G Kerdivel

A Bézos

C La

Keywords: DOLERITE, STONE AXE, GEOCHEMISTRY, NEOLITHIC

This study presents new geochemical data on dolerites from the Plussulien and Beulin Neolithic quarries in the Massif Armoricain (France) and for dolerite samples from their surrounding local regions. Using the major and trace element data obtained on these rocks, the two quarries and regional dolerite occurrences appear to be clearly distinct. Consequently, a set of chemical criteria is proposed to identify the dolerite axes produced uniquely at the Beulin quarry and to discriminate between the axes produced in the surrounding local region of Beulin, but outside the quarries, and those produced in the local region of Plussulien. These results could also be used, for example, to identify the existence of undiscovered quarries in the Beulin region. This work may provide the breakthrough needed to understand stone axe exchanges during the Neolithic times in north-western France and beyond.

INTRODUCTION

The social organization of Neolithic societies may be explored, for example, through the knowledge of Neolithic axe exchange and of the localization of their source of production. The petrological and geochemical studies of these axes and their raw materials are without any doubt the necessary approaches to unravel such exchanges in Neolithic societies [START_REF] Cogné | Étude pétrographique des haches polies de Bretagne[END_REF][START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF]. Most of the Neolithic axes from Brittany (France) are made of crystalline rocks and only a very few of them are made of flint (~4%). The considerable petrographic diversity observed for the stone axes made of crystalline rocks, led [START_REF] Cogné | Étude pétrographique des haches polies de Bretagne[END_REF] to classify these axes into three petrographic types. The first one, which represents ~8% of known Neolithic stone axes, corresponds to eclogite rocks composed mainly of sodic pyroxene (i.e., jadeite). This is by far the most studied petrographic type among all stone axes [START_REF] Pétrequin | La hache de pierre: carrières vosgiennes et échanges de lames polies pendant le Néolithique (5400-2100 av[END_REF][START_REF] Ricq De Bouard | Pétrographie et sociétés néolithiques en France méditerranéenne: l'outillage en pierre polie[END_REF][START_REF] Pétrequin | JADE Grandes haches alpines du Néolithique européen: V e et IV e millénaires av[END_REF]. Most of the eclogite axes were found in deposits under big dolmens or in Carnac-style tumuli in the Gulf of Morbihan area (southern Brittany). The analyses of their diffuse reflectance (spectroradiometry) suggest a link with the Mont Viso outcrops in the Italian Alps [START_REF] Errera | Spectroradiométrie, référentiel naturel et étude de la diffusion des haches alpines[END_REF]. However, eclogites can also be found in the Brière river area of the Loire-Atlantique department (south-eastern Brittany). This is a much closer source than the Italian outcrops and their possible exploitation by Neolithic peoples cannot be excluded [START_REF] Mens | Mégalithes et premiers agriculteurs[END_REF][START_REF] Tsobgou Ahoupe | Matières et techniques de la préhistoire récente du Massif armoricain: pétrographiegéochimie-mécanique-technologies[END_REF]. The second petrographic type, named 'fibrolite', represents 22% of the inventory of Neolithic stone axes of Brittany [START_REF] Cogné | Étude pétrographique des haches polies de Bretagne[END_REF]. The use of spectroscopic methods (i.e., spectroradiometry, and Raman and infrared spectroscopy) on stone axes from this group has provided significant information about their sources of production, suggesting only a few axe factory sites in the Massif Armoricain [START_REF] Guiavarc'h | La fibrolite du Massif armoricain. Étude pétrographique et spectrométrique d'échantillons naturels et de haches polies néolithiques: conséquences géologiques et archéogemmologiques[END_REF][START_REF] Pailler | Neolithic fibrolite working in the west of France[END_REF][START_REF] Pailler | L'exploitation des fibrolites en Bretagne et ses liens avec les productions alpines[END_REF][START_REF] Guiavarc'h | La fibrolite du Massif armoricain: état des recherches sur les gisements et la caractérisation des haches polies néolithiques[END_REF]. The results emerging from these works on 'fibrolite' and eclogite axes have contributed to the development of the theory of a social inequality system during the Neolithic in some parts of France and Europe [START_REF] Pétrequin | À propos du dépôt de La Bégude: haches alpines et haches carnacéennes pendant le V e millénaire[END_REF][START_REF] Pétrequin | L'Unique, la Paire, les Multiples: a propos des dépôts de haches polies en roches alpines en Europe occidentale pendant les Ve et IVe millénaires, in Du matériel au spiritual: réalités archéologiques et historiques des 'dépôts' de la préhistoire à nos jours[END_REF]. Finally, the third and last petrographic type, which designates 'greenstones'-embracing, among others, dolerites, diorites and amphibolites-represents ~66% of the Neolithic stone axes stored in the museums of Brittany [START_REF] Cogné | Étude pétrographique des haches polies de Bretagne[END_REF]. Most of these axes are made of metamorphic dolerites (metadolerites) and can be further subdivided into three petrographic types, A, B and C (see the review in [START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF]. Type A dolerite, which is the type relevant to our study, has a fine-grained doleritic texture; it is composed of strongly altered plagioclase (saussuritized) and augite (uralitized), with elongated crystals of ilmenite having leucoxene rims [START_REF] Cogné | Étude pétrographique des haches polies de Bretagne[END_REF]. Le [START_REF] Le Roux | Etude pétrographique des haches polies de Bretagne: VI découverte des ateliers de dolérite de type A[END_REF] proposed that the petrographic characteristics of type A dolerites match those from a dolerite outcrop directly quarried at the Plussulien-Roc'h Pol Neolithic site located in Brittany (Fig. 1), therefore identifying the source of production of type A dolerite axes. The discovery of this type A dolerite quarry in the Massif Armoricain has provided valuable information on the diffusion of Breton stone axes along the Loire valley (Le Roux 1999) and elsewhere. Plussulien was the only known Neolithic quarry until the recent discovery of the Beulin quarry (Mayenne, France), 250 km to the east [START_REF] Kerdivel | Exploitation de la dolérite dans le nord-ouest de la Mayenne au Néolithique: données préliminaires[END_REF]Kerdivel 2012a).

The discovery of Neolithic dolerite axes in the Massif Central [START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF] led to the question as to their origin of production. Dolerite rocks are indeed ubiquitous in both the Massif Armoricain and the Massif Central and the possibility of local production in the latter cannot be excluded. In fact, the comparison of the chemical compositions of 20 stone axes discovered in the Massif Central with those of dolerites outcropping in both massifs unambiguously indicates the existence of a local production area in the Massif Central that remains to be discovered [START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF].

In this study, we characterize the chemical compositions of dolerites from the point sources of the Plussulien and Beulin Neolithic quarries and from their surrounding local regions. We use this information to describe the means by which axes from the two sites and their local regions may be distinguished from one another.

QUARRY EVIDENCE FROM THE PLUSSULIEN AND BEULIN NEOLITHIC SITES

Archaeological field surveys around Plussulien in Brittany (Fig. 1 (a); Le Roux 1999, 2011) reveal dolerite artefacts to be widespread over an area of ~1800 m 2 lying between the villages of Quelfenec and Keregan and the Daoulas River to the north (Fig. 1 (a)). The distribution of artefacts near the villages of Quelfenec and Keregan displays four high-density clusters scattered over an area of 500 m 2 [START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF][START_REF] Le Roux | Une 'production de masse' dès le Néolithique: les ateliers de Plussulien (Côtes-d'Armor) et les haches polies en métadolérite du 'type A[END_REF]. Le [START_REF] Le Roux | Etude pétrographique des haches polies de Bretagne: VI découverte des ateliers de dolérite de type A[END_REF] first discovered this area near Plussulien (Côtes d'Armor) and identified the now well-known Roc'h Pol quarry (Fig. 1 (b)). In the following, we will refer to this site as the Plussulien quarry. The geomorphological situation of the archaeological site is a significant ridge formed by dolerite rocks that occasionally occur as 3-4 m wide outcrops. The excavations of Le [START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF][START_REF] Le Roux | Une 'production de masse' dès le Néolithique: les ateliers de Plussulien (Côtes-d'Armor) et les haches polies en métadolérite du 'type A[END_REF] focused on two different outcrops that are very close to each other (~18 m apart). The most important outcrop is named Roc'h Pol (Fig. 1 (b)). The second one, located to the east of Roc'h Pol, is a small outcrop characterized by abundant veins of quartz, which certainly degrade the mechanical properties of the rocks there [START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF][START_REF] Le Roux | Une 'production de masse' dès le Néolithique: les ateliers de Plussulien (Côtes-d'Armor) et les haches polies en métadolérite du 'type A[END_REF]. The Roc'h Pol outcrop displays abundant evidence of quarrying, such as fine-grained dolerite rocks with sharp edges, negatives flakes, and trimming and polishing marks [START_REF] Le Roux | Stone axes of Brittany and the Marches, in Stone axe studies: archaeological, petrological, experimental and ethnographic[END_REF][START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF][START_REF] Le Roux | Une 'production de masse' dès le Néolithique: les ateliers de Plussulien (Côtes-d'Armor) et les haches polies en métadolérite du 'type A[END_REF]. Three different excavations have been conducted at the Roc'h Pol site over an area of ~250 m 2 . The N1/O1 excavation (Le Roux 1979) provides the reference stratigraphic profile, reaching a depth of 4 m. The deepest soil consists of altered rocks, clays and sands resulting from the alteration of the dolerite; these form earth heaps visible in profile as a consequence of Neolithic quarrying. This first period of dolerite extraction has been radiocarbon-dated to around 4000 BC [START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF]. Two blocks of dolerite are also associated with this stratigraphic level and are interpreted as anvils set up by Neolithic people for trimming stages of the axe-making process. The second period of dolerite extraction is the direct quarrying of the Roc'h Pol outcrop. The technique of extraction takes advantage of the natural rock fracturing, which varies in spacing and orientation, leading to extraction of dolerite blocks of different sizes. During this period of extraction, dated between 3800 and 3200 BC, the dolerite wastes progressively bury both anvils [START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF][START_REF] Le Roux | Une 'production de masse' dès le Néolithique: les ateliers de Plussulien (Côtes-d'Armor) et les haches polies en métadolérite du 'type A[END_REF]. The third stratigraphic level displays evidence of the use of fire-setting methods that seems to have been well known at the time, although it was only intermittently used prior to 3200 BC [START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF]. The extraction at this stratigraphic level was less intensive and limited to the prominent visible ridges of the outcrop. Dolerite axes produced at the Plussulien quarry have been recognized in the South of England as well as in the Rhone valley [START_REF] Le Roux | Stone axes of Brittany and the Marches, in Stone axe studies: archaeological, petrological, experimental and ethnographic[END_REF][START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF][START_REF] Thirault | Echanges néolithiques: les haches alpines[END_REF][START_REF] Pétrequin | JADE Grandes haches alpines du Néolithique européen: V e et IV e millénaires av[END_REF]. Geochemical data on axes and corresponding quarried material would certainly help to support the reality of such an important geographical diffusion of axes [START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF].

The recent discovery of the Beulin Neolithic quarry, near Saint-Germain-le-Guillaume in Mayenne (France; Fig. 1 (a)), differs from the Plussulien quarry in its lack of massive dolerite outcrops and it was only the presence of clusters of dolerite flakes over an area of ~115 m 2 that led to its discovery [START_REF] Kerdivel | Exploitation de la dolérite dans le nord-ouest de la Mayenne au Néolithique: données préliminaires[END_REF]Kerdivel 2012a). The field morphology at the Beulin site shows a scatter of small mounds corresponding to the presence of near-surface dolerite. The Beulin quarry was excavated over an area of ~50 m 2 (Figs 1 (c) and 1 (d)) revealing a quarry organized like an open-pit mine, with several quarrying sites [START_REF] Kerdivel | Exploitation de la dolérite dans le nord-ouest de la Mayenne au Néolithique: données préliminaires[END_REF]Kerdivel 2012a). The Neolithic people preferentially quarried dolerite characterized by widely spaced fractures-mostly joints-as indicated by the use of fire-setting methods. Notably, the organization of dolerite blocks in the excavation suggests the extraction of blocks weighing ~150 kg. Flakes with a thick bulb and a great width were used to knap axes at this site. Three radiocarbon ages (Beta-287649, Lyon-8821 and Lyon-8820) on Malus (apple tree) and Quercus (oak) charcoal yielded ages between 4200 and 3600 BC, which indicate concurrent production of axes at the Beulin and Plussulien sites.

THE SCIENTIFIC APPROACH, THE GEOLOGICAL SETTINGS AND SAMPLING

The scientific approach The use of chemical compositions of rocks may be used to pinpoint the origin of production of stone axes (e.g., [START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF]. However, this approach requires a good knowledge of the regional chemical variation of outcropping dolerites-and, of course, of the chemical analyses of the stone axes themselves. In this study, we intend to set out a method by which to characterize the geochemical compositions of dolerites quarried by Neolithic people at the Beulin and Plussulien sites in the Massif Armoricain. In addition, we spread the net wider to characterize the local regional geochemical variation of outcropping dolerites around both quarries, to provide a geochemical catalogue of the dolerites that might have been available to the Neolithic people. Combining the use of this geochemical catalogue with the chemical analyses of the dolerite axes allows identification and distinction of the axes produced at the Beulin and Plussulien sites, or at least the definition of their region of production.

The geological setting and samples

First, a brief geological overview is presented of the Châteaulin basin sills and Mancellian dyke swarms where the Plussulien and Beulin quarries were, respectively, opened during the Neolithic. The Mancellian domain in the northern Massif Armoricain extends from Caen at its eastern end to Guingamp at its western end, and is bounded to the south by the North Armorican Shear Zone (NASZ; Fig. 1 (a)). A vast network of dyke swarms cross-cuts the Mancellian domain in a north to south direction. All the geological observations suggest that these dykes were injected during a brief period between the Devonian and Carboniferous (Le Gall 1999). Palaeomagnetic and K-Ar geochronology have given, for example, an age of 330 ± 10 Ma for the St Brieuc doleritic dykes [START_REF] Perroud | Palaeomagnetism and K-Ar dating of Lower Carboniferous dolerite dykes from northern Brittany[END_REF].

The Plussulien Neolithic quarry was opened on a dolerite sill intruding cleaved shales of Lower Carboniferous age in the Châteaulin basin [START_REF] Chauris | Gîtes minéraux de la France, volume I, Massif armoricain[END_REF] (Fig. 1). These sill rocks display doleritic textures varying from fine to coarse grained, with interstitial pyroxene (augite) and Fe-Ti oxide (ilmenite) embedded in a network of plagioclase laths. The dolerite outcrops at the Neolithic site are characterized by a fine-grained texture and strong hydrothermal alteration (for more petrological details, see the supplementary online material). During our field campaigns, we sampled dolerites 73 and 74 (Fig. 1 (b)) at the Plussulien site, the same as excavated by Le Roux (1999), and dolerites 71 and 72, which correspond to archaeological artefact samples (a nucleus and a flake, respectively) from the same area as Figure 1 (b). Our samples from the local region of Plussulien (four samples) were collected in an area restricted to a few km 2 around the Plussulien site and they belong to the same sill unit. The extent and number of sills (two or three) in this basin are severely restricted when compared to the vast geographical coverage of the Mancellia dyke swarm. There is, additionally, no evidence that the Plussulien sill and Mancellian Guingamp dyke swarm are related to the same magmatic event.

The Beulin Neolithic quarry was opened on a dyke that belongs to the south-eastern part of the Mancellian dyke swarm. The quarried rock is a dolerite with a medium-grained doleritic texture, showing the same mineralogical composition as dolerites from the Plussulien site (plagioclase, augite and ilmenite) but with less pronounced hydrothermal alteration (see the supplementary online information). Seven dolerites were collected at, or in close proximity to, the Beulin site (Fig. 1 (d)). Dolerites 65 and 66 come from a zone of axe production (trench 1), dolerites 61, 62 and 63 were sampled in the continuity of the production zone (trench 2) and dolerite 67 was sampled in close proximity to the production zone (trench 3). Dolerite 64 is an artefact collected on the quarry site. We have also collected a total of 27 rocks from the dyke swarm occurring in the Beulin local region over an area of ~120 km 2 (Figs 1 (c) and 1 (d)). All these local regional rocks are dolerites except for samples 33 and 161, which are more dioritic, with higher abundances of green amphiboles and plagioclase and less abundant pyroxene (See Petrographic descriptions). All sample locations are reported in Table 1.

ANALYTICAL METHODS

Major and trace elements were analysed at the laboratory of LPG-Nantes in Nantes, France, and samples were prepared as follows: the freshest parts of dolerites were first crushed into chips of ~2 mm diameter using a steel jaw crusher. The chips were then rinsed multiple times in ultrasonic baths of milli-Q water, dried and finely powdered in an agate grinder. Major elements were analysed by ICP-OES (iCAP-6300, Thermo), following the procedure described by [START_REF] Cotten | Origin and anomalous rare-earth element and yttrium enrichments in subaerially exposed basalts: evidence from French Polynesia[END_REF]. Samples were dissolved in closed Teflon PFA beakers using 0.5 mL of HNO 3 65% and 40 drops of HF 40% for 125 mg of rock powder. After 12 h at 110 °C, the acid mixture and dissolved sample were transferred to a 100 mL bottle that contained 5 g of our internal standard solution of 80 ppm Ge and Co, and diluted up to 50 g with a boric acid solution at 20 g L À1 . This final solution for analysis was then left for a minimum of 48 h prior to analysis. The geostandards materials BE-N, BHVO-2, BIR-1, JB-2, MO-5 and W-2 were used for external calibration, using the recommended values from [START_REF] Govindaraju | compilation of working values and sample description for 383 geostandards[END_REF] for all standards except for BHVO-2 [START_REF] Jochum | GeoReM: a new geochemical database for reference materials and isotopic standards[END_REF]. To ensure our reproducibility over time, during each analytical session we have analysed the geostandard WS-E and sample 61 from our sample collection (for the results, see the supplementary online material). Loss on ignition was determined after heating the sample powder at 900 °C for 3 h. All the major element and loss on ignition results are reported in Table 1. Trace elements were analysed by ICP-MS (820MS, VARIAN). Samples were dissolved in closed Teflon PFA beakers using 0.5 mL milli-Q water, 0.5 mL of doubledistilled HNO 3 65% and 14 drops of double-distilled HF 40% for 50 mg of rock powder. After 12 h at 120 °C, the dissolved samples were evaporated at 90 °C, then re-dissolved in 1 mL of double-distilled HNO 3 65% at 120 °C and then evaporated to dryness at 90 °C. The final solutions for analysis were obtained by dissolution of sample residues in 250 g of 1 N HNO 3 with the following internal standards: 2 ppb for Ge and 0.8 ppb for Rh, In, Tm and Bi. The geostandards materials BE-N, BHVO-2, BIR-1, JB-2 were used for external calibration. All the trace element results are reported in Table 2. In the same way as for major elements, the geostandard material W-2 and sample ID-61 were analysed throughout our studies to ensure the good reproducibility of our analyses (for the results, see the supplementary online material). All the trace element results are reported in Table 2.

RESULTS

Major elements

Dolerites from the Neolithic quarries in Figure 2 show distinct and quite homogeneous compositions in their SiO 2 and MgO contents, except for dolerite 67 from the Beulin quarry, which displays lower SiO 2 and higher MgO contents compared to other dolerites from the same quarry. Dolerite 67 was sampled in trench 3, which is adjacent to trenches 1 and 2 that relate to the Neolithic quarry sensu stricto (Fig. 1 (d)). The major element composition of dolerite artefact 64 displays a similar composition to those of the dolerite samples from trenches 1 and 2. Dolerites from the Plussulien quarry display on average lower SiO 2 and higher MgO contents when compared to the dolerites from the Beulin quarry. The bounding lines in Figure 2 illustrate the compositional fields for dolerite outcrops sampled around the Beulin and Plussulien quarries.

For the purpose of clarity, these dolerites will be referred to as 'local regional' dolerites. The inverse relationship found in the Beulin local regional dolerites in Figure 2 suggests that these rocks are related to each other by a fractional crystallization process. Interestingly, the Beulin quarry dolerites plot outside the local regional Beulin compositional field and show, for a given MgO content, an SiO 2 excess of ~4 wt%. The inspection of other major element diagrams (not shown) indicates that the Beulin quarry dolerites are also characterized, for a given MgO content, by slightly lower Fe 2 O 3 total and TiO 2 and slightly higher K 2 O contents, compared to the Beulin local regional dolerites.

As mentioned earlier, the geographical coverage of our sampling around the Plussulien area is far less advanced and widespread compared to that of our sample collection from the local region of Beulin. This is partly related to the occurrence of a restricted number of sills in the Plussulien region when compared to the Mancellian dyke swarm in the Beulin region. For this reason, we cannot be sure that the Plussulien compositional field defined in Figure 2 is fully representative of the chemical variations displayed by other dolerites potentially related to this magmatic event (i.e., the Mancellian Guingamp dyke swarm). Bearing this in mind, we do not observe any differences in chemical composition between the Plussulien quarry dolerites and those sampled in the same local region. Finally, we note in Figure 2 that the Plussulien local regional dolerites are clearly distinguishable from the Beulin local regional and quarry dolerites.

Trace elements

The incompatible trace element patterns of dolerites, normalized to the primitive mantle values [START_REF] Mcdonough | The composition of the Earth[END_REF], are presented in Figures 3 (a) and 3 (b). In such diagrams, the trace elements are ordered from the most incompatible element (left) to the least incompatible element (right). The incompatibility of an element refers to its preferential partitioning into magmas relative to the solid phases at equilibrium. The trace element patterns of the Beulin local regional dolerites (grey patterns in Fig. 3 (a)) reveal, relative to primitive mantle values, an overall increasing enrichment from Lu to Nb-Ta, then a decrease of enrichment from Nb-Ta to Ba, and finally a noticeable increase of the Rb content relative to the Ba content at the most incompatible end. The high field strength element (HFSE) pairs Nb-Ta and Zr-Hf also display positive anomalies relative to their neighbouring elements U-La and Sm-Gd, respectively. Such overall geochemical features are commonly diagnostic of intra-plate (hotspot) magmatism. Interestingly, dolerites from the Beulin quarry (black patterns in Fig. 3 (a)) do not display the positive Nb-Ta anomaly observed for dolerites from the local region of Beulin, but instead display a wellmarked positive Th-U anomaly relative to neighbouring elements Nb and Ba. Dolerite 67 from trench 3 does not display the positive Th-U anomaly observed for the quarried dolerite and therefore conforms to the trace element description of the Beulin local regional dolerites. Finally, we note that the trace element composition of dolerite artefact 64 cannot be distinguished from that of the other dolerites from the quarry.

The trace element patterns of the Plussulien local regional dolerites (grey patterns in Fig. 3 (b)) also display the geochemical characteristics of intra-plate volcanism. This result agrees well with previous studies of the Mancellian dyke swarm [START_REF] Lahaye | Le volcanisme fissural paléozoïque du domaine nord-armoricain[END_REF][START_REF] Vuaillat | Les haches néolithiques limousines. Etude géochimique des matériaux méta-doléritiques. Conséquences archéologiques et géologiques[END_REF][START_REF] Caroff | Continental tholeitic magmatism associated with the Hercynian orogeny: the Kerroc'h Visean volcanism, Armorican Massif[END_REF] 1996). However, the Plussulien quarry dolerites display slightly negative Zr-Hf anomalies (relative to Sm and Gd) that clearly separate them from the marked positive anomalies observed for the Beulin quarry and its local regional dolerites (Fig. 3 (a)). This observation is reflected by higher Sm/Zr ratios for the Plussulien dolerites compared to those for Beulin (Fig. 3 (c)). Nonetheless, the Plussulien archaeological artefacts tend to show Sm/Zr ratios akin to those from the Beulin area dolerites (Fig. 3 (c)). This observation points to our still poor characterization of the local regional Plussulien dolerites.

DISCUSSION

The geochemical signature of the dolerites from the Beulin and Plussulien quarries

We have demonstrated that the Beulin quarry dolerite is characterized by distinct major and trace element compositions compared to the Plussulien quarry dolerite. This is clearly illustrated in Figures 3 (c) and 3 (d), where the chemical compositions of dolerites from the two quarries barely overlap. These differences are remarkable and beyond the analytical errors, which are smaller than the drawn symbols in Figures 3 (c) and 3 (d). From this observation, we have drawn up a list of chemical criteria (Table 3) that can easily be used to discriminate between the rocks that originate from these two quarries. However, these chemical criteria do not have any meaning without knowledge of the chemical variations displayed by the corresponding local regional dolerites in both areas. The question of as yet undiscovered Neolithic quarries of dolerite with similar chemical compositions to those of dolerites from the Beulin or Plussulien quarries certainly needs to be addressed. As an example, in Figure 3, dolerites from the Plussulien local region display similar chemical compositions to dolerites from the Plussulien quarry. This implies that dolerites from the Plussulien quarry cannot be specifically distinguished from other local regional dolerites on the basis of their chemical compositions. As mentioned earlier, our sample collection from the Plussulien region is restricted to only a few samples that, furthermore, are located in close proximity to the quarry. This illustrates the need for a detailed geochemical study of the Châteaulin basin sills and the Guingamp dyke swarm to fully understand the regional chemical variability of dolerites in the local region of the Plussulien site. At a greater geographical scale, a comparison of the Beulin and Plussulien local regional dolerites reveals different and distinct major and trace element characteristics (Figs 2 and 3). Such differences can certainly be used to discriminate between the axes produced in these two regions by using the geochemical criteria listed in Table 3.

In contrast to the Plussulien dolerites, dolerites from the Beulin quarry display distinct and different geochemical features when compared to its local regional dolerites. They show, for Figure 2 SiO 2 versus MgO contents for dolerite rocks analysed in this study: ■, dolerite from the Beulin Neolithic quarry; ▲, dolerite from the Plussulien quarry; □, dolerite from the Beulin local region; Δ, dolerite from the Plussulien local region; ---, compositional field of Beulin local regional dolerites; À --, compositional field of Plussulien local regional dolerites.

Figure 3 (a,b) Trace element patterns for dolerites with MgO contents higher than 5 wt% MgO. (a) Dolerite from the Beulin local region (grey) and the Beulin Neolithic quarry (black). Note that sample 67 shows a trace element pattern that is not matched by any dolerite from the Beulin quarry. (b) Dolerites from the Plusssulien local region (grey) and Plussulien Neolithic quarry (black). Note the differences in the trace element patterns for the Th, U, Nb and Ta contents when comparing dolerites from the Beulin quarry with those of the Beulin local region. Note also the differences in the Sm, Zr, Hf, and Eu contents when comparing dolerites from the local regions of Beulin and Plussulien. (c) The Sm/Zr ratio versus the MgO content of the dolerite rocks: ---, compositional field of Beulin local regional dolerites; À --, compositional field of Plussulien local regional dolerites. (d) The Nb/U ratio versus the SiO 2 content of the dolerite rocks: the grey curve is the calculated mixing curve between the chemical composition of the upper continental crust and the chemical composition of the rock (sample 121) derived from a magma characterized by a mantle-like U/Nb ratio.

example, a relatively high SiO 2 content for a given MgO content (Fig. 2) and a particularly low Nb/U ratio of ~23 (Fig. 3 (d)). Such geochemical characteristics for highly incompatible trace element ratios are at odds with the expected values for mantle-derived magmas, which would be characterized by an Nb/U of 55 ± 10 [START_REF] Hofmann | Nb and Pb in oceanic basalts: new constraints on mantle evolution[END_REF]. Note that most dolerites analysed in this study, including the Beulin local regional dolerites, plot within the compositional field labelled 'mantle-derived magmas' in Figure 3 (d). The combination of a low Nb/U ratio and a high SiO 2 content strongly suggests that the magma from which the Beulin quarry dolerite originates has assimilated significant amounts of continental crust during its emplacement. Rocks from the continental crust are indeed characterized by a low Nb/U ratio of ~4.5, and high silica contents of ~67 wt% [START_REF] Hawkesworth | Evolution of the continental crust[END_REF], which strongly contrast with the expected mantlederived magma values mentioned just above (see the cross in Fig. 3 (d)). Such a crustal contamination process in the context of intra-continental plate magmatism is quite common and has been widely documented [START_REF] Patchett | Thermal effects of basalt on continental crust and crustal contamination of magmas[END_REF][START_REF] Fodor | Petrology of Serra Geral (Paraná) continental flood basalts, southern Brazil: crustal contamination, source material, and South Atlantic magmatism[END_REF][START_REF] Caroff | Continental tholeitic magmatism associated with the Hercynian orogeny: the Kerroc'h Visean volcanism, Armorican Massif[END_REF]. We have calculated the mixing relationship expected between a pristine magma composition with Nb/U = 55 ± 10 and SiO 2 = 48 ± 2 wt% (e.g., dolerite 121) and the average composition of the continental crust. The result is illustrated in Figure 3 (d) by the thick grey line connecting the end-member compositions labelled 'continental crust' and 'mantle-derived magmas'. The good agreement between our mixing model and the data (Fig. 3 (d)) suggests that all the Plussulien and Beulin dolerites have experienced significant crustal contamination. More importantly, this model shows that dolerites from the Beulin quarry are the most affected by this process, with up to 25 wt% assimilation of continental crust by the magmas en route to the surface. This extensive contamination has therefore imprinted a specific geochemical signature on dolerites from the Beulin quarry relating to both major and trace elements. Although this decline has not been dated, it might be connected to the discoveries of new Neolithic dolerite quarries at that time [START_REF] Cogné | Etude pétrographique des haches polies de Bretagne. V[END_REF][START_REF] Le Roux | L'outillage de pierre polie en métadolérite du type A. Les ateliers de Plussulien (Côtes-d'Armor): production et diffusion au Néolithique dans la France de l'ouest et au-delà[END_REF][START_REF] Kerdivel | Occupation de l'espace et gestion des ressources à l'interface massifs anciens/bassins secondaires et tertiaries: l'exemple du Massif armoricain et de ses marges au Néolithique[END_REF]. The opening of the Beulin quarry might be one of these new resources competing with the Plussilien quarry [START_REF] Kerdivel | Exploitation de la dolérite dans le nord-ouest de la Mayenne au Néolithique: données préliminaires[END_REF]. Given the unique geochemical signature of the Beulin quarry (Table 3), we propose that it is now possible to identify the axes produced at the Beulin quarry and provide new constraints to understand how the discovery of new doleritic resources might impact the social structures during Neolithic.

Neolithic knowledge of raw materials

There is no doubt that Neolithic people had a very good knowledge of the raw materials in their environment. This knowledge was probably transmitted from generation to generation as an increasing heritage, with its origins going back as far as Mesolithic times. Tsobgou and Dabard (2010) have shown, for example, that in the Massif Armoricain during the Late Mesolithic, specific phtanite (radiolarian chert) was used inland as a substitute for flint, which was the main usage near the coast. This is certainly related to the higher abundances of phtanite relative to flint rocks inland and to the mechanical properties of phtanite, which bears some similarities to flint-they are both siliceous. [START_REF] Rodríguez Rellán | Shooting out the slate: working with flaked arrowheads made on thin-layered rocks[END_REF][START_REF] Valcarce | Gestión del cuarzo y la pizarra en el Calcolítico peninsular: el 'Santuario' de El Pedroso (Trabazos de Aliste, Zamora)[END_REF][START_REF] Rodríguez Rellán | Shooting out the slate: working with flaked arrowheads made on thin-layered rocks[END_REF] have also shown, in the western Iberian Peninsula, that schists were used during prehistoric and Bronze Age times due to their suitability for the making of good arrowheads. The Neolithic people in the area of Sablé-sur-Sarthe favoured flint from a specific source -that is, the Vion quarry (Sarthe, France)-rather than from other random flint outcrops in the region [START_REF] Georges | Habitat et site d'extraction de silex au début du Néolithique moyen: les sites de la Croix-Sainte-Anne à Juigné-sur-Sarthe et du Camp de César à Vion (Sarthe)[END_REF][START_REF] Georges | Approvisionnement en silex au Néolithique entre Massif armoricain et Bassin parisien: Sablé-sur-Sarthe et ses environs[END_REF]. In another example of Neolithic discrimination, the type A dolerites outcropping at the Plussulien site display two different types of texture: fine-grained and coarse-grained (Fig. 1 (b)); however, the Plussulien quarry was opened exclusively to exploit the fine-grained variety. [START_REF] Tsobgou Ahoupe | Matières et techniques de la préhistoire récente du Massif armoricain: pétrographiegéochimie-mécanique-technologies[END_REF] has shown that the mechanical properties of coarse-grained dolerites are less suitable than those of finergrained dolerites, which tends to indicate preferential choice by the Neolithic people based on experience. In the same way, the presence of dolerite axes competing with flint axes, which are less hard than dolerites [START_REF] Tsobgou Ahoupe | Matières et techniques de la préhistoire récente du Massif armoricain: pétrographiegéochimie-mécanique-technologies[END_REF], outside the Massif Armoricain may indicate educated choices by Neolithic people that are certainly related to cultural distinctions that remain to be elucidated. We have shown that dolerites from the Beulin quarry display, for a given MgO content, a significantly higher SiO 2 content compared to other dolerites from the Beulin area. We think that the Neolithic quarrying of this specific high-silica dolerite is not fortuitous and might be correlated with its better knapping capabilities, probably approaching the mechanical properties of flint owing to its high SiO 2 content. As an experiment to challenge our hypothesis, we found out that sculptor J. Huard, who lives in Mayenne, close to the Neolithic Beulin quarry, uses this specific dolerite as a raw material because of its mechanical properties. Interestingly, the technique of identification developed by J. Huard when looking for a raw material is based on the specific sound produced by a shock or blow between two such blocks of dolerite. This demonstrates that basic skills of field prospection can be developed to allow the identification of this rock without the need for modern analytical facilities, and that this specific dolerite is particularly well suited for sculpture. We suggest, therefore, that a Neolithic population in the area did not choose this dolerite dyke for its axe source at random. This study provides new evidence for the knowledge of rocks held by Neolithic peoples.

CONCLUSION

In this paper, we have characterized the major and trace element compositions of dolerites from the Beulin and Plussulien Neolithic quarries and from their respective local regions. The data shows that dolerites from the Beulin quarry display a unique geochemical signature among all the dolerites analysed in the study. This chemical singularity, which can be recognized in both major and trace elements, arises from the particularly extensive assimilation of continental crust by the magma at the origin of the Beulin quarry dolerite. This geochemical singularity of the Beulin quarry dolerite can be used to fingerprint the chemical composition of Neolithic axes that originate from this specific production site. We provide a set of geochemical parameters that are usable in such identifications. We have also shown that the local regional dolerites from Plussulien differ in both major and trace elements from those from Beulin. This result can be used to argue in favour of new sites of axe production in the local regions of Plussulien and Beulin beyond the context of known dolerite quarries. Unfortunately, the dolerites from the Plussulien quarry do not display any unique chemical signature when compared to the local regional dolerites. Among the chemical specificities of the Beulin quarry dolerites, we note the particularly elevated SiO 2 content for a relatively high MgO content. We propose that such high-silica dolerite might have specific physical properties that enhance its knapping capabilities and that these were recognized by Neolithic populations. The results of this study also open up new perspectives on the study of Neolithic stone axe exchange beyond the boundaries of the Massif Armoricain.

Figure 1

 1 Figure 1 (a) A simplified geological map of the Massif Armoricain (north-western France): white, Bassin parisien; light grey, Massif Armoricain; dark grey, distribution of artefacts related to the Plussulien quarry; black dots, dolerite samples; white dots, main cities (after Sagon 1976). (b) Details of the geological map and sampling at the Plussulien quarry (Roc'h Pol): black dots, sample locations with sample numbers; hatched zone, coarse-grained dolerite; white, fine-grained dolerite; other grey lines are fields and roads. (c) Details of the sampling of the Beulin area: grey lines, local map of the Mancellia dyke swarm. (d) Details of the geological sampling at the Beulin quarry: dark grey, observed outcrops of dolerite in the excavations; light grey, extrapolation of the dolerite outcrop that may define the orientation of the dykes observed in (c).

  ARCHAEOLOGICAL PERSPECTIVESThe geological fingerprint of Neolithic axes Fifty years after the discovery of the type A dolerite quarry by Le Roux and Giot (1965), Kerdivel et al. (2011; see also Kerdivel 2012a) discovered the Beulin site, a new dolerite axe source in the eastern part of the Massif Armoricain. This finding opens up new perspectives

Table 1

 1 The localization and major element compositions of the dolerite samples analysed in this study, with results for geochemical reference material WS-E (SARM, CRPG,

	Nancy, France)

Table 2

 2 The trace element compositions of dolerite samples, with results for geochemical reference material WS-E (SARM, CRPG, Nancy, France)

	Sample	Localization	Li	Be	Sc	V	Cr	Co	Ni	Cu	Ga	Rb	Sr
	61	Beulin quarry	33.3 1.55 30.0 276 194	32	33	18	20.5 32.7
	62	Beulin quarry	33.2 1.63 29.7 277 194	32	34	19	21.8 28.3
	63		32.6 1.73 29.1 264 190	36	35	22	21.8 42.4
	65		29.7 1.48 28.5 259 188	33	34	21	19.9 40.2
	66		30.0 1.44 29.3 272 196	35	36	26	21.0 30.1
	67		39.6 1.29 32.3 298 216	38	37	29	20.4 28.5
	64	Beulin artefact	35.8 1.59 30.3 270 208	34	36	24	20.9 36.7
	13	Local region	16.9 1.71 32.6 422	38	40	31	44	23.6 24.0
	15	of Beulin	18.7 1.75 29.6 381	26	40	26	41	24.5 22.5
	22		20.0 1.71 32.3 436	28	41	27	46	24.9 19.4
	23		17.9 2.35 30.8 156	1	27	2	12	27.2 20.1
	32		32.5 2.55 32.5 168	29	30	8	11	25.5 81.3
	33		21.7 3.26 25.8 146	54	21	6	7	26.7 61.4
	41		30.2 1.82 29.4 278	69	36	31	31	23.5 23.1
	42		32.7 1.74 28.4 277	65	37	33	38	23.9 20.0
	51		40.9 1.47 30.7 341 138	43	62	78	21.9 24.7
	91		22.2 1.69 32.5 441	51	43	42	37	23.9 22.6
	101		23.6 1.76 31.2 413	35	40	31	27	23.8 20.7
	111		16.3 1.63 36.0 483	39	49	33	48	24.2	9.9
	121		19.7 1.57 31.1 369	67	43	44	65	23.1 18.8
	131		48.4 1.72 14.9 110	28	14	14	15	19.2 79.4
	141		43.0 1.45 31.8 378	23	38	27	45	22.4 19.3
	151		35.6 1.64 28.2 284 167	40	66	60	21.5 14.8
	171		24.8 1.81 25.9 270	76	38	47	52	22.2 33.5
	181		22.5 1.50 30.5 324	97	42	62	66	22.5 19.3
	191		26.0 1.34 30.6 309 156	42	75	76	21.0 24.2
	201		18.8 1.83 26.7 289	60	36	40	49	24.3 13.3
	211		20.9 1.64 29.6 339	86	42	60	78	23.0 25.7
	221		30.6 1.47 31.7 338 114	46	72	76	21.5 24.6
	231		25.8 1.69 30.7 370	60	43	49	66	23.3 27.1
	241		30.7 1.26 35.1 410	66	51	31	45	21.9 21.4
	251		26.7 0.79 25.5 249 187	43	102	54	19.7 13.8
	252		18.8 1.72 31.0 389	70	38	50	44	25.2 14.9
	253		20.1 1.57 33.0 428	77	42	54	59	24.8 11.6
	73	Plussulien quarry	34.8 0.91 31.1 251 372	41	109	78	18.9 10.7
	74		34.1 0.84 31.6 255 398	39	116	34	18.9	9.2
	71	Plussulien artefacts	34.0 1.33 33.3 294 221	40	80	93	21.1	9.6
	72		30.1 1.31 32.5 289 229	40	82	97	20.8 12.2
	75	Local region of	30.2 0.90 41.4 318 360	56	133 108 17.3 16.1
	76	Plussulien	31.9 1.10 32.9 292 228	41	81	140 20.1	9.4
	77		36.3 1.14 33.3 301 218	37	77	35	20.8 31.3
	78		40.4 1.73 33.2 285	87	37	11	27	22.3	6.9
	et al.

Table 2 (

 2 Continued)

	Sample	Y	Zr	Nb	Cs	Ba	La	Ce	Pr	Nd	Sm	Eu	Gd
	61	31.9		20.7	1.35	158	17.6	40.3	5.44	23.8	5.96	1.92	6.49
	62	32.6		21.5	1.17	145	18.3	41.9	5.62	24.5	6.15	1.86	6.77
	63	33.2		20.7	1.26	231	18.5	42.8	5.74	25.1	6.32	1.96	6.95
	65	31.0		19.1	1.50	168	17.1	39.9	5.31	23.1	5.86	1.80	6.43
	66	34.0		19.9	0.96	152	17.9	41.7	5.64	25.1	6.35	1.95	6.67
	67	32.8		19.4	1.94	130	15.7	37.0	5.18	24.0	6.14	2.07	6.55
	64	32.4		20.6	1.23	165	17.9	41.1	5.56	24.4	6.11	1.86	6.77
	13	36.7		30.0	2.26	134	18.4	44.9	6.39	29.2	7.57	2.58	8.20
	15	43.8		32.8	2.28	154	23.6	58.1	8.27	38.2	9.55	2.99	10.05
	22	38.8		32.5	2.06	136	18.2	45.2	6.64	30.7	8.02	2.82	8.66
	23	62.2		47.8	2.57	175	32.9	81.4	11.74	55.3	14.26	5.46	15.25
	32	52.8		34.7	10.41	306	36.3	81.4	10.95	47.8	11.64	3.62	12.27
	33	58.4		36.2	3.26	406	38.7	88.0	11.79	50.1	12.03	3.62	12.64
	41	41.7		34.8	1.75	138	23.9	58.8	8.33	38.8	9.72	3.55	10.42
	42	50.5		36.6	3.37	180	28.7	70.4	10.16	47.3	11.71	4.12	11.63
	51	35.9		34.8	6.47	70	20.9	50.4	7.03	31.7	7.92	2.54	8.45
	91	42.6		32.0	1.81	172	22.1	52.5	7.35	33.5	8.48	2.81	9.24
	101	44.2		31.5	1.87	131	21.4	51.5	7.21	33.0	8.46	2.87	8.87
	111	49.3		41.9	1.59	115	23.7	58.0	8.48	40.1	10.42	3.34	11.39
	121	41.1		33.7	1.33	168	22.3	54.2	7.64	34.9	8.79	2.87	8.84
	131	29.8		6.0	2.60	344	16.1	35.4	4.49	18.2	4.51	1.07	4.97
	141	37.1		28.2	3.12	143	19.7	48.0	6.77	31.4	7.95	2.65	8.62
	151	36.3		29.3	1.99	63	20.7	49.1	6.73	30.0	7.47	2.24	7.70
	171	41.6		31.4	1.36	186	26.1	62.2	8.62	38.0	9.39	2.86	9.81
	181	37.7		29.6	1.73	103	19.9	48.6	6.95	32.1	8.14	2.65	8.32
	191	34.2		23.6	4.46	116	17.3	41.1	5.71	26.2	6.70	2.14	7.04
	201	46.2		36.0	1.58	98	25.7	63.4	8.99	41.6	10.33	3.23	10.26
	211	38.4		29.5	2.25	116	21.6	53.1	7.36	34.8	8.42	2.68	8.36
	221	36.3		27.5	2.16	161	20.0	48.4	6.80	30.4	7.76	2.42	8.26
	231	40.8		33.3	1.68	100	23.2	56.4	7.94	36.4	9.06	2.92	9.30
	241	31.8		23.2	2.51	116	16.3	39.6	5.58	25.4	6.48	2.10	7.07
	251	23.3		15.4	2.82	69	10.6	24.5	3.37	15.9	4.14	1.55	4.88
	252	43.4		32.1	1.09	158	23.3	56.4	8.03	36.8	9.40	3.17	10.14
	253	40.2		30.1	0.53	91	21.5	51.7	7.35	33.8	8.63	2.86	9.43
	73	23.3	88	14.0	0.37	63	12.0	28.3	3.89	17.3	4.49	1.57	5.06
	74	24.0	83	13.6	0.29	53	11.5	26.7	3.81	17.6	4.45	1.52	4.85
	71	31.2		21.4	0.57	111	15.6	37.4	5.28	23.7	6.01	1.93	6.72
	72	30.3		21.4	0.52	101	15.1	36.2	5.03	22.7	5.81	1.90	6.48
	75	26.1		15.3	0.94	118	12.5	30.2	4.19	19.1	4.94	1.60	5.68
	76	31.1		20.2	0.49	42	15.8	37.4	5.16	23.8	5.98	1.84	6.38
	77	32.1		21.7	0.17	20	16.5	38.6	5.47	24.9	6.30	2.11	6.67
	78	41.7		22.3	1.16	97	23.6	53.6	7.15	31.1	7.58	2.24	8.33

Table 3

 3 Analytical criteria to discriminate between Neolithic axes produced using Massif Armoricain dolerites. Note that averages have been calculated for samples with MgO > 5 wt%, and that averages for local regions do not include data from the quarries the study of the social and territorial organization of Neolithic populations in the north-west of France through Neolithic axe exchange. Le Roux (1999) suggested a noticeable decrease of interest in type A dolerite material (i.e., from Plussulien) in the east of the Massif Armoricain.

		Neolithic quarries
				Plussulien region	Beulin region
		Plussulien (Roc'h Pol)	Beulin
	Sm/Zr	0.05	0.0295 ± 0.0005	0.04 ± 0.01	0.033 ± 0.003
	Nb/La	1.18	1.14 ± 0.03	1.3 ± 0.1	1.5 ± 0.1
	Nb/U	41	22.8 ± 0.5	47 ± 3	52 ± 10
	Th/Nb	0.08	0.155 ± 0.004	0.079 ± 0.004	0.06 ± 0.01
	Ce/Pb	15	15 ± 3	16 ± 4	25 ± 9
	SiO 2 (wt%)	48.51	51.4 ± 0.3	49.5 ± 0.2	47 ± 1
	MgO (wt%)	7.33	5.6 ± 0.1	6.8 ± 1.3	5.6 ± 0.5
	TiO 2 (wt%)	1.98	2.55 ± 0.04	2.5 ± 0.3	3.9 ± 0.7

for

ACKNOWLEDGMENTS

For their interest in our investigations, we wish to thank Guy San Juan, Nelly Le Meur, Sophie Bernard, Yann Le Jeune and Emmanuel Georges (Archaeological Regional Service). We also wish to thank Charles-Tanguy Le Roux, Jean-Yves Tinevez (Minister of Culture), Emilie Veneau and Yvon Pellerin (Conseil Général of Côtes d'Armor), who authorized our new sampling at Plussulien, and Serge Cassen for providing us with samples 71 and 72. For their help, we would like to thank Bernard Bodinier, Julien Huard and Gilbert Foucher (Maine and Anjou Archaeological Investigation Group). Finally, we would like to thank J. Renouf and G. Cornen for their friendly reviews and J. Renouf and F. Chotard for assisting with the English.

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article at the publisher's web-site: Table A1. Major elements replicate analyses of Dolerite 61 and reference material WS-E. Table A2. Trace elements replicate analyses for dolerite 61 and referenced material W-2. Petrographic descriptions.


N Reuge
email: reuge@free.fr

F Collet

S Pretot

S Moisette

M Bart

O Style

A Shea

C Lanos

Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies

Keywords: Bio-based building materials, Local kinetics, Sorption, Hygrothermal transfer, Mass transfer, Modeling

A bio-based multi-layered reference wall has been developed within the framework of the European ISOBIO project. One of the key points of this project was to be able to perform proper simulations of the hygrothermal transfers occurring inside such walls. Previous published investigations, also performed in the framework of this project, have demonstrated that the classic assumption of instantaneous equilibrium between local relative humidity and water content according to the sorption isotherm is not relevant for bio-based porous materials, where, in practice, a rather slow kinetics of sorption occurs. The theoretical background developed in this previous study is used here to determine the kinetic constants of the bio-based construction materials and to perform 1D hygrothermal simulations. The kinetics constants are determined thanks to a 1D cylindrical tool based on the local kinetics approach, validated against several experiments of sorption. Then, heat and hygric transfers recorded on a demonstrator building (The HIVE, Wroughton, UK) are analyzed and are simulated using two modeling tools: TMC based on the Künzel approach and TMCKIN based on the local kinetic approach. From the simulations, the local kinetics improves the small timescale RH dynamics. The comparison with measurements performed in the demonstrator confirms the relevance of the local kinetics approach.

Introduction

The aim of the European ISOBIO project was to develop multi-layered wall solutions made of biobased materials featuring very low carbon footprints and high insulating properties. The present study has been done in this framework. One of the key points of this project was to be able to perform proper simulations of the hygrothermal transfers occurring inside the ISOBIO reference wall. Sorption of water in porous media involves interdependent phenomena such as vapor / liquid water mass transport by Fickian diffusion and equilibrium isotherms of sorption also called "water storage functions" associated with hysteretic phenomena. The diffusion coefficients can be determined in A c c e p t e d M a n u s c r i p t steady state exchange by permeability measurements (i.e. "wet cup method" [START_REF] Kumaran | Interlaboratory Comparison of the ASTM Standard Test Methods for Water Vapor Transmission of Materials (E 96-95)[END_REF]). The equilibrium isotherms of sorption can be determined by gravimetric methods [START_REF] Iglesias | Handbook of Food Isotherms: Water Sorption Parameters for Food and Food Components[END_REF]. Actually, the equilibrium water contents evolve as a function of the relative humidities between the main adsorption and desorption equilibrium isotherms depending on the material's hygric history and this complex phenomenon can be described by hysteretic models [START_REF] Carmeliet | Hysteresis and moisture buffering of wood[END_REF][START_REF] Huang | A novel hysteresis model in unsaturated soil[END_REF]. Note that heat and mass transfer phenomena have to be properly modeled and coupled, as highlighted in [START_REF] Perré | On the importance of heat and mass transfer coupling for the the characterization of hygroscopic insulation materials[END_REF]: heat transfers in walls can have a significant effect on the hygric transfers and inversely. But despite the reliability of these models, it seems that inside some porous materials, and particularly in bio-based materials, simulations largely underestimate the time required for the water content to reach the equilibrium: this has been established for bio-based materials in [START_REF] Nyman | Numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF][START_REF] Eitelberger | The sorption behavior of wood studied by means of an improved cup method[END_REF][START_REF] Alexandersson | Triphasic model of heat and moisture transport with internal mass exchange in paperboard[END_REF] and by Reuge et al. [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], but also for more traditional material such as cement compounds or concretes [START_REF] Johannesson | A numerical approach for non-linear moisture flow in porous materials with account to sorption hysteresis[END_REF][START_REF] Janssen | Experimental study of dynamic effects in moisture transfer in building materials[END_REF][START_REF] Zengh | A two-parameter stretched exponential function for dynamic water vapor sorption of cement-based porous materials[END_REF]. These considerations take on their full meaning in the cases of hygrothermal transfers with permanent fluctuations such as in materials of building envelopes, in soils or in food materials.

Classic simulation tools predicting hygrothermal transfers in building materials are based on the assumption that for a given local relative humidity ϕ, the associated equilibrium local water content w is reached instantaneously. In our previous studies [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF][START_REF] Reuge | Modèle de cinétique locale de sorption couplé au phénomène d'hystérésis pour les matériaux biosourcés[END_REF], three hemp-lime concretes were studied and it was demonstrated that such an assumption led to serious inconsistencies. Thus, as reported in the aforementioned literature, our previous studies have established that a local kinetics of sorption exists (from water vapor to liquid water and inversely) which can be slow compared to the diffusive fluxes. Obviously, this invalidates the classic assumption.

The first part of this study deals with the classic hygric and thermal properties obtained from characterizations performed on samples of ISOBIO materials. From the knowledge of these classic properties, a simple steady-state sensitivity study is performed to determine the most sensitive layers in the ISOBIO reference wall in term of thermal transmittance and resistance to water vapor diffusion. Then, the theoretical background necessary to model the water sorption / kinetics of sorption is presented, relying on the study [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF]. Thanks to this theoretical background, the kinetics constants of some of the studied ISOBIO materials are determined numerically and analytically by adjustments on sorption experiments. The last part of this study compares the results of the hygrothermal simulations based on the classic model with and without taking into account solar radiation and the local kinetics model to the measurements performed inside the ISOBIO reference wall at the HIVE demonstrator (Wroughton, UK) over a wide range of hygric and thermal operating conditions.

Classic hygrothermal properties of the ISOBIO materials

Reference ISOBIO wall

The reference ISOBIO wall is composed of: a BCB TM lime-hemp render (BCB), a CAVAC TM Rigid insulation panel made of hemp shiv and an organic binder (CAV), a Biofib Trio flexible insulation panel from CAVAC TM made of hemp flax and cotton (BIO), an OSB3 panel, a Proclima TM INTELLO membrane (INT), a Lignicell CSB TM panel made of compressed straw (CSB) and a CLAYTEC TM clayhemp plaster (CLA). Note that this wall is supported by a timber frame which will not be considered in the simulations. The configuration and the thicknesses of the different layers are given in Figure 1.

Note that the local hygric variables given at the macroscopic scales will be written as lower case letters (e.g. the local water content w) while the hygric variables given at the sample scales will be written as upper case (e.g. the global water content W).

Experimental characterizations

The experimental characterizations of the ISOBIO materials hygrothermal properties have been performed by Collet et al. [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF]. Therefore, the experimental methods of measurement will not be described here but only the values of the properties necessary to perform the simulations.

Table 1 is a compilation of the following properties measured at a temperature of 23°C: the bulk densities at dry state ρ 0 , the porosities ε 0 , the vapor diffusion resistance factors at dry state µ 0 , the thermal conductivities at dry state λ 0 and the specific heat capacities at dry state Cp 0 . Note that while most of these properties have been determined by Collet et al. [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF], a few others have been determined by other ISOBIO partners (University of Bath for BCB permeability) or obtained from trustable technical sheets.

The adsorption behavior of representative samples of the ISOBIO materials (CAV, BIO, OSB3 and CSB) have been studied in [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF]: they have measured their water content W (kg of water per m 3 ) temporal evolutions until quasi stabilization (or in other words, their global kinetics of adsorption) after several instantaneous increments of ambient relative humidity RH at a temperature T of 23°C. The final stabilized W are actually the equilibrium water contents W eq at the corresponding RH, allowing to determine the adsorption isotherms of the materials. The moisture storage functions of the other ISOBIO materials come from technical sheets and/or F-IBP databases (BCB, INT and CLA). The data are shown in Figure 2.

Models of properties

From the collected data of W eq as a function of RH, the Van Genuchten model VG [START_REF] Van Genuchten | A closed-form equation for predicting the hydraulic conductivity of unsatured soils[END_REF] has been used to model the adsorption isotherms. Note that the VG model is claimed valid even at high RH (>90%). It is expressed as follow:

( ) ( ) ( ) 1 1 sat 1 ln eq W RH W h RH h h -   = + -   (1)
where h and η are adjustment coefficients. 2 and the Figure 2 shows the adjustments. Note that the maximum water contents W sat have been considered equal to the measured porosities ε 0 multiplied by the liquid water density (i.e. 1000 kg.m -3 ) excepted for BIO.

The evolutions of the vapor diffusion resistance factors µ as a function of the local water content w or RH have been ignored except for the Proclima INTELLO membrane because it is a hygrovariable material evolving very significantly as a function of RH. The data provided by Proclima/F-IBP have

W (kg.m -3 ) RH (-)
A c c e p t e d M a n u s c r i p t been fitted by a logistic power as shown in Figure 3. Because of its great values, this parameter must be carefully modeled. Note that at 100% RH, µ decreases to 553. Finally, the evolution of the thermal conductivities as a function of the water content has been modeled by the self-consistent scheme [START_REF] Collet | Thermal conductivity of hemp concretes: Variation with formulation, density and water content[END_REF], which takes the following expression:

( ) ( ) ( )( ) ( ) { ( ) ( )( ) ( ) ( ) ( )
s s s W W W λ λ ε ε ε λ ε λ - -  = + - + + -    ⋅ -- - ⋅ +     (2)
The coefficient λ s (which can be seen as the thermal conductivity of the material skeleton) have been adjusted such as λ(W=0) equals λ 0 . The values of λ s are given in Table 2. A c c e p t e d M a n u s c r i p t

Sensitivity study

Based on the materials thermal conductivities λ 0 and the vapor diffusion resistance factors µ 0 at dry state, the total thermal transmittance U and vapor resistance R of this wall are of 0.155 W.m -2 .K -1 and 1.95.10 11 Pa.m 2 .s.kg -1 respectively.

Then, by individually varying λ 0 and µ 0 of each layer (±10%), a sensitivity study has been performed. The sensitivities S U and S R given by eqs ( 3) and ( 4) of each layer are reported in Table 3. This means that if λ 0 or µ 0 is modified by x%, U and R of the wall are modified by x.S U % or x.S R % respectively.

( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 0 0 10% 10% 0.2 10% 10% 0.2 λ λ λ + - -  =    + - -  =   U R U U S U R µ R µ S R µ (3,4)
Table 3: Sensitivity study Regarding U, the most sensitive material is obviously the Biofib Trio BIO (which is actually implemented in two layers of a total thickness of nearly 20 cm and which shows the lowest thermal conductivity) with a S U of 0.77 and, to a much lesser extent, CAV and CSB.

Regarding R, the most sensitive material is obviously the membrane INT with a S R of 0.83 and, to a much lesser extent, OSB3 and CSB. Note that the S R of INT is given at dry state and will decrease very significantly with RH as this is a hygrovariable membrane.

Therefore, if the global characteristics of the ISOBIO reference wall need to be modified regarding any standard requirement, this sensitivity study can be of a precious help.

Mass transport governing equations

In this section, (i) air transport is ignored. In the porous samples, water is present in gaseous form (water vapor) and in liquid form. Therefore, there are two mass balance equations to consider. Assuming that (ii) the convective transport is negligible, they take the following form:

S U (-) S R (-) BCB 0.
, , v p v v s l p l l s D R t D R t ρ ρ ρ ρ ∂  -∇ ⋅ ∇ = -   ∂  ∂  -∇ ⋅ ∇ =  ∂  (5,6)
where v ρ and l ρ are the local water vapor and liquid water partial densities, D p,v and D p,l are the water vapor and liquid water diffusivities and R s is the rate of sorption. The local relative humidity can be expressed as follow:

v v sat w sat P RT P M P ρ ϕ = = (7)
and the local liquid water partial density l ρ (i.e. the local water content) will be written by convention as w. Thus, eqs [START_REF] Perré | On the importance of heat and mass transfer coupling for the the characterization of hygroscopic insulation materials[END_REF][START_REF] Nyman | Numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials[END_REF] can be rewritten as follow:

( ) ( ) ( ) , , sat v p sat s w w p l s P RT RT P R t M M w D w R t ϕ δ ϕ ∂   -∇ ⋅ ∇ = -     ∂    ∂  -∇ ⋅ ∇ =  ∂  (8,9)
where the porous media vapor permeability

, v p v v w D M RT δ δ µ µ = =
, the water vapor diffusion resistance factor being given by:

, , v v p v p v D D µ δ δ = = .
It is commonly assumed that the rate of sorption R s is very fast compared to the vapor diffusive flux leading to the so-called Künzel mass transfer equation [START_REF] Künzel | Simultaneous Heat and Moisture Transport in Building Components -One-and Two-Dimensional Calculation Using Simple Parameters[END_REF].

Note that the coupling of eqs (8,9) with a hysteretic model (e.g. [START_REF] Huang | A novel hysteresis model in unsaturated soil[END_REF]) can easily be done: the reversal points (i.e. transitions between adsorption and desorption phases) are obtained when the sign of R s changes.

As demonstrated and validated in the study of Reuge et al. [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF] based on three different hemp concretes, the following expression for the sorption rate seems appropriate for the bio-based materials:

( ) ( ) 2 0 s eq R k w w ϕ = - (10)
where k 0 is the local kinetic constant of sorption (adsorption or desorption) and w eq is the equilibrium local water content given by the sorption isotherm at a local relative humidity φ. Note that this is a second order kinetics and consequently the unit of k 0 is expressed in day -1 /(kg.m -3 ). In [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], the values obtained for the studied hemp concretes are around 1 day -1 /(kg.m -3 ).

The classic heat transport governing equation is not given here but it is obviously taken into account considering latent heat of vaporization. At the wall surface, a convective heat transfer coefficient h T is specified and the short-wave radiative flux is considered via an absorptivity coefficient α.

Determination of the kinetics constant of the ISOBIO materials

The time-dependent adsorption curves have been experimentally determined by gravimetric methods for CAV, BIO, OSB3 and CSB [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF]. Regarding BCB, desorption experiments have been performed by an industrial partner (BCB). The characteristic diameter of the samples was of 4 cm.

A c c e p t e d M a n u s c r i p t

If the sorption rate is slow compared to the vapor diffusive flux, the adjustments of 1D cylindrical calculations based on the local kinetics approach allow to determine the kinetic constant k 0 . According to Reuge et al. [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], k 0 should be constant in the range of 20% to 70% RH, for higher RH, k 0 tends to decrease because most of the sorption sites are already occupied. And actually, at RH higher than 80%, both local kinetics and diffusive mass transport are limiting phenomena [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF]. Note that liquid diffusivity tends to usually initiate at RH of about 60% and becomes really significant from RH of about 80% as demonstrated in [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois en béton de chanvre[END_REF] and evidenced in the Fraunhofer Institute for Building Physics (FIBP) database. The 1D cylindrical calculations will be performed considering µ always equal to µ 0 (as a first step) and ignoring the liquid diffusivities.

CAVAC Rigid Panel

Experiments

Initially, the samples have been stabilized at a given ambient RH, and then the RH have been suddenly increased to a higher given value. For CAV, the following RH steps have been tested: 0-30%RH, 30-50%RH, 50-65%RH, 65-80% RH and 80-95% RH. Regarding the 0-30% RH and 50-65 %RH steps, one of the samples was weighted continuously, for the other steps the samples were weighed discontinuously [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF]. Four representative samples were used for each measurement, the differences were lower than 5%. The results of the measurements are shown in Figure 4: the stabilizations occur in more than 5 days. Note that regarding the 80-95% RH step, the measurements have been stopped before the stabilization because of initiation of mold development.

1D simulations

First, 1D simulations based of the Künzel approach have been performed: for the 0-30% RH, 30-50% RH, 50-65% RH steps, the times of stabilization are lower than 1 day and therefore greatly underestimated: this approach is invalidated (see Fig. 4 for the 30-50% RH step).

The adjustments of the 1D simulations based of the local kinetics approach leads to the following values of k 0 : 0.56, 0.3, 0.3, 0.12 and 0.08 day -1 /(kg.m -3 ) for the 0-30% RH, 30-50% RH, 50-65% RH, 65-80% RH and 80-95% RH steps respectively, as shown in Figure 4. Therefore, as expected, k 0 is the same for 30-50% RH and 50-65% RH steps (i.e. inside the range of 20% to 70% RH). The adjustments are globally very good with correlation coefficients greater than 0.99. However, note that the simulations and the values of k 0 obtained for the 65-80% RH and 80-95% RH steps can be unreliable since the liquid diffusivity is not taken into account. As noticed in [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF] for hemp concretes, at moderate RH (< 80%), the limiting parameter is k 0 and the calculation is insensitive to µ 0 . At high RH, both the kinetics and diffusive mass transport have an effect on the global sorption rate.

Biofib Trio flexible

The adjustments of the 1D simulations based of the local kinetics approach on adsorption curves [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF] leads to the following values of k 0 : 20, 9, 13 and 1.5 day -1 /(kg.m -3 ) for the 30-50% RH, 50-65% RH, 65-80% RH and 80-95% RH steps respectively (the 0-30% RH step measurements are too noisy to be exploited). Therefore, k 0 is around 14 day -1 /(kg.m -3 ) at common RH: this is a relatively high kinetic constant

A c c e p t e d M a n u s c r i p t

CSB Lignicell panel

This material is quite specific: it has a rather high µ 0 of 27 and both kinetics and diffusive mass transport are limiting. From 50% RH, both k 0 and µ have to be adjusted to obtain good agreements of the 1D simulations with the measurements. The adjustments showed in Figure 5 have been obtained with the following k 0 : 0.25, 0.25, 0.25, 0.01 and 0.001 day -1 /(kg.m -3 ) and the following µ: 27 (i.e µ 0 ), 27, 22, 8.5 and 8.5 for the 0-30%RH, 30-50%RH, 50-65%RH, 65-80%RH and 80-95%RH steps respectively. Note that the value of 8.5 corresponds the apparent µ "humid" measured by Collet et al. [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF] at 53-88% RH.

OSB3

This material is also a particular case because its µ 0 of 138 is so high that diffusive mass transport is the only limiting phenomena. This does not mean that no local kinetics exists but that the local kinetics is fast compared to the diffusive fluxes. Consequently, the Künzel approach is justified in this case. Performing 1D simulations based on this approach, a good agreement is obtained with the measurements adjusting µ to the following values: 275, 100, 100, 40 and 10 for the 0-30%RH, 30-50%RH, 50-65%RH, 65-80%RH and 80-95%RH steps respectively. The results are shown in Figure 6.

Note that the µ 0 of 138 measured at 0-50% RH in [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF] is indeed between 100 and 275 and that the measured µ "humid" (53-88% RH) of 45 [START_REF] Collet | Hygric propeties of materials used for ISOBIO wall solution for new buildings[END_REF] is close to the adjustment value of 40 for the 65-80%RH step.

Under these conditions, the kinetic constant cannot be determined. lead to the following values of k 0 : 0.0045 and 0.0055 day -1 /(kg.m -3 ) for the 100-65% RH and 100-50% RH steps respectively. Therefore, this is a quite slow kinetics constant of around 0.005 day -1 /(kg.m -3 ); note that from [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF], the kinetic constants of adsorption and desorption are the same (at least for the three hemp concretes studied in the cited study).

BCB plaster

Compilation of the kinetic constants

From this study, in the 20-70% RH range, the kinetics constants k 0 can be very different according to the material: from 0.005 day -1 /(kg.m -3 ) for BCB to about 14 day -1 /(kg.m -3 ) for BIO, i.e. a difference of almost 4 orders of magnitude. The values determined for RH greater than 80% are not reliable because the liquid diffusivities are unknown and have not been taken into account (see [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF] for deeper explanations and investigations). For the simulations performed in the next section, the values of k 0 compiled in Table 4 will be considered. For the materials for which k 0 remains unknown, i.e. OSB3, INT and CLA, a median value of 0.25 day -1 /(kg.m -3 ) will be considered; note that the thicknesses of the layers of these three materials in the reference ISOBIO wall are relatively small, particularly INT with 0.25 mm thickness and note that the value of k 0 of CLA is of minor importance when the RH fluctuations at the indoor boundary conditions are almost non-existent (see section 5.2).

* Unknown, median value The good adjustments of the calculations on the measured sorption curves is in themselves a selfconsistent validation of the proposed kinetics approach. It should be emphasized that considering a kinetic order different from 2 would not lead at all to such good adjustments. And although lab-scale MBV (Moisture Buffer Value) test measurements had been performed in the framework of the ISOBIO project, at the moment they cannot serve as a second validation step of the kinetic approach for two reasons: for these experiments, (i) most hygric phenomena occur under the vicinity of the material surface and then are highly sensitive to the surface mass transfer coefficients which are extremely difficult to determinate precisely and (ii) by the fact that mass sample weight determinations (and then liquid content dynamics) are much less sensitive to the sorption kinetics than the relative humidity dynamics. Thus, the next part deals with in-situ RH measurements performed in a demonstrator: this is arguably the most consistent approach.

Note that for CAV and BIO, the analytical expression given in [START_REF] Reuge | Water transport in bio-based porous materials: A model of local kinetics of sorption-Application to tree hemp concretes[END_REF] allow to straightly estimate k 0 without the need of performing simulations.

Simulations of the HIVE demonstrator

In this final part, the hygrothermal behavior of the ISOBIO reference wall installed at the HIVE demonstrator (Wroughton, UK) is studied under the local climate during winter 2018. This consists in comparing the measurements and the simulations. To our knowledge, this is the first modeling work studying a multi-layered fully bio-based wall in real climatic conditions while various studies have already been carried out under controlled conditions and/or only one bio-based layer. Moujalled et al. [START_REF] Moujalled | Experimental and numerical evaluation of the hygrothermal performance of a hemp lime concrete building: A long term case study[END_REF] has studied the effect of real climatic conditions (Périgueux, FR) on a bio-based building with a wall of three layers: a hemp-lime concrete but with classic internal and external renders. Their simulations took into account the solar radiation and their results of the simulations were in globally good agreements with the measurements but the small time scale (on a few hours) RH dynamics was very notably underestimated. Piot et al. [START_REF] Piot | Hygrothermal behaviour of a hemp concrete wall: experimental and numerical study of coating[END_REF] has also studied a three-layered wall (Savoie, FR) in real climatic conditions: a hemp concrete but also with classic internal and external renders. Again, the calculated small time scale RH dynamics was very notably underestimated compared to the measurements. In [START_REF] Lelievre | Hygrothermal behavior of bio-based building materials including hysteresis effects: Experimental and numerical analyses[END_REF][START_REF] Colinart | Experimental and numerical analysis of the transient hygrothermalbehavior of multilayered hemp concrete wall[END_REF][START_REF] Rahim | Numerical investigation of the effect of non-isotherm sorption characteristics on hygrothermal behavior of two bio-based building walls[END_REF][START_REF] Colinart | Temperature dependence of sorption isotherm of hygroscopic building materials. Part 2: Influence on hygrothermal behavior of hemp concrete[END_REF][START_REF] Fabbri | Impact of the determination of the sorption-desorption curves on the prediction of the hemp concrete hygrothermal behaviour[END_REF][START_REF] Seng | Scale analysis of heat and moisture transfer through biobased materials -Application to hemp concrete[END_REF], the authors have studied the response of hemp concrete panels to controlled indoor and outdoor conditions. Even in these controlled operating conditions without solar radiation, most of these studies [START_REF] Lelievre | Hygrothermal behavior of bio-based building materials including hysteresis effects: Experimental and numerical analyses[END_REF][START_REF] Colinart | Experimental and numerical analysis of the transient hygrothermalbehavior of multilayered hemp concrete wall[END_REF][START_REF] Seng | Scale analysis of heat and moisture transfer through biobased materials -Application to hemp concrete[END_REF] lead to simulation results that underestimate clearly the small time scale RH dynamics. From that point of view, [START_REF] Rahim | Numerical investigation of the effect of non-isotherm sorption characteristics on hygrothermal behavior of two bio-based building walls[END_REF][START_REF] Colinart | Temperature dependence of sorption isotherm of hygroscopic building materials. Part 2: Influence on hygrothermal behavior of hemp concrete[END_REF][START_REF] Fabbri | Impact of the determination of the sorption-desorption curves on the prediction of the hemp concrete hygrothermal behaviour[END_REF] seem to obtain better results playing on some parameters which have an effect on the hysteretic behavior of the sorption phenomena such as the initial water content (which is usually unknown) or the considered hysteretic model.

HIVE demonstrator: experimental setup

The ISOBIO test wall dimensions were 1.95mx1.95mx33.45cm. Inside the demonstrator, a CS215 SDI-12 Sensirion-based sensor was installed to measure air room T and RH. Heating equipment was used to maintain a constant indoor air temperature (BioGreen Phoenix electrical resistance heater with inbuilt air circulation fan). Outside the demonstrator, a weather station was installed to measure: RH and T (Rotronic HC2S3 sensor within 9-element ventilated solar shield), the wind speed (2-axis Gill Instruments Ultrasonic anemometer), precipitation (RM Young Tipping Bucket rain gauge) and horizontal global and diffuse solar radiation (Delta T Devices SPN1 Sunshine Pyranometer). Three RH and T sensors were installed inside the wall (CS215) at:

-position 1: CAV / BIO1 interface, -position 2: BIO1 / OSB3 interface, -position 3: INT / BIO2 interface.

In standard operating conditions, the accuracy of the CS215 SDI-12 Sensirion sensor measurements is of ±2%RH and ±0.4°C for T.

Figure 7 presents the external view of the ISOBIO wall panel under test at the HIVE test facility. At the center of the external face of the test panel, the external surface temperature is measurement using a thermistor encapsulated in an epoxy-filled aluminum housing clipped to the surface of the BCB render. This sensor is protected in a solar shielded and ventilated space. Offset from the center of the panel, the first of three embedded CS215 RHT sensors is fixed at the interface of CAV and BIO1, (i.e. position 1, approx. 75 mm from the external surface of the wall); the second CS215 RHT sensor is fixed at an approximate depth of 220 mm at the interface of BIO1 and the OSB3 board (position 2); and the third CS215 RHT sensor is at an approximate depth of 232 mm at the interface of the INT membrane and BIO2 (position 3). To avoid penetrations through the vapor control membrane, For the simulations, typical values have been considered for outdoor and indoor heat transfer coefficients, 17 and 8 W.m -2 .K -1 respectively [START_REF] Schaube | Wärmeübergangskoeffizient unter natürlichen Klimabedingungen[END_REF][START_REF] Erhorn | Überprüfung der Wärme-und Feuchteübergangskoeffizienten in Außenwandecken von Wohnbauten[END_REF]. A value of 0.4 has been considered for the white wall render (BCB) absorptivity α in accordance with RT2012 French standards [START_REF]RT 2012 -Règles Th-S : Caractérisation du facteur de transmission solaire des parois du bâtiment -CSTB Ed[END_REF]. For outdoor and indoor mass transfer coefficients, typical values of 7.4.10 -8 and 2.6.10 -8 kg.Pa -1 .m -2 .s -1 have been considered respectively [START_REF] Schaube | Wärmeübergangskoeffizient unter natürlichen Klimabedingungen[END_REF][START_REF] Erhorn | Überprüfung der Wärme-und Feuchteübergangskoeffizienten in Außenwandecken von Wohnbauten[END_REF]. Note that TMC has been numerically validated on simple cases against WUFI TM 1D (a commercial tool) calculations.

Assumptions

For the mathematical models, assumptions are given in section 3.1. Regarding the sorption isotherms, the measurements done in adsorption conditions at 23°C (Fig. 2) were considered: consequently, no temperature effect or hysteresis phenomena were considered. Constant vapor resistance factor coefficients at dry state µ 0 were considered (Table 1) excepted for INT for which µ as a function of RH was considered (Fig. 3). Liquid diffusivities were neglected. The effects of wind and rain and long-wave radiation on outdoor boundary conditions were neglected for the simulations.

For TMCKIN simulations, kinetics constants k 0 given in Table 4 were considered. As clearly demonstrated in (Reuge, 2019), the actual values of k 0 and of the liquid diffusivities of the bio-based materials are strongly interdependent at high RH (>70-80%). Since the liquid diffusivities associated with the ISOBIO materials are unknown, the most reasonable approach is to consider the values of k 0 constant even at high RH.

Results of the simulations and discussion

The initial hygrothermal conditions in the wall have been chosen as follow: Obviously, these initial conditions do not correspond to the reality. Consequently, an iterative procedure has been used: the first simulations (with TMC and TMCKIN) have been performed over a full cycle of 18 days considered the aforementioned initial conditions. A second set of simulations have been run considering as initial conditions the final profiles of ϕ, w and T in each layer inside the wall. Finally, a third set of simulations have been run considering as initial conditions the final hygrothermal profiles of the second simulations in each layer. Only the results of this third set of simulations will be presented here. It worth noting that this procedure does not guarantee that the third simulations were run with exactly the good initial conditions but at least that they were more realistic than the aforementioned constant values used for the first simulations.

The results of the simulations (TMC and TMCKIN) are given at the aforementioned positions. Figures 10a, 11a and 12a show the measured and calculated RH over the full cycle (18 days) at pos. 1, 2 and 3 respectively. Figures 10b, 11b and 12b show the measured and calculated T at pos. 1, 2 and 3 respectively. Broadly, the RH obtained from the simulations are in good agreement with the measurements: the discrepancies are in a range of ±4%. Regarding the temperature evolutions, the agreements are good provided the solar radiations is taken into account, the peaks of temperature corresponding to intense solar radiation periods are almost perfectly reproduced.

Then, it is particularly interesting to analyze the dynamics of the RH fluctuations at relatively small time scales (within at time interval of 24 h): at pos. 1 (Fig. 10a) and pos. 2 (Fig. 11a), they are patently underestimated by the TMC if the solar radiation is not taken into account and better but still largely underestimated predicted by TMC if the solar radiation is taken into account. The dynamics is better predicted when the solar radiation is considered because the temperature peaks resulting from the radiative flux increase the variations of water vapor saturation pressure and then of RH. The best agreements are obtained with TMCKIN: this is a straight effect of the local kinetics delaying adsorption / desorption of the water vapor, this is particularly observable at pos. 1 and pos. 2 (Fig. 10a and11a). Extracting the main RH minima and maxima from the data, it is possible to estimate average RH variations: at pos1, they are of 2.8, 0.84, 1.4 and 3.2 respectively from the measurements, the TMC simulation without solar radiation, the TMC simulation and the TMCKIN simulation. Thus, the TMC simulation (with solar radiation) underpredicts the RH dynamics by 51% whereas the TMCKIN simulation slightly overpredict it by 12bb%. At this point, it must be reminded that the liquid water transport is ignored (because the liquid diffusivities are unknown for the studied materials) but its effect would undoubtfully soft the small time scale RH dynamics at such high RH of pos1. At pos2, the TMC simulation underpredicts the RH dynamics by 56% whereas the TMCKIN simulation slightly overpredict it by 16%. At pos3, the TMC simulation overpredicts the RH dynamics by 11% and the TMCKIN simulation by 31%: the overpredictions at this last position are questionable.

The measured and predicted RH dynamics tend to be of a lesser extent at pos. 3 (Fig. 12a), this can be explained by the lesser effect of the solar radiation heat flux at such a deepness in the wall and by the filtering effect of the INT membrane on hygric variations. considered 18 days is studied on the total wall water content considering every time the hygric state of the end of a run as initial conditions for the next run. This has been repeated 10 times with TMC and TMCKIN. Initially, the wall water content W w is of 4.71 kg.m -2 . As aforementioned, the hygric state of the end of runs 2 had been considered as initial conditions for runs 3 which have been studied previously. From Fig. 14, the differences of W w predicted with TMC and TMCKIN doesn't cease to increase run after run. At the end of run 10, the predicted total wall water contents W w by TMC and TMCKIN are of 3.32 kg.m -2 and 3.88 kg.m -2 respectively, i.e. a difference as much as 17%. Thus, after a long period of time, the hygric states of the wall predicted by TMC and TMCKIN can be very significantly different. It deserves to be emphasized, for instance in the perspective of durability studies.

Sensitivity study

It seems interesting to study the sensitivity of various intrinsic properties of the studied materials on the small time scale RH fluctuations. The properties studied here are: the vapor resistance factor coefficient µ 0 ±20%, the kinetic constant k 0 ±20% and the thermal conductivity parameter λ s ±20%. At a given position, the average RH fluctuation obtained with TMCKIN is named ∆RH . The sensitivity S of a given properties, for instance µ 0 , on ∆RH is given by: ( ) ( ) ( )

0 0 0 20% 20% 0.4 ∆ + -∆ - = ∆ RH µ RH µ S
RH µ [START_REF] Janssen | Experimental study of dynamic effects in moisture transfer in building materials[END_REF] This means that if µ 0 is modified by x%, the predicted ∆RH is modified by x.S% (at least in the range of µ 0 ±20%).

Three sensitivity studies have been performed:

-the first one varying the properties of the CAV layer, -the second one varying the properties of the BIO1 and BIO2 layers,

-and the third one varying the properties of the INT layer.

For this last layer, only the µ 0 parameter was tested (the other properties of this very thin layer do not impact the results of the simulations).

The values of the sensitivities S, at pos1, pos2 and pos3, are reported in Table 5. Note that when the calculated S is lower than 0.01, a dash has been reported instead of a value.

From these results, it appears that the sensitivity S to the studied parameters is relatively low, i.e.

taking into account the uncertainties given in Table 1, the effect on ∆RH is relatively limited and does not put into question the considerations of the previous section. That beeing said, the most sensitive parameter for CAV and BIO1/BIO2 is µ 0 and therefore must be measured very carefully. For INT, variations of µ 0 in the ±20% range does not have any effect, its value remains anyway too high.

In further investigations, the effect of the slopes of the isotherms of sorption can be analyzed, but this parameter is straightly linked with the effects of the hysteresis phenomena which is outside the scope of the present study.

Conclusion

This study has allowed to determine the kinetic constants of the key (on a hygric point of view) ISOBIO materials. According to these various materials, these kinetics constants can differ by four orders of magnitude. When the material vapor diffusion resistance factor µ 0 is too high (> 100, i.e. OSB3), the kinetic constant cannot be determined by the proposed 1D numerical method.

The simulations of the HIVE demonstrator have been performed and compared to the measurements. This is the first modeling study of a multi-layered bio-based wall and, despite some assumptions, the simulations have led to overall good agreements with the measurements. Regarding the heat transfers, taking into account the solar radiation is required to obtain accurate agreements on temperature with the in-situ measurements. Regarding the hygric transfer, it has appeared that taking account both the solar radiation and the kinetics of sorption (TMCKIN) are required to reasonably predict the small time scale (less than 24 h) RH dynamics. In the perspective of simulations of RH variations inside a whole building, this work tends to show that the commercial simulation tools may fail to lead to reliable hygric results because they do not take into account the local kinetics effects.

In further investigations, the effects of an alternative climate and of internal RH loads on the ISOBIO reference wall will be studied. Moreover, alternative configurations of the ISOBIO wall will be investigated.

Figure 1 :

 1 Figure 1: ISOBIO reference wall

Figure 2 :

 2 Figure 2: Isotherms of adsorption of the ISOBIO materials -Experimental data (symbols) and adjustments with the VG model

Figure 3 :

 3 Figure 3: Vapor diffusion resistance factors µ of the Proclima INTELLO membrane as a function of RH -Measurements (points) and adjustment by a logistic power law -a = 7.3310 -6 , b = 1.8.10 -3 and c = 7.644

Figure 4 :

 4 Figure 4: CAV sample -Adsorption measurements (symbols and black lines) -Adjusted 1D simulations (colored lines)

Figure 5 :Figure 6 :

 56 Figure 5: CSB sample -Adsorption measurements (symbols) -Adjusted 1D simulations (colored lines)

A c c e

  p t e d M a n u s c r i p t cabling for sensors between the membrane and the outer face of the test wall are routed to the outside and those inboard of the membrane are routed to the interior of the test enclosure.

Figure 7 : 5 . 2

 752 Figure 7: Outer face of the instrumented ISOBIO wall -HIVE demonstrator (Wroughton, UK)

Figure 8 :

 8 Figure 8: Indoor and outdoor RH (a) and T (b) measurements

Figure 9 : 5 . 3

 953 Figure 9: Solar short-wave radiation measurements

  s c r i p t -a constant RH of 80% in each layer, -water contents w corresponding to RH of 80% according to the sorption isotherm in each layer, -a constant temperature T of 10°C.

Figure 13 showsFigure 10 :

 1310 Figure13shows the evolutions of local water content w as a function of local relative humidity ϕ at position 1 during the studied period of time (18 days) obtained with TMC and TMCKIN simulations. As expected, (ϕ, w) moves along the sorption isotherm of CAV according to TMC simulation whereas (ϕ, w) moves around it according to TMCKIN simulation. TMC simulation is always in an equilibrium

Figure 11 :

 11 Figure 11: Measurements and simulations (TMC without solar radiation, TMC, TMCKIN) at position 2 -Temporal evolution of (a) relative humidity and (b) temperature

Figure 12 :Figure 13 :Figure 14 :

 121314 Figure 12: Measurements and simulations (TMC without solar radiation, TMC, TMCKIN) at position 3 -Temporal evolution of (a) relative humidity and (b) temperature

A c c e p t e d M a n u s c r i p t

Table 1 :

 1 ISOBIO materials properties at dry state at T = 23°C

		Biofib Trio Flexible
	CAVAC Rigid Panel	(BIO1) (BIO2)	Lignicell CSB Panel
	(CAV) -50 mm	145 mm 45 mm	(CSB) -40 mm
				Claytec Plaster
	OUTDOOR			(CLA) -15 mm
	BCB Render			INDOOR
	(BCB) -25 mm
		OSB3	Proclima INTELLO
		12 mm	Membrane (INT) -0.25 mm

Table 2 :

 2 Adjustment coefficients -VG model and self-consistent scheme

	µ (-)
				RH (-)
		W sat (kg.m -3 )	h (-)	η (-)	λ s (W.m -1 .K -1 )
	BCB	546	8524	1.38	0.312
	CAV	874	27490	1.435	0.53
	BIO	348	228504	1.473	1.055
	OSB3	609	11360	1.325	0.367
	INT	85	2091	1.42	2.74
	CSB	720	23172	1.334	0.38
	CLA	294	271	1.656	0.995

Table 4 :

 4 ISOBIO materials kinetic constants k 0

Table 5 :

 5 Sensitivity study -Values of S (-)

Acknowledgments

This work has been performed and funded in the framework of the European project ISOBIO -(http://isobioproject.com) within the scope the of the research and innovation program Horizon A c c e p t e d M a n u s c r i p t 2020 (agreement No. 636835). This work has also been supported by the French region Bretagne Loire (UBL).

Special acknowledgments go to Prof. M. Lawrence (University of Bath) and Ronelvy Nivesse (BCB) for their works on the characterization of the BCB render.