Franck Bourrier
email: franck.bourrier@inrae.fr

David Toe

Bruna Garcia

Julien Baroth

Stéphane Lambert

Experimental investigations on complex block

Keywords: Rockfall, Experiments, Block propagation models, Topography effects, Trajectory measurements

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Introduction

The assessment of rockfall hazard, i.e. of rockfall triggering conditions and block propagation, is essential to develop mitigation strategies involving hazard zones determination and protection structures, in particular.

The analysis of rockfall triggering conditions requires field studies to identify prone-to-fall rock compartments and analysis of rockfall activity, given by historical inventories, surveys of deposited boulders or remote sensing methods, to assess triggering frequencies [START_REF] Dussauge-Peisser | Probabilistic approach to rock fall hazard assessment: potential of historical data analysis[END_REF][START_REF] Glover | Rockfall hazard and risk assessment in the Yosemite Valley, California, USA[END_REF][START_REF] Corominas | Quantitative assessment of the residual risk in a rockfall protected area[END_REF][START_REF] Rabatel | Rock falls in high-alpine rock walls quantified by terrestrial lidar measurements: A case study in the mont blanc area[END_REF][START_REF] Agliardi | Integrating rockfall risk assessment and countermeasure design by 3d modelling techniques[END_REF][START_REF] Hantz | Quantitative assessment of diffuse rock fall hazard along a cliff foot[END_REF][START_REF] Abellan | Detection and spatial prediction of rockfalls by means of terrestrial laser scanner monitoring[END_REF][START_REF] Dewez | Probabilistic coastal cliff collapse hazard from repeated terrestrial laser surveys: case study from Mesnil Val (Normandy, northern France)[END_REF].

Block propagation can be evaluated at the district scale based on empirical approaches that estimate the maximum block propagation distance using historical surveys of rockfall events. Among these approaches, the commonly used energy line method, initially developed by [START_REF] Heim | Der Bergsturz und Menschenleben[END_REF], assesses the maximum propagation distance from the intersection between the topography and a line passing by the top of the cliff, characterized by its angle with the horizontal direction [START_REF] Jaboyedoff | Technical note: Preliminary estimation of rockfall runout zones[END_REF]. Complementary, block propagation models are routinely used for the quantitative assessment of rockfall hazard (e.g. [START_REF] Dincer | Rockfall at the heritage site of the tatlarin underground city (cappadocia, turkey)[END_REF]; [START_REF] Sarro | Rockfall simulation based on uav photogrammetry data obtained during an emergency declaration: Application at a cultural heritage site[END_REF]; [START_REF] Macciotta | Preliminary approach for prioritizing resource allocation for rock fall hazard investigations based on susceptibility mapping and efficient three-dimensional trajectory modelling[END_REF]) and their use is almost exclusively limited to studies on small areas. In these models, one of the major difficulties is the development of physically consistent and field applicable approaches to model the interaction between the block and the natural terrain. Two types of propagation models exist. They either consider the block as a single material point or explicitly account for the fragment shape [START_REF] Bourrier | chap Rockfall Dynamics: A Critical Review of Collision and Rebound Models[END_REF][START_REF] Bourrier | Rockfall rebound: comparison of detailed field experiments and alternative modelling approaches[END_REF]. Although both types of approaches provided representative results on different study sites [START_REF] Jaboyedoff | Technical note: Preliminary estimation of rockfall runout zones[END_REF][START_REF] Labiouse | Half-scale experimental study of rockfall impacts on sandy slopes[END_REF][START_REF] Glover | Rockfall hazard and risk assessment in the Yosemite Valley, California, USA[END_REF][START_REF] Lu | Modelling rockfall impact with scarring in compactable soils[END_REF], several limitations of these models have been identified in the literature. The more commonly reported ones are limited capacities to model block propagation for complex topographies, e.g. ledges due to road building or complex 3D topographies [START_REF] Bourrier | Toward objective rockfall trajectory simulation using a stochastic impact model[END_REF][START_REF] Lambert | Improving three-dimensional rockfall trajectory simulation codes for assessing the efficiency of protective embankments[END_REF], and for block motion almost analogous to rolling, e.g. propagation on gentle slopes or soft soils [START_REF] Bourrier | chap Rockfall Dynamics: A Critical Review of Collision and Rebound Models[END_REF][START_REF] Spadari | In situ rockfall testing in new south wales, australia[END_REF].

Various experiments have been conducted in view of analyzing the interactions between the block and the slope surface, the block propagation processes at the slope scale, as well as for calibrating and evaluating the predictive capacities of propagation models. These studies were conducted either in the field [START_REF] Giani | Experimental and theoretical studies to improve rock fall analysis and protection work design[END_REF][START_REF] Dorren | Real-size experiments and 3-d simulation of rockfall on forested and non-forested slopes[END_REF][START_REF] Bourrier | Toward objective rockfall trajectory simulation using a stochastic impact model[END_REF][START_REF] Bourrier | Rockfall rebound: comparison of detailed field experiments and alternative modelling approaches[END_REF][START_REF] Spadari | In situ rockfall testing in new south wales, australia[END_REF][START_REF] Caviezel | Reconstruction of four-dimensional rockfall trajectories using remote sensing and rock-based accelerometers and gyroscopes[END_REF] or in laboratory conditions (e.g. [START_REF] Chau | Rockfall problems in hong kong and some new experimental results for coefficients of restitution[END_REF]; [START_REF] Labiouse | Half-scale experimental study of rockfall impacts on sandy slopes[END_REF]; [START_REF] Hu | Field, experimental, and numerical investigation of a rockfall above a tunnel portal in southwestern china[END_REF]; [START_REF] Asteriou | Effect of impact velocity, block mass and hardness on the coefficients of restitution for rockfall analysis[END_REF]; [START_REF] Garcia | Experimental and dem analysis of the dissipation involved in the collision of a boulder with a substratum[END_REF]). Most of these experiments focused on the detailed analysis of few block rebounds or block trajectories, or on the effect of specific parameters (e.g. block shape) for specific propagation conditions (e.g. propagation as a succession of flight and rebound phases). In addition, only few of these studies provide substantial and exhaustive data on blocks propagation at the slope scale. In particular, data concerning both block stopping positions and kinematics are scarce, specifically for study sites where block propagation is complex to model because of problematical topography or propagation processes.

In practice, the limited amount of available exhaustive and accurate experimental data at the slope scale entails that most of propagation models are not calibrated exhaustively and thoroughly. For a particular study site, the assessment of the accuracy of propagation simulations is limited to the analysis of the simulated stopping points of the blocks in comparison with past-events, mainly because the kinematics of the blocks cannot be easily quantified from the analysis of past events. Consequently, the assessment of the relevance of block propagation simulation works is challenging. These simulation works strongly depend on the expertise of the operator, because of incomplete model calibrations, based on scarce data available, generally limited to few past events in the study site.

In this context, the objective of this study was to provide and analyze experimental data of block propagation for the assessment of propagation models relevance on a configuration where propagation simulations is potentially problematical. For that purpose, an experimental campaign involving exhaustive measurements of block propagation on a complex study site has been designed to provide exhaustive and statistically representative data for assessing the model capacities and identifying their potential limitations for complex study sites.

First, the characteristics and the complexity sources of the study site as well as the experimental protocol are presented. Second, the experimental results are exposed in detail, considering the various data recorded. Finally, these results are discussed focusing on the analysis of the prevailing effects leading block propagation and highlighting the difficulties in modeling these trajectories.

Experiments

The study site was chosen because its topography and slope surface materials were prone to induce complex block propagation processes. Specific attention was also paid to set up controlled experimental conditions in order to quantify the parameters classically identified in the literature for having an effect on block propagation (release conditions, block mass and shape, local variability of soil properties, in particular). Finally, one major concern was the acquisition of a significant amount of data with sufficient accuracy despite non negligible constraints of safety and practical feasibility. The details of the experiments are presented in the following.

Study site

The study site, located in a quarry (Authume -France, owner: Pernot S.A, Figure 1), was selected because it offers significant complexity and variability in terms of topography and surface characteristics. The propagation paths were chosen to favor challenging-to-model block trajectories. The two selected paths exhibit combinations of gentle slopes and soft soils, favoring block motion almost analogous to rolling, and complex topographies with rapid changes in slope inclination and/or orientation. These paths are described in the following. The soils are characterised considering classifications commonly used in trajectory simulation codes that are available to design engineers. The first profile, referred to as Path A (Figures 1 and2), is characterized first by a gentle slope section, 30m in length along the horizontal axis with a 32 o inclination. The slope material is made of dry newly deposited quarry waste, mixing sand, clay and limestone fragments. This upper slope is terminated by a flatter and rougher part where boulders are more numerous, overhanging a 18m in height subvertical rock cut inclined by 10 o towards the vertical and made of compact limestone rock. The 7m in width horizontal track at the toe of this wall consists of compact quarry waste. A second 13m in height rock cut, with same characteristics as the first one, separates this track from the quasi-horizontal platform acting as terminal deposit area. The slope profile along the perpendicular to the steepest slope direction is rather uniform. On such a path, numerous block trajectories are possible. A block could directly stop on the uphill gentle slope just after release or on its terminal flatter part. It could also propagate on the gentle slope, fall on the intermediate track, and stop or propagate down to the platform. Alternatively, when reaching the upper ledge on top the first rock cut, it could directly bounce over the intermediate track and directly reach the platform. None of these potential trajectory archetypes can be a priori identified as preferential mainly because the propagation on the uphill slope is difficult to predict by expert knowledge only because its low inclination and soil mechanical characteristics limit block rebound. The second profile, referred to as Path B (Figures 1 and3) is characterized in its upper section by a 32 o in inclination slope, 40m in length along the horizontal axis. At mid-distance, the path is bordered by a rock cut on one side and by a talus on the other. This creates a so-called corridor. The soil in this upper section is made of medium soft quarry waste, mixing sand, clay and limestone fragments. Above the corridor, the soil is revegated while it was newly deposited within the corridor.

The intermediate section of Path B is characterised by two successive tracks 7m in width each. These tracks exhibit slight inclinations in opposite directions and are separated by a slope inclined by 32 o which is made of medium soft quarry waste. The second track is followed by a 27m in horizontal length and 32 o in inclination slope also made of medium soft quarry waste, terminated by a globally horizontal deposit area.

This path was chosen because of potentially substantial 3D effects in the blocks trajectories, as compared to Path A. Such effects were expected to result from the corridor in the second half of the upper section, creating a preferential propagation path, and from the presence of the slightly sloping tracks perpendicular to the mean steepest direction in its intermediate section, favouring lateral deviation.

For both paths, the tracks are bordered by a rock pile forming a more or less rounded berm, typically 0.5m in height.

These two paths thus exhibit significantly different topographical features. Path A is characterized by two subvertical rock cuts, compared to Path B mainly showing slight changes in slope inclination. Along the perpendicular to the steepest slope direction, Path A is rather uniform contrary to Path B. These differences are expected to result in different blocks kinematics evolution along these two paths. For example, high amplitude topographical discontinuities favor the occurrence of normal impacts and are thus expected to induce higher block kinetic energy dissipation as well as complex rebounds involving couplings between the components of the velocity [START_REF] Bourrier | Rockfall rebound: comparison of detailed field experiments and alternative modelling approaches[END_REF].

Overall, the two paths complement one another. Path A focuses on the effects of topographical discontinuities, gentle slopes, and soft soils, and Path B allows to investigate the influence of complex 3D topography in addition to the previous effects.

Experimental and measurements protocols

Experimental procedure

Preliminary experiments, consisting of ten block releases on each propagation path, were first conducted to identify optimal block release conditions, to set up the experimental and measurement protocols, and to design the data analysis procedure.

The main experiments consisted in the successive release of approximately fifty blocks on each propagation path using a power shovel. The number of blocks released on each profile corresponds to the larger amount of releases possible given the limited duration of the experiments. However, it is not sufficient to guarantee statistical representativeness for all the quantities explored, especially for the extreme quantiles of quantities distributions.

A release zone (4m x 4m horizontal area) was delimited at the top of each path. The vertical release heights were set at 4m for Path A and 2m for Path B. The height was larger for Path A to prevent block stopping directly on the uphill gentle slope, as observed in the preliminary experiments.

Block characteristics assessment

The blocks were extracted from the quarry and visually selected to obtain block volumes approximately ranging between 0.1 and 0.75m 3 . The weight of each block was measured using a piezoresistive force sensor (Chatillon SLC10000accuracy ±20kg). Each block was installed in a wire mesh basket connected to the force sensor. The block was weighed lifting up the sensor using the crane of a power shovel. Additionally, three principal lengths have been measured for each block. These lengths characterize the minimal parallelepiped of dimensions L 1 , L 2 and L 3 , with L 1 > L 2 > L 3 that incorporates the block. This data was used for block shape characterisation according to the classification proposed in [START_REF] Sneed | Pebbles in the lower colorado river, texas a study in particle morphogenesis[END_REF], which was recently adapted for the assessment of block shape in the field of rockfall [START_REF] Van Veen | Effects of sampling interval on the frequency -magnitude relationship of rockfalls detected from terrestrial laser scanning using semi-automated methods[END_REF][START_REF] Bonneau | Threedimensional rockfall shape back analysis: methods and implications[END_REF]. In this classification (Figure 4 -adapted from Blott and Pye ( 2008)), four main types of block shapes are differentiated : compact, platy, blade and elongate. Blade and elongate shapes potentially favour high rebounds compared to the others (compact and platy) [START_REF] Labiouse | Half-scale experimental study of rockfall impacts on sandy slopes[END_REF][START_REF] Glover | Rockfall hazard and risk assessment in the Yosemite Valley, California, USA[END_REF] while platy blocks have been identified in the literature [START_REF] Glover | Rockfall hazard and risk assessment in the Yosemite Valley, California, USA[END_REF][START_REF] Leine | Simulation of rockfall trajectories with consideration of rock shape[END_REF] for their predisposition to travel further by rolling motion.

Data concerning the blocks mass and shape are given in the section dedicated to the influence of these parameters on the block propagation.

Block trajectories assessment

Precise determination of the blocks stopping point location was conducted after each series of five blocks release to limit the duration of the experimental campaign. The theodolite used for this purpose (Leica TS02) provided measurements with an estimated accuracy of 0.1m, mainly resulting from uncertainties associated with the visual assessment of blocks gravity centres. In case of breakage of the block, the stopping point considered was the stopping point of the larger resulting fragment, if it could be identified, or the last impact point before breakage, if the block broke in several small pieces. Complementary to the stopping points location determination, the trajectory of each block was filmed to provide information on the trajectories and kinematics. Given the configuration of the study site, the safety rules established and the capacities of the cameras, it was not possible to install safely cameras covering the complete propagation paths with sufficient resolution for accurate measurements of the complete trajectories. Consequently, the quantitative analysis of block kinematics focused on measurements at specific locations of the site, called Evaluation Screens (ES) (Figures 5 and6), using cameras with shooting range focused on the ES. The locations of the evaluation screens were chosen in view of measuring the velocities at the transitions between homogeneous zones of the paths in terms of soil and slope properties. These transitions correspond to the location of topographical discontinuities. For Path A, the first evaluation screen (ES1-A) was located at the end of the uphill gentle slope, just before the first rock cut, and the second one (ES2-A) at the top of the downhill rock cut (Figure 5). For Path B, ES1-B is the contour line defined by the elevation of the corridor beginning while ES2-B was located at the downstream extremity of the first sloping track (Figure 6). Additionally, two cameras were installed to fully cover the propagation paths. The video footage from these cameras were used for global qualitative analyses of the trajectories since their low resolution did not allow accurate determination of the trajectories.

A protocol for the analysis of the video footage was designed to assess the translation and rotation velocities as well as heights of the blocks when passing through the evaluation screens. The analysis of the video footage required building a Digital Terrain Model (DTM) of the study site. A DTM (resolution: 0.2m) was thus built from a set of images, taken from a UAV and from the ground. The images were treated using photogrammetry techniques (software Agisoft V1.2.6). 20 control points covering the site, and located in a local coordinate system using a theodolite (Leica TS02), were used in the building process. Two GPS points and one geodesic point were also recorded to georeference the DTM.

The process for assessing the translation velocity consisted, first, in identifying two block positions at the slope surface (just before and just after the evaluation screen). Second, the location of these positions was identified in the three dimensions. Finally, the translation velocity was calculated from this tri-dimensional location and the block travel time between these two positions determined from the digital footage.

This process slightly differed between the case of a block passing through the evaluation screens with significant height, i.e. for a propagation by successive rebounds and flights phases, from the case where the block motion was almost analogous to rolling. In the first case, the block positions just before and just after the evaluation screen correspond to the impact points just before and just after the evaluation screen. In the second one, the two positions were selected to guarantee a distance between them significantly larger than the resolution of the point location detection process, estimated around 0.5m. The calculation of the tri-dimensional positions from the digital footage was similar for both cases. The images associated with the positions were extracted from the video footage and projected onto the digital terrain model (DTM) so that the tri-dimensional position could be identified. Finally, the calculation of the translation velocity was different. In the case of block motion almost analogous to rolling, the velocity at the evaluation screen was assimilated to the mean velocity between the two positions. For significant block passing heights, the exact translation velocity was calculated from the same quantities assuming a parabolic trajectory of the block. Details of this calculation can be found in [START_REF] Bourrier | Rockfall rebound: comparison of detailed field experiments and alternative modelling approaches[END_REF].

Complementary, a qualitative assessment of the passing height was done by visualisation of the video footage and estimation of the passing heights of the block gravity centre, discretized into four classes (contact with soil, small height : approx. 0.5m to 1m, medium height : approx. 1m to 3m, large height : >3m approx.). The passing height is defined as the distance along the vertical axis between the soil surface and the block gravity center. The rotational velocity at the evaluation sche block between the two positions with an accuracy of 1/8 revolution.

Experimental results

The experiments provided data concerning a total of 104 block releases on the two paths (Table 1). All blocks were used to assess the passing probabilities at the evaluation screens. Almost all final positions were also measured, except for two blocks released on Path A due to safety problems. Consequently, the number of measured final positions is smaller than the number of block releases. In addition, several video recordings were missing or not usable for analysis(ES1-A: 14%, ES2-A: 11%, ES1-B: 29%, ES2-B: 33% ). Indeed, the cameras batteries available had been consumed before the end of the experiments. In addition, the lighting conditions changed during the experiments and, as the experiments were done in limited duration conditions, it had not been possible to stop the experiments to modify the camera settings accordingly.

Block fragmentation occurred more frequently for Path A (16 blocks -33% of the total) than for Path B (1 block -1.7% of the total). For Path A, 11 blocks (23% of the total) fragmented into many small parts after a normal impact on a sub-horizontal or horizontal surface (i.e. track or downhill platform). No significantly large fragments propagated after fragmentation, in these cases. A main fragment was identified for the other fragmented blocks. The main fragment did not travel further than approximately 1m for 4 blocks. For one block, a small fragment broke away from the block just after ES1-A and the main fragment propagated after ES2-A. The only block fragmentation observed for Path B is very similar to the latter case. Block fragmentation occurred after ES1-B and the main fragment propagated after ES2-B. For all fragmented blocks, the initial masses and shapes were considered in the analyses of the influence of these parameters on block propagation. This has no consequence on the observed and discussed trends as only one block per path propagated down the slope after fragmentation.

Spatial distributions of the stopping points

The stopping points shown in Figure 7 suggest differences in terms of propagation distance, preferential deposit zones and lateral dispersion. Visually, it seems that Path B led to longer propagation distances and a larger dispersion. These points are addressed in the following results presentation, before detailing the data collected at the evaluation screens.

For Path A, four deposition zones can be identified (Figure 7). One block propagated few meters after release (zone 1A) and another one stopped when reaching the flatter part above the first rock cut, after propagating along the uphill slope, (zone 2A). More significant amounts of block stopped on the track, just before ES2-A, (zone 3A) and on the downhill platform (zone 4A).

Similarly as for Path A, four deposit zones were identified for Path B (Fig. 7). Five blocks stopped near screen ES1-B (zone 1B) without reaching the corridor. Three of these blocks remained blocked on the top of the crest of the rock cut, on one side of the corridor. The two others encountered a locally flat surface near the corridor entry, on its other side. Several blocks passed the evaluation screen ES1-B and stopped on the uphill track (zone 2B) or passed also evaluation screen ES2-B and stopped on the second track (zone 3B). Among these, two were significantly diverted by the gentle slope of the track. Finally, some blocks reached the downhill platform (zone 4B) . Table 2 summarizes the percentage of blocks arrested in the different zones.

The deposit zones can also be clearly identified on the cumulative distribution functions (CDFs) of the block propagation distances for Path A and Path B (Figure 8). These CDFs confirm that, for both paths, just few blocks stopped in the first meters of propagation, around 5% for P athA (zones 1A, 2A) and around 10% for P athB (zone 1B). A significant amount of blocks reached large propagation distances: around 40% reached zone 4A and around 20% reached zone 4B. Finally, a majority of blocks stopped at intermediate distances, corresponding to zone 3A for P athA and to zones 2B and 3B for P athB.

As for the lateral dispersion, or deviation, Figure 7 suggested a difference between the two paths. In order to quantify this difference, Figure 9 the corridor in Path B, which channeling effect globally dominates over the dispersion effect of the two inclined tracks.

Trajectories at the evaluation screens

For Path A, the translation velocities of the block at the evaluation screen ES1-A vary through a large range (0.1 to 8.9m/s -Figure 10a). Their distribution is rather continuous but it is not symmetrical : half of the block velocities are smaller than 2m/s and only 10% of the velocities are larger than 5m/s. At evaluation screen ES2-A level (Figure 10b), the velocity distribution shows a pronounced bi-modal distribution : 32% of the velocities are smaller than 5m/s while 68% are comprised between 18m/s and 19.5m/s.

For Path B, the translation velocities variation is narrower and the velocity distribution is almost symmetrical at the evaluation screen ES1-B except few block experiencing small velocities, smaller than 2.5m/s for 6% of the blocks. The velocity distribution exhibits a bi-modal character at evaluation screen ES2-B. Two variation range can be differentiated : 71% of the velocities range from 0 to 5m/s and 29% range from 6m/s to 14m/s.

Tables 3 provides velocity statistics for both paths and each screen: means, medians, 95% quantiles and standard deviations. These quantities confirm that the distributions of the velocities are not symmetric: means and medians being clearly different. In addition, the very large standard deviations compared to the means, observed for all evaluation screens, except for ES1-B, confirm the large variability of the velocities.

The comparisons between the velocities at the evaluation screens and the stopping points (Figure 11) do not show significant correlations between these quantities. These comparisons only confirm rather obvious relationships. For example, for Path A, only the block passing at ES2-A with large velocities were able to reach large propagation distances (Figure 11c): it corresponds to blocks that bounced near the berm or flew over it. For Path B, the velocities of the blocks at the evaluation screen ES2-B are slightly correlated with those at ES1-B (Figure 11b) because there is no substantial topographical discontinuity between the two evaluation screens. In addition, most of the blocks that reached large propagation distances passed through ES2-A with large velocities (Figure 11c).

Path A Path B ES1-A ES2-A ES1-B ES2
The rotational velocities are homogeneously distributed between with values ranging between 3rad/s and 20rad/s. They are globally smaller for Path A than for Path B (Figure 10 -Table 4) and their variability is smaller than the variability of the translation velocities, as shown by the smaller values of coefficients of variations, in particular.

The qualitative analysis of the passing heights highlights an interesting tendency of the blocks to propagate through the evaluation screens at almost nil passing heights (Table 5). For P athA, all the blocks passed through ES1-A in contact with the soil and only few of them passed through ES2-A with significant, i.e. medium or large, heights. For P athB, only one block (2%) was observed at a significant passing height while all other passed, for both ES1-B and ES2-B, in contact with the soil or at small height. It is interesting to note that, for ES2-A, the very few amount of blocks passing with significant heights seems not consistent with the significant large passing velocities observed (more than 60% larger than 18m/s). This apparent inconsistency is due to the fact that many blocks impacted the slope surface just at the location of ES2-A after a long flight phase. For these blocks, we considered the velocity just before impact in the analysis because it was more conservative in terms of protective measures design. Table 5 Blocks passing heights.

Effect of the blocks characteristics

The released blocks were characterised in terms of their mass and shape. The influence of both these parameters on the blocks trajectory, classically considered as significant, is addressed in the following.

The map of the blocks stopping points classified according to blocks mass (Figure 13) denotes that most of the blocks presenting higher mass have reached longer propagation distances. On the contrary, some of these heavier boulders stopped earlier compared to small blocks, showing that no univocal relationship exists between the block mass and its propagation distance. How- ever, these observations remain speculative because the block masses are not evenly distributed (Figure 14).

The analysis of the blocks shape (Fig. 15) highlights that, most of the blocks belong to compact block categories (compact, compact platy, compact bladed and compact elongated) while only few of them are classified as platy, bladed, elongate and very elongate ones. Some shape categories (very platy and very bladed) are not even present. As shape categories proposed are not equiprobable among the blocks used in the experiments, the analysis of the effect of block shape on the propagation remains incomplete. However, the map of the stopping points classified according to the block's shape (Figure 16), shows that the block having more regular shapes -compact blocks in particular but also compact platy and compact bladed blocks -tend to produce longer propagation distances. Indeed, most of the stopping points of these blocks are located in the downhill part of the study site. In comparison, elongate blocks (including compact elongate, elongate and very elongate) seem to reach smaller propagation distances than compact ones. Concerning other block categories, no conclusion should be drawn due to the small number of concerned blocks.

Cumulative distribution function a) ES1-A b) ES2-A c) ES1-B d) ES2-B

Discussion

Prevailing effects

The analysis of the effects prevailing over the block propagation was done with the objective to identify the leading parameters as well as the physical processes which should be considered for accurately modeling the blocks propagation in this study site.

The spatial distribution of the stopping points emphasizes clear preferential deposit zones of the blocks at the topographical discontinuities and delimits clear preferential propagation paths mainly driven by the global characteristics of the propagation path. In particular, topography determines simple but essential characteristics of the blocks propagation such as the zones where the block cannot propagate, e.g. zones separated from the main corridor by impassable obstacles. Topography also determines the zones where blocks will preferentially stop, for instance on nearly horizontal surfaces at the toe of rock cuts provided that soil properties guarantee a minimum block energy dissipa- tion at impact, as well as against obstacles such as the berms. Consequently, these experimental results confirm that topography is a parameter of major influence on block propagation and stopping.

Nevertheless, topography is not the only parameter with influence on block propagation, as illustrated by the substantial variability in the block trajectories for both propagation paths. This is revealed by the distribution of both the stopping points and the velocities at the evaluation screens. In addition, the experiments showed that there exist several possibilities for the blocks to get through a local topographical discontinuity. For example, at the level of Evaluation screen 2 for Path B, the blocks can bounce on the middle of the track and jump over the berm or make several small bounces on the track to roll over the berm. This variability shows that many other factors than topography influence block propagation. Among the various parameters, the soil properties on both paths are rather homogeneous for each type of soil (quarry waste, rock cut, track,...). The variability in the trajectories cannot be explained by the variability in the soil properties inside each homogeneous zone. As for the blocks characteristics, the analysis of the experimental results suggested a qualitative influence of the block shape on the propagation distance but did not reveal any trend in relation to the block mass. Despite the speculative character of the latter observation, it is worth noting that it contrasts with the commonly believed influence of the mass on the propagation distance of the blocks. As regards to the influence of block shape, it is also interesting to mention that a reduced influence of block shape has already been observed in a similar context [START_REF] Preh | Stochastic analysis of rock fall dynamics on quarry slopes[END_REF].

In addition to these rather well characterised parameters, the block propagation may also depend on other parameters. The variability may thus stem from other parameters that were not measured in these experiments because it is not practically feasible at the site scale. These parameters concern local features, i.e. in the impact point vicinity and small scale quantities such as, in particular, the details of block shape, the orientation of the block at impact, the local topography or locally specific properties of the soil.

More generally, the variability in the trajectories is also thought to result from an interdependence between the various parameters in terms of their influence on the block propagation. In this study, three main parameters were considered: topography, block mass and block shape. It is believed that the influence of one parameter depends on the value of the two others. There is a competition between the parameters in their ability in influencing the block propagation at the local scale. For instance, a high topographical discontinuity (berm for example), may modify or neutralise the influence of the block mass or shape on the block propagation. This results in a variability in the trajectories on this site and suggests that studies focusing on the influence of one parameter on sites where the other parameters are uniform provide qualitative evidences and quantitative trends that should not be extrapolated for cases in other situations.

In summary, in the context of these controlled experiments, the propagation process is driven by topography and several local parameters. The latter parameters, which entail significant variability of the results, cannot be easily identified at the slope scale for propagation modelling purposes in operational contexts. They can be identified but their relative influences can hardly be quantified.

Towards block propagation modelling

The analysis of the processes leading block propagation on the study site provides important information to model this propagation and to assess the relevance of block propagation models in this site. In particular, the experiments showed that block propagation is mainly influenced by topography and that substantial variability of the block trajectories exists.

First, as topography plays a major role on block propagation, it is mandatory to perform propagation simulations with 3D Digital Terrain Models, or 2D profiles if 3D simulations are not feasible for technical or economical reasons, that represent topography in details. In particular, the quality of the representation of the topographical discontinuities is essential because these continuities induce propagation options. Automatically generated digital terrain models (DTM) are not necessarily relevant in that sense, even for high resolution DTM. They have to be checked and improved manually by expert knowledge. For example, the presence of slope discontinuities (ledges, mounds, etc.) has to be checked and the terrain model has to be modified if the slope discontinuities are not accurately represented. Such problem can occur if the resolution of the DTM is too low or if the DTM format is not adapted (for example, raster DTM may not allow reproducing sharp slope changes [START_REF] Lambert | Improving three-dimensional rockfall trajectory simulation codes for assessing the efficiency of protective embankments[END_REF].

Second, even if the influence of soil properties, block mass and block shape on the propagation has not been clearly identified in the experiments, these parameters are classically identified in the literature for playing an important role on block propagation [START_REF] Bourrier | chap Rockfall Dynamics: A Critical Review of Collision and Rebound Models[END_REF]. They thus have to be quantified in the field and integrated into the modelling process. This stage is classical in block propagation modelling but it remains important. A field survey of the soil mechanical properties is thus mandatory to identify homogeneous zones and quantify the model parameters associated with soil properties at the global scale of the study site. Quantitative procedures to assess block mass and shape have also to be performed.

In addition to the above mentioned procedures, it is of primary importance to traduce the variability of the trajectories. As the soil properties are rather homogeneous for each type of soil (quarry waste, rock cut, track,...), the variability cannot be fully attributed to this parameter. In addition, the analyses showed that block mass or shape were not the main causes of variability. On the contrary, the experiments showed the substantial influence of local conditions in the vicinity of the impact point, that cannot be easily quantified in the field, on the propagation. These conditions are of several nature. They may be related with the local terrain properties, both in terms of geometry and mechanical properties, and with the local impact conditions (block orientation, in particular). Random variables sampled from calibrated distributions [START_REF] Li | Probabilistic modeling of rockfall trajectories: a review[END_REF] are classicaly used to account for the variability induced by the latter conditions. The propagation models either use one single random variable that traduces the complete variability associated with all local parameters or different random variables associated with the different local sources of variability. The main difficulty related with the practical use of such probabilistic modelling approaches is the calibration of the distributions of the random variables chosen.

Finally, the conclusions drawn from the experiments illustrate the misleading character of several classical practices for the qualitative assessment of the relevance and accuracy of propagation simulations. For example, as there is no clear relationships between the block size, shape and the propagation distance, it is not possible to assess the quality of simulations from the presence of size or shape sorting in the deposit. In the same vein, the local parameters influenced the block trajectories in such an important way that no clear relationships exist between the velocities at the different evaluation screens and the stopping points (Figure 11). The consequence is that, contrary to our initial expectations, it is not possible to identify archetype trajectories at the slope scale. As no archetype trajectories can be identified at the slope scale, the presence of such archetypes in the simulations does not guarantee their relevance. Consequently, the assessment of the relevance and accuracy of propagation simulations remains limited to the comparison between the simulations and previous rockfall events on the site or on similar study sites. This assessment can consist of comparing the preferential deposit zones, or the preferential transit zones. For that purpose, the mapping of the deposited blocks in the sites or the use of dendrogeomorphology techniques to identify preferential transit zone constitute valuable tools.

Conclusion

The dataset obtained from the analysis of block propagation on the two propagation paths allowed to assess the complexity stemming from the presence of topography discontinuity and of combinations of gentle slopes and soft soils, favoring block motion almost analogous to rolling, in the study site. This dataset could be used by researchers or practitioners that would like to assess the relevance of propagation modelling tools on such a complex study site.

On both propagation paths, preferential transit and deposit zones were identified. Complementary, significant variability of the stopping points and of the block kinematics at the evaluation screens was observed. This variability revealed not to be clearly correlated with specific block properties, except a qualitative influence of block shape on the propagation distance. In addition, the joint analysis of the block kinematics evolution between the evaluation screens and of the stopping points did not allow to identify archetype trajectories at the slope scale.

While the presence of preferential transit and deposit zones highlights the substantial influence of topography, the absence of archetype trajectories at the slope scale illustrates the effects of local conditions, e.g. block shape, orientation, local topography, specificity of soil properties, in the vicinity of the impact point. For example, in the presence of a topographical discontinuity different propagation options exist but the occurrence of one of these options depends mainly on local conditions.

Given the predominant effect of topography, in particular of topographical discontinuities, block propagation simulations should be based on accurate digital terrain models that traduces these discontinuities. In addition, the predominant effect of local conditions, whose deterministic quantification would require substantial field effort, tends to favor the use of probabilistic modelling of block propagation using sound random variables that traduce the influence of local conditions. Finally, the absence of archetype trajectories and of correlations between block properties and propagation entails difficulties in evaluating the quality of block propagation simulations.

The detailed analysis of the propagation on the study site and of the associated prevailing effects provides additional information of primary importance for the researchers or practitioners that would like to assess the relevance of propagation modelling tools on such a complex study site. It also highlights two major challenges in the field of block propagation modelling: the identification of sound random variables for the probabilistic modelling of block propagation and the assessment of propagation simulations results relevance based on statistical comparisons with relevant field surveys or experiments.

Fig. 1

 1 Fig. 1 Overview of the study site. The release zones correspond to the blue polygons and the potential block propagation zones to the red contours.

Fig. 2

 2 Fig. 2 2D profile along the main rockfall path, for Path A.

Fig. 3

 3 Fig. 3 2D profile along the main rockfall path, for Path B.

Fig. 5

 5 Fig. 5 Views of propagation path A (a: top view, b: side view, c: front view). Blue squares and red lines respectively show the block release zone and evaluation screens location.

Fig. 6

 6 Fig. 6 Views of propagation path B (a: top view, b: side view, c: front view). Blue polygons and red lines respectively show the block release zone and evaluation screens location.

Fig. 7

 7 Fig. 7 Final positions of blocks represented using black points. Preferential deposit zones are represented on the right, denoted "A" for Path A and "B" for Path B.

Fig. 8

 8 Fig. 8 Cumulative distribution functions of block propagation distances for Path A (a) and Path B (b).

Fig. 9

 9 Fig. 9 Distribution of block deviation indicators for Path A (a) and Path B (b).

Fig. 10

 10 Fig. 10 Cumulative distribution functions of block translation velocities (Path A: a,b and Path B : c,d).

Fig. 11

 11 Fig. 11 Relations between block velocities at ES1 and at ES2 and between horizontal propagation distance and block velocity at ES2 (Path A: a, c and Path B : b, d).

Fig. 12

 12 Fig. 12 Cumulative distribution functions of the blocks rotational velocity (Path A: a,b and Path B : c,d).

Fig. 13

 13 Fig. 13 Map of the blocks stopping points classified according to the mass of the blocks.

Fig. 14 Fig. 15

 1415 Fig. 14 Distribution of the mass of the blocks according to the classes used to analyse the influence of the mass of the blocks on the stopping points.

Fig. 16

 16 Fig. 16 Map of the blocks stopping points classified according to the shape categories.

  Shape classification diagram (adapted from[START_REF] Blott | Particle shape: a review and new methods of characterization and classification[END_REF]).

		C
	0.7		0.7
	L3 / L1	CP CB CE	L2 / L1
	0.5		0.5
	P	B	E	C :Compact CP : Compact Platy
	0.3		0.3	CB : Compact Bladed
				CE : Compact Elongate
	VP	VB	VE	P : Platy B : Bladed
				E : Elongate
	(L1-L2) / (L1-L3) 0.33 0.67	VE : Very Elongate VP : Very Platy VB : Very Bladed
	Fig. 4

Table 1

 1 Summary of available data.

		Path A Path B
	Number of released blocks	48	56
	Number of measured final positions	46	56
	Number of trajectories (screen 1)	38	37
	Number of trajectories (screen 2)	17	31

Table 2

 2 Percentage of deposited blocks in the different zones along paths A and B.

	Deposit zone	A	B
	1	2.2%	8.9%
	2	2.2%	8.9%
	3	54.3% 62.5%
	4	41.3% 19.6%

Table 3

 3 Statistical indicators related with block velocity distributions at the evaluation screens

	-B

Table 4

 4 Blocks rotational velocities.

Acknowledgements The topography of the study site and the results of the experiments are available in supplementary materials attached to this article or upon request (franck.bourrier@inrae.fr).

This research work has been held in the context of the french national project C2ROP, which provided financial support for the experiments. The authors would like to thank all the partners involved in these experiments, including research laboratories and institutes, stakeholders, and private engineering companies.

Conflict of interest

The authors declare that they have no conflict of interest.


Nicolas Martin
email: nicolas.martin@b-com.com

Martin Ragot
email: martin.ragot@b-com.com

Vincent Savaux
email: vincent.savaux@b-com.com

Acceptability and 5G in the Medical Field: The Impact of the Level of Information

The issues around 5G are considerable: sovereignty, smart city, industry 4.0, energy, connected healthcare. However, 5G is currently raising many questions from the general public and professionals. To better understand these questions related to acceptability, a quantitative experimental study was conducted with 81 healthcare professionals, via an online questionnaire. The objective is to analyse the impact of the level of information on acceptability. The participants were divided into two experimental groups, confronted either with a low level of information or a high level of information about 5G. Several dimensions were analyzed (perceived usefulness and usability, intention to use, harmfulness and perceived environmental impact). The results show a significant influence of the level of information related to 5G on the number of "I don't know" responses participants. More broadly, this study demonstrates the influence of respondents' level of information on their ability to express an opinion. These results provides insights for the construction of survey and public policies around 5G and new technologies acceptability.

I. INTRODUCTION

The fifth generation (5G) of mobile communications and networks enables a broadband and reliable connectivity to a constantly growing number of devices of many kinds [START_REF] Ahmad | Overview of 5G Security Challenges and Solutions[END_REF], [START_REF] Peisa | 5G evolution: 3GPP RELEASES 16 and 17 OVERVIEW[END_REF]. Unlike the previous generations, the 5G technology does not only focus on the connectivity of individuals' user equipment, but also takes part in the digital transformation of the so-called verticals [START_REF] Vannithamby | 5G Verticals: Customizing Applications, Technologies and Deployment Techniques[END_REF], among which the transport, the industry 4.0, or the e-health. The acceleration of the 5G deployment inherently raises the issue of the acceptability of this technology by the users, not only in their personal life, but also in their professional use. In fact, forms of distrust and resistance towards 5G has been recently observed in some countries where it is being deployed.

In this paper, we focus on the acceptability of 5G in a professional use within the field of healthcare. Thus, the current study aims to evaluate the effect of the level of information about 5G on acceptability among potential healthcare users, i.e. all people working in hospital and healthcare centers. The presented results reveal that the higher the level of information, the more people are able to assess their perception of 5G. Indeed, more Don't Know (DK) responses are present within the low level of information group, comparatively to the second group "high level of information. Such a study could then help the operators of public and private 5G networks to manage the acceptability of the users in their professional field.

A. State of the Art

Numerous studies have been conducted to understand the adoption of new technology, as evidenced by the number of meta-analyses on this topic (e.g., [START_REF] Dwivedi | A Metaanalysis of the Unified Theory of Acceptance and Use of Technology (UTAUT)[END_REF]- [START_REF] Schepers | A meta-analysis of the technology acceptance model: Investigating subjective norm and moderation effects[END_REF]). Relying on acceptability theory, it aims to discover the factors that facilitate or inhibit technological product adoption (e.g., [START_REF] Dillon | User Acceptance of Information Technology: Theories and Models[END_REF]). One of the best-known theoretical models of acceptability is probably the Technology Acceptance Model (TAM) [START_REF] Davis | Perceived Usefulness, Perceived Ease of Use, and User Acceptance of Information Technology[END_REF] which supposes the influence of two variables on the intention to use: the perceived usefulness and the perceived ease of use. The TAM seems to be appropriate, with additional variables, to predict the usage of 5G [START_REF] Akbari | Acceptance of 5 G technology: Mediation role of Trust and Concentration[END_REF].

5G is still a technology in development. Studies have already been carried out on technical performance (e.g., [START_REF] Li | Performance analysis of a novel 5G architecture via Content-Centric Networking[END_REF]), on issues and costs related to its deployment (e.g., [START_REF] Oughton | Assessing the capacity, coverage and cost of 5G infrastructure strategies: Analysis of the Netherlands[END_REF]) on public health and environmental implications (e.g., [START_REF] Russell | 5 G wireless telecommunications expansion: Public health and environmental implications[END_REF], [13]) and in terms of quality of experience perspective (e.g., [START_REF] Pierucci | The quality of experience perspective toward 5G technology[END_REF]). Nevertheless, few studies have focused on investigating user acceptability towards 5G. According to [START_REF] Akbari | Acceptance of 5 G technology: Mediation role of Trust and Concentration[END_REF], there are "insufficient in-depth discussions of intention to use from the potential user perspective" ( [START_REF] Akbari | Acceptance of 5 G technology: Mediation role of Trust and Concentration[END_REF], p. 7). These authors study the acceptance of 5G among students. They show for example that trust mediates the relationships among perceived ease of use, perceived usefulness, and the intention to use 5G. Trust seems to to be an important factor in driving behavioral intentions (i.e., [START_REF] Warkentin | Social identity and trust in internet-based voting adoption[END_REF], [START_REF] Kaushik | Tourist behaviour towards self-service hotel technology adoption: Trust and subjective norm as key antecedents[END_REF]). For Akbari (2020), "trust refers to specific beliefs about the way that technology operates through a work environment" ( [9], p. 3). Trust refers to specific beliefs about how technology works in a professional environment [START_REF] Mcknight | Trust in a Specific Technology: An Investigation of Its Components and Measures[END_REF]. Some authors have also investigated the factors influencing the intention to use 5G mobile communication service, based on an extended version of TAM (ETAM) [START_REF] Jeong | A Study on the Factors Affecting the Usage Intentions of 5G Mobile Communication Service[END_REF]. For [START_REF] Koh | Factors Affecting Risk Perception of Electromagnetic Waves From 5G Network Base Stations[END_REF], "perhaps owing to the newness of the 5G network's development, no study has been published on risk perception of electromagnetic waves from 5G network base stations" ( [START_REF] Koh | Factors Affecting Risk Perception of Electromagnetic Waves From 5G Network Base Stations[END_REF], p. 492). In parallel, [START_REF] Lin | SURVEY ON CONSUMER USER SATISFACTION THROUGH 5G NETWORK MEDICAL SYSTEM[END_REF] focused on user satisfaction with 5G, via online questionnaires [START_REF] Lin | SURVEY ON CONSUMER USER SATISFACTION THROUGH 5G NETWORK MEDICAL SYSTEM[END_REF]. Along with these different variables influencing acceptability and intention to use, it seems that the framing information or the level of information can have also an impact on the adoption of new technologies. For example, [START_REF] Vishwanath | From Belief-Importance to Intention: The Impact of Framing on Technology Adoption[END_REF] has shown that there could be a "framing effect" related to the adoption of new technologies [START_REF] Vishwanath | From Belief-Importance to Intention: The Impact of Framing on Technology Adoption[END_REF]. Indeed, the type of words used, which can have a potentially framing effect, and therefore the type of information conveyed to the user about a technology has consistently been shown to be one of the strongest biases in decision making [START_REF] Ragot | Effect of wordings on public perception toward Artificial Intelligence[END_REF]. However, to the best of our knowledge, no study has been carried out on the impact of level information on 5G acceptability. In this period of intense debate around 5G, where the information is abundant and possibly influencing, it seems necessary to propose a study that comes to address this issue, i.e., to better understand the impact of communication policies on the perception of users towards 5G.

B. Contributions

The contributions of the paper are multiple:

• The study is original since, to the best of our knowledge, studies on the acceptability of 5G are rare, even when distrust towards 5G is observed in many countries deploying this new technology. • It is based on an experimental and robust protocol, and in the same times, it suggests to test news dimensions such as the perceived impact on health or environment, as these are key issues inherent to 5G. The protocol could then be reused in larger scale studies in different professional fields where 5G will be used.

• It provides results about the acceptability of 5G that could help operators in the deployment of public or private 5G networks.

• It provides crucial insights in terms of public policies, on the impact of the level of information on the ability of respondents to express an opinion and respond to acceptability surveys around new technologies and 5G in particular.

The rest of the paper is organized as follows: Section II describe the methodology of the study. Section III provides the obtained results, which are then discussed in Section IV. Finally, Section V concludes this paper.

II. METHODOLOGY

A. Participants

The data has been collected from the responses to an online questionnaire, whose items are available at URLLINK. A set of 81 participants (44 women, 18 men & 19 others/don't want to answer; mean age = 43.03 years, SD age = 11.35) have been involved in this study. Volunteers were recruited by email using a professional network, composed of french hospitals and healthcare institutes. The participants were randomly divided in two conditions : half of the participants are assigned to the condition "low level of information", the other half to the condition "high level of information". These conditions are different in the type and amount of information provided to participants about 5G.

B. Protocol

The participants filled the survey using the online Survey-Monkey platform. The survey started by the presentation of the following instruction (in French):

"The French Institute of Research and Technology b<>com is currently carrying out a study on the perception of healthcare professionals towards 5G. For this, we need your advice. The data collected during this survey will be only processed confidentially and anonymously for statistical purposes. The results will be used for scientific purposes. There are no right or wrong answers, only your opinion matters. This study is intended for all professionals in the medical field and does not require specific knowledge about 5G.".

Then, the participants were randomly distributed in both conditions (i.e., low level of information and high level of information). In the condition "low level of information", the participants had to read the following description: "5G is the fifth generation of mobile telephony, allowing high-speed connectivity / connection to any type of mobile terminal (smartphones but also vehicles, sensors, etc.)".

In the condition "high level of information", in addition to the description of the condition "low level of information", the participants had to read the following description: "It is characterized by higher throughput (up to 100 times more data transmitted per second), lower latency (i.e., shorter response time) for better energy efficiency and higher high reliability than previous generations of mobile telephony (e.g., 3G / 4G). 5G could allow significant progress in telemedicine and thus improve access to healthcare for as many people as possible. It would thus promote the emergence of certain applications: telemedicine, for remote medical, reliable, highspeed and secure monitoring; Operating rooms and connected ambulances for better patient monitoring; Secure data transfers for scientific research purposes; etc."

After reading this instruction, participants had to complete the survey. Data collection took place without supervision and participants could leave the questionnaire whenever they wished. The order of items in the questionnaire was randomized to avoid order effects [START_REF] Benton | A Question Order Effect in a Local Government Survey[END_REF].

C. Measures

Such as aforementioned, the TAM [START_REF] Davis | Perceived Usefulness, Perceived Ease of Use, and User Acceptance of Information Technology[END_REF] and related questionnaire has been used to evaluate the acceptability of medical professionals towards 5G. Thus, perceived usefulness, perceived ease of use, and intention to use has been evaluated. In addition, personal innovativeness [START_REF] Agarwal | A Conceptual and Operational Definition of Personal Innovativeness in the Domain of Information Technology[END_REF] as well as perceived impact on health, perceived impact on environment and perceived level of information have been assessed. The trust and distrust dimensions were also studied [START_REF] Jian | Foundations for an Empirically Determined Scale of Trust in Automated Systems[END_REF].

To evaluate all these dimensions, participants were asked to indicate their agreement based on five-point Likert scales (1 = totally disagree; 5 = totally agree). Completion of each item was mandatory. However, for each item, a "don't know" (DK) response was made possible for the participants. They therefore had the option of not responding to the item, if they wished, by checking this case. Finally, in order to identify inattentive respondents and to ensure that participants correctly classified the level information of each condition, an item of attention check was introduced. At the end of the questionnaire, the instructions were as follows (in french): "Please choose the title that best corresponds in your opinion to each of the following paragraphs describing 5G". The two descriptions used in the experimental groups were presented to all participants. For each description, participants had to choose between two items:

• Factual description of 5G • Description of 5G, its characteristics and applications In summary, the following dimensions have been evaluated using 36 items:

• Acceptability -TAM -Usefulness -4 items (e.g., "Using 5G would improve my job performance") -Ease of use -4 items (e.g., "My interaction with 5G medical applications would be clear and understandable") -Intention to use -3 items (e.g., "Assuming that I have access to the 5G in the medical field, I intend to use it")

• Trust -6 items (e.g., "I can trust 5G in the medical field")

• Distrust -4 items (e.g., "I am wary of 5G in the medical field") • Personal Innovativeness -4 items (e.g., "Among my peers, I am usually the first to try out new information technologies") • Perceived impact on Health -3 items (e.g., "5G will be harmful to my health") • Perceived impact on environment -3 items (e.g., "5G will make it possible to be more respectful of the environment in the medical field") • Perceived level of Information -3 items (e.g., "I believe I have access to enough information about 5G") • Demographic variables -2 items (i.e., Gender and Age)

III. RESULTS

In this section, we provide and analyze the results obtained from the responses of the questionnaire. They will be further discussed in Section IV. The data analyzes were performed using R [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF], and the results regarding the impact of the conditions (i.e., the level of information) have been gathered and displayed using Matlab.

In order to verify the relevance of the proposed level of information (i.e., low level of information and high level of information), we evaluated that participants correctly classified the level information of each condition. For the condition "low level of information", 91.5% of participants correctly classified the description. For the condition "high level of information", 78.7% of participants correctly classified the description. These results show that the levels of information provided are relevant and that it is possible to analyze their effects in depth.

A. Influence of level information on "Don't know" responding

The influence of level information on DK responses was evaluated using the usual chi-square analysis. The results are presented using the American Psychological Association (APA) style, i.e.

Dimension(χ 2 (D, N ) = X, p), (1)
where "Dimension" is the tested dimension (e.g. the usefulness), D is the degree of freedom of the data, N represents the size of the sample (the number of responses), X is the result of the χ 2 test, and p is the p-value. The latter indicates the significance of the level of information on the propensity of the participants to answer/not answer with a DK response (the lower the p-value, the more significant the result).

Analyzes showed that level information has a significant impact on the number of "I don't know" responding on show that the participants are more inclined to not respond with DK when the level of information is high, for the usual TAM items measuring the acceptability of a technology (e.g., usefulness, ease of use). Thus, the level of information increases their capability to build an opinion about 5G regarding these dimensions. Conversely, the level of information has a weaker influence on the amount of DK responses related to the dimensions we added such as "perceived impact on environment" (the number of DK response is low in both cases). This result shows that the participants have an a priori opinion regarding these new dimensions we tested. To summarize, these analyzes show that the level of information makes it easier to assess the qualities of 5G for future users. But this does not change their judgment on impacts related to health or the environment.

B. Influence of level information on judgement

The effect of level information on judgement toward 5G was evaluated using the Student's t-test. The results of the t-test are presented using the same style as the previous results for the χ 2 tests.

The results showed only a significant effect on Perceived level of Information (t(73.17) = -3.13, p = .003). The participants in the condition "high level of information" perceived actually a higher level of information about 5G (M = 3.62, SD = 0.96) compared to condition "low level of information" (M = 3.23, SD = 0.93). All descriptive statistics are listed below and reported in Fig. 1 in the form mean/standard deviation.

No significant effect was found on:

• Usefulness: t(74.36) = -1.17, p = .245

• Ease of use: t(69.83) = -0.99, p = .326

• Trust: t(70.70) = -1.31, p = .195

• Distrust: t(75.99) = 1.47, p = .145

• Intention to use: t(71.95) = -0.94, p = .348

• Personal Innovativeness: t(78.13) = -1.84, p = .069

• Perceived impact on Health: t(68.95) = 0.06, p = .951

• Perceived impact on environment: t(66.94) = 0.57, p = .571 • Perceived level of Information: t(73.17) = -3.13, p = .003 Although no significant effect of the level of information on the judgement toward 5G has been clearly highlighted, Fig. 1-(a) nevertheless shows that, in average, the participants with the higher level of information are more inclined to use, trust, or find useful the 5G than the participants with low level of information. Conversely, the level of information seems to have no effect on the judgement toward the new tested dimensions (impact on health and environment), according to Fig. 1-(b). However, the standard deviation is too high to highlight further statistics, due to the low number of participants.

IV. DISCUSSION

An experimental study was done in order to evaluate the influence of information level on acceptability towards 5G among healthcare professionals. For the participants evaluating 5G (participants which don't answer "I don't know"), the level of information did not significantly directly influence their judgment, but this should be confirmed with a much larger number of participants. Nevertheless, the results showed an effect on "don't know" responding. Participants exposed to a lower level of information tend to be significantly less able to evaluate their perception towards 5G. Conversely, technical details provided on 5G and associated use cases tend to promote the ability of participants to respond. It is then possible to use the concept of "framing effect" to qualify the influence of the first provided information on the perception of respondents. Indeed, some authors have previously raised the question of framing information on user perceptions [START_REF] Binns | It's Reducing a Human Being to a Percentage': Perceptions of Justice in Algorithmic Decisions[END_REF]- [START_REF] Ragot | Ai-generated vs. human artworks. a perception bias towards artificial intelligence?[END_REF].

Our results are different from [START_REF] Frank | The Effect of Negativity Bias on Trust in the Adoption of Innovations: A Longitudinal Study[END_REF]: Their results show that individuals consistently show lower scores on trust in technology after being exposed to negatively (compared to positively) biased information. Conversely, the positively skewed information does not appear statistically different from the control condition, in which no additional information was Fig. 1. Mean and standard deviation on evaluated dimensions according to the experimental condition: purple for low level of information and orange for high level of information presented. In [START_REF] Jeong | A Study on the Factors Affecting the Usage Intentions of 5G Mobile Communication Service[END_REF], two variables have positive effects on the intention to use 5G: the perceived usefulness/enjoyment and the personal innovativeness. As [START_REF] Vishwanath | From Belief-Importance to Intention: The Impact of Framing on Technology Adoption[END_REF], our results highlight the importance of frames in perception and technology adoption. But this influence differs because he shows that positive frames (that positively highlighted performance and ease of use of the innovation), by creating specific expectations towards this innovation, can cause rejections within participant evaluations. [START_REF] Hay | I Don't Know" My Cancer Risk: Exploring Deficits in Cancer Knowledge and Information-Seeking Skills to Explain an Often-Overlooked Participant Response[END_REF] show that Don't Know (DK) responses are correlated with lower education, lower numeracy, lower income, and minority status [START_REF] Hay | I Don't Know" My Cancer Risk: Exploring Deficits in Cancer Knowledge and Information-Seeking Skills to Explain an Often-Overlooked Participant Response[END_REF]. Our study also shows that the level of information proposed (frames) also influences the number of DK responses.

Frei (2020) assessed the perception of risk associated with 5G within a population group. It appears that 65 percent of respondents perceived the risks of 5G as medium to high (responses above 50, within a scale ranging from 0 to 100) [START_REF] Frey | Psychological drivers of individual differences in risk perception: A systematic case study on 5g[END_REF]. In his Study 2, Frei (2020) shows that objective knowledge about 5G are related inversely to risk perception. Regarding the influence of the level of knowledge on the risks perception towards technology, [START_REF] Seo | The Relationship between Risk Perception of Cell Phones and Objective Knowledge of EMF in Korea[END_REF] find similar results to our current study, despite a different experimental protocol. Indeed, among several other psychological factors, the level of Personal knowledge influenced risk perceptions of cell phones, as in our study where the level of information influences similar variables.

Finally, it should be noted that the difference in terms of level of information represents both a quantitative and a qualitative difference. Indeed, beyond the difference in terms of the number of information proposed between the two experimental conditions, there are also differences in terms of types of information. The first conditions "low level of information" is based on a factual description of 5G. The second conditions, also focuses on the characteristics of 5G and its possible applications. Thus, beyond a quantity of information, these details provide insights on the type of information to be provided and its impact on participants' responses, It might be interesting to replicate this type of study using the prompt method [START_REF] Denman | Reducing "I Don't Know" Responses and Missing Survey Data: Implications for Measurement[END_REF], that is to say encouraging people to respond if they checked the DK response. Indeed, the authors compare three methods to treat DK responses in the medical field (exclude this data, recode them at a neutral point on the response scale; recode them to the mean) with the their technique of prompt. It appears that, compared to excluding data related to DKs responses, the prompt improved the data quality and the correlations between constructs.

V. CONCLUSION

Many debates are currently taking place among the population around the deployment of 5G. Many use cases are mentioned, in particular in terms of connected healthcare. As the technology is not yet accessible to the majority of professionals in the hospital field, it seems necessary to assess their perception and acceptability before use. Many factors seem to influence acceptability and risk perception related to technology. However, few studies focus on acceptability with 5G, especially in the medical field. To the best of our knowledge, few studies show the impact of public policies in terms of information provided on the adoption of new technologies and 5G in particular. Nevertheless, for evidencebased policy-making, experimental data on the impact of the level of information provided on the acceptability of new technologies, and 5G in particular, appear to be essential. This study therefore attempts to answer the question of the impact of users' level of knowledge and of the level of information provided on their perception of 5G. This study highlights the impact of respondents' level of information on their number of Don't Know (DK) responses, related to their ability to position themselves and express a point of view. It appears that participants have more difficulty in positioning themselves (more DK responses) when they are given low information. In parallel, when the participants know how to position themselves, the level of information does not significantly influence the other factors. These results are essential for the establishment of current public policies in terms of communication, especially in the field of health, where 5G represents significant challenges.

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  Usefulness: χ 2 (1, N = 114) = 17.43, p < .001 • Ease of use: χ 2 (1, N = 114) = 11.48, p < .001 • Trust: χ 2 (1, N = 114) = 21.33, p < .001 • Distrust: χ 2 (1, N = 114) = 5.96, p = .001 • Intention to use: χ 2 (1, N = 114) = 18.01, p < .001 However, no significant difference was observed on: • Personal innovativeness: χ 2 (1, N = 114) = 0.01, p = .918 • Perceived impact on health: χ 2 (1, N = 114) = 3.70, p = .055 • Perceived impact on environment: χ 2 (1, N = 114) = 1.49, p = .222 • Perceived level of Information: χ 2 (1, N = 114) = 2.44, p = .110 These results

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  s e fu ln e s s E a s e o f u s e T ru s t D is tr u s t In te n ti o n to u s e P e rs o n n a l in n o v a ti v n e

VI. ACKNOWLEDGMENTS

This study was carried out by b<>com within the "Handicap Innovation Territory" project, supported by the French Government as part of "Territoires d'innovation" (French program for innovative territories), administered by the "Banque des Territoires".