Accurate ab initio full-dimensional dipole moment surfaces of ethylene are computed at 82 542 nuclear configurations using coupled-cluster approach and its explicitly correlated counterpart CCSD(T)-F12 combined respectively with cc-pVQZ and cc-pVTZ-F12 basis sets. Their analytical representations are provided through 4-th order normal mode expansions. First-principles predictions of line intensities in rotationally resolved spectra using variational method up to J = 30 are in excellent agreement with experimental data in the range 0-3200 cm -1 . Errors of 0.25 -6.75% in integrated intensities for fundamental bands are comparable with experimental uncertainties. Overall calculated C 2 H 4 opacity in 600-3300 cm -1 range agrees with experimental determination better than to 0.5%. The improved accuracy permitted to resolve some controversial issues related to the qualitative behavior of intensity patterns.

Introduction

Radiative properties of hydrocarbons, including the ethylene (ethene) C 2 H 4 molecule, are of major importance in various domains of science particularly for remote gas sensing applications [1]. In the Earth atmosphere ethylene is a natural gas pollutant [2,3,4] produced by various sources as forest fires, volcanic eruptions, combustion processes and also by anthropogenic emissions due to motor vehicle exhaust. It is involved in bio-chemical processes acting as a hormone in plant biology regulating growth and development and is used for fruit ripening control [5].

Together with other simple hydrocarbons ethylene is one of key molecules for various astrophysical applications [6,7]. They dominate the opacity of some brown dwarfs and asymptotic-giant-branch (AGB) stars and are considered among "standard" building blocks for carbon-rich atmospheres of many exoplanets [7]. Spectral signatures of ethylene have been observed in the outer planets Jupiter, Saturn, Neptune, and satellites [6]. Accurate knowledge of line and band intensities as well as of their temperature dependence is essential for reliable remote sensing diagnostics. Rotationally resolved ethylene spectra are known to be quite complex due to irregular couplings of twelve vibrational modes. Their analyzes represent difficult tasks because of accidental resonance perturbations in congested patterns of overlapping bands including hot ones. For this reason the ethylene line-by-line information in available spectroscopic databases [8,9] is far from being complete.

Ab initio theoretical studies of triatomics and small polyatomic molecules of planetological and astrophysical interest such as ammonia NH 3 , phosphine PH 3 , methane CH 4 grew up during last decades along with the improvement of ab initio surfaces and computational codes solving the rovibrational Schrödinger equation (see for example Refs. 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and references therein). This has helped resolving many issues related to spectra analyzes at high energy ranges [20,21,14,22,23] (the list being not exhaustive). Quantitatively accurate ab initio rovibrational spectra of five-atomic hydrocarbon isotopologues have been recently reported [16,24,25] together with detailed comparison against experimental data. Examples of global hightemperature methane spectra predictions for astrophysical applications can be found in Refs. 26, 27. Concerning the ethylene molecule, data assignments and analyzes present in databases remain much more sparse, although many recent studies [28,29,30,31,32,33] tend to extend the informations. For these reasons it is a perfect candidate to take the next step in accurate ab initio spectra calculations.

Accurate dipole moment surfaces (DMS) are mandatory for first principles intensity predictions [10,11,14,34,15,35,16,19]. This requires high-level electronic structure calculations on an extended grid of points, an appropriate modeling of full-dimensional surfaces and converged nuclear motion variational calculations. These tasks become very demanding with increasing number of vibrational degrees of freedom and represent a considerable challenge for the theory in case of rotationally resolved spectra of six-atomics. This may explain a lack of related studies for the ethylene molecule at the theoretical level similar to that of three-to-five atomic molecules. Despite of promising accuracy of ab initio calculations for ethylene energy levels [36,37,38] and line intensities [34], there exist very limited public available information on the ethylene DMSs.

This works aims at filling this gap. We provide analytical symmetry-adapted representation of full 12-dimensional (12D) ethylene DMSs computed at large extent of nuclear configurations (82 542 points) using the coupled-cluster approach CCSD(T) and its explicitly correlated counterpart CCSD(T)-F12 combined with cc-pVQZ and cc-pVTZ-F12 basis sets. The comparison with experimental spectra suggests that the corresponding first principle intensity calculations are currently the most accurate ones. This Letter is structured as follows. Section 2 describes computational approach to the construction of ab initio DMSs together with a brief review of the previous works. Sections 3 and 4 are devoted to the variational method of intensity calculations in the normal mode representation and to the comparison of intensities in the 0-3200 cm -1 range with recent calculations, experimental spectra and databases. The summary and conclusions are given in Section 5.

Electronic structure calculations

Force field constants of C 2 H 4 have been calculated by Martin et al. [36] at a CCSD(T)/cc-pVTZ level. Avila and Carrington [37] have modified this field using Morse representation of the potential energy surface (PES) and computed vibrational energies of up to 4200 cm -1 . In our previous work the ethylene PES [38] have been computed on the grid of 82 542 nuclear configurations.

The analytical PES modeling using sixth order expansion in curvilinear symmetry adapted coordinates involving about 2650 parameters [38] have permitted a considerable improvement of rovibrational energy predictions for several isotopologues.

Carter, Sharma and Bowman [34] computed ethylene DMS at the MP2/cc-pVTZ level of the theory over 22 219 nuclear configurations and reported line intensities in the range below 3200 cm -1 . To our knowledge these were the only ab initio intensities reported for ethylene. Although their study was encouraging with a good agreement for the fundamental bands [34] giving a typical accuracy of ∼10-20% , the corresponding DMSs have not been published.

In this work we compute new DMSs with larger electronic basis set at extended grid of points. For this purpose, we applied coupled cluster approach including single and double excitations [39] with the perturbative treatment of triple excitations, usually denoted as CCSD(T) method [40] that has proven its efficiency for high-resolution spectroscopy applications in recent years (see 18,19 and references therein).

Calculations were carried out using well established Dunning's correlation consistent basis sets cc-pVQZ [41]. In addition, explicitly correlated calculations, which are expected to improve the basis set convergence of CCSD correlation energies, were considered for comparison purpose. A second set of DMS surfaces was calculated at the CCSD(T)-F12 level of the theory combined with specially optimized correlation consistent F12 basis set cc-pVTZ-F12 [42]. As generally advised, CCSD(T)-F12a method was employed with this VTZ-F12 basis set. The Molpro program package version 2010.1 [43] was used to carry out all the ab initio calculations of electronic ground state energies. Dipole moments were computed as the derivative of the energy with respect to the weak external uniform electric field using the finite difference scheme with the field variation of ±0.001 a.u. around at the zero field strength. The dependence of the dipole moments on the size of finite steps external field derivatives was not significant in the range of 0.002 -0.0001 a.u. We have checked this for various nuclear configurations with three field variation steps: 0.0001, 0.001 and 0.002 a.u. This gave relative differences in the determined dipole moment values of the order of 10 -5 or 10 -4 .

Most of the calculations were done using the regional "Romeo" multiprocessor computer (Reims), "IDRIS" computer center of CNRS in Orsay and "JADE" cluster at CINES computer center in Montpellier. As a first step for the DMS construction, the dipole moment values in the electronic ground state were calculated with cc-pVQZ basis set on a grid of the 82 542 nuclear configurations described in Ref. 38. The distribution of the density of the DMS geometrical configurations which corresponds to the same grid choice as for our PES has been given in Fig. 1 of Ref. 38, with a maximum number of configurations near 5000-7000 cm -1 but a significant number of points extends up to 12 000-13 000 cm -1 . The number of contracted functions was 178 for VTZ-F12 and 230 for VQZ bases. Full DMS calculations for these large basis sets were quite demanding in terms of computer resources. Altogether, these calculations took about 90 000 hours (CPU time) for VTZ-F12 basis and 180 000 hours for VQZ basis.

In this work, we used our best equilibrium geometry parameters values r

He = 1.080565 Å , r Ce = 1.330898 Å, α e = 121.40176 Degrees [Table I of Ref. 38],
obtained by an empirical optimization as described in Ref . 38]. As already pointed out in previous works, these parameters are of primary importance for accurate description of rotational spectra, and were fixed to the same value for all calculations involving different basis sets.

The DMS components µ α in the molecular fixed Eckart frame were repre-sented as power series of normal modes coordinates q

i µ α (q 1 , q 2 , • • • , q 12 ) = n K n α B p n (q k ) (1)
where

k ∈ {1, 2, • • • 12} and α B p n (q k ) = (q p1 1 Ag q p2 2 Ag q p3 3 Ag q p4 4 Au q p5 5 B 2g q p6 6 B 2g q p7 7 B 2u q p8 8 B 3g q p9 9 B 3u q p10 10 B 3u q p11 11 B 1u q p12 12 B 1u
) Γα

(2)

with Γ α ∈ B 1u , B 2u , B 3u for α = z, y, x, p = 12 m=1 p m ∈ {1, 2, • • • 4}
and n is a string of low case indices in Eq. ( 2).

The shape of normal modes and the relation of rectilinear normal coordinate

with Cartesian ones were defined on the PES [38] computed at the same level of the theory. The techniques of related transformations have been described in the previous work [16] (and references therein). We fitted K n parameters of the DMS expansion (1) to our ab initio dipole moment values using the weight function that depends on energy E/hc expressed in cm -1

w(E) = tanh(-a(E -E 0 ) + b) 1 + b . ( 3
)
where a = 0.0005 cm, b = 1.002002002 and E 0 = 9000 cm -1 . With this weighting function, which has been originally employed by Schwenke and Partridge in Ref. 44 for the fit of methane PES, the weight of ab initio points decrease for electronic energies above the E 0 value.

In total 254 + 254 + 194 parameters up to fourth order were statistically well determined in this fit on the entire grid of all 3 × 82542 ab initio points.

The details of the fit as well as the number of parameters involved in the fit of each component µ α are given in Table 1. Note that the number of ab initio geometries was considerably larger than the number of fitted DMS parameters.

Figure 1 shows the VQZ DMS error distribution of the final fit. The fit errors (defined as ab initio dipole moment value minus the value of the analytical DMS representation) are quite small up to energies ∼ 9 000 cm -1 . A larger scatter of points above this range occurs because the weighting function (3) quickly de-emphasizes energies above this threshold [44]. In order to further improve the fit, it would be necessary to include some higher order terms in the DMS expansion (1). We plan to do this in a future work, but the fourth order should be sufficient to check the accuracy of the ab initio surfaces for the fundamental and low overtone and combination bands.

Both CCSD(T)/cc-pVQZ and CCSD(T)-F12a/cc-pVTZ-F12 ab initio DMSs fitted in normal modes coordinates up to fourth order are provided as the electronic Supplementary Materials of this work.

First principles variational intensity calculations: computational procedure

In order to check the accuracy of obtained DMSs we used these surfaces for rovibrational line intensities in the infrared. Rovibrational energies and wavefunctions were determined using our recent ethylene PES reported in Ref. 38, which is referred to as DNRST PES hereafter. As described in details in our previous works [16,38,19], the rovibrational model used in our homemade Tensor code is based on the complete normal-mode nuclear Hamiltonian in Eckart frame [45]. Besides providing all necessary transformations for a systematic symmetry- As described in details in previous works [16,38], rovibrational line posi-170 tions and intensities were obtained following a two steps procedure. First, band centers were calculated using F(9) basis of primitive normal mode vibrational functions satisfying the condition

F (v max ) ⇔ i κ i v i ≤ v max .
When available, vibrational J = 0 levels were matched to observed band centers [29,33] using the VSS empirical corrections [16,38]. In order to make rovibrational calculations up to J = 30 feasible, we employed at the second step (J > 0) the eigenfunctions

Comparisons of ab initio intensities with empirical values and with spectroscopic databases

An example of the comparison of predicted spectra using DNRST PES [38] and our ab initio DMSs with empirically based HITRAN line list of 12 Figure 2: Comparison of spectra calculated from ab initio DMS using VQZ and VTZ-F12 basis sets with HITRAN 2012 and with latest experimental spectra analyzes [33] in 650 -800 cm -1 region. In all calculations the DNRST PES [38] was used for line positions and vibration-rotation basis functions.

Figure 3: Comparison of spectra calculated from ab initio DMS using VQZ and VTZ-F12 basis sets with HITRAN 2012 and with latest experimental spectra analyzes [33] in 850 -1100 cm -1 region. In all calculations the DNRST PES [38] was used for line positions and vibration-rotation basis functions.

and with the results of recent analyzes [33] of high-resolution experimental spectra in three ranges. On these scales both VQZ and VTZ-F12 DMSs give very similar band shapes.

Due to better accuracy of our PES [38] and to the technique of VSS band center shifts [16] in two-step variational calculation, the deviations between calculated and observed line positions up to J = 30 appears to be of the order of 0.1 cm -1 .

This allows better description of accidental rovibrational resonances than in previous theoretical studies. Figure 6 illustrates the line to line matching in the ν 10 -ν 7 range.

Carter et al. [34] have reported good qualitative agreement for fundamental bands with some exceptions. They pointed out problems with the ν 10 band in HITRAN suggesting mis-assignments. Here we confirm their finding concerning unsatisfactory representation of ν 10 in HITRAN. Indeed the HITRAN intensities were too low and many of high-J transitions were missing in the center of the band and in the band edges that is clearly seen in Figures 2 and5. However irregular strong lines (example at 951 cm -1 ) appear here not because of misassignments but due to resonance intensity borrowing as further discussed in Section 5. This conclusion is supported by recent results of new experimental spectra analyzes [33] which are in excellent agreement with our calculations (Figures 2 and5).

Table 2 summarizes integrated intensities for six fundamental C 2 H 4 bands for which the results of line-by-line high-resolutions spectra analyzes have been included in HITRAN database [8]. Integrated intensity in a range R is the sum

S = Si(min)
i in R S i of line intensities S for all calculated or observed transitions in this range. The cutoff S i (min) = 1.10 -26 cm/molecule was applied for all bands. This accounts for the major part of the opacity at room temperature conditions.

For known fundamental bands in case of VTZ-F12 DMS the deviations from empirical integrated intensity data (up to J = 30) range from 0.3% to 7%. The strongest ν 7 band deviates by 2.5% only. This is unprecedented accuracy of ab initio results for six-atomic molecules. Note that the RMS deviations in Table 2 and in further tables should not be entirely attributed to the errors in ab initio calculations as all available observed and empirical line lists used for the comparisons contain their own uncertainties which could amount to several percent as well. Another possible source of discrepancies is related to interference intensity effects among various bands, which are treated somewhat differently in experimental data reduction and in global theoretical predictions.

For the total absorbance by six fundamentals accounting for 13 663 assigned rovibrational transitions (last line in Table 2) the difference with empirical data drops down to about 1%.

Second type of tests concerns interval-by-interval comparison of integrated

intensities with low-resolution measurements (Table 3). Lebron and Tan [46] have reported Fourier transform experimental determination of the absorbance area in ethylene infrared spectra at a resolution of 0.5 cm -1 with various gas pressures. They have distinguished five spectral intervals given in Table 3 where the ethylene infrared opacity was the most significant.

The advantage of such comparison is that this implicitly involves contributions from line of all bands in the considered range including weak overtone, combination and hot bands which are not yet analyzed in high-resolution ex- , line positions RMS errors (last column) are in cm -1 . All "empirical" rovibrational lines assigned to known fundamental bands are taken from HITRAN-2012 database [8] except for ν 10 . a For ν 10 empirical data are replaced by recent more accurate analysis [33]. b Number of lines used for the calculation of integrated band intensities. c Relative deviations [(S emp -S calc )/S emp ] in % between empirical line lists and variational calculations using ab initio PES and DMSs. c Deviations between empirical and calculated line positions up to J = 30. a In wavenumbers cm -1 . b Bands providing main contributions to considered interval. c Measured by the total absorbance area in each interval [46]. d Obtained as a sum of VQZ ab initio line intensities for all bands contributing to each interval up to J max = 30. e Relative deviations [(S obs -S calc )/S obs ] in % between Ref. [46] and calculations for integrated line intensities. periments. Also, this permits getting round very tedious line-by-line analyzes of rotationally resolved spectra and in a sense compensate incompleteness of HITRAN-like databases. For the comparison of Table 3 we have included between 2 and 10 times more theoretical lines than those presently available in HITRAN depending on the range. This gives an idea of a lack of information for ethylene data in existing databases. A shortcoming of the low resolution method is that it is locally less accurate and that contributions of impurities could hardly be totally excluded.

Bearing in mind above considerations, the agreement of our ab initio results with low-resolution Lebron and Tan measurements is also very good, particularly for the most absorbing regions 640 -1200 cm -1 and 2920 -3260 cm -1 were the deviations are of 0.75% and of 4%, respectively. In the middle ranges 1340 -1540 cm -1 and 1820 -1950 cm -1 the low resolution measurements show slightly larger absorption but could possibly be biased by a contribution of water vapor due to very large and strong ν 2 band centered at about 1600 cm -1 .

Finally we compared our intensities with previous ab initio results [34].

Carter et al. [34] have published large table including their calculated tran-sitions for J = 0, 1, 2 for six bands ν 7 , ν 8 , ν 11 , ν 12 , ν 2 + ν 12 and 2ν 10 + ν 12 . They qualify their absolute intensities as quite acceptable. The agreement for strong bands was better than for the overtone bands where some lines were off up to 15-20 cm -1 in positions and up to factor 2-3 in intensities. In Table 4 we summarize these results by adding intensities of lines belonging to the same bands.

This gives a sort of smoothing effect for outliers due to weaker lines. For the same reason the contributions at the highest range 2980 -3125 cm -1 including two combination bands were summed up. With this averaging of J = 0, 1, 2 transitions the deviations of Carter et al. [34] from empirical data are in the range from 7% to 25% that can be considered as a good match for the first ab initio results. With our DMS the discrepancies for the same sample of data fall down to the range 0.4%-3% (Table 4).

Discussion and summary

After the pioneering work of Carter et al. [34], this study presents further improvement in theoretical predictions of ethylene intensities in the infrared.

Few percent of Emp.-Calc. in Tables 2, 3, 4 are of the same order of magnitude as typical uncertainties of line intensity measurements and as errors in empirical models of experimental data reductions. In the Supplementary Electronic Materials we provide 12D ab initio DMSs that permit the accuracy of first principles intensity calculations comparable with available experimental precision. To our knowledge such a step forward in the computational spectroscopy becomes possible for the first time in case of rotationally resolved spectra of hexatomic molecules. Also, the improved accuracy permitted resolving some controversial issues in qualitative intensity behavior. The first one concerns the intensity repartition between P and R branches depending on the band type. The P/R ratio for the strongest lines was not the same for certain bands in HITRAN and in the previous ab initio calculations [34]. For example, for the ν 11 band the theoretical predictions of Ref. 34 gave weaker P-branch (P/R<1) in agreement with HITRAN, whereas the opposite results occurred for the ν 12 band: (P/R<1) in HITRAN and (P/R>1) in ab initio calculations [34]. In the present study the P/R ratios are in agreement with experimental data for all investigated bands. For example in the ν 12 band we have the intensity ratio for the strongest lines (P/R) ab initio ν12 = 0.957 that agrees well with the empirical ratio (P/R) HIT RAN ν12 = 0.958. The corresponding calculated transitions are J, K a , K c = 10, 0, 10 → 9, 0, 9 at 1425.015 cm -1 in P-branch and 10, 0, 10 → 11, 0, 11 at 1461.701 cm -1 in R-branch. Note that the errors in our line position calculations for these transitions were only about 0.001 cm -1 .

The second controversy concerned irregular lines of the ν 10 band. Carter et al. [34] attributed the most intense HITRAN line of ν 10 at 951 cm -1 to an experimental mis-assignment as this did not appear in their calculated Fig. 11 of ν 10 [34]. By investigation of the wavefunction mixing coefficients we conclude that this is a case of so called "unstable transitions" [15,22] whose intensities are known to be extremely sensitive to the accuracy of the PES and of the energy level calculations. In our calculations the upper state level (J, K a , K c ) ν10 = (18, 6, 12) at 1273.37 cm -1 of this transition is in accidental Coriolis resonance with the nearby level (J, K a , K c ) ν7 = (18, 2, 17) at 1273.60 cm -1 . A very small energy difference of only 0.23 cm -1 between these two upper state levels produces a strong resonance coupling between corresponding ν 10 and ν 7 rovibrational states. In our calculations we have the normal mode decomposition for the wavefunction ψ V 10 (70%) + V 7 (21%) + ... of the first level. Consequently the line J, K a , K c = 18, 1, 17 → 18, 6, 12 with the intensity I = 3.71 × 10 -21 at 951.279 cm -1 has to be attributed to the ν 10 band according to the major normal mode coefficient. This line appears as anomalously strong one due to the resonance intensity transfer from the line J, K a , K c = 18, 1, 17 → 18, 6, 12 of ν 7 at 951.066 cm -1 that has the intensity I = 1.19×10 -20 . At this point we only partly confirm the statement of Carter et al. [34]: the effect of the intensity mixing with ν 7 indeed occurs but the first anomalously strong line at 951.279 cm -1 belongs to the ν 10 band according to the wavefunction projection in agreement with HITRAN. The most recent new experimental spectra analysis [33] in this range confirms our conclusion as seen in Figure 4. Note that in our calculation the position error is below 0.001 cm -1 for the first ν 10 line and below 0.01 cm -1 for the second ν 7 line.

In higher energy ranges a correct description of "unstable lines" is a major challenge in computational spectroscopy both for first principle calculations and for assignment of crowded experimental spectra using effective polyad models [28,30,29,31,32]. In the first case small errors of few wavenumbers in energy levels would false the effects of "resonance intensity borrowing". On the other hand it is well known that the second types of methods suffer from ambiguity [47,48,49] of an empirical determination of the resonance coupling parameters responsible for these effects. One of possible solutions would be applying a mixed "ab initio → polyad model" approach, that permits characterizing various resonance couplings using ab initio information as was recently discussed for methane spectra [22].

This Letter was focused essentially on accurate DMS calculations and on the analytical surface model parametrization. More detailed comparisons with recent experimental data [31,33] are planned in future works together with the study of nuclear basis convergence effects. Extended nuclear motion calculations using independent theoretical methods would help to produce accurate and sufficiently complete theoretical line lists in large infrared range for assignments and analyzes of experimental spectra.

Acknowledgments

The supports of the CNRS (France) and RFBR (Russia) in the frame of Laboratoire International Associé SAMIA , of Tomsk State University Academic D.

Mendeleev funding Program, of IDRIS/CINES computer center of France and of the ROMEO computer center Reims Champagne-Ardenne are acknowledged.

  m p o n e n t Y c o m p o n e n t Z c o m p o n e n t F i t e r r o r / a . u . W a v e n u m b e r / c m -1

Figure 1 :

 1 Figure 1: Errors of the ethylene DMS fit to ab initio values computed with the CCSD(T)/cc-pVQZ ansatz. Components x, y, z are represented in red, green and blue, respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

  schemes. With such basis size the rovibrational line positions would not yet be fully converged for high vibrational excitations. However, the previous work on phosphine and methane molecules has shown that this should not have a big impact on fundamental and low overtone and combination bands, particularly for integrated band intensities.

C 2 H 4

 4 for fundamental bands in the 600 -3200 cm -1 range is given in Figures2, 3 and 4. Globally, all calculations with VQZ and VTZ-F12 basis sets are in a very good agreement with experimental intensities. In order to compare integrated intensities we extended line calculations up to rotational quantum number J = 30. In Tables 2, 3 and 4 integrated intensities in the ranges of fundamental bands are collected at 296 K and compared with various empirical data including HITRAN-2012 database, Lebron et al.[46], Bourgeois et al.[33] and with ab initio results of Carter et al.[34]. In all cases we use the HITRAN intensity units cm/molecule. Natural abundance factor 0.97729 of 12 C 2 H 4 was taken into account in all our calculated intensities.First type of comparisons concerns rotationally resolved spectra. Figures2, 3, 4show a very good overall agreement of our line-by-line intensity calculations using ab initio VQZ and VTZ-F12 DMS with HITRAN spectroscopic database[8]

Fig. 2

 2 corresponds to the lowest edge of infrared active 205 ethylene bands, Fig. 3 to ν 10 wagging mode, ν 7 out-of-plane and ν 4 twisting vi-

Figure 4 :

 4 Figure 4: Comparison of spectra calculated from ab initio DMS using VQZ and VTZ-F12 basis sets with HITRAN 2012 in 2900 -3250 cm -1 region. In all calculations the DNRST PES [38] was used for line positions and vibration-rotation basis functions.

Figure 5 :

 5 Figure 5: Comparison of the ν 10 band of C 2 H 4 calculated from ab initio DMS using VQZ and VTZ-F12 basis sets with HITRAN 2012 and with latest experimental spectra analyzes[33] in 600 -1100 cm -1 region. In all calculations the DNRST PES[38] was used for line positions and vibration-rotation basis functions. It is clearly seen that HITRAN intensities were underestimated by about 30% with respect to new experimental analyzes and to our ab initio results.

Figure 3

 3 Figure 3 and 4 correspond to the ranges of the strongest ethylene absorbance.

Figure 6 :

 6 Figure 6: Comparison of spectra calculated from ab initio CCSD(T)/VQZ DMS with HI-TRAN 2012 in 935 -958 cm -1 region. In our calculation the DNRST PES [38] was used for line positions and vibration-rotation basis functions. The VSS band center shift of -0.74 cm -1 was applied for ν 7 .

Table 1 :

 1 Statistics for the fit of ab initio points with analytical DMS representations for the two basis sets. Component a StDev b VQZ W-StDev c VQZ W-StDev c VTZ-F12 nb. param. Symmetries labeled with respect to I r representation. b Standard deviations between ab initio values and DMS analytical representation, in Debyes. c Weighted standard deviations between ab initio values and DMS analytical representation, in Debyes.

	d

d Number of parameters in analytical representation used for the surfaces fit.

Table 2 :

 2 Comparison of ab initio integrated intensities S is for fundamental bands using VTZ-F12 and VQZ DMSs with empirical data deduced from high-resolution analyzes of rotationally resolved C 2 H 4 spectra up to J = 30. Intensities are in HITRAN units cm.molecule -1

			S is			Diff.(%) c	RMS d
	Band	VTZ-F12	VQZ	Empirical	Nb. trans. b VTZ-F12 VQZ pos.
	ν 4	1.325×10 -19 1.313×10 -19 1.304×10 -19	461	-1.62	-0.66 0.056
	ν 7	1.190×10 -17 1.187×10 -17 1.161×10 -17	3010	-2.50	-2.19 0.080
	ν 10 3.497×10 -19 3.509×10 -19 3.674×10 -19a	4217	4.82	4.49 0.086
	ν 12 1.364×10 -18 1.321×10 -18 1.463×10 -18	2378	6.75	9.69 0.062
	ν 9	2.879×10 -18 3.097×10 -18 2.979×10 -18	2365	3.34	-3.98 0.131
	ν 11 1.734×10 -18 1.752×10 -18 1.738×10 -18	1232	0.24	-0.80 0.160
	Sum 1.836×10 -17 1.852×10 -17 1.829×10 -17	13663	-0.38	-1.26 0.070
	Note:

Table 3 :

 3 Interval-by-interval comparison of ab initio C 2 H 4 integrated intensities with low resolution measurements of Lebron and Tan [46]. 3260 ν 9 , ν 11 , 2ν 10 + ν 12 , ν 2 + ν 12

	Ranges a	Principal bands b	Empirical [46] c This Work d Diff.(%) e
	640 -1200	ν 7 , ν 10 , ν 4 ,...	1.33×10 -17	1.34×10 -17	0.75
	1340 -1540	ν 12 ,...	1.66×10 -18	1.48×10 -18	10.84
	1820 -1950	ν 7 + ν 8 ,...	8.75×10 -19	7.27×10 -19	16.91
	1990 -2100	ν 6 + ν 10 ,...	1.04×10 -19	1.07×10 -19	-2.88
	2920 -6.50×10 -18	6.76×10 -18	-4.00
	Sum		2.24 ×10 -17 2.25 ×10 -17	-0.45
	Intensities are in cm.molecule -1 .

Table 4 :

 4 Summed up intensities of J = 0, 1, 2 ethylene transitions: comparison between ab initio predictions and HITRAN empirical data in the range of fundamental bands. is per band or per interval of all line intensities from TableVof Ref. 34. b The same sample computed with our VQZ DMS. c The same sample with empirical data from HITRAN-2012 database. d Relative deviations [(S emp -S calc )/S emp ] in % between HITRAN and calculations. e Wavenumber range in cm -1 including ν 2 + ν 12 and 2ν 10 + ν 12 combination bands.

		S is		Discrepancies (%) d
	Range	Carter [34] a This Work b	Hitran c	Carter [34] This Work
	ν 7	1.26 ×10 -19 1.12×10 -19 1.14×10 -19	-12.46	-1.93
	ν 12	1.47 ×10 -20 1.36×10 -20 1.37×10 -20	-7.89	-0.35
	ν 9	2.24 ×10 -20 3.01×10 -20 3.07×10 -20	25.53	-2.24
	ν 11	1.36 ×10 -20 1.61×10 -20 1.66×10 -20	15.13	-3.14
	2980 -3125 e 3.97 ×10 -20 5.22 ×10 -20 5.18 ×10 -20	23.95	0.79
	Note: Intensities are in cm.molecule -1 .

a S

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://www.sciencedirect.com/science/article/pii/S0009261415007319.

Both CCSD(T)/cc-pVQZ and CCSD(T)-F12a/cc-pVTZ-F12 ab initio DMSs fitted in normal modes coordinates up to fourth order are provided.


Othman Omikrine Metalssi
email: othman.omikrine-metalssi@ifsttar.fr

Bruno Godart
email: bruno.godart@ifsttar.fr

François Toutlemonde
email: francois.toutlemonde@ifsttar.fr

Effectiveness of Non-Destructive Methods for the evaluation of structures affected by Internal Swelling Reactions: Electric, seismic and acoustic methods

Keywords: Nondestructive Testing, Structural Testing, Wave Propagation, Mechanical, Materials Behaviors Topic : Civil Structures Testing, Structural Test Society for Experimental Mechanics, Inc. Experimental Internal Swelling Reaction, AAR, DEF, ND Techniques, Concrete structures durability, assessment of structures, structures survey

Internal swelling reactions (ISR) (which mainly comprise alkali-silica reaction, alkali-carbonate reaction, delayed ettringite formation, etc) are pathologies that affect the long term durability of concrete structures. The reactions are apparently characterized by series of closely spaced, tight map cracks with wide cracks appearing at regular intervals and excessive tensile stresses in rebars. This phenomenon is alarming for affected structure managers as it deals with people safety and structures operation. Moreover, there is no easily implemented way to stop the reactions. Prediction of concrete expansion, structural degradation and assessment of efficiency and periodicity of repair works are crucial issues.

The aim of this work is to explore the applicability of some Non Destructive Techniques (NDT) of investigations (electric, seismic and acoustic methods) to differentiate the structure zones affected and not affected by the ISR for different exposure conditions. The results highlight that the coupling between some of those ND Methods can reduce the measurement uncertainty and eliminate the factors that may influence the characterisation of the structure parts affected by the ISR. Nevertheless, for the complete structure reassessment, it is desirable to also refer to global geometrical/topographical survey and to destructive analysis methods on some cored samples for chemical analysis, petrography and dimensional measurements.

Introduction:

Internal swelling reactions (ISR) can affect concrete structures by causing cracking and material expansions which lead to degradation of structures mechanical behaviour. These pathologies mainly consist in alkaliaggregate reaction (AAR) and/or delayed ettringite formation (DEF). These chemical reactions can cause internal disorders non directly visible, and external disorders that may be observed at the surface of structures [START_REF] Divet | Les réactions sulfatiques internes au béton : contribution à l'étude des mécanismes de la formation différée de l'ettringite[END_REF][START_REF] Larive | Apports combinés de l'expérimentation et de la modélisation à la compréhension de l'alcaliréaction et de ses effets mécaniques[END_REF][START_REF]Aide à la gestion des ouvrages atteints de réactions de gonflement interne[END_REF][START_REF]Manuel d'identification des réactions de dégradation interne du béton dans les ouvrages d'art[END_REF] .

The visual measurements of the cracking index and the relative distance measurement are currently used to characterize the overall cracking and the global swelling. Following the survey methodology based on these informations, the structural diagnosis approach is well controlled and documented [START_REF]Méthodes de suivi dimensionnel et de suivi de la fissuration des structures[END_REF][START_REF] Li | Modélisation chimico-mécanique du comportement des bétons affectés par la réaction d'alcali-silice. Expertise numérique des ouvrages d'art dégradés[END_REF] . Moreover, these informations are quantitatively used for the numerical analysis of the structure in its present state and prognosis validation of possible repair [START_REF] Baghdadi | Modélisation du couplage chimico-mécanique d'un béton atteint d'une réaction sulfatique interne[END_REF][START_REF] Omikrine-Metalssi | Integration of contact elements in RGIB-modulus of the Finite Element program « CESAR-LCPC » : application to structures affected by internal swelling reactions[END_REF][START_REF] Omikrine-Metalssi | Integration of contact elements and creep in RGIB-modulus of the Finite Element program "CESAR-LCPC": Application to structures affected by internal swelling reactions[END_REF][10] . However, it requires monitoring over time and the condition of the structure must have reached a sufficiently advanced level to take the decision to monitor the structure effectively.

On the other hand, Non Destructive Techniques (NDT) could be interesting in the case of a preliminary diagnosis before the occurrence of visible disorders due to ISR at a given time of the structure-life when the sensitivity of the structure or risk analysis based on general documentation rise such a concern. In fact, it would be interesting to develop a NDT-based diagnosis methodology by comparing two areas made of the same concrete within the structure that may be respectively affected and not affected by the ISR (possibly due to different exposure conditions). This method would be instantaneous and could help rapidly evaluate a large number of structures. However, it is clear that this preliminary NDT diagnosis should be confirmed by microscopic examination, petrography and chemical analysis of some cored samples.

Presently, there are still no reliable procedures involving non-destructive techniques for the characterization and assessment of damage associated with ISR. Therefore, very few structures have been monitored by NDT methods and laboratory research has been mainly limited to the methods of ultrasonic waves velocity measurements [11][12][13][14][15] . This paper aims to describe and qualify the electric, seismic and acoustic NDT methods that could be used to measure some characteristic parameters of the causes and consequences of ISR at the material scale, aiming at a preliminary diagnosis approach.

Presence of water in the heart of the material (at a saturation degree above 80% for ASR, possibly 90% for DEF) is a condition which is apparently necessary for the chemical reactions to occur 16,17 . Electric, seismic and acoustic methods are sensitive to this parameter but also to changes of the elasticity modulus E and to the presence of cracks caused by ISR development. Indeed, the ISR induces mechanical alterations with a decrease -4 -of elasticity modulus E and evolution of the tensile and compressive strengths [START_REF] Baghdadi | Modélisation du couplage chimico-mécanique d'un béton atteint d'une réaction sulfatique interne[END_REF] . The effectiveness of electric resistance, mechanical wave propagation and seismic tomography methods for the evaluation of structures affected by ISR has thus been studied and is discussed in the following.

Electrical and electromagnetic methods

Water content has a critical influence on concrete durability and its evaluation is necessary for the prediction of structure aging. Water in concrete pores makes it possible for some endogenous chemical reactions to occur leading to concrete cracking, such as AAR and DEF. Furthermore, this presence of water in concrete structures is important for other processes engaging the structures durability as the penetration of chloride ions and/or concrete carbonation which are two causes of embedded steel corrosion. For those reasons, concrete water content on site evaluation is highly desirable.

However, the electrical and electromagnetic methods are sensitive to this moisture content of the material and to the ion concentration in the pores solution, even if they can permit to characterize the internal chemical processes in the concrete. In this context, three techniques have been tested and discussed: radar technique, capacitive method and electrical resistivity measurement.

Radar

Ground Penetrating Radar (GPR) is a geophysical non-destructive testing technique for the evaluation of structural elements and materials and is very useful for the detection of embedded objects (steel reinforcement, prestressing/post-tensioning strands, ducts, etc…), material interfaces (such as a slab to sub-base interface), and significant internal defects such as large voids and flaws in concrete 18,19 . The technique involves the use of a high-frequency radar antenna which transmits electromagnetic radar pulses along a longitudinal scan at the surface of the concrete. The frequency of the antenna will provide deeper scans with less detail or shallower penetration depths with more detail. This method is based on measurement of the propagation time and the waves attenuation that are either reflected on a steel reinforcement or on the opposite side of the concrete structure, or transmitted at the surface between the transmitter and receiver. This latter configuration has the main advantage of not being dependent of any reflector, whose position, form or nature is never completely controlled. The depth of investigation depends on the material, its condition and on the frequency of measurement used. For a "normally dry" concrete, it can exceed one meter depending on the frequency.

Many research teams have studied the influence of the propagation velocity of radar pulses and their amplitude versus the water and chloride content of concrete [20][21][22] . Indeed, they noticed the high sensitivity of these two electromagnetic observables, namely waves velocity and amplitude decrease when the water content increases. As regards more particularly the chloride content, there is a greater attenuation of the signal amplitude because the material becomes more conductive.

However, little information is available on radar tests performed on concrete structures affected by ISR. Some works have shown that the expansion of some structures leads to damping of the wave amplitude. Their interpretation is that the ISR generates micro-cracks which increase the porosity and therefore the water content.

To study the effectiveness of the GPR technique in detecting structure zones affected by ISR, a series of measurements was carried out on a bridge located in Northern France. This bridge is affected by ISR on one side of its pier caps, caused by water infiltration [START_REF] Klysz | Auscultation non destructive du chevêtre du pont de la Marque (59) : combinaison de techniques[END_REF] .

The GPR technique was applied along two horizontal profiles of 12.60 m long at the middle of transverse reinforcement, so sixty points measurement in total have been carried out.

The measurements presented in Figs 1 and2 show the effects of ISR, in the zones where it has been detected, on the amplitude and the estimated dielectric constant which is directly deduced from the velocity of the direct wave. Two zones can be highlighted from these observables which correspond to those characterizing the presence or absence of ISR in the pier cap. Indeed, the zone located beyond 9 meters is potentially affected by ISR since the amplitude of the radar waves is clearly damped in this zone compared to that not affected (where this amplitude remains almost constant). These results are confirmed by the measurements of the dielectric constant which show that this last one becomes important in the affected zone of the pier cap (Fig. 2).

These results are confirmed by the study of Rivard et al [START_REF] Rivard | Assessing alkali-silica reaction damage to concrete with non-destructive methods: From the lab to the field[END_REF] which shows a variation of about 75% between the measured amplitude of a non affected concrete and the zone most affected by the ISR.

The attenuation of the Radar waves amplitude is particularly due to the micro-cracking generated by ISR leading to an increase in porosity and to the increase in water content of concrete which occur by adsorption. Thus, the dielectric polarization and electrical conduction become higher which explains the dielectric constant increasing (Fig. 2).

The use of the radar technique can delimit suspicious zones in the structures. As the electromagnetic waves are sensitive to local variations in the concrete mix-proportions, current knowledge does not distinguish the presence of the ISR from other ageing phenomena. However, signs of decrease in wave velocity and amplitude in all cases are associated with high water presence (which may be associated to chlorides attack or ISR), and therefore may be associated with a pathology risk. The radar technique should be used to target zones to be studied more precisely, either with other non-destructive techniques, or by destructive methods investigations (on cored samples taken from suspicious zones).

Capacitive methods

The capacitive method for measuring moisture is based on the functional relationship between the permittivity of a substance and its moisture content. Permittivity is determined from the value of the capacitive transducer which is filled with the tested substance. The value of this transducer, including its dielectric loss, is determined by comparing it with a parallel tuned circuit which comprises inductance and capacitance, and is coupled through an inductance or a capacitance to a high-frequency generator 19 .

The principle of this technique relies on measuring the resonant frequency of an oscillating circuit (around 30-35 MHz) between two electrodes placed on the concrete. If we consider these two metal electrodes, they form with the surrounding material a dielectric capacitor, the capacity depends on the geometry of the electrodes and on the value of the relative dielectric constant of the material. In practice, this results in a resonant frequency that varies depending on the dielectric nature of concrete, which is mainly related to its water content, the nature of aggregates and the W/C ratio 19 .

Capacitive measurements were performed on concrete slabs (50*25*12 cm) with different W/C ratio (0.30, 0.45, 0.55, 0.65, 0.90) in order to evaluate the dielectric permittivity. The results show that for all the specimens tested in this study, the capacitive measurements vary linearly and depend on concrete texture [START_REF] Villain | Complémentarité de techniques non destructives pour déterminer les propriétés de différents bétons hydrauliques[END_REF] (Fig. 3).

Until now, there is no example in the literature about capacitive results on concrete affected by ISR. The technique seems to be complementary of the radar technique in the sense that it can be carried out at lower frequency (~35 MHz) in a zone where the permittivity changes are important and where it can give an idea about the evolution of the saturation degree with depth.

(Figure 3)

Electrical resistivity

The electrical resistivity is the ability of a medium to oppose the passage of an electric current. The measurement principle consists in injecting an electric current through the concrete and measuring the electrical response of the medium (resistance or potential difference). It is a direct current with a very low frequency (static regime).

According to the application case, this measure involves two or four electrodes.

The resistivity is sensitive to a number of parameters related to the nature and condition of the medium. These include: the mineralogical nature of cement, aggregates and additions, the relative proportions of these components, the porosity, the water content and salinity of the pore solution, the temperature. Thus, logically the -7 -resistivity depends on the W/C ratio and on the compressive strength (the latter being correlated to the porosity of concrete). The resistivity also depends on structural features (normal and pathological) being able to prevent or to promote the current flow, e.g. the presence of reinforcement or cracking.

According to the concrete mix-design, age and exposure conditions, the resistivity varies in a range covering several decades (from some Ω.m for the fresh concrete to thousands of Ω.m for an old and very dry concrete).

The resistivity should be therefore an appropriate and sensitive physical quantity to characterize a concrete, particularly its water content, its cracking state and the presence of chemical agents.

Currently, resistivity techniques are mainly applied, in addition to other techniques, to detect areas of possible corrosion of steel reinforcement [START_REF] Breysse | Méthodologie d'évaluation non destructive de l'état d'altération des ouvrages en béton[END_REF][START_REF] Polder | RILEM TC 154-EMC: Electrochemical techniques for measuring metallic corrosion -Test methods for on site measurement of resistivity of concrete[END_REF][START_REF] Lataste | Évaluation Non Destructive de l'état d'endommagement des ouvrages en béton armé par mesures de résistivités électriques[END_REF] . New applications are developed and used also to map the surface of a concrete and detect areas of resistivity contrasts.

The publications related to ISR diagnosis using electrical resistivity measurements are very few [START_REF] Lataste | Évaluation Non Destructive de l'état d'endommagement des ouvrages en béton armé par mesures de résistivités électriques[END_REF] . Only Rivard and Saint-Pierre appear to have conducted a pilot program with the necessary precautions [START_REF] Rivard | Assessing alkali-silica reaction damage to concrete with non-destructive methods: From the lab to the field[END_REF] . Their results do not distinguish clearly the concrete affected by ISR. Their analysis is that resistivity is sensitive to several parameters, the effects of which compensate each other in the presence of ISR. Fig. 4 shows an example of result which highlights the effect of the dry density and the water content on the electrical resistivity of the material [START_REF] Beck | Evaluation de l'état hydrique d'un sol fin par méthodes électriques et électromagnétiques : Application géotechnique[END_REF] . Indeed, the ISR development is favoured by a high water content and the presence of alkaline agents 20 . These two factors contribute in principle to reduce the resistivity. However, the chemical processes of ISR lower the concentration of alkali on one hand, and produce an electrically resistant gel on the other hand. Moreover, the cracking induced by the swelling of the concrete, and the filling of the cracks by the gel contribute to the increase in resistivity.

At first, Rivard et al. [START_REF] Rivard | Suivi et caractérisation de la RAG par techniques non destructives[END_REF] have made preliminary measurements of resistivity. They have shown a good correlation between resistivity and compressive strength, and especially a small but significant time evolution of the resistivity of the "reactive" slabs versus the "non reactive" slabs. The cracks filled with gel would help to increase the apparent resistivity in opposing the current flow.

The same authors estimate that the anisotropy of resistivity is correlated to the expansion degree of the specimens studied: the resistivity anisotropy is induced by the cracking degree of damaged concrete and is therefore a possible indicator of the induced cracking [START_REF] Rivard | Couplage de méthodes non destructives pour l'évaluation de l'endommagement du béton[END_REF] . However, the measured apparent resistivities appear to have decreased with this expansion [START_REF] Klysz | Auscultation non destructive du chevêtre du pont de la Marque (59) : combinaison de techniques[END_REF] .

(Figure 4) [START_REF] Klysz | Auscultation non destructive du chevêtre du pont de la Marque (59) : combinaison de techniques[END_REF] . This bridge is affected by ISR pathology on one side of the pier caps, activated by water infiltration. According to the authors, the profile of apparent resistivity along the cap allows observing significant variations (Fig. 5). The low apparent resistivity values (less than 120 Ω.m) coincide with the zone where ISR has developed and produced significant expansion. The local decrease of resistivity is explained by the higher humidity of concrete in the area affected by ISR. In fact, a high moisture degree is necessary to the ISR chemical process. In addition, higher humidity reduces the problems of electrode-concrete coupling and improves the quality of measurements [START_REF] Klysz | Auscultation non destructive du chevêtre du pont de la Marque (59) : combinaison de techniques[END_REF] .

(Figure 5)

In sum, studies linking the electrical resistivity to ISR phenomena in concrete are too few, and the available results and analysis have just permitted to delimit the affected zone of the structure.

Seismic and acoustic methods

The seismic and acoustic parameters are sensitive to certain physical properties and characteristics of concrete, but also to its composition and its microstructure. Indeed, all the contrasts and differences in shape, nature, size, density, mechanical properties in a structure have an influence on changes in wave propagation and hence in the ultrasonic measurements [START_REF] Sargolzahi | Effectiveness of nondestructive testing for the evaluation of alkali-silica reaction in concrete[END_REF] . ISR generates isotropic and/or anisotropic micro-cracks and ASR produces a gel which can change the propagation of mechanical waves with regard to a sound material.

Three techniques based on waves propagation have been investigated: ultrasonic volume waves, resonant frequency method and seismic tomography.

Measurement of ultrasonic volume waves in transmission

The most usual temporal ultrasonic technique consists in simple measurements. The inferred velocity of the waves in the material is the key parameter. The European standard (EN 12504-4) defines the method for determining the speed of ultrasonic waves in concrete [START_REF]Testing concrete in structures -Part 4: Determination of ultrasonic pulse velocity[END_REF] . This one may be related to the mechanical characteristics of the material and geometric characteristics of specimens. This requires a rigorous calibration [START_REF] Bungey | The validity of ultrasonic pulse velocity testing of in-place concrete for strength[END_REF] .

Correlations are often volatile and are valid in controlled conditions in terms of measurement and environment [START_REF] Jenkins | Non destructive testing: an evaluation tool[END_REF] .

The European norm (EN 13791) defines the conditions for establishing these correlations [START_REF]Assessment of concrete compressive strength in structures or in precast concrete products[END_REF] .

The velocity measurement has to be captured at the time signal of the first arrival. This measure can be relative (between two synchronous receivers) or not (between the source and one receiver). In the latter case the starting time of the wave must be known. The attenuation measurement consists of measuring the amplitude of the signal and quantifying its decrease. This less usual technique can also characterize the concrete, but industrial applications are not yet operational 15 . However, initial results suggest a high sensitivity of this parameter to changes in the concrete and particularly to the disorders resulting from the ISR. Indeed, these expansion phenomena lead to the appearance of cracks which change the sign of the wave velocities evolution from positive to negative values.

For the sake of qualification of this method, measurements of ultrasonic wave propagation have been performed on concrete samples with different expansion rates (0, 50, 75 and 100% of maximal sample expansion) [START_REF] Guedon | Recherche CEBTP-LCPC sur l'alcali-réaction : techniques de mesures[END_REF] . The states of degradation and degrees of micro-cracking of concrete could be distinguished. Indeed, the representation of the wave velocities over time may indicate the progression of cracking which is a consequence of swelling. When the evolution of the velocities is positive, it reflects the filling of cracks. Under the effect of internal stresses caused by the swelling reactions, cracks appear and lead to the change of sign of the wave's velocities evolution which becomes negative. The created cracks are sealed which causes further cracking and the crack-filling cycle continue, that reflects the oscillations observed in the results of measurements of ultrasonic wave velocity (Fig. 6).

(Figure 6)

Other tests have been performed on reactive and non-reactive concrete samples kept in two different environments (20 and 38 °C) [START_REF] Guedon | Recherche CEBTP-LCPC sur l'alcali-réaction : techniques de mesures[END_REF] . Fig. 7 shows that the propagation velocity of ultrasonic waves for non-reactive samples remains high in comparison with that of the reactive samples. This result is due to the changes in the concrete microstructure occurring with the ongoing expansive ISR (e.g., ASR gel product formation, ettringite formation and precipitation in the cracks, aggregate/paste debonding, cracking in the aggregate and paste). These observations have been confirmed by other authors who worked on in situ and laboratory concrete samples [START_REF] Saint-Pierre | Measurement of alkali-silica reaction progression by ultrasonic waves attenuation[END_REF][START_REF] Wardany | Condition assessment of concrete in hydraulic structures by surface wave non-destructive testing[END_REF] .

They have shown that the velocity wave propagation decreased very slightly with the concrete expansion which (in the studied case of ASR) varied from 0 to 0.2%. However, the results obtained on in situ cores are less convincing than those in the laboratory. Two explanations are proposed: the heterogeneity of in situ concrete is larger and uncontrolled as compared to laboratory concrete, and the non-representativeness of the core sampling, because concrete of the samples may have evolved once extracted from the structure [START_REF] Saint-Pierre | Measurement of alkali-silica reaction progression by ultrasonic waves attenuation[END_REF][START_REF] Wardany | Condition assessment of concrete in hydraulic structures by surface wave non-destructive testing[END_REF] .

(Figure 7) An other technique of data processing, namely the measure of the wave attenuation, seems relevant. The spectral response of the concrete specimen, subjected to an ultrasonic pulse, is measured in order to calculate the loss of -10 -spectral gain (i.e. the attenuation). All the studies in this domain confirm the significant reduction of volume waves in the presence of ISR, which means the attenuation increasing with the structure expansion [START_REF] Gudmundsson | Detection and mapping of alkali-silica damaged areas in concrete structures with nondestructive techniques[END_REF][START_REF] Nakagawa | Prediction method for properties of concrete on ultrasonic non-destructive testing[END_REF][START_REF] Hiroi | Experimental study on the long-term properties of prestressed concrete members affected by alkali-silica reaction (ASR)[END_REF][START_REF] Wang | Formulae for estimating AAR expansion in concrete structures based on ultrasonic pulse velocity measurement[END_REF] .

Resonant frequency method

The resonant frequency method is one of the most interesting techniques for structural health monitoring applied to civil engineering structures [START_REF] Doebling | Damage Identification and Health Monitoring of Structural and Mechanical Systems From Changes in their Vibration Characteristics: A Literature Review[END_REF][START_REF] Alvandi | Contribution à l'utilisation pratique de l'évaluation dynamique pour la détection d'endommagements dans les Ponts[END_REF][START_REF] Ren | Output-only Modal Parameter Identification of Civil Engineering Structures[END_REF] . The changes of the physical properties of the structure cause the variations of the modal parameters (mode shapes, resonant frequencies, modal damping) [START_REF] Siegert | Resonant frequencies monitoring of Alkali Aggregate Reaction (AAR) damaged concrete beams[END_REF] . Nevertheless, the capacity to detect a reduction of the stiffness resulting from ISR-induced damage depends on the environmental variability of the modal properties 48 .

The principle of this method is to check periodically the structure by the impact of the force hammer. The transmission of the wave is initiated on one side of the structure and the reception takes place on the opposite side by using an accelerometer positioned directly opposite the force hammer. The resonant frequencies caused by the force hammer allow characterizing the mechanical condition of the structure. Thus, this method relies on the feasibility of vibration based health monitoring in controlled conditions.

An experimental study was performed on six beams subjected to ISR [START_REF] Siegert | Resonant frequencies monitoring of Alkali Aggregate Reaction (AAR) damaged concrete beams[END_REF] . Possible ISR influence on the resonance frequencies of ultrasonic waves caused by a force hammer was checked. The six beams (reinforced and unreinforced) had been manufactured with reactive and non-reactive aggregates and had been equipped with a series of accelerometers 49 . The interpretation of the signals was carried out thanks to an analysis of the spectral density of acceleration measured [START_REF] Siegert | Resonant frequencies monitoring of Alkali Aggregate Reaction (AAR) damaged concrete beams[END_REF] (Fig. 8).

(Figure 8) Fig. 9 shows the evolution of ultrasonic waves frequencies with time. Before immersion in water, the resonant frequencies of concrete beams (reinforced and unreinforced) manufactured with non-reactive aggregates have turned out relatively constant and higher than those of beams with reactive aggregates (Fig. 9). Resonant frequencies of beams made with reactive aggregates show an early decrease that has reached 6 to 10% of initial values and then an increase with time. These results correspond to a loss of about 12 to 20% of stiffness for beams affected by ISR. After partial immersion in water, the values of the resonante frequencies increase and remain higher for beams with non-reactive aggregates. As previously well known, the presence of water in concrete increases the resonant frequencies [START_REF] Siegert | Resonant frequencies monitoring of Alkali Aggregate Reaction (AAR) damaged concrete beams[END_REF] In sum, the dynamic evaluation of structures is therefore a possible method of monitoring the development of damage caused by ISR in the structures, but there are still many issues to be clarified before its operational application.

(Figure 9)

Seismic tomography

The overall objective of this last type of investigation method is to produce an image describing the distribution of materials and/or their properties (based on mechanical vibratory response) in the structure. The different zones investigated correspond to the variations in the propagation velocity of compression waves, called "primary waves", through the concrete 50 . The tomographic image is based on three steps: data acquisition, simulation of these data in a synthetic model and finally the definition of solutions. The experimental data are the travel times of the seismic waves between each source point and each sensor location. The model is defined by the wave velocity considered in each node of a grid covering the whole tested structure. Fig. 10 shows an example that illustrates the type of seismic tomography visual output which can be obtained on a real structure 50 . The variations observed in the velocities are very important and indicate a significant alteration of the material for the upper zones of the dam. The velocities measured vary between 2000 and 4500 m/s. Low velocities are assumed to be caused by cracks in the concrete, rather than by a simple reduction in the modulus of elasticity. When the velocity values are higher than 3000 m/s, the concrete is considered of good quality 50 .

(Figure 10)

The application of this method in the case of real structures, with repeated investigations over time, is clearly possible and allows differentiating the zones affected by ISR from the non-affected ones 51 (even though there may be artefacts due to distribution of moisture supply).

Discussion

This review has aimed to explore the applicability of some NDT of investigation to delimit the structure zones affected and not affected by ISR for different exposure conditions. As is clearly known, the ISR evolution generates micro-cracking and thus an increase in porosity and water content of concrete. This reduces the amplitude of the radar signal due to the increase of the attenuation by adsorption (dielectric polarization and electrical conduction). The attenuation by diffusion (diffraction of radiation on heterogeneities of dimensions comparable to the wavelength) can also intervene in this case due to the presence of cracks and thus an increase in the heterogeneity of the material. So all these phenomenon explain the effect of damage caused by ISR on the amplitude attenuation of the radar signal. This GPR technique can be implemented in a complementary manner with the capacitive method. Since the capacitive technique can provide accurate results with respect to cover concrete, prior to extensive GPR investigations.

The resistivity measurement for on site concrete damage characterisation, in the frame of the non-destructive evaluation methods, can be complementary to the GPR and capacitive methods. This technique, easier to use and adapted to on site constraints, is also sensitive to the moisture degree and presents an interesting ability to characterise concrete damage and more particularly its cracks (the ability to assess cracks depth and opening). In any way, the coupling between the three methods may help engineers to give an original response to their problems of assessing damage degree of structures.

However, it has been shown that the sensitivity of pulse velocity method is too low to establish damage criteria associated with ISR whereas the attenuation variation associated only with ISR increase highly with the structure expansion. The variability of the reduction of the volume waves would make the ISR-structures characterization semi-quantitative (e.g. no damage, very low damage, low damage, high damage, etc…).

The applicability of the wave attenuation method can be effective if the investigated area of the damaged structure is reduced. In this case, the use of another ND method, namely the seismic tomography, can be helpful.

In fact, in addition to its interest in allowing full accounting of the whole structure (and enabling a major tensile crack in the gallery to be located 50 ), this method can help in determining the more damaged areas on the structure by targeting zones of different quality.

Finally, the dynamic evaluation of structures seems to be a possible method of monitoring the development of damage caused by ISR. However, this method has to be applied with another ND technique for more accurate results (and identification of possible artefacts due to moisture distribution).

Conclusion

Six non-destructive methods were compared to assess their applicability regarding ISR damage in concrete structures. The following conclusions can be drawn:

• The use of the radar technique does not distinguish the presence of the ISR from other ageing phenomena, but it may delimit suspicious zones in the structures. The affected zones are characterized by a decrease in the amplitude of the radar wave according to the level of concrete expansion. The radar allows determining the zones with higher water content which is an indicator of ISR risk.

• The capacitive method could complement the radar technique and give information about the water content evolution with depth in the structures. • The ultrasonic waves attenuation has been one of the most important techniques used for our purpose. It allows locating the zones where the mechanical properties decrease with the concrete expansion.

• The use of dynamic evaluation can inform about the stiffness reduction of the structures affected by ISR.

Nevertheless, this method has to be applied combined with another technique due to sensitivity to moisture.

• The seismic tomography is one of the methods which permits full coverage of the whole structure and can locate a major tensile crack and its estimated depth.

All these conclusions give confidence in using non-destructive methods to detect the ISR-damaged areas in a structure suspected to be affected. However, all studies that could be used as references in the present review show that ND method described for the purpose are not effective when used alone to assess the damage of structures caused by ISR. Monitoring of structures affected by these pathologies should only be carried out by combining two or more techniques (acoustic, electric and seismic) for an accurate detection of damaged areas. 12. Monette, L.J., Gardner, N.J., Grattan-Bellew, P.E., "Residual strength of reinforced concrete beams damaged by alkali-silica reaction -Examination of Damage Rating Index method". ACI Materials Journal, 99 (1), 42-50, (2002). 15. Amasaki, S., and Takagi, N., "The estimate for deterioration due to alkali-silica reaction by ultrasonic spectroscopy". Proc. de la 8 e CIRAG, Kyoto (Japon), 839-844, (1989).

16. Poyet S., "Etude de la dégradation des ouvrages en béton atteints par la réaction alcali silice : Approche expérimentale et modélisation numérique multi-échelles des dégradations dans un environnement hydrochemo-mécanique variable", PhD thesis, university of Marne la Vallée, France, (2003). 17. Martin R-P., "Analyse sur structures modèles des effets mécaniques de la réaction sulfatique interne du béton", PhD thesis, university of Marne la Vallée, France, (2010).

18. Laurens S., Balayssac J.-P., Rhazi J., Klysz G., Arliguie G., "Non-destructive evaluation of concrete moisture by GPR: experimental study and direct modeling", Materials and Structures, 38, 827-832, (2005).

19. Dérobert X., Iaquinta J., Klysz G., Balayssac J.-P., "Use of capacitive and GPR techniques for the nondestructive evaluation of cover concrete", NDT&E international, 41, 44-52, (2008). 20. Barnes C., Trottier J.-F., Forgeron D., "Improved concrete deck evaluation using GPR by accounting for signal depth-amplitude effects", NDT&E international, 41, 427-433, (2008). Experimental Techniques

  study of Klysz et al. presents the measurement campaign carried out on the deck of the Marque Bridge located in Northern France

  . A thorough and careful interpretation is thus required to avoid artefacts due to moisture when monitoring structures affected by ISR.

•

  The electric resistivity is very sensitive to different parameters such as moisture content and presence of chemical agents in the interstitial solution. Application of this technique could differentiate the more or less affected zones.

  B., Mahut B., Fasseu P., Michel M., "The guide for aiding to the management of structures damaged by concrete expansion in France", Proc. of the 12 th Int. Conf on Alkali-Aggregate Reaction in Concrete, Beijing, China, Oct. 15-19, 1219-1227, (2004). 11. Swamy, R.N. and Al-Asali, M.M., "Engineering Properties of concrete affected by alkali-silica reaction". ACI Materials Journal, 85, (5), 367-374, (1988).

  13. Ono, K. and Taguchi, M., "Long-term behavior of AAR bridge pier and the internal deterioration". Proc. de la 11 e CIRAG, Québec (Canada), 1167-1174, (2000).14. Kojima, T., Hayashi, H., Kawamura, M., Kuzume, K., "Maintenance of highway affected by AAR". Proc. de la 11 e CIRAG, Québec (Canada),1159-1166, (2000).

Figure 1 .

 1 Figure 1. Amplitude of the Radar direct wave for each position of pier cap 21

Figure 2 .

 2 Figure 2. Dielectric constant variation measured on the bent affected by ISR 21

Figure 3 .

 3 Figure 3. Evolution of dielectric permittivity vs. volume water content for mixes with different W/C ratios 23

Figure 4 .

 4 Figure 4. Evolution of resistivity vs. dry density for different water contents in concrete material 27

Figure 5 .

 5 Figure 5. Resistivity variation measured on the pier cap side affected by ISR[START_REF] Rivard | Suivi et caractérisation de la RAG par techniques non destructives[END_REF]

Figure 6 .

 6 Figure 6. Variation of ultrasonic wave velocity of samples with different deformation rates[START_REF]Assessment of concrete compressive strength in structures or in precast concrete products[END_REF]

Figure 7 .

 7 Figure 7. Ultrasonic wave velocity measurements of reactive and non-reactive concrete samples[START_REF]Assessment of concrete compressive strength in structures or in precast concrete products[END_REF]

Figure 8 .

 8 Figure 8. Tested beam in the climatic chamber (38°C)[START_REF] Ren | Output-only Modal Parameter Identification of Civil Engineering Structures[END_REF]

Figure 9 .

 9 Figure 9. Resonant frequency monitoring of the tested beams[START_REF] Ren | Output-only Modal Parameter Identification of Civil Engineering Structures[END_REF]

Figure 10 .PageFigure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .Figure 10 .

 1012345678910 Figure 10. Comparison between visual observation and tomography analysis of dam 48

Society for Experimental Mechanics, Inc.Experimental Techniques

Acknowledgements

The authors would like to thank the members of Electricité De France (EDF) (especially Mr M. Lion), for their financial and technical support. The authors are also grateful for the participation in this work of Géraldine Villain, Xavier Dérobert, Odile Abraham, Philippe Côte and Sergio Palma-Lopez.