Nour Hattab
email: nour.hattab@univ-orleans.fr

Ridha Hambli
email: ridha.hambli@univ-orleans.fr

Mikael Motelica-Heino

Xavier Bourrat

Michel Mench

Application of neural network model for the prediction of Chromium concentration in phytoremediated contaminated soils

Keywords: Artificial neural networks (ANN), Soil contamination, Chromium prediction, pH, EC, DOC

The assessment of chromium concentrations in plants requires the quantification of a large number of soil factors that affect their potential availability and subsequent toxicity and a mathematical model that predicts their relative concentrations. Many soil characteristics can change the availability of chromium (Cr) to plants in soils. However, accurate, rapid and simple predictive models of metal concentrations are still lacking in soil and plant analysis. In the present work a novel artificial neural network (ANN) model was developed as an alternative rapid and accurate tool for the prediction of Cr concentration in dwarf bean leaves grown in the laboratory on phytoremediated contaminated soils treated with different amendments. First, sixteen (4x4) soil samples were harvested from a phytoremediated contaminated site located in south-western France. Second, a series of measurements were performed on the soil samples.

The inputs are the soil amendment, the soil pH, the soil electrical conductivity and the dissolved organic carbon of the soil and the output is the concentration of Cr in the dwarf bean leaves. Third, an ANN model was developed and its performance was evaluated using a test data set and then applied to predict the exposition of the bean leaves to the Cr concentration versus the soil inputs. The performance of the ANN method was compared with the traditional multi linear regressions method using the training and test data sets. The results of this study show that the ANN model trained on experimental measurements can be successfully applied to the rapid prediction of plant exposition to Cr.

Introduction

Chromium in plants has received relatively little attention from researchers in comparison with other trace elements such as Cu, Cd, Ni, Al and As. Soils contaminated with Cr have serious consequences for terrestrial ecosystems, agricultural production and human health [START_REF] Adriano | Trace elements in terrestrial environments; Biochemistry, bioavailability and risks of metals[END_REF]. Chromium has been considered as the 16 th most toxic pollutant and it has become a serious health concern because of its carcinogenic and teratogenic effects [START_REF] Kowalski | Treatment of chromic tannery wastes[END_REF]. Chromium is also considered a serious environmental pollutant [START_REF] Kotas | Commentary: chromium occurrence in the environment and methods of its speciation[END_REF], due to its widespread use in the metallurgical and chemical industries.

Improper disposal, poor storage and leakage of Cr from waste discharge through the soil can release Cr to the environment, causing contamination of groundwater and adverse biological and ecological effects.

Chromium is present in the environment in the form of Cr(III) and Cr(VI). These two forms show different chemical, physico-chemical and biochemical properties. Species of Cr(VI) are more soluble, more mobile, more bioavailable and more toxic than Cr(III) [START_REF] Murti | Toxic Metals in the Indian environment and its human health implication[END_REF][START_REF] Katz | The biological and environmental chemistry of chromium[END_REF][START_REF] Fendorf | Surface reactions of chromium in soils and waters[END_REF][START_REF] James | Oxidation-reduction chemistry of chromium: Relevance to the regulation and remediation of chromate contaminant soils[END_REF]. This may be due to the fact that Cr(VI) penetrates mammalian cells more readily than Cr(III) [START_REF] Wetterhahn | Molecular basis of hexavalent chromium carcinogenicity: Effect on gene expression[END_REF]. Compounds of Cr(VI) are toxic at low concentrations for both plants and animals. The presence of Cr(VI) in water, soil and wastewater has, therefore, been of great concern. Many factors can influence its migration process, such as pH [START_REF] Mclean | Behaviour of metals in soils. Ground water issue[END_REF], dissolved organic carbon or DOC [START_REF] Heijerick | The combined effects of hardness, pH and dissolved organic carbon on the chronic toxicity of Zn to D. magna: development of a surface response model[END_REF], electrical conductivity or EC [START_REF] Förstner | Chemicals forms and reactivities of metals in sediments in "chemical methods for assessing bio-available metals in sludges and soil[END_REF] and soil characteristics such as cation exchange capacity, clay content and competition from other metal ions [START_REF] Sauerbeck | The nickel uptake from different soils and its prediction by chemical extractions[END_REF][START_REF] Smith | Effect of soil pH on availability to crops of metals in sewage sludge-treated soils. 1. Nickel, copper and zinc uptake and toxicity to ryegrass[END_REF]. Soluble chromates are converted to insoluble Cr(III) salts and the subsequent availability for plants decreases [START_REF] Wetterhahn | Molecular basis of hexavalent chromium carcinogenicity: Effect on gene expression[END_REF]. However, soil amendments such as pH [START_REF] Kabata-Pendias | Trace Elements in Soils and Plants[END_REF][START_REF] Jackson | Soil solution chemistry of a fly ash-. poultry litter-. and sewage sludge-amended soil[END_REF], DOC [START_REF] Hsu | Characterisation and extractability of copper. manganese. and zinc in swine manure composts[END_REF], and EC [START_REF] Laing | Factors affecting metal concentrations in reed plants (Phragmites australis) of intertidal marshes in the Scheldt estuary[END_REF][START_REF] Hatje | Kinetics of trace element uptake and release by particles in estuarine waters: effects of pH, salinity, and particle loading[END_REF] can be used to change the soil condition and reduce the high concentration of Cr in contaminated soils [START_REF] Mench | Assessment of ecotoxicity of topsoils from a wood treatment site[END_REF][START_REF] Bes | Remediation of copper-contaminated topsoils from a wood treatment facility using in situ stabilisation[END_REF]. Amendments that induce solubility can be used to clean polluted sites by leaching the contaminating trace elements or by facilitating their uptake by plants (phytoextraction) [START_REF] Kolbas | Copper phytoextraction in tandem with oilseed production using commercial cultivars and mutant lines of sunflower[END_REF].

Quantifying Cr mobility in a given soil is a critical aspect of predicting its toxicity.

Since performing experimental measurements to investigate the relationship between soil parameters and Cr mobility in soil is time-consuming, difficult and expensive, the development of models simulating soil processes has increased rapidly in recent years [START_REF] Minasny | The neuro-m methods for fitting neural network parametric pedotransfer functions[END_REF]. Generally two common methods are used to develop prediction models, regression methods and artificial neural networks (ANN). Several multiple linear regression (MLR) models have been developed over the past 20 years to predict the sorption of trace metals in soils (van der Zee and [START_REF] Van Der Zee | Transport of reactive solute in spatially variable soil systems[END_REF][START_REF] Andersen | Distribution coefficients of Cd, Co, Ni and Zn in soils[END_REF][START_REF] Reinds | Critical loads and excess loads of cadmium, copper and lead for European forest soils[END_REF][START_REF] Streck | Heavy metal displacement in a sandy soil at the field scale: I. Measurements and parameterization of sorption[END_REF][START_REF] Römkens | Cd, Cu and Zn solubility in arable and forest soils: consequences of land use changes for metal mobility and risk assessment[END_REF][START_REF] Tiktak | Modeling cadmium accumulation at a regional scale in the Netherlands[END_REF][START_REF] Elzinga | General purpose Freundlich isotherms for cadmium, copper and zinc in soils[END_REF][START_REF] Schug | Improved cadmium sorption isotherms by the determination of initial contents using the radioisotope 109 Cd[END_REF]. With MLR methods, the relationships between soil inputs (properties) and soil output characteristics have to be stated a priori in the regression models. An alternative to MLR is the application of ANN models where such relationships do not need to be formulated beforehand [START_REF] Anagu | Estimation of heavy metal sorption in German soils using artificial neural networks[END_REF][START_REF] Sarmadian | Modeling of Some Soil Properties Using Artificial Neural Network and Multivariate Regression in Gorgan Province, North of Iran[END_REF]Schaap and Leij, 1998;[START_REF] Hambli | Real-time deformation of structure using finite element and neural networks in virtual reality applications[END_REF][START_REF] Hambli | Statistical damage analysis of extrusion processes using finite element method and neural networks simulation[END_REF][START_REF] Minasny | Neural networks prediction of soil hydraulic functions for alluvial soils using multistep outflow data[END_REF][START_REF] Mcbratney | On digital soil mapping[END_REF][START_REF] Behrens | Digital soil mapping using artificial neural networks[END_REF][START_REF] Buszewski | A new model of heavy metal transport in the soil using non-linear artificial neural networks[END_REF][START_REF] Gandhimathi | Analysis of Heavy Metal for Soil in Coimbatore by using ANN Model[END_REF].

It has been reported that ANNs provide superior predictive performance compared to conventional mathematical methods including MLR models (van der Zee and [START_REF] Van Der Zee | Transport of reactive solute in spatially variable soil systems[END_REF][START_REF] Andersen | Distribution coefficients of Cd, Co, Ni and Zn in soils[END_REF][START_REF] Streck | Heavy metal displacement in a sandy soil at the field scale: I. Measurements and parameterization of sorption[END_REF][START_REF] Römkens | Cd, Cu and Zn solubility in arable and forest soils: consequences of land use changes for metal mobility and risk assessment[END_REF][START_REF] Tiktak | Modeling cadmium accumulation at a regional scale in the Netherlands[END_REF]Schaap and Lei, 1998;[START_REF] Elzinga | General purpose Freundlich isotherms for cadmium, copper and zinc in soils[END_REF][START_REF] Sarmadian | Modeling of Some Soil Properties Using Artificial Neural Network and Multivariate Regression in Gorgan Province, North of Iran[END_REF]. In regression models in many soil engineering situations, the input-output relationships are highly complex and are not well understood. The lack of physical understanding and of a powerful general tool for mathematical modeling leads to either simplifying the problem or incorporating several assumptions into mathematical models.

Consequently, many mathematical models fail to simulate the complex behavior of most soil engineering problems.

ANNs have been widely used in the field of soil science for prediction of soil hydraulic properties (Schaap et al., 1998;[START_REF] Minasny | Neural networks prediction of soil hydraulic functions for alluvial soils using multistep outflow data[END_REF] generation of digital soil maps [START_REF] Mcbratney | On digital soil mapping[END_REF][START_REF] Behrens | Digital soil mapping using artificial neural networks[END_REF] and modeling of the behavior of trace metals [START_REF] Buszewski | A new model of heavy metal transport in the soil using non-linear artificial neural networks[END_REF][START_REF] Anagu | Estimation of heavy metal sorption in German soils using artificial neural networks[END_REF][START_REF] Gandhimathi | Analysis of Heavy Metal for Soil in Coimbatore by using ANN Model[END_REF].

In the cases, ANN are trained to find model input-output relations using an iterative calibration process (training phase). Moreover, ANNs have the advantage of not imposing restrictions on inputs and outputs and can be easily applied to carry out inverse calculation [START_REF] Jenkins | An introduction to neural computing for the structural engineer[END_REF][START_REF] Rafiq | Neural network design for engineering applications[END_REF][START_REF] Hambli | Real-time deformation of structure using finite element and neural networks in virtual reality applications[END_REF].

In the present study, a novel ANN model was developed as an alternative rapid and accurate tool for the prediction of Cr concentration in dwarf bean leaves (BL) grown in the laboratory on phytostabilized contaminated soils treated with different amendments. The inputs are soil amendment, soil pH, soil EC and soil DOC, whereas the output is Cr concentration in the dwarf BL. The performance of the ANN method was compared with a traditional MLR method using the same training and test data sets. The comparative study revealed that ANN provided a better performance than MLR method in predicting soil properties. Results showed that the neural network model led to a very rapid and accurate prediction of the soil outputs.

Material and Methods

Site, soil sampling and soil characterization

Soil samples were collected from southwestern France, Gironde County (44°43'N; 0°30'W). This site has been contaminated with high concentrations of copper sulfate and chromated copper arsenate. The history of the site and the origin of these pollutants are described in detail by [START_REF] Mench | Assessment of ecotoxicity of topsoils from a wood treatment site[END_REF].

The study site is divided into 15 sub-sites labeled A to E and P1 to P10 depending on total topsoil Cu concentration (Fig. 1a) [START_REF] Mench | Assessment of ecotoxicity of topsoils from a wood treatment site[END_REF][START_REF] Bes | Spatial variation of plant communities and shoot Cu concentrations of plant species at a timber treatment site[END_REF]. Long-term phytostabilization experiments have been established at the P3 and P7 sub-sites by [START_REF] Bes | Remediation of copper-contaminated topsoils from a wood treatment facility using in situ stabilisation[END_REF]; [START_REF] Mench | Assessment of ecotoxicity of topsoils from a wood treatment site[END_REF]. Plant communities in the zone of the field trial included Agrostis capillaris, Elytrigia repens, Rumex acetosella, Portulaca oleracea, Hypericum perforatum, Hypochaeris radicata, Euphorbia chamaescyce, Echium vulgare, Agrostis stolonifera, Lotus corniculatus, Cerastium glomeratum, and Populus nigra [START_REF] Bes | Spatial variation of plant communities and shoot Cu concentrations of plant species at a timber treatment site[END_REF].

The field trial zone (150 m²) was established at site P3, which consists of two plots; that were further divided into 16 (3 m x 1 m) sub-plots (Fig. 1b). On these 16 sub-plots, four different amendments were applied, one per subplot (Latin square design) and carefully mixed in the top soil (0-0.30 m) with a stainless steel spade with four replicates: untreated soil (UNT), 0.2% of dolomite limestone (DL), 5% of compost of poultry manure and pine bark (CPM), and a mixture of 0.2% DL and 5% CPM (DLX CPM). Sixteen soil samples (four replicates) were collected from the four plots treated with the different amendments (4X (UNT), 4X (DL), 4X (OM) and 4X (DLX OM)) to a depth of 0.25 m (Fig. 1b).

Soil pH (7.0 ± 0.23) was measured in a 1:1 soil:water suspension using a glass electrode pH meter [START_REF] Jackson | Soil Chemical Analysis[END_REF]. Total nitrogen (0.534 mg kg -1 ) was determined at the INRA Laboratoire d'Analyses des sols (LAS), Arras, France using standard methods (INRA LAS, 2007). The organic matter content was determined by a modified Walkely-Blak method: 0.5 g soil was placed in a 500 ml conical flask and mixed with 10 ml of 0.17 M K 2 Cr 2 O 7 , followed by addition of 20 ml of H 2 SO 4 , 200 ml of water, 10 ml of H 3 PO 4 and 1 ml of diphenylamine indicator. Finally, the contents were titrated with 0.5 M FeSO 4 .7H 2 0. The main characteristics of site P3 (0-0.25 m soil layer) are given in Table 1. The cation exchange capacity (CEC) (3.49 Cmol+/kg) was determined using cobaltihexamine chloride (Ciesielski and Sterckeman, 1997). Total metal content in P3 site was determined by ICP-AES after wet digestion with HF and HCIO 4 (AFNOR NF X 31-147; Ciesielski et al., 1997) (Table 1,column 2). Total soil metal concentrations were in the common range of French sandy soil for Cr, As and Zn, but total soil Cu was in excess for these coarse sandy soils (Table 1, column 3). Total Cr concentrations in each of the 16 potted soil samples were measured by laser ablation inductively coupled plasma-mass spectrometry (LA-ICP-MS). Prior to metal content measurements, the accuracy of the metals determination was checked by performing calibrations with a homogeneous combination of certified reference materials such as NIST-610 (artificial glass), GOR-128-G (komatiite natural glass) and . Little difference was found between the measured and the reference results. In our case, the LA-ICP-MS measurements produced an averaged error in the range of -1.2% to 1.17%. After the calibration phase, 4 repeated measurements were performed for each soil generating 64 testing results (4 soils  4 amendments 4 replicates). The precision of the metal content measurement was assessed by the standard deviation (SD) and the coefficient of variation (COV) (Table 2).

⁎⁎

Highly significant for p < 0.001.

Germination tests

A phyto-toxicological test was applied to the 16 soil samples to assess whether the use of amendments on the field trial zone, assisted by phytostabilisation, is able to reduce the concentrations of bioavailable fractions of Cr for plants. To achieve this objective, one kilo of each soil (4X (UNT), 4X (DL), 4X (OM), 4X (DLX OM)) was placed in a pot after sieving (2 mm). Then, four seeds of dwarf beans (Phaseolus vulgaris) were sowed in each potted soil and cultivated for 18 days in controlled conditions (16 h light/8 h darkness). Soil moisture was maintained at around 50% of the field water capacity with additions of deionized water after weighing. Then, the soil moisture was raised to 80% (11-13% of air-dried soil mass) at the beginning of the germination stage of the grains. At the end of the growing period, the plants were harvested and then the dry weights of roots, shoots, and primary leaves were determined after drying at 70 C°.

The 4), then the Cr concentration in a given dry weight, expressed here, the mineral masses (g per pot) were determined by multiplying Cr concentration in the BL (mg.kg-1) in dry weight of BL (g DW) (Table 4).

Characterization of soil solution

After harvesting the dwarf beans, the soils were watered with distilled water, and maintained daily at 80% of field capacity (11-13% of air-dried soil mass) for 15 days. After 15 days, three Rhizon soil-moisture samplers from Rhizosphere Research Products (Wageningen, Holland) were inserted for 24 h with a 45 o angle into each potted soil (416 soil) to collect (30 ml) of soil solution from each pot. DOC was analyzed in the solution of soils by a Shimadzu © TOC 5000A analyzer. Before DOC measurements, the accuracy of the analyzer was checked by performing calibration with standard reference solution (potassium hydrogen phthalate (KHP) (1000 mg C/L)). In our case, the measurements produced an R²=0.999. After the calibration, 4 repeated measurements of DOC were performed for each soil solution. The precision of the DOC measurement was assessed by the SD and the COV (Table 2). Soil pH and EC were determined in the same soil solutions by pH meter and the EC meter (Table 2).

Selection of soil factors

The mobility of trace elements plays a major role in the behavior and transfer of metals in soils. Mobility, availability and/or bioavailability of metals is controlled by several factors such as the soil's chemical and physical properties (pH, EC, DOC, temperature, ion charges, etc.), plant species and their related factors [START_REF] Soon | Chemical pools of Cd, Ni and Zn in polluted soils and some preliminary indications of their availability to plants[END_REF][START_REF] Sauerbeck | The nickel uptake from different soils and its prediction by chemical extractions[END_REF][START_REF] Davies | Inter-relationships between soil properties and the uptake of cadmium, copper, lead and zinc from contaminated soils by radish (Raphanus sativus L.). Water, Air[END_REF], Smith, Fisher, 2002;[START_REF] Weng | Complexation with dissolved organic matter and solubility control of heavy metals in a sandy soil[END_REF][START_REF] Kerndorff | Sorption of metals on humic acids[END_REF][START_REF] Velleman | Definition and comparison of robust nonlinear data smoothing algorithms[END_REF]Vogeler et al., 2009). It has been reported that the relationships between the mobility of metal concentrations in plants and a given soil are mainly influenced by the soil properties related to the ion charges (Fisher, 2002;[START_REF] Weng | Complexation with dissolved organic matter and solubility control of heavy metals in a sandy soil[END_REF]Kerndorffand Schnitzer;[START_REF] Velleman | Definition and comparison of robust nonlinear data smoothing algorithms[END_REF]Vogeler et al., 2009). Therefore, in the current preliminary study, the soil inputs for the ANN model were limited to the three measurable factors considered to be the most influential (pH, DOC and EC)

on the mobility and availability of metals in the soil. [START_REF] Kabata-Pendias | Trace Elements in Soils and Plants[END_REF] and [START_REF] Jackson | Soil solution chemistry of a fly ash-. poultry litter-. and sewage sludge-amended soil[END_REF] reported that the addition of amendments to soil increased the soil pH compared to the untreated soil, leading to a reduction in the mobility and the availability of metals to plants. The second variable used in our work was DOC. [START_REF] Hsu | Characterisation and extractability of copper. manganese. and zinc in swine manure composts[END_REF] noted that the addition of amendment to the soil increased the soil DOC compared to that of untreated soil, which led to increasing plant mass, reducing the bioavailability of metals by forming ligands with dissolved organic matter. The third parameter was EC. Du [START_REF] Laing | Effect of salinity on heavy metal mobility and availability in intertidal sediments of the Scheldt estuary[END_REF][START_REF] Laing | Factors affecting metal concentrations in reed plants (Phragmites australis) of intertidal marshes in the Scheldt estuary[END_REF] and [START_REF] Hatje | Kinetics of trace element uptake and release by particles in estuarine waters: effects of pH, salinity, and particle loading[END_REF] found that an increase in conductivity (salinity) led to increasing the mobility of some metals such as Cd and Zn, thereby increasing the availability and bioavailability of these metals to plants.

To prepare the training data for the ANN, 64 different measurements (4 soils  4 amendments 4 replicates) were performed on the four different soils subjected to four different treatments (UNT, DL, CPM and DLX CPM). Because of the noise (uncertainty)

concerning the inputs measurement which can be characterized by a given a set of scattered input data, the 64 experiments were used for the training phase instead of 16 (the total number of experimental replicates) to ensure a more robust processing of the scattered measurements (Table 2).

The 64 experiments were used for the training phase instead of 16 (the total number of experimental replicates) to ensure a more robust processing of the scattered measurements.

Presenting the entire patterns (64) ensured the reduction of the ANN prediction sensitivity to noise related to inputs [START_REF] Velleman | Definition and comparison of robust nonlinear data smoothing algorithms[END_REF][START_REF] Kafadar | Choosing among two-dimensional smoothers in practice[END_REF][START_REF] Hambli | Statistical damage analysis of extrusion processes using finite element method and neural networks simulation[END_REF]. The inputs and their minimum/maximum levels are given in Table 3.

Statistical analysis

The total soil solution concentrations of Cr, pH, DOC, EC, foliar elemental concentrations, foliar mineral masses of elements and leaf dry weight (DW) yields were statistically analyzed by ANOVA (Statistica) to evaluate the influence of the treatment and the different effects of soil variables on each other. All analytical determinations were performed in four replicates.

Differences were considered statistically significant at p < 0.05.

Artificial neural network

The ANN architecture is composed of an input layer, a certain number of hidden layers and an output layer in forward connections. Each neuron in the input layer represents a single input parameter. These values are directly transmitted to the subsequent neurons of the hidden layers. The neurons of the last layer represent the ANN outputs (Fig. 2). The output m i y of neuron i in a layer m is calculated by [START_REF] Jenkins | An introduction to neural computing for the structural engineer[END_REF][START_REF] Rafiq | Neural network design for engineering applications[END_REF][START_REF] Hambli | Real-time deformation of structure using finite element and neural networks in virtual reality applications[END_REF]: Among activation functions, the sigmoid (logistic) function is the one most usually employed in ANN applications. It is given by [START_REF] Jenkins | An introduction to neural computing for the structural engineer[END_REF][START_REF] Rafiq | Neural network design for engineering applications[END_REF][START_REF] Hambli | Real-time deformation of structure using finite element and neural networks in virtual reality applications[END_REF]:

  m i m i v f y  (1)       L j m i m j m ji m i b y w v 1 1 1 (2)
    m i m i v v f     exp 1 1 (3)
where  is a parameter defining the slope of the function (

9 . 0   ).
The training process in ANNs involves presenting a set of examples (input patterns) with known outputs (target output) [START_REF] Jenkins | An introduction to neural computing for the structural engineer[END_REF][START_REF] Rafiq | Neural network design for engineering applications[END_REF][START_REF] Hambli | Real-time deformation of structure using finite element and neural networks in virtual reality applications[END_REF][START_REF] Hambli | Statistical damage analysis of extrusion processes using finite element method and neural networks simulation[END_REF]. The system adjusts the In the present work, an in-house ANN program called Neuromod written in Fortran [START_REF] Hambli | Real-time deformation of structure using finite element and neural networks in virtual reality applications[END_REF][START_REF] Hambli | Statistical damage analysis of extrusion processes using finite element method and neural networks simulation[END_REF] In order to avoid data saturation and artifacts related mainly to the coding of the amendments (non-numeric data), the input and output variables were normalized between 0 and 1 using:

min max min i i i i norm i x x x x x    (

Coding of the amendments

The amendments are model independent inputs, therefore, they can be represented using sequential codes (integer) as a non-numeric indexes from 1 to 4 (UNT=#1, CPM=#2, DL=#3, DLX CPM=#4). Such non-numeric data encoding is common when applying ANN models [START_REF] Haykin | Neural Networks and learning machine[END_REF]. An alternative approach is to use the one-of-N encoding technique, which consists of transforming a many-state variable (four states in our case) into several binary variables (one for each state) to represent a single nominal variable. The number of numeric variables equals the number of possible values; one of the N variables is set to one, and the others are set to zero. In the current case, the input variable -amendment‖ was replaced by 4 binary variables, (e.g., UNT= 1000, DL= 0100, CPM= 0010, DLX CPM= 0001; where 0 denotes to inactive and 1 active [START_REF] Ruggiero | Cybernetic Trading Strategies[END_REF]).

In certain cases, a nominal variable with a large number of states would require a prohibitive number of numeric variables for one-of-N encoding, which can increase In addition, during the training phase the assigned codes for the amendments [1,4] are converted in the normalized range [0, 1] using Eq. ( 4) to avoid coding artificial effects and de-normalized after prediction in the range of [1, 4] using Eq. ( 5).

Multiple linear regression model

The most common method used to quantify relationships between inputs and outputs is to employ multiple linear regressions in the form:

    n j i i i i X Y 1   (6)
where i Y is the output variable i, i X are the input variables related to the sample, i, i  and i  are the model regression coefficients determined by a fitting procedure using generally least squares method.

Results and Discussion

Experimental results

Soil solution characteristics

Table 2 shows the physico-chemical parameters (i.e., pH, DOC and EC) of the 16 soil solutions and the total soil Cr concentration measured in the 16 contaminated soils. These measurements concerned the 16 pots containing the 16 types of soils: 4X UNT, 4X DL, 4X CPM, and 4X DLX CPM. Amendment incorporation into the soil increased soil pH slightly in the treated soil compared to the untreated one. This effect was in decreasing order based on mean values from 4 replicates): DL (7.5±0.14) > CPM (7.4±0.27) > DLX CPM (7.3±0.29) > UNT (7.2±0.15).

The organic matter added to the soil (i.e., CPM) resulted in reduction of EC (856.75±122.00 µS.cm -1 ) compared to the DL (1243.75±308.27 µS.cm -1 ), DLX CPM (1278.75±152.18 µS.cm - 1 ) and the UNT (1172.75±214.72 µS.cm -1 ). The soil amendments had no significant effect on the pH and EC of the four types of soil. In contrast, the addition of amendments significantly increased the DOC in the soil solution compared to the untreated soil (p= 0.019). This effect was in the following order: DLX CPM (34.6±2.50 mg.l -1 ) > DL (29.2±6.14 mg.l -1 ) > CPM (26.8±5.49 mg.l -1 ) > UNT (19.0±4.72 mg.l -1 ). The amendments also had a significant effect on the total Cr concentration in the soils (p= 0.000501). A good correlation was observed between soil pH and DOC (R² = 0.589), but poorer or lack of correlations were observed between the other variables used in our experiment.

Concentration and Mineral mass of Cr in the bean leaves

Table 4 shows that the measured Cr concentrations in the BL were less than the toxic concentrations measured in the tops of plants reported by Kitagishi andYamane (1981), Gough et al. (1979) and [START_REF] Davis | Critical levels of twenty potentially toxic elements in young spring barley[END_REF]. The mean value of foliar Cr concentrations in the beans decreased from 1.438±1.23 in the UNT soil to 0.733±0.08 in the soil amended with CPM, to 0.588±0.17 in the soil amended with DL and to 0.652±0.012 in the soil amended with DLX CPM. However, the soil amendments (CPM, DL, DLX CPM) had no significant effects on the Cr concentrations in the BL (p= 0.436) (Table 4).

Leaf Cr mineral mass (g.ha -1 ) was computed with foliar Cr concentrations (mg.kg -1 DW) and foliar biomass (g DW per pot). We can clearly note in Table that soil amendments decreased the mineral mass of Cr in the BL compared to the UNT plants (0.094±0.03 g per pot). The lowest Cr mineral masses were observed for the DLX CPM plants (0.067±0.01 g per pot). This difference in the mineral masses is notably driven by the lower foliar Cr concentrations and dry weight in the DLX CPM plants. The DL and DLX CPM additions decreased the Cr mineral masses more than those for CPM and UNT. While amendments added to soil had a significant effect on the total Cr concentration (p=0.000501) in the four soils UNT (15.52 mg.kg -1 ), CPM(14.81 mg.kg -1 ), DL(17.05 mg.kg -1 ) and DLX CPM(16.07 mg.kg -1 ), there was no significant effect of soil amendments on the concentration and the mineral masses of Cr in the plants.

Table 4. Dry weight (g), concentration (mg kg -1 ) and mineral mass of Cr (g per pot) measured in the BL.

Soil amendments

Dry weight (g)

Cr concentration in the plant (mg kg -1 ) Mineral mass (g per pot) UNT 0.087 ± 0.04 1.438 ± 1.23 0.094 ± 0.03 CPM 0.112 ± 0.02 0.733 ± 0.08 0.083 ± 0.01 DL 0.122 ± 0.02 0.588 ± 0.17 0.069 ± 0.00 DLX CPM 0.103 ± 0.00 0.652 ± 0.012 0.067 ± 0.01

Neural network modeling results

The ANN was trained with 3 x 10 4 epochs (number of training cycles). The training performance was assessed by the root mean square error (RMSE). At the end of the training phase, the RMSE convergence value was 1 x 10 -5 . Table 5 shows the experimental and ANN predicted values of Cr concentration in the BL for the four soil groups (four different amendments) and their corresponding correlation coefficients.

= 0.9998 R 2 = 0.9986 R 2 = 0.9989 R 2 = 0.9991
An average correlation coefficient of 0.9998 between the measured and ANN predicted values as found. This indicates that the ANN model was able to predict the Cr concentration in the BL rapidly and accurately. In order to investigate the effects of the soil amendments, soil pH, soil EC and DOC inputs on the Cr concentration in the BL, a parametric study of the ANN output with respect to the inputs was performed for each soil treatment with the trained ANN.

For each input factor, four values in the interval between the minimum and maximum values of each input were applied here to capture the non-linear response (Table 6). Full factorial design generated 256 ( ) combinations to study the effect of each input on the Cr response.

The computation time was about 2 seconds. To explore the relationships between the inputs and the output, several response surfaces (RS) were plotted consisting of 3D graphical representation of a response between two independent variables (inputs) and the output. The 3D RS plots provide insight into the behavior of the system and enable investigation of the parametric Cr concentration results

versus the levels of the effecting factors predicted by the ANN model. Figure 3 shows the coupled effects of the pH and EC on the Cr concentration in BL for two different values of DOC (14 and 34 mg.l -1 ). decreased the Cr concentration in the BL to 1, 1.2 and 1.4 mg.kg -1 , respectively, compared to the untreated soil which presents a reference Cr concentration of about 2.4 mg.kg -1 . The same effect of soil amendments can be observed when the DOC value increased to 34 mg.l -1 (Fig. 3 right-hand column). If we compare the right and left columns of Figure 3, we can see that the increase in DOC concentration from 14 to 34 mg.l -1 in the soil slightly increased the availability of Cr to plants in the treated (CPM, DL, DLX CPM) and UNT soils by 0.3, 0.2, 0.2, 0.4 mg.kg 1 ,respectively. [START_REF] Barcelona | Oxidation-reduction capacities of aquifer solids[END_REF]Holm (1991), Pantsar-Kallio et al. (2001) and [START_REF] Seaman | Immobilization of nickel and other metals in contaminated sediments by hydroxyapatite addition[END_REF] reported that oxidation and reduction reactions are important in the fate, transport, and toxicity of Cr in the soil. These reactions are governed by many factors including organic matter, pH, aeration, soil moisture content, wetting and drying, microbial activity, the content in clay minerals and availability of electron donors and acceptors. Moreover, the amendments added to the soil have the capacity to change the Cr from Cr(VI), which has a high mobility and toxicity and facilitates leaching, to Cr(III), which is relatively insoluble and resistant to leaching [START_REF] James | Oxidation-reduction chemistry of chromium: Relevance to the regulation and remediation of chromate contaminant soils[END_REF]. [START_REF] Fendorf | Surface reactions of chromium in soils and waters[END_REF] also reported that the reduction of Cr in soils is accelerated by the presence of organic matter and divalent iron. If Cr in the soil is converted to trivalent oxide or co-precipitated with Fe hydrous oxide or organic matter, it is likely to remain stable for a long time. Our results agree with those of [START_REF] Hsu | Characterisation and extractability of copper. manganese. and zinc in swine manure composts[END_REF], who reported that the high affinity of metals for CPM had two-sided consequences. The first is that in the presence of DOC the mobility of trace elements increases by forming complexes with the humic acid and fulvic acid, leading to the high mobility and availability of metals to plants. Secondly, non soluble high molecular weight organic acids can retain significant concentrations of trace metals in soil upon soil acidification, thus decreasing their mobility [START_REF] Chirenje | Effects of acidification on metal mobility in a papermill-ash amended soil[END_REF].

The concurrent effect of the three studied factors can be observed clearly in the soil treated with CPM (Fig. 3-right-hand column), where it can be seen that the increase in the DOC value (34 mg.l -1 ) led to an increase in the Cr availability to the plant from 1.2-1.4 mg.kg -1 in the case of DOC=34 mg.l -1 compared to soil treated with CPM containing less DOC (14 mg.l - 1 ) where it decreased from 1.2 to 0.8 mg.kg -1 . The increase in pH leads to a slight decrease in Cr concentration in plants, whereas the decrease in EC leads to a strong increase in Cr concentration in the BL from 0.2 at EC=1100 mg.kg -1 to 1.3 at EC=800 mg.kg -1 in the case of DOC=34 mg.l -1 . This result can be explained by the fact that in the case of anions (Cr(VI)), the decrease in pH promotes the release of HO-ions. This then leads to a decrease in competition between anions and HO-ions, which then accelerates the formation of new phases. Thus, the solubility of Cr anions decreases when pH decreases. [START_REF] Dzombak | Surface Complexation Modeling -Hydrous Ferric Oxide[END_REF] reported that when soil pH increases, the mobility of metals decreases, thereby decreasing the uptake of Cr by living species as in the case of soil treated with DL, CPM at DOC=14 mg.l -1 . Another important factor that has a major effect on the bioavailability of Cr is EC. Increases in chloride, sulfate, carbonate, bicarbonate, nitrate and phosphate concentrations in solution lead to the formation of metallic salts, which increase the EC of the soil solution. An increase in salinity is associated with an increase in the concentration of major elements (Na, K, Ca, Mg), which compete with trace metals for sorption sites [START_REF] Tam | Mangrove soils in removing pollutants from municipal wastewater of different salinities[END_REF]. This is different from our results where we found that the increase in DOC and pH and decrease in EC lead to an increase in Cr concentration in plants.

The predicted findings suggest that due to the large variation of Cr concentration in the BL with different treatments, the best amendment for reducing soil Cr toxicity is the (CPM) treatment. This reduced Cr concentration from 2.4 mg.kg -1 in the untreated soil to 1 mg.kg -1 (case of DOC=14 mg.l -1 ) and from 2.8 mg.kg -1 in the untreated soil to 1.2 mg.kg -1 (case of DOC=34 mg.l -1 ). These two DOC values result in non-linear Cr variation versus pH and EC.

However, the DL and DLX CPM treatments generated intermediate Cr concentration levels but with a more stable (linear) variation compared to that of the CPM treatment.

When all the results are considered, it can be seen that the Cr tends to evolve from nonlinear responses for UNT and CPM soils to linear responses for DL and DLX CPM soils.

UNT soil generated the highest non-linear variation in Cr concentration, suggesting that the results are sensitive to pH and EC. Such a variation is reduced, however, with the addition of CPM and DL or with a combined treatment (DLX CPM). We found that among the investigated factors, pH and DOC are the most important parameters affecting the Cr concentration in BL.

However, there are only a limited number of published studies available for describing the techniques of stabilization of Cr in the soil. Because of the low reactivity of its common species in soils, even if Cr is added to soil in the mobile form Cr(VI), it can be converted to its stable form Cr(III). [START_REF] Jop | Comparative toxicity and speciation of two hexavelant chromium salts in acute toxicity tests[END_REF] reported that the dominant species of Cr(V1) at pH > 6.5 is chromium oxide (the case of our soil). As Cr(VI) species are negatively charged, they do not complex with anionic particulate matter and are more bioavailable. In our experience, we have noted that the addition of both organic and inorganic amendments to the soil can decreased the bioavailability of Cr with reference to untreated soil.

Comparison of MLR and ANN performance

Four MLR experiments were performed, one each of the four soil training data pertaining to every amendment, to quantify the relationships between Cr concentration in BL After determining of these equations, comparison between predictive results of the ANN and MLR models was performed for the training and test data sets. The obtained coefficients of correlations among the results (Table 7). This indicates that the results of ANN model are better than that of MLR models for all amendment cases. Our finding agrees well with those of van der Zee and van Riemsdijk (1987), [START_REF] Andersen | Distribution coefficients of Cd, Co, Ni and Zn in soils[END_REF], [START_REF] Streck | Heavy metal displacement in a sandy soil at the field scale: I. Measurements and parameterization of sorption[END_REF], [START_REF] Römkens | Cd, Cu and Zn solubility in arable and forest soils: consequences of land use changes for metal mobility and risk assessment[END_REF], [START_REF] Tiktak | Modeling cadmium accumulation at a regional scale in the Netherlands[END_REF], Schaap and Lei (1998), [START_REF] Elzinga | General purpose Freundlich isotherms for cadmium, copper and zinc in soils[END_REF], [START_REF] Sarmadian | Modeling of Some Soil Properties Using Artificial Neural Network and Multivariate Regression in Gorgan Province, North of Iran[END_REF]. The interactions of the soil factors in the form of response surfaces were analyzed and compared to existing published results. This methodology could be effectively used to study the importance of individual, cumulative and interactive effects of the selected soil inputs in Cr concentration in bean leaves. The predictive ANN models used to evaluate the Cr concentration corresponded well with the experimental results reported in the literature. The ANN models developed here showed that a plausible innovative low-cost strategy for in situ remediation of Cr contaminated soils using organic and inorganic amendments, modified vegetation, or a combination of the two approaches. It should be noted that the ANN approach proposed here does not take into account all the possible factors that may influence soil toxicity. The primary aim was to illustrate the potential of the ANN method in its ability for rapid and accurate prediction of soil toxicity. The ANN model can be extended by including additional factors and their combinations to capture complex Cr behavior.

Overall, the ANN modeling outperforms MLR modeling. The effort required to calibrate the ANN and MLR models were similar, and both require about the same amount of time and processing resources. Despite their good performance, ANNs suffer from a number of limitations. First, they are not able to explain the physical relationships between the inputoutput data. Secondly, there are no general guidelines for the design of ANN architecture for a given problem. There is a need for more research to develop such guidelines to enable the extensive application of ANNs for non-specialists. Nevertheless, ANNs have a number of significant benefits that make them a powerful, rapid and practical tool for solving many soil engineering problems. The implementation of ANN modeling for the robust and reliable prediction of metal concentration in plants using additional soil data such as soil particle size and moisture levels in a practical sensor system appears very promising. Future significant work is required to achieve this goal. The results of ANN testing (prediction) allow for the investigation of the soil factors' interactions. This methodology could therefore be effectively used to study the importance of individual, cumulative and interactive effects of the soil parameters. Moreover, the ANN method can be used in conjunction with mechanistic models at the research level as a method to determine the most important parameters in a design that could then be used to formulate a mechanistic model and to determine where future research efforts should be directed. The tables [START_REF] Baize | Un Point sur Les Teneurs Totales des Eléments Traces Métalliques dans les Sols[END_REF][START_REF] Baize | Les Éléments Traces Métalliques dans les Sols -Approches Fonctionnelles et Spatiales[END_REF]. b common As mean values for all French soil types [START_REF] Baize | Les Éléments Traces Métalliques dans les Sols -Approches Fonctionnelles et Spatiales[END_REF].

Fig. 1

 1 Fig. 1. a) Location of studied sites from A to E. The arrows indicate the studied site P3 (adapted from Mench and Bes, 2009). b) The two plots of soil with the different types of amendment (adapted from Bes, 2008).

  dwarf beans were weighed (35-150 mg) directly into Savillex polytetrafluoroethylene PTFE 50 ml vessels. To each vessel 2 ml H 2 O and 2 ml supra-pure 14 M HNO 3 were added and the vessels were heated open at 65 °C for 2 h. Then, the vessel caps were closed and the containers were left overnight at 65 °C (12-14 h). After that they were opened, 0.5 ml of H 2 O 2 (30%) was added to each sample and left at 75 °C open for 3 h. Then, 1.5 0.5 ml of fluorhydric acid HF (48%) was added to each sample, vessel caps were closed and the samples were left at 100 °C overnight. Then, vessels were opened and kept at 120 °C for 4-5 h evaporating to dryness, taken off heat, 1 ml HNO 3 + 5 ml H 2 O + 0.1 ml H 2 O 2 were added to each vessel, gently warmed up and after cooling down made up to 50 ml. Trace element concentrations in digests were determined by ICP-MS (Varian 810-MS) using standard solution of measured trace elements, in our case, Reference Standard Solution of Chromium (1000ppm ±1%/Certified) was used. The accuracy of the metals determination was checked by performing calibrations with standard reference solution. Strong correlation was found between the measured and the reference results (R 2 =0.998). After the calibration phase, 4 repeated measurements were performed for each digest generating 64 testing results (4 repeated  16 digests). The precision of the metal content measurement was assessed by the standard deviation (SD) (Table

  Measured soil variables included soil pH, soil EC, DOC and Cr concentration in the BL with 4 replications for each measurement (4  4 measurements) for the ANN training. Then, a neural network model was developed and trained to predict the exposition of the BL to the high Cr concentration in the soil. The inputs are the soil amendment, soil pH, soil EC and DOC. The output is Cr concentration in the BL.

Fig. 2 .

 2 Fig. 2. Neural network architecture composed of four input layers, two hidden layers and one output layer.

  outputs of the layer m, f is the activation function, L is the number of connections to the previous layer, bias, representing the constant part of the activation function.

  internal connections to minimize errors between the network output and target output (Levenberg-Marquardt back-propagation or BP training algorithm in the current work). The knowledge is represented and stored by the strength (weights) of the connections between the neurons.

  was applied. The basic ANN configuration employed in this study has a double hidden layer with six neurons of each layer with a learning rate . The learning rate coefficient  and the momentum term  are two user-defined BP algorithm training parameters that affect the learning procedure of the ANN. The training is sensitive to the choice of these net parameters. The learning rate coefficient, employed during the adjustment of 1  m ji w , was used to speed up or slow down the learning process. A larger learning coefficient increases the weight changes, hence large steps are taken towards the global minimum of error level, while smaller learning coefficients increase the number of steps taken to reach the desired error level. Tests performed for more than two hidden layers and different  and  parameters showed no significant improvement in the obtained results.A total of 64 measurements were performed. The proportion of ANN training set from the available data ranged generally from 25% to 80%. The proportion of ANN testing set from the available data is about 15 to 20% and the proportion of the validation data set is about (5 to 15%)[START_REF] Haykin | Neural Networks and learning machine[END_REF]. In the current work, the experimental data (64 cases) were subdivided in three sets: 62.5% of the data were used for training (40), 25% for testing (16) and 12.5% for validation (8) covering a wide range of the experiments for validation (2 samples from every experiment variant). The testing data were not used for training. The testing data provided cross validation during the ANN training for verification of the network prediction accuracy. The validation data were used to measure the performance of the predictive capability of the ANN after complete training.

  considerably the ANN size and making the training difficult. If such is the case, it is possible to model the nominal variable using a single numeric sequential encoding if these non-numeric data are inputs. These sequential codes are not quantities or values related to the treatments or any classification of them. In the current ANN model, these codes are treated by the ANN algorithm in the following general form: o In case #1 (UNT amendment), the prediction model is determined by the ANN learning phase related to the case 1 representing the UNT treatment. o In case #2 (CPM amendment), the prediction model is determined by the ANN learning phase related to the case 2 representing the CPM treatment. o In case #3 (DL amendment), the prediction model is determined by the ANN learning phase related to the case 3 representing the DL treatment. o In case #4 (DLX CPM amendment), the prediction model is determined by the ANN learning phase related to the case 4 representing the DLX CPM treatment.

Fig. 3 .

 3 Fig. 3. Chromium concentration in BL in mg kg -1 : effects of soil pH and EC for two different limit values

FiguresFigure1. a )Figure 2 .Figure 3 .

 a23 Figures

Table 1 .

 1 Main characteristics of site P3 (0-0.25 m soil layer).

	Parameters

Site P3 Background values in French sandy soils a

	Sand %	83.5 ± 1.1
	Silt %	11.5 ± 0.9
	Clay %	3.8 ± 1.2
	C/N	17.2
	OM (g kg -1 )	15.9
	CEC (cmol + kg -1 ) 3.49
	Organic C (g kg -1 ) 9.19
	total N (g kg -1 ) 0.534
	pH	7.0 ± 0.23
	As (mg kg -1 )	9.8	1.0-25 b
	Co (mg kg -1 )	2	1.4-6.8
	Cu (mg kg -1 )	674 ± 126 3.2-4.8
	Cr (mg kg -1 )	23	14.1-40.2
	Mn (mg kg -1 )	181	72-376
	Ni (mg kg -1 )	5	4.2-14.5
	Zn (mg kg -1 )	46	17-48
	A : Median and high vibrissae values except for As (Baize, 1997 and Baize and Tercé, 2002).
	B : Common As mean values for all French soil types (Baize and Tercé, 2002)

Table 2 .

 2 The experimental values (pH, EC, DOC and Cr).

	Four replications were

Mean EC (μS cm -1 ) SD- COV (%) Mean DOC (mg l -1 ) SD- COV (%) Mean Cr concentration in the soil (mg kg -1 )

										SD-
										COV
										(%)
	B4-9	DL	7.34 NS		1308 NS		38.46 ⁎		16.93 ⁎⁎
	B1-3	DLX CPM	7.45 NS		1192 NS		33.12 ⁎		16.09 ⁎⁎
	B2-6	DLX CPM	7.00 NS	0.32-	1347 NS	152.2-	34.26 ⁎	2.50-	15.91 ⁎⁎	0.2-
	B3-13	DLX CPM	7.07 NS	4.46%	1457 NS	11.90%	29.16 ⁎	7.02%	15.93 ⁎⁎	1.27%
	B4-12	DLX CPM	7.59 NS		1119 NS		29.75 ⁎		16.35 ⁎⁎

NS (non significant).

⁎ Significant for p < 0.05.

Table 3 .

 3 Selected inputs and output for ANN training (UNT = #1, CPM = #2, DL = #3, DLX CPM = #4).

	Inputs	Level Min value Max value
	Soil treatment 4	#1	#4
	pH	4	6.98	7.6
	EC (μS cm -1 ) 4	754	1654
	DOC (mg l -1 ) 4	14.337	34.260
	Output
	Cr concentration in the bean leaves (mg kg -1 )

Table 5 .

 5 Comparison between averaged measured and ANN predicted values of Cr concentration in the bean leaves for the four soil groups. The determination coefficient R 2 is based on the eight experimental samples kept for validation.

	Soil (UNT)	Soil (CPM)	Soil (DL)	Soil (DLX CPM)
	Measured NN Measured NN Measured NN Measured NN
	3.29	3.285 0.762	0.764 0.519	0.519 0.524	0.523
	0.748	0.746 0.709	0.710 0.775	0.773 0.819	0.820
	0.601	0.600 0.392	0.391 0.892	0.890 0.805	0.804
	0.661	0.662 0.498	0.496 0.618	0.616 0.781	0.780
	R 2

Table 6 .

 6 Selected four inputs for the ANN prediction. Full factorial combinations generate 256 (4 × 4 × 4 × 4) data to investigate their effects on soil response.

	Inputs	Min Max Level 1 Level 2 Level 3 Level 4
	Soil treatment #1	#4	UNT CPM DL	DLX CPM
	pH	6.98 7.6	7.0	7.2	7.4	7.6
	EC (μS cm -1 ) 754 1654 800	1100 1400 1600
	DOC (mg l -1 ) 14.337 34.260 14	20	28	34

  and the soil factors (pH, EC and DOC). The software used for the purpose of statistical analyses was Statistica 10. These four MLR equations are:

		Amendment							MLR equations per amendment
			UNT	BL Y		255 . 2		0623 . 0			x	pH		e 44 . 6	 4		x	EC		00128 . 0		x	DOC
			DL	Y			987 . 2		113 . 0		x			e 26 . 1	 3		x		00097 . 0		x
				BL												pH			EC	DOC
			CPM	Y			851 . 1		0124 . 0		x			e 67 . 6	 4		x		00115 . 0		x
				BL												pH			EC	DOC
		DLX CPM	Y			986 . 1				0118 . 0			x			e 61 . 6	 4		x		00101 . 0		x
				BL													pH			DOC
	where	x ,	x and	x	denote, respectively, values of pH, EC and DOC.
		pH	EC	DOC

Table 7 .

 7 Correlation coefficients obtained by ANN and MLR methods.Reducing the concentration of Cr in contaminated soils can be performed by adding soil amendments. These amendments reduce Cr mobility by promoting the formation of insoluble precipitates or by enhancing the soil's capacity to bind Cr to the soil. The latter can be achieved directly through the addition of adsorbent materials or indirectly by adjusting the soil's pH-EC combination to provoke Cr absorption onto the soil. In this preliminary study, three factors were retained (pH, EC and DOC) in combination with four soil amendments (UNT, CPM, DL and DLX CPM). The present study confirmed that organic matter (CPM) is one of the best soil amendments, as it reduced the concentrations of Cr in the BL more than the other amendments.

		UNT	CPM	DL	DLX CPM
	Method	Trainin	Trainin	Trainin	Trainin	Trainin	Trainin	Trainin	Trainin
		g data	g data	g data	g data	g data	g data	g data	g data
	Neural network	0.999	0.998	0.998	0.996	0.998	0.997	0.999	0.995
	Linear
	regressio	0.876	0.695	0.792	0.702	0.765	0.637	0.882	0.802
	n

Table 1 .

 1 Main characteristics of site P3 (0-0.25 m soil layer).

	Parameters	Site P3	Background values in
			French sandy soils a
	Sand %	83.5 ± 1.1
	Silt %	11.5 ± 0.9
	Clay %	3.8 ± 1.2
	C/N	17.2
	OM (g.kg -1 )	15.9
	CEC (cmol + .kg -1 )	3.49
	Organic C (g.kg -1 )	9.19
	total N (g. kg -1 )	0.534
	pH	7.0 ± 0.23
	As (mg.kg -1 )	9.8	1.0-25 b
	Co (mg.kg -1 )	2	1.4-6.8
	Cu (mg.kg -1 )	674 ± 126	3.2-4.8
	Cr (mg.kg -1 )	23	14.1-40.2
	Mn (mg.kg -1 )	181	72-376
	Ni (mg.kg -1 )	5	4.2-14.5
	Zn (mg.kg -1 )	46	17-48

a median and high vibrissae values except for As

Table 2 .

 2 The experimental values (pH, EC, DOC and Cr). Four replications were performed for each measurement generating 64 testing results (4 soils  4 amendments 4 replicates) allowing for the determination of the mean values, standard deviations (SD) and coefficient of variations (COV).

	Soil reference	Amendments	Mean pH	SD-COV (%)	Mean EC (µS.cm -1 )	SD-COV (%)	Mean (mg.l -1 ) DOC	SD-COV (%)	Mean Cr (mg.kg -1 ) concentration in the soil	SD-COV (%)

Table 4 :

 4 Dry weight (g), concentration (mg.kg -1 ) and mineral mass of Cr (g per pot) measured in the BL.

	Soil amendments	Dry Weight (g)	Cr concentration in the plant (mg.kg -1 )	Mineral mass (g per pot)
	UNT	0.087±0.04	1.438±1.23	0.094±0.03
	CPM	0.112±0.02	0.733±0.08	0.083±0.01
	DL	0.122±0.02	0.588±0.17	0.069±0.00
	DLX CPM	0.103±0.00	0.652±0.012	0.067±0.01

Table 5 .

 5 Comparison between averaged measured and ANN predicted values of Cr concentration in the bean leaves for the four soil groups. The determination coefficient R² is based on the eight experimental samples kept for validation.

	Soil (UNT)	Soil (CPM)	Soil (DL)	Soil (DLX CPM)
	Measured	NN	Measured	NN	Measured	NN	Measured	NN
	3.29	3.285	0.762	0.764	0.519	0.519	0.524	0.523
	0.748	0.746	0.709	0.710	0.775	0.773	0.819	0.820
	0.601	0.600	0.392	0.391	0.892	0.890	0.805	0.804
	0.661	0.662	0.498	0.496	0.618	0.616	0.781	0.780
	R²=0.9998	R²=0.9986	R²=0.9989	R²=0.9991

Table 6 .

 6 Selected four inputs for the ANN prediction. Full factorial combinations generate 256 () data to investigate their effects on soil response.

	Inputs	min	max	Level 1	Level 2	Level 3	Level 4
	Soil treatment	#1	#4	UNT	CPM	DL	DLX CPM
	pH	6.98	7.6	7.0	7.2	7.4	7.6
	EC (µS.cm -1 )	754	1654	800	1100	1400	1600
	DOC (mg.l -1 )	14.337	34.260	14	20	28	34

Acknowledgements

Our work was financially supported by ADEME (Projects PhytoDEMO and CWdemo), Department of Brownfields and Polluted Sites, Angers, France, the Aquitaine Region Council (Project Phytorem), Bordeaux, France, and the European Commission under the Seventh Framework Programme for Research (FP7-KBBE-266124, GREENLAND). The authors would like to thank the anonymous reviewers for their valuable efforts, comments and suggestions to improve the manuscript.


Julien Thébault

Denis Solas

Colette Rey

Thierry Baudin

Olivier Fandeur

Michel Clavel

POLYCRYSTALLINE MODELLING OF UDIMET 720 FORGING

Keywords: Deformation, Dynamic Recrystallization, Crystalline Approach, Coupling, Forging

A crystalline modelling of deformation implemented in a finite element code coupled to a recrystallization Cellular Automaton code is proposed and applied to forging processes of superalloys. The coupled modelling is used in order to obtain a better understanding of the microstructural evolution of superalloys during high temperature forging at different strain rates and temperatures. The framework of the modelling is large plastic deformation and large lattice rotation. The used internal variables are dislocations densities on slip systems of the different phases. Modelling is based on viscoplatic constitutive and hardening laws at the scale of the slip systems and describes local strain and stress fields as well as the stored energy and the rotation of the lattice in the grains of the microstructure. At different steps of deformation, formation of subgrains, annihilation of dislocations, nucleation, growth and new orientation of grains are computed. The 3D aggregates representing the superalloy, are built up from Electron Back Scattered Diffraction method (EBSD) by means of a high resolution Scanning Electron Microscope. The phases are identified by means of EBSD, chemical analysis (EDS) and observations with a Scanning Electron Microscope. In this paper the studied aggregate is realised from a semi product of Udimet 720. Such technique is able to give us, a realistic description of the crystalline orientation, morphology and position of grains in the aggregate. The Finite Element meshing is deduced from the EBSD analysis. At high temperature, the Udimet 720 is constituted by a γ matrix with a Face Centred Cubic structure and γ' precipitates (Ni 3 (Ti,Al)) with a Simple Cubic structure. The various material parameters used for the coupled modelling are previously determined from compression tests performed at several strain rate and temperature; The dislocation densities are measured from Transmission Electronic Microscope.

Introduction

The Udimet 720 1 alloy is a promising material to build turbine discs. It has been developed to replace classical grades such as Waspaloy and Inconel 718. The strength improvement, obtained by addition of hardening elements, reduces ductility and requires a γ' subsolvus forging. Indeed, for temperatures above the solvus, the γ' phase is solved causing a strong hardening of the matrix. The grains boundaries behave like weakest links and forging become impossible. In the forging temperature range, the material is composed of two phases with γ matrix of FCC structure and an hardening phase γ' under a precipitate shape (Ni 3 (Ti,Al)) with a SC structure. 1

Material supplied by Aubert & Duval who cofinance this study with Ecole Centrale Paris

The aim of this study is to predict the microstructural evolution of Udimet 720 during forging at 1100°C, through a crystalline approach. During high temperature forging, the microstructure is ruled by the simultaneous influence of deformation and dynamic recrystallization. The different mechanisms (plastic deformation, nucleation, grain growth, annealing) depending on temperature, strain rate and deformation ratio respectively, lead to a decrease of the stress (softening) during forging.

In this paper, a crystalline approach using Finite Element method (Cristalecp) is coupled at different steps of the deformation to a recrystallization scheme based on a Cellular Automaton modelling (Reclpces). The used crystalline approach [START_REF] Hoc | Experimental and numerical analysis of localization during sequentials tests for IF-Ti steel[END_REF][START_REF] Delaire | Plastic Heterogeneities of a Copper Multicrystal Deformed in Uniaxial Tension : Experimental study and Finite Element Simulations[END_REF][START_REF] Erieau | Modelling of deformation and rotation bands and of deformation induced grain boundaries in IF steel aggregate during large plane strain compression[END_REF] can describe the interactions between the two phases and can compute the evolution of the local strain and stress fields as well as the density of dislocations and the rotation of the lattice in the different grains. Such crystalline modelling is now well known technique to determine the microstructure effect on the mechanical local behaviour of aggregates [START_REF] Peirce | Material rate dependence and localized deformation in crystalline solids[END_REF][START_REF] Beaudoin | A hybrid finite element formulation for polycrystal plasticity with consideration of macrostructural and microstructural linking[END_REF][START_REF] Becker | Effects of grain interactions on deformation and local texture in polycrystals[END_REF][START_REF] Acharya | Grain-size effect in viscoplastic polycrystals at moderate strains[END_REF][START_REF] Barbe | Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results[END_REF][START_REF] Barbe | Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model[END_REF][START_REF] Meissonier | Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains[END_REF][START_REF] Bhattacharyya | Evolution of grain scale microstructure during large strain simple compression of polycrystalline aluminium with quasi columnar grains: OIM measurements and numerical simulations[END_REF].

Cellular Automaton (CA) and Monte Carlo (MC) algorithms are also standard techniques in computer simulation of static recrystallization processes. The use of such models helps us to understand experimental observations and improves our knowledge of the recrystallization process. In past years, the input microstructure and texture was most often assumed randomly [START_REF] Srolovitz | Computer simulation of recrystallization-I. Homogeneous nucleation and growth[END_REF][START_REF] Srolovitz | Computer simulation of recrystallization-II. Heterogeneous nucleation and growth[END_REF]. However these assumptions are seldom verified and different procedures were developed to introduce real deformed microstructure [START_REF] Baudin | Simulation of the anisotropic growth of goss grains in Fe3%Si sheets (grade HiB)[END_REF][START_REF] Baudin | Simulation of primary recrystallization from tem orientation data[END_REF] or simulated deformed microstructure [START_REF] Solas | Deformation and recrystallization of hexagonal metals: modeling and experimental results for zinc[END_REF][START_REF] Erieau | Experimental study and numerical analyze of the influence of heterogeneities induced by cold deformation on the primary recrystallization of IF-Ti steel[END_REF][START_REF] Baudin | Influence of thermo-mechanical treatments on the stored energy simulated by FEM for two low carbon steels[END_REF][START_REF] Volovitch | Monte Carlo modeling of low carbon steel recrystallization: role of thermo-mechanical treatment and chemical composition[END_REF] as input data in the recrystallization simulation.

The studied aggregate deduced from a semi product by Electron Back Scattered Diffraction method (EBSD), is described in section 2. The two above mentioned approaches are detailed and the material parameters are given in section 3. The results are presented in section 4. A discussion and a conclusion end this paper.

Material and Aggregate

The simulated aggregate corresponds to a sample cut in the centre of a semi-product (disc=254mm) supplied by the Aubert&Duval company. The microstructure aggregate was characterized by Scanning Electron Microscopy (SEM), EBSD and Energy Dispersive Spectroscopy (EDS).

The microstructure of the semi product is given in Figure 1. The matrix (γ phase) is constituted by secondary and tertiary γ' precipitates (=100nm) which are not visible at the scale of the Figure 1. These precipitates being solved in the matrix at the

                    ) sgn( 1 0   0  s    u u su s c h    
forging temperature, the matrix is considered as CFC. The grain size of the matrix is the 5-50µm range and many grains present Σ3 twin boundaries. The most part of the primary precipitates γ' (grain size 1-5µm) is situated at the grain boundaries. The γ' structure is SC. The material presents a weak texture coming from the different processes before forging. Experimental compression curves, performed at 1100°C for different strain rates, point out a large dependence of behaviour with the strain rate (see Figure 2).

Figure 2. Stress-strain curves for 0.7 10 -1 s -1 , 0.7 10 -2 s -1 , 0.7 10 -3 s -1 , 0.7 10 -4 s -1 respectively

Modelling of the forging

Crystalline approach

The Udimet is considered as a two phase material, the matrix and the primary precipitates γ' are assumed as a FCC and SC structures respectively. The crystalline approach applied for each phase is implemented in the Finite Element Code ABAQUS. The crystalline plasticity constitutive law uses a large deformation framework, based on the multiplicative composition of the deformation gradient into elastic and plastic parts [START_REF] Peirce | Material rate dependence and localized deformation in crystalline solids[END_REF][START_REF] Teodosiu | Finite implementation of the large elastoplastic deformation of multicrystals[END_REF].   as a reference slip rate. As long as slip occurs, hardening is caused by the interactions between different slip systems. This is usually represented through a phenomenological relationship between a critical shear stress increment and all the slip strain increments weighted with a hardening matrix su h .

(

) 2
The critical shear stress is also related to the densities of dislocations u  on the different glide systems by:

(

) 3
where 0

 contains the friction of the lattice, increased by the effect of alloying elements. a su is an interaction matrix which coefficients depend on the interactions between dislocation families (s) and (u).

The hardening matrix expression can be deduced of equations ( 2),

(3) and ( 4). The hardening matrix su h evolves with increasing deformation, but depend on internal variables (dislocation densities on all slip systems) in order to take into account the physical aspects of plasticity [START_REF] Hoc | Experimental and numerical analysis of localization during sequentials tests for IF-Ti steel[END_REF][START_REF] Delaire | Plastic Heterogeneities of a Copper Multicrystal Deformed in Uniaxial Tension : Experimental study and Finite Element Simulations[END_REF][START_REF] Erieau | Modelling of deformation and rotation bands and of deformation induced grain boundaries in IF steel aggregate during large plane strain compression[END_REF]. On a given slip system (s), the evolution of the dislocation density s

 is governed by a production term based on Orowan's relationship and by an annihilation term which takes into account the dynamic recovery during deformation. Thus, it may be:

         u u su s c a   
K L u t t u 1 1 1      (5)
 and b are respectively shear modulus and Burgers vector magnitude; c g is proportional to the annihilation distance of dislocation dipoles; K is a material parameter and D is the average polycrystal grain size. Only self a ss and latent a su hardening are considered here. The physical meaning of all the parameters set is detailed in [START_REF] Erieau | Modelling of deformation and rotation bands and of deformation induced grain boundaries in IF steel aggregate during large plane strain compression[END_REF].

The parameters used for this simulation were identified using a polycrystalline model and an inverse method from experimental results obtained at different temperatures and deformation rates.

At high temperature and for the two phases, the interaction matrix [START_REF] Franciosi | Glide mechanisms in B.C.C. crystals : an investigation of the case of -iron through multislip and latent hardening tests[END_REF] is assumed weak, which means that dislocations can easily pass through the obstacles due to the latent dislocations.

The material parameters are usually determined by inverse method using results on different mechanical tests. In this case, for high temperature (1100°C), only experimental compression curves are available, the initial dislocations density in the two phases being determined by TEM. The parameters are presented in Table I.

where: [START_REF] Acharya | Grain-size effect in viscoplastic polycrystals at moderate strains[END_REF] where m  is the energy of high-angle grain boundaries, *  is the misorientation limit for low angle boundaries (taken as 15° in the present simulations), ' ss  is the crystallographic misorientation between two neighbours sites s and s'. The grain boundary energy as the function of the misorientation corresponds to the well-known Read-Shockley equation. The mobility M of the boundary between the two sites is calculated according to: [START_REF] Barbe | Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results[END_REF] where M m is the average mobility of high angle grain boundaries and the misorientation angle is expressed in degrees.

In this simulation, one type of nucleation was implemented: site nucleation with high stored energy, which allows to reproduce the discontinuous dynamic recrystallization mechanism. When the stored energy is larger than a critical value, nucleation occurred. The orientation remains the same and its stored energy is set to zero. Concerning the growth step, the reorientation of each site is estimated. For each site, one of its six neighbours is selected at random, this site 2 has to be already in a recrystallized configuration. Then the orientation of site 2 is attributed to site 1 and its stored energy is set to 0. The variation of the energy E between the two configurations is computed. As soon as the driving force is positive the reorientation is not accepted. The velocity V of the grain boundary is expressed as: [START_REF] Barbe | Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model[END_REF] Where M is the mobility and E is the driving force. During a time increment t inc the grain boundary moves along a distance d.

           u c u t t st su su g L a a µ h   1 2 ' ' ss s s gb E                           * ' * ' * ' * ' ' ln 1            ss m ss ss ss m ss when when E M V                              



This distance is compared to the cell size d 0 . The probability of reorientation is expressed as: [START_REF] Meissonier | Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains[END_REF] When all the sites are visited, the microstructure is updated. With this model, a length scale is introduced. As a consequence, using a coherent system of units for the driving force and the grain boundary mobility, a real time scale can be used during the growth step.

Meshing and boundary conditions

The finite element mesh is constituted by 8 nodes hexahedron with reduced integration (C3D8R) obtained directly from EBSD acquisitions. This analysis has been performed on a semi-product supplied by Aubert & Duval with a FEG-SEM (LEO 1530) using a 0.6µm step (Figure 3a). Each element of the meshing is characterized by a constitutive law and a dislocation evolution law as well as the initial dislocation density, the initial crystalline orientation and spatial coordinates. By this method, morphology of grains, spatial distribution of phases and crystallographic orientation are taken into consideration, enabling us to describe grains and phases interactions effect on the local mechanical fields. In order to represent the forging process, boundary conditions of simple compression type are applied on the aggregate. The sequential steps (deformation-recrystallization) correspond to a deformation of 0.1. To avoid buckling for these large strains, the pattern thickness is set to 2µm. In this study, the 3D aggregate is composed of five similar layers and its dimensions are 48.6 x 48.6 x 10µm 3

Results

This chapter presents the results of the computation obtained after two and a half cycles on the aggregate composed by five similar layers. In order to reduce the computation time, only the intermediate layer is submitted to the sequential coupling.

First deformation: For the first deformation step, it is used parameters shown in Table 1 (named -state 0‖). The aggregate is 10% deformed at a 10 -2 s -1 strain rate. To trace stress evolution during sequential coupling, the stressstrain curve is drawn after each deformation step. In the first deformation step, Figure 5 shows that the yield strength is well represented and that the hardening is slightly higher than the experimentally observed one. Thus, during recrystallization, the stress decreases leading to an important microstructural evolution. Recrystallization: After 10% of deformation, dislocation densities are heterogeneous and nucleation takes place in sites where the energy is higher than a critical value. The comparison of the map at the deformed state (fig7a) and the deformed and recrystallized ones (called state 2) (Figure 7b), points out that some grains have grown and are exempt of dislocations (grain 2) whereas others retain a deformation sub-structure with a crystallographic orientation spread (grain 3) (see Figure 7c). One can also notices that some twin boundaries have vanished. The aggregate is again submitted to a 10% deformation with a strain rate of 10 -2 s -1 . After the second deformation (E=20%), the crystallographic orientation of some grains has evolved (grain 4)

and the misorientation of some sub-boundaries (located in deformed grains) has increased (Figure 9). One of the main features of the sequential coupling is to consider, at each step of the computation, all the sub-grains whose misorientation is higher than 2°. Some sub-boundaries created during the first deformation step and not annihilated by the recrystallization can increase their misorientation during the second deformation step.

Microstructural evolution after several cycles: Now the microstructural evolution of the intermediate layer after two and a half cycles is shown on Figure 10. Second recrystallization Second deformation this way it is used a sequential coupling of models of deformation -Cristalecp‖ and recrystallization -Reclpces‖. Currently the method is operational and the first results are promising. However it still remains to determine more precisely the mechanical parameters for deformation modelling and to take into consideration recrystallization mechanisms identified during experimental analyzes.

Figure 1 .

 1 Figure 1. Microstructural analysis of Udimet 720 by SEM/EBSD/EDS

  For a FCC material, glide occurs on the 12 {111}<110> slip systems and for SC material on the 6 {100}<110> slip systems. The resolved shear stress s  , the critical shear stress s c  and the slip rate s   are related by a viscoplastic power law:

  Udimet 720: matrix γ (orientation of the normal to the sample measured by EBSD) (a) Udimet 720: quality image SEM/EBSD (b) Udimet 720: Precipitates distribution (SEM/EDS) (d) Udimet 720: precipitates γ' (orientation of the normal to the sample measured by EBSD) mean free path of the mobile dislocations gliding on the system u.

D

Figure 3 . 1 Figure 4 .

 314 Figure 3. (a) Example of inverse pole figure map showing the position of the normal axis in the stereographic triangle, (b) phase map, (c) aggregate picture.Sequential couplingDuring high temperature forging, the microstructure evolves under the influence of dynamic recrystallization leading to softening. To perform a sequential coupling of the two modellings, we need to determine the deformation ratio (with -Cristalecp‖) and the recrystallization time (with -Reclpces‖). In this way a third model has been developed. This model corresponds to a macroscopic dynamic recrystallization where

Figure 5 .

 5 Figure 5. Comparison of simulated and experimental stress-strain curves (first step of deformation) During deformation, the microstructure evolves by crystal lattice rotation, leading to the formation of intragranular misorientations

Figure 6 .

 6 Figure 6. Grain boundary map and orientation map before and after deformation

Figure 7 .

 7 Figure 7. (a) Orientation map after 10% of deformation, (b) orientation map after recrystallization,(c) dislocation densities after recrystallization Second deformation: After the first cycle (deformation + recrystallization), the intermediate recrystallized layer (state2) is inserted in the aggregate at the state 0 (Fig 8.). The role of the surrounding layers is to apply more realistic mechanical fields on the intermediate layer. The intermediate layer differs from the

Figure 8 .

 8 Figure 8. Inserting a deformed and recrystallized layer into an aggregate at state 0

Figure 9 .

 9 Figure 9. (a) Orientation map after E=10% and recrystallization, (b) orientation map after 20% of deformation and (c) grain boundary map after the second deformation.

Figure 10 . 4 First

 104 Figure 10. Orientation evolution for two and half cycle of deformation and recrystallization

Table I .

 I Material parameters at 1100°C

		E (GPa)	υ	a su	0 (s -1 ) 	n	g c (nm)	K	τ 0 (MPa)	ρ 0 (m -2 )	D (µm)	b (nm)
	γ	126	0.3	8.10 -3	5.10 -5	6.2	10	100	5.5	10 14	10	0.26
	γ'	129	0.3	8.10 -5	10 -5	6.2	10	100	5	10 13	3	0.26
	The recrystallization model -Reclpces‖
	After deformation, a recrystallization step is performed. An
	energy is assigned to each cell as the sum of the stored energy
	E

stored and the grain boundary energy E gb . The stored energy is the result of the Finite Element calculation which gives the local dislocation density. The grain boundary energy depends on the misorientation of a given site with respect to its 6 neighbours

[START_REF] Solas | Deformation and recrystallization of hexagonal metals: modeling and experimental results for zinc[END_REF]

: