F Gatuingt

G Pijaudier-Cabot

Coupled Damage and Plasticity Modelling in Transient Dynamic Analysis of Concrete

In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to as many mode of rupture. Close to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, confinement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be reflected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present in this paper a model aimed at describing these three failure modes. It is based on visco-plasticity and rate dependent damage in which a homogenisation method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on confined concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented.

INTRODUCTION

Modelling of concrete structures subjected to dynamic loading such as explosions, impacts and perforations is very demanding, both from the point of view of computer codes and from the point of view of material modelling. As far as computer codes are concerned, the major difficulties deal with a fast integration of the equation of motion (compatible with large three dimensional modelling), contact modelling in dynamics and in the case of perforation, the evolution of the concrete structure boundaries and large deformations. Explicit time integration, reduced spatial integration with hourglass control, specialised contact algorithms and adaptive meshing or erosive techniques exist nowadays in computer codes (such as LS-DYNA3D, ABAQUS and others). With such techniques, which for sure could be improved, it is possible to carry out, with a large but still reasonable amount of computer time, three dimensional computations of concrete structures in dynamics.

It seems, however, that constitutive modelling of concrete has not reached the same level of sophistication as computer methods. Most approaches are inspired by existing constitutive relations for alloys and ceramics, where a split between the spherical and deviatoric parts of the stress-strain relations is assumed (see e.g. [START_REF] Whirley | DYNA3D: A Nonlinear Explicit Three-Dimensional Finite Element Code for Solid and Structural Mechanics[END_REF][START_REF] Hallquist | LS-DYNA 3D -Theoretical Manual[END_REF]). The deviatoric part is modelled with a plasticity-based, or viscoplastic model while the spherical part, also called "equation of state", is fitted with a cap model [START_REF] Lubarda | Brittle-Ductile transition in porous Rock by Cap Model[END_REF]. In the present paper, which is a sequel of recent research efforts carried out at LMT-Cachan [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF][START_REF] Burlion | Experimental Analysis of Compaction of Concrete and Mortar[END_REF], we present a new constitutive relation for concrete in dynamics based on viscoplasticity combined with rate dependent continuum damage. This relation is restricted to cases with moderate strain rates in concrete, corresponding typically to explosions and impacts of projectiles at a velocity less than 350 m/s, yielding a hydrostatic pressure in the material which is less than 1 GPa.

The constitutive relation is detailed in section two. Three mechanisms will be combined: compaction which is modelled with a homogenisation technique, tensile damage which is described with a rate dependent damage model, and compression failure which is modelled with viscoplasticity combined to damage. Section three presents several examples of computations of laboratory tests (Split Hopkinson tests, dynamic tension tests) and of a concrete slab subjected to an explosion.

CONSTITUTIVE EQUATIONS

Let us consider the schematic case of an impact on a concrete slab depicted on Fig. 1 and look at the various modes of deformation and failure in concrete. Near the striker, inertial forces in concrete are such that the material is confined. Concrete experiences a very high state of triaxial compression. In statics, the response of concrete for such a state of stress has been characterised experimentally [START_REF] Bazant | Confined Compression tests of Cement Paste and Concrete up to 300 Ksi[END_REF][START_REF] Burlion | Experimental Analysis of Compaction of Concrete and Mortar[END_REF]. The equation of state, (e.g. the curve relating the volumetric deformation to the hydrostatic stress), exhibits an increase of the tangent and secant volumetric moduli with residual plastic strains upon unloading. Recently Gary et al. [START_REF] Gary | Testing concrete at high strains and high rates of strain[END_REF] obtained similar results in dynamics and observed a substantial rate effect. The hydrostatic stress at a given volumetric strain increases with the strain rate. Although the physical mechanisms responsible for the rate effect are not clearly explained at the moment (it might be due to intersticial water trapped in the porous microstructure of the material), it is generally accepted that the hardening shape of the equation of state is due to irreversible material compaction at a given strain rate.

Farther from the impactor, concrete is subjected to compression with a moderate amount of confinement. Its response is essentially controlled by microcracking in compression and internal friction. This state of stress can be captured by constitutive relations based on plasticity or plasticity coupled to damage [START_REF] Feenstra | Computational Aspects of Biaxial Stress in Plain and Reinforced Concrete[END_REF][START_REF] Yazdani | Combined Plasticity and Damage Mechanics Model for Plain Concrete[END_REF]. Two characteristics of the material response ought to be recalled:

• The coupling between the volumetric and deviatoric responses of concrete has been experimentally demonstrated by Burlion et al. [START_REF] Burlion | Experimental Analysis of Compaction of Concrete and Mortar[END_REF], by comparing hydrostatic and uniaxial tests on confined specimens.

• In uniaxial compression, it has been demonstrated with three dimensional computations that rate effects are very small compared to the confinement generated by inertial forces which are opposite to the lateral expansion of the specimen during loading [START_REF] Donze | Study of the Behavior of Concrete at High Strain Rate Compressions by a Discrete Element Method[END_REF][START_REF] Gatuingt | Prévision de la rupture des ouvrages en béton sollicités en dynamique rapide[END_REF] (see Fig. 2a). The increase of the material strength, which is classically observed (see e.g. Ref. [START_REF] Bischoff | Compressive Behaviour of Concrete at High Strain Rates[END_REF]) can be almost totally explained (in the range of strain rates considered in this paper) by such a transient confinement.

The third failure mechanism is scabbing and occurs on the back of the impacted structure. It is due to the interaction between the compressive wave generated by the impactor and the free surface. The compression wave is transformed into a tensile wave which might produce tensile cracking if the material strength is reached. This failure mechanism is rate dependent. Contrary to compression, inertial forces in uniaxial tension induce a three dimensional state of tensile stresses in the material (Fig. 2b) and cannot contribute to an increase of apparent strength. The response of the material in tension can be captured with a rate dependent damage model [START_REF] Dube | A Rate Dependent Damage Model for Concrete in Dynamics[END_REF][START_REF] Simo | Strain and Stress Based Continuum Damage Models -I Formulation[END_REF] or a rate dependent smeared crack model [START_REF] Sluys | Analysis of Impact Fracture in a Double -Notched Specimen Including Rate Effects[END_REF].

An accurate description of the response of concrete subjected to impacts and explosions requires at least the combination of the above three features. For instance, scabbing is controlled by the material tensile strength and by the wave speed in the material which increases with compaction. During perforation, a large amount of energy can be dissipated. The consequences on tunelling, scabbing and on the output speed of the impactor after perforation can be important. Most constitutive relations implemented in existing computer codes are not entirely satisfactory because they do not account for the interaction between the deviatoric response of the material and its volumetric response and they hardly combine the above three mechanisms.

Bazant and co-workers have used the microplane approach for such a combination [START_REF] Bazant | Microplane Model M4 for Concrete: I Formulation with Work-Conjugate Deviatoric Stress[END_REF]. This microplane model has been implemented in a large scale computation code which includes finite strain description (not intended in the present paper). Note that the rate effect on the equation of state is not considered in the microplane model. Burlion et al. [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF] proposed a coupled damage-plasticity model in which compaction and tensile cracking are combined into a single damage variable, which has the merit of being quite simple. It was however delicate to obtain a good description of uniaxial compression with such a model, which did not include strain rate effects too.

The constitutive relations presented in this paper are an extension of this model, aimed at a more accurate description of the material response, with a moderate degree of complexity. These relations are based on three main characteristics:

• The variation of porosity of concrete, which remains lower than 30 %, is taken into account with the help of a homogenisation technique. The method due to Mori-Tanaka is selected because it provides explicit expressions of the shear and bulk moduli of (uncracked) concrete. Thus, the elastic properties of material are functions of the variation of porosity, especially during hydrostatic compaction.

• Microcracking is captured with a rate dependent damage model [START_REF] Dube | A Rate Dependent Damage Model for Concrete in Dynamics[END_REF], which uses two damage variables in order to provide a realistic response of the material in uniaxial compression while preserving a good description of tension, which is a characteristic of damage models. Rate effects are necessary in order to represent dynamic experiments (mostly dynamic tensile tests).

In addition, rate dependency preserves well posedness of the equations of motion when strain softening occurs [START_REF] Sluys | Wave Propagation, Localisation and Dispersion in Softening Solids[END_REF].

• In order to describe the material response in triaxial compression, a viscoplastic model is implemented, based on Perzyna's approach associated to a modified Gurson's yield function [START_REF] Needleman | An analysis of ductile rupture in notched bars[END_REF]. This yield function was already used by Burlion et al. [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF] in order to introduce the coupling between the spherical and deviatoric response of the material on the growth of plastic strains. Rate effects are necessary in order to capture the increase of stress with strain rate in hydrostatic compression observed experimentally in dynamics [START_REF] Gatuingt | Prévision de la rupture des ouvrages en béton sollicités en dynamique rapide[END_REF].

Damage model

The relation between the stress σ ij and the reversible strains ε e ij is:

σ ij = (1 -D)[Kε e kk δ ij + 2G(ε e ij - 1 3 ε e kk δ ij )] (1)
where K and G are the bulk and shear moduli of concrete respectively. These moduli are assumed to remain constant in this section. Their variation, due to material compaction will be introduced later.

We use the formulation due to Mazars which combines compression damage and tension damage [START_REF] Mazars | A description of micro and macroscale damage of concrete structures[END_REF]. The combination of these two types of damage is:

D = α c D c + α t D t (2)
where D c and D t represent the compressive and tensile damage respectively, while α c and α t are parameters defined as:

     uniaxial tension α c = 0 uniaxial compression α t = 0 general loading α t + α c = 1 (3)
The definition of these parameters is given in the original work of Mazars [START_REF] Mazars | Application de la mecanique de l'endommagement au comportement non lineaire et a la rupture du beton de structure[END_REF][START_REF] Mazars | A description of micro and macroscale damage of concrete structures[END_REF]. The growth of the two damage variables is governed by the elastic equivalent strain [START_REF] Mazars | A description of micro and macroscale damage of concrete structures[END_REF]:

εe = i ( ε e i + ) 2 (4)
where ε e i is the ith component of the tensor of the principal strains and x + is the positive part of x. The growth of D c and D t is defined by the following equations which are similar to the equations used by Dube et al. [START_REF] Dube | A Rate Dependent Damage Model for Concrete in Dynamics[END_REF]: Figure 3a shows the response of the damage model in uniaxial tension tests carried out at various strain rates. The response is strongly dependent on the rate of strain, which is in agreement with experiments [START_REF] Bailly | Rapport final, première partie, expérimentation", Comportement des ouvrages en dynamique rapide-Comportement dynamique du béton[END_REF]. Figure 3b shows the response of the damage model in uniaxial compression. We have chosen to have a behaviour in compression which is only slightly dependent on the strain rate. This is again quite consistent with test data. It should be pointed out, however that the model response will be substantially modified in compression, due to the coupling with a viscoplastic model.

Ḋc = < εe -ε D0 -1 ac Dc 1-Dc (1/bc) > m Dc n Dc
On these figures and in all the subsequent computations, the same material is modelled. It is a microconcrete on which many experiments have been performed within an experimental research program of the french network GEO carried out by several French laboratories [START_REF] Bailly | Rapport final, première partie, expérimentation", Comportement des ouvrages en dynamique rapide-Comportement dynamique du béton[END_REF][START_REF] Gatuingt | Prévision de la rupture des ouvrages en béton sollicités en dynamique rapide[END_REF][START_REF] Gary | Testing concrete at high strains and high rates of strain[END_REF][START_REF] Darve | Mecanique des geomateriaux[END_REF]. Its compressive and tensile strengths are 50 MP a and 4 MP a respectively. Its Young's modulus is 23.000 MP a with a Poisson's ratio of 0.17. The same material has been modelled by Le Nard and Bailly [START_REF] Nard | Dynamic Behaviour of Concrete: the Structural Effect of Compressive Strength Increase[END_REF].

Viscoplastic model

The experiments developed within the French network GEO showed that there was a dependence of the loading rate on the curve relating the volumetric strain to the hydrostatic stress [START_REF] Gatuingt | Prévision de la rupture des ouvrages en béton sollicités en dynamique rapide[END_REF], in addition to permanent plastic strains and to the material compaction which induces an increase of the bulk and shear moduli of the material. It is thus pertinent to implement a viscoplastic model which will be coupled in the next section to the above damage model. In the absence of damage (which will be added later), the stress-elastic strain relation is:

σ ij = [Kε e kk δ ij + 2G(ε e ij - 1 3 ε e kk δ ij )] (7)
and

εij = εe ij + εvp ij ( 8
)
where εvp ij is the viscoplastic strain rate. The shear and bulk moduli are functions of the material porosity denoted as f * . It is the ratio of the volume of the voids in concrete divided by the apparent volume of the porous material. These functions are computed using Mori-Tanaka homogenisation technique [START_REF] Mori | Average stress in matrix and elastic energy of materials with misfitting inclusions[END_REF]:

K = 4K M G M (1-f * ) 4G M +3K M f * G = G M (1-f * ) 1+ 6K M +12G M 9K M +8G M f * (9)
where K M and G M are the bulk and shear moduli of the material without pores respectively.

The viscoplastic strains are obtained following Perzyna's approach:

εvp ij = λ ∂F N T ∂σ ij (10)
F N T is the modified Gurson's yield function proposed by Needleman and Tvergaard [START_REF] Needleman | An analysis of ductile rupture in notched bars[END_REF]:

F N T (σ ij , σ M , f * ) = 3J 2 σ 2 M + 2q 1 f * cosh q2 I 1 2σ M -(1 + (q 3 f * ) 2 ) = 0 (11)
where σ M is the stress in concrete without voids and q 1 , q 2 , q 3 are scalars parameters. Colantonio and Stainier [8] proposed a similar model in which the definition of the plastic multiplier accounts for the variation of porosity of the material. We follow here the same approach and define the viscoplastic multiplier as :

λ = f * (1 -f * ) F N T m vp nvp (12)
where m vp and n vp are material parameters. The limiting case where the porosity tends to 1 (material failure) should not be considered because tension or compression damage reaches 1 before it may happen. When the pores are completely closed (f * = 0), the viscoplastic incremental strains vanish.

The principle of maximum plastic work for materials with voids was given by Needleman and Tvergaard [START_REF] Needleman | An analysis of ductile rupture in notched bars[END_REF]:

σ ij dε p ij = (1 -f * )σ M dε p M ( 13
)
where ε p M is the equivalent irreversible strain in the matrix (concrete without voids and cracks) associated to the equivalent stress σ M . The relation between the equivalent strain and the equivalent stress in the matrix is elastoplastic, with isotropic work hardening:

ε M = σ M E if σ M ≤ σ y ε M = σy E σ M σy n if σ M > σ y ( 14
)
where E is the elastic modulus of the material without void, σ y a yield stress and n the hardening exponent.

The variation of the material porosity f * is controlled by the plastic flow, keeping in mind that in practice the material is always compacted (the porosity always decreases because in tension cracking occurs first). Just like in Ref. [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF], we assume that the evolution of the porosity is controlled by the irreversible volumetric strain:

df * = k(1 -f * )f * dε p kk (15)
a parameter k is introduced in order to be able to calibrate the velocity with which porosity is closed. Figure 4 shows a comparison of the hydrostatic responses between static and dynamic simulations and the corresponding experiments taken from Ref. [START_REF] Bailly | Rapport final, première partie, expérimentation", Comportement des ouvrages en dynamique rapide-Comportement dynamique du béton[END_REF].

Coupled response of the viscoplastic and rate dependent damage models

The micromechanical phenomena responsible for damage by shearing or extension are completely different from those corresponding to a collapse of the material porosity. The first one is microcracking in tension and tension-shear, while compaction is due to a crushing of the porous cementitious matrix and it is controlled by the hydrostatic stress in triaxial compression. Therefore, it is natural to separate these two mechanisms, one being represented by the damage variable D, the other one being represented by the porosity f * . These two mechanical effects are combined in the final relationships which relate the stresses to the elastic strains:

σ ij = (1 -D)[Kε e kk δ ij + 2G(ε e ij - 1 3 ε e kk δ ij )] (16)
where the shear G and bulk moduli K are defined in Eq. ( 9) by Mori-Tanaka's expressions and damage growth as defined in section 2.1.

In tension, the Gurson's yield function is not activated. Viscoplastic strains do not grow and the model described in paragraph 2.1 is recovered. Conversely, when the loading history is such that the positive equivalent strain is always zero (hydrostatic compression or confined uniaxial compression), we will have only the Gurson's yield surface which is activated and the viscoplastic model described in paragraph 2.2 is recovered.

Figure 5a shows the response of the model for hydrostatic compression followed by hydrostatic tension. We observe a hardening behaviour when the porosity of the material decreases. We see also that during unloading, the modulus of elasticity of material is higher than at the beginning of the loading (this is due to the decrease of porosity). Finally, when tension is reached, the rate dependent damage model is recovered, with the elastic constants K and G which have increased due to compaction. A static loading and a dynamic loading were carried out in order to show the influence the strain rate on the model response. As expected, the material stiffness and strength are lower in statics than in dynamics. Hardening occurs later with a stiffer slope in dynamics too.

With regard to the material behaviour in uniaxial compression, the values of the model parameters (particularly m Dc and σ y ) provide a behavior which is either coupled or not, in the sense that the viscoplastic criterion and the damage criterion can be activated at the same time or not. Figure 5b shows, in the case of a dynamic loading, a curve where the model parameters are such as in one case the damage criterion is activated only (no irreversible strains) and in the second case the two criteria are activated simultaneously. In the second case, a decrease of stiffness occurs at the same time that incremental viscoplastic strains are non zero. Obviously, the first case is much easier to handle as far as calibration is concerned because viscoplasticity is restricted to cases where the material is subjected to compression with a significant amount of confinement.

Calibration and numerical implementation

Overall, the constitutive relations contains two parameters which define the elastic behaviour (the shear and bulk moduli of concrete without voids), five parameters which control the material response in tension (including the damage threshold), four parameters which control damage growth in compression. Four parameters enter in the viscoplastic model and two enter in the equation which governs the variation of porosity, including the initial material porosity (the quantities q 1 , q 2 , q 3 assume fixed values usually, see Ref. [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF]). The total number of model parameters might be considered to be quite high. In view of the three mechanisms described by the model and the various rate effects, it seems difficult to arrive at a significantly smaller amount of parameters.

The initial porosity depends on the concrete mix. It is usually in the range of 0.3. The other model parameters are obtained by fitting the following test data: quasistatic experiments in tension, uniaxial compression and triaxial compression (such as uniaxially confined tests [START_REF] Burlion | Experimental Analysis of Compaction of Concrete and Mortar[END_REF][START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF]), test data obtained for different strain rates, including scabbing tests, and split hopkinson tests on confined and unconfined specimens [START_REF] Bailly | Rapport final, première partie, expérimentation", Comportement des ouvrages en dynamique rapide-Comportement dynamique du béton[END_REF]. This amounts to a large experimental database to be obtained for the same material, which is available for the microconcrete modelled in the present contribution. Of course, one may use the fact that some model parameters can be identified on separate tests independantly. This is the case of the tension and compression damage evolution laws, and of the viscoplastic part of the model which solely controls the nonlinear response of the material in confined compression, when the elastic equivalent strain is zero (no positive strains). The following general procedure can be implemented: (i) Quasistatic tensile tests and a scabbing test provide the parameters entering in the damage model in tension. (ii) The viscoplastic part of the model is calibrated independantly with the help of compression tests on confined specimens where there is no damage, just viscoplasticity, and the variation of porosity is deduced from loading unloading cycles on such experiments (quasistatic tests). (iii) Finally, uniaxial quasistatic compression tests and split Hopkinson compression tests on unconfined specimens provide the remaining parameters, entering into the evolution law of damage in compression. When viscoplasticity enters in the response of the material in uniaxial compression, the calibration is the same, which is the reason why the parameters of the compression damage evolution laws ought to be determined after those of the viscoplastic part of the model.

The model has been implemented in the finite element code LS-DYNA3D in an explicit format. The objective of the numerical implementation of the model is to be able to calculate the new state of stress at time t + ∆t knowing the increment of strain ∆ε and the state of material at time t as quickly as possible. We have implemented an explicit (Euler forward) integration scheme. All the incremental variables during the time increment ∆t starting at time t are computed from the state variables evaluated at time t . The nonlinear response of the material is obtained by an explicit correction of the elastic prediction at each time steps [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF].

It is well known that explicit time integration is not accurate if the time increment is too large (i.e. if the viscoplastic incremental strains, damage or incremental porosity are too high). In the case of rate independent plasticity combined to damage, Burlion et al. [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF] have used the same integration scheme. It was observed that in practical cases where the three dimensional finite element mesh is sufficiently fine in order to achieve an accurate description of the irreversible phenomena in the structure, the critical time step due to the explicit integration of the equations of motion is so small that the explicit integration of the constitutive relations is accurate enough. Given the fact that both the constitutive relations and the equations of motion are integrated explicitely, error accumulation might occur at these two levels. The balance between the internal, kinetic and dissipated energy is monitored in order to detect such situations. Finally, LS-DYNA3D has an erosion option which can be activated in the course of a numerical simulation in order to remove elements in which failure occurs. This element removal implies a loss of mass which is not very important in our problems. This erosion procedure can, for instance, be indexed on critical values of some internal variables in the model, as we will see further.

NUMERICAL SIMULATIONS

In the following, we are going to discuss several examples of numerical simulations. The foregoing results have been obtained within the framework of a research sponsored by Thomson Daimler Armements in France. For confidentiality reasons, the numerical values of the model parameters of the constitutive relations cannot be provided. Nevertheless, we will show comparisons between the computations and the experiments in order to illustrate the capabilities of the constitutive relations developed in the previous section. All these computations have been performed with the same set of model parameters since concrete is the same. The main characteristics of this material have been provided in the previous section. More comprehensive test data can be found in Ref. [START_REF] Bailly | Rapport final, première partie, expérimentation", Comportement des ouvrages en dynamique rapide-Comportement dynamique du béton[END_REF], and for the sake of comparison, an attempt of modelling the same material with a different constitutive relation can be found in Ref. [START_REF] Nard | Dynamic Behaviour of Concrete: the Structural Effect of Compressive Strength Increase[END_REF].

Dynamic confined compression tests

Dynamic compression tests have been performed by Gary and co-workers [START_REF] Gary | Testing concrete at high strains and high rates of strain[END_REF] on concrete cylinders of length 40 mm and diameter 30 mm confined by a metallic ring (Fig. 6). Hopkinson bars have been used in order to apply on the specimens several strain rates. A sample is placed between two long identical bars (length 6 m) with high elastic limit (here 1000 MPa) compared to that of material tested (Fig. 7). With a striker, a longitudinal compressive wave is generated in the input bar. Part of this wave is reflected on the interface bar-sample, another part transmitted to the sample, and then in the output bar. Strain gauges glued on the two bars record the signals associated with these three waves. In the assumption of a unidimensional wave propagation, strain, stress and particulate velocities applied to the specimen are linearly related. The experimental velocities and forces (along the cylinder axis) applied on the two faces of the concrete specimen are computed.

In the present experiment, the metallic ring is made of steel [START_REF] Gatuingt | Prévision de la rupture des ouvrages en béton sollicités en dynamique rapide[END_REF]. The steel ring controls the radial deformation of the specimen and therefore applies a confinement stress on concrete which avoids splitting. The friction between the concrete sample and the metallic ring has been neglected because, experimentally the contact surface is coated with Teflon. Figure 10 shows the 3D finite element mesh used in the computations. It is made of 8 nodded finite elements with a single integration point. The biggest disadvantage of the one-point integration is the need to control the zero energy modes, called hourglassing modes, which arise. Undesirable hourglass modes tend to have periods that are typically much shorter than the periods of the structural response, and they are often observed to be oscillatory. The method used in LS-DYNA3D is the Flanagan-Belytschko approach [START_REF] Flanagan | A uniform strain hexahedron and quadrilateral and orthogonal hourglass control[END_REF]. It is used throughout the computations presented in this paper. The input and output bars are not represented in the finite element model. Only the confined concrete specimen is described with special boundary conditions which account for wave transmission and reflection. In the simulations, the input and output experimental velocities are prescribed to the confined concrete specimen and numerical results of the input and output forces are compared with experimental data.

It should be stressed that the model has been calibrated in compression with the help of the same experiments. The interpretation of the test data differs only. For the calibration, the longitudinal strains and stresses in concrete are calculated with the formulae employed classically for the uniaxial interpretation of the split Hopkinson tests. The difference between the input and output velocities divided by the specimen length provides the average longitudinal strain rate and the stress is computed from the average of the input and output forces. The confinement pressure is computed from the transverse strain on the outer part of the steel ring, assuming it remains elastic. The results obtained from the three dimensional computation are just a validation of the data interpretation and model calibration.

Figure 8 shows the input and output velocities at the specimen boundaries when the striker hits the hopkinson bar at a speed of 6 m/s. Figure 9a shows the comparison between the experimental and computed output forces. We have reported also on this figure a similar comparison in the case where the striker speed is 20 m/s (Fig. 9b). The good agreement between the experiments and the computation had to be expected since the model has been calibrated using these tests results among others. On these figures, results obtained with the rate independent model devised by Burlion et al. [START_REF] Burlion | Compaction and tensile damage in concrete: constitutive modelling and application to dynamics[END_REF] have also been reported. The comparison shows that the rate independent model does not provide accurate results as the speed of the striker, e.g. the strain rate in concrete, is increased. However, the present solution deviates from the experiment with progressing time, due to an overestimation of the reduction of the material porosity.

Dynamic tension test

A tension test by scabbing was performed by Brara [START_REF] Brara | Nouveau dispositif expérimental d'étude de la rupture par écaillage du béton[END_REF]. Fig. 11a shows the principle of the test, similar to the Hopkinson set-up, without the output bar. The entering (impacting) bar has a diameter of 40 mm and a length of 1 m, while the concrete sample has the same diameter as the entering bar and a length of 120 mm.

The finite element mesh used is shown in Fig. 11b. The same finite elements as in the previous computation have been used. The experimental (measured) velocity of the bar end in contact with the concrete specimen is applied to the sample (same as in the previous example). The radial displacement for the impacted surface is blocked, while the other boundaries conditions are free. In the course of the calculation, a crack should occur in the specimen, upon waves reflection at the free end of the concrete specimen and interaction. In the experiment, a single crack at the distance X = 66 mm approximately from the impacted face was obtained.

Fig. 12a shows the state of stress obtained during the numerical simulations. We obtain a homogeneous state of stress in a vertical cross section of the specimen. Figure 12b shows the state of damage associated with this state of stress. When it is subjected to compression (t = 4, 8.10 -5 s) the transverse strains imposed by the boundary condition are not sufficiently high to damage the material. In other words, the damage criterion is not activated. When the compression wave is reflected on the free (opposite) surface of the specimen, it becomes a tensile wave and the strains can become sufficiently large (at time t = 7, 2.10 -5 s) so that damage grows suddenly up to 1 in a cross section of the sample. This cross section, which represents the place where a macrocrack propagated, is located at a distance ranging between 64 and 69 mm far from the impacted face. This prediction is in good agreement with the experimental data.

In order to complement the model, erosion can be added as a function of the state of damage: an element is removed if the value of the damage variable D at its gauss point is greater than a fixed limit value (note that the elements used possess only a single integration point). Fig. 13 shows the result of simulations when the criterion of erosion is activated. If the criterion of erosion is based on a relatively low value of the damage (D 1 ), the rupture obtained is very diffuse because many elements will be removed in the course of the damage process. Conversely, if the criterion of erosion on D is too high (D 3 ), very few elements will be removed. Fig. 14 shows the evolution of the velocity of the free face versus time. On this figure we can see that when the criterion of erosion is low, the velocity of ejection of the broken part of the specimen is close to 6,5 m/s, while if the criterion is equal to high it is approximately equal to 3 m/s. An experimental measurement the scab speed associated with a rather physical criterion (width of crack equal to twice the diameter of the coarsest aggregate approximately), would make it possible to obtain a realistic value of the criterion of erosion.

Simulation of an explosion

In order to evaluate the proposed model on a case more representative of a real application, a test where an explosive is placed in contact with a concrete slab was carried out [START_REF] Bailly | Rapport final, première partie, expérimentation", Comportement des ouvrages en dynamique rapide-Comportement dynamique du béton[END_REF]. For the sake of simplicity, the explosive as well as the concrete slab were axisymmetric. The circular concrete slab had a diameter of 1 meter and a thickness of 20 cm (Fig. 15). These dimensions were such that the boundary conditions at the edge of the concrete slab did not influence the loading process, as the wave generated by the explosive travelled back and forth through the thickness of the slab. This test was instrumented by strain and pressure gauges embedded in concrete. Fig. 15 and Fig. 16 show the location of the gauges, the P2 plane corresponding to the mid-thickness of the slab.

Figure 16 shows also the mesh used for the numerical simulations. The concrete slab is separated in three distinct parts in order to be able to refine the mesh on the level of the contact between the explosive and concrete. It is a 2D mesh, essentially for computational speed reasons, compared to a full 3D mesh (note that as axisymmetric mesh could have been used as well). The displacements perpendicular to the plane containing the finite element mesh are blocked. This condition represents the symmetry of revolution approximately. It should be pointed out that many problems were encountered in the numerical representation of the contact between the concrete slab and the explosive. A way of limiting these problems was to increase the number of element describing this contact significantly. This is the reason why a full 3D computation is not presented.

The equation of state used to model the detonation in the explosive is of the JWL type, which defines the pressure p induced by the explosion as:

p = A 1 - ω R 1 V exp(-R 1 V ) + B 1 - ω R 2 V exp(-R 2 V ) + ωE V (17)
where A, B, R 1 , R 2 , ω are material parameters, E, V represent the internal energy and the volume of the explosive, respectively. The numerical values are given in table 1. Detonation starts at the center of the explosive. It generates a pressure wave which is transmitted to the slab through the contact conditions in between the two materials. Fig. 17 shows the evolution of the damage during the calculation. In this calculation, the criterion of erosion was also activated in order to visualise the scab which might be ejected from the back face of the slab. Although a significant mesh effect was observed at the interfaces between the regions of the finite element model where the element density is changed abruptly, the computed size of the scab is: diameter = 26 cm, depth = 4 cm. This is quite close to the experimental values measured on the slabs equipped with the embedded strain gauges. Fig. 18 shows the evolution of axial stress versus to time for planes P 1, P 2 and P 3. We can see that the model is also able to capture quite well the velocity and amplitude of the compression wave within the thickness of the slab.

CONCLUSIONS

A constitutive relation aimed at describing the response of concrete in dynamics has been presented. It contains a description of microcraking in tension and compression, and of compaction due to hydrostatic compression. The model combines viscoplasticity with a rate dependent damage model. Compaction is described with a homogenisation technique, assuming that concrete is a homogeneous material with voids.

Several conclusions have been obtained from the computations :

• The comparison of the results of the Hopkinson tests on confined specimens reveal that rate effects on the volumetric strain versus hydrostatic compression curve are needed in order to achieve a good description of the tests, at different strain rates.

• The finite element computation of the tensile test shows that scabbing can be well captured with the model. A technique of finite element removal at failure indexed on the state of damage of the material has been implemented (note that this technique is standard in the computer code which we used, only the criterion of erosion is left to be defined by the user).

• The prediction of the response of a concrete slab subjected to an explosion is quite consistent with the experiments, which lends some confidence in the capabilities of the proposed model at describing, with a sufficient amount of details, the response of concrete structures subjected to explosions and impacts.

As a final remark, it ought to be noted that the present approach does not account for the presence of interstitial water in concrete. The model has been calibrated with test data on the material not saturated with water (Humidity ≈ 60%). The influence of water should be expected on compaction and on the rate effect.

A 9.8968e11 B 1.586e10 R 1 4.72 R 2 1.0 ω 0.4 E 0 0.0

m

  Dt , n Dt , m Dc and n Dc are material parameters which control the rate effect. a c , a t , b c , b t are material parameters which govern the growth of damage in quasistatic tension and compression. ε D0 is the initial threshold of damage.

Figure 1 :Figure 2 :

 12 Figure1: Schematic case of an impact on a concrete slab, after Ref.[START_REF] Kennedy | A review of procedures for the analysis and design of concrete strutures to resist missile impact effects[END_REF]

Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 3456 Figure 3: Model response for several strain rate: a) uniaxial tension test, b) uniaxial compression test.

Figure 7 :Figure 8 :

 78 Figure 7: Split Hopkinson pressure bar set-up

Figure 9 :Figure 11 :

 911 Figure 9: Comparison between experimental and computed output forces: a) striker at a speed of 6 m/s, b) striker at a speed of 20 m/s

Figure 12 :Figure 15 :Figure 17 :Figure 18 :

 12151718 Figure 12: Tensile test: a) stress evolution, b) damage evolution.

Table 1 :

 1 Parameters of the JWL law for the explosive.

	Spalling

Acknowledgements : Financial support from Thomson Daimler Armements and the french network GEO is gratefully acknowledged.

Confinement cell

Metallic plugs


M Lionard
email: marie.lionard@ugent.be

F Aze´mar

S Bouleˆtreau

K Muylaert

M Tackx

W Vyverman

Grazing by meso-and microzooplankton on phytoplankton in the upper reaches of the Schelde estuary (Belgium/The Netherlands)

Keywords: Schelde estuary, grazing, rotifers, mesozooplankton, phytoplankton, HPLC, CHEMTAX

In contrast with the marine reaches of estuaries, few studies have dealt with zooplankton grazing on phytoplankton in the upper estuarine reaches, where freshwater zooplankton species tend to dominate the zooplankton community. In spring and early summer 2003, grazing by micro-and mesozooplankton on phytoplankton was investigated at three sites in the upper Schelde estuary. Grazing by mesozooplankton was evaluated by monitoring growth of phytoplankton in 200 mm filtered water in the presence or absence of mesozooplankton. In different experiments, the grazing impact was tested of the calanoı¨d copepod Eurytemora affinis, the cyclopoid copepods Acanthocyclops robustus and Cyclops vicinus and the cladocera Chydorus sphaericus, Moina affinis and Daphnia magna/pulex. No significant grazing impact of mesozooplankton in any experiment was found despite the fact that mesozooplankton densities used in the experiments (20 or 40 ind. l ÿ1 ) were higher than densities in the field (0.1e6.9 ind. l ÿ1 ). Grazing by microzooplankton was evaluated by comparing growth of phytoplankton in 30 and 200 mm filtered water. Microzooplankton in the 30e200 mm size range included mainly rotifers of the genera Brachionus, Trichocerca and Synchaeta, which were present from 191 to 1777 ind. l ÿ1 . Microzooplankton had a significant grazing impact in five out of six experiments. They had a community grazing rate of 0.41e1.83 day ÿ1 and grazed up to 84% of initial phytoplankton standing stock per day. Rotifer clearance rates estimated from microzooplankton community grazing rates and rotifer abundances varied from 8.3 to 41.7 ml ind. ÿ1 h ÿ1 . CHEMTAX analysis of accessory pigment data revealed a similar phytoplankton community composition after incubation with and without microzooplankton, indicating non-selective feeding by rotifers on phytoplankton.

Introduction

In contrast to the downstream, marine reaches of estuaries, where the zooplankton community is usually dominated by marine calanoid copepods (e.g. Castel and Veiga,1990;[START_REF] Soetaert | Spatial and temporal patterns of the zooplankton in the Westerschelde estuary[END_REF][START_REF] Tackx | Copepod feeding in the Westerschelde and the Gironde[END_REF][START_REF] Roman | Temporal and spatial patterns of zooplankton in the Chesapeake Bay turbidity maximum[END_REF], freshwater zooplankton species tend to become more important in the upper reaches of estuaries, where the water is fresh or slightly brackish. In the upper reaches of estuaries, rotifers are often numerically the dominant zooplankton group.

Rotifers have been found to dominate the zooplankton community in the upper reaches of the Hudson River estuary [START_REF] Pace | Zooplankton in advective environments: the Hudson River community and a comparative analysis[END_REF], the Hawkesbury-Nepean River estuary [START_REF] Kobayashi | Grazing by a river zooplankton community: importance of microzooplankton[END_REF], Chesapeake Bay [START_REF] Park | The trophic contributions of rotifers in tidal freshwater and estuarine habitats[END_REF] and the Schelde estuary (Muylaert et al., 2000a;[START_REF] Tackx | Zooplankton in the Schelde estuary, Belgium and The Netherlands. Spatial and temporal patterns[END_REF]. In this respect, the upper reaches of estuaries strongly resemble the lowland reaches of large rivers (e.g. [START_REF] Pourriot | Influence de quelques facteurs du milieu sur la composition et la dynamique saisonnie`re du zooplancton de la Loire[END_REF][START_REF] Gosselain | The phytoplankton community of the River Meuse, Belgium: seasonal dynamics (year 1992) and the possible incidence of zooplankton grazing[END_REF]. Rotifers have a short generation time compared to crustacean zooplankton and are therefore well adapted to survive in ecosystems like rivers and estuaries, which often have a short retention time. Freshwater crustacean mesozooplankton like cladocera or cyclopoid copepods may occasionally become abundant in the upper reaches of estuaries, but rarely during prolonged periods.

Despite the fact that the upper reaches of estuaries tend to be very turbid they often show dense phytoplankton blooms. Phytoplankton biomass in upper estuarine reaches is often higher than in the marine reaches. It is not unusual for chlorophyll a concentrations in the upper reaches of estuaries to exceed 50 mgl ÿ1 (e.g. [START_REF] Schuchardt | Phytoplankton maxima in the tidal freshwater reaches of two coastal plain estuaries[END_REF][START_REF] Muylaert | Phytoplankton growth in the freshwater tidal reaches of the Schelde estuary (Belgium) estimated using a simple light-limited primary production model[END_REF]. While many studies have dealt with zooplankton grazing on phytoplankton in the marine zone of estuaries (e.g. [START_REF] Heinle | Detritus as food for estuarine copepods[END_REF][START_REF] Tackx | Copepod feeding in the Westerschelde and the Gironde[END_REF][START_REF] Roman | Temporal and spatial patterns of zooplankton in the Chesapeake Bay turbidity maximum[END_REF], much less is known about the fate of phytoplankton in the upper estuary. [START_REF] Park | The trophic contributions of rotifers in tidal freshwater and estuarine habitats[END_REF] suggested that rotifers may play an important trophic role in the upper reaches of estuaries. Grazing experiments carried out in the freshwater tidal Potomac River seem to confirm this hypothesis [START_REF] Sellner | Zooplankton grazing in a Potomac river cyanobacteria bloom[END_REF]. In the lowland reaches of rivers, of which the upper reaches of estuaries form a downstream continuation, rotifers were found to graze a considerable fraction of phytoplankton production or standing stock. In the River Meuse, rotifers grazed up to 113% of phytoplankton standing stock per day [START_REF] Kobayashi | Grazing by a river zooplankton community: importance of microzooplankton[END_REF][START_REF] Gosselain | Can a community of small-bodied grazers control phytoplankton in rivers?[END_REF]. Using riverine ecosystem models, rotifers were predicted to exert a significant control on phytoplankton during summer (Seine river: [START_REF] Billen | Modeling phytoplankton development in whole drainage networks: the Riverstrahler model applied to the Seine river system[END_REF]Meuse river: Everbecq et al., 2001;Rhine river: Schol et al., 2002).

The Schelde estuary is one of the few European estuaries with an extensive freshwater tidal zone in its upper reaches. This freshwater tidal zone is characterized by the occurrence of dense phytoplankton blooms and a zooplankton community that is dominated by rotifers [START_REF] Tackx | Zooplankton in the Schelde estuary, Belgium and The Netherlands. Spatial and temporal patterns[END_REF]. The first goal of this study was to determine whether zooplankton can exert a significant grazing pressure during phytoplankton blooms in the upper reaches of the Schelde estuary. The experiments were carried out during the spring and the summer blooms at three sites representative of riverine, freshwater tidal and oligohaline conditions. Grazing by mesozooplankton and microzooplankton (dominated by rotifers) were determined separately to evaluate the relative roles of rotifers and mesozooplankton in phytoplankton grazing. Using CHEMTAX analyses of HPLC derived pigment data phytoplankton groups selective grazing on the major was evaluated.

Materials and methods

Study site

The Schelde estuary (Fig. 1) is a macrotidal coastal plain estuary situated in Western Europe. In contrast to many other European estuaries, where locks have been constructed at the freshwater seawater interface, the Schelde estuary still possesses an extensive freshwater tidal zone in its upper reaches. In these upper reaches, dense phytoplankton blooms occur during spring and summer. The spring bloom tends to be mainly imported from the tributary river Schelde while the summer bloom reaches its maximum within the upper estuary. These phytoplankton blooms are dominated by diatoms but chlorophytes can be co-dominant in the tributary rivers and near the head of the estuary in summer (Muylaert et al., 2000b). The zooplankton community in the upper estuary is dominated by rotifers, which frequently attain abundances of about 1000 ind. l ÿ1 [START_REF] Soetaert | Spatial and temporal patterns of the zooplankton in the Westerschelde estuary[END_REF]Muylaert et al., 2000a;[START_REF] Tackx | Zooplankton in the Schelde estuary, Belgium and The Netherlands. Spatial and temporal patterns[END_REF]. Mesozooplankton densities rarely exceed 20 ind. l ÿ1 . The crustacean zooplankton in the freshwater tidal reaches and river is dominated by the cyclopoid copepod Acanthocyclops robustus with other cyclopoid copepods or cladocera like Cyclops vicinus, Bosmina longirostris, Moina spp. and Daphnia spp. often being codominant. Towards the brackish reaches of the estuary, the calanoid copepod Eurytemora affinis replaces the cyclopoid copepods and cladocera. This species has recently moved upstream into the freshwater tidal zone, possibly due to improved water quality [START_REF] Appeltans | Zooplankton in the Schelde Estuary (Belgium The Netherlands). The distribution of Eurytemora affinis: effect of oxygen[END_REF].

For the experiments, water and zooplankton were collected in 2003 in spring (March) and early summer (June) at three sites situated at the upper reaches of the Schelde estuary (Fig. 1): the river Schelde just before it enters the estuary, the freshwater tidal reaches of the estuary in Dendermonde and the oligohaline reaches in Antwerpen. March and June were representative for the two phytoplankton blooms that occur annually in the upper Schelde estuary. Water and zooplankton for the experiments were sampled from the river bank using bucket hauls. A quantitative mesozooplankton sample (50 l) was collected by means of a 200 mm mesh size plankton net. Salinity and temperature were measured in situ using an YSI 650 MDS multimeter with an YSI 600 R sensor.

Experimental setup

Grazing rates of meso-and microzooplankton on phytoplankton were estimated by comparing phytoplankton growth rates in the presence and absence of grazers. Phytoplankton was separated from micro-and mesozooplankton by filtration over a 30 mm nylon mesh. Exploratory tests had demonstrated that this filter did not significantly retain phytoplankton. Mesozooplankton was separated from microzooplankton by filtration over a 200 mm nylon mesh. Microzooplankton grazing on phytoplankton was estimated by comparing phytoplankton development in the !200 mm and !30 mm filtrates. Microzooplankton therefore only included grazers in the 30e200 mm size range. Mesozooplankton grazing on phytoplankton was estimated by comparing phytoplankton development in !200 mm filtrates with and without added mesozooplankton. Mesozooplankton was collected at each sampling site by filtering 200e300 l of water through a 200emm mesh size plankton net. A known number of individuals were picked out using a wide-bore pipette and a dissecting microscope to be added to the treatments. Two mesozooplankton treatments were set up for each experiment. If two species were co-dominant in the mesozooplankton community, the grazing impact of these two species was assessed separately. If only one species was dominant, this species was added to the treatments in different densities. The treatments were incubated in 1 l polycarbonate bottles during 1 day. Three replicates were prepared for each treatment. The bottles were incubated in a temperature and light controlled incubator. Temperature was set within approximately 1 C of the field temperature (10 C in March and 20 C in June). Light intensity was set at 22 mmol m ÿ2 s ÿ1 , which corresponds to the mean underwater irradiance at Dendermonde in spring. The mean underwater irradiance was estimated from a typical spring surface irradiance, the vertical light extinction coefficient and mean water column depth. The mean underwater irradiance experienced by phytoplankton will have been different at the other two sites and in summer. Therefore, growth rates measured in the experiments cannot be extrapolated to the field situation. In March, light was (accidentally) supplied continuously while a 12 h darke12 h light cycle was supplied in June. Bottles were incubated on a rotating table (100 rpm) to keep the phytoplankton in suspension. All bottles were sampled for phytoplankton and microzooplankton at the start and at the end of the experiment.

Phytoplankton pigments were sampled by filtering 50e100 ml water over 25 mm GF/F filter. Filters were quickly dried between blotting paper and stored frozen at ÿ80 C until analysis. Microzooplankton was sampled by filtering 50e100 ml water over a 30 mm nylon mesh. Samples were fixed with formalin at a final concentration of 4%. Samples for quantification of ciliates were fixed according to the Lugol-formalinthiosulphate method [START_REF] Sherr | Simultaneous measurements of bacterioplankton production and protozoan herbivory in estuarine water[END_REF]. In the mesozooplankton treatments, mesozooplankton individuals added to the bottles were collected on a 200 mm mesh at the end of the experiment for identification up to the species level. Mesozooplankton was fixed in a 4% formalin solution.

Gent

Analysis of samples

Phytoplankton biomass and community composition were investigated by means of HPLC pigment analysis. Pigments were extracted from the filters in 90% acetone by means of sonication (tip sonicator, 40 W for 30 s). Pigment extracts were filtered over a 0.2 mm nylon filter to remove particulates. Pigments were injected into a Gilson HPLC system equipped with an Alltima reverse-phase C18 column (25 cm!4.6 mm, 5 mm particle size). Pigments were analysed according to the method of [START_REF] Wright | High-resolution HPLC system for chlorophylls and carotenoids of marine phytoplankton[END_REF], which is an adaptation of the method of [START_REF] Wright | Improved HPLC method for the analysis of chlorophylls and carotenoids from marine phytoplankton[END_REF] for marine phytoplankton. This method uses a gradient of three solvents: methanol 80%eammonium acetate 20%, acetonitrile 90% and ethyl acetate. Three detectors were connected to the HPLC system: an Applied Biosystems 785A Programmable Absorbance Detector to measure absorbance at 785 nm, a Gilson model 121 fluorometer to measure fluorescence of chlorophylls and their derivates and a Gilson 170 diode array detector to measure absorbance spectra for individual pigment peaks. Pigments were identified by comparison of retention times and absorption spectra with pure pigment standards (supplied by DHI, Denmark).

Mesozooplankton added to the bottles, the quantitative mesozooplankton samples and microzooplankton present in the !200 mm filtrates were identified and enumerated using a dissecting microscope. Identification was based on Ruttner-Kolisko (1972), [START_REF] Pontin | A key to British Freshwater Planktonic and semiplanktonic Rotifera of the British isles[END_REF] and [START_REF] Segers | Ritifera 2, Guides to the Identification of the Microinvertebrates of the Continent Waters of the World[END_REF]. Ciliates were counted using an inverted microscope. Ciliates were identified up to class level [START_REF] Foissner | Identification and ecology of limnetic plankton ciliates. Informationsberichte des Bayer[END_REF]. Samples for microzooplankton and ciliates were stained with Bengal Rose to aid in distinguishing between plankton and detritus.

Data analyses

One-way ANOVA was used to compare densities of potential grazers of phytoplankton and concentrations of total chlorophyll a at the end of the experiments between the treatments.

The CHEMTAX software was used to calculate the contribution of different algal groups to total chlorophyll a using concentrations of accessory pigments. This software package was developed specifically for the analysis of phytoplankton pigment data [START_REF] Mackey | CHEMTAX-a program for estimating class abundances from chemical markers: application to HPLC measurements of phytoplankton[END_REF]. The CHEMTAX software makes use three matrices: (1) a matrix containing concentrations of all marker pigments in the samples; (2) an initial matrix containing marker pigment to chlorophyll a ratios for all algal groups; and (3) a ratio limit matrix defining limits on the theoretical marker pigment to chlorophyll a ratios. The CHEMTAX program optimizes the contribution of different algal groups to total chlorophyll a based on measured pigment concentrations (matrix 1), using the pigment ratio matrix (matrix 2) as a starting point and allowing pigment ratios to vary according to constraints defined in the limit matrix (matrix 3). The initial pigment ratio matrix (Table 1) was obtained from previous monitoring studies of phytoplankton pigments in the Schelde estuary in which biomass of major phytoplankton groups estimated by means of HPLC-CHEMTAX analyses was verified with data obtained by microscopical analyses (M. Lionard, unpublished data). Pigment data were processed separately using CHEMTAX for each experiment.

Community grazing rates and individual clearance were calculated according to [START_REF] Walz | Rotifer life history strategies and evolution in freshwater plankton communities[END_REF] and [START_REF] Frost | Effects of size and concentration of food particles on the feeding behaviour of the marine planktonic copepod, Calanus pacificus[END_REF]. Grazing rates were calculated as gZ lnðC t =C zt Þð1=tÞ where C t and C zt are the concentrations of the prey at the end of the incubation period, respectively in the absence and in the presence of the predator, and t is the incubation time (in days). The percentage of initial phytoplankton biomass grazed per day was calculated as 100 ÿ 100 e ÿlnðgÞ . The individual clearance rate was calculated as FZgðV=PÞ, where P is the density of predators and V is the bottle volume. For P the average density of predators during the incubation period was used, which was calculated according to [START_REF] Marin | Measuring feeding rates of pelagic herbivores: analysis of experimental design and methods[END_REF]

Results

As shown in Table 2 salinity was !0.5 in spring, as well as in summer, in Gent and Dendermonde. In Antwerpen, salinity was !0.5 in spring but was 1.75 in summer, which is indicative of oligohaline conditions. Temperature was 9.5 C at all sites in spring and varied between 21.5 and 23.5 C in summer. In spring, chlorophyll a concentration was highest in Gent and decreased in downstream direction towards Dendermonde and Antwerpen. In summer, chlorophyll a concentration was highest in Dendermonde and was lower in the river in Gent and in the oligohaline reaches in Antwerpen. The contribution of different algal groups to total chlorophyll a was assessed by means of CHEMTAX analysis of accessory pigment concentrations. In Gent and Dendermonde in spring and in Dendermonde in summer diatoms dominated the phytoplankton community with at least 78% of total chlorophyll a. In Gent in summer, chlorophytes were dominant (58% of total chlorophyll a) with diatoms being co-dominant. In Antwerpen, diatoms and chlorophytes were co-dominant in spring as well as in summer, with both groups contributing 60e80% to total chlorophyll a. In spring, euglenophytes contributed 11% to total chlorophyll a in Gent and 18% in Antwerpen. The contribution of other algal groups to total chlorophyll a was always !10%.

Total mesozooplankton density was !1 ind. l ÿ1 in spring and summer in Gent and in spring in Dendermonde. Highest mesozooplankton densities were observed in Dendermonde in summer (about 7 ind. l ÿ1 ) and in Antwerpen in spring (about 9 ind. l ÿ1 ). Cyclopoid copepods (Acanthocyclops robustus, Cyclops vicinus) dominated the mesozooplankton community at all sites By comparing the !30 mm and !200 mm treatments we evaluated grazing by microzooplankton in the 30e 200 mm size range on phytoplankton. Potential grazers in the 30e200 mm size range included ciliates, copepod nauplii and rotifers. Ciliate densities never differed significantly between the !30 mm and !200 mm size fractions indicating that ciliates were not significantly retained by the 30 mm mesh (Table 3). Densities of rotifers and copepod nauplii, on the contrary, were always significantly higher in !200 mm than in the !30 mm treatments. Densities of rotifers in the !200 mm size fraction at the start of the experiment varied from 191 to 1777 ind. l ÿ1 . Rotifer densities were highest in Gent in spring as well as in summer. The rotifer community in Gent and Dendermonde was dominated by Brachionus calyciflorus in spring and by Trichocerca sp. in summer. In Antwerpen, the rotifer community was dominated by the genera Synchaeta and Brachionus in spring and by Trichocerca in summer. Densities of copepod nauplii were usually much lower than densities of rotifers. Densities of copepod nauplii exceeded rotifer densities by O10% only in spring in Antwerpen (16%) and summer in Dendermonde (13%). Abundances of rotifers and copepod nauplii often changed during the incubation period. Increases up to 340% and decreases down to 61% of initial densities were observed.

No significant difference in final chlorophyll a concentration was observed between the !200 mm treatments and the mesozooplankton treatments (Fig. 2)i n any of the experiments, indicating no significant grazing by mesozooplankton on phytoplankton. Except for the experiment in Antwerpen in summer, chlorophyll a concentration at the end of the experiments was always significantly lower in the !200 mm treatments when compared to the !30 mm treatments, indicating significant grazing by microzooplankton on phytoplankton. Microzooplankton community grazing rates varied between 0.4 and 1.8 day ÿ1 (Table 4). The fraction of initial phytoplankton biomass grazed per day by microzooplankton varied between 33 and 84%. Given the fact that rotifers dominated the microzooplankton community it can be assumed that microzooplankton grazing was dominated by rotifers. Individual rotifer filtration rates were therefore estimated using average abundances of rotifers and total community grazing rates. Individual filtration rates varied between 8.3 and 41.7 ml ind. ÿ1 day ÿ1 (Table 4).

To evaluate whether selective grazing by microzooplankton on phytoplankton may influence the composition of the phytoplankton community, the phytoplankton community composition was compared at the end of the experiments in the presence and absence of microzooplankton (Fig. 3). No large differences in phytoplankton community were observed after incubation in the presence or absence of microzooplankton.

Discussion

The goal of this study was to investigate whether microand/or mesozooplankton can exert a significant grazing pressure during phytoplankton blooms in the upper reaches of a macrotidal estuary, the Schelde estuary. The March experiments were typical for the phytoplankton spring bloom in the upper estuary, when phytoplankton is mainly imported from the river and the phytoplankton community is dominated by diatoms. The June experiments were typical of the summer bloom, when autochthonous phytoplankton populations develop in the freshwater tidal reaches and a succession in the phytoplankton community occurs from chlorophytes in the river to diatoms in the freshwater tidal and brackish zones (Muylaert et al., 2000a). Abundance and community composition of the microzooplankton community at the time of our experiments was typical for the upper Schelde estuary, being dominated by rotifers of the genera Brachionus, Synchaeta and Trichocerca [START_REF] Tackx | Zooplankton in the Schelde estuary, Belgium and The Netherlands. Spatial and temporal patterns[END_REF]. Similar microzooplankton communities occur in other freshwater tidal estuaries (Rhode River estuary: [START_REF] Dolan | Trophic role of planktonic rotifers in the Rhode River Estuary, spring-summer 1991[END_REF]; Elbe estuary: [START_REF] Meister | Untersuchung zum Plankton der Elbe und ihrer gro¨sseren Nebenflu¨sse. Investigation of the River Elbe and its most important tributaries[END_REF]; Chesapeake Bay estuary: [START_REF] Park | The trophic contributions of rotifers in tidal freshwater and estuarine habitats[END_REF] or in lowland rivers (Loire river: [START_REF] Pourriot | Influence de quelques facteurs du milieu sur la composition et la dynamique saisonnie`re du zooplancton de la Loire[END_REF]Meuse river: Gosselain et al., 1994). Mesozooplankton densities in the field at the time of the experiments were relatively low compared to previous observations. The mesozooplankton densities used in the present experiments, however, were comparable to the maximal densities that have been observed in previous years. In at least two independent mesozooplankton experiments, the grazing impact of the two dominant mesozooplankton species that occur in the upper Schelde estuary was evaluated: Eurytemora affinis, which is dominant in the brackish zone of the estuary, and Acanthocyclops vicinus, which is the dominant species in the freshwater tidal reaches [START_REF] Tackx | Zooplankton in the Schelde estuary, Belgium and The Netherlands. Spatial and temporal patterns[END_REF]. In addition, the impact of other species that are frequently encountered in the freshwater tidal and brackish reaches of the Schelde estuary but that are rarely dominant: was also tested the cyclopoid copepod Cyclops vicinus and the cladocera Chydorus sphaericus, Daphnia pulex/magna and Moina affinis.

No significant effect of mesozooplankton on phytoplankton was observed in any of the experiments. This was not due to the low mesozooplankton densities at the time of the experiments as mesozooplankton in the experimental bottles was at a density comparable to the maximal densities that occur in the estuary. This suggests that mesozooplankton did not exert a significant grazing pressure on phytoplankton during the spring and summer blooms and that its impact on phytoplankton blooms is probably insignificant even when higher densities occur. Because mesozooplankton densities in that bottles were higher than those in the field, that results should be interpreted with some caution as increasing mesozooplankton densities in experimental bottles may perturb the zooplankton feeding behaviour [START_REF] Roman | Containment effects in copepod grazing experiments-a plea to end the black-box approach[END_REF]. The lack of a significant grazing impact of mesozooplankton on phytoplankton does not necessarily imply that mesozooplankton does not feed on phytoplankton in the upper Schelde estuary. Eurytemora affinis, one of the species used in this study has been shown to exert a clearance rate up to 1 ml ind. ÿ1 h ÿ1 on diatoms in the brackish reaches of the Schelde estuary [START_REF] Tackx | Selective feeding of Eurytemora affinis (Copepoda, Calanoida) in temperate estuaries: model and field observations[END_REF]. In the upper Schelde estuary and river, chlorophyll a concentrations are often high (up to 215 mgl ÿ1 in this study) relative to the densities of mesozooplankton. While mesozooplankton may feed on phytoplankton in the upper Schelde estuary, their impact on phytoplankton standing stocks may have been too low to be measurable by means of the method used in this study.

In contrast to mesozooplankton, a significant effect of microzooplankton on phytoplankton was observed in all experiments except in Antwerpen in June. In the experiments, the microzooplankton included organisms between 30 and 200 mm in size. This size range encompasses rotifers, copepod nauplii and ciliates. As ciliates were not retained by the 30 mm mesh, microzooplankton grazing on phytoplankton in the present experiments did not include grazing by ciliates. Both copepod nauplii and rotifers were strongly retained by the 30 mm mesh. Grazing by microzooplankton in the experiments should mainly be attributed to copepod nauplii and/or rotifers. On all occasions, abundance of copepod nauplii was much lower (maximal 16%) than rotifer abundance and in two experiments copepod nauplii were even absent. Grazing by microzooplankton in the present experiments should probably mainly be attributed to rotifers. To evaluate whether rotifers were capable of exerting the observed grazing pressure on phytoplankton, individual rotifer filtration rates were estimated from total rotifer densities and microzooplankton community grazing rates and compared these filtration rates with literature data. These estimated individual filtration rates should be interpreted with caution as they do not take into account additional grazing by copepod nauplii. Moreover, individual filtration rates are difficult to assess when rotifer abundances change during the incubation, which was the case in several experiments. Apart from the high filtration rate of 76 ml ind. ÿ1 h ÿ1 measured in Dendermonde in spring, the estimated filtration rates were in the range of published rates measured for the same species as those occurring in the upper Schelde estuary using radioactively labelled prey method in previous laboratory or field experiments [START_REF] Starkweather | Feeding in rotifer Brachionus calyciflorus. 2. Effect of food density on feeding rates using Euglena gracilis and Rhodotorula glutinis[END_REF]4 5 e50 ml ind. ÿ1 h ÿ1 for Brachionus calyciflorus in a laboratory study; Rothhaupt, 1990a: 30 ml ind. ÿ1 h ÿ1 for Brachionus calyciflorus in a laboratory study; Sellner et al., 1993: 5.4 ml ind. ÿ1 h ÿ1 for Brachionus angularis in a field study; [START_REF] Gosselain | The phytoplankton community of the River Meuse, Belgium: seasonal dynamics (year 1992) and the possible incidence of zooplankton grazing[END_REF]1 4 ml ind. ÿ1 h ÿ1 for Brachionus calyciflorus in a laboratory study, and from 2.14 to 19.71 ml ind. ÿ1 h ÿ1 for Brachionus calyciflorus in a field study in the Meuse river; Havens, 1991:3 0 ml ind. ÿ1 h ÿ1 for Brachionus calyciflorus and 30 ml ind. ÿ1 h ÿ1 for Synchaeta stylata in a field study). The high value estimated for Dendermonde in spring may have been due to an overestimation of clearance rates related to the large increase in rotifer abundance during the incubation period.

The importance of rotifers as grazers of phytoplankton in the upper reaches of the Schelde estuary is in contrast with the marine reaches of the estuary, where mesozooplankton is often assumed to dominate grazing on phytoplankton (e.g. [START_REF] Soetaert | Living in the twilight: estimating net phytoplankton growth in the Westerschelde estuary (The Netherlands) by means of an ecosystem model (MOSES)[END_REF]. Dilution experiments, however, have indicated that microzooplankton may also be important grazers of phytoplankton in the marine reaches of estuaries [START_REF] Mcmanus | Phytoplankton pigments and growth-rates, and microzooplankton grazing in a large temperate estuary[END_REF][START_REF] Ruiz | Microzooplankton grazing in the estuary of Mundana, Spain, and its impact on phytoplankton distribution along the salinity gradient[END_REF]. In these studies, however, ciliates were identified as the dominant microzooplankton grazers while, in the present study, microzooplankton grazing was mainly ascribed to rotifers and grazing by ciliates was not taken into account. A similar microzooplankton grazing pressure on phytoplankton has been observed in lowland rivers where phytoplankton biomass and rotifer abundances were in the same order of magnitude as in the upper reaches of the Schelde estuary (e.g. [START_REF] Billen | Modeling phytoplankton development in whole drainage networks: the Riverstrahler model applied to the Seine river system[END_REF][START_REF] Descy | Development and ecological importance of phytoplankton in a large lowland river (River Meuse, Belgium)[END_REF][START_REF] Kobayashi | Grazing by a river zooplankton community: importance of microzooplankton[END_REF].

In this study, the grazing pressure of microzooplankton on phytoplankton varied from non-significant (in Antwerpen in June) to a maximum of 1.83 day ÿ1 (in Gent in March). That the grazing pressure of rotifers on phytoplankton in Antwerpen in June was non-significant can probably be ascribed to the absence of efficient phytoplankton grazers, as the rotifer community at that time was dominated by 74% by the small rotifer Trichocerca. In the experiments where microzooplankton had a significant impact on phytoplankton biomass, the grazing rate varied considerably (from 0.41 to 1.83 day ÿ1 ). No clear relationship could be observed between microzooplankton grazing rate and rotifer abundance, community composition or temperature. The minimal grazing rate occurred at relatively high rotifer abundance (in Gent in summer). Brachionus spp. dominated the rotifer community both when the highest and the lowest grazing rates were measured. Both high and low grazing rates were measured during the spring as well as the summer bloom, despite a difference in water temperature of more than 10 C. The lack of a clear pattern in microzooplankton grazing rates may be due to the importance of alternative food sources of rotifers in the Schelde estuary. Rotifers have a broad diet and are capable of feeding on bacteria, heterotrophic flagellates or ciliates [START_REF] Dolan | Trophic coupling of rotifers, microflagellates, and bacteria during fall months in the Rhode River estuary[END_REF][START_REF] Arndt | Rotifers as predators on components of the microbial web (bacteria, heterotrophic flagellates, ciliates) e a review[END_REF][START_REF] Gilbert | Rotifers as predators on small ciliates[END_REF][START_REF] Ooms-Wilms | Are bacteria an important food source for rotifers in eutrophic lakes[END_REF]. These alternative food sources may be important in the Schelde estuary, which is a net heterotrophic ecosystem [START_REF] Soetaert | Living in the twilight: estimating net phytoplankton growth in the Westerschelde estuary (The Netherlands) by means of an ecosystem model (MOSES)[END_REF]. Certainly, more studies are needed to investigate what regulates seasonal and spatial variations in grazing pressure of rotifers on phytoplankton.

Despite the high biomass of phytoplankton during the spring and summer blooms, microzooplankton nevertheless grazed a large fraction of phytoplankton standing stock per day (up to 84%). The impact of microzooplankton on the development of phytoplankton blooms in the upper Schelde estuary might be significant, especially because phytoplankton growth rates are low due to severe light-limitation [START_REF] Muylaert | Phytoplankton growth in the freshwater tidal reaches of the Schelde estuary (Belgium) estimated using a simple light-limited primary production model[END_REF]. The potential impact of microzooplankton feeding on phytoplankton seasonal succession in upper reaches of the Schelde estuary remains unclear. In the Schelde estuary, dense rotifer populations occur from spring onward (Muylaert et al., 2000b). Despite the presence of these rotifer populations and the strong grazing impact they may have on phytoplankton, dense phytoplankton blooms develop in the upper Schelde estuary in summer. These blooms are only terminated when discharge increases in autumn (Muylaert et al., 2000b), suggesting that discharge is more important in regulating phytoplankton blooms than rotifer grazing. The reason why rotifers are incapable of controlling phytoplankton biomass or causing a clear water phase in the upper Schelde estuary may be twofold. First, rotifers require high food levels for growth [START_REF] Hansen | Particule grazing efficiency and specific growth efficiency of the rotifer Brachionus plicatilis (Muller)[END_REF][START_REF] Walz | Rotifer life history strategies and evolution in freshwater plankton communities[END_REF] and can therefore never reduce phytoplankton to very low levels without becoming food-limited. Second, rotifers in the upper Schelde estuary may never reach sufficiently high population densities to control phytoplankton biomass because rotifer populations are kept low by the short retention time of the water (!10e12 days for the freshwater tidal reaches, Muylaert et al., 2000b).

Selective feeding by rotifers has frequently been reported in the literature (e.g. [START_REF] Pourriot | Food and feeding habits of the Rotifera[END_REF][START_REF] Starkweather | Aspects of the feeding behaviour and trophic ecology of suspension-feeding rotifers[END_REF][START_REF] Bogdan | Body size and food size in freshwater zooplankton[END_REF]. Selective grazing by the microzooplankton community on different phytoplankton groups was evaluated by comparing the composition of the phytoplankton community after incubation in the presence (!200 mm treatments) and absence (!30 mm treatments) of microzooplankton grazing. No difference in phytoplankton community composition was observed between the !30 mm and !200 mm treatments, indicating no strong selective grazing by the microzooplankton. Algal groups were consumed in approximately the same proportion as in which they occurred in situ. This was surprising because diatoms were always an important component of the phytoplankton community and selection against diatoms was expected as diatoms are difficult to ingest by rotifers due to their silica frustules. The lack of significant selective feeding in these experiments may be related to the importance of Brachionus spp. in the rotifer community. Compared to other rotifers, members of the family Brachionidae are considered to be rather non-selective filter feeders [START_REF] Bogdan | Body size and food size in freshwater zooplankton[END_REF]. Moreover, several studies have shown that Brachionus spp. are capable of ingesting diatoms or other large phytoplankton species that are similar in size to the Stephanodiscus and Cyclotella species that occur in the upper Schelde estuary [START_REF] Hansen | Particule grazing efficiency and specific growth efficiency of the rotifer Brachionus plicatilis (Muller)[END_REF][START_REF] Hotos | Growth, filtration and ingestion rate of the rotifer Brachionus plicatilis fed with large (Asteromonas gracilis) and small (Chlorella sp.) celled algal species[END_REF].

Fig. 1 .

 1 Fig. 1. Map of the Schelde estuary indicating the position of the sampling sites with black points. The grey arrows indicate the position of upper limit of tidal influence.

Fig. 2 .

 2 Fig. 2. Concentrations of chlorophyll a (mgl ÿ1 ) in the different treatments of the six experiments at the end of the incubation period.The mesozooplankton species and densities used in the ''zoo1'' and ''zoo 2'' are presented in Table3. Error bars correspond to the standard deviation. The p-value of ANOVA analyses comparing the different treatments is shown above the bars.

Fig. 3 .

 3 Fig. 3. Comparison of phytoplankton community composition at the end of the experiment in the !30 and !200 mm treatments.

:

  PZðP t ÿ P o Þ=lnðP t =P o Þ where P t is Table 1 Initial matrix with accessory pigments to chlorophyll a ratios in the major algal groups used in the CHEMTAX analyses

	the final predator density and P o is the initial predator
	density.
		Peridinin	Fucoxanthin	Diatoxanthin	Alloxanthin	Lutein	Zeaxanthin	Echinenone	Chlorophyll b
				diadinoxanthin
	Chlorophytes	0	0	0	0	0.162	0.025	0	0.229
	Cryptophytes	0	0	0	0.212	0	0	0	0
	Cyanophytes	0	0	0	0	0	0.036	0.085	0
	Diatoms	0	0.701	0.160	0	0	0	0	0
	Dinophytes	0.760	0	0.302	0	0	0	0	0
	Euglenophytes	0	0	0.333	0	0	0	0	0.372

Table 2

 2 Environmental conditions and phytoplankton and zooplankton biomass or abundance and community composition at the sampling sites at the time of the experiments. n.d. indicates that no data were collected and e indicates zero abundance or biomass

		Spring			Summer
		Gent	Dendermonde	Antwerpen	Gent	Dendermonde	Antwerpen
	Abiotic factors
	T ( C)	9.47	9.45	9.54	23.7	23.1	21.51
	Salinity	0.35	0.34	0.43	0.36	0.34	1.75
	ph	9.58	7.76	7.64	7.37	7.43	7.53
	O 2 (%)	82	65	35	49	41	22
	Phytoplankton
	Chl a (mgl ÿ1 )	92.2	8.7	2.9	28.8	214.9	12.9
	Diatoms (%)	78	79	27	35	89	43
	Chlorophytes (%)	4	8	37	58	7	41
	Euglenophytes (%)	11	3	18	1	0	5
	Dinoflagellates (%)	6	4	0	1	0	0
	Cryptophytes (%)	1	4	9	1	3	7
	Cyanophytes (%)	1	1	9	4	0	5
	Microzooplankton
	Rotifers (ind. l ÿ1 )	1157	191	860	1777	1433	796
	Brachionus calyciflorus (%)	53	31	33	34	1	1
	Brachionus angularis (%)	5	6	2	18	15	3
	Polyarthra sp. (%)	11	7	7	0	9	0
	Syncheata sp. (%)	5	11	35	1	3	18
	Trichocerca sp. (%)	0	0	0	17	55	74
	Other rotifers (%)	26	45	23	30	17	4
	Copepod nauplii (ind. l ÿ1 )	e	9.5	140	e	190	7
	Ciliates (ind. ml ÿ1 )	n.d.	80.8	46.5	75.4	55.3	31.7
	Mesozooplankton (ind. l ÿ1 )
	Acanthocyclops robustus	ee	e	0.2	6.9	e
	Chydorus sphaericus	0.1	e	0.5	ee	e
	Cyclops vicinus	0.4	0.5	4.1	ee	e
	Daphnia pulex	ee	e	ee	0.2
	Daphnia magna	ee	e	ee	0.2
	Eurytemora affinis	ee	4	ee	1.5
	Moina affinis	ee	e	0.8	ee

Table 3

 3 Comparison of densities of potential phytoplankton grazers in the !30 mm and !200 mm filtrates. The two values separated by a hyphen represent densities measured at the start and at the end of the experiments, respectively. The p-level resulting from a one-way ANOVA test comparing densities of grazers in the 30 mm and 200 mm is given for each experiment. n.d. indicates that no data were collected and e indicates zero abundance

		Spring			Summer
		Gent	Dendermonde	Antwerpen	Gent	Dendermonde	Antwerpen
	Ciliates (cells ml ÿ1 )
	30 mm	n.d.	91e83	57e193	70e288	57e98	28e124
	200 mm	n.d.	81e81	46e137	75e241	55e74	32e111
	ANOVA p-level	e	0.566	0.361	0.541	0.394	0.948
	Rotifers (ind. l ÿ1 )
	30 mm	117en.d.	10e47	n.d.en.d.	107e410	n.d.en.d.	360e140
	200 mm	1157e1693	191e843	860e550	1777e1720	1433e2893	797e610
	ANOVA p-level	!0.001	0.008	e	!0.001	e	!0.001
	Copepod nauplii (ind. l ÿ1 )
	30 mm	1.5en.d.	0e0	n.d.en.d.	0e0	n.d.en.d.	0e0
	200 mm2 0 e16.7	9.5-0	140e107	3.3e27	190e220	6.5e10
	ANOVA p-level	ee	e	e	e	e
	Mesozooplankton (ind. l ÿ1 )
	30 mm0 e00 e00 e00 e00 e00 e0
	200 mm0 e01 0 e21	0e00 e00 e00 e0
	Zooplankton 1	Chydorus (20) Eurytemora (20) Eurytemora (20) Moina (20)	Acanthocyclops (20) Eurytemora (20)
	Zooplankton 2	Cyclops (20)	Cyclops (20)	Cyclops (10)	Acanthocylops (40) Acanthocyclops (40) Daphnia (12)

Table 4

 4 Mean rotifer abundance, contribution of rotifers to combined abundance of rotifers and copepod nauplii, microzooplankton community grazing rate, fraction of initial phytoplankton biomass grazed and estimated individual filtration rates for rotifers (estimated from microzooplankton community grazing rate and rotifer abundance). Data are presented only for the experiments where microzooplankton exerted a significant grazing pressure on phytoplankton

	Spring			Summer
	Gent	Dendermonde	Antwerpen	Gent	Dendermonde

Acknowledgements

The research presented in this paper was carried out in the framework of the OMES project ('Onderzoek naar de Milieu-Effecten van het Sigmaplan') coordinated by Prof. Patrick Meire. Marie Lionard was financially supported by the Belgian Federal Science Policy Office (SiSCO project, contract nr. EV/11/17A). We thank J.P. Descy for assistance with the CHEMTAX analyses. We are also indebted to D. Van Gansbeke for technical assistance during HPLC analyses.