Paul-Ayme Toulemonde
email: paul-ayme.toulemonde@ensam.eu

Julie Diani

Pierre Gilormini

Geneviève Lacroix

Nancy Desgardin

Paul-Aymø Toulemonde

Genevive Lacroix

P. -A Toulemonde

P. -A Toulemonde

G Lacroix

Roles of the Interphase Stiffness and Percolation on the Behavior of Solid Propellants

Keywords: Propellants, Matrix/particle interface, Interphase, Mechanical behavior, Finite element analysis [a]

Introduction

Composite solid propellants are elastomers highly filled with explosive particles( up to 90 wt-%) [START_REF] Davenas | Technologie des Propergols Solides[END_REF].T he primary function of this material is to burn and deliver aphenomenal thrust for av ery limited period. However,t oe nsurep redictable burning kinetics and properi ntegration into industrial applications, specific stressa nd strain at failure are targeted. In this respect, the use of matrix/filler bonding agents has drawn significant attention. Mixed to the matrix, the bondinga gent migrates to the filler surrounding and reacts in presenceo ff iller or matrix, the latterr eaction strengthening the filler/matrix bonds. Variants of this technique have beenp atented [START_REF] Allen | Composite Solid Propellant with Additive to Improve the Mechanical Properties Thereof,U SP atent 3745074[END_REF][START_REF] Consaga | Bonding Agent for Composite Propellants[END_REF][START_REF] Kim | Filler Reinforcement of Polyurethane Binder Using aN eutral Polymeric Bonding Agent,U SP atent 4915755[END_REF] for two of the main chemical systems of propellants:h ydroxyl-terminated polybutadiene (HTPB) filled with ammonium perchlorate (AP) and glycidyl azidep olymer (GAP) or polyethylene glycol (PEG) filled with organic particles. Lookingc losely at the experimental sections supporting these patents claims, one notes that adding some bonding agents in propellants enhances the stress at break significantly for HTPB/AP systems [START_REF] Allen | Composite Solid Propellant with Additive to Improve the Mechanical Properties Thereof,U SP atent 3745074[END_REF][START_REF] Consaga | Bonding Agent for Composite Propellants[END_REF][START_REF] Oberth | T ear Phenomena around Solid Inclusions in Castable Elastomers[END_REF] and for systems with organic fillers [START_REF] Kim | The Mechanism of Filler Reinforcement from Addition of Neutral Polymeric Bonding Agents to Energetic Polar Propellants, Propellants Explos[END_REF][START_REF] Landsem | Neutral Polymeric Bonding Agents (NPBA) and Their Use in Smokeless Composite Rocket Propellants Based on HMX-GAP-BuNENA[END_REF].A sr egards the strain at break, the presence of ab onding agent can either reduce or improvei t, changes ranging from À25 %t o + 150 %f or HTPB/AP propellants and from À58 %t o+ 25 % for systems with organic fillers are reported by the same authors. As ar esult, it appears that adding af iller/matrix bonding agent in ap ropellant can have three distinct beneficial effectso nt he failure properties of propellants:( i) improve the strain at break while reducing the failure stress, (ii)i mprove the stressw ithoutr educing the strain at break, and (iii)i mprove both properties at the same time.

Varying matrix/filler interface properties has demonstrated that the two first cases can be explained by changes of interface properties [START_REF] To Ulemonde | On the Account of aC ohesive Interface for Modeling the Behavior Until Break of Highly Filled Elastomers[END_REF].S uch strengthening of the matrix/ filler interface is conventionally targeted by propellants manufacturers. However,u ntil now,t he modification of the interface properties only does not seem sufficient to explain the increase of both failure stressa nd failure strain at the same time.T hat is why another phenomenon has been proposed [START_REF] Kim | The Mechanism of Filler Reinforcement from Addition of Neutral Polymeric Bonding Agents to Energetic Polar Propellants, Propellants Explos[END_REF] to understand the effect of bonding agents: the appearance of am atrix stiffness gradient around the particles. An increase of the initial Young modulus is observed for systemsw here bonding agents enhance both failure properties [START_REF] Kim | The Mechanism of Filler Reinforcement from Addition of Neutral Polymeric Bonding Agents to Energetic Polar Propellants, Propellants Explos[END_REF].T his increase could stem from al ocal enhancement of the matrixs tiffness due to an interphase created by the bondinga gent.

The presence of an interphase at the filler/matrix interface has been accounted for in ar ange of composites. AFM nano-indentationh as proved to be av aluable technique to characterize both the morphology and the mechanical properties of this interphase [START_REF] Gao | C haracterisation of Interphase Nanoscale Property Variations in Glass Fibre Reinforced Polypropylene and Epoxy Resin Composites[END_REF][START_REF] Lee | Evaluation of Interphase Properties in aC ellulose Fiber-Reinforced Polypropylene Composite by Nanoindentation and Finite Element Analysis[END_REF] through the use of con-Abstract:A tomic force microscopy has provided accesst o local modulif or propellants prepared with bondinga gents, which create as tiffness gradient in the matrix producing as tiffer interphases urrounding the fillers. The reinforcing impact of the bondinga gent appears up to some distance and interphase percolation is observed. In order to better understand the impact of bonding agents on the stress and strain at break of propellants, finite element simula-tact mechanics [START_REF] Derjaguin | To porov,E ffecto fC ontact Deformations on the Adhesion of Particles[END_REF].I th as already been used to reveal the presenceo fm atrix/filler interphasesi nn anofiller [START_REF] Pakzad | G radient of Nanomechanical Properties in the Interphase of Cellulose Nanocrystal Composites[END_REF] and microfiller [START_REF] Wang | AFM Characterization of the Interfacial Properties of Carbon Fiber Reinforced Polymer Composites Subjected to Hygrothermal Treatments[END_REF] composites. This technique is also successful for soft materials [START_REF] Young | The Use of the PeakForce Quantitative Nanomechanical Mapping AFM-Based Method for High-Resolution Young'sM odulus Measurement of Polymers[END_REF].M icro-mechanicalm odels based on homogeneization theories [START_REF] Fisher | Viscoelastic Interphases in PolymerÀ Matrix Composites:T heoretical Models and Finite-Element Analysis[END_REF] and FEA analysis [START_REF] Lee | Evaluation of Interphase Properties in aC ellulose Fiber-Reinforced Polypropylene Composite by Nanoindentation and Finite Element Analysis[END_REF][START_REF] Fisher | Viscoelastic Interphases in PolymerÀ Matrix Composites:T heoretical Models and Finite-Element Analysis[END_REF][START_REF] Wang | Finite Element Analysis of the Effecto fa nI nterphase on To ughening of aP article Reinforced Polymer Composite[END_REF][START_REF] Spring | Computational Homogenization of the Debonding of Particle Reinforced Composites:T he Role of Interphases in Interfaces[END_REF] have been proposed to evaluate the influence of the characterized interphase on composites macroscalem echanical properties. However,t hese contributions focuso nc omposites with af iller volume fraction of maximum 30 %, whereas propellants typically encompass over 70 %f illers volume fraction. Considering that the amounta nd thus the effect of an interphase are directly related to the fillers specific surface, af ull new study of propellants interphase influence on the mechanical behavior is required.

In the presented contribution,o riginal experimental evidence of the existence of the matrix/filler interphasei s shown and key characteristics of this interphase are identified. Next, 2D finite element simulations of am odel material represented by ap eriodicc ell of randomly dispersed fillers surrounded by an interphase and embeddedi n ar ubber matrix are presented. Finally,aqualitative study of the effectso ft he interphase parameters on the mechanical responsea nd failure of thec ompositei sc onducted. It provides an explanation for the possible effects of bonding agents on solid propellants.

Experimental Section

In this work, the material of interest is aB utalane TM solid propellant such as produced by Herakles. It consists of ac ompound of 68 wt %o fammonium perchlorate, 20 wt % of aluminum, and 12 wt %o fam odified PBHT-based matrix that were mechanically mixed and crosslinked. In order to avoid surface roughness that would hinder AFM measurements, smooth surfaces were ultramicrotomed at À70 8C with ag lass/diamond knife. The AFM measurement were carried out by BiophyResearch company with aB ruker Multipode 8N anoscopeV TM machine using Peak-force QNM TM for peak-force tappingm ode with scanasyst-Air TM probes with stiffness1 2Nm À1 . Figure 1a nd Figure 2p resentt he local map of the recorded Young modulus on Butalane TM samples. Three main phases appear on these images:( i) the matrix in dark grey, (ii)t he filler particlesi nw hite,a nd (iii)a ni nterphase surroundingt he particlesi nl ight grey.I nF igure 1, ap article with ar adius seemingly over 30 mma nd particlesm uch smaller are observed. At this scale, it appears that the interphase is locateda round the particles and spreado ver the microstructure. It also appearst hat the interphase thickness varies from one particle to another. In some cases,t he interphase thicknessi sa sl arge as the surrounded particle radius and in otherc ases it is difficult to acknowledge the presenceo fsuch an interphase.

Looking closely at ac ouple of small particleso nF igure 2b, it is notedt hat the interphase encircles allt he parti- cles to create as hell. This figure also emphasizest hat contact points exist betweent hese shells. Consequently,d ue to the high specific surface of fillers enhanced by the presence of small particles into the material, the interphase may percolate through the microstructure.

Figure 2c presentst he evolutiono ft he Young modulus through matrix/filleri nterphases in three different locations illustrated on Figure 2a andb. The local values of the phases stiffness are thusm easured and it appearst hat:( i) the matrix displays aY oung modulus of 5M Pa, (ii)t he stiffness of the particlesi st oo high to be measured with the probe, and (iii)t he interphasei sa pproximately five times stiffer than the matrix.

Numerical Simulations

Experimentale vidences of filler/matrix debonding have been obtainedonmodel [START_REF] Oberth | T ear Phenomena around Solid Inclusions in Castable Elastomers[END_REF] and industrial highly filled elastomers [START_REF] Bencher | Microstructural Damage and Fracture Processes in aC omposite Solid Rocket Propellant[END_REF][START_REF] Ta O | 12th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials[END_REF].T his damaging process playsakey role in the mechanical response of these materials in unixial tension [START_REF] Vratsanos | APredictive Model for the Mechanical Behavior of Particulate Composites. Part II:C omparison of Model Predictions to Literature Data[END_REF].M odeling efforts were conducted recently in order to understand and predict the behavioro ft hese composites. In ordert oa ccount for the filler/matrix debonding, ac ohesive zone model was introduced to represent the filler/matrix damageable interface. Micromechanical modeling was performed [START_REF] Ta N | The Cohesive Law for the Particle/Matrix Interfaces in High Explosives[END_REF][START_REF] Inglis | Cohesive Modeling of Dewetting in Particulate Composites:M icromechanics vs. Multiscale Finite Element Analysis[END_REF] to account for small strain behaviors with large amounts of fillers or for hyperelastic behaviors with moderate amounts of fillers [START_REF] Brassart | An Extended Mori-Tanaka Homogenization Scheme for Finite Strain Modeling of Debonding in Particle-Reinforced Elastomers[END_REF]. Some authors also carried out two-dimensionala nd threedimensional finite element analysis. The numerical feasibility of these calculations was assessed in the literature [START_REF] Segurado | AN ew Three-Dimensional Interface Finite Element to Simulate Fracture in Composites[END_REF][START_REF] Matous | Finite Element Formulation for Modeling Particle Debonding in Reinforced Elastomers Subjected to Finite Deformations[END_REF][START_REF] Matous | Multiscale Modeling of Solid Propellants:F rom Particle Packing to Failure[END_REF].I nsight was gained on the effect of filler size on the mechanical behavior of compositesd escribedb yaperiodic lattice of particles [START_REF] Zhong | Analysis of Interfacial Failure in Particle-Filled Elastomers[END_REF] or by randomly dispersed particles [START_REF] To Ulemonde | On the Account of aC ohesive Interface for Modeling the Behavior Until Break of Highly Filled Elastomers[END_REF].T he effect of the cohesive zone parameters on the mechanical response was studied [START_REF] Moraleda | Effecto fI nterface Fracture on Tensile Deformation of Fiber-Reinforced Elastomers[END_REF] and comparisonsw ith multiscale modeling were proposed [START_REF] Inglis | Cohesive Modeling of Dewetting in Particulate Composites:M icromechanics vs. Multiscale Finite Element Analysis[END_REF][START_REF] Ngo | On the Constitutive Relation of Materials with Microstructure Using aP otential-Based Cohesive Model for Interface Interaction[END_REF].T he presence of an interphase around the particles was also accounted for in the case of elastomers filled up to a2 6% volume fraction of fillers [START_REF] Spring | Computational Homogenization of the Debonding of Particle Reinforced Composites:T he Role of Interphases in Interfaces[END_REF].

In this work, since our interest focuses on the behavior up to failure of propellants, microstructures containing ah igh volume fraction of fillers are submitted to large strains. In order to detect damage localization, randomly dispersed fillers arec onsidered. Ac ohesive zone model is also introduced to modelt he damageable filler/matrix interface. In ordert oa ccount for the matrix stiffness gradient around particles,l ayerso fi nterphase that may percolate or not are added. To reducet he complexityo ft he calculations, two-dimensionals imulationsa re consideredh ere. They will provideq ualitative comparisons withe xperiments andw ill allow testing morep arameters due to the reduced computationalc ost. First, we presentt he microstructures, next the material and interface models,a nd finally the implementationinthe Abaqus/Standard [START_REF]Abaqus/Standard,D assault Systmes Simulia Corporation[END_REF]finite elementcode.

Microstructure

It has beend emonstrated [START_REF] To Ulemonde | On the Account of aC ohesive Interface for Modeling the Behavior Until Break of Highly Filled Elastomers[END_REF][START_REF] Zhong | Analysis of Interfacial Failure in Particle-Filled Elastomers[END_REF][START_REF] Moraleda | Effecto fI nterface Fracture on Tensile Deformation of Fiber-Reinforced Elastomers[END_REF] that the presence of small particles mainly strengthenthe matrix without noticeably influencing the composite failure properties in the case of ap ropellant with al arged istribution of particles size. As outlined in the Experimental Section, it also appears that in the presenceo fa ninterphase, the small particles promote the percolation of the interphase through the microstructure thanks to their high specific surface. For these reasons, the propellant microstructure is represented by 2D periodic cells containing distributions of 49 round particlesw ith as ingle particle size representing only the large particles and ag iven particle surface fraction of 50 %. In order to build the cell, the procedure presented in reference [START_REF]To rquato, Random Heterogeneous Materials[END_REF] is applied. Al ayer of interphase of relative thickness e (evaluated as af raction of the particle radius)i s added around each particle. Figure 3s hows that, depending on the interphase relative thickness e,o verlapping of the particle interphase may conduct to percolation of the interphase (Figure 3a) or not (Figure 3b).

Due to expected numerical behaviora nd failure scattering, four randomm icrostructures are created and testedf or each set of parameters considered.

Material and InterfaceModel

The matrix is considered as quasi-incompressible and hyperelastic and defined byi ts strain energyd ensity W.I n order to reduce the complexityo ft he numerical model ac ompressible neo-Hookean law is chosen (W = E m / 6(I 1 À3) + K m /2(DV/V 0 À1) 2 , I 1 being the first strain invariant). The matrix behaviori sd efined by its small strain Young modulus E m and its bulk modulus K m .I th as beend emonstrated that such modely ields results that are consistent with propellants mechanical behaviorsi nt erm of stressstrain relationa nd failure properties [START_REF] To Ulemonde | On the Account of aC ohesive Interface for Modeling the Behavior Until Break of Highly Filled Elastomers[END_REF].

Despite the lack of directe vidence it can be assumed safely thatt he interphasei sa lso aq uasi-incompressible and hyperelastic material with ag radiento fs tiffness throughi ts thickness,w hich may be averaged to model its behavior by ac ompressiblen eo-Hookean law with aY oung modulus E i (respectively ab ulk modulus K i )l argert han E m (respectively K m ). The ratio H of interphaseY oung modulus over matrix Young modulus is therefore equal to

H = E i /E m .
The particles are regarded as rigid.

The microstructures contain two kinds of interfaces: am atrix/interphase interface and an interphase/filleri nterface. Considering the chemicals imilarity of the interphase/ matrix pair,t his interface is regarded as perfectly bonded and thus undamageable. As explaineda bove, debonding around filler particles is ak ey feature to understand the mechanical response of propellants up to failure. Therefore, ac ohesive zone modeli si ntroduced at the interphase/filler interface to account for this debonding. This model represents the interface through an elastic-damageable traction-separation law.P ark and Paulino [START_REF] Leon | AU nified Library of Nonlinear Solution Schemes[END_REF] haver eviewed multiple variantso ft he cohesive zone models that account for ar ange of phenomena linked to decohesion (damageb ehavior,m ode-mixing, in 3D especially). Among the models reviewed, ab ilinear traction-separation law deriving from ap otential energyi ndependent of mode-mixing and ensuring the same fracture energy for any loading path has been proposed [START_REF] Tvergaard | The Influence of Plasticity on Mixed Mode Interface To ughness[END_REF].I ts simplest variant is illustrated in Figure 4a nd it is described by four parameters: K (initial "pseudo-rigidity"), G (adhesion energy), d i (critical displacement for damage initiation), and d f (criticald isplacement for interface failure). Only three of these parameters are independent since they are related by G = Kd i d f /2.F urthermore, to model the fact that no debonding is allowed before the appearance of the interface damage, K is chosen as high as computation allows. Thus the chosenc ohesive zone model is defined by two parameters: d f and G.

Implementation

The simulations are run with Abaqus/Standard [30] using 4node hybrid plane strain elements with reduced integration. Periodic displacementb oundary conditions werea pplied to the cell. So as to ensure ar atio of 3b etween the critical length d f of the cohesive zone model and the element size [START_REF] Turon | An Engineering Solution for Mesh Size Effects in the Simulation of Delamina-tion Using Cohesive Zone Models[END_REF],t he structuresw ere meshed with an average of 300 000 elements. It was verified on aperiodic lattice of particles with the same microstructurala nd material parameters that for the chosen mesh size or lowerm esh sizes, the mechanical behavior is independent of the element size.

The particles radiusi s0 .1 mm, whichi si nt he rangeo f commons olid propellants fillers radii for large particles [START_REF] Matous | Finite Element Formulation for Modeling Particle Debonding in Reinforced Elastomers Subjected to Finite Deformations[END_REF][START_REF] Matous | Multiscale Modeling of Solid Propellants:F rom Particle Packing to Failure[END_REF][START_REF] Ta N | The Uniaxial Te nsion of Particulate Composite Materials with Nonlinear Interface Debonding[END_REF].T he filler surface fraction is 50 %, which suitably represents the volumefraction of large particles in standard solid propellants [START_REF] Azoug | MicromØcanismes et Comportement Macroscopique d'un Élastomre Fortement ChargØ[END_REF].T he neo-Hookean stiffness of the propellants matrix is E m = E m 0 = 5MPa as was evaluated in AFM measurements on Figure 2a nd remains fixed, whereas the interphase behavior is givena sE i = HE m with H = 2o r5 or 10. Thesev alues of H provide ar ealistic range of values according to the AFM measurements. Valueso fK m = 4000 MPa and K i = HK m were chosen to obtain aq uasi-incompressible behavior.T he parameters of the cohesive zone model are taken from the literature [START_REF] Ta N | The Uniaxial Te nsion of Particulate Composite Materials with Nonlinear Interface Debonding[END_REF][START_REF] Yan-Qing | AM icromechanical Model for Predicting Combined Damage of Particles and Interface Debonding in PBX Explosives[END_REF] to represent am atrix/filler interface of energetic materials: K = 1000 MPa, d f = 0.1 mm and G = 0.083 MPa mm. Relative thickness e values were chosen in ordert oe xperience possible percolation of the interphase through the microstructure, as suggested by AFM observations. Values e = 0.01 and 0.035 do not produce percolation, whereas e = 0.1 and 0.12 do.

Results and Discussion

Failure Criterion

Rivlin and Thomas [START_REF] Rivlin | Rupture of Rubber.I .C haracteristic Energy for Te aring[END_REF] introduced ac ritical elastic energy density based failure criterion for elastomers. This criterion is am ere applicationo ff racture mechanics and is consequently widely used. In the presented case, the underlying principle that failure initiates in material elements with high elastice nergy density is extended. Indeed, starting from av irgin microstructure (Figure 5a), early damage of the interphase/filler interface initiates homogeneously throughout the microstructure (Figure 5b).A ts ome point, debonding localizes orthogonally to the loading direction (Figure 5c), and interphase-matrix fibrils form highlighting very high levels of elastic energy density.T hereforet he strain energy based failure criterion may be equivalently defined by the appearance of the fibrillar microstructure due to debonding localization. From ap ractical point of view,ast his localized debonding occurs, the two remaining parts of the microstructure move as rigid bodies. Experimental evidence attestso fs uch al ocalized failure mechanism [START_REF] Liu | Monitoring Microstructural Evolution and Crack Formation in aS olid Propellant under Incremental Strain Condition using Digital Radiography X-ray Techniques[END_REF].

The elastic energy density W normalized by the smallstrain Young modulus E m is ad imensionless measureo ft he elastic energy density and allows comparisons between simulations with different materialp arameters. Figure 6i llustratest he case, where no debonding localization occurs and the proposedf ailure criterion does not apply,c ompared to Figure 5c, where localization occurs. At 36 %m acroscopic strain, the no-localization microstructure does not display peaks of normalized elastic energy (Figure 6) in contrast with the case of debonding localization (Figure 5c).

Figure 7p resents the results of four identical simulations except for the particlesr andom layout. Very good reproducibility is achieved on the behavior, while expected scattering is observed on failure. Therefore, averageb ehaviorsa re presented in whatf ollows with mean values and standard deviations of the strain at break. As regardst he comparison to experimental data on propellants [START_REF] Landsem | Neutral Polymeric Bonding Agents (NPBA) and Their Use in Smokeless Composite Rocket Propellants Based on HMX-GAP-BuNENA[END_REF][START_REF] Ozupek | C onstitutive Modelling of High-Elongation Solid Propellants[END_REF],i ta ppears that the shape of the stress-strain curve is well reproduced on Figure 7: first al inear portion is obtained, then the structure undergoes softening and ap lateau is observed. Also, the range of strain at whichs oftening begins and the failure strain are consistent. The order of magnitude of the simulated stressi sc onsistent with propellants behavior at low temperature (typically À40 8C) and overestimates propellants stress-strain response at room temperature.

Effect of the Interphase Thickness

Figure 8s hows the impact of the interphase relativet hickness e on the mechanical behavior of the composite until failure with H = 5( when the interphase is five times stiffer than the matrix). As reference, the behavior of model materials with no interphase is also represented. First,a ts mall strain, before any interface debonding has occurred, the stiffness of the structure increases with the relativet hick- ness e,t he interphase being stiffer than the matrix. As for fracture,t wo casesc an be distinguished. When the interphase is thin, the composite shows similarb ehavior until break as the reference presenting no interphase and aY oung modulus E m = E m 0 .W hen the interphase is thick, no debonding localization occurs. In this case, the composites sustain larger strain and stress at break and display asimilar evolution to the one of the reference material without interphase and aY oung modulus E m = H.E m 0 .F rom am icrostructural point of view,i ti st on otice that, the interphase percolates for the second group only.T hus,apath to transmit the load through the microstructure exists and relieves the softer matrix. Consequently the structure is stiffer and behaves verys imilarly to ac omposite with as tiffm atrix without interphase.

Hence, for H = 5, the presenceo fastiff interphase has as ignificant impact when the interphase percolates and none whenitd oes not percolate.

According to these results, the presence of ap ercolating interphase enhances both stress and strain at break of the composite,w hich is consistent with experimental results on HTPB/APa nd organic filler systems [START_REF] Allen | Composite Solid Propellant with Additive to Improve the Mechanical Properties Thereof,U SP atent 3745074[END_REF][START_REF] Kim | The Mechanism of Filler Reinforcement from Addition of Neutral Polymeric Bonding Agents to Energetic Polar Propellants, Propellants Explos[END_REF] reported in the Introduction. Introducing an interphase in the simulated microstructures also leads to an increase in the initial Young modulus as observed experimentally for organic filler systems [START_REF] Kim | The Mechanism of Filler Reinforcement from Addition of Neutral Polymeric Bonding Agents to Energetic Polar Propellants, Propellants Explos[END_REF].H owever,s tress (respectively strain) at break of the numerical results for non-percolating microstructure does not show am arked increase( respectively decrease) as could be expectedf rom experimental results. This difference could stem from the fact that on the one hand, in the calculations, the presence of ab onding agent was solely accounted for throught he introduction of an interphase but no modification of the filler/matrix properties was implemented. Whereas, on the other hand, bonding agent are designed to reinforce the matrix/filler bond [START_REF] Hori | On the Adhesion Between Hydroxyl-Terminated Polybutadiene Fuel-Binder and Ammonium Perchlorate. Performance of Bonding Agents[END_REF].Y et, it has been demonstrated [START_REF] To Ulemonde | On the Account of aC ohesive Interface for Modeling the Behavior Until Break of Highly Filled Elastomers[END_REF][START_REF] Moraleda | Effecto fI nterface Fracture on Tensile Deformation of Fiber-Reinforced Elastomers[END_REF] that ac hange of the critical strength or of the debonding energy of the cohesive zone, which both representamodification of the interface,c an produce sucha nincrease in the stressa tbreak.

Effect of the Interphase Stiffness

Figure 9i llustrates the influence of the H ratio on the beneficial effect of interphase percolation on the failure of the composite. Twoi nterphase relative thicknesses with (e = 0.12) and without (e = 0.035)p ercolation were tested, each with two values of the ratio H,2a nd 10, compared to the reference case H = 5. For at hin interphase (Figure 9a), the stiffer the interphase, the stiffer the composite and the larger its stress at failure. As regardst he strain at failure, at low values of ratio H,i ti ss imilart ot he reference case E m = E m0 :t he failure remains unaffected by the presence of the interphase. At ah igher valueo fr atio H the strain at break increasess ignificantly.

For ap ercolated interphase (Figure 9b), the stiffer the interphase, the stiffer the composite at small strain. Concerning the failure properties, two cases appear:( i) for stiff interphases (H = 5a nd 10) a5 0% increase of the stress and strain at break is achieved, whereas (ii)f or as oft interphase (H = 2) no noticeable influence on the failure behaviori s observed. Notet hat for this relative thickness e and as ufficiently high valueofthe H ratio, the mechanisms are similar to the one observed for the reference case without interphase and high matrix stiffness.

According to these results, the presence of ap ercolating interphase is not always sufficient to achieve an improvement of both stress and strain at break, as ufficiently stiff interphase in comparison to the matrix is also necessary. Besides,anon-percolated interphase can also yield improvement of the failure strain but not of the failure stress. Very local measurements such as AFM peak force are required to check these conditions and they cannot be easily predicted when formulating the material. For these reasons the presence of an interphasec an have ar ange of effects on the stress and strain at break -i mproving both or not affectingt hem -t hat cannot be interpreted without local measurements. This could explain the discrepant experimental results foundi nt he literature and the difficultiese xperienced to consistently interpret them.

Conclusions

AFM observations with Young modulus measurements at the microscale were conducted. The presence of an interphase between matrix and fillers in industrial solid propellants was experimentally observed and its morphology and Young modulus were evaluated. An interesting feature of this interphase is to possibly percolate through the matrix. So as to understand the effect of this interphase on the mechanical behavior, ap ropellant-like highly filled elastomer wasm odeled by 2D periodic cells containing randomly dispersed rigid particles coated by an elastomer interphase and embedded in an elastomer matrix. Debonding of the interphase/filler interface was permittedt hrough the use of ac ohesive zone model. Af ailure criterion was proposed as the appearanceofafibrillar microstructure and two constitutive parameters of the interphase were varied:t he relative thickness of the interphase e and the ratio H of interphase stiffness over matrix stiffness. Changing e revealed the significant impact of the percolation of the interphase by reducing the localization of filler/matrix debonding and therefore increasing the stressa nd strain at failure. Nonetheless, as variations of H have shown, conditions on the interphases tiffness are preponderant. At low interphase stiffness, there is no room for improvement of failure properties. At medium interphase stiffness, the interphase percolation is an ecessary condition to obtain an increase of both strain and stress at failure. At high interphase stiffness, the failure strain can be improved without percolation but it is required to enhance the failure stress.

According to these mechanisms, adding bondinga gents to propellants formulations can have af avorable impact on both stress and strain at failure in two cases: for as tiff percolatingi nterphase,a nd in am ore limited respect, for av ery stiff interphase. In the other cases, no significant impact is observed if it is assumed that the interface properties are unchanged. These conditions on the interphase are very local properties that are difficult to predict precisely ap riori. This can explain the discrepant results obtained

Figure 1 .

 1 Figure 1. AFM observations of ap ortion of al arge particle surrounded by smaller particles in Butalane TM .

Figure 2 .

 2 Figure 2. AFM observations of acouple of small particles:(a) topological image, (b) Young modulus map, and (c) evolution of the phases stiffness along the matrix/filler interphase in three different locations.

Figure 3 .

 3 Figure 3. Modelled microstructures:( a) with interphase percolation (e = 0.12), (b) without interphase percolation (e = 0.035).

Figure 4 .

 4 Figure 4. Illustration of the chosen cohesive zone model for apositive normal traction applied to the interface.

Figure 5 .

 5 Figure 5. Evolution and ratio of the elastic energy density W normalized by Young modulus E m for am icrostructure without interphase submitted to uniaxial tension. (a) Initial microstructure, (b) early damage (20 %m acroscopic strain), and (c) further damage evolution with the appearance of matrix fibrils (36 %m acroscopic strain) (E m = E m 0 ).

Figure 6 .

 6 Figure 6. Microstructure and normalized elastic energy density W at 36 %m acroscopic strain for am icrostructure without interphase when debonding localization does not appear due to ah igh matrix stiffness (E m = 5 E m 0 ).

Figure 7 .

 7 Figure 7. Uniaxial tension responses of four microstructures of identical constitutive parameters and differing by the particles layout only.

Figure 8 .

 8 Figure 8. Effecto fthei nterphase thickness on the uniaxial behavior of composites with interphase stiffness characterized by H = 5. The case e = 0( respectively e = 1)r epresents am icrostructure without interphase and E m = E m 0 (respectively E m = HE m 0).

Figure 9 .

 9 Figure 9. Comparison of the uniaxial behaviors of microstructures for different rigidity ratios H with fixed interphase relative thickness:( a) e = 0.035, (b) e = 0.12. In the cases E m = E m 0 (respectively E m = 5 E m 0 ), there is no interphase but am atrix with stiffness E m

(respectively 5 E m 0 )only.

Acknowledgments

The authors wish to thank DGA for its financial support.

by authors when evaluating the effect of ag iven bonding agent on the mechanical response.


H Mastori

P Piluso

J.-F Haquet

R Denoyel

M Antoni

Limestone-Siliceous and Siliceous concretes thermal damaging at high temperature

Keywords: Concrete, Porosity, Thermal stress, Molten metal, Corium

Limestone-siliceous and siliceous concretes are used in reactor pits of French nuclear power plants. In case of severe nuclear reactor accident, failure of the reactor vessel would lead to interaction between molten corium (hot melt of nuclear fuel) and concrete. This paper focuses on the thermal degradation of both limestone-siliceous and siliceous concretes till 1000°C. Thermo-Gravimetric Analysis (TGA) and Mercury Intrusion Porosimetry (MIP) are used to measure mass loss and porosity modification. As concretes are heterogeneous materials, sampling and representativeness have been addressed. TGA experiments show larger mass loss for limestone-siliceous concretes due to the decarbonation of calcium carbonate gravels when T>800°C. MIP experiments demonstrate a 100% increase of porosity for limestone-siliceous (resp. siliceous) concretes when T> 500°C (resp. T> 800°C). The consequences of these results are discussed in the frame of experimental tests on prototypical corium systems aimed at describing the key-phenomena involved in molten corium concrete interaction.

Introduction

Concretes are the most widely used building materials. They have excellent performances at room temperature but exhibit critical behavior when subjected to high temperatures [START_REF] Aitcin | Cements of yesterday and today: Concrete of tomorrow[END_REF], [START_REF] Piasta | Heat deformations of cement paste phases and the microstructure of cement paste[END_REF]. Concretes consist of mortar (cement paste and sand) and gravels and are therefore highly heterogeneous systems. Their modeling at the microstructure level is still for many aspects empirical and making predictions of their properties when subjected to extreme thermal stresses raise challenging open questions. This problem is particularly acute when focusing on nuclear accidents ranked at a level higher than 5 on the INES scale [START_REF] Piasta | Heat deformations of cement paste phases and the microstructure of cement paste[END_REF]. In such situations, a partial (or total) meltdown of the nuclear fuel is reached and a complex mixture, called corium, is formed consisting mainly of structural materials of the reactor. It may come in contact with the concrete of the reactor pit and potentially disseminate in the environment [START_REF] Jacquemain | Les accidents de fusion du coeur des réacteurs nucléaire de puissance[END_REF]. A detailed knowledge of the driving phenomena involved in the Molten Corium-Concrete Interaction (MCCI) is fundamental for the reliability of models and simulations [START_REF] Journeau | Two-dimensional interaction of oxidic corium with concrete: The VULCANO-VB series[END_REF], [START_REF] Journeau | Contributions of the VULCANO experimental programme to the Understanding of MCCI phenomena[END_REF]. Most of reactor pits of the pressurized water reactors of the French nuclear power plants consist of either Limestone-Siliceous (L) or Siliceous (S) concretes. Both L and S concretes were used to simulate the MCCI conditions in the VULCANO facility of the PLINIUS CEA-Cadarache platform that is dedicated to the study of severe nuclear accidents. The tests were carried out at high temperatures (up to 2400°C) using prototypical corium (by means of depleted uranium dioxide) and a semi-cylindrical concrete test section. Post-test analysis revealed unexpected ablation profiles of concretes and metal/oxide phase separation phenomena [START_REF] Journeau | Contributions of the VULCANO experimental programme to the Understanding of MCCI phenomena[END_REF]. For S concretes, anisotropic ablation profiles were evidenced with enhanced radial ablation, while L concretes exhibited isotropic ablation. Such differences in concrete damaging is key for nuclear security. One of the goals of this work is to provide new insights into the understanding of this phenomenon by focusing only on the thermal degradation of concretes. No molten nuclear material will therefore come into play hereafter. A comparative description of the changes in the physical and chemical properties of L and S concretes, after exposure to different temperatures, is investigated. A characterization, for temperatures up to 1000°C, of the porosity, mass loss as well as the specific surface area is presented.

The description of the microstructure and properties of the components of concretes and their interaction is essential to understand their damaging kinetics with increasing temperature. Each component plays a well-defined role: hydraulic binder for cement paste, resistance to compression and volume enhancement for gravels. These latter occupy 60 to 75% of the volume and are therefore key for the tensile modulus and the overall stability of concretes. At room temperature, these properties are determined by physical rather than chemical characteristics [START_REF] Mehta | Concrete: Microstructure, properties and materials[END_REF]. But when investigating heated concretes, physico-chemical transformations have to be accounted for as they strongly modify their microstructure [START_REF] Hager | Behaviour of cement concrete at high temperature[END_REF]. Successive degradation mechanisms are activated. At moderate temperatures (T<100°C) evaporation of water, dehydration processes of hydrates constituting the cement matrix and decomposition of ettringite take place [START_REF] Alonso | Dehydration and rehydration processes of cement paste exposed to high temperature environments[END_REF], [START_REF] Castellote | Composition and microstructural changes of cement pastes upon heating, as studied by neutron diffraction[END_REF]. The first signs of decomposition of the CSH gel are observed at T≈180°C and persist up to 400°C [START_REF] Fordham | A simple thermogravimetric study of hydrated cement[END_REF]. Between 400°C and 600°C, decomposition of portlandite (Ca(OH)2) prevails [START_REF] Hager | Behaviour of cement concrete at high temperature[END_REF], [START_REF] Alarcon-Ruiz | The use of thermal analysis in assessing the effect of temperature on a cement paste[END_REF], [START_REF] Pei | Effects of severe heating and rehydration on poro-mechanical properties of a mortar[END_REF] while for 600°C<T<1000°C, calcite decomposes into lime (CaO) with a significant release of carbon dioxide [START_REF] Alarcon-Ruiz | The use of thermal analysis in assessing the effect of temperature on a cement paste[END_REF], [START_REF] Akca | Effects of re-curing on microstructure of concrete after high temperature exposure[END_REF]. Finally, for T>1000°C, the remaining concrete components melt down [START_REF] Hager | Behaviour of cement concrete at high temperature[END_REF]. All these mechanisms can be modified by additives. For example, the improvement of concrete high temperature resistance and limitation of its susceptibility to damage can be achieved thanks to the use of the addition of siliceous fly ash [START_REF] Golewski | An assessment of microcracks in the Interfacial Transition Zone of durable concrete composites with fly ash additives[END_REF], [START_REF] Golewski | The influence of microcrack width on the mechanical parameters in concrete with the addition of fly ash: Consideration of technological and economical benefits[END_REF], [START_REF] Golewski | Estimation of the optimum content of fly ash in concrete composite based on the analysis of fracture toughness tests using various measuring systems[END_REF].

The study of the morphological transformations of CSH gel during heating emphasizes the fundamental role of the water content of concretes before heating. The bonds between the gel layers are controlled by Van der Waals forces which are weak when compared to chemical ones. CSH gel has a surface area of 250 to 300 m²/g that turns 1000 times larger than that of cement (0,3 m²/g). Thus, when temperature increases, evacuation of water modifies its mechanical properties. Dehydration is the dominant mechanism occurring in the cement paste when heated up and results in a reduction of the CSH gel volume. But, as water vapor fills the porous network and tends to escape from concrete, the pressure increases [START_REF] Laing | Thermal energy storage for direct steam generation[END_REF]. This phenomenon, called internal autoclaving, activates hydrothermal reactions that modify the microstructure of hydrates [START_REF] Hager | Behaviour of cement concrete at high temperature[END_REF], [START_REF] Piasta | Changes in the structure of hardened cement paste due to high temperature[END_REF]. The decrease of the volume of anhydrous compounds and the expansion of the cement paste due to autoclaving generate an increase of porosity [START_REF] Piasta | Heat deformations of cement paste phases and the microstructure of cement paste[END_REF], [START_REF] Hager | Behaviour of cement concrete at high temperature[END_REF]. Free space between CSH layers can indeed vary from 5 up to 25Å. But this is too low to have a significant role on mechanical resistance. Nevertheless, water residing in these small voids can be maintained by weak hydrogen bonds (C-S-H gel) [START_REF] Baroghel-Bouny | Caractérisation des pâtes de ciment et des bétons. Méthodes, analyse, interprétations[END_REF] and its removal can contribute to shrinkage, drying and creeping of concrete [START_REF] Hager | Behaviour of cement concrete at high temperature[END_REF]. Macropores (i.e. pores of diameter greater than 50 nm) are essential for mechanical strength and permeability, while mesopores (i.e. pores with diameters between 2 nm and 50 nm) play an important role in the drying and shrinking processes. A small amount of air is usually trapped in the cement paste during the mixing phase and forms millimetric air bubbles. Trapped air bubbles and the space occupied by entrained air in the cement paste are much larger than the capillary voids and are likely to adversely affect the resistance [START_REF] Salem | Effect of air entrainment on compressive strength, density and ingredients of concrete[END_REF].

After this introduction, material and methods are presented in section 2. Concretes being heterogeneous at different scales, sampling technique is discussed. Thermo-Gravimetric Analysis and Mercury Intrusion Porosimetry results of L and S concretes are exposed in section 3. Mass losses after heating for five days are further analyzed. Conclusions and perspectives for future work are finally presented.

Materials and Methods

Materials

Table 1 presents the composition of L and S concretes under study and Table 2 the cements (respectively CEM I for L and CEM II for S) supplied by CALCIA© cement plant (Beaucaire -France). The sand and gravels content is given in Table 3. The analyzed samples were cast on June 6 th 2006 and November 23 rd 2007 respectively and extracted from parallelepiped concrete blocks of approximately 7cm×20cm×30cm and about 7 kilograms each. As they're more than 12 years old, they're assumed to be representative of nuclear pits. Error! Reference source not found. shows two representative photographs of sections of L and S concretes. Siliceous gravels show up in black. Other gravels are calcium carbonate. This figure illustrates the granulometry of the samples that turn similar and the larger fraction of calcium carbonate in L concretes. In the mix design the following materials were used for L concrete : 15,3%w of Portland cement CEM I 52.5N, gravel with 4-16 mm, gravel with 6-14 mm, sand with 0-3 mm, sand with 0-4 mm and sand with 3-6 mm and 6,7%w of water. For S concrete the following materials were used: 15,3%w Portland cement CEM II/A-S 52,5N, sand with 0-2 mm, sand with 0-6 mm and gravel with 5-8 mm, gravel with 8-11, gravel 11-16 mm and 6,7%w of water. Prior to mixing, mass of each compound was measured with a balance (reliability ± 1 In the first stage of mixing plan, the sands and cement were added and mixed with onethird of the mixing water in a bucket in order to get a homogeneous paste. Manually mixing is performed using a shovel. Then, the gravels were added gradually and the remained water was poured to the mixture. The mixing is stopped when a homogeneous mix is obtained. The mix is finally poured in prismatic molds. From each type of concrete, 3 prismatic specimens were cast (50x5x5 cm 3 ). Prior to the experimental campaign, to reduce the risk of spalling, the samples were cured at laboratory environment for 28 days. Depending on the analyzes to be carried out, the samples were prepared in different ways. For Thermo-Gravimetric Analysis, samples consist of small fragments of about 100 mg. This low weight exclude large gravels. Sampling is therefore key here. For Mercury Intrusion Porosimetry, samples consist of either Crushed Samples (CS) or samples in the form of Monoliths (MS). CS consists of coarse and dispersed chunks obtained by hammering and MS are cylinders of about 3 cm high and 1.5 cm in diameter (see Figure 2). The weight of MS varies between 25 and 35 g and they are obtained by coring concrete blocks at slow speed without using lubrication liquid. A jet of cold compressed air has been used to prevent chemical alteration due to temperature rise.

Component

Methods

Thermo-Gravimetric Analysis (TGA)

TGA is an adapted technique for studying the mass variation of samples submitted to temperature stress. Samples are placed in a platinum crucible and mass variations are measured with a balance monitored in real time as function of temperature. In current TGA experiments, atmosphere must be inert to prevent samples from reacting with environment. In this paper argon is used. TGA experiments were performed using a Q-500 thermo-balance from TA Instrument© which makes possible to reach a maximum temperature Tmax=850°C with a sensitivity of 0.1 μg. Temperature ranges from room temperature up to 850°C at a rate of 5°C/minute with an accuracy of ±1°C. In order to be as representative as possible, 15 samples of L and S concretes were analyzed. This is sufficient to provide reliable trends. Some TGA measurements were carried out for aggregates and cement paste separately to distinguish the contribution of the different components of the samples.

Furnace Heating and direct weighting of samples (FH)

In FH experiments samples were exposed for five days at a fixed temperature. This relatively long period aims to ensure a deep calcination and thus to avoid any inhomogeneities due to non-uniform temperature gradients within the samples. Two Thermolyne © Furnaces 38000 and 68000 and alumina crucibles were used for this purpose. Four experimental campaigns, identified by the temperature at which the concrete samples were exposed, were carried out. In the first, they have not undergone any heat treatment. For the other three, they were calcined at 500°C, 820°C and 1000°C and analyzed 2 to 3 hours after their extraction from the furnace. This time range was long enough for their temperature to return to the ambient one and sufficiently short to avoid rehydration process to occur. Samples were weighed before and immediately after extraction of the furnaces with an accuracy of ±1 mg. For heat treatments at high temperatures (T>500°C) their mechanical strength decreases considerably. This fragility results from cracks that are mainly due to the pressure of water vapor and CO2 [START_REF] Georgali | Microstructure of fire-damaged concrete. A case study[END_REF] and requires careful handling to avoid samples disaggregation.

Mercury Intrusion Porosimetry (MIP)

The samples used for FH were further analyzed by MIP. MIP is based on the concept of forced penetration of a non-wetting, non-reactive liquid into a porous material. It gives information on the size distribution of accessible pores in the range of diameters from 3 nm to 300 μm . The Washburn equation describes the relationship between pore diameter, applied pressure and contact angle. The porosimeter used in this work is a Quantachrome POREMASTER-60©. It includes a low-pressure and a high-pressure measuring station. High pressure measurements were carried out from ambient temperature up to maximal value Pmax=4140 bar. A 5 cm 3 macrocell has been used to allow experiments with large samples (see Figure 2). Mercury intrusion is preceded by degassing of the samples at a pressure smaller than 10 -5 bar. Samples weight about 30 g (see section materials) but the weight of the analyzed samples that have undergone calcination is smaller (about fifteen grams) suggesting larger porosity. It is therefore necessary to pay attention to the volume of the stem of the macrocell. For large porosities, if volume is too small, maximum pressure cannot be reached making smallest pores (few tens of nanometers) not accessible. CS have typically large interparticle porosity. This is why smaller cells and smaller masses (5 g) were used for such samples. Finally, all MIP plots consist in averages for at least 5 samples for each temperature.

Three characteristic volumes are measured when operating MIP. The apparent volume Vapp that corresponds to the volume of the sample regardless to its porosity, the absolute volume Vabs = Vapp -Vp where Vp is the porous volume that is defined when maximal pressure Pmax is reached. Vp writes :

V p = M Hg ρ Hg
Eq. 1

with MHg the mass of mercury intruded in the sample at Pmax and ρHg the density of mercury. Vp is therefore the volume of mercury intruded in the sample at Pmax. It is referred to as the porous volume and is expressed in cm 3 /g. With this definition, Vabs turns out to be the volume occupied by the solid phase (skeleton) of the concrete. Both Vabs and Vapp are further used to define the absolute and apparent density :

ρ abs = M sample V abs , ρ app = M sample V app Eq. 2
where Msample is the sample's weight. The apparent density, ρapp is accounting for sample porosity whereas ρabs, also called skeletal density of the solid matrix, describes the dense phase (ρapp < ρabs).

For a given temperature, the outputs of TGA, FH and MIP presented hereafter result from averages over 15 samples for TGA and a minimum of 3 samples for MIP and FH. As experiments are independent, error bars in the plots are obtained using a student test with a confidence interval set to 80%.

Results and discussion

Thermo-Gravimetric Analysis

The properties of the concretes are first studied considering gravels and mortar separately. The interest of this approach is to highlight the differences in thermal stability between mortar and gravels. Samples are crushed and gravels separated from mortar by sieving. Figure 3 plots the sample averaged thermo-gravimetry (TG) and DTG (Differential Thermo-Gravimetry) curves for S concretes. For mortar samples, mass decreases progressively in the full temperature range. For T<200°C, a mass loss of about 4% is observed due to water release. Free water evaporates first, followed by adsorbed water. Water chemically combined with hydrates is evacuated last. When looking mortar DTG curve in detail, the peak at T≈70°C is the signature of the evaporation of free water. For higher temperatures and up to 200°C mass loss associated to calcium sulphoaluminate hydrates (i.e. ettringite) decomposition comes in addition to water release [START_REF] Fernandes | Microstructure of concrete subjected to elevated temperatures: physico-chemical changes and analysis techniques[END_REF], [START_REF] Innocentini | Drying stages during the heating of High-Alumina, Ultra-Low-Cement Refractory Castables[END_REF]. This explains most probably the presence of the secondary peak at T≈140°C. For T>200°C, temperature rise causes complete drying. At T≈450°C, the pronounced peak in the DTG curve is associated to CSH gel decomposition that yields an additional mass loss of about 2%. For 450°C<T<550°C portlandite undergoes decomposition with again a mass loss of 2% [START_REF] Alonso | Dehydration and rehydration processes of cement paste exposed to high temperature environments[END_REF], [START_REF] Castellote | Composition and microstructural changes of cement pastes upon heating, as studied by neutron diffraction[END_REF], [START_REF] Schneider | Effect of temperature on steel and concrete for PCRV[END_REF]. Portlandite content falls rapidly and, as it decomposes into quicklime and water, leads to an additional water release. The dehydration of CSH gel is already activated at T≈180°C but this mechanism becomes prevailing only above 750°C, where decomposition into calcium silicates β-C2S, β-CS and water occurs. All these phenomena are accompanied by volume changes induced by thermal expansion. During heating, cement paste indeed undergoes an expansion of 0.2% when temperature is increased from ambient to 150°C [START_REF] Cruz | Thermal expansion of Portland Cement Paste, Mortar and Concrete at high temperatures[END_REF]. This expansion results from the pressure increase generated by the evacuation of free water. It is followed by a shrinkage when T>500°C due to the reduction of the interlayer space between CSH sheets [START_REF] Bazant | Concrete at High Temperatures: Material Properties and Mathematical Models[END_REF].

When considering gravels only, Figure 3 shows that they remain almost inert when T<600°C. DTG curve shows a weak peak at T=400°C, due to CSH decomposition. It actually results from the thin residual mortar layer covering the gravels. For T>600°C, calcium carbonate gravels are submitted to intense decarbonation that is at the origin of a sharp mass loss. Calcium carbonate is decomposed into quicklime and carbon dioxide. Unlike mortar, gravels only expand under the effect temperature. An additional source of volume expansion comes from the quartz phase transition from quartz-α phase to quartz-β that occurs for T≈570°C. It generates a volume dilation ranging between 1 and 1,4% [START_REF] Khoury | Strain of concrete during first heating to 600°C under load[END_REF]. It is important to note here that quicklime may rehydrate during sample cooling and form Portlandite after recombination with water molecules of the ambient air. This can create an expansion of more than 40% [START_REF] Delhomme | Influence de la substitution du ciment Portland par du laitier de haut fourneau sur des éprouvettes de mortier portées à hautes températures[END_REF]. This expansion comes in addition to the gaseous stresses and therefore favors outward gas flows. Figure 4 shows the average TG and DTG curves for both L and S concretes. When T<600°C, curves are similar and display a mass loss smaller than 8%. Only mortar contributes since gravels are not modified for T<600°C (see Figure 3). Physicochemical changes occur at the same temperatures and therefore do not depend on the type of concrete. When T>600°C, decarbonation occurs and yields a mass loss larger for L concrete due to larger calcium carbonate content. From a quantitative point of view, three temperature domains can be roughly identified here:

• In the first domain denoted D1, temperature ranges from 30°C to 120°C. In this domain, the release of water prevails and mass loss is smaller than 2% for both concretes [START_REF] De Toledo Pereira | Comparative analysis between properties and microstructures of geopolymeric concrete and Portland concrete[END_REF]. • The second domain, D2, shows up for 400°C<T<600°C. Mass loss for S (resp. L) reaches 4% (resp. 5%) at T=500°C. Dehydration of portlandite comes into play and CSH gel decomposes [START_REF] Caetano | Effect of the high temperatures on the microstructure and compressive strength of high strength fiber concretes[END_REF]. According to the literature, the dehydration of CSH gel occurs over a wide range of temperature [START_REF] Huang | Mechanical properties and microstructure of ultra-weight cement composites with fly ash cenospheres after exposure to high temperatures[END_REF]. Some authors have denoted that it occurs for temperatures less than 400°C where mass loss combines the release of capillary water (for T≈180°C), interlayer water (for T≈350°C) and finally adsorbed water (for T≈400°C) [START_REF] Fordham | A simple thermogravimetric study of hydrated cement[END_REF]. • The third domain, D3, corresponds to T>700°C. Decarbonation takes place. Mass loss becomes important and reaches at T=900°C, 29% (resp. 12%) for L (resp. S) concrete.

The definition of D1 to D3 relies on the maxima reached in the -DTG curves. Other definitions could be used here such as, the temperatures domains bounded by successive inflexion points of the TG curves. But, as concretes are heterogeneous materials, this would not affect the main outcomes of this work as the mechanisms taking place in two adjacent domains actually coexist as suggested by the continuous trend of the TG curves of Figure 4.

Furnace Heating and direct weighting of samples

Besides imposing small mass samples, one additional limitation of TGA experiments comes from the fact that they do not allow fast heating of the samples. Fast heating is important in the frame of this work since it occurs in the VULCANO-MCCI experiments. One way to get insights into such a scenario is to introduce directly the concrete samples into a preheated furnace. This is what is done next. Figure 5 shows the typical mass loss, noted W(S) and W(L) of S and L concretes, obtained from FH experiments at five different temperatures. The analyzed samples are either MS or CS. Figure 5 clearly indicates common trends.

• In D1, W(L) and W(S) remains smaller than 0.5% (about 1% for TG). FH and TG measurements therefore almost coincide. • In D2, FH and TG measurements still show moderate mass losses when T≤500°C. They result essentially from the physico-chemical changes in the mortar. These latter being the same for S and L concretes, no significant differences should again be observed here. At T=500°C, W(S)=0.9±0,02% while W(L)=1.3%±0,3. They are therefore much smaller than the values obtained from TG (4% and 5% respectively). For T=570°C, a jump is expected in the data due to the phase transition from quartz-α to quartz-β. It produces an expansion of quartz gravels from 1.0 to 1.4%. This volume expansion is accompanied by their fracturing and by the occurrence of cracks at the Interfacial Transition Zone (ITZ) [START_REF] Xu | Impact of high temperature on PFA concrete[END_REF]. Gases have then the possibility migrate thought a network of cracks and therefore yield the drastic increase of mass loss observed in D2. • In D3, T>700°C, two important differences show up. First it appears that W(L) is more than twice larger than W(S) (W(L)/W(S)~2.5). Second when comparing Figure 4 and Figure 5, for example at T=820°C, W(S)=4±0,01% (resp. W(L)=10%±0.5%) for FH while W(S)=12% (resp. W(L)=28%) for TG. Hence, it turns out that, for a same temperature, mass loss is much larger for FH than for TGA. FH and TGA measurements are observed for the same concretes, the same temperatures, but not in the same conditions regarding to atmosphere control and heating rate. As no inert gas flow is used in FH, samples are submitted to the water vapor pressure of the target temperature. This contributes both to the presence of capillary water and to the inhibition of dehydration. Moreover, unlike samples analyzed by TGA that undergo smooth temperature ramps, in FH, samples are subjected to a thermal shock. Such a process can induce water retention phenomena. The moisture in the vicinity of the sample surface is indeed in an unsaturated state while the moisture deeper in the sample is in a supersaturated state. The variation in temperature with depth causes therefore larger water vapor pressure that migrates inside the sample due to pressure gradients. But this also creates moisture clog [START_REF] Harmathy | Effect of moisture on the fire endurance of building materials, Moisture in relation to fire tests[END_REF], [START_REF] Jansson | Fire spalling of concrete -A historical overview[END_REF]. At a high heating rate, samples are indeed far from thermodynamic equilibrium: bounded water can rapidly turn in capillary water. This generates the formation of a saturation barrier that prevents water from migrating through the porous network of the concrete. Similarly to water, calcium carbonate decomposition has been shown to affect heat transfer kinetics [START_REF] Caldwell | Effect of Thermal Transport Mechanisms on the Thermal Decomposition of CaCO3[END_REF]. It is a highly endothermic reaction and the resulting cooling plays an important role in the overall mass flows [START_REF] Gallagher | The Effects of Sample Size and Heating Rate on the Kinetics of the Thermal Decomposition of CaCO3[END_REF]. Partial pressure of carbon dioxide actually modifies the decomposition temperature due to Le Chatelier law that is shifted to higher temperatures [START_REF] Caldwell | Effect of Thermal Transport Mechanisms on the Thermal Decomposition of CaCO3[END_REF], [START_REF] Galan | Calcium carbonate decomposition[END_REF]. As the decomposition reaction of calcite is reversible and is dependent on the partial pressure of carbon dioxide, a retardation in the reaction rate can occur [START_REF] Willburn | The effect of procedural variables on TG, DTG and DTA curves of calcium carbonate[END_REF]. Finally, the sample size may also affect the decomposition since the larger the sample size, the longer the diffusion paths and hence the greater is the build-up of partial pressure of carbon dioxide [START_REF] Gallagher | The Effects of Sample Size and Heating Rate on the Kinetics of the Thermal Decomposition of CaCO3[END_REF].

Overall, while it is FH that would have been expected to affect the most aggressively the concretes due to thermal shocks, it appears here that it is actually TGA that creates the largest mass losses and therefore the strongest damages. This is surprising and suggests that concrete damaging in MCCI is most likely, in its initial stage, driven by the physics of fracturing due to increasing inner pressure and not by chemical alteration.

Mercury Intrusion Porosimetry

First point to verify here is to ensure that MS and CS give comparable results. Figure 6 displays the pore size distribution, denoted in the following by fL(d,T) for L concretes (fS(d,T) for S concretes), as a function of pore diameter, d, for L concretes exposed to temperatures T=20°C (a) and T=820°C (b). An absolute maximum in fL(d,T) close to d=170 nm appears at 20°C. For 820°C, maxima are slightly shifted but remain within the range 300 -500 nm. Amplitudes have moreover similar for d < 2 µm. It is therefore reasonable to consider here that, for a given temperature, the morphology of the samples (MS or CS) does not strongly affect MIP results in this size range. Similar outcomes are obtained for S concretes. Averaging the data regardless to sample morphology make therefore sense here. This similarity of MIP curves gives also hints about porous structure. In CS accessible porosity is indeed expected to be larger because of the opening of closed pores in the preparation procedure and larger contact surface with mercury. For example when T=20°C, Figure 6 Figure 7 shows sample averaged cumulative intrusion curves for S and L concretes for T<500°C (a) and T > 800°C (b). For clarity, curves for S concretes are plotted with dashed lines while the ones for L correspond to full lines. In Figure 7(a) two regimes show up. The first one can be identified for pore diameter d > 3 μm for which volume of intruded mercury remains small. It corresponds to the filling of the largest pores carried out at low pressure (0 to 1 bar). In the second regime (d < 3 μm), this volume monotonously increases and pores sizes down to few nanometers are explored. S and L concrete curves do not display clear saturation at high pressure indicating that the porous volume is not yet fully probed in the operating conditions and that pores with d<3 nm are probably present. For such experiments, pressure spans from 1 to 4000 bars and several milliliters of mercury per experiment are needed.

Figure 7(a) illustrates that at T=20°C, S and L concretes have similar porosity since intrusion curves show the same trend. For T=500°C however, clear discrepancies show up. The porous volume of S appears now almost twice smaller than the one of L (Vp(S) ≈0.9 cm 3 /g and Vp(L)≈0.5 cm 3 /g). This temperature falls in temperature domain D2 (see Figure 4) where CSH decomposes and dehydration of portlandite comes into play [START_REF] Caetano | Effect of the high temperatures on the microstructure and compressive strength of high strength fiber concretes[END_REF]. Figure 4 and Figure 5 indicate only limited mass differences in D2 (about 1%). The porosity change cannot therefore be attributed to differentiation in mass loss mechanisms. Structural changes in the material are instead to be considered here like porosity opening and increase of pores interconnection (for example by the modification of bottleneck shaped pores). For T=500°C, the thermal expansion of the siliceous gravels, generated by the quartz phase change, contributes to the increase of their apparent volume, which can lead to the crushing of the porous network. This phenomenon may explain the fact that the pore volume of S concretes for this temperature is smaller than that for T=20°C when d<1µm.

For T > 800°C, temperatures are in D3. Intrusion curves are plotted in Figure 7(b). They saturate and therefore indicate that larger and open pores prevail. For T=820°C (resp. T=1000°C), L has porous volume Vp(L)≈0.35 cm 3 /g while for S, Vp(S)≈0.15 cm 3 /g (resp. Vp(L)≈0.8 cm 3 /g and Vp(S)≈0.55 cm 3 /g). For T=1000°C, millimetric sized pores are present. Mechanical and chemical alteration of the concrete is then sufficient for a relevant amount of mercury to already be intruded at low pressure. For such large temperatures, all the mechanisms discussed in the TGA section, like free and capillary water evaporation, portlandite and CSH dehydration and calcium carbonate decomposition come into play. This latter explains the larger porous volume for L concretes due to larger content in calcium carbonate.

Mercury intrusion curves of Figure 7 could be supplemented by the extrusion curves obtained after pressure decrease back to the atmospheric one. When performing such an intrusion/extrusion cycle, hysteresis appears. A small volume of mercury remains indeed trapped in the samples. This is the signature of constrictions in the topology of the porous network. Good reproducibility however is evidenced when proceeding with more intrusion/extrusion cycles indicating that the microstructure of the concretes resist to MIP measurements.

Figure 8 shows the pore diameter distribution obtained from the derivative of the intrusion curves displayed in Figure 7. This figure is interesting since it provides information about the evolution in the typical entrance size of the pores when changing temperature (it accounts for constriction modification). It will be mentioned as pore size in the following. Similarly to Figure 7, dashed lines correspond to S concretes while full lines show the trends for L concretes. Curves are complex but some specific properties can be discussed here in particular in the mesopore range. When considering the range d>8µm, Figure 8(a) demonstrates for example that large scales pores are formed when T=500°C. This is expected as pores open with increasing temperature and becomes strongly pronounced at even larger temperatures with, for example, at T=1000°C and d=10 µm, values of f(d) larger than 0.1 cm 3 /g.μm. Clear peaks are also present for both L and S concretes when d≈0.012 µm. This last value is denoted as d1 in the following. At T=20°C, the fraction of mesopores for L concretes is fL(d1,T)=9.10 -3 cm 3 /g.μm and for S concretes fS(d1,T)≈4.10 -3 cm 3 /g.μm (see Figure 8(b)). As curves are averages over several samples (see section 2), one can consider here mesopores in L concretes have a diameter typically twice larger than in S concretes. A similar trend also prevails for T=500°C as fL(d1,T)=1.9 10 -2 cm 3 /g.μm and fS(d1,T)≈1.1 10 -2 cm 3 /g.μm. For T=820°C and 1000°C, the maximum at d1 vanishes and a new one shows up at d2≈4 nm (see Figure 8(c)) with fL(d2,T)≈fS(d2,T)≈3.10 -3 cm 3 /g.μm for T=820°C and fL(d2,T)≈1.6 10 -2 cm 3 /g.μm (resp. fS(d2,T)≈9 10 -3 cm 3 /g.μm for T=1000°C.

The above observations demonstrate how L and S concretes are damaged when exposed to increasing temperatures. Mesoporosity turn twice larger in L concretes and clear signature of microporosity is evidenced although not accessible with MIP. They do moreover evidence that in D2 and D3 different levels of mesoporosity comes into play. The fact that the typical mesopore size remains close to a constant value when increasing T from 20°C to 500°C is surprising since opening of the pores is expected. This should lead to a shift of the typical pore size to larger values. But it is actually their fraction that increases indicating not only a good robustness towards thermal stress but also the presence of micropores that are destroyed and turned into mesopores of typical size d1. This behavior is prevailing for temperatures in D2 and is the consequence of the water release generated by CSH gel dehydration [START_REF] Bodnarova | Effect of high temperature on cement composite materials in concrete structures[END_REF] and of the opening of fractures in the vicinity of the ITZ due to differentiated expansion of cement paste and gravels [START_REF] Kong | Effect of elevated temperature on geopolymer paste, mortar and concrete[END_REF]. Another interesting observation here is the occurrence of new peaks when T is in D3. They are also created by micropore breakage but now produce smaller mesopores (d=4 nm instead of 12 nm). This is particularly clear for T=1000°C (Figure 8(c)). [START_REF] Hernandez | Porosity estimation of concrete by ultrasonic NDE[END_REF]. At 1000°C 𝜌 𝑎𝑏𝑠 (𝑆)~𝜌 𝑎𝑏𝑠 (𝐿)~2.5 ± 0.2 𝑔/𝑐𝑚 3 . Density therefore does not depend significantly on temperature. For 900°C < T < 1000°C the possibility of a liquid phase has been demonstrated and shown to generate vitreous phases [START_REF] Schneider | The behaviour of concrete under attack of liquid steel[END_REF]. This phenomenon is expected to create a densification of the material by sintering and can therefore to increase density. The regular trend of ρabs shown in Figure 9(a) indicates that such phenomenon, if it occurs, is not measurable in the present experiments. Figure 9(b) displays the variation of the apparent density ρapp as a function of T. It behaves in a non-monotonous way. At T=20°C, ρapp(S) ≈ ρapp(L) = 2.30.17 g.cm -3 . As temperature increases, the physicochemical changes taking place in the concretes are expected to produce a decrease in ρapp [START_REF] Bazant | Concrete at High Temperatures: Material Properties and Mathematical Models[END_REF], [START_REF] Pazdera | Non-Linear Characteristics of Temperature Degraded Concrete at High Temperature[END_REF]. Figure 9(b) shows instead an increase, especially for L concretes, for which ρapp (L)=3.00.1 g.cm -3 at T=500°C. It is attributed to the compaction of the CSH sheets following their dehydration for T in D2 [START_REF] Schneider | Effect of temperature on steel and concrete for PCRV[END_REF]. For 500°C<T<650°C, the thermal expansion of siliceous aggregates, generated by the quartz phase change, contributes to the increase of apparent volume. This may be the reason why ρapp(S) is smaller that ρapp(L) in D2. When T is in D3, the expansion of siliceous gravels and degassing that accompanies the decomposition of calcite in limestone gravels explain the sharp fall of ρapp [START_REF] Bazant | Concrete at High Temperatures: Material Properties and Mathematical Models[END_REF]. Thermal exchanges in concretes are determined by their thermal conductivity that depend upon their apparent density. Figure 9(a) showed that absolute densities are similar and Figure 7 that Vp(L)>Vp(S) when T>500°C. Gaz content is therefore larger in L concretes. Thermal conductivity of degraded L concretes is hence expected to be smaller than that of degraded S concretes. But in porous media, when investigating transfer mechanisms, specific surface area is also a fundamental input since it corresponds to the available surface for mass exchanges to occur. It monitors the kinetics of the exchanges and, in addition to porous volume, determines the properties of the flows inside the material. Large values of specific area contribute to enhance exchanges. The above MIP experiments have the great interest to give access to this parameter [START_REF] Rootare | Surface areas from mercury porosimeter measurements[END_REF].

Figure 10(a) displays the behavior of the specific area as a function of T. Similarly to porous volumes Vp(L) and Vp(S), important differences between L and S concretes are again evidenced. The specific area A(L) of L concretes turns larger than the one, A(S), of S concretes in the entire temperature range. This is naturally the consequence of larger porous volumes resulting from the higher mass fraction of limestone in L concrete. The measurement points in Figure 10(a) were interpolated by fitting parabolas and suggest that A(S) (resp. A(L)) reaches a maximum at T~540°C (resp. T~690°C) with Amax(S)≈6.3 m 2 /g and Amax(L)≈10.0 m 2 /g. The temperature at which these maxima occur is uncertain due to the large error bars in the measurements at 700°C. The ratio A(L)/A(S) plotted in Figure 10(b) turns larger than 1.5 and increases up to 2.3 for T=1000°C. For a same temperature, L concretes offer therefore larger surfaces for exchanges than S ones. This last result, in addition to the fact that Vp(L)>Vp(S) (Figure 7) and ρapp(S) ≈ ρapp(L) (Figure 9(a)) suggest that mass flows and heat exchanges should be more favorable in L than is S concretes.

VULCANO-ICB experiments

The above results can now help to propose some hints for the understanding of coriumconcrete interaction in the VULCANO-MCCI experiments. In these experiments, concrete ablation profile is isotropic for L concretes and anisotropic for S ones. Enhanced radial ablation is also observed for S concretes suggesting locally higher heat flows. A scenario that can be invoked here relies on the ability of L concretes to support more efficient degassing and therefore to generate stronger turbulence in the molten corium. As mixing is more developed, homogeneity of the corium bath is improved. This enhances heat transfers within the corium and, consequently, at the corium/concrete interfaces that finally get damaged the same way and with the same kinetics. Conversely to L concretes, in S concretes hot points may develop and yield locally stronger damages. The plausibility of this scenario is reinforced by FH experiments that demonstrated a weight loss due to degassing more than twice larger for L concretes when T is in D3 (see Figure 5).

The loss of mechanical strength resulting from degassing is also key here. As heat transfer within L concretes is isotropic, concrete disaggregation is also isotropic. This contributes to maintain degassing rate homogenous along the corium/concrete interface as corium cools down to ambient temperature. This most likely cannot occur in S concretes where corium cooling rate may become locally larger when running along the corium/concrete interface and therefore prevent degassing and concrete ablation to proceed with the same kinetics everywhere.

Conclusion

Two concretes, siliceous and limestone-siliceous, used in the construction of the pit of the French nuclear reactors have been characterized by thermo-gravimetric analysis and mercury intrusion porosimetry after exposition to temperatures ranging from room temperature up to 1000°C. Concretes being heterogeneous composite materials, the influence of temperature is first studied for crushed and monolith samples with TGA. Main results are the following:

• Thermo-gravimetric analysis allowed the identification of three temperature domains in which specific degradation mechanisms are activated. • Evaporation of free water has led to define a first domain, dehydration, fracturing and decomposition of concrete hydrates including CSH and portlandite occur in a second domain.

• Finally, decarbonation of the calcium carbonate occur in a third domain. At moderate temperatures, mass losses range between 1 and 3% and turn similar for both siliceous and limestone-siliceous concretes. For large temperatures decarbonation affects mainly limestone-siliceous concretes because of their higher limestone content. Besides TGA, samples were introduced in preheated furnaces and exposed to strong thermal gradients. This procedure creates moisture clog and is shown to generate a drastic reduction of mass loss when compared to thermo-gravimetric analysis. Measurements show that:

• The modifications in the microstructure of the concretes is further characterized by mercury intrusion porosimetry. • Increase of porous volume with temperature is evidenced for macropores for both concretes. At T=1000°C, the porous volume of limestone-siliceous concretes is shown to be more than 40% larger than the one of siliceous concretes. • In the mesopore range an increase of the number of pores is observed at moderate temperature and attributed to the destruction of micropores. Specific areas have been further estimated. At T=1000°C, limestone-siliceous concretes have specific areas that turn more than twice larger when compared to siliceous ones. Finally, a scenario based on larger degassing rates in limestone-siliceous concretes is finally proposed to explain the differences in the ablation profiles evidenced in the VULCANO-MCCI experiments.

Figure 1 :

 1 Figure 1: Photo of a section of L (a) and S (b) concretes. Scale is given bottom left of (a).

Figure 2 :

 2 Figure 2: Left: Crushed sample (CS). Right: Monolith sample (MS). The left image also displays the macro-cell used for MIP measurements.

Figure 3 :

 3 Figure 3: Thermal degradation of S concrete. Orange curves correspond to sample consisting in gravels only, while green curves to mortar. Solid lines (resp. dashed lines) show TG (resp. DTG) curves.

Figure 4 :

 4 Figure 4: Thermal degradation of L and S concretes. Blue (resp. red) curves correspond to L (resp. S) concrete. Solid lines (resp. dashed lines) correspond to the TG (DTG) curves.

Figure 5 :

 5 Figure 5: Average mass loss W as a function of temperature resulting from FH experiments. Red: S concrete. Blue: L concrete

  (a) shows that CS gives larger values of fL(d,T) than MS when d < 20 nm and d > 2 μm. This suggest that closed mesoporosity of MS is partially open in CS.

Figure 6 :

 6 Figure 6: L concrete pore size distribution for CS (dashed line) and MS (full line) after exposition for 5 days to temperature 20°C (a) and 820 °C (b).

Figure 7 :

 7 Figure 7: Sample averaged cumulative intruded mercury volume as function of pore diameter for S (dashed lines) and L (full lines) concretes for various exposition temperatures: In (a) T≤500°C in (b) T≥800°C.

Figure 8 :

 8 Figure 8: (a) Pore size distribution obtained from the intrusion curves displayed of Figure 6(a) (legends and colors are the same). (b) zoom of (a) in the range d < 0.1 μm. (c) pore size distribution in the same range than (b) for T=820°C and T=1000°C.

Figure 9

 9 Figure 9 presents the variation of 𝜌 𝑎𝑏𝑠 (a) and of 𝜌 𝑎𝑝𝑝 (b) (see Eq. 2) of S and L concretes as a function of T. When T=20°C, S and L concrete absolute densities have comparable values with 𝜌 𝑎𝑏𝑠 (𝑆)~𝜌 𝑎𝑏𝑠 (𝐿) = 2.6 ± 0.2𝑔/𝑐𝑚 3[START_REF] Hernandez | Porosity estimation of concrete by ultrasonic NDE[END_REF]. At 1000°C 𝜌 𝑎𝑏𝑠 (𝑆)~𝜌 𝑎𝑏𝑠 (𝐿)~2.5 ± 0.2 𝑔/𝑐𝑚 3 . Density therefore does not depend significantly on temperature. For 900°C < T < 1000°C the possibility of a liquid phase has been demonstrated and shown to generate vitreous phases[START_REF] Schneider | The behaviour of concrete under attack of liquid steel[END_REF]. This phenomenon is expected to create a densification of the material by sintering and can therefore to increase density. The regular trend of ρabs shown in Figure9(a) indicates that such

Figure 9 :

 9 Figure 9: Temperature dependency of 𝜌 𝑎𝑏𝑠 (a) and 𝜌 𝑎𝑝𝑝 (b) for L (blue) and S (red) concretes. Temperature domains, D1, D2 and D3 are represented (see Figure 4).

Figure 10 :

 10 Figure 10: (a) Specific area as a function of temperature for L (blue) and S (red) concretes. Lines results from a quadratic fit. (b) Specific surface area ratio A(L)/A(S). Dashed line is the ratio of the fitting curves displayed in (a).

Table 1 :

 1 Common buildings have indeed a life expectancy of about 50 years and up to 100 years for civil engineering structures. Composition of analyzed concretes

	Component	S concrete (%weight)	L concrete (%weight)
	Ca(OH)2	12.89	13.00
	CaCO3	16.20	55.95
	SiO2	65.89	25.16
	Free H2O	2.87	6.7
	Al2O3	2.15	2.31

Table 2 :

 2 CEM I and CEM II composition

		Component	Sand	Sand	Sand	Gravels	Gravels
	L concrete	(granulometry)	(0-3)	(0-4)	(3-6)	(4-16)	(6-14)
		%weigh	5.55	19.50	5.55	31.20	16.20
		Component	Sand	Sand	Gravels	Gravels	Gravels
	S concrete	(granulometry)	(0-2)	(0-6)	(5-8)	(8-11)	(11-16)
		%weigh	12.20	18.40	16.60	20.40	10.40

Table 3 :

 3 Sand and gravels characteristics

Acknowledgements:

The authors gratefully thank Electricité de France for financial support.