H Shariati

A Bouterf

M Saadati

P.-L Larsson

F Hild

Probing Constitutive Models of Bohus Granite with In Situ Spherical Indentation and Digital Volume Correlation

Keywords: Damage, digital volume correlation (DVC), friction, granite, indentation, inelastic behavior

Spherical indentation of granite was investigated using Digital Volume Correlation (DVC) aiming at probing constitutive laws of the studied rock. In situ indentation was performed within an X-ray tomograph. Finite element simulations of the problem, using different constitutive models, were carried out and their trustworthiness was assessed thanks to DVC residuals. Three laws were investigated, namely, pure elasticity, then compressible elastoplasticity, and finally compressible elastoplasticity coupled with damage. Frictional contact effects were studied as well. The results show that compressible elastoplasticity should be accounted for to achieve high accuracy of results, and that frictional effects are of importance in terms of damage extent. If macrocrack initiation is also sought, then damage features should be included in the model.

Introduction

Percussive drilling is widely used as an industrial method in which rocks are fragmented under contact loading. The mechanical problem includes spherical contact between drill bit buttons and rocks. To improve the efficiency of the drilling process, an understanding of rock failure under such conditions is required. Tkalich et al. [START_REF] Tkalich | Experimental and numerical study of Kuru granite under confined compression and indentation[END_REF] presented an experimental and numerical investigation on the response of Kuru granite under confined compression and quasi-static indentation tests with a spherical indentor. Finite element (FE) simulations (with an axisymmetric model) of static indentation were carried out by the previous authors. The influence of the material model features was discussed, and the effect of confining pressure during indentation was evaluated. The numerical simulation showed that the peak force of indentation increased with confining pressure compared to unconfined cases. Conversely, the confining pressure had a limited influence in the contact region due to high stresses induced by indentation. Based on continuum damage mechanics concepts [START_REF] Lemaitre | A Course on Damage Mechanics[END_REF], Mazars' model [START_REF] Mazars | A description of microscale and macroscale damage of concrete structures[END_REF] was used to simulate the extent of the damaged zone within rocks (i.e., granite, limestone and sandstone) in the vicinity of spherical drill insert during single-and double-indentation tests [START_REF] Souissi | Numerical Modeling of Rock Damage during Indentation Process with Reference to Hard Rock Drilling[END_REF].

The inelastic behavior of Bohus granite, as prototypical of hard rocks, was experimentally and numerically investigated [START_REF] Shariati | On the Inelastic Mechanical Behavior of Granite: Study Based on Quasi-oedometric and Indentation Tests[END_REF]. Several quasi-static spherical indentation tests were performed on specimens made of such material. The resulting force-penetration curves were predicted by the established compressible plasticity model, namely the Drucker-Prager law [START_REF] Drucker | Soil mechanics and plastic analysis of limit design[END_REF] with variable dilation angle. Any inelastic deformation associated with crushing at high pressures under the contact area as well as multiple microcracking were captured by such model. Then, an anisotropic damage model was added to capture mode I cracking due to tensile stress states close to the specimen surface [START_REF] Shariati | A damage model for granite subjected to quasi-static contact loading[END_REF]. This stress state may lead to rock cracking, and subsequently material removal on the surface. Furthermore, the frictional effects under quasi-static spherical indentation were numerically studied [START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF]. It was observed that the simulated force-penetration response was not affected by friction. It was also shown that the predicted fragmentation pattern was similar in both cases (i.e., frictional and frictionless cases) but with a larger size in the frictional case.

One of the main challenges of indentation tests is that most of the deformation of the medium remains confined close to the zone beneath the indentor, which is not accessible by surface observations. Conversely, 3D imaging techniques (e.g., computed tomography [START_REF] Maire | Quantitative X-ray tomography[END_REF]) coupled with in situ tests may be considered and the deformation of the medium can then be measured by digital volume correlation (DVC) [START_REF] Bouterf | Digital Volume Correlation Applied to X-ray Tomography Images from Spherical Indentation Tests on Lightweight Gypsum[END_REF][START_REF] Mostafavi | 3D Studies of Indentation by Combined X-Ray Tomography and Digital Volume Correlation[END_REF][START_REF] Vertyagina | In situ quantitative three-dimensional characterisation of sub-indentation cracking in polycrystalline alumina[END_REF]. Such approaches then allow deformation mechanisms to be revealed and quantified, as well as constitutive models to be calibrated and/or validated. The aim of the present work is to further validate the afore-mentioned observations by performing in situ indentation in an X-ray scanner.

With DVC analyses, deformation mechanisms were revealed and quantified via in situ indentation. Cracking mechanisms were studied for indented polycrystalline alumina and it was shown that radial cracks experienced mixed mode opening displacements [START_REF] Vertyagina | In situ quantitative three-dimensional characterisation of sub-indentation cracking in polycrystalline alumina[END_REF]. Compaction and cracking in plaster was analyzed thanks to micro-and nano-tomography [START_REF] Bouterf | Analysis of compaction in brittle foam with multiscale indentation tests[END_REF]. Very early damage was observed. Pore collapse and its gradual development was detected in contrast with mesoscale studies where compaction appeared very abrupt. Deformation mechanisms of (elephant) dentin were reported [START_REF] Lu | Anisotropic crack propagation and deformation in dentin observed by four-dimensional X-ray nano-computed tomography[END_REF]. The authors showed that the strain levels beneath the indentor exceeded the yield strain of dentin. The fracture development in shales was reported very recently [START_REF] Ma | In-situ synchrotron characterisation of fracture initiation and propagation in shales during indentation[END_REF]. The cracking pattern was evidenced thanks to strain fields derived from measured displacement fields.

More ductile materials were also studied. Deformation mechanisms (e.g., dilatancy, liquid flow, macrosegregation, and intra-granular deformation) were reported for semi-solid Al-Cu alloy [START_REF] Cai | Synchrotron X-ray Tomographic Quantification of Deformation Induced Strain Localisation in Semi-solid Al-15wt[END_REF] and for semi-solid granular alloy with an equiaxed dendritic microstructure [START_REF] Cai | Time-resolved synchrotron tomographic quantification of deformation during indentation of an equiaxed semi-solid granular alloy[END_REF]. Strain localization was quantified and the role of the underlying microstructure was highlighted.

Another route consists in the extraction of material parameters and the validation of constitutive models. Elastoplastic finite element simulations were compared to DVC measurements for ductile aluminum-silicon carbide composite (Al-SiC) [START_REF] Mostafavi | 3D Studies of Indentation by Combined X-Ray Tomography and Digital Volume Correlation[END_REF]. Because of high strain uncertainties, computed and measured displacements were preferred and led to a good agreement. For a SiC-SiC composite, axial displacements and strains were compared with FE simulations at macroscopic and microscopic scales [START_REF] Saucedo-Mora | Observation and simulation of indentation damage in a SiC-SiC f ibre ceramic matrix composite[END_REF]. The damage model was qualitatively validated by using experimental and simulated axial displacements and strains. Ramberg-Osgood parameters could be extracted from an indentation test on an Al-SiC composite [START_REF] Mostafavi | Yield behavior beneath hardness indentations in ductile metals, measured by three-dimensional computed X-ray tomography and digital volume correlation[END_REF]. The difference between experimentally measured and simulated (normalized) axial displacements was minimized. Such type of analysis was extended to a nano-structured oxide dispersion strengthened steel [START_REF] Mostafavi | Quantifying yield behaviour in metals by X-ray nanotomography[END_REF]. In particular, it was shown that the effect of friction was very limited on the reported results. The compaction of glass was experimentally studied and numerically described by an approximate solution [START_REF] Lacondemine | Direct observation of the displacement field and microcracking in a glass by means of X-ray tomography during in situ Vickers indentation experiment[END_REF]. In indented plaster, a crushing criterion was proposed, calibrated thanks to indentation tests, and validated with oedometric tests [START_REF] Bouterf | Identication of the Crushing Behavior of Brittle Foam: From Indentation to Oedometric Tests[END_REF]. Predictions with Mohr-Coulomb and crushable foam models were compared with macroscopic and microscopic data. Both models reproduced the (macroscopic) load-displacement response of the indentation test. Conversely, poor predictions of the experimental crushed zone were obtained by both models.

In the afore-mentioned studies, various DVC schemes were considered. Most of the analyses were performed with so-called local DVC [START_REF] Mostafavi | 3D Studies of Indentation by Combined X-Ray Tomography and Digital Volume Correlation[END_REF][START_REF] Vertyagina | In situ quantitative three-dimensional characterisation of sub-indentation cracking in polycrystalline alumina[END_REF][START_REF] Cai | Synchrotron X-ray Tomographic Quantification of Deformation Induced Strain Localisation in Semi-solid Al-15wt[END_REF][START_REF] Mostafavi | Yield behavior beneath hardness indentations in ductile metals, measured by three-dimensional computed X-ray tomography and digital volume correlation[END_REF][START_REF] Cai | Time-resolved synchrotron tomographic quantification of deformation during indentation of an equiaxed semi-solid granular alloy[END_REF][START_REF] Saucedo-Mora | Observation and simulation of indentation damage in a SiC-SiC f ibre ceramic matrix composite[END_REF][START_REF] Mostafavi | Quantifying yield behaviour in metals by X-ray nanotomography[END_REF][START_REF] Lu | Anisotropic crack propagation and deformation in dentin observed by four-dimensional X-ray nano-computed tomography[END_REF][START_REF] Ma | In-situ synchrotron characterisation of fracture initiation and propagation in shales during indentation[END_REF], in which independent sub-volumes were registered. FE-based DVC was also considered, registration residuals and strain fields were utilized to characterize cracks [START_REF] Bouterf | Digital Volume Correlation Applied to X-ray Tomography Images from Spherical Indentation Tests on Lightweight Gypsum[END_REF][START_REF] Bouterf | Identication of the Crushing Behavior of Brittle Foam: From Indentation to Oedometric Tests[END_REF][START_REF] Bouterf | Analysis of compaction in brittle foam with multiscale indentation tests[END_REF][START_REF] Lacondemine | Direct observation of the displacement field and microcracking in a glass by means of X-ray tomography during in situ Vickers indentation experiment[END_REF]. Furthermore, reduced bases based on elastic simulations tailored to indentation tests enabled mechanical fields (e.g., stresses) to be accessible [START_REF] Bouterf | Digital Volume Correlation Applied to X-ray Tomography Images from Spherical Indentation Tests on Lightweight Gypsum[END_REF][START_REF] Bouterf | Identication of the Crushing Behavior of Brittle Foam: From Indentation to Oedometric Tests[END_REF]. Such analyses may allow different constitutive models to be probed. In the present case, the faithfulness of elastic and two nonlinear models was probed in addition to friction via integrated DVC in which the selected kinematic bases included simulated displacement fields.

The paper is organized as follows. First, the spherical indentation experiment is discussed including the tomographic scans that were acquired during load application (i.e.,in situ test).

Then, the integrated DVC framework is introduced. The latter was specifically tailored to the studied test. Finite element simulations were performed to construct kinematic bases for DVC analyses with different constitutive laws. Last, the integrated DVC results are presented and discussed in particular regarding the appropriateness of the three constitutive models, namely, elasticity, compressible elastoplasticity, and compressible elastoplasticity accounting for damage to describe the behavior of Bohus granite when indented by a hard material.

2 Indentation Experiment on Bohus Granite

In Situ Test

A cylinder (45 mm in diameter and 40 mm in height) made of Bohus granite was indented in situ with a 12-mm in diameter sphere made of silicon nitride (Si 3 N 4 ). Bohus granite mainly contains quartz (33 vol%), plagioclase (32 vol%), potassium feldspar (29 vol%) and biotite (6 wt%) [START_REF] Saadati | On the mechanical behavior of granite: Constitutive modeling and application to percussive drilling[END_REF].

The sample size was chosen to enable for high resolution (i.e., 30.8 µm/voxel) to be compared to the mean grain size of the order of 1 mm. The TTC testing machine of LMPS was utilized [START_REF] Buljac | Digital Volume Correlation: Review of Progress and Challenges[END_REF].

Its axial load capacity is ±20 kN (Figure 1(a)). indentation force vs. stroke. Five tomographic acquisitions (red lines) were performed (Table 1).

The green circle depicts the first drop induced by the indentation load apart from those associated with scan acquisitions

The hardware parameters of the X-ray tomograph are gathered in Appendix A. load increments (Table 1). One scan was also acquired post-failure (i.e., F i = 19850 N ). Once reconstructed, the volumes prior to failure were registered via DVC analyses. In Figure 1

Reduced Basis for DVC Analyses

In the present study, an integrated DVC framework was developed, which was specifically designed to compare different constitutive laws. It consisted in performing numerical simulations to construct reduced kinematic bases in which the displacement fields were mechanically (i.e., statically and kinematically) admissible contrary to standard DVC algorithms that do not make such hypotheses [START_REF] Bay | Methods and applications of digital volume correlation[END_REF][START_REF] Buljac | Digital Volume Correlation: Review of Progress and Challenges[END_REF]. For indentation experiments, reduced bases can be constructed [START_REF] Bouterf | Digital Volume Correlation Applied to X-ray Tomography Images from Spherical Indentation Tests on Lightweight Gypsum[END_REF]. Contrary to the afore-mentioned work that did not model the crushing zone so that boundary conditions became the unknown degrees of freedom, the volume in the close vicinity of the indentor was analyzed. Within such framework, three different scales of analysis are possible for any considered constitutive law. First, the applied force is compared to simulation results. Second, the displacement fields are computed at a scale compatible with numerical convergence. Third, the quality of the model is probed at the voxel scale thanks to the gray level residuals.

The reduced displacement basis consisted of seven fields

u rbt (t x , t y , t z ) = t x e x + t y e y + t z e z u rbr (x, ω x , ω y , ω z ) = ω x r yz (y, z) + ω y r zx (x, z) + ω z r xy (x, y) u ind (x, F i , f, CE) = u F E (x, F i , f, CE) -u F E (x, F 0 , f, CE) (1)
where u rbt denotes the rigid body translation vector, u rbr the displacement field induced by three rigid body rotations, and u ind the so-called indentation displacement field. Given the fact that the first scan was acquired in a pre-loaded state (F 0 ), the reference configuration was not the unloaded state. Consequently, the indentation field was corrected by the displacement field computed for the corresponding indentation force F 0 (Equation ( 1)). In the present case, small rotations occurred, which explains the linearity with respect to the rotation amplitudes and leads to simple expressions for the corresponding fields (e.g., r xy (x, y) = xe y -ye x ). The fields u F E were constructed with finite element (FE) simulations that provided results for different indentation forces F i , friction coefficients f between the indentor and Bohus granite, and various constitutive equations (CE). In the FE simulations, the reference configuration was the load-free state.

One key parameter that is introduced hereafter allows the faithfulness of the FE simulations to be quantified. If the latter ones are fully consistent with the experiment, it should vanish.

Therefore, the smaller the absolute value of this new parameter, the more trustworthy the model prediction. The seventh degree of freedom thus becomes this correction factor c that allows small offsets to the reference solution to be accounted for (i.e., (1 + c)u ind ). The DVC analyses consisted in determining the following seven amplitudes

• three rigid body translations t x , t y , t z

• three rigid body rotations ω x , ω y , ω z

• one correction factor c (at convergence) through the minimization of the sum of squared gray level residuals over the considered region of interest (ROI)

2 (t x , t y , t z , ω x , ω y , ω z , c) = ROI ρ 2 (x, t x , t y , t z , ω x , ω y , ω z , c) (2)
with

ρ(x, t x , t y , t z , ω x , ω y , ω z , c) = I 0 (x) -I i (x + u m (x, t x , t y , t z , ω x , ω y , ω z , c)) (3)
where the measured displacement field u m read

u m (x, t x , t y , t z , ω x , ω y , ω z , c) = u rbt (t x , t y , t z ) + u rbt (x, ω x , ω y , ω z ) + (1 + c)u ind (x, F i , f, CE) (4)
and I 0 denotes the gray level volume in the reference configuration, I i the volumes in the deformed configurations. In the minimization scheme with respect to the sought degrees of freedom, c was not updated. Its value was only assessed at convergence so that the reference solution was probed as well as its first order deviation at convergence for which the rigid body motions were properly accounted for. Consequently, the predictive capacity of each model is assessed in terms of this correction factor c (i.e., the closer c to zero, the better the model).

The volumes were processed using the Correli 3.0 framework [26] in which A Gauss-Newton scheme was implemented for the minimization of the sum of squared gray level residuals. The kernels of Correli 3.0 only process meshes made of 4-noded tetrahedra (T4) [START_REF] Hild | Toward 4d mechanical correlation[END_REF]. In the present case, the FE and DVC meshes shared the same nodes even though the interpolation hypotheses

were not identical (Figure 3). The Hessian matrix [H] and the right hand side vectors {b} were computed with the selected discretization (Figure 3)

H ij = ROI (∇ ∇ ∇I 0 (x) • N i (x)) (∇ ∇ ∇I 0 (x) • N j (x)) (5)
and

b i = ROI (I 0 (x) -I t (x + u(x)) (∇ ∇ ∇I 0 (x) • N i (x)) ( 6
)
where u is the current estimated of the displacement field, and N j (x) the vectorial shape functions.

Congruential transformations were performed on the previous DVC system to account for the reduced basis in a non intrusive way. They consist in writing a master-slave transformation matrix

[T] in which the master degrees of freedom are the seven amplitudes x, t x , t y , t z , ω x , ω y , ω z , c, which are gathered in the column vector {a}, and the slaves are the nodal displacements of the finite element mesh (i.e., column vector {υ})

{a} = [T]{υ} (7)
Each column of matrix [T] then corresponds to one of the seven selected displacement fields (Equation ( 1)). The minimization scheme then consisted in iteratively updating the amplitude corrections δ{a} by solving linear systems

[T] [H][T] δ{a} = [T] {b} (8)
In the present case, the correction parameter was not updated but, at convergence, it was assessed as the first order correction to be applied to the indentation field u ind . With such an implementation, the Dirichlet boundary conditions of the finite element simulations were made consistent with the experiment, and thus the quality of the selected constitutive could be probed in terms of applied force, of its faithfulness with the correction factor c, and with gray level residuals computed for each voxel belonging to the considered ROI.

To assess u ind , FE analyses were performed using the commercial code Abaqus explicit [START_REF]Abaqus analysis user's manual version[END_REF].

The rock geometry was meshed with linear reduced integration (C3D8R) brick elements (Figure 3).

The bottom surface of the sample was motionless. The indenter was modeled as a 3D analytical rigid surface. A vertical displacement with constant velocity was applied to the indenter. The contact force was captured by outputting the reaction force. As a result, the numerical forcepenetration response could be obtained. Two contact assumptions were made, namely, frictionless and Coulomb friction with a coefficient f = 0.4, noting that results for intermediate frictional coefficients did not provide much effect [START_REF] Carlsson | On frictional effects at inelastic contact between spherical bodies[END_REF]. The mesh was adapted (i.e., refined) in the contact area. In the most advanced constitutive equation, the Drucker-Prager law [START_REF] Drucker | Soil mechanics and plastic analysis of limit design[END_REF] was considered with variable dilation angle coupled with an anisotropic damage model [START_REF] Denoual | Dynamic fragmentation of brittle solids: A multi-scale model[END_REF][START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF]. The constitutive equations were introduced in Abaqus explicit via a VUMAT subroutine [START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF]. Additional details of such FE analyses can be found in Ref. [START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF]. In the following analyses, the present model, which accounts for two different inelastic mechanisms, will be compared to predictions with the elastoplastic part (i.e., with no damage), and an elastic Ansatz. The parameters of the three constitutive models are gathered in Table 2. The elastic (E), elastoplastic (EP), and elastoplastic coupled with damage (EPD) models are detailed in Appendix B.

Sensitivity analysis for the selected constitutive laws

For the investigated models, the following sensitivity analysis was performed. First, the macroscopic response in terms of indentation force F i vs. penetration depth h was computed for the three laws (Figure 5). There is no significant effect of the friction coefficient on the macroscopic response. This observation is in agreement with the results reported by Carlsson et al. [START_REF] Carlsson | On frictional effects at inelastic contact between spherical bodies[END_REF] and Mostafavi et al. [START_REF] Mostafavi | Quantifying yield behaviour in metals by X-ray nanotomography[END_REF]. It was also confirmed by a recent study on the same material [START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF]. Conversely, with increasing applied force, the difference between elastic and nonlinear simulations increases.

Both nonlinear models lead to the same macroscopic response. This observation is related to the fact that the damage state at the maximum simulated penetration is still very limited in terms of level and region over which it is active (see Section 4). Therefore, the force-penetration response is not affected by introducing damage, which was also reported in Ref. [START_REF] Shariati | A damage model for granite subjected to quasi-static contact loading[END_REF]. Since DVC analyses used two different ROIs, the same type of analysis was performed for the simulated displacement fields over two different regions. First, the whole DVC ROI (Figure 3) was considered and displacement differences were assessed for identical indentation depths. For any comparison, the standard displacement difference (SDD) was computed. For any given constitutive model, the SDD between results with and without friction remains very small (when expressed in voxel, Figure 6(a)). It is therefore expected that it will hardly be detectable via DVC since measurement uncertainties are generally higher than these levels [START_REF] Buljac | Digital Volume Correlation: Review of Progress and Challenges[END_REF]. Conversely, the SDD is larger for nonlinear simulations with respect to elastic calculations, especially for higher indentation depths. The differences between the two nonlinear models remain limited and of the same order of magnitude as for friction.

It was decided to consider a smaller region centered about the indentation point such that |x| < 1.85 mm, |y| < 1.85 mm, and -1.85 < z < 0 mm (see Figure 3). It is referred to as reduced ROI. Overall, the SDDs are higher in the reduced ROI (Figure 6(b)) than in the first ROI (Figure 6(a)). Yet, they remain too small to capture the effect of friction, and possibly that of the two nonlinear models. The reduced ROI is more sensitive for discriminating elastic vs. nonlinear kinematic bases. It will therefore be considered in the following discussions. The displacement differences in the axial direction between elastoplastic and elastic predictions are shown in Figure 7. For the first scan, these differences are small (i.e., in the micrometer range) because elasticity was the dominant deformation mechanism even in the reduced ROI. As the applied load increases, the differences between the two models become more pronounced. However their magnitude remains small in comparison with the selected resolution (i.e., 30.8 µm per voxel). Figure 8 shows the displacement differences in the axial direction between the elastoplastic (EP) and damage (EPD) predictions. Their levels are very small in comparison to the physical size of each voxel. The major differences occur along the periphery of the contact area where damage initiates (Figure 18), which leads to softening that induced these small differences.

DVC Results

The DVC analyses were run on the ROI shown in Figure 3. Even though this ROI is less sensitive than the reduced ROI considered in the sensitivity study (Figure 6), it was selected to use more voxels to evaluate the seven degrees of freedom (i.e., ≈ 30 Mvx for the DVC ROI vs. 864 kvx for the reduced ROI).

Elastic (E) analyses

For each scan, DVC analyses were run for different simulated load levels F i . The root mean square (RMS) gray level residuals were computed over the reduced ROI and are reported in Figure 9.

For any analyzed scan, the residuals are sensitive to the selected load levels and minimum levels are clearly observed for all three load levels. As the indentation load is increased, the residuals gradually increase as the proposed solutions describe less precisely the experiment. Conversely, there is virtually no difference between the case with and without friction.

In terms of minimum RMS residual levels (see table in Figure 9), except for the second scan for which the load level is fully consistent with its experimental counterpart, the load levels at minimum residual over-estimate the experimental level. This is particularly true for the third scan (i.e., the highest indentation force). One additional piece of information extracted from the DVC analyses is related to the correction factor c for all reported results. As explained in Section 2.2, the closer c to zero, the more faithful the considered model. Figure 10 displays, for all three scans, how the correction factor changes with increasing load. In all cases, there is a unique solution for which c = 0, which indicates that the corresponding displacement field is the best with the selected parameters. Interestingly, the load levels for the first two scans are very close to the actual level. Conversely, this is no longer the case for the third scan. All these observations indicate that linear elasticity was not able to properly describe all the physical phenomena involved in the reduced ROI especially for the third scan. (thick lines) and f = 0.4 (thin lines). The force level when c = 0 is reported in the table for each analyzed case.

Elastoplastic (EP) analyses

The second set of results is related to elastoplastic simulations. Figure 11 shows that the overall trends observed in elastic simulations are equivalent. However, from a quantitative point of view, the minimum levels of RMS residuals were very close to the experimental observation. They still departed for the third scan but not as much as with elastic simulations (Figure 9). The effect of friction was even more limited in the present simulations compared to the previous ones. All the conclusions drawn from the RMS residuals are confirmed by the correction coefficient reported in Figure 12. In particular, load levels that cancel out the correction factor c were very close to the experimental value except for the third scan. Even though the relative sensitivity of the elastic and elastoplastic models was shown to be in the sub-voxel range (Figure 6), the present results show that the elastoplastic model better captured the kinematics in the reduced ROI. The two complementary quantities, namely, the RMS residuals and the correction factor proved to be very useful for discriminating the two models.

Damage (EPD) Model

The complete EPD model is now investigated. The minimum RMS residuals (Figure 13) were virtually identical to those observed with the elastoplastic model (Figure 11). This result is due to the fact that the kinematic sensitivity (Figure 8) between the two models was very low (i.e., well below the physical voxel size). The effect of friction was essentially insignificant. The correction factors c are reported in Figure 14. When compared to those reported for the elastoplastic model (Figure 12), it is concluded that both models captured in the same way the overall material response beneath the indentor, and that friction did not play a significant role.

Discussion

The first set of simulations assumed frictionless contact between the indentor and Bohus granite (i.e., f = 0). The RMS residuals and correction factors are gathered in Table 4. For the first load level, all models had the same quality in terms of gray level residuals. This observation was still true for the second scan (with a very slight advantage for the nonlinear models). Conversely, the difference was more significant for the last scan for which the RMS residuals were lower for the two nonlinear models in comparison with the elastic response. The correction factor was also closer to 0 for the nonlinear models. All these observations show that the nonlinear models better captured the deformations beneath the indentor. At this stage, there was no clear difference between the two nonlinear models. Finite element analyses were also run with a non vanishing friction coefficient (f = 0.4). When comparing the results reported in Table 5 with f = 0.4 to those of Table 4 (when f = 0), it is concluded that the effect of friction was very limited. When nonlinear models were considered, virtually identical results were obtained. This observation is in line with all the previous results and those reported on nano-structured oxide dispersion strengthened steel [START_REF] Mostafavi | Quantifying yield behaviour in metals by X-ray nanotomography[END_REF]. It was also numerically observed that the predicted force-penetration response was not affected by frictional effects [START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF]. In Figure 15, the predicted equivalent plastic strain fields using the EPD model are displayed when the indentation force was equal to 15230 N (i.e., scan #3) and 19850 N (i.e., ultimate load).

The fields are only shown for one half of the DVC ROI (Figure 3). The plastic zone is associated with crushed material due to high pressures under the contact surface as well as shear zones with multiple microcracks. The plastic region extent is similar in both frictionless and frictional cases (i.e., 4 mm in diameter and 3.6 mm in depth for the ultimate load), and consequently the force-penetration response was not significantly affected by frictional effects. Figure 16 displays three sections of the last volume (i.e., scan #4), which corresponds to the post-mortem state of indented Bohus granite (Table 1). The dark zones on the upper parts of the sagittal and coronal sections highlight the comminuted material, which underwent inelastic deformations. The extent of the comminuted zone was compared with the predicted plastic zone (yellow circles). A very good correspondence is observed, which further validates the elastoplastic predictions of the two nonlinear models. The EPD model enables the initiation probability P I to be computed using the Weibull parameters (Table 2), which would correspond to the failure probability P F if the weakest link assumption applied (Appendix B). Figure 17 shows the change of the initiation probability with the indentation force when friction was accounted for or not. Very similar predictions are observed. In the present experiment, the first load drop (green circle in Figure 1) occurred around 9 kN. This level is consistent with the indentation force interval that yields initiation probabilities such that 0 < P I < 1 (i.e., 7 < F < 12 kN). In the present case, the weakest link assumption did not apply and damage grew beyond the first load drop as the applied load could be doubled prior to final failure (Figure 1(b)). Figure 18 shows damage fields associated with the first principal stress when the indentation force was equal to 15230 N (i.e., scan #3) and 19850 N (i.e., ultimate load). Damage occurred at the periphery of the plastic zone (Figure 15), where the confining stresses were not very high. For this field, there are differences in terms of damaged zone size when friction was accounted for or not. It is interesting to note the elongated damaged zone along the dominant crack in the simulations, which was also observed experimentally (Figure 16(c)) and in terms of damage extent, the frictional case was closer to the experimental observations. The EDM model predicted the formation of two splitting cracks. From the experimental observation (Figure 19), it is concluded that one of them propagated earlier than the other one.

Conclusion

Spherical indentation of Bohus granite was investigated using Digital Volume Correlation (DVC).

The aim was to evaluate the faithfulness of different constitutive laws of the indented granite and the contact properties between the rock and the indentor. A new integrated DVC framework was introduced in which the measured quantities were associated with mechanically admissible (i.e., computed) displacement fields. Each investigated law could be independently probed against global data (i.e., indentation force), its kinematic trustworthiness assessed with the so-called correction parameter associated with simulated displacement fields using meshes with 200 µm long elements, and gray level residuals computed at the voxel scale (i.e., ca. 30 µm). Therefore, three different scales of analyses were covered by such framework.

The most important results concerning the investigated constitutive models are summarized as follows:

• Compressible elastoplasticity should be accounted for to achieve high accuracy in terms of predicted load level and displacement fields underneath the indentor. For the latter ones, DVC residuals enabled for the differentiation of linear elastic vs. nonlinear models even though displacement differences remained less than one voxel. Furthermore, the introduced correction factor (further probing the faithfulness of each model) proved very useful in determining the predicted indentation load levels with the selected models.

• Even though the frictional effects between the indentor and the tested granite remained very limited in terms of plastic zone size and applied load, they led to an extended damage pattern by influencing the corresponding (damage) variables.

• The damage model based on Weibull statistics was able to determine the indentation fracture pattern prior to extensive failure, in addition to the level of first initiation event (i.e., load drop).

Such results are further evidence of the suitability of the coupled elastoplastic/damage model for predicting nonlinear mechanisms that occur in indented hard rocks such as Bohus granite.

where E denotes the Young's modulus, ν the Poisson's ratio, and 1 the second order identity tensor. In elasticity, the elastic strain tensor e is equal to the infinitesimal strain tensor .

Elastoplasticity (EP)

Since the strain levels are assumed to remain small, the strain tensor is additively partitioned into elastic and inelastic parts

= e + i ( 10
)
where i denotes the inelastic strain tensor. The Drucker-Prager [START_REF] Drucker | Soil mechanics and plastic analysis of limit design[END_REF] yield function F y reads

F y = q -p tan(β) -d ( 11
)
where q is von Mises' equivalent stress, p the hydrostatic pressure (i.e., p = -1/3(σ σ σ : 1)), d the cohesion, and β the friction angle.

The flow potential reads

G = q -p tan(ψ) ( 12
)
where ψ is the dilation angle [START_REF] Shariati | On the Inelastic Mechanical Behavior of Granite: Study Based on Quasi-oedometric and Indentation Tests[END_REF] ψ = tan -1   3 3

˙ i a ˙ i v -1   (13)
˙ i a the inelastic axial strain rate, and ˙ v a the inelastic volumetric strain rate.

Elastoplasticity Coupled With Damage (EPD)

The previous model essentially describes the behavior in compressive (i.e., confined) states. In the present case, it is activated in the immediate vicinity of the indentation zone [START_REF] Shariati | On the Inelastic Mechanical Behavior of Granite: Study Based on Quasi-oedometric and Indentation Tests[END_REF][START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF]. Farther away from this compacted zone, cracks may initiate due to tensile stresses [START_REF] Shariati | A damage model for granite subjected to quasi-static contact loading[END_REF]. To describe the early stages of such mechanism, the so-called DFH model is considered [START_REF] Denoual | Dynamic fragmentation of brittle solids: A multi-scale model[END_REF][START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF] and coupled with the previous one. It was already applied in the study of dynamic fragmentation of Bohus granite [START_REF] Saadati | Granite rock fragmentation at percussive drilling -experimental and numerical investigation[END_REF][START_REF] Saadati | A numerical study of the influence from pre-existing cracks on granite rock fragmentation at percussive drilling[END_REF][START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF].

An anisotropic damage model is considered. In the principal frame, the compliance tensor of damaged elements becomes

[S D ] = 1 E       1 1-D1 -ν -ν -ν 1 1-D2 -ν -ν -ν 1 1-D3       (14)
and the growth law of each damage variable D i associated with principal stress σ i reads

d 2 dt 2 1 1 -D i dD i dt = 6S(kC 0 ) 3 λ t ( σ i (t)) if σ i > 0 and dσ i dt > 0 (15)
with

V F E λ t ( σ i (t)) =      0 if σ i (t) < σ k max 1, V FE λ 0 σi(t) σ0 m otherwise ( 16
)
where σ i is the i-th effective principal stress (i.e., σ i = σ i /(1 -D i ), with no index summation),

V FE the volume of the considered finite element, m and σ m 0 /λ 0 the Weibull parameters [START_REF] Weibull | A statistical theory of the strength of materials[END_REF], C 0 the longitudinal wave speed so that the crack propagation velicity is kC 0 (with k = 0.38), and S = 3.74 the dimensionless shape parameter of the relaxation zones [START_REF] Saadati | A numerical study of the influence from pre-existing cracks on granite rock fragmentation at percussive drilling[END_REF]. The stress σ k is randomly selected for each finite element as the initiation level for the first crack according to the Weibull model

σ k = σ 0 - log(1 -P k ) λ 0 V FE 1/m (17)
where P k denotes the initiation probability, which is randomly selected in a uniform distribution ranging from 0 to 1. If the weakest link hypothesis applies, the initiation probability is equal to the cumulative failure probability of the considered element

P F = 1 -exp -λ 0 V FE σ k σ 0 m ( 18
)
and the corresponding mean failure stress becomes

σ F = σ 0 (λ 0 V FE ) 1/m Γ 1 + 1 m ( 19
)
where Γ is the Euler function of the second kind [START_REF] Abramowitz | Handbook of Mathematical Functions[END_REF]. If the failure probability of the whole structure is to be evaluated, the volume V FE of any element has to be replaced by the effective volume V eff [START_REF] Davies | The statistical approach to engineering design in ceramics[END_REF].

Figure 1 :

 1 Figure 1: (a) In situ testing machine utilized for the reported indentation test. (b) Corresponding

Figure 2 :

 2 Figure 2: (a) 3D rendering of the volume in the reference configuration (scan # 0). (b) Corresponding gray level histogram

Figure 3 :

 3 Figure 3: C3D8R mesh for numerical simulations (left) and T4 mesh (right) used for DVC analyses. The origin of the frame is located at the indentation point. The reduced ROI is such that |x| < 1.85 mm, |y| < 1.85 mm, and -1.85 < z < 0 mm (see blue box)

Figure 4

 4 Figure4shows the displacement fields u z (in the axial direction) for the elastoplastic predictions when damage was included (EPD). Most of the deformation concentrates around the indentation point. The maximum amplitude is about 90 µm (or 3 vx) for the first scan, 160 µm (or 5.3 vx) for the second scan, and 220 µm (or 7.3 vx) for the third scan. Such levels are compatible with DVC analyses and validate the selected resolution (i.e., 30.8 µm per vx).

Figure 4 :

 4 Figure 4: Axial displacement fields u z (expressed in µm) predicted by the elastoplastic model for the three scans. Top row: complete FE model, bottom row: DVC ROI (see Figure 3). (a,d) Scan #1, (b,e) Scan #2, (c,f) Scan #3

Figure 5 :

 5 Figure 5: Sensitivity of the indentation depth vs. applied force response for elastic (E), elastoplastic (EP) and Damage (EPD) simulations without and with friction (w/ fr.)

Figure 6 :

 6 Figure 6: Sensitivity analysis of displacement differences between elastic analyses (E) with or without friction, elastoplastic analyses (EP) with or without friction, damage analyses (EPD) with or without friction, elastic and elastoplastic simulations (E-EP) with no friction, damage and elastoplastic simulations (EPD-EP) with no friction. Standard displacement differences computed over the whole DVC ROI (a) and the reduced ROI (b). The physical size of one voxel is 30.8 µm

Figure 7 :

 7 Figure 7: Axial displacement differences δu z (expressed in µm) between the elastoplastic and the elastic models for the three scans. The physical size of one voxel is 30.8 µm. Top row: complete FE model, bottom row: DVC ROI (see Figure 3). The blue boxes depict the reduced ROI. (a) Scan #1, (b) Scan #2, (c) Scan #3

Figure 8 :

 8 Figure 8: Axial displacement differences δu z (expressed in µm) bewteen the elastoplastic (EP) and damage (EPD) models for the three scans. The physical size of one voxel is 30.8 µm. Top row: complete FE model, bottom row: DVC ROI (see Figure 3). The blue boxes depict the reduced ROI. (a) Scan #1, (b) Scan #2, (c) Scan #3

Figure 9 :

 9 Figure9: Root Mean Square (RMS) residual as a function of applied force in elastic (E) simulations when f = 0 (thick lines) and f = 0.4 (thin lines). In the present cases, the results are very close (i.e., the two lines can barely be distinguished). The minimum level for each analyzed case is reported in the table.

Figure 10 :

 10 Figure 10: Correction factor c as a function of applied force in elastic (E) simulations when f = 0

Figure 11 :

 11 Figure 11: Root Mean Square (RMS) residual as a function of applied force in elastoplastic (EP) simulations when f = 0 (thick lines) and f = 0.4 (thin lines). The minimum level for each analyzed case is reported in the table.

Figure 12 :

 12 Figure 12: Correction factor c as a function of applied force in elastoplastic (EP) simulations when f = 0 (thick lines) and f = 0.4 (thin lines). The force level when c = 0 is reported in the table for each analyzed case.

Figure 13 :

 13 Figure 13: Root Mean Square (RMS) residual as a function of applied force in elastoplastic (EP) simulations when f = 0 (thick lines) and f = 0.4 (thin lines). The minimum level for each analyzed case is reported in the table.

Figure 14 :

 14 Figure 14: Correction factor c as a function of applied force in elastoplastic (EP) simulations when f = 0 (thick lines) and f = 0.4 (thin lines). The force level when c = 0 is reported in the table for each analyzed case.

Figure 15 :

 15 Figure 15: Plastic zones predicted with the EPD model for DVC ROI (see Figure 3). (a) Plastic zones for 15230N when f = 0 and (b) when f = 0.4. (c) Plastic zones for 19850N when f = 0 and (d) when f = 0.4.

Figure 16 :

 16 Figure 16: Post-mortem (scan #4) and predicted comminuted zone. (a) x -z (sagittal), (b) y -z (coronal), (a) x -y (transverse) sections. The cyan circles depict the boundary of the predicted plastic zone (Figure15). The red circles show the extent of the damage zone (Figure18) when f = 0 (dashed line) and f = 0.4 (solid line).

Figure 17 :

 17 Figure 17: Initiation probability P I predicted by the EPD model for f = 0 and f = 0.4.

Figure 18 :

 18 Figure 18: (a) Damage field from FE simulations. (b) Damage fields for 15230N when f = 0 and (c) when f = 0.4. (d) Damage fields for 19850N when f = 0 and (e) when f = 0.4.

Figure 19 :

 19 Figure 19: (a) Top transverse view of the Post-mortem (scan #4) state where one splitting crack eventually led to the fracture of the tested sample. The green box shows the sub-region shown in Figure 16(c). (b) 3D rendering of thresholded scan #4 to reveal the comminuted zone and splitting crack.

Table 2 :

 2 Material parameters for the three selected models after Ref.[START_REF] Saadati | On the mechanical behavior of granite material with particular emphasis on the influence from pre-existing cracks and defects[END_REF], 2 after Refs.[START_REF] Saadati | On the mechanical behavior of granite material with particular emphasis on the influence from pre-existing cracks and defects[END_REF][START_REF] Shariati | On the Inelastic Mechanical Behavior of Granite: Study Based on Quasi-oedometric and Indentation Tests[END_REF],3 after Ref.[START_REF] Shariati | A damage model for granite subjected to quasi-static contact loading[END_REF], 4 after Ref.[START_REF] Shariati | Study of frictional effects of granite subjected to quasi-static contact loading[END_REF]

	Model	E 1	EP 2	EPD 3 (f = 0) EPD 4 (f = 0.4)
	Young's modulus, E (GPa)	52	52	52	52
	Poisson's ratio, ν	0.25	0.25	0.25	0.25
	Mass density (kg/m 3 )	2630	2630	2630	2630
	Cohesion, d (MPa)		153	153	153
	Friction angle, β (°)		51.7	51.7	51.7
	Dilation angle, ψ		see Eq. (13)	see Eq. (13)	see Eq. (13)
	Weibull modulus, m			24	12
	Mean failure stress, σ F (MPa)			120	75
	Effective volume, V eff (mm 3 )			1	2
	1

Table 3

 3

		: DVC analysis parameters
	DVC software	Correli 3.0 [26]
	Image filtering	none
	Element length (mean) 7 vx (220 µm)
	Shape functions	linear (T4)
	Mesh	see Figure 3
	Matching criterion	sum of squared differences (Equation (2))
	Reduced basis	see Equation (4)
	Interpolant	cubic

Table 4 :

 4 Model comparison for the three analyzed scans in terms of RMS gray levels computed over the reduced ROI ( ) and correction factor c when f = 0

			E		EP
	scan #	(GL)	c	(GL)	c	(GL)	c
	1	6.70	2.5 × 10 -3	6.70	-2.4 × 10 -2	6.70	-2.4 × 10 -2
	2	7.25	6.9 × 10 -2	7.21	1.6 × 10 -3	7.21	2 × 10 -4
	3	8.82	3.1 × 10 -1	8.29	1.0 × 10 -1	8.29	1.0 × 10 -1

Table 5 :

 5 Model comparison for the three analyzed scans in terms of RMS gray levels computed

	over the reduced ROI ( ) and correction factor c when friction is account for (f = 0.4)
			E		EP		EPD
	scan #	(GL)	c	(GL)	c	(GL)	c
	1	6.70	1.6 × 10 -2	6.70	-2.4 × 10 -2	6.70	-2.4 × 10 -2
	2	7.25	8.7 × 10 -2	7.21	3.5 × 10 -3	7.21	2 × 10 -4
	3	8.89	3.4 × 10 -1	8.30	1.0 × 10 -1	8.30	1.0 × 10 -1

Acknowledgments

The authors would like to thank Dr. Kenneth Weddfelt at Epiroc Rock Drills AB for helpful discussions. This work was partially funded by Agence Nationale de la Recherche under grant ANR-10-EQPX-37 (MATMECA) and by Epiroc Rock Drills AB.

Conflict of interest

The authors declare that they have no conflict of interest.

Appendix A: DVC hardware parameters

Appendix B: Constitutive Laws

In this appendix, the three investigated constitutive models are detailed. The last two models required user defined subroutines to be developed within the explicit version of Abaqus.

Elasticity (E)

Isotropic elasticity is assumed. The Cauchy stress tensor σ σ σ is related to the elastic strain tensor

e by e = 1 + ν E σ σ σ -ν E (σ σ σ : 1)1 [START_REF] Maire | Quantitative X-ray tomography[END_REF]


Antoine Mazières
email: antoine.mazieres@gmail.com

Alexandre Thomas

Romuald De La Cruz
email: romuald.de-la-cruz@gendarmerie.interieur.gouv.fr

Notes on building an open data portal for a French police force

Keywords: open data, open government, police, gendarmerie, France

Le Baromètre Numérique is a dedicated open data portal developed by the French Gendarmerie Nationale. It provides data with respect to digital services maintained by or related to this civil service. These notes document some background elements and development directions of this project. We aim to update these notes as the project evolve.

Context Open government

By the end of the 1990's, the significance of the Internet as a governance platform started to be widely acknowledged, and considered through various analogies with emerging open source and open data communities. Several public initiatives throughout the 2000's led to the Open Government Partnership1 in 20112 which brought together 77 countries around principles and commitments towards digital transformation, bearing on a number of areas such as governance, justice, citizenship, health and the fight against corruption. Broadly speaking, open government endeavors aim at adapting democratic principles of public accountability and transparency into the digital age, and empowering citizens participation and contribution to the public decision making process.

Though generally supported by government doctrine and public opinion, these axioms still have to overcome numerous cultural and practical challenges to be implemented within the structures and processes of every administration and political entity.

Public tech fellowships

One of the many pitfalls to navigate is the tight tech labour market where big tech and startup companies seem to have a greater advantage in alluring the relevant workforce, such as programmers, designers, data scientists and jurists. To get around the lack of manpower, a number of so-called public tech fellowships have been set up to attract necessary talents. Pioneered in 2012 by the Presidential Innovation Fellows program3 in the United States, it has been followed by likely minded initiatives such as the Public Interest Entrepreneurs program4 in France (2017, Entrepreneurs d'Intérêt Général, EIG), Tech4Germany5 in Germany (2018) and the Innovation Fellowships6 in the United Kingdom (2020) 7 .

These institutional set-ups are generally open through a competitive selection for well-funded short-term contracts with the mandate to swiftly explore and prototype high-impact services with a strong use of digital tools and methods. Participants usually have a high-level reporting line which contribute to the program prestige while helping to ease the relation with the administrations involved in the project.

The open data portal described here was developed in the context of the 5 th cohort of the Entrepreneur d'Intérêt Général program, between September and June 2022, at the Gendarmerie Nationale.

Gendarmerie Nationale

Gendarmerie Nationale (GN) is, along with Police Nationale (PN), one of the two main police forces in France. While PN has authority mainly in big cities, GN is the default police force in most of the rural and suburban areas which are less populated. As a result, GN's authority reaches, like PN, around 50% of the French population but covers 95% of the French territory.

The Gendarmerie inherits from policing institutions as far as from the middle-age (Maréchaussée), making it one of the most ancient French institutions. It has approximately 100, 000 agents, mostly under military status, while being, since 2009, under the authority of the Minister of Home Affairs (Ministère de l'Intérieur).

With the digitalisation of their activities since the early 2000's, GN has gained a certain visibility in several open source communities by implementing on an institution-wide scale tools such as Open Office and Linux 8 and making contributions to several codebases 9 .

Project From data intelligence to data transparency

Over the course of the last decade, GN has developed a number of digital services to interact with French citizens, such as a fully featured website, recruitment processes, a 24/7 online chat and numerous interfaces to fill administrative forms related to frauds or offences. The underlying systems have been developed along the way by different teams relying on a diverse set of technologies, sometimes with the support of external companies and third-party services.

The initial project 10 joined the EIG program with the perspective of developing a data intelligence platform for internal use. It entailed gathering and 8 https://ubuntu.com/blog/la-gendarmerienationale-upgrades-85000-pcs-to-ubuntu-desktopedition 9 Among which LemonLDAP and OCS Inventory.

10 https://eig.etalab.gouv.fr/defis/cyberimp-ct/ analyzing data from multiple sources in order to identify and represent relevant indicators for the national and territorial commands to monitor the above-mentioned digital services.

For a couple of months, we met with all the teams involved in the 15 data sources considered by the project. This data diplomacy helped us to lay down the information available and the technical challenges to process it. What appeared is that, first, only aggregated data would be available in the shortterm, yielding predefined variables that would make it difficult to craft indicators tailored to the command expectations. Second, and more importantly, that the data protection regulation implies a formal approval from the National Commission on Informatics and Liberty (CNIL) in order to centralize several data sources for a new purpose. This approval takes time and couldn't be sought in the short-term.

However, we realized that, given that we trim the available data from personal information, the legal hassle to process it for internal use would be equivalent to the one of releasing the data publicly. Therefore, instead of crafting a internal platform with limited value for the interested parties, we could endeavor developing a dedicated open data portal for GN.

Open data & police

As it joined the Open Government Partnership in 2014, the French government released two consecutive National Action Plans (2015-2017, 2018-2020) 11 to lay down the principles on which it would foster a "transparent and collaborative government". In 2016, the Law for a Digital Republic12 enforced some of these commitments, including making it mandatory for administrations to publish their data.

One caveat to this obligation is to protect personal information and the proper functioning of the administration. Police forces are both processing sensitive personal information and their activity require a certain amount of discretion if not secrecy, usually enforced by law. Therefore, police forces have generally initiated their journey to opening their data with caution, and there are not as many of them throughout the world who have opened their data as other types of civil services may have.

However, numerous initiatives are being carried out, such as the Police Data Initiative13 in the USA which gathers the publication of 120 police forcesmore than 200 datasets -and puts forward the openended "purposes of enhancing trust, understanding, innovation, and the co-production of public safety". In the UK, a national dedicated platform14 offers both datasets and APIs which enable users to access programmatically the latest information about a range of topics spanning from street-level crimes to neighborhood policing priorities. Other salient instances include the platforms from Toronto15 and New Zealand16 police forces.

In France, since 2019, administrations must publish their data on data.gouv.fr which -as of todayindexes more than 40, 000 datasets, several hundreds of which are related to police forces and published by the statistical service of the Minister of home affairs17 .

Target audiences & interfaces

We developed the Baromètre Numérique bearing in mind a number of possible audiences and use cases, among which:

• Citizens willing to know more about the underlying activity of the digital services they are using to interact with an administration.

• Journalists and researchers willing to report on these digital services or the underlying facts their activity are a proxy to.

• Other administrations or companies willing to embed this data into their own services.

• GN's agents and services themselves as a way to evaluate and emphasize their work.

Meeting, at least partially, the requirements of these different use cases requires to avoid some commons options considered for data portals, for instance:

• A list of datasets available for download along with a short description which tends to require that the user will have the time and knowledge to exploit the data with some specialized software.

• A complex dashboard with numerous and complex visualizations which might necessitate a certain amount of expertise to interpret the data or even to identify the topic at hand.

In order to try meet various degrees of police and tech savviness, we decided to provide both a minimalist visual interface and a programming interface (API).

Each page deals with only one digital service and is composed of simple isolated blocks, starting with a highlighted key figure and description. The whole site is used composed of only 3 types of visualisation, an interactive map of France and 2 bar charts, one for categories and one for timelines. A simple tag system enables the user to modify the underlying query for a set of different periods (week, month, year). A simple calendar to manage this input should enable finer queries from the web interface.

The API enables advanced usages. Similarly to a static file or a database, it allows users to access all the data but adds also the possibility to programmatically access and embed the specific up-to-date elements from a third-party program or website. However, this interface doesn't combine well with the use of traditional spreadsheet softwares and we will automate promptly regular dumps of the data on the platform data.gouv.fr.

https://www.opengovpartnership.org/

Joined by France in 2014: https://www.etalab.gouv.fr/ gouvernement-ouvert/

https://presidentialinnovationfellows.gov/

https://eig.etalab.gouv.fr/

https://tech.4germany.org/

https://no10innovationfellows.campaign.gov.uk/

The similarities between these various programs have been discussed by several members of their management teams during an international panel at the EIG 4 th cohort demo day: https://www.dailymotion.com/video/x82ilbt

https://www.etalab.gouv.fr/plan-dactionnational/

 12 Loi n o 2016-1321 pour une République numérique: https://www.legifrance.gouv.fr/dossierlegislatif/ JORFDOLE000031589829/

https://www.policedatainitiative.org/

https://data.police.uk/

https://data.torontopolice.on.ca/

https://policedata.nz/

SSMSI, https://www.interieur.gouv.fr/Interstats/


Audrey Leblanc

Facing the daily life of photojournalism: the Black Star agency's photography library and its 'métiers de femmes'

Facing the daily life of photojournalism: the Black Star agency's photography library and its 'métiers de femmes' 1 Photographic press agencies are much studied from a news perspective, a specificity by which they claim the historical role of their images and on which the history of photojournalism is built for the most part, especially from the second half of the 20 th century 2 . Black Star is one of the flagships in this prestigious history, especially known for civil rights cover in USA 3 . But this prestigious narrative of the agency's history comes up against an archive in which known images of Black Star are poorly represented and which original indexing, kept becoming the Black Star Collection at the RIC, is organized by subject, location, and author.

"Appropriate and efficient in the commercial environment of a press agency, […] this organization rarely responds to researchers' expectations", according to Thierry Gervais and Vincent Lavoie 4 . My first methodological choice is facing this heterogeneous set of black and white prints, getting back to the materiality of the collection, and considering it as an object to be apprehended as a whole 5 . It is then difficult to understand alone the meaning of the classifications and marks of which it is important, moreover, to distinguish the various temporal strata to read their function. However, these elements of organization of the collection (indexes, keywords, inventories...) outcome of the work of lesser known professions in the history of photojournalism 6 : they leave few traces in the narratives or in the archives -apart from the results of their professional actions. Facing these jobs with diverse names -librarians, researchers, picture editor and later, because of « the displacement of the Black Star Collection from a corporate press agency to a public cultural institution 7 », archivist, documentalist…8 -, is my second methodological choice to better understand the collection as it is accessible today.

A genealogy of women then appears. The first ones managed the Black Star picture library of the agency, composed of prints for black and white and slides for color. They were replaced/ succeeded by other women when the black and white part of this library was transferred to the RIC, becoming The Black Star Collection.

These women have been invisibilized -rarely mentioned in narratives of the agency's history or evoked through the prism of seduction 9 . These "métiers de femme" 10 are indeed considered ancillary to other activities that are presented as central to the funds. However, their interviews and their reports document (the history of) this ensemble/this whole, each being the heir ti the previous ones [START_REF] With | Nadya Bair for the RIC[END_REF] . The black and white prints Black Star Collection of the RIC thus asserts/assumes itself as part of a tool for the exploitation of visual production by the Black Star agency for the years 1935-1990: its photo library. Set up at the beginning/early days, the photo library collected/recovered the photographs produced with the commercial partners of the agency. Its classification was organized more systematically during the 1970s and 80s. It fell into disuse with the start in 1997 of the digitization of the items that the agency continues to sell.From this point of view, evaluated in the name of its historical importance for the visual history of the 20th century, this part of the library -which, for the black and white, circulated at the time in the form of prints -became, at the time of its institutional acquisition, an incomplete, useless, outdated object, expensive to preserve/to keep and cumbersome for the agency [START_REF] Coleman | Archive and Artefact. The Black Star Photo Agency[END_REF] . Black Star disposes of it in a general context of sales of these photo libraries by the media companies and of restructuring of the press images markets in the early 2000s [START_REF] Panzer | The Meaning of the Twentieth-Century Press Archive[END_REF] .

The despised testimonies of the women who managed the photo library and then the collection, highlight a daily history of this photography market. This oral 14 and feminine history reveals a gendered distribution of tasks, ignored by the history of photojournalism, hierarchical and largely constructed by men on the photographers and agency managers of the period, who were also men. However, the strategies adopted by the company to multiply markets, to make the whole production profitable and to limit the losses, testify to an empirical relationship to photographs, whose interpretation of the visual content and the dissemination on the markets of the illustration depend entirely on the work of these women's teams.

A genealogy of unknown women, recipients of the history of the Black Star agency's photo library

Emma Gurry is part of the staff of the agency in its early days as head of the picture library Emma 15 . Yukiko Launois, wife of photographer John Launois, begins working as a researcher at the library in 1964, when Howard Chapnick became president of the agency. She gradually increases her working time, participated in a more systematic structuring of the classification of images, becomes editor and then, shortly after the departure of Emma Gurry, takes over the responsibility of the photo library in 1973 until the end of the 1980s, early 1990s 16 .

VISUEL n°1 : Yukiko director of the photo library, devant ses tiroirs en remerciant NB pour le partage d'archives

Managed by women at Black Star, the library is taken in hand by other women at the time of its institutional patrimonialization. These women become the custodians of the memory of the past uses and functioning of the library. In 2003, Penelope Dixon and Associates is commissioned by the Canadian Cultural Property Export Review Board 17 to appraise Black Star's collection of black-and-white prints, with RIC becoming responsible for the care of the collection 18 . She recommends/advocates maintaining the collection as a whole in order to add cultural -and therefore economic -value to the transaction. The collection is officially donated to the RIC in 2005, however it is stored at the offsite warehouse until 2012 when the building is completed. Valérie Matteau 19 becomes responsible for it (2005-2012) and maintains the link with Benjamin Chapnick, the president of Black Star Agency. She organized six exhibitions between 2006 and 2009. Then, she participated in the installation of the collection in the final building of the RIC in 2012, at their opening after renovation work.In this transfer, and thanks to the expertise of these professional women, the order of the drawers is scrupulously respected. Original craft envelopes and folders, revised one by one, are kept in their initial classification, with their key words written in marker, as soon as they contain the slightest document (tear sheets, order forms, typed stories, detached captions, etc.): they form the Black Star Ephemera collection at the RIC, whose materiality "allows researchers to look at a glance at what is in the drawer, but also how the overall archive was arranged by Black Star" 20 . Especially since, according to Yukiko Launois "black and white's system didn't evolve too much from the beginning. I guess it stayed in a primitive state 21 ".

VISUEL n°2: craft envelopes

The library: an autonomous operating tool that recycles assignments for other markets

The well-known narrative of the history of photojournalism in which Black Star's fame fits suggests that the library would be the archive of its production; in particular of that valued in the stories, the news. But the library does not have a conservation function: it is another instrument of exploitation of the images produced on assignment, whatever they are, which it recovers to sell them in otherwise, on other markets. In the flow, indeed, photographs fall into the library, available for all uses and no longer only those related to their newsworthiness for a specific moment: "The agency's holdings developed in large part through commissioning or, less frequently, through purchase of work produced by photographers on speculation. The best of these pictures subsequently became part of the working picture collection and were maintained by the Black Star agency and re-used in future" 22 As Benjamin Chapnick explains, the library is autonomous and has its own activity:

"There were two aspects to the business, one was assignment, and one was existing material, our library was almost always developed from material that was left over from assignment, nobody in those days shot for library sales" 23

The two sales channels for the photographs produced do not overlap pr reflect each other: each operates according to its own logic. The assignment is an economic agreement between companies with sharing of the expenses at the time of the production of the images -at Black Star "[they] always tried to do it as an assignment" 24 . The press editorial staff, a priori the most frequent partner, bears the cost of developing the films in exchange for the scoop on the images. It does its own editing and most often keeps its own prints.

The rest is sent to Black Star, which edits these leftovers to offer them to other distribution channels 25 , such as foreign sales (by building new stories) and library's files. The library is intended to respond to iconographic requests 26 : they came in the form of letters from publishing companies mostly but also from press magazine.

The OA -"On Approval" -mark on the back of some of the prints in the collection means that the prints were considered by the editors of Life for reproduction in the magazine 27 . The proportions of published photographs from the Black Star collection found in Look (1937-1971) and Life (1936-1972) indicate that these types of sales (illustrations, series) massively irrigate these publications 28 .

VISUEL n°3 : camemberts workshop TG

The iconographic exploitation is an important daily activity that requires the agency to adapt its team and premises to respond to it 29 . The agency cannot be satisfied only with "good shots": the librarians, at the interface of the daily sales, multiple and regular over time, also make it live. Presented as secondary for its business -"at no point was the library worth more than 25% of our annual income, minimum 75% came from the assignments, and even though it created a cash turnover, it wasn't a profit center" 30 -, the agency does not however make the economy of this activity and the various markets -in which it makes profitable an 29 "as the stock grew, librarians staff grew (…) at one point we had 42 or 43 people and 25 or 27 of them were working directly with the library", BC : 11 30 BC : 13 expensive production -are strategically thought out together. The library recycles images produced once the assignment time has passed -and the assignment concerns all image productions:

-You said that stock was never more than 25% -I'm pretty sure that's accurate yes. -That's mean the other 75% is editorial -The other 75% was assignment, the editorial could corporate, but it was assignment work 31 The Black Star Ephemera Collection contains, in fact, the same type of accompanying documents (list of captions for example) for photographs of Birth of a Delphin, Atomic Blast Explosion, Roller disco, etc.

Remainders of reports sold in news; remnants of reports produced for the internal reports of companies which the agency has made a specialty in corporate; portraits of celebrities; returns of shipments abroad... Contrary to its apparent homogeneity, the library brings together very diverse prints in their production dates, their initial functions, their circulation, their status and their generations. Upon entering this operating tool, all are relieved of their assignment production description in favor of a new description in accordance with the needs of the library's activities: subjected to the same system of keywords established according to their content iconographic, the library permanently assigns all photography to its illustrative dimension. A photographer like Charles Moore thus sees his images classified for a quarter under the generic word "civil rights" when the rest becomes "women, telephone, motoring, school, indians...". However, this classification is the result of actions and human decisions of women who, on the one hand, receive the different prints for the files and, on the other hand, respond to the iconographic requests for which these prints of the library are intended.

Women at the origin of our visual culture

"I mean big lists of requests used to come from textbooks, and one researcher was assigned to filed their request. So for instance, they would say they want to illustrate infinity -some image which signifies infinity" 32 . The library team chooses the prints that could correspond to this request, sends them to the client who makes his choices and then returns them : they are reintegrated into the library -possibly as is under the term "infinity".

"The collection is divided into four series based on the original arrangement by the agency found in the filing cabinet drawers. These series are: 1. Countries and Places (drawers 1-63 or boxes 1-32); 2. World War II (drawers 64-72 or boxes 32-39); 3. Personalities (drawers 73-141 or boxes 40-71); and 4. Subject (drawers 142-206 or boxes 72-81 and portfolio) with corresponding sub-series following each series description." 33 VISUEL n°4 : schéma de Laura Potter Of the four large sections that compose it, "Countries and Places" (3.62m linear) and "Personalities" (3.82m) occupy three times more space than the other two and largely dominate the whole. They testify of the 31 BC : 46 32 YL 33 POTTER, Lauren: 25 important proportion of banal images produced and diffused as well as of the mass of potential requests to which they correspond. All are sub-organized by thematic keywords: « Within these there are a myriad of finer categories, ranging from astronomy to demonstrations, ecology to industry, military to urban renewal, Brando to Odetta, Nastase to Thatcher, Eisenhower to Reagan, Argentina to Zimbabwe, etc. » 34 At the time of Emma Gurry, there is no indexing system: everything was in Emma's head and Howard's head.

Yukiko Launois initiates a cataloguing of her husband's photographs. Then Emma Gurry generalizes this principle and builds a catalog card which allows, in addition to classifying them, to track down each image of the photo library to monitor its commercialization 35 . The resale potential of the images guides the structure of the photo library and the interpretation of the images. In order to meet the widest range of requests, the thematic keywords chosen by the librarians remain as general as possible and depend on their interpretation of the images:

"The most appropriate place to file a photography by subject is also a matter of interpretation and current application. For instance, a photograph of Martin Luther King arrested at a demonstration could be files under Demonstrations, Martin Luther King, or Civil Rights. Had the demonstration just taken place and was a topic of current news stories, it would make sense to file under Demonstrations. After King was assassinated, it would make more sense to file it under the general category of the subject's name. In more recent years, as the Civil Rights era has become an important historic subject, it would be logical to file the image under Civil Rights. A photo-researcher at Black Star would also know to look for photographs of King (or negative and contact sheets) under the name of Charles Moore, the most wellknown of the Civil Rights photographers, whose photographs were in some cases files separately at Black Star as they were so frequently requested." 36 VISUEL n°5 : exemple de BSE ex. NASA "do not file under industry"

Only few of them -as Yukiko Launois -edited for files but all the picture librarians are those who created the folder categories and chose the keywords. If a picture came in and that category did not exist, they create a new file and label it. The researchers could take initiative, but the librarian would know when that happened without monitored it neither documented how the subject headings changed: there was no ledger or list, "it was very physical going through" 37 . The organization of the library is done organically, as requests come in, without any real plan, in an empirical classification of the prints -several envelopes sometimes following/succeeding each other under the same keyword, without chronological order. The date is not necessarily associated with the visual content: it is only useful for the agency's photo library if it facilitates the availability of the image. Otherwise, it gets lost.

NB: Not all the pictures are dated. YL: No, that's very primitive. NB: So was there any system or code to dating some and not others?

34 PD: 7 35 The catalog card was thrown away, VM 36 PD: 21 37 "Still even colour photographs, which were filed under each photographer, researchers had to resort to the imagination and memory a lot", YL YL: I don't know. At some point they started including the date. In my time there was no system. We had a numbering system but it didn't correspond with the date the picture was taken; it was about the date the picture was put in the file so that doesn't help very much. We had a number system like 31978xxxxit meant it was put into the file in March 1978. NB: And what would the other four numbers (xxxx) have correlated to? YL: That would be consecutive numbering of the take, I guess. But that has nothing to do with the subject matter or day of the event.

Librarians filter the production and, in this description of the images reduced to their visual content, generate the added value that allows them to be sold; they select them to propose their dissemination and keep the memory of them:

Larry Levin (sales man) -But we were pack (…) because you never knew what was going to sell. And never knew what we needed. (…) when a librarian left, they didn't know where all your work was. And then your sales went down. (…) But the best researcher, I mean the best computers that we had, were the researchers. When I said, Oh I need a picture of such and such, I would go to one of the researchers, to Lynn or to Annie or Ann, and they note, or Joyce... (…) Dennis Brack (photograph) -(…) I think that half the money that I made from Black Star was because they knew my files so well, and the Presidents, and you know, "I need a red-headed juggler on a bicycle." (…) Jim Pickerell (photograph)-But it was filed under some different story name. That had nothing to do with it. DB-Oh yeah, they never went to the index cards unless they really had to." 38 Whether at the time of the classification of the photograph or at the time of its selection to be proposed in response to a request, it is the library staff who interprets the content of the images put into circulation on the illustrated markets, anticipated in the long term. Dependent on the expertise of these women, still largely ignored by the history of photojournalism, our visual culture has been established, at least as much as by photojournalists, by these shadowy, professional figures whose names and importance should be made known.

VISUEL n°6 : la fiche de circulation de Yukiko à Enid, de 1993

The preservation of the media past, a question of gender

The iconographic requests for which the agencies set up a photo library correspond to a daily office activity, unspectacular, described as secondary in their economic life by the professionals who hardly mention them. Transmitted by an ephemeral oral history, more difficult to make known and minimized, it has been neglected by historians of photojournalism who have preferred spectacular, punctual events and heroised male figures. However, it is the images exploitation tool linked to these activities that stands out here as a central archive in the history of photojournalism. Howard Becker demonstrated it in Art Worlds 39 , these "small" trades, affiliated to the technical services in the branch, could not be held/considered as secondary.

Librarians tell the daily sales of the image fonds, manage customer requests and explain the filing choices for an efficient global exploitation of these fonds ; when they are not at the initiative very often of the good

1

  I warmely thank all the women who helped me: Valérie Matteau, Gaëlle Morel, Charlene Heath, Anna Jedrzejowski, Denise Birkhofer at the RIC ; Nadya Bair and Bibia Pavard 2 HILL, Jason E., SCHWARTZ Vanessa R. (dir.) (2010) : Getting the Picture. The Visual Culture of the News, Londres, New Delhi, New York, Sidney, Bloomsbury, 2015. LAVOIE, Vincent, Photojournalismes -Revoir les canons de l'image de presse, Paris, Hazan 3 SEALY, Mark, MATTEAU (2013) ; NEUBAUER, Hendrick (1997) ; SMITH, C. Zoe. (1984) ; TOROSIAN, Michael, HIGDON, Peter (2013). And CHAPNICK, Howard (1994) ; MORRIS, John G. (2002). See bibliography and chronology by Valérie Matteau and Alexandra Gooding 4 GERVAIS, Thierry, LAVOIE, Vincent, Symposium Open up the Morgue ! How press archive are enabling a New history of Photojournalism, 2 july 2021, Rijksmuseum, Amsterdam 5 MAUUARIN, Anaïs (2020): "Images for Sale: Cards and Colours at the Photothèque of the Musée de l'Homme", in J. Bärnighausen et C. Caraffa, S. Klamm, F. Schneider, P. Wodtke (ed.). Photo-Objects. On the materiality of Photographs and Photo-Archives in the Humanities and Sciences, Berlin, Max-Planck-Institut 6 BIHL, Laurent, DOGUE, Philippe L.-J. (2020) : « Dans la caverne de l'iconographe. Entretien avec Philippe L.-J. Dogué, réalisé par Laurent Bihl », Sociétés & Représentations, n o 50, p. 119-139. LUGON, Olivier (2019) : Nicolas Bouvier iconographe, Genève, Bibliothèque de Genève/Gollion, Infolio. Photographica n°4, « Derrière l'image », Paris, Ed. de la Sorbonne, avril 2022 7 GERVAIS, Thierry, LAVOIE, Vincent (2021)

38

  Panel Discussion (2010): 8-9 39 BECKER, Howard S. (1982): Art Worlds, Berkeley: University of California Press conservation of the funds of media images for historical purposes 40 . As a true memory of still image collections, they ensure, regardless of their cultural (de)valuation, the durability of photojournalism images on the illustrated markets over time. Thus actively contributing to the structuring of the visible, the archive here renews the history of photojournalism, including at the level of the gender. 40 TIBLE, Anna (2019) : « Les documentalistes audiovisuel.les et la création des formats à base d'archives », Congrès de la Société Française de l'Information et de la Communication « Création, créativité et médiations », Actes vol. 2 « Modèles et stratégies d'acteurs »

  16 YL part avant la mise en place de la section Prostock en 1997, qu'elle ne connaît pas 17 https://www.ccperb-cceebc.gc.ca/en/index-en.html 18 Explanation of Outstanding Significance and National Importance, To Canadian Cultural Property Export Review Board, From Peter Higdon, Curatorial Manager, Ryerson University's Mira Godard Study Centre, School of Image Arts, 10 November, 2004 19 after a Master of Arts in Photographic Preservation and Collections Management à Ryerson, graduated in 2006 20 POTTER, Lauren (2013): , A Journey in Collections Management: The Creation of a Finding Aid for The Black Star Ephemera Collection At the Ryerson Image Centre, BA, Agnes Scott College, Toronto, Ontario, Canada: 12 21 YL : 28

  John Morris told it to VM 28 Black Star Research Workshop leaded by Thierry Gervais with students (2010 -2012), on Publications of Credited Black Star Photographs, in Life (p. 41), Look (p. 39)

	22 Explanation: 9
	23 BC: 3
	24 BC: 34. "The assignments were the sales department (…) If the photographer and agency initiates the story we call it a spec story",
	YL
	25 YL : 44
	26 LEBLANC, Audrey, DUPUY, Sébastien (2017) : « Le Fonds Sygma exploité par Corbis. Une autre histoire du photojournalisme »,
	Études photographiques n°35 : 88-111
	27

LUGON, Olivier, « Iconographe indépendant : émergence d'un métier dans les années 1960-70 », Journée d'étude « Iconographe et documentaliste dans les médias depuis les années 1960 », Audrey Leblanc (dir.), 10 juin 2021, Institut Pour la Photographie, Lille ; INA ; Université de Lille https://clinoeil.hypotheses.org/2890