domain: sde sdu sdu.stu.ag

text:
Thomas Gillot

Isabelle Cojan
email: isabelle.cojan@mines-paristech.fr

Haurine Frédéric

Poirier Catherine

Marie-Anne Bruneaux

Gillot Thomas

Cojan Isabelle

Haurine Frederic

Catherine Poirier

Bruneaux Marie-Anne

Demonstrating the influence of sediment source in dredged sediment recovery for brick and tile production

Keywords: dredged sediment recovery, brick and tile production, provenance fingerprinting, technological properties, Principal Component Analysis

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

Introduction

In a context of sustainable development, waste management has become an important target in terms of natural resource preservation and environmental issues (Azapagic et al., 2004).

Among the multiple non-hazardous wastes, this paper focuses on fine-grained dredged sediments that can be recovered by substitution of natural material in tile and brick building materials [START_REF] Hamer | Brick production with dredged harbour sediment. An industrial-scale experiment[END_REF]Agostini et al., 2007;[START_REF] Mezencevova | Utilization of Savannah Harbor river sediment as the primary raw material in production of fired brick[END_REF][START_REF] Cappuyns | Dredged sediments as a resource for brick production: Possibilities and barriers from a consumers' perspective[END_REF]. Composition of raw mixtures for ceramic materials has an influence on the sintering temperature and final properties of the produced material [START_REF] Dondi | Technological and compositional requirements of clay materials for ceramic tiles[END_REF][START_REF] Cultrone | Influence of mineralogy and firing temperature on the porosity of bricks[END_REF]. Mineralogical studies on fine-grained dredged harbor sediment [START_REF] Hamer | Brick production with dredged harbour sediment. An industrial-scale experiment[END_REF][START_REF] Mezencevova | Utilization of Savannah Harbor river sediment as the primary raw material in production of fired brick[END_REF]Benyerou et al., 2015) or river material (Manap et al., 2016) have shown that silt carried in suspension can be valuable material for the ceramic industry based on appropriate grain-size distribution and significant content in clay minerals combined with quartz and some carbonates [START_REF] Xu | The use of urban river sediment as a primary raw material in the production of highly insulating brick[END_REF][START_REF] Cappuyns | Dredged sediments as a resource for brick production: Possibilities and barriers from a consumers' perspective[END_REF][START_REF] Haurine | Caractérisation d'atterrissements d'argiles récents sur le territoire français, en vue de leur valorisation dans l'industrie des matériaux de construction en terre cuite[END_REF][START_REF] Haurine | Development of an industrial mineralogical framework to evaluate mixtures from reservoir sediment for recovery by the heavy clay industry: Application of the Durance system (France)[END_REF].

Fine-grained sediments silting in dam reservoirs or estuaries are regularly dredged for harbor, water resource or maintenance management, and a vast majority is disposed at sea or inland as a waste product. The re-use of dredged sediments in the heavy clay industry as an alternative to fossil sedimentary rocks requires further investigation to provide fingerprint of these fine-grained sediment composition with respect to the geology of sediment source.

Provenance studies, traditionally focus on mineralogical composition of sand which is easier to analyze with standard petrography techniques (Zuffa, 2013 and references therein).

Mineralogy of silt and clay carried in suspension by rivers is determined by X-ray powderdiffraction analyses (XRD), composition is generally related to sediment provenance [START_REF] Klages | Suspended solids carried by the Gallatin River of southwestern Montana: II. Using mineralogy for inferring sources[END_REF]Benedetti et al., 2006;[START_REF] Garzanti | Quantifying sand provenance and erosion (Marsyandi River, Nepal Himalaya)[END_REF][START_REF] Garzanti | Mineralogical and chemical variability of fluvial sediments 2. Suspended-load silt (Ganga-Brahmaputra, Bangladesh)[END_REF], it may change along the river course, influenced by sediment dilution or concentration from tributaries, chemical weathering during transport and seasonal input [START_REF] Walling | Linking land use, erosion and sediment yields in river basins[END_REF].

The aim of this study is to achieve a resource-efficient evaluation for the recovery of finegrained dredged sediments in the heavy clay industry by investigating relationship between sediment provenance and industrial properties. Spot sampling of fine-grained sediment was conducted in French dam reservoirs and estuaries, collecting sediments from a large diversity of source rocks and geomorphic contexts. At first broad compositional pattern of surficial sediments is described from two large dam reservoirs, Lake Serre Ponçon (Alps) and Lake Grandval (Massif Central). Then, a resource-efficient evaluation using principal component analysis (PCA) is conducted between provenance, geomorphic context, sediment composition and scores during the technological tests of the heavy clay industry. Finally, consistency between proposed fingerprint categories from PCA, Mineralogical Industrial Framework domains (MIF, [START_REF] Haurine | Development of an industrial mineralogical framework to evaluate mixtures from reservoir sediment for recovery by the heavy clay industry: Application of the Durance system (France)[END_REF] and technological tests is discussed.

Setting

Among the numerous dams built along the course of the French rivers and estuaries, we selected sites fed from great diversity of sediment sources (plutonic, volcanic, metamorphic and sedimentary rocks) and geomorphic contexts (active mountain range, remains of ancient volcanoes and chains, sedimentary basins) (Fig. 1). Fig. 1. Site location on the lithological map of France (BRGM, 2008). Sites labeled per river system and color-coded according to the geology of the dominant source (see supplementary material 1 for details).

Variability of sediment composition was investigated from two large dam reservoirs located in an active mountain range (Lake Serre Ponçon, Alps), and in an ancient chain (Lake Grandval, Massif Central), respectively. Lake Serre-Ponçon (water volume 1,272 10 6 m 3 ) (Fig. 1, site 10) gathers waters from two major streams; the Durance (watershed 2170 km²) and Ubaye (watershed 1011 km²) rivers, and a minor one the Blanche River (watershed 205 km²) and two mountain creeks (Vachères and Boscodon) (Fig. 2a). The watershed is characterized by mountain reliefs, heterogeneous lithologies (granite, metamorphic and is five times smaller (water volume 272 10 6 m 3 ) (Fig. 1, site 22). It is fed by the Truyère River (watershed 1782 km²) and minor creeks (L'Ander, watershed 310 km²; and Le Bès, watershed 283 km²) (Fig. 2b). The watershed corresponds to low mountain reliefs, heterogeneous lithologies (granite, gneiss with some volcanic rocks), the erosion rate is moderate [START_REF] Colmar | Démarche de validation régionale par avis d'experts du modèle MESALES d'estimation de l'aléa érosif[END_REF]. Climate in both watersheds is mountainous with some Mediterranean influence favoring seasonal high peak discharges during which sediment accumulates at the mouth of the feeding rivers forming deltas that prograde into the dam reservoir. Fine-grained sediment accumulates in distal depositional environments fed by suspension. Estuaries are located along the English Channel and the Atlantic coast (Fig. 1). To the north, the Somme (site 80) and the Seine (sites 07) estuaries are fed by fluvial systems dominantly flowing over sedimentary substrates (marl and limestone, clay and sand). Estuaries along the north coast of the Massif Armoricain are fed by rivers flowing over mixed plutonic and metamorphic rocks (sites 60 and 70). Those from the Atlantic coast are fed by rivers flowing over mixed plutonic, metamorphic and sedimentary rocks (sites 42, 43, 57 and 59). Finally, the Arcachon bay (site 30) is fed by a river flowing over sedimentary substrate composed of sandy deposits.

Selected sites provide a variety of sediment sources in different physiographic settings: active mountain range (Alps -sites 10 to 13), ancient chain (Massif Central -sites 01-03, 20 to 21, 40 to 41), remnant of a chain (Massif Armoricain -sites 50-55, 60 and 70) or sedimentary basin (Paris basin -sites 04-07, 80; Aquitaine basin -sites 30, 42-43, 53, 56-59).

Material and Methods

Material

A total of 86 surficial spot samples were collected from 37 dam reservoirs and estuaries (Fig. 1; supplementary material 1). About two third of the samples come from dam reservoirs (69%). Sediment sources are distributed as follow: sedimentary rocks (28%), plutonic and metamorphic rocks (27%), plutonic, metamorphic and sedimentary rocks (28%), plutonic rocks (7%), metamorphic rocks (4%) and dominant volcanic rocks (6%). In addition, 11 industrial mixtures from the French heavy clay industry were analyzed to enlarge the industrial dataset built by [START_REF] Haurine | Caractérisation d'atterrissements d'argiles récents sur le territoire français, en vue de leur valorisation dans l'industrie des matériaux de construction en terre cuite[END_REF], now representative of 90% of the French production over the last 15 years. For reasons of confidentiality, data from industrial mixtures are not detailed in this paper.

Sampling (up to 20 kg per site) was conducted using a spade during low water levels to access the distal part of the reservoir sediment wedge where fine-grained sediment accumulate by silting. Lake Serre Ponçon sediment was sampled at the end of winter when lake level is at minimum, some 10 m below the high level. Lake Grandval and Lake Sarran were sampled during the maintenance period; the nearly emptied reservoir gave access to lake-bottom sediment. Similarly, estuaries were sampled at low tide, away from tidal channels. In addition, four samples of dredged sediments were included, three from the Seine estuary (provided by Le Havre seaport) and one from the Cadarache settling pond (Durance River -provided by EDF). Samples were first oven dried at 40°C and stored in a dry room. Analyses were conducted on samples dried in a forced-air drying oven at 40°C for 4 to 8 days.

Analytical methods

Particle size analysis

Dried samples were suspended in an excess of water, mixed to separate particles, and separation at 40 µm was obtained by wet sieving. Particle size distribution was determined by dry sieving (fraction > 40 µm) and by sedimentation with SediGraph 5100 Particle Size Analyser (Micrometrics) (fraction < 40 µm). A dispersing and deflocculating agent (sodium polymetaphosphate, 1%, pH 6.5-7.2) was added to the aqueous suspension. Error is ± 10%.

Results are presented for the particle-size classes used in the heavy clay industry: 0.5, 2.5, 40, 200, 500 and >500 µm (supplementary material 2). Particle-size analysis was conducted on 53 sediment samples, representative of the varied sediment sources and geomorphological contexts (supplementary material 2). Results are plotted on the Winkler diagram [START_REF] Winkler | Bedeutung der Korngrössenverteilung und des mineral-bestandes von Tonen für die Herstellung grobkeramischer erzeugnisse[END_REF], a ternary plot of three particle size fractions (< 2.5 μm, 2.5-25 μm and > 25 μm)

(Supplementary material 2). Domains from the French tile and brick raw materials are also indicated on the ternary plot.

Mineralogical analyses

Mineralogical analyses were conducted on the silt fraction (< 40 µm). They were carried out via X-ray diffraction (XRD) using PANalytical's X-ray diffractometer (Phillips), CuKα radiation. Quantitative mineral analysis of the bulk sample was performed using random powder mounts. EVA software (Bruker DIFFRACPlus 2007) was used for identification and quantitative phase analysis based on scan wavelength (lambda) and the normalized intensity ratio (RIR) method [START_REF] Chung | Quantitative interpretation of X-ray diffraction patterns. I. Matrix flushing method of quantitative multicomponent analysis[END_REF], (supplementary material 3). Relative Error is ± 5%.Following the removal of carbonate by weak acid, particles smaller than 2 μm were separated by sampling the upper 2 cm of the clay suspension after 100 min. Identification of the clay minerals was performed according to the position of the (00l) series of basal reflections on three XRD diagrams (air-drying, ethylene-glycol salvation and heating at 490 °C for 2 h, [START_REF] Moore | X-Ray Diffraction and the Identification and Analysis of Clay Minerals[END_REF]. Identification and relative proportion of clay minerals was performed using recommended protocol by [START_REF] Kahle | Review of XRD-based quantitative analyses of clay minerals in soils: the suitability of mineral intensity factors[END_REF] (supplementary material 4). Error estimate is ± 5%.

Mineralogical analyses were performed on the 86 samples (supplementary materials 3 and 4)

to investigate the compositional pattern within dam reservoirs (Lake Serre Ponçon, 21 samples, Fig. 2a, Lake Grandval, 5 samples, Fig. 2b); and to compare silting sites fed by different lithological sources (Fig. 3a,b).

Extrusion

A representative subsample of 8 kg of dried sediment was gently crushed to eliminate the aggregates that formed during the drying. The loose sediment was then weighted, mixed with the suitable quantity of water to obtain a plastic paste with extrusion shaping capacity (for shaping water content see supplementary material 6). For each sample, several specimen bars were extruded to conduct tests at the laboratory scale (10 x 2 x 2 cm 3 for shrinkage and water absorption measurement, and 13 x 2.5 x 1 cm 3 for bending strength test) (supplementary material 5). The plastic paste was weighted to evaluate the proportion of water in the paste (water shaping). Raw specimen bar plasticity was appraised in a semi-quantitative way using an index ranging from poor, fair, good, very good (plasticity raw) (supplementary material 6).

Technological tests

Technological tests were performed on the 24 successfully extruded samples (i.e. with a suitable plasticity) (Fig. 4, 3c, supplementary material 5, 6 and 7). Extruded specimen bars dedicated to the determination of the drying behavior were dried at room temperature for 24 h. During this period, the drying behavior was measured with a barrelatograph (Adamel), which traces the Bigot's curve, representing the humidity in percentage of the dry weight (and thus the moisture loss) as a function of the longitudinal shrinkage in percentage of the dry length (shrinkage dry).

Specimen bars dedicated to the study of the characteristics of the material after firing (water absorption, aspect changes, and mechanical resistance, i.e. flexural strength) were dried at room temperature for one week. Then, they were placed for 48 h at 105 °C in ovens to complete drying, before being fired. The firing cycle consisted in a slow heating gradient of 100° C/h followed by a 2 h steady stage at maximum temperature (50 °C steps from 850 to 1150 °C), before cooling. Tests were only conducted on specimen bars fired at 950 °C, average temperature of industrial kiln between that of bricks [START_REF] Johari | Effect of the change of firing temperature on microstructure and physical properties of clay bricks from Beruas (Malaysia)[END_REF] and tiles [START_REF] Cultrone | Influence of mineralogy and firing temperature on the porosity of bricks[END_REF]. For each sample, a visual inspection of the fired specimen bar at 950 °C evaluated the bar alteration during the firing process by comparison with the crude specimen bar: occurrences of cracks, scum, lime blowing, shape deformation (shape 950) (supplementary material 5). Finally, flexural strength was investigated through 3-points flexural bending tests (press LFPlus-Lloyd Instruments LTD-1KN) on unfired (F. strength dry) and fired at 950 °C (F. strength 950) specimen bars.

PCA analysis

Identification vs. F2 was coded according to the geology of the dominant sediment source and the results of the extrusion process (Fig. 3, observations).

Results

Particle-size distribution

Particle-size analysis of the 53 samples representative of the varied sediment sources showed that they correspond to silt (supplementary material 2). Half of the samples are medium to fine silt with less than 5% of particles larger than 200 μm. Sediments showing a poor sorting (30 to 50% of particles larger than 200 µm) correspond to 25% of the samples.

Plot of the particle size distribution on the Winkler diagram [START_REF] Winkler | Bedeutung der Korngrössenverteilung und des mineral-bestandes von Tonen für die Herstellung grobkeramischer erzeugnisse[END_REF] shows that most of the samples fall within or close to the tile hollow brick or solid brick domains (supplementary material 2). Samples with more than 70% of large particles (>25 µm) are from dam reservoirs (plutonic and metamorphic sources); and those with less than 10% are from dam reservoirs and estuaries (mainly mixed sources). Some contain a high percentage (> 60%) of particles between 2.5-25 µm, they were collected in dam reservoirs.

Particle-size distributions of industrial materials -i.e. crushed sedimentary rocks extracted from quarries -are distributed between the three industrial domains (supplementary material 2). Those of industrial mixtures cluster within the respective industrial domains, industrial mixtures for brick production contain slightly more coarse-grained particles than those dedicated to tiles.

Mineralogical composition

Compositional pattern at the scale of a dam reservoir -Lake Serre Ponçon and Lake Grandval

In Lake Serre Ponçon, the average mineralogical composition of the silt fraction (Fig. 2a) comprises carbonate (29%), quartz (19%), and clay minerals (36%). Carbonate content (dominantly calcite) shows the highest variability (σ = 13). Carbonates in the upstream reach (30%) and lacustrine delta of the Durance (22%) are present in fairly similar proportion than in the Ubaye River sediments (28%). The largest carbonate content is observed in the Boscodon (58%) and Blanche (36%) delta sediments and close by beaches (36%).

Downstream of the Serre-Ponçon dam, the carbonate content (30%) of the Durance sediment is very similar to that of the upstream Durance or Ubaye sediments, reflecting the major contribution from these two streams draining large basins. Clay minerals and non-expandable clay mineral chlorite, muscovite, quartz and feldspar contents are less variable, fluctuations (σ < 6%) are within the error range. The average clay mineral assemblages are composed of illite (60%) and chlorite (40%) (Fig. 2a). Kaolinite is present in the upstream Durance delta samples (20%) resulting in lower illite (50%) and chlorite (30%) contents. Mixed layers (I/S) were identified in the Vachère creek sediment (10%).

In Lake Grandval, the average composition of lake-bottom sediment is dominated by clay minerals (40%), feldspars (24%), muscovite (19%), quartz (17%) (Fig. 2b). Fluctuations are within the error range (σ ≤ 7). Clay mineral content shows the highest variability: from 38% in the proximal sediments of the Truyères River and Ternes Creek, to 20% in the distal lake deposits. The average clay mineral association comprises illite and mixed-layer clays (illite/smectite and chlorite/smectite) in equal proportions (30%), then kaolinite (20%) and chlorite (20%) (Fig. 2b). No smectite was identified. Mixed-layer clays are present in lower proportion in the proximal delta sediment (25%) than in the distal ones (40%).

Sediments

Sediments are composed of a limited number of minerals, but with contrasted proportions.

Sediments comprise quartz (∼ 30%) in association with K-feldpars (10 to 40%), clay minerals (25 to 55%), muscovite (<10%) and calcite (0 to 35%) (supplementary material 3). Clay mineral assemblages are composed of kaolinite (25 to 45%), illite (15 to 40%), chlorite (0 to 20%), and mixed-layer clays (0 to 40%); smectite (5 to 35%) is present in less than 25% of the samples (supplementary material 4). Other minerals -albite, microcline and dolomite -are generally present in very low proportion (≤ 5%). In the following, albite and microcline are included in the feldspar group with K-feldspars; and dolomite in the carbonate group with calcite.

Industrial mixtures

Mean composition of industrial mixtures is dominated by clay minerals (39%) and quartz (35%) associated to feldspar (10%), muscovite (7%) and calcite (6%). Clay mineral assemblages comprise kaolinite (34%), mixed-layer clays (24%), illite (22%), smectite (14%)

and chlorite (6%).

Minerals as provenance indicators of sediments

The PCA results of the mineralogical associations of the sediments and industrial mixtures are presented in Figure 3a, b. In this study we only considered the first two eigenvalues, accounting for 61% of the total variance of the mineralogy dataset (Fig. 3a); and 74% of the clay mineral dataset (Fig. 3b).

Fig. 3. PCA results from sediments and industrial mixtures (detailed results in supplementary material 8).

In the mineralogical analysis, 32% of the total variance is captured by the first principal component (F1) whereas the second component (F2) captures 29% (Fig. 3a). Variable plot and associated factor loadings on F1 vs. F2 axes show that the first axis (F1) mostly exhibits the opposition between the clay mineral and carbonate variables, and the feldspar and quartz variables. The second component (F2) shows that the chlorite and muscovite variables are Industrial mixtures are scattered on the left side of the score plot.

Technological tests

Extrusion success rate (24 samples out of 53) is very high for samples that plot within the tile domain or show a lower content in particles larger than 25 µm. It is lower for samples that plot within the brick domain (50%). Finally samples plotted within the solid brick domain or with more than 50% of particles between 2.5 -25 µm or >25 µm could not be extruded (supplementary material 2). Half of the specimen bars (12 samples) had excellent plasticity, an even shape, sharp edges and a smooth surface (sample 22a presents some cracks). More than half of the specimen bars with a medium plasticity (7 samples) presents irregular shapes (samples 23a, 23b) or cracks along the edges (samples 22a, 22d). Specimen bars with low plasticity show either a rough surface (samples 07b, 07d), an irregular shape (sample, 80), or cracks along the edges (sample 25). shaping the raw material from the sediment samples shows a large dispersion (15 to 42%), far larger than that observed from the industrial mixtures (16 to 26%) (Fig. 4a), resulting in median (25%) and mean (27%) values higher than those of the industrial mixtures (21% bricks, 20% tiles). Shrinkage during drying shows similar trends (Fig. 4b), minimum values (around 2%) are comparable to the industrial ones (bricks 4%, tiles 2%), maximum ones (13%) are nearly two times larger (bricks 6.5%, tiles 7%). Mean values of sediment bars (15%) are also higher than those from the brick (5%) or tile (7%). Data from the bending mechanical strength test on dried bars indicate a larger dispersion for the sediment values than the industrial mixture ones, mean and median values are quite comparable for all materials (sediment 5MPa, bricks 4 MPa, and tiles 6 MPa) (Fig. 4c).

Examination of the fired bars showed that more than half of the sediment bars of excellent to good quality kept their original shape (supplementary material 5 and 6). Several fired bars of good quality present some defects developed during firing such as deformation (samples 57a, 59b), cracks (samples 12a, 23a, 54b), lime blowing (samples 04b, 42), and deformation in association to some lime blowing (samples 06b, 07a, 07b). Lime blowing can be easily eliminated by immersion in slightly acidic water after firing, a process that is used in the firing industry [START_REF] Kornmann | Matériaux de construction en terre cuite -fabrication et propriétés[END_REF]. One sample is of medium quality with soluble salts efflorescence (80).

Data from water absorption of sediment specimen bars after firing at 950 °C show a large dispersion (12 to 47%), mean values (around 37%), higher than those of the industrial mixtures (bricks 13%, tiles 11%) (Fig. 4a). Mean values of shrinkage associated to firing (0.9%) are very close of those obtained from the industrial mixtures (bricks 0.5%, tiles 0.7%) with a good overlap (80% of the sediment data fall within the industrial values) (Fig. 4b).

Results from mechanical strength tests on fired bars are in the range of the industrial values with a larger dispersion (Fig. 4c). Mean values from fired sediment bars (around 13 MPa) are slightly higher than those from the industrial mixtures (around 10 MPa).

PCA results of the technological tests of the sediment samples and industrial mixtures are negative to slightly positive values).

Discussion

Representativeness of spot sediment samples

Particle-size distribution of spot samples in environment dominated by silting processes shows some variability partly controlled by external parameters (erosion process, hydrological regime) and internal ones (geometry of the water body and the sediment wedge) [START_REF] Lane | Making stratigraphy in the Anthropocene: climate change impacts and economic conditions controlling the supply of sediment to Lake Geneva[END_REF][START_REF] Loizeau | Taux d'accumulation de sédiments récents et bilan de la matière particulaire dans le Léman (Suisse-France)[END_REF][START_REF] Valero-Garcés | Sediment sources and siltation in mountain reservoirs: a case study from the Central Spanish Pyrenees[END_REF]. Low variability at the scale of a dam reservoir or estuary is attributed to efficient particle sorting such as series of dam along the river or tidal currents in estuaries [START_REF] Bertin | Tidal inlet response to sediment infilling of the associated bay and possible implications of human activities: the Marennes-Oléron Bay and the Maumusson Inlet, France[END_REF].

Sediment composition -mineralogy and clay minerals does not vary significantly at the scale of a dam reservoir or estuary. Changes in proportion are larger for minerals than clay minerals; this is likely to be attributed to the lower dependence of the clay minerals to the sampling site during silting. Sediment composition may be locally influenced by the input from tributaries draining areas with distinct substrates and by calcite precipitation that may occur in the lakes during summer [START_REF] Filippi | Monitoring detrital input and resuspension effects on sediment trap material using mineralogy and stable isotopes (δ18O and δ13C): The case of Lake Neuchâtel (Switzerland)[END_REF].

Despite their limitations, results of the spot sediment samples serve to demonstrate the potential of the fingerprinting approach in establishing composition patterns -mineralogy and clay minerals -from silted sediment in water bodies fed from a diversity of sediment sources.

Sediment source fingerprinting

In this study, attention focused on the <40 µm sediment fraction with the objective of the recovery of dredged sediments, as full or partial substitution of fossil resource in the heavy clay industry. Although particle-size distribution and proportion of plastic clays play a significant role in the extrusion process, sediment composition is also crucial. Thus, extrusion process failed on 52% of the sediments with particle-size distribution similar to those of the industrial domains on the Winkler diagram (supplementary material 2).

Provenance fingerprinting method is based on sediment mineralogical composition. The multivariate statistical analysis (PCA) is supportive in predicting the potential of sediment for the heavy clay industry based on five broad provenances (S, P, M, P-M-(V), P-M-S). Four groups of sediment sources have been categorized according to the sample clustering in the principal component F1-F2 plot (Fig. 3).

The first category shows the fingerprint of particles produced by the erosion of sedimentary rocks (S source). Composition varies widely between carbonate and siliciclastic sources, but is dominated by quartz (20 to 70%), carbonates (20 to 60%) and clay minerals (5 to 40%).

Clay mineral assemblages comprise mixed-layer clays and kaolinite, with around 10% of smectite. This group (despite being projected in the hollow brick domain on the Winkler diagram) had poor technological results such as high water absorption and low shrinkage after firing certainly because of carbonate decomposition between 700-900 °C observed on the DTA/GTA diagrams, the loss of weight and the endothermic specific peaks of magnesium or calcium carbonates decomposition [START_REF] Haurine | Caractérisation d'atterrissements d'argiles récents sur le territoire français, en vue de leur valorisation dans l'industrie des matériaux de construction en terre cuite[END_REF][START_REF] Haurine | Caractérisation d'atterrissements d'argiles récents sur le territoire français, en vue de leur valorisation dans l'industrie des matériaux de construction en terre cuite[END_REF], or high quartz content associated to a low clay mineral one (siliciclastic source).

The second category shows the fingerprint of detritus produced by the weathering of plutonic, metamorphic and/or volcanic rocks of ancient orogen (P, M, P-M-(V) sources). Composition consists of silicates (60 to 80% -quartz, feldspars, mica and chlorite) and clay minerals (20 and 40%).They include a large content of mixed-layer clays associated to chlorite and illite.

This group had also poor technological results despite particle-size distribution falling within the brick and solid brick domains. The need of high quantity of water to be extruded without a high drying shrinkage, high water absorption et low mechanical strength at 950°C are put in relation to a lack of melting compounds like soda or potassic feldspars.

The third category corresponds to the fingerprint of the erosion of basement and sedimentary cover of active or ancient orogen (P-M-S source). Composition comprises relatively high percentages of clay minerals (40 to 60%) associated to quartz (20 to 50%) and low amount of carbonates (10-20%) and feldspars and mica (10 to 30%). Clay mineral assemblages are quite dispersed, mainly consisting of mixed-layer clay and smectite in association with some chlorite and illite. High smectite content (35%) is observed in some samples. Best results for the technological tests were obtained for this group of particle-size distribution mainly characterizd by a low content in particles > 25 µm. High mechanical strength on dried and fired samples, poor firing shrinkage but high drying shrinkage (that could be problematic for drying) are attributed to the smectite content and the presence of diatoms in the estuary sediments (Paulmier, 1994), these are mechanically resistant, with a high porosity and without transformation or decomposition during firing [START_REF] Escalera | The production of porous brick material from diatomaceous earth and Brazil nut shell ash[END_REF].

The fourth one is composed of sediments from P, M and P-M-(V) sources that could not be extruded. Composition is dominated by quartz and feldspars (60 to 100%), no specific pattern is observed for the clay mineral association. Extrusion results may have also been influenced by the particle-size distribution, mostly with a large amount of medium (2.5 to 25 µm) or coarse grained particles (> 25 µm), certainly because of a lack of clay minerals that permits sliding and cohesion between particles.

Mineral association reflects the sediment provenance from the rocks of the watershed. Clay Dispersion suggests that refined classifications might capture specific sediment composition in relation to provenance (e.g. siliciclastic vs carbonate-rich sedimentary rocks, types of metamorphic or volcanic rocks).

Consistency between PCA results and the Mineralogical Industrial

Framework

The Mineralogical Industrial Framework (MIF, [START_REF] Haurine | Development of an industrial mineralogical framework to evaluate mixtures from reservoir sediment for recovery by the heavy clay industry: Application of the Durance system (France)[END_REF]) is a decision tool based mineralogy and clay mineral assemblages of industrial mixtures clustering in domains on each of four ternary diagrams (Fig. 5). Plot of the composition of the industrial mixtures analyzed in this study falls within the originally defined industrial domains, complementing areas with few data. As for the original data set, no specific pattern is observed between the tile or brick industrial mixtures. Samples that could not be extruded (all samples from P, M sources and some samples from P-M and S sources) plot outside of the ternary diagrams because of low clay content associated to very high silicate content (quartz, or feldspar and mica) (P, M, P-M sources), or a very high carbonate content (S source) (Fig. 5a). Nearly all samples fall within the industrial domains on the clay ternary diagrams (Fig. 5b). These results indicate that the further the sediment samples plot outside the industrial domains, the lesser is the possibility to extrude the wet paste, or the lower are the scores of the technological tests.

Consistent results between the PCA categories for sediment source fingerprinting and the MIF domains based on mineralogy and scores of technological tests indicate that sediments originating from P-M-S sources show the closest properties to those of industrial mixtures.

Properties of other sediments could be easily enhanced by mixing with materials having Composition is dominated by clay minerals and quartz with some carbonates, chlorite and muscovite. Sediments from S and P-M sources obtained less effective scores attributed to the high content in carbonates (S source) or silicates (P-M sources, chlorite, muscovite and feldspars). Sediment from P or M sources could not be extruded partly due to the low clay mineral content and coarser particle-size.

Consistent results between the PCA fingerprinting method, MIF industrial domains, and technological tests show that even though the sediment source categories are simplified, they constitute a reference to predict the potential of sediment as raw material for the heavy clay industry. The MIF decision tool proved to be an efficient reliable tool as it only necessitates sediment composition.

In an industrial scale perspective, environmental chemical analyses (such as S, F, Cl compounds and CO2) should be conducted to further characterize the silted sediments. Costs associated to sediment transport and treatments should also be taken into account keeping in mind that environmental standards of the industry are evolving due to the awareness of the benefits of a sustainable environment policy. This classification should be useful to the heavy clay industry managers when making decision regarding the fossil resource preservation by substitution with dredged sediments.

Fig. 2 .

 2 Fig. 2. Sediment compositional pattern at the scale of large dam reservoirs: Lake Serre-

  coupled and negatively correlated to the quartz variable. Plot of the samples (observations) on F1 vs. F2 shows that F1 allows a separation between the sediment sources dominated by sedimentary (S sources), a mixture of plutonic, metamorphic and sedimentary rocks (P-M-S sources), mixed plutonic-metamorphic-(volcanic) rocks (P-M-(V) sources) and plutonic (P source) or metamorphic (M source) rocks. The second component F2 allows a fairly good separation between the S and M sources, and those dominated by P, P-M-(V) and P-M-S rocks. Four main sample clusters are identified in relation to the sediment provenance: 1) S sources (F1, F2 positive values), 2) P-M-S sources (F1 positive and F2 negative values), 3) P-M-(V) sources (F1 and F2 negative values), and 4) M sources and some samples from P-M sources (F1 negative and F2 positive values). Industrial mixtures are mainly clustered in the middle of the score plot with a slight distribution towards the right side of F1 and upper side of F2.In the clay mineral analysis, 39% of the total variance is captured by the first principal component (F1) and 31% by the second one (F2) (Fig.3b). Variable plot and associated factor loadings on F1 vs. F2 axes show that the chlorite and illite variables are coupled, and negatively correlated to the kaolinite and smectite variables (component F1). The second component (F2) shows that the mixed-layer clay variable is negatively correlated to the smectite variable. Plot of the samples (observations) on F1 vs. F2 shows that F1 allows a slight separation between the sediment sources dominated by sedimentary rocks (S sources) and the other sources (P, M, P-M-(V) and P-M-S sources). The second component F2 also allows a slight separation between the sediment sources dominated by S sources or P source or P-M-(V) sources, and those corresponding to M source, and P-M-S sources, in fluvial dam reservoirs. Samples from coastal sites fed by P-M-S sources are scattered over the plot.Despite some overlapping, it is possible to identify three main sample groups for the fluvial samples: 1) S sources (F1 negative values); 2) P, P-M-(V) sources (F1, F2 positive or slightly negative values); 3) M sources and P-M-S sources (F1 positive and F2 negative values).

Fig. 4 .

 4 Fig. 4. Box plot of technological tests of sediments and industrial mixtures: affinity with

  presented in Figure3c. The first principal component (F1) captures 39% of the total variance whereas the second component (F2) captures 27% Variable plot and associated factor loadings on F1 vs. F2 axes show that the first axis (F1) mostly exhibits that plasticity of extruded material (plasticity raw), fired specimen bar quality (quality 950 °C) and water absorption after firing at 950 °C (water absorbed 950 °C) variables are coupled. The second component (F2) shows a high loading factor for the water shaping variable. Plot of the samples (Fig.3c, observations) on F1 vs. F2 shows that F1 allows a separation between the sediment sources dominated by P-M-S rocks (fluvial and coastal sites) and those by P-M-(V) rocks. Samples from S sources are scattered along F1. No specific distribution is observed along the second component F2. It is possible to identify two main sample clusters: the first one contains samples from P-M-S sources (F1, F2 positive values), the second one corresponds to samples from P-M-(V) sources (F1 negative and F2 positive values). Industrial mixtures are mainly clustered in the lower right-hand of the score plot (F1 positive values, F2

  minerals are more complex to relate to a specific sediment source because they depend on dominant weathering processes, i.e. physical in active mountain ranges (illite and chlorite) vs chemical in ancient orogen (mixed-layer clays and smectite) or sedimentary basins (mixedlayer clays and kaolinite). In addition to the fluvial input, a contribution from marine origin may be observed in macrotidal estuaries as for example in the Seine estuary, where sediments from the erosion of the Cotentin peninsula are brought in by the longshore drift(Walter- Simmonet, 2008).Although simplified, the proposed categories of sediment provenance help defining the dredged sediment properties for substitution of fossil material in the heavy clay industry. Best technological results are obtained from P-M-S sources either in fluvial or estuaries.

Fig. 5 .

 5 Fig. 5. Projection of sediment samples on the Mineralogical industrial framework (MIF), a

  of indicator minerals from sampled sediments can help trace related sediment source; identify sediment with the most appropriate properties for a use by the heavy clay

industry. With this scope, we carried out Principal Component Analysis (PCA) with XLStat software, three dataset including sediment and industrial mixtures were considered: mineralogy, clay minerals, and technical properties. Loading plot, scree plot and projection of observations on the first two components (F1 vs. F2) are given in Fig.

3

. Eigenvectors, factor loadings for each component are given in supplementary material 8. Plot of the samples on F1

Acknowledgements

This work benefited from an ANRT support (convention N°2012-093) and is associated to the SEDIBRIC project financed by ADEME and Région Normandie, AMI funding CPIER VDS.

complementary properties (in-between sites or with fossil material), or by addition of correcting agents (quartz sand, grinded calcined clay wastes…), a conventional practice in the heavy clay industry [START_REF] Haurine | Development of an industrial mineralogical framework to evaluate mixtures from reservoir sediment for recovery by the heavy clay industry: Application of the Durance system (France)[END_REF].

Environmental studies (emission, carbon, metals) are needed to further characterize the silted sediments. Estuary sediments are rich in chlorine and sulphur, seawater containing more dissolved ions than most rivers (supplementary material 9). Some compounds could be transformed during firing between 850 and 1100 °C on gaseous pollutants and be emitted on atmosphere; which environmental impact should be evaluated.

Conclusions

Sediment provenance was identified as the main parameter controlling the recovery of dredged sediment in the characterization of silted in the heavy clay industry, thus contributing to reduce the proportion of quarried fossil materials by substituting part of a non renewable resource by material from dredging in dams, canals and harbors, by material presented considered as waste. Mineralogy plays an important role as indicated by the contrasted results during technological tests of samples having similar particle-size distributions.

In this context, PCA analyses (mineralogical composition) showed four categories of samples based on their provenance, confirming the fingerprinting approach from spot sampling of fine grained sediments in dam reservoirs and estuaries. Mineralogy proved to be more discriminating than clay-mineral associations, the later being controlled by weathering processes in geomorphic contexts. Samples from sites fed from the erosion of P-M-S rocks obtained the best scores during the technological tests, close to the industrial values.

Authors wish to thank the heavy clay producers for providing industrial mixtures. We also wish to acknowledge F. Théry, W. Pesle and G. Vuarand (EDF); F. Bourdin and S. Brasselet


Diana Vitiello

Benoit Nait-Ali

Nicolas Tessier-Doyen

Thorsten Tonnesen

Luís Laím

Lionel Rebouillat

David S Smith

Thermal conductivity of insulating refractory materials: comparison of steadystate and transient measurement methods

Keywords: thermal conductivity, refractories, heat losses, humidity, anisotropy, heterogeneity

Measurements of thermal conductivity with the heat flow meter, laser flash method, hot disk method and hot wire method are compared on two kinds of refractory materials: Insulating Boards and Insulating Fireclay Bricks. Heat losses, humidity, anisotropy and heterogeneity can explain the variation in thermal conductivity values obtained with the different techniques. If they are taken into account in the analysis, discrepancy within 10% can be found. The choice of the technique depends on the investigated material and on the level of information required.

1 HFM : heat flow meter HWM : hot wire method IB-LD : low density insulating boards IB-MD : medium density insulting boards IB-HD : high density insulating boards IFB : insulating fireclay bricks

Introduction

For steel making, the need to reduce heat losses through the lining of steel ladles becomes increasingly important due to the higher energy costs and new laws on environmental impact in industrial situations. The ladle is the vessel to hold and transport the hot liquid steel, in which all the secondary metallurgical operations take place. These operations require large energy input to maintain the liquid steel above the casting temperature. Therefore, the design of the steel ladle lining plays an important role. Many steel manufacturers added an insulation layer between the external steel shell and the safety lining. Its main purposes are: i) reducing heat losses through the lining and ii) keeping the lining in a stable compressed condition [START_REF] Santos | Steel ladle energy saving by refractory lining design[END_REF] [START_REF] Vitiello | Thermal properties characterization of refractory materials used in the insulation layer of steel ladles[END_REF].

Therefore, the selection of an appropriate insulating refractory material becomes crucial. This kind of refractory is usually a highly porous material with low thermal conductivity < 1 W m -1 K -1 . The conductivity may vary with temperature and can evolve with the state of the microstructure [START_REF] Vitiello | Thermal properties characterization of refractory materials used in the insulation layer of steel ladles[END_REF]. In other words, the initial behaviour characterized at room temperature can differ from that in service conditions. For these reasons, a careful and detailed evaluation of the thermal conductivity is an important aspect for the development and the performance of these materials.

Several methods are used for determining the thermal conductivity of a material. These can be classified into two main categories: steady-state and transient methods. In steady-state methods, the sample is tested after a stable temperature distribution is achieved. The thermal conductivity is obtained by evaluating the one dimensional heat flux due to the temperature gradient across the specimen [START_REF]Springer Handbook of Metrology and Testing[END_REF]. The main disadvantage is that this approach requires a long time in order to achieve the equilibrium temperature distribution inside the material. Large sample size and low conductivity increase the time to reach equilibrium. For instance, the samples measured in this work with the heat flow meter needed between 40 and 60 minutes to reach the equilibrium. On the other hand, individual measurements with transient methods are much quicker, typically less than a minute. In some techniques, such as the hot disk method, it is even possible to evaluate thermal conductivity and thermal diffusivity with a single experiment.

However when different methods are compared, the obtained values can show some variation. Tonnesen et al. [START_REF] Tonnesen | A modified equipment for determination of thermal conductivity of refractories by the hot-wire method-a critical review and comparison with the laser-flash-method[END_REF] compared the hot disk and the laser flash methods on fireclay bricks, chromia/alumina bricks and high alumina bricks. They found a difference between 5% and 20%, depending on the investigated temperature. Bourret et al. [START_REF] Bourret | Thermal conductivity of geomaterial foams based on silica fume[END_REF] compared the heat flow meter and the laser flash method on geomaterial foams revealing a maximum discrepancy of 21%. Mathis [START_REF] Mathis | Transient thermal conductivity measurements: Comparison of destructive and nondestructive techniques[END_REF] compared the hot disk and the laser flash methods on homogeneous solid samples with different amounts of conductive alumina filler in a continuous matrix, yielding differences of 20%. Thus, the discussion about which is the best technique for the refractory field is still open. The main purpose of this paper is to compare four methods: a steady-state method involving a heat flow meter [START_REF]Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus[END_REF] and three transient methods namely the laser flash [START_REF]Standard Test Method for Thermal Diffusivity by the Flash Method 1[END_REF], the hot disk [START_REF] Gustafsson | Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials[END_REF] and the hot wire methods [START_REF] Healy | The theory of the transient hot-wire method for measuring thermal conductivity[END_REF]. Attention will be focused on the advantages and disadvantages of each of them. The measurements will be made on two kinds of refractory materials: Insulating Boards and Insulating Fireclay Bricks, which both present rather little variation of thermal conductivity with temperature.

Materials and methods

Heat flow meter

The heat flow meter (HFM), supplied by CAPTEC (France), is a steady-state method used to measure the thermal conductivity of insulating materials at ambient temperature [START_REF]Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus[END_REF]. Samples are cut in the form of square slabs with two flat parallel faces and different thicknesses.

The specimen is placed between two thin copper plates equipped with thermocouples and heat flow sensors. An electrical resistance is embedded in the top plate, which acts as a heat source. The power dissipation is chosen in order to impose a temperature difference ∆T of around 4 °C between the upper and lower plates. To improve the thermal contact between the sample and the two plates, a weight is placed on top of the upper plate [START_REF] Bourret | Thermal conductivity of geomaterial foams based on silica fume[END_REF]. A simplified schematic of the measurement is shown in Figure 1a: The method measures the apparent thermal resistance Rapp [m 2 K W -1 ] using Eq. 1: ∆ /2 Eq. 1

where sup is the heat flow supplied to the sample by the upper plate [W m -2 ], inf is the heat flow coming out of the sample absorbed by the lower plate [W m -2 ] and ΔT the temperature difference between the two plates [K]. The apparent thermal resistance is the sum of two contributions: the thermal resistance of the sample Rth [m 2 K W -1 ] and the contact resistance Rc [m 2 K W -1 ] between the sample and the two plates (Eq. 2).

/

Eq. 2

where d is the thickness of the sample [m] and λ the thermal conductivity [W m -1 K -1 ]. Assuming the contact resistance does not vary between specimens, plotting the experimental data as a function of the thickness should yield a linear relation (Figure 1b). The thermal conductivity is the inverse of the slope and the contact resistance is obtained by the intercept of the linear extrapolation with the y-axis.

In terms of precision, the main factor that affects the values is the thickness. If the samples are too thick, the lateral heat losses will become significant. The overall thermal conductivity increases by up to 8% for the data in Figure 1b. However, if they are taken into account the accuracy is ± 1%. Furthermore, the samples are assumed to have two perfectly parallel faces, but a difference of ± 2% is estimated. Thus, the uncertainty of this method at room temperature is taken to be ± 3% [START_REF]Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus[END_REF] [START_REF] Iso Standard | Thermal insulation -Determination of steady-state thermal resistance and related properties -Heat flow meter apparatus[END_REF].

Laser flash method

The laser flash method (LFA) is a transient technique developed by [START_REF] Parker | Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity[END_REF] for evaluating the thermal diffusivity of different kinds of materials in a short measuring time [START_REF]Standard Test Method for Thermal Diffusivity by the Flash Method 1[END_REF] [START_REF] Parker | Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity[END_REF]. The main advantages are: i) no contact resistance between the sample and the heat source; ii) easy sample preparation; iii) rapidity of measurements.

The principle consists of sending a light energy pulse to impact on the front face of a disk sample. The temperature inside and outside the sample is assumed to be the same before the pulse and it is measured by a thermocouple, placed close to the specimen. An infrared detector records the increase of temperature on the back face as a function of time (Figure 2a). A layer of graphite covers the sample. This layer is very important in the case of semi-transparent materials which are typically white in appearance [START_REF] Albers | Effect of testing conditions on the laser flash thermal diffusivity measurements of ceramics[END_REF]. The purposes of this layer are: i) to increase the heat absorbed on the front face; ii) to increase the radiation emitted by the back face; iii) to keep the absorption constant even if the sample changes colour; iv) to prevent the laser from passing directly through the sample to the detector [START_REF] Albers | Effect of testing conditions on the laser flash thermal diffusivity measurements of ceramics[END_REF] [START_REF] Hahn | Transient Heat Transfer in Coated Diathermic Media: a theoretical study[END_REF]. A simplified schematic of the measurement set up is shown in Figure 2a. A typical temperature -time response is presented in Figure 2b. Assuming that there are no heat losses, the evaluation of the thermal diffusivity from the T-t behaviour can be made using Parker's equation (Eq. 3) [START_REF]Standard Test Method for Thermal Diffusivity by the Flash Method 1[END_REF]: where α is the thermal diffusivity [m 2 s -1 ], d the thickness of the sample [m] and t1/2 the time necessary for the back face to reach half of the maximum temperature [s]. However, the hypothesis of negligible heat losses is not always applicable, especially at high temperatures. For this reason, many other models were developed, for taking into account this effect, such as those of Cape-Lehman [START_REF] Cape | Temperature and finite pulse-time effects in the flash method for measuring thermal diffusivity[END_REF] and Degiovanni [START_REF] Degiovanni | Une nouvelle technique d'identification de la diffusivité thermique pour la méthode « flash[END_REF]. Furthermore, in the case of semi-transparent materials, another aspect to consider is the direct transmission between the two faces due to radiation effects (e.g. Mehling's model [START_REF] Mehling | Thermal diffusivity of semitransparent materials determined by flash laser method applying a new analytical model[END_REF]). For these reasons, the analysis of thermal diffusivity in the following paper was made using the Mehling's model for all the investigated temperatures.

The thermal conductivity is, then, calculated using Eq. 4:

!" # Eq. 4
where λ is the thermal conductivity [W m -1 K -1 ], α the thermal diffusivity [m 2 s -1 ], ρ the bulk density [kg m -3 ] and Cp the specific heat capacity [J kg -1 K -1 ]. For more complex formulations, Cp can be estimated from data for simple components using the rule of mixtures [START_REF] Günther | Mixing rules for the specific heat capacities of several HFCmixtures[END_REF].

The measurements were performed using a Netzsch LFA 427 in an argon atmosphere (100 mL min -1 ). The apparatus is characterized by a vertical setup: the laser system (laser wavelength ~ 1050 nm) is placed at the bottom and connected to the measurement cell by an optical fibre, while the detector (type: InSb) is positioned on the top and cooled by liquid nitrogen.

In terms of precision, the main factors that influence the thermal conductivity results are: i) density (± 2%), because the faces might be not perfectly parallel; ii) Cp (± 3%), this is affected by the technique used to estimate the chemical composition since it is evaluated with the rule of mixtures; iii) precise knowledge of sample thickness (± 0.5%). Thus, the uncertainty in conductivity values for this method is considered to be ± 5% at room temperature according to the ASTM report [START_REF]Standard Test Method for Thermal Diffusivity by the Flash Method 1[END_REF]. At high temperatures, the uncertainty in values can increase up to 10 -15% depending on the material and on the quality of the T-t curve, which can exhibit noise due to the hot environment and radiation effects.

Hot disk method

The transient plane source (TPS) technique is also known as the hot disk method or the Gustafsson probe [START_REF] Gustafsson | Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials[END_REF] [START_REF] Gustavsson | Thermal conductivity, thermal diffusivity, and specific heat of thin samples from transient measurements with hot disk sensors[END_REF]. One of the advantages of this technique is the possibility to measure simultaneously the thermal conductivity and the thermal diffusivity, and then to deduce the heat capacity per unit volume (ρ Cp) [START_REF] He | Rapid thermal conductivity measurement with a hot disk sensor: Part 1. Theoretical considerations[END_REF].

A TPS probe is a double nickel spiral supported by two thin sheets of an insulating material [START_REF] Log | Transient plane source (TPS) technique for measuring thermal transport properties of building materials[END_REF] [START_REF]Hot Disk Thermal Constants Analyser: Instruction Manual[END_REF]. It is placed between two halves of the sample material (Figure 3a) and has a double function: on one hand, it constitutes the heat source for increasing the temperature of the samples; on the other hand, it works as a "resistance thermometer" for recording the increase of temperature as a function of time (Figure 3b). The theory assumes that the probe is placed in a medium of infinite dimensions [START_REF] Log | Transient plane source (TPS) technique for measuring thermal transport properties of building materials[END_REF]. To adapt the theory and the reality, two parameters must be chosen: the radius (r) of the probe and the measurement time (t). In the first case, the probe external surface should be restrained to the central part of the samples. In the second case, the chosen measuring time t should guarantee a thermal penetration depth smaller than the real dimensions of the samples in all directions. For this reason, during the analysis of the thermal conductivity, a tmax is chosen in order to take into account the finite dimensions of the samples. Furthermore, the mathematical solution assumes a perfect contact between the probe and the two faces in contact. Taking into account the probe-sample contact thermal resistance, some of the initial points recorded (from t = 0 to tmin) are removed from the calculation.

The calculation method for evaluating the thermal properties is based on an iteration procedure, which yields the thermal diffusivity (α) as an optimised variable. The result is a linear relation (Figure 3c) between ΔT(τ) (temperature increase) and D(τ) (dimensionless specific time function) [START_REF] Iso Standard | Plastic -Determination of thermal conductivity and thermal diffusivity -Part 2: Transient plane source method[END_REF] [START_REF] Carslaw | Conduction of heat in solids[END_REF]. The function D(τ) depends on the geometrical parameters of the nickel spiral and also τ given by Eq. 5:

$ % &
Eq. 5

D(τ)

where α is the thermal diffusivity [m 2 s -1 ], t the measurement time [s] and r the radius of the probe [m]. The temperature increase is the sum of two contributions: i) the temperature increase of the sample surfaces facing the TPS probe ΔTs(τ) and ii) the temperature increase which stems from the insulating layers of the nickel spiral, as well as from the contact resistance between the sample and the probe ΔTi(τ). The slope of the linear relation yields the ΔTs(τ) and the intercept with the vertical axis gives the ΔTi(τ) [START_REF] Iso Standard | Plastic -Determination of thermal conductivity and thermal diffusivity -Part 2: Transient plane source method[END_REF].

In the case of isotropic materials, the thermal conductivity is then calculated using Eq. 6 [START_REF] Iso Standard | Plastic -Determination of thermal conductivity and thermal diffusivity -Part 2: Transient plane source method[END_REF][24]:

∆ $ ' ( )* +/ & , -. $ Eq. 6
where P0 is the heating power [W], r the radius of the probe [m] and λ the thermal conductivity [W m -1 K -1 ]. The specific heat per unit volume (ρ Cp) is calculated using Eq. 4.

In the case of anisotropic materials, the specific heat per unit volume is an important parameter, which must be used as input data for the analysis software at the beginning of the calculation. If the value inserted is wrong, the ratio between radial and axial results would be false [START_REF]Hot Disk Thermal Constants Analyser: Instruction Manual[END_REF]. In this case, the iteration procedure gives the value of radial thermal diffusivity (αrad) corresponding to the plane of the probe (disk). The radial thermal conductivity (λrad) is then calculated using Eq. 4. Finally, the axial thermal conductivity (λax) is calculated using Eq. 7 [START_REF] Iso Standard | Plastic -Determination of thermal conductivity and thermal diffusivity -Part 2: Transient plane source method[END_REF][24]:

∆ $ / 0 ' ( 1* +/ & / 0 2 / 3 -. $ / 0
Eq. 7

The measurements were performed both at the Department of Civil Engineering in Coimbra (FCTUC) using a TPS 2500S and at IRCER using a TPS 1500 in air atmosphere. At room temperature, two Kapton sensors were used: r = 14.61 mm and r = 6.403 mm.

In terms of precision, the thermal conductivity values depend on the accuracy of the output power, on the radius of the TPS probe and on the time. Furthermore, in the case of anisotropic materials, the values in the two directions strongly depend on the accuracy of the specific heat per unit volume. Thus, the uncertainty of this method is estimated to be around 2 -5% for the thermal conductivity and 5 -10% for the thermal diffusivity [START_REF] Iso Standard | Plastic -Determination of thermal conductivity and thermal diffusivity -Part 2: Transient plane source method[END_REF].

Hot wire method

The hot wire method (HWM) is a transient method, which is often used for determining the thermal conductivity of refractory bricks. Furthermore, this method has different configurations: the standard technique, which is a cross wire method (the thermocouple is connected to the middle of the wire in the perpendicular direction) [START_REF] Boer | Hot wire technique for determining high thermal conductivities[END_REF]; the parallel method [START_REF] Santos | Hot-wire parallel technique: A new method for simultaneous determination of thermal properties of polymers[END_REF]; the resistance technique [START_REF] Boer | Hot wire technique for determining high thermal conductivities[END_REF]; the two thermocouple technique [START_REF] Boer | Hot wire technique for determining high thermal conductivities[END_REF] etc. In this paper, the measurements were made with the hot wire parallel technique with a configuration developed at the Institute of Mineral Engineering (GHI) in Aachen [START_REF] Tonnesen | A modified equipment for determination of thermal conductivity of refractories by the hot-wire method-a critical review and comparison with the laser-flash-method[END_REF]. Three samples are necessary. Between the bottom and the central samples, a thermocouple and a platinum wire are placed in two parallel ground grooves, which are distant 15 mm (Figure 4a). The reference thermocouple is placed between the central and the top sample in a perpendicular direction compared to the platinum wire (Figure 4a). The theory is fairly similar to the hot disk method. The difference is that in this case, the heat source is a platinum wire, which is assumed to be infinitely thin and long and surrounded by an infinite medium [START_REF] Healy | The theory of the transient hot-wire method for measuring thermal conductivity[END_REF] [START_REF] Santos | Advances on the hot wire technique[END_REF]. When a constant electrical current is applied, a constant amount of heat flux is generated all along the wire and this causes a transient temperature field, which for a given position is logarithmically dependant on time (Figure 4b). The non-linearity at the beginning of the temperature-time response (from t = 0 to tmin) is due to the contact resistance between the samples and the wire, while the non-linearity at the end (t > tmax) is due to the finite dimensions of the samples [START_REF] Tonnesen | A modified equipment for determination of thermal conductivity of refractories by the hot-wire method-a critical review and comparison with the laser-flash-method[END_REF].

For the parallel method, the thermal conductivity is calculated using Eq. 8 [START_REF] Carslaw | Conduction of heat in solids[END_REF][25]: Eq. 8

where λ is the thermal conductivity [W m -1 K -1 ], q the heat flow [W m -1 ], α the thermal diffusivity [m 2 s -1 ], r the distance between the wire and the thermocouple [m], T(t) the temperature rise compared to the reference temperature [K] and t the time to reach that temperature [s]. Ei is a function given by Eq. 9:

47 8 4; < = -/ > 2
Eq. 9

where ;

/ ? @A
The measurements were performed at the Institute of Mineral Engineering (GHI) in Aachen using a Netzsch TCT 426 in an air atmosphere.

The accuracy of the thermal conductivity values is related to: i) nonzero heat capacity of the wire, ii) thermal radiation, iii) outer boundary conditions (axial and radial heat losses), iv) non-constant power dissipation in the Pt wire, v) finite integration time of the voltmeter, vi) temperature drift of the sample surroundings and vii) radius of the wire [START_REF] Hammerschmidt | Transient hot wire (THW) method: Uncertainty assessment[END_REF]. Therefore, the uncertainty of this method is taken to be ± 6% for small power levels and ± 1% for high power levels [START_REF] Hammerschmidt | Transient hot wire (THW) method: Uncertainty assessment[END_REF]. Furthermore, in the case of an anisotropic material, the obtained result represents an average value over different heat flow directions through the sample.

Materials

Two kinds of refractory materials were studied: Insulating Boards (IB), which are vermiculite-based materials (Figure 6a), and Insulating Fireclay Bricks (IFB), clay-based materials (Figure 6b). For the IB, three kinds were analysed: Low Density Insulating Boards (IB-LD), Medium Density Insulating Boards (IB-MD) and High Density Insulating Boards (IB-HD). Table 1 summarizes required physical properties of each material. The porosity was estimated using the following equation:

' % 1 4 ! /! / • 100
Eq. 10

where ρapp is the bulk density [kg m -3 ] and ρr the true density [kg m -3 ] measured using a helium pycnometer. For each material, ten measurements were made. Both investigated refractories are used in the insulating lining (Figure 5) to reduce heat losses through the wall of the vessel. Samples of different sizes were prepared for each material, depending on the technique. A summary of the dimensions is shown in Table 2.

Table 2 : Sample's dimensions for each method (Ф = diameter, d = thickness, A = area).

Methods

Typical dimensions

Laser flash method Φ = 10 mm, d = 2 mm An important aspect to underline is the anisotropic behaviour of Insulating Boards due to the layer structure of the vermiculite (Figure 6a). This implies that the thermal conductivity should be evaluated in at least two directions. For the laser flash method, the samples were prepared so that the cross sectional area was in one case perpendicular to the pressing direction (called "cross-plane" direction) and in the second case parallel to the pressing direction (called "in-plane" direction). For the hot disk method, the anisotropic behaviour was studied using an anisotropic analysis software module, which gives the values of thermal conductivity in the two directions with one measurement. For the hot wire method and the heat flow meter, it was not possible to take into account this aspect. In the first case, the reason is related to the technique itself, which gives an average value of λ. Secondly, for the heat flow meter measurements there was insufficient volume available in the board for extracting samples with the heat flow axis in two different orthogonal directions.

Hot-disk method

On the other hand, the Insulating Fireclay Bricks were considered macroscopically isotropic and thus, only the "cross-plane" direction was analysed. This hypothesis was verified experimentally using the laser flash method on samples cut in two different directions.

Results and discussions

The analysis in Table 3 gives the thermal conductivity values for the four refractory materials at room temperature using three techniques: the laser flash method, the hot disk method and the heat flow meter. Room temperature measurements were not made with the hot wire method because the time to achieve the equilibrium temperature distribution inside the material was too long. Only the results for the "cross-plane" direction are shown in the table. This is the most important direction since these kinds of refractory materials are used to reduce heat losses through the lining of the steel ladle.

For the laser flash method, two samples per direction were analysed. For each sample, three measurements were made. In the case of the hot disk method, three pairs of specimens were analysed and for each couple, four measurements were made. Finally, for the heat flow meter, between five and six samples with different thicknesses were measured twice. The percentage value in Table 3 gives the standard deviation, representing the amount of variation in a set of repeated measurements.

Table 3: Thermal conductivity values obtained with the laser flash method (LFA), the hot disk method (TPS) and the heat flow meter (HFM). The refractory materials were measured at room temperature in the "cross-plane" direction. λ (W m -1 K -1 ) Each result is reproducible. The standard deviations are around 3% for the HFM, between 1% and 4% for the TPS and between 1% and 3.5% for the LFA.

LFA

TPS λ (W m -1 K -1 ) HFM λ (W m -1 K -
It is evident from Table 3 that the three techniques give different values of thermal conductivity, with a maximum discrepancy of around 38%. This value is sufficiently high to merit a more detailed investigation. However, it can be noted that the discrepancy is less for the isotropic material. Several aspects were taken into account in order to better interpret the obtained results.

Heat losses

Heat losses are an important aspect for both the LFA and the HFM measurements. In the first case, they modify diffusivity values obtained using Parker's relation (Eq. 3), especially at high temperatures. For this reason, the values were corrected using Mehling's model [START_REF] Mehling | Thermal diffusivity of semitransparent materials determined by flash laser method applying a new analytical model[END_REF], which has been built into the LFA software. In the case of HFM measurements, it was possible to observe that the heat flow supplied to the sample was greater than the heat flow coming out of the sample. This is due to heat losses by convection on the lateral surfaces, which can be expressed with Newton's law (Eq. 11):

D EFG 4Hℎ 8/ 4
Eq. 11

where Фconv is the rate of the heat transfer by convection [W], A the lateral surface area [m 2 ], Tair the temperature of the air [K] and T the temperature of the sample [K]. Furthermore, the difference became larger with the increase of the thickness. These heat losses can be considered as a parallel thermal resistance, which decreases the overall thermal resistance of the material and consequently increases the apparent value of thermal conductivity. A correction was made by introducing heat losses through a heat sink term in the one-dimensional steady-state heat equation (Eq. 12) [START_REF] Trojan | O: One-dimensional analytical models of frictional heating during braking[END_REF]:

J 4ℎ 8/ 4 J K 0
Eq. 12 where h is the heat transfer coefficient [W m -2 K -1 ]. For natural convection in air a value of h = 15 W K -1 m -2 can be used. Tair is the temperature of air [K], T(z) the temperature of the material [K], L the length of the sample [m] and λ the thermal conductivity [W m -1 K -1 ] estimated considering only the values for d < 6 mm. This thickness value was chosen with the approximation that for small thicknesses, the lateral heat losses are negligible. The corrected values are shown in Table 4. In the case of IFB, the three methods now give rather close results. The discrepancy is within 10%. In the case of IB, the difference between the heat flow meter and the other two methods in the "cross-plane" direction is now around 26%. A similar discrepancy was found by Bourret et al. on geomaterial foams comparing the HFM and the LFA [START_REF] Bourret | Thermal conductivity of geomaterial foams based on silica fume[END_REF]. This means that some other aspects should be taken into account.

Humidity

Porous solids in humid atmospheres exhibit higher overall thermal conductivity. This is explained by replacing the air in the pores with a thermal conductivity of 0.026 W m -1 K -1 [START_REF] Wu | Characterization of thermal cross-talk in a MEMS-based thermopile detector array[END_REF] by water with a thermal conductivity equal to 0.6 W m -1 K -1 [START_REF] Ramires | Standard Reference Data for the Thermal Conductivity of Water[END_REF]. Work on humidity effects and drying suggests that this water is located as a film layer on the inside of the pore surface [32][33]. This can help to understand why the LFA gives the lowest values of thermal conductivity.

The LFA measurements were made in an argon atmosphere. To be sure, that inside the furnace there was only Ar, the samples were first subjected to three cycles of vacuum followed by filling with argon. As a consequence, the samples were effectively dried before the measurements. On the other hand, the TPS and the HFM were measured in the air atmosphere of standard laboratory conditions, with a typical humidity of 50%. In fact, the nature of the Insulating Boards containing layered vermiculite grains makes these IB samples particularly sensitive to their thermal and hydric history.

However, to verify the influence of the presence of the humidity, one pair of samples for each IB was left 24 h in the oven at 200 °C, cooled down up to room temperature in a desiccator and then measured again. This temperature was chosen in order to remove the physically adsorbed water and the water molecules residing in the particle spaces of the vermiculite [START_REF] Pérez-Maqueda | Study of natural and ion exchanged vermiculite by emanation thermal analysis, TG, DTA and XRD[END_REF] [START_REF] Kresten | The thermal decomposition of vermiculite[END_REF]. The same temperature was also used in the case of IFB to have comparable experimental conditions. For each material, the water content (W) on the dry basis was estimated using the following equation [START_REF] Oummadi | Optical method for evaluation of shrinkage in two dimensions during drying of ceramic green bodies[END_REF]:

L % 9 M 8 4 M N M N : • 100
Eq. 13

where mi is the mass of the sample before drying [kg] and mf the mass of the sample after drying [kg]. The results of this simple experiment are shown in Table 5. The table shows two behaviours. The isotropic IFB material seems to not be affected by the humidity. Thermo-gravimetric analysis (TGA) on IFB showed no loss in mass up to 1000 °C, which is also confirmed by the estimation of the water content (< 0.05% wt.). In the case of the anisotropic materials, by removing 4 -5% wt. of water, the thermal conductivity decreases by around 25%. Therefore, drying is an important step to avoid overestimating λ.

The same correction was made on the results obtained with the heat flow meter. The values have been adjusted to equivalent "dry" conditions of the LFA and TPS trials. Table 6 summarizes the values obtained with the three methods at room temperature taking into account the effects of the heat losses and the humidity.

Table 6: Thermal conductivity values obtained with the heat flow meter (HFM), the hot disk method (TPS) and the laser flash method (LFA) at room temperature in the "cross-plane" direction after considering the effects of heat losses and humidity. HFM values have been adjusted considering equivalent "dry" conditions of the LFA and TPS results. It is possible to observe that the values obtained with the HFM and the LFA are now rather close, even in the case of the anisotropic materials. The maximum discrepancy is within 10%. In contrast, the TPS method gives higher thermal conductivity values in the case of the anisotropic materials with a maximum discrepancy of around 26%. It is important to underline that the three methods do not correspond to exactly the same experimental conditions. For instance, the LFA and the HFM involve similar heat flow directions (linear in both cases), while for the TPS, the heat flow is spherically radial from the disc shape probe. Furthermore, the hot disk method uses larger sample dimensions, yielding a better average value of thermal conductivity in the case of heterogeneous materials.

LFA λ (W m -1 K -1 ) TPS λ (W m -1 K -1 ) HFM λ (W m -1 K -

Heterogeneity and anisotropy

The Insulating Fireclay Bricks have a fine microstructure which, at the macroscale, is homogeneously distributed (Figure 6b). This means that small mm sized samples can be representative of the entire brick. This interpretation is also confirmed by the results shown in Table 6, in which the maximum discrepancy between the three techniques is within 10%.

On the other hand, the Insulating Boards have microstructures with greater heterogeneity, mostly linked to the layer structure of the vermiculite and its orientation (Figure 6a). After the correction of the effects of the heat losses and the humidity, the difference between the HFM and the LFA is within 10%, while the difference between the TPS and the other two methods is within 26%. This might be related to the effect of the heterogeneous microstructure.

The effect of heterogeneity is linked to the anisotropic conductivity of individual grains. Furthermore, orientation of these grains in brick forming leads to anisotropic thermal conductivity at the macroscopic scale. If this factor is not taken into account, the input value in the modelling studies of the heat transfer through the lining of steel ladles will be higher than the real value and thus, the thickness of the insulation to apply will be overestimated with economic consequences.

To verify this interpretation, hot wire measurements were made on IB samples (Figure 7). The results are compared to those obtained with the LFA method in the two directions. The graphs for the three refractory materials show that the thermal conductivity values given by the HWM are between those obtained with the LFA. In particular, they are higher than the values obtained in the "cross-plane" direction, which is the most important direction. This supports the interpretation of a slight overestimation of the thickness of the insulation layer based on HWM values. Furthermore, Figure 7 also shows that with the reduction of the pore volume fraction the effect of the anisotropy becomes more significant. High Density Insulating Boards (Figure 7c) exhibit a higher difference between the λ values in the two directions compare to Low Density (Figure 7a) and Medium Density (Figure 7b) Insulating Boards. This validates the hypothesis that the anisotropic behaviour is related to the orientation of the layer structure of the vermiculite. The higher proportion of solid phase in the IB-HD emphasizes this characteristic compared to the homogenizing effect of the isotropic pores.

Conclusion

Thermal conductivity is an input parameter, which is required for modelling of heat transfer through a steel ladle lining. Therefore, its estimation is of primary importance. Several methods can be used to evaluate the thermal conductivity, but each of them can give a different value. Differences can be explained by considering parameters such as:

• Heat losses: it can increase the apparent value of thermal conductivity by 5 -10%;

• Humidity: it can increase the thermal conductivity by 15 -25% in a porous material;

• Heterogeneity and anisotropy: it can vary the thermal conductivity by 10 -15%.

For each method, the effects of these factors were analysed and where needed, corrections were made to the obtained values. Table 7 summarizes the main advantages and disadvantages of each technique. Therefore, the answer to the question, which is the best technique, is linked to the type of material investigated and to the level of information required.

If the analysis is made on a homogenous isotropic material, the methods give rather close results. Discrepancy may be within 10% if heat losses and humidity effects are taken into account. On the other hand, for heterogeneous materials, the hot disk and the hot wire methods give more accurate values due to the larger dimensions of the samples. However, if the material is anisotropic, the hot wire method provides less detailed information in the form of an average value over the radial direction to the hot wire axis.

Another important aspect to consider is the time: transient methods are faster than steady-state methods and this time increases with the decrease of the thermal conductivity.

Considering all these aspects, in the following paper the best technique seems to be the hot disk method, both for the Insulating Boards and the Insulating Fireclay Bricks.

Figure 1 :

 1 Figure 1: a) Schematic diagram of the heat flow meter; b) an example of the results obtained with this method for a set of six samples (apparent thermal resistance -Rapp vs thicknessd).

Figure 2 :

 2 Figure 2: a) Schematic diagram of the laser flash method; b) evolution of the temperature increase ΔT on the back face as a function of time t.

Figure 3 :

 3 Figure 3: a) Schematic diagram of the hot disk method; b) increase of the temperature as a function of time; c) linear relationship between the temperature increase and the dimensionless specific time function D(τ). The dotted lines underline the two limit values: tmin and tmax for the analysis of the thermal conductivity.

Figure 4 :

 4 Figure 4: a) Schematic diagram of the hot wire method; b) difference between the theoretical and the real temperature-time curve.

Figure 5 :

 5 Figure 5: Schematic representation of a steel ladle lining.

A = 70x70 mm 2 ,

 2 d= 25-35 mm Hot-wire method A = 250x114 mm 2 , d = 50 mm Heat flow meter A = 30x30 mm 2 , d = 1.5-15 mm

Figure 6 :

 6 Figure 6: a) SEM micrograph of Insulating Boards, showing the layer structure of the vermiculite; b) SEM micrograph of Insulating Fireclay Bricks, where it is possible to observe porous alumina grains and denser alumina-silica phases, the darkest phase corresponding to the embedding resin required for the specimen preparation.

Figure 7 :

 7 Figure 7: Comparison between the hot wire and the laser flash methods on Insulating Boards (Low Density (a), Medium Density (b) and High Density (c)).

1 ) 1 )

 11 _ hot wire IB-LD (cross-plane) _ laser flash IB-LD (in-plane) _ laser flash IB-MD _ hot wire IB-MD (cross-plane) _ laser flash IB-MD (in-plane) _ laser flash IB-HD _ hot wire IB-HD (cross-plane) _ laser flash IB-HD (in-plane) _ laser flash Temperature (°C)

Table 1 :

 1 Summary of the density and porosity of each investigated insulating refractory material.

	Materials	Density (g/cm 3 )	Porosity (%)
	IB-LD	1.0 ± 7%	55-65
	IB-MD	1.2 ± 7%	45-55
	IB-HD	1.5 ± 7%	35-55
	IFB	0.9 ± 7%	70-75

1 )

	IB-LD	0.19 ± 1%	0.29 ± 2.6%	0.26 ± 3%
	IB-MD	0.22 ± 1.7%	0.35 ± 1.5%	0.36 ± 3%
	IB-HD	0.27 ± 1.5%	0.43 ± 1%	0.36 ± 3%
	IFB	0.36 ± 3.5%	0.38 ± 3.9%	0.45 ± 3%

Table 4 :

 4 Thermal conductivity values obtained with the heat flow meter, both experimentally (before) and (after) correction taking into account the heat losses.

		before	after
	IB-LD	0.26 ± 3%	0.24 ± 3%
	IB-MD	0.36 ± 3%	0.30 ± 3%
	IB-HD	0.36 ± 3%	0.33 ± 3%
	IFB	0.45 ± 3%	0.40 ± 3%

HFM

λ (W m -1 K -1 )

Table 5 :

 5 Thermal conductivity measurements on Insulating Boards and Insulating Fireclay Bricks before and after drying in the "cross-plane" direction. The measurements were made with the hot disk method. The table also shows the water content on the dry basis.

		TPS		W
		λ (W m -1 K -1 )		(%)
		before	after
	IB-LD	0.29 ± 2.6%	0.23 ± 2.6%	4-5% wt.
	IB-MD	0.35 ± 1.5%	0.28 ± 1.5%	4-5% wt.
	IB-HD	0.43 ± 1%	0.34 ± 1%	4-5% wt.
	IFB	0.38 ± 3.9%	0.38 ± 3.9%	< 0.05% wt.

Table 7 :

 7 Summary of the main advantages and disadvantages of each investigated technique. * It is possible to determine the anisotropic behaviour of a material, if sufficient volume of the material is available to cut samples in different directions

	Method	Measured parameter	Range*	Uncertain ty*	Sample shape	Sample dimensions	Heat source	Anisotropy	Heat losses	Heterogeneity
	LFA	α	0.1-1000 mm 2 s -1	± 5%	Cylindrical	Φ: 10 mm d: 2 mm	Light energy	2 values -2 samples	Model correction	-
	TPS	λ α	0.005-500 W m -1 K -1	2-5% 5-10%	Square / cylindrical	70x70x25-35 mm 3	Electrical resistance	2 values -1 measurement	-	More precise average value
	HWM	λ	< 15 W m -1 K -1	1-6%	Square	250x114x50 mm 3	Electrical resistance	Average value	-	More precise average value
	HFM	λ	< 1 W m -1 K -1	± 3%	Square	30x30x1.5-16 mm 3	Electrical resistance	2 values -2 samples**	Model correction	-

*ASTM and ISO standards. *

Acknowledgements

This work was supported by the funding scheme of the European Commission, Marie Skłodowska-Curie Actions Innovative Training Networks in the frame of the H2020 European project ATHOR -Advanced THermomechanical multiscale mOdelling of Refractory linings [grant number 764987].


Marie Lebreton

Katia Melnik
email: melnik@ehess.univ-mrs.fr.

Greqam

Katia Greqam

‡ Melnik

Jean-Benoît Zimmermann

Anne Peguin-Feissolle

Voluntary Participation as a Determinant of Social Capital in France : Allowing for Parameter Heterogeneity

Keywords: JEL classication: C12, C22 Social capital, Parameter heterogeneity, Neural network models

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