María Elena Perdomo

Ricardo Picón

María Eugenia Marante
email: emarante@ucla.edu.ve

François Hild

Stephan Roux

Julio Flórez-López

EXPERIMENTAL ANALYSIS AND MATHEMATICAL MODELING OF FRACTURE IN RC ELEMENTS WITH ANY ASPECT RATIO

Keywords: Reinforced Concrete Elements, Experimental Analysis, Numerical Analysis, Shear Damage, Flexural Damage, Damage Mechanics

In this paper, it is proposed a new model of the behavior of elements of arbitrary aspect ratio.

The model allows for the analysis of large and complex structures and it is based on concepts of classic fracture mechanics and continuum damage mechanics. The model considers independent variables that measure the degree of shear and flexural damage separately. This paper also presents an experimental analysis of the behavior of RC elements with the use of digital image correlation technique which allows for the classification and quantification of the different failure mechanisms in a much better way than the classic procedures.

INTRODUCTION

Real RC structures present components of very diverse nature. Including all of them in the analyses is essential for realistic numerical simulations of severe nonlinear behavior such as in cases of earthquake loading, displacement of supports, impacts or explosions. One of the most difficult aspects is the modeling of structural elements with arbitrary aspect ratios; this is however a fundamental issue. Dual systems are often used as a good structural alternative for buildings and facilities in earthquake-prone areas; this kind of structures combines frames with short elements and walls. Even in framed structures, short or intermediate columns and beams may appear as a result of inadequate disposition of masonry walls or other non-structural components.

The models for RC components subjected to bending using plastic hinges or distributed plasticity are the most abundant, models for walls and squat elements with bending and shear are less numerous but still there is a large choice of options (some of the most recent are [1][2][START_REF] Mohr | A frame element model for the analysis of reinforced concrete structures under shear and bending[END_REF][START_REF] Mergos | A distributed shear and flexural flexibility model with shear-flexural interaction for R/C members subjected to seismic loading[END_REF]).

The goal of this work is to propose a new model of the behavior of elements of arbitrary aspect ratio within the framework of the classic analysis of structures. The model is based on concepts of classic fracture mechanics and continuum damage mechanics. Many other models are also included within the latter sub-field, but they are limited to slender elements only [START_REF] Cipollina | A simplified damage mechanics approach to nonlinear analysis of frames[END_REF][START_REF] Perera | A fatigue damage model for seismic response of RC structures[END_REF][START_REF] Kaewkulchai | Beam element formulation and solution procedure for dynamic progressive collapse analysis[END_REF][START_REF] Valipour | Nonlocal damage formulation for a flexibility-based frame element[END_REF][START_REF] Rahasankar | Modelling inelastic hinges using CDM for nonlinear analysis of reinforced concrete frame structures[END_REF][START_REF] Sisniegas | Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures[END_REF][START_REF] Faleiro | Plastic-damage analysis of reinforced concrete frames[END_REF][START_REF] Araujo | Application of a lumped dissipation model to reinforced concrete structures with the consideration of residual strains and cycles of hysteresis[END_REF], or walls exclusively [START_REF] Thomson | Simplified model for damage in squat RC shear wall[END_REF][START_REF] Hua-Jing | Plastic-damage model for reinforced concrete shear walls[END_REF].

This paper also presents an experimental analysis of the behavior of RC elements.

Experimental analyses aim for the determination of the resistance and deformation capacity in order to predict the inelastic response of slender elements or walls (see for instance [START_REF] Greifenhagen | Static cyclic test on lightly reinforced concrete shear walls[END_REF][START_REF] Güray | Shear strength of reinforced concrete beams with stirrups[END_REF][START_REF] Sezen | Seismic test of concrete columns with light transverse reinforcement[END_REF].

These studies show that for beams and columns of large aspect ratios the most important effect is bending but with its reduction, shear stresses become progressively more important and may be the dominant failure mechanism.

The experimental study presented in this paper differs from the aforementioned references in the use of digital image correlation (DIC), see for instance [START_REF] Besnard | Finite-element displacement fields analysis from digital images: application to Portevin-Le Châtelier bands[END_REF]. This method allows for the classification and quantification of the different failure mechanisms in a much better way than the classic procedures, which are either local or performed by visual inspection.

EXPERIMENTAL ANALYSIS

The experimental analysis [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF] was carried out using DIC. In this method the specimens to be tested are marked randomly using dark paint dots. A first digital photo of reference is taken before the test. Next, further pictures are taken during the experiment while the chosen external forces are applied. A computer program [START_REF] Besnard | Finite-element displacement fields analysis from digital images: application to Portevin-Le Châtelier bands[END_REF] processes first the reference digital image; the program divides this photo into small portions that may be imagined as small "finger prints" and identifies each of them. Then, the program analyses the following picture, looks for the same "finger prints" and determines their new position in the picture. This procedure gives the average displacement vector of each specific portion. Next, the program feeds a finite element mesh with those displacements. In this way the displacement field of the specimen is measured. Notice that the nodal displacements are experimentally measured and not mathematically computed. The same procedure is followed sequentially with each digital photo of the test. With the displacement FE field, the program computes the strain field using the conventional techniques. Cracks in concrete appear as concentrations of strains. For instance, Fig. 2 shows diagonal tension cracks and/or flexure cracks in beams. Notice that the program also provides for an automatic and objective quantification (independent of the observer) of the intensity of cracking.

The first series of tests was designed to show and quantify the modifications of the cracking patterns with the aspect ratio. Three specimens that represent RC beams in cantilever with different aspect ratios were tested (see Fig. 1). The properties of these specimens can be found in [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF]. The variation of the aspect ratio was achieved using identical specimens but changing the position of the lateral force. Specimen B4 is a slender beam with an aspect ratio of 7.11; specimens B2 and B3 represent intermediate beams with, respectively, aspect ratios of 3.56 and 5.36 [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF]. The loading history is shown in Fig. 1b. It is cyclic and displacementcontrolled in the loading phase with increasing maximum displacements after each cycle; the unloading phase is load-controlled and the final force at the end of each cycle is always zero. This kind of test is denoted in this paper "mono-sign" since both, displacements and forces are cyclic but never change sign. Several RC walls with different aspect ratios [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF] were also tested with mono-sign loadings; in this paper, the results of only one of them (see Fig. 3) are shown in Fig. 4. In that case, dominant shear cracks appear in the specimen. The longitudinal reinforcement of this wall was over-dimensioned in order to minimize as much as possible flexure damage. Fig. 4 Cracking pattern in a wall revealed by DIC It was observed [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF] that the presence of an axial force on the specimens does not modify significantly the cracking pattern; it just alters slightly the orientation of the shear cracks.

SIMPLIFIED MODELING OF FRACTURE USING INTERNAL VARIABLES

Consider a RC structure composed of n nodes and m elements of any aspect ratio. A node i of the structure has three degrees of freedom: the displacements u i and w i in the directions of the global axis X and Z and the rotation  i . The generalized deformations of an element b between nodes i and j are represented by the matrix    is the elongation (see Fig. 5a). The generalized stress matrix is denoted

) , , ( } { b b j b i t b n m m  M and
includes the bending moments at the end sections and the axial force (see Fig. 5b). If the forces distributed on the element are small with respect to the nodal forces, then the shear force is approximately constant and can be computed as: The experimental analysis showed that RC elements with arbitrary aspect ratio may have flexural cracks in the plastic hinge zone and/or shear cracks along the element. A simplified representation of the fracture process is obtained using the damage variables indicated in Fig.

b b j b i b j i L m m V v v     (1)

6.

Those parameters take values between zero and one as in continuum damage mechanics [START_REF] Lemaitre | Mechanics of Solids Materials[END_REF] but, in the present case, they represent densities of macro-cracks instead of microdefects. Flexural damage may be lumped at the plastic hinges [START_REF] Cipollina | A simplified damage mechanics approach to nonlinear analysis of frames[END_REF]; the flexural damage matrix The second mechanism is related to the yielding of the transverse reinforcement that produces plastic distortions. They may be represented by the plastic distortion matrix

CONSTITUTIVE EQUATIONS: STATE LAW

Constitutive laws in classic continuum damage mechanics are based on two simple but very powerful concepts: the effective stress  and the hypothesis of equivalence in deformations [START_REF] Lemaitre | Mechanics of Solids Materials[END_REF]:

     1 ; ) ( E ) 1 ( ) ( E p p              (2)
where  is the dimensionless continuum damage variable taking values between zero and one.

Instead of writing the state law in terms of stiffness as in Eq. (2c), it is better for the purpose of this paper to express it in terms of flexibility:

        E p ) 1 ( 1 p d        e where   E e 1  ; and     ) 1 (   E d (3)
Notice that the term e  is an elastic strain, p  is the plastic strain and d  can be interpreted as an additional damage-related one. Correspondingly, there is an initial elastic flexibility E 1 and a damage-related one:

) 1

(    E
. If damage is equal to zero, the damage strain is zero too; if damage tends to one, the damage-related flexibility and deformation tend to infinity.

Notice the existence of three strain terms for the three phenomena under consideration: elasticity, damage and plasticity.

Return to the case of RC elements. In the previous section, five main phenomena were identified; thus, according to the hypothesis of equivalence in deformations, total deformation is decomposed into five terms: an elastic deformation, a shear damage term, a flexural damage one, the plastic distortion matrix and the plastic hinge rotation matrix:

b p b p b d b d b e b } { } { } { } { } { } { Φ γ Φ γ Φ Φ      (4)
The elastic deformations may be written as a function of stresses using the conventional flexibility matrices: The third deformation term in Eq. ( 4) can be written, according to the hypothesis of equivalence in deformation, as:

b b 0 b e } { ] [ } { M F Φ  ; where                                           0 0 0 0 1 1 0 1 1 0 0 0 3 6
b b s s b d } { )] d ( [ } { M C γ  where                       0 0 0 b b s s s s L GA L GA L GA L GA d d d C (6)
Notice that if the shear damage is zero then the damage deformations are also zero. If the shear damage tends to one, the Timoshenko flexibility tends to infinity.

Similarly, the fourth term of Eq (4) is:

b b f b d } { )] ( [ } { M D C Φ  where                      0 0 0 0 3 1 0 0 0 3 1 )] ( [ b b j j b b i i b f EI L d d EI L d d D C (7)
This time, the Bernoulli flexibility terms tend to infinity when the damages tend to one. The combination of (4-7) gives the state law of a RC element:

    b } { M D F γ Φ Φ s b p p d , } {    (8)                                                b b s b b j b b s b b b b s b b b b s b b i b b s EA L d L GA d EI L d L GA EI L d L GA EI L d L GA d EI L d 0 0 0 1 1 1 3 1 1 6 0 1 1 6 1 1 1 3 , D F The local stiffness matrix is, of course, the inverse of     s d , D F
and its computation is immediate using any symbolic manipulation program but the resulting expression is too complex to be read easily.

GENERALIZED GRIFFITH CRITERIA

The theory of linear elastic fracture mechanics states that crack propagation is only possible if the energy stored in the structure is sufficient to overcome the fracture energy of the material.

The same Griffith balance energy can be used in the present case. The complementary deformation energy W b of the element can be computed from the state law (8):

b b s t b b p p t b b d W } { )] , ( [ } { 2 1 } { } { 2 1 M D F M γ Φ Φ M     (9)
Assuming that the damage mechanisms are uncoupled, the energy release rate for shear

damage s G is:   2 2 1 2 s b b b s b s d GA V L d W G      (10)
Notice that this variable depends indeed on the shear force b V . The use of a generalized form of the Griffith criterion allows for the computation of the shear-damage:

         if if 0 0 s s s s s s d R G R G d ( 11
)
where R s is the shear damage resistance function and This generalized form of the Griffith criterion was also discussed in [START_REF] Thomson | Simplified model for damage in squat RC shear wall[END_REF].

The shear damage resistance R s can be identified experimentally using the test on the wall described in Section 2. Fig. 8a shows the plot of deflection vs. lateral force obtained in that test. This test was chosen for the identification because the DIC analysis indicated very small, negligible, flexure damage. In this particular case, with the corresponding boundary conditions, the state law (8) becomes:

) )( ( p s t t d Z V   ; L t p p   ;   ) 3 ( 1 3 ) ( 2 2 EI GAd L GA L L d GA EI d Z s s s     ( 12
)
where t is the lateral displacement and V the lateral force. Notice that Eq.( 12) corresponds to the straight lines represented in Fig. 8a. Therefore, the slopes Z may be measured in the test. Thus, an experimental value of shear damage can be determined for each unloading in the test using:

) 3 ( 3
3 3 3 Z L EI GA GA L Z EI L Z EI GA d s     ( 13
)
Notice that this is simply an extension of the elastic stiffness variation method well-known in fracture and continuum damage mechanics [START_REF] Lemaitre | Mechanics of Solids Materials[END_REF].

It is possible to plot shear damage against shear energy release rate (Fig. 8b) because experimental values of the latter variables can be obtained using Eq. [START_REF] Sisniegas | Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures[END_REF]. With this plot it is possible to propose the following expression for the crack resistance function:

s s s s s d d q R d R     1 ) 1 ln( ) ( 0 ( 14
)
Notice that there are an initial value of crack resistance s R 0 and a logarithmic hardening term.

The latter is due to the action of the reinforcement that obstructs shear cracks propagation. In practical applications, the parameters s R 0 and s q does not need to be measured experimentally; they may be determined from well-known concepts of the reinforced concrete theory as it is explained in the following paragraph.

Consider again the Griffith equation:

s s R G 
. This expression defines a general relationship between shear force and shear damage:

               s s s s s b b b d d q R d GA V L 1 ) 1 ln( 1 2 0 2 2 (15)
This equation gives the plot of damage vs. shear force indicated in Fig. 9. Notice that the values of the first cracking shear force V cr and ultimate shear force V u in Fig. 9 can be indeed computed using RC theory [START_REF]Building code requirement for structural concrete[END_REF][START_REF] Sezen | Seismic behavior and modeling of reinforced concrete building columns[END_REF] with a reasonable accuracy. Those values enable for the computation of the parameters s R 0 and s q in the shear crack resistance function.

Flexure-damage can also be computed using the same procedure. The damage driving moments are:

b i b i b i d EI m L d W G      ; 2 2 ) 1 ( 6 i
j b j b j b j d EI m L d W G      2 2 ) 1 ( 6
Notice that these new energy release rates depend now on the flexural moments and not on the shear force. Similar generalized forms of the Griffith criterion can also be proposed and the corresponding flexure crack resistance function identified [START_REF] Cipollina | A simplified damage mechanics approach to nonlinear analysis of frames[END_REF]. The same method of the variation of the elastic stiffness can also be adapted to the experimental measurement of flexure-damage [START_REF] Cipollina | A simplified damage mechanics approach to nonlinear analysis of frames[END_REF] but in this case DIC technique is used to check that shear cracks are negligible. It is interesting to note that the flexure damage resistance function of a plastic hinge i may have the same general expression as Eq.( 14) but, of course, with different values for the parameters:

i i f f i d d q R d R     1 ) 1 ln( ) ( 0 (17)
It appears that the function Eq. ( 17), or [START_REF] Hua-Jing | Plastic-damage model for reinforced concrete shear walls[END_REF], can be considered as a general expression for damage resistance in RC elements.

YIELD FUNCTIONS

The last components of the model are the yield functions needed for the computation of the plastic distortion and the plastic rotations. The starting point is the conventional yield functions with linear kinematic hardening; next, the hypothesis of equivalence in deformation is used again with the following effective shear force and effective flexural moment:

L d m m d V V s j i s ) 1 ( 1     
; and

i i i d m m   1 (18) 0 ) 1 (          os p s s j i os p s s k c L d m m k c V f   ; 0 1 0      i p i i i i i k c d m f  (19)
where c s , c i, k oi and k os are, too, model parameters. All of them can also be computed using reinforced concrete theory [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF].

The last expressions for a full analysis of RC structures are the kinematic and equilibrium equations. Both of them are exactly the same as those for the analysis of nonlinear elastic frames.

NUMERICAL VALIDATION OF THE MODEL

The model was included into the library of a well-known commercial structural analysis program [23] as a new finite element [START_REF] Perdomo | Fractura y Daño en Estructuras Duales de Concreto Armado[END_REF]; then, all the tests presented in Section 2 were simulated. 1-2). The results of the numerical simulation are also very good. The histories of damage are different (Fig. 11c); the final value of flexure damage is also very large (0.74) but now shear damage is not negligible (0.33). Again, this is in agreement with DIC observations (see specimen B3 in Fig. 2). The results for the shorter intermediate beam (specimen B2) are shown in Fig. 12. The numerical simulation is good and now the relationship between flexure damage and shear damage are reversed, with final values of 0.47 and 0.85 respectively. This is again in good agreement with DIC results (see specimen B2 in Fig. 2).

EXPERIMENTAL ANALYSIS AND NUMERICAL SIMULATION OF A TWO-ELEMENTS STRUCTURE

The last validation was carried out using the structure shown in Fig. 14a. This is a continuous beam of two elements, one short and one slender, separated by a chunk that represents a column; the beam is embedded at its ends in two heavy RC blocks that represent fixed supports. A mono-sign loading was applied at the column. The goal of this test is to reproduce the short element effect similar to the one shown in Fig. 14b, to test the ability of the model to simulate it and to recognize the different patterns of cracking in the structure. As expected, the experimental results show moderate flexure damage in the plastic hinge regions of both elements and severe shear damage in the short beam. In this test, the DIC analysis was not carried out, the software was not available at that time.

The quality of the numerical simulation can be evaluated in the plots of deflection vs. force for the column shown in Fig. 15. It must be underlined the great potential that DIC offers for the development of new methods in the analysis and design of RC structures. The results presented in this paper are just a small example of a large spectrum of possibilities. This technique allows not only for an objective and automatic determination of fracture patterns but also for its quantification. This feature was very important for the validation of the computed values of damage.

Fig. 1 Fig

 1 Fig.1

Fig. 2

 2 Fig.2

Fig. 2

 2 Fig. 2 Cracking patterns revealed by DIC in beams with different aspect ratios

Fig. 3

 3 Fig.3

Fig. 3

 3 Fig. 3 RC wall

  rotations of the element end-sections with respect to the cord and b

Fig. 5 Fig. 5 a

 55 Fig.5

Fig. 6

 6 Fig.6

Fig. 6

 6 Fig. 6 Flexure and shear damage variables

  . 7b[START_REF] Thomson | Simplified model for damage in squat RC shear wall[END_REF].

Fig. 7

 7 Fig. 7

Fig. 7

 7 Fig. 7 Plastic deformations in a RC element a) Plastic rotation b) Plastic distortion

F

  is the Bernoulli elastic flexibility matrix and the second term is the Timoshenko elastic flexibility matrix. The parameters b EI and b GA are the usual rigidities to, respectively, bending and shear of the element.

Fig. 8 Fig. 8 a

 88 Fig.8

Fig. 9 Fig. 9

 99 Fig.9

Fig. 10a -

 10a Fig. 10a-b shows the experimental results and numerical simulation of the slender column

Fig. 10

 10 Fig. 10 Behavior of a slender RC beam in cantilever a) Experimental deflection vs. lateral force

Fig. 11

 11 Fig.11

Fig. 11

 11 Fig. 11 Behavior of an intermediate RC beam in cantilever a) Experimental deflection vs. lateral

Fig. 12

 12 Fig. 12

Fig. 12

 12 Fig. 12 Behavior of an intermediate RC beam in cantilever a) Experimental deflection vs. lateral

Fig. 13

 13 Fig.13

Fig. 13

 13 Fig. 13 Behavior of a RC wall in cantilever a) Experimental deflection vs. lateral force b)

Fig. 14

 14 Fig.14

Fig. 14 a

 14 Fig. 14 a) Continuous two-element beam b) Failure of a short column in a RC structure [24]

Fig. 15

 15 Fig.15

Fig. 15

 15 Fig. 15 Deflection vs. force a) Experimental analysis b) Numerical simulation

Fig. 16

 16 Fig.16

Fig. 16

 16 Fig. 16 Cracking pattern in the continuous beam a) Short element and corresponding damage

ACKNOWLEDGMENT

The results presented in this paper were obtained in the course of an investigation sponsored by FONACIT (G-2001001210, PI-2005000762) and CDCHT-UCLA (002-IC-2005).


Paul George

Indira Thouvenin

Vincent Frémont

Véronique Cherfaoui

DAARIA: Driver Assistance by Augmented Reality for Intelligent Automotive

Taking into account the drivers'state is a major challenge for designing new advanced driver assistance systems. In this paper we present a driver assistance system strongly coupled to the user. DAARIA 1 for Driver Assistance by Augmented Reality for Intelligent Automotive is an augmented reality interface informed by a several sensors. The detection has two focus: one is the obstacles position and the quantification of their dangerousness. The other is the driver behavior. Via a suitable visualization metaphor the driver can at any time perceive the location of relevant hazards while keeping his eyes ont the road. First results show that our method could be applied to vehicle but also to aerospace, fluvial or sea navigation.

I. INTRODUCTION

Driving relies on key concerns such as security and mediated perception for the driver: driving accidents are the 10th leading cause of death worldwide, killing every year 1,2 million people. The automotive industry has turned to support driving systems such as ABS (Anti-lock braking) or ESP (Electronic-Stability Program). These systems attempt to correct driving errors when they are happening. An original method is proposed in this paper : a Mobile Augmented Reality and Interactive Driving Assistance which provides the user the possibility to avoid obstacles and to anticipate driving difficulties. We designed a display module with Augmented Reality (AR) linking a module of obstacles perception and a module of observation of the driver's behavior. We present in part 2 a state of the art of visualization metaphors for driving. Then in part 3 we describe our approach, and part 4 provides the DAARIA system design and realization for obstacle detection. The first results are given in part 5 and a conclusion is proposed in part 6.

II. REVIEW OF EXISTING METAPHORS FOR THE DRIVER

The visualization metaphor is defined by Averbukh [START_REF] Averbukh | Interface and visualization metaphors[END_REF] as "a map establishing the correspondence between concepts and objects of the application domain under modeling and a system of some similarities and analogies. This map generates a set of views and a set of methods for communication with visual objects." These metaphors are used to inform the user by reusing standard interface concepts. It is essential to avoid cognitive overload when learning to use the new system. In this section we will extract from literature some existing visualization metaphors for car driving application. 1 The authors are with University of Technology of Compiègne(UTC), CNRS Heudiasyc UMR 7253, firstname.familyname@utc.fr

A. Metaphor for navigation and planning assistance

The navigation assistance helps the driver to choose a direction while the planning assistance allows the user to reach its destination without prior knowledge on the road topology or on the followed path. We present in this section different metaphors related to the navigation and planning aid systems.

Narzt et al. [6] [7] describe two metaphors types in the field of car assistance system. The metaphor of the augmented road (Fig. 1a) provides the user a highlighted way to follow when looking directly at the road. For example, it allows to notice that a back exit has been missed or to find the right exit on a roundabout without having to check. This metaphor is for planning assistance even if the information presented to the user is a middle term one (usefull till the next intersection). Another metaphor present a virtual car to follow as it accelerates, brakes or activates turn signal. In this case, the information is a short term one (about one second) (cf Fig. 1b). The metaphor of unrolled map [START_REF] Kim | Simulated augmented reality windshield display as a cognitive mapping aid for elder driver navigation[END_REF] is an improvement of the metaphor of the augmented road. The aim is to give the user global knowledge of the environment. A map is held as and when the vehicle is moving. The part which is on the ground indicates the path to be taken immediately. The other part in the sky shows the structure of the surrounding road network. A curved area allows a continuous transition between the two modes of representation (Fig. 1c). It provides a knowledge of the road network in the medium term, using the technique of LOD (Level Of Detail). The results of tests in simulation (i.e. virtual reality) show a reduction in navigation errors and problems caused by divided attention. This metaphor has been developed by CMU on the new HUD system "full windshield" of General Motors in order to verify these results in real situations.

B. Metaphor for driving safety

We define the driving safety assistance as all resources used to provide the user with information needed to drive as safely as possible. The aim is to overcome inattention and to compensate the ability to detect hazards.

The metaphor of the highlighter shown in Fig. 1d allows to highlight some of the details existing in the driver's field of view in order to draw his attention. It is possible to highlight other vehicles, pedestrians, and the lane limits [START_REF] Narzt | A new visualization concept for navigation systems[END_REF]. We can notice that the highlight of the road is similar to the augmented road metaphor. However, the context and the goals are not the same. Indeed, in the first case, the aim is to guide the driver along a route. In the second case,the aim is to help the user to locate the path when the lane is not clear or when the visibility is poor.

The metaphor of the radar [START_REF] Tonnis | Effective control of a car driver's attention for visual and acoustic guidance towards the direction of imminent dangers[END_REF] looks like a top view of the vehicle in two dimensions. Imminent hazards are marked with an arrow indicating their direction. The user can see the dangers that are on front of the vehicle (Fig. 1e). This metaphor is exocentric (i.e. external to), also the user must perform mental transformations to bring the information in the egocentric reference. The exocentric metaphors are not suitable for driving assistance.

The metaphor of the vane [START_REF] Tonnis | Effective control of a car driver's attention for visual and acoustic guidance towards the direction of imminent dangers[END_REF] is presented as a threedimensional arrow pointing to imminent danger (Fig. 1f). The arrow is attached to a virtual pole in front of the car, and helps preventing cognitive changes (otherwise some subjects perform a mental translation of the arrow to the location of their head). Unlike the metaphor of the radar, the metaphor of the wind vane keeps an egocentric view while providing the driver with information on items that are not in his visual field. The advantage of staying in egocentric visualizations is that it frees the driver to perform mental transformations before processing information.

C. Metaphors to discover points of interest

The discovery of points of interest is a mean to provide the user with additional knowledge without distraction. Narzt [START_REF] Narzt | A new visualization concept for navigation systems[END_REF] offers the annotation metaphor with contextual information. He suggests to take into account the vehicle's state in order to provide information suitable to the driver's needs such as: location of a gas station and the fuel price when missing (Fig. 2a). A variant of the annotation metaphor is the use

D. Conclusion on metaphors uses for driving assistance

Many metaphors are available in the context of car driving. Displayed all together they would lead to an overload of the driver's visual space. Our first objective will be to design a relevant metaphor. In addition, with existing metaphors, authors often assume that a future technology will be able to display on the whole windshield. We assume we have not this possibility. Our second objective will be to develop a prototype in order to conduct experiments for our solution and to realize an adapted interface.

III. PROPOSED APPROACH

Our objective is to integrate the visualization metaphor in the design process of driving assistance system. In order to propose a visualization metaphor adapted to the driving situation, it is necessary to know what is the current situation and what the driver looks at. So we propose the coupling of an obstacle detection module with a system monitoring the driver in order to develop a display module for an application of Augmented Reality (AR). This section is organized as follows : we describe first the obstacle detection and the eye tracking system used for this study; then we describe our metaphor.

A. Obstacle detection and eye tracking system.

To achieve obstacles detection, we will use the ADAS (Advanced Driver Assistance Systems and Driver Assistance) Mobileye c . A camera is mounted on the windshield of the vehicle (Fig. 3a) and a computer (chipset) retrieves the video stream and processes it to extract more useful information for driver assistance applications: positions of pedestrians and vehicles ( Cars, trucks, bicycles and motorcycles), vehicle speed, road markings etc... The public version of Mobileye offers an interface for driver assistance notifying the presence of vehicles, pedestrians and lane (Fig. 3b). The system is also equipped with loudspeakers to broadcast warnings. The professional version provides access to information calculated by the system and allows to exploit them differently from the original system. The data produced are broadcasted on the CAN bus of the vehicle. Video signal is not an output of the system. To adapt the display to the metaphor, we have chosen to integrate the driver's behavior to the system, especially his gaze. The idea is to inform the driver only when he needs help. FaceLab c is a system able to capture head and eyes position and orientation. Two infrared emitters illuminate the user's face, two cameras are located in the configuration of the stereo vision (cf Fig. 4a). A computer processes the images to extract the following information : the position and orientation of the head, the position and orientation of the eyes, opening of the eyelids, pupil size, the frequency of eye blinking as shown in fig. 4b). FaceLab is a commercial product and outputs are saved in a file or sent in the network.

B. The visualization metaphor

In order to help the driver with obstacle detection, we have chosen the metaphor of the weathervane. This metaphor has two main advantages : it is egocentric and it can be used to indicate several dangers at once. The metaphor proposed for the restitution to the driver is defined as follow.

1) Indication of the type of danger: Rather than using a color code to indicate the nature of the dangers, we will refer to symbols which are familiar to the driver: those of the highway code (Fig. 5a).

2) Indication of dangerousness: To highlight the most critical dangers, we have adopted an intuitive color-code : the gradient green / yellow / orange / red. Indeed, it is generally accepted that red and green are associated respectively danger and safety (Fig. 5b).

3) Indication of criticality: In order to solve the problem of overlapping arrows and prioritize the display of arrows indicating the most critical dangers, we decided to convey information on the criticality of the danger through the height of the arrows. They are sorted so that the more dangerous, the more visible, thus allowing the driver to process them in an optimal way (Fig. 5c).

4) Animation of metaphor: To make the metaphor more pleasing to the eye, and give it a more credible behavior, we decided to animate it. In practice, the arrows motions are physics-driven, hence smoothing variations of metaphor states. Fig. 5d is a diagram showing the design of our metaphor building on the original weathervane metaphor. The experimental platform CARMEN has been used to develop DAARIA. CARMEN is an experimental vehicle dedi-cated to research on intelligent vehicles. The Figure 7 shows the cameras of Mobileye and FaceLab systems. Another camera (scene) has been added in order to have a video output of the scene and to monitor the system. In the same way, the display allows to check that all components are working correctly when experimenting.

B. Calibration method

The data to combine in DAARIA come from heterogenous sources : Mobileye, FaceLAB and a wide angle camera. Since the geometrical informations are expressed in different frames (see Fig. 8) , it is crucial to perform an extrinsic calibration procedure between the systems [START_REF] Rodriguez | Extrinsic Calibration between a Multi-Layer Lidar and a Camera[END_REF]. For each camera system, we use the Caltech Calibration toolbox [12] to estimate the intrinsic parameters of each camera. If the cameras have enough overlapping, the calibration toolbox can be used to estimate the extrinsic parameters i.e. rotation and translation between the cameras frames. In our case, the Mobileye and the FaceLAB cameras are looking at opposite direction, therefore classical calibration procedure is impossible. Moreover, it is impossible to access to the video images in the FaceLAB system. The only available information comes from the gaze tracker which gives the eyes direction in the FaceLAB frame.

Therefore we developed a new idea to solve the calibration problem (see Fig. 9 ):

• We take pictures of the calibration target with the Mobileye System. • During the pictures acquisition, someone seats on the driver side, looking at some reference point on the target and we save the gaze direction vector. • Simultaneously, we place a Laser pointer on the driver's forehead pointing on the calibration target, and we save the measured distance. • If one repeats the procedure several times, one obtains 3D points in the Mobileye frame and in the FaceLAB frame. Then we use a classical registration approach such as ICP [START_REF] Arun | Least-squares Fitting of Two 3-D Point sets[END_REF] to estimate the transformation between the two frames.

C. Objects and driver gaze restitution in scene image

This module is developed in order to have the possibility to check and monitor the metaphor computation. It calculates the projection of the driver's gaze direction and detected objects on two views : a bird view (Fig 10a) and a scene view given by the scene camera (Fig. 10b). This is done thanks to calibration data. The blue boxes represent pedestrians, the green boxes represent the cars and red line or circle gives the direction of the driver gaze. The metaphor computation module calculates the configuration to be taken by the metaphor of the weathervane. To achieve this, we combine information from the viewing direction (FaceLAB) and the obstacles location (Mobileye) and can get obstacles information looked at. Determining obstacles dangerousness relies on several criteria:

• Object dynamics : the stationary objects are not considered for the metaphor. • Driver's visual activity: it avoids to point out a danger checked by the driver. The current implementation is very simple : it carries out tests of intersection between the eye direction and obstacles. • Time-to-Collision (TTC) : using the status of egovehicle and information about the detected objet, we can approximate a TTC. The lower, the more dangerous.

The arrows in the weathervane metaphor are ordered by level of danger.

E. Display device

The most suitable device for an AR interface compatible with the the driving task would be the HUD (Head Up Display). Its main advantage over the HDD (Head Down Display) is the driver time saving. Indeed, the eyes back and forth between the road and the dashboard deprive the driver of valuable time, as the need to constantly refocus his eyes to distance changes. HUD solves both problems: it is close to the road, which limits the round-trip of gaze and in addition the image formed is located behind the windshield, which reduces the visual rehabilitation. We proposed a lowcost solution that uses a tablet-PC as a HUD. The solution is to put it under the windshield of the car and to display our metaphor as shown in Fig. 11 The first real road tests allowed us to validate the choice of components as well as the feasibility of our approach. CARMEN is able to collect data that we can replay for analysis (Figure 12).

A. Characterization of the consideration of an obstacle

To integrate the driver's behavior in our system, we chose a very simple rule based on the intersection of vector of the gaze of the driver and detected obstacles. This simple rule has several basic flaws: no consideration of gaze tracking, the field of view is not a vector, the imprecise or incorrect detection can lead to wrong conclusions. We could propose several improvements concerning the visual attention model, the finer characterization of the obstacle consideration and the cognitive map managing of the driver taking into account the information life cycle.

B. Characterization of dangerous obstacles

To integrate the situation analysis to DAARIA, we chose a simple rule: the closer the obstacle, the more dangerous. More information could be taken into account: the obstacle nature (pedestrian or vehicle), its trajectory and its speed, its behavior (a pedestrian about to cross the street), the consideration of traffic (for example, priority of the drivers on the right).

VI. CONCLUSION AND OUTLOOKS

A prototype of driver assistance system in augmented reality has been presented. It is based on the weathervane metaphor adapted for a use in real conditions. The metaphor is computed according to the driving situation and the driver's attention. The driver can perceive at any time the location of the dangers without leaving the eyes of the road. The system adapts its behavior to provide him the most relevant information. A lot of problem of integration (calibration, synchronization -not described here-and data exchange) have been resolved to conduct first experiments and prove the feasibility.

Future works concern three major directions. The first one is the uncertainties consideration propagated in this complex system and especially the uncertainties of detected objects [START_REF] Fayad | Updating confidence indicators in a multi-sensor pedestrian tracking system[END_REF] and of the driver's attention. The second axe for future research is focused on the metaphor improvement. The third axe is the analysis of metaphor performances in virtual environnement [START_REF] Fricoteaux | Heterogeneous Data Fusion for an Adaptive Training, Informed Virtual Environment. Systems (VECIMS)[END_REF] in order to validate it and test it with critical scenarios.

Fig. 1 :

 1 Fig. 1: Metaphors for navigation, planning and driving assistance

Fig. 2 :

 2 Fig. 2: Metaphors to discover Points of interest

Fig. 3 :

 3 Fig. 3: The system Mobileye and the public interface

Fig. 4 :

 4 Fig. 4: The eye-tracker Facelab

Fig. 5 :

 5 Fig. 5: Metaphors for obstacle detection assistance

Fig. 6 :

 6 Fig. 6: DAARIA Architecture

Fig. 7 :

 7 Fig. 7: Integration on board CARMEN

Fig. 8 :Fig. 9 :

 89 Fig. 8: Frames

Fig. 10 :

 10 Fig. 10: Objects and Driver gaze Restitution

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Fig. 11 :

 11 Fig. 11: Tablet as HUD, displaying the metaphor of the weathervane

Fig. 12 :

 12 Fig. 12: Replay for result analysis

VII. ACKNOWLEDGMENTS

The authors gratefully acknowledge the contribution of Gérald Dherbomez.