E Rozière

A Loukili
email: ahmed.loukili@ec-nantes.fr

R El Hachem

F Grondin

Durability of concrete exposed to leaching and external sulphate attacks

Keywords: C, Durability C, Sulfate attack Leaching D, Sulfate Resistant Cements C, Expansion

Leaching and external sulphate attack on concrete lead to dissolution of hydration products, mainly portlandite, and in case of ingress of sulphate ions to formation of expansive products such as gypsum and ettringite. Durability of concrete exposed to these environments is still based on prescriptive specifications. The aim of the study is to provide experimental data to design performance based tests and specifications for a comparative approach. Tests have been developed to study these degradations in controlled conditions at constant pH. A leaching test has been performed on concrete. Indicators can be deduced from the leaching test and they are sensitive to the variations of potential durability. An accelerated test using a high sulphate concentration has been performed on mortars. Expansion results are sensitive to mortar mix proportions and the test could be used to qualify cements or binders in a comparative approach. Concrete specimens are exposed to external sulphate attack at two levels of sulphate concentration to provide long-term data that can be used to study the relevance of the accelerated tests and models which are being developed. Results from both series of tests show a correlation between the resistance to leaching and the resistance to external sulphate attack.

Introduction

Leaching is a diffusion-reaction phenomenon which takes place when concrete is exposed to poorly mineralized or acid water. Degradation consists in dissolution of calcium and hydroxide ions out of the matrix, which causes an increase in porosity and transport properties of surface concrete [START_REF] Carde | Modelling the loss of strength and porosity increase due to the leaching of cement pastes[END_REF][START_REF] Mainguy | Modelling of leaching in pure cement paste and mortar[END_REF]. Leaching is accelerated in neutral and acid solutions [START_REF] Adenot | Modelling of the corrosion of the cement paste by deionized water[END_REF][START_REF] Kamali | Modelling the leaching kinetics of cementbased materialsinfluence of materials and environment[END_REF], and it may be coupled with the ingress of aggressive ions such as chloride, sulphate, magnesium [START_REF] Moranville | Physicochemical equilibria of cement-based materials in aggressive environmentsexperiment and modeling[END_REF]. These issues need to be taken into consideration in the design of concrete structures in contact with ground water-such as nuclear waste containers [START_REF] Planel | Long-term performance of cement paste during combined calcium leaching-sulphate attack: kinetics and size effect[END_REF]-and also nuclear cooling towers, wastewater treatment plants and precast concrete products such as water tanks and sewage pipes. The mechanism of degradation of concrete exposed to external sulphate attack depends on exposure conditions, such as temperature [START_REF] Crammond | The thaumasite form of sulphate attack[END_REF][START_REF] Lipus | Sulfatwiderstand unterschiedlich zusammengesetzter Betone, Tl.1 -Sulphate Resistance of Concretes with Different Compositions (Part 1)[END_REF], associated cation [START_REF] Duval | Chapitre 9: La durabilité du béton vis-à-vis des eaux agressives, dans La durabilité des bétons[END_REF][START_REF] Neville | The confused world of sulphate attack on concrete, Review[END_REF] and sulphate concentration [START_REF] Santhanam | Sulphate attack researchwhither now?[END_REF][START_REF] Higgins | Resistance of Concrete Containing ggbs to the Thaumasite Form of Sulphate Attack[END_REF][START_REF] Dehwah | Effect of sulphate concentration and associated cation type on concrete deterioration and morphological changes in cement hydrates[END_REF]. The best known mechanism involves C 3 A and portlandite in the cement matrix and sulphate ions [START_REF] Duval | Chapitre 9: La durabilité du béton vis-à-vis des eaux agressives, dans La durabilité des bétons[END_REF][START_REF] Irassar | Microstructural study of sulphate attack on ordinary and limestone Portland cements at ambient temperature[END_REF][START_REF] Tixier | Modeling of damage in cement-based materials subjected to external sulphate attack. I: formulation[END_REF][START_REF] Maltais | Predicting the durability of Portland cement systems in agressive environmentslaboratory validation[END_REF]. The first stage of this mechanism is based on a diffusion-reaction based phenomenon. Sulphate ions react with portlandite to form gypsum, which can in turn react with the hydration products of C 3 A to form ettringite. The formation of gypsum and ettringite can be expansive. During the second stage of degradation the expansive products that have filled the porosity of concrete cause swelling, damage and finally a strength loss of concrete.

The everyday durability approach of concrete exposed to leaching and external sulphate attack is prescriptive. Standards [START_REF]NF EN 206-1 Béton -Partie 1: Spécification, performances, production et conformité, AFNOR, French standard, from European standard EN 206 Concrete -Performance, production and conformity[END_REF] are based on limiting values of the maximum water/binder ratio, minimum cement content, minimum compressive strength, and in case of sulphate attack prescriptions on binder are added. In the French standard on concrete NF EN 206-1 [START_REF]NF EN 206-1 Béton -Partie 1: Spécification, performances, production et conformité, AFNOR, French standard, from European standard EN 206 Concrete -Performance, production and conformity[END_REF], the maximum proportion of mineral admixtures such as fly ash and slag is 15% of the mass of binder, and socalled 'sulphate-resisting' cements are required. Sulphate resistance of cements is defined in other standards [START_REF] Nf P | Liants hydrauliques -Ciments pour travaux en eaux à hautes teneurs en sulphates[END_REF][START_REF]ASTM C 150 -04a Standard Specification for Portland Cement[END_REF]. It generally consists in limiting maximum C 3 A content (5% in both standards). Such cements are designed either by increasing the C 4 AF/C 3 A ratio of Portland cements or by increasing the slag proportion in blended slag cementswhich is contradictory to limits on binder from the standard on concrete.

However cost-effectiveness, environmental and technical issues have shown the need for performance based specifications for the same durability [START_REF] Rozière | A performance based approach for durability of concrete exposed to carbonation[END_REF]. In existing test procedures resistance of binders to external sulphate attacks is assessed on mortar prisms. Acceleration is obtained by decreasing the volume/exposed surface ratio of specimens and increasing sulphate concentration: 34 g/L in ASTM C 1012 [START_REF]ASTM C 1012 -95a Standard Test Method for Length Change of Hydraulic-Cement Mortars Exposed to a Sulphate Solution[END_REF] and NF P 18-837 [START_REF] Nf P | Produits de calage et/ou scellement à base de liants hydrauliques, Essai de tenue à l'eau de mer et/ou à l'eau à haute teneur en sulphates[END_REF], 29.8 g/L in Wittekindt procedure [START_REF] Wittekindt | Sulfatbeständige Zemente und ihre Prufung[END_REF]. But in field exposure conditions sulphate concentration is usually much lower: about 2.7 g/L in seawater [START_REF] Bucea | Chemical and physical attack of salts on concrete[END_REF], from 0.2 to 6 g/L in groundwater according to the definition of XA exposure classes in European standard EN 206 [START_REF]NF EN 206-1 Béton -Partie 1: Spécification, performances, production et conformité, AFNOR, French standard, from European standard EN 206 Concrete -Performance, production and conformity[END_REF]. Mehta [START_REF] Mehta | Evaluation of sulphate-resisting cements by a new test method[END_REF] and Brown [START_REF] Brown | An evaluation of sulphate resistance of cements in a controlled environment[END_REF] have shown the influence of pH on sulphate attack. In a laboratory study, it is typical to use only sodium sulphate, but not magnesium sulphate that would induce a coupled mechanism of degradation involving magnesium ions and CSH [START_REF] Duval | Chapitre 9: La durabilité du béton vis-à-vis des eaux agressives, dans La durabilité des bétons[END_REF][START_REF] Neville | The confused world of sulphate attack on concrete, Review[END_REF].

In this study, the effect of the exposure conditions has been taken into account to develop a representative test on concrete, using automatic control of pH and two levels of sulphate concentration (3 g/L and 30 g/L). Six concrete mixtures have been designed to study the sensitivity of the performance tests. Concrete specimens have been exposed to pH controlled leaching test and sulphate test. The corresponding cements and binders were studied by means of the test on mortar. Mass, dynamic elastic modulus (from resonance frequencies), and expansion have been monitored in order to understand the main mechanisms of degradation, and to find the most sensitive indicators of the damage degree, and the main composition parameters.

The aims of the study were: assessing the sensitivity of the test on mortar and the leaching test, and designing a representative test on concrete. The test is new because pH is automatically controlled, sulphate concentration is low (3 g/L), and it is done on concrete. pH controlled tests have been done on concrete at high sulphate concentrations (Brown [26]) and on cement pastes at low sulphate concentrations (Planel [6]).The results provided information on the mechanisms by comparing the results of the leaching test and sulphate attacks (Section 4.2.2), and analysing the results of the test from the compositional differences, for each exposure condition.

Characteristics of materials and mixture proportions

Cementitious materials and binders

The test on mortars was designed to assess chemical resistance of cements or binders of concrete exposed to sodium sulphate attacks. Chemical and physical properties of the cements, ground granulated blast-furnace slag (GGBS) and fly ash (FA) are given in Table 1. FA (Cordemais, France) has low calcium content and can be compared to ASTM Class F fly ash [START_REF] Lawrence | Mineral admixtures in mortars effect of type, amount and fineness of fine constituents on compressive strength[END_REF] Their compositions are significantly different. They may be used as reference binders to study the sensitivity of the test. Three other binders were designed to investigate the influence of the chemical composition of binders on sulphate resistance of concrete:

-Portland cement CEM I 52.5 R (2) (high C 3 A content: 7.6%), Saint Pierre La Cour -Portland cement CEM I 52.5 R + 62% GGBS.

Mortars

The reference mixes M1, M2, and M3 were designed according to standard NF EN 196-1. The mixtures were made of three parts of normalized sand (1350 g), one part of cement (450 g) and half part of water (225 g). The six previously described binders were respectively used in M1-M6 mortars, keeping a constant w/b ratio.

M7, M8, M9 mortars mixtures are made of the three reference cements to study sensitivity of the test and they have higher w/b ratio, in order to accelerate the test. M10, M11, M12 mortars have lower w/ b ratio to study the effect of an increase in compactness on resistance to external sulphate attack. The twelve mortars mixtures given in Table 2 were designed keeping the paste volume (water + binder volumes) constant.

Concrete mixtures

Six concrete mixtures were designed using the same cementitious materials (Table 3). Siliceous sand gravels were used to avoid coupled degradations due to calcium carbonate [START_REF] Higgins | Resistance of Concrete Containing ggbs to the Thaumasite Form of Sulphate Attack[END_REF] in case of use of limestone aggregates. Two concrete mixtures C2 and C4 comply with two levels of prescriptive requirements (XA2 and XA3 exposure classes) from standard NF EN 206-1 [START_REF]NF EN 206-1 Béton -Partie 1: Spécification, performances, production et conformité, AFNOR, French standard, from European standard EN 206 Concrete -Performance, production and conformity[END_REF] for exposure to leaching and sulphate attacks, in terms of minimum Equivalent Binder content (Eq. Binder) and maximum W eff. /Eq. Binder ratio. C3 and C6 concrete mixtures do not comply with maximum SCM/(SCM+C) ratio, equal to 0.15 in sulphate rich waters or soils. Binder of C5 concrete mixture is not sulphate-resisting, because its C 3 A content is higher than 5%. C1 concrete mixture was made of this same cement and has high W eff. / Eq. Binder ratio. Such mixture often leads to poor resistance to leaching and sulphate attacks [START_REF] Sahmaran | Effects of mix composition and watercement ratio on the sulphate resistance of blended cements[END_REF], but C1 was designed to investigate the sensitivity of the test.

Experimental procedures

Concrete specimens were exposed to a leaching test and external sulphate attacks in order to assess relevance and sensitivity of these tests and related performance based indicators. Moreover a test was performed on mortars to design a performance test for binders exposed to sulphate attack (Table 4).

Leaching test

The procedure was adapted from existing tests [START_REF] Planel | Long-term performance of cement paste during combined calcium leaching-sulphate attack: kinetics and size effect[END_REF][START_REF] Bourdette | Durabilité du mortier: prise en compte des auréoles de transition dans la caractérisation et la modélisation des processus physiques et chimiques d'altération[END_REF]. Two identical experimental devices were built in order to study the repeatability and to use the test in a comparative performance based approach (Fig. 1). For each test a 25-mm thick specimen was sawed from a Ø 11 × 22 cm specimen. The specimen was circumferentially coated with a waterproof vinylester resin, and hence was exposed to leaching only on its two plane surfaces.

Specimens were immersed in 1.5 L of demineralised water. The temperature was kept constant at 20 °C using a jacketed beaker of 2 L and a regulator. As pH tends to increase because of the dissolution of portlandite Ca(OH) 2 , it is controlled by adding appropriate volumes of 0.5 mol/L nitric acid solution, through a controlled burette. The set point of pH was 5, and the measured value was 5.0 ± 0.1. The solution was renewed whenever 30 mL of nitric acid had been added. The calcium concentration was assessed by atomic absorption spectrometry [START_REF] Badoz | A performance test to estimate durability of concrete products exposed to chemical attacks[END_REF]. C2, C3, C4, C5, C6(1), C6(2) concrete samples were tested at 43, 56, 42, 68, 45, 38 days after batching respectively. A nitrogen flow was used to avoid carbonation.

External sulphate attacks

Tests on mortars

The procedure followed for the test on mortar is close to those described in French standard NF P 18-837 [START_REF] Nf P | Produits de calage et/ou scellement à base de liants hydrauliques, Essai de tenue à l'eau de mer et/ou à l'eau à haute teneur en sulphates[END_REF] and ASTM standard C 1012 [START_REF]ASTM C 1012 -95a Standard Test Method for Length Change of Hydraulic-Cement Mortars Exposed to a Sulphate Solution[END_REF]. It consists in immersing prismatic mortar specimens in concentrated sodium sulphate solution. For each mortar mixture, six 4 × 4 × 16 cm 3 prismatic specimens and six 2 × 2 × 16 cm 3 specimens were cast and sealed cured for 24 h. They were stored in water for 14 days then for 14 days at 40 °C. Three control specimens were vacuum saturated with tap water and immersed in water and three others specimens were saturated with sodium sulphate solution and immersed in the solution. The sulphate concentration is 30 g/L. The solution was prepared using demineralised water and renewed once a month. 2 × 2 × 16 cm 3 specimens have gauge studs to measure expansion with length comparators. The elastic modulus was determined on 4 × 4 × 16 cm 3 prisms with a Grindosonic apparatus. This device gives the frequency of a vibration created by a slight shock on the sample. The elastic modulus is calculated from this frequency with the Spinner and Teft model [START_REF] Spinner | A method for determining mechanical resonance frequencies and for calculating elastic modulus from these frequencies[END_REF]. All tests were carried out on three samples and the given results are average values.

Tests on concrete

7 × 7 × 28 cm 3 prismatic concrete specimens were sealed cured until they reach 50% of required compressive strength (NF EN 206-1) for the corresponding exposure class (X0, XA2, XA3) and stored at 20 °C and 50% RH. After 28 days they were immersed in two different sodium sulphate solutions [START_REF] Rozière | Etude de la durabilité des bétons par une approche performantielle[END_REF]. Solutions were made of demineralised water and sodium sulphate. The sulphate concentration of the first solution was 3 g/L, and pH is controlled using 0.02 mol/L sulphuric acid solution. The sulphate concentration of the second solution was 30 g/L, and pH is controlled using 44 g/L sodium sulphate + 0.04 mol/L sulphuric acid solution. Solutions were renewed every month. Mass, length and elastic modulus of concrete samples were monitored.

Results and discussion

Results of leaching tests

The quantity of leached hydroxide ions was assessed through the added volumes of nitric acid HNO 3 solution, and that of leached calcium by the titration of the solutions. These quantities are plotted against square root of time in Figs. 2 and3.

The parameters of leaching kinetics may be deduced from quantity of leached ions versus square root of time curves. Steady state was assumed to be reached after 1 day. Corresponding parameters are given in Table 5, for the following Eq. ( 1):

N t ð Þ = a: ffiffi t p + b: ð1Þ
Ratios of leaching rates a OH /a Ca are close to 2 (Table 5) suggesting leaching had mainly come from dissolution of portlandite Ca(OH) 2 (Eq. ( 2)).

CaðOHÞ 2 + 2H 3 O þ Y Ca 2+ + 4H 2 O: ð2Þ
Ratios are actually above 2, so a part of leached calcium ions could come also from CSH.

After taking out from immersion phenolphthalein solution was sprayed over a fresh fracture to measure the damaged depth using the coloration front. Results in Table 6 show that corroded layer is very thin, for all concrete mixtures, so a more precise and sensitive criterion was looked for. Assuming that calcium ions only came from binder and that no portlandite remained in corroded layers, equivalent damaged depths may be calculated, dividing the total amount of leached calcium by the theoretical initial total calcium content of binder. From experimental data of the leaching test and CaO content of the cementitious materials, the following ratio can be calculated and give an equivalent damaged depth (EDD). The Total leached calcium is the ratio of the total leached calcium on specimen surface area (in mol/m 2 ) and Initial calcium content in binder is in mol/m 3 .

EDD =

Total leached calcium Initial calcium content in binder :

Equivalent damaged depths of C3 and C5 concrete samples were assessed assuming a ratio of leaching rates a OH /a Ca equal to 2.

From microstructural analyses on concrete specimen after the same testing procedure, the equivalent damaged depth would actually underestimate the damaged depth, because the corroded layer was not totally decalcified, which was an assumption of the previous calculation [START_REF] Badoz | A performance test to estimate durability of concrete products exposed to chemical attacks[END_REF].

The amounts of leached calcium or hydroxide ions can be considered as criteria for a comparative approach of durability of concrete. The leaching rates of C6 (1) and C6 (2) concrete specimens were 8.4% higher or lower than the mean value for the two tests, which was 2.44 mmol/ dm 2 /day 1/2 , so significant differences may be deduced from experimental results.

Leaching increased with an increase in Water/Binder ratio, which can be explained by corresponding variations of porosity and diffusivity. But this does not account for all the differences. C3 should have a better behaviour than C2 concrete, and leaching rate has reduced by 18%. So incorporating 30% of FA in binder would improve resistance to leaching, and behaviour would not only depend on porosity but on chemical composition of binder. Blended cements or binder incorporating such pozzolanic materials actually produce less portlandite, with equal or enhanced compactness of the matrix.

Among the concrete tested, the concrete with high amounts of GGBS (62%) leads to good resistance to leaching. C4 and C6 concrete mixtures showed the lowest leaching rates and total amounts of leached calcium and hydroxide ions. They have the same leaching rates (respectively 2.45 and 2.44 mmol/dm 2 /day). So including GGBS in concrete mixture instead of using blended cement had not significant effect with these materials.

Finally three indicators can be assessed from the test, namely: the Total leached calcium at the end of the test, the Experimental Damaged Depth and the Equivalent Damaged Depth. For a given type of aggregates, classifications of performances based on these three indicators were the same. Equivalent Damaged Depth is assessed from the hypothesis that the calcium is totally leached in damaged depth. The good correlation between the Experimental Damaged Depth and the Equivalent Damaged Depth suggests that the hypothesis is mainly true. Classifications of performances from the first indicator, Total leached calcium, are the same because the variations of total leached calcium are higher than the variations of initial calcium content. Higher initial calcium concentrations in binder came from lower water/cement ratios and lower diffusivities and thus lead to better resistance to leaching.

Results of external sulphate attack tests

We can suppose sulphate ions are likely to react with portlandite and C 3 A-rich hydration products, according to the following equations [START_REF] Tixier | Modeling of damage in cement-based materials subjected to external sulphate attack. I: formulation[END_REF]:

CaðOHÞ 2 + SO 2 - 4 + 2H 3 O þ Y CaSO 4 ;2H 2 O + 2H 2 O: ð4Þ
Gypsum (CaSO 4 ,
C 3 A + 3CSH 2 + 26HY C 6 AS 3 H 32 : ð6Þ

External sulphate attacks on mortars

As shown on Fig. 4, some samples have shown the typical expansion and cracking of concrete exposed to sodium sulphate solution with high sulphate concentration, i.e. equal to 20 g/L or higher [START_REF] Lipus | Sulfatwiderstand unterschiedlich zusammengesetzter Betone, Tl.1 -Sulphate Resistance of Concretes with Different Compositions (Part 1)[END_REF].

Expansion was observed before cracking by the monitoring of length (Figs. 5 and6) and mass (Figs. 7 and8). As absorption of water and hydration are likely to occur after immersion, differences between measures on control specimens and specimens exposed to sulphate solution were calculated to focus on the effects of sulphate ions. They are plotted in Figs. 6 and8. Relative mass decrease occurs during the period of latency, when no significant expansion occurred. The mass decrease is due to leaching. The mass increase is due to swelling caused by gypsum and/or ettringite formation in damaged mortar specimens. As the sulphate attack is external, the effect of the Exposed surface/Specimen volume ratio is important and this can be seen in Figs. 4, 7 and8, where damage and mass increase are greatest in the specimens with the higher surface/volume ratio.

Elastic modulus (Fig. 9) does not appear as a sensitive indicator of damage during the first stage, as the modulus of attacked specimens remains equal or higher than modulus of control specimens even if significant expansion and damage can be observed. Lee et al. [START_REF] Lee | Sulfate attack and role of silica fume in resisting strength loss[END_REF] and Sahmaran et al. [START_REF] Sahmaran | Effects of mix composition and watercement ratio on the sulphate resistance of blended cements[END_REF] have also shown the positive effect of sulphate attack on mechanical properties, before they finally decrease. Decrease of elastic modulus became significant after about 120 days (Figs. 9 and 10), but mass variation appeared earlier (Fig. 7) so this would be a better indicator for a performance test.

Mortar mixtures M1 to M6 were designed keeping water/binder ratio and paste volume constant. Mass variations and expansions of these mortars are plotted in Figs. 11 and12. Even mortar including sulphate resisting cement (M2) shows significant expansion (Fig. 12), which has already been observed in other studies using the same kind of test on mortar [START_REF] Sahmaran | Effects of mix composition and watercement ratio on the sulphate resistance of blended cements[END_REF]. Tian and Cohen [START_REF] Tian | Does gypsum formation during sulphate attack on concrete lead to expansion?[END_REF] have shown that gypsum could also cause expansion in sulphate environments. So analysis of microstructure is necessary to know whether expansion is actually due to ettringite. Irassar [START_REF] Irassar | Microstructural study of sulphate attack on ordinary and limestone Portland cements at ambient temperature[END_REF] has found high gypsum concentration in the outer layer of damaged specimens by means of XRD analysis. An ettringite inner layer has also been found on the same samples, but The two stages of the degradation may be distinguished in Figs. 11 and12. The first step corresponds to the period of latency, when no significant expansion can be measured. The second stage corresponds to significant expansion. It starts at about 60 days for M4 mortar specimens.

The difference between the mass variations of control and damaged specimens is plotted against the square root of time, which shows a linear dependency. This can be clearly seen for mortars M2, M3, and M4. That corresponds to leaching and diffusion-reaction processes between sulphate solution and hydration products, mainly portlandite Ca(OH) 2 [START_REF] Planel | Long-term performance of cement paste during combined calcium leaching-sulphate attack: kinetics and size effect[END_REF]. This could explain why the cements used in mortars M2, M3, and M4 showed the highest expansion, even if cement used in M2 is considered as sulphate resisting. The three cements actually have approximately the same proportion of CaO and high proportions of C 3 S. They produce comparatively greater amounts of portlandite on hydration than blended cements or binders. Leaching of portlandite can thus increase ingress of sulphate ions in cement matrix. Moreover reaction with sulphate is likely to produce more gypsum (CaSO 4 ) and more ettringite (C 3 A.3CaS0 4 .32H 2 O), which are responsible for expansion and damage.

Gypsum has actually been observed on cracked mortar samples. Fig. 13 shows scanning electron microscopy and energy dispersive spectroscopy (SEM/EDS) analysis on M4 polished mortar sample. EDS analysis (Table 7, Fig. 14) was performed at accelerating voltage of 20 keV and takeoff angle of 37°. High silicon concentrations come from siliceous aggregate and calcium comes from cement paste. High concentrations of sulphur can be observed in cracks, especially between paste and aggregates. Normalized weight concentrations and atomic proportions given by quantitative analysis are closed to composition of gypsum CaSO 4 , and Ca/S ratio is equal to 1.1. This confirms the part played by gypsum in expansion due to sulphate attacks.

Fig. 15 confirms the influence of the chemical composition of binder on expansion of mortar. Expansion after 180 and 360 days has been plotted as a function of the sum of CaO and Al 2 O 3 proportions, as these two oxides are the main compounds of C 3 S and C 3 A, so they potentially lead to production of ettringite and gypsum in sulphaterich environments. Two behaviours can be distinguished. Portland cements, i.e. the two high-C 3 A cements and the sulphate-resisting cement, have the same CaO + Al 2 O 3 content (68.4%). They showed significant expansions for water/binder ratios equal or higher than 0.5. Even if C 3 A content is known as a major parameter, this result suggests that C 4 AF could also play an important part. Mortars made of the same cements but with lower water/binder ratio (0.35) did not show any significant expansion. Reducing the water/binder ratio actually improves strength and resistance to the ingress of the sulphate ions by diffusion [START_REF] Sahmaran | Effects of mix composition and watercement ratio on the sulphate resistance of blended cements[END_REF][START_REF] Khatri | Role of permeability in sulphate attack[END_REF]. The slag cement and the binders made of Portland cement and slag (62%) or fly ash (30%) showed much lower expansion, even for high water/binder ratios [START_REF] Thomas | Use of ternary cementitious systems constaining silica fume and fly ash in concrete[END_REF][START_REF] Osborne | Durability of Portland blast-furnace slag cement concrete[END_REF][START_REF] Higgins | Increased sulphate resistance of ggbs concrete in the presence of carbonate[END_REF]. But expansion of M6 (30% FA, w/b = 0.50) and M7 (62% GGBS, w/b = 0.65) had not stabilized after 420 days, so w/b ratio and chemical composition of binder are both important parameters and slight variations can completely change behaviour of mortars or concrete, from stabilization to unlimited expansion. The water-binder ratio influences the diffusivity and the strength of mortar or concrete. The CaO + Al 2 O 3 content is related to the potential amount of gypsum and ettringite and the forces due to formation of these products. The result of the test is global and influenced by both factors, namely: the forces coming from the formation of expansive products, and the resistance (tensile strength) of the material. The diffusivity influences the kinetics. Slight changes of composition parameters can thus significantly affect the potential expansion or the strength, thus the behaviour of mortar.

The behaviours distinguished in Fig. 15 are consistent with expansion data from ASTM C 1012 tests. According to ASTM Subcommittee C01-29 [START_REF] Patzias | The development of ASTM method C1012 with recommended acceptance limits for sulphate resistance of hydraulic cements[END_REF], cements satisfying the expansion limits of 0.10% (1000 µm/m) and 0.05% (500 µm/m) at 26 weeks are considered as moderate sulphate resistant and high sulphate resistant, respectively and the expansion limits of 0.10% (1000 µm/m) at 52 weeks are considered as high sulphate resistant [START_REF] Sahmaran | Effects of mix composition and watercement ratio on the sulphate resistance of blended cements[END_REF]. But expansion at a given time does not give information on future stability of mortar or concrete. Monteiro and Kurtis [START_REF] Monteiro | Experimental asymptotic analysis of expansion of concrete exposed to sulphate attack[END_REF] have proposed a predictive approach based on experimental asymptotic analysis, from the 40-year study on concrete conducted by the U.S. Bureau of Reclamation (USBR).

During the first stage of sulphate attacks, leaching occurs and the dominant phenomenon is the diffusion-reaction as shown in Fig. 11. During the second stage of expansion, other phenomena occur such as the formation of expansive products, damage and, in some cases, coupling with hydration and healing. The aim of this approach is to obtain similitude laws for phenomena from experimental results [START_REF] Monteiro | Experimental asymptotic analysis of expansion of concrete exposed to sulphate attack[END_REF]. The scaling law for the expansion ε of concrete or mortar is expressed as follow:

e = K t-t 0 ð Þ α ð8Þ
where K is a constant, t the time, t 0 the effective origin of time and α the scaling exponent. α can be assessed by plotting log(ε) as a function log(t). Therefore the curve ε 1/α versus t is linear (Fig. 16). The value of t 0 is given by the intercept with the horizontal axis. The same graph provides the initiation time t i , which represents the initiation of the expansion stage. Mortars M1, M5, M10, M11 and M12 did not show expansion. Instead, they show saturation behaviour, as expansion increases but remains limited. Forces due to expansion of the products of sulphate attack are lower than the strength of the material. The saturation process repeats itself (Fig. 17). It was defined by the following equation:

e = e lim 1 -e -βt : ð9Þ
Based on data from the USBR tests on concrete, Monteiro and Kurtis [START_REF] Monteiro | Experimental asymptotic analysis of expansion of concrete exposed to sulphate attack[END_REF] defined a potential damage Pd to predict the initiation time or saturation behaviour from the composition of concrete and cement:

Pd = C 3 A 1:39 C 3 S 2:9 C 4 AF 0:77 w= c ð Þ 7:80 : ð10Þ
As shown in Fig. 18, this model gives a good assessment for the behaviour of mortars exposed to the same kind of test. It is difficult to find the limit of tendency to saturation behaviour. For instance, M12 mortar has not shown significant damage but saturation behaviour, whereas M6 mortar has shown self-similar behaviour. So slight changes in cement properties or w/b can significantly affect performance of concrete exposed to sulphate attacks according to this test procedure [START_REF] Sahmaran | Effects of mix composition and watercement ratio on the sulphate resistance of blended cements[END_REF][START_REF] Monteiro | Experimental asymptotic analysis of expansion of concrete exposed to sulphate attack[END_REF]. All expansion data are presented in Table 8.

Results from this study on mortars are consistent with other studies on the same test. As the sulphate concentration could modify the conditions of sulphate attack, especially the relative amounts of gypsum and ettringite, the tests on concrete were designed to take into account sulphate concentration and control of the pH of the solution.

External sulphate attacks in concrete

The mass of control and attacked specimens was monitored. Control specimens stored in tap water showed a slight mass increase, which corresponds to hydration, whereas specimens stored in sulphate solution showed much lower increase or slight loss of mass. In order to separate the effect sulphate attack from phenomena of absorption and hydration, differences of relative mass variations are plotted against square root of time in Fig. 19. The graph shows linear variations, which can be due to diffusion-reaction phenomenon, such as leaching and ingress of sulphate ions [START_REF] Planel | Long-term performance of cement paste during combined calcium leaching-sulphate attack: kinetics and size effect[END_REF].

In order to compare these variations to the kinetics assessed from the leaching test, the kinetics from Fig. 19 were converted into loss of portlandite per unit area of sample (Table 9). They are of the same order of magnitude and they show the influence of composition parameters such as water/binder ratio and chemical composition of the binder. Significant differences appear for concrete mixtures C2, C3, and C5. The corresponding binders are mainly made of Portland cement.

Damaged depths can not be deduced only from leaching kinetics. As the sulphate test is still in progress, it is not possible to use a colorimetric indicator on a fracture of specimens. Visual observation can bring useful information on the degree of degradation, in a comparative approach [START_REF] Irassar | Microstructural study of sulphate attack on ordinary and limestone Portland cements at ambient temperature[END_REF]. Classification is given in Table 10 and shows good correlation with the classification from leaching test (Table 6).

The cement used in concrete mixtures C1B and C5B (see Fig. 21) is the high-C 3 A cement used in mortars M3, M9, and M12 but concrete mixtures are the same as C1 and C5. After immersion, expansion is due to absorption of water and depends on the magnitude of drying shrinkage before test. After this first stage, neither monitoring of mass nor monitoring of length shows expansion due to sulphate attack at both sulphate concentrations (Figs. 20 and21). Even if controlled pH accelerates degradation [START_REF] Tixier | Modeling of damage in cement-based materials subjected to external sulphate attack. II: comparison with experiments[END_REF], the sulphate attack is external and an Reference: mass before immersion. increase in volume/surface ratio of specimens causes a corresponding increase in initiation time of degradation of paste [START_REF] Planel | Long-term performance of cement paste during combined calcium leaching-sulphate attack: kinetics and size effect[END_REF], mortar (Fig. 4) and concrete specimens [START_REF] Lagerblad | Long-term test of concrete resistance against sulphate attack[END_REF][START_REF] Tixier | Microstructural development and sulphate attack modelling in blended cement-based materials[END_REF]. The test is actually not meant to classify performances of concrete mixtures by accelerated degradation, but to provide data on behaviour of concrete exposed to sulphate attack in realistic and controlled conditions. So these data can be useful to conclude on relevance of accelerated tests or models of external sulphate attacks [START_REF] Rozière | Modelling of the sulphate attack in cement-based materials[END_REF] based on the evolution of the microstructure of concrete [START_REF] Grondin | A multi-scales approach for the physico-chemical deformations of solidifying cement-based materials[END_REF].

Conclusions

The aim of the study was to provide comparative performance-

  . GGBS (Moerdijk, Netherlands) complies with technical agreement (ATG) in Belgium, BRL 9325 (KIWA) and 9340 (BMC) in the Netherlands and standards NF in France. Three reference cements were used, namely: -Portland cement CEM I 52.5 R (1) (high C 3 A content: 10.6%), Beffes -Sulphate resisting Portland cement CEM I 52.5 N PM ES (low C 3 A content: 2%), Le Havre -Sulphate resisting blended cement CEM III I 42.5 PM ES made of 62% ground granulated blast-furnace slag (GGBS), Le Havre.

Fig. 1 .

 1 Fig. 1. Schematic diagram of leaching test.

Fig. 2 .

 2 Fig. 2. Leached hydroxide ions.

Fig. 3 .

 3 Fig. 3. Leached calcium ions.

Fig. 4 .Fig. 5 .

 45 Fig. 4. M9 mortar specimens after 105 and 150 days in 30 g/L sulphate solution.

Fig. 6 .

 6 Fig.6. Expansion of 2 × 2 × 16 cm 3 specimens. Difference between sulphate and control specimens.

Fig. 7 .

 7 Fig. 7. Mass variations of mortar specimens.

Fig. 8 .

 8 Fig. 8. Mass variations of mortar specimens. Difference between sulphate and control specimens.

Fig. 9 .

 9 Fig. 9. Elastic modulus of 4 × 4 × 16 cm 3 specimens.

Fig. 10 .

 10 Fig. 10. Elastic modulus of 4 × 4 × 16 cm 3 specimens. Difference between sulphate and control specimens.

Fig. 11 .

 11 Fig. 11. Mass variations of 4 × 4 × 16 cm 3 specimens. Difference between sulphate and control specimens. Water/Binder = 0.50.

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Expansion of 2 × 2 × 16 cm 3 specimens. Difference between sulphate and control specimens. Water/Binder = 0.50.

Fig. 14 .

 14 Fig. 14. EDS analysis on M4 mortar sample (circled zone): spectrum.

Fig. 15 .Fig. 16 .

 1516 Fig. 15. Influence of chemical composition of binder on expansion of mortar.

Fig. 17 .

 17 Fig. 17. Saturation curves of mortar M5.

Fig. 18 .

 18 Fig. 18. Analysis of expansion data by scaling law.

Fig. 19 .

 19 Fig. 19. Difference of mass variations of immersed concrete specimens. [S0 4 2-] = 3 g/L.

  based tests and indicators to assess durability of concrete exposed to leaching and external sulphate attacks. Sensitivities of existing tests have been investigated and a new test has been developed for external sulphate attacks on concrete. • Leaching test on concrete has shown good sensitivity: varying water/binder ratio and chemical composition of binder lead to significant changes in the behaviour of concrete. Three indicators can be assessed from test data, namely: total leached calcium at the end of the test, experimental damaged depth and equivalent damaged depth (for siliceous aggregates). This test is under evaluation for standardization. • Test on mortar could be used to qualify binders, for a given water/ binder ratio and volume of paste. Conditions of exposure are not totally controlled and high sulphate concentration could be responsible for decreasing potential durability of sulphate-resisting Portland cements because of gypsum formation. The test is sensitive enough to show different behaviours of the studied reference binders, namely: high-C 3 A Portland cement, low-C 3 A sulphateresisting Portland cement, and sulphate-resisting slag cement. Experimental asymptotic analysis developed by Monteiro and Kurtis [39] from long-term study on concrete has been shown to be reliable to analyse data from the test. • A new test has been developed to expose concrete to external sulphate attack in controlled conditions: pH is automatically controlled and two tests are still in progress at two sulphate concentrations (3 g/L and 30 g/L SO 4 2-). The long-term objective is to provide data to study relevance of the accelerated tests and models which are being developed. • As classifications of performances are consistent, studies of external sulphate attack on mortars and concrete have both shown that leaching plays a predominant role. Leached portlandite would facilitate ingress of sulphate ions and produce reactants to form expansive products such as gypsum and ettringite. Portlandite comes from hydration of C 3 S and C 2 S. So substitution of high-C 3 S Portland cement by 30% of fly ash improved behaviour of mortar or concrete exposed to leaching and sulphate attack. The best behaviour was obtained when Portland cement was substituted by 62% of ground granulated blast-furnace slag, either by using commercial slag cement or by blending Portland cement and slag in concrete.

Fig. 20 .

 20 Fig. 20. Expansion of immersed concrete specimens. [S0 4 2-] = 3 g/L.

Fig. 21 .

 21 Fig. 21. Expansion of immersed concrete specimens. [S0 4 2-] = 30 g/L.

Table 1

 1 Characteristics of cementitious materials.

	Cements

Table 2

 2 Proportions of mortar mixtures.

	(kg/m 3 )	M 1	M 2	M 3	M 4	M 5	M 6	M 7	M 8	M 9	M 1 0	M 1 1	M 1 2
	Sand	1484	1494	1490	1490	1490	1490	1484	1494	1490	1484	1494	1490
	Cement
	CEM III PM ES	495						419			591
	CEM I PM ES		498				368		420			597
	CEM I R (1)			497						420			593
	CEM I R (2)				497	190
	GGBS					316
	FA						158
	Superplasticizer					4.4					8.8	8.9	9.9
	W eff.	247	249	248	248	237	231	272	273	273	207	209	208
	W eff. /Eq. Binder	0.50	0.50	0.50	0.50	0.50	0.50	0.65	0.65	0.65	0.35	0.35	0.35

Table 3

 3 Proportions of concrete mixtures.

	Exposure classes	X0	XA2		XA3
	(kg/m 3 )	C 1	C 2	C 3	C 4	C 5	C 6
	Siliceous gravels Palvadeau
	12.5/20	365	374	358	372	374	366
	8/12	268	275	264	274	275	269
	4/8	410	421	403	419	421	412
	Siliceous sand Palvadeau
	2/4	56	57	55	57	57	56
	1/4	238	244	234	243	244	239
	0.5/1	130	133	127	132	133	130
	0.315/1	192	197	189	196	197	193
	0/0.315	103	106	102	105	106	104
	0/0.160	22	23	22	23	23	23
	Cement (C)
	CEM III PM ES	-	-	-	385	-	-
	CEM I PM ES	-	352	280	-	-	-	Table 4
	CEM I R (2)	280	-	-	-	385	156	Experimental program.
	SCM									Mortar	Concrete
	Fly ash Cordemais (k = 0.6)	-	-	120	-	-	-	External	Specimens	Prisms:	Prisms:
	GGBS ECOCEM (k = 0.9)	-	-	-	-	-	254	sulphate attacks		2 × 2 × 16 cm 3 ,	7 × 7 × 28 cm 3
	Effective water (W eff. )	205	174	174	154	154	154			4 × 4 × 16 cm 3
	Superplasticizer	0	0.73	1.29	4.14	3.16	3.38		Sulphate	30 g/L	3 g/L, 30 g/L
	Eq. Binder content (C+k.SCM)	280	352	352	385	385	385		concentration
	E eff. /Eq. Binder	0.73	0.49	0.49	0.40	0.40	0.40		[SO 4 2-]
	SCM/(SCM+C)	0	0	0.30	0	0	0.62	Leaching	Specimens	-	Cylinder:
	Volume of paste Vp (L/m 3 )	296	286	308	282	278	293				Ø11 × 2.5 cm

Table 5

 5 Parameters of leaching kinetics.

			C2	C3	C4	C5	C6 (1)	C6 (2)
	OH a (mmol/dm 2 /d 1/2 )	6.97	5.82	2.45	6.17	2.23	2.64
		b (mmol/dm 2 )	-3.44 -3.59	4.19 -3.23	-0.15	-0.35
	Ca	a (mmol/dm 2 /d 1/2 )	3.81	2.90	1.59	-	1.24	1.48
		b (mmol/dm 2 )	-2.95	-1.97	0.58	-	0	-0.21

Table 6

 6 Experimental and equivalent damaged depths.

	C2	C3	C4	C5	C6 (1) C6 (2)

Table 7

 7 EDS analysis on M4 mortar sample (circled zone): quantitative analysis.

	Element	Normalized	Precision	Atomic prop.	Line
		conc. (wt.%)		(%)
	O	58.7	3.75	75.8	K line
	Al	0.31	0.16	0.23	K line
	Si	3.70	0.34	2.72	K line
	S	15.7	0.59	10.2	K line
	Ca	21.7	0.78	11.2	K line
	Total	100.00		99.99

Table 8

 8 Analysis of expansion data.

		α	t 0	t i	Pd
		Measured	Origin of time	Initiation time	Potential of damage
	M1	-	-	-	536
	M2	1.70	0.016	0.24	22,315
	M3	2.47	0.019	0.27	110,622
	M4	1.68	0.032	0.28	71,718
	M5	-	-	-	492
	M6	1.16	0.001	0.47	3671
	M7	-	-	-	4150
	M8	1.44	0.048	0.20	172,729
	M9	3.08	0.045	0.15	856,252
	M10	-	-	-	33
	M11	-	-	-	1382
	M12	-	-	-	6849

Table 9

 9 Kinetics of loss of mass, from sulphate attack test and leaching test.

	Sodium sulphate solution, [S0 4 2C1 0.039 2.01	-
	C2 0.035	1.83	3.81
	C3 0.027	1.41	2.90
	C4 0.025	1.33	1.59
	C5 0.023	1.22	3.27
	C6 0.025	1.32	1.36

-] = 3 g/L, pH = 7 Nitric acid solution, pH = 5 k (mass %/day 1/2 ) a Ca(OH)2 (mmol/dm 2 /day 1/2 ) a Ca(OH)2 (mmol/dm 2 /day 1/2 )

Table 10

 10 Classification of performances from external sulphate attack test on concrete.

		Time of immersion	Surface appearance	Classification of performances
	C1	597	Porous -severe attack	5
	C2	609	Porous -severe attack	5
	C3	463	Slight attack	3
	C4	578	Very slight attack	1
	C5	560	Moderate attack	4
	C6	519	Very slight attack	1

Acknowledgement

The Fédération Nationale des Travaux Publics (from the French building industry) is gratefully acknowledged for its funding of the project.


Xavier Polanco
email: xavier.polanco@inist.fr

Co-word Analysis Revisited: Modelling Co-word Clusters in Terms of Graph Theory

Introduction

The idea that graph theory would be useful in coword analysis was suggested to us by social network analysis, where both graph theory and matrix operations have been widely used (Wasserman & Faust, 1999;Degenne & Forsé, 2000). In co-word analysis tradition, Courtial (1986) had started to explain the co-word clusters in terms of graphs. However, he did not take this idea to its logical next step, which we will attempt here. We distinguish two analytical units: clusters and the network of clusters. In the network each cluster represents a node. In addition, we will consider each cluster as a "super vertex" (according to the "reduced model approach" in Everett & Borgatti, 1999)

Co-word Analysis Components

Recall the main components of the standard co-word analysis (cf. Callon et al. 1993, c. VII). The input dataset in co-word analysis is a matrix D (n, m) where n is the number of documents, and m the number of keywords. From this matrix two other matrices are derived, initially a matrix of occurrence of the keywords (columns) in the document collection (rows), and then a co-occurrence matrix making it possible to constitute pairs of terms (or dyads). A normalised weight is attributed to the coword associations. This is calculated by an association coefficient. In this case, it is called "equivalence coefficient" (Michelet, 1988) and defined as:

2 ( ) ( ) ( ) ij ij i j C E C C ×     =
, where C(ij) is the total number of co-occurrences of words i and j, and C(i) is the total number of occurrences of the word i. The huge normalised and weighted co-occurrence network is submitted to a cluster analysis with the objective to constitute readable sub-sets (or clusters). The clusters are then disposed on a map, which essentially is a bi-dimensional plan. The members of a co-word cluster are also normalised weighted elements. For each internal or external item a of the cluster Cl we calculate this weight w as follows:

Using Graph Theory

A graph G consists of two sets of information: a set of nodes, N = {n 1 , n 2 , …, n N }, and a set of undirected relations, R = {r 1 , r 2 , …, r R } between pair of nodes, denoted G (N,R). A weighted graph, denoted by G W (N, R, W), consists of three sets of information: a set of nodes, N = {n 1 , n 2 , …, n N }, a set of relations, R = {r 1 , r 2 , …, r R }, and a set of weights, W = {w 1 , w 2 , …, w R }, attached to the relations. A directed graph or digraph, G D (N, R), consists of two sets of information: a set of nodes, N = {n 1 , n 2 , …, n N }, and a set of directed relations (or arcs), R = {r 1 , r 2 , …, r R } between pairs of nodes. Each arc is an ordered pair of distinct nodes, r k = <n i , n j >. The arc <n i , n j > is directed from n i (the origin or sender) to n j (the terminus or receiver).

Co-word clusters are considered as graphs, G (N,R), because the intra-cluster relations between two internal terms (internal associations) constitute nondirectional relations. We use the weighted graphs, G W (N, R, W), for representing co-word clusters, since cluster relations always are valued by a normalised weight. Following this, we use a directed graphs, G D (N, R), and we then propose the weighted directed graphs as a model for representing intercluster relations (external associations) between two clusters (in the network of clusters), since the external associations can be analysed like sending or receiving relations between two clusters. This is a consequence of the clustering algorithm that we applied (cf. Grivel et al., 1995).

Types of relations between clusters in the network

The external associations can be analysed by pairs of clusters and the possible arcs between them. The classes of ties between the pairs of clusters can be null, asymmetric, and mutual. A pair of clusters (i.e. a dyad) is null, that is, when neither arc is present, when neither of the arcs <Cl i , Cl j > nor <Cl j , Cl i > is contained in the set of arcs. An asymmetric pair of clusters has an arc between the two clusters going in one direction or the other, but not both, that is, one of the arcs <Cl i , Cl j > or <Cl j , Cl i >, but not both, is contained in the set of arcs. Asymmetric pairs of clusters are represented by one-way arcs, <Cl i → Cl j > or <Cl j → Cl i >. Mutual or reciprocal pairs of clusters have two arcs between the nodes representing them, one going in one direction and the other going in the opposite direction. Both arcs <Cl i , Cl j > and <Cl j , Cl i > are contained in the set of arcs. The arc with a double-headed arrow between two nodes indicates a mutual pair of clusters, <Cl i ↔ Cl j > (cf. Wasserman & Faust, 1999, p.124).

Types of clusters in the network

According to in-and out-degrees, we can distinguish four types of nodes in a directed graph. We can use this information for analysing the network of clusters in terms of isolate nodes (if d in-degree (n i ) = d out-degree (n i ) = 0), transmitter nodes (if d in-degree (n i ) = 0 and d out-degree (n i ) > 0), receiver nodes (if d in- degree (n i ) > 0 and d out-degree (n i ) = 0), and carrier nodes (if d in-degree (n i ) > 0 and d out-degree (n i ) > 0). Transmitter is the node, which only has arcs originating from it; receiver is the node that only has arcs terminating at it; carrier is the node that has arcs both to and from it (cf. Wasserman & Faust, 1999, p.128).

Conclusion

We try in this article to translate the standard coword analysis in graph language, following the example of the social network analysis. Graph theory provides us the analytical tools and indicators for analysing co-word clusters as non-directional weighted graphs. In contrast, the network of clusters is defined as a directional weighted graph.

A real co-word analysis application on a bibliographic dataset has been used for illustrating this translation. We have used as example a data set of 228 publications indexed by 164 keywords on rough set theory, and its applications in the field of information science, through 1999-2004. This dataset was collected from PASCAL database.

The issue that remains to be considered is the alternative to apply directly a graph algorithm to the weighted co-occurrence matrix. Thus, a clustering process will be done on the graph structure that has been generated from the weighted co-occurrence matrix. This is in progress using CPCL algorithm introduced by Ibekwe-SanJuan (1998), and revisited by Berry et al. (2004). We will demonstrate in this case that the model only is an undirected weighted graph in conformity with the non-directional cooccurrence relation between keywords.

We have not yet revisited the cluster centrality and density structural properties, nor have we addressed the issue of the different class of centrality (degree, closeness, and betweenness), and density (in a graph, a directed graph or a weighted graph). We will address these issues in a following article.

  = the number of its internal and external terms, n Clin = the number of its internal associations, n Clex = the number of its external associations, k Cl (a) = the number of occurrences of internal or external term a (a = 1, m Cl ) in the internal or external associations of Cl. The term with most weight serves to label clusters.

  COLING-ACL'98, Montréal, 10-14 August, p. 564-570. Michelet B. (1988). L'Analyse des Associations.Thèse de Doctorat, Université de Paris 7. Wasserman S. & Faust K.(1999). Social Network Analysis. Methods and Applications. Cambridge: Cambridge University Press.

	Figure 1: The network of clusters represented by a
	directed weighted graph
	References
	Berry A., Kaba B., Nadif M., SanJuan E., Sigayret
	A. (2004). Classification et désarticulation de
	graphes	de	termes,	7èmes	Journées
	Internationales d'Analyse Statistique des
	Données Textuelles, JADT 2004, Louvain-la-
	Neuve, Belgique, 10-12 March, vol. 1, p. 160-
	170.
	Callon M., Courtial J-P., Penan H. (1993). La
	Scientométrie. Paris, Presses Universitaires de
	France, (coll. Que sais-je? Vol. 2727).
	Courtial J-P.(1986). Technical issues and
	developments in methodology. In M. Callon, J.
	Law & A. Rip (Eds), Mapping the Dynamics of
	Science and Technology. London: The
	Macmillan Press, c.11, p.189-210.
	Degenne A. & Forsé M. (2001). Les réseaux
	sociaux. Paris: Armand Colin.
	Everett M.G. & Borgatti S.P. (1999). The Centrality
	of Groups and Classes, Journal of Mathematical
	Sociology, vol. 23, num. 3, p. 181-201.
	Grivel L., Mutschke P., Polanco X. (1995).
	Thematic Mapping on Bibliographic Databases
	by Cluster Analysis: A Description of the SDOC
	Environment	with		SOLIS,	Knowledge
	Organization, vol. 22, num. 2, p. 70-77.
	Ibekwe-SanJuan	F.	(1998).	Terminological
	variation, as a means of identifying research
	topics from texts, Proceedings of the Joint
	International Conference on Computational
	Linguistics,