Jordan Seira
email: jordan.seira@ensiacet.fr

Catherine Claparols

Claire Joannis-Cassan

Claire Albasi

Mireille Montréjaud-Vignoles

Caroline Sablayrolles
email: caroline.sablayrolles@ensiacet.fr

Optimization of pressurized liquid extraction using a multivariate chemometric approach for the determination of anticancer drugs in sludge by ultra high performance liquid chromatography-tandem mass spectrometry

Keywords:

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Pharmaceutical residues in the environment and their possible biological or side effects on non-target organisms are an emerging research in environmental sciences [1]. The interest about their occurrence, their fate and their toxicity in the environment really took off at the end of 1990s and the number of publications has been constantly increasing since then [2].

After administration, large fractions of pharmaceuticals are not completely assimilated or metabolized in the body and then excreted as parent compounds or metabolites via urine and feces [3]. These compounds are collected and mixed in wastewaters, in which their concentrations can reach some g/L [4]. Pharmaceutical compounds suffer from partial removal during activated sludge treatment, the most common wastewater treatment plant (WWTP). Consequently, WWTP effluents are recognized as the primary spreading source of pharmaceutical pollution in the environment.

During activated sludge treatment, trace pollutants can mainly be affected by three mechanisms: volatilization, biodegradation or sorption onto sludge, depending on both compound and sludge physico-chemical properties. Therefore, volatilization is usually neglected for pharmaceuticals because of low Henry's constant [5]. While biodegradation has sometimes the signification of complete elimination, sorption onto sludge can be considered as a displacement of the pollution from the aqueous to the solid phase. Monitoring trace pollutants in solid part could be of crucial importance because of (1) possible influence toward bioavailability (i.e. biodegradation) to microorganisms and (2) stabilized-sludge landfill applications which can introduce sludge-born trace pollutants in the environment, increasing potential exposure risks. Consequently, investigating occurrence of trace compounds in biosolids could be a key factor for (1) upgrading WWTPs and trace pollutants removal and (2) the establishment of new regulations which are only focused on heavy metals, polychlorobiphenyls (PCBs) and polycyclic aromatic hydrocarbons (PAHs) for trace pollutants in sludge-amended soil applications.

Among the broad spectrum of available pharmaceutical products, there is still one class that paid little attention in spite of an environmentally devastating potential: the anticancer drugs. Including antineoplastic and endocrine-therapy drugs, these compounds are designed to prevent or disrupt cellular proliferation in cancer treatment schemes [6]. Unlike some other therapeutic classes, anticancer drugs exhibit very different physico-chemical properties. To name a few, some examples are log Kow ranging from -2.46 to 6.3 and pK a ranging from 1.45 to 9.8 [2]. Most of the anticancer drugs possess a strong carcinogenic, mutagenic and teratogenic potential and are thought as one of the most hazardous contaminants in water cycle [7]. Due to their mode of action, it is assumed that almost all eukaryotic organisms are vulnerable to genetic damages at very low concentrations [8]. As highlighted by the literature, their consumption is increasing and trends, including type of consumed drugs and practices of consumption, are diversifying [6].

The monitoring of anticancer drugs in the environment has encountered a tremendous interest for the last 3 years. Comprehensive overviews including analytical methods for their analysis [9], data about their environmental occurrence and fate [2] and assessment of environmental exposure [6] have been published under this period. These states-of-art revealed that environmental occurrence of anticancer drugs in water samples are few documented but data about their occurrence in solid samples are definitively scarce. Although analytical development for their determination in liquid samples is still of concern but fairly common, there is a great need of accurate analytical method focused on their detection in more challenging matrices such as solid part of sludge.

Performing extraction of trace pollutants from solid matrices is not easy to handle. A variety of procedures has been defined in the literature and can be divided in two distinct groups: classical and recent extraction techniques [10]. Classical techniques include mechanical stirring, Soxhlet and Soxtec, and ultrasound extraction (USE), the later has been used one time for the extraction of anticancer drugs in sludge samples [11]. Most of them are labor-intensive, time-consuming and require large amounts of solvents. Their application to solids is noticeably dropped and replaced with more time-saving and eco-friendly processes. Recent extraction techniques include micro-wave assisted extraction (MWE) and pressurized liquid (including hot water) extraction (PLE) among many examples. A comprehensive overview about the extraction of trace pollutants from sludge according different extraction techniques is available [10]. Due to the increasing number of published papers, PLE and its derivatives appear as the most promising technique for efficient extraction [12,13]. Up to now, only one application of PLE has been reported for the extraction of anticancer drugs in sludge samples [14].

Depending on the extractive conditions applied, the recovery of variable amounts of co-interfering compounds during PLE is possible [15]. To address this well-known drawback, a clean-up extract is often required. In most of cases, this step is performed by solidphase extraction (SPE). With the emergence of mixed-mode SPE implying polar, non-polar and ionic interactions with the sorbent, selective purification is allowed. Thus, mixed-mode SPE could be promising for recovering analytes with different physico-chemical properties and enhancing method specificity. Mixtures containing anticancer drugs are usually separated by liquid chromatography [2,9]. The trace level occurrence of these drugs in environmental samples justifies the use of sophisticated systems such as mass spectrometry (MS) detection. Thus, ultra high pressure liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) appears as the most powerful and adequate tool for fast separation and very selective and sensitive detection in complex matrices [10].

In light of these concerns, one of our objectives was to develop and validate an analytical method for determining the occurrence of anticancer drugs in the solid part of sludge. The drugs of interest are the alkylating cytotoxics cyclophosphamide (CP) and ifosfamide (IFO) and the antiestrogen hormonally active tamoxifen (TAM). Some of their relevant physico-chemical properties are given in Fig. 1. Among all the anticancer drugs, the investigation of their fate has recently been defined as preferential due to their consumption data, their behavior in WWTP and related predicted environmental concentrations (PEC) in the literature [6]. The method is based on the extraction from the solid matrix using semi-exhaustive PLE, extract clean-up using tandem Oasis MAX/MCX selective SPE and analysis by UHPLC-MS/MS. To highlight the influence of experimental conditions, optimization of PLE parameters was realized according to an experimental design. The method was validated for seven sludge samples representative of the French WWTPs profile. Some efforts have been carried out to identify which analytical step was detrimental in the determination of anticancer drugs. The use of deuterated standards has also been applied to check for possible complete compensation of losses through the analytical procedure. To our knowledge, this is the first time that anticancer drugs have been investigated in sludge originated from French WWTPs.

Experimental

Analytical standards and chemicals

Analytical standards cyclophosphamide monohydrate (CP), ifosfamide (IFO), tamoxifen (TAM) were purchased from Sigma-Aldrich (Saint-Quentin de Fallavier, France) and deuterated cyclophosphamide-d 4 (CP-d 4 ), ifosfamide-d 4 (IFO-d 4 ), tamoxifend 5 (TAM-d 5 ) were purchased from Toronto Research Chemicals (North York, Ontario, Canada) as chemical powders.

Methanol (MeOH), acetonitrile (ACN) and acetone were HPLC grade and purchased from Scharlau (Spain). Hydrochloric acid (HCl) 37% and formic acid (HCOOH) 99% were purchased from VWR Prolabo (Fontenay-sous-Bois, France). Ammonium hydroxide (NH 4 OH) 35% was purchased from Fischer Chemical (Loughborough, Leicestershire, UK). Ammonium acetate (NH 4 CH 3 COO) 98% was purchased from Merck (Damstadt, Germany). Na 2 EDTA was purchased from ICN BioMedicals (Aurora, OH, USA). The ultra pure water used for laboratory purposes as well as LC mobile phase was produced from demineralized water by a MilliPore system (Molsheim, France).

Stock solution (∼1000 mg/L) of each individual standard was prepared every 4 months by dissolving the appropriate amount in MeOH. Before any experiment, working solutions (i.e. dilution of the stock solution) were prepared in MeOH to the required concentration. Two distinct mixtures of standards CP (∼2 mg/L), IFO (∼2 mg/L), TAM (∼0.5 mg/L) and deuterated CP-d 4 (2 mg/L), IFO-d 4 (2 mg/L), TAM-d 5 (0.3 mg/L) were prepared in this way. For convenience, the terms MIX Standards and MIX Deuterated will now be used throughout this document. To minimize degradation of standards, stock and working standards solutions were wrapped in aluminum and stored at -20 • C after preparation.

Analytical procedure

Determining the anticancer compounds in sludge was carried out according to a procedure of several determinative steps including sample pre-treatment, extraction, purification and analysis (Fig. 2).

Sample collection and pre-treatment

Sludge samples used in this study were originated from different full-scale or pilot-scale WWTPs in Midi-Pyrenees and Languedoc-Roussillon regions (France). Samples were collected during grab sampling campaigns between March 2009 and November 2011. For each sampling campaign, a sufficient amount of sludge (>5 L) was retrieved and transferred to polypropylene cans. Samples were originated from three conventional activated sludge (CAS), one full-scale (FS) internal membrane bioreactor (IMBR), two pilot-scale (PS) IMBR and external MBR (EMBR) and one thickened primary-secondary (TPS) sludge. Details about WWTPs and some related features such as sludge acronyms used throughout this document are given in Table 1. All the above mentioned samples were characterized and distinguished according to volatile suspended solid (VSS) measurement. VSS was obtained after calcination of total suspended solid (TSS) at 525 • C during 2 h in a furnace. TSS measurement was determined by filtration of a known volume of sludge according to AFNOR regulation NF EN 872 [START_REF] Afnor | Qualité de l'eau -Dosage des matières en suspension -Méthode par filtration sur filtre en fibres de verre[END_REF].

Briefly after transport to the laboratory, each sludge sample was allowed to settle and supernatant was discarded. The remaining sludge was then centrifuged to ensure a complete separation between particular and aqueous phases. A great amount of settled sludge (1 L for each run) was centrifuged during 20 min at 5000 × g with a Megafuge 40 R centrifuge from Fischer Scientific (Illkirch, France) operated at sludge temperature. All the pellets were combined and frozen at -20 • C. Iced sludge pellets were then freeze-dried at obscurity and -60 • C under 0.045 bar vacuum (Christ Alpha 1-2 LD, Bioblock Scientific, Illkirch, France), ground to thin particles (<0.5 mm) using a mortar and pestle and stored at -20 • C prior to use.

Sample extraction

A Dionex accelerated solvent extraction (ASE) 200 device (Dionex, Sunnyvale, USA), which is the trade name for PLE, was used for the extraction of anticancer drugs from sludge.

At the bottom of each extraction cell, one glass-fiber filter (Dionex, Voisins-le-Bretonneux, France) was placed to ensure the filtration of semi-aqueous extracts. A thin sand layer (Fisher Scientific, Loughborough, UK) was then applied for pre-filtration. The dried biosolid sample was weighted (0.35 g), spiked with 100 L of MIX Deuterated and mixed thoroughly with sand as dispersing agent to prevent aggregation during extraction process and reduce clumping and channeling. The ratio between sample and sand weight was about 0.04. The mixture was then placed in the extraction cell and covered with an additional layer of sand. The cell was not completely filled with sand. A dead space about 0.25 cm was left to keep threads and sealing surfaces safe. To allow more representative adsorption of spiked analytes in sludge, built cells were left at room temperature for a minimum of 24 h before extraction.

The extraction solvent and operating conditions were optimized according to a multivariate experimental design shortly detailed in this paper. MeOH/ultra pure water mixture (65/35, v/v) was used as extraction solvent. The operating conditions were as follows: extraction pressure, 85 bar; extraction temperature, 100 • C; no preheat period; static extraction time, 9 min; number of static cycles, 4; flush volume, 60% of the cell; purge time, 120 s. This procedure led to a final extract volume of 15 ± 2 mL for all the samples.

Extract clean-up

Extracts were transferred to rocket-shaped bottles (200 mL) and evaporated to around 5 mL with a TurboVap II concentration workstation (Caliper Life Sciences, Hopkinton, USA) operating at 30 • C under a nitrogen N 2 pressure of 1 bar. The evaporation lasted 2 h. The clean-up procedure has already been submitted for aqueous samples [START_REF] Seira | [END_REF] and was adapted to our purposes. Clean-up has been carried out using selective SPE tandem approach Oasis MAX/MCX cartridges from Waters (Saint-Quentin-en-Yvelines, France). The solvent mixtures used for SPE were prepared every week.

The 5-mL extract was dissolved in 150 mL of ultra pure water. ASE vial collection was also rinsed with 50 mL (5× 10 mL) of ultra pure water and transferred to the mixture for a final volume about 200 mL. Sample pH was adjusted to 12 with NH 4 OH 35% and mixed thoroughly with EDTA 5% (0.01% in the sample, w/w). A MAX cartridge (6 cm 3 , 150 mg) was initially conditioned with 4 mL of MeOH, 4 mL of acetone and 4 mL of NH 4 OH 0.5%. A 70-mL SPE propylene sample reservoir from Macherey-Nagel (Hoerdt, France) was stacked on the cartridge before loading the sample at a flow rate of 1 mL/min. A wash solution of 4 mL NH 4 OH 0.5% in MeOH/ultra pure water mixture (5/95, v/v) was applied and followed by the elution of targeted analytes with 4 mL of MeOH and 6 mL of acetone collected in a same fraction. The volume of the fraction was concentrated down to 2 mL and dissolved in 70 mL of ultra pure water corrected at pH 2 with HCl 37%. A MCX cartridge (6 cm 3 , 150 mg) was then conditioned with 4 mL of MeOH, 4 mL of acetone and 4 mL of ultra pure water at pH 2. The sample was loaded (1 mL/min) on a 70-mL SPE propylene adaptator. The cartridge was rinsed with 4 mL of MeOH/ultra pure water (pH 2) mixture (5/95, v/v). The excess water present in the cartridge was removed with a strong vacuum during 15 min and the sorbent was completely dried under N 2 stream during 20 min. The elution of neutrals IFO and CP was performed with 4 mL of MeOH followed by the elution of basic TAM with 6 mL of NH 4 OH 2% in acetone in two distinct fractions. Details of SPE procedure, retention mechanisms and interest of cartridges combination are given elsewhere [START_REF] Seira | [END_REF]. The volume of the extracts was reduced down to 1 mL and transferred to vials from Agilent Technologies (Massy, France). The extracts were then evaporated to dryness and redissolved in 1 mL of (A)/(B) mobile phase mixture (75/25, v/v) (see Table 2 for composition) using a vortex apparatus from Fischer Scientific (Illkirch, France). A filtration on a Spartan RC 0.45 m syringe filter from VWR (Fontenay-sous-Bois, France) was performed for each extract. The extracts were finally stored at 4 • C and obscurity during a maximum duration of 7 days prior to analysis.

UHPLC-MS/MS analysis

LC separation was carried out using an Ultimate 3000 UHPLC System from Dionex (France). The column used for separation was an ACQUITY UPLC ® BEH C 18 (50 mm × 2.1 mm) with a 1.7 m particle size diameter (Waters, Saint-Quentin en Yvelines, France). All details about LC conditions such as injection volume, flow rate, auto sampler and column temperatures, elution gradient are given in Table 2. Detection was achieved with an Applied Biosystems Sciex QTRAP ® hybrid linear ion-trap triple quadrupole mass spectrometer (Foster City, USA) equipped with a Turbolon-Spray Interface. The instrument was operated in ElectroSpray (ESI) positive (+) in Multiple Reaction Monitoring (MRM) mode (dwell time, 80 ms). The operating parameters were: capillary voltage, 5000 V; source temperature, 450 • C; gas N 2 ; curtain gas, 20; Ion source gas 1, 20; ion source gas 2, 70. Before any experiment, a soft cleaning of the cone entrance was performed to maintain top instrumental performance. For each compound, cone voltage and collision energies of the main transitions were optimized. MS and MRM conditions are summarized in Table 3. For MS spectra and chromatogram acquisition and exploitation, Analyst 1.6.1 software from Applied Biosystems Sciex (Foster City, USA) was used.

A minimum of 3 identification points were applied to unambiguously identify the analytes in environmental samples. Each compound was characterized according to (1) its retention time t R in comparison with the corresponding standard for each batch process with a tolerance of ±5%, (2) the monitoring of two transitions per analyte and (3) its presence in one of the 2 SPE extracts. A typical chromatogram of targeted analytes in real sample is given in Fig. 1.

For quantification, MRM transitions were used. Six-point calibration curves were generated. From working solutions, identical amounts of deuterated analytes were added to the calibration standards, which contained related analytes in concentration spanning about 2 orders of magnitude. The calibration standards were evaporated to dryness, redissolved in 1 mL of (A)/(B) mobile phase mixture (75/25, v/v) and filtered at 0.45 m. Calibration curves were performed at the beginning of each batch process. Curves were built by calculating the ratios between the peak area of each analyte and the peak area of corresponding deuterated standard using weighted 1/x model for linear regression. Along the sequence, quality control (QC) samples were also analyzed to confirm their validity. QC samples were a high-and low-concentration level of the curves (1 order of magnitude). No significant (<12%) deviation has been observed. As sludge extracts may content many interfering compounds, blank samples (mobile phase mixture without analytes) were included every 5 injections. No cross-contamination has been observed. At the end of each sequence, chromatographic column was washed thoroughly with acidified water (pH 3) and pure ACN. Instrumental detection limits (IDL) and instrumental quantification limits (IQL) were determined by serial dilution of each standard down to 2 pg injected. The IDL and IQL were set as a signal-to-noise (S/N) ratio of 3 and 10 of the chromatographic response respectively.

Method performances

The performances of the analytical procedure were evaluated for each analyte through the estimation of method efficiency, repeatability and reproducibility, sensitivity and matrix effect. Estimation of the linearity was also considered as part of the validation.

Validation procedure

To demonstrate the robustness of the analytical procedure, the seven sludge samples defined in Table 1 were submitted to the validation process. For each freeze-dried biosolid, 4 samples were spiked with 100 L of both MIX Standards and Deuterated and 1 sample was spiked with 100 L of MIX Deuterated for native analyte concentration. All the samples were then submitted to the previously described protocol. This experimental set-up allows for the determination of the efficiency of the entire procedure (i.e. method efficiency MEff) and not for each analytical step. The determination of the MEff was calculated following Eq. (1):

method efficiency MEff (%) = Q preextract -Q back Q spike × 100 (1)
where Q preextract is the amount in the extract after complete procedure (ng), Q back is the amount present in the native sample (background quantity) (ng) and Q spike is the quantity of the spike (ng).

For three freeze-dried sludges (FS LCAS, FS MCAS, FS IMBR), MEff was also determined over a range of 4 concentrations. For each sludge candidate, 4 samples were spiked with 100 L of MIX Deuterated and different volumes of MIX Standards (10, 50, 100, 200 L) to achieve concentrations in the samples of 60, 300, 600, 1200 g/kg of dry matter (DM) and then submitted to the entire protocol. Measured analyte concentrations were plotted as a function of their related spiked concentrations and the corresponding slope was determined (Slope plotted ). Four-concentration MEff was determined for each analyte according to Eq. ( 2 where Slope plotted is the slope previously defined, Slope calibration is the slope of the calibration curve. In both experiments, absolute and relative MEff were calculated. For relative MEff, all the values were corrected relative to the deuterated analogues. Repeatability (intra-day precision) was expressed as the relative standard deviation (RSD, %) obtained from the MEff experiment at a single concentration and extracted, purified and analyzed in the same batch. Reproducibility (inter-day precision) was defined and conducted in the same conditions but on different batches and was determined only for three freeze-dried sludges (FS LCAS, FS MCAS, FS IMBR).

The sensitivity of the analytical method was determined according to the definitions of method detection limits (MDL) and method quantification limits (MQL). MDL and MQL were calculated using Eq. ( 3):

method limits ML (g/kg DM ) = IL × V extract MEff abs × m ( 3
)
where IL is the considered instrumental limit (g/L), V extract is the volume of the final extract (=1 mL), MEff abs is the absolute method efficiency calculated for a single concentration (0 < MEff abs < 1), m is the dried sample weight (=0.35 g).

Analytical limitation

To evaluate the performances of each analytical step, freezedried samples and subsequent extracts were spiked at different steps of the procedure with 100 L of both MIX Standards and Deuterated. The experimental scheme was inspired from the literature [18] and conducted in triplicate for FS MCAS and FS IMBR. Spikes were applied: Absolute and relative recoveries were determined in the same way as for MEff estimation. The following Eq. ( 4) was used for calculation:

recovery (%) = Q step -Q back Q spike × 100 (4)
where Q step is the amount in the final extract after spike to the corresponding analytical step (ng). For relative recovery, all the values were corrected relative to the deuterated analogues.

The spiking procedure applied in (e) also allows for the determination of matrix effect (ME), according to Eq. ( 5):

matrix effect ME (%) = A postextract -A back A spike -1 × 100 ( 5
)
where A postextract is the area in the extract spiked just before the analysis, A back is the area in the extract of native unspiked sample (background area) and A spike is the area of the corresponding spike. Absolute ME calculation was based on the area of analyte without correction while relative ME was calculated related to the deuterated analogue area. The accurate determination of the recoveries for each analytical step was possible. The efficiency of each detailed step was determined according to Eq. ( 6):

analytical step n efficiency (%) = R n R n+1 × 100 ( 6
)
where R is the absolute or relative recovery (%) at a given spiking step, n is a value ranging from 1 to 4 and describing a specific analytical step. Thus, the corresponding steps are:

. Selection of extraction solvent

The solvent must be able to solubilize the targeted analytes from the matrix with few interfering compounds as far as possible. Since the analytes vary in physico-chemical properties, the choice of solvent mixtures was crucial but also limited. Our strategy for selecting mixtures relies on (1) solvents previously applied with success in the literature and (2) close polarity matching between analytes and solvent mixtures. Different pure and binary solvents were tested. Pure solvents were acetone, MeOH, ACN, water (pH 7) and binary mixtures were acetone/ACN (1:1), MeOH/ACN (1:1), acetone/water (1:1), MeOH/water (1:1) and ACN/water (1:1). As no detectable concentration of targeted anticancer drugs was measured, FS LCAS sludge was selected, spiked with 100 L of both MIXs and submitted to the whole analytical process. All the experiments were performed in duplicate. Initial PLE conditions were applied from the literature: extraction pressure, 138 bar; extraction temperature, 100 • C; no pre-heat period; static cycle extraction time, 5 min; number of static cycles, 3; flush volume, 60% of the cell; purge time, 120 s [14]. The solvent mixture efficiency was investigated by comparing the mean areas of targeted analytes for each tested condition (data not shown). Areas of deuterated analogues were also compared. In the same time, extraction cells filled with dispersing agent were spiked and extracted in the same conditions to investigate the thermal degradation of analytes. No significant losses occurred under chosen parameters, thus confirming the stability.

For the tested solvents, all targeted analytes were recovered in different amounts. Extracts exhibiting different aspects were also obtained. Pure and mixed organic solvents led to highly colored and clear extracts while water led to brown and very turbid ones. Semi-organic mixtures gave intermediate profiles. Turbid aqueous samples were responsible for the clogging of the cartridge during the purification. Consequently, water (pH 7) was not selected as extraction solvent in our experimental scheme. Higher areas were obtained for IFO and CP using MeOH/water (1:1) and for TAM using pure MeOH. No discrepancies were observed for deuterated analogues areas. ACN and derived mixtures gave the worst results for each compound. The lower efficiency of ACN for extracting pharmaceuticals from solid samples has already been reported [13,18,19]. Unsurprisingly, water mixtures were efficient to extract polar analytes IFO and CP while pure organic solvents were efficient to extract apolar TAM. As TAM analysis was more sensitive than for IFO and CP, MeOH/water as extraction solvent was found to be a good compromise. From the literature and our findings, the superior capability of MeOH/water mixture to extract pharmaceuticals from solid samples has been found [13,[18][19][20][21][22][23].

Optimization using experimental design

The number of parameters affecting PLE is very high so the one variable at a time (OVAT) strategy was not to consider here. Finding the best operating conditions for maximizing recoveries with few experiments was achieved using a central composite design (CCD). According to the literature, the parameters of interest were the solvent (MeOH/water) ratio (variable A), the extraction temperature (variable B), the extraction pressure (variable C), the static cycle duration (variable D) and the number of cycles (variable E) [24]. The CCD consisted in a fractional factorial design including the five variables at two levels (2 5-1 ), each augmented by ten star points and 6 center points. The total number of extractions was 32. The low and high levels (domain boundaries) for each parameter were common PLE values determined from the literature [10,24]. These values were 10-90% (MeOH/water ratio), 70-110 • C (temperature), 70-130 bar (pressure), 4-16 min (cycle duration) and 1-5 (number of cycles). The complete definition of the experimental design applied is given in Supplementary Content 1. FS LCAS sludge was chosen for optimization as no targeted analytes have been detected. To evaluate the efficiency of extraction, 100 L of MIX Standards were spiked prior to extraction and 100 L of MIX Deuterated were spiked into the corresponding extract.

Supplementary material related to this article found, in the online version, at http://dx.doi.org/10.1016/j.chroma.2013.01.114.

The recoveries obtained for each analyte and experiment are given in Supplementary Content 2. Some yields were superior to 100% which could be attributed to method errors, sludge sample inhomogeneity [25] or signal ion enhancement during analysis. In the defined experimental domain, TAM displayed strong variability with values ranging from 0 to 205%. Moreover, the variability was remarkably high for the 6 center points (experiments [27][28][29][30][31][32]. It suggested that TAM extraction was affected by an unconsidered parameter or any other unknown process. A simple experiment was conducted by washing thoroughly with organic solvent the laboratory vessel and analyzing the solvent. Quantifiable amounts of TAM have been measured, confirming adsorption phenomena. Determination of TAM was therefore not possible. For the other analytes, the variability at the 6 center points has been determined (Supplementary Content 2). IFO exhibited less variability than CP with a relative standard deviation (RSD) of 6% versus 13%.

Supplementary material related to this article found, in the online version, at http://dx.doi.org/10.1016/j.chroma.2013.01.114.

The Minitab ® software was used for the statistical study. Owing to the CCD, the coefficients of a second order polynomial model describing the effects of the 5 variables on IFO and CP recovery have been estimated. The two models adequately represented the data as lack-of-fit p-values were superior to 0.05 (0.21 for IFO and 0.26 for CP). The correlation between predicted and observed recoveries was up to 99% for IFO and 98% for CP.

In order to see which variables (i.e. parameters) were the most influent on the response, standardized Pareto charts were constructed and are given in Fig. 3. Trends between IFO and CP were rather similar. In both cases, the solvent ratio was probably the most determining factor for extraction efficiency. However, its influence was difficult to assess, as this parameter was implied in several significant interactions sometimes of opposite trends. Indeed, it appeared that some interactions between parameters, such as A * D and A * E for example, were strongly influent. It means that variations in extraction recovery were not strictly assigned to a single parameter but could also be due to synergistic effects of two or more variables. These results justify the use of experimental design rather than OVAT strategy.

Our objective was to determine the best values of the five parameters that allow a recovery of around 100% with a 5% tolerance. Due to the second order of the models, an infinite combination of the factors allows to reach this goal. So response surface methodology was used to determine the area where the criterion is fulfilled. The values of the five parameters were chosen in these areas, taking into account the following experimental considerations.

First, aqueous or highly aqueous extracts were not recommended in our experimental scheme due to possible cartridge clogging. Moreover, the more polar the solvent mixture, the less selective extraction is [15]. Consequently, semi-organic content was preferential (middle of domain). Then, the application of high temperature in PLE decreases the viscosity of the solvent, thus allowing its better penetration into sample matrix and increasing its capacity to solubilize the analytes [20]. Faster extraction rates are also expected with high temperatures [15]. Nevertheless, high temperature could also lead to loss in method selectivity due to the extraction of more co-extractable compounds [20]. Relatively high temperature was thus preferential (upper part of domain). Next, pressure seemed to be the less significant parameter, which is a common finding in the literature for PLE [13,25,26]. Its role is to maintain the solvent in the liquid state at extraction temperature. Low pressure was sufficient (lower part of domain). Finally, the duration and number of cycles were determined simultaneously. Long cycle time could lead to a better diffusion of analytes but the multiplication of short cycle could be favorable to recovery [20]. Indeed, the introduction of fresh solvent at each cycle could allow new equilibrium between analytes and solvent, which could be interesting for strongly entrapped analytes. Consequently, low cycle duration (lower part of the domain) and many cycles (upper part of the domain) were preferential. Taking account of these reasons, surface responses were plotted and displayed in Supplementary Contents 3 and 4. The chosen experimental conditions were the following: MeOH/water 65/35 (v/v), extraction temperature 100 • C, extraction pressure 85 bar, static cycle duration 9 min and 4 cycles.

Supplementary material related to this article found, in the online version, at http://dx.doi.org/10.1016/j.chroma.2013.01.114.

Extract clean-up

Extract clean-up was required to concentrate the analytes and to remove the interfering components. As sludge was expected to contain much more interferents than wastewater samples, high sorbent weights (150, 500 and 1000 mg) were applied. Briefly, three types of sorbents were selected: reversed phase, hydrophilic-lipophilic balance (HLB) and mixed-mode anionic-cationic exchange. FS LCAS sludge PLE extracts were generated and spiked prior to purification. Reversed phase sorbent yielded very low recoveries for IFO and CP and were rejected. HLB yielded better recoveries but the major part of interfering compounds were concentrated in the final extract, which could introduce analytical troubles (i.e. strong matrix effect) with more complex sludge samples. Therefore, HLB sorbents were rejected. In our previous study [START_REF] Seira | [END_REF], mixed-mode anionic-and cationic-exchange SPE has proven value in the selective recover of targeted analytes in sludge aqueous samples with relatively low matrix effect. This procedure has been retained. As the sorbent weight for purification was two times and a half higher, the conditioning, washing and eluting volumes were multiplied by two. Lightly colored and clear extracts were obtained for most of the samples. Purification procedure was then considered satisfactory.

Performances of the analytical method

As no CRM was available for validation, in-house material was used. In-house material was freeze-dried sludge spiked with a known amount of targeted analytes. Seven different types of sludge were studied to demonstrate the complete suitability of the procedure.

The linearity of the internal calibration curves was satisfactory (R 2 > 0.995) for IFO and CP over the tested concentrations (1-500 g/L) and validation period (2 months). Indirectly, method linearity was also studied during MEff estimation over four concentrations (see Section 2.3.1) for FS LCAS, FS MCAS and FS IMBR. Linearity was observed (R 2 ≥ 0.990) for each analyte and sludge tested (data not shown). Thus, the method showed good specificity for the analysis of targeted analytes.

Recoveries of selected drugs for different types of sludge are given in Table 4. Both absolute and relative method recoveries were distinguished as recommended in the literature [12]. Absolute MEff values were very different and dependent on the compound and sludge considered. Absolute MEff ranges were 1.5-33% for IFO and 2.2-47% for CP. For FS LCAS, FS MCAS and FS IMBR, the agreement between MEff at a single and four concentrations validate the "single-point" procedure for each sludge. The absolute recoveries for IFO and CP were limited for all the samples (<50%) but not critical for their determination due to the high sensitivity of MS/MS detection. No significant correlation has been found between the recoveries and sludge features according to pH, VSS and the biological process (see Table 1). The very low method efficiency for TPS sludge impedes the quantitative determination of IFO and CP. Since VSS was the lowest, other characteristic might be more relevant to explain the very low method efficiency. As TPS sludge appeared partially digested, harsh chemical surroundings of TPS sludge could have been detrimental for IFO and CP recovery during the extraction or purification. Strong matrix effect occurring during analysis was also possible.

Table 4

Analytical method performances and validation data. Sludge For the different sludges, relative MEff values were considered excellent and ranged from 99 to 110% for IFO and from 92 to 105% for CP (see Table 4). Therefore, deuterated standards were completely suitable for IFO and CP determination in each case. Moreover, the use of only one surrogate standard along the entire protocol provided more accurate results in comparison with analytical methods using at least two surrogate standards, one for extraction and one for analysis, as encountered in the literature [20,21].

The repeatability of the method was calculated from the standard deviations given in Table 4 for each sludge. For IFO, RSD for absolute and relative MEff were in the range 0.8-15% and 2.4-12% respectively. For CP, RSD were in the range 2.4-14% and 1.0-11% respectively. These values have the significance of good overall repeatability (<15%) in each case. The reproducibility of the method has been calculated as the same manner and was below 14% and considered satisfactory (<15%) for FS LCAS, FS MCAS and FS IMBR (data not shown). Therefore, the robustness of the procedure has been proven.

For IFO and CP, MDL ranged from 3.9 to 74 g/kg DM and from 2.5 to 51 g/kg DM respectively (Table 4). With the exception of TPS sludge, all the MDLs were lower than 10 g/kg DM displaying good overall method sensitivity. The conclusions are the same for MQLs lower than 20 g/kg DM which are the best quantification limits reported in the literature for both compound [11]. The uncommonly low sample and purification sorbent weights applied in the experimental scheme were not limiting in the achievement of low method limits, reaching possible environmental requirements.

In the overall, our analytical strategy proved good sensitivity, selectivity and specificity due to the validation on seven sludge samples from different origins. However, it is important to note that recoveries obtained for spiked samples could overestimate the efficiency of the method for incurred native analyte [25]. Because of limitations in diffusion and kinetics of the sorption process, spiked analytes will always be less retained than the native ones [27], To assess the representativeness of freshly spiked compared to incurred analytes, an additional experiment on PS EMBR sludge has been carried out. PS EMBR has been continuously contaminated with anticancer drugs during 80 days. This procedure allows analytes to penetrate much more into the volume of the matrix rather than on the surface. Sludge was sampled on days 10, 30 and 60 during campaign, which corresponds respectively to 0.5, 1.5 and 3 times the sludge age. Each sample was freeze-dried and split equally in two. The second aliquot received an additional spiking of 10 L of MIX Standards. All the samples were then submitted to the whole analytical procedure. The measured concentration of the freshly spiked sample was corrected by subtracting the amount of the spike to assess the native concentration. The corrected value was compared to the concentration measured in the sample without additional spike. No significant differences were measured for IFO (RSD < 4%) and CP (RSD < 3%). It appears that the proposed analytical method is not specific to freshly spiked samples and can be applied to aged samples. This could be attributed to the numerous extraction cycles in PLE, allowing the exhaustion of the matrix from easily accessible compartments (spiked) to less accessible ones (incurred). The sorptive interactions of IFO and CP in freshly spiked and aged samples could also be comparable.

Which analytical step is the most limiting?

As sludge matrix components can strongly influence the efficiency of the sample treatment stage, the objective here was to determine whether the limited absolute recoveries were linked to a same analytical stage or if they were related to different stages depending on the sludge nature. To do so, two types of sludge with different organic content (i.e. VSS) have been selected and spiked at different analytical steps described in Section 2.3.2. FS MCAS was selected for its high organic content (91%) and FS IMBR for its relatively low organic one (75%). TPS sludge (71%) was rejected due to the analytical challenge previously described.

The profiles obtained for IFO and CP are displayed in Fig. 4a and b respectively. The absolute recoveries displayed the true efficiency of the spiking stages. Even if recoveries related to the analysis are comparable or somewhat higher than those related to the whole method, the quantification of IFO and CP is deeply disturbed by the matrix effect (ME) in each sample, possibly due to the use of semiorganic solvent during PLE. For IFO, recoveries associated with the couple "Whole method; Analysis" are 14%; 45% for FS MCAS and 26%; 25% for FS IMBR. For CP, recoveries are 22%; 51% and 38%; 51%. The use of (semi-) organic solvent during PLE could be responsible for the extraction of many interfering compounds as suggested in the literature [10,15,24] thus decreasing clean-up efficiency and resulting in relatively high ME.

The efficiency of each analytical step from the pretreatment until the analysis has been calculated following Eq. ( 6) given in Section 2.3.2. The results are displayed in Fig. 5. Only absolute recoveries were used for calculation. The profiles are very different between sludges but not between analytes. For a given sludge sample, it suggests that IFO and CP are submitted to the same or close processes during each stage. The high variability observed for some analytical steps is fully explained by the addition of variances implied by Eq. ( 6) but not critical for trend explanation.

Pretreatment stage did not imply any significant losses for IFO and CP in each case. Freeze-drying is often required because wet samples can prevent from efficient PLE [15]. Grinding ensures shorter diffusion path-lengths during extraction and enhances solvent penetration [15]. Both steps can be responsible for losses but are usually neglected during method development. From our result it is demonstrated that non-volatile analytes, which is the case of pharmaceuticals, are not sensitive to freeze-drying and grinding. Therefore, the use of spiked freeze-dried samples during method validation was effectively sufficient. The extractive step led to satisfactory recoveries between 78 and 105% in each case. For sludge samples, the versatility of the optimized PLE method has been demonstrated. The purification stage efficiency was strongly dependent on the sludge nature. For both analytes, higher losses were observed for FS MCAS sludge. It could be explained by the nature of interfering compounds present in the PLE extract, which may have competed for binding sites and lowering the clean-up efficiency. It is also important to note that evaporative steps along the procedure were not responsible for any analyte loss.

In the overall, the analysis was the most limiting factor in the quantification. CP suffered from ME up to 49% for both sludges while IFO suffered from ME of 55 and 75% for FS MCAS and FS IMBR sludges respectively. Additionally, it appeared that sludge organicity according to VSS measurement was not sufficient to explain ME as no correlation between VSS, analytes and ME was found. Even if VSS is an easy-to-handle and quick measurement, it seems that the characterization of the sludge matter and related extract could be more relevant in the understanding of ME origins.

Application to environmental samples

Optimized method was applied to the biosolid samples described in Table 1. Measured mean concentrations are given in Table 5.

Except for FS LCAS, one or two of the targeted drugs were detected or quantified in our samples thus confirming the occurrence of anticancer drugs in solid part of sludge. Concentrations in solid phase for IFO ranged from 11.4 to 42.5 g/kg DM while CP was quantified only in FS MCAS at a concentration of 12.6 g/kg DM . This concentration is of the same order of magnitude than one reported in the literature for excess sludge [14]. From our data, contaminated sludges are mostly those of WWTPs treating each day large amounts of wastewater. It could be thought that the contamination is much more related to the treated person equivalent number than the sludge physico-chemical nature. The quantification of IFO in FS IMBR could be attributed to a possible accumulation as sludge age is long (100 days) and biodegradation is not expected [28][29][30][31][32]. In the overall, very low levels of anticancer drugs were determined in our solid samples originated from different WWTPs. This is in good agreement with levels of concentration found or predicted in the literature [6,11,30]. It could be explained by the relatively low consumption and the possible low sorption affinity for sludge due to high polarity of IFO and CP. However, low concentrations in sludge may not have the significance of low toxicity for microorganisms and more. Some other field results are requested to confirm or not these first conclusions.

Conclusion

In this paper, an original analytical method was proposed to recover anticancer drugs from solid part of sludge. The experimental set-up consists of extraction from the solid matrix using PLE, clean-up by selective SPE and analysis by UHPLC-MS/MS. Some efforts focused on the extraction efficiency, the method validation and the analytical limitation. The use of an experimental design to optimize the extraction revealed the concomitant effect of some parameters during extraction, which helped to understand the true functioning of PLE. The validation of the method was applied to seven different sludge samples. Method validation requirements implying linearity, repeatability, and reproducibility were fulfilled. The analytical performances were very different between sludge samples with method efficiencies and MDLs spanning more than one order of magnitude. Thus, method validation should be systematically applied for each new sample and could be of great interest for monitoring programs. Matrix effect occurring during analysis was demonstrated as the most limiting factor for the quantification of each analyte. However, the use of deuterated standards spiked at the very beginning was efficient to overcome analytical troubles regardless of the matrix composition. Various sludge samples were analyzed, confirming the environmental occurrence of anticancer drugs in sludge. Up to now, the proposed method is only the third analytical procedure available in the literature for the extraction of anticancer drugs from environmental solid samples, each of them dealing with sludges. The developed method is also the most sensitive (up to low g/kg DM ), detailed and versatile. The need of analytical methods and environmental data about anticancer drugs is still of concern to establish their occurrence in the water cycle at national and international scales.

Fig. 1 .

 1 Fig. 1. MRM chromatogram of spiked FS IMBR sludge sample.

Fig. 2 .

 2 Fig. 2. Methodology applied for the determination of anticancer drugs in sludge.

  (a) Before freeze-drying on rehydrated freeze-dried samples to assess true MEff; (b) Before extraction to evaluate the combined recovery of extraction, purification and analysis (MEff defined in Section 2.3.1); (c) Before purification on Oasis MAX to evaluate the recovery of both purification and analysis; (d) Before purification on Oasis MCX to evaluate the recovery of second purification and analysis; (e) Before analysis to evaluate the recovery of the analysis.

(n = 1 )

 1 pretreatment (i.e. freeze-drying) by comparing experiments (a) and (b) (n = 2) extraction by comparing experiments (b) and (c) (n = 3) purification I (i.e. Oasis MAX) by comparing experiments (c) and (d) (n = 4) purification II (i.e. Oasis MCX) by comparing experiments (d) and (e)

Fig. 3 .

 3 Fig. 3. Standardized Pareto chart highlighting the effect of PLE parameters in applied experimental design for IFO (up) and CP (down). The vertical straight line is the limit of significance.

  efficiency; SD: standard deviation; MDL: method detection limit; MQL: method quantification limit; DM: dry matter. a Calculated for a single concentration (n = 4). b Calculated over a four-concentration range.

Fig. 4 .

 4 Fig. 4. (a) Mean recoveries ± standard deviation for IFO in FS MCAS sludge (up) and FS IMBR sludge (down) for the different steps of the analytical procedure (n = 3). (b) Mean recoveries ± standard deviation for CP in FS MCAS sludge (up) and FS IMBR sludge (down) for the different steps of the analytical procedure (n = 3). The recoveries were determined according to Eq. (4).

Fig. 5 .

 5 Fig.5. Recovery profiles for IFO (up) and CP (down) in two types of sludge. The recoveries were determined according to Eq. (6).

Pretrea tmen t ExtracƟo n PurificaƟon 1. Analy sis EvaporaƟon PurificaƟon 2.

	Raw slud ge sa mple
		Cent rifu gaƟon
		Aqueous phas e discarded
	Freezin g, lyop hilisa Ɵon and grin ding
		0.35 g of slud ge
		PLE cell pr eparaƟon
	PLE
	MeOH/wat er (65 /35), 85 bar, 100 °C, 9 min, 4 cycles
		15-mL ex trac t
	TurboVap evaporaƟon to 5 mL-extrac t
		Dissol uƟon with 200 mL UHQ wat er pH 12
		AddiƟon of EDTA 0.1% (w/w)
	Oasis MAX 150 mg cartrid ge
		EluƟon with 4 mL MeOH and 6 mL acet one
		EvaporaƟon to 2 mL
		Dissol uƟon with 70 mL UHQ water pH 2
	Oasis M CX 150 mg cartrid ge	EluƟon of neutrals with 4 mL MeOH
		EluƟon of basics with 6 mL NH4OH 2% in acetone
		EvaporaƟ on t o dryness
	UHPLC-MS/MS	Recon sƟt uƟon to 1 mL and filtraƟon at 0.45 µm

Table 1

 1 Features of sludges used in this study.

	Sludge	Scale	Person equivalent	Organic load	Technology	pH	VSS (%)
	FS VLCAS	Full	300 000	Very low	CAS	8.3	79
	FS LCAS	Full	2000	Low	CAS	-	83
	FS MCAS	Full	800 000	Medium	CAS	7.25	91
	FS IMBR	Full	9000	Very low	Internal MBR	7.55	75
	LS EMBR	Lab (20 L)	-	Low a	External MBR	7.7	84
	LS IMBR	Lab (15 L)	-	Low b	Internal MBR	7.5	89
	TPS	Full	>30 000	-	Thickener	7.8	71

CAS: conventional activated sludge; MBR: membrane bioreactor; VSS: volatile suspended solids; FS VLCAS: FullScale VeryLowCAS; FS LCAS: FullScale LowCAS; FS MCAS: FullScale MediumCAS; FS IMBR: FullScale InternalMBR; LS EMBR: LabScale ExternalMBR; LS IMBR: LasScale InternalMBR; TPS: thickened primary secondary.

a Semi-synthetic influent using same wastewater as FS MCAS.

b Fed with the same wastewater as FS MCAS.

Table 2

 2 Liquid chromatography conditions.

	Parameter		Applied condition
	Injection volume		10 L
	Flow rate		400 L/min
	Auto sampler temperature	15 • C
	Column oven temperature	25 • C
	Mobile phase	Eluent A		Eluent B
		Ultra pure water/ACN (90/10, v/v)	Pure ACN
		NH4CH3COO 1 mM
		HCOOH 0.3%
	LC gradient	% Eluent A		% Eluent B
	Time (min)
	0	100		0
	0.5	100		0
	2	78		22
	3.5	77		23
	4	0		100
	6	0		100
	8	100		0
	10	100		0

Table 3

 3 MS and MRM conditions used to identify and quantify pharmaceuticals.

	Pharmaceutical	Detection	Transitions (m/z)	DP a (V)	EP b (V)	CE c (V)	CXP d (V)
	IFO	Positive	261.1 > 92.0 (Q)	65	10	30	12
			261.1 > 153.8 (q)	65	10	24	12
	CP	Positive	261.1 > 139.8 (Q)	65	10	27	12
			261.1 > 105.9 (q)	65	10	22	12
	TAM	Positive	372.4 > 72.0 (Q)	65	10	40	15
			372.4 > 128.9 (q)	65	10	35	15

Q: quantification transition; q: confirmatory transition. a Declustering potential. b Entrance potential. c Collision energy. d Collision cell exit potential.

Table 5

 5 Anticancer drugs concentrations in collected biosolid samples.

	Sludge	Pharmaceuticals a (g/kgDM)
		IFO	CP
	FS VLCAS	11.4 ± 2.1	<MQL
	FS LCAS	<MDL	<MDL
	FS MCAS	41 ± 23	12.6 ± 4.9
	FS IMBR	42.5 ± 14.6	<MQL
	PS EMBR	<MQL	<MDL
	PS IMBR	<MQL	<MQL
	TPS	<MQL	<MQL

MDL: method detection limit; MQL: method quantification limit.

a n = 2, medium concentration ± standard deviation.

Acknowledgment

This work form part of the project ANR-09-JCJC-0005 "BioMed-Boue" supported by ANR (French Research Agency).


M L Raffa

F Lebon

E Sacco

H Welemane

A Multi-Level Interface Model for Damaged Masonry

Keywords: Masonry, interfaces, damage, homogenization, microcracks, unilateral effects, asymptotic analysis

.

Introduction

Historically, the masonry is considered one of the oldest building material although its mechanical behaviour is still the subject of many research activities. It is usually described as a composite material formed by units (bricks, natural stones, marble, granite, limestone, concrete block, etc.) and joint, with or without adhesive component (mortar, concrete, clay, etc.), and different bond arrangements. Masonry is still used nowadays to build houses because of its qualities of strength, solidity, durability and fire resistance, and its elegant appearance, etc. It is certain that the problems associated with modelling ancient and modern masonry structures are very different. Physical evidence shows us that ancient masonry is a very complex material with three-dimensional internal arrangement, usually unreinforced, but which can include some form of traditional reinforcement. Moreover, these materials are associated with complex structural systems, where the separation between architectural features and structural elements is not always clear. However, masonry, which is not generally thought to be a highly technological material, shows highly complex behaviour, due in particular to the interactions between the components and the anisotropy induced by the direction of the joints, which are a source of weakness. Even for simple geometries and far from failure loadings, masonry structures exhibit a mechanical response affected by extreme stiffness contrast between constituents, randomness of contact points between bricks where unilaterality and Coulomb friction dominate. The interplay between extreme stiffness contrast and randomness on the one hand and regularity of the fabric on the other, yields stress distributions within masonry walls that may present localized stress paths, evidencing stress concentrations and stress relieves. It is classically held that the seismic vulnerability of masonry buildings depends strongly on their resistance to shear forces. It is therefore of great interest to model and test the shear responses of building components subjected to loading of this kind, especially cyclic loading. These responses have generally been characterized by a peak load, loss of rigidity and energy dissipation. To summarize considerably, two methods of modelling masonry structures have been used so far. The first method involves macroscopic models, in which the wall is assumed to be a single structural element characterized by a non linear response when it is exposed to shear forces [START_REF] De Buhan | A homogenization approach to the ultimate strength of brick masonry[END_REF][START_REF] Gabor | Modelling approaches of the in-plane shear behaviour of unreinforced and frp strengthened masonry panels[END_REF][START_REF] Luciano | Homogenization technique and damage model for old masonry material[END_REF][START_REF] Oliveira | Implementation and validation of a constitutive model for the cyclic behaviour of interface elements[END_REF][START_REF] Pela | Continuum damage model for orthotropic materials: Application to masonry[END_REF][START_REF] Quinteros | Nonlinear homogenization techniques to solve masonry structures problems[END_REF][START_REF] Sacco | A nonlinear homogenization procedure for periodic masonry[END_REF]. In continuum macro-models bricks, mortar and brick-mortar interfaces are smoothed out into a homogeneous continuum, the average properties of which are identified at the level of the constituents, taking their geometric arrangement into account [START_REF] Lourenco | A plane stress softening plasticity model for orthotropic materials[END_REF][START_REF] Lourenco | Continuum model for masonry: Parameter estimation and validation[END_REF]. This technique is particularly indicated in global modelization of unreinforced masonry structures in which the very low tensile strength of the material renders the use of non-linear constitutive behaviour more obvious. This is particularly true in the assessment of existing structures and in seismic analysis. To describe the inelastic behaviour of structural masonry, some authors have combined homogenization techniques with a continuum damage mechanics approach [START_REF] Alfano | Combining interface damage and friction in a cohesivezone model[END_REF][START_REF] Zhu | Homogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks[END_REF]. On the other hand, some models of micro-analysis school have been developed for predicting the evolution of damage into interface between two initially bonded deformable bodies [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF][START_REF] Fremond | Adhesion of solids[END_REF][START_REF] Lebon | Asymptotic analysis of some nonlinear soft thin layers[END_REF][START_REF] Lekhnitsky | Theory of elasticity of an anisotropic elastic body[END_REF][START_REF] Mauge | Effective elastic properties of an anisotropic material with arbitrarily oriented interacting cracks[END_REF][START_REF] Monchiet | A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite[END_REF][START_REF] Raous | A consistent model coupling adhesion, friction, and unilateral contact[END_REF][START_REF] Tsukrov | Anisotropic material with arbitrarily oriented cracks and elliptical holes: Effective elastic moduli[END_REF]. Two main modelling approaches used for this purpose are phenomenological modelling and deductive modelling. In the first approach, the thickness of the interface is taken to be zero and the mechanical properties are obtained from physical considerations and experiments (see for example [START_REF] Bonetti | Analytical results on a model for damaging in domains and interfaces[END_REF][START_REF] Freddi | Damage in domains and interfaces: A coupled pre-dictive theory[END_REF][START_REF] Fremond | Adhesion of solids[END_REF][START_REF] Fremond | Damage, gradient of damage and principle of virtual power[END_REF] and references therein). The second approach consists in focusing on the thin layers materials at the micro-mechanical level, which are usually called the interphase. Several authors [START_REF] Abdelmoula | Asymptotic behavior of an elastic thin layer[END_REF][START_REF] Lebon | Asymptotic analysis of a thin interface: The case involving similar rigidity[END_REF][START_REF] Lebon | Asymptotic behavior of a hard thin linear elastic interphase: An energy approach[END_REF][START_REF] Lebon | Asymptotic modelling of interfaces taking contact conditions into account: Asymptotic expansions and numerical implementation[END_REF][START_REF] Lotfi | Interface model applied to fracture of masonry structures[END_REF][START_REF] Lourenco | Multisurface interface model for analysis of masonry structures[END_REF][START_REF] Pelissou | Asymptotic modeling of quasi-brittle interfaces[END_REF] have established that the interface elements reflect the main interactions occurring between bricks and mortar. For this reason, various studies have been presented for modelling the behaviour of interfaces with zero thickness and predicting their failure modes. Some studies [START_REF] Del Piero | A unified model for adhesive interfaces with damage, viscosity, and friction[END_REF], for example, expressed the constitutive law at the interface in terms of contact traction and the relative displacements of two surfaces interacting at the joint. The fracture of the joint and the subsequent sliding are associated with the interface yield condition. Method based on limit analysis combined with a homogenization technique was shown [START_REF] De Buhan | A homogenization approach to the ultimate strength of brick masonry[END_REF] to be a powerful structural analysis tool, giving accurate collapse predictions. The brittle damage model developed in [START_REF] Alfano | Combining interface damage and friction in a cohesivezone model[END_REF][START_REF] Pelissou | Asymptotic modeling of quasi-brittle interfaces[END_REF] involves an elementary cell composed of units, mortar and a finite number of fractures at the interfaces. In this paper, a multi-level model for interfaces based on homogenization and asymptotic techniques is presented. This model is based on a previous study proposed by A. Rekik and F. Lebon [START_REF] Rekik | Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry[END_REF][START_REF] Rekik | Homogenization methods for interface modeling in damaged masonry[END_REF]. The first part of this paper gives an accurate version of the mechanical modelling approach used. The multi-level approach used is described. This approach takes into account the mechanical characteristics of the mortar and bricks, the presence of micro-cracks and the thickness of the interface into. In the second part, the numerical procedure used and implemented using a finite element software program is presented and some numerical examples are given and compared with experimental data [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF][START_REF] Gabor | Modelling approaches of the in-plane shear behaviour of unreinforced and frp strengthened masonry panels[END_REF].

An accurate version of the Rekik-Lebon model [31, 32]

Masonry units have generally been discretized using continuum elements, whereas joints have been modelled in the form of weakness planes, using interface elements. The main limitation of this approach is the fact that the interactions between joints and brick units cannot be satisfactorily described. The most original feature of this kind of model is that it includes a third material inserted between the units and the mortar, which accounts for the noticeable differences generally existing between the mechanical properties of bricks and mortar. In order to model interface damage to masonry structures, the present method based on homogenization theories, asymptotic techniques and finite element methods was developed. The main steps involved in this method will be described below. Most studies on masonry structures have dealt with only two materials: brick and mortar. In the present work, it is assumed the existence of a third material: the brick/mortar interface, which is considered as a mixture of brick and mortar with a crack density ρ. To obtain the effective properties of the damaged intermediate material, three steps are performed. First it is calculated the exact effective properties of the crack-free material using homogenization techniques for laminate composites, for the sake of simplicity it is considered to have the same volume fraction for both constituents, and thus define a first homogeneous equivalent medium, which will be referred below as HEM-1. In the second step, it is assigned a proper crack density ρ to the previous material. To model the macroscopic behaviour of the cracked material HEM-1, it is used the Kachanov model and then it is defined a new homogeneous equivalent medium HEM-2. Finally, in order to be sandwiched between the brick and mortar, this material is given a small thickness, and its mechanical behaviour is derived using asymptotic techniques to shift from the micro to the macro level. With this interface law, the masonry structure problem can be solved using finite element methods. The following overall scheme (Fig. 1) describes the principles underlying the proposed model:

Undamaged stratified composite homogenization

It is proposed first to obtain the mechanical properties of the 3D interphase material by homogenizing those of brick and mortar. Both constituents are assumed to be isotropic and linear elastic materials. In the compliance form, their constitutive law reads:

ε ζ i j = S ζ i jkl σ ζ ik = 1 + ν ζ E ζ σ ζ i j - ν ζ E ζ σ ζ kk δ i j (1)
where

ε = S0 : σ where ε = ∑ ζ =b, m f ζ ε ζ = ∑ ζ =b, m f ζ S ζ : σ ζ (2)
where f ζ denotes the volume fractions of phase ζ and S0 is the effective fourth-order compliance tensor of the homogeneous equivalent crack-free material supposed to be transversely isotropic . According to the modified Voigt notation, the macroscopic law (2) reads:

        ε11 ε22 ε33 √ 2ε 23 √ 2ε 13 √ 2ε 12         =         S0 1111 S0 1122 S0 1133 0 0 0 S0 1122 S0 1111 S0 1133 0 0 0 S0 1133 S0 1133 S0 3333 0 0 0 0 0 0 2 S0 1313 0 0 0 0 0 0 2 S0 1313 0 0 0 0 0 0 S0 1111 -S0 1122                 σ11 σ22 σ33 √ 2 σ23 √ 2 σ13 √ 2 σ12        
(3) The five independent coefficients of the compliance tensor S0 are determined by applying three independent loads. The same results may be found in [START_REF] Boutin | Microstructural effects in elastic composites[END_REF], where the macroscopic law of the laminate is given in the stiffness form C0 = S0 -1 . For the sake of simplicity the model is developed assuming the plane stress hypothesis in direction e 2 on the effective material, so that the 3D problem is reduced to a 2D problem in the (e 1 , e 3 ) plane.

Homogenization of the micro-cracked composite

In this section, the material HEM-1 is assumed to contain an arbitrary distribution of rectilinear cracks located on the plane (e 1 , e 3 ) in a representative area A = L 0 ε, where L 0 is the bed mortar length and ε is the thickness of the micro-cracked HEM-2 material. Kachanov et al. [START_REF] Mauge | Effective elastic properties of an anisotropic material with arbitrarily oriented interacting cracks[END_REF][START_REF] Tsukrov | Anisotropic material with arbitrarily oriented cracks and elliptical holes: Effective elastic moduli[END_REF] provided an accurate approximation of the effective behaviour of such a material for open cracks; the average strain ε in a solid with N families of microcracks can be written in the form:

ε = S : σ = ( S0 + ∆ S) : σ (4)
where S (resp. S0 ) is the effective compliance of the cracked (resp. crack-free) material and

∆ Si jhl = 1 2A N ∑ k=1 [n (k) i n (k) h B jl + n (k) i n (k) l B jh + B ih n (k) j n (k) l + B il n (k) j n (k) h ](l (k) ) 2 (5)
in which 2l (k) and n (k) are mean length and normal of the k th family of cracks and A is the area of the representative 2D-domain.

The second rank symmetric tensor B (k) can be called the crack compliance tensor of the k th family of cracks, which depends on the anisotropy of the virgin material [START_REF] Tsukrov | Effective moduli of an anisotropic material with elliptical holes of arbitrary orientational distribution[END_REF]:

B (k) = (C(1 -D)e 1 ⊗ e 1 +C(1 + D)e 3 ⊗ e 3 ) (6)
where

                 C = π 4 E 0 1 + E 0 3 E 0 1 E 0 3   1 G 0 13 -2 ν 0 13 E 0 1 + 2 E 0 1 E 0 3   1 2 D = E 0 1 -E 0 3 E 0 1 + E 0 3 ( 7
)
E 0 1 , E 0 3 , ν 0 13 and G 0 13 are the effective elastic engineering constants of the crack-free material HEM-1. These constants are easily derived from the effective elastic compliances S0 as follows:

                       E 0 1 = 1 S 0 1111 E 0 3 = 1 S 0 3333 ν 0 13 = - S 0 1133 S 0 1111 G 0 13 = 1 4S 0 1313 (8)
We note in [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF] the dependence of the sign of D on the anisotropy ratio E 0 1 /E 0 3 . We consider here a single family of microcracks normal to direction e 3 with mean length 2l. Substituting ( 7) and ( 8) into (6), we obtain the change of elastic compliance: where ρ = 1/A ∑(l) 2 is the proper scalar crack density parameter in 2D case The compliance of the cracked material HEM-2 is thus given by:

∆ Si jhl = 1
           S 1111 = S 0 1111 S 3333 = S 0 3333 + 2ρC(1 + D) S 1133 = S 0 1133 S 1313 = S 0 1313 + 1 2 ρC(1 -D) (10)
The elastic constants C and D are given by [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF]. The engineering constants E 1 , E 3 , ν 13 and G 13 of the cracked material HEM-2 are given by relations similar to (10) thus:

                 E 1 = E 0 1 E 3 = E 0 3 1 + 2ρC(1 + D)E 0 3 ν 13 = ν 0 13 G 13 = G 0 13 1 + 2ρC(1 -D)G 0 13 ( 11
)

Third step: asymptotic analysis and interface law

In this section, it is considered a thin joint composed of the material defined above, which is sandwiched between brick and mortar. Since the joint is thin and soft, it is natural to use asymptotic techniques, to study the limit problem (by tending the thickness to zero) and to replace the joint by an interface law defined along the limit surface. It is taken ε to denote the thickness of the joint, which is assumed to be constant and S to denote the limit surface of the joint (a line in 2D), corresponding to a thickness equal to zero (see fig. 2). We take C to denote the elasticity tensor of the joint and lim c i jkl /ε = ci jkl . The limits are assumed to exist. We take [ ] to denote the It is found an interface law which links the stress vector to the jump in the displacement via a diagonal matrix. It is important to remark that this is a simplified choice to reduce the continuous model of interface material to a simple mechanistic model obtained considering springs in the normal and tangential direction. In this case, the terms C N and C T in this matrix (corresponding to the normal and the tangential springs stiffnesses) are given by

     C N = C3333 (ε → 0) where C3333 = C3333 ε C T = C1313 (ε → 0) where C1313 = C1313 ε (12)
Using expressions [START_REF] Goidescu | Microcracks closure effects in initially orthotropic materials[END_REF] and writing the crack density scalar in the form: ρ = l 2 /ε L 0 , where L 0 denotes the joint length, it can be established that the normal and tangential joint stiffnesses read:

     C N = L 0 2C(1 + D) l 2 C T = L 0 2C(1 -D) l 2 (13)
Note that the choice of HEM-1 is quite irrelevant because the same functions C N and C T can be obtained with various combinations of HEM-1 and material parameters. The present model takes the evolution of the micro-crack into account by taking a Figure 3: Function describing the evolution of the crack half length with respect to the applied shear stress variable crack half length l depending on the load. For the sake of simplicity, it is first assumed that the half length l depends only on the predominant tangential stress τ by neglecting its dependence on the normal stress. For its evolution, it is assumed that l remains constant l = l c until a certain value τ c of the shear stress has been reached. From this value, the crack half length l evolves linearly with respect to the shear stress τ up to a second value of the crack length l u reached at the maximum shear stress value τ u . It is experimentally proved that this evolution law can accurately model the response of a quasi-brittle non-confined masonry structure subjected to a shear load. Fig. 3 describes the evolution of the half crack length with respect to the shear stress τ. The first step (where l is constant) corresponds to a stable state of the interface material in which crack propagation occurs. The second step (where l evolves linearly as a function of the shear stress τ) includes the crack propagation, which leads to the failure of the interface. The values of the shear stresses τ c and τ u are fixed in advance, based on experimental 'stress-displacement' diagrams obtained on various masonries subjected to shear conditions. The values of the crack evolution law parameters (l c and l u ) result from the minimization of the difference between the numerical and experimental 'stressdisplacement' diagrams.

Numerical modelling

In this section, some numerical results are illustrated and a brief review of the experiments which validate this damage model is done. The main goal is to evaluate the strain and damage distribution in the unreinforced and strengthened masonry panels which are submitted to a predominant shear load, taking into account the nonlinear behaviour of the material. It is known from the laboratory experiences that this strongly non-linear shear behaviour of the masonry is mainly governed by phenomena that occur at the brick/mortar interface.

An outline on experimental validations

The local behaviour of the interfaces at mode I and mode II fracture of brick masonry bed joints, which are typical quasi-brittle interfaces has been studied by various laboratory experiments [START_REF] Gabor | Modelling approaches of the in-plane shear behaviour of unreinforced and frp strengthened masonry panels[END_REF]. In the following, the capability of the proposed interface constitutive model in representing the behaviour of the brick/mortar joints under different load conditions is validate by experimental results obtained by F. Fouchal et al. [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF]. The experimental device (Fig. 4) was designed to study on the local scale the shear behaviour of a simple assembly consisting of two and three full or hollow bricks (210 mm × 100 mm × 50 mm) connected by a mortar joint 10 mm thick. The samples were subjected to a monotonous increasing load up to failure.

Figure 4: a) Experimental device involving two bricks, b) Experimental device involving three bricks

The following findings were obtained :

• occurrence of two kinds of fracture processes, the fracture can occur along the interface or it can begin along the interface and then it propagates into the mortar joint;

• the variations in the shear stresses show that the stress concentration develops in the regions containing the discontinuities

• rigid elastic behaviour up to the failure, followed by friction sliding behaviour;

• the behaviour of full bricks was fragile beyond the limit strength;

• the behaviour of hollow bricks was quasi-fragile beyond the limit strength;

• hollow brick samples showed great dispersion, mainly due to the non uniform distribution of the mortar spikes and local defects in the components of the bricks;

• samples consisting of two and three bricks showed similar behaviour, so the choice of basic cell therefore has no effect on the local scale.

Numerical processing

For the first numerical processes and in according to experiments is chosen to study a simple model: a triplet of three full bricks bounded by two mortar joints. The geometrical and mechanical properties of the sample are totally in agreement with those used in Fouchal's experiments (Tab.1). The boundary conditions are given in Fig. 5. The finite element method is used to perform the spatial discretization. In the subsequent modelling study, only the interface's behaviour will therefore be of importance and not the basic components used. The principal goal of the model is to analyze interface's stiffness degradation caused by microcracks. To begin with a model as simple as possible brick and mortar are assumed to be linear elastic isotropic materials. A plane stress modelling is pursued using a regular mesh of four node quadrangular elements having two degree of freedom per nodes, four Gauss integration points and lagrangian polynomials as shape functions in displacement formulation. This classical mesh choice is used both for brick and mortar elements. For brick/mortar interface elements quadrangular finite elements are chosen also. Their modelling is made explicit below.

Let us briefly recall the weak formulation of a standard elastic problem, having the following form :

Ω A ε(u) . ε(v) dΩ - Γ s C [u].[v] dΓ s = Ω f v dΩ + Γ 1 s . v
C = C T 0 0 C N ( 15
)
Writing the displacement jump [u] = N δ [u], the discretization of the surface term is obtained as follows:

Γ s C [u].[v] dΓ s = ∑ seg seg δ [v] N t C N δ [u] dx = ∑ seg seg δ [v] Ṽ δ [u] dx (16)
A linear interpolation is performed (Fig. 6.a), taking x to denote the abscissa associated with the segment of length h. V el is the order (8 ×8) elementary matrix associated with the length of the segment h, .

V el = h 0 Ṽ dx = h 0 N t C N dx ( 17
)
After proceeding to the assembly of the matrix, we then obtain the linear system where K and V are the rigidity matrix and the matrix associated with the damage interface, respectively. An incremental explicit algorithms is used to solve the local problem. Due to the contact conditions, a fairly small increment is chosen. The mesh consists of 665 Q4 finite elements for the whole domain and of 76 Q4 finite elements for brick/mortar interfaces (Fig. 7). The loading on the middle brick ranges from 0 to 53 KN. The main goal of computation consists in determining the stiffness values of the interfaces, C N and C T . The values of the load parameters F c and F u (or stresses τ c and τ u ) are determined from the experimental "load-displacement" curves [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF]. The values of the lengths l c and l u are chosen so that the numerical global response matches the experimental "stress-strain" (or "stress-displacement") diagram satisfactorily. The rigidity of the assembly depends mainly on the interface stiffness as expected. Since the problem is highly non linear, even small perturbations in the stiffness coefficients can greatly affect the numerical responses. In Figs. 8 e 9 stiffnesses C N and C T degradation with respect to load increments and with respect to the micro-crack length l evolution are plotted.

K δ u -V δ [u] = F (18)
The analysis of the shear stresses σ xy distribution map (Fig. 11) reveals that the stress concentration develops in the regions containing the discontinuities, or more specifically, at the interface level. Moreover, Figs. It is possible to conclude that the future failure of the triplet model occurs in brick/mortar interface zone by the excess of the strain capability of this interphase, which agrees with the experimentally observed failure mode.

Conclusions

An accurate version of the multi-scale model proposed by A. Rekik and F. Lebon [START_REF] Rekik | Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry[END_REF][START_REF] Rekik | Homogenization methods for interface modeling in damaged masonry[END_REF] it is presented here. It is successfully used to simulate the experimental tests in which failure occurred at the brick/mortar interface presented in [START_REF] Fouchal | Contribution to the modelling of interfaces in masonry construction[END_REF], which provided the coefficients required to model the interface, namely the stiffness parameters and the length of the micro-cracks. The model is sensitive to these characteristics but the results obtained are in line with the experimental data. From the practical point of view, an optimization routine is needed to systematically determine the values of the parameters describing the evolution of the crack length. This idea will be applied to more complex masonry structures in a future study.

It is proposed in the future to enrich this model with a more complete homogenization technique, in particular the one performed by C. Goidescu and H. Welemane [START_REF] Goidescu | Microcracks closure effects in initially orthotropic materials[END_REF][START_REF] Welemane | Isotropic brittle damage and unilateral effect[END_REF]. Their work is devoted to a continuum micromechanics-based investigation of the anisotropic multi-linear response of orthotropic materials containing microcracks. This response is often a very complex combination of two specific features of such deteriorating phenomenon. First, the oriented nature of microcracks induces an evolution of the material symmetry. Secondly, a change in the elastic response of the material is expected, based on opening-closure microcracks state with respect to loading situations. Their procedure leads to the proposal of a closed-form expression of the macroscopic free energy corresponding to two dimensional initially orthotropic materials weakened by arbitrarily oriented microcracks systems.

In a future study, it is planned to implement and validate this enriched model with a software suite for finite element analysis and computer-aided engineering like ABAQUS.

Figure 1 :

 1 Figure 1: Principle of the proposed model

  S ζ , E ζ and ν ζ are respectively the compliance tensor, the Young's modulus and the Poisson ratio of phase ζ (ζ = b for the brick, ζ = m for the mortar). The macroscopic behaviour law of the laminate brick/mortar reads:

2 ρ[(e 3 ⊗ e 3 )

 33 ih B jl + (e 3 ⊗ e 3 ) il B jh + B ih (e 3 ⊗ e 3 ) jl + B il (e 3 ⊗ e 3 ) jh ] (9)

Figure 2 :

 2 Figure 2: the principle of the asymptotic techniques in a 2-D case

Figure 5 :

 5 Figure 5: Initial geometrical configuration and loading conditions imposed

Figure 6 :

 6 Figure 6: a) Displacement jump, b) Quadrangular element at the interface.

Figure 7 :

 7 Figure 7: Meshing detail

Figure 9 :

 9 Figure 9: Variation of the overall elastic coefficients C N and C T as function of the crack length

Figure 10 :Figure 11 :

 1011 Figure 10: Shear stresses at the brick/mortar interface

Table 1 :

 1 Mechanical properties of the three-fold masonry constituents

	dΓ 1	(14)

  [START_REF] Fremond | Damage, gradient of damage and principle of virtual power[END_REF] show the evolution of the jump

		2	x 10 12
		1.8
											Ct
											Cn
		1.6
	C N , C T [KN/m 3 ]	1 1.2 1.4
		0.8
		0.6
		0 0.4	10	20	30	40	50	60	70	80	90	100
							load increment δF/F
	Figure 8: Variation of the overall elastic coefficients C N and C T with respect to load
	incrementation
		2	x 10 12
		1.8
										Ct
		1.6								lc lu
										Cn
	C N , C T [KN/m 3 ]	1 1.2 1.4
		0.8
		0.6
		3.4 0.4	3.6	3.8	4	4.2	4.4	4.6	4.8	5	5.2	5.4
							micro-crack length [m]			x 10 -4