G Rimpault
email: gerald.rimpault@cea.fr

V Huy

I Kodeli
email: ivan.kodeli@ijs.si

Integral Experiment Analyses in support to the OECD/NEA benchmarks on Uncertainty Analysis in Modelling (UAM) for Design, Operation and Safety Analysis of SFRs (SFR-UAM)

Sodium fast reactors can answer three major challenges:

 Using the whole uranium ore ( 238 U and not only 235 U),  Burning radioactive waste (Plutonium or minor actinides) in order to reduce the size of the ultimate storage,  An enhanced safety. Designing reactors with improved safety performance while preserving a sustainable source of energy at an economically competitive cost requires to improve the performance of the modelling tools. It is the purpose of the OECD/NEA sub-group on Uncertainty Analysis in Modelling (UAM) for Design, Operation and Safety Analysis of Sodium-cooled Fast Reactors (SFR-UAM).

 (available from the ICSBEP and in the IRPhE experimental data bases) have been identified as relevant to the SFR-UAM core characteristics, with the use of sensitivities. These experiments have been analysed here with JEFF3.1.1 and provide a base

1.

Validation Exercises The methods that were applied for the analysis of the specified theoretical exercises shall be used for the calculation of experiments. The calculated output quantities can be compared to the experimental values while considering the obtained uncertainties.

The validation experiments were chosen based on a similarity assessment between various experiments from the International Criticality Safety Benchmark Experiment Handbook (ICSBEP) [START_REF] Nea | International Criticality Safety Benchmark Experiment Handbook[END_REF] and in the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhE) [START_REF] Nea | International Handbook of Evaluated Reactor Physics Benchmark Experiments[END_REF] on one hand and the MET1000 and MOX3600 core assemblies, on the other hand [START_REF]Benchmark For Uncertainty Analysis In Modelling (UAM) For Design, Operation and Safety Analysis of SFRs, Core Definitions[END_REF].

List of selected Experiments

The experiments used in this work are listed in Table 1 along with their fuel and structural material characteristics. The spectrum hardness indicator r is also given for mock-up reactors. This value r is the inverse of the difference between the average lethargy of neutrons disappearing through absorption or leakage and the one of neutrons emmited by fission :

1 One can note that this experimental database include international benchmarks from the IRPhE and ICSBEP database, as well as the experimental programmes performed in the CEA MASURCA facilities, not yet integrated in IRPhE.

Fuel
The representability rRE of an integral experiment E to a reactor concept R is a global indicator used to evaluate the similarity of the sensitivity profiles of two experiments. It is calculated (using the sensitivity of a target parameter, such as keff, to nuclear data SE and SR and a nuclear data covariance matrix D) by applying the following formula:

E T E R T R E T R RE DS S DS S DS S r 
Sensitivities have been calculated with the ECCO/ERANOS code system [START_REF] Rimpault | The ERANOS code and data system for fast reactor neutronic analyses[END_REF] using JEFF3.1.1 nuclear data to which the COMAC-V1 matrix is associated for uncertainties [START_REF] Archier | COMAC { Nuclear data covariance matrices library for reactor applications[END_REF]. Critical mass representability values of several Pu-fueled configurations to the SFR oxide core are given in One has to note that representability calculations depend on the set of covariance matrices used. This indicator is thus particularly useful for transposition studies, for instance to foresee how an experiment could help reducing the uncertainty associated to a reactor concept.

Jezebel is a critical assembly made by the Los Alamos Scientific Laboratory in 1951. A total of three sub-assemblies was built: one made up of 95.5% at. of 239Pu (PUMET-FAST-001 according to the ICSBEP benchmark nomenclature), one consisting of 20.1% at.240Pu (PU-MET-FAST-002) and the last consisting of 98.0% at. 233U (U233-MET-FAST-001).This critical assembly has almost a spherical shape and is composed of four major pieces, of similar mass, for safety reasons. The critical masses from the ICSBEP database (FLATTOP 239 Pu, JEZEBEL 239 Pu and 240 Pu) are the only experiments that are likely to greatly affect nuclear data only in the high energies range, above 1-2MeV.

For 238 U inelastic and capture cross section, we benefit from a great number of experiments of Plutonium-fueled critical masses that are highly sensitive to this cross section,. Moreover, the simultaneous use of JEZEBEL and FLATTOP 239 Pu is particularly interesting to get access to 238 U inelastic cross sections. Indeed, JEZEBEL is a bare 239 Pu sphere and FLATTOP 239 Pu is similar to JEZEBEL (both in its geometry and its Plutonium content) except that it is surrounded by a natural Uranium . Also, it seems important to use integral data sensitive to different isotopes (graphite, 56 Fe, 23 Na, 16 O, etc.) present in structural material. Indeed, this allows having access to different neutron flux spectra (and thus sensitivity profiles). For instance, 23 Na elastic scattering resonance at 2.85 keV causes a flux depression. This motivates the use of experiments which do not include 23 Na such as SNEAK7A/7B. Moreover, one has to keep in mind that eventual bias in structural material isotopes evaluations could induce large C/E for some experiments. ZPR-6 Assembly 7 is a fast reactor core with mixed (Pu,U)-oxide fuel and sodium with a thick depleted-uranium reflector. A description of this experiment including the detailed specifications is given in the International Handbook of Evaluated Reactor Physics Benchmark Experiments under the acronym ZPR-LMFR-EXP-001. A variant of this assembly exhibits a central zone with a high Pu240 content.

The MASURCA ZONA2 core is part of an extensive experimental programme called BERENICE (Beta Effective Reactor Experiment for a New International Collaborative Evaluation) whose main objective was the measure of the effective fraction of delayed neutrons (βeff) by various methods. The programme is currently being evaluated in the IRPHE data base. Fuel pins are made of mixed oxide (U , Pu) O2 with a Pu / (U + Pu) content from about 25 to 27% , clad steel . The cross section of a fuel sub-assembly consists of a checkerboard of 16 fuel cells 2x2 pins , for a total 32 strips (U , Pu) O2 and sodium strips 32 (see Figure 15 ) . The mostly used pins are the so-called " PIT " (Pu 18% 240Pu/Pu ) pins and at the core periphery, a small amount of so-called " POA " ( 8% Pu 240Pu/Pu ) pins are being used.

C/E results on critical masses

Critical masses have been calculated with TRIPOLI4 [START_REF] Brun | TRIPOLI-4®, CEA, EDF and AREVA reference Monte Carlo code[END_REF] with the JEFF3.1.1 library. The JEFF3.1.1 library includes Probability Tables for a proper self-shielding of resonances in the Unresolved Resonance Region (URR). The geometry used is an as-built geometry hence without modelling approximations. Such calculations can be considered as benchmark values and incorporate no method approximation nor geometrical modelling errors.

C/E ratios as presented in The nuclear data uncertainties lie in the 1200-1660 pcm range which is far bigger than the experimental uncertainties. There is a possibility of improving nuclear data through an integral assimilation technique and hence the possibility to reduce the final SFR-UAM core characteristics uncertainty.

 eff experimental validation

There are a number of available experiments for assessing the calculation of βeff in the ICSBEP and in the IRPhEP experimental databases among which are JEZEBEL, SNEAK7A and SNEAK 7B. To these experiments, one can add the BERENICE experiments performed in MASURCA [START_REF] Kodeli | Uncertainty Analysis of Kinetic Parameters for Design, Operation and Safety Analysis of SFRs[END_REF]. The importance of a neutron is needed for calculating β , for which, the Iterated Fission Probability method (IFP) [START_REF] Truchet | Computing adjoint weighted kinetics parameters in TRIPOLI-4 by the Iterated Fission Probability method[END_REF] is the most accurate method to obtain it with Monte Carlo, and has been implemented in various codes quite recently. Based on the interpretation calculations of Rossi and eff measurements, a series of calculation versus experiment comparisons is being done with modern tools such as MCNP, TRIPOLI4, SUSD3D, SERPENT and the latest evaluated nuclear data ENDF/B-VII.1, JEFF3.2, JENDL4.0. Uncertainty assessments due to nuclear data (including those for delayed neutron constant values) have been done using the SUSD3D and ERANOS tools. Uncertainties on delayed neutron constant values are only available in the JENDL4.0 library. The calculations of uncertainties were carried out by JSI, CEA and, GRS for a series of experimental benchmarks: SNEAK 7A, SNEAK 7B, JEZEBEL, POPSY, BERENICE ZONA2, and, the SFR 3600MWth. These calculations of uncertainties have been done with various sets of covariance matrices including JENDL4.0 on which one can compare the calculations done at JSI, CEA and at GRS. The use of Monte-Carlo code TRIPOLI4® [START_REF] Brun | TRIPOLI-4®, CEA, EDF and AREVA reference Monte Carlo code[END_REF] and its recent development of the Iterated Fission Probability method [START_REF] Truchet | Computing adjoint weighted kinetics parameters in TRIPOLI-4 by the Iterated Fission Probability method[END_REF] allow us to improve the C/E ratio for calculating βeff. The detailed representation of cores and the use of an energy dependency of the delayed neutron emission to the incident neutron energy are the major contributions to this improvement. Also, the improvement comes from the calculated terms used to derive βeff from raw experimental measurements. The C/E ratios are greatly improved when using the reliable Noise measurement technique with 1.2% ± 3.2% for the ZONA2 core.

The uncertainty quantification process has been done using the deterministic code ERANOS, with the sensitivity analysis and uncertainty propagation leading to a 2.8% uncertainty for the ZONA2 cores whose main contributors are the delayed neutron fission yield and the fission cross section of 238 U.

Since uncertainties for delayed neutron constant values are available only in the JENDL4.0 library, a series of actions (differential measurements, models) are studied at CEA, ILL and Subatech-Nantes in order to provide in the future, new recommended values. The construction of the covariance matrices of the delayed fission yields of the 235 U, 238 U and 239 Pu isotopes, including the correlations among these isotopes, is also underway in the scope of the cooperation between JSI and ENSIIE [START_REF] Tarride | Mathematical Aspects of Nuclear Data Covariance Matrix Preparation -An Example of Delayed Neutron Data[END_REF].

5.

Doppler measurements Doppler coefficient is an important dynamic characteristic of the core. A review of relevant experiments in the IRPhEP database has identified a lack of experiments on Doppler. The SEFOR reactor has been built for the purpose of measuring the Doppler coefficient [START_REF] Noble | Experimental program results in SEFOR Core II[END_REF]. SEFOR documentation is not in the IRPhEP standard but has been used in the past [START_REF] Hazama | Re-Evaluation of SEFOR Doppler Experiments and Analyses with JNC and ERANOS systems[END_REF] and is worth being investigated. Computational uncertainties in Doppler coefficient lie in the 100eV-100keV energy domain as illustrated by Figure 1 and are mainly due to the uncertainty in the flux level at the bottom edge of the fast reactor flux. The SEFOR static tests were performed at power levels up to 20 MW while maintaining the average core coolant temperature constant at 678K. The reactivity effects due to power changes were measured by the reflector positions, adjusted to compensate the reactivity feedback. The Doppler coefficients were then evaluated by subtracting the contributions from the fuel axial expansion. Since SEFOR was particularly designed, using segmented fuel rods and dished fuel pellets, the reactivity change due to the axial expansion is as small as 5% of the total feedback, and its uncertainty has little affect on the Doppler reactivity evaluation.

Hence, the SEFOR static tests are recommended as an experimental validation of the Doppler calculations.

Careful attention should be given to the different sources of experimental uncertainties (fuel thermal conductivity, temperature increase, etc…). The resulting Doppler constants divided by βeff (Tdρ/dT/βeff) for Core I and II are -2.61$ and -2.03$, respectively, according to the new analysis from Hazama & Tommasi [START_REF] Hazama | Re-Evaluation of SEFOR Doppler Experiments and Analyses with JNC and ERANOS systems[END_REF]. The experimental uncertainty is reduced to 7%.

In the standard 2D cell representation, the heterogeneity of the B4C pin absorbers (12 in SEFOR l, 5 in SEFOR 2) must be taken into account. A calculation using the ECCO code is performed in which the B4C rod is surrounded by a corresponding part of the reactor and compared with an equivalent homogeneous calculation.

In Table 1, we present the values calculated using three different approximations, a homogeneous cell model, a 2D heterogeneous model in which the boron pins are represented as an outer annular region and the third case in which a correction is made for the treatment of the boron pins. C/E values are within a ± 7 % range of uncertainties.

Modelling

Conclusions

The design of a SFR core implies the development and validation of scientific calculation tools. Notably, the use of neutronic codes aims at defining the characteristics of reactor cores with well-mastered accuracies. Nuclear data, the input parameters of these codes, constitute the main source of uncertainty in neutronic calculations.

The re-analysis of several experimental programmes in support to the SFR-UAM core benchmarks has been done in this paper. Reducing the bias on critical masses C/E due to deterministic methods and modeling approximations are of major concern. Thus, critical mass calculations were performed using the Monte-Carlo code TRIPOLI-4 on "as-built" geometries.

A great number of critical masses from the ICSBEP database (JEZEBEL 239 Pu, JEZEBEL 240 Puand FLATTOP 239 Pu), the IRPhE database (ZPR 6/7 assemblies, SNEAK 7A and 7B…) and MASURCA experimental programmes (ZONA2 etc.) have also been used. They provide both complementary and redundant information on nuclear data with a great diversity of sensitivity profiles which cover the energy range of interest. Moreover, their experimental uncertainties are much smaller than current nuclear data uncertainties calculated using COMAC-V1, so they have the capability to greatly reduce nuclear data uncertainties when used in an integral data assimilation.

As a perspective, performing an integral data assimilation would be a contribution to the improvement of our knowledge on nuclear data of interest for the SFR-UAM cores. Depending on the more or less urgent need of the core designers, assimilation results can be used as there are for core design or be used as guidelines for new evaluations.

Figure 3 .

 3 Figure 3. Doppler Effect (Nominal Temperature -> Fuel Melting Temperature) of an oxide SFR

Table 1 . Characteristics of the integral experiments critical masses used

 1

	Fertile blanket	Diluant	r
	or reflector

Table 2 .

 2

	Configuration	Representativity rRE
	ZPR-6/7	0.87
	ZPR-6/7 High 240 Pu	0.90
	SNEAK 7A	0.76
	SNEAK 7B	0.84
	MASURCA ZONA2	0.39

Table 2 . Representability of the critical mass of Pu-fueled configurations to the SFR-UAM 3600 MWth oxide core critical mass. Values were calculated using COMAC-V1.

 2

Table 3 . C/E values for critical masses considered using JEFF3.1.1

 3 Table 3 show values larger than one. It means that JEFF3.1.1 calculations are far bigger that measurement, however at less than 2 .

		C/E with TRIPOLI4 and JEFF3.1.1	Exp unc.	Nuclear data unc.	C/E-1²/Total unc ²	C/E-1²/Exp unc ²
	FLATTOP_Pu239_keff	1.00396	0.00300	1.30E-02	9.32E-02	1.74E+00
	JEZEBEL_Pu239_keff	1.00009	0.00250	1.24E-02	5.28E-05	1.30E-03
	JEZEBEL_Pu240_keff	1.00433	0.00200	1.36E-02	1.01E-01	4.69E+00
	SNEAK_7A_keff	1.00445	0.00400	1.30E-02	1.17E-01	1.24E+00
	SNEAK_7B_keff	1.00140	0.00350	1.66E-02	7.10E-03	1.60E-01
	MASURCA_ZONA2_keff	1.00447	0.00090	1.25E-02	1.29E-01	2.47E+01
	ZPR6_7_keff	1.00196	0.00230	0.01514	1.68E-02	7.26E-01
	ZPR6_7_High_Pu240_keff	0.99993	0.00220	1.48E-02	2.22E-05	1.01E-03

Table 4 . Comparison of eff computational results with experiments

 4

	Benchmark	Exp. SUSD3D PARTISN	MCNP5	ERANOS TRIPOLI	MCNP6.1	SERPENT
	experiment			k-ratio	k-ratio		IFP	IFP	IFP
				ENDF7.0/-7.1*	JEFF3.2 ENDF7.1	ENDF7.1	ENDF7.0
							/JEF3.2	/JEFF3.2	/JEFF31
	Jezebel	194 ±10 185	186	186			187±1
								/188±1
	Skidoo	290 ±10 296	297				295±1
								/294±1
	Popsy	276 ±7	277	278	284			277±2
								/287±2
	Flat-top 23 360 ±9 374	375				374±2
								/381±2
	SNEAK-7A 395 ± 20 373	379	369	383	370 ± 3/	363 ± 3/	371±2
							391± 3	391± 8	/385±2
	SNEAK-7B 429 ± 22 419	429	415	426 417 ± 3/	427 ± 8/	417±2
							441± 3	425 ± 8	/433±2
	SNEAK-9C2 426 ± 19				384		383±2
								/398±2
	ZONA2	346 ± 11 344	351		362	335 ± 1/
							350 ± 1
	BFS-61	371 ± 60				383	370 ± 3/	363 ± 3/
							391± 3	391± 8
	FCA-XIX-2 364 ± 9						368±2
								/383±2
	FCA-XIX-3 251 ± 4						250±1
								/256±1
	* ENDF7.1 stands for ENDF/B-VII.1

Table 5 . SEFOR 1 & 2 modelling with ECCO/ERANOS The

 5 C/E comparisons are presented for the two experiments with the corrected experimental values by[START_REF] Hazama | Re-Evaluation of SEFOR Doppler Experiments and Analyses with JNC and ERANOS systems[END_REF] and the calculations using ECCO/ERANOS with a 2D heterogeneous model in which a correction is made for the treatment of the boron pins..

	SEFOR 1	SEFOR 2

Table 6 . SEFOR 1 & 2 C/E with ECCO/ERANOS

 6

Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 10 -13, 2018


H Saur

P Sénéchal

T Boiron

C Aubourg

H Derluyn

P Moonen

First investigation of quartz and calcite shape fabrics in strained shales by means of X-ray tomography

Keywords: High resolution XCT, calcareous shale, cleavage, shape preferred orientation, quartz, calcite

Highlights:

-Fine-grained rock fabric is investigated by X-ray tomography and SEM-EDS.

-Samples cover all stages of cleavage development along a strain gradient.

-Shape preferred orientation of quartz, calcite and pores is studied.

-Deformation imprints differently on the grain shape fabric of quartz and calcite.

-Grain fracturing, rotation and pressure-solution identified as dominant processes.

Introduction

The fabric of fine-grained rocks is commonly studied by means of optical microscopy, electronimaging techniques (Secondary Electron Microscopy and Transmission Electron Microscopy) or Xray diffraction techniques. These techniques have been used to determine the evolution of the phyllosilicate fabric and the main deformation mechanisms of these platy minerals along a strain gradient in the transition from mudstone to slate at Lehigh gap, Pennsylvania [START_REF] Lee | Evidence for syntectonic crystallization for the mudstone to slate transition at Lehigh gap, Pennsylvania[END_REF][START_REF] Ho | Reorientation mechanisms of phyllosilicates in the mudstone-to-slate transition at Lehigh Gap, Pennsylvania[END_REF][START_REF] Van Der Pluijm | Contradictions of slate formation resolved?[END_REF]. While imaging techniques can provide 2D shape fabrics of grains, the X-ray diffraction techniques, such as the X-ray pole figure goniometry [START_REF] Oertel | The relationship of strain and preferred orientation of phyllosilicate grains in rocks-a review[END_REF][START_REF] Van Der Pluijm | High-resolution X-ray texture goniometry[END_REF] and high-energy synchrotron X-rays [START_REF] Wenk | Preferred orientation and elastic anisotropy of illite-rich shale[END_REF], aim mostly at determining the lattice-preferred orientation (LPO) of phyllosilicates in these rocks. Another powerful technique to determine the fabric of deformed fine-grained rocks is the Anisotropy of Magnetic Susceptibility or AMS [START_REF] Tarling | Magnetic anisotropy of rocks[END_REF][START_REF] Borradaile | Anisotropy of magnetic susceptibility (AMS): magnetic petrofabrics of deformed rocks[END_REF][START_REF] Parés | Sixty years of anisotropy of magnetic susceptibility in deformed sedimentary rocks[END_REF]. The AMS provides a bulk magnetic fabric, through a magnetic susceptibility tensor, retracing the preferred orientation (shape or magnetocrystalline) of both ferromagnetic, diamagnetic and paramagnetic minerals. In the case of mudrocks, paramagnetic minerals (i.e. phyllosilicates) are generally the main contributors to the AMS signal and the magnetic fabric often reflects the clay fabric [START_REF] Hirt | Magnetic and mineral fabric development in the Ordovician Martinsburg Formation in the Central Appalachian Fold and Thrust Belt, Pennsylvania[END_REF][START_REF] Parés | Sixty years of anisotropy of magnetic susceptibility in deformed sedimentary rocks[END_REF]. Using AMS and other magnetic analyses, [START_REF] Hirt | Magnetic and mineral fabric development in the Ordovician Martinsburg Formation in the Central Appalachian Fold and Thrust Belt, Pennsylvania[END_REF]; [START_REF] Housen | Slaty cleavage development and magnetic anisotropy fabrics[END_REF] proposed deformation mechanisms associated to slaty cleavage development in a fine-grained matrix at Lehigh gap. However, little attention has been given to other shale bearing minerals such as quartz and calcite and information on the 3D shape fabrics of these common minerals in gradually deformed pelitic rocks is scarce. Shape fabrics or Shape Preferred Orientation (SPO) determination of grains can be done thanks to numerous techniques. As mentioned, AMS can provide the SPO of ferromagnetic minerals such as magnetite if they are the main magnetic carriers in the rock matrix. Other techniques mostly rely on 2D (digital) image analysis and we can cite the intercept counting method [START_REF] Launeau | Shape preferred orientation of object populations: automatic analysis of digitized images[END_REF][START_REF] Launeau | Two-and three-dimensional shape fabric analysis by the intercept method in grey levels[END_REF][START_REF] Launeau | Fabric analysis using the intercept method[END_REF], the wavelet transformation [START_REF] Gaillot | Wavelet transform: a future of rock fabric analysis[END_REF] and the autocorrelation function [START_REF] Heilbronner | The autocorrelation function: an image processing tool for fabric analysis[END_REF][START_REF] Pfleiderer | Magnetic pore fabric analysis: Verification through image autocorrelation[END_REF]. More recently, [START_REF] Thissen | An autocorrelation method for three-dimensional strain analysis[END_REF] have developed a method to estimate rock fabric and to evaluate the strain using the autocorrelation function on 3D X-ray computed tomography data. Generally, to obtain 3D information from 2D image analysis only, three orthogonal pictures of outcrop microstructures, images of thin sections or polished surfaces are combined. It refers to the discipline of stereology [START_REF] Underwood | Quantitative Stereology[END_REF]. This technique has been successfully applied by [START_REF] Grégoire | Magnetite grain shape fabric and distribution anisotropy vs rock magnetic fabric: a three-dimensional case study[END_REF]; [START_REF] Launeau | Magmatic fabric acquisition mechanisms in a syenite: Results of a combined anisotropy of magnetic susceptibility and image analysis study[END_REF] and by [START_REF] Hastie | Significance of magnetic and petrofabric in Karoo-feeder dykes, northern Lebombo[END_REF][START_REF] Hastie | Characterisation of grain-size, shape and orientation of plagioclase in the Rooi Rand dyke swarm, South Africa[END_REF] in igneous rocks. It is however desirable to obtain a 3D characterization of SPO of rock constituents in a faster and non-destructive way and for this purpose X-ray tomography is particularly appealing. X-ray computed tomography (XCT) is now a well-established, powerful and non-destructive method to investigate the microstructure of rocks in three dimensions [START_REF] Ketcham | Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences[END_REF][START_REF] Ketcham | Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography[END_REF][START_REF] Carlson | Three-dimensional imaging of earth and planetary materials[END_REF][START_REF] Baker | An introduction to the application of X-ray microtomography to the threedimensional study of igneous rocks[END_REF][START_REF] Cnudde | High-resolution X-ray computed tomography in geosciences: A review of the current technology and applications[END_REF]. The advantage of this imaging technique relies on its ability to provide the 3D shape fabric, for each individual object (grain or pore space) and makes the quantitative analysis statistically robust. The study of SPO of minerals by laboratory XCT or synchrotron XCT has proven to be valuable within various coarse-grained materials [START_REF] Ketcham | Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography[END_REF][START_REF] Zucali | The 3D quantitative lattice and shape preferred orientation of a mylonitised metagranite from Monte Rosa (Western Alps): Combining neutron diffraction texture analysis and synchrotron X-ray microtomography[END_REF][START_REF] Sayab | Highresolution X-ray computed microtomography: A holistic approach to metamorphic fabric analyses[END_REF][START_REF] Sayab | Orthogonal switching of AMS axes during type-2 fold interference: Insights from integrated X-ray computed tomography, AMS and 3D petrography[END_REF][START_REF] Kahl | 3-D microstructure of olivine in complex geological materials reconstructed by correlative X-ray μ-CT and EBSD analyses[END_REF] but also in fine-grained sedimentary rocks [START_REF] Kanitpanyacharoen | Mineral Preferred Orientation and Microstructure in the Posidonia Shale in Relation to Different Degrees of Thermal Maturity[END_REF][START_REF] Wenk | Slate -A new record for crystal preferred orientation[END_REF]. XCT does not measure the chemical composition of a rock sample but reflects the density and atomic number of its components. However, chemical identification can be performed by taking account of differences at elemental absorption edges, with synchrotron X-rays [START_REF] Gualda | Quantitative 3D petrography using X-ray tomography 3: Documenting accessory phases with differential absorption tomography[END_REF] or by using a lab-based instrument equipped with a spectroscopic imaging detector [START_REF] Egan | 3D chemical imaging in the laboratory by hyperspectral X-ray computed tomography[END_REF]. Recently, phasecontrast (holo-)tomography, X-ray fluorescence tomography and X-ray diffraction were used together in order to study chemical features of zircons [START_REF] Suuronen | 3D nanopetrography and chemical imaging of datable zircons by synchrotron multimodal X-ray tomography[END_REF]. Otherwise, laboratory XCT can be easily combined with other techniques, such as energy dispersive X-ray spectroscopy (EDS), to determine the chemical nature of rock constituents. This 2D-3D registration method has been commonly used in studies related to the characterization of reservoir rocks [START_REF] Golab | 3D porosity and mineralogy characterization in tight gas sandstones[END_REF][START_REF] Golab | 3D characterisation of potential CO2 reservoir and seal rocks[END_REF][START_REF] De Boever | Data-fusion of high resolution X-ray CT, SEM and EDS for 3D and pseudo-3D chemical and structural characterization of sandstone[END_REF] but also in metamorphic studies [START_REF] Macente | The strain-dependent spatial evolution of garnet in a high-P ductile shear zone from the Western Gneiss Region (Norway): a synchrotron X-ray microtomography study[END_REF]. Because of its accessibility, simplicity and quick implementation, we chose to use EDS to supplement information from lab-based X-ray absorption-contrast images.

Here we propose a novel methodology to study the shape fabric of common shale-bearing minerals (quartz, calcite), but also pore spaces, in three dimensions by combining of XCT and EDS. The proposed method is then applied to study deformed shales from the South Pyrenean foreland. Results demonstrate that the shape fabric of quartz and calcite exhibit a contrasting evolution along a kmlong strain gradient. The purpose of this work is however not to go through details about the geological setting but more to emphasize the usefulness of the method that can be applied on finegrained rocks in various geological context.

Geological setting and sampling

The Jaca basin is a piggyback basin of the South Pyrenean foreland, incorporated in the Pyrenean Orogeny from the Eocene to the Early Miocene [START_REF] Labaume | Evolution of a turbiditic foreland basin and analogy with an accretionary prism: Example of the Eocene South-Pyrenean Basin[END_REF][START_REF] Hogan | Evolution of the Jaca piggyback basin and emergence of the External Sierra, southern Pyrenees[END_REF][START_REF] Izquierdo-Llavall | On the origin of cleavage in the Central Pyrenees: Structural and paleo-thermal study[END_REF][START_REF] Crognier | Syn-orogenic fluid flow in the Jaca basin (south Pyrenean fold and thrust belt) from fracture and vein analyses[END_REF]. The Northern part of the Jaca Basin is made up of the Hecho turbiditic group. The Sierra de Leyre (Fig. 1a) bounds the southern part of the Hecho group. We focus on the Hecho Marls Formation (Eocene), which outcrop near the Sigües locality, and more precisely on the footwall of a steep thrust, which delineates the southern anticline of the Sierra de Leyre. The bedding (S0) of Hecho marls is sub-horizontal (Fig. 2a), except at few meters from the emerged thrust, where footwall syncline developed, marked by overturned bedding dipping to the North (Fig. 2e).

In this study, we observed a strain gradient associated to cleavage development (S1) north of Sigües, correlated to the distance from the thrust. Cleavage develops as axial planes parallel to the major folds axes (mostly oriented N100o) but damage is induced by thrust propagation. At ~2 km south from the emerged thrust, there is no cleavage, and shales are only affected by a fracture network [START_REF] Crognier | Syn-orogenic fluid flow in the Jaca basin (south Pyrenean fold and thrust belt) from fracture and vein analyses[END_REF]. We refer to this type of petrofabric, corresponding to a low strain area, as "cleavage-free" throughout the text. In this domain, bedding has a dip of 15° towards the South (Fig. 2a). In the range ~1 km-0.5 km from the thrust, a pencil cleavage develops, dipping to the North and oblique to the bedding. The spacing between cleavage planes is metric at ~1 km and evolves gradually to millimetric at ~0.5 km. We refer to this petrofabric, corresponding to an intermediate strain area, as "pencilcleavage". In this study, the bedding is still well observed in the pencil-cleavage domain (Fig. 2b-c).

The dip of the bedding is 10° towards the South. At a distance below 0.5 km from the thrust, the cleavage intensity increases and the cleavage spacing becomes infra millimetric. We refer to this petrofabric, corresponding to a high strain area, as "slaty-cleavage". Here cleavage is strongly oblique to a horizontal bedding (Fig. 2d). Continuing towards the North, the bedding is now barely detectable and the change between sub-horizontal to overturned beds is difficult to observe near the thrust. The slaty cleavage, strongly dipping to the North, superimposes the bedding that has a dip of 60° towards the North forming a transposition structure (Fig. 2e). This is the slaty-cleavage domain where cleavage and bedding are nearly parallel due to high strain. The Sigües site exhibits therefore an exceptional exposure where it is possible to monitor, meter by meter, the evolution of a fine-grained sedimentary matrix in response to cleavage development.

In this study, five calcareous shale samples (A1, A2, A3, A4, A5) have been collected from the South to the North, with respectively a cleavage-free petrofabric (A1, 1.95 km from thrust), an incipient pencil-cleavage petrofabric (A2, 0.95 km), a pencil-cleavage petrofabric (A3, 480 m) and two slaty cleavage petrofabrics (150 and 15 m for A4 and A5 respectively). For the A4 sample, the bedding is sub-horizontal, superimposed by a steep cleavage. For the A5 sample, located near the thrust in the footwall syncline, overturned bedding and cleavage are nearly parallel due to the transposition of the two structures.

Methods

Workflow

The complete acquisition workflow applied in this study is described in Fig. 3. The workflow includes:

1) Extraction of a drill core from a georeferenced cylindrical field sample. A 'T' shaped orientation marker respecting the strike of the field sample is reported on the top of the extracted drill core (Fig. 3a).

2) Performing a first X-ray tomographic acquisition of the drill core. Image processing enables to extract different phases corresponding to shale constituents (Fig. 3b).

3) Polishing the drill core in the longitudinal direction (Fig. 3c). 4) Performing an EDS analysis on this polished surface (Fig. 3d), 5) Performing a second X-ray tomographic acquisition permitting to position the 2D EDS dataset within the 3D X-ray data set of the entire drill core and to fuse the data (Fig. 3e).

The following sections shortly present the principles of XCT and EDS and describe more precisely how the data fusion is performed and how it enables to perform detailed shape fabric analysis.

High resolution X-ray computed tomography 3.2.1 Acquisition and reconstruction of data

Laboratory X-ray computed tomography (XCT) is a technique, which enables inner inspection of a sample at high resolution and in a non-destructive way. The sample is placed between a source and a detector. During an acquisition, a conical X-ray beam illuminates the sample and a series of 2D projection images are recorded for various sample orientations. The pixel values of each of these images correspond to the intensity of the transmitted X-ray beam and depend on the attenuation of the sample material [START_REF] Ketcham | Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences[END_REF][START_REF] Ketcham | Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography[END_REF][START_REF] Baker | An introduction to the application of X-ray microtomography to the threedimensional study of igneous rocks[END_REF]. The attenuation is function of the density and the atomic number of the material and of the incident X-ray spectrum [START_REF] Ketcham | Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences[END_REF][START_REF] Baker | An introduction to the application of X-ray microtomography to the threedimensional study of igneous rocks[END_REF]. The recorded dataset of 2D projection images is subsequently converted into a three-dimensional dataset in which every voxel (i.e. a pixel in 3D) reflects the average attenuation of the physical material located at that voxel position. As attenuation coefficients are material-specific, different mineral phases yield different grey values in the reconstructed 3D images. Analysis of the spatial distribution of the reconstructed images hence permits to determine the geometry and location of the mineral phases. Attenuation-based X-ray tomography however does not provide crystallographic information nor direct chemical information.

In this work, five shale drill cores (A1-A5) were scanned with a Zeiss Xradia Versa 510 X-ray tomograph at DMEX (UPPA). This tomograph combines geometric and optical magnification, enabling the acquisition of high-resolution images for relatively large sample sizes. The 16-bit CCD detector is capable of acquiring radiographs with 2048 2 pixels. The acquisition parameters are selected in view of optimizing the image contrast, the signal-to-noise ratio and the acquisition duration (Table 1). The set of recorded radiographs are reconstructed with XRM Reconstructor® (Zeiss,version 11) in order to obtain a stack of cross-sections forming a digital volume of the sample. This reconstruction software is based on the standard filtered back projection algorithm [START_REF] Ramachandran | Three-dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions instead of Fourier Transforms[END_REF].

Data processing

The XCT data were processed, visualized and interpreted using Avizo® (FEI, Version 9.0.0). A twostep image processing is applied to the data. In a filtering step the signal-to-noise ratio is improved.

The subsequent segmentation step enables extracting mineral phases and pore spaces for further quantitative analysis in 3D. Note that for each sample, image processing is done for a subvolume (volume of interest) located in the central part of the image (Fig. 3f) as the structure near edges of the drill core might be affected by the coring.

Filtering

The noise in the reconstructed XCT dataset can be reduced by applying pre-processing filters which are mathematical algorithms that act on each pixel or voxel of the image [START_REF] Kaestner | Imaging and image processing in porous media research[END_REF][START_REF] Russ | The Image Processing Handbook, Seventh Edition[END_REF]. The aim of the filtering process is to make the interpretation of the image easier by increasing the contrast between the objects [START_REF] Kaestner | Imaging and image processing in porous media research[END_REF][START_REF] Russ | The Image Processing Handbook, Seventh Edition[END_REF]. In our study, an anisotropic diffusion filter proposed by [START_REF] Bernard | Constrained sintering of glass films: Microstructure evolution assessed through synchrotron computed microtomography[END_REF] is applied to each dataset. This filter is a modified version of the classical anisotropic diffusion filter [START_REF] Perona | Scale-space and edge detection using anisotropic diffusion[END_REF]. It smoothens noisy but relatively uniform regions of the image (i.e. each individual phase), while preserving the boundaries between the phases (i.e. the contours of the objects). Additionally, the Despeckle module is applied to remove residual noise based on a mean calculation of neighborhood voxels values.

Segmentation

Segmentation enables to partition the image into regions so that each region is homogeneous with regard to certain properties, such as gray level or texture [START_REF] Dougherty | Digital image processing methods[END_REF]. Here, it is sought to extract five phases which are associated to different gray levels ranging from black (lowest X-ray attenuation, phase 1) to white (highest X-ray attenuation, phase 5) (Fig. S1). In the case of finegrained sedimentary rocks, the structure of the rock is complex due to various sized minerals of different densities and a multi-scale porosity. Indeed, porosity varies over a wide range of length scales in shales and can only be fully characterized using multi-scale imaging techniques.

Consequently, the histogram of the gray levels shows overlapping values that make it difficult to distinguish each phase. The comparison of results obtained by different methods of thresholding

shows that global manual thresholding is the most suitable in this context. Morphological filters [START_REF] Serra | An overview of morphological filtering[END_REF][START_REF] Dougherty | Digital image processing methods[END_REF] have also been applied as post-segmentation image processing, when it was necessary, to discriminate two phases and to reduce misclassification errors near phase interfaces (Fig. S1). The thresholds are chosen to dissociate the different phases and to respect their boundaries. As this choice could be considered as subjective, upper and lower bounds on the thresholds are determined that encompass all reasonable choices of an experienced operator. These permit to assess the uncertainties on the volume of each phase from ±15% to ±5% depending on the considered phase. Once the tomographic phases have been segmented (Fig. 3b), we desire to identify them chemically using EDS.

Energy-Dispersive X-ray Spectroscopy

Energy dispersive X-ray spectroscopy (EDS) enables acquiring a chemical map at nanometer resolution of the elements from Li to U situated on the analyzed surface. Associated with SEM devices, EDS uses X-rays generated by the interaction of an electron beam with a sample to characterize the elemental composition [START_REF] Goldstein | Scanning electron microscopy and x-ray microanalysis[END_REF].

In this work, we use EDS in a qualitative approach to identify the major constituents of the shale samples. A grid of scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) images is acquired to compose a chemical map of a plane surface obtained after the core has been polished in the longitudinal direction (Fig. 3c-d). SEM-EDS data acquisition is performed at the Raimond Castaing Microanalysis Centre (Toulouse, France). SEM images are collected as backscattered electrons (BSE) with a JEOL JSM-7800F Prime equipped with a Silicon Drift Detector from Oxford Instruments to generate the EDS images. The acceleration voltage used for our study is 10 kV. One EDS map is obtained for each detected chemical element. Two samples (A1 and A2) are characterized to identify major constituents of the rock, EDS parameters are summarized in Table S1.

SEM images are not used in this work because they are redundant with the X-ray dataset.

Image registration and fusion

Registration of the EDS images and the XCT volume is done in order to propagate chemical identification given by EDS images into the whole XCT volume. First, the registration of the initial XCT image with the final XCT image after polishing is performed. This operation is essential to precisely locate the surface analyzed by EDS inside the initial XCT volume. The Mutual Information method from Avizo® is used to register these datasets and the plane that corresponds to the polished surface is extracted from the initial volume. This plane and the EDS image are not strictly superimposable because they are not exactly parallel, nor do they have the same resolution.

Furthermore, the EDS image integrates information over a thickness of several microns. Therefore, we fine-tune the registration based on landmarks (i.e. characteristic features in the image).

Four out of five XCT phases can be directly associated to a mineral, namely quartz, clayey matrix, calcite and pyrite for phases two to five, respectively. Light elements cannot be detected by EDS, and therefore phase 1 (lowest X-ray attenuation) can be associated with the air-filled pores of the material.

This procedure enables propagating the chemical information from 2D EDS maps to the entire XCT volume and to subsequently perform a shape fabric analysis of each phase.

Shape fabrics analysis

The shape of each individual phase (grain or pore) corresponds to the distribution of its voxels in the three-dimensional XCT image. In our case, the shape is approximated by a best-fit ellipsoid (Fig. 3g)

having the same moments of inertia as the original object [START_REF] Jähne | Digital Image Processing: Concepts, Algorithms, and Scientific Applications[END_REF]. The inertia matrix of each object is obtained by the calculation of the second-order moments. The diagonalization of the matrix provides three eigenvalues which correspond to the principal moments of inertia and the associated three orthogonal eigenvectors which correspond to the principal axes of inertia. The major, intermediate and minor eigenvectors give information on the spatial orientation of the object in the coordinate system of the sample. As the strike and dip of each sample is known, the local coordinate system can be converted into the geographic coordinate system. The shape of the object is approximated by the eigenvalues, which are related to the best-fit ellipsoid's semi-axes. Truncated objects placed at the edges of the volume were excluded, as they would bias the shape-analysis.

The shape of each object is further characterized by three non-dimensional shape parameters, namely anisotropy, elongation and flatness.

-The anisotropy is defined by 1 -𝑒 3 /𝑒 1 where 𝑒 3 and 𝑒 1 are the smallest and largest eigenvalues of the inertia matrix respectively. A spherical object has anisotropy equal to zero.

-The elongation is defined by 𝑒 2 /𝑒 1 where 𝑒 2 and 𝑒 1 are the medium and largest eigenvalues respectively.

-The flatness is defined by 𝑒 3 /𝑒 2 where 𝑒 3 and 𝑒 2 are the smallest and medium eigenvalues respectively.

Results

General observations

Distribution of phases

The results concerning quartz, calcite and pores phases are provided in this work. The study of the phyllosilicate matrix is discarded because of insufficient XCT resolution while the study of pyrite is outside the scope of this paper. The number of objects belonging to each phase (calcite, quartz and pore spaces) and their relative abundance in the volume of interest of the samples are reported in Table 2. In this study, objects under 729 µm 3 (corresponding to 216 voxels in A1, 332 voxels in A2, 729 voxels in A3, 422 voxels in A4 and A5) are considered as noise and are eliminated. Thus, the volumetric contribution of each phase obtained with XCT underestimates the real quantity present in the samples to some extent. All together, the three phases represent 3.5 to 7.6% of the volume of interest. In comparison, the rock matrix represents around 92.4 to 96.5%. We thus focus on a small fraction of the rock volume (Table 2). The volume distribution of the objects ranges from 729 to near 2*10 6 µm 3 for the biggest calcite grains. Nevertheless, among each mineralogical phase (quartz and calcite), around 95% of the studied particles have a size ranging from 729 to 20729 µm 3 . The respective distributions, in the five samples, of quartz and calcite ranging from 729 to 20729 µm 3 , are represented in Fig. S2 and show a remarkable similarity. 4 presents a vertical north-south cross section through each sample, illustrating the horizontal bedding orientation from A1 to A4, the appearance of a cleavage plane from A3 onwards, as well as the rotation of this plane from A3 to A5. As the depicted cross-section intersects each cylindrical sample in an oblique fashion, the shapes of the cross-sections differ from one sample to the next.

Images in the samples reference frame are available in Fig. S3.

Fig. 4 shows that most of the calcite grains are rounded shaped and correspond to microfossils and shell fragments. On the contrary, quartz grains are more angular. At this micron scale, we observe a preferred alignment of grains in the least deformed samples (A1 and A2). This fabric is attributed to bedding as this planar structure is sub-horizontal, which is in accordance with field observations. In sample A3, a secondary planar fabric becomes slightly visible, it corresponds to cleavage that crosscut bedding structures at low angle. Cleavage domains are subtle in this XCT image, sometimes marked by preferred alignment of calcite bioclasts and spaced by more than 1 mm in this sample. In samples A4 and A5, the traces of cleavage domains are deduced from high porosity surfaces, which appear as microcracks in the XCT images (see Fig. S3 for more images). Because clay minerals are known to concentrate in cleavage domains (seams), clays may have dehydrated during storage of the samples and formed microcracks. From these structures, we can infer the presence of pressure solution seams. Furthermore, the calcite bioclasts are often truncated by the seams and confirm that pressure solution has been responsible of the growth of these surfaces [START_REF] Engelder | Disjunctive cleavage formed at shallow depths in sedimentary rocks[END_REF][START_REF] Passchier | Microtectonics[END_REF]. The truncation of calcite by pressure solution seams is supported by optical microscopy observation (Fig. 5). The cleavage domains are more penetrative in A5 than in A4.

Average spacing between cleavage domains is of 212 µm ± 65 µm in A4 and of 116 ± 16 µm in A5.

However, the measure of the spacing of cleavage depends on the scale of observation and the true spacing is certainly less than these values. In our case, spatial resolution depends on the voxel size of the XCT images. In A4, the seams are discontinuous, subparallel to slightly anastomose around grains and rather rough. In A5, the seams appear discontinuous, subparallel and smoother. In both samples A4 and A5, grains within or close to the cleavage domains are strongly aligned, parallel to the seams.

In between the cleavage domains of A4, grains are whether subparallel, orthogonal (related to the bedding fabric) or randomly oriented. In between the cleavage domains of A5, calcite grains are mostly aligned parallel to seams giving a strong planar fabric to the rock. Quartz grains are rather randomly oriented in A5. We remark that cleavage domains are heterogeneously spaced in A4 compared to cleavage domains in A5, which are equally spaced throughout the rock volume.

4.2 Grain and pore spaces shape.

At first glance, the distribution of the shape parameters of quartz, calcite and pores highlights a global transition towards more anisotropic, more elongated and flatter objects from the cleavage-free domain (A1) to the slaty-cleavage domain (A5) (Fig. 6). However, the evolution of the shape parameters is not the same for each phase.

Concerning the quartz (Fig. 6), the major shift in distributions of both anisotropy, elongation and flatness takes place between A1 and A2. After what, the distribution of these parameters is not really distinguishable between samples A2, A3, A4, A5. However, we should note that distributions in A3 feature the most anisotropic, elongated and flattened quartz grains.

Concerning the calcite (Fig. 6), there is a regular shift of the distribution of the three parameters from A1 to A5. As strain increases, calcite grains gradually become more deformed. This is particularly well illustrated by evolution of anisotropy and flatness. However, we should note that distributions of anisotropy and elongation in A3 are close to that in A5. The distribution of flatness in A3 is similar to that in A4. We should note that quartz and calcite have similar distributions of anisotropy, elongation and flatness in A1 and A2.

Concerning the pore spaces (Fig. 6), the distribution of anisotropy and flatness are delicate to interpret due to a high proportion of very anisotropic and flattened pores in A1 and A5. These pores may in fact correspond to microcracks present in A1 and A5. Elongation of the pore spaces is similar for the five samples.

As significant results, we thus retain common shape features of quartz and calcite grains in samples A1 and A2, the change of quartz shape between A1 and A2 solely, contrasting with the continuous and regular evolution of calcite shape across the five samples. We also note that quartz grains seem to be more deformed in sample A3. It has been verified that the specific segmentation thresholds (cf.

segmentation paragraph) for each phase have no influence on the evolution of shape parameters.

Shape preferred orientation of quartz, calcite and pores.

We plot density contours of the short (L3) and long (L1) axes corresponding to thousands of objects (grains, pore spaces) in equal area and lower hemisphere projections representing a geographic coordinate system (North-East-Down) (Fig. 7-8), using the OpenStereo software [START_REF] Grohmann | OpenStereo: Open Source, Cross-Platform Software for Structural Geology Analysis[END_REF]. In fabric analysis, it is generally common to assign L3 as the pole of foliation (Fig. 7) and L1 as the lineation (Fig. 8). Poles of the bedding and cleavage planes measured on the XCT images from the alignment of grains (Fig. 4) are also reported onto these stereographic plots in a common geographic coordinate system (North-East-Down).

In the cleavage-free domain (sample A1), all objects display foliation parallel to the bedding plane (Fig. 7). Pore spaces are well-organized with a maximum density near 30% around the pole of bedding. Quartz and calcite display almost the same degree of dispersion and have maximum densities coinciding with the pole of bedding (3.5% and 3.8% respectively, which mean 3.5%/1% area and 3.8%/1% area respectively). Lineation of individual ellipsoid long axes (L1) spread subhorizontally in the bedding plane with a slight NW-SE trend (Fig. 8). At the onset of the pencilcleavage domain (sample A2), all poles of foliation spread near the bedding pole. Here again, quartz and calcite have similar maximum densities (3.3% and 3.7% respectively). Poles of the pores are more disorganized. No evident lineation is observed but we can notice a slight preference towards NW-SE for quartz and calcite (Fig. 8). Lineation is related to bedding. In the pencil-cleavage domain,

where cleavage is oblique to bedding (sample A3), we observe notable differences. Quartz displays a scattered foliation related to the bedding pole with a maximum density of 2.2% (Fig. 7). Calcite shows a NNE-SSW directed girdle of the pole of foliation between the pole of cleavage and the pole of bedding. However, calcite foliation mostly indicate a cleavage related fabric with a maximum density of 3.0% around the pole of cleavage. The pole of foliation of pore spaces seems to be scattered between the pole of cleavage and the pole of bedding. The lineation is sub-horizontal and related to bedding for quartz grains but still displays a preference towards NW-SE as in A1 and A2 (Fig. 8). As of now, the lineation tends ESE-WNW for calcite grains and correspond to an intersection lineation of bedding and cleavage planes. Calcite lineation also displays incipient contours in the cleavage plane. The lineation of pore spaces cannot be assessed. In the slaty cleavage domain, where cleavage is strongly oblique to bedding (sample A4), we also observe notable differences. Quartz displays a N-S directed girdle of the pole of foliation between the pole of cleavage and the pole of bedding (Fig. 7). Quartz grains are thus influenced by these two planes. In contrast, calcite grains and pore spaces have a well concentrated foliation near the pole of cleavage. At this strain state, quartz and calcite show different maximum densities around the pole of cleavage, 2.3% for quartz compared to 6.6%

for calcite. The lineation tends slightly E-W for quartz, close to an intersection lineation (Fig. 8). For calcite and pore spaces, the intersection lineation mostly lies E-W sub-horizontally but is also depicting the cleavage great circle with some steep lineations within the cleavage plane. In the slatycleavage domain, where bedding and cleavage are parallel to each other (sample A5), all foliation poles are grouped parallel to the bedding/cleavage pole (Fig. 7). However, quartz foliation is still quite disorganized and show a weak maximum density of 2.9%. Maximum density at the pole of cleavage reaches 11.4% for calcite foliation. The dispersion of the quartz foliation may indicate that bedding and cleavage planes are not exactly parallel. The pole of foliation of pores is well defined and displays a maximum density of 38.2%. The lineation is relatively scattered, sub-horizontal in trend for quartz but also with a girdle around the dip of the cleavage plane (Fig. 8). Calcite and pore spaces display a down-dip stretching lineation with a maximum density of 4.0% and 7.0%

respectively. We should note as a general trend that foliation of grains and pore spaces is better defined than their lineation.

Discussion

Results of this microscale study are fully consistent with field data. Cleavage development along the strain gradient is well recorded in XCT images and is demonstrated by our microstructural approach on quartz, calcite and pores. Although we have worked on a small rock volume (volume of interest between 1 to 6 mm 3 ), results are well correlated to field observations and show clear trends, indicating that the samples are representative. The representativeness of sample is also illustrated by the volume distribution remarkably similar for calcite and quartz, independently of strain. Moreover, the amount of investigated objects from XCT data of each sample (~10000 for quartz and calcite, more than 100 for pores) makes the study statistically robust.

In the cleavage-free domain (A1), quartz and calcite have similar shape features (Fig. 6) and SPO (Fig. 7-8-9). In these shales, quartz grains may mostly be provided by detrital inputs whereas calcite grains may be provided by carbonates pelagic particles. Grain shape may result from compaction both during burial/diagenesis and tectonic compression. SPO of quartz and calcite is governed by a typical bedding-parallel fabric with short axis L3 normal to the bedding plane and no specific orientation of the long axis L1 (Fig. 7). SPO of pores is also governed by the bedding.

At the onset of pencil-cleavage domain (A2), we observe similar shape features (Fig. 6) and SPO (Fig. 7-8-9) for quartz and calcite but they have evolved with respect to the undeformed sample A1.

Particles are more deformed (Fig. 6) but their foliation remains close to the pole of bedding, lineation is almost the same as in A1. No specific change in SPO is recorded in this low strain intensity area.

Grain shape may change due to microfracturing, as illustrated in Fig. 10. Evolution of grain shape and SPO is reported in a sketch presented in fig. 10 that follows this discussion.

In the pencil-cleavage domain (A3), where cleavage is oblique to the bedding orientation, shape features and SPO differ between quartz and calcite. Quartz and calcite grains are more deformed in this sample as shown by the distribution of shape parameters (Fig. 6). Quartz SPO is still related to bedding but disturbed (Fig. 7-8-9). Calcite SPO is developing a cleavage foliation and is depicting an intersection lineation. Some calcite grains might still be related to the bedding as described by the girdle of L3. The fabric of pore spaces in this sample is more difficult to interpret because of the weak number of pore spaces. Mechanical rotation, pressure-solution and new crystallization of phyllosilicates grains have been commonly proposed as the major processes acting during cleavage development associated to the transition from mudstones to shales and slates [START_REF] Engelder | Disjunctive cleavage formed at shallow depths in sedimentary rocks[END_REF][START_REF] Lee | Evidence for syntectonic crystallization for the mudstone to slate transition at Lehigh gap, Pennsylvania[END_REF][START_REF] Ho | Reorientation mechanisms of phyllosilicates in the mudstone-to-slate transition at Lehigh Gap, Pennsylvania[END_REF][START_REF] Ho | Contrasting roles of detrital and authigenic phyllosilicates during slaty cleavage development[END_REF][START_REF] Passchier | Microtectonics[END_REF]. van der Pluijm et al. (1998) discussed the possible roles of thermal and strain energy in determining which process dominates.

Generally, mechanical rotation is said to be the dominant process affecting detrital grains in early stages of cleavage development, as proposed by works on phyllosilicates grains [START_REF] Ho | Reorientation mechanisms of phyllosilicates in the mudstone-to-slate transition at Lehigh Gap, Pennsylvania[END_REF][START_REF] Ho | Contrasting roles of detrital and authigenic phyllosilicates during slaty cleavage development[END_REF][START_REF] Hirt | Magnetic and mineral fabric development in the Ordovician Martinsburg Formation in the Central Appalachian Fold and Thrust Belt, Pennsylvania[END_REF] and on magnetite grains [START_REF] Housen | Slaty cleavage development and magnetic anisotropy fabrics[END_REF]. This would be consistent with our observations on the quartz and calcite grains in the pencil-cleavage domain.

Changes in shape features and SPO of quartz and calcite may result from mechanical processes such as grain rotation. Alternatively, one could assume that grain rotation does not take place during deformation (Fig. 10), especially for grains located in between the cleavage domains. Since both scenarios are end-members in between we can find intermediate models that may explain the dispersion of the poles of foliation and low maximum densities. Brittle fracturing of grains may also erode grain contours and affect their shape. At this intermediate strain intensity, we cannot detect evidences for pressure-solution in the XCT image so we propose that grain rotation and grain fracturing are the dominant deformation processes to accommodate shortening. However, we do not exclude the play of pressure-solution. It is important to note that this strain state shows the weakest maximum densities of foliation and lineation which attest for the most disturbed shape fabrics of grains and pores.

In the slaty-cleavage domain (A4), where cleavage is strongly oblique to the bedding orientation, shape features and SPO differ between quartz and calcite. The shape of the quartz grains remains the same as in A2, while the calcite grains continue to deform (Fig. 6). The major step in the SPO evolution of grains is apparent in this sample and well demonstrated by differences in the maximum density of quartz and calcite foliations (Fig. 9). Quartz foliation is now related to poles of both bedding and cleavage (Fig. 7). More precisely, one third of the total quartz grains keep a bedding influenced fabric in this sample, compared to calcite and pores particles which are strictly governed by cleavage. We have compared the shape of the quartz grain population related to both the pole of cleavage and the pole of bedding, by selecting particles having a dip above or under 45°, but no differences have been observed in their respective size distribution. Therefore, these different orientations are not related to the size of the quartz grains. In this sample, we have seen some evidence for pressure-solution such as and truncated calcite grains (Fig. 5 & Fig. S3). It should be noticed that in XCT data, truncated grain and its pressure shadows (tails) are assimilated as one grain because of equal densities, as opposed to what can be seen in optical microscopy. Furthermore, fine grains present in pressure shadows are beyond XCT image resolution. It explains the high degree of anisotropy of calcite grains obtained by XCT data processing which encompass many submicrometric grains to define one grain. In this sample, the increasing deformation of calcite grains and changes in their SPO could be explained by pressure-solution. We suppose that this process may be the reason of the divergent evolution of the shape features and SPO between quartz and calcite in A3 (Fig. 10). Pressure-solution may proceed on calcite grains but may be less effective or may not happen for quartz grains. It is well-known that pressure solution is a function of the thermodynamics conditions, especially temperature [START_REF] Houseknecht | Influence of grain size and temperature on intergranular pressure solution, quartz cementation, and porosity in a quartzose sandstone[END_REF][START_REF] Bjorkum | How important is pressure in causing dissolution of quartz in sandstones?[END_REF][START_REF] Tournier | Mécanismes et contrôle des phénomènes diagénétiques en milieu acide dans les grès de l'Ordovicien glaciaire du bassin de Sbaa[END_REF], of the size and the composition of grains as well as of the stress conditions [START_REF] Gratier | Chapter 2 -The Role of Pressure Solution Creep in the Ductility of the Earth's Upper Crust[END_REF]. Another paramount parameter is the role of phyllosilicate in enhancing dissolution process of grains such as calcite and quartz [START_REF] Dewers | Influences of clay minerals on sandstone cementation and pressure solution[END_REF][START_REF] Renard | Pressure solution in sandstones: Influence of clays and dependence on temperature and stress[END_REF][START_REF] Meyer | Experimental investigation of the dissolution of quartz by a muscovite mica surface: Implications for pressure solution[END_REF]. More precisely, illite and mica are known to favor quartz dissolution in sandstones [START_REF] Weyl | Pressure solution and the force of crystallization: a phenomenological theory[END_REF][START_REF] Houseknecht | Intergranular pressure solution in four quartzose sandstones[END_REF][START_REF] Bjorkum | How important is pressure in causing dissolution of quartz in sandstones?[END_REF][START_REF] Tournier | Mécanismes et contrôle des phénomènes diagénétiques en milieu acide dans les grès de l'Ordovicien glaciaire du bassin de Sbaa[END_REF][START_REF] Kristiansen | Pressure solution -The importance of the electrochemical surface potentials[END_REF]. Even though both types of these phyllosilicates are present in our shales, the results of this study is not conclusive on their role in quartz dissolution. These shales have only experienced a peak temperature near 180°C [START_REF] Izquierdo-Llavall | On the origin of cleavage in the Central Pyrenees: Structural and paleo-thermal study[END_REF] and we can propose that the thermodynamics conditions were prone to pressuresolution of calcite while they were not for quartz grains, or at least to a lesser extent. In particular, temperature may be the limiting parameter for quartz dissolution. It should be noticed that the distribution of the size of quartz and calcite (Fig. S2) remains similar in the five samples, which is particularly stunning considering the amount of strain recorded by the samples in the slaty-cleavage domain. It seems that even though calcite grains are affected by pressure-solution processes, these processes have no influence on the grain size. The grain shape evolves due to the processes mentioned above but the removed material is probably only redistributed and grain size remains stable.

In the slaty-cleavage domain (A5), where cleavage and bedding are parallel, shape features and SPO of quartz and calcite are still displaying differences. Quartz shows the same shape as in A2 and A3

while calcite becomes more strained (Fig. 6). Quartz SPO is mostly related to cleavage but still scattered both in terms of foliation and lineation (Fig. 78). Calcite and pores' foliation are governed by cleavage and are well defined. Calcite lineation, which is close to the dip of cleavage, may correspond to a stretching lineation. Evidences for pressure-solution on calcite grains are also highlighted in this sample A5 (Fig. 5 & Fig. S3). Thus, evolution of calcite shape and enhancement of its SPO at this strain state could be explained by pressure-solution (Fig. 10). Here also, quartz grains might not be affected by this process.

Information issued from textural analysis, e.g. by means of the electron backscatter diffraction (EBSD) technique, could complete this study. In particular, EBSD would provide more information on the type of grains (authigenic vs detrital) and their relations and overgrowths patterns for authigenic grains. This approach could also be completed and compared with the study of preferred orientation of matrix phyllosilicates at a higher resolution thanks to XCT synchrotron devices or the well-established X-ray texture goniometry. Also, the analysis of phyllosilicates and their interactions with quartz and calcite could be useful, to determine if they play a role in the pressure-solution process. Overall, this work offers new perspectives of investigations for the study of fine-grained rock fabric in 3D and in various geological contexts.

Conclusions

The combination of XCT and EDS data is a reliable and fast way to produce a three-dimensional chemical and structural characterization of a representative volume of a fine-grained rock sample at a micrometric scale. It is possible to identify the major rock constituents, to extract shape parameters and to gain insight in shape-preferred orientation of thousands of mineral grains and hundreds of pores. Therefore, investigating fine-grained rock fabric by means of XCT appears as a promising tool.

According to this approach, we document for the first time the 3D shape fabrics of quartz and calcite and their evolution across a km-long strain gradient in the South Pyrenean foreland:

In five gradually more deformed calcareous shale samples (A1 to A5), we demonstrate that:

quartz and calcite grains embedded in the matrix have analogous shape and SPO in the cleavage-free and at onset of pencil-cleavage domain (A1 and A2);

quartz and calcite have distinct shape and SPO in the pencil-cleavage domain (A3) and in the slaty-cleavage domain (A4 and A5);

pore fabric mimics calcite fabric along the strain gradient.

We envisage grain fracturing, grain rotation and pressure-solution as dominant processes acting in the matrix but affecting differently quartz and calcite. Quartz deformation may be mostly induced by grain fracturing and rigid rotation of grains and occurs preferentially in the first stages of cleavage development (onset of pencil-cleavage domain and pencil-cleavage domain). Detrital quartz grains could appear as rigid markers of strain. Calcite deformation may be favored by pressure-solution in the slaty-cleavage domain whereas it is not the case for quartz. Calcite could be a useful strain gauge as shown by its regular shape fabric evolution according to strain intensity. onwards, a first one featuring grain rotation and a second one without grain rotation. A1: no deformed grain; A2: grain fracturing; A3: grain fracturing, pressure-solution may occur; A4: no further deformation of quartz grain, pressure-solution of calcite grain; A5: no further deformation of quartz grain, enhanced pressure-solution of calcite grain.

Fig. 1 :

 1 Fig. 1: (a) Simplified geological map between Sigües and Salvatierra in the Southern Pyrenees, Spain (adapted from Puigdefàbregas (1975)). Sampling locations are indicated on the map. (b) North-south cross-section corresponding to the A-A' profile on the geological map (adapted from Labaume et al.(1985). Projected positions of the samples with respect to the cross-section are indicated. Poles of bedding (S0) and cleavage (S1) measured in the field are reported onto equal area and lower hemisphere projections using density contouring.

Table 1 :

 1 sample parameters of X-ray tomography (XCT) for each studied sample.

	Sample	A1	A2	A3	A4	A5
	Diameter (mm)	2.5	1.9	1.8	1.8	1.8
	Field of View (mm)	2.9	2.5	1.95	2.35	2.35
	Acceleration tension (kVp) 50	50	40	40	40
	Target current (µA)	80	80	75	75	75
	Power (W)	4	4	3	3	3
	Exposure time (s)	18	12	40	40	40
	Number of projections	2001	2001	2001	1601	1601
	Voxel size (µm)	1.5	1.3	1.0	1.2	1.2
	Total acquisition time	12	8.5	24	22	22
	(hours)

Table 2 :

 2 Volume of interest for each sample. Number and volume fraction of quartz, calcite and pores particles in this volume, obtained after segmentation.

	Sample	A1	A2	A3	A4	A5
	Volume of interest (mm 3 )	6.12	2.10	1.76	2.34	2.15
	Number of quartz grains	13,451	5,282	13,109	8,311	7,371
	Volume fraction of quartz (1)	1.63 %	1.48 %	2.92 %	2.07 %	1.74 %

Acknowledgments

The authors thank E2S UPPA for financially supporting the lead author of this article H. Saur, ISIFoR for financially supporting the reported field survey and the SEM-EDS analyses, as well as the company Total for providing UMS 3360 DMEX with the tomograph used to carry out the XCT acquisitions described in this article. We are grateful to the editor T. Takeshita and two reviewers for their helpful comments on the manuscript.