Louise Devigne

Tom Carlson

Marie Babel

A shared control solution for safe assisted power wheelchair navigation in an environment consisting of negative obstacles: a proof of concept

Power wheelchairs allow people with motor disabilities to have more mobility and independence. However, driving safely such a vehicle is a daily challenge particularly in urban environments while navigating on sidewalks, negotiating curbs or dealing with uneven grounds. Indeed, differences of elevation have been reported to be one of the most challenging environmental barrier to negotiate, with tipping and falling being the most common accidents power wheelchair users encounter. It is thus our challenge to design assistive solutions for power wheelchair navigation in order to improve safety while navigating in such environments. To this aim, we propose a shared-control algorithm which provides assistance while navigating with a wheelchair in an environment consisting of negative obstacles. We designed a dedicated sensor-based control law allowing trajectory correction while approaching negative obstacles e.g. steps, curbs, descending slopes. This shared control proposed method takes into account the humanin-the loop factor. In this study, our solution the ability of our system to ensure a safe trajectory while navigating on a sidewalk is demonstrated through simulation, thus providing a proof-of-concept of our method.

I. INTRODUCTION

Motorized mobility is not without risk and accidents can occur while driving a power wheelchair. In a study on the prevalence of wheelchair-related accidents involving 95 participants, 54.7% of them reported at least 1 accident in the past 3 years [START_REF] Chen | Wheelchair-related accidents: relationship with wheelchair-using behavior in active community wheelchair users[END_REF]. In this context, robotic assistive solutions can increase wheelchair navigation safety. Indeed, navigation support can be supplied in the form of autonomous [START_REF] Baklouti | Autonomous wheelchair navigation with real time obstacle detection using 3d sensor[END_REF] [START_REF] Kokosy | SYSIASS -An Intelligent Powered Wheelchair[END_REF] or semi-autonomous [START_REF] Horn | Smart wheelchairs: Past and current trends[END_REF] assistance [START_REF] Ezeh | Probabilistic vs linear blending approaches to shared control for wheelchair driving[END_REF]. However, the existing navigation assistance technologies are currently restricted to indoor environment. Indeed, they do not detect outdoor environmental barriers such as differences in elevation (step, curb, etc.). Yet, recent studies highlight the benefits of power mobility in the case of outdoor activities [START_REF] Löfqvist | Mobility and mobility-related participation outcomes of powered wheelchair and scooter interventions after 4-months and 1-year use[END_REF] [START_REF] Samuelsson | Powered wheelchairs and scooters for outdoor mobility: a pilot study on costs and benefits[END_REF]. Indeed, it is reported that power mobility can improve the user self-esteem and sense of independence as it allows to go outdoors more easily and to have the opportunity to socialize and enjoy daily activities such as shopping. Therefore, outdoor navigation solutions have to be developed to increase navigation safety. Among the 3 categories of wheelchair-related accidents identified in [START_REF] Chen | Wheelchair-related accidents: relationship with wheelchair-using behavior in active community wheelchair users[END_REF], 87.7% were tips and falls. In some cases, this type of accident can have serious consequences such as traumatic brain injury or spinal cord injury [START_REF] Opalek | Wheelchair falls: 5 years of data from a level i trauma center[END_REF]. Moreover, [START_REF] Korotchenko | Power mobility with collision avoidance for older adults: User, caregiver, and prescriber perspectives[END_REF] highlights that environmental obstacles impact the outdoor driving safety and that one of the biggest challenges is to negotiate curb drop-offs and curb cuts. While a lot of works have been done in the robotics field on detecting and avoiding obstacle, there is significantly less research on detection of negative obstacles to improve outdoor robot navigation. In [START_REF] Larson | Lidar based off-road negative obstacle detection and analysis[END_REF] an algorithm analyzes the terrain using a 3D laser range finder. They classify the obstacles and populate a grid map of obstacles and terrain features. In [START_REF] Murarka | Detecting obstacles and drop-offs using stereo and motion cues for safe local motion[END_REF], a stereo-based scene reconstruction is used to detect drop-offs and also relies on the definition of a grid map. The few proposed methods are used for autonomous robot navigation and are typically based on stereo-vision detection or use expensive sensors such as LIDARs and generally rely on computationally expensive localization methods within local maps of the environment. As for wheelchair navigation, only a few research teams have worked on assistive solutions for power wheelchair driving in outdoor environments. While the intelligent wheelchairs presented in [START_REF] Simpson | The smart wheelchair component system[END_REF] simply stops when a drop-off is detected, [START_REF] Coughlan | Terrain analysis for blind wheelchair users: Computer vision algorithms for finding curbs and other negative obstacles[END_REF] proposes an algorithm relying on depth information using stereo vision for finding obstacle edges. Then, if some efforts have been made in order to detect drop-offs using a robotized power wheelchair, no control law is given in order to assist the user while driving. In [START_REF] Devigne | Low complex sensor-based shared control for power wheelchair navigation[END_REF] we presented an approach dealing with obstacles that a wheelchair cannot cross (e.g. walls, furniture). In this paper, we present a complementary approach providing navigation assistance in an environment consisting of negative obstacles which are defined here as curbs, steps and descending slopes. Here, we use distance sensors mounted all around the wheelchair to detect distances to the floor and to extract local floor orientations information. With this method, no map is required and the proposed solution is able to smoothly correct the trajectory of the wheelchair while approaching a negative obstacle while respecting user intention. The paper is organized as follows. Section II deals with the modeling related to the robotized wheelchair. Section III presents the computation of the constraints deduced from sensors measurements on which the method relies and then details the proposed sensor-based wheelchair assisted navigation method. Section IV presents simulations of the system, thus highlighting the behavior of the servoing process in presence of negative obstacles while driving on a virtual sidewalk. The results are discussed in section V.

II. MODELING

We model a 6 wheeled robotic wheelchair composed of 2 actuated wheels and 4 passive caster wheels. It is controlled with 2 variables, namely the linear velocity u and the rotational velocity ω.

The wheelchair is equipped with distance sensors. As shown on Fig. 1, we define the following notations

• let F R (R, X R , Y R , Z R
) be the frame attached to the robotic wheelchair, • let F si (S i , X i , Y i , Z i ) be the frame attached to the sensor s i , • let u = (υ, ω) be the 2-DoF control input of the wheelchair, • let v si be the velocity of the sensor s i ,

• let a i and b i be the distances from the robot frame to the sensor frame respectively along the robot x-axis and y-axis.

• let φ i be the orientation of the sensor s i with respect to the robot frame Oxy plane, • let d i be the distance measured by the sensor s i ,

• let θ i be the orientation of the sensor s i with respect to the robot frame z-axis,

• let e i be the difference between the measured distance

x i and its desired value x * i . Each sensor s i is rigidly fixed to the robot frame so that the translation vector r t si between F si and F R is such that

r t si =   a i b i 0   . (1)
The rotation matrix si R r relative to sensor s i frame F si with respect to the robot frame F R is given by

si R r = si R r (φ i ) si R r (θ i ) (2) with si R r (φ i ) =   cos φ i 0 -sin φ i 0 1 0 sin φ i 0 cos φ i   (3)
and si R r (θ i ) =   cos θ i sin θ i 0 -sin θ i cos θ i 0 0 0 1   (4)
The translation si t r between the robot F R frame and the sensor s i frame F si is obtained from si R r with

si t r = si R r r t si . (5)
From si R r and si t r , the velocity screw transformation matrix is given by

si W r = si R r [ si t r ] × si R r 0 3×3 si R r (6)
with [ ] × the skew matrix expression.

The velocity v si of the sensor s i in the sensor frame F si is derived from the robot 2-DoF control input u in the robot frame using

v si = si T r u, (7)
with si T r = si W r r J r , (8)
where r J r is the robot jacobian expressed in the robot frame such that

r J r = 1 0 0 0 0 0 0 0 0 0 0 1 T . (9)

III. SENSOR-BASED SERVOING FOR ASSISTED NAVIGATION ON A SIDEWALK

In [START_REF] Devigne | Low complex sensor-based shared control for power wheelchair navigation[END_REF], we presented a semi-autonomous approach providing adaptive assistance in the form of an intuitive obstacle avoidance. This method consists in merging the user control coming from a wheelchair controller with a set of constraints deduced from the sensors. This shared control law is based on the definition of two distinct areas in the wheelchair velocity domain that represent allowed and forbidden wheelchair control input values. So far, we applied this method to indoor navigation. In this section, we present the assisted power wheelchair navigation in an environment consisting of environment obstacles by detailing the features extracted from the sensors measurements and we present the computation of the constraints in the velocity domain. The resulting computation of the wheelchair control values from user velocity input by minimizing a cost function is directly applied from [START_REF] Devigne | Low complex sensor-based shared control for power wheelchair navigation[END_REF].

A. Distance sensor features

In this method, we want to extract relevant information from each sensor distance measurement. Considering a sensor able to measure multiple distances within different regions of interest, we are able to collect information about floor differences of elevations by means of local floor orientation computation obtained for each sensor. This leads to the definition of two features in the form of angles characterizing the orientation of the detected floor area. As shown on Figure 2, let (α xi , α yi ) be the set of angles defining the orientation of the floor with respect to the wheelchair Oxy plane with α xi and α yi being defined respectively around the sensor s i x-axis and y-axis.

B. Velocity regulation controller design

Within the context of power wheelchair navigation assistance in an environment consisting of negative obstacles, a velocity controller is designed to ensure the wheelchair to navigate safely. We propose here to progressively adapt the wheelchair control input to avoid hazardous situations caused by negative obstacles.

To do so, we define the error e si for each sensor s i such that e si = d i -d * i where d i , d * i ∈ R + are respectively the distance measured by a sensor s i to the floor and a configurable fixed value corresponding to the maximum allowed distance from the sensor s i to the floor.

1) Interaction matrix computation: With the 2 features α xi and α yi defined in III-A, we can design a dedicated control law that regulates the error e si by taking into account local floor area orientation into each sensor s i interaction matrix.

For the present case, the interaction matrix L xi is such that

L d i = -1 tan αx i sin φ i 1 tan(φ i +αy i ) 0 d i tan(φ i +αy i ) d i tan(αx i ) sin φ i , ( 10
)
where α xi and α yi are depicted in Figure 2.

2) Shared control method: The objective is to regulate the wheelchair velocity control input to avoid hazardous situations involving negative obstacles when needed while still allowing full control to the user when there is no negative obstacle close to the wheelchair, we propose to gradually activate the regulation of each distance sensor s i feature d i to a desired value d * i corresponding to the distance measured when no negative obstacle is detected. This is achieved by using an interval d s- i , d s+ i that we define to trigger the sensor-based servoing when the distance d i leaves the safe interval. This hybrid control law method has been introduced in [START_REF] Kermorgant | Combining ibvs and pbvs to ensure the visibility constraint[END_REF] and applied to wheelchair navigation in [START_REF] Pasteau | Vision-based assistance for wheelchair navigation along corridors[END_REF] within a wall avoidance task. The idea is to adapt this framework to our semi-autonomous navigation task in an environment consisting of negative obstacles. We propose the following sensor-based control law aiming to keep the distance feature d i within the interval d s- i , d

s+ i ḋi = h di L di v si (11)
with L di ∈ R 1×6 the interaction matrix introduced in [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF] and , we propose here to define the weight h di by the following smooth function

h di ∈ R + * a
h di (d i ) =                    1 -cos π d i -d s+ i d + i -d s+ i /2 if d s+ i < x < d + i 0 if d s- i < x < d s+ i 1 -cos π d i -d s- i d - i -d s- i /2 if d - i < x < d s- i 1 otherwise (12) where d - i , d + i ⊃ d s- i , d s+ i
is a tolerated interval whose fixed limits represent the distance values corresponding to distances measured to obstacles the wheelchair should avoid. The evolution of the weighting term h di is given in Fig. 3.

where λ ∈ R + * is a gain and e si = d i -d * i the difference between the measured distance to the floor d i and its desired value d * i . In this framework, d * i value is the distance which is measured by the sensor s i while detecting no obstacle.

This way, we constrain ḋi by a minimum value -λe si . When considering the relationship ḋi = L di si T r u between the 2 DoF wheelchair control input u and the variation ḋi of the distance d i measured by the sensor s i , we obtain

h di L di si T r u ≥ -λe si (14)
i.e.

J si u ≥ -λe si , (15)
where J si = h di L di si T r is the sensor s i jacobian. The system (15) is a linear equation system which can admit an infinity of solutions in the form of a 2D half-plane in the wheelchair velocity domain.

Defining A i = J si and B i = -λe si , inequation (15) can also be written as

A i u ≥ B i . ( 16
)
This defines 2 half-planes in the (u, ω) such as shown on Fig. 4a. The green and red half planes respectively represent allowed and forbidden wheelchair control input values.

In the particular case where h di is null (i.e. when no negative obstacle is detected), the forbidden half plane is not defined, therefore the constraint deduced from sensor s i is not involved in the regulation of the wheelchair control input. This way, user full control is ensured.

When considering N sensors, we rewrite [START_REF] Pasteau | Vision-based assistance for wheelchair navigation along corridors[END_REF] as

A u ≥ B ( 17
) using A =    A 0 . . .

C. Computing control values

• Let u op = (u op , ω op ) be the user desired velocity,

• let u cmd = (u cmd , ω cmd ) be the robot velocity. u cmd is computed from u op under constraints ( 17) by minimizing a cost function f . This can be written as an optimization problem using

u cmd = min u f (u op , u) A u ≥ B (18)
The details of the computation of the wheelchair control values from user velocity input by minimizing the function f are given in [START_REF] Devigne | Low complex sensor-based shared control for power wheelchair navigation[END_REF].

IV. SIMULATIONS

In this section, we present the results of a simulation we performed as a first step to develop the proposed solution of power wheelchair navigation assistance on a sidewalk.

A. Simulation framework

As a part of our research activities, we developed a simulator for assisted power wheelchair navigation. This simulator has been designed with Unity3D and consists of a Virtual Environment in which we operate a virtual robotized wheelchair equipped with virtual distance sensors [START_REF] Devigne | Design of an immersive simulator for assisted power wheelchair driving[END_REF]. In this study, we use a framework designed to control a wheelchair in a virtual environment with any type of assistance (Fig. 5). This framework allows us to develop, test and tune driving assistance solutions more rapidly than while working with a real ground prototype. With such a simulator, we are able to modify the environment and the tests conditions with rapidity and flexibility. The virtual wheelchair (Fig. 6b) is here equipped with 12 distance sensors divided into 4 detection modules placed at each corner of the virtual wheelchair (Fig. 6a). The virtual environment is displayed on a computer screen as it is only used to demonstrate the properties of the proposed solution for assisted power wheelchair navigation on a sidewalk. As shown on Fig. 7, it consists of a 20 cm height sidewalk. The velocity parameters of the wheelchair are chosen to mimic a typical commercially-available wheelchair, such that the maximum forward speed is 0.7 m.s -1 and the maximum rotational speed is 0.5 rad.s -1 . Fig. 7: Virtual environment for the simulation.

B. Simulation results

Multiple simulation tests have been performed with different initial wheelchair positions. Fig. 8 shows the wheelchair trajectories for 3 different initial positions. In order to demonstrate the behavior of the wheelchair and evolution of wheelchair control inputs, we present the results of a single trial on Fig. 9. The user's linear and angular inputs are constant and respectively set to the maximum linear velocity value and zero for angular velocity. This leads the wheelchair to go forward at maximum speed. At the beginning, no negative obstacle is detected: the wheelchair is going towards the curb. Then, when the curb is detected, the linear velocity progressively decreases and the rotational velocity is modified in order to follow the curb. When the wheelchair drives parallel to the curb, the linear velocity increases as there is no danger to fall from the curb. Then, when the wheelchair is driving close to the curb dropoff, an adaptation of both velocities is performed in order to provide a curb-following behavior. When the wheelchair arrives at the end of the corridor in front of a drop-off, it stops and prevents the fall.

V. DISCUSSION

The purpose of this study was to provide a proof-ofconcept of a sensor-based shared control method providing navigation assistance in an environment consisting of negative obstacles. The resulting sensor-based driving assistance solution uses 12 low-cost distance sensors detecting distances to the floor around the wheelchair. Considering the sensors being able to detect multiple distances within different regions of interest local floor orientations could thus be determined around the wheelchair. Therefore, each constraint deduced from a sensor measurement is used to define 2 half-planes in the wheelchair velocity domain representing respectively allowed and a forbidden set of values induced by the sensor constraint. Wheelchair control is then computed from user input and sensors constraints so that it respects as much as possible user intention given by u op . The proposed Fig. 9: Simulation results: (a) Forward velocity applied to the wheelchair (b) Rotational velocity applied to the wheelchair (c) Representation of the trajectory of the virtual wheelchair in the simulated environment (which we recorded for visualization purpose only). The rectangles represent the wheelchair at the beginning (red) and at the end (green) of the simulation. solution has been developed and tested in simulation in the case of navigation in an environment with steep negative obstacles (e.g. curb, drop-off). Simulation results with different initial positions show our smart power wheelchair ability to avoid negative obstacles while respecting user intention (here driving forward). This is achieved by means of a smooth trajectory correction resulting from progressive regulation of the 2DoF wheelchair control inputs. The presented method necessitates an extrinsic calibration of the sensors as we use the sensor position information in our distance calculations. This consideration is easily respected when rigidly attaching the detection modules to the wheelchair frame thus ensuring a fixed position of the sensors. The findings obtained with the simulation framework encouraged us to equip a power wheelchair with such detection technology. Therefore, a standard M400 power wheelchair from permobil has been equiped with low-cost compliant Time-of-Flight (ToF) VL53L1X distance sensors from STMicroelectronics. The sensor-based shared control solution proposed in this paper is currently under tests. Videos showing wheelchair behavior in real environment conditions will be available soon at https://team.inria.fr/rainbow/fr/louise-devigne/. Finally, based on these results, simulations and tests will also be performed on the ability of the algorithm to provide relevant progressive assistance while negotiating a slope or a ramp.

VI. CONCLUSION

In this paper, we presented a shared-control solution for safe assisted power wheelchair navigation in an environment consisting of negative obstacles. This method regulates wheelchair control input values from constraints deduced from each sensor measured distance to the floor as well as local floor orientations. A gradual activation of the assistance allows the user to keep full wheelchair control when no obstacle is detected. When an obstacle such as a step is detected, a modular level of assistance allows progressive control input regulation. Therefore, in order to respect as much as possible user intention, user input is blended with a set of constraints deduced from the sensors. This provides an intuitive shared control scheme capable of assisting the user while needed without inducing a non-compliant trajectory. This approach coupled with the framework presented in [START_REF] Devigne | Low complex sensor-based shared control for power wheelchair navigation[END_REF] will allow a safe navigation indoors and outdoors.

The behavior of the system in simulation leads to validate our method. This proof-of-concept step is essential in order to technically validate the system before obtaining an ethical agreement for performing trials with non disabled volunteers as well as performing clinical trials with people with disabilities. The shared control model presented here is flexible, computationally inexpensive and independent of the range measurement sensor type. Moreover, this work showed the versatility of our method and encourages us to go further in our research process. In particular, future work will focus on improving the simulator physical engine in order to be able to test this solution of assisted power wheelchair navigation on a sidewalk to negotiate ramps.

  (a) Details for one sensor si (top view). (b) Details for one sensor si (right view).

Fig. 1 :

 1 Fig. 1: Definition of the robot frame

  (a) Definition of αy i . (b) Definition of αx i .

Fig. 2 :

 2 Fig. 2: Definition of α xi and α yi .

Fig. 3 :

 3 Fig. 3: Weighting function h di defined for feature d i . The weight is null in the safe interval and smoothly increases up to 1 in the tolerated intervals d - i , d s- i

Fig. 4 :

 4 Fig. 4: Wheelchair setup for the simulation.

Fig. 5 :

 5 Fig. 5: Framework used for this study on the wheelchair driving simulator.

Fig. 6 :

 6 Fig. 6: Wheelchair setup for the simulation.

Fig. 8 :

 8 Fig. 8: Wheelchair corrected trajectory for different initial positions.

Fig. 10 :

 10 Fig. 10: On-going test on a real power wheelchair.

Univ Rennes, INSA, CNRS, Inria, Irisa-UMR6074, Rennes, France.

Aspire Centre for Rehabilitation Engineering and Assistive Technology, University College London, UK.

ACKNOWLEDGEMENT

The authors would like to thank Éric Bazin from the IETR laboratory at INSA Rennes who was of great help during the development process.

This work has been funded by Inria associated team ISI4NAVE and by Institut des Neurosciences Cliniques de Rennes (INCR). This work is carried out as part of the INTERREG VA FMA ADAPT project "Assistive Devices for empowering disAbled People through robotic Technologies" http://adapt-project.com/index.php. The Interreg FCE Programme is a European Territorial Cooperation programme that aims to fund high quality cooperation projects in the Channel border region between France and England. The Programme is funded by the European Regional Development Fund (ERDF).


Virginie Lahaye
email: vlahaye@univ-lr.fr

Paco Bustamante

Willy Dabin

Olivier Van Canneyt

Franck Dhermain

C Cesarini

Graham J Pierce

Florence Caurant

New insights from age determination on toxic element accumulation in striped and bottlenose dolphins from Atlantic and Mediterranean waters

Keywords: Stenella coeruleoalba, Tursiops truncatus, Mercury, Cadmium, Diet, Exposure

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Due to their terminal position in the food web and their long life span, carnivorous marine mammals accumulate particularly high levels of mercury (Hg) and cadmium (Cd) [START_REF] Wagemann | Concentrations of heavy metals and organochlorines in marine mammals of northern waters: overview and evaluation[END_REF][START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans[END_REF]. The natural occurrence of these trace elements in seawater [START_REF] Nriagu | A history of global metal pollution[END_REF] has involved adaptations of marine organisms over geological time scales to the presence of toxic metals in their environment. Thus, marine mammals have developed efficient detoxification capacities to support elevated exposure to these metals (see reviews by [START_REF] Cuvin-Aralar | Mercury and selenium interaction: a review[END_REF][START_REF] Cuvin-Aralar | Mercury and selenium interaction: a review[END_REF]Das et al., 2000a). The demethylation of organic Hg in the liver leads to the production of non-toxic granules of tiemannite [START_REF] Koeman | Mercury-selenium correlations in marine mammals[END_REF][START_REF] Martoja | Identification of tiemannite as a probable product of demethylation of mercury by selenium in cetaceans. A complement to the scheme of the biological cycle of mercury[END_REF]. The accumulation of tiemannite granules makes the liver the ultimate organ of retention of Hg [START_REF] Wagemann | Methylmercury and total mercury in tissues of arctic marine mammals[END_REF]2000). Since these granules are not excreted [START_REF] Nigro | Intracellular storage of mercury and selenium in different marine vertebrates[END_REF], inorganic Hg would be stored in this organ for nearly the whole life. This detoxification process results in particularly elevated Hg concentrations in the liver, which is not the case when considering levels in the kidneys, where no storage of Hg under tiemannite would occur [START_REF] Cuvin-Aralar | Mercury and selenium interaction: a review[END_REF]. Like Hg in the liver, Cd levels can also be particularly elevated in the kidneys of marine mammals [START_REF] Wagemann | Concentrations of heavy metals and organochlorines in marine mammals of northern waters: overview and evaluation[END_REF][START_REF] Dietz | Have artic marine mammals adapted to high cadmium levels?[END_REF]. Its potential toxic effects are mitigated by the binding to metallothioneins both in the liver and the kidneys [START_REF] Klaassen | Role of metallothioneins in cadmium-induced hepatoxicity and nephrotoxicity[END_REF]Teigen et al., 1999). In other mammals such as humans, the biological half-life of Cd has been estimated to be a few months in liver and between 10 to 30 years in kidneys [START_REF] Friberg | Cadmium in the Environment[END_REF], and Cd could also be stored over very long time in the renal tissue of marine mammals.

In addition, Cd and Hg concentrations display an important variability in marine mammal tissues, which may be the result of biological and ecological influences [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans[END_REF].

At the individual scale, the most important parameter to be considered is the age, since these metals potentially accumulate throughout the life. Other factors such as growth features, gender, reproductive status and/or health aspects may also be important. At the population scale, feeding preference is probably the key factor controlling Cd and Hg levels because upper-level predators are mainly exposed to metals through their food [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans[END_REF].

Feeding on cephalopods is probably a major source of Cd for small cetaceans both because of the high Cd levels in these prey and because Cd is present mainly in bioavailable forms in their tissues [START_REF] Bustamante | Cephalopods as a vector for the transfer of cadmium to top marine predators in the north-east Atlantic Ocean[END_REF]2002). In both fish and cephalopods, Hg occurs mainly in organic forms which are highly bioavailable for the predators [START_REF] Bloom | On the chemical form of mercury in edible fish and marine invertebrate tissue[END_REF]Bustamante et al., submitted). As a result, species or populations that consume an important proportion of cephalopods can be expected to exhibit higher Cd levels in their tissues than piscivorous upper-level predators. The effects of feeding preferences on metal exposure may also be combined with other characteristics inherent to the species, the habitat and the geographical location, as concentrations in prey would reflect concentrations in their environment (e.g. Law et al., 1991;[START_REF] Bloom | On the chemical form of mercury in edible fish and marine invertebrate tissue[END_REF].

The present study aims at determining the main biological and ecological factors influencing

Cd and Hg concentrations in two small cetacean species inhabiting the French waters, the striped dolphins (Stenella coeruleoalba) and the bottlenose dolphins (Tursiops truncatus) (e.g. [START_REF] Forcada | Distribution of common and striped dolphins in the temperate waters of the Eastern North Atlantic[END_REF][START_REF] Goujon | Incidental catches of cetaceans by the French albacore tuna fishery: preliminary results[END_REF][START_REF] Gannier | Les Cétacés de Méditerranée nord-occidentale : estimation de leur abondance et mise en relation de la variation saisonnière de leur distribution avec l'écologie du milieu[END_REF][START_REF] Liret | English and French coastal Tursiops from Cornwall to the Bay of Biscay. Photo-Identification Catalogue[END_REF]. The two geographical areas involved are the Mediterranean Sea and the Bay of Biscay. These areas are characterised by different oceanological features which are likely to affect metal exposure to small cetaceans. Indeed, the Mediterranean Sea is well-known for its natural Hg enrichment (e.g. [START_REF] Bacci | Mercury in the Mediterranean[END_REF][START_REF] Cossa | The distribution and cycling of mercury species in the western Mediterranean[END_REF]. Furthermore, a previous study has reported that striped dolphins from the Mediterranean Sea exhibited much higher Hg levels than those from the Atlantic [START_REF] André | Comparative study of mercury accumulation in dolphins (Stenella coeruleoalba) from French Atlantic and Mediterranean coasts[END_REF]. However, this report did not take age into account, only body length, which may introduce a bias. Indeed, the use of length as a covariate to detect differences in pollutant levels between areas does not permit comparisons between individuals having reached their asymptotic length or/and between groups with different growth curves [START_REF] Monaci | Trace elements in striped dolphins (Stenella coeruleoalba) from the western Mediterranean[END_REF]. Striped dolphins from the Mediterranean Sea are smaller than those from the Atlantic [START_REF] Di-Méglio | Growth comparison in striped dolphins, Stenella coeruleoalba, from the Atlantic and Mediterranean coasts of France[END_REF], which may affect Hg levels in these two populations.

As a consequence, understanding accumulation of toxic elements with age is mandatory to establish the effective metal impregnation state of small cetaceans from the Mediterranean and Atlantic waters and to allow further comparison between both areas. Renal Cd and hepatic Hg are measured in order to provide a long-term overview of the impregnation. In addition, the influence of diet on metal exposure to striped and bottlenose dolphins is investigated using metal concentrations in reported prey from each area. Thus, the influence of diet on metal levels in these small cetaceans could be clarified both at the intra-and interspecific scale.

Material and methods

Studied areas

The Bay of Biscay is situated in the north-eastern Atlantic and extends from 1 to 10°W and 43 to 48°N (Fig. 1). This area is characterised by a variable distance of the shelf-edge from the coastline, the continental shelf width varying from 60 to 100 nautical miles (NM) in the northern part of the Bay (up to 45°N) to 25-30 NM in the southern part, and reaching 3 NM at the latitude of the Capbreton trough. Within this area, Arcachon Bay (see Fig. 1) constituted a semi-enclosed shallow habitat for bottlenose dolphins until 2001, when the last individual of this small resident population was found stranded [START_REF] Ferrey | Statut et comportement social du grand dauphin Tursiops truncatus dans le bassin d'Arcachon[END_REF]J.J. Boubert, pers. comm.).

In contrast, the continental shelf width is very limited along the French Mediterranean coasts, with the largest width encountered in the Gulf of the Lion (15 to 45 NM, see Fig. 1), as compared to 2.5-10 NM at the eastern of 5°30 E. These latter areas are characterised by an abrupt shelf-edge, with deep canyons (up to -2000m) close to the coastline.

Biological material

Small cetaceans

Between 1999 and 2004, 55 stranded small cetaceans were sampled along the whole French Mediterranean (n = 15) and Atlantic coasts (n = 40) by the Réseau National Echouage (RNE) co-ordinated by the Centre de Recherche sur les Mammifères Marins (CRMM) of La Rochelle (France). Striped dolphins were the most common species (n = 40) whereas only 15 bottlenose dolphins were collected. Among the 10 Atlantic bottlenose dolphins, 3 animals were identified as the last bottlenose dolphins from the small resident group of Arcachon Bay (J.J. Boubert, pers. comm.), the history of which is well-known [START_REF] Ferrey | Statut et comportement social du grand dauphin Tursiops truncatus dans le bassin d'Arcachon[END_REF]. During the necropsies, teeth (n = 55) were collected for age determination, and liver (n = 55) and kidney (n = 48) for trace element analyses (Table 1). These samples were stored at -20°C until being processed in the laboratory.

Age was determined at the CRMM, following the recommendations of [START_REF] Perrin | Age determination of toothed whales and sirenians[END_REF]. Briefly, this procedure consists of counting Growth Layer Groups (GLGs) from teeth sections, assuming that one GLG equals one year. All carcasses were in good post-mortem condition, except a single striped dolphin from the Mediterranean Sea. Owing to the small number of dolphins collected along the Mediterranean coast (see Table 1), the single putrefied animal has been included in the study. This individual can be identified in figures since it is the oldest striped dolphins (i.e. 27 years-old).

Prey

Selected prey from each area were also sampled for toxic element analyses. The selection of species and their size was based upon previous dietary studies on bottlenose and striped dolphins originating from the study areas [START_REF] Würz | Mediterranean cetaceans and fisheries: do they exploit the same resource?[END_REF][START_REF] Blanco | Diet of the bottlenose dolphin (Tursiops truncatus) in the western Mediterranean Sea[END_REF][START_REF] Spitz | Le régime alimentaire des petits cétacés et sa variabilité temporelle: un indicateur des changements environnementaux ? EPHE[END_REF]Astruc et al., in press;Pusineri et al., in press;Spitz et al., submitted). Prey sampling occurred during IFREMER groundfish surveys, in winter and spring 1997 and in autumn 2001-2003 (RESSGASC andEVHOE campaigns, respectively). For the Mediterranean Sea, sampling was conducted in May and October 2004 (MERMED campaigns). Whereas RESSGASC and MERMED surveys occurred only on the continental shelf, EVHOE surveys extended to the shelf-edge, allowing the collection of mesopelagic species. All prey samples were immediately frozen at -20°C on board and then stored until being processed in the laboratory.

After species determination, each prey was weighed and measured. Metal analyses were carried out using the whole prey in order to reflect the exposure to predators. As cephalopods represent a major pathway of Cd exposure [START_REF] Bustamante | Cephalopods as a vector for the transfer of cadmium to top marine predators in the north-east Atlantic Ocean[END_REF]2002) and since Cd levels are particularly low in fish (Lahaye et al., in press), Cd levels were assayed in cephalopods but not in fish. In contrast, the presence of Hg in its bioavailable form in both fish and cephalopod [START_REF] Bloom | On the chemical form of mercury in edible fish and marine invertebrate tissue[END_REF]Bustamante et al., submitted) necessitates measurements of Hg concentrations in both prey items.

Metal analyses

All equipment used in the sample processing was cleaned, and subsequently decontaminated for 24 h in a solution composed of 35 ml HNO 3 (65%) and 50 ml HCl (36%) for 1 L of Milli-Ro quality water. Fresh samples were freeze-dried and ground to powder. The mean ratio between dry weight (d.wt.) and wet weight (w.wt.) was 0.28 for liver and 0.23 for kidney.

Each sample was then treated in duplicate.

For total Hg measurements, aliquots ranging from 0.2 to 2 mg of dried-material were analysed in an Advanced Mercury Analyser spectrophotometer (Altec AMA 254). Hg determination in the AMA 254 involved evaporation of Hg by progressive heating to 800°C under oxygen atmosphere for 3 min, and subsequent amalgamation on a gold net. The net was then heated to liberate the collected Hg, which was measured by UV atomic-absorption spectrophotometry.

For Cd analyses, 2 aliquots of approximately 200 mg of each homogenised dry sample were digested with 3.5 ml of 65% HNO 3 at 60°C for 3 days. The digested contents were then diluted to 10 ml in milli-Q quality water. Then Cd contents were assayed using a flame (Varian 250 Plus) and graphite furnace (Hitachi Z-5000) atomic absorption spectrophotometer with deuterium and Zeeman background correction, respectively. Quality controls were made using standard reference materials (National Research Council of Canada). These standards were treated and analysed under the same conditions as the samples and results were in good agreement with the certified values (Table 2). In addition, intercalibration exercices were carried out on material from the International Atomic Energy Agency. Detection limits were determined with blank analyses and the obtained values were 0.005 µg.g -1 d.wt. for Hg, 0.4 and 0.002 µg.g -1 d.wt. for Cd, respectively using flame and furnace AAS.

Data treatment

Metal concentrations were expressed as µg.g -1 wet weight (w.wt.). All concentrations below the detection limit were replaced with "dummy values" that were half of the detection limit in order to allow further statistical comparisons [START_REF] Gibbons | Statistical methods for detection and quantification of environmental contamination[END_REF]. Figures showing metal concentrations against age were presented on a logarithmic scale in order to better describe the relationship of metals with age in the youngest dolphins since they constituted a large part of the sampling (see Table 1). Statistical analyses were performed using XL-STAT Pro 7.0. Metal concentrations were natural log-transformed in order to reduce skewness when striped dolphins were taken into account. When the relationship of metal concentrations with age was linear, analysis of covariance (ANCOVA, Quinn & Keough 2002) was used to determine the influence of gender and area, with age as the covariate. When no influence of age on metal concentrations was established, analyse of variance (ANOVA) was used to compare groups (i.e. per gender or area).

Results

Metal levels in bottlenose dolphins

Concentrations of both metals displayed high variability: overall coefficients of variations (CV) were 96% for Hg in liver and 103% for Cd in kidneys. Hepatic Hg concentrations ranged from 1.5 to 331 µg -1 w.wt. (Fig. 2a) and renal Cd concentrations ranged from 0.06 to 3.05 µg.g -1 w.wt. (Fig. 2b).

Correlation with age was significant for both hepatic Hg (p = 0.001) and renal Cd (p < 0.0001, Table 3). As the three bottlenose dolphins from Arcachon Bay constituted a particular social unit, these individuals were not taken into account for the global geographical comparison (Mediterranean Sea vs Atlantic Ocean). Figure 2 shows that Mediterranean bottlenose dolphins exhibited much higher Hg levels in liver than Atlantic ones (p = 0.032, Table 3) whereas Cd levels were rather similar in these two groups (p = 0.207, Table 3).

The three 3 individuals from Arcachon Bay exhibited very low Cd levels compared to the other Atlantic animals (Fig. 2b). Among the Arcachon Bay animals, two individuals exhibited hepatic Hg concentrations as high as those of Mediterranean bottlenose dolphins (Fig. 2a).

Metal levels in striped dolphins

The global CV of hepatic Hg was particularly elevated for striped dolphins (i.e. 221%). The highest concentration was found in a 27-year-old Mediterranean striped dolphin (1033 µg.g -1 w.wt; see Fig. 3a), which was also the single putrefied specimen of the overall sampling.

Concentration variability was much lower for renal Cd, with a CV of 94%. Surprisingly, the maximal value of renal Cd was obtained in a relatively young Atlantic striped dolphin (age estimated to be 1.3-year-old) reaching 40.2 µg Cd.g -1 w.wt. (see Fig. 3b).

Metal accumulation with age in striped dolphins was only apparent for hepatic Hg (Fig. 3a; p < 0.0001, Table 3). In addition, no influence of the geographical area on the bioaccumulation rates was observed for this metal (p = 0.691, Table 3). In contrast, renal Cd concentrations would increase until 2 years-old, and then would remain independent of the age (Fig. 3b).

However, when looking at calves of 2 years-old and less, Cd concentrations in the kidneys were more influenced by the geographical area (p = 0.018) than the age (p = 0.635) and the interaction between these two parameters was not significant (p = 0.741, Table 3). In addition, although the Mediterranean sampling was limited compared to the Atlantic sampling, the two adult Mediterranean striped dolphins exhibited quite similar renal Cd concentrations to the Atlantic ones (Fig. 3b).

The high number of striped dolphins sampled along the Atlantic coast (n = 30; see Table 1) allowed us to consider the influence of gender on metal accumulation. No influence of gender on metal concentrations was established for either hepatic Hg (p = 0.637) or renal Cd (p = 0.515, Table 4).

Inter-specific comparisons

Owing to the limited Mediterranean sampling, inter-specific comparisons were carried out only for the Atlantic. Since bottlenose dolphins from Arcachon Bay had lived isolated for a long time and therefore displayed different metal concentrations compared to the other individuals from the Atlantic coast, they were not included in the inter-specific comparison.

Bioaccumulation rates of Hg in liver with age were similar in Atlantic bottlenose and striped dolphins (p = 0.774) whereas Cd bioaccumulation in the kidneys with age was significantly higher in striped dolphins than in bottlenose dolphins (p = 0.026, Table 5).

Metal levels in prey

Mediterranean prey displayed higher Hg levels than Atlantic ones, the mean length of the prey analysed being equivalent for both areas. In addition, cephalopod and fish exhibited similar Hg concentrations, the highest level being reached in a cephalopod specimen, Illex coindetii, from the Mediterranean Sea (490 ng.g -1 w.wt). Among fish, the Myctophid Notoscopelus kroeyeri from the Atlantic displayed the highest Hg level (105 ± 80 ng.g -1 w.wt.). However, no Myctophids from the Mediterranean area could be sampled.

Cd concentrations in cephalopods displayed high intra-and inter-specific variability, and especially for the Mediterranean Sea where samples had the lowest variability in their mean length (Table 6). For example, the squid Loligo vulgaris was characterised by the lowest Cd levels in both Atlantic and Mediterranean Sea (132 ± 54 and 99 ± 111 ng.g -1 w.wt., respectively) but also by the highest CV (41 and 112%, respectively). In the Atlantic, Cd levels in cephalopods could be described following this pattern: Teuthowenia megalops (Cranchids) > Histioteuthis reversa (Histioteuthids) > I. coindetii (Ommastrephids) > L. vulgaris (Loliginids).

Discussion

Metal concentrations displayed high variability in storage tissues of striped and bottlenose dolphins from the Mediterranean and Atlantic areas. The extreme CV values obtained in our study (i.e. 94 to 221%) have previously been reported in other marine mammal species for these toxic elements (e.g. [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Bustamante | Trace element bioaccumulation in grey seals Halichoerus grypus from the Faroe Islands[END_REF]. This underlines the fact that metal levels in upper-level predators are likely to be influenced by numerous factors, such as age, gender, body condition, geographical location and/or dietary preferences [START_REF] Aguilar | Biological factors affecting variability of persistent pollutant levels in cetaceans[END_REF].

Concerning the influence of gender, no effect was detected in striped dolphins stranded along the Atlantic coast for either hepatic Hg or renal Cd concentrations (Table 4). This result is consistent with those obtained for striped dolphins from the Pacific Ocean [START_REF] Honda | Heavy metal concentrations in muscle, liver and kidney tissue of striped dolphin, Stenella coeruleoalba, and their variations with body length, weight, age and sex[END_REF]. Some differences of Cd concentrations between genders have been reported for other marine mammals, e.g. long-finned pilot whales Globicephala melas and grey seals Halichoerus grypus, and were attributed to their sexual dimorphism [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Bustamante | Trace element bioaccumulation in grey seals Halichoerus grypus from the Faroe Islands[END_REF]. Although male striped dolphins from the Atlantic Ocean are slightly bigger than females [START_REF] Di-Méglio | Growth comparison in striped dolphins, Stenella coeruleoalba, from the Atlantic and Mediterranean coasts of France[END_REF], this sexual dimorphism might not be sufficient to induce differences in Cd levels between genders. This also suggests that the transfer of Cd to offspring during pregnancy and lactation is not an important route of excretion for female striped dolphins.

Mercury

Age was the major factor affecting hepatic Hg concentrations in bottlenose and striped dolphins from the Atlantic and Mediterranean waters (Table 3). Such an increase of Hg concentrations with age has previously been demonstrated in several cetacean species (e.g. [START_REF] Honda | Heavy metal concentrations in muscle, liver and kidney tissue of striped dolphin, Stenella coeruleoalba, and their variations with body length, weight, age and sex[END_REF]Paludan-Müller et al., 1993;[START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Monaci | Trace elements in striped dolphins (Stenella coeruleoalba) from the western Mediterranean[END_REF].

Comparisons between the two studied species do not reveal any difference in Hg accumulation in the Atlantic (Table 5). Such similar Hg accumulation trends between bottlenose (i.e. mainly fish-eaters in this area: [START_REF] Spitz | Le régime alimentaire des petits cétacés et sa variabilité temporelle: un indicateur des changements environnementaux ? EPHE[END_REF]) and striped dolphins (i.e. mixed item-eaters: Pusineri et al., in press; Spitz et al., submitted) are consistent with the high bioavailability of Hg in both fish and cephalopods [START_REF] Bloom | On the chemical form of mercury in edible fish and marine invertebrate tissue[END_REF]Bustamante et al., submitted). However, geographical comparisons highlighted two different patterns: 1) bottlenose dolphins from the Mediterranean Sea displayed higher Hg concentrations than Atlantic ones whereas 2) Mediterranean and Atlantic striped dolphins exhibited similar Hg concentrations at a given age (Fig. 2a, Fig. 3a, Table 3).

Firstly, the Hg accumulation in Mediterranean bottlenose dolphins compared to Atlantic animals resulted in mean Hg levels about 5 times higher in Mediterranean bottlenose dolphins than Atlantic animals (i.e. 204 ± 121 vs 38 ± 41 µg.g -1 w.wt., respectively). Mediterranean prey displayed higher Hg levels than Atlantic prey (Table 6). Thus, higher Hg levels in Mediterranean prey and Mediterranean bottlenose dolphins were in agreement with the Hg enrichment in Mediterranean food webs, due to higher methylation rates of Hg in the anoxic layer waters of this area [START_REF] Bacci | Mercury in the Mediterranean[END_REF][START_REF] Cossa | The distribution and cycling of mercury species in the western Mediterranean[END_REF].

Surprisingly, and conversely to bottlenose dolphins, no difference in Hg bioaccumulation was established between Mediterranean and Atlantic striped dolphins. The highest Hg concentration (1033 µg.g -1 w.wt.) was encountered in a putrefied 27 year-old Mediterranean dolphin. Such an extreme elevated level has been previously reported for several striped dolphins from the Mediterranean Sea (see Table 7), but without taking into account their age or body condition. In their previous report on Hg levels in striped dolphins from the Atlantic and the Mediterranean Sea, [START_REF] André | Comparative study of mercury accumulation in dolphins (Stenella coeruleoalba) from French Atlantic and Mediterranean coasts[END_REF] used mostly mature animals, which had reached their asymptotic length. As the life-span of striped dolphins might reach 40 years [START_REF] Miyasaki | An outline of the biological studies on Stenella coeruleoalba[END_REF][START_REF] Honda | Heavy metal concentrations in muscle, liver and kidney tissue of striped dolphin, Stenella coeruleoalba, and their variations with body length, weight, age and sex[END_REF], these individuals could also have been from about 10 to 40 years old, which makes it difficult to establish geographical comparisons for these individuals. Therefore, the previous report of higher Hg levels in Mediterranean striped dolphins compared to Atlantic ones [START_REF] André | Comparative study of mercury accumulation in dolphins (Stenella coeruleoalba) from French Atlantic and Mediterranean coasts[END_REF] can not be assessed. This underlines the fact that relationships of metal concentrations with body length is not appropriate for geographical comparisons, especially when growth curves are clearly different [START_REF] Di-Méglio | Growth comparison in striped dolphins, Stenella coeruleoalba, from the Atlantic and Mediterranean coasts of France[END_REF]. However, if the environmental chemistry of water mass was considered alone, the Mediterranean striped dolphins would display higher Hg concentrations than the Atlantic ones. Hence, feeding and habitat preferences need to be taken into account.

In the Bay of Biscay, striped dolphins are mainly found in oceanic waters, where they primarily feed upon on mesopelagic fish and cephalopods (Pusineri et al., in press). Some intrusions over the continental shelf could also occur [START_REF] Forcada | Distribution of common and striped dolphins in the temperate waters of the Eastern North Atlantic[END_REF]Kiszka et al., in press), as underlined by the simultaneous occurrence of neritic and oceanic species in stomachs of stranded animals (Spitz et al., submitted). In contrast, in north-western Mediterranean waters, striped dolphins would occur equally over the continental shelf, the shelf-edge and in deeper waters [START_REF] Gannier | Les Cétacés de Méditerranée nord-occidentale : estimation de leur abondance et mise en relation de la variation saisonnière de leur distribution avec l'écologie du milieu[END_REF]. The diet of stranded Mediterranean striped dolphins is mainly based on cephalopods and demersal fish from the upper shelf, at comparable proportions in terms of reconstructed biomass (Astruc et al., in press). Regarding Hg levels in the Atlantic prey, Myctophid fish were the prey with the highest concentrations (Table 6). Indeed, these mesopelagic fish are well-known to exhibit particularly high Hg levels [START_REF] Monteiro | Mercury concentrations in prey fish indicate enhanced bioaccumulation in mesopelagic environments[END_REF]Thompson et al., 1998). No Mediterranean Myctophids could be sampled in this study but these mesopelagic fish could be expected to also present elevated mercury levels, probably higher than those from the Atlantic as a result of the Hg enrichment in this area [START_REF] Bacci | Mercury in the Mediterranean[END_REF]. Our results concerning Hg concentrations in the liver of the striped dolphins strongly suggest that they do not feed on mesopelagic prey on a long time-scale in the Mediterranean waters in contrast to those from the Atlantic. Thus, different feeding behaviour could explain similar Hg tissue concentrations because mesopelagic prey species in the Atlantic display similar Hg levels to demersal prey in the Mediterranean, leading to similar Hg exposure in both areas.

Cadmium

Contrary to Hg, different patterns of Cd bioaccumulation occurred between the two studied species. Indeed, despite the limited number of bottlenose dolphins sampled (see Table 1), comparisons between the two species in the Atlantic revealed far lower Cd levels at a given age in bottlenose dolphins than in striped dolphins (Table 5). Some piscivorous marine mammals such as harbour porpoise (Phocoena phocoena), belugas (Delphinapterus leucas), grey seals (H. grypus) and bottlenose dolphins from other areas also accumulate low levels of Cd (e.g. [START_REF] Falconer | Trace metals in the common porpoise, Phocoena phocoena[END_REF][START_REF] Wagemann | Overview and regional and temporal differences of heavy metals in artic whales and ringed seals in the Canadian Arctic[END_REF]Szefer et al., 2002;[START_REF] Bustamante | Trace element bioaccumulation in grey seals Halichoerus grypus from the Faroe Islands[END_REF][START_REF] Decataldo | Association of metals (mercury, cadmium and zinc) with metallothionein-like proteins in storage organs of stranded dolphins from the Mediterranean sea (Southern Italy)[END_REF]. The low Cd levels encountered in bottlenose dolphins would be induced by a diet dominated by fish [START_REF] Spitz | Le régime alimentaire des petits cétacés et sa variabilité temporelle: un indicateur des changements environnementaux ? EPHE[END_REF], which contain low Cd levels (Amiart-Triquet et al., 1983;[START_REF] Bustamante | Bioaccumulation des éléments traces (métaux et terres rares) chez les mollusques céphalopodes et bivalves pectinidés. Implication de leur biodisponibilité pour le transfert vers les prédateurs[END_REF]Lahaye et al., in press). In contrast, regarding elevated Cd levels in striped dolphins, high Cd concentrations have also been reported in the tissues of teuthophageous species (e.g. [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF][START_REF] Holsbeek | Heavy Metals, Organochlorines and Polycyclic Aromatic Hydrocarbons in Sperm Whales Stranded in the Southern North Sea During the 1994/1995 Winter[END_REF][START_REF] Bustamante | Trace elements in two odontocete species (Kogia breviceps and Globicephala macrorynchus) stranded in New Caledonia (South Pacific)[END_REF]. As feeding on cephalopods constitutes a major source of Cd for small cetaceans [START_REF] Bustamante | Cephalopods as a vector for the transfer of cadmium to top marine predators in the north-east Atlantic Ocean[END_REF]2002), the elevated Cd concentrations in striped dolphins wellreflected their important squid consumption in the Atlantic area (Pusineri et al., in press; Spitz et al., submitted).

No difference in Cd accumulation was found in bottlenose dolphins from the Atlantic and Mediterranean areas (Table 3). However, the 3 individuals from Arcachon Bay displayed particularly low Cd concentrations compared to the individuals stranded along the Atlantic coast (Fig. 1b). Consequently, the low Cd levels encountered in the resident bottlenose dolphins from Arcachon Bay may be the result of a specialised diet resulting from particular prey availability in this restricted area. Most of the fish encountered are coastal species rather than demersal ones and the main source of cephalopods in this bay is common cuttlefish (Sepia officinalis). Indeed, Arcachon Bay is a mating area for this species, which die after the spawning, adults therefore being present in this area only during a very limited period of the year [START_REF] Poulard | Interaction between marine populations and fishing activities: temporal patterns of Landing of La Rochelle trawlers in the Bay of Biscay[END_REF]. Consequently, the Cd levels obtained in the bottlenose dolphins from Arcachon Bay were clearly due to the even more limited occurrence of cephalopods in their feeding regime compared to the other individuals from the Atlantic area, for which stomachs generally contain about 10% of cephalopods in term of reconstructed biomass [START_REF] Spitz | Le régime alimentaire des petits cétacés et sa variabilité temporelle: un indicateur des changements environnementaux ? EPHE[END_REF].

In addition, Cd accumulated significantly with age in bottlenose dolphins which was not the case for striped dolphins (Table 3). Like bottlenose dolphins, harbour porpoises and belugas would exhibit increasing concentration of renal Cd during their life [START_REF] Falconer | Trace metals in the common porpoise, Phocoena phocoena[END_REF][START_REF] Wagemann | Overview and regional and temporal differences of heavy metals in artic whales and ringed seals in the Canadian Arctic[END_REF]Szefer et al. 2002). Concerning striped dolphins, the apparent increase of Cd in the kidneys until 2 years old, and then followed by a plateau (Fig. 3b), can not be statistically confirmed with our sampling. Indeed, when looking at calves of 2 yearsold and less, renal Cd concentrations were more influenced by the geographical area than the age (Table 3). Because it was opportunistic, our sampling is however limited to a few individuals for the Mediterranean area (see Table 1). Our results fall within the range of Cd concentrations reported in previous studies in the Mediterranean Sea but such a comparison with previous studies also showed that immature Mediterranean striped dolphins from our study were smaller and also younger than those from other studies (see Table 7). The particularly low Cd levels encountered in Mediterranean calves compared to Atlantic calves may also be the consequence of the sampling characteristics of this study. Indeed there is no significant difference when interaction between age and area is considered (Table 3). In addition, the proportion of cephalopods in the diet did not seem to differ between Atlantic and Mediterranean striped dolphins, as revealed by stomach content analyses (Astruc et al., in press; Pusineri et al., in press; Spitz et al., submitted). Given that Mediterranean cephalopods displayed similar or even higher Cd levels compared to Atlantic cephalopods (Table 6), the similar Cd concentrations measured in the kidneys of two Mediterranean striped dolphins compared to Atlantic ones may reflect a similar Cd impregnation state for these two populations.

A larger sample size is also required to better understand Cd accumulation with age in Atlantic and Mediterranean striped dolphins. Indeed, a logarithmic pattern of Cd accumulation was previously described for Pacific striped dolphins [START_REF] Honda | Heavy metal concentrations in muscle, liver and kidney tissue of striped dolphin, Stenella coeruleoalba, and their variations with body length, weight, age and sex[END_REF], as well as in long-finned pilot whales G. melas [START_REF] Caurant | Ecological and biological factors controlling the concentrations of trace elements (As, Cd, Cu, Hg, Se, Zn) in delphinids Globicephala melas from the North Atlantic Ocean[END_REF], and arctic narwhals Monodon monoceros [START_REF] Dietz | Regional and inter annual patterns of heavy metals, organochlorines and stable isotopes in narwhals (Monodon monoceros) from West Greenland[END_REF], which consume a large proportion of squids. A rapid increase of Cd concentrations in calves could be explained by transfer of the metal through milk during the suckling period [START_REF] Honda | Heavy metal concentrations in muscle, liver and kidney tissue of striped dolphin, Stenella coeruleoalba, and their variations with body length, weight, age and sex[END_REF] as well as a higher absorption efficiency generally exhibited by young mammals [START_REF] Underwood | Trace elements in human and animal nutrition[END_REF]. Hence, Cd concentrations increased rapidly in calves to levels closed to the threshold likely to induce toxic effects [START_REF] Dietz | Have artic marine mammals adapted to high cadmium levels?[END_REF] (i.e. up to 40 µg.g -1 w.wt., see Fig. 3b). The fact that these concentrations would be maintained constant for the rest of the striped dolphin's life (Fig. 3b) suggests an efficient adaptation of accumulation processes in response to high exposure to Cd through the consumption of cephalopods.

Conclusions

The present study underlines the importance of considering age when making geographical comparisons of toxic element accumulation in upper-level predators. Hence, taking into account age as a covariate has permitted us to control for biometric differences in the two populations of striped dolphins considered in this study. Thus, the similar Hg levels obtained in Atlantic and Mediterranean striped dolphins highlighted the influence of feeding behaviour on Hg concentrations and suggested that striped dolphins feed in mesopelagic waters of the Atlantic whereas striped dolphins from the Mediterranean Sea feed on other species over shallower waters. Further investigations on feeding behaviour of striped dolphin and quantitative estimation of exposure to metals through the diet are needed, and especially for other areas of the Mediterranean Sea. Moreover, Cd concentrations in the kidneys would well-reflect the occurrence of cephalopods in the diet on a long time-scale, as underlined by the particular Cd impregnation state of animals that have inhabited Arcachon Bay throughout their life. Concerning striped dolphins, the similar Cd impregnation state in Mediterranean and Atlantic populations obtained when taking age into account will have to be reinvestigated in the future with a larger sample size. Overall, our results suggest that metal measurements could constitute efficient additional tracers to better understand long-term feeding preferences of these pelagic upper-level predators. Spitz, J., Richard, E., Meynier, L., Pusineri, C., Ridoux, V., submitted With: %H, percent of humidity; nd not determined. * Length refers to standard length for fish and mantle length for cephalopod.

  . Dietary plasticity of the oceanic striped dolphin, Stenella coeruleoalba, in the neritic Bay of Biscay. Journal of Sea Research. Storelli, M.M., Ceci, E., Marcotrigiano, G.O., 1998. Comparison of total mercury, methylmercury, and selenium in muscle tissues and in the liver of Stenella coeruleoalba (Meyen) and Caretta caretta (Linnaeus). Bulletin of Environmental and Contaminant Toxicology 61, 541-547. Szefer, P., Zdrojewska, I., Jensen, J., Lockyer, C., Skora, K., Kuklik, I., Malinga, M., 2002. Intercomparison studies on distribution and coassociations of heavy metals in liver, kidney and muscle, of harbor porpoise, Phocoena phocoena, from southern Baltic and coastal waters of Denmark and Greenland. Archives of Environmental Contamination and Toxicology 42, 508-522. Teigen, S., Andersen, R., Daae, H.L., Skaare, J.U., 1999. Heavy metal content in liver and kidneys of grey seals (Halichoerus grypus) in various life stages correlated with metallothioneins levels: some metal-binding characteristics of this protein. Environmental Toxicology and Chemistry 18, 2364-2369. Thompson, D.R., Furness, R.W., Monteiro, L.R., 1998. Seabirds as biomonitors of mercury inputs to epipelagic and mesopelagic marine food chains. Science of the Total Environment, 213, 299-305.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Relationships between age and (a) hepatic Hg and (b) renal Cd concentrations (µg.g -1 w.wt.) in bottlenose dolphins stranded along the French Atlantic (white squares) and

Figure 3 .

 3 Figure 3. Relationships between age and (a) hepatic Hg and (b) renal Cd concentrations (µg.g -1 w.wt.) in striped dolphins stranded along the French Atlantic (white squares) and

  Figure 1

Table 2 .

 2 Toxic element levels (mean ± SD; µg.g -1 d.wt.) in standard reference materials (with 6 replicates).

	Species	Tissue	Age category		Gender
	Sampling area	liver kidney < 2 y. old older	♂	♀	nd
	Stenella coeruleoalba
	Bay of Biscay	30	30	12	18	17	13	-
	Mediterranean Sea	10	6	6	4	6	3	1
	Tursiops truncatus
	Bay of Biscay	10*	9*	3	7	5	5	-
	Mediterranean Sea	5	3	1	4	1	4	-

Table 3 .

 3 Influence of age and area on metal levels in small cetaceans stranded along the French Mediterranean and Atlantic coasts, determined by ANCOVA. Influence of the studied parameters is given with Fisher's F and its associated p-value (in brackets). * ANCOVA on renal Cd concentrations refers to young striped dolphins (≤ 2 years old), for which Cd accumulation with age was linear.

						Studied parameters
	Species	Metal	ddl	R²
					Age	Area	Age x Area
	T. truncatus	hepatic Hg	8	0.900	26.714 (p = 0.001)	1.286 (p = 0.290) 6.721 (p = 0.032)
		renal Cd	5	0.978	156.768 (p < 0.0001) 5.198 (p = 0.072) 2.105 (p = 0.207)
	S. coeruleoalba	hepatic Hg	36	0.820	155.5 (p < 0.0001)	0.116 (p = 0.735) 0.160 (p = 0.691)
		renal Cd*	12	0.767	0.237 (p = 0.635)	7.453 (p = 0.018) 0.115 (p = 0.741)

Table 4 .

 4 Influence of age and gender on metal levels in Atlantic striped dolphins. Influence of the studied parameters is given with Fisher's F and its associated p-value (in brackets).

	Metal	Statistical test	ddl	R²	Age	Studied parameters Gender	Age x Gender
	hepatic Hg	ANCOVA	26	0.778	155.5 (p < 0.0001) 0.442 (p = 0.512) 0.229 (p = 0.367)
	renal Cd	ANOVA	28	0.002	0.051 (p = 0.822) 0.435 (p = 0.515)	nd

Table 5 .

 5 Variations of metal concentrations between species at the Atlantic scale, determined using ANCOVA. Influence of the studied parameters is given with Fisher's F and its associated p-value (in brackets).

					Studied parameters
	Metal	ddl	R²
				Age	Species	Age x species
	hepatic Hg	33	0.790	70.36 (p < 0.0001)	0.075 (p = 0.786)	0.084 (p = 0.774)
	renal Cd	32	0.599	6.25 (p = 0.018)	37.547 (p < 0.0001)	5.426 (p = 0.026)

Table 6 .

 6 Toxic element levels (ng.g -1 w.wt.) in prey from the Atlantic and the Mediterranean Sea.

	TAXON			Length (mm)*	[Hg] (ng.g -1 w.wt)	[Cd] (ng.g -1 w.wt)
	Family
	Species	Area n % H mean ± sd	range	CV% mean ± sd	range	CV% mean ± sd	range	CV%
	FISH
	Clupeidae
	Sardina pilchardius	Atl. 6	61	154 ± 4 148 -159 2.6	23 ± 7	19 -34	26	nd	nd	nd
		Med. 6	61	145 ± 6 137 -150 3.8	94 ± 22	67 -127	24	nd	nd	nd
	Engraulidae
	Engraulis encrasicolus	Atl. 6	70	118 ± 4 112 -122	3	28 ± 20	26 -32	7.2	nd	nd	nd
		Med. 6	73	109 ± 4 104 -113 4.1	50 ± 9	43 -61	17	nd	nd	nd
	Gadidae
	Micromesistius poutassou Atl. 3	75	141 ± 2 139 -144 1.7	16 ± 1	16 -17	5.2	nd	nd	nd
		Med. 3	75	135 ± 4 131 -138 2.7	21 ± 2	20 -23	8.5	nd	nd	nd
	Merluccidae
	Merluccius merluccius	Atl. 3	79	257 ± 42 225 -305 16	33 ± 14	18 -46	42	nd	nd	nd
		Med. 3	79	222 ± 6 215 -226 2.7	45 ± 12	34 -58	26	nd	nd	nd
	Myctophidae
	Notoscopelus kroeyeri	Atl. 6	70	93 ± 23 70 -125	23	105 ± 80	29 -210	77	nd	nd	nd
	CEPHALOPOD
	Cranchidae
	Teuthowenia megalops	Atl. 1	83	181			34			1320
	Histioteuthidae
	Histioteuthis reversa	Atl. 5	85	40 ± 24	20 -80	59	15 ± 5	10 -24	34	383 ± 196 148 -665	21
	Loliginidae
	Loligo vulgaris	Atl. 26 77	148 ± 50 73 -256	34	56 ± 22	24 -97	40	132 ± 54	58 -238	41
		Med. 12 74	173 ± 54 120 -265 31	146 ± 66	68 -250	45	99 ± 111	20 -434	112
	Ommastrephidae
	Illex coindetii	Atl. 22 79	130 ± 54 73 -272	42	41 ± 17	14 -69	41	290 ± 94 150 -520	32
		Med. 6	67	138 ± 19 118 -161 14	277 ± 150 110 -490	54	697 ± 391 380 -1290 56

Acknowledgements

We are very grateful to all the participants of the French stranding network (RNE) for the collection of dolphin samples and to IFREMER for facilitating the prey sampling. Thanks to V. Loizeau and C. Melon for collecting Mediterranean prey, and to C. Churlaud from the Centre Commun d'Analyses from La Rochelle for technical assistance. We also wish to thank A. Guerra and A. González of the Instituto de Investigaciones Marinas of Vigo for the species determination of oceanic squids and J.J. Boubert of the Réserve Naturelle du Banc d'Arguin for providing information about the bottlenose dolphins from the Arcachon Bay. This work was funded by the European program BIOCET (EC: EVK3-CT-2000-00027) and through a research grant from the Conseil Régional de Poitou-Charentes of V.L.

Table 7. Hepatic Hg and renal Cd levels (µg.g -1 w.wt.) in striped dolphins obtained in previous works.

With: a d.wt. converted in w.wt. on the basis of the d.wt. : w.wt. ratio obtained in this study; and b refers to median. NB: maturity has been assumed to be "immature" when body length was < 175 cm for Mediterranean animals, and < 200 cm for other animals.


Nicolas Ducoulombier
email: nicolas.ducoulombier@enpc.fr

Camille Chateau
email: camille.chateau@enpc.fr

Michel Bornert
email: michel.bornert@enpc.fr

Jean- François Caron
email: jean-françois.caron@enpc.fr

Jonathan Perrin
email: jonathan.perrin@synchrotron-soleil.fr

CHARACTERISATION AND MODELLING OF INTERFACIAL DAMAGE IN FIBRE-REINFORCED CONCRETE FOR 3D PRINTING IN CONSTRUCTION

Keywords: Fiber-Reinforced Concrete, Interface, Damage, Tomography, 3D Printing, Micromechanical Testing

Extrusion-based additive manufacturing of cementitious material is a promising technology for the future of construction. Nevertheless, new solutions need to be proposed to provide either ductility or even reinforcement in areas in tension. Using fibres to reinforce the structure made by extrusion seems to be promising and needs to be fully understood at different scales. Moreover, the efficiency of reinforcement depends mainly on the interfacial properties between matrix and fibres. Decohesion between matrix and fibre is studied at two different scales. A mesoscopic analytical mechanical model of a so-called tension stiffening test has been proposed to quantify resistance and friction along the interface from the force-elongation curve. Secondly, the same experimental test is performed inside the microtomography setup of the Anatomix beamline of Synchrotron Soleil permitting to identify the microscopic nature, shape and the evolution of decohesion between matrix and fibres for different loading. Different types of fibres are compared and different damaging mechanisms are observed.

INTRODUCTION

Additive fabrication of concrete is a promising technology for the future of construction, offering new architectural opportunities, increased flexibility and productivity. While additive manufacturing refers to various processes, we focus here on extrusion based additive fabrication. Because of the low resistance and brittle behaviour of traditional concrete in tension, new solutions need to be proposed to fully print complex structures, including areas in tension. Different strategies to reinforce the extruded concrete by adding short fibres or long cable are under development [START_REF] Soltan | A selfreinforced cementitious composite for building-scale 3D printing[END_REF][START_REF] Bos | Experimental Exploration of Metal Cable as Reinforcement in 3D Printed Concrete[END_REF][START_REF] Bos | Ductility of 3D printed concrete reinforced with short straight steel fibers[END_REF]. Thanks to the alignment of fibres during the extrusion process, this process seems to be efficient and promising. Indeed, one can make a full use of reinforcement in a given direction corresponding to the printing path. Short carbon fibres reinforced cement paste made by extrusion have been shown to exhibit very high tension strength [START_REF] Hambach | Portland cement paste with aligned carbon fibers exhibiting exceptionally high flexural strength (> 100 MPa)[END_REF]. Nevertheless, micromechanical explanations need to be provided to enhance the high potential of this family of material.

To better understand mechanical behaviour at different scale, this work focuses on the fibre/matrix interface as it strongly governs mechanical resistance and induces ductility of the reinforced material at macroscale. A socalled "tension-stiffening" micromechanical test has been developed to characterise the interfacial decohesion both at mesoscale using force-elongation curve and at microscale using microtomography 3D imaging. On one hand, a mesoscopic analytical mechanical model of this experiment has been proposed to quantify resistance and friction along the interface from the force-elongation curve. Then, this model is used to identify interfacial decohesion from comparison to experimental force-elongation curve obtained by digital image correlation (DIC) [START_REF] Ducoulombier | Micromechanical testing for a 3D-printed long fiber reinforced concrete[END_REF]. On the other hand, 3D images from X-Ray microtomography are analysed using Digital Volume Correlation (DVC) and associated image subtraction techniques [9], to quantify the associated kinematic discontinuities, detect and characterise in 3D the microscopic nature and the evolution of the interfacial debonding.

DETERMINATION OF INTERFACIAL MECHANICAL PROPERTIES USING MESOSCOPIC FORCE-ELONGATION CURVE

Interfacial properties between matrix and fiber in composite material has broadly been studied. Numerous experimental tests have been proposed in literature to quantify strength and mechanical behavior depending on the material used and fiber geometry at different scale. Reviews of these investigations can be found in [START_REF] Teklal | A review of analytical models to describe pull-out behavior -Fiber/matrix adhesion[END_REF][START_REF] Zhandarov | Characterization of fiber/matrix interface strength: applicability of different tests, approaches and parameters[END_REF].

Here, a so-called "tension-stiffening" (TS) micromechanical test has been developed to characterise the interface bonding, evolution of decohesion and friction. It consists in pulling on a single fibre locally embedded in the matrix on a ten to twenty mm long area (see Figure 1).

It was inspired by the traditional macroscale "tension stiffening" test used for the determination of rebar/concrete interfacial properties. It has been preferred over other existing micromechanical tests because of the simplicity of the boundary conditions and its capacity to identify mechanical properties of free fiber at the same time. General information about experimental and modelling part are specified hereafter.

Fabrication of specimens and properties

A specimen is made of a given fiber embedded on its central parts in a prismatic cementitious matrix.

Embedded fiber area

Free fiber areas A special printable OPC mortar has been formulated (denominated Nav) and associated with two types of fibers. The first one is a single 100-micron diameter filament stainless steel fiber and the second one is a five hundred approx. 10 micron diameter filament basalt fiber. Fibers here can then refer either to single filament or multifilament fibers. Mechanical parameters are gathered in Table 1. The specimen is elaborated by casting the concrete in a 3D printed molds with one fiber passing through it. The mold is then cut or diluted to obtain the concrete specimen with a unique fiber at the center of the mortar section. Next, free basalt fiber areas (Figure 1) are impregnated with epoxy resin using a brush on area non-embedded in mortar. Later, the fiber is glued between two sheets of heavy paper. This permits to protect the specimen from unattended load when manipulated and to trap them in the clamping jaw during the test. Finally, a speckle pattern is applied on free fiber area using paint spray what provides the required image texture to apply DIC.

Experimental set-up

The test is perform using a universal uniaxial machine. The force value is measured by a 100N load cell and recorded by a national instruments (NI) card. The deformation of both embedded and free area of the fiber are measured by DIC. The set-up is composed of two cameras from Allied Vision equipped with optics from Schneider Kreuznach providing the appropriate optical magnification, close to unity, that record the same scene from two different viewpoints. The acquisition was led by MatLab thanks to an academic code based on the Image Acquisition and the Data Acquisition toolboxes of MatLab.

At any given time, it acquires and gathers one image per cameras and the force data from the NI cards. The optic of each camera was chosen to find a good compromise between getting enough pixels in the fiber diameter to be able to follow its movement during the test and showing a sufficient length in the longitudinal direction to measure the deformation of both embedded and free areas of the fiber. The experimental curves are given in Figure 4. * For multifilament fibers, diameters and mechanical properties are indicative. They are calculated fixing the diameter to d=0.2mm and Poisson Ratio to υ=0.25 and calculating the young modulus E=4*K/πd 2 and the shear modulus G= E/2(1+υ) with K being the free fiber stiffness experimentally measured by the setup.

Data processing

In order to get the experimental forceelongation curves, deformation from both free and embedded fiber parts are obtained using multiple DIC. This technique is used to remove from the apparent deformation of one camera, the contribution due to the out-of-plane rigid motion detected by the other camera. Only final curves are presented here for brevity.

Modelling

A mesoscopic analytical model of this test has been proposed to quantify resistance and friction along the interface from the force-elongation curve. It is derived by associating a reduced multi-particle 1D model and a particular mechanical behaviour at the interface. The reduction from 3D model to 1D model is performed using Hellinger-Reissner formulation. This technique was first developed and was successfully used from 3D to 2D to efficiently model a multi-layer material in [START_REF] Thai | Bending analysis of laminated and sandwich plates using a layer-wise stress model[END_REF].

Here, only main notations, hypothesis and the final set of equations are provided:

-Notations: Fm : Matrix internal force Ff : Fiber internal force τext : Matrix external shear stress τi : Interfacial shear stress Qext : Generalized matrix external shear stress Qi : Generalized interfacial shear stress Uf : Generalized 1D fiber displacement Um : Generalized 1D matrix displacement εf : Generalized 1D fiber displacement εm : Generalized 1D matrix displacement Ef : Fiber young modulus Em : Matrix young modulus Gf : Fiber shear modulus Gm : Matrix shear modulus -Hypothesis: 1) Fibres and matrix are isotropic and elastic 2) Only one dimensional interfacial inelastic effect is kept. 3) Supposed to be a plastic-softening -Equilibrium:

m f R 2 * (z) ) ( and R 2 * (z) ) ( with 0 ) ( ) ( 0 ) ( ) ( ) (     ext i i i f i ext m z Qext z Q z Q dz z dF z Q z Q dz z dF        -Boundary conditions: given = (0) F := CL2 given = (l) F := CL1 given = Q f f ext -Elastic behavior:                                               2 2 f 2 m 4 m 2 f 2 m 4 f 4 m m m 2 f 2 m m m f 2 f f f R - R * * R 3 R * R 4 R R * R ln * 4 1 * 8 ) ( ) ( ) ( ) ( E * ) R - (R * (z) F ) ( (z) E * R * (z) F ) ( (z) pi G R G z Q z U z U z U dz z dU dz z dU m f f i f m m f      -Interfacial decohesion: Strength domain writes:                  f Q i u d K Q if f Q i Q ) i f(Q f Q i u d K Q if i u d K Q i Q ) i f(Q max max max
Radial return writes:

i Q f u        i Inelastic interfacial behavior:   ) ( ) ( ) ( ) ( x u x U x U K x Q i f m i i    
Here, interfacial decohesion is seen as a plastic softening behavior. But this could also be transposed to a damage behavior using one parameter affecting the interfacial stiffness. The best choice between those two visions is difficult without more information on the decohesion nature at smaller scale.

Identification of interfacial properties

From now, we keep our plastic modelling of interfacial decohesion and choose a trilinear curve for elastic, softening and frictional behavior of the interface represented in Figure 3. This analysis shows a good agreement between experimental and simulated curves. The stainless curves are interesting because their late superposition shows that interface is completely debonded at the end of the test. Compared to these reference curves, the basalt ones highlight the fact that interfacial properties of multifilament basalt fiber is much higher than single filament stainless steel fiber. The beginning of the basalt composite force-elongation curves seems to be due to fiber curvature and stress repartition at the beginning of the test.

IDENTIFICATION OF DAMAGE NATURE BY MICROTOMOGRAPHY AND IN SITU TESTING

In order to confirm (or to enhance) the assumption and to explain results of the mesoscopic model, microtomography imaging is used to fully characterize the damage mechanisms at microscopic scale involved in the load distribution between mortar and fibers. The aim is to detect and characterize in 3D the microscopic nature and the evolution of interfacial debonding and associated damage mechanisms in the matrix close to the reinforcement. The 3D images were acquired at synchrotron Soleil on the recently developed beamline Anatomix [10], with a voxel size of 0.65 µm and an image definition of 2048 3 voxels per acquisition, so that one acquisition covers an area of 1.3 3 mm 3 . As the diameter of the mortar prism is approximately three millimeters. Only surrounding mortar around the fiber is included in the 3D images. In order to get a volume including all the interface along the sample, successive acquisitions at subsequent heights were performed along the embedded fiber area. One acquisition lasts approximately 3 min.

Experimental Set-up

A specific set-up has been designed and made to be able to realize the same experiments on the same kind of specimen inside the microtomograph. Details are shown on Figure 5.

A reference acquisition was performed with a very small loading but sufficient to straighten the specimen. Then, loading was applied by hand using the micrometric screw until the aimed force value, monitored by the load sensor, was reached. The operation was

Images processing

For each subvolume, three main action should be performed. The first one is to reduce 32 bits volumes to 8 bits volume that are easier to process thanks to smaller memory allocation. In this step, grey level bounds needs to be chosen carefully to insure that no information on microstructure are lost.

The second one consists in applying DVC algorithms to map the reference volume and a volume under load at a certain level. DVC is performed using CMV3D, an academic software developed by Bornert and al [9 ou Bornert et al 2004]. A regular grid of points is first generated. And, in order to guaranty a good accuracy of measurement, only points with sufficient local mean value and variance of grey levels are kept for deformation mapping by DVC, respectively superior to 50 and 0.05 and calculated on 30 3 voxels subvolumes for each point of the initial grid. As a consequence, final points that will be used for DVC are mostly located in the cement paste. The correlation window is set to 30 3 voxels and the critical correlation coefficient (Zero-mean Normalized Cross Correlation) value is set to 0.15. Finally, appropriate image substraction is performed. The principle is to rebuild the damaged volume in the reference position. More precisely, the correspondent grey level in damaged volume can be attributed for each pixel in the reference position using local transformation fitted over a set of nearest correlated points, the size of which defines the local smoothing of the mapping. Then, the subtraction between the rebuilt damage volume and the reference volume can be performed. The resulted volume should suppress all the microstructure information and only contain the difference between both images associated with high frequency kinematic phenomena not described in the smoothed mapping, including essentially cracks as shown in Figure 7 and Figure 8. More information about the substraction technique can be found in [9].

Damage nature

As in situ experimental tests were performed very recently, the full processing of all data is still underway. In the present paper, we thus focus on the very first remarkable result, which shows that two remarkable and very different decohesion mechanisms are observed, depending on the considered fiber. These events are obtained when processing two subvolumes obtained at the reference and the last force value before ruin, centered on the fibers axis and located at approximately 2mm inside the mortar. Two main kinds of damage pattern can be observed, respectively in Figure 7-Figure 9 and Figure 8-Figure 10:

The first damage pattern shows cohesive cracks in the surrounding matrix. Cracks are conical and emitted from the interface. The cracks propagation seems to be limited in a small matrix cylinder centered on the fiber, the precise extension still needs to be quantified. Moreover, the cones are more or less flattened depending on the fiber shape. This kind of damage is very efficient as it produces multi cohesive cracking of the matrix that allows for a great energy dissipation. This observation confirms the result obtained from the study of the force-elongation curve and calls for a damage or fracture mechanics analysis rather than plasticity. The second damage pattern does not show any crack in the matrix. But one can guess a tiny decohesion area located along the fiber from Figure 8 and Figure 10. Here, debonding is located at the immediate vicinity of the fiber with no propagation to the surrounding matrix. This observation confirms that the anchorage of steel fiber should be much lower than basalt fiber. Moreover, elastoplastic modelling of the interface seems this time more fitted.

CONCLUSION

The present paper aims to study interfacial decohesion of different fibers in a printable OPC mortar at two different scale from the same tension stiffening experiment. From the mesoscopic point of view, a reduced model is proposed and associated with an elastoplastic interfacial law, allows for simulating theoretical force-elongation curve. By comparison with experimental results, interface mechanical parameters can be identified. Key results are listed here:

 Good agreement is found between simulated and experimental Force-Elongation curve  Multifilament basalt fiber interfacial properties are remarkable and much higher than single filament stainless steel fiber.  The interfacial stress up to 33MPa does not have a clear physical meaning and requires for more investigation. The same experimental test is run inside microtomography setup of the Anatomix synchrotron beamline. First observations of damage nature give important complementary results:

 Multifilament basalt fiber shows cohesive multi cracking of the surrounding matrix.  Single filament steel fiber shows a much more located interfacial decohesion. By gathering analysis at two different scales, the paper shows that depending on the fiber, different decohesion mode can occur at interface, what will affect the force elongation curve.

 Very localized decohesion around the steel fiber confirms the proposed modelling and lead to interfacial properties that are controlled by the immediate vicinity of the fiber surface.  Interfacial decohesion in multifilament basalt fiber, involves cohesive multicracking of the surrounding matrix. This increases drastically the interface properties and calls for a modification in the modelling assumptions that was made in the present work, using damage or fracture mechanics hypothesis rather than elastoplasitcity.

Figure 1 :

 1 Figure 1: Schematic Tension Stiffening test

Figure 2 :

 2 Figure 2: Protected and textured steel fiber TS specimen

Figure 3 :

 3 Figure 3: Trilinear Interfacial Behavior.

Figure 4 :

 4 Figure 4 : Comparison between experimental and simulated Force-Elongation curves

Figure 5 :

 5 Figure 5: In situ experimental tension stiffening set up

Figure 6 :

 6 Figure 6: Cross section of reference volume of basalt fiber embedded in mortar

Figure 7 :

 7 Figure 7: Zoomed cross section of basalt reference subvolume (top), rebuilt damaged subvolume at 35N (top), substracted subvolume (bottom)

Figure 8 :

 8 Figure 8: Zoomed cross-section of stainless steel reference subvolume (top), rebuilt damaged subvolume at 15N (top), substracted subvolume (bottom)

  Chateau, Michel Bornert, Jean-François Caron and Mario Scheel

Figure 9 :

 9 Figure 9: Longitudinal section of basalt subvolume obtained by image substraction.

Figure 10 :

 10 Figure 10: Longitudinal section of stainless steel subvolume obtained by image substraction.

Table 1 :

 1 Material mechanical properties.

	Material Diameter	Young	Shear
		(mm)	Modulus	Modulus
			(GPa)	(GPa)
	Nav	3	40	16,3
	Stainless	0.1	175	67,3
	steel
	basalt*	0.2*	100*	38.5*

Table 2 :

 2 Identified interface mechanical properties.

	Interface	Ki	Kd	τmax	τf
		(GPa/	(GPa/	(MPa	(MPa
		mm)	mm)	)	)
	Basalt	40	0	33	?
	Stainless	inf	0.24	9	0.2
	steel
	Figure 4 presents comparison between
	experimental and simulated force-elongation
	curves for the two different specimens.
	Identified interfacial properties are then
	gathered in

table 4 .

 4