Gerard Gary

Patrice Bailly

Behaviour of quasi .. brittle material at high strain rate. Experiment and modelling

ABsTRAcr.-Strain-rate effects on the beha'<iour and on failure of concrete under quasi-static and dynamic loading (with uniaxial strain-rates up to 1000 s-1) are investigated from both experimental testing and modelling point of views. The main damaging process taken into account is the brittle tensile response induced by Poissons' effects under compression loading.

The proposed meso-rnechanical model is based on a description of mechanisms observed at a microscopic level after failure has started. The strain-rate sensitivity then appears as a consequence of the motions of such mechanisms, with the introduction of the time derivative of the strain-rate (€) in the formulation. Dynamic loadings under compression are performed with a Split Hopkinson pressure bar (SHBP) apparatus. To investigate the response of concrete under multiaxial loading, a specific device presented in the paper is specially built to produce dynamic compression under various controlled lateral confinement pressures, allowing for an independent evaluation of radial inertia and lateral pressure effects.

It is found that a small number of parameters, mostly deduced from a classical pure compression or traction test, allow for correct modelling of the response under multiaxial loading for a wide range of speeds of loading.

Introduction

In recent years, progress in computer technology and development of explicit codes (or hydrocodes) have made possible the calculation of the transient response of concrete structures under dynamic loading (earthquakes, collisions of cars, ships or planes with civil engineering structures). The need for constitutive laws taking account of strain-rate effects has given an impulse to experimental and theoretical investigations of the dynamic behaviour of concrete and other rock-like materials.

A rather significant literature exists on rate sensitivity of rock tested at medium strain rates, for example in previous papers [START_REF] Cheatam | The effect of pressure, temperature, and loading rate on the mechanical properties of rocks, Mechanical Behaviour of rock under Dynamic Loads[END_REF][START_REF] Lindholm | The dynamic strength and fracture properties of Dressel basalt[END_REF], (Christensen et al., 1972) and more recently [START_REF] Klepaczko | Behaviour of rock salt in uniaxial compression at medium and high strain rates[END_REF]. The early tests on concrete under dynamic loading have been performed with pendulum and drop weight tests. The lack of precision of these tests does not allow for an accurate determination of material behaviour, as shown in a review given by Green [START_REF] Green | The impact testing of concrete, Mechanical properties of non-metallic brittle materials[END_REF]. The arrangement using an impulse loading in a cylindrical specimen made of concrete is used by Goldsmith and eo-workers [START_REF] Goldsmith | Dynamic behaviour of concrete[END_REF] to study the tensile fracture feature of concrete. Results obtained from different loading devices are compared and discussed by the state of the art report of the RILEM committee in 1975 (RILEM, 1975). Application of the tensile SHPB arrangement to the concrete specimen has been reported by Reinhardt and eo-workers [START_REF] Reinhardt | The split Hopkinson bar, a versatile tool for the impact testing of concrete[END_REF]. The use of the compressive SHPB to determine the rate sensitivity of concrete can be found in recent works [START_REF] Gong | Dispersion investigation in the split Hopkinson pressure bar[END_REF], Tang et al., 1972).

Another type of dynamic test pe1formed on rocks is high strain-rate impulse loading, for example presented in (Grady & Kipp, 1979;[START_REF] Forrestal | An experimental method to estimate the dynamic fracture strenght of oil shale in the 103 to the 104 s-1 strain rate regime[END_REF]. At those very high rates of loading (i > 1000 s-1 ) , hydrodynamic models are often used and the deviatoric parts of the stress and strain tensors are disregarded.

In this paper, we are looking at medium strain rates (1 s-1 < i < lOOos-1 ). In corresponding real loadings (collision of a car with a concrete civil structure for instance), the influence of deviatoric components of stress on the behaviour cannot be neglected. In this domain, as is generally the case for brittle materials, concrete shows an asymmetric ultimate behaviour (with a failure strength in tension much lower than in compression) under quasi-static loading and a strong sensitivity to the triaxiality of the loading [START_REF] Cedolin | Triaxial Stress-Strain Relationship for Concrete[END_REF]. The same asymmetry is found for the strain-rate sensitivity, which, for concrete, remains small in traction [START_REF] Reinhart | Joint investigation of concrete at high rates of loading[END_REF] and strongly increases in compression [START_REF] Tang | Rate effects in uniaxial dynamic compression of concrete[END_REF].

Such an effect is often attributed to the lateral confinement induced by inertia effects [START_REF] Klepaczko | Behaviour of rock salt in uniaxial compression at medium and high strain rates[END_REF].

It is thus important to take account of those effects in the physical analysis of the dynamic behaviour of concrete. Following the rather classical description of concrete plastic behaviour (Chen and Ting, 1980), one could use a global visco-plastic model to describe dynamic effects [START_REF] Sluys | Wa ve propagation and localisation in rate-dependent cracked medium-Model formulation and one-dimensional example[END_REF]. One could also try to use methods closer to the physical microscopic behaviour (Rossi, 1994) but such methods cannot easily be introduced in classical computer codes. Using a mesa-mechanical approach, to allow for industrial efficiency by the introduction of the model in commercial explicit codes, and following [START_REF] Bailly | Une modelisation d'un materiau fragile avec prise en compte d'effets dynamiques[END_REF][START_REF] Economou | Evaluation of strain rate dependent model for concrete under tension applications, Material and Structure Modeling in Collision Research[END_REF]Reid, 1992), a model is proposed in which local inertia effects are introduced in the constitutive law through the strain acceleration (i).

Checking the validity of this model needs a minimum of experimental results under dynamic multiaxial loading. Those results are obtained using a special device for dynamic tests on rocks under confined pressure, developed in one of the authors' Laboratories and presented in this paper.

The experiment

1. THE SHPB DEVICE

The SHPB (Split Hopkinson Pressure Bar) system, also called Kolsky's apparatus is a commonly used experimental technique in the study of constitutive laws of materials at high strain rates. The first use of a long thin bar to measure stresses in impact conditions has been reported in [START_REF] Hopkinson | A Method of measuring the pressure in the deformation of high explosive by impact of bullets[END_REF]. The experimental setting with two long bars widely used today is pioneered by Kolsky [START_REF] Kolsky | An investigation of mechanical properties of materials at very high rates of loading[END_REF]. This ingenious technique for a compression test has been extended to the tensile loading by Harding [START_REF] Harding | Te nsile testing of materials at impact rate of strain[END_REF] treatment allows for the knowledge of forces and particle velocities at both faces of the specimen. Conditions of the homogeneity of mechanical fields in the specimen can be discussed depending on those measures.

Signal processing

According to the wave propagation theory, stress and particle velocity associated with a wave are simply related to the strain measured by the gages. Thanks to the superposition principle and the shifting of waves (propagation theory), these values are known not only at the measured points but everywhere in the bar and in particular at bar-specimen interfaces.

Following Davies' and other authors works (Davies, 1948; Malinowsky and [START_REF] Malinowski | A unified analytic and numerical approach to specimen behavior in the split Hopkinson pressure bar[END_REF][START_REF] Malvern | Dynamic testing of laterally confined concrete, Micromechanics of fa ilure of quasi brittle materials[END_REF], we use a complete data processing of the waves, including wave dispersion correction-recently extended to linear viscoelastic bars [START_REF] Zhao | A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques[END_REF]and an assisted delay setting based on the elastic transient response of the specimen, (Gary et al., 1992, Gary et al., 1993). The use of that precise data processing is specially important for testing concrete (or brittle materials) that cannot support large strains without damage because it insures correct measurements at low strains (in the range of 1%) where rupture occurs and where the maximum stress is measured [START_REF] Zhao | Measurements of the dynamic behaviour of concrete under impact loading[END_REF].

Forces and velocities at both sides of the specimen being known, assumptions for the specimen response must be chosen to obtain the constitutive law. The standard analysis assumes the homogeneity of strains in the specimen. In the case of concrete, transient simulations [START_REF] Zhao | Analyse de l'essai aux barres de Hopkinson, Application a la mesure du comportement dynamique des materiaux[END_REF][START_REF] Zhao | Utilisation de la barre de Hopkinson pour !'etude du comportement dynamique des materiaux fragiles, I I' Congres Franr[END_REF][START_REF] Zhao | A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques[END_REF] show that correct results are obtained using the so-called improved standard analysis-or three waves' analysis-using the average of the two forces to calculate the stress [START_REF] Lindholm | Some experiments with the split Hopkinson pressure bar[END_REF]. The nominal values for average strain rate and stress applied to the specimen are, in that case, the following ones:

(1), (2)

( t) = Vlnput -Vouput L.s (t) _ Flnput + Fouput O's ' - 2 Ss
where Ls and Ss are the initial length and section area of the specimen.

The processing of the signals recorded with gauges is based on a one-dimensional description of the bar (even the dispersion correction, due to a 3D calculation, only takes account of the ID projection of those results on the bars' axes). Consequently, measurements at bar-specimen interfaces are integrated values: total force applied to the specimen, mean speed of its faces. A 3D modelling of the specimen response is always possible but it needs additional assumptions for loading conditions.

Tests result analysis

Non-constant strain-rate

A typical average strain-rate for the specimen obtained with those assumptions is presented in Figure 2. It would be convenient to fix the strain rate at a constant value in an idealised test, but this is obviously impossible (at least since the strain-rate equals zero at the beginning of the test). The assumption of a constant strain-rate is accepted when the rise time of the strain-rate is small compared with the duration of the test and when the strain-rate is almost constant during the test (as in quasi-static tests or approximately for some dynamic tests on metals). A different situation is shown in Figure 2. The strain rate is not constant for a SHPB test on concrete and the measured stress-strain relation cannot be simply related to a constant value of the strain rate. In the following, when a nominal value of the strain-rate will have to be attached to a particular test, it will be chosen as the value associated with the maximum stress. Nevertheless, it must be kept in mind that the response depends on the strain-rate evolution. This point is illustrated in Figure 3. (two simulations, using the behaviour modelled in section 3, with the same nominal value for the strain rate).

the model presented in the following: two different loadings with the same nominal value of the strain rate produce close, but different, stress-strain responses.

Contact conditions

Experimental problems found in concrete testing in compression have already been investigated by [START_REF] Gorisse | Les essais mecaniques, Le beton Hydraulique[END_REF][START_REF] Toutlemonde | Resistance au choc des structures en beton[END_REF]. They show, in particular, that fretting effects can induce an over estimated measure of the failure strain. The influence of fretting conditions appears almost only in the post-peek response of the specimen. In [START_REF] Kotsovos | Effect of testing techniques on the post-ultimate behaviour of concrete in compression[END_REF], it is directly illustrated with constant length specimens and various fretting conditions as in (van Mier, 1986) it indirectly appears through the effec t of the specimen length. Following those authors it is found that the natural explanation of this effect is the presence of an undesired confined loading induced by fretting effects near specimen ends.

Under dynamic compression, lateral inertia effects will become active as soon as lateral displacements appear (this is one of the ideas introduced in the model proposed in this paper). If the additional lateral pressure due to friction effects is the same as in a quasi-static loading, one can expect that it will be relatively less important with respect to the fi nite overall lateral pressure induced by inertia. Furthermore, our main purpose is to investigate the effects of lateral pressure and compare them to inertia effects. We are then always in loading situations where a significant lateral pressure appears. An indication of less apparent fretting effects, is given in a similar case, using bars with a Poisson's ratio close to the one of concrete: strain measurements with a strain gauge glued on the specimen show results very close to the SHPB ones [START_REF] Tang | Rate effects in uniaxial dynamic compression of concrete[END_REF].

Specimen length

Platens used in our tests are the ends of 40 mm diameter aluminium bars. Specimens have the same diameter and length (40 mm diameter, 40 mm length). Considering contact condition, this length is rather small and it is due to the dynamic loading conditions. The analysis of the test is based on the assumption of homogeneous stress and strain fi elds. Consequently, the rise time .of the loading signal must be long compared to the travelling time of the waves through the specimen therefore long specimens must be avoided. On the other hand, the small-scale specimen tested, with a maximum aggregate size of 10 mm, would not have been correctly represented with a shorter specimen.

A second point is that changing the specimen length could not be independent of changing the speed of loading in order to keep the strain-rate constant. All the tests have been done with similar specimens.

THE SPECIFIC DEVICE FOR CONFINED PRESSURE TESTS

Different methods can be used to provide multiaxial loading conditions. A very simple one consists of making oedometric tests. Such a method has given good results for sand testing [START_REF] Semblat | Sols sous sollicitations dynamiques et transitoires : reponse dynamique aux barres de Hopkinson, propagation d'ondes en milieu centrifuge[END_REF][START_REF] Semblat | Dynamic response of sand using 3D Hopkinson bar[END_REF] but cannot be easily applied to concrete because of unknown (and probably strong) longitudinal friction effects induced by the differential strains betweeen the specimen and the thick confining cylinder.

To avoid longitudinal friction, another method exists using a thin metallic ring compressed with the specimen. This method, used by Gong and Malvern [START_REF] Malvern | Dynamic testing of laterally confined concrete, Micromechanics of fa ilure of quasi brittle materials[END_REF] and others [START_REF] Bragov | Use of the Kolsky Method for Studying Shear Resistance of Soils, Dymat[END_REF] needs a special specimen preparation and the use of a strain-gage on the ring. It allows for a simultaneous measurement of the radial pressure and strain of the specimen, but without the ability of an easy control of the lateral pressure.

1. Sealing problems

Using a significant lateral pressure of oil (20 MPa) a test without a specimen (bar against bar) has been performed to investigate the influence of seals on waves propagating in the bars. The complete data processing has been applied to the recorded incident and transmitted waves measured in this test. Input and output forces have been calculated. those forces, presented in Figure 5, are not very different. This good agreement proves that the influence of seals can be disregarded.

Force OdU 158 2.2.2. Lateral pressure It seems reasonable to assume that a static confined pressure applied with air will not be significantly aff ected by the increase in the diameter of the specimen induced by the deformation (in this device, the chamber is 120 mm long and has a diameter of 75 mm so that with a 40 mm long and 40 mm diameter specimen, the volume of the fluid in the chamber is almost 10 times the volume of the specimen).

The situation is not so clear with oil and it is not sure, because of transient effects in the fluid, that a measurement of the oil pressure during the test at a point in the chamber would give an exact measure of the pressure applied to the specimen. To evaluate this point, tests with oil and with air have been performed, using the same initial confinement pressure and other initial conditions. Results under oil pressure look very much like the ones presented in (Malvern et al., 1991) using a very similar device where water lateral pressure was used.

When lateral pressure is applied with air, the stress strain relation shows a much lower apparent strain hardening, as presented in Figure 6. The same kind of results have been obtained in tests on sand specimens [START_REF] Semblat | Sols sous sollicitations dynamiques et transitoires : reponse dynamique aux barres de Hopkinson, propagation d'ondes en milieu centrifuge[END_REF] showing that oil pressure increases during the test. In that case, for similar tests (same specimen, same speed of loading, same initial lateral pressure), the stress associated with a given strain was minimum for air pressure tests, maximum for oedometric {zero lateral strain) tests, and in-between for oil pressure tests.

Consequently, all the test results presented in the following to support our model, are obtained under a confined pressure of air, assumed constant during the test and equal to the initial imposed and measured value. 3. Modelling of a quasi-brittle material

BACKGROUND OF THE MODELLING

.1.1. The general case

Many constitutive models to describe the macroscopic behaviour of concrete can be found in the literature [START_REF] Cedolin | Triaxial Stress-Strain Relationship for Concrete[END_REF]Chen and Ting, 1980;[START_REF] Bazant | Endochronic Theory of Inelasticity and Failure of Concrete[END_REF][START_REF] Bicanic | Constitutive model for concrete under dynamic loading[END_REF]. Depending on physical phenomenon observed in different situations, the non linear behaviour of a concrete-like material is described by three different classes of models. The first class ("a") is associated with uniaxial loading or loading with a small mean stress. The main physical behaviour involved is micro-cracking. The second class ("b") is associated with significantly multiaxial loading: the mechanical behaviour shows plastic flow. The third class ("c") is associated with high pressure loading where significant compaction of the material occurs. When this process is involved, the rate sensitivity is generally neglected, even at very high strain rates like those found during impact producing shock waves.

For "c" -class models, the compacting process can be modelled by an "equation of state", i.e. a pure spherical relation between the mean stress and the volumetric strain. When a plastic flow is observed ("b"-class), the macroscopic behaviour is naturally modelled using a plastic or visco-plastic theory [START_REF] Pietruszczaks | An elastoplastic constitutive model for concrete, lnt[END_REF][START_REF] Chen | Constitutive relations for concrete[END_REF]. Rather sophisticated models are found in this case, using for example a non associated fl ow rule [START_REF] Elwi | A 3D hypoelastic concrete consitutive model[END_REF][START_REF] Han | A non uniform hardening plasticity model for concrete materials[END_REF]. The addition of a deviatoric behaviour, described by a plastic model, and of a spherical behaviour has also been proposed (Mariotti et al., 1994). Other authors associate damage and plasticity theory [START_REF] Ulm | Un modele d'endommagement plastique : application au beton de structure, These de doctoral de I[END_REF]. In the case of general plastic behaviour, it is natural to introduce the rate dependence with the visco-plastic theory [START_REF] Suaris | Rate sensitive damage theory for brittle solids[END_REF]. The more sophisticated models available for dynamic problems concern loading with medium or high pressures [START_REF] Holmquist | A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressure[END_REF] where the sophistication is associated with a great number of parameters (to be identified).

Our approach is for "a" -class models. The micro-cracking can be introduced with damage theory [START_REF] Mazars | Application de la mecanique de l'endommagement au comportement non lineaire et a la rupture du beton de structur�[END_REF][START_REF] Kachanov | Continuum model of medium with cracks[END_REF][START_REF] Andrieux | Un modele de materiau microfissure pour les betons et les roches[END_REF]. Another approach is based on the study of mechanisms observed at a microscopic level [START_REF] Deng | Dynamic Damage Evolution of solids in compression: Microcracking, Plastic Flow, and Brittle-Ductile Transition[END_REF][START_REF] Kusano | Impulse local damage analysis of concrete structure by the distinct element method[END_REF]. It should be expected that a constitutive law based on such an approach needs a reduced number of parameters and that it will contribute to the understanding of the physical response of the material. The rate sensitivity of the concrete and other semi-brittle material has for a long time been a subject for experimental investigations and theoretical modelling in this field.

In any case, when an apparent macroscopic rate sensitivity of the material is observed it raises the question whether it is due to a rheological material behaviour or is a simple consequence of the structural dynamic response of a finite volume dynamically loaded. In the latter case, especially when numerical finite elements' models are used-with elements, as they can be found in civil engineering, that are large compared with local mechanisms due to failure-, the question would remain of how to find a macroscopic rate-sensitive model. This question has already been widely discussed. On the rheological side, time dependent effects have been found. It has been proved that the crack velocity cannot exceed the speed of Rayleigh's waves [START_REF] Bui | Mecanique de la rupture fragile[END_REF][START_REF] Deng | Dynamic Damage Evolution of solids in compression: Microcracking, Plastic Flow, and Brittle-Ductile Transition[END_REF]. The presence of free water in the open porosity of the concrete could also explain a part of a rheological viscosity (Rossi, 1991 ). The opening of micro-cracks creates motion at a micro-level which could also induce inertial effects at the macro-level [START_REF] Economou | Evaluation of strain rate dependent model for concrete under tension applications, Material and Structure Modeling in Collision Research[END_REF]Kusanov et al:, 1992). On the macroscopic side, one could expect that a correct transient dynamic calculation of a concrete structure would be sufficient to describe the apparent rate sensitivity response. In recent works (Daudeville, 1996;Le Nard, 1996), it has been observed that a rate effect in the response of a cylindrical sample can be found, through a dynamic (including inertia effects) transient 3D calculation using a model that is not rate sensitive. Nevertheless, the agreement of such calculations with experimental results becomes better when the confining presure increases, showing that the rate sensitivity of a constitutive model is specially needed when lateral extension can occur, as it is the case when the confining pressure is closed to zero.

One purpose of the present modelling work is to contribute to the understanding of the basic physical principles involved in the behaviour, using a micro-mechanical model with a small number of parameters. This model is then not intended to provide an exact mechanical description of a specimen in compression and our proposed comparisons between simulations and experiments are only a first step for a general qualification of basic ideas. The domain of validity investigated concerns loading paths of the structure leading to extensions in the material. In this case special attention is focused on the post-peak phase where failure in extension is under development. It is then expected that the response of our model and, in particular, the time sensitivity, will depend on inertia or viscous effects involved in the motion of basic mechanisms.

Construction of the model

In the construction of the model, the following observations concerning the general behaviour of concrete will be kept in mind:

-the damage criterion is a function of the strain in extension [START_REF] Mazars | Application de la mecanique de l'endommagement au comportement non lineaire et a la rupture du beton de structur�[END_REF], -effects of internal friction are observed in the fractured material (Attia, 1991), -structural effects like buckling of the fractured material (Janach, 1979) and inertia of micro cracking [START_REF] Klepaczko | On the Role of Microcracking Inertia in Rate Sensitivity of Coal at High Strain Rates[END_REF][START_REF] Klepaczko | Behavior of Rock-like Materials at High Strain Rate in Compression[END_REF] are involved in the dynamic behaviour. The fractured material is described through a virtual continuum the behaviour of which includes structural effects. Those effects are obtained by introducing a mass in a rheological model, following previous authors [START_REF] Economou | Evaluation of strain rate dependent model for concrete under tension applications, Material and Structure Modeling in Collision Research[END_REF][START_REF] Bischoff | Compressive Behaviour of Concrete at High Strain Rate[END_REF]). An analogical scheme, used as a rheologica1 model, is built in two dimensions, as shown in Figure 7. This model is then to be used when there is at least one direction in extension producing cracks. Consequently, and as mentioned before, the behaviour under high pressure, as described in [START_REF] Holmquist | A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressure[END_REF] is not investigated in this paper. The explicit formulation of the behaviour is deduced from the governing equations of the two�dimensional mechanism. Those equations are written in the principal axes of the stress tensor. The first equation describes the current state of the geometry of the mechanism (Fig. 7).

RADIAL LOADING

(3)

1 + c22 tga = tgao --- 1 + e:n
The second and the third ones describe the equilibrium of forces on the mechanism. Where the principal strains are named in increasing order (en < e22)-R a stiffness, Pm an equivalent specific mass and 7J a viscosity coefficient.

a is a geometric parameter (ao is relative to the virgin material) described in Figure 7.

In equation ( 5), the first term describes a buckling effect, the third an inertial one and the fourth a viscous one. Function Pt• that appears in the second term, will influence the overall evolution of the response of the model. This function describes an extension process and should depend only on the tensile behaviour of the material. A tensile behaviour has been experimentally measured, by [START_REF] Terrien | Emission Acoustique et Comportement Mecanique Post Critique d'un Beton Sollicite en Trac tion[END_REF]. It is described here by an elastic model complete with damage and friction:

-if e2m < c:d <TJ (.:: 22) = E e22 -if e2m > C d
where: e d is the strain limit of tension, e2m = max (e22)b, is the maximum of the value of e22 (t) before the current time.

E is classical Young's modulus.

When damage has occurred (c: z 111 2 c:d ), the term (J.f is the result of two effects: crf, is a residual strength after cracking, for the most part due to bridging in the heterogeneous material, that is characterised by a damage parameter as written below, and rJfs is a stress due to friction in the cracks. If the loading is tensile (cr11 0)

the behaviour is directly governed by equation ( 5). n is an empirical power law exponent.

It is important to note that, with such a model, the continuity of the stress is always verified with respect to time (or during the evolution), even when cracking occurs. When softening appears, the size of the strain localisation domain is a consequence of the effects of the equivalent specific mass and the viscosity coefficient in the equations of motion (de Borst, 1993; Zaki, 1995 and[START_REF] Zaki | Reponse dynamique d'un milieu quasi-fragile[END_REF]. For a small and reversible strain this model gives a response very close to classical linear elasticity. It is then easy to obtain relations between coefficients of the model and usual elastic constants:

(8) tgao = v
The rate sensitivity introduced in (5) is associated with the opening of cracks in two different ways: First, r1 is a viscosity coefficient (io is then a reference strain rate, for instance io = w-5 /s) that will not play an important role (see § 4.2.1).-Second, the time dependence is related to an equivalent density P m that describes inertia effects associated with structural movements and a similarity can be found with the buckling of a column [START_REF] Gary | Dynamic Buckling of an Elastoplastic Column[END_REF]. This effect will be shown to dominate at high strain rates. This modelling approach can be extended to the three dimensional case when there is at least one principal stress in compression. The mechanism is then completed by the superimposition of a second (identical) one, chosen in a perpendicular plane, both planes being parallel to the compressive (loading) stress. Using the same analysis as in the single case (20), the model is described by the following equations:

(9) 1 + f:ji tg ai tg ao --- 1 + E"ll <Ju _ R ( 1 + c:u _ 1 )
-IT cos ai IT cos ai cos 2 ao ai ( ) .. O'fi (Eii) = E (1-�i) Eii + (-vO'u ) \ 1 -E�:) si g n ( i22) with �i = 1-( Ea ) 11 and Eim :::: : rnax (Eii )b f1m

I (ii i)

An important area for this kind of model is the explicit formulation of the behaviour which is suitable for a dynamic computation. In the case of a radial loading, the stress is given by equations depending on the strain, the strain rate, the strain acceleration and damage parameters ;;_ ::::

( �i) (11)
The thermodynamic consistency of the model is verifi ed: the reversible energy is close to the one of a pure elastic material with actual moduli depending on damage parameters. A specific internal kinetic energy, Pb is associated to inertial effects by: ( 12)

i = 2, 3
The dissipated power is due to damage, friction, and viscosity:

(13) 1 2 •

1. I ( l iii l ( ) / Ea ))

D = Z E Eii �i + Eii TJ l o g io + -vO'u \ 1 -E i i
lts positiveness follows from the model construction.

THE GENERAL CASE (NON-RADIAL LOADING

) i = 2, 3
The model is simple to apply in the case of proportional loadings, frequently found in common dynamic loadings on real structures.

Its extension to general loadings is still theoretically possible (provided that the three principal strains are not in tension). Nevertheless, when the principal axis of the strain tensor varies during the loading, it becomes difficult to describe in a simple way the anisotropy of the damage and its evolution and it is necessary to introduce complementary assumptions. A simple criterion can be found to determine the first direction of the mechanism.

For example, when the principal strain E 3, which is an extension, reaches the limit Ea, it is assumed that the cracks of the corresponding elementary volume are orthogonal to the corresponding direction. One direction of the mechanism is then fixed. The determination of the second direction, chosen orthogonal to the first one, is not so natural. Furthermore, the axes of the mechanism become different to the principal axis of the strain tensor and complementary relations, not provided by the mechanism, are needed between stress and strain components.

Following this kind of frame, a theoretical generalisation of the model has been proposed [START_REF] Bailly | Une modelisation d'un materiau fragile avec prise en compte d'effets dynamiques[END_REF].

Knowing that dynamic test results under non radial loading are not generally available, such a generalisation is not developed in this paper. The response of the model for a typical quasi-static loading is shown in Figure 8. In that case, a constant low strain-rate of loading is applied (1 0 -4 s-1 ) with no lateral pressure (o-2 = 0) The compressive streng th fc is the maximum value of the axial stress (/c = 65 MPa). The behaviour obtained with the model presents the classical phases of a compression test on concrete:

1. o-1 � 20 MPa (cz � cd), the behaviour is close to linear elasticity.

2.

o-1 > 20 MP a (! !c), damage appears and there is a non linear radial expansion but damage is still not visible on the axial stress-strain curve. The volume change is still negative in this region and• becomes positive at about o-= 0 . 75 le• 3. o-1 � fc, a very high radial expansion is observed and the failure looks like an unstable phenomenon.

The simulation of a confined compressive quasi-static test has been carried out (with the set of previously identified parameters). The triaxial test is divided in two phases: in the first phase, a hydrostatic pressure is applied (o-t = o-2) whieh leads to a confined state (10 MPa); in the second phase a deviatoric loading is app lied where the radial stress is constant. An experiment has been performed on a concrete specimen the compressive strength of which is about 65 MPa. The results of the simulation are compared with experimental ones in Figure 9 showing a good agreement in the ultimate strength (which is about 1 30 MPa).

DYNAMIC COMPRESSION TESTS

The capability of the model to describe quasi-static tests under lateral pressure indicates that the proposed mechanism provides a good description of some bi-axial loading effects. A more important goal is nevertheless to have a model working in the dynamic range.

Pure compression tests

Many results found in the literature show an increase of the maximum stress with the average strain rate.

Experimental results presented here have been obtained in a joint research program [START_REF] Klepaczko | Essai de compression dynamique sur beton[END_REF] on a large range of strain-rates, see Figure 10. They show a change in the strain-rate sensitivity of the maximum stress, for a strain-rate about 10 s-1 , that could be due to inertial effects. Below this value, only a strain rate effect due to the viscosity may be visible. This viscous effect is small and is attributed to the presence of free water in the concrete (Rossi and Boulay, 1990; Rossi, 1991). For high strain rates(£ > 100 s-1), the structural effect is very important and becomes the major contribution to the apparent increase of the maximum strength.

Parameters used in the model have already been identifi ed with a quasi-static test except the specifi c mass Pm• This last value is now chosen to give the best fi t with dry concrete test results. In the simulation, nominal strain-rate is that defined in section 2.1. The maximum value of the stress as a function of strain-rate is shqwn in Figure 10 and compared with experimental points. ------------------------------------------- The experimental device for confined dynamic compressive tests is described in section 2. Simulations with the model are performed in the same way as for previous cases. An example of the axial stress-strain evolution is presented in Figure 11. The model provides a good evaluation of the maximum stress. The effect of the lateral pressure produces a post-peak residual stress which is also correctly described. Figure 12 presents results at two different strain rates. Experimental results show that the strain rate has an influence on the maximum stress (apparent strength), as in the unconfined compression tests. It seems that the residual stress (post-peak phase) only depends on the confinement. The model provides good evaluations of those "apparent" and "residual" stresses. At high strain rates (i :;:::i 600 s�1 ), it produces oscillations in the softening phase of the stress-strain curve that are not observed in experimental results. This discrepancy could be due to transient effects in the specimen (propagation of waves through the specimen) which are neglected in the analysis of the test and are not introduced in the modelling. Indeed, stress and strain fields are assumed homogeneous in the model and the experimental average strain-rate used as input data is based on the same hypothesis. In the case of higher velocity impacts, very high strain rates can be locally produced that will not appear in the average strain rate history. The simulation of high velocity tests then requires a transient analysis of the specimen which is not developed in this paper.

strength (MPa) 150 �-

In Figure 13, the effect of the lateral pressure on the stress-strain curve is presented (with approximately the same axial strain rate for the different tests). The maximum stress and the "residual" stress both depend on the value of the pressure. The model correctly describes those effects.

Conclusion

Experimental results have been presented for concrete specimens under dynamic compression and quasi-static lateral loading. The original use of air pressure for lateral loading allows for a constant controlled value of this pressure during the test facilitating comparisons between experimental and theoretical results.

This model allows inertia effects to be taken into account by introducing the second time-derivative of the strain in the constitutive relation. A rather small number of parameters is needed so that an easy identification of the model is possible. It gives good agreement with experimental results in the dynamic range where it also correctly describes the effect of lateral pressure.

Our purpose was to investigate the capability of taking account of inertia effects with the derivative of the strain rate and the model has been constructed to describe the behaviour of concrete when damage has already occurred. Dynamic results being mostly obtained under radial loadings, the use of such a model in a complex 3D loading situation will need further development.

Results presented here are obtained under the assumption of homogeneous stress and strain fields in the specimen, even in the dynamic range, as is commonly done in similar situations. Considering now the specimen as a structure itself, the same model has to be validated in the case of transient loadings. The measure of input and output forces and speeds at both ends of the specimen provides sufficient data to support such calculations [START_REF] Rota | An inverse approach for identification of dynamic constitutive equations[END_REF]. The transient simulation of the specimen response in which certain input conditions are prescribed (velocities for instance) provides calculated values of the other quantities (forces for instance) which can be compared with measured-or assumed-values. Results already obtained in this direction [START_REF] Zaki | Reponse dynamique d'un milieu quasi-fragile[END_REF] further validate the proposed model.

  Fig. I. -SHPB set-up.

Fig. 2 .Fig. 3 .

 23 Fig. 2. -Average strain rate as a function of time.

  For sake of simplicity, and following(Christensen et al., 1972;[START_REF] Malvern | Dynamic testing of laterally confined concrete, Micromechanics of fa ilure of quasi brittle materials[END_REF], the specimen is introduced into a cylindrical quasi-static pressure cell. The bars are acting as pistons and are introduced into the cell through sealing rings. A scheme of the complete set-up is shown in Figure4. The lateral pressure can be applied with oil (up to 50 MPa), or with air (up to 10 MPa).

  Fig. 4. -Set-up for confined pressure tests.

Fig. 5 .

 5 Fig. 5. Input and output forces for a confined "bar against bar,. test

Fig. 6 .

 6 Fig. 6. -Comparison between different lateral loading conditions.

Fig. 7 .

 7 Fig. 7. -Elementary volume of concrete and analogical rheological model.

  cos a cos acos ao(5) o-22 == o-11 tg a + a f ( e22) + Pm i22 + 7J log ( i :

  <Jjp = E (1-�) czz or afe = E (.!!i_ ) n c:zz with 1 < n < 2 C:zm afs =(-van)/ 1-�d )sign(izz) (wbere(a) rnax(O, a)) \ C 2 2 v is classical Poisson' s ratio, .; is a damage parameter.

  aii = <Jll +a fi €ii +Pm Eii + 71 o g -;

4.Fig. 8 .

 8 Fig. 8. -Stress-strain relation for the simulation of a quasi-static compressive test.

Fig. 9 .

 9 Fig. 9. -Stress-strain relation for the simulation of a quasi-static confined compressive test. (solid line: experiment, dotted line: simulation).

  Fig. 10. -The apparent compressive strength function of the strain rate (experimental data from Gary and Klepaczko. 1992).

  2. Dynamic compression tests under lateral pressureAll parameters used in the model are now fixed, a new loading condition is introduced with lateral pressure.

Fig

  Fig. 11. -Stress-stmin relations for a confined dynamic compressive test. (solid line: experiment, dotted line: simulation) (confinement pressure= 5 MPa, nominal strain rate= 250 s-1 ).

58 a

 58 Fig. 12. -Confined compressive test (left hand side) and simulation (right hand side).Influence of the strain rate (confi nement pressure 5 MPa).


Achour Mostéfaoui

Matthieu Perrin

Michel Raynal

Extending the Causal Consistency Condition to any Object Defined by a Sequential Specification

Keywords: Causality, Causal order, Concurrent object, Consistency condition

This paper presents a generalization of causal consistency suited to the family of objects defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects (concurrent operations are not ordered), it follows that causal consistency allows different processes to have different views of each object history.

Processes and Concurrent Objects

Let us consider a set of n sequential asynchronous processes p 1 , ..., p n , which cooperate by accessing shared objects. These objects are called concurrent objects. A main issue consists in defining the correct behavior of concurrent objects. Two classes of objects can be distinguished according to way they are specified.

• The objects which can be defined by a sequential specification. Roughly speaking, this class of objects includes all the objects encountered in sequential computing (e.g., queue, stack, set, dictionary, graph). Different tools can be used to define their correct behavior (e.g., transition function, list of all the correct traces -histories-, pre and post-conditions, etc.).

It is usually assumed that the operations accessing these objects are total, which means that, whatever the current state of the object, an operation always returns a result.

As an example, let us consider a bounded stack. A pop() operation returns a value if the stack is not empty, and returns the value ⊥ if it is empty.

A push(v) operation returns the value ⊤ if the stack is full, and returns ok otherwise (v was then added to the stack). A simpler example is a read/write register, where a read operation always returns a value, and a write operation always returns ok.

• The objects which cannot be defined by a sequential specification. Example of such objects are Rendezvous objects or Non-blocking atomic commit objects [START_REF] Gray | Notes on database operating systems: an advanced course[END_REF]. These objects require processes to wait each other, and their correct behavior cannot be captured by sequences of operations applied to them.

In the following we consider objects defined by a sequential specification.

Strong Consistency Conditions

Strong consistency conditions are natural (and consequently easy to understand and use) in the sense that they require each object to appear as if it has been accessed sequentially. In a failure-free context, this can be easily obtained by using mutual exclusion locks bracketing the invocation of each operation.

Atomicity/Linearizability

The most known and used consistency condition is atomicity, also called linearizability 1 . It requires that each object appears as if it was accessed sequentially, this sequence of operations belonging to the specification of the object, and complying with the real-time order of their occurrences.

Sequential consistency This consistency condition, introduced in [START_REF] Lamport | How to make a multiprocessor computer that correctly executes multiprocess programs[END_REF], is similar to, but weaker than, linearizability, namely, it does not require the sequence of operations to comply with real-time order. Figure 1 presents an example of a sequentially consistent computation (which is not atomic) involving two read/write registers R1 and R2, accessed by two processes p 1 and p 2 . The dashed arrows define the causality relation linking the read and write operations on each object (also called read-from relation when the object is a read/write register). It is easy to see that the sequence of operations made up of all the operations issued by p 2 , followed by all the operations issued by p 1 , satisfies the definition of sequential consistency.

R1.write(2)

R1.write [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF] R2.write( 5)

R2.read() → 5 p 1 p 2 R1.read() → 2 R1.read() → 1
Figure 1: A sequentially consistent computation (which is not atomic) Implementing a strong consistency condition in an asynchronous messagepassing system Shared memories usually provide processes with objects built on top of basic atomic read/write objects or more sophisticated objects accessed by atomic operations such as Test&Set or Compare&Swap [START_REF] Herlihy | Wait-free synchronization[END_REF][START_REF] Herlihy | The art of multiprocessor programming[END_REF][START_REF] Raynal | Concurrent programming: algorithms, principles and foundations[END_REF][START_REF] Taubenfeld | Synchronization algorithms and concurrent programming[END_REF]. This is no longer the case in message-passing systems where all the objects (except communication channels) have to be built from scratch [START_REF] Attiya | Distributed computing: fundamentals, simulations and advanced topics[END_REF][START_REF] Raynal | Distributed algorithms for message-passing systems[END_REF].

Implementations of sequentially consistent objects and atomic objects in failurefree message-passing systems can be found in [START_REF] Attiya | Sequential consistency versus linearizability[END_REF][START_REF] Attiya | Distributed computing: fundamentals, simulations and advanced topics[END_REF][START_REF] Cholvi | A methodological construction of an efficient sequentially consistent distributed shared memory[END_REF][START_REF] Raynal | Sequential consistency as lazy linearizability[END_REF][START_REF] Raynal | Distributed algorithms for message-passing systems[END_REF]. These implementations rest on a mechanism which allows a total order on all operations to be built. This can be done by a central server, or a broadcast operation delivering messages in the same order at all the processes. Such an operation is usually called total order broadcast (TO-broadcast) or atomic broadcast. It is shown in [START_REF] Raynal | Sequential consistency as lazy linearizability[END_REF] that, from an implementation point of view, sequential consistency can be seen as a form of lazy linearizability. The "compositional" power of sequential consistency is addressed in [START_REF] Ekström | A fault-tolerant sequentially consistent DSM with a compositional correctness proof[END_REF][START_REF] Perrin | On composition and implementation of sequential consistency[END_REF].

Implementations of a strong consistency condition (such as atomicity) in failureprone message-passing systems is more difficult. More precisely, except for a few objects including read/write registers (which can be built only in systems where, in each execution, a majority of processes do not crash [START_REF] Attiya | Sharing memory robustly in message passing systems[END_REF]), it is impossible to implement an atomic object in the presence of asynchrony and process crashes [START_REF] Fischer | Impossibility of distributed consensus with one faulty process[END_REF]. Systems have to be enriched with additional computing power (such as randomization or failure detectors) to be able to implement objects defined by a strong consistency condition.

3 Causal Consistency on Read/Write Objects (Causal Memory)

Causality-based consistency condition A causal memory is a set of read/write objects satisfying a consistency property weaker that atomicity or sequential consistency. This notion was introduced in [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF]. It relies on a notion of causality similar to the one introduced in [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF] for message-passing systems.

The main difference between causal memory and the previous strong consistency conditions lies in the fact that causality is captured by a partial order, which is trivially weaker than a total order. A total order-based consistency condition forces all the processes to see the same order on the object operations. Causalitybased consistency does not. Each process can have its own view of the execution, their "greatest common view" being the causality partial order produced by the execution. Said differently, an object defined by a strong consistency condition is a single-view object, while an object defined by a causality-based consistency condition is a multi-view object (one view per process).

Another difference between a causality-based consistency condition and a strong consistency condition lies in the fact that a causality-based consistency condition copes naturally with process crashes and system partitioning.

Preliminary definitions As previously indicated, a causal memory is a set of read/write registers. Its semantics is based on the following preliminary definitions (from [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF][START_REF] Herlihy | Linearizability: a correctness condition for concurrent objects[END_REF]). To simplify the presentation and without loss of generality, we assume that (a) all the values written in a register are different, and (b) each register has an initial value written by a fictitious write operation.

• A local (execution) history L i of a process p i is the sequence of read and write operations issued by this process. If the operations op1 and op2 belong to L i and op1 appears before op2, we say "op1 precedes op2 in p i 's process order". This is denoted op1 i → op2. • Two operations not related by po → are said to be independent or concurrent.

• The projection of H on a register R (denoted H|R) is the partial order H from which are suppressed all the operations which are not on R.

• A serialization S of an execution history H (whose partial order is po →) is a total order such that, if op1 po → op2, then op1 precedes op2 in S .

A remark on the partial order relation As we can see, the read-from relation mimics the causal send/receive relation associated with message-passing [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF]. The difference is that zero, one, or several reads can be associated with the same write. In both cases, the (write-into or message-passing) causality relation is a global property (shared by all processes) on which is built the consistency condition. It captures the effect of the environment on the computation (inter-process asynchrony), while process orders capture the execution of the algorithms locally executed by each process.

Causal memory Let H i+w be the partial order po →, from which all the read operations not issued by p i are suppressed (the subscript i + w means that only all the operations issued by p i plus all write operations are considered).

As defined in [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF], an execution history H is causal if, for each process p i , there is a serialization S i of H i+w in which each read from a register R returns the value written in R by the most recent preceding write in R.

This means that, from the point of view of each process p i , taken independently from the other processes, each register behaves as defined by its sequential specification. It is important to see, that different processes can have different views of a same register, each corresponding to a particular serialization of the partial order po → from which the read operations by the other processes have been eliminated. An example of a causal memory execution is depicted in Figure 2. Only one write-into pair is indicated (dashed arrow). As R1.write [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF] and R1.write(2) are independent, each of the operations R1.read() by p 2 and p 3 can return any value, i.e., u, v ∈ {1, 2}. For the same reason, and despite the write-into pair on the register R2 involving p 1 and p 3 , the operation R1.read() issued by p 3 can return w ∈ {1, 2}. This shows that different processes can obtain different "views" of the same causal memory execution. Once a read returned a value, a new write-into pair is established.

Implementations of a causal read/write memory (e.g., [START_REF] Ahamad | An adaptive protocol for implementing causally consistent distributed services[END_REF]) rest on an underlying communication algorithm providing causal message delivery [START_REF] Birman | Reliable communication in the presence of failures[END_REF][START_REF] Raynal | The causal ordering abstraction and a simple way to implement it[END_REF]. It is shown in [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF][START_REF] Raynal | From causal consistency to sequential consistency in shared memory systems[END_REF] that, in executions that are data race-free or concurrent write-free, a causal memory behaves as a sequentially consistent read/write memory.

Causal Consistency for any Object

The problem Albeit it was introduced more than 20 years ago, it appears that, when looking at the literature, causal consistency has been defined and investigated only for read/write objects (the only exception we are aware of is [START_REF] Perrin | Causal consistency: beyond memory[END_REF]). This seems to be due to the strong resemblance between read/write operations and send/receive operations. Hence, the question: Is it possible to generalize causal consistency to any object defined by a sequential specification? This section answers positively this question.

Preliminary definitions

The notations and terminology are the same as in the previous section, but now the operations are operations on any object O of a set of objects O, each defined by a sequential specification.

Considering a set of local histories and a partial order po → on their operations, let Assignment i ( po →) denote the partial order po →, in which, for each operation op() not issued by p i , the returned value v is replaced by a value v ′ , possibly different from v, the only constraint being that v and v ′ belong to the same domain (as defined by the corresponding operation op()). Let us notice that Assignment i ( po → ) is not allowed to modify the values returned by the operations issued by p i . Moreover, according to the domain of values returned by the operations, a lot of different assignments can be associated with each process p i .

Given a partial order po →, and an operation op, the causal past of op with respect to po → is the set of operations {op ′ | op ′ po → op}. A serialization S i of a partial order po → is said to be causal past-constrained if it is such that, for any operation op issued by p i , only the operations of the causal past of op appear before op.

Causal consistency for any object Let H = L 1 , . . . , L n be a set of n local histories (one per process) which access a set O of concurrent objects, each defined by a sequential specification. H is causally consistent if there is a partial order po → on the operations of H such that for any process p i : The first requirement states that the partial order po → must respect all process orders. The second requirement states that, as far as each process p i is concerned, the local view (of po →) it obtains is a total order (serialization S i ) that, according to some value assignment, satisfies the sequential specification of each object O. 2Let us remark that the assignments Assignment i () and Assignment j () associated with p i and p j , respectively, may provide different returned values in S i and S j for the same operation. Each of them represents the local view of the corresponding process, which is causally consistent with respect to the global computation as captured by the relation po →.

• (op1 i → op2) ⇒ (op1
When the objects are read/write registers The definition of a causal memory stated in Section 3 is a particular instance of the previous definition. More precisely, given a process p i , the assignment Assignment i allows an appropriate value to be associated with every read not issued by p i . Hence, there is a (local to p i ) assignment of values such that, in S i , any read operation returns the last written value. In a different, but equivalent way, the definition of a causal read/write memory given in [START_REF] Ahamad | Causal memory: definitions, implementation and programming[END_REF] eliminates from S i the read operations not issued by p i .

While such operation eliminations are possible for read/write objects, they are no longer possible when one wants to extend causal consistency to any object defined by a sequential specification. This come from the observation that, while a write operation resets "entirely" the value of the object, "update" operations on more sophisticated objects defined by a sequential specification (such as the operations push() and pop() on a stack for example), do not reset "entirely" the value of the object. The memory of such objects has a richer structure than the one of a basic read/write object. An example As an example illustrating the previous general definition of a causally consistent object, let us consider three processes p 1 p 2 and p 3 , whose accesses to a shared unbounded stack are captured by the following local histories L 1 , L 2 , and L 3 . In these histories, the notation op i (a)r denotes the operation op() issued by p i , with the input parameter a, and whose returned value is r.

• L 1 = push 1 (a)ok, push 1 (c)ok, pop 1 ()c. • L 2 = pop 2 ()a, push 2 (b)ok, pop 2 ()b. • L 3 = pop 3 ()a, pop 3 ()b.
Hence, the question: Is H = L 1 , L 2 , L 3 causally consistent? We show that the answer is "yes". To this end we need first to build a partial order po → respecting the three local process orders. Such a partial order is depicted in Figure 3, where process orders are implicit, and the inter-process causal relation is indicated with dashed arrows (let us remind that this relation captures the effect of the environment -asynchrony-on the computation). The second step consists in building three serializations respecting po →, S 1 for p 1 , S 2 for p 2 , and S 3 for p 3 , such that, for each process p i , there is an assignment of values returned by the operations pop() (Assignment i ()), from which it is possible to obtain a serialization S i belonging to the specification of the stack. Such assignments/serializations are given below.

• S 1 = push 1 (a)ok, pop 3 ()a, push 1 (c)ok, pop 2 ()⊥, push 2 (b)ok, pop 1 ()c, pop 2 ()b, pop 3 ()⊥.

• S 2 = push 1 (a)ok, pop 2 ()a, push 2 (b)ok, pop 2 ()b, pop 3 ()⊥, pop 3 ()⊥, push 1 (c)ok, pop 1 ()c.

• S 3 = push 1 (a)ok, pop 3 ()a, pop 2 ()⊥, push 2 (b)ok, pop 3 ()b, pop 2 ()⊥, push 1 (c)ok, pop 1 ()c.

The local view of the stack of each process p i is constrained only by the causal order depicted in Figure 3, and also depends on the way it orders concurrent operations. As far as p 2 is concerned we have the following, captured by its serialization/assignment S 2 . (The serializations S 1 and S 3 are built similarly.) We have considered short local histories, which could be prolonged by adding other operations. As depicted in the figure, due to the last causality (dashed) arrows, those operations would have all the operations in L 1 ∪ L 2 ∪ L 3 in their causal past.

1. Process p 2 sees first push 1 (a)ok, and consequently (at the implementation level) updates accordingly its local representation of the stack.

2. Then, p 2 sees its own invocation of pop 2 () which returns it the value a.

3. Then, p 2 sees its own push 2 (b) and pop 2 () operations; pop 2 () returns consequently b.

4. Finally p 2 becomes aware of the two operations pop 3 () issued by p 3 , and the operations push 1 (c) and pop 1 () issued by p 1 . To have a consistent view of the stack, it considers the assignment of returned values that assigns the value ⊥ to the two operations pop 3 (), and the value c to the operations pop 1 (). In this way, p 2 has a consistent view of the stack, i.e., a view which complies with the sequential specification of a stack.

A universal construction Algorithm 1 is a universal construction which builds causally consistent objects from their sequential specification. It considers deterministic objects. This algorithm is built on top of any underlying algorithm ensuring causal broadcast message delivery [START_REF] Birman | Reliable communication in the presence of failures[END_REF][START_REF] Raynal | The causal ordering abstraction and a simple way to implement it[END_REF] 3 . Let "co_broadcast MSG(a)" denote the causal broadcast of a message tagged MSG carrying the value a. The associated causal reception at any process is denoted "co-delivery". "?" denotes a control value unknown by the processes at the application level.

when p i invokes O.op(param) do (1) result i ← ?;

(2) co_broadcast OPERATION(i, O, op(param));

(3) wait (result i ?); (4) return (result i ).

when OPERATION( j, O, op(param)) is co-delivered do (5) r, state i [O] ← δ O (state i [O], op(param)); (6) if ( j = i) then result i ← r end if.
Algorithm 1: Universal construction for causally consistent objects (code for p i ) 3 Interestingly, the replacement of the underlying message causal order broadcast by a message total order broadcast, implements linearizability. When a process p i invokes an operation op(param) on an object O, it cobroadcasts the message OPERATION(i, O, op(param)), which is co-delivered to each process (i.e., according to causal message order). Then, p i waits until this message is locally processed. When this occurs, it returns the result of the operation.

When a process p i co-delivers a message OPERATION( j, O, op(param)), it updates accordingly its local representation of the object O. If p i is the invoking process, it additionally locally returns the result of the operation.

Conclusion

This short article extended the notion of causal consistency to any object defined by a sequential specification. This definition boils down to causal memory when the objects are read/write registers.

The important point in causal consistency lies in the fact that each process has its own view of the objects, and all these views agree on the partial order on the operations but not necessarily on their results. More explicitly, while each process has a view of each object, which locally satisfies its object specification, two processes may disagree on the value returned by some operations. This seems to be the "process-to-process inconsistency cost" that must be paid when weakening consistency by considering a partial order instead of a total order. On another side and differently from strong consistency conditions, causal consistency copes naturally with partitioning and process crashes.

returns 3 Figure 2 :

 32 Figure 2: Example of an execution of a causal read/write memory

po→

  op2), and • ∃ an assignment Assignment i and a causal past-constrained serialization S i of Assignment i ( po →) such that, ∀ O ∈ O, S i |O belongs to the sequential specification of O.

Figure 3 :

 3 Figure 3: Example of a partial order on the operations issued on a stack

  Each object O is defined by a transition function δ O (), which takes as input parameter the current state of O and the operation op(param) applied to O. It returns a pair r, new_state , where r is the value returned by op(param), and new_state is the new state of O. Each process p i maintains a local representation of each object O, denoted state i [O].

  op1 is the write of a value v into a register R and op2 is a read operation of the register R which returns the value v.

	• An execution history H is a partial order composed of one local history per process, and a partial order, denoted po →, defined as follows: op1 po → op2 if
	-op1, op2 ∈ L i and op1	i → op2 (process order), or
	-op1

• The write-into relation (denoted wi →) captures the effect of write operations on the read operations. Denoted wi →, it is defined as follows: op1 wi → op2 if wi → op2 (write-into order), or -∃ op3 such that op1 po → op3 and op3 po → op2 (transitivity).

Atomicity was formally defined in[START_REF] Lamport | On inter-process communications, part I: basic formalism[END_REF][START_REF] Misra | Axioms for memory access in asynchronous hardware systems[END_REF] for basic read/write objects. It was then generalized to any object defined by a sequential specification in[START_REF] Herlihy | Linearizability: a correctness condition for concurrent objects[END_REF]. We consider these terms as synonyms in the following.

This definition is slightly stronger than the definition proposed in[START_REF] Perrin | Causal consistency: beyond memory[END_REF]. Namely, in addition to the introduction of the assignment notion, the definition introduced above adds the constraint that, if an operation op precedes an operation op ′ in the process order, then the serialization required for op must be a prefix of the serialization required for op ′ . On the other hand, it describes precisely the level of consistency achieved by Algorithm 1 presented below.

Acknowledgments

This work has been partially supported by the Franco-German DFG-ANR Project 40300781 DISCMAT (devoted to connections between mathematics and distributed computing), and the French ANR project DESCARTES (devoted to layered and modular structures in distributed computing).


Chawki El Zant

Nathalie Klement

Belgacem Bettayeb

M'hammed Sahnoun

Vincent Havard

CONFERE'18/N° UV-ROBOT SUPERVISION SYSTEM DESIGN AND DEVELOPMENT

Keywords: GUI, Supervision system, Mobile robots, UV-Robots, Autonomous vehicles

Introducing the supervision system architecture of an agricultural robotic system enable the improved performance overcoming the complexity that current autonomous robots face due to the dynamic and unstructured agriculture environment. This requires the design of a human-robot interface. When designing a user interface several principles must be considered aiming to improve the usability of the user interface. This paper describes the design of the GUI web application and the coverage planner suitable for controlling the UV-Robot for typical coverage style greenhouse mildew treatment operations. The cross-platform user interface allows the farmer to specify their farm including fields, roads and docking stations, as well as controlling the whole operation. The contribution of this paper is to specify the design guidelines and the development of a user interface for a human-agricultural robot, in the case of UV treatment. Along with identifying the supervision system architecture and the communication control development, connecting the farmer, the UV-Robot and the cloud server associated.

INTRODUCTION

Fungi are multicellular organisms which include mildew, molds, and mushrooms. As with all fungi, mildew grows on organic material in conditions of humidity and within a certain temperature range. Fungi reproduce by spreading airborne spores that can establish new colonies elsewhere. Extremes of cold and heat can kill mildew, but fungal spores can tolerate these conditions and remain dormant until the environment is ideal for growth.

Though part of the fungi family, "mildew" refers to a mold which is growing on fabric or any other covering made of organic matter. As with all fungi, mildew does not produce food by photosynthesis; it extrudes roots, or "hyphae" into the material it is growing in. The hyphae secrete enzymes which breaks down organic matter into compounds the mildew fungus can absorb for nutrition. This leads to damage to whatever the mildew colony is growing on. Optimal conditions for mildew growth are 60 percent humidity in the environment, with a temperature of between 10 to 32 degrees Celsius.

Ultraviolet or "UV" light is a wavelength of radiation. It is part of the electromagnetic spectrum, which includes microwaves, visible light, and infrared radiation. Each wavelength of radiation is composed of an electric and magnetic field, with energy moving back and forth between them. All radiation vibrates at a particular frequency and moves at the speed of light. Ultraviolet light has energy characteristics which make it effective in destroying microorganisms such as fungi. When exposed to UV light, the genetic material in cells is damaged as chemical bonds are severed within the DNA structure. Prolonged exposure to UV light inflicts more damage to the point where the DNA cannot be repaired and cells die as a result. UV light is used to control fungal growths in homes after water damage and to treat items infested with molds, such as books and museum exhibits [START_REF] Conceicao | Effect of uv light on mildew[END_REF].

In the North West European countries (NWE), fruit, fresh vegetable, and spice production is a prosperous and innovative component of the economy, but the intensive use of pesticides is still widespread. An important disease in many crops is downy mildew, the chemical treatment of which contaminates other crops. In the case of strawberries, the spray against powdery mildew can leave up to 6 active ingredients (40% of the residues). Several research studies have shown that Ultra Violet Type C (UV-c) is effective for the physical control of mildew and can become a sustainable alternative [START_REF] Janisiewicz | Use of low-dose UV-C irradiation to control powdery mildew caused by podosphaera aphanis on strawberry plants[END_REF]. For strawberries, this treatment can reduce the rate of residues by up to 10%. Due to the high degree of manual labor and the risk of exposure to the radiation, the UV-c technique is not yet used in NWE horticulture [START_REF] Xie | Effects of preharvest ultraviolet-c irradiation on fruit phytochemical profiles and antioxidant capacity in three strawberry (fragariax ananassa duch.) cultivars[END_REF].

The aim of the "UV-Robot" European project is to develop autonomous mobile robots able to analyze and to disinfect the mildew disease affecting widely various kind of the agricultural crops specifically strawberry, cucumber, tomato, lettuce, and basil, using the UVc rays. To well operate this disinfection mission, ensure targets and complete tasks, an intelligent supervision system along with an adapted user interface is to be designed and developed. Several technological, functional and temporal constraints must be taken into account in order to ensure effective use of these robots. The supervision of these robots represents a challenge for development. Indeed, the efficiency of these robots requires a graphical interface facilitating the programming of robots and allowing the farmer to choose the best options for treatments.

In fact, farmers are under growing pressure to increase production, a challenge that robotics has the potential to address. A possible solution is to replace large farm machinery with numerous smaller robots. However, with a large number of robots it will become increasingly time-consuming for the farmer to monitor and control them all, hence the need for an effective user interface and automatic multi-robot coordination [START_REF] Richards | User interface and coverage planner for agricultural robotics[END_REF]. CESI's LINEACT laboratory participates in the "UV-Robot" project for the development of an ergonomic and efficient supervision system for planning and monitoring the tasks of the processing robots. In this project, we work on the development of a supervision system usable from several types of terminals (computer, tablet, mobile phone) along with specifying the communication protocols between the different elements in the system. Two main features of the interfaces will be developed; the first one for the definition of the mission of the robot and the supervision of its execution, and the second one for the direct control of the robot (manual control). This system allows the UV-robots to accomplish tasks autonomously. A specific and safe plan is optimized according to the field specification and disease potential. Through the user interfaces, the robot is controlled manually and automatically by the farmer and/or by the cloud management, all connected, coordinated and supervised through an intelligent network and communication control system. This constitutes a kind of Internet of Robotic Things IoRT, an innovative and emerging vision that brings together pervasive sensors and objects with robotic and autonomous systems as claimed by Simoens et al. [START_REF] Simoens | The internet of robotic things: A review of concept, added value and applications[END_REF].

The rest of this paper is organised as follows. Section 2 presents the innovative UV-Robot project in comparison with some existing relevant projects. In section 3 we define the middleware challenges of the mildew treatment in the agriculture greenhouses. Section 4 shows the UV-Robot graphical user interface. Finally, the supervision system architecture is targeted in Section 5.

UV-ROBOT, AN INNOVATIVE MIX

Robots applications have been increasing since the last few decades, from civilian search and rescue, agriculture and medicine to military missions. In agriculture, they are used to ensure the human's safety from unhealthy and risky tasks, the high productivity and the precision agriculture. A problem that comes up when it is necessary to work with a robot or a fleet of robots in the field is having an adequate supervisory system [START_REF] Arruda | Development of a mobile robots supervisory system[END_REF]. In the following, we firstly review the existing robots and the relevant projects in the agriculture sector. Secondly, we present the innovative UV-Robot project in details.

Existing robots and relevant projects

Many robotic projects already existed in the agricultural field providing several activities and serving the cultivation process. On the other hand, the robots are well integrated into the healthcare domain, assisting the disinfection process in the hospitals and working alongside with the Clinical Lab Technicians. The robot, called "Bonirob", has been developed to reduce the environmental impact of farming by optimizing fertilization and monitoring crop growth. It also makes farm work easier and greener by automating the weeding process without the use of controversial herbicides [START_REF] Biber | Navigation system of the autonomous agricultural robot Bonirob[END_REF].

The project "Robot Fleet for Highly Effective Agricultural and Forestry Management" (RHEA) was implemented to integrate smart and autonomous robots to farms, in order to develop the concept of the "farm of the future". The global approach consists of conducting experiments and evaluating a new generation of automatic systems and fleets of robots for chemical and physical weed management and crop spraying. The aim of this project is to reduce the use of chemicals in agriculture and to decrease production costs while improving crop quality, health, and safety to both humans and animals [START_REF] Gonzalez-De Santos | Fleets of robots for environmentally-safe pest control in agriculture[END_REF].

In the healthcare sector, disinfecting UV-rays robots developed by "Xenex", are portable, automatic and selfcontained. Some units use low-pressure mercury lamps, non-mercury, and xenon-lamp. These robots have increased in popularity and are being trialed and implemented in hospitals to perform the disinfection of patient rooms and operating rooms.

UV-Robot in the agricultural field

The UV-robot is an innovative project mixing both the agricultural and the disinfection facilities. As part of the European project "UV-Robot" mobile robots (see Figure 1) will be developed and tested in order to make the UV-c treatment for crop protection against mildew in horticulture [START_REF] Preter | Autonomous navigation of a platform with UVc-light to prevent crop infestation by powdery mildew[END_REF]. The goal is to develop a UV-c strategy for five crops (strawberry, tomato, cucumber, lettuce, basil). The automation of the UV-c application is essential for the implementation of this technology and will increase innovation in horticulture. This automation aims to reduce the labor cost of this treatment and to improve health and safety of the production operators. UV-robots will be developed to move through different crop types. For each crop type, a specific version of the robot will be designed to treat mildew in a typical greenhouse cultivation system. To stabilize the UV lamps when driving through the crop an adapted suspension should be implemented to deal with soil undulation. An autonomous localization system will be integrated into the robot; this will make it possible for the robot to move through the crop along a pre-set path. Each robot needs to optimally treat the cultivation with UVc-light.

A unique system will be delivered to autonomously localize the robot.

Existing sensors will be adapted to detect the specific strains of mildew. The E-nose will incorporate an environmental sampler, developed by "RoboScientific", which pumps air from around the plants through an absorbent pad to concentrate the Volatile Organic Compounds VOCs to be measured by the sensors. A number of operating parameters (sampling period, sensitivity, digital VOC fingerprint) will need to be fine-tuned to optimize the performance of the system. Three sensors will detect specific species of powdery and downy mildew. First of all, the grower uses the interface to implement the cultivation area to determine the path planning for the treatments. Second, while driving through the crop the robot will monitor for mildew presence.

Visualized on an interactive map, the grower can evaluate the treatments. Finally, the grower can adapt the next treatment and avoid further infestation in certain locations in the greenhouse. The user interface allows the grower to define the working surfaces of the UV-robot on which the path planning should be based on. Using this input the robot can navigate through the crop with the autonomous localization. The output will show on an interactive map the localization and the severity of mildew in the greenhouse. An interactive map will allow the grower to adapt the next UV-c treatment. As the vehicle should work autonomously in treating crops for mildew, it should be safe in all aspects: human, crops, and environment. An elaborate risk analysis will be performed on the operation vehicle and the use of UV-c lamps to avoid human and plant damage. During field tests, the vehicle will be monitored and safety-critical situations will be evaluated by clearly describing the scene and the conditions of the robot. Accordingly, procedures will be set in order to guarantee the safe operation in greenhouse cultivation.

MIDDLEWARE CHALLENGES

The past decade has witnessed a huge increase in the number of proposed middleware solutions for robotic operating in unstructured environments. As a result, it has become difficult to decide which middleware is the most appropriate for a specific application or domain. This section gives an overview of the most relevant challenges to be considered when designing the middleware of the supervision system of the UV-Robot.

Global design challenges

Drenjanac and Tomic [10] proposed a classification of middleware challenges according to their specific domains of concern. These challenges are derived from a specific precision agriculture use-case based on the robotic fleet for weed control, which was elaborated within the framework the European project RHEA-robot fleets for highly effective agriculture and forestry management. When a new application is being developed, understanding the challenges of a specific application domain is the first important step towards making the decision which middleware to use. According to this analysis, several criteria and missions have to be defined, aiming to well develop the treatment strategy. After the mission is defined, it is decomposed into a set of tasks and assigned to corresponding robots. The centralized control system is responsible for both task-robot mapping and robots' coordination during the mission execution. During the mission, distributed robots report their status to the base station (user) who supervises the mission and acts as a central point in the system. The base station is a place that manages, coordinates, makes decisions, collects data, instructs, and monitors all robots in the network. The result is the classification of middleware design challenges, addressing three domains of design decisions [10]: General Fleet Realization Challenges, Environmentally Imposed Challenges, and Task Dependent Challenges.

Power supply availability, limits, and constraints

Another main challenge in our project case is the power supply. Power consumption is mainly due to: the robot's movements, the UV lighting, sensors, the network and communication center, the towers or access points, and the user interfaces (tablets, PCs, phones). The strategy of the power supply and resources could be developed by defining the required power consumption of each component of the system after choosing the best technology and optimizing the power saving ones. Then leading the power system size can be reduced. Moreover, the installation of the docking station (refuel or rechargeable stations) is necessary to complete tasks according to an efficient optimization architecture, and considering each field specifications.

Input and output data to be exchanged

Precision agriculture is about applying the right treatment, at the right place and at the right time [11]. The key factor behind the right treatment and the overall robot scout technology is the ability to communicate with the swarm at each moment transferring and receiving data and orders through the network. Some of these data transferred to the swarm are coming from the cloud management system or the base, while some others are collected by the robots' sensors. Referring to this fact, we divide our data into two categories: input and output data. With the aim of avoiding conflicts, this categorization is classified from an operator point of view: -Input data: This data category contains any information added to the system, which can be added manually by the farmer or automatically analyzed and visualized by the robots. Basically, the information (or the sensors' data) in need can be listed as follow: Navigation (row detection, ground detection, mapping, turning control, ...), Localization (Global Positioning System GPS or the Global Navigation Satellite System GNSS), and Autonomy. -Output data: These data correspond to the order received by the robots, coming from the user interface or the base station, the web user or the system itself. Several kind of orders are to be developed depending on the operating mode either manual or automatic: UV doses or treatment level, the greenhouse dimension and the architecture specifications, the path planning and the operation instructions, the operation schedule and timing, the day or night operation with the specified starting time, testing and regulation purposes. Other tools can be fitted into the system for other applications when necessary, which collect data for the accomplishment of the good treatment: measuring soil density (soil can be examined to a depth of 800mm per example), measuring air temperature and moisture, etc...

GRAPHICAL USER INTERFACE GUI

There are many factors to consider in Human-Robot Interaction HRI design, such as ease of use, user workload, information flow, software maintenance, and robot maintenance. Although, the GUI display is essential to supervise the whole system by allowing the visualization of internal state, it can become cluttered and inefficient, if it is not designed properly [12].

GUI functionalities and design principles

In order to well design our user interface, it is relevant to start by defining the main functionalities: the GUI design usability and acceptability [13], and the GUI awareness (location awareness, activity awareness, status awareness, surroundings awareness, overall mission awareness) [14]. Several design guidelines and principles are considered based on many studies concerning the GUI design [14]: visibility, safety, simplicity, feedback, extensibility, and cognitive load reduction.

GUI development

When developing user interfaces there are two approaches: web-based and a native application. The web-based approach is the development of a website in languages such as HyperText Markup Language (HTML), JavaScript, Cascading Style Sheets (CSS), and Hypertext Preprocessor (PHP), and takes advantage of web browsers to provide support for multiple devices. Alternatively, native applications are developed for a specific device and can be optimized to run more efficiently in some specific cases. Typically, these applications are precompiled and installed on the target device. Each platform requires a software development kit and framework. Native applications can also employ a variety of networking techniques to communicate to any robot middleware [15].

Otherwise, taking into consideration the GUI objectives, referring to the project management strategy, it is relevant to respect the project development sequences and goals, in order to achieve the well done operation monitoring regarding all constraints and aspects. In our case, at the early stage of the system development, and in order to boost the treatment trial operations along with testing carefully the optimized system, the GUI is implemented as a web application. The UV-Robot web application has the major role in running the system properly, as a result of the trials feedback concerning the supervision coverage, the treatment itself and the optimized treatment plan efficiency, and the whole system reliability. The GUI web application gives the user a wide range of flexibility in terms of end-use devices, and offers the quick ability to develop a specific IPhone Operating System (IOs) or android phone application in advanced stages, if needed.

Starting from the greenhouse specifications and the mildew level divisions, a lightweight data-interchange format JSON (JavaScript Object Notation) or XML (Extensible Markup Language) file is generated. This file lists the main field specification. It could be generated through the web application directly, uploaded from any PC, or even accessed from the system web server by an admin user.

After choosing the desired option, the specification file is transmitted to the web server, where it can be treated with the simulator, sending back a new generated file (with the same format) containing the optimized treatment plan, along with the docking (recharging) stations number and framing grid, according to each field architecture.

In order to set up the settings and run the robot, this file is then sent through the communication control system as a light packet to the UV-Robot micro-controller. In fact, the JSON and the XML formats are frequently used between a server and a web application. In addition, it must be noticed that working with these formats facilitates the robot micro-controller python programming and enhances the processing speed. As it is well known, the JSON and the XML modules enable the simple convert and parse processes into Python Objects fluently. On the other hand, what makes the GUI application light and facilitates the communication system development is the fact that the system is not supposed to handle and transmit some heavy data such as live streaming videos or pictures.

The application gives the user the ability to supervise the whole treatment operation, showing instantly the treatment evolution and the robot position as well as the treatment estimated and remaining time (see Figure 2). The code is well developed thanks to the Extensible HyperText Markup Language (Xhtml) web pages, the CSS formatting, the JavaScript applications using React library for building user interfaces, jQuery (JS library) and AJAX technique for accessing web servers from a web page, which stands for Asynchronous JavaScript and XML). The layout of the interface consists of several windows (see Figure 3,4):

-The welcome page window.

-A window for setting the greenhouse specifications.

-A window for the mildew treatment configuration: doses, day and night treatment.

-A window for the greenhouse treatment plan configuration.

-The main window displaying the running treatment operation. The robot control is the main function of the interface. This allows the operator to have access to all the functions available for interacting with the robot, which are:

CONFERE'18/N° -Overview Map of the Environment: This area is used to display the generated map of the environment. The map includes the location of the robot in the greenhouse.

-Robot Sensor and Actuation Display: Displaying the status indicators of the robot, currently robot velocity, level of battery, etc... -Autonomous/Manual Mode control: Allows the operator to change the level of autonomy of the UV-robot.

-The user interface is able to run on a variety of platforms including Windows, and Linux.

-Through the GUI, the user can get an approximation of the needed time for the treatment operation execution regarding the current disease presence and the greenhouse specifications.

-Stop option: When the stop button is clicked, all processes will be terminated.

SUPERVISION SYSTEM ARCHITECTURE

The definition of the network system depends on the level of automation required, the level of supervision required, and the resources availability. Several network technologies can be used separately or combined depending on the data transfer awareness such as the General Packet Radio Service GPRS/3G/4G, Bluetooth, Wi-Fi or ZigBee. The challenges in using any communication protocol are the field coverage, the data transfer package, the power consumption and the cost. The aim of choosing any transmission mode and data formats is to improve the Human Machine Interface functions during the treatment operation execution.

Network and communication control

The definition of the UV-robot network and communication system components includes: the base station, the field communication towers or routers, the robot devices sub-system, the cloud-based system and the web server. In order to be a platform for different developments, the system hardware needs to be designed to support not only a specific task but also a wide range of applications. In our system, the hardware design is divided into: the communication configuration, the sensor and actuator, and the user interaction; each is to be developed with the feasibility, the flexibility and the extendibility in mind.

Transmission modes and data formats

There are two modes of transmission: either broadband landlines or alternative mobile long-range transmission technologies, e.g. 3G, Short Message Service (SMS), and Multimedia Messaging Service (MMS) [16]. The regional combination of sensors, Wi-Fi, 3G, RFID, NFC (near field communication), and Bluetooth will allow significantly improved measurement and monitoring methods of the agricultural cultivation. In addition, the sensor technology is becoming available at much lower cost and with built-in support for network connectivity and remote monitoring. In the UV-robot supervision system we will examine the following cases of data transmission: The Global System for Mobile Communications, Bluetooth, The Radio-Frequency Identification RFID, The Wireless Local Area Network (WLAN), and ZigBee (see Table 1

Supervision system architecture

Our work focuses on three of the available technologies for data transfer, in mobile communication, SMS, GPRS, and Wi-Fi/ADSL (Asymmetric Digital Subscriber Line) technology, which are currently the dominant ones and which are expected to remain important in years to come as well. In our scenario, the UV-robot may have any kind of sensor devices, enabled with Bluetooth, Wi-Fi, NFC, RFID, cabling or any other kind of technology collecting information and allowing for data registration and communication with a mobile phone or a PC. The Robot's position can be determined through GPS technology, if the mobile device supports it, or alternatively through possible Wi-Fi technology in that area, or even through mobile telephony antennas, providing different levels of accuracy. Some kind of appropriate mobile or web application exchanges data with a web service, and depending on the technology used for the data transfer, two architectures arise, which are briefly described below.

-In the 1st architectural approach, the mobile application is connected to the internet through its Mobile Telecommunications Provider, using GPRS technology. After the connection is established, the application sends data directly to the robot also connected to the internet. A 3G USB (Universal Serial Bus) device with an internal mobile Subscriber Identity Module (SIM) card can be used. The USB is to be plugged into the computer inside the robot and registered to a mobile phone service provider allowing it to have access to the Internet. This simple configuration enables the robot to connect to the Internet without any restrictions in physical distance, as far as the 3G mobile signal is presented almost everywhere. -In the 2nd architectural approach, the mobile application exploits the established ADSL internet connection and the existence of a wireless router. Data are sent to the wireless router using Wi-Fi technology and then are forwarded to the robot and vice versa. Using Wi-Fi technology, which is already included in many mobile phones provides a benefit in enabling the agricultural robot control. The connectivity aspect is to take the data from a smartphone or PC and send it to the robot.

CONCLUSION

The need of an effective supervision system for the robots in the agricultural field has guided the researchers and the engineers to improve and implement several user interface designs and communication control architectures. Depending on the operation configuration, the mission tasks, and the field specifications, the supervision system design and development is a big challenge to be addressed, in order to run the project properly. Based on our review concerning the development of a robotic supervisory system in the agricultural field, the guidelines of the research work and the implementation of the UV-robot GUI web application are defined. A suitable design of a user interface and coverage planner for controlling and monitoring the UV-robot for typical coverage style farm treatment operations are proposed. The cross-platform user interface allows the farmer to specify the greenhouses including disease potential, roads, docking stations and all needed specifications, well optimized to fit the field requirements. Many factors are to be addressed in order to create the ideal network architecture, mainly the coverage planner, the power consumption and the operation efficiency. In an advanced stage, an innovative task to be defined, addressing the development of the cloud management and a web server, aiming to collect data information about the treatment operations and to set the optimal management plan for a specific mission and using an autonomous fleet of UV-Robots.

Figure 1

 1 Figure 1 UV-Robot, by "Octinion".

Figure 2

 2 Figure 2 UV-Robot web application use case diagram

Figure 3 UV

 3 Figure 3 UV-Robot web application, sign in and settings pages.

Figure 4

 4 Figure 4 UV-Robot web application, specification sheet and GUI.

Table 1

 1 ). Comparison of parameters of various wireless technologies [17].

	Technology	WIFI 802.11 Bluetooth 802.15.1 ZigBee 802.15.4
	Frequency	2.4 GHz	2.4 GHz	2.4GHz-868/915 MHz
	Modulation	OFDM	FHSS/BPSK	DSSS/QPSK
	MAC	CSMA/CA	TDMA/TDD	CSMA/CA
	MAX. data rate	54 Mb/s	1 Mb/s	20/40/250 Kb/s
	Device types	One	One	FFD/RFD
	No. of channels	11-14	79	26
	No. of devices	32	8	Up to 65 535
	Battery life	Days	Weeks	Months
	Coverage (m)	100	10	15/50
	Topology	Star	Star	Star and cluster-tree

ACKNOWLEDGMENT "This research was made possible thanks to € 1.35 million financial support from the European Regional Development Fund provided by the Interreg North-West Europe Programme in context of UV-ROBOT".

Conference' Intensive and environmentally friendly agriculture: an opportunity for innovation in machinery and systems ',Paris,France,25