Sarah Regina Pereira Camelo

Sophie Franceschi

Emile Perez

Sophie Girod Fullana

Maria Lnês Ré
email: maria-ines.re@mines-albi.fr

PhD Maria Inês Ré

Factors influencing the erosion rate and the drug release kinetics from organogels designed as matrices for oral controlled release of a hydrophobie drug

Keywords: Efavirenz, lipid formulation, multiparticulate dosage form, oral drug delivery, organogel, poorly soluble drugs, prilling process, release profile models

This article proposes solid-like systems from sunflower oil structured with a fibrillar network built by the assembly of 12-hydroxystearic acid (12-HSA), a gelator molecule for an oil phase. The resulting organogels were studied as oral controlled release formulations for a lipophilic drug, Efavirenz (EFV), dissolved in the oil. The effects of the gelator concentration on the thermal properties of the organogels were studied by Differential Scanning Calorimetry (DSC) and showed that drug incorporation did not change the sol-gel-sol transitions. The erosion and drug release kinetics from organogels under conventional (filling gelatin capsules) or multiparticulate (beads obtained by prilling) dosage forms were measured in simulated gastric and intestinal fluids. EFV release profiles were analyzed using model-dependent (curve-fitting) and independent approaches (Dissolution Efficiency DE). Korsmeyer-Peppas was the best fitting release kinetic model based on the goodness of fit, revealing a release mechanism from organogels loaded with EFV different from the simple drug diffusion release mechanism obtained from oily formulations. From organogels, EFV probably diffuses through an outer gel layer that erodes releasing oil droplets containing dissolved EFV into the aqueous medium .

Introduction

Interest in lipid-based drug delivery has developed over the past 15 years, largely driven by the growing need for novel drug delivery systems to deal with the vast majority of the new chemical entities (NCE) that have poor solubility, or permeability or to improve the delivery of existing drugs 1 • The diversity of commercialized lipid excipients (e.g. fatty acids, glycerides, polyoxyethylene glycols derivatives, ethoxylated glycerides and polyalcohol fatty acid esters) has created a large platform for lipid-based formulation design. Depending on the choice of lipid excipients and formulation techniques, it is possible to obtain a variety of systems in the forms of emulsions, microemulsion s, micelles, liquid crystalline particles, solid lipid particles and various self-emulsifying systems.

Successfully marketed oral lipid-based drug products, currently conceming S4% of the global pharmaceutical market, are mostly formulated as bulk liquid solutions or liquid-filled gelatin capsules 2 • Clinical translation of novel lipid-based formulations is clearly related to the rate of discovery of pipeline drugs exhibiting poor aqueous solubility, which is predicted to increase from 30% to 70% 3 . Major barriers for attaining full commercial potential for lipid-based formulations are associated with challenges in their physical stability, non-ideal drug encapsulation and unpredictable delivery performance.

The primary mechanism of action by which a lipid formulation leads to improved bioavailability is usually avoidance of the slow dissolution process that limits the bioavailability of hydrophobie drugs from solid dosage forms. A formulation keeping the drug in a dissolved state throughout its transit in the gastrointestinal tract (Gl tract) appears preferable. In this context, a gel vehicle and especially an organogel could be useful to improve the bioavailability of a hydrophobie drug. Ingeneral, a gel may be defined as a semi-solid formulation having an external solvent phase, apolar (organogel) or polar (hydrogel) immobilized by a 3D-network scaffold. Organogels may be regarded as bi-continuous systems consisting of a gelator and an apolar solvent. The gelators may undergo physical or chemical interactions so as to form selfassembled entangled fibrous structures leading to the formation of a three-dimensional scaffold. The 3D-networked structure, hence formed, entraps and immobilizes the apolar phase.

In the last 20 years, there has been an explosive growth in research on organogels, and on publications related on them4- [START_REF] Bhatia | Tamoxifen-loaded lecithin organogel (LO) fur topical application: development, optimization and cbaracterization[END_REF] as another category of lipid system. Most of these publications report the discovery and/or the synthesis of new organogelators, the properties of organogels including the gel microstructures and the manner in which the gelator molecules could be arranged in 3-D network structures. The large diversity in terms of the possible microscopie structures available for organogels originated the interest for applications of these soft materials in the petrochemical industry for gelling flammable solvents for storage and transport [START_REF] Abdallah | Organogels and low molecular mass organic gelators[END_REF] , in the food industry for structuring edible oils [START_REF] Pernetti | Structuring of edible oils by alternatives to crystalline fat[END_REF] , in the cosmetic field [START_REF] Anand | Applications of organogels in pharmaceuticals[END_REF] and more recently as part of pharmaceutical drug delivery systems. As far as drug delivery is concerned, organogels appear as suitable carriers for lipophilic drugs. Consequently, in recent years, the possibility of using organogels as drug delivery vehicles has been explored for parenteral [START_REF] Motulsky | Characterization and biocompatibility of organogels baSC<l on 1-alaninc for parenteral drug delivery implants[END_REF] and transdermal delivery8• [START_REF] Lim | Pbysicochemical effects of terpenes on organogel for transdermal drug delivery[END_REF] •". Nevertheless, so far, only few studies have been carried out on oral drug delivery 15 -17 . Starting from these considerations, this study proposes the application of organogels to integrate attractive and nove! lipidbased delivery systems for controlled release of a hydrophobie drug, Efavirenz (EFV), via oral administration. EFV is a nonnucleoside reverse transcriptase inhibitor, used for the treatment of the human immunodeficiency virus (HIV). EFV is a molecule of class IIof the biopharmaceutical class system [START_REF] Amidon | A theoreti.cal basis for a biopharmaceutic drug classification: the correlation of in vitro drug product dissolution and in vivo bioavailability[END_REF] that presents low aqueous solubility (4 µg/ml) [START_REF] Chiappetta | Efavirenz-loaded polymeric micelles for pediatric anti-IIlV pbarmacotherapy witb significantly higher oral bioavailability [corrected][END_REF] and high permeability. Efavirenz (EFV) is a first-line anti-HIV drug largely used as a non-nucleoside reverse transcriptase inhibitor as part of antiretroviral therapies. EFV as active pharmaceutical ingredient (APT) is commercially available as microni zed powder. Sorne papers 20 -22 have been published focusing on EFV innovative solid forms, but there is no clear evidence of solubility or dissolution improvement. Other studies 23 -27 have led to an amorphous system that was inherently unstable, could recrystallize and had low physical stability. Organogels for oral administration of EFV could represent an innovative drug delivery system, particularly under multiparticul ate forms.

Among the different physical methods available to obtain multiparticulate forms, such as spray drying, fluid bed coating or extrusion, prilling is able to produce microparticles or beads (prills) with very narrow dimensional range and high encapsulation efficiency. These beads are produced by breaking apart a laminar jet of molten organogel into a row of monosized drops by means of a vibrating nozzle device. The aim of this study was also to show that prilling technique could be used as a simple method to prepare organogel beads with narrow particle size distribution loaded with Efavirenz, as multiparticulate dosage forms. Multiparticulate dosage forms are known to overcome the poor and variable GI tract absorption of drugs and have shown the ability to reduce or eliminate the influence of food on bioavailability 28 . ln view of the above, the control release of EFV from sunflower oil-based organogel structured with 12-hydroxystearic acid (12-HSA) as gelator has been studied. The 12-HSA was chosen because it is one of the most studied molecular gelators for cosmetics [START_REF] Cri Cir | Am.ended final report on tbe safety assessm.ent of hydroxystearic acid[END_REF] and more recently for food [START_REF] Lupi | Olive oil/policosanol organogels for nuttaceutical and drug delivery purposes[END_REF] and drug delivery applications [START_REF] Sumizawa | Cbaractcrization of organogel as a novel oral controlled release formulation for lipophilic compounds[END_REF] in part due to its inexpensive cost, versatility in gelling numerous solvents 30 and safety2 9 . The effect of different parameters (gelator concentration, temperature of the gel formation, EFV loading, composition of the release media) on the thermal properties of the gels and drug release kinetics was investigated. The erosion rate was also investigated for the gel capsules.

Materials and methods

Materials

A food grade sunflower oil (density of 0.92 g/mL) provided by a local supplier was chosen as the vegetable oil for organogel preparation. Sunflower oil is mainly composed of linoleic acid (60--703w/w), but it also contains oleic acid (14-353w/w), palmitic acid (3-103w/w) and stearic acid (1-103w/w) 31 . 12-Hydroxystearic acid (12-HSA 853, C18H3603, MW 300.48 g/mol) was purchased from Alfa Aesar (France) and used as gelling agent. Efavirenz (EFV) was obtained from Cristalia S.A. (!tapira, Brazil). Acetonitrile used in solubility, pepsin and pancreatin used in the erosion/drug release studies were supplied by Sigma-Aldrich (France). Sodium dodecyl sulfate (SDS) was supplied by VWR (Prolabo, France).

Methods

Drug solubility in gel and oil phases

EFV soluhility in molten organogels. The enthalpies of solution of EFV in molten organogels were carried out isothermally (90.0 ± 0.5 °C) using a heat flux in a Calvet calorimeter model-C80 (Setaram, France) equipped with two mixture cells, one for reference. Each ceII has an upper and lower compartment separated by a displaceable lid that allows the connection of compartments during the analysis. The sample cell was filled with accurately weighed amount of drug (30, 60, 70, 75 and 80mgEFv/ g0rganoge1) in the lower compartment and 1g of organogel in the upper compartment. After thermal stabilization, the vesse! was rotated by 180° several times, which displaces the lid between the drug and solution leading to their mixing. The signal was automatically recorded on the strip chart recorder. Experiments were conducted in duplicate.

EFV soluhility in sunjlower oil. The solubility of Efavirenz in sunflower oil was determined at 37 ± 1 °C by adding excess drug (5 g) to the oil (50 g). The suspensions were equilibrated in a constant temperature shaking water bath during 24, 48 and 72 h. An aliquot of the filtered samples ( 1 mL) was transferred to a volumetric flask for appropriate dilution with acetonitrile (ACN); subsequently, 1mL of the resultant solution was diluted with the mobile phase acetonitrile: acetate buffer (60:40) and analyzed by High Performance Liquid Chromatography (HPLC) (LaChrom Elite, Hitachi) to determine the amount of dissolved EFV. The HPLC was equipped with reversed-phase column C18, 250 x 4.6 mm, 5 µm (Kinetex™ -Phenomenex, France) and the HPLC column operating conditions were optimized [mobile phase ACN: acetate buffer (60:40), 1.0mL/min flow rate, volume injection of 40 µL, UV-detector 252 nm]. Experiments were conducted in triplicate.

Thermal analys is

12-HSA was added to sunflower oil over a range of compositions (2-303 w/w). Samples were prepared by dissolving the weighed solid organogelator in a weighed amount of liquid oil at 85 °C under stirring (300rpm). The heated solutions were subsequently cooled to room temperature (25 °C) and stored at this temperature for further analysis. For the formulations including EFV in the organogel (30 or 60 mg EFV/g0rganoge1), both EFV and 12-HSA were weighed and added to sunflower oil. The mixture was then heated at 85 °C with gentle stirring during 30 min to melt the organogel and dissolve EFV. The heated solutions were subsequently cooled to room temperature and stored under the same conditions for further analysis. AU concentrations are expressed as a weight percentage (wt3).

Thermal properties of organogels, unloaded or loaded with EFV, were determined by Differential Scanning Calorimetry (DSC) using a FRS5 calorimeter (Mettler Toledo, France). Samples (5-10mg) were hermetically sealed in aluminum standard pans. Temperature was heated and cooled at a rate of 3 °C/min from 15 to 85 °C for two cycles. Before the second cycle, the system was kept al 15°C for 20 min. A nitrogen gas purge was used at 20 mL/min. Melting (Tm) and crystallization (Tc) points were determined from DSC data (onset, peak and end temperatures as well as the associated specific enthalpies).

Erosion and release kinetics from organogel in a conventional dosage form (cylindrical shape)

The erosion mode of the delivery system is one of the factors controlling drug release. In order to understand the release kinetics in relation to their weight changes, both erosion rate and release rate were determined and correlated.

Molten organogels loaded with EFV were solidified in hard shell gelatin capsules (size #00: i.e. 0.95 mL of capacity volume; length of 23.3mm and diameter of 8.2mm) at 25 or 5 °C. The dissolution of gelatin capsules after five minutes of contact with the dissolution media did not affect erosion nor release rate. Two gelator concentrations were used (5 and 20 wt% of 12-HSA). Erosion and drug release were measured from the organogels in a SOTAX AT7 (Switzerland) dissolution bath at 37 ± 0.5 °C. The organogels capsules were weighed, placed in a USP dissolution basket and immersed in 500 mL dissolution media at 50rpm. The simulated gastric solution comprised pepsin (800 U/L of enzyme activity) dissolved in 0.1 N hydrochloric acid (pH 1.2) and the simulated intestinal solution included pancreatin (1750 U/L of protease activity and 140 U/L of lipase activity) 32 dissolved in phosphate-buffered saline (pH 6.8). Both solutions contained 1.0wt% SDS according to dissolution monograph of Efavirenz. The organogels were removed from the test solution (1, 2, 3, 4, 6 and 8 h after starting) and dried under ambient conditions during 24 h. Determination s were performed in duplicate.

Organogel erosion was determined by difference in weight, taking the amount of the drug release into account. Percentage of organogel erosion (E) at time t was calculated from Equation (1).

E(%) = ( mo -m, -mEFVreleased ) X lOO (l) mo
Where m0 is the initial weight of the organogel, m1 the weight of the organogel subjected to erosion for time t and mEFVreleased the weight of EFV released at time t.

When the organogel was removed from the test solution, 5 mL of the medium was also withdrawn from the incubation vesse!. The amounts of EFV dissolved were determined by HPLC (LaChrom Elite, Hitachi), utilizing a reversed-phase column Cl8, 250 x 4.6 mm, 5 µm (Kinetex™ -Phenomenex, France); UVdetector 252 nm; 1.0mL/min flow rate; 40 µL volume injection and mobile phase ACN: acetate buffer (60:40).

Methods used ta compare EFV release profiles from the cylindrical organogels

Efavirenz (EFV) release profiles were analyzed using modeldependent (curve-fitting) and independent approaches (Dissolution Efficiency -DE). The free open source software KinetDS® [START_REF] Mendyk | KinetDS: an open source software for dissolution test data analysis[END_REF] was used to fit the release curves to the Korsmeyer-Peppas, Weibull and Hixson-Crowell mathematical models [Equations (2-4), respectively, Table 1). The accuracy and prediction ability of these models were compared by calculation of coefficient of determination (R 2 ), AIC (Akaikes's information criterion) and RMSE (root mean square error).

The dissolution (or release) efficiency (DE), calculated by KinetDS® according to Equation (8) (Table 1), is a modelindependent parameter that was also used to evaluate the EFV release performance under different formulations and test conditions. The differences for DE were statistically examined by oneway analysis of variance (ANOVA) followed by Tukey test, in order to find the source of difference (p<0.05). ln this method, DE (n =2) was the dependent variable, and Formulation was the factor. The calculations were performed using the software Statistica version 12.0 (Data Analysis Software system, StatSoft, Inc., Tulsa, OK). Throughout the study, p ::;0.05 was used as the criterion to assess statistical significance.

Organogel beads for drug delivery purpose

Preparation method. Before beads production, the organogel formulation was preliminary selected. The concentration of 12-HSA was fixed at 20 wt% and the drug loading at 60 mg/g, an interesting composition for controlled drug release. Blank organogels (without drug) were also prepared under the same conditions for comparison. Organogel beads were generated using prilling equipment (Spherisator M, BRACE -GmbH, Germany). After melting 12-HSA in sunflower oil at 90°C, EFV was added to the melt under stirring up to its complete dissolution in the molten matrix. By applying air pressure (50 mbar), the mixture was extruded towards a thermostated nozzle (inner diameter: 0.4 mm). The extruded liquid jet was broken up into droplets of equal size by the application of a vibrational frequency (250 Hz). The droplets were allowed to form and fall into a thermostated vesse! containing water at 25 °C. The distance between the nozzle and the collector bath was adjusted to 90 mm. A surfactant (0.2 wt% Tween-20) was added into the collector bath to prevent the formation of bead aggregates. The beads were collected immediately, rinsed thoroughly with distilled water and then stored in dry atmosphere at ambient temperature until further experiments.

Characterization methods

Bead size and shape. Beads were observed by optical microscopy (OM) and scanning electron microscopy (SEM). The OM was performed by numerical microscope (Keyence VHX-5000, France) equipped with objective-glass Z20 and ZlOO. Concerning SEM, a XL30 ESEM-FEG equipment (Philips, USA) was utilized . At least 1OO beads were analyzed from each batch. An average value for ail beads has been calculated as the mean particle size.

Raman microscopie mapping. To further characterize the beads, complementary Raman analyzes were undertaken focusing on the evaluation of the spatial distribution of the components within the gel beads. Raman microscopie mapping was performed using the Alpha 300AR Confocal Raman-AFM microscope (Witec, Germany) equipped with a double laser Nd:Y AG at a wavelength of 532 nm. Cross-sections of beads were scanned by a 50 x long working distance objective lens, which allowed 432 nm of lateral resolution and 1320 nm of axial resolution. Ail spectra were acquired using an exposure time of 10s and a step size of 0.2 µm. The area mapped was approximately 15 µm x 30 µm. The resulting images provide information about the distribution of EFV within the organogel beads.

Drug release studies from organogel beads

Dissolution profile of the organogel beads generated by prilling, composed with 20 wt% of 12-HSA and loaded with 60 mg/g of Efavirenz was performed using an USP4 apparatus (Sotax CH-4008, Switzerland) equipped with three flow-through cells. Twenty beads were placed into each cell operating at a flow rate set of 16mL/min in a closed circuit. In order to simulate the GI tract, two dissolution media were successively used according to Pharmacopeia recommendations (2 h at pH 1.2 and then 8 h at pH 6.8). About 1wt% SDS was added in the media as previously described. According to the literature, the equilibrium concentration of the drug in simulated gastrointestinal fluid containing l wt% is close to 2.5 mg/g,01ution at 37 °C34 . The drug Higuchi

Mt = 1-exp(-( •Ti)b) (3) (1 -Mt/Mo) 113 = KHc.t (4) Mt = KHi.t 05 NE(5) Best mode/ criteria RM. SE = L., ' • = -' (yiobs-yipred) 2 ( 6 ) n AIC = 2k + n.[zn ( (yiobs -yipred ) 2 ) ] (7) Model-lndependent Dissolution efficiency (DE) DE = ( f M i Mtdt)
x 100 (8) trnax .t

Mt: amount of drug released in time t.

Mo: initial amount of drug in the dosage form.

KHi is the release constant in Higuchi mode!. KHc is the release constant in Hixson-Crowell mode!. KKP is the release constant incorporating structural and geometric characteristics of the drug-dosage for; n is the diffusional exponent indicating the drug-re ease mechanism. Mtmax = maximum amount of drug released (=100%). N = number of time points. Ti = lag time before the onset of the release process (in most cases will be zero). a = time scale of the process. b = shape parameter. concentration used in the dissolution tests was 0.04 mg/gsotution• Samples were withdrawn at predefined time intervals up to 10h

i "' .±-• • ••• •• / .. ...• • •••• • • . . +-+=:• . f.-----+ • • ••• •• ... ..

Results and discussion

Drug solubility in molten organogels

Organogels were prepared for prilling at 90 °C. The determination of the drug solubility in the molten organogel (for the highest organogelator concentration tested) was necessary to ensure the complete dissolution of the drug in the molten organogel and prevent nozzle clogging during prilling. Solution calorimetry measured the heat change generated from the dissolution of the solid EFV by the molten organogel constituted of sunflower oil and 20 wt% of 12-HSA. The creation of a saturated solution at 90 °C involved dissolving the solute (EFV) up to the maximum and constant concentration that also corresponds to a constant value of heat of solution. As shown in Figure 1, incremental amounts of EFV added to the molten organogel resulted in a straight line increase in the magnitude of the heat of solution until a plateau was reached when the concentration of the solute equaled the saturation point. From Figure 1, the EFV mass where the two straight lines cross corresponds to the amount of solute that saturates the solvent contents in the vesse!. The solubility value corresponds to 75 mg/g for EFV in the molten organogel at 90 °C. From these results, we choose to work with a concentration below the saturation (30 and 60 mg of EFV per gram of organogel). It is also important at this stage to keep in rnind the organogel concept, in which oil is entrapped in a network self-assembly of the gelator molecules creating a gel. In this study, sunflower oil is entrapped in the self-assembled fibrillar networks of 12-HSA. The aim is to entrap EFV amounts smaller than its solubility lirnits at 37 °C in the oil phase in order to keep the drug always dissolved when exposed to the release medium. This condition is achieved for the EFV concentrations equal or lower than 60 mg per gram of organogel containing 20% 12-HSA (corresponding to 75 mg per gram of sunflower oil), since the equilibrium concentration determined experimentally after 72 h is equal to 79.8 ± 0.6 mg of EFV per gram of sunflower oil as shown in Table 2.

Thermal analysis

The effects of the gelator concentration and the drug incorporation on the thermal properties of the organogels were studied by DSC. DSC thermograms for the second The thermal point of technical-grade 12-HSA is roughly 76 °C with a melting enthalpy of 182J/g 35 . 12-HSA/sunflower organogels display the following melting characteristics: as gelator concentration is increased, so does the melting enthalpy and the onset of melting, i.e. the gel melts at a higher temperature. For example, a 2wt% HSA sunflower oil gel has a Tm of approxi-0 u::: Temperature (°C) temperature, and even higher than 40 °C to combine environmental and storage aspects. All fractions of 12-HSA used in this study to produce sunflower oil gels are able to lead to a structured network of 12-HSA since the onset for melting is approximately 48 °C for the lower gelator concentration (2 wt%).

" GI ' -0.2 -0.3 ------4wt% --5wt% (03) --6wt% (04) • • •• • • -• •-8wt% (05) -••-••-••-•10wt% (06) • ., " • . \ • : • • ,
Besides the gelator and its concentration, the effect of the drug on the gel structures should be an important parameter to be taken into account when developing organogels for drug delivery purposes. In previous studies reported in the literature, the drug was mostly suspended in the gel medium and had a little or no impact on the structures of the drug-loaded gels, which possessed nearly identical physical properties with blank gels 15 -17 • In other cases, although no impact was observed on the gelation temperature, the presence of some dissolved drug in the gel apparently shortened the time of phase inversion while raising drug content [START_REF] Jiao | Self-assembly and headgroup effect in nanostructured organogels via cationic amphiphile-graphene oxide composites[END_REF] .

The effect of the drug incorporation in the thermal transition temperatures of the organogels was also studied by DSC. EFV was incorporated (30 mg/g0rganogel or 60 mg/g0rganogeJ in 12-HSA/ heating-cooling cycle of the organogels without EFV (Samples 01-09) are shown in Figure 2(a) and (b), respectively. The position of the melting and the crystallization peaks shifts to higher temperatures as the concentration of 12-HSA is increased and they become broader and shallower at low concentrations of 12-HSA as shown in the bottom curves in Figure 2(a) (melting) and in the top curves in Figure 2(b) (crystallization). As expected, the organogels were thermoreversible as identical thermal parameters were obtained over the two melting/crystallization cycles (data not shown).

Table 3 shows the thermal parameters that describe the crystallization and melting behavior of organogels over the range of compositions from 2% to 30% (w/w) HSA. Tm(onset)> Tm and Tm(enctset) are the temperatures at the beginning, peak and end of the melting endotherm, respectively. Tc(onset) • Tc and Tc(endset) are the temperatures at the beginning, peak and end of the crystallization exotherm, respectively. AHm and AHc are the melting and crystallization enthalpies, respectively, determined by integrating the area of each peak, melting and crystallization respectively. sunflower oil gels containing different gelator concentrations (5%, 10%, 20% and 30wt%). The DSC thermograms for the second heating-cooling cycle of EFV-loaded organogels formed with 20%wt HSA are shown in Figure 3(a) and (b). The same trend was systematically seen for the whole gelator concentrations studied. The temperatures and heats of melting (i.e. Tm and AHm) and crystallization (Tc and AHc ) are reported in Table 3.

The organogel melting enthalpy (AHm ) combines at least two distinct energetic contributions: (l) the melting enthalpy of the fibers (which should be more or Jess constant and independent of the solvent used if the fibers comprise pure gelator molecules organized in a similar and regular structure) and (2) the enthalpy of dissolution of the gelator in the solvent phase, which is related to the molecular affinity between the two species and should depend on the solvent used 37 ' 38 . A decrease of the melting enthalpy could be taken as a sign of some re-arrangements in the microstructure and/or packing of the 12-HSA molecules occurring in the presence of the dissolved drug in the oil. However, the data shown in Table 3 suggest that the introduction of EFV in the gelling system did not result in evident changes on AHm or AHc of the formulations, but apparently reduced the thermal transition temperatures (Tm, Tc) by a few degrees while raising drug content. This is quite visualized for low gelator concentrations, the differences decreased when the HSA fraction increased, both Tm HSA concentration (Figure 4). The sol-gel transition is sometimes interpreted as dissolution or melting of the "crystal " gelling molecules. In this sense, the solubility of "crystals gelling" corresponds to the concentration of gelling agent in an ideal solution at a given temperature by the following Equation ( 9), called Schroeder-van Laar equation -ôHm (B) 1.2 .,, Where R is the universal gas constant and /'<;.Hm corresponds to the melting enthalpy apparent (sol-gel) of the pure gelling and C its molar concentration in the gel. According to this equation, a plot of L111 C versus 1/ Tm should be a straight line. This linear dependency is confirmed in Figure 5. The melting and crystallization enthalpies likewise increased in a linear manner with an increase of the 12-HSA concentration (Figure 6). Similar To clarify the mechanism of drug release from organogels, the weight loss and the amount of drug released were measured as a fonction of time. Experimental data plotted in Figure 7 highlights an initial slow release during the first hour, during which probably the drug diffuses slowly, followed by a second step characterized by a faster release. This faster release could be attributed to the onset of an erosion phenomenon, which makes the entrapped drug . -----------1--•---:-= fluid. The corresponding organogel erosion percents were 4 and 12%, respectively. lt was also observed that the same organogels when formed at 5 °C eroded more easily (7 and 22% mass losses in gastric and intestinal conditions, respectively), although minor differences were observed on the amounts of drug released (24 and 34%), compared to those at 25 °C. In summary, the data presented here evidenced that both erosion and drug diffusion from the 12-HSA sunflower organogel are dependent on the matrix network (directly correlated to HSA concentration and temperature of gel formation) and slightly affected by the EFV presence, especially at low concentration of HSA. Therefore, the more structured the system the lower should be the matrix erosion, yielding to a lower drug release as a final result. More structured gels were obtained with the higher gelator more available. Combined drug diffusion and erosion may contribute to a faster release than erosion alone [START_REF] Iwanaga | Application of organogels as oral controlled release formulations of bydrophilic drugs[END_REF] . The data shown in Figure 7 include the influence of four different parameters: gelator concentration (5 or 20 wt% HSA), temperature of gel formation (5 °C or 25 °C), and composition of the release media (pH 1.2 containing pepsin or pH 6.8 containing pancreatin) to simulate the GI tract.

0 " c " w -2wt% (01) ----4wt% (02) . .. . -5wt% (03) . ' -6wt% (04) • • •••-•Bwto/o (05) ='i • ••-•••10wt 0 /o (06) -•-•-• 15wto/ o (
C =--+ constant e R.Tm (9)
At the end of 8h of release, the mass lost (erosion) and the amount of drug released were more pronounced for organogels less concentrated in 12-HSA (5 wt%) formed at lower temperature (5 °C). In fact, organogels containing 5 wt% HSA (OEFVl) formed at 5 °C released 34% of EFV under simulated gastric conditions against 51% in simulated intestinal fluid. The corresponding organogel erosion percents were 25 and 41%, respectively. The temperature of gel formation influenced the amount of drug released and the organogel mass Joss. lncreasing the temperature of organogel formation to 25 °C led to an increased drug release (36% of EFV released in gastric and 45% in intestinal conditions; 27 and 39% of organogel mass Joss, respectively).

In tum, organogels formed at 25 °C, loaded with 20 wt% 12-HSA (OEFV7) provided the smaller amounts of drug released and mass losses. They released approximately 24% of EFV under simulated gastric conditions against 32% in simulated intestinal concentration (20 wt% HSA) and the higher temperature of gel formation (25 °C). Both erosion and drug diffusion from more structured gels were less affected by the pH of the medium. These findings are also in agreement with the few works found in the literature related to drug delivery from organogels in simulated gastric and intestinal test solutions 15 -17 . Release profiles from the cylindrical organogels Dependent models (curve fitting ) ln a general manner, the drug release from organogels may involve processes of diffusion, erosion or drug dissolution 16 • 17 . Diffusion and erosion are expected to be the processes controlling drug release from the organogels since EFV at the concentrations tested, is completely dissolved within the organogels, as expected from the measured solubility data and confirmed by DSC studies. The drug is then immediately available for diffusion.

A large number of models (both empirical and mechanistic mathematical models) have been proposed to describe drug release mainly for polymer matrices characterized by a 3D network. Even though organogels have different structures, the models already proposed for more investigated polymeric carriers can be useful to fit experimental values to compare the release profiles obtained from different formulation (gelator concentration, EFV loading) and conditions (gel formation temperature) studied here.

The in vitro drug release data from the different organogels contaimng EFV were evaluated kinetically using the Korshmeyer-Peppas, Weibull and Hixson-Crowell models [Equations (2-4), Table 1]. Korsmeyer-Peppas mode!is expected to be valid only up to 60% cumulative drug release, so the data for analysis were restricted to this range. The coefficient of determination (R 2 ), root-mean-square error (RMSE) and Akaike's information criterion (AIC) values of these models were determined for evaluation of accuracy and prediction ability of these models using KinetDS 3.0 rev. 2010 software (Krakow, Poland). The result of the curve fitting into varions mathematical models is given in Table 4. The best fitting of models was based on goodness of fit, i.e. the highest coefficient of determination (R 2 ) (doser to unity) and lowest RMSE and AIC values (definition in Table 1).

From the obtained results, it is observed that for all formulations the drug release mechanism is best described by Korsmeyer-Peppas model. This model is a semi-empirical mode!, relating exponentially the drug release to the elapsed time. Tt is used to analyze the release of pharmaceutical polymeric dosage forms, when the release mechanism is not well known or when more than one type of release phenomena could be involved 43 . The release exponent (n) is used in order to characterize different release mechanism. Ifthe n value is 0.5 or Jess, the release mechanism follows Fickian diffusion. Higher values of n (0.5 <n < 1) correspond to a non-Fickian model denominated anomalous transport The drug release follows Zero-order drug release or Case-II transport if the n value is 1. For the values of n higher than 1, the mechanism of drug release is regarded as super Case-II transport, describing the influence of polymeric hydration and swelling on drug release for polymeric and swellable systems, and which can be related to matrix erosion for nonswellable systems.

The values of diffusional exponent (n) determined from Korsmeyer-Peppas model ranged from 0.81 to 1.39 (Table 4) for all organogels loaded with EFV (Fl-Fl6, refer Table 5 for formulation code description), indicating that the drug release from these systems followed the super case-II transport mechanism. However, the n value determined from this mode! for Reference (when EFV-60 mg/g0;1 is dissolved in non-gelled oil) is 0.30 (Fl7, Table 4), denoting a Fickian diffusion mechanism. In conclusion, the release mechanism from organogels loaded with EFV is different from the diffusion mechanism obtained with simple oil formulations. From organogels, EFV probably diffuses through an outer gel layer that erodes, releasing oil droplets containing dissolved EFV into the aqueous medium. This conclusion is supported by the visual observation of the cylindrical organogels before and after release in the test solutions. The photographs shown in Figure 8 were taken at the end of the erosion/release studies. It is clearly visible that the organogels undergo changes in thickness (decrease in diameter) mainly for organogels containing 5 wt% HSA , while the capsule length remained essentially unchanged. These findings evidence erosion occurring at the organogel surface (Figure 8) depending on the gelator concentration.

The results from the evaluation of drug release mechanism using varions kinetic models confirmed the experimental observations that both erosion and drug diffusion mechanisms take place, depending on the matrix network . To evaluate the difference among the 17 formulations, a post hoc Tukey test was performed on the results of ANOVA. With the application of the Tukey test it was possible to observe that, with a level of significance of 5%, DE of formulations Fl, F2, F3, F4, F6, F7, F8, FlO, Fll, F12 and F16 were equal and significantly smaller than the DE found for the formulation F17. Moreover, Fl7 is not significantly different from F5, F9, Fl3, F14 and F15 (p >0.05), which are not significantly different from one other.

From these results, it could be concluded that the drug release was delayed by the gelled oil as already discussed, i.e. an oilstructured system is expected to present lower drug release rate. However, the different parameters studied such as the gelator concentration, the drug loading, the temperature of organogel formation and even the pH of the release media showed no significant difference on DE.

Organogel beads for drug deli very purposes

Beads characterization

Size and shape. Figure 9 reveals that the organogel beads consist of large micron-scale beads, spherical in shape and very uniform in diameter {610 ± 5 µm). l]. The coefficient of determination (R 2 ), root-mean-square error (RMSE) and Akaike's information criterion (AlC) values of these models were determined for evaluation of accuracy and prediction ability of these models using KinetDS 3.0 rev. 2010 software. The result of the curve fitting into various mathemati cal models is given in Table 6. Figure 10 also confirms the correlation of the EFV release profile with the theoretical profile predicted by these model s (see fitting curves). The best fitting was based on goodness of fit, i.e. the highest coefficient of determination (R 2 ; Incubation time, h Raman mapping. The Raman spectra of the individual components (HSA, sunflower oil and organogel beads) are compared in Figure 10. The Raman spectrum of 12-HSA displays a strong peak at around 2850-2900cm-1 (C-H), peaks at 1440cm-1 (CH2) and two peaks around 1068-1135 cm-1 characteristics of C-0 stretching bands. In turn, the characteristic peaks are identified in the Raman spectrum of the sunflower oil: at 1660cm-1 (C =C stretching band s) and the peaks at 1306 and 1272cm-1 ( =C-H deformation), already reported in the literature 44 . For the Raman spectrum of pure EFV, the CF3 stretching modes have been assigned at 1146cm-I, with a typical C =0 stretching bands at 1791cm-1 , one distinguishing intensive band at 2250cm-1 assigned to C C stretching bands, which was not evident in the other gel components.

The pure component Raman spectrum of 12-HSA could not be separated from that of sunflower oil using cluster analysis due to the homogeneous (molecular) dispersion of EFV within the organogel. Comparison of the Raman spectra of the samples revealed that, except for the EFV vibrational bands at 2250 cm-I, there were no distinguishable vibrations bands. EFV was found uniformly distributed within the organogel.

Release studies from organogel beads Figure 11 shows the cumulative amount of EFV release profiles from organogel beads comprising 20wt% of 12-HSA and loaded with 60mg/g of EFV. The organogel beads exhibited a slow dissolution profile with 80% of the drug being released after 8 h, closer to unity) and lowest RMSE and AlC values (Table 1). From the obtained results, it is observed that the drug release mechanism is also best described by Korsmeyer-Peppas model. The release exponent n calculated from Korsmeyer-Peppas mode! for predicting drug release mechanism was 0.62, corresponding to a non-Fickian mode! denominated anomalous transport, revealing that the EFV release is strongly influenced by the size of the organogel system. For the organogel beads an anomalous transport is the main release mechanism, whereas for cylindrical organogels (larger size) erosion and diffusion are the mechanisms controlling the release. The 3D-fibrillar network with 12-HSA as gelator is well documented in the literature and already observed in some of our previous works 46 -4 9 . The driving force of controlled release is the entanglement of the network which represents a physical barrier to the diffusion of the entrapped oil containing the dissolved drug. Sorne interaction between EFV and 12-HSA could delay the free EFY diffusion through the 12-HSA network. However, it was not detected in this study by the Raman mapping of the organogel beads.

Conclusions

This study underlines the interest of gelling sunflower oil with 12-HSA for the controlled release of a hydrophobie drug like EFV. With organogels of different shapes and sizes, exposed to different release conditions, it could be demonstrated that the drug release was controlled mainly by diffusion with a minor participation of erosion in absence of enzymes, or controlled by more than one process, a coupling of diffusion and erosion mechanisms, the later accelerated by enzymatic activities.

Based on the drug release kinetics and mechanism models, EFV release from organogels could be described by the Korsmeyer-Peppas mode!with the highest coefficient of determination and lowest RMSE and AIC values. The release exponent (n) allows highlighting the different EFV release mechanisms with sunflower oil-based delivery systems: drug diffusioncontrolled (sunflower oil, n = 0.30), anomalous transport (organogel beads, n =0.62) and super Case-II transport (cylindrical organogels 0.81<n <1.39). Even though further data will be necessary to investigate EFV release k:inetics in the 12-HSA sunflower oil gel more deeply, the obtained results have &bown that is possible to modify the drug release from the oil phase by gelling the system. Furthermore, prilling is a useful and simple technique to prepare organogel beads with spherical shape and narrow size distribution. The beads could be applied fur the manufacture of multiparticulate dosage furms where a suitable controlled release rate could be designed to takc advantage of beads properties. The multiparticulate nature of beads as a dosage form (filled into capsules) can offer important pharmacological and technological advantages over conventional single-unit solid dosage forms.

Further optimization of formulation wi11 be required before moving onto any in vivo studies.

2 .

 2 ---------------and directly analyzed. The amount of drug released at each time point was determined by the previously described HPLC-UV method. Ali experiments were performed in triplicate.The free open source software KinetDS®[START_REF] Chowdary | Preclinical pharmacokinetic evaluation of Efavirenz solid dispersions in two new modified starches[END_REF] was used to fit the release curves to the Korsmeyer-Peppas, Weibull, Hixson-Crowell and Higuchi mathematical models [Equations(2-5), Tablel]. The accuracy and prediction ability of these models were compared

Figure 1 .

 1 Figure 1. Enthalpy of dissolution of EFV in molten organogel comprising 12-HSA (20 wt%) and sunflower oil at 90 °C. Means with error bars for two experiments (n = 2) are shown.

  e

.

  , against 75 °C for a 20 wt% HSA. It is perhaps appropriate to remember that the main goal of this study is the optimization of a structured organogel matrix in which EFV could be solubilized to control its delivery in the GI tract after oral:I: -0.4 -0.5 -0.6 w -•-• -•-•-15wt% (07).... 20wt% (08) ------30wt% (09) ' , . .. . . administration . Thus, the best formulation for EFV-loaded organogels should take into account the melting temperature of these systems. In fact, organogels being thermoreversible, they should guarantee both the thermal stability and solid-like behavior higher than or equal to the human body

Figure 2 .

 2 Figure 2. DSC second-heating for gelled sunflower oil over the range of 12-HSA compositions from 2% to 30wt%. Melting (A) and Crystallization (B).

3 .and

 3 Thermal parameters obtained from the melting and crystallization thermograms of organogel with different concentrations of 12-HSA in sunflower oil, neat and loaded with EFV. ....... . . .. .... ... . ..•• ...._ ((_---------Tc are almost constant and only fonction of the gelator amount. A similar effect in onset temperatures was reported for soy organogel with different gelators: myristic, palmitic, stearic and arachidic acids 39 .The onset of Tc is the last point associated with the solution state and the onset of Tm is the last point of the gel state. Anyway, the peak melting Tm and onset of crystallization temperatures of the gels increased as 12-HSA concentrations increased, whatever the gel studied, in the presence and absence of drug. Both thermal parameters scaled in a logarithmic fashion in relation to the12-

  ..........20wt% (OEFV3) ..------20wt% (OEFV7)

Figure 3 .

 3 Figure 3. DSC second-heating for gelled 12-HSA (20wt%) -sunflower oil loaded with EFV (30 mg/gorganogel or 60 mg/gorganogeÙ• Melting (A) and Crystallization (B).

40 eFigure 4 .Figure 6 .

 4046 Figure 4. Transition phase diagrams of organogels in different 12-HSA concentrations made without active pharmaceutical ingredient, with 30mg/g and 60mg/g of Efavirenz. Blank symbols correspond to crystallization and black symbols correspond to melting. Means with error bars for two experiments (n =2) are shown.

1 Figure 5 .

 15 Figure 5. Representation of Schroeder-van Laar equation for the analysis of the influence of gelling agent concentration on the sol-gel transition temperature. Means with error bars for two experiments (n =2) are shown.

40 .

 40 --........,.. t --------..-------.... ...... ----,, --..----

Figure 7 .

 7 Figure 7. Weight Joss and release studies of organogels containing EFV at 37 °C. (a, c) Simulated gastric solution at pH 1.2 inclucling pepsin 800 U/L enzyme activity; (b, d) Simulated intestinal solution at pH 6.8 including pancreatin 1750 U/L protease activity. Means with error bars for two experiments (n = 2) are shown.

Figure 9 .Figure 1O .

 91O Figure 9. SEM image of organogel beads produced by prilling process.

11 40%

 11 during the first 2 h under simulated gastric condition s (pH 1.2). Despite an increase in the EFY solubility at pH 6.8[START_REF] Pinto | Estudo de dissoluçâo intrfnseca de Efavirenz como ferramenta para antecipaçâo de suabiodisponibilidade[END_REF] , drug dissolution exhibited a slow release reaching 80% after 4 h of immersion into the simulated intestinal fluid.The data obtained during the release test were examined according to Korsmeyer-Peppas, Weibull, Hixson-Crowell and Higuchi equations [Equations (2-5), respectively, Table

Figure 11 .

 11 Figure 11. Release amount of EFV from the organogel beads containing 20%wt 12-HSA as gelling agent during the release test at 37 °C (2 h in pH 1.2, 8 h in pH 6.8). Means with error bars for three experiments (n = 3) are shown.

Table 1 .

 1 Dependent and independent kinetic models applied to analyze the drug release

	data. Approach	Method	Equations
	Model-dependent	Korsmeyer-Peppas	Mt = KKP.t" (2)
		Weibull
		Hixson-Crowell

Table 2 .

 2 EFV equilibrium concentration in sunflower oil at 37 ± 1°C as a fonction of time.

	Equilibrium lime (h)	24	48	72	Median value*
	EFV concentration (mg/g oil)	82.47 ± 2.18	79.14 ± 3.49	79.78± 0.65	80.02

*The median of ail measured values from 24 to 72 h because we cannot see differences among concentrations al different limes, the differences being smaller than standard deviations.

Table 4 .

 4 Results of curve fitting of the in vitro release data from different cylindrical organogels containing EFV.

	Formulation code (Table 5)

Table 5 .

 5 Comparison of EFV-loaded organogel release profiles using the independent mode! values of dissolution efficiency DE (done using oneway [ANOVA] followed by Tukey's test).

		R2			0.9989	0.9999	0.9993	0.9992	0.9997	0.9998	0.9998	0.9997	0.9975
	Korshmeyer-Peppas	RMSE			1.0503	l.2482	1.5821	0.7897	1.2178	1.5781	1.6493	1.5383	3.4737
		AIC			18.3		2.07	24.04	14.32	20.38	24.08	24.63	23.65	24.45
		K			5.48		4.52	7.82	3.37	9.01	4.10	4.21	1.83	29.20
		n			1.02		0.89	0.65	1.07	0.85	0.99	1.05	1.39	0.30
		DR (%)4h		22.55		15.46	19.22	14.94	29.24	16.16	18.03	12.63	44.00
		R2			0.9999	0.9998	0.9994	0.9987	0.9999	0.9998	0.9997	0.9995	0.9980
	Weibull	RMSE			1.1189	1.2339	1.5218	l.3811	0.9910	1.6369	2.057	3.4710	3.251
		AIC			19.19		20.56	2.35	22.14	17.49	24.52	27.72	35.04	23.84
		Rz			0.7726	0.7573	0.6457	0.7931	0.7228	0.7665	0.7890	0.8352	0.4353
	Hixson-Crowell	RMSE			8.199	6.6980	8.0967	5.4566 11.380	6.1924	6.9713	3.8616 21.05
		AIC			47.08		44.25	46.90	41.38	53.67	43.15	44.81	36.54	42.51
	Model-independent method DE			22.86		15.33	18.04	15.20	28.64	16.18	18.44	13.95	40.74
		Number of time points	7		7	7	7	7	7	7	7	5
					Dissolution
	Formulation	Formation	EFV		efficiency, DE
	code	temperature mg HSA% pH mean (n =2)*
	Fl7 (oil formulation) Fl4	25 5	60 60	0 5	6.8 6.8	40.38" 30_97•.b
	F13	5	30	5	6.8	29_07•.b
	FS	25	30	5	6.8	22.86a,b
	F9	5	30	5	1.2	21.46•-b
	FIS	5	30	20	6.8	19.29•.b
	F7	25	30	20	6.8	18.04b
	FI	25	30	5	1.2	17.68b
	Fll	5	30	20	1.2	17.43b
	FIO	5	60	5	1.2	17.43b
	F3	25	30	20	1.2	15.57b
	F8	25	60	20	6.8	15.53b
	F6	25	60	5	6.8	15.33b
	F16	5	60	20	6.8	14.46b
	F2	25	60	5	1.2	14.36b
	Fl2	5	60	20	1.2	14.17b	Figure 8. 12-HSA sunflower oil gel formed in gelatin capsules (size #OO)
	F4	25	60	20	1.2	12.65b	removed after 8 h of incubation into simulated intestinal solution at 37 °C,

*Values represent the mean of two independent determinations. Same letters at the same colurnn indicate that there is no statistical difference (p <0.05).

lndependent model Dissolution efficiency (DE) results are shown in Table 5. The analysis of variance (ANOVA) revealed a statistical difference (p <0.05) between the formulations. Differences in the DE pH 6.8 including pancreatin 1750 U/L protease activity. (A) 20 wt% HSA and (B) 5 wt% HSA. Both organogels were loaded with EFV (60mg/g). A calibrated vernier cal iper was used for diameter and thickness evaluation of the gel capsules.

data may be related to the release profiles since factors such as 12-HSA concentration, drug loading, gel formation temperature and pH of the release medium may influence the release of the drug molecule from the organogels.

Table 6 .

 6 Results of curve fitting of the in vitro release data from organogel beads containing EFV.Test conditions: media at 37 °C containing 1wt% SDS with changing pH values (2 h at pH 1.2 and then 8 h at pH 6.8), without enzyme

	Model-dependent method

Acknowledgements

Authors thank Gala® technological platform (France) for technical support, Cristali.a (Brazil) fur providing the drug (EFV) and EA-CIDAM (Conception Ingénierie et Développement de /'Aliment et du médicament) for dissolution studies.

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper. This study was partially financially supported by the CNPq (Brazil).


M Caudron

F Emeriault

R Kastner

M Al Heib

Numerical modeling of the soil structure interaction during sinkholes

This article focuses on the simulation of soil-structure interactions during a sinkhole by the use of a coupled numerical approach. The 2D model uses a Finite Difference computer code coupled with a Distinct Elements code (FLAC 2D and PFC 2D from Itasca Consulting Group) to optimize the performances of both softwares.

INTRODUCTION

Sinkholes are caused by natural or man-made cavities. The very sudden nature of this phenomenon may be damaging for the buildings and endangers the life of the population. The soil-structure interactions occurring during this phenomenon are not well understood. The commonly employed approach (in which the soil movements obtained in greenfield condition are applied to a structure) is not satisfying.

The main purpose of this paper is the presentation and the validation of a numerical model allowing a satisfying modeling of the soil-structure interactions during this phenomenon (Figure 1). Two codes are used jointly: FLAC 2D uses the Finite Differences Method whilst PFC 2D is based on the Distinct Element Method. The results obtained in greenfield condition will be compared with those taking into account a building on the ground surface. Moreover a relevant comparison can be made between this numerical simulation and the results of an experimental campaign carried out on a small-scale model, illustrated by Figure 1 (For more details on this experimentation, the reader can refer to [START_REF] Caudron | Sinkhole and soil-structure interactions: Development of an experimental model[END_REF].

THE CASE STUDY

The experimental small-scale model uses a geometric scale of 1/40 to model a 10 m wide and 2 m high gallery with a 8 m thick cover. It corresponds to the usual dimensions of the Parisian quarries that are responsible for several disorders each year. The soil mass modeled is 30 m wide and 20 m high.

The ground cover is composed of several different layers that can be roughly considered as two homogenous layers from a mechanical point of view: a 6 m thick cohesionless material overlies a 2 m thick cohesive layer. Their mechanical characteristics are presented in Table 1. In the small scale physical model, the cohesion of the material is reproduced by the addition of an aqueous solution of glue to cohesionless metallic Schneebeli rods - [START_REF] Caudron | Sinkhole and soil-structure interactions: Development of an experimental model[END_REF]. The structure corresponds, with a 1/40 scaling factor, to a dwelling with three spans and two stories. Its total width is 10 m, each story is 2.7 m high and it comprises a crawl space of 1.2 m in height (more details are given in Table 2). The left foundation is located directly above the center of the cavity. The structure is made of standard steel beams and columns and the applied payloads are determined in order to induce stresses on the foundations corresponding to the Serviceability Limit State. The creation of the cavity follows a simple procedure and five steps are necessary to obtain the 10 m total opening. The first step implies the creation of a small cavity: 2 m in width with the nominal 2 m height. Then, for each of the four following steps, one meter of cavity is opened on each side of the cavity until the final width is reached. On the other hand, it can reduce computation times by using a faster numerical resolution algorithm (such as the Finite Difference Method) in the rest of the soil where only small deformations will appear and for the modeling of the building and structural elements such as beams.

Figure 2 shows a schematic view of the coupled model that uses FLAC 2D and PFC 2D (both softwares have been developed and are commercialized by Itasca Consulting Group -2005). FLAC 2D uses a Finite Difference formulation applied to a continuum, whereas PFC 2D is based on the Distinct Elements Method. They can exchange informations with one another through a socket connection, in particular the data required to satisfy at any step of the calculation the interface conditions between the FD mesh and the particle assembly. The simple coupling procedure illustrated on Figure 4 can be strictly followed in a "simple" case, i.e. when no loss or creation of contact can occur between the particles and the border elements. Nevertheless, in the present case, it is necessary to be able to take into account major modifications in the geometry of the border elements (when the cavity is gradually created by deleting FLAC 2D grid elements) and also losses or creations of contacts of the border elements with moving particles. Therefore, a specific scheme has been developed. This scheme includes the basic one (presented in Figure 4) and determines automatically when it is necessary to update the list of slave particles (PFC 2D particles linked to FLAC 2D border elements).

Step 1: The user specifies a total number X of calculation cycles to compute.

Step 2: A specific Fish function determines the maximum value of the particle velocities in the assembly, V max . Given the smallest particle radius in the assembly, the program then determines the number of cycles x that can be safely achieved:

max min V R x = (1)
In Equation 1, it is assumed that in x cycles the displacement of the fastest particle can not exceed a maximum value arbitrarily taken equal to the smallest particle radius in the assembly, otherwise the list of slave particles has to be updated.

Step 3: y calculation cycles are computed using the coupling scheme detailed above where y is the minimum of x and X.

Step 4: PFC 2D frees the slave particles, get the new border elements list from FLAC 2D and defines the new list of slaves particles.

Step 5: The procedure goes back to Step 2 after replacing X by X-y. The loop is followed until the total number of calculation cycles X introduced in Step 1 is achieved.

When the FLAC 2D grid has to be modified during calculations, the same scheme is used: the required modifications of the border elements and their geometry are performed between Steps 4 and 5.

Between two stages of the creation of the cavity, stabilization of the soil is ensured: the maximum particle velocity in the assembly should be smaller than 10 -11 m/calculation cycle. Finally, Figure 2 shows that the structure represented by FLAC 2D beam elements is not directly in contact with PFC 2D particles but via small FLAC 2D grids. This modeling enables to cope with the limitation of the coupling scheme to the exchange of data between PFC 2D particles and FLAC 2D grid elements

4 INTERPARTICLE CONTACT PARAMETERS (PFC 2D )
The determination of the interparticle contact parameters required by the DEM and PFC 2D is based on the results of biaxial tests (q -ε 1 and ε v -ε 1 curves) performed on the cohesionless and cohesive materials [START_REF] Caudron | Sinkhole and soil-structure interactions: Development of an experimental model[END_REF]). The main parameters describing the behaviour of the particles are:

k n and k s , the normal and tangent stiffness of the contact between two particles, fric, the intergranular coefficient of friction.

-c_n and c_s, the normal and tangent strength of the contact bonds used to represent the overall soil cohesion [START_REF] Potyondy | A bonded-particle model for rock[END_REF].

For the sake of simplicity, two assumptions are made reducing to 3 the number of independent parameters: the ratio k n /k s is supposed to be equal to 2 and the ratio c_n/c_s to 1.

Two sets of parameters are determined (Table 3), respectively for the granular soil (standard metallic Schneebeli rods assembly) and for the cohesive material (Schneebeli rods soaked in an aqueous glue solution). Figure 5 gives an example of the results obtained for the cohesive soil.

The evolution of the deviatoric stress during biaxial compression is generally accurately reproduced, in particular the initial modulus and the deviatoric strength (as shown in Figure 5). The comparison of the experimental and computed volumetric strains presents more discrepancies. The DEM and its implementation in PFC 2D lead to an initial contractancy of the sample under shear stress whereas in the experiments dilatancy is observed even in the early stages of the loading. Nevertheless, after 1 or 2 % of axial strain, the same dilatancy angle is observed. Figure 5. Deviatoric stress and volumetric strain for the cohesive soil (biaxial test performed with 50 kPa confining stress).

SIMULATIONS AND RESULTS

Two subsidence tests have been performed:

-one corresponds to greenfield conditions, i.e. without any structure, and will be considered as a reference, -in the second one, the small scale model of building is positioned at ground level, with its left foundation located directly above the center of the cavity, in order to observe soilstructure interaction effects. [START_REF] Deck | Etude des conséquences des affaissements miniers sur le bâti. Propositions pour une méthodologie d'évaluation de la vulnérabilité du bâti[END_REF] showed that several main parameters are representative of the potential damage to a building induced by the soil movements induced by sinkholes. They include the maximum subsidence or vertical displacement, the shape of the settlement trough, the differential horizontal displacements and the slope of the ground surface in the vicinity of the building (or where it should be positioned if one explicitly takes soil-structure interaction).

The greenfield case

The cavity is created in five steps, it remains stable as it is observed in experimental test. The cohesive layer is then locally weakened in order to cause failure. Weakening is induced in the middle of the cavity roof by simultaneously applying a reduction factor to c_n and c_s the normal and tangential strength limits of the contact bonds in this area. When the crack development reaches a critical state, collapse appears in a very brutal manner and total failure of the cavity is observed. Figure 6 illustrates the stress distribution at the end of the creation of the cavity when a stable state is obtained. The stress concentration on the vertical walls of the cavity is obvious, as the presence of tensile stress in the central lower part of the stiff bench and in its upper part above the side walls of the cavity.

Figure 7 shows the final state, i.e. after failure, and the induced ground surface deformation. The corresponding subsidence or settlement trough is presented on Figure 8 and compared with the results of the experimental test and with a semi-empirical approach.

The latter is a modified version of Peck's semiempirical approach proposed by [START_REF] Caudron | Effondrement de cavités souterraines et interaction avec les ouvrages en surface : approche expérimentale sur modèle analogique bidimensionnel[END_REF] for rectangular shaped cavities. The total volume of the settlement trough is computed from the volume of the cavity multiplied by a factor depending on the expansion coefficient K (K≈0.5 in this particular case study):

cavity trough V K V + = 1 1 (2)
An equivalent cavity radius R eq is also calculated from the trough volume. [START_REF] Caudron | Effondrement de cavités souterraines et interaction avec les ouvrages en surface : approche expérimentale sur modèle analogique bidimensionnel[END_REF] have shown that this enables the computation of i, the distance from the center of the settlement trough to the point of inflexion using Oteo & Sagaseta's empirical expression (1982). (3)

and S max the maximum subsidence above the center of the cavity by:

i V S trough × = 51 . 2 max ( 4
)
where H is the cavity cover. -the numerical simulation gives a better description of the overall volume of the settlement trough, -the width of the predicted trough is smaller than that resulting from the semi-empirical approach and closer to the observed experimental value, -therefore the maximum settlement and the maximum slope observed on the trough are in closer agreement with the experiments. However, it must be noted that the failure mechanism observed in the physical test (shown on Figure 9) is different from that considered in the numerical and semi-empirical approaches (leading to symmetric settlement trough). Only the left part of the cohesive layer felt into the cavity, the right part remained overhanging.

Soil-structure interaction

The coupled model that explicitly considers the presence of a building at ground surface uses the same procedure for the cavity creation and the weakening of the cohesive layer. The final state reached is illustrated on Figure 10. The failure is quite similar to the one observed in greenfield conditions. It appears that the left foundation is not completely resting on the particles. A void is clearly visible under this foundation as well as in the upper part of the rigid bench directly above the cavity sidewalls.

The subsidence trough is plotted on Figure 11 with the position of the three foundations laying in the particles assembly. The results of the physical test with the structure on the ground surface are compared with the outcome of the coupled numerical simulations a) in greenfield condition and b) with the building. The main differences are located on the right part of the curves where the building model is situated. Table 5 summarizes the main characteristics of the observed and computed settlement troughs. The computed trough volumes are smaller than the average value obtained from the physical tests. The values of S max, i and the maximum slope predicted by the numerical model with structure are closer to the experimental results than the greenfield simulation. Both numerical models predict a maximum differential settlement between foundation 2 and 3, i.e. in the central span. However, in the case with structure, the predicted maximum slope is smaller than that observed value in the greenfield case and also smaller than the experimental value. This can be partly explained by the stiffness of the link between the right foundation (foundation 4) with the FLAC 2D grid (Figure 10).

F 2 -F 3 F 2 -F 3 F 2 -F 3
Figure 12 illustrates the impact of the structure on the distribution of the horizontal displacements: the numerical simulation roughly reproduces the reduction in horizontal displacements in the vicinity of the structure and the dissymmetry of the distribution. On the left part of the trough, the experimental and numerical results almost coincide with the greenfield semi-empirical approach

The induced stresses and efforts in the structure may be analyzed from a qualitative point of view. It appears that the two left columns concentrate the maximum efforts and more particularly their lower part (between the foundation and the first floor): an increase of bending moments of about 13kN.m is observed. Moreover, the opposite signs of the moments indicate that the left span is subjected to horizontal compression during the test. This is confirmed by comparing the horizontal displacement vectors on Figure 12.

For the horizontal elements of structure, the coupled numerical approach predicts that the maximum induced bending moment is localized in the central span of the lower floor (more exactly near the junction with the third column). Similar results have been obtained in the physical test: it appeared that the maximum stress (measured by strain gauges) is located in the column 1 and 2 and in the span F 1 -F 2 of the lower beam.

Finally, during the simulation, the total force acting on the sidewalls and away from the cavity can be computed. Figure 13 clearly shows that each step of the creation of the cavity leads to an increase of this vertical force and that the effect of the stress redistribution is limited a 2 to 3 m thick zone from the sidewalls. The computed values presented in Figure 13 are relevant with the conclusions of the smallscale test [START_REF] Caudron | Sinkhole and soil-structure interactions: Development of an experimental model[END_REF]). Nevertheless, it should be mentioned that in both numerical and physical tests, the walls of the cavity are largely stiffer than the soil which is generally not true in real situations where the deformability of the material constituting the walls leads to smaller stress concentration.

CONCLUSION AND PROSPECTS

This paper demonstrates that a coupled FLAC 2D -PFC 2D approach can be used to reproduce in a satisfying manner the soil-structure interaction phenomena induced by sinkholes.

Further research should improve the ability of the model to quantitatively describe the volume of the subsidence trough (smaller than the experimental values in the present analysis). Even if the efforts induced in the structure by the soil movements are complex, the coupled approach gives qualitatively similar results to the experimental observations. An in-depth analysis of the stresses and efforts induced in the structure is required to the global understanding of the phenomenon.

After improvement, the FLAC 2D -PFC 2D numerical model will be used for parametric studies in order to determine the influence of each parameters of the problem: geometry of the cavity and position with respect to the building, mechanical characteristics of the soil mass and nature of the structure.

Figure 1 .

 1 Figure 1. Laboratory small-scale model.

Figure 2 .

 2 Figure 2. Schematic view of the coupled model.

Figure 3 .

 3 Figure 3. Dimensions of the considered building.

Figure 4 .

 4 Figure 4. Basis for the FLAC-PFC coupling scheme.

Figure 6 .

 6 Figure 6. Stress distribution in the soil mass.

Figure 7 .

 7 Figure 7. Final state after failure for the greenfield test.

Figure 8 .

 8 Figure 8. Subsidence troughs for the FLAC-PFC model, the physical test and the Peck approach.

Figure 9 .

 9 Figure 9. Partial failure during the small-scale physical test in greenfield condition.

Figure 10 .

 10 Figure 10. Final state for the model with the building.

Figure 11 .

 11 Figure 11. Subsidence trough for the computation with the soil-structure interaction.

Figure 12 .

 12 Figure12. Horizontal displacement profiles (compared with the semi-empirical approach in greenfield condition).

Figure 13 .

 13 Figure 13. Vertical forces acting at the level of the roof of the cavity.

Table 1 .

 1 Soil properties of the documented case study.

		Granular soil	Cohesive soil
	E (MPa)	50-100	50-100
	ν	0.30	0.30
	ρ (kg/m 3 )	2200	2200
	φ (°)	~26	~26
	c (kPa)	0	~100

Table 2 .

 2 Characteristics of the building.

	Beam length	3.2 m
	Foundation width	1.65 m
	Story height	2.7 m
	Crawl space	1.2 m
	Element section (m²/m)	0.051 m²
	Element inertia (m 4 /m)	60.4 10 -4 m 4
	Number of spans	3
	3 THE COUPLED NUMERICAL MODEL
	The use of a coupled numerical approach based on
	two different numerical schemes (in the present case
	DEM and FDM) presents two main advantages:
	On one hand, it is possible to refine the description
	of the behaviour of a soil mass in certain locations

Table 3 .

 3 PFC parameters.

	Parameters	Granular material	Cohesive material
	k n (MN/m)	16.0	16.0
	k s (MN/m)	8.0	8.0
	Fric	0.50	0.45
	Density	7.85	7.85
	c_n & c_s (N)	0	1000

Table 4 .

 4 Geometric characteristics for the troughs in greenfield condition.

	Characteristic	Physical test	Semi-empirical approach	FLAC-PFC model
	S max	176 cm	108 cm	120 cm
	I	~3.5 m	~5 m	~4 m
	% of V cavity	60%	66%	58%
	Maximum slope	39%	13%	24%

Table 4

 4

summarizes the main parameters of the settlement troughs resulting from the experimental, semi-empirical and coupled numerical approaches. It appears that:

Table 5 .

 5 Quantitative results for the models with the building.

	Characteristic	Physical test with SSI	FLAC-PFC in greenfield	FLAC-PFC with SSI
	S max	127 cm	120 cm	151 cm
	i	~4.5 m	~4 m	~4 m
	% of V cavity	64%	58%	54%
	Maximum slope	35%	24%	34%
	Maximum slope on the building	~18%	~15.3%	~11%
	Situation (span)

ACKNOWLEDGEMENTS

The authors would like to thank the French Ministry of Environment and Sustainable Development for partial funding of INERIS and its research project DRS02.