A Pelfrêne

N Gassama

D Grimaud

Mobility of major-, minor-and trace elements in solutions of a planosolic soil: distribution and controlling factors

Keywords: Soil solutions, Planosol, trace metals, speciation, Al, Fe, controlling factors, mobility

Subsurface waters circulating in an unpolluted soil of a planosolic horizon (Massif Central, France) were studied in order to determine their physico-chemical characteristics. Three water sampling sites were chosen along a toposequence according to topography. For each site, two piezometers were placed above and in the gravely and concretion-rich horizon (Fe-and Mn-oxyhydroxides). Concentrations of major-, minor-(cations, anions, iron, manganese, phosphorus, silica) and trace elements (Al, Cd, Co, Cr, Cu, Ni, Pb, Zn, U) were monitored on bulk and filtered water (0.45 µm) to study both the particulate and the dissolved components, from 2004 to 2006, during the soil saturation period (i.e. from November to May). Chemical characteristics of soil solutions provide evidence for various chemical water compositions and for time variations of the water quality, pointing out that the hydrodynamic and chemical reactivity in the solution is different for the three sites.

Calculations of pe values allow to give an information about a range of the redox state of soil solutions. The pe ranges are different for each piezometer but correspond to anoxic solution. For all piezometers, distribution between the dissolved and the particulate fraction and correlations between the various elements in the soil solutions indicate that: (i) Al and Fe show similar behaviour, (ii) Al is mainly present as oxyhydroxides and (iii) some trace metals are mainly associated with particles which

Introduction

Trace metals are naturally present in soils reflecting their occurrence in the parent material. They are, however, also present as environmental contaminants, particularly since soil pollution has become a major problem due to anthropogenic activities. As a consequence, assessment of this pollution requires a good knowledge of the distribution of trace metals in unpolluted soils, the so-called pedogeochemical background level.

The total concentration of trace metal is not the only factor to be considered to assess toxicity hazard. The speciation of trace metals (i.e., the distribution of their physicochemical forms) ultimately determines their bioavailability and their mobility in the soil [START_REF] Alloway | Soil processes and the behaviour of metals[END_REF]. These characteristics of trace metals in soils, sediments and aquatic systems depend largely upon their interaction with organic compounds and/or minerals like clays, hydrous oxides of Fe, Al and Mn [START_REF] Stumm | Aquatic chemistry: an introduction emphasizing chemical equilibria in natural waters[END_REF]. Adsorption of trace metals onto solid compounds and associated surface coatings is considered very important in controlling metal activity [START_REF] Sposito | Electrochemical phenomena[END_REF][START_REF] Sigg | Chimie des milieux aquatiques[END_REF][START_REF] Alloway | Soil processes and the behaviour of metals[END_REF].

Moreover, pH and redox conditions are factors that also affect the chemistry of metals in soils, and their uptake by organisms [START_REF] Singh | Soil and water contamination by heavy metals[END_REF].

Planosols are characterised by a vertical succession of clay-poor horizons overlying a clay-rich horizon that drastically restricts the vertical flow of water and induces the occurrence of a seasonal water table [START_REF] Baize | Planosols in the "Champagne Humide" region, France. A multiapproach study[END_REF]. According to the water hydrodynamic during the year, oxide concretions may develop at the base of the last horizon. In this horizon, trace elements can be accumulated or released depending on the dynamic of oxide formation/dissolution.

The Planosol studied here is developed from metamorphic parent material. Naturally rich in trace elements due to the geology, this soil is subject to seasonal water saturation during winter and spring [START_REF] Salvador-Blanes | Déterminisme de la distribution spatiale des éléments majeurs et traces dans les sols en contexte métamorphique (Plateau d'Aigurande, nord du Massif Central[END_REF]. In this hydromorphic soil, water circulation, notably lateral underflow above clayey horizons, can involve specific chemical reactions and transfers [START_REF] Bourrié | Mise en évidence de deux dynamiques saisonnières du fer dans les sols hydromorphes en climat tempéré[END_REF]. Soil solutions were collected above and in a gravely and concretion-rich (Fe and Mn oxides) horizon, in order to assess its impact on the distribution of trace metals in the soil waters. The objectives of this paper are (i) to determine the range, distribution and behaviour of major-, minorand trace elements in these unpolluted soil solutions, (ii) to identify the main physical and chemical controlling factors of their distribution, and (iii) to assess the impact of the concretion-rich horizon on the trace metal distribution. The soil solutions have been monitored for three years. Concentrations both in the soluble and in the particulate fraction have been considered. Redox conditions have been assessed to provide evidence for particular mechanisms. The study of chemical speciation of some trace elements has been developed in a further paper [START_REF] Pelfrêne | Dissolved Cu(II) speciation in unpolluted soil solutions of a planosolic horizon[END_REF].

Environmental settings

The study area is located on the Aigurande plateau in the northern part of the Massif Central (France). The substratum is composed of Paleozoic metamorphic formations (gneiss and amphibolite) and intrusive granitic rocks [START_REF] Quenardel | Paleozoic evolution of the Plateau d'Aigurande (NW Massif Central, France)[END_REF]. The area is a grassland in a hedged farmland district. The studied soil is a Planosol developed from gneissic parent material. Planosols are characterized by the vertical succession of horizons (Fig. 1a). The upper horizon (sandy and organic-rich horizon) is allochthonous and derived from colluvial materials of amphibolitic (site 1, piezometers 1a and 1b) and gneissic (sites 2 and 3, piezometers 2a, 2b, 3a and 3b) origin [START_REF] Salvador-Blanes | Influence des substrats et des formations de versant sur la variabilité spatiale des teneurs naturelles en chrome de sols issus de roches métamorphiques[END_REF] (Fig. 1b). The gravelly and concretion-rich horizon below comprises concretions which are mainly composed of several types of cements (Fe-rich, Si-and Al-rich, Mn-rich and Ti-rich) surrounding grains of quartz, feldspars, micas and accessory minerals [START_REF] Salvador-Blanes | Déterminisme de la distribution spatiale des éléments majeurs et traces dans les sols en contexte métamorphique (Plateau d'Aigurande, nord du Massif Central[END_REF][START_REF] Cornu | Trace element accumulation in Mn-Fe-oxide nodules of a planosolic horizon[END_REF]. The deeper horizons (a silty horizon and alterite) are developed in gneissic material (mainly quartz with feldspars, micas and clay minerals) [START_REF] Salvador-Blanes | Déterminisme de la distribution spatiale des éléments majeurs et traces dans les sols en contexte métamorphique (Plateau d'Aigurande, nord du Massif Central[END_REF]. The horizons are waterlogged during winter and spring. The mean annual rainfall in the area was 872, 667 and 772 mm for 2004, 2005 and 2006, respectively. The main rainfall occurs between December and March.

Sampling and analytical methods

Three water sampling sites were chosen along a toposequence according to topography (Fig. 1). Two piezometers were placed in each site, in November 2003: above (noted 1a, 2a, 3a respectively for sites 1, 2 and 3) and in (noted 1b, 2b and 3b respectively for sites 1, 2 and 3) the gravelly and concretion-rich horizon. Piezometers were made of a strainer (20 cm height) in order to collect free water circulating in the soil horizon. Soil solution samples were collected from March 2004 to May 2006 (every 15 days) during the soil saturation period (i.e. from November to May). In 2004, sampling began in March in order to allow the soil to reach equilibrium. Bulk and filtered water were sampled to study both the particulate and the dissolved phases. The concentrations of the particulate fraction were determined by subtracting concentration measured in the bulk solution from concentration measured in the dissolved fraction. Soil waters were filtered in the field through 0.45 µm membrane filters (acetate of cellulose) with a frontal-flow system in order to separate dissolved and particulate fractions. Prior to use, each membrane was rinsed with deionized water (18 MΩ) and then with the sample.

Filtered and bulk water samples were acidified to pH ≈ 2 with Suprapur ® grade nitric acid for aliquots intended for cation, phosphorus, dissolved silica, TOC, DOC and trace metal analysis. The samples were stored in previously washed polypropylene containers. Physico-chemical parameters (temperature, pH and electrical conductivity C) were measured in the field. Alkalinity was measured the same evening by the Gran method [START_REF] Gran | Determination of the equivalent point in potentiometric titrations[END_REF] with a HCl solution. Bicarbonate concentrations were calculated considering alkalinity mainly due to carbonate. Total organic C (TOC, on unfiltered water samples) and dissolved organic C (DOC) were determined by using a C analyzer (Shimadzu TOC-V CSH , NPOC method). Particulate organic C (POC) was obtained by difference between TOC and DOC. Calcium and Mg, in the bulk and filtered waters (0.45 µm), were determined by flame atomic absorption spectrometry, and Na and K by flame atomic emission spectrometry. Chloride, F -, NO 3 -and SO 4 2-in the filtered waters were measured by ionic chromatography. Total and dissolved P and Si were measured by molecular spectrometry.

Iron and Mn in the bulk and filtered waters were measured by graphite furnace atomic absorption spectrometry. Trace elements (Al, Cd, Co, Cr, Cu, Ni, Pb, Zn and U) in the different fractions were measured by ICP-MS. Bulk solutions were analyzed by ICP-MS after successive HNO 3 digestions in order to destroy organic matter and to dissolve amorphous particles. However, the clayey fraction and other silicates were not destroyed. Therefore, the particulate fraction corresponds to amorphous particles (plus carbonates) and ions adsorbed on the clay minerals.

All samples exhibited a charge imbalance lower than 10%.

Blank filters were run out in the field to check for possible contamination. Deionized water passed through filters was also analyzed. Blank tests showed that the filtration introduces insignificant levels of contamination for all the elements of interest.

Results

Major elements and nutrients

In the dissolved fraction, wide ranges of concentrations are recorded for the three sites from 2004 to 2006 for major-and minor-elements ( Concentrations of major cations do not differ significantly between sites except Ca 2+ , which is higher in 1a and 1b (Fig. 2). This Ca-rich content could be explained by the origin of colluvial materials. Amphiboles which are the main minerals of amphibolites might cause high Ca values at sites 1a and b. Low values for Ca at sites 2 and 3 indicate a different circulation system, perhaps via lateral input of water from a low Ca source (gneisses).

For each piezometer, the cation concentrations do not show important temporal evolution (less than 20%, Fig. 2). Results for the anion distribution are different (Table 2). Strong temporal variations are observed for (i) HCO 3 -, mainly in 3a and 3b, and (ii)

NO 3 -and Σ(Cl -+ SO 4 2-
) in 2a, 2b, 3a and 3b. For 3b in 2005, HCO 3 -concentrations were high (3.70 ± 0.23 mM), and no correlation exists between HCO 3 -and Ca 2+ .

Because waters circulate in crystalline rocks, HCO 3 -cannot originate from bedrock weathering. During this period, concentrations of some other elements (Ca, Na, Mn and Fe) are also high. Calculations show that soil solutions are in a thermodynamic equilibrium with a pCO 2 (5.11x10 -2 atm in 2005) higher than medium pCO 2 (2004-2006, 1.72x10 -2 atm).

For sites 2 and 3 NO 3 -concentrations exhibit strong temporal variations (Table 2), with low values during spring, indicating vegetation assimilation, absorption and/or denitrification.

Fe, Mn, Al, Si and organic matter

For each piezometer, results on soluble/particulate form distributions (Table 3) show that Fe (excepted in 1a) and Al are mainly associated with particles, while Mn, Si and organic matter have an ubiquitous behaviour. The particulate phases in the soil waters are rich in Fe, Al and Si. The composition of particles varies spatially and temporally.

In the sites 1 and 3, particles are richer in Si. Silicium percentage increases from March 2004 to May 2006, while Fe and Al decrease in all sites.

In the dissolved and particulate fraction, Al is not linked to Si (no correlation between these elements is recorded), indicating that the source of Al may not be aluminosilicate minerals but rather Al oxyhydroxides.

Correlations between Al, Fe, Mg and POC are observed in the particulate fraction.

These relationships will be discussed site by site.

In January 2005, soil waters at site 3b exhibited more reducing characteristics with a maximum recorded concentration of dissolved Fe (4.31x10 -5 mol/L) and dissolved Mn (3.82x10 -5 mol/L) (Table 2).

Trace elements

Concentrations of trace elements are presented in Table 4.

Site 1

In the particulate fraction, three groups of trace elements can be distinguished. In 1a, Cr is linked to Al (R 2 = 0.986); Co, Pb and Zn are strongly linked to Fe (R 2 = 0.999; 0.992 and 0.992 respectively). In 1b, Co, Cr, Cu, Ni, Pb, U and Zn are linked to Mg, Fe and Al (Table 5). No relationship between trace metals and organic matter is recorded.

In the dissolved fraction, it was observed that (1) in 1a and 1b, some elements are linked to HCO 3 -; the relationships are particularly significant for Ca (R 2 = 0.726 in 1a and 0.813 in 1b), Mg (R 2 = 0.831 in 1a and 0.902 in 1b), Sr (R 2 = 0.868 in 1a and 0.907 in 1b) and Ba (R 2 = 0.874 in 1a and 0.813 in 1b); (2) in 1a and 1b, Cr is linked to Al (R 2 = 0.986 and 0.906, respectively).

The correlations between HCO 3 -and some elements (Ca, Mg, Sr and Ba) could indicate that these elements are linked to carbonate dissolution.

Chromium is linked to Al both in the dissolved and particulate fraction (1b).

In 1b, the similar behaviour of Al, Fe and Mg suggests that these elements are controlled by the same mechanism. If Al is present as Al oxyhydroxide, Fe as Fe oxyhydroxide, Mg as clay, which are particles exhibiting different properties, this result could also suggest the presence of mixed particles, which is corroborated by a link between Al and Mg (R 2 = 0.978).

The absence of correlation between organic matter content and trace metals could be attributed to the fact that the reactive fraction of the organic matter could not be assessed in the relationship [START_REF] Harter | Effect of soil pH on adsorption of lead, copper, zinc, and nickel[END_REF][START_REF] Mcbride | Solubility control of Cu, Zn, Cd and Pb in contaminated soils[END_REF]. No evidence of mixed particles is recorded in 2a.

Site 3

In the particulate fraction, the correlation diagrams delineate several groups of elements.

In 3a, Pb and U are correlated with Si (R 2 = 0.850 and 0.888 respectively); Al, Co and Cr are correlated with Mg (R 2 = 0.943; 0.900 and 0.919 respectively); Co, Cr, Pb and Zn are strongly correlated with Al (Table 8). In 3b, no correlation exists between Si, Mg and metals; Co, Cr, Cu, Ni, U and Zn are correlated with Fe (Fig. 4) and Al (except Ni) (Table 8); Cr and Cu are correlated with POC (R 2 = 0.980 and 0.987, respectively).

In the dissolved fraction, in 3a, Co and Mn are correlated with Fe (R 2 = 0.947 and 0.964, respectively), and in 3b, Cu, Mn, Sr and U are correlated with HCO 3 -and Ca (Table 9).

In 3a, some trace metals exhibit interaction with clay and Al oxyhydroxide where a relationship between Al and Mg (R 2 = 0.943) is recorded in particles. In 3b, observed relationships between POC and Fe (R 2 = 0.985), Al and Mg (R 2 = 0.971), and Al and Fe (R 2 = 0.940) suggest mixed particles made of a combination of clay + Al-Fe oxyhydroxides + POC. But here trace metals exhibit interaction mainly with Al and Fe oxyhydroxides. Also, in site 3, mixed particles can also assumed but with different composition and/or reactivity (interaction with carbonate in solution for 3b) according to horizon.

Discussion

Chemical characteristics of soil solution and water circulation

Waters circulating in sites 2 and 3 are more mineralized than that in the site 1. The soil solution composition seems to depend on the water residence time. The Ca-rich content in the site 1 may evidence that water circulating in the sites 2 and 3 does not mainly come from vertical infiltration but rather from lateral flow.

Between Chloride and SO 4 2-variation could be linked to the hydrodynamic of the soil solution, which is controlled both by the effective rainfall variations and vegetation uptake.

During high rainfall, transfer and dilution processes can occur. Autumn rainfall flushes evaporated and thus concentrated superficial waters, whereas winter rainfall causes dilution.

From November 2004 to May 2005, the high pCO 2 recorded in site 3 may indicate that confined waters circulated in the studied horizon. This could be explained by a shoaling of the water table. This explanation has also been proposed by Alberic et al.

(Unpublished study), based on redox data.

The reduction in NO 3 -content recorded at sites 2 and 3 in spring 2005 and 2006 may be linked to denitrification, because the concentration of dissolved Fe and mainly dissolved Mn increase at this same time.

The subsurface water circulation pattern is not in agreement with topography. Site 2 seems to receive mainly lateral waters. Site 3 water may originate from site 2, from the side, or from a confined aquifer. Also, the evolution of trace element behaviour upstream/downstream cannot be discounted.

Range of the redox state of soil solutions

Redox reactions play an important role in the chemistry of natural water systems and influence the mobility and availability of many elements. In this work, the range of pe values in soil solutions was calculated in order to determine the degree of oxidation of trace metals and to study the links between metals and Fe/Mn/Al oxyhydroxides.

Temporary waterlogging of soils may cause the redox potential to decrease.

In the soil solutions, Fe and Mn are redox sensitive elements and can be used to evaluate the pe values, which were calculated using a pe-pH diagram, considering different redox couples and solids. Here pe-pH diagrams were constructed considering the following species: Fe 2+ , Fe 3+ , FeOH 2+ , Fe(OH) 2 , FeOOH and Mn 2+ , MnO 2 . For the Fe pe-pH diagram, it was considered that soluble Fe was at equilibrium with FeOOH (pKs = -1, [START_REF] Michard | Equilibres chimiques dans les eaux naturelles[END_REF] and not with Fe(OH) 3 because of Fe-minerals (mainly goethite) present in the studied soil [START_REF] Cornu | Trace element accumulation in Mn-Fe-oxide nodules of a planosolic horizon[END_REF] (for Fe(III) solid). The highest calculated pe values for Fe and Mn are +1.3 and +2.2, respectively, and the lowest are -6.0 and -2.5, respectively. For all piezometers, Mn pe calculated values are higher than Fe pe. Differences of up to 1.2-2.5 (pe) are observed between Fe and Mn redox couples, indicating a disequilibrium in the soil solutions. The redox reaction rates are typically slow. In this dynamic system where several redox reactions can occur simultaneously, redox species can hardly reach an equilibrium. Nevertheless, these calculations provide a range of the redox states of soil solutions.

The pe ranges are different for each piezometer (Fig. 5), but correspond to anoxic conditions (pe values < +2.5) from November to May (for each year). When pe < 0, electrons are available for SO 4 2-reduction. In this case, typical products in soil solution are H 2 S, bisulphide (HS -) or thiosulphates (S 2 O 3 -) ions. However, in the field, the typical smell of these products was only present for site 3. The pe values for site 3 are lower than for site 2 and site 1. Upstream (site 1), waters are recently infiltrated and contain little O 2 . Then, during water circulation in the soil (site 2 and then site 3), mineral reactions result in a decrease in O 2 content and pe values.

Behaviour of trace elements

Binary correlations provide evidence when one mechanism prevails in the regulation of an element's behaviour. If several mechanisms with the same impact are involved, they cannot be identified.

At the scale of the 3 sites, various behaviours are highlighted, notably: (i) good correlations between Co and Mn in the soluble phase (R 2 = 0.908; Fig. 6a), (ii) strong correlations between U and Fe in the particulate phase (R 2 = 0.958; Fig. 6b), (iii) some trace metals are mainly associated with particles (Table 4) and (iv) very few elements are correlated in the dissolved fraction. In the narrow range of calculated redox states, no difference is really noticed from site 1 to site 3, perhaps excepted for Cr and U in the particulate fraction.

The relationship between Co and Mn reflects the well-known affinity and adsorption (or co-precipitation)/desorption of Co onto amorphous MnO 2 . Cobalt associated with Mnoxide phases is probably released (or maybe reduced) when the oxides are reduced [START_REF] Spencer | Aspects of the distribution and trace element composition of suspended matter in the Black Sea[END_REF][START_REF] Murray | The interaction of cobalt with hydrous manganese dioxide[END_REF]. Significant correlations were also found between dissolved Co and dissolved Mn in aquatic systems by [START_REF] Lienemann | Association of cobalt and manganese in aquatic systems: chemical and microscopic evidence[END_REF]. Most of the Co in the soils is contained in or associated with Mn in mineral form. Indeed, there is a large literature on the adsorption of cobalt by MnO 2 : in soils and sediments (Means et al., 1978b;[START_REF] Alloway | Soil processes and the behaviour of metals[END_REF], in fresh waters [START_REF] Hem | Thermodynamic stability of CoOOH and its coprecipitation with manganese[END_REF], in lakes [START_REF] Balistrieri | The biogeochemical cycling of trace metals in the water column of lake Sammamish, Washington: response to seasonally anoxic conditions[END_REF] and in sea water [START_REF] Knauer | Cobalt in north-east Pacific waters[END_REF][START_REF] Hem | Thermodynamic stability of CoOOH and its coprecipitation with manganese[END_REF][START_REF] Santschi | Factors controlling the biogeochemical cycles of trace elements in fresh and coastal marine waters as revealed by artificial radioisotopes[END_REF][START_REF] Shaw | Early diagenesis in differing depositional environments: the response of transition metals in pore water[END_REF]. Studies of adsorption of Co(II) on synthetic birnessite have been carried out too by Crowther et al. (1983). They proposed several mechanisms of Co incorporation into Mn-rich phases of minerals. In the soil solutions, co-precipitation and adsorption seem to be the mechanisms which explain the link between Co and Mn.

Some studies have shown a high sorptive capacity of Mn oxyhydroxides and MnO 2 towards some trace metals. In various natural settings [START_REF] Jenne | Controls on Mn, Fe, Co, Ni, Cu and Zn concentration in soils and water: the significant role of hydrous Mn and Fe oxides[END_REF][START_REF] Carpenter | Fe-Mn oxide coatings in stream sediment geochemical surveys[END_REF][START_REF] Robinson | Adsorption of Cu, Zn and Pb near sulfide deposits by hydrous manganese-iron oxide coatings on stream alluvium[END_REF][START_REF] Dillard | The oxidation states of cobalt and selected metals in Pacific ferromanganese nodules[END_REF][START_REF] Lind | Manganese minerals and associated fine particulates in the streambed of Pinal Creek, Arizona, U.S.A.: a mining-related acid drainage problem[END_REF] and in a series of laboratory experiments, many metals are closely associated with Mn oxyhydroxides, including: Zn [START_REF] Balistrieri | The surface chemistry of sediments from the Panama Basin: the influence of Mn oxides on metal adsorption[END_REF][START_REF] Catts | Adsorption of Cu, Pb and Zn by (delta)MnO 2 : applicability of the site binding-surface complexation model[END_REF][START_REF] Hem | Synthesis and stability of hetaerolite, ZnMn 2 O 4 , at 25°C[END_REF], Cu and Ni [START_REF] Balistrieri | The surface chemistry of sediments from the Panama Basin: the influence of Mn oxides on metal adsorption[END_REF][START_REF] Hem | Coprecipitation and redox reactions of manganese oxides with copper and nickel[END_REF], Cd [START_REF] Hem | Coprecipitation mechanisms and products in manganese oxidation in the presence of cadmium[END_REF], Pb [START_REF] Catts | Adsorption of Cu, Pb and Zn by (delta)MnO 2 : applicability of the site binding-surface complexation model[END_REF]; but also in deep-sea sediments (Cu, Ni, Pb and Zn) [START_REF] Thomson | Redox zonation of elements at an oxic / post-oxic boundary in deep-sea sediments[END_REF], in sea water (Ni, Cu and V) [START_REF] Shaw | Early diagenesis in differing depositional environments: the response of transition metals in pore water[END_REF] and as coating on quartz [START_REF] Manceau | Natural speciation of Ni, Zn, Ba and As in ferromanganese coatings on quartz using X-ray fluorescence, absorption, and diffraction[END_REF]. The importance of processes occurring at reaction sites on solid-phase surface in contact with Mn-bearing solutions has long been recognized, but these results are not observed here. In this work, redox equilibrium and oxidation kinetics of Mn are important factors in the speciation of trace metals.

Significant correlations exist between U and Fe in the particulate fraction. Uranium transport is dominated by U sorbed to Fe oxyhydroxides which are >0.45 µm in size. In spite of the dynamic redox environment expected in soil solutions, this result shows that U comprised of both U(IV) and U(VI) species. Some authors [START_REF] Ragnarsdottir | Environmental mineralogy: microbial interactions, anthropogenic influences, contaminated land and waste management[END_REF] have shown that the most important species for near neutral waters are the uncharged UO 2 (OH) 2 0 and U(OH) 4 0 species.

The trace metal concentration is governed by a number of interrelated processes, including inorganic and organic complexation, precipitation/dissolution reactions, adsorption/desorption reactions and redox reactions [START_REF] Evans | Chemistry of metal retention by soils[END_REF][START_REF] Singh | Soil and water contamination by heavy metals[END_REF]. These observed results indicate the high impact of particles on the regulation of trace mobility (Table 10). In addition, they intend to assess the mixed nature of particles. If Al is mainly present as oxyhydroxides (no correlation with Si) its links with

Mg suggest an association with clay mineral. This result is also observed for Fe. An adsorption of Fe and Al oxyhydroxides can occur on clay minerals and involves various types of binding between metals (M n+ ) and oxyhydroxides and/or clay minerals: (i) M n+ -Al/Fe oxyhydroxides, (ii) M n+ -clay minerals, and/or (iii) M n+ -Al/Fe oxyhydroxides -clay minerals. Some authors have provided evidence for similar mechanisms. [START_REF] Robinson | Adsorption of Cu, Zn and Pb near sulfide deposits by hydrous manganese-iron oxide coatings on stream alluvium[END_REF] showed that the chemical properties of the Mn oxides are associated with the clay minerals. [START_REF] Jenne | Controls on Mn, Fe, Co, Ni, Cu and Zn concentration in soils and water: the significant role of hydrous Mn and Fe oxides[END_REF] noted the probable occurrence of Fe and Mn oxides as partial coatings on other minerals (and notably clay minerals). Clay minerals and oxyhydroxide minerals have long been recognized as the main metal sorbents in soils [START_REF] Jenne | Controls on Mn, Fe, Co, Ni, Cu and Zn concentration in soils and water: the significant role of hydrous Mn and Fe oxides[END_REF][START_REF] Evans | Chemistry of metal retention by soils[END_REF] and in aquatic systems [START_REF] Förstner | Metal pollution in the aquatic environment[END_REF][START_REF] Benjamin | Multiple-site adsorption of Cd, Cu, Zn and Pb on amorphous iron oxyhydroxide[END_REF][START_REF] Bilinski | Trace metal adsorption on inorganic solid phases under estuarine conditions[END_REF].

Soil solutions were collected above and in the gravely and concretion-rich horizon, in order to assess the impact of the concretion-rich horizon on the distribution of trace metals in the soil waters. In this horizon, concretions are Fe-and Mn-rich coatings and can stabilize trace metals by adsorption or co-precipitation processes with Fe-Mn oxyhydroxides under oxidizing conditions [START_REF] Jenne | Controls on Mn, Fe, Co, Ni, Cu and Zn concentration in soils and water: the significant role of hydrous Mn and Fe oxides[END_REF][START_REF] Stumm | Aquatic chemistry: Chemical equilibria and rates in natural waters[END_REF].

When soils become reduced, trace metals (in soluble or particulate form) can be released into the soil solution by reductive dissolution of Fe-Mn oxyhydroxides. Much higher correlations were found between Fe/Al/Mg and/or POC and trace metals in the concretion-rich horizon. This can be linked to (i) concretion composition or (ii) hydrodynamic (reaction time between water and soil due to porosity) and chemical reactivity of the solution circulating.

Conclusions

This study highlights the distribution, behaviour and controlling factors of some trace metals in unpolluted soil solutions of a planosolic horizon and enhanced knowledge of these kinds of solution. The relationships between the different parameters and trace metals are complex and can not be related to only one parameter. However, results

show Fe and Al oxyhydroxides, clay minerals and organic matter play an important role in trace metal distribution and mobility. In these weakly reductive waters, trace metals are mainly linked to particles. In addition, the concretion-rich horizon has an impact both on the trace element composition and on the particle composition, although this impact cannot be linked to the chemical distribution of the horizon. Table 1: Analytical results (mean, min, max and median) for samples from 1a, 1b, 2a, 2b, 3a and 3b in the dissolved phase.

T°C pH C HCO 3 - Na + K + Ca 2+ Mg 2+ H 4 SiO 4 Cl - SO 4 2- NO 3 - ΣPO 4 F - µ S / c m m M m M µ M m M µ M m M µ M µ M µ M µ M µ M
Mean 9 . 0 6 . 2 5 7 9 0 . 7 1 0 . 1 5 7 . 0 3 0 . 2 4 6 2 . 1 0 . 1 8 2 9 . 0 2 2 . 0 1 4 . 4 0 . 6 5 7 . 0

Min -Max 3.1 -14.3 5.57 -6.60 62 -100 0.41 -1.03 0.12 -0.18 2.20 -12.50 0.16 -0.33 42.8 -86.8 0.16 -0.22 8.8 -65.6 3.5 -38.2 1.5 -32.0 0.28 -0.87 5.2 -8.4 Median 9 . 5 6 . 3 2 8 1 0 . 7 9 0 . 1 5 6 . 6 1 0 . 2 3 6 3 . 5 0 . 1 7 1 5 . 6 2 6 . 5 1 1 . 6 0 . 7 0 7 . 2 Mean 7 . 2 5 . 9 3 8 5 0 . 8 1 0 . 1 6 4 . 5 4 0 . 2 6 6 7 . 1 0 . 1 9 2 2 . 9 1 8 . 2 9 . 8 0 . 5 9 5 . 9

Min -Max 1.6 -13.5 5.56 -6.62 54 -106 0.46 -1.13 0.14 -0.20 2.64 -8.09 0.15 -0.37 38.5 -89.5 0.15 -0.26 Min -Max 1.8 -14.0 5.91 -7.25 217 -525 0.60 -1.70 0.91 -1.17 0.00 -3.14 0.40 -0.56 211.0 -321.0 0.14 -0.27 222.3 -972.3 205.7 -309.0 0.9 -970.0 0.43 -0.65 3.5 -7.5 Median Min -Max 3.7 -15.3 6.09 -7.08 106 -295 0.81 -2.11 0.79 -1.09 0.59 -43.30 0.25 -0.50 259.8 -456.0 0.22 -0.54 97.4 -614.0 170.0 -321.0 5.6 -500.0 0.00 -0.71 7.6 -18. Min -Max 1.2 -15.5 6.25 -7.40 185 -372 1.13 -3.88 0.61 -1.02 3.90 -90.30 0.46 -0.86 274.0 -657.0 0.10 -0.21 34.0 -686.0 37.0 -553.0 0.0 -29.0 0.00 -0.85 8.0 -12.

  March 2004 to May 2006, for sites 2 and 3, some constituents (, Fe, Mn) exhibit interesting temporal patterns.

Figure 1 a

 1 Figure 1 a) Schematic diagram of the studied toposequence (modified from Cornu et al., 2005). b) Study area and location of three water sampling sites (piezometers 1a, 1b, 2a, 2b, 3a and 3b) (modified from Alberic et al., Unpublished study).

Figure 2 :

 2 Figure 2: Cation and anion distribution (expressed in % mol/L) in the three soil solution sites from 2004 to 2006.

Figure 3 :

 3 Figure 3: Correlations between some trace elements and Fe in 2b, the particulate phase of soil solutions.

Figure 4 :

 4 Figure 4: Correlations between some trace metals and Fe in 3b, the particulate phase of soil solutions.

Figure 5 :

 5 Figure 5: pE range calculated for the soil solutions from the six piezometers (see text for explanation).

Figure 6 :

 6 Figure 6: a) Correlations between Co and Mn in the soluble phase (piezometers 1a, 1b, 2a, 2b, 3a and 3b). b) Correlations between U and Fe in the particulate phase (piezometers 1b, 2a, 2b and 3b).

Table 1

 1

	, exhaustive data are

Table 2 :

 2 Concentrations of HCO 3

						-, Cl -, SO 4	2-, NO 3	-, Mn and Fe in the dissolved fraction
	for each year.
			HCO 3	-	Cl	-	SO 4	2-		NO 3	-	Mn	Fe
			mM		µM	µM		µM	µM	µM
		2004	1.33 ±0.18	332.5 ±38.5	269.5 ±7.5	30.0 ±1.1	0.09 ±0.06	0.14 ±0.04
	2a	2004-2005	1.35 ±0.36	597.3 ±375.0 256.4 ±50.7 395.4 ±381.2	0.96 ±0.88	1.41 ±0.98
		2005-2006	0.96 ±0.36	607.0 ±349.0 289.5 ±19.5 485.4 ±484.6	1.08 ±1.02	1.59 ±1.25
		2004	1.59 ±0.26	414.5 ±105.5 181.0 ±11.0	75.0 ±51.0	9.60 ±9.59	1.25 ±1.15
	2b	2004-2005	1.84 ±0.27	361.7 ±252.3 229.7 ±36.7 121.2 ±101.6	2.65 ±2.50	1.32 ±0.96
		2005-2006	1.42 ±0.60	340.7 ±243.3 248.5 ±72.5 252.8 ±247.2	4.69 ±4.59	0.97 ±0.46
		2004	1.76 ±0.01	77.5 ±17.5	136.0 ±33.0	14.5 ±14.5	0.81 ±0.47	1.10 ±1.00
	3a	2004-2005	3.48 ±0.41	323.6 ±289.6	85.4 ±48.4	19.1 ±0.4	14.62 ±4.09	7.02 ±1.78
		2005-2006	1.43 ±0.30	578.5 ±107.5 436.0 ±117.0		2.4 ±1.0	0.87 ±0.68	1.77 ±0.49
		2004	1.75 ±0.05	93.0 ±32.0	144.5 ±37.5	14.0 ±14.0	1.16 ±1.01	1.29 ±1.19
		2004-2005	3.70 ±0.23	337.4 ±239.4 122.8 ±66.7	83.7 ±65.1	29.71 ±8.47 21.60 ±21.50
		2005-2006	1.90 ±0.75	439.7 ±256.3 356.1 ±191.9		2.9 ±2.9	6.68 ±4.92	2.89 ±1.58

Table 3 :

 3 Concentrations of Al, Mn, Fe, Si and organic matter in the dissolved and particulate fraction for each piezometer (expressed as mol/L of solution). diss Al part Al part Mn diss Mn part Mn part Fe diss Fe part Fe part Si diss Si part Si part DOC POC POC Zn diss Zn part Zn part U diss U part U part Ba diss Ba part Ba part Rb diss Rb part Rb part Sr diss Sr part Sr part

			Al µM	µM	%	µM	µM	%	µM	µM	%	mM	mM	%	mg/L	mg/L	%
		mean	2.74	184.3	88.3	1.28	2.05	48.1	2.17	90.2	75.6	0.18	0.32	55.6	11.2	1.4	13.2
	1a	min max	0.28 9.99	5.6 693.8	62.5 100.0	0.08 2.60	0.08 8.74	6.5 97.8	0.10 5.20	1.53 341.0	37.4 99.9	0.16 0.22	0.03 0.60	12.5 77.0	4.9 17.5	0.0 6.1	0.0 55.8
		median	1.76	26.5	95.3	1.24	0.48	49.2	2.39	7.34	78.6	0.17	0.36	68.5	10.9	0.6	3.6
		mean	1.59	149.8	95.6	3.19	2.21	34.7	1.59	159.4	87.6	0.19	0.37	58.1	10.8	1.6	14.8
	1b	min max	0.27 4.89	13.9 769.1	83.7 100.0	0.25 8.10	0.06 11.00	1.6 76.5	0.10 2.82	2.26 1010.0	61.5 99.9	0.15 0.26	0.00 0.73	0.0 80.5	4.7 21.8	0.0 4.4	0.0 44.3
		median	1.06	74.3	98.5	2.42	1.80	36.5	1.40	29.71	95.4	0.18	0.41	68.8	10.5	1.6	14.0
		mean	1.89	101.5	95.7	0.53	0.77	61.0	1.18	39.81	93.3	0.17	0.24	41.1	9.8	3.2	22.6
	2a	min max	0.10 5.85	25.4 305.7	82.9 99.9	0.03 2.10	0.00 1.97	0.0 98.2	0.10 2.84	8.27 130.0	75.2 99.9	0.14 0.22	0.00 0.66	0.0 81.7	4.3 18.3	0.0 10.5	0.0 50.4
		median	1.09	77.3	98.4	0.12	0.52	72.8	1.18	29.8	96.2	0.18	0.10	38.4	8.5	2.5	26.6
		mean	0.96	1033.8	99.7	2.98	5.73	61.8	1.06	466.7	99.0	0.33	0.62	50.1	12.7	10.0	38.1
		min	0.10	61.7	99.3	0.01	0.20	4.8	0.10	22.68	96.5	0.22	0.01	3.7	5.4	0.0	0.0
		max	2.88	3999.0 100.0	19.20	31.10	99.9	2.40	4185.0 100.0	0.54	2.45	90.8	27.2	41.0	75.7
		median	0.89	258.1	99.7	1.22	2.25	65.9	0.97	85.74	99.1	0.31	0.36	47.2	11.9	8.6	37.4
		mean	2.18	435.9	97.3	5.21	2.78	54.0	3.21	103.77	91.6	0.14	0.17	43.3	21.4	2.5	10.5
	3a	min max	1.31 3.64	32.3 3199.0	94.5 99.9	0.18 18.70	0.55 10.18	4.0 96.8	0.10 8.80	13.82 620.0	76.4 99.9	0.10 0.21	0.01 0.40	2.6 79.8	15.8 33.5	0.0 8.7	0.0 35.3
		median	1.81	73.4	97.7	1.28	2.31	67.1	2.09	38.36	91.8	0.12	0.14	40.2	19.9	2.0	10.0
		mean	1.53	719.5	97.7	14.32	8.39	26.0	6.06	974.9	88.4	0.24	0.28	51.5	18.3	3.6	14.1
	3b	min max	0.26 3.60	29.1 6466.4	91.8 99.9	0.15 38.18	0.00 64.88	0.0 97.6	0.10 43.10 11165.0 99.9 3.85 46.3	0.13 0.67	0.00 0.53	0.0 74.1	11.4 26.2	0.0 18.6	0.0 54.6
		median	1.07	64.0	99.2	7.63	2.31	16.5	2.25	57.52	90.0	0.21	0.25	57.3	17.0	1.6	8.2

Acknowledgments

This work was supported by Le Conseil Régional du Centre as part of the METALOE program. We gratefully acknowledge Martine Bouhnik-Le-Coz (CAREN Géosciences Rennes) for ICP-MS analysis and Mrs Narbone (IUT Tours) for a part of AAS and AES analysis. Two anonymous reviewers supplied very useful comments. Pr. Gabriel Filippelli, Associate Editor, proposed important comments which improved the present manuscript.


Ambre Assor
email: ambre.assor@inria.fr

Arnaud Prouzeau
email: arnaud.prouzeau@inria.fr

Pierre Dragicevic
email: pierre.dragicevic@inria.fr

Martin Hachet
email: martin.hachet@inria.fr

Exploring Augmented Reality Waste Data Representations for Eco Feedback

Keywords: Visualization, Concrete Scales, Augmented Reality, Embodied Interactions

Figure 1: Illustrative examples of ARwavs we prototyped. (a) On the top left hand corner, a user looks at the amount of waste produced by his corporate restaurant in a week. The waste is represented by virtual trash bags which are displayed directly in the restaurant using augmented reality. (b) On the top right hand corner, 9 Litres of water represented using water bottle next to the toilets (average flush amount of water).(c) On the bottom left, the approximate amount of material displaced and emitted to manufacture 8 smartphones . (d) Bottom right, the quantity of single-use plastic cups accumulated for a given period of time. Captured with Hololens.

The negative impact humans have on the environment is partly caused by thoughtless consumption leading to unnecessary waste. A likely contributing factor is the relative invisibility of waste: waste produced by individuals is either out of their sight or quickly taken away. Nevertheless, waste disposal systems sometimes break down, creating natural information displays of waste production that can have educational value. We take inspiration from such natural displays and introduce a class of situated visualizations we call augmented-reality waste accumulation visualizations or ARwavs, which are literal representations of waste data embedded in users'

INTRODUCTION

The adverse impact humans have on the environment (through, e.g., air pollution, plastic pollution, soil erosion, or damage to biodiversity) is one of the biggest challenges currently faced by our society. Although the causes are complex and numerous, individual behavior and lifestyles have been identified as among the key contributors [START_REF] Alpizar | A framework for selecting and designing policies to reduce marine plastic pollution in developing countries[END_REF][START_REF] Masson-Delmotte | Global warming of 1.5°C: an IPCC special report on the impacts of global warming of 1.5°C above pre-industrial levels and related global greenhouse gas emission pathways[END_REF]. A factor that likely contributes to the excessive consumption and unnecessary waste production is the invisibility of waste there: when we buy a new smartphone, we do not see the metal mines that went into its construction; Even when we directly create waste, it quickly goes away and becomes invisible (dirty water flow to the treatment plant after showering or flushing, trash is picked up by garbage collectors). We propose to use augmented reality to recreate these accumulations in the direct surroundings of users. These visualizations fill a gap in eco-feedback research [START_REF] Froehlich | The design of eco-feedback technology[END_REF], where most systems convey resource consumption and waste production using units and visual representations that are useful but often abstract and potentially difficult to grasp intuitively. Because ARwavs use literal representations of waste amounts [START_REF] Chevalier | Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures[END_REF] (e.g., 300 litres of garbage can be represented with ten 30-litres trash bags), we expect them to give a more visceral sense of quantities and stand as more engaging representations. However, ARwavs may not be self sufficient in some situations, as when a quick value judging is necessary. Hence, we are starting to explore embodied transitions with 3D classic aggregates (barplots, tables...) and include them in our demonstration. We already conducted a study suggesting that ARwavs yields more emotions compared to less immersive display modalities (3D on screen) and simpler information representations (numerals); results are under review and available as a preprint [START_REF] Assor | Augmented Reality Waste Accumulation Visualizations[END_REF]. In this interactivity paper, we : (1) Present the prototypes we plan to demonstrate: several 1:1 scale ARwavs pictured within scenarios and an embodied way of transitioning with 3D aggregates. (2) Explain the advantages of participating in this interactive experience and clarify the opportunity of initiating novel discussions among the community.

BACKGROUND

In this section we give an overview of AR-HCI research on ecofeedback, i.e., "technology that provides feedback on individual or group behaviors with a goal of reducing environmental impact" [START_REF] Froehlich | The design of eco-feedback technology[END_REF] and will present some related work in information visualization. A complete related work review is available at https://hal.inria.fr/hal-03907474.

AR Eco-Feedback interfaces

Some explorations in AR has been considered for eco-feedback technologies like AR overlays of energy consumption on physical building models [START_REF] Ens | Uplift: A Tangible and Immersive Tabletop System for Casual Collaborative Visual Analytics[END_REF], and heat cameras to visualize thermal loss [START_REF] Boomsma | Improving the visibility of energy use in home heating in England: Thermal images and the role of visual tailoring[END_REF]. But as far as we know, enhancing real-world environments with AR for eco-feedback purposes has been only mentioned as a possibility in past research (e.g., in [START_REF] Carneiro | Comprehensible and interactive visualizations of spatial building data in augmented reality[END_REF][START_REF] David Fredericks | Visualising the Invisible: Augmented Reality and Virtual Reality as Persuasive Technologies for Energy Feedback[END_REF][START_REF] Santos | Changing environmental behaviors through smartphone-based augmented experiences[END_REF]).The only example of ARwav we currently know of is a mobile app where users can visualize a year worth of trash bags in augmented reality [START_REF] Stark | Visualizing Impact Through Augmented Reality -Using Concrete Scales To Combat Waste[END_REF]. This prototype has directly inspired our work, but has not been discussed in the academic literature, nor has it been generalized to other cases or evaluated. This paper fills this gap.

Information Visualization

Strategies for representing large quantities or unfamiliar units next to familiar landmarks have been formalized in information visualization under the concrete scale framework [START_REF] Chevalier | Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures[END_REF]. Inspired by this framework, Lee et al. [START_REF] Lee | Data Visceralization: Enabling Deeper Understanding of Data Using Virtual Reality[END_REF] introduced the concept of data visceralization focusing on VR experience, as "a data-driven experience which evokes visceral feelings within a user to facilitate intuitive understanding of physical measurements and quantities". These article does not discuss eco-feedback as a possible application and the latter identify AR as a possible direction for future work. Following Drucker and Fernandez [START_REF] Drucker | A unifying framework for animated and interactive unit visualizations[END_REF] definition, ARwavs are unit visualizations: "each data item becomes a unique visual mark; such visualizations strictly maintain the identity of each visual mark and its relation to a corresponding data item."1 . However they may not be adapted to every situations: one could benefit from the advantages of aggregates regarding value judging or readability. Animations and transitions on on-screen unit representations are already explored to tackle its weaknesses [START_REF] Drucker | A unifying framework for animated and interactive unit visualizations[END_REF]. In our scope direct interactions enabled by AR units and 3D representations of classic aggregates 1 (barplot, graph...) opens of wide range of explorations toward embodied transitions.

IMPLEMENTATION

The ARwavs were implemented with a Microsoft Hololens 2. The see-through holographic display was equipped with 4 visible light cameras for head tracking and map building. IR-reflectivity steams are used to compute depth along with a depth camera that operates in two modes: high-frequency (45 FPS) near-depth sensing used for hand tracking and low-frequency (1-5 FPS) far-depth sensing used by spatial mapping. The display is equipped with speakers enabling built-in spatial sound. We developed with Unity 2020.3.18f1 and used the MRTK toolkit2 . We enabled hands, head tracking, and set the spatial awareness module to scan the environment at start (update interval of 3.5 seconds). The objects making up the ARwavs (trash, bottle, mud and plastic cup) where either found on the Unity Asset Store or download and adapted from free 3D models browsers 3 . The abstract representation have been adapted from Unity Packages 4 . They have been modified to take input from csv files with the data shown. We adapted the visualizations to make them AR compatible, enable manipulation of elements and make them dynamic to interact with units.

WALK-THROUGH

Augmented-reality waste accumulation visualizations or ARwavs aim to help people better perceive the quantitative impact of their actions and decisions in order to inform them, raise their awareness, or encourage them to change their habits. Figure 1 (a) illustrates a scenario where employees can perceive directly in their corporate restaurant a week of collective waste production represented with virtual trash bags. In the following sections we introduce the ARwavs we'll present at the venue. The last scenario put in context our current explorations on transitions with more classical representations such as 3D bar charts.

Scenario 1: Personal motivation, water use. Water is a resource that many of us abundantly use at home when we take a shower, wash our hands, flush our toilets, or use appliances like washing machines. As water immediately disappears through the pipes, it can be hard to get a good impression of the amount we use over time. Knowing numbers is a good start, but is likely not enough. For instance, it might not seem a lot to consume 5 m 3 of water in a month, but it actually represents about 28 full bathtubs, or an average bathroom filled with water up to 2 m high. ARwavs can literally show these volumes of water to make abstract numbers more concrete. Figure 1 (b) shows an example where a user sees the amount of water used for a flush next to the used toilets.

Scenario 2: Group dynamics, ecological rucksack. Computers and mobile devices are powerful tools with many useful applications, but they have a significant ecological footprint. One way to capture this footprint is the concept of ecological rucksack, which is the amount of matter displaced to build an object. 5 A smartphone requires an ecological rucksack of about 70kg, which includes the amount of soil mined to obtain the metals that go into its fabrication, and the amount of CO2 emitted during transportation and manufacturing. 6 Since the metal mines and the CO2 emissions are typically situated far away from where the phone is purchased and used, it is hard for people to have a vivid picture of them in their mind, even when they heard about them. In addition, computing devices often look clean and beautiful, so looking at them does not bring about any association with mines, soil, or greenhouse gases. With ARwavs, we can make those waste products more salient to users. For example, imagine a research team discussing whether to buy eight new smartphones for a project or use old ones. An eco-conscious member of the team could use AR to show them the size of the ecological rucksack necessary to build the new phones, as a pile of soil (Figure 1 (c)). Having this heap of soil appear as if it was in the room (as opposed to, e.g., on a computer screen or a magazine) could give the team members a more visceral sense of quantity and size. It also adds a dramatic dimension, which can help make environmental issues more salient and more influential in the discussion. Scenario 3: Support for policies, plastic cups. Single-use plastic cups have a negative repercussion on the planet. It is estimated that more than 50 billions are used in the US in one year. 7Yet manufacturing them is costly in energy and resources, they are hard to recycle, and they are one of ten most commonly found waste items in European beaches 8 . However, plastic cups are still routinely given away in cafés, shops and companies, and thus it remains easier for many people to use them instead of bringing a reusable cup. In this third scenario, a company chooses to ban plastic cups as part of a program to reduce its ecological footprint, but is afraid that not all of its employees will agree. The company has already communicated about the issue through figures and charts, but they went largely ignored. Therefore, the company decides to organize an event, with a booth in front of the coffee machine, where employees can observe through an AR-HMD (Head-Mounted Display) an ARwav composed of all plastic cups typically used over a week (see Figure 1 (d)). With this immersive experience, most employees get a much better sense of the amount of plastic cups accumulated over time, and many become more willing to make the effort to bring their own reusable cup.

Scenario 4: Transitioning with classic representations in the 3D space. In scenario 3, a company organized an event for plastic cups usage awareness. The organizers have in mind to recreate this meet-up to sensitize about the company's waste. However, the charts they want to communicate are large datasets and the ARwavs they want to use (50L trash bags) are quite voluminous. This makes the experience difficult to put up. The marketing team choose to keep charts as they present advantages including easiness on value judging or readability on large datasets; however they don't want to drop ARwavs that were appreciated for their emotions raising. To keep both, they introduced a 3D barplot in the AR space and allowed embodied transitions with ARwavs. Employees can grab a bar from the barplot and throw it on the floor to see the amount of trash bags it represents appear and get the scaled reality of it. They can grab the trash bags and put them back in the chart to clean the space and continue to navigate in the dataset.

DEMONSTRATION

In the demo booth, we plan on showing the average amount of water used for a 6'30 min lasting shower with water bottles, the amount of soil needed to build 5 and 10 smartphones, the amount of plastic cups use in a day at our lab (before the no-plastic recent policy) and an example of transitions between a barplot about trash emission and ARwavs.

ARwavs act as situated information displays that are unique in their ability to convey waste production in a way that is immediately understandable by a large audience and can carry emotional impact. Testers get to experience these with integrated scaled Holograms that may raise some awareness and initiate self-reflections. They will also be able to appreciate several embodied ways of transitioning from more classic representations of the same data. To tackle the potential layout issues and people flow abundance, we developed a 1:10 scale scene showing ARwavs, see Figure 2. This mini mode allow observers to see the entire ARwav without having to move their head or step back. This version will not be showed systematically, but will be if it is appropriate within the discussion with the tester or if it is more convenient due to the layout business. Not only this version tackles layout limits but it also fits Hololens 2 boundaries; indeed, the display FoV is (43 • x 29 • ) which does not allow to get the full AR scene without moving. Through this scaled version, users can have a first appreciation of the possible trade-offs that can be operated for such AR visualizations and these elements will be even more relevant for HCI or visualization researchers. This large-scale expert conference is a great opportunity to put light on of the challenges of eco-feedback. More broadly this interactive experience will potentially generate discussions in the community to imagine and design around environmental issues. The conference already shows sustainable HCI interests through workshops and talks and this demo will suitably feed these exchanges. Also, experts feed-backs are precious to push our work in the best direction.

Figure 2 :

 2 Figure 2: Miniature view of an ARwav, with a car and standing man silhouette as reference points.

They are distinguished from aggregate visualizations (i.e. in which multiple data item are merged into visual aggregates that cannot be separated and that does not keep identity properties)

https://docs.microsoft.com/fr-fr/windows/mixed-reality/develop/unreal/unrealmrtk-introduction

[START_REF] Boomsma | Improving the visibility of energy use in home heating in England: Thermal images and the role of visual tailoring[END_REF] https://free3d.com/, https://www.turbosquid.com/fr/, https://sketchfab.com/store/3dmodels

https://assetstore.unity.com/packages/tools/gui/3d-interactive-barchart-157887

https://www.gdrc.org/sustdev/concepts/27-rucksacks.html

https://ec.europa.eu/environment/ecoap/about-eco-innovation/expertsinterviews/friedrich-schmidt-bleek_en

https://plastic.education/the-problem-with-disposable-cups/

https://ec.europa.eu/environment/pdf/waste/single-use_plastics_factsheet.pdf

CONCLUSION

In this paper, we presented augmented-reality waste accumulation visualizations or ARwavs, which are literal representations of accumulated waste embedded in users' physical environments. We went through several examples of ARwavs to illustrate the variety of situations where they can be useful. Minimizing the negative impact of humans on the environment is an incredibly complex problem, and ARwavs could play a useful role if they usefully inspire future research or demonstrate to successfully engage visitors.


Guoying Dong

Grace Wijaya

Yunlong Tang

Yaoyao Fiona Zhao

Optimizing Process Parameters of Fused Deposition Modeling by Taguchi Method for the Fabrication of Lattice Structures

Keywords: Additive Manufacturing, Fused Deposition Modeling, Lattice structure, Optimization, Taguchi method

The lattice structure is a type of cellular material that can achieve a variety of promising physical properties. Additive Manufacturing (AM) has relieved the difficulty of fabricating lattice structures with complex geometries. However, the quality of the AM fabricated lattice structure still needs improvement. In this paper, the influence of parameters of the Fused Deposition Modeling (FDM) process on lattice structures was investigated by the Taguchi method. S/N ratio analysis was used to find the optimal process parameters that improve the printing quality, and ANOVA provided a significance ranking of the various factors analyzed in this paper. It was found that the optimum level and significance of each process parameter vary for horizontal and inclined struts. In addition, compression tests investigate the influence of process parameters on the mechanical properties of lattice structures. The results show that process parameters optimized by print quality can also improve the elastic modulus and the ultimate strength of these lattice structures.

Introduction

The lattice structure is a truss-like structure with intersecting struts and nodes with a certain repeated arrangement over a volumetric region. Compared to other cellular materials such as foams and honeycombs, lattice structures have more flexibility to achieve a variety of physical properties including high stiffness-weight ratio [START_REF] Deshpande | Effective properties of the octet-truss lattice material[END_REF], low thermal expansion coefficient [START_REF] Lehman | Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization[END_REF], negative Poisson ratio [START_REF] Yang | Non-stochastic Ti-6Al-4V foam structures with negative Poisson's ratio[END_REF], and high heat dissipation rate through active cooling [START_REF] Zhang | Ultralight X-type lattice sandwich structure (I): Concept, fabrication and experimental characterization[END_REF]. Due to these excellent characteristics, lattice structures have been extensively implemented in engineering applications, including ultralight structures [START_REF] Tang | Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing[END_REF][START_REF] Rosen | Computer-aided design for additive manufacturing of cellular structures[END_REF], energy absorbers [START_REF] Ozdemir | Energy absorption in lattice structures in dynamics: Experiments[END_REF], low thermal expansion structures [START_REF] Lehman | Stiff, strong, zero thermal expansion lattices via material hierarchy[END_REF], and conformal cooling [START_REF] Brooks | Design of conformal cooling layers with self-supporting lattices for additively manufactured tooling[END_REF]. In addition, lattice structures can be used as biocompatible materials for orthopaedic implant [START_REF] Khanoki | Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem[END_REF] and tissue engineering [START_REF] Masood | The design and manufacturing of porous scaffolds for tissue engineering using rapid prototyping[END_REF][START_REF] Cheah | Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 1: Investigation and Classification[END_REF].

In the past, the complexity of lattice structure design was severely restricted by traditional manufacturing techniques such as casting, sheet metal forming and wire bonding [START_REF] Wadley | Multifunctional periodic cellular metals[END_REF]. Only simple topologies and structures on a macro scale could be fabricated, unable to fully exploit the considerable potential of lattice structures. However, Additive Manufacturing (AM) technology provides an alternative approach to directly or indirectly [START_REF] Lee | Rapid investment casting: Direct and indirect approaches via fused deposition modelling[END_REF] fabricate highly complex lattice structures via its layer by layer manufacturing principle. Powder bed fusion [START_REF] Yan | Evaluations of cellular lattice structures manufactured using selective laser melting[END_REF][START_REF] Parthasarathy | Mechanical evaluation of porous titanium (Ti6Al4V) structures with electron beam melting (EBM)[END_REF] and material extrusion [START_REF] Lee | Rapid investment casting: Direct and indirect approaches via fused deposition modelling[END_REF][START_REF] Karamooz Ravari | Numerical investigation on mechanical properties of cellular lattice structures fabricated by fused deposition modeling[END_REF] are the most common AM techniques for manufacturing lattice structures.

However, each manufacturing technology has its limitations, and AM is no exception. A wellknown limitation of AM is the need for support structures on down-facing surfaces [START_REF] Atzeni | Study on unsupported overhangs of AlSi10Mg parts processed by Direct Metal Laser Sintering (DMLS)[END_REF]. Some support structures are difficult to remove, which leads to inferior surface quality or failed fabrication. To better understand the capability of AM to fabricate overhanging structures, the manufacturability and accuracy of self-supporting surfaces need further investigation.

A previous analysis on the effects of the process parameters of SLM on the roughness of selfsupporting surfaces [START_REF] Fox | Effect of Process Parameters on the Surface Roughness of Overhanging Structures in Laser Powder Bed Fusion Additive Manufacturing[END_REF] had limited experimental results and did not show a clear dependency on process parameters. Therefore, the relationship between process parameters of AM and the manufacturing quality of overhangs needs further analysis.

In addition, several attempts have been made to investigate process parameters of different AM approaches to enhance the print quality including surface roughness [START_REF] Pupo | Influence of process parameters on surface quality of CoCrMo produced by selective laser melting[END_REF], density [START_REF] Kamath | Density of additivelymanufactured, 316L SS parts using laser powder-bed fusion at powers up to 400 W[END_REF] and dimensional accuracy [START_REF] Wang | A model research for prototype warp deformation in the FDM process[END_REF]. However, they focus on simple geometry rather than complex structures with many overhangs. Overhangs include horizontal struts and inclined struts, which are found in lattice structures and challenge the manufacturability of AM processes. Due to the lack of research relating the effect of process parameters on overhanging structures, there are no guidelines for finding the optimal process parameters of AM for the fabrication of lattice structures. Therefore, it is imperative to investigate the relationship between process parameters and the manufacturing quality of lattice structures to improve manufacturability.

In this paper, an optimization approach using the Taguchi method is proposed to find optimal parameters to fabricate lattice structures through Fused Deposition Modeling (FDM), a type of material extrusion AM process. The Taguchi method has been immensely used to optimize process parameters in product design through comprehensive experimental investigation. Since AM technology is influenced by many process parameters and currently has a high cost, the quantity and cost of a full factorial method experiment will be quite considerable. The design of experiment using Taguchi's method can significantly simplify the experimental plan. The Orthogonal Array (OA) is implemented here to give unique combinations between parameters and their levels to minimize the number of experiments while still investigating the entire parameter space.

In the Taguchi method, the analyses of experimental results have three primary objectives [START_REF] Roy | A primer on the Taguchi method[END_REF]. Firstly, studying the main effects of each factor gives the general influence of each factor. Secondly, by knowing whether higher or lower values produce the preferred result, the best levels of factors can be predicted. Finally, the contribution of each factor is established by analysis of variance (ANOVA), a statistical treatment to determine the relative percent influence and significance of each factor. After predicting the optimum conditions and expected performance, a confirmation test is usually conducted for verification. This is because the OA represents only a small fraction of all possibilities, so the optimum condition may not be present among the experimental combinations already carried out. Additionally, Signal-to-Noise (S/N) ratio analysis are conducted over the replicates to determine the most robust set of operating conditions from variations within the results.

In recent years, a lot of research have assessed the influence of the process parameters on the quality characteristics of FDM by the Taguchi method. For example, Anitha et al. [START_REF] Anitha | Critical parameters influencing the quality of prototypes in fused deposition modelling[END_REF] used the Taguchi method to investigate layer thickness, road width and the speed deposition to minimize the surface roughness. ANOVA revealed that layer thickness is the most significant parameter; and from S/N analysis, the optimum levels are 0.3556mm layer thickness, 0.537mm road width and 200mm speed of deposition. Another study used the Taguchi method to evaluate the elastic performance and optimize the throwing distance of an FDM fabricated bow made with flexible ABS [START_REF] Lee | Optimization of rapid prototyping parameters for production of flexible ABS object[END_REF][START_REF] Laeng | Optimizing Flexible Behaviour of Bow Prototype Using Taguchi Approach[END_REF]. It was found that air gap, slice height and raster angle most significantly impacted the elastic performance and optimum FDM parameter combinations were obtained. In addition, the Taguchi method with gray relational analysis has been used. One study used gray Taguchi to analyze the ultimate tensile strength, dimensional accuracy and surface roughness to optimize the FDM process [START_REF] Chung | Optimizing the rapid prototyping process by integrating the Taguchi method with the Gray relational analysis[END_REF]. The results demonstrate that for different objectives, the optimal combinations and most essential parameters may be different. Sood et al. [START_REF] Sood | Improving dimensional accuracy of Fused Deposition Modelling processed part using grey Taguchi method[END_REF] investigated the dimensional accuracy of FDM processed ABS400 part to minimize the percent change in length, width and height. The results indicated that optimum settings for each performance were different, so the gray relation grade combined three responses into a single response to simultaneously optimize parameters. The gray Taguchi method has also evaluated the influence of process parameters on the mechanical properties of FDM fabricated parts [START_REF] Liu | Mechanical property parametric appraisal of fused deposition modeling parts based on the gray Taguchi method[END_REF].

In this research, the design of experiment based on the Taguchi array evaluates the fabrication of lattice structures. S/N ratio analysis finds the best level of process parameters, the ANOVA method investigates the significance of each process parameter, and the compression test evaluates the correlation between the print quality and mechanical performance of the lattice structure. This proposed approach is not limited to the FDM process; rather, the flow of experiments and method of data analysis is applicable to other AM processes for the selection of appropriate manufacturing parameters. This paper is organized as follows: Section 2 introduces the basic concepts used in this approach, Section 3 illustrates the design of experiments, and Section 4 presents the results of data analyses and compression test, and results discussion. Finally, the paper ends with conclusions and future research directions.

Basic concepts 2.1 Manufacturable Element (ME)

To link the design and manufacturing process of lattice structures, a concept called the Manufacturable Element (ME) [START_REF] Tang | Lattice Structure Design and Optimization With Additive Manufacturing Constraints[END_REF] is used in this paper. This concept is defined by Rosen [START_REF] Rosen | Computer-Aided Design for Additive Manufacturing of Cellular Structures[END_REF] as a predefined, parametrized decomposition of a volumetric region of a part. Applied to the characteristics of lattice structures focused in this paper, a ME of lattice structure is defined as a lattice strut with its related geometry, material and process information. To parametrically represent each ME of lattice structures, a data structure of ME is proposed and its graphic view is shown in Figure 1. The ME of lattice structures consists of geometrical data, material data and process data. The objective of this paper is to find the best process parameters for lattice structures fabricated by FDM. From the perspective of ME, it is to find the relationship between the process and geometrical data, while the material data is set to be constant. For better printing quality, the fabricated geometry should be as precise as the designed geometry. However, less error in the fabricated geometry does not mean a better mechanical performance. As a result, the compression test is also conducted to investigate the relationship between the mechanical properties of lattice structure and the process parameters. Figure 1. Graphic view of data structure of ME for lattice structures [START_REF] Tang | Lattice Structure Design and Optimization With Additive Manufacturing Constraints[END_REF].

In this research, the samples are single struts, which is what lattice structures are constructed of. This is because it is difficult to evaluate the dimensional accuracy of the interior of as built lattice structures. Based on the geometrical data of ME, there are three types of lattice struts: horizontal struts, vertical struts and inclined struts. In addition, the cross section of the lattice strut will be circular, resulting in similar toolpaths for vertical struts and inclined struts [START_REF] Tang | Lattice Structure Design and Optimization With Additive Manufacturing Constraints[END_REF]. Therefore, the vertical strut can be regarded as a special case of inclined struts with a 90 degree incline. Consequently, there are two lattice strut groups in this experiment: the horizontal group and the inclined group as shown in Figure 2. The controlled geometrical data include strut diameter for both groups, strut overhanging length for only the horizontal group, and strut incline angle for the inclined group.

Failure Method

In the evaluation of the printing quality, is defined to represent the difference between the maximum and minimum thickness on a single strut. It is calculated by [START_REF] Deshpande | Effective properties of the octet-truss lattice material[END_REF] The definition of and for both type of struts is shown in Figure 3. In general, the parts with the smallest difference had geometries closest to the modeled shape. However, because the levels tested a wide range of printing parameters, there were runs where the geometry was not printable or badly printed that cannot be measured as shown in Figure 4, resulting in missing information. Four different failure methods account for the missing data: omit the missing information, set to the maximum deviation of the parts of the same geometry, to the part diameter, and to twice the part diameter. These failure methods may overestimate or underestimate the quality of the failed strut. Careful comparison between these methods is necessary to find the optimal process parameters in the fabrication of lattice struts.

Design of Experiment

In the experiment, the material data of ME is Acrylonitrile Butadiene Styrene (ABS) with no grade. Process data of ME include an Ultimaker 2 Extended+ for the machine, and FDM process for fabrication strategy. Based on the design parameters in Section 2.1, the lattice struts are divided into two groups: inclined group and horizontal group. Detailed information about the design parameters are summarized in Table 1. Before selecting the controlled process parameters, preliminary experiments are conducted to investigate the influence of process parameters on the manufacturing quality of lattice structures.

During preliminary experimentation, inclines and horizontal struts are printed under various process conditions to identify the most significant parameters. The parameters which created significant variations between parts are nozzle temperature, fan speed, print speed, and layer height. For each parameter, different levels are tested to find the range and levels to test. The range of the parameters are located at the limits of manufacturability, resulting in poor parts. In some cases, the machine's limitations define these limitsnozzle temperature hit a maximum at 255ᵒC, and fan speed can only be set between 0 and 100%. The intervals are chosen to show a significant difference in part quality between levels. After preliminary testing, four printing parameters (2 with 4 levels, 1 with 3 levels, and 1 with 2 levels) were considered. Interactions between these parameters were not considered. The control parameters and their levels are summarized in Table 2. Other parameters held constant during the manufacturing process and are listed in Table 3. These parameters have little impact on part geometry during preliminary testing.

An orthogonal array is modified to test the design parameters. The initial array, L16, can hold a maximum of 215 or 45 factors. The linear graph in Figure 5 is used to merge nine 2 level columns into three 4 level columns [START_REF] Taguchi | Taguchi's Quality Engineering Handbook[END_REF]. This is done by combining the 2 level columns specified at the nodes of the linear graph, forming one 4 level column located in the column number specified by the line joining the nodes. To create the 3 level factor, dummy treatment changes 'level 4' to 'level 1*' [START_REF] Roy | A primer on the Taguchi method[END_REF]. Level 1 was chosen to be repeated for more runs because a fan speed of 0% is an absolute measure, whereas 50% and 100% are relative values that depend on the printer used. The orthogonal array is shown in Table 4. Each set of parameters are used to print two types of structures: bridges with varying diameter and length, and inclined parts with varying diameter and angles listed in Table 1. Design parameters are tested with the full factor method. There are 9 horizontal samples and 12 inclined samples in each set of process parameters and each set is printed 3 times.

Results and Discussion

4.1 Analysis of S/N Ratio S/N ratios measure the variation in the data. Since the best case is to have no difference between the maximum and minimum dimensions of the data, the target value is 0. Therefore, the S/N ratio of is calculated by the lower-the better formula [START_REF] Roy | A primer on the Taguchi method[END_REF],

(

The results are analyzed according to their geometry: inclines and horizontal struts. The process and design parameters varied for horizontal struts are temperature, print speed, fan speed, layer height, diameter, and length. The parameters varied for inclines are temperature, print speed, fan speed, layer height, angle, and diameter. The level response of each factor level is found by taking an average of the S/N ratios within that factor level.

(

) 3
In addition, the response range for each factor was calculated by

Response range = Level Response max -Level Response min [START_REF] Zhang | Ultralight X-type lattice sandwich structure (I): Concept, fabrication and experimental characterization[END_REF] The main effects of different process parameters at different levels are shown in Figure 6 for inclined struts and Figure 7 for horizontal struts. A higher S/N ratio indicates better printing quality. The main effects charts demonstrate that the failure methods of taking maximum deviation, strut diameter, and twice the strut diameter follow similar trends; while the omitted method does not. This is because the failed parts have extremely poor printing quality which is not reflected when results are omitted. The omission will underestimate the negative influence of process parameters on those failed parts. Therefore, taking the equal to maximum deviation, strut diameter, and doubling the strut diameter are more reasonable approximations to treat missing data due to failed prints and will be considered to find the optimal process parameters. However, there are still some inconsistencies between these three failure methods for some parameters, so additional experiments are conducted to further investigate those parameters and will be discussed in the next subsection. The optimal levels of the process parameters can be selected from Figure 6 and Figure 7, indicated by the levels which produce the highest S/N ratio values. For inclined struts, the trends for nozzle temperature, printing speed and fan speed are the same for all the failure methods. That means the optimal level for those parameters can be determined by the failure methods. The optimal levels are level 4 or 255 for nozzle temperature, level 2 or 1200mm/min for print speed, and 50% for fan speed. The best level for layer height cannot be determined because the trends for the S/N value are different in the three failure methods. This indicates that some failure methods may overestimate or underestimate the influence of the layer thickness on inclined struts.

The print failure of struts interferes with the determination of optimal process parameters. The failure is because the OA cannot guarantee combinations of good printing quality. However, since the other three optimal process parameters have been found, the three settings can be used to re-fabricate the inclined struts with better printing quality regardless of layer thickness. This will eliminate the influence of the failed samples, and the optimal level of layer thickness for inclined struts can be found. This additional experiment is conducted in the confirmation test to further investigate the undetermined process parameters.

As for horizontal struts, three parameters: nozzle temperature, layer height and printing speed can be determined by failure methods while the fan speed shows some inconsistency among failure methods. Through finding the highest S/N ratio for those three process parameters in Figure 7, it is found that the best level for nozzle temperature is level 3 or 245 , for printing speed is level one or the slowest speed, and for layer height is level 2 or 0.2mm printing thickness. However, for the fan speed, different failure methods show different trends, for the reasons explained above. Therefore, additional confirmation testing is required to determine the optimal fan speed for horizontal struts.

Confirmation test

In Section 4.1, the main effect charts did not show consistency for the layer thickness of inclined struts, and fan speed of horizontal struts between the three different failure methods. Additional tests are conducted to further investigate the optimal level of layer thickness for inclined struts and fan speed for horizontal struts. Five additional tests are designed and the process parameters of each test are shown in Table 5. For inclined struts, the layer height is set to 0.1mm and 0.2 mm, and for horizontal struts, the fan speed was set to 0%, 50% and 100%. The other parameters were set at the optimal level for inclined and horizontal struts respectively as obtained in the S/N Ratio analysis. The optimal level chosen will minimize print failure in these five tests. The results of these tests are shown in Figure 8. A higher S/N ratio refers to a better print quality.

It can be concluded that the 0.1mm layer height is better than 0.2mm layer height for inclined struts. This is because slicing over a smaller layer height will reduce the overhang length of the layer. Additionally, the 0% fan speed is better than 50% and 100% for horizontal struts. During the print, the first layer is very weak because of the large overhang, and the fan's airflow in the printing chamber will cause oscillation of the unsolidified layer. Therefore, reducing airflow without a fan will result in better printing quality for the horizontal struts. Via S/N ratio analysis and confirmation test, the optimal level of each process parameter is obtained and summarized in Table 6. It is found from the result that best process parameters for different types of the lattice struts are totally different, due to the differing geometrical characteristics between horizontal struts and inclined struts. Therefore, if the parameters are dynamic during the printing process to optimize for different types of lattice struts, the printing quality of the entire structure can be further improved. In addition, tests No.1 and No.3 can be regarded as the confirmation test for inclined struts and horizontal struts because all the process parameters are optimum. It can also be concluded that the S/N ratio of the optimized process parameter is larger than the S/N ratio of the L16 array, which means that the optimized result improves the printing quality of both horizontal and inclined struts.

ANOVA

Analysis of variance for means is performed on the data to find the most significant process parameter for both inclined and horizontal struts. Three sets of ANOVA tables are calculated for each geometry type based on three failure methods which are maximum deviation, strut diameter, and doubling the strut diameter. Interactions are not considered as factors were assumed to be independent. Degrees of freedom for factor A is calculated by

= m -1 ( 5
)
Where m is the total levels of A. The total degrees of freedom is the number of observations, subtracted by 1. The number of samples are 576 and 432, for inclines and horizontal struts respectively. Therefore, dfTot inclines = 575, and dfTot hor = 431. Finally, degrees of freedom for error is calculated by dfE = dfTot - [START_REF] Rosen | Computer-aided design for additive manufacturing of cellular structures[END_REF] where n denotes the total number of factors, and dfA i is the degree of freedom for each factor. The mean is calculated for each set of replicated trials, where the levels for each factor are held constant. This is calculated by i. = [START_REF] Ozdemir | Energy absorption in lattice structures in dynamics: Experiments[END_REF] where n is the number of observations values within the level. The grand mean is calculated by

.. = (8)
where i and j represent all the factors and their levels respectively. The sum of squares of factor A is obtained by [START_REF] Christensen | Analysis of variance, design, and regression: applied statistical methods[END_REF] SS A = 2 [START_REF] Brooks | Design of conformal cooling layers with self-supporting lattices for additively manufactured tooling[END_REF] In this case, N is the number of observations at each factor level. The fan speed parameter requires unbalanced ANOVA (Eq. 10) because the dummy variable used doubles the number of observations for a fan speed of 0%.

SS A = 2 [START_REF] Khanoki | Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem[END_REF] where is the number of observations of each factor level i. Then the mean sum of squares can be obtained: [START_REF] Masood | The design and manufacturing of porous scaffolds for tissue engineering using rapid prototyping[END_REF] The total sum of squares is calculated by Eq. 12 for each set of data: inclines and horizontal struts SS T = 2 [START_REF] Cheah | Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 1: Investigation and Classification[END_REF] The sum of squares error is given by

SS err = SS T - ( 13
)
where n is the total number of factors and is the mean sum of squares for each factor. The F ratio of factor is calculated by

F ratio A = (14)
P-contribution, is the mean sum of squares of a factor divided by the total mean sum of squares of all the factors, including error. It is calculated by Eq. 15.

P A = ( 15
)
where n is the total number of factors, and is the mean sum of squares for each factor. The results of the AONVA through three failure methods are shown in Figure 9 and Figure 10 for inclined struts and horizontal struts, respectively. The contributions of each factor for horizontal struts and inclined struts are different. Small error contributions indicate that it is reasonable to assume no interactions between factors. Although the P-value varies slightly for different failure methods, the process parameters which gives the maximum P-value do not change with failure method. Furthermore, the rank of the influence is almost the same, except ranks 3 and 4 in the maximum deviation method for horizontal struts. However, it can be concluded that these parameters have little influence on the printing quality of horizontal and vertical struts.

The average P values demonstrate that for inclines, the contribution of fan speed is 81.00%, nozzle temperature is 11.97%, print speed is 3.05%, and layer height is 1.42%. For horizontal struts, the contribution of layer height is 69.84%, temperature is 15.14%, print speed is 11.52%, and fan speed is 1.74%. Therefore, the most significant process parameters are fan speed for inclined struts and layer height for horizontal struts. The reason is that for inclined struts, the overhang area can be cooled down quickly by the fan which maintains the overhang's shape. Without a fan, the overhang area remains soft and will sag due to the gravity. As for horizontal struts, the first layer of the overhang is very important. With a larger printing thickness, the first layer of the overhang is more robust to support the following layers. Therefore, these two process parameters are significant for inclined struts and horizontal struts respectively. Figure 11 summarizes average S/N value ranges, in which a higher value indicates greater influence on the printing quality. By comparing ANOVA and S/N response range, the ranks for the S/N value range and P contribution are similar, and the largest range between the lowest and highest S/N values in all levels of the factor correspond to the largest contribution of that factor. It can also be concluded that the most significant process parameter for both types of struts obtained by the S/N value range is the same as obtained by ANOVA analysis. Therefore, both S/N value range and ANOVA analysis can be used to determine the significance of each parameter. The influence of these parameters on the mechanical property of lattice structures will be discussed in the next subsection. After S/N ratio analysis and ANOVA, the optimal process parameters for both horizontal struts and inclined struts are obtained, and the most significant parameter for each type of strut is determined. However, these analyses only focus on single struts and dimensional accuracy. To understand the influence of the process parameters on the entire lattice structure, the compression test is conducted to evaluate the mechanical performance of lattice structure fabricated by different process parameters. This test also verifies whether process parameters optimized by dimensional accuracy improves mechanical performance. In this experiment, geometrical data is set to be constant. All the lattice structures have the same dimension with a cubic-center topology with horizontal, inclined, and vertical struts. The length of the unit cell is 15mm and the strut thickness is 2mm. The lattice structure has three unit cells along each direction, as shown in Figure 12(a). The relative density is 12.8%.

The lattice structure is fabricated with the process parameters in Table 4, and each run is shown in Figure 12(b). Half the fabrications have failed due to the process parameters in OA. If the optimization process had been directly applied on the entire lattice structure instead of single lattice struts, half the data would not be obtainable for the S/N ratio analysis and ANOVA. This demonstrates the benefit of using single struts, as most struts are still measurable and the missing data is only a small portion of the whole. Via the failure methods proposed in this research, the S/N ratio and ANOVA methods can find the optimal process parameters and the most significant process parameters. In contrast, manufacturing error accumulates in an entire lattice structure at each layer, which leads to the failure of subsequent struts. Therefore, it is difficult to optimize the process parameters due to plenty of failed fabrications.

To verify the improvement of optimization process, the lattice structure is also fabricated by the optimized process parameters found from S/N ratio analysis and ANOVA. Because optimal levels of horizontal struts and inclined struts are different, overall optimal parameters have to be determined. From ANOVA, the most significant parameter is fan speed for inclined struts and layer thickness for horizontal struts. Therefore, the fan speed is set to 50%, the best level for inclines; and the layer thickness set to is 0.2mm, the best level for horizontal struts. Printing speed has little influence on the inclined struts, so 600mm/min is selected because it is the best level for horizontal struts. The temperature has equivalent significance for both types of struts and an average value of the two optimal temperatures is chosen, which is 250ᵒC. The overall optimal parameters create a lattice structure, whose mechanical performance will be compared to the lattice structures fabricated by process parameters in the Taguchi array.

Test result and discussion

The compression test is conducted by a TestResources 313 Universal Test Machine as shown in Figure 12(c) at a strain rate of 2mm/min. The loading direction is perpendicular to the build direction of the FDM machine coordinate system for two reasons. The first is that the bonding strength between each layer of the lattice structure can be tested in this direction. Because loading along the build direction would compress each layer, which does not expose the weak bonding strength between layers. The second reason is that the horizontal strut deflects during the fabrication process, which is vulnerable to bulking. The compression load perpendicular to the build direction causes bulking on horizontal struts so that manufacturing defects are more clearly seen.

The results of the compression test are shown in Figure 13, with no test results for the failed lattice structures. The effective elastic modulus and the ultimate strength are summarized in Figure 14. It can be concluded that lattice structures fabricated with different process parameters are likely to exhibit different mechanical properties. However, the lattice structure fabricated by the optimized process parameters exhibits the highest effective Young's modulus and ultimate strength. Also, Lattice structures from Runs 2, 3 and 13 demonstrate better mechanical performance compared to the other runs. This is because all these runs have a 0.2mm layer thickness, the most significant parameter at the optimal level for horizontal struts. Furthermore, Runs 2 and 13 have 50% fan speed, which is the most significant parameter at optimal level for inclined struts; Run 3 with its 100% fan speed had lower effective Young's modulus and ultimate strength compared to Runs 2 and 13. In addition, while lattice structures are successfully fabricated in Runs 6, 7, 9 and 12, they exhibit worse mechanical performance compared to Runs 2 and 13 because their 0% fan speed is the worst level for inclined struts. Therefore, the optimal level of process parameters from S/N ratio analysis, and most significant process parameters from ANOVA can be used to improve the mechanical performance of as built lattice structure.

Another conclusion is that all the lattice structures fabricated with 0.1mm layer thickness fail except in Run 11 where the other process parameters are exact or close to the optimal level. As a result, layer thickness is the most significant parameter in the fabrication of lattice structure by FDM process.

One main failure mechanism in the compression test of lattice structures is fracture between layers of the vertical strut as shown in Figure 12(c). A higher nozzle temperature will strengthen the bond between each layer in the FDM process. The Optimized Run has the same process parameter levels as Run 2, except a nozzle temperature that is 25ᵒC higher, which is reflected in a 12% higher ultimate strength in the Optimized Run compared to Run 2.

Another important failure mechanism in Figure 12(c) is the bulking of the horizontal strut. Some horizontal struts are badly fabricated with large deflection, making them vulnerable to bulking when the compression force is along their orientation. This can be seen by comparing Run 13 and the Optimized Run. While they both have the same layer thickness and fan speed, the Optimized Run's 600mm/min printing speed is the best level for horizontal struts and Run 13 uses 1200mm/min. In addition, the nozzle temperature in the Optimized Run is 250ᵒC which is closer to the optimal nozzle temperature for horizontal struts. Consequently, the effective Young's modulus and ultimate strength in the Optimized Run are 13% and 8% higher respectively than those in Run13.

Figure 13 The result of the compression test Figure 14 The comparison of the effective young's modulus and ultimate strength of lattice structures fabricated with different process parameters

Conclusions

In this paper, the process parameters of FDM have been optimized for lattice structures. The concept of the Manufacturable Element is proposed to link the geometrical information of lattice structures and the manufacturing process. The lattice structure is deconstructed into horizontal and inclined struts. Taguchi method is implemented to investigate the optimal process parameters for both types of struts. Failure methods are used to represent the data of failed fabrication. It is shown that except for omitted method, the other three failure methods can well represent the missing data. S/N ratio analysis and ANOVA has been used to optimize the process parameter.

The result shows that the most significant process parameter for inclined struts is fan speed; but for horizontal struts it is layer height. The optimal values for inclined struts are 255˚C nozzle temperature, 1200mm/min print speed, 50% fan speed and 0.1mm layer height. However, for horizontal struts, the optimum is 245˚C nozzle temperature, 600mm/min print speed, 0% fan speed and 0.2mm layer height. Furthermore, compression tests have been conducted to investigate the mechanical performance of lattice structures fabricated by different process parameters. Experimental result shows that the proposed optimization method can improve the mechanical performance of lattice structure, even though the optimization is based on the printing quality of lattice struts. All fabrications in this research use constant process parameters. Nevertheless, the S/N ratio analysis shows that optimized process parameters are different for different features. Future work will investigate the printing quality of lattice structures fabricated by FDM via dynamic process parameters.

Figure 2 .

 2 Figure 2. Examples of horizontal group and inclined group, L is the horizontal length, θ is the inclined angle, D is the diameter of both struts [30].

Figure 3 .

 3 Figure 3. the difference between the minimum thickness and the maximum fabricated thickness for (a) horizontal strut and (b) inclined strut [30].

Figure 4 .

 4 Figure 4. Poorly fabricated struts that are not measurable

Figure 5 .

 5 Figure 5. Linear graph used to merge nine 2 level columns, into three 4 level columns[START_REF] Taguchi | Taguchi's Quality Engineering Handbook[END_REF].

Figure 6 .Figure 7 .

 67 Figure 6. Main effects charts for the effect of process parameters on average S/N Ratio for inclines

Figure 10 P

 10 Figure 10 P values for horizontal struts for three failure methods respectively

Figure 12

 12 Figure 12 The lattice structure for compression test, (a) the geometrical model, (b) the as built lattice structure by the process parameters in the Taguchi array, (c) the failure of the lattice structure during the compression test.

Table 1 .

 1 Design parameters and their levels

	Geometry Group Design Parameter	Units Level 1 Level 2 Level 3 Level 4
	Inclines	Angle from horizontal ˚	15	30	60	90
		Diameter	mm	2	4	6	-
	Horizontal Struts Length	mm	10	30	50	-
		Diameter	mm	2	4	6	-

Table 2 .

 2 Controlled printing parameters and their levels

	Symbol	Printing Parameter	Unit	Level 1	Level 2	Level 3	Level 4
	A	Nozzle Temperature	˚C	225	235		245	255
	B	Print Speed	mm/s	600	1200		1800	2400
	C	Fan Speed	%	0	50		100	-
	D	Layer Height	mm	0.1	0.2		-	-
			Table 3. Non-design process parameters
	Machine	Bed	XY Travel	Z Speed Layer	Retraction	Retraction
			Temperature	Speed		Width	Distance	Speed
	Ultimaker 2	100	3900	1000	0.48mm 4.5mm	1800
	Extended+		mm/min	mm/min			mm/min

Table 4 .

 4 Experimental runs with an L16 (42 x 31 x 21) orthogonal array

	Run	A	B	C	D
	1	1	1	1	1
	2	1	2	2	2
	3	1	3	3	2
	4	1	4	1*	1
	5	2	1	3	1
	6	2	2	1*	2
	7	2	3	1	2
	8	2	4	2	1
	9	3	1	1*	2
	10	3	2	3	1
	11	3	3	2	1
	12	3	4	1	2
	13	4	1	2	2
	14	4	2	1	1
	15	4	3	1*	1
	16	4	4	3	2

Table 5 .

 5 Process parameters in additional tests

		Test No. nozzle temp print speed fan speed layer height
		1				0.1
	Inclines	2	255	1200	50	0.2
		3			0
	Horizontals	4	245	600	50	0.2
		5			100

Table 6 .

 6 Optimal process parameters for inclined struts and horizontal struts

		13.3						7.6
	Ratio	13.2 13.25					Ratio	7.2 7.4
	S/N	13.15					S/N	7
	Average	13 13.05 13.1					Average	6.4 6.6 6.8
		12.95						6.2
		0.05	0.1	0.15	0.2	0.25		0	20	40	60	80	100	120
			Layer Height (mm)					Fan Speed (%)
			(a) inclined strut					(b) horizontal strut
				Figure 8. The S/N result of additional tests
					nozzle	print	fan		layer
					temp		speed	speed		height
			Inclined struts	255		1200	50			0.1
			Horizontal struts	245		600	0			0.2

Corresponding author, E-mail: yaoyao.zhao@mail.mcgill.ca, Tel: +1 (514) 398-2523

Acknowledgement

This research work is supported by National Sciences and Engineering Research Council of Canada Discovery Grant RGPIN436055-2013.