS sample of 1494 galaxies. The tree representation is unrooted, but the lower masses are at the top. The colors of the branches correspond to the groups and are the same as in Fig. 4. of curvature of the Sersic profile describing how the intensity of a galaxy varies with distance from its center), Hα/NII, Gband, Mg and Na.

PRE-CLUSTERING

Phylogenetic methods are intended to find relationships between classes (species) of objects. But there is no multivariate classification of galaxies (Fraix-Burnet et al., 2015). This would be however useful since it is easier and physically more relevant to study different types of objects rather than millions of individuals. This dimension reduction is also necessary in the era of the huge databases brought by current and future telescopes.

This multivariate classification is one objective of astrocladistics. However, we are limited by the size of the samples to study. There are other phylogenetic techniques that tackle this problem efficiently, but they are based on distances, and most often adapted for the specific evolutionary processes of living organisms and their traits (e.g. [START_REF] Saitou | The neighbor-joining method: a new method for reconstructing phylogenetic trees[END_REF][START_REF] Gascuel | Neighbor-joining revealed[END_REF]). Some work should be done to assess their applicability to astrophysics. There are also many statistical tools for unsupervised classification (or clustering, [START_REF] De | Comparison among clustering and classification techniques on the basis of galaxy data[END_REF]), but they gather objects according to their similarities, not to their evolutionary relationships.

We will discuss this big issue with possible solutions in another paper (Fraix-Burnet in prep.), and here show the results of a first approach we have implemented. The idea behind this approach is rather intuitive: we are looking for structures in the parameter space, structures that both gather and relate the objects of our sample. Since we have too many of these objects, we try to reduce the resolution of our data by replacing very close (similar) objects into meta-objects that we call pre-clusters. These pre-clusters take the median properties of their components. In other words, we postulate that there may be some redundancies in our data. Then we can perform the cladistic analysis on these pre-clusters that can subsequently gathered into groups from the tree. This idea is also mentioned by [START_REF] Murtagh | Wards hierarchical agglomerative clustering method: Which algorithms implement wards criterion[END_REF] that recommends to perform a preclustering using a hierarchical classification method (that builds a hierarchy of clusters, (Fraix-Burnet et al., 2015)) for the k-means analysis (a partitioning method, (MacQueen, 1967;Fraix-Burnet et al., 2015)). While for our problem many pre-clustering algorithms could a priori be used, we here choose the hierarchical clustering one. Note that this technique requires a huge amount of CPU time with very large samples.

The number of pre-clusters is arbitrary. Obviously it should not be too low otherwise we probably mix together different kinds of objects. It cannot be too high either because of the limitation of the cladistics analysis. We have found that 300 pre-clusters is here a good choice compromise because the cladistic analaysis takes only a few hours allowing many runs to test this strategy.

RESULTS

The tree (Fig. 3) is obtained with the 300 pre-clusters. Each leave (ending branch) of the tree is thus one pre-cluster. We have gathered these pre-clusters depending on the substructures of the tree, and the groups are represented by different colors. Each group of galaxies thus corresponds either to a single branch or to a bunch of branches on the tree.

The boxplots (Fig. 4) show the statistics of several parameters for each of the groups. The order of the groups is arbitrary and has been chosen to underline the increase of the mass. On the tree in Fig. 3 this parameter increases from top to bottom.

The color progression from blue to red grossly matches the increase in mass of galaxies, as well as other clear trends as visible on the boxplots. Interestingly, the morphological type decreases along the tree downward, and possibly the distance to the cluster center as well even though the in-group scatters are large.

Sometimes, some groups stand out from these trends in some parameters, such as the group 6 for the mass or group 12 for Mg. These groups will be further investigated since they could be either the results of some weird data or, more interestingly, a new peculiar species of galaxies that could lead us to a better understanding of the evolution of galaxies than simply redder colors or larger masses.

The WINGS sample galaxies belong to X-ray brights clusters, which are rather evolved systems, predominantly close to a state of viral equilibrium. We find that most of the groups have a representant in all the clusters, or conversely all clusters span the entire tree. Despite the low statistics in some of the clusters, this would indicate that the classification scheme depicted on the tree in Fig. 3 could be well of general validity for galaxies at low redshift.

We have also analysed a control sample of 497 higher redshift field galaxies. It is impossible to root the tree such that the boxplots show as many monotonic trends as for the cluster sample above, indicating that the field galaxies of our sample may not possess a "common ancestor", that is they could be made of two distinct populations with different origins. Another possibility is that their evolution is more complex, but the sample is probably too small to conclude in this direction. The fact that the cluster sample of lowredshift galaxies is compatible with a common ancestor can be due to: i) the general influence of clusters on galaxy evolution, ii) time smoothing out somewhat the different origins of these galaxies, iii) a lower diversity by a sort of volume selection effect.

CONCLUSION

Categorizing quasars or galaxies is usually made through a handful of properties at most. Multivariate clustering is still rare (Fraix-Burnet et al., 2015), but only phylogenetic tools like cladistics provide relationships that emerge from the data. Here [START_REF] Fraix-Burnet | The phylogeny of quasars and the ontogeny of their central black holes[END_REF], the quasar sample is small and relatively well contained in redshift, so probably in diversity. Indeed, the diversity of the quasar sample

Figure 2 .

 2 Figure 2. Boxplots for the groups in the 85 quasar sample as defined on the tree in Fig. 1. The parameters shown are: the radio loudness parameter (RK), the intensity ratio between Feλ4570 and Hβ (RFE), the Full Width at Half-intensity Maximum (FWHMHb) and the line centroid displacement at quarter maximum (c1o4Hb) of the Hβ line, the equivalent width (WOIII) and the peak shift (vOIII) of the [OIII]λ5007 line, the bolometric luminosity (Lbol), the Black Hole Mass (MBH), the Eddington ratio L/L edd (LoLedd), the soft X-ray photon index (Gamma), the centroid displacement at half maximum (c1o2CIV) and the equivalent width of the CIVλ1549 line (WCIV).

Figure 4 .

 4 Figure 4. Boxplots for the groups in the WINGS sample as defined on the tree in Fig. 3

https://astrocladistics.org

This is a provisional file, not the final typeset article

Frontiers

MacQueen J. Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics (Berkeley, Calif.: University of California Press)(1967), vol. 1, 281-297. This is a provisional file, not the final typeset article

(which is exclusively low-z, z 0.7) can be organized along a 1D sequence, the eigenvector-1 main sequence.

To extend this study to larger samples at higher redshifts, we present a possible strategy to perform the same kind of analysis by performing a pre-clustering using a hierarchical clustering technique, followed by a cladistic analysis on the pre-clusters. This is applied on a galaxy samples due to the current lack of larger samples of quasars with similar parameters as above.

Even though this diversity is much larger for the WINGS galaxy sample, our proposed strategy successfully establishes a phylogenetic scheme that points to several evolutive properties (like color, mass, metallicity but also D4000 and the Sersic index n) characterizing a level of diversification (or evolution). Some of these evolutive correlations are very probably not causal, unlike the quasar evolution with MBH. Some caution is necessary when interpreting the cladograms presented here. One should not conclude that every quasar or every galaxy follows some linear evolution along the tree. There are bunches of branches (sub-structures of the trees) that could suggest some dead ends, or the lack of more ancestral objects. For instance, starting from the low luminosity Pop A quasars (group 1), how to understand the branch of more luminous Pop A quasars (group 2)? Regarding WINGS galaxies, the true ancestors of the objects studied here are at higher redshifts: where the connection to the presented trees would take place? This is impossible to answer these questions without further pursuing the present work.

DISCLOSURE/CONFLICT-OF-INTEREST STATEMENT

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

AUTHOR CONTRIBUTIONS

The contributions is mainly as follows: DFB performed the cladistic analyses, MDO and PM worked on the WINGS project and gathered the sample. PM also provided the quasar sample. All three authors equally participated to the elaboration of the documents.


Didier Fraix

Didier Fraix-Burnet
email: didier.fraix-burnet@univ-grenoble-alpes.fr

Astrocladistics: Sixteen Years Later

Keywords:

come

Some results on galaxies Initial motivation: renewal of the classification of galaxies.

First "general" multivariate classification of ( 1000) galaxies:

But this is only for 1000 galaxies...

Why it works

Demonstration with the evolutionary tracks of stellar evolution using 11 parameters (traits). The PHYLOCODE project initially inspired us, similar difficulties?

Pre-classification with Hierarchical Clustering 1494 galaxies have been pre-clustered into 300 pre-groups with a hierarchical clustering method followed by a cladistic analysis. Eleven parameters are used: B-V, logRe, surface brightness, Hβ, D4000, Mass, Sersic index n, Hα+NII, Gband, Mg and Na.

Most parsimonious tree on the 300 "pre-groups" (leaves). The nine groups ("clades") shown in colour are the larger ones with more than 30 galaxies.

Some properties of the nine main groups.

Conclusion

Phylogenetic tools: marvelous techniques to reconstruct evolutionary paths, whatever the nature of evolution.

Great success in astrophysics, more and more applications.

Connections with physical models to be improved.

Still no multivariate classification of galaxies.

Networks better suited to represent galaxy diversification?


Alaa Eddin Iskef
email: iskef@lmt.ens-cachan.fr

Fabrice Gatuingt
email: gatuingt@lmt.ens-cachan.fr

Frédéric Ragueneau
email: raguenea@lmt.ens-cachan.fr

Cédric Giry
email: giry@lmt.ens-cachan.fr

Eddin

Gatuingt Fabrice

Ragueneau Frédéric

Giry Cédric

Modeling the nonlinear mechanical response of reinforced concrete structures by simplified approaches

Keywords: (5): RC Structures, Finite element, Macro-element, Nonlinear analyses, experiments Main subthemes: Modeling of structures (AMS)

Introduction

Context and objective of the research

Constructive deficiencies of buildings are generally not known before earthquakes tragically highlight them. Several recent seismic events have shown weaknesses of buildings having a reinforced concrete (RC) structure built with wrong "Capacity Design" principles. Moment resisting frames (MRF) built until the end of the 1970s are generally very sensitive to lateral actions and their poor performance results often in brittle collapse during an earthquake (see Figure 1-1). In most cases, the reasons of such undesirable behavior for theses RC structures can be identified as being due to a deficient design of beam-column connections and in particular of exterior beam-column joints (see Figure 1-1).

In the past few decades some researches has highlighted that the causes of low joint shear strength and consequent brittle behavior of joints can be found in the lack of shear reinforcement in the core and an inadequate anchorage of the beam reinforcement bars in the joint panel. Although a significant research effort has been spent on this topic, there is still major uncertainness in the seismic assessment of so-called substandard exterior beam-column joints. A large variety of typologies of beam-column connections can be found in RC structures (see Figure 1-2) but to simplify our approach, only a 2D case of an exterior joint is considered in this paper. Therefore, in this study the development of numerical tools based on macro-element to describe the behavior of such substandard beam-column connections is targeted.

Mechanics of RC exterior beam-column joints

From a structural point of view, a beam-column joint can be considered elastic if the plastic deformations of the connection occur only in the beam and/or the column and if the joint panel remains uncracked during the entire loading history. Conversely, a beam-column joint is defined as plastic if, during the loading reversals, there is some inelastic behaviors in the joint panel (cracking, rebar debonding, …).

A beam-column joint can also be described as the region formed by the intersection of beams and columns. Therefore, each of the three elements can fail under different modes: beam flexural failure, beam shear failure, column flexural failure, column shear failure, joint shear failure, bond failure of the reinforcement or combination of the various modes. It is well know that some of these failure modes should be avoided if the beam-column connection undergoes large plastic deformations (shear failures of beam, column or joint and bond failure of reinforcement). Due to the limited deformation capacity of such brittle plastic mechanism, a collapse of the whole frame may result (see Figure 1-1).

Numerical investigation of the mechanical behavior of joint-element

A large number of numerical approaches for the simulation of beam-column joints have been developed. These approaches include, lumped plasticity models, multi-spring models, finite element simulations and fracture mechanics based approaches. These methods may be divided into two groups with reference to the ultimate aim of the numerical analysis. The first group of models aims to simulate the joint strength and rotation within a MRF (Moment Resisting Frame). They are due to the observation that the plastic behavior of a frame cannot be properly simulated taking into account only the strength-deformation contribution of beam and column while neglecting the joint shear strength and distortion. In this type of models, the behavior of the joint is assumed to be known. Examples of this type of models are (Figure 2-1):

-Rotational hinge models : [START_REF] Alath | Modeling inelastic shear deformations in RC beam-column joints[END_REF] -Multi-spring models : [START_REF] Biddah | Modelling of shear deformation and bond slip in reinforced concrete joints, s[END_REF] , [START_REF] Lowes | Modeling Reinforced-Concrete Beam-Column Joints Subjected to Cyclic Loading, s.l[END_REF] -Complex joint response model : [START_REF] Elmorsi | Modeling bond-slip deformations in reinforced concrete beam-column joints, s.l[END_REF] -Fiber models : [START_REF] Braga | Modeling of the bond-slip behavior in the response mecanisms of RC beam-coloumn joints with plain round bars[END_REF] The models of the second group are more sophisticated. They usually involve a Finite Element (FE) model and are often developed with the investigation of the joints load-deformation behavior and the effect of different parameters. These types of models are very demanding in terms of computational requirements and are usually not suitable for the analysis of a entire 3D structure. They are usually be used to save much more expensive experimental tests, as in [START_REF] Eligehausen | 3D Analysis of Seismic Response of RC Beam-Column Exterior Joints before and after Retrofit[END_REF], [START_REF] Genesio | Seismic retrofit solution for reinforced concrete exterior beam-column joints using a fully fastened haunch -Part 2-1: As-built joints, s.l[END_REF].

3D analysis

This analysis aims to point out different sources of nonlinearity under cyclic and seismic loading and to complete the information given by experimental tests about the failure mode, the ultimate force or the displacement capacity up to failure. This kind of 3D modeling studies allow us to justify our future choice of internal variables of a macro-model and to quantify their evolution that will be introduced in the constitutive behavior of the macro-model. Until the date of preparation of this paper, we have not yet experimental results, so, the aim of these analyses is to test different concrete behavior laws on the 3D modeling of exterior beam-column joint by using software Cast3M in order to verify their limits, application domain and their computing capabilities.

Constitutive law for concrete and bar reinforcement

A perfectly plastic model is used for the steel reinforcement bars and two models based on isotropic damage mechanisms are introduced for the concrete behavior as described below:

-MAZARS (Mazars, 1984) : a single scalar damage variable is introduced to reproduce the stiffness degradation experimentally observed. The dissymmetry between tension and compression strength is also taken into account. This model is very simple and robust but it is not really suitable to model the behavior of concrete under cyclic loading (Figure 2-2).

-DAMAGE_TC [START_REF] Costa | Implementation of the damage model in tension and compression with plasticity in cast3m, s.l[END_REF] The parameters introduced in the computation are given in the following tables based on characteristic test of all materials used for the experimental analysis.

Modeling and discretization

In this work, the concrete is modeled with eight nodes 3D hexahedral elements. The reinforcement steel is modeled using 1D truss elements. The 1D-truss elements are only able to transfer the tension and compression forces, but not a bending moment. A perfect connection between this reinforcement bars and the concrete elements is also assumed.

Load and boundary conditions, were applied as nodal loads and constraints in the FE model (schematically shown in Figure 2-4). To prevent local failure of the concrete elements due to the concentration of high stresses in the vicinity of the supports and at the point of application of lateral load, the concrete behavior was assumed as linear elastic in these regions. -Appearance of a plastic hinge in the beam at the beam-column interface as soon as the elasticity limit is exceeded.

Preliminary analyses

-After formation of the plastic hinge, diagonal cracks through the joint region and cracks due to bending in beam are noted.

-Flexural yielding of the beam reinforcement bars occurred after joint shear cracking (brittle behavior).

-Ultimate stregnth and flexural yielding of bars predicted by Mazars model slightly exceeded DAMAGE_TC model, whereas Mazars behavior was more brittle. -Mazars model could not reproduce the hysteretic behavior because it doesn't take into account the unilateral effect and frictional sliding at the concrete crack interfaces.

-The hysteretic behavior predicted by DAMAGE_TC was symmetric and without permanent deformations.

-In the case of deformed bars, the assumption of a perfect bond between steel and concrete leads to a slight overestimation of the ultimate strength and a less realistic cracking pattern and postpeak behavior especially under cyclic loading if compared to the use of the discrete-bond model [START_REF] Sharma | Nonlinear dynamic analysis using microplane model for concrete and bond slip model for prediction of behavior of nonseismically detailed RCC beamcolumn joints, s.l[END_REF].

From 3D modeling to simplified macro-element model

Avoiding the high computational costs of classical three-dimensional (3D) analysis of RC structures, different kind of models can be adopted in order to reduce the structural kinematic complexity in describing the numerical responses of large-scale structures subjected to complex loadings (cyclic and seismic). Elements joints (beam-column and wall-slab connections) can be treated thanks to macro-elements linking global loads vector (Forces and Moments) to global kinematic variables (displacement and rotation) [START_REF] Nguyen | Macroscopic modeling of reinforced concrete joints: Application to thermal break elements subject to earthquake loadings[END_REF].

Kinematics of connection element: finite element framework

The joint element used in our work contains three nodes (Figure 23456789).Each node has three degrees of freedom in 2D space: two displacements and one rotation. The vectors of nodal displacement and force of an element with three nodes have the form shown below. In general cases, the relation between the generalized displacements and forces (stiffness matrix) are directly computed using elastic beam theory.

Where is the stiffness matrix.

Stiffness matrix of proposed macro-element

In order to find the different components of the stiffness matrix , based on 3D Finite Element numerical analyses (using elastic model for concrete and steel), we can set one component of the displacement vector to non-zero value (and at the same time set the other displacement components to zero), and evaluate the resulting reaction forces . The values components of the stiffness matrix column, corresponding to this component, can be calculated by dividing the reaction forces obtained by the imposed displacement value. In order to find the stiffness matrix degradations of the proposed macro-element (during loading applied at beam tip in direction z), we need to know which components in the stiffness matrix will degrade during this loading. Therefore, firstly, we have done 3D analysis using Mazars model to obtain damage state of the joint. Secondly, we have done 3D analysis using elastic model for concrete with the value of the damage Young's modulus . Figure 2-10 shows the evolution of stiffness matrix degradations for four increasing stages of the monotonic loading at beam tip in direction Z. IL FAUT COMMENTER LES VALEURS OBTENUES

Experimental investigations

Many researchers carried out experimental investigations on monotonic and cyclic loading of beamcolumn joints in order to understand the behavior of RC beam-column joints [START_REF] Hamil | Reinforced Concrete Beam-Column Connection Behaviour[END_REF], [START_REF] Youssef | Experimental Investigation on the Seismic Behavior of Beam-Column Joints Reinforced with Superelastic Shape Memory Alloys, s.l[END_REF], [START_REF] Kam | Influence of slab on the seismic response of sub-standard detailed exterior reinforced concrete beam column joints[END_REF]. In this work, the experimental test series considered for the validation of the FE and macro-element models will include three or four exterior beam-column joint subassemblies designed without seismic detailing (i.e., without transverse reinforcement in the core) and subjected to different cyclic loadings (unidirectional and bidirectional displacementcontrolled quasi-static) applied at the beam tip. The specimens have been designed, built, instrumented, tested, and analyzed in the LMT-Cachan.

Details of Specimens

All specimens will have similar properties (identical beam and column sizes). Until the date of preparation of this paper, only one specimen was manufactured. This specimen was designed to fit the machine capacity (Hexapod, Figure 3-2.) and to have a shear failure in the joint region before the yielding of beam or column reinforcement bars. Figure 3-1 shows the cross section and reinforcement configurations for the specimen.

Test Setup and procedure

The test setups is shown in Figure 3-2. The specimen will be placed horizontally. Both two ends of the column will be fixed in all directions. The specimen will be cyclically loaded at beam tip in the horizontal plan. The loading consists of cycles at increasing displacement level with 2 cycles at each stage. The loading rate was chosen to reproduce quasi-static loading conditions. No axial load will be applied. A load cell (6 DOF) developed and calibrated will be used for loading and to get an overall idea of displacement of the test body, displacement fields and cracking patterns a digital image correlation [START_REF] Hild | A software for displacment field measurements by digital image coorelatin[END_REF] will be used.

Conclusions

Considering the nonlinear behavior of beam-column connections in buildings, an experimental and numerical analysis of the mechanical response of exterior joint is proposed in this paper. Proposed experiment will allow to identify the behavior of connection under complex loading. Finite elements analysis based on 3D nonlinear behaviors helps one to discriminate the fundamental thermodynamic variables to be introduced and to evaluate their respective evolution laws linked to the global displacements. At last, a simplified model, based on the beam theory assumption is proposed to predict the nonlinear response of building connections subject to cyclic loading. Depending on the material parameters choices and identification, it can reproduce brittle to softener joints.

Figure 1

 1 Figure 1-1: Joint failures in RC buildings during past earthquakes

  : In this model, damage and plasticity are combined. The mechanism of degradation of the tensile material has been decoupled from the compression by introducing two variables of damage, one for the tension and other one for compression. The model can be energetically calibrated through the cracking energy and a characteristic length. The unilateral effect (cracks closure in compression) is taken into account to model the behavior under cyclic loading (Figure 2-3).

Figure 2

 2 Figure 2-1: Macro-element models

Figure

  Figure 2-3 : DAMAGE_TC model in traction and compression

Figure 2 - 5 and

 25 Figure 2-5 and Figure 2-6 show the results of the numerical local analysis of the exterior BC joint under monotonic loading. The numerical simulations show:

Figure 2 -

 2 Figure 2-7 and Figure 2-8 show the results of the numerical local analysis of the same joint under cyclic loading. In these simulations we can observed:

Figure 2 - 5 :

 25 Figure 2-5 : Global response (monotonic loading)

Figure 2 Figure

 2 Figure 2-7 : Hysteretic behavior (cyclic loading)

Figure 2 -

 2 Figure 2-10 : Evolution of stiffness matrix degradations of the proposed macro-element

Figure 3

 3 Figure 3-1: Reinforcement details of the specimens

Table 1 :

 1 Material features for the 3D nonlinear computations

Table 2 :

 2 Mazars model parameters

	Parameter	Description	Value
	'KTR0'	Threshold in deformation for the tension	1.50943E-04
	'ACOM'	Parameter for the compression	1.276
	'BCOM'	Parameter for the compression	1060
	'ATRA'	Parameter for the traction	0.9
	'BTRA'	Parameter for the traction	11925
	'BETA'	Correction for the shear	1.06

Table 3 :

 3 DAMAGE_TC model parameters

	Parameter	Description	Value
	'HLEN'	Characteristic length (cf. mesh)
	'GVAL'	Fracture energy (J/m 2 )	120
	'FTUL'	Tension limit strength (Pa)	4.18E+06
	'REDC'	Drop Factor for Peak Tensile Stress (Pa)	2.92E+06
	'FC01'	Elastic Limit Compressive Stress (Pa)	-1.00E+07
	'RT45'	Equi-biaxial Compressive Ratio	1.18
	'FCU1'	Compressive Peak Stress (Pa)	-4.51E+07
	'STRU'	Ultimate Limit Strain	-0.035
	'EXTP'	Reference Strain for Plastic Parameter	-0.00153
	'STRP'	Reference Stress for Plastic Parameter	-3.00E+07
		(Pa)
	'EXT1'	Fitting Point 1 (Strain)	-0.003
	'STR1'	Fitting Point 1 (Stress) (Pa)	-4.00E+07
	'EXT2'	Fitting Point 2 (Strain)	-0.005
	'STR2'	Fitting Point 2 (Stress) (Pa)	-3.00E+07
	'NCRI'	Exponential softening in tension	1