Sébastien R David

Dris Ihiawakrim

Robert Regis

Valérie A Geoffroy
email: valerie.geoffroy@unistra.fr

Efficiency of pyoverdines in iron removal from flocking asbestos waste: an innovative bacterial bioremediation strategy

Keywords:

The use of asbestos-containing products has been banned in many countries since the beginning of the 80's due to its carcinogenic properties. However, asbestos is widely present in private and public buildings, resulting in the need to process a vast amount of asbestos-containing waste.

Among the current technologies for the destruction of asbestos fibers, biodegradation by fungi, lichens, and, more recently, bacteria has been described. We previously reported the involvement of the bacterial siderophore pyoverdine in the release of iron from the two asbestos groups, serpentines and amphiboles. Among the large diversity encountered in the pyoverdine family, we examined whether these siderophores can alter flocking asbestos waste as well. All the tested pyoverdines were efficient in chrysotile-gypsum and amosite-gypsum weathering, although some exhibited higher iron dissolution. Iron was solubilized by pyoverdines from Pseudomonas aeruginosa and mandelii in a time-dependent manner from chrysotile-gypsum within 24 hours.

Renewal of pyoverdine-containing supernatant every 24 or 96 hours allowed iron removal from chrysotile-gypsum at each cycle, until a limit was reached after 42 days of total incubation. Moreover, the dissolution was concentration-dependent, as demonstrated for the pyoverdine of

Introduction

Asbestos has been extensively used because of its excellent properties, such as thermal conductivity, high mechanical strength, resistance to chemical attacks, and low cost. Asbestos is composed a group of fibrous silicate minerals that belong to the serpentine and amphibole families. Amphiboles can contain up to 36% iron by weight, whereas the serpentine form of asbestos contains only 2 to 3% iron by weight [START_REF] Chao | Effect of long-term removal of iron from asbestos by desferrioxamine B on subsequent mobilization by other chelators and induction of DNA singlestrand breaks[END_REF]. Iron can be present as part of the mineral structure in the amphibole or as an exchangeable element in the chrysotile [START_REF] Douguet | Effets sur la santé des principaux types d'exposition à l'amiante[END_REF][START_REF] Virta | Asbestos: Geology, mineralogy, mining, and uses[END_REF]. The iron encountered in asbestos is able to catalyze many reactions, such as lipid peroxidation, oxygen consumption, ROS formation, and DNA damage, precursors for tumor development [START_REF] Toyokuni | Mechanisms of asbestos-induced carcinogenesis[END_REF][START_REF] Valko | Redox-and non-redox-metalinduced formation of free radicals and their role in human disease[END_REF]. The various types of toxic effects in humans include fibrogenesis and stomach, ovarian, and lung cancer [START_REF] Scherpereel | Amiante et pathologie respiratoire[END_REF]. Due to the associated health problems, asbestos was banned after more than 30 years of intense use. As a consequence, we are confronted with the generation of a vast amount of asbestos-containing waste (ACW).

Today, most waste is packed and deposited in controlled landfills, an inexpensive technique that does not remove the toxicity or potential health risk of waste related to fiber inhalation (Spasiano and Pirozzi, 2017). ACW treated by stabilization aims to reduce the fibers released, without modifying the crystalline structure, and ends up in landfills. The second type of treatment, called inertization, consisting of thermal treatment (vitrification or microwave), or hydrothermal, chemical, or mechanochemical treatment, involves the total transformation of the fibers, providing an inert and harmless material, considered to be a resource. However, such thermal treatment is expensive due to energy consumption and may release emissions into the atmosphere. Chemical treatment requires chemical products and their disposal, but has allowed confirmation of the potential Mg released [START_REF] Paolini | Asbestos treatment technologies[END_REF]. At the laboratory scale, bioremediation experiments have been carried out on raw asbestos using various organisms (fungi, lichens, or bacteria) or metabolites (organic acids or siderophores), whereas few studies have focused on ACW. A few studies have focused on asbestos-cement waste, whereas none have investigated biological treatment of flocking asbestos waste (FAW), of which the matrix composition differs, containing gypsum to allow flocking to walls instead of cement. For example, lichens are able to cover asbestos-cement roofs and modify the surface reactivity, leading to bioavailable iron and magnesium liberation [START_REF] Favero-Longo | Lichens on asbestos-cement roofs: Bioweathering and biocovering effects[END_REF]. Moreover, modification of the fibers has been described, by which they became amorphous, due to oxalic acid production [START_REF] Favero-Longo | Chrysotile asbestos is progressively converted into a non-fibrous amorphous material by the chelating action of lichen metabolites[END_REF] and nitrous and nitric acid produced by nitrifying bacteria, such as Nitrosomonas and Nitrobacter, inducing corrosion of a cement-roof, thus increasing porosity and reducing the strength of the material [START_REF] Wasserbauer | Nitrifying bacteria on the asbestos-cement roofs of stable buildings[END_REF].

Moreover, [START_REF] Wang | Bacteriological challenges to asbestos cement water distribution pipelines[END_REF][START_REF] Wang | Biodeterioration of asbestos cement (AC) pipe in drinking water distribution systems[END_REF]) also highlighted the porous structure of cement pipes after microorganism colonization. They showed that acid-producing bacteria together with slimeforming and heterotrophic bacteria contribute to corrosion of the inside surface of asbestoscement pipes of water distribution systems. Innovative bio-chemical processes have been recently proposed, in which the cement phase is dissolved by lactic acid produced by Lactobacilli or by dark fermentation, before hydrothermal end treatment [START_REF] Balducci | Process for treating an asbestos containing material[END_REF]Spasiano et al., 2017). Siderophore production is a common mechanism shown in fungal and bacterial weathering of native asbestos, leading to iron dissolution from fibers [START_REF] Daghino | Fungal weathering and implications in the solubilization of metals from soil and from asbestos fiber[END_REF][START_REF] Rajkumar | Biotechnological applications of serpentine soil bacteria for phytoremediation of trace metals[END_REF]. Siderophores are a well-known strategy that many living organisms use to access iron, an essential element for growth. In mineral-bacterial weathering, various siderophores have been implicated in iron dissolution, resulting in leaching of the material, and pyoverdine (PVD) has been described to interact with iron-bearing silicates, such as smectite [START_REF] Ferret | Siderophore-promoted dissolution of smectite by fluorescent Pseudomonas[END_REF] and municipal waste-bottom ashe [START_REF] Aouad | Interactions between municipal solid waste incinerator bottom ash and bacteria (Pseudomonas aeruginosa)[END_REF]. However, this mechanism has not yet been investigated on ACW. We thus investigated the impact of the bacterial siderophore PVD, produced by fluorescent Pseudomonas, on FAW. In building construction, two types of FAW have been described, varying in texture, thickness, and density.

The first type used in this study contained 50 to 90% chrysotile fibers ((Mg 3 Si 2 O 5 (OH) 4 ) and 10 to 50% gypsum (CaSO 4 , 2H 2 O), whereas the second contained 5 to 30% chrysotile fibers and 95 to 70% gypsum. Amphibole fibers, such as amosite ((Fe, Mg) 7 Si 8 O 22 (OH) 2 ), have also sometimes been combined with FAW. The ability of pyoverdine to extract iron from fiber has already shown on chrysotile and amphibole raw asbestos. However, two main difficulties such as the iron pollution present in the matrix and the fiber accessibility may interfere with the iron extraction by pyoverdine.

Among the 100 PVDs so far described by siderotyping fluorescent Pseudomonas, their affinity for iron is not yet known. We therefore tested several representatives from the PVD laboratory collection to determine their ability to scavenge iron from ACW and selected the most efficient. Iron removal was tested as a function of PVD concentration and the optimum time for FAW alteration determined. Long-term alteration experiments by the best identified PVDs determined the iron extraction limit.

Experimental

Asbestos wastes preparation

Two types of flocking asbestos wastes were used, chrysotile-gypsum and amosite-gypsum.

These wastes come from the asbestos removal site of Jussieu University of Paris and kindly provided by the Mediterranean Company of Zeolites (SOMEZ). To obtain amosite-gypsum, FAW samples were incubated in an acidic bath with sulfuric acid (8 mol/L), until total dissolution of the chrysotile brucite layer. All asbestos samples (0.2 g) were sterilized by autoclave (121°C for 20 min) and incubated at 70°C for 14 days before experiments. Before each experiment, asbestos samples were washed with 20 mL of sterile succinate medium to remove free Fe and Mg.

Bacterial strains

Bacteria used in this study were listed in table 1. Strains were stored in LB-20 % glycerol stock at -80°C. Pseudomonas cells were grown routinely overnight at 30°C in Luria Bertani medium (LB) under shaking condition (220 rpm).

Production of pyoverdines

1 mL of overnight LB culture of Pseudomonas strains was centrifuged (3 min at 9871 g).

For iron starved cells, the iron-deficient succinate medium (composition in g.L -1 : K 2 HPO 4 , 6.0; KH 2 PO 4 , 3.0; (NH 4 ) 2 SO 4 , 1.0; MgSO 4 .7H 2 O, 0.2; sodium succinate, 4.0; pH adjusted to 7.0 by addition of NaOH), sterilized by 0.2 µm filtration, was used [START_REF] Meyer | The fluorescent pigment of Pseudomonas fluorescens: Biosynthesis, purification and physicochemical properties[END_REF]. The pellet, washed twice with 1 ml of sterile succinate medium, was suspended in 1 ml of sterile succinate medium and inoculated in 15 mL of sterile succinate medium, incubated at 30°C under shaking condition (220 rpm). After 24 h of growth, 7.5 mL of this culture was transferred in an Erlenmeyer flask containing 1 L of sterile succinate medium. After 24 h of incubation at 30°C under shaking condition (220 rpm), the culture was centrifuged (2664 g for 40 min). The supernatant was filtered twice with glass microfibre filters (Whatman, GF/C) and once on nitrocellulose filter (0.45 µm porosity). To determine pyoverdine concentration, OD 400 was measured with a Specord 205 spectrophotometer (Analytik Jena). When needed, the PVD concentration was adjusted with purified PVD according to the method described so far.

Siderophore containing supernatant was loaded, after acidification (pH 6.0), on XAD-4 column, washed with two volume of purified water and eluted with one volume of 50% ethanol. The eluate was concentrated under vacuum on a rotary evaporator and lyophilized.

Asbestos dissolution by pyoverdines

To evaluate the effect of various PVDs on the dissolution of iron from chrysotile-gypsum and amosite-gypsum, 20 mL of PVD-containing supernatants adjusted to 100 µM were incubated with materials in 50 mL Falcon tubes. After 24 h of incubation at 30°C under shaking condition (220 rpm), the assays were centrifuged 30 min at 9871 g to recover supernatants. Assays were done in 3 to 5 replicates.

Kinetics of iron dissolution from chrysotile-gypsum in 20 mL of PVD-containing supernatant of P. aeruginosa and P. mandelii respectively adjusted to 100 µM were followed on 24 hours with regular sampling of the solution at 1, 2, 4, 6, 8 and 24 h. Assays were done in 5

replicates.

Long-term alteration of chrysotile-gypsum by PVD-containing supernatant of P. aeruginosa and P. mandelii was performed by renewal cycles at 30°C under shaking condition (220 rpm). Nine cycles of 24 hours and seven cycles of 96 h were realized in the presence of 100 µM of PVD-containing supernatant, followed by a 24 and a 96 h cycles with 200 µM of PVDcontaining supernatant. Assays were done in 5 replicates.

To determine the effect of pyoverdine concentrations produced by P. mandelii on iron and magnesium dissolution from chrysotile-gypsum, material was incubated during 48 h at 30°C under shaking condition (220 rpm) with 20 mL of supernatant adjusted to 25, 50, 100, 150 and 200 µM. Assays were done in 5 replicates.

Materials were eliminated from supernatants by filtration (0.22 µm porosity). Iron and magnesium content were measured depending on the experiment.

Determination of Fe and Mg contents

In order to determine iron content, we used the bathophenanthroline method, which is a sensitive colorimetric method for determining ferrous iron content. To determine the total iron, ferric iron was converted to ferrous iron by thioglycolic acid. Each sample was analyzed in triplicate. 20 µL of sample were dispensed into each well of a 96-well plate (Greiner, PS flatbottomed microplate). 40 µL of saturated sodium acetate (5.5 M) (Sigma-Aldrich), 80 µL of cold distilled water, 10 µL of a thioglycolic acid solution diluted 10 times in water (Sigma-Aldrich)

and 10 µL of bathophenanthroline (5 mg.mL -1 ) (Sigma-Aldrich) were additionned per well.

After shaking, microplates were stored overnight at 4°C. Absorbance was measured at 535 nm in a Tecan microplate reader (Infinite M200, Tecan) and iron concentration (mg.L -1 ) was determined by reference to a standard curve.

For the magnesium content, calmagite method was used. Magnesium formed a coloured complex with calmagite. EGTA (Ethylene Glycol Tetraacetic Acid) was used to eliminate any calcium interference. Each sample was analyzed in triplicate. To prepare the reactive solution, one volume of reagent 1 (1 mol.L -1 of 2-Methyl-2-Amino-1-Propanol and 215 µmol.L -1 of EGTA) with one volume of reagent 2 (300 µmol.L -1 of calmagite) were mixed. 3 µL of sample were dispensed into each well of a 96-well plate (Greiner, PS flat-bottomed microplate) and 300 µL of reactive solution mixed were added. After shaking and 30 seconds of incubation, absorbance was measured at 500 nm in a Tecan microplate reader (Infinite M200, Tecan) and magnesium concentration (mg.L -1 ) was determined by reference to a standard curve.

STEM-EDX of asbestos fibers

TEM (Transmission Electron Microscopy) images were recorded with a JEOL 2100 microscope, with a 200 kV potential applied on a LaB6 filament as an electron source.

Resolution of the TEM is 0.21 nm. TEM mapping was performed in STEM (Scanning transmission electron microscopy) mode (resolution 2 nm) and using an SSD-EDX (Silicon Drift

Detector-Energy Dispersive X-ray) spectrometer to determine the chemical composition.

Statistical analysis

Results presented in all figures correspond to mean values of three to five replicates.

Significant statistical differences among values were determined using Kruskal-Wallis test (RStudio v1.0.153) followed by a Conover post-hoc analysis. Values with the same letter are not significantly different at p = 0.05.

Results and discussion

Efficiency of pyoverdines on iron removal from flocking asbestos wastes

PVDs, yellow-green fluorescent pigments, are composed of three moieties: (i) a peptide chain varying in the nature, number, and order of amino acids, (ii) a dihydroxyquinoline chromophore, conferring the yellow-green color of the molecule, and (iii) an acyl chain radical made of dicarboxylic acid residue which can be either succinate, malate, or their amide forms, or alpha-ketogluratate or glutamate, depending on the producing strain and growth conditions.

Based on these structural differences, PVDs have been purified from various Pseudomonas strains to obtain a large family composed of more than 100 different structures, depending on their peptide chain and radical R [START_REF] Meyer | Siderotyping of fluorescent pseudomonads: Characterization of pyoverdines of Pseudomonas fluorescens and Pseudomonas putida strains from Antarctica[END_REF]. PVD binds to Fe 3+ in a 1:1 stoichiometry with a stability constant for Fe(III) of approximately 10 32 M -1 for PVD produced by P.

aeruginosa PAO1 [START_REF] Albrecht-Gary | Bacterial iron transport: Coordination properties of pyoverdin PaA, a peptidic siderophore of Pseudomonas aeruginosa[END_REF]. From this bank, we selected nine PVDs produced by various Pseudomonas species based on their different isoelectrofocusing profile related to the length, nature, and presence of cycle rings in the peptide chain (Table 1). These selected PVDs were tested to investigate potential differences in their ability to chelate iron. We previously showed that purified PVDs can extract iron from the three native asbestos types, chrysotile, amosite, and crocidolite, and with the same efficiency as PVD-containing supernatant [START_REF] David | Iron removal from raw asbestos by siderophores-producing Pseudomonas[END_REF]. Therefore, we used PVD-containing supernatants to determine the effect of these siderophores on FAW, chrysotile-gypsum, and amosite-gypsum (Fig. 1). The nine selected PVDs (at a concentration of 100 µM) were incubated with each FAW for 24 h. The control medium (sterile succinate medium) had no visible effect on iron dissolution from waste, whereas all tested PVDs exhibited significant iron extraction from both types of waste, ranging from 0.24 mg.L -1 to 1.22 mg.L -1 iron dissolved for chrysotile-gypsum and 0.63 to 5.39 mg.L -1 for amositegypsum. For chrysotile-gypsum, 25% of the siderophores were in the PVD-Fe complex form, whereas PVD was almost saturated at 100% for amosite-gypsum, a factor that may have limited material weathering. A higher amount of extracted iron was obtained for amosite-gypsum, which is consistent with the chemical composition of this material, which contains more iron than chrysotile-gypsum. Iron removal was not the same for all PVDs. Moreover, the PVD which extracted the most iron was different, depending on the type of waste: PVD from P. mandelii for chrysotile-gypsum, with 1.22 mg.L

-1

, and P. fluorescens for amosite-gypsum, with 5.39 mg.L -1 .

In addition, the amount of iron extracted from samples incubated in fresh supernatants for 48 h was the same as that measured after 24 h (data not shown). Studies examining siderophoremediated iron dissolution from chrysotile waste are lacking. A few studies have focused on the effect of the commercial bacterial siderophore desferrioxamine, produced by Streptomyces pilosus, on asbestos fibers. Iron removal from crocidolite and amosite by this siderophore is also effective [START_REF] Chao | Effect of long-term removal of iron from asbestos by desferrioxamine B on subsequent mobilization by other chelators and induction of DNA singlestrand breaks[END_REF]. Moreover, [START_REF] Mohanty | Siderophore-mediated iron removal from chrysotile: Implications for asbestos toxicity reduction and bioremediation[END_REF] showed that desferrioxamine releases exchangeable and structural iron from chrysotile fibers in a concentration-dependent manner. Other studies have shown that fungal strains can extract iron from asbestos, likely promoted by siderophores [START_REF] Daghino | Bioweathering of chrysotile by fungi isolated in ophiolitic sites[END_REF]. [START_REF] Mohanty | Siderophore-mediated iron removal from chrysotile: Implications for asbestos toxicity reduction and bioremediation[END_REF] showed that desferrioxamine was as effective as the fungi siderophore, ferrichrome, in removing iron from chrysotile fibers.

Kinetics of iron extraction from chrysotile-gypsum by pyoverdines

We then focused on the most representative ACW among waste, chrysotile-gypsum. Based on the results show in Fig. 1, we carried out waste alteration using the two PVD-containing supernatants from P. aeruginosa (PVD aeruginosa ) and P. mandelii (PVD mandelii ), adjusted to a final concentration of 100 µM (Fig. 2). We sampled and measured iron solubilization during the first 8 h and at the end of the incubation to better understand the iron extraction kinetics. The kinetic profiles of dissolution by the two PVDs were very similar and achieved the same iron extraction (0.9 mg.L -1 ) at the end of the experiment, consistent with the results presented in Fig.

1. We detected dissolved iron for PVD mandelii and PVD aeruginosa after only 1 h of contact (0.12 and 0.17 mg.L -1 , respectively), which progressively increased during the next 8 h of dissolution (0.59 and 0.54 mg.L -1

, respectively). The same time scale of 24 h was used by [START_REF] Mohanty | Siderophore-mediated iron removal from chrysotile: Implications for asbestos toxicity reduction and bioremediation[END_REF] to reach an iron dissolution equilibrium for chrysotile fiber weathering by desferrioxamine. However, we cannot compare the iron concentrations because our experiment focused on chrysotile waste embedded in gypsum for flocking purposes in housing, whereas that of Mohanty et al. used raw asbestos fibers.

Long-term alteration of chrysotile-gypsum by pyoverdines

Our experiments clearly show that the optimum time for chrysotile-gypsum alteration is 24 h without renewal of the medium. We conducted a second set of experiments, with periodic medium renewal, for 42 days on FAW to determine the limit of iron extraction by PVDs produced by P. aeruginosa and P. mandelii. The supernatant was replaced by fresh apo-PVD supernatant at each cycle. PVD aeruginosa and PVD mandelii showed equivalent iron release over time, which is consistent with the previous results. Succinate medium alone had no effect on iron dissolution, as only low iron concentrations were detected in the control (0.01 to 0.08 mg.L -1 ) (Fig. 3). During the 24 h cycles (T24-1 to T24-8), using siderophore concentrations of 100 µM, iron extraction decreased from 0.92 to 0.28 mg.L -1 for PVD aeruginosa and 0.88 to 0.22 mg.L -1

for PVD mandelii . We observed an unexpected increase to 0.42 for PVD aeruginosa and 0.37 for PVD mandelii for T24-9, due to a longer stand-by period (a week) between T24-8 and T24-9 than for the other cycles, for which the duration was < 72 h. Thus, the cycles were extended to 96 h for seven cycles. At T96-1, iron dissolution was 0.55 mg.L -1 for PVD aeruginosa and 0.45 mg.L -1

for PVD mandelii . After T96-2, released iron decreased to 0.24 mg.L -1 for PVD aeruginosa and 0.25 mg.L -1 for PVD mandelii and remained constant between T96-5 and T96-7. Then, we incubated the chrysotile-gypsum in a 200 µM PVD-containing supernatant for 24 and 96 h to determine whether additional iron could be extracted. However, the concentration of solubilized iron was very low (0.17 for PVD aeruginosa and 0.09 mg.L -1 for PVD mandelii after 96 h). The waste contains chrysotile, with a theoretical composition of Mg 3 Si 2 O 5 (OH) 4 , which is a sheet silicate composed of inner tetrahedral silicate layers and outer magnesium oxide octahedral layers (brucite). Since asbestos originated from soils where iron is highly abundant, magnesium in the outer layer may be replaced by ferrous and ferric iron. The same phenomenon may occur in the inner silicate layer, where silicon may be exchanged by ferric iron only [START_REF] Pollastri | The chemical environment of iron in mineral fibres. A combined X-ray absorption and Mössbauer spectroscopic study[END_REF]. In our study, some iron appeared to be more easily solubilized during short-term assay (24 h), whereas we needed to increase the exposure time to 96 h to continue iron dissolution. It is well known that siderophore-mediated iron removal leads to siderophore adsorption on the ironbearing mineral surface. For example, PVD has already been shown to dissolve structural iron from smectite upon contact [START_REF] Ferret | Siderophore-promoted dissolution of smectite by fluorescent Pseudomonas[END_REF]. A few studies have focused on siderophore dissolution mechanism for mineral asbestos. [START_REF] Mohanty | Siderophore-mediated iron removal from chrysotile: Implications for asbestos toxicity reduction and bioremediation[END_REF] studied iron release from chrysotile fibers, depending on the concentration of desferrioxamine in long-term experiments with no solution renewal. The low concentration of desferrioxamine (1 µM) released some iron from the surface of the brucite layer, whereas increasing the concentration of desferrioxamine to 10 µM led to better surface coverage. Exhaustion of surface sites could provide easier access to the iron present in the silica tetrahedron. In our experiment, the concentration of both siderophores remained predominantly constant (100 µM) and the solutions were renewed at regular intervals of 24 h or 96 h. Our results tend to point to the same conclusion as those of [START_REF] Mohanty | Siderophore-mediated iron removal from chrysotile: Implications for asbestos toxicity reduction and bioremediation[END_REF], in which short renewal cycles appear to release iron from the brucite layer, leaching the fiber surface and potentially providing access to iron from the silica layer.

The increase in iron removal by the 96 h renewal cycles could be explained by two mechanisms: i) better siderophore surface coverage and the ii) release of iron from the silica layer. As iron dissolution from the silica tetrahedron could be slow, our long renewal cycles may have facilitated such weathering.

Analysis of chrysotile fibers by STEM-EDX (Fig. 4) showed a large decrease of iron content after long-term alteration with both PVDs and confirms that iron was removed from the structure. Interestingly, the silica content tended also to decrease after PVD contact. These results confirm active dissolution driven by the siderophores.

Effect of pyoverdine concentrations on iron and magnesium dissolution from chrysotile-gypsum

Various concentrations of PVD mandelii were added to FAW over 48 h to evaluate iron and magnesium release. We observed iron removal from chrysotile fibers in a dose-dependent manner (Fig. 5A). The control (succinate medium alone) showed only weak dissolution (0.034 mg.L -1 ), whereas iron release was significantly higher in the presence of PVD from 0.30 mg.L -1 at 25 µM to 0.96 mg.L -1 at 150 µM. The amount of iron released by 200 µM PVD was similar to that released by 150 µM, showing that the PVD concentration was not a limiting factor. Indeed, 10% of the siderophore was in a PVD-Fe complex form at 200 µM. Thus, the reaction involved a proportion of apo-PVD which could be high enough to extract iron, indicating that the limiting factor could be the availability of iron. [START_REF] Mohanty | Siderophore-mediated iron removal from chrysotile: Implications for asbestos toxicity reduction and bioremediation[END_REF] showed that iron removal from chrysotile fibers increased if the concentration of desferrioxamine was raised from 1 to 10 µM.

Our results confirm this study and suggest that iron release is limited by iron availability.

Siderophores are well known for their high affinity for iron and recently [START_REF] Schalk | New roles for bacterial siderophores in metal transport and tolerance[END_REF] demonstrated that other metals can also be chelated by the PVD of P. aeruginosa. However, no data are available on the capacity of PVD to complex magnesium. Given that the studied FAW contains chrysotile with an external brucite layer composed of magnesium, fiber alteration may result in magnesium solubilization. We thus evaluated the effect of PVD mandelii on magnesium dissolution as well as that of iron (Fig. 5B). We observed no effect on magnesium dissolution at any tested concentrations. A relatively high magnesium concentration was measured in the control (5.5 mg.L -1

), with no significative difference from the amount of magnesium dissolved by PVD mandelii (3.85 mg.L -1 to 6.89 mg.L -1 ), regardless of the concentration tested. pH is a well-known parameter that has been described to influence the dissolution of the chrysotile brucite layer [START_REF] Choi | Kinetic study of dissolution of asbestos fibers in water[END_REF][START_REF] Gronow | The dissolution of asbestos fibres in water[END_REF]. An acidic environment could strongly favor magnesium ion leaching, whereas slower dissolution kinetics may occur at neutral pH. All solutions in our study were adjusted to pH 7 and thus measured magnesium release may have been due to the pH.

Conclusions

We investigated the efficiency of various PVDs to scavenge iron from FAW and the ability of the best identified PVDs to degrade asbestos waste. Our results showed a significant iron extraction from FAW by all tested PVDs but with differences in efficiency according to the pyoverdines and the type of waste. PVD from P. mandelii extracted the higher amount of iron from chrysotile-gypsum, while PVD from P. fluorescens was the most efficient for amositegypsum. The kinetic profiles of iron extraction from chrysotile-gypsum by these pyoverdines highlighted a time-dependent dissolution. A long-term alteration of chrysotile-gypsum by PVD aeruginosa and PVD mandelii revealed an extraction limit after renewal cycles for a total of 42 days leading to a large decrease of iron content from chrysotile fibers structure. Moreover, PVD mandelii extracted iron from chrysotile-gypsum in concentration-dependent manner. Our research identified efficient pyoverdines in biodegradation of asbestos waste. The resulting PVD-Fe complex could be exploited as a valuable iron source. Further investigations might allow to consider the development of an eco-friendly asbestos treatment, using pyoverdines, in order to reduce asbestos-related environmental and health problems. In color online Graphical Abstract

FIGURE LEGENDS: Fig. 1 .Fig. 2 .Fig. 5 .

 125 FIGURE LEGENDS: Fig. 1. Concentration of iron dissolved from flocking asbestos waste, chrysotile-gypsum (A) and amosite-gypsum (B), in the presence of various pyoverdine-containing supernatants (SN) after 24 h of contact. Error bars indicate the standard errors of the means of three or five replicates. Bars with the same letter are not significantly different (p > 0.05, Kruskal-Wallis test, three or five replicates).

Fig. 1 .FigureFig. 2 .Fig. 3 .Fig. 4 .

 1234 Fig. 1. Concentration of iron dissolved from flocking asbestos waste, chrysotile-gypsum (A) and amosite-gypsum (B), in the presence of various pyoverdine-containing supernatants (SN) after 24 h of contact. Error bars indicate the standard errors of the means of three or five replicates. Bars with the same letter are not significantly different (p > 0.05, Kruskal-Wallis test, three or five replicates).

Fig. 5 .

 5 Figure Click here to download Figure: Figure 4.pdf Texte

Acknowledgements

This work was supported by the French Environment and Energy Management Agency (ADEME), the French R&D plan for asbestos removal (PRDA) and SOMEZ (Mediterranean Company of Zeolites).

Weathering efficiency varies according to the pyoverdines and the type of waste. Pyoverdines solubilize iron in a time-dependent manner. Chrysotile-gypsum weathering by pyoverdines decreases iron concentration in fibers. Iron removal from chrysotile-gypsum is concentration-dependent of pyoverdines. Pyoverdines could be used in bioremediation process of asbestos waste. εLys: lys linked by its ε-NH2; OHAsp: threo-β-hydroxy-aspartic acid; aThr: allo-Thr; cOHOrn: cyclo-hydroxy-ornithine; FOHOrn: δN -formyl-δN -hydroxy-ornithine; AOHOrn δN -acetyl-δN -hydroxy-ornithine.

Highlights (for review)

Texte

Parentheses indicate cyclic structures. D-amino acids are underlined. A broken line means that the two enantiomers were detected among the underlined residues. ND: not determined.


Maxime Redondin
email: maxime.redondin@vedecom.fr

Laurent Bouillaut

Dimitri Daucher

A Clustering-based Approach to Segment a Pavement Markings Line

Keywords: pavement marking, retroreflection luminance, Agglomerative Hierarchical Clustering

The maintenance of road infrastructure is a classic social challenge, especially in the context of a decreasing maintenance budget and the advent of autonomous vehicle traffic. Road markings need an accurate replacement strategy to guarantee that the markings remain perceptible. The retroreflective luminance of markings is currently dynamically quantifiable only by using a retroreflectometer such as the Ecodyn from MLPC. The main objective of this research is to construct a performance-based approach for retroreflective marking replacement adapted to a given road network. This approach involves three main tasks: localize the strategic area based on past inspections, determine an adapted decay model for a given area, and evaluate the economic impact of replacing markings. This paper focuses on the first task. We apply the Agglomerative Hierarchical Clustering (AHC) method to a given dataset to obtain a suitable markings line segmentation. Markings whose retroreflective luminance exhibits similar evolution over time are interpreted to belong to a specific area of the road network. When no follow-up replacement has occurred, a replacement detector deduces the date at which markings were laid from the clusters. The broken center line of the French National Road 4 illustrates the proposed approach; the road is divided into 5 clusters and 34 lifecycles. A study of markings laid in 2008 and replaced in 2012 shows important variations in the decay of the retroreflective luminance as identified by the clustering approach. Even for a single road, an optimal replacement strategy for retroreflective road markings is necessary and is composed of several local maintenance strategies.

Introduction

The maintenance of one given road infrastructure is a classic social challenge, especially in the context of a decreasing maintenance budget and the advent of autonomous vehicle traffic. The first motivates the development of an original maintenance strategy according to a given budget over several years. The second will define different maximum degradation thresholds on the pavement, the surface signing, and road equipment. An autonomous vehicle employs several different sensors to analyse the road on which it travels. VEDECOM chooses a multi-agent approach based on a camera [START_REF] Revilloud | A Lanemarker Estimation Method for Improving Lane Detection[END_REF]. A reliable marking line is more than 95% detected with fewer than 2% of false alarms [START_REF] Revilloud | A Lanemarker Estimation Method for Improving Lane Detection[END_REF]. Applied on a degraded road infrastructure, 85% of the emergency line is correctly detected and the center line is not seen by the system [START_REF] Revilloud | A New Multi-Agent Approach for Lane Detection and Tracking[END_REF]. A global preventive maintenance strategy based on given degradation thresholds represents a solution to solve these two issues. A preventive replacement strategy that is able to guarantee perceptible pavement markings is an adapted solution to optimize lane detection. A clear road surface marking is more important than a pavement in good condition for an autonomous vehicle guidance system. However, up to now most efforts have been focused on pavement quality only. For example, Wang et al [START_REF] Wang | Survival Analysis of Fatigue Cracking for Flexible Pavements based on Longterm Pavement Performance Data[END_REF] compares different stochastic processes to model road fatigue cracking and Zouch et al [START_REF] Zouch | A Condition-based Imperfect Maintenance Model with Action Dependent Deterioration[END_REF] proposes a condition-based imperfect maintenance of the wearing course.

An autonomous vehicle may inspect the road infrastructure and more specifically, inspect pavement markings during its journey. Nowadays, no example of a marking line regularly inspected by an autonomous vehicle is known. The current method for evaluation of marking degradation is based on the retroreflection luminance (from vehicle headlights). This strictly positive integer variable is measured in millicandela per square meter and by lux (mcd/m²/lx). It is the only dynamically quantifiable measure and has become the only measure surveyed to evaluate marking degradation and its evaluation is subject to the strict conditions described in the NF EN 1436 rules [START_REF] Afnor | NF EN 1436 + A1 -Road Marking Material -Road Marking Performance for Road Users[END_REF].

Figure 1(a) illustrates the perception of a marking by nighttime according to their retroreflection luminance. For waterborne markings, this property is guaranteed by glass spheres mixed into the paint during application. A high level (> 150) guarantees a visible white marking. Their main degradation over time is induced by traffic, environmental conditions, and the material properties of markings and pavements. Markings progressively lose paint and glass beans, causing their retroreflective luminance to decrease over time. These results in a below-threshold level (< 150) and a visible grey object in the best case. When a marking's retroreflectivity has degraded sufficiently, replacement is the only possible maintenance action. European infrastructures require a minimum threshold of 150 mcd/m²/lx for a new marking [START_REF] Afnor | NF EN 1436 + A1 -Road Marking Material -Road Marking Performance for Road Users[END_REF]. Marking retroreflectivity can be dynamically inspected using a retroreflectometer such as the Ecodyn from MLPC. A retroreflectometer is fitted to the side of a car and connected to a laptop inside the car (Figure 1(a)). A white light is shone on the markings (Figure 1(b): "Emission") and the quantity of the retro-reflected light is measured (Figure 1(b): "Reception"). Associated software automatically creates a database in which each measurement is associated with a reference location (a kilometric point for example). The standard configuration analyses the retroreflective luminance every 40cm but stores only the average over 100m. Several degradation models exist in the current literature that are mainly based on a regression model. Two common weaknesses are observed: they are difficult to apply directly to a given road network and they suppose an available followup of the replacement. A single line is also not systematically replaced in its entirety. For logistic and safety reasons, road managers maintain only specific areas at a time. A first task for a surface marking replacement strategy is to identify strategic areas. A follow-up of the replacement is necessary to identify all the lifecycles. The constitution of feedback data is therefore key to developing a degradation or a lifetime model and finally deducing an adapted preventive replacement strategy. Thus, the main objective of this study is to construct a clustering-based approach for retroreflective marking replacement that is adapted to a given lane. This approach involves three tasks: localize strategic areas based on a feedback database, determine an adaptive lifetime model for the given area, and evaluate the economic impact of marking replacement. This paper focuses on the first task and proposes a clustering approach to localize the strategic areas.

First, Section 2 presents a state of the art main degradation model for pavement retro-reflective markings. Such models provide a prediction of failure occurrences and a preventive replacement is engaged before this instant. Then, Section 3.1 proposes a segmentation of one given line using an Agglomerative Hierarchical Clustering (AHC) approach [START_REF] Tufféry | Data Mining and Statistics for Decision Making[END_REF]. Markings with similar retroreflective luminance evolution over time are identified and each cluster is interpreted with respect to a specific area of the road network. Section 3.2 completes this approach with a replacement detector to estimate the date at which markings were laid. The detector searches for a median retroreflection luminance gain between two inspections. In Section 4, an illustration of this approach is proposed, using a part of the broken centerline of the French National Road 4 (NR4). The surface signing is inspected once a year, but replacement follow-up is not available. However, every replacement campaign for marking is done in March. This situation runs counter to the literature, which assumed monthly road network inspections and completed follow-ups of required replacement. The road is divided into 5 clusters with 34 lifecycles. The study of markings laid in March 2008 and replaced in March 2012 shows that even on the same line and under the same cycle, important variations in the degradation of retroreflection luminance occur. The proposed clustering approach can isolate each different degradation mode. Finally, this example shows that even for a single road, an optimal replacement strategy for retroreflective road markings consists of several local maintenance strategies.

State of the Art of Current Degradation Model of Retroreflective Marking

The two main research fields regarding pavement markings are its detection by visibility sensors and its degradation. Hillel et al [START_REF] Hillel | Recent Progress in Road and Lane Detection: A Survey[END_REF] presents research on lane detectors. The preferred sensor is a camera used with a clustering process able to extract markings from each image. The VEDECOM Institute proposed a multi-agent approach previously presented [START_REF] Revilloud | A Lanemarker Estimation Method for Improving Lane Detection[END_REF][START_REF] Revilloud | A New Multi-Agent Approach for Lane Detection and Tracking[END_REF]. Independently: Xiao et al [START_REF] Xiao | Road Marking Detection based on Structured Learning[END_REF] and Lee et al [START_REF] Lee | Vpgnet: Vanishing Point Guided Network for Lane and Road Marking Detection and Recognition[END_REF] propose different options based on cameras. Kumar et al [START_REF] Kumar | Automated Road Markings Extraction from Mobile Laser Scanning Data[END_REF] proposes a solution based on a LIDAR and a cartographical approach is proposed by Hazelhoff et al [START_REF] Hazelhoff | Exploiting Automatically Generated Databases of Traffic Signs and Road Markings for Contextual Co-Occurrence Analysis[END_REF]. A basic idea is to consider a lane detector as an inspection process. For example, Costello et al [START_REF] Costello | Life-Cycle Planning Methodology for Ancillary Highway Assets[END_REF] proposed an inspection policy by camera and introduced five degradation levels. A stochastic maintenance strategy based on this model. However, this is a non-standard strategy and no example of a feedback database created by a lane detector is known. The current inspection process is based on a retroreflectometer and current degradation models evaluate the retroreflection luminance. This variable is explained by a regression method as a function of time, traffic, marking material, or lateral locations of markings. Such models provide a prediction of failure occurrences and a preventive replacement is engaged before this instant. A recent development is proposed by Owusu et al [START_REF] Owusu | Degradation of Retro-Reflectivity of Thermoplastic Pavement Markings: A Review[END_REF]. This paper presents the main degradation models currently used to evaluate retro-reflective markings.

The age of markings variables is present in all such models. It is also the only variable used on the exponential model proposed by Lu [START_REF] Lu | Performance of Traffic Markings in Cold Regions[END_REF], linear models proposed by Scheuer et al [START_REF] Scheuer | Paint-Line Retroreflectivity Over Time[END_REF], Taek et al [START_REF] Taek | Pavement Making Material Evaluation Study in Michigan[END_REF], Sarasua et al [START_REF] Sarasua | Evaluation of Interstate Pavement Marking Retroreflectivity[END_REF] and Thamizharasan et al [START_REF] Thamizharasan | A Methodology for Estimating the Lifecycle of Interstate Highway Pavement Marking Retroreflectivity[END_REF], and the inverted quadratic equation model proposed by Bahar et al [START_REF] Bahar | Pavement Marking Materials and Markers: Real-World Relationship Between Retroreflectivity and Safety Over Time[END_REF]. Abboud and Bowman [START_REF] Abboud | Cost-and Longevity-based Scheduling of Paint and Thermoplastic Striping[END_REF], Lindly and Wijesundera [START_REF] Revilloud | A Lanemarker Estimation Method for Improving Lane Detection[END_REF], and Lee et al. proposed independently the Vehicle Exposure (𝑉𝐸) variable defined as a weighted product of the Annual Average Daily Traffic (𝐴𝐴𝐷𝑇) and the age of markings. Each one proposed a logarithmic model function of the 𝑉𝐸. Road infrastructure characteristics such as the traffic or the locations of markings are also considered by Karwa and Donnell [21] or Sitzabee et al [START_REF] Sitzabee | Pavement Marking Degradation Modeling and Analysis[END_REF]. The first proposed a multi-layer perceptron. The second proposed a multilinear model optimized to thermoplastic markings and is a function of time, the initial retroreflection value, the 𝐴𝐴𝐷𝑇, the lateral locations of markings, and marking color. This model admits an alternative for waterborne markings and the number of snowplow transits is added by Mull and Sitzabee [START_REF] Mull | Paint Pavement Marking Performance Prediction Model[END_REF].

At least three papers bring into question a degradation model based on a regression technique. Ozelim and Turochy [START_REF] Ozelim | Modeling Retroreflectivity Performance of Thermoplastic Pavement Markings in Alabama[END_REF] recommend only models proposed by Sitzabee et al. [START_REF] Sitzabee | Pavement Marking Degradation Modeling and Analysis[END_REF] and Thamizharasan et al. [START_REF] Thamizharasan | A Methodology for Estimating the Lifecycle of Interstate Highway Pavement Marking Retroreflectivity[END_REF]. Migletz et al. [START_REF] Migletz | Service Life of Durable Pavement Markings[END_REF] and Kopf [START_REF] Kopf | Reflectivity of Pavement Markings: Analysis of Retroreflectivity Degradation Curves[END_REF] show an important variation between models attributed to the road design, the marking material, the laying technique and the winter maintenance strategy. Some alternatives exist. Andrady [START_REF] Andrady | Pavement Marking Materials: Assessing Environment Friendly Performance[END_REF] proposed an estimator of the useful lifetime of a retroreflective marking. Sathyanarayanan et al. [START_REF] Sathyanarayanan | Pavement Marking Retroreflectivity Inspection Data: A Weibull Analysis[END_REF] predicts the failure of given markings with a Weibull distribution. Asdrubali et al. [START_REF] Asdrubali | Assessment of the Performance of Road Markings in Urban Areas: The Outcomes of the CIVITAS Renaissance Project[END_REF] proposed the first known preventive replacement strategy for urban markings while respecting the NF EN 1436 rules [START_REF] Afnor | NF EN 1436 + A1 -Road Marking Material -Road Marking Performance for Road Users[END_REF]. Chimba et al [START_REF] Chimba | Evaluating the Service Life of Thermoplastic Pavement Markings: Stochastic Approach[END_REF] proposes a different degradation model based on a Markov chain.

Presented models are based on various assumptions. For example, Sitzabee et al [START_REF] Sitzabee | Pavement Marking Degradation Modeling and Analysis[END_REF] suggested an inspection after each replacement action, a follow-up of the replacement to estimate the age of markings, its material, one description of the road infrastructure, and an estimation of the 𝐴𝐴𝐷𝑇. Thus, this model is not adapted to a retroreflective line yearly inspected where its follow-up of the replacement is not available. Operationally, proposed degradation models must be applied directly on the whole line. This assumption doesn't consider an eventual local degradation process or different maintenance strategies on the same road infrastructure. For example, this paper presents a road infrastructure segmented into open country roads, suburban areas, bypass, and a short highway. The proposed clustering-based approach consists of first segmenting a line into different sections correlated to one specific local infrastructure. Each one is then interpreted as a replacement strategic area and admits its own evolution of the retroreflection luminance but also its own replacement strategy. This last property could then be used to define an estimation of the follow-up of the replacement in respect of the NF EN 1436 rules [START_REF] Afnor | NF EN 1436 + A1 -Road Marking Material -Road Marking Performance for Road Users[END_REF] and be based on the median evolution of the retroreflection luminance. The Agglomerative Hierarchical Clustering (AHC) method [START_REF] Tufféry | Data Mining and Statistics for Decision Making[END_REF] is chosen to segment a given line.

Segmentation of a Markings Line by an AHC

In this paper, any markings line is composed of 𝑛 > 0 retroreflectometer measures defined by 𝑖 = 1, ⋯ , 𝑛. Each one is localized by a Point of Reference (PR). To simplify, one measure is analyzed as one pavement marking localized by a PR. The retroreflection luminance of marking 𝑖 at the inspection point 𝑡 is denoted 𝑅𝐿 𝑡 (𝑖) ∈ 𝑁. The whole monitoring of markings according to inspections (𝑇 > 1) realized is done by 𝐼 (1). One given marking 𝑖 ∈ 𝐼 is described only by its 𝑇 > 1 inspection data. The monitoring is not completed by a description of the road infrastructure for example. A graphical representation of 𝐼 analyzes simultaneously the evolution of all markings from the first to the last inspection. A classic clustering approach, such as the AHC, identifies several clusters of markings that exhibit a similar retroreflection evolution over time.

𝐼 = {

(𝑅𝐿 1 (𝑖); ⋯ , 𝑅𝐿 𝑇 (𝑖)) 𝑖 = 1, ⋯ , 𝑛 } (1)

Identification of Strategic Areas

The AHC interprets 𝐼 as vectors in the vectorial space 𝑅 𝑇 . Applying AHC results in sequences of partitions with increasing heterogeneity between partitions, resulting in 1 < 𝑁 < 𝑛 clusters in which data is first isolated and then partitioned into clusters that include all similar objects [START_REF] Tufféry | Data Mining and Statistics for Decision Making[END_REF]. General steps of the clustering process are: 1) each data point is initially assumed to be a cluster, 2) the distances between clusters are calculated, 3) the two closest clusters are merged, and 4) repeat from

Step 2 until only one cluster remains containing all data.

Steps 1) and 3) do not present any difficulties.

Step 2) introduces a distance measurement between two clusters. The Ward distance (2) is selected, where 𝑑 is the Euclidean distance. Here, 𝐼 𝑥 and 𝐼 𝑦 denote two clusters; 𝐼 𝑥 and 𝐼 𝑦 are their average profiles; #𝐼 𝑥 and #𝐼 𝑦 represent their numbers. Various choices for distance measurements exist, such as the minimum or median distance [START_REF] Tufféry | Data Mining and Statistics for Decision Making[END_REF]. The Ward distance merges the two clusters that cause the smallest decrease in betweenclass inertia. In fact, the Ward distance is defined as the reduction in the loss of between-class inertia between two clusters.

Step 4) introduces the need for a stopping criterion. The classic approach is to represent the whole clustering process by an associated dendrogram. As shown in figure 5, this graphic is specific to the AHC and indicates the Ward distance between two given clusters. A classic stopping criterion is cutting the dendrogram when a compromise between a few clusters and a large average inter-cluster distance is found. A double cut is proposed in this paper. The first cut is empirically optimized according to geographical and logistical considerations. Indeed, to accumulate many clusters is logistically difficult to maintain for safety reasons. To control the quality of the cut, clusters may be projected on a road map. Consider now 𝑁 ≥ 2 clusters associated to the first cut denoted by 𝐼 1 , ⋯ , 𝐼 𝑁 .

𝑑 𝑤 (𝐼 𝑥 ; 𝐼 𝑦 ) = 𝑑 (𝐼 𝑥 ; 𝐼 𝑦 ) 1 #𝐼 𝑥 + 1 #𝐼 𝑦 (2)
When no follow-up of the replacement has occurred, marking deposition dates must be estimated. A replacement detector is proposed and is based on three observations: the retroreflection luminance decreases over time, a sudden gain in retroreflection luminance signals that a replacement occurred and the AHC tends to identify important gains in retroreflection luminance. A second cut of the dendrogram looks for a partition of sub-clusters defined only by some replacement actions. Sub-clusters created by this second cut are denoted by 𝐼 1 , ⋯ , 𝐼 𝑀 where 𝑀 ≥ 𝑁.

Identification of Replacement Action

The proposed detector compares systematically two inspections on every sub-cluster 𝐼 1 , ⋯ , 𝐼 𝑀 . Consequently, it is unable to estimate replacement before the first inspection and estimated deposition dates are defined between two inspections. According to the NF EN 1436 [START_REF] Afnor | NF EN 1436 + A1 -Road Marking Material -Road Marking Performance for Road Users[END_REF], a minimum of 150 mcd/m²/lx is selected to represent a new marking. For a given cluster 𝐼 𝑗 ∀𝑗 = 1, ⋯ , 𝑀, five maintenance actions can be identified:

• A Full Replacement (𝐹𝑅) operation involves a replacement of all the markings. • A Full Stressed Replacement (𝐹𝑆𝑅) operation involves a replacement of all the markings but the initial or the sudden gain retroreflection luminance is relatively low. An over maintenance action is an example. • A Partial Replacement (𝑃𝑅) operation consists of replacing only a part of the markings.

• A punctuated Replacement (𝑝𝑅) operation consists of replacing only a part of the sub-cluster.

• A maintenance operation of Nothing (∅) is applied when no maintenance operation was conducted.

Let 𝐴 = {𝐹𝑅, 𝐹𝑆𝑅, 𝑃𝑅, 𝑝𝑅, ∅} be the set of possible replacement actions. The action detected for a marking 𝑖 during the inspection t is denoted as 𝐴 𝑡 (𝑖). For all inspections and all clusters, the number of replaced markings is counted. As shown in Figure 2, the replacement detector is based on two steps: the marking step and the clusters step.

The marking step analyzes whether the marking was replaced between inspections 𝑡 and 𝑡 -1 (Figure 2(a)). The variation between inspections 𝑡 and 𝑡 -1 is done by 𝛥𝑅𝐿 𝑡 [START_REF] Zouch | A Condition-based Imperfect Maintenance Model with Action Dependent Deterioration[END_REF]. If 𝛥𝑅𝐿 𝑡 (𝑖) > 100 and 𝑅𝐿 𝑡 (𝑖) > 150 then the marking was replaced, and 𝐴 𝑡 (𝑖) = 𝑝𝑅. This step cannot determine whether this replacement action was isolated or is part of a wider replacement campaign. An increasing value of (at least) 100 mcd/m²/lx indicates a replace marking and can also be used to anticipate the degradation during the period between the deposition date and the inspection.

𝛥𝑅𝐿 𝑡 (𝑖) = 𝑅𝐿 𝑡 (𝑖) -𝑅𝐿 𝑡-1 (𝑖) (3)
𝛥𝑅𝐿 𝑡 𝐼 𝑗 = 1 2 [𝛥𝑅𝐿 𝑡 ( #𝐼 𝑗 2 ) + 𝛥𝑅𝐿 𝑡 ( #𝐼 𝑗 2 + 1)] (4)
Let us suppose 𝑅𝐿 𝑡 𝐼 𝑗 to be the median retroreflection luminance at inspection 𝑡 observed on the sub-cluster 𝐼 𝑗 . If 𝛥𝑅𝐿 𝑡 𝐼 𝑗 < 0 and 𝑅𝐿 𝑡 𝐼 𝑗 < 150 , then the cluster was not replaced: ∀𝑖 ∈ 𝐼 𝑗 𝑎𝑛𝑑 𝐴 𝑡 (𝑖) ≠ 𝑝𝑅, 𝐴 𝑡 (𝑖) = ∅ . This step meets replacement objectives: the cluster has a larger retroreflection luminance than is required by NF EN 1436 rules. A defined part of the broken center line of the French National Road 4 (NR4) is considered to illustrate the proposed approach. The road is presented by Figure 3. The NR4 runs between Paris and Strasbourg. The direction heading toward Strasbourg is chosen. Since 2007, the section between Courgivaux and Vauclerc (~102km) has been managed by the DIR Est. Pavement markings are yearly inspected in late September in collaboration with CEREMA Est. The selected retroreflectometer is an Ecodyn from MLPC which annotates each measure with a Point of Reference (PR). The surface signing is replaced according to inspections and the current maintenance budget in March. However, there is no follow-up of these replacement campaigns for markings. The same marking product is supposed to be fit. In this paper, only the feedback data base created by the Ecodyn is considered. Between 2007 and 2016, 970 markings were monitored (95% of the considered NR4 section). Contrary to the previous analysis, different punctual replacements are identified in 2008 (cluster 2, 4 and 5), 2009 (cluster 4), and 2013 (cluster 1). Each inspection presents an important group which exhibits a low retroreflection luminance ( < 150 mcd/m²/lx ). Finally, the segmented monitoring confirms and completes the cartographical representation. However, at least one cluster could be divided into two: Fè re-Champenoise presents two different evolutions between 2007 and 2010. Otherwise, the part replaced in 2008 is localized around the local highway. This observation could justify a finer segmentation of the line. Finally, the segmentation into five clusters seems to be a good compromise between limiting the number of clusters and producing clusters correlated to a specific characteristic of the road infrastructure. The replacement follow-up is not available and should thus be estimated.

𝑅𝐿 𝑡 𝐼 𝑗 = 1 2 [𝑅𝐿 𝑡 ( #𝐼 𝑗 2 ) + 𝑅𝐿 𝑡 ( #𝐼 𝑗 2 + 1)] (5)

Segmentation of the Broken Center Line

Estimation of the Broken Center Line Replacement Follow-up

As presented in Figure 6, the second cut associated with the replacement detector is fixed at 15 clusters. This cut corresponds to a larger acceptable number of clusters. Contrary to the previous segmentation, sub-clusters are not necessarily correlated to a specific characteristic of the NR4: the sub-cluster 2 corresponds to the previous mentioned cluster 6 and is defined by a complete replacement in 2015, but the sub-cluster 10 corresponds to the bypass of Vitry-le-Franç ois. However, each one is associated with one cluster. Open country roads are composed of six sub-clusters: 1, 2, 3, 4, 5 and 6. Suburban areas are composed of four sub-clusters: 7, 8, 9 and 10. Sé zanne is the sub-cluster 11. Fè re-Champenoise is composed of three sub-clusters: 12, 13 and 14. The local highway cluster is the sub-cluster 15. Unsurprisingly, larger clusters are decomposed into several sub-clusters. On average, a given cluster is decomposed into 3 sub-clusters. Table 1 presents the follow-up of the replacement estimated using the replacement detector presented in Section 3.2. It indicates only the frequency of markings replaced. The last line is the whole broken center line. The two main replacement campaigns are estimated in 2012 (59%) and 2015 (77%). Few replacements are estimated in 2010 (3%), 2013 (3%) and 2015 (< 1%). Otherwise, the line benefits from targeted replacements. Each cluster is divided into its subclusters. For example, the open country road cluster is composed of 6 sub-clusters. Its sub-cluster 2 was partially replaced (56%) in 2008 and completely replaced in 2015. The whole cluster 1 was completely replaced in 2015 and no replacement was observed in 2010.

(1) Open country roads were completely replaced in 2015. Its sub-clusters exhibit on average 1.8 complete replacements since 2008. In 2012 (84%), its three larger sub-clusters 1, 4 and 5 were completely replaced.

(2) Suburban areas have never been completely replaced. In 2014 (41%), its larger sub-cluster 7 was completely replaced. The other sub-clusters are completely replaced next year (62%). On average, sub-clusters exhibit 1.25 complete replacements since 2008. Three complete replacements are observed on the sub-cluster 10 (bypass of Vitry-le-Franç ois).

(3) Sé zanne was completely replaced in 2011 and 2014.

(4) Fè re-Champenoise was completely replaced in 2012 and 2015. Sub-clusters show on average 3.6 complete replacements since 2008. Most of the observed complete replacements are stressed replacements. The 2015 replacement corresponds mainly to an over-maintenance action due to an opportunist action (77% of the whole line was replaced), in combination with a complete replacement the previous year. Other stress replacements are mainly attributed to the important retroreflection luminance observed on the figure 9 combined with a slow degradation process.

(5) The local highway was completely replaced in 2008, 2012, 2014. The 2008 stress replacement corresponds to an over-replacement action. This summarized follow-up of the replacement shows that sub-clusters are built according to several complete replacement campaigns, occasionally supported by punctual replacement. For example, Sé zanne was replaced twice since 2008. Larger clusters take advantage of targeted replacements. For example, the sub-cluster is included in the open country road cluster and is defined by only one important replacement in 2015. This follow-up provides additional information on the current maintenance strategy. For example, an important replacement campaign was done in 2015 (77%). This is the reason why no replacement was detected in 2016 (< 1%). A similar situation is presented in 2012 (59%) and 2013 (3%).

The replacement detector estimated 34 lifecycles between 2008 and 2016. Figure 7 presents the cycle of 92 markings deposited in May 2008 and replaced in May 2012. However, inspections are done once a year in September between 2008 and 2011. Retroreflective degradation clearly involves two steps. The first step, between 2008 and 2010, is a fast-decay period (median -625 mcd/m²/lx between 2008 and 2010). The second step shows a stable variation of +14 mcd/m²/lx. This pattern is in accordance with other reports in the literature from Sathyarayanan [START_REF] Andrady | Pavement Marking Materials: Assessing Environment Friendly Performance[END_REF] or Sarazura [START_REF] Sarasua | Evaluation of Interstate Pavement Marking Retroreflectivity[END_REF]. This example clearly shows the differences in the degradation rate with respect to the clusters. The local highway clusters have the highest retroreflection luminance. The open country road and suburban clusters have the lowest retroreflection luminance. However, the degradation rate is more stable in the suburban cluster. The Fè re-Champenoise cluster has an intermediate retroreflection luminance between 2008 and 2010. Within the same lifecycle, four different degradation rates were identified by the AHC.

Finally, the NR4 broken center line example shows that clusters are localized to areas such as a city, a bypass, and so on. The current maintenance strategy could be estimated from the segmentation. For example, the local highway of Sommesous is isolated in the segmentation. The identification of several strategic areas shows the difficulty in directly applying a single degradation model for retroreflective markings, even on a given single road. Each cluster degrades at a specific rate, and more broadly, requires its own replacement strategy. A preventive replacement strategy adapted to this line should comprise several local replacement strategies. AHC applied across all inspections was able to define the entire strategic area.

Conclusion

Road infrastructure maintenance is a classic social challenge in the context of a decreasing maintenance budget. One important equipment to maintain are pavement markings which define traffic lanes. This is the reason why autonomous vehicle guidance systems include a lane detector. However, this option must be optimized by a preventive replacement strategy able to guarantee perceptible pavement markings and improve the quality and reliability of the road infrastructure. Currently, evaluation of degradation is based on retroreflection luminance. This measure evaluates the nighttime visibility and is dynamically quantifiable by a retroreflectometer such as the Ecodyn from MLPC.

The degradation is currently explained by a regression method as a function of time, traffic, or marking material. The associated preventive replacement strategy provides a prediction of failure occurrences. And finally, the replacement is engaged before this instant. However, these models present three main difficulties. First, the prediction quality shows an important variation from one model to another. Second, the follow-up of the replacement is known. Third, proposed degradation models must be applied directly on a whole line. However, a line is only observed by retroreflectometers and the follow-up of the replacement may not be available. Also, current assumptions do not consider an eventual local degradation process or different maintenance strategies on the same road infrastructure.

In this paper, the feedback database describes completely one given markings line and is generated by retroreflectometers. The monitoring over time of the retroreflection luminance is the first and only indicator to develop a preventive replacement strategy. A clustering approach simplifies the analysis. Each cluster presents one specific evolution over time, including each replacement action and be projected on a road map. Without additional information on the feedback database, the markings line is segmented into several maintenance strategic areas defined by both a specific evolution of the retroreflection luminance and a specific geographic position.

The Agglomerative Hierarchical Clustering (AHC) is chosen to segment the line. The clustering process is represented by a dendrogram which opens a discussion on the number of clusters to choose. This is the main reason why this approach was chosen. A double cut is proposed. The first cut segments a line into several sections correlated to one specific local infrastructure. The NR4 broken center line is segmented into five clusters. Each one is correlated to the road infrastructure: a bypass, a local highway or an open country road. This paper introduces the situation where the follow-up of the maintenance is not available. A replacement detector is based on the following two observations. First, each cluster of the first segmentation exhibits its own evolution of the retroreflection luminance as well as its own maintenance strategy. Second, the retroreflection luminance decreases over time. The median gain of retroreflection luminance between two inspections per cluster is an accepted indicator to estimate the follow-up of the replacement. This detector is optimized by a second cut of the dendrogram. Sub -clusters deduced from it correspond to the larger acceptable number of clusters and are empirically defined by several gains of retroreflection between two inspections. The final replacement detector is also based on different decisions in respect of the NF EN 1436 rules.

The detector estimates 34 lifecycles between September 2008 and September 2016. The current replacement strategy is now known. The bypass of Sé zanne has been completely replaced two times since 2008, for example. Complete life cycles are extracted from the estimated follow-up of the replacement and are similar to those presented in the literature. This paper presents the cycle of markings laid in March 2008 and replaced in March 2012. This monitoring is also segmented into four clusters. Each one exhibits its own degradation process. For example, the retroreflection luminance is strong on the local highway but the degradation process is very fast. This example shows that the segmentation of the whole line is also represented on a given life cycle.

Three limits are identified on the proposed approach. First, the segmentation is not perfect. For example, the section between Soudé and Maisons-en-Champagne is mainly classified as open country roads. However, small sections of 1 km classified in suburban clusters are included and correspond to some small cities such as Coole. In future work, the authors suggest completing the feedback database with a description of the road infrastructure and the complete surface signing. A first approach based on a factorial analysis presents a thinner segmentation based mainly on the traffic lane organization. These first encouraging results motivate an extending study including the French Government Open Data. Second, the clustering process is empirically stopped by a comparative study between the associated dendrogram and the representation on a road map. An automatic stopping criterion is advisable. Finally, the proposed replacement detector must be compared to a line regularly inspected with a complete follow-up of the replacement. Obviously, this work is necessary to estimate the prediction level of the detector. An additional interest is to optimize different steps, which are currently mainly influenced by the NF EN 1436 [START_REF] Afnor | NF EN 1436 + A1 -Road Marking Material -Road Marking Performance for Road Users[END_REF]. This paper proposed an original clustering-based approach to segment a pavement markings line. Even for a single road, an optimal preventive replacement strategy for retroreflective road markings is necessary and is composed of several local maintenance strategies. A line is now a segment on a different replacement strategic area. Each one could be associated with one degradation model based on a regression method. In future work, the reliability approach proposed by Sathyanarayanan et al [START_REF] Andrady | Pavement Marking Materials: Assessing Environment Friendly Performance[END_REF] may be preferred because it represents an opportunity to develop a stochastic preventive maintenance strategy for road markings.

Figure 1 .

 1 Figure 1. (a) Perception of a white marking according to it retroreflection luminance (mcd/m² /lx); (b) Inspection process

Figure 2 .

 2 Figure 2. (a) The marking step to estimate marking deposition date; (b) The clustering step to estimate marking deposition date Let us consider a given sub-cluster 𝐼 𝑗 at inspection 𝑡. The cluster step analyzes whether the cluster was partially or completely replaced between 𝑡 and 𝑡 -1 (Figure 2(b)). The process is split into four operations. Let us suppose 𝛥𝑅𝐿 𝑡 𝐼 𝑗 to be the median retroreflection luminance variation between inspections 𝑡 and 𝑡 -1 observed on the sub-cluster 𝐼 𝑗 . If 𝛥𝑅𝐿 𝑡 𝐼 𝑗 > 150, then the cluster was fully replaced: ∀𝑖 ∈ 𝐼 𝑗 , 𝐴 𝑡 (𝑖) = 𝐹𝑅. This step detects all clear replacements.

Figure 3 .

 3 Figure 3. Presentation of the considered section of the French National Road 4

Figure 4 ( 1 )

 41 Figure 4 introduces a cartographic AHC representation of a NR4 broken center line over time. Each cluster is represented by its median profile and is named based on the nearest city or by a remarkable observation. The follow-up of replacement is not available. From now, both the median variation and the median retroreflection identify possible complete replacement. The last line represents the whole broken center line and presents some general observations. Except in 2012, 2015 and 2016, the median retroreflection luminance is always under 150 mcd/m²/lx . Two possible important replacement campaigns are observed in 2012 and 2015: 𝛥𝑅𝐿 12 = 105 and 𝛥𝑅𝐿 15 = 173. The longest decreasing period is observed between 2009 and 2011: 𝛥𝑅𝐿 09 + 𝛥𝑅𝐿 10 + 𝛥𝑅𝐿 11 = -82. The segmentation of the NR4 completes these observations. (1) The cluster 1 corresponds to open country roads. It is the largest (43% of markings) and shows a weak median retroreflection luminance between 2007 and 2011: 𝑅𝐿 07 1 = 103, 𝑅𝐿 08 1 = 118, 𝑅𝐿 09 1 = 103, 𝑅𝐿 10 1 = 53, 𝑅𝐿 11 1 = 55. Two possible complete replacements are observed in 2012 and 2015: 𝛥𝑅𝐿 12 1 = 221, 𝛥𝑅𝐿 15 1 = 260.

( 2 )( 3 )( 4 )( 5 )

 2345 The cluster 2 is localized on different suburban areas. It is the second largest (35% of markings) and shows the weakest median retroreflection luminance over time: The cluster 3 is the bypass of Sé zanne. This area was clearly replaced in 2011: 𝛥𝑅𝐿 11 3 = 529 and 𝑅𝐿 11 3 = 577. A strong degradation is also observed the next year: 𝛥𝑅𝐿 12 3 = -406. A possible complete replacement is observed in 2014: The cluster 4 is the bypass of Fè re-Champenoise. This area shows a good median retroreflection luminance over the time: 𝑅𝐿 10 4 = 160, 𝑅𝐿 13 4 = 179, 𝑅𝐿 15 4 = 365. Four possible complete replacements are observed in 2009, 2012, 2014 and 2015: The cluster 5 corresponds to a local free highway near the city of Sommesous. It is the smallest cluster (4% of markings) and shows the strongest median retroreflection luminance over the time: 𝑅𝐿 07 5 = 826, 𝑅𝐿 08 5 = 946, 𝑅𝐿 09 5 = 510, 𝑅𝐿 14 5 = 307. Two possible complete replacements are observed in 2008 and 2014: 𝛥𝑅𝐿 08 5 = 141 and 𝛥𝑅𝐿 14 5 = 183. An important decrease is observed between 2008 and 2010: 𝛥𝑅𝐿 09 5 + 𝛥𝑅𝐿 10 5 = -760.

Figure 4 .

 4 Figure 4. AHC representations of NR4 broken center line over time, showing the median profile of each clusterThe global analysis introduces two possible replacement campaigns in 2012 and 2015. This cartographical representation shows at least three additional pieces of information. First, the line is segmented into five clusters that are heterogeneous in size. Second, each cluster is correlated to some characteristic of the road infrastructure. Third, this segmentation identifies another possible replacement campaign. The two main examples are the clear complete replacement of Sé zanne in 2011 and a possible replacement campaign on the three last clusters. However, this graphic does not represent the retroreflection monitoring and the clustering process remains to be verified.

Figure 5 (

 5 Figure 5(a) shows the segmented monitoring of the broken center line between 2007 and 2016. Each cluster exhibits its own monitoring. For example, the local highway cluster shows a strong decrease between 2008 and 2010 ( -760 in median), a small increase between 2013 and 2015 (+219 in median) and the retroreflection luminance remains high over time. Otherwise, the Fè re-Champenoise and local highway clusters have been similar since 2010. Between 2007 and 2009, Fè re-Champenoise presented clearly that two sub-clusters have been replaced in 2008 and 2009 respectively.Contrary to the previous analysis, different punctual replacements are identified in 2008 (cluster 2, 4 and 5), 2009 (cluster 4), and 2013 (cluster 1). Each inspection presents an important group which exhibits a low retroreflection luminance ( < 150 mcd/m²/lx ). Finally, the segmented monitoring confirms and completes the cartographical representation. However, at least one cluster could be divided into two: Fè re-Champenoise presents two different evolutions between 2007 and 2010. Otherwise, the part replaced in 2008 is localized around the local highway. This observation could justify a finer segmentation of the line.

Figure 5 (

 5 Figure 5(b) shows the dendrogram associated with the clustering process segmenting into five clusters. Two alternatives are identified. A cut into three clusters would join on the one hand the local highway and Fè re-Champenoise and on other hand Sé zanne and suburban areas. The current segmented monitoring justifies the merge between the local highway and Fè re-Champenoise because their retroreflection luminance is similar since 2010. However, three distinct evolutions are presented between 2007 and 2010. Otherwise, Sé zanne is clearly isolated on the map representation and focuses on an important replacement campaign in 2011. The second alternative proposes a cut into six clusters. According to the dendrogram, this sixth cluster is a distanced part of the open country road clusters. However, it corresponds to a discontinuous section of only 1.5 km and is defined by only one important replacement in 2015.

Figure 5 .

 5 Figure 5. (a) Dendrogram associated with the AHC results of the NR4 broken center line; (b) Segmented monitoring between 2007 and 2016

Figure 6 .

 6 Figure 6. Dendrogram associated with the AHC results of the NR4 broken center line and associated median profile

Figure 7 .

 7 Figure 7. The 2008-2012 lifecycle segmented into the four presented clusters

  Let us suppose 𝑞 1 [𝛥𝑅𝐿 𝑡 𝐼 𝑗 ] and 𝑞 1 [𝑅𝐿 𝑡 𝐼 𝑗 ] are the first quartile of the retroreflective luminance between 𝑡 and 𝑡 -1 and the first quartile of the retroreflective luminance at 𝑡 on 𝐼 𝑗 . If 𝑞 1 [𝛥𝑅𝐿 𝑡 𝐼 𝑗 ] > 0 and 𝑞 1 [𝑅𝐿 𝑡 𝐼 𝑗 ] > 150, then the cluster was fully replaced but the markings it contains are stressed: ∀𝑖 ∈ 𝐼 𝑗 , 𝐴 𝑡 (𝑖) = 𝐹𝑆𝑅. By the first quartile definition, 75% of 𝐼 𝑗 involves a gain of retroreflection luminance and the markings meet the NF EN 1436 rules. According to the first two operations, this gain is between 0 and 150 mcd/m²/lx. An over replacement action is included in this situation. be the subset of 𝐼 𝑗 to the markings where 𝛥𝑅𝐿 𝑡 > 0. This step constraints 𝐼 𝑗 to the markings that involve a gain in retroreflection luminance. If 𝛥𝑅𝐿 𝑡

	𝑞 1 [𝛥𝑅𝐿 𝑡 𝐼 𝑗 ] = 𝛥𝑅𝐿 𝑡 ( #𝐼 𝑗 4	)	(6)
	𝑞 1 [𝑅𝐿 𝑡 𝐼 𝑗 ] = 𝑅𝐿 𝑡 ( #𝐼 𝑗 4	)	(7)
	Let's suppose 𝐼 𝑗 𝑓 (𝑡) 𝐼 𝑗 𝑓 (𝑡)	≥ 100 and 𝑅𝐿 𝑡 𝐼 𝑗 𝑓 (𝑡)	≥ 150, then ∀𝑖 ∈ 𝐼 𝑗 𝑓 (𝑡), 𝐴 𝑡 (𝑖) = 𝑃𝑅.
	𝐼 𝑗 𝑓 (𝑡) = { 𝛥𝑅𝐿 𝑡 (𝑖) ≥ 0 𝑖 ∈ 𝐼 𝑗	}	(8)
	4. Presentation of the French National Road 4 Broken Center Line
	4.1. Presentation of the French National Road 4

Table 1 .

 1 Estimated follow-up of the replacement of the NR4 broken center line

	Cluster	Sub-cluster 2008 2009 2010 2011 2012 2013 2014 2015 2016
		1	13% 2%		3% 100%	2% 100% 1%
		2	56% 4%			37% 4%	4% 100%
		3	11% 6%		100% 14%	100%
	Open country road	4		1%			100%	12% 100%
		5	1%			3% 100%	100%
		6				14% 5% 100% 5% 100%
		Total	9%	1%		12% 84% 5%	3% 100% < 1%
		7	29% 7%		10% 15%	100% 4%	1%
		8	6%	7%		6% 39% 1%	1% 100%
	Suburban	9	9% 11%		2%	2%	2% 100% 2%
		10	100%		100%		7%	100%
		Total	23% 7%	8%	7% 21% < 1% 41% 62% 1%
	Sézanne				100%	100% 11%
		12	12% 100% 8% 23% 100% 8%	100%
	Fère -	13		100%			100%	100% 100%
	Champenoise	14	100%			13% 100%	100% 100%
		Total	24% 79% 2%	8% 100% 4% 77% 100%
	Local highway	100%				100%	100% 11%
	Global	18% 12% 3% 15% 59% 3% 35% 77% < 1%
	Legend:

Partial Replacement Stress Replacement Complete Replacement

Acknowledgements

VEDECOM Institute and IFSTTAR thank CEREMA Est and DIR Est for inspection data of the National Road 4.