Loris Verron

Erwan Hamard
email: erwan.hamard@univ-eiffel.fr

Bogdan Cazacliu

Andry Razakamanantsoa

Myriam Duc

Théo Vinceslas

Arthur Hellouin De Menibus

Blandine Lemercier

Rhoda Julia Ansaa-Asare

Thibaut Lecompte

Estimating and mapping the availability of earth resource for light earth building using a soil geodatabase

Keywords: earth building, light earth, pedology, soil suitability, material flow analysis

Introduction

Buildings insulation: a social and environmental necessity

The building and construction sector is responsible for 36% of final energy consumption and 39% of global CO2 emissions in 2018 (Global Alliance for Buildings and Construction (GABC) 2019).

11% of GHG emissions from the building sector result from the manufacture of modern building materials alone (GABC 2019). In Europe, 67% of the energy consumed by the residential buildings is attributed to the heating of buildings [START_REF] Brevik | Shelter, clothing, and fuel: Often overlooked links between soils, ecosystem services, and human health[END_REF].

In countries with rapid population growth and strong rural exodus, the construction of new buildings is inevitable and necessary. Therefore, optimizing the energy efficiency (embodied energy and service life energy) of new buildings is an important lever for reducing energy consumption for these countries (GABC 2017).

On the contrary, population growth is low and building is slowly being renewed in Europe: 65% of the buildings that will exist by 2060 have already been built (GABC 2017). In order to reduce the energy consumption of the building sector in an efficient way, it is ecologically interesting to improve the energy efficiency of existing buildings (Oury et Parissin-Fabert 2019). In addition, new construction consumes 40 times more materials than renovation, and 80 times more in collective housing (ADEME 2019a). Renovation also leads to less soil artificialization (French Ministry of Agriculture, 2020).

Use of local natural materials for insulation

The use of local materials can reduce the embodied energy of the building sector by a factor of 2 and GHG emissions related to transportation by 4.5 [START_REF] Morel | Building houses with local materials: means to drastically reduce the environmental impact of construction[END_REF]UNEP DTIE IETC, 2003).

Depending on local socio-economic conditions, the use of local materials and vernacular building techniques also allows for easier access to construction materials, the development of sustainable local industries and the creation of jobs that cannot be relocated [START_REF] Hamard | Rediscovering of vernacular adaptative construction strategies for sustainable modern building: application to cob and rammed earth 183[END_REF][START_REF] Khoso | INVESTIGATIVE CONSTRUCTION OF BUILDINGS USING BAKED CLAY POST-REINFORCED BEAM PANELS[END_REF][START_REF] Sameh | Promoting earth architecture as a sustainable construction technique in Egypt[END_REF].

Raw earth construction is the use of earth that has not been stabilized with non-biodegradable binders as a building material. It has the potential to decrease the GHG emissions compared with conventional materials. For example, cob building can reduce 75-82% of such emissions compared with concrete masonry block building (Lola Ben-Alon et al., 2019). At the end of life of the building, the resource can:

1) return to the surrounding environment. The eventual bio-based additives such as vegetal fibres or granulates are 100% biodegradable when they are not supplemented with non-biodegradable materials [START_REF] Holzhueter | The Potential for Light Straw Clay Construction in Japan: An Examination of the Building Method and Thermal Performance[END_REF].

2) be reused infinitely for raw earth building [START_REF] Morel | What are the barriers affecting the use of earth as a modern construction material in the context of circular economy?[END_REF][START_REF] Van Damme | Earth concrete. Stabilization revisited[END_REF].

Using earth or bio-based materials would therefore reduce construction waste, which today constitutes 50% of the mass of waste in the European Union [START_REF] Llatas | A model for quantifying construction waste in projects according to the European waste list[END_REF].

The use of natural materials from local and sustainable sources requires adapting, within each territory, to the resources available locally. While the production of bio-based materials for construction may compete with other uses, some are considered as "residues", "co-products" or "by-products" of agriculture [START_REF] Valbuena | Identifying determinants, pressures and tradeoffs of crop residue use in mixed smallholder farms in Sub-Saharan Africa and South Asia[END_REF]. A good example of this is the hemp shiv, which is derived from the hemp stem. Its use in hemp concretes or in light earth could support the development and durability of the hemp sector and therefore its introduction in crop rotations. Indeed, hemp cultivation often has a positive impact on soil properties and requires few inputs [START_REF] Finnan | Hemp: A more sustainable annual energy crop for climate and energy policy[END_REF][START_REF] Struik | Agronomy of fibre hemp (Cannabis sativa L.) in Europe[END_REF]Zegada-Lizarazu and Monti, 2011).

Assuming that natural material insulation can have adequate insulation performances (see 1.3), it is potentially an efficient solution to insulate existing buildings and therefore reduce energy consumption in the building sector.

Currently, the use of natural or recycled materials for insulation is not very widespread: in 2011, mineral wools and plastics represented 93% of the world market share of insulation materials [START_REF] Asdrubali | A review of unconventional sustainable building insulation materials[END_REF]. However, the current trend is upward: over the period 2015-2050, the total consumption of biobased insulation products would vary from 2.4 to 7 Mt and that of wood from 1.5 to 3.5 Mt, according to different scenarios (French Ministry of Agriculture, 2020).

Approximately 1 to 10 mm of soil is formed every 100 years in temperate climates [START_REF] Egli | Soil formation rates on silicate parent material in alpine environments: Different approaches-different results?[END_REF]. Therefore, this material cannot be considered a renewable resource at human time scale. Besides, European soils are already facing many anthropogenic threats such as water erosion, soil capping and sealing due to the high urbanization rate and extensive contamination of the soils (FAO, 2015). The use of soil as a construction material raises the question of its sustainable management. Yet, till date, soil scientist have paid little attention to earthen building materials [START_REF] Brevik | Shelter, clothing, and fuel: Often overlooked links between soils, ecosystem services, and human health[END_REF].

In most cases, extensively building with raw earth should not threaten soil resource availability. However, particular cases such as the excavation of fertile surface soils should be avoided. Indeed, it can lead to a degradation of the agricultural or ecological potential of the soil, and abuses have already been identified by the scientific community [START_REF] Biswas | The Drivers and Impacts of Selling Soil for Brick Making in Bangladesh[END_REF][START_REF] Hashemi | Environmental Impacts and Embodied Energy of Construction Methods and Materials in Low-Income Tropical Housing[END_REF].

On the other hand, excavated soil is available in large quantities, 2.8 million tons per year in Brittany [START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF], often in close proximity to the construction site. The valorisation of this resource is interesting since it has no other function today and is considered as a waste of the construction industry. Using excavated soil for earth construction would reduce the environmental and economic cost of earth collection and transportation [START_REF] Marrero | Assessing the economic impact and ecological footprint of construction and demolition waste during the urbanization of rural land[END_REF].

Technical references for earth-hemp insulation

Raw earth building is often little or not considered in French construction standards [START_REF] Harries | The geological and geotechnical properties of earth material from central Devon in relation to its suitability for building in 'cob[END_REF][START_REF] Delgado | The selection of soils for unstabilised earth building: A normative review[END_REF], and has been the subject of few research programs compared to the most commonly used materials (metal, cement, wood) [START_REF] Ciancio | An overview of some current recommendations on the suitability of soils for rammed earth 6[END_REF][START_REF] Morel | What are the barriers affecting the use of earth as a modern construction material in the context of circular economy?[END_REF].

The French code of practice for light earth (Confédération de la Construction en Terre Crue (CCTC), 2018) defines light earth as a building material that is:

-non-load-bearing -composed of an earth slip (earth at liquid state) matrix coating vegetable or mineral aggregates -implemented in various ways: compacted in a temporary or lost formwork, manually applied with a trowel or by mechanized spraying, or implemented after drying.

Generally, it has a dry density ranging from 200 to 1200 kg/m³. However, our study focuses on light-earth for insulation purpose, which narrows the density range to 200-500 kg/m 3 .

Earth-hemp concrete, or earth-hemp, refers to a light earth material whose aggregate is hemp shiv. It combines the insulation performance of hemp shiv to the thermal inertia and hygroscopic exchange capacity of raw earth [START_REF] Cagnon | Hygrothermal properties of earth bricks[END_REF][START_REF] Soudani | Assessment of the validity of some common assumptions in hygrothermal modeling of earth based materials[END_REF]. These performances are similar to limehemp concretes and are attractive for renovation and construction in temperate or hot climates [START_REF] Volhard | Light earth building: a handbook for building with wood and earth[END_REF]. However, the Life Cycle Assessment (LCA) of hemp-lime concrete shows that the production of lime results in significant GHG emissions [START_REF] Peinemann | Effect of Clay Minerals and Organic Matter on the Cation Exchange Capacity of Silt Fractions[END_REF][START_REF] Sagastume Gutiérrez | Evaluation of the environmental performance of lime production in Cuba[END_REF][START_REF] Shan | CO2 emissions from China's lime industry[END_REF]. Using earth as a binder in plant-based concretes eliminates the need for lime, and ultimately reduces the embodied energy of the insulation system by a factor of 20 and GHG emissions by a factor of 5 [START_REF] Vinceslas | Light Earth Performances For Thermal Insulation: Application To Earth-Hemp[END_REF]. It also limits the impact and cost of end-of-life management, and decreases the price of the material by a factor of 1.5, while maintaining similar physical performance (thermal conductivity, compressive strength) [START_REF] Vinceslas | Light Earth Performances For Thermal Insulation: Application To Earth-Hemp[END_REF].

Paper objectives

In a context where raw earth building techniques are flourishing in the building sector, understanding where and how earthen construction can be developed while preserving the soil resource is essential. The evaluation of soil suitability for light earth building, and the quantification of the locally available resource is a way to better understand the eventual impacts of the development of light-earth building on the local soil resource availability for other uses. Furthermore, it is an interesting way to evaluate the reuse potential of excavated earth in order to include raw earth construction in a circular economy approach [START_REF] Kirchherr | Conceptualizing the circular economy: An analysis of 114 definitions[END_REF].

From [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF] insights on earth suitability for light earth building and expert craftsmen advices (see 2.5.3), and from [START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF] method on how to use a pedological database to estimate suitable soil availability for cob building (see 2.6), this work presents a method to evaluate local soil resource availability for light earth building. A pedological database (DoneSol3 Brittany) is crossed with earth suitability thresholds. Earth suitability is considered as dependant on multiple building steps, that represent on-field easiness of implementation as much as final mechanical performance of the material. The methodology is applied to Brittany (France), but may be applicable to any other territory disposing of an adequate soil map database.

Methods

Soils of Armorican Massif

This study covers the territory of Brittany region, located in the Armorican Massif geological domain. In this 27,040 km 2 area, the local pedological database is the Regional Pedological Referential of Brittany [START_REF] Lemercier | Sols de Bretagne[END_REF]. Generally, geological formations strongly impact on the pedogenesis of the overlying soils and especially in the Armorican Massif. The dominant soil mechanisms in the Armorican Massif are browning and clay leaching [START_REF] Berthier | Démarche qualité et cartographie régionale des sols dans le cadre du programme Sols de Bretagne[END_REF][START_REF] Jamagne | Grands paysages pédologiques de France, Collection Synthèses[END_REF]. DoneSol3 (InfoSol, 2021) is the French national database structuring and regrouping the point and surface data of the pedological studies of the Pedological Regional Referential (RRP) [START_REF] Lemercier | Guide d'utilisation des bases de données sol pour la production de cartes thématiques 112[END_REF].

Soil database structure

The surface data of DoneSol are derived from the synthesis of point and landscape observations by the soil-mapper. The expert defines Soil Type Units (STUs) ("pedon" equivalent), which are vertically divided into layers ("horizon" equivalent). On this territory, [START_REF] Vincent | Spatial disaggregation of complex Soil Map Units at the regional scale based on soil-landscape relationships[END_REF] carried out a predictive map of STUs using DoneSol data and soil landscape relationships. The resulting 50 m raster predicted the occurrence of a STU accurately up to 72.3% of the cases.

Earth parameters terminology

Earth is the constituent material of soil; where the properties of interest and study methods vary according to the discipline. In geotechnics, attention is often focused on the nature and particle size of soil constituents [START_REF] Lcpc | Fascicule 1&2 du Guide des Terrassements Routiers[END_REF]. In pedology, the analysis of constituents is one of the main dimensions of study, but also their organization at different scales, and the variability of these two parameters in time and space [START_REF] Jamagne | Grands paysages pédologiques de France, Collection Synthèses[END_REF]. Following the example of [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF], the word "soil" will be used here to indicate the complete soil profile in place (the "solum"). The word "horizon" will be used to describe a pedological horizon, i.e. a volume of soil in place with properties quite homogenous and generally delimited by a horizontal discontinuity. The word "earth" will be used to qualify any earth resource, including extracted soil resource.

In order to study soil's particle size distribution, the soil particles are grouped according to the particle size fractions. The limits of these fractions vary according to disciplines and national and international standards. In this article, we will use the size fractions commonly used by soil scientist in France, in particular those used in the DoneSol3 database. The 2000 µm sieve fraction, commonly referred to as the "fine fraction", is separated from the 2000 µm sieve non-passing fraction, commonly referred to as the "coarse fraction". The coarse fraction is called "F2000/D" and is measured as a % of the initial mass of earth. The fine fraction is divided into 3 size fractions, each of which is measured in g.kg -1 of the fine fraction:

-the 0 to 2 µm size fraction (F0/2), commonly termed "clays"; -the 2 to 50 µm size fraction (F2/50), commonly termed "silts"; -the 50 to 2000 µm size fraction (F50/2000), commonly termed "sands". F0/2 is often referred to as "clays" or "clay fraction", because F0/2 often gathers the majority of clay minerals. This creates ambiguity with mineralogical clays (Mitchell and Soga, 2005). Indeed, the particle size definition of "clays" differs from the mineralogical definition [START_REF] Peinemann | Effect of Clay Minerals and Organic Matter on the Cation Exchange Capacity of Silt Fractions[END_REF]. On one hand because non-clay particles (quartz) are present in F0/2 [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF], and on the other hand because F2/50 and F50/2000 contain clays, either in aggregate form or in mantle on other particles [START_REF] Brady | The nature and properties of soils[END_REF][START_REF] Curtin | Estimation of Components of Soil Cation Exchange Capacity from Measurements of Specific Surface and Organic Matter[END_REF][START_REF] Peinemann | Effect of Clay Minerals and Organic Matter on the Cation Exchange Capacity of Silt Fractions[END_REF]. In this article, the term clay will therefore refer only to mineralogical clays.

Earth suitability for earth-hemp building

Earth suitability

A suitable earth material for a raw earth building technique can be defined as an earth whose properties (composition, mechanical properties, etc.) enables the earthen building element to reach the desired building performance. The scientific community considers the functional building element performances (Figure 1) such as its mechanical strength parameters or sometimes hygrothermal performances when dealing with earth suitability for raw earth building. However, when masons evaluate an earth material suitability, they also consider its suitability for other stages of the building process, including its excavation, preparation and implementation. Indeed, these stages also introduce constraints on the composition or mechanical properties of the earth material, that often depend on the building techniques employed or mechanization intensity.

Suitability properties can thus be identified throughout the life cycle of earth material in raw earth building. As earth in raw earth building techniques is 100% reusable [START_REF] Morel | What are the barriers affecting the use of earth as a modern construction material in the context of circular economy?[END_REF][START_REF] Van Damme | Earth concrete. Stabilization revisited[END_REF], we can consider the earth material's life cycle along earth building process as circular.

For each suitability property, we define a suitability criterion, which is a threshold above/under which the material is considered suitable for the corresponding building stage.

Earth suitability for light earth building is not significantly impacted by the type of vegetal aggregate/fiber used [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF] or by the implementation method. This study focuses on earth-hemp implemented in a formwork, however the results are likely applicable to other light clay mixes with similar aggregates, such as linen or reed, or to other implementation techniques, such as projected earth-hemp.

Five suitability properties have been identified along with earth-hemp building process. They are summarized in Figure 1.

Excavation

An excavation step can be necessary. Although earth can be excavated by hand, nowadays it is usually excavated by mechanical means. During this step, different soil horizons can be excavated separately. In this study, we consider that the excavation machines have a limited excavation precision. Therefore, the cumulated thickness of the suitable soil horizons must be greater than this precision.

2.4.3

Ease of sieving F2000/D earth particles usually do not contribute significantly to the cohesive strength but they increase earth density. In order to maximise the insulation property of the material, a sufficiently low density must be obtained. To this end, the earth can be sieved to remove coarse particles (see appendix A, Figure A.1).

Glove test practicability

Earth is mixed with water until it reaches an adequate liquid state. The earth slip is then mixed with hemp shiv in order to distribute and coat the fibers. The homogenization/coating process requires adequate consistency of the earth in its fluid state. In addition, the slip consistency must have an adequate yield stress for the implementation step (see 2.4.5).

The "glove" test is currently the most common test for characterizing an earth slip used in light earth (see appendix A, Figure A.2). Craftsmen dip the hand into the slip, remove it, and observe the flow and cohesion of the slip on the hand, the result resembling a glove. Because this is the most effective test carried on field to characterise the adequate consistency of the earth [START_REF] Vinceslas | Methods to evaluate earth slip cohesion to build with light earth[END_REF], the earth material must allow its good execution.

Fresh state mechanical behaviour

The earth-hemp mix is partially compacted in a formwork that will be removed soon to allow the earth mix to dry. Therefore, the compacted mix must be cohesive enough to stick together at fresh state, even when the formwork is removed.

Earth slip behaves as a Bingham fluid, i.e. fluid with a yield stress [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF]. The yield stress represents the threshold at which the earth slip and hemp mixture "slips" along the wall, under its own weight. Thus, the yield stress can be seen as the capacity of a fresh earth-hemp mixture to stick on the wall [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF]. At this step, the yield stress of the earth slip must be high enough for the compacted mix to stick together when the formwork is removed.

Dry state mechanical behaviour

After drying, the cohesion provided by the earth in the dry earth-hemp mix must be sufficient to support the mass of a coating.

Suitability properties: an approximation using soil database proxies

Proxies

Proxy: In environmental sciences, when a data is not directly measurable or estimable, we use estimation parameters of this data, called "proxies". For example, satellite spectroscopic data is often used as a proxy to estimate organic content and texture of topsoil [START_REF] Knadel | Visible-Near Infrared Spectra as a Proxy for Topsoil Texture and Glacial Boundaries[END_REF].

In this study, we use proxies to approximate earth suitability properties. Therefore, a proxy is a pedological property of the earth material that 1) is considered representative of one or more suitability properties and 2) is available in the DoneSol pedological database.

Proxy threshold: As a proxy approximates a suitability property, the proxy threshold will approximate the suitability criterion i.e. the theoretic limit above/under which the earth material is no longer considered suitable for light earth building.

Proxy threshold variation range:

The suitability criterion along earth life cycle in earth-hemp building can vary depending on many parameters, e.g. implementation method, type of earth, building performances objectives, etc. This leads to a wide possible range of proxy thresholds values. In order to quantify an earth material suitability for earth-hemp building, at this stage, we reduce this variability to one predetermined proxy threshold for each suitability property. In order to consider the impact of the variability of the proxies' thresholds, the model will be submitted to a sensitivity analysis. The thresholds will be allowed to vary inside an interval (proxy threshold variation range) using a Monte Carlo analysis (see 2.6 part. 3). The intervals are defined by knowledge from expert masons and from literature, and represent a realistic variation range of the proxy thresholds in real conditions.

Proxy threshold concealment

As explained in [START_REF] Rojat | Towards an easy decision tool to assess soil suitability for earth building[END_REF], when earth suitability proxies thresholds are proposed in the literature, they fail to give full account of the diversity of earth employed for construction. This can be explained by the variability of the materials or techniques employed by present or past masons, mason's ability to adapt their practices to the earth material behaviour, and the complexity of earth suitability prediction for raw earth building.

Examples of abuse in the use of suitability thresholds have already been recorded. The grading envelopes published in [START_REF] Houben | Earth Construction: A Comprehensive Guide[END_REF] are used by several designers and control offices to define suitability criteria imposed in specific technical specifications in France, despite the authors' warning [START_REF] Luquain | La terre crue veut se libérer de l'analyse granulométrique[END_REF].

Thus, in order to avoid potential abuses in the use of the thresholds used in this study, they will not appear explicitly in the article's body. They will be replaced by an artefact: "[proxy name]unit" (ex: [F2000/D]%). They will be available on simple request to the authors. However, the proxy thresholds variation ranges will be left explicit.

The proxies' thresholds and their variation ranges for every suitability criterion are explained below. They are summarized in Table 1.

Sources of the data

The proxy thresholds and proxy thresholds' variation ranges for light earth suitability have been obtained from two sources. For T, OC, CEC, F50/2000, Vinceslas (2019) thesis data, based on 6 earth samples collected in the Armorican Massif, has provided us with hypothetical thresholds, that were validated by expert masons. For F2000/D, expert masons provided us with theoretical thresholds based on their field observations.

Excavation (T)

Soil horizons suitable for earth-hemp building must be accessible and must be separated easily from other non-suitable soil horizons. Therefore, the cumulated suitable horizons thickness must be thick enough to be excavated separately from others.

The proxy used, consecutive suitable layers cumulated Thickness (T) is calculated from the database (see 2.6). The proxy threshold variation range goes from 10 cm (manual excavation) to 60 cm (biggest mechanic diggers).

Ease of sieving (F2000/D)

As mechanical sieving is not common on light earth building sites, suitable earth should be easy to sieve manually (see 2.4.3). The proxy F2000/D will be used to approximate the ease of sieving. It must be low enough for manual sieving to be practicable.

The proxy threshold variation range is defined according to experts and goes from 5% (where a sieving process becomes necessary), to 30% if a mechanized sieving is performed.

Glove test practicability (OC)

Vinceslas ( 2019) noticed experimentally that a high soil organic matters content can perturbate the glove test used on field to characterise the adequate consistency of the earth (see 2.4.4). In addition, masons using local earth are trained to identify earths that are poor in soil organic matters (CCTC 2018). Therefore, a maximum limit of soil organic matters content in the earth is set in this study.

Organic Carbon (OC) content is used as a proxy for the presence of soil organic matters, via the van Bemmelen coefficient (1.724) [START_REF] Baize | Du taux de carbone à celui de matières organiques dans les sols -Les Mots de l'agronomie[END_REF], which allows one to switch between the two (Eq. 1).

Eq. 1 : 𝑆𝑜𝑖𝑙 𝑂𝑟𝑔𝑎𝑛𝑖𝑐 𝑀𝑎𝑡𝑡𝑒𝑟𝑠 (𝑔. 𝑘𝑔 -1 ) = 𝑂𝑟𝑔𝑎𝑛𝑖𝑐 𝐶𝑎𝑟𝑏𝑜𝑛 (𝑔. 𝑘𝑔 -1 ) × 1.724

In the experiments of Vinceslas ( 2019), the richest earth in soil organic matters that did not perturbate the glove test had an OC content of [OC] g.kg -1 . Above, there is a risk that the soil organic matters content perturbates this field test.

The proxy threshold variation range goes from 33.0 g.kg -1 corresponding to the second higher OC content of [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF] samples that did not perturbate the test, to 63.1 g.kg -1 which corresponds to the OC content of the earth material disturbing the glove test in the experiment.

Fresh state mechanical behaviour (F50/2000)

The earth slip yield stress must be high enough for the earth-hemp mix particles to stick together when the shutter is removed (see 2.4.5). The relationship between yield stress and water content is affected by the composition of the mixture, including clay content, nature of the clays, and particle size [START_REF] Bolleni | Understanding the role of yield stress in the quality of Light earth samples[END_REF][START_REF] Nguyen | Effect of clay fraction and water content on rheological properties of sand-clay mixtures[END_REF][START_REF] Vinceslas | Methods to evaluate earth slip cohesion to build with light earth[END_REF]. At equivalent water content, the dominant parameter of the liquid state behaviour is the specific surface area of the particles, which is maximized by increasing F0/2 and F2/50, i.e. reducing F50/2000 [START_REF] Bolleni | Understanding the role of yield stress in the quality of Light earth samples[END_REF][START_REF] Coventry | Specification development for the use of Devon cob in earthen construction[END_REF][START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF]. Therefore, F50/2000 is used as a proxy of the earth slip cohesion at fresh state.

The proxy threshold and proxy threshold variation range [308 g.kg -1 to 829 g.kg -1 ] are defined according to the results of [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF]. The proxy threshold used is in adequation with [START_REF] Brouard | Caractérisation et optimisation d'un composite biosourcé pour l'habitat[END_REF] experimental results. Above this proxy threshold, the earth material is considered not cohesive enough.

Dry state mechanical behaviour (CEC)

The cohesion provided by the earth must be sufficient for the dry earth-hemp material to support the mass of a coating. The mechanical parameters of raw earth materials depend primarily on the phenomena of electronic cohesion and suction. These two types of electronic interactions vary depending on the type and amount of clay [START_REF] Curtin | Estimation of Components of Soil Cation Exchange Capacity from Measurements of Specific Surface and Organic Matter[END_REF][START_REF] Meimaroglou | Cation Exchange Capacity (CEC), texture, consistency and organic matter in soil assessment for earth construction: The case of earth mortars[END_REF]Weil and Brady, 2016). Clay bonding capacity is provided by the combined action of clay specific surface area and electronical charge [START_REF] Meimaroglou | Cation Exchange Capacity (CEC), texture, consistency and organic matter in soil assessment for earth construction: The case of earth mortars[END_REF]. Cation Exchange Capacity (CEC) is the amount of positive electronic charges in the form of cations that can replace present cations or be retained by negative charges, in an earth material [START_REF] Coventry | Specification development for the use of Devon cob in earthen construction[END_REF]Mitchell and Soga, 2005). In non-organic earths these charges originate mainly from clays [START_REF] Ersahin | Estimating specific surface area and cation exchange capacity in soils using fractal dimension of particle-size distribution[END_REF][START_REF] Farrar | The Correlation of Surface Area with Other Properties of Nineteen British Clay Soils[END_REF][START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF][START_REF] Hepper | Clay mineralogy, cation exchange capacity and specific surface area of loess soils with different volcanic ash contents[END_REF]Weil and Brady, 2016). CEC is therefore a good indicator of the potential for electronic interactions in an earth material [START_REF] Coventry | Specification development for the use of Devon cob in earthen construction[END_REF][START_REF] Meimaroglou | Cation Exchange Capacity (CEC), texture, consistency and organic matter in soil assessment for earth construction: The case of earth mortars[END_REF], and therefore in an earth building material [START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF][START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF]. In this study, the proxy CEC is used to approximate the mechanical strength of the dry light-earth material.

The proxy threshold and the proxy threshold variation range [3.9 g.kg -1 to 6.6 g.kg -1 ] are defined according to the results of [START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF].

Table 1 : Suitability parameters and associated suitability criteria, corresponding proxies, proxy thresholds and proxy thresholds variation range.

Data processing

The calculation method is based on the methodology proposed by [START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF] where a pedological database is used to estimate suitable soil availability for cob building. It was encoded in Python for reproducibility purposes and to run a Monte Carlo sensitivity analysis, and it was modified to fit the predictive STU raster map produced by [START_REF] Vincent | Spatial disaggregation of complex Soil Map Units at the regional scale based on soil-landscape relationships[END_REF] and light earth suitability thresholds.

Part. 1: Calculation of volume and % of suitable earth

STU and STU layers properties were extracted from DoneSol database (see appendix B, Figure B.1). For each layer, the parameters were compared to the proxies' thresholds, and assumed as suitable or not suitable. Then the consecutive suitable layers of every STU were compared to the cumulated Thickness threshold (T). If the layer satisfies T threshold, it is assumed as suitable. The sum of all suitable layers' thickness of the STU is calculated and called suitable thickness. The total thickness of the STU is also calculated. From the predicted STU raster map, STU surface is quantified and extracted. STU total soil volume and STU suitable soil volume were obtained by multiplying respectively STU total thickness and STU suitable thickness by STU surface.

Building stage stage of earth material life cycle

Suitability property earth material property impacting suitability

Suitability criterion criterion of success of the suitability property

Proxy

Finally, all STU total volumes and STU suitable volumes were summed in order to obtain a total soil volume and suitable soil volume over Brittany territory. The Suitable Soil Percentage (SSP) was calculated after the suitable soil volume % of the total soil volume.

Part. 2: Sensitivity analysis on the proxies' thresholds

In order to consider the impact of the variability of the proxies' thresholds on these soils' suitability, the model is submitted to a Monte Carlo sensitivity analysis. The Pearson correlation coefficients between the 4 input proxies were calculated from the data extracted from the DoneSol3 database ( Overall, the input proxies are not closely correlated, allowing the input thresholds to be submitted to a Monte Carlo sensitivity analysis. The proxy thresholds were randomly selected inside the proxy threshold variation range, that is to say on the whole realistic range of possible values. Exception is made for T, as it is not directly available in the database. However, to be able to evaluate its variability, T varied randomly on 3 fixed values: the two proxy threshold variation range values (10cm, 60cm) and the proxy threshold value ([T]cm).

Then, each set of 4 input proxies and T proxy was used to run the model. The Suitable Soil Percentage (SSP) was calculated. This process was repeated 10 000 times. The results are plotted on (Figure 3).

Smoothing curves were plotted in order to be able to compare the impact of the different proxies' threshold choices on the SSP. For each proxy, one smoothing curve was plotted for every T value.

For every input proxy, the difference between the maximum and minimum value of the T=[T]cm smoothing curve was calculated and plotted as a red broken line.

Part. 3: Mapping Brittany's soils suitability

STU suitable thickness was assigned to each raster pixel of the STU map proposed by [START_REF] Vincent | Spatial disaggregation of complex Soil Map Units at the regional scale based on soil-landscape relationships[END_REF] (Figure 4a.).

An estimation of the earth mass required for earth-hemp insulation of all dwellings on the territory of Brittany was carried out (see [START_REF] Verron | Availability of earth for light earth building: modelling using spatialized pedological data in Brittany[END_REF]. The estimated mass was allocated to every municipality by population proportion (Figure 4b.).

Using municipality vector map (DREAL Bretagne & IGN-F 2020), STUs surface proportion was calculated for every municipality. Municipality suitable earth mass was then deduced, by increasing the estimated volume by a factor of 1.3, the commonly used density of soils value. The municipality Resource Availability Ratio (RAR) was then calculated (Eq. 2).

Eq. 2: 𝑅𝐴𝑅 = 𝑛𝑒𝑒𝑑𝑒𝑑 𝑒𝑎𝑟𝑡ℎ 𝑚𝑎𝑠𝑠 𝑓𝑜𝑟 𝑙𝑖𝑔ℎ𝑡 𝑒𝑎𝑟𝑡ℎ 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔 𝑒𝑎𝑟𝑡ℎ 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒 "Non-accessible soils" were defined when DoneSol non-accessible soils cover more than 50% of municipality surface.

Processing tools

Data format and analysis were processed through Microsoft Access 2018, Spyder 4.1.4 (Python 3.8.3 64bit), QGIS 3.10.0 (2020) with GRASS 7.8.3, running on Windows 10. The model was tested on DoneSol3 Bretagne database. In an effort to make this work replicable, reproducible and reusable as proposed by Cohen-Boulakia et al. ( 2017), the complete data workflow and the high-resolution figures of this work have been published [START_REF] Verron | Availability of earth for light earth building: modelling using spatialized pedological data in Brittany[END_REF]. They can be consulted freely by all or even reproduced provided getting the rights to access DoneSol database by the owners [START_REF] Grolleau | Le système d'information national sur les sols: DONESOL et les outils associés[END_REF].

Results

DoneSol3 data statistics

The distribution of the database layers cumulated volume according to the 4 input proxies thresholds values allows to visualize the commonly found values for these soil properties in Brittany's soils (Figure 2). Additionally, it allows the reader to locate the proxy thresholds variation range along the values distribution. Indeed, for CEC, F50/2000 and F2000/D, the variation range covers approximately 50% of the volume of the soil horizons. Therefore, we expect a high sensitivity of the model to the variation of these proxies' thresholds.

Sensitivity Analysis

The suitability increases with the proxy when the threshold is a maximum, and decreases when it is a minimum (Figure 3).

T and CEC are the proxies having the highest impact on the Soil Suitability Percentage (SSP), with a variation of 24 and 30% respectively inside their proxy threshold variation range. However, T proxy variation was not calculated exactly in the same way as the other input proxies (see 2.6.2). Therefore, comparison with the other SSP variation results is only illustrative.

F50/2000 and F2000/D have an SSP variation of 16 and 12%, whereas OC only 5%. This was expected, as the thresholds variation range covered only 10% of the volume distribution curve (see 3.1).

Suitable soil volume and percentage

The estimated total soil volume in Brittany is more than 27 558 000 000 m 3 . The estimated total volume of suitable soil for earth-hemp building is more than 13 277 000 000 m 3 (17.3 Bt). Therefore, the Suitable Soil Percentage (SSP) is 48%. If the "coarse elements" (F2000/D) volume is deduced from the suitable volume, to represent the earth actually available after sieving, the suitable earth volume goes down to 12 636 347 046 m 3 which represents 46% of the total soil volume.

Soil suitability mapping

The thickest suitable soils for earth-hemp building (Figure 4a.) are located in a zone starting along the north-eastern coast of Brittany and expanding to the east to reach Rennes city. This trend follows particularly suitable soils: Cambisols, Luvic Cambisols and Luvisols developed from deep aeolian silts deposits [START_REF] Jamagne | Grands paysages pédologiques de France, Collection Synthèses[END_REF], rich in F0/2 and F2/50, and poor in coarse elements. The municipality Resource Availability Ratio (RAR) ranges from 0 to 6802 (Figure 4b.). Almost all municipalities show a ratio above 10, predicting an abundant resource. The RAR decreases with municipalities' population, and increases with soil suitability. The RAR is logically lower near major cities, where the population is high, hence the potential need is high. However, there is still a significant amount of locally available material. Conversely, it is higher in the centre of Brittany, where the inhabitant density is the lowest, and in the northern part of Brittany, where deep suitable soils are found. Distances to suitable soils

The maximum acceptable transport distance of the earth resource varies and depends on many criteria (economical, ecological or practical). Experts estimate that today's maximum distance is between 30 and 50 km. The soil suitability map (Figure 4a.) shows that 99,5% of Brittany territory is at less than 1 km of a suitable soil resource for earth-hemp building. The further point from a suitable resource is located 2,3 km away from a suitable soil. Thus, earth resource for earth-hemp can be considered a very local resource in Brittany.

Discussion

Availability of total soil resource

According to the model, 46% of the total soil volume in Brittany could be used for light earth building. Considering that the mass of annually excavated earth is 2.8 Mt [START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF], 1.3 Mt should then be suitable for light earth building. The broken line on Figure 5 represents this mass, cumulated over the years.

To put these findings into context, the mass of earth required to insulate all buildings in Brittany that need insulation with light earth is estimated. Data from the French government is used to estimate the amount of earth material required per house, the number of houses that must be insulated, and the number of houses built each year [START_REF] Cgdd | Le parc des logements en France métropolitaine en[END_REF]INSEE, 2020INSEE, , 2017)). The details of the calculation can be found in the metadata [START_REF] Verron | Availability of earth for light earth building: modelling using spatialized pedological data in Brittany[END_REF]. The total mass of earth required to insulate all building that need insulation in Brittany with light earth is estimated to be 7.4 Mt. This corresponds to less than 6 years of suitable excavated earth. In addition, to insulate every new building with a light earth, the estimated requirement is 0.3 Mt annually, which is less than 1/4 th of annually suitable excavated earth.

A scenario where the reuse of suitable excavated earth in light earth building is maximised would consist in insulating all new buildings with light earth using 0.3 Mt/year of suitable earth, and using the 1 Mt/year left to insulate existing buildings (Figure 5). In this scenario, it would take only 8 years to finish the insulation of all existing buildings that require insulation (in 2020). In reality, other materials are used for insulation, therefore the requirement is considerably lower and the stream of excavated earth should meet light earth building earth needs in most of the contexts. Figure 5: Scenario maximising the reuse of suitable excavated earth in light earth building in a period of 10 years. Estimations of volumes extracted, and used to insulate new and existing buildings. Building requirements estimated from French government data [START_REF] Cgdd | Le parc des logements en France métropolitaine en[END_REF]INSEE, 2020INSEE, , 2017)), see [START_REF] Verron | Availability of earth for light earth building: modelling using spatialized pedological data in Brittany[END_REF].

Due to the different benefits of earth material and driven demand for sustainable constructions, there is a growing interest in this material for construction [START_REF] Walker | Rammed earth: design and construction guidelines[END_REF]. Even if the earth resource seems abundant in total, the soil is also a support for other human and non-human uses. All soils should be preserved as high-value and essential ecosystems for human and non-human well-being. Furthermore, reusing excavated earth in light earth insulation does not mean that the excavation operations don't have to be reduced, or that this insulating solution is the most ecologically efficient for every building project.

A complete analysis of the positive and negative externalities should always be performed before using a building material, for example conducting life cycle assessment.

Thresholds sensitivity

The Monte Carlo sensitivity analysis shows that the Soil Suitability Percentage (SSP) is particularly sensitive to the Cation Exchange Capacity (CEC) and the consecutive layers cumulated suitable Thickness (T) proxies' thresholds.

As discussed in 2.4.2, T is greatly dependent on the building context and on the excavation precision. The sensitivity to T is high, but we can notice that soil suitability remains stable for T values between approximately 10 and 30 cm. This would mean that it probably won't increase soil suitability to use excavation means more precise than 30 cm. The reason may be that the majority of Soil Type Unit (STU) layers are thicker than 20 cm, and that the thinner layers correspond to O (organic) and A (mixed organic and non-organic) horizons (AFES 2008) which are often already evicted from suitability by the OC threshold. The actual precisions of the common mechanic diggers being around 15 to 30 cm, this parameter is probably not the most impacting on soil suitability.

CEC is an interesting proxy for raw earth building techniques properties, as it indicates clay bonding capacity, which is the combined action of clay specific surface area and electronical charge [START_REF] Hamard | A new methodology to identify and quantify material resource at a large scale for earth construction -Application to cob in Brittany[END_REF][START_REF] Meimaroglou | Cation Exchange Capacity (CEC), texture, consistency and organic matter in soil assessment for earth construction: The case of earth mortars[END_REF]. This parameter is sensitive in the suitability model, notably because the defined threshold is located on a peak of the earth volume distribution curve. As it is a key parameter of earth suitability, there is a need for more investigation on the link between CEC and earth properties for earth building.

In this study, Organic Carbon (OC) threshold variation impacts the suitable soil volume percentage by only 5%. But as organic matter content is generally higher in the surface layers of soil [START_REF] Girard | Etude des sols[END_REF], it could be more impacting depending on field excavation conditions, as it forces to dig deeper to extract the resource.

Model limitations

All of the numerical modelling choices can be accessed and questioned as the complete data workflow of this study is available in the metadata of the article [START_REF] Verron | Availability of earth for light earth building: modelling using spatialized pedological data in Brittany[END_REF]. The suitability calculation model has been designed with the objective of underestimating the potential resource when an adequate estimation process was not possible. This open-source numerical model is flexible and could be reused for future estimations and mapping of soil suitability for earth building techniques.

We can imagine that all of the suitability criteria used to limit earth suitability for light earth building in this model could be more or less overcome in different building conditions: by the discovery or rediscovery of new building techniques, by technology, with highly mechanized means, or by the addition of natural or artificial additives, etc. Therefore, the model parameters, chosen collaboratively with local masons, represent a realistic possibility of parameters actually used on field along the earth material life cycle in light earth building, rather than absolute thresholds that must be satisfied.

The spatialized pedological data employed in this study, like any map, does not accurately depict reality.

The results of this model highly depend on the accuracy of this data. Because this accuracy was not assessed in our study, it remains a possible source of inaccuracies.

The results of this study have been obtained by considering the 5 previously defined suitability criteria. In real field conditions, the earth resource choice must consider other criteria such as private property, natural or anthropic physical or chemical contaminations of the soil, and other technical accessibility parameters of the resource. Indeed, some studies record urban chemical contamination to around 10% of urban soils [START_REF] Ferreira | Chapter Six -Urban Areas[END_REF]. As the major part of the excavated earth comes from urban areas, it could impact significantly the suitability results. Yet, as the available amounts are considerably bigger than the estimated needs, it is probable that this study conclusions about earth availability for light-earth insulation would remain similar.

Furthermore, the maps precision does preclude their use at field scale for resource prospection, or to validate earth suitability for an earth-hemp building project. On field, the mason's expertise and manual tests are the only reliable source of information concerning an earth material suitability for earth building.

Conclusion

Soil suitability was estimated using 5 proxies based on previous research and experts' advices. Using spatialized pedological data in Brittany (France), suitable soils for light earth building were quantified and mapped.

The abundance of excavated earth, and the potentially low resource selectivity and quantity that is required for light earth indicates that the availability of the earth resource should not be an obstacle to develop light earth building in Brittany.

According to our estimations, 48% of the total soil volume in Brittany could technically be used for light earth building, which corresponds to 17 Bt. Furthermore, using only the annually excavated earth of the construction sector, all existing and new buildings could be insulated with light earth in less than 8 years. It was also found that, suitable earth for light earth building can be found locally almost anywhere in Brittany. Indeed, 99.5% of Brittany territory is at less than 1 km of a suitable soil resource, the farthest point being 2,3 km away.

Cation Exchange Capacity (CEC) is a parameter that has a high influence on the model results. It is notably because a great fraction of Brittany's soils has CEC values close to realistic CEC thresholds. Little information is available about the potential impacts of CEC on light earth building, and particularly its interaction with clays and soil organic matters. Therefore, more research is needed to understand CEC and soil organic matters impact on the properties of earth building materials.

The model parameters, chosen collaboratively with local masons, represent a realistic possibility of parameters actually used on field along the earth material life cycle in earth-hemp building, rather than absolute thresholds that must be satisfied. On field, the mason's expertise and manual tests are the only reliable source of information concerning earth suitability. Furthemore, the accuracy of the model depends on the spatialized pedological data used. Therefore, the model thresholds and the mapping accuracy are not operational field data and cannot be used as references for earth selection for earthhemp or other light earth building techniques.

However, this model is an innovative way to raise awareness on the availability of earth resource for light earth building. For example, it could help territorial institutions to understand the development potential for sustainable building techniques on their territory. This open-source model could be reused to investigate other raw earth building techniques resource availability in other territories.

Funding

This study is part of the Eco-terra research program (Eco-Terra, 2017), funded by ADEME. This work is based on the previous works of the research program [START_REF] Bolleni | Understanding the role of yield stress in the quality of Light earth samples[END_REF][START_REF] Vinceslas | Caractérisation d'éco-matériaux terre-chanvre en prenant en compte la variabilité des ressources disponibles localement[END_REF].

Acknowledgements

The data analysis is performed via the cross-referencing of the proxies thresholds with the DoneSol database of the Référentiel Régional Pédologique de Bretagne [START_REF] Lemercier | Sols de Bretagne[END_REF] (see 0), complimentarily provided by l'institut agro -AGROCAMPUS Ouest. We would like to express our profound recognition to Samuel Dugelay, Corentin Mouraud and Fabrice Auvé, the masons that accepted to share their knowledge to help us understanding the complexity of earth suitability for light earth building.

Figure 1 :

 1 Figure 1 : Distribution of suitability properties along the life cycle of earth in earth-hemp building and corresponding proxies.

Figure 2 :

 2 Figure 2 : Comparison of the cumulated distribution of DoneSol3 layer volume and its derivative (earth volume repartition), with proxy threshold variation range.

  Weil, R.R.,Brady, N.C., 2016. The Nature and Properties of Soils, Global Edition. Pearson Education. Zegada-Lizarazu, W., Monti, A., 2011. Energy crops in rotation. A review. Biomass and Bioenergy 35, 12-25. https://doi.org/10.1016/j.biombioe.2010.08

Figure A. 1 :

 1 Figure A.1: Manual dry sieving prior to an earth-hemp formwork. On this building site, the sieve mesh size was close to 1 cm, illustrating the variability of sieving objectives on field. Liquid state sieving is also a common practice.

Table 2 :

 2 Table 2). DoneSol3 database input proxies Pearson correlation coefficient.

	CEC	OC	F2000/D
	F50/2000 -0.27 -0.17	0.32
	CEC	0.51	-0.19
	OC		-0.11


E Halter

C Thiam

C Bobin

J Bouchard

D Chambellan

B Chauvenet

M Hamel

L Rocha

M Trocmé

R Woo

First TDCR measurements at low energies using a miniature x-ray tube

Keywords: TDCR method, Radionuclide metrology, X-ray tube, Geant4 simulation

Developed for radionuclide standardization using liquid scintillation, the Triple to Double Coincidence Ratio (TDCR) method is applied using coincidence counting obtained with a specific three-photomultiplier system. For activity determination, a statistical model of light emission is classically used to establish a relation between the detection efficiency and the experimental TDCR value. At LNE-LNHB, a stochastic approach of the TDCR modeling was developed using the Monte Carlo code Geant4. The interest of this TDCR-Geant4 model is the possibility to simulate the propagation of optical photons from their creation in the scintillation vial to the production of photoelectrons in photomultipliers.

As an alternative to the use of radionuclide sources, first TDCR measurements are presented using a miniature x-ray tube closely coupled to the scintillation vial. The objective of this new set-up was to enable low-energy depositions (lower than 20 keV) in liquid scintillator in order to study the influence of both time and geometrical dependence between PMTs already observed with radioactive sources. As for the statistical TDCR model, the non-linearity of light emission is implemented in the TDCR-Geant4 model using the Birks formula which depends on the kB factor and the scintillation yield. Measurements performed with the x-ray tube are extended to the assessment of these parameters and they are tested afterwards in the TDCR-Geant4 model for activity measurements of 3 H.

Introduction

The Triple to Double Coincidence Ratio (TDCR) method is widely applied in National Metrology Institutes for primary radionuclide standardization [START_REF] Broda | Radionuclide metrology using liquid scintillation counting[END_REF]. Based on a specific liquid scintillation (LS) counter equipped with three photomultiplier tubes (PMTs), the activity is determined using the experimental TDCR ratio given by double and triple coincidences of emitted scintillation photons between PMTs. To this end, a statistical model of light emission is implemented according to several assumptions such as stochastic independence between PMTs (Bobin et al., 2012a), Poisson distribution of photoelectrons in PMTs, etc. In the statistical modeling, double and triple coincidences between PMTs are calculated using an analytical expression based on the probability to count at least one photoelectron as a result of an energy deposition. However, the statistical approach does not account for the optical and geometrical properties of the detector in terms of refraction and reflection processes of optical photons.

At LNE-LNHB (Laboratoire National Henri Becquerel), an alternative to the statistical TDCR model is studied using the Geant4 simulation toolkit [START_REF] Agostinelli | Geant4a simulation toolkit[END_REF] in order to simulate the transport of charged particles and optical photons resulting from scintillation and the Cherenkov effect. With the TDCR-Geant4 model, optical photons are simulated from their creation in the optical cavity to the generation of photoelectrons in PMTs leading to double and triple coincidences. From previous studies, several results were obtained from the application of the TDCR-Geant4 model in the case of low-energy depositions (lower than 20 keV). In particular, simulations carried out for mono-energetic depositions (5 keV, 8 keV and 12 keV) revealed the existence of a stochastic dependence between PMTs due to geometrical optics (or geometrical stochastic dependence). This effect results from the sensitivity of the photon distribution between PMTs to the location of light emission inside the scintillator volume combined with reflection and refraction processes occurring at the different interfaces of the optical cavity. As shown with the TDCR-Geant4 model for discreteenergy emitters, the consequence is an overestimation of detection efficiencies obtained with the standard statistical model. These simulation results were experimentally confirmed in the case of 51 Cr standardization (this radionuclide disintegrates by electron capture with maximum energies of x-ray photons and Auger electrons mainly comprised between 4 keV and 6 keV).

The influence of the geometrical stochastic dependence (i.e. due to geometrical optics) on detection efficiencies is directly observed by a shift of the counting rates for the same experimental TDCR value when using diffusive polyethylene vials instead of glass vials. This shift observed between the two types of vials leads to an increase of the activity calculation which was also mentioned by [START_REF] Simpson | Fe-55 activity measurements at the NMISA revisited[END_REF] in the case of 55 Fe measurements.

In the present paper, first TDCR measurements using a miniature x-ray tube are presented as an alternative to radionuclide sources. In order to obtain interactions of low-energy x-rays in the liquid scintillator, the end-window transmission-target x-ray tube (MAGNUM ® 40 kV manufactured by Moxtek) was coupled to a scintillation vial. The first objective was to test the reproducibility with the x-ray tube of the two types of stochastic dependence identified with radioactive LS sources: 1) when the coincidence resolving time is too short with regard to the time distribution of photons between PMTs; 2) due to geometrical optics as previously discussed. These two types of stochastic dependence were first investigated experimentally for a low-energy deposition set to 2.7 keV. The influence of the liquid scintillator on the evolution of the counting rates according to the resolving time was checked. The modification due to geometrical optics of the relation between the detection efficiency of double coincidences and TDCR values was also tested using glass and polyethylene vials.

As for the statistical model, the Birks formula is implemented in the TDCR-Geant4 model to account for the non-linearity of light emission as a consequence of ionization quenching. The associated parameters [kB factor; scintillation yield] were assessed using measurements performed with the x-ray tube for 3 different x-ray energies (2.7 keV, 8.7 keV and 17.3 keV). These parameters are tested afterwards in the case of the standardization of 3 H with the TDCR-Geant4 model.

Experimental TDCR set-up with a miniature x-ray generator

As already described in previous studies [START_REF] Thiam | Radiopharmaceutical 11 C activity measurements by means of the TDCR-Cerenkov method base on a Geant4 stochastic modeling[END_REF], the detection system is composed of three XP2020Q photomultipliers equipped with a fused silica window. Counting vials (glass or polyethylene) are hung inside a spherical cavity made of Teflon ® . For coincidence counting, the electronics chain is composed of a fast amplifier (Phillips scientific model 777) and a Constant Fraction Discriminator (CFD) module (Canberra Quad CFD 454). The logical signals provided by these front-end electronics are used to feed either a MAC3 module [START_REF] Bouchard | MAC3: an electronic module for the processing of pulses delivered by three photomultiplier liquid scintillation counting system[END_REF] that has been modified to set variable resolving times or an FPGA (Field Programmable Gates Array)-based digital system which is also used as a time-to-digital converter combined with the processing of counting losses according to the live-time technique using extendable dead-times (Bobin et al., 2012b).

The interest of integrating a miniature x-ray tube into the detection set-up is the ability to perform TDCR measurements with low-energy x-ray photons in the liquid scintillator as an alternative to radionuclide sources. As depicted in Fig. 1, this small-size x-ray generator (~55 mm length, ~29 mm diameter) is directly coupled to the counting vial (for the x-ray beam, a small hole is machined in the plastic cap). The x-ray tube is designed with a transmission-target end-window configuration with tungsten for the anode material. Three energies have been selected for this study: 2.7 keV, 8.7 keV and 17.3 keV. The x-ray-beam energy is tuned by applying an appropriate high-voltage potential and by using an attenuation film placed at the output of the x-ray tube. The upper-energy cutoff is defined by the K-shell absorption edge of the film component. The x-ray energy spectrum is sharpened using a suitable attenuation thickness (see Table 1 for the settings used for the 3 x-ray energies). For instance, the 2.7 keV-energy emission is obtained using the following settings: high voltage set to 3 kV, and PVC film of ~100 μm thickness (K-shell electron binding energy of chlorine equal to ~2.82 keV). The spectrum shapes at the end-window were measured with a Silicon Drift Detector (SDD, AXAS-M manufactured by KETEK) calibrated using 55 Fe and 241 Am sources.

Fig. 1. Geometrical modeling with Geant4 of the LS-counter vial coupled with the miniature x-ray tube. The collimator (used for [kB; S] measurements) is also included inside the vial, which was hung between PMTs in the optical cavity.

X-ray energy (keV)

Attenuation film

2.7

Polyvinyl chloride (100 µm)-cutoff energy: 2.8 keV 8.7 Pure copper (300 µm)-cutoff energy: 9 keV 17.3 Pure zirconium (800 µm)-cutoff energy: 18 keV Table 1. Attenuation films used with the x-ray tube set for several energies. The cut-off energy is defined by the K-shell electron binding energy of the film component.

Experimental results

The sensitivity of coincidence counting with varying resolving times has already been observed by several laboratories in the case of low-energy radionuclides [START_REF] Steele | FASEA: a FPGA acquisition system and software event analysis for liquid scintillation counting[END_REF], Bobin et al., 2010a). According to complementary investigations, this effect occurs when the coincidence resolving time is too short with regard to the arrival-time distribution of photoelectrons, leading to coincidences between PMTs. As observed for the standardization of 3 H, the consequence can be a deviation of detection efficiencies calculated with the statistical TDCR model. This deviation is due to the stochastic time dependence between PMTs, which is not considered in the statistical TDCR model (Bobin et al., 2012a).

The evolution of double-coincidence counting rates according to increasing resolving times was compared for a 2.7 keV-energy emission using two liquid scintillators, Hionic Fluor (HF) and Ultima Gold (UG). For these measurements, the x-ray beam was not collimated in order to have interactions through the whole surface of the liquid scintillator. The experimental results given by the time-to-digital converter especially designed for TDCR measurements are plotted in Fig. 2, taking the counting rates for a coincidence resolving time set at 40 ns as a reference (~220 s -1 for HF; ~400 s -1 for UG). Similarly to the results previously obtained with radioactive LS sources, double-coincidence counting rates are sensitive to increasing resolving times (especially below 120 ns for HF and 200 ns for UG). The difference of behavior between the two scintillators is in agreement with the hypothesis proposed in Bobin et al. (2012a), that the PMT-PMT coincidence timing distribution depends on the scintillation lifetime of the liquid scintillator used. The higher sensitivity observed for UG can be explained by the fact that the solvent is a naphthalene derivative molecule (diisopropylnaphthalene) which is known to generate triplet-triplet annihilation that yields delayed fluorescence applied for alpha/beta discrimination [START_REF] Aupiais | Some rules to improve the energy resolution in alpha liquid scintillation with beta rejection[END_REF].

Fig. 2. Comparison between two liquid scintillators (Hionic Fluor and Ultima Gold) of the evolution of double-coincidence counting rates with increasing resolving times for an energy deposition of 2.7 keV (the collimator was not used). The relative differences are calculated using a reference value given by counting rates corresponding to a resolving time of 40 ns.

Additional measurements carried out with the UG scintillator have shown that the type of vial (glass or polyethylene) has no significant impact on counting rates with regard to the influence of coincidence resolving times. On the other hand, as displayed in Fig. 3, a significant shift is observed for the relation between the double coincidence rates and the experimental TDCR value. As previously studied with the TDCR-Geant4 model, this effect reflects the influence of the geometrical stochastic dependence between PMTs (i.e. due to geometrical optics) on triple and double coincidence counting (Bobin et al., 2012a).

Fig. 3. Comparison between polyethylene and glass vials of double-coincidence counting rates versus TDCR values for x-ray photons of 2.7 keV (the collimator was not used).

TDCR-Geant4 modeling

The Monte Carlo Geant4 code was chosen for its capability to simulate the transport of ionizing and electromagnetic radiations [START_REF] Agostinelli | Geant4a simulation toolkit[END_REF]. The simulation results obtained in the present study were performed with the Geant4.9.4 version using the lowenergy electromagnetic physics based on PENELOPE models [START_REF] Apostolakis | Geant4 Low Energy Electromagnetic Models for Electrons and Photons[END_REF]. The model also includes the atomic relaxation using the Livermore Evaluation Atomic Data Library, which contains the radiative and non-radiative transition probabilities for each subshell of each element, for Z=1-100 [START_REF] Perkins | Tables and Graphs of Atomic Subshell and Relaxation Data Derived from the LLNL Evaluated Atomic Data Library (EADL)[END_REF]. The Geant4 package allows for the transport of optical photons using the UNIFIED model developed for the DETECT project [START_REF] Levin | A more physical approach to model the surface treatment of scintillation counters and its implementation into DETECT[END_REF]. For that purpose, the geometrical model of the LS counter is constructed with the optical properties (according to the photon wavelengths) attached to each element of the optical cavity. Optical photons are simulated taking into account refraction and reflection processes (depending on refractive indexes of medium boundaries) and spectral transmittance of materials (borosilicate vial, PMT windows).

As already described in previous studies, the TDCR-Geant4 modeling has been first investigated with the application of the TDCR-Cherenkov technique (Bobin et al., 2010b[START_REF] Thiam | Radiopharmaceutical 11 C activity measurements by means of the TDCR-Cerenkov method base on a Geant4 stochastic modeling[END_REF]. The TDCR-Geant4 benchmark is able to simulate the transport of ionizing particles emitted in aqueous solutions and subsequent Cherenkov photons. Optical photons are tracked from their creation (considering the anisotropy of Cherenkov emission) inside the optical chamber (aqueous solution, glass vial, PMT windows) to their conversion into photoelectrons at the PMT photocathode. For each energy deposition following a disintegration, a binomial trial is applied to all the photoelectrons produced in the PMTs in order to determine if they are detected or not, and then to calculate double and triple coincidences between PMTs. This trial represents the probability for a photoelectron to reach the first PMT dynode and it is used to simulate the PMT defocusing for the detection efficiency variation. The probability to count at least one photoelectron in a PMT calculated with the TDCR-Geant4 model differs from the statistical modeling by taking into account potential stochastic dependence between PMTs. Activity measurements based on Cherenkov emission were carried out for various radionuclides: 90 Y, 11 C, and 32 P (Bobin et al., 2010b[START_REF] Thiam | Radiopharmaceutical 11 C activity measurements by means of the TDCR-Cerenkov method base on a Geant4 stochastic modeling[END_REF]. Because of the anisotropy of Cherenkov emission, these results are considered as a validation step of the geometrical modeling. As for the classical statistical model, the extension of the TDCR-Geant4 model to scintillation counting is based on the Birks formula with regard to the non-linearity of light emission as a consequence of ionization quenching. In that case, the TDCR-Geant4 model has been applied to activity measurements of 63 Ni, 51 Cr and 60 Co in UG (Bobin et al., 2012b, Thiam et al., 2012).

Estimation of the kB factor and scintillation yield used in the Birks formula

When the statistical TDCR method is implemented, the activity is usually determined from the experimental TDCR values obtained by variation of the detection efficiency. An optimal kB factor is estimated in order to obtain the most consistent activities over a range of experimental TDCR values. As it is included in a free parameter, the value of the scintillation yield (characterizing the liquid scintillator) is not explicitly specified for the activity determination [START_REF] Broda | Radionuclide metrology using liquid scintillation counting[END_REF]. In the case of TDCR-Geant4 model, the scintillation process is also implemented using the Birks formula but the scintillation yield has to be defined in terms of photons emitted per keV. The measurement of this parameter was previously carried out using the 4π(LS)β-γ coincidence technique (Bobin et al., 2012a).

For a given liquid scintillator and x-ray energy, pairs of kB factor and scintillation yield are calculated with the TDCR-Geant4 model using the TDCR measurement obtained with the xray tube coupled to the LS counter. For the preliminary tests of this system, the measurements were carried out using a glass vial containing 10 mL of UG. The size of the x-ray beam was collimated using a Delrin collimator (Ø=8 mm) in order to decrease the diameter of the volume where x-ray photons interact in the liquid scintillator. In this configuration, the geometrical stochastic dependence on TDCR measurements resulting from the photon distribution between PMTs is reduced (Bobin et al., 2012a). The aim was also to minimize possible biases due to the transport of particles and photons in the meniscus region which is considered in the Geant4 modeling [START_REF] Thiam | Radiopharmaceutical 11 C activity measurements by means of the TDCR-Cerenkov method base on a Geant4 stochastic modeling[END_REF]. The experimental TDCR values obtained for x-ray energies equal to 2.7 keV, 8.7 keV and 17.3 keV are respectively 0.137 (2), 0.646 (2) and 0.928 (2). As expected with the TDCR-Geant4 model, the collimation increases the measured TDCR values: for instance, at 2.7 keV TDCR=0.128 (2) without the collimator.

In the TDCR-Geant4 modeling, the x-ray emission is implemented according to a beam flux with energies randomly generated using the spectra measured with the SDD for each energy. The spectrum obtained in the case of 2.7 keV x-ray photons is displayed in Fig. 4. Simulations were carried out for 2.7 keV photons according to different configurations of energy distribution: mono-energy, monoenergy convoluted with a Gaussian function (using the energy resolution of the SDD) and the x-ray spectrum measured with the SDD. The results have shown no significant differences within uncertainties. The atomic rearrangement resulting from x-ray interactions with the main components of the UG scintillator (~79% carbon, ~10% hydrogen, ~9% oxygen and ~1.4% phosphorus) is also considered in the Geant4 simulations. The simulated photoelectron spectrum given by 2.7 keV x-ray interactions in UG is shown in Fig. 5. Most of the energy distribution is comprised between 2 keV and 2.7 keV (~85%). The photoelectron spectrum also features a non-negligible component at about 600 eV (~12%) due to the photoelectric effect with phosphorus in the liquid scintillator. For each photon energy obtained with the x-ray tube, several simulations with the TDCR-Geant4 model were carried out for kB factors ranging from 0.07 to 0.13 mm MeV -1 (corresponding to usual values drawn from the literature) and scintillation yields (ranging from 7 to 10 photons keV -1 ). The pairs of kB factor and scintillation yield displayed in Fig. 6 were obtained by minimizing the difference between measured and calculated TDCR values (e.g. in the case of the 2.7 keV x-ray energy, each pair of kB factor and scintillation yield corresponds to a TDCR value equal to 0.137 (2)). In the range of kB factors and scintillation yields investigated, it appears that the plots follow a straight line with a slope which decreases when x-ray energy increases. Considering that the pair of kB factor and scintillation yield is constant with energy in the Birks formula, a coherent pair can be obtained: kB=0.13 mm MeV -1 associated with a scintillation yield equal to 8.9 (1) photons keV -1 . In future, the range of the kB factor will be extended above 0.13 mm MeV -1 for further simulations. Based on detection efficiencies measured with 4π(LS)β-γ coincidence counting (Bobin et al., 2012a), a [kB; scintillation yield] pair equal to [0.1 mm MeV -1 ; 8.2 (3) photons keV -1 ] in the liquid scintillator UG was previously assessed from 54 Mn measurements (photon energy mainly comprised between 5 and 6 keV). This first result is in agreement with those reported in this work for 8.7 keV photons given by the x-ray generator: [0.1 mm MeV -1 ; 8.3 (1) photons keV -1 ] with the same detection set-up.

Application of the TDCR-Geant4 model to the standardization of 3 H

The results obtained with the x-ray generator [kB=0.13 mm MeV -1 ; 8.9 (1) photons keV -1 ] were used in the TDCR-Geant4 model for activity measurements of 3 H (β-emitter; E max =18.6 keV) in UG. Activity concentrations were calculated from measurements obtained by PMT defocusing (TDCR values ranging from 0.49 to 0.54) using both the TDCR-Geant4 and statistical models. As observed in Fig. 7, the activity concentrations are about 1.3% higher in the case of the TDCR-Geant4. Moreover, the slope featuring activity concentration as a function of TDCR values is lower for the results given by the statistical model. Additional plots in Fig. 7 were obtained with the TDCR-Geant4 model by limiting the electron emission at the center of the scintillator volume: the slope difference between both models vanishes. Because this configuration of Geant4 simulations attenuates stochastic dependence due to geometrical optics, it is considered to be closer to the statistical model (Bobin et al., 2012a). Due to the low energies of emitted electrons, the standardization of this β-emitters such as 3 H is sensitive to the kB factor. In that case, the kB factor is generally used as a second free parameter for the activity calculation with the statistical TDCR model. The usual practice is to optimize the kB value by minimizing the fitting slope of the function giving the activity concentration versus TDCR. Flat slope is considered as an indicator of the goodness of the model. For the present study, the optimal kB factor given by the statistical model is equal to 0.10 (1) mm MeV -1 leading to an activity concentration equal to 29.5 (2) kBq/g (the activity concentration corresponding to kB=0.13 mm MeV -1 is equal to 29.95 (20) kBq/g). In the case of the TDCR-Geant4, the slope (activity concentration versus TDCR) is less sensitive to the variation of the kB factor. As a result, the activity determination performed by minimization of the kB factor is not applicable with the TDCR-Geant4 model. This effect was already observed in the case of the standardization of 63 Ni (β --emitter; E max =66.98 keV) but the activity concentrations given by both Geant4 and classical models were in good agreement [START_REF] Thiam | Application of TDCR-Geant4 modeling to standardization of 63 Ni[END_REF].

Further studies are needed to understand the differences observed between both TDCR-Geant4 and statistical models for the standardization of 3 H. In particular, the influence of the stochastic dependence due to geometrical optics on the kB-optimization procedure will be investigated.

Discussion and perspectives

First measurements performed with an x-ray generator coupled with a TDCR detection set-up were presented. The first aim of this new system was the possibility to reproduce with lowenergy x-ray photons (less than 20 keV) the observations related to stochastic dependence between PMTs previously obtained with radioactive LS sources. Resulting from geometrical optics, the influence of the vial type (glass and polyethylene) observed by a shift of the relation between double-coincidence rates versus TDCR values was confirmed with an x-ray beam tuned at 2.7 keV (liquid scintillator: Ultima Gold). Due to the sensitivity of PMT-PMT coincidence timing distribution to scintillation lifetime, a difference in the evolution of double-coincidence rate with coincidence resolving time was also presented when comparing two commercial liquid scintillators (Ultima Gold and Hionic Fluor). These results have shown that the effect due to stochastic dependence between PMTs first identified with interactions in the whole LS volume can be also observed with x-ray interactions taking place in a smaller volume close to the surface of the liquid scintillator (50% of 2.7 keV x-ray photons are absorbed in a thickness of about 70 μm). Thus, the new experimental TDCR set-up including the x-ray tube can be used to test or to refine the TDCR-Geant4 model for activity measurements of low-energy emitters.

A technique using the x-ray tube has been tested to assess the pair of kB factor and scintillation yield used in the Birks formula for a given liquid scintillator. Calculations were based on the minimization of the difference between an experimental TDCR value obtained for a given x-ray energy and calculations performed with the TDCR-Geant4. From measurements obtained with three x-ray energies (2.7 keV, 8.7 keV and 17.3 keV), a preliminary estimation of a pair of kB factor and scintillation yield is proposed: [0.13 mm MeV -1 ; 8.9 (1) photons keV -1 ]. This estimated kB factor was higher compared with the value given by the statistical model (kB=0.10 mm MeV -1 ) obtained by minimizing the fitting slope of the function of the 3 H activity concentration versus TDCR values. The origin of the higher kB factor given by the TDCR-Geant4 model needs to be investigated. As previously observed for the standardization of 63 Ni, the slope (activity concentration versus TDCR) is not as sensitive to the variation of the kB factor as for the statistical model. As a result, the activity calculation with the TDCR-Geant4 model cannot be implemented by minimizing the slope with the variation of the kB factor. This result could be due to the fact that the TDCR-Geant4 model includes geometrical and optical properties of the LS counter. Finally, further investigations are planned to understand the difference between both TDCR models on activity measurement of 3 H by using other scintillation cocktails (e.g. containing no phosphorus) or by measuring other low-energy emitters ( 55 Fe, 241 Pu).

Fig. 4 .

 4 Fig. 4. Energy spectrum obtained with a SDD of x-ray photons emitted by the miniature x-ray tube tuned to 2.7 keV. The energy resolution is mainly due to the detector.

Fig. 5 .

 5 Fig. 5. Simulated photoelectron spectrum resulting from 2.7 keV x-ray interactions in UG.

Fig. 6 .

 6 Fig. 6. Evolution of [kB factor; scintillation yield] pairs for three different energies obtained with the miniature x-ray tube.

Fig. 7 .

 7 Fig. 7. Activity concentration versus TDCR value in the case of 3 H in UG obtained with both statistical and TDCR-Geant4 models (kB equal to 0.13 mm MeV -1 ).