Ayodele Adessina

Ben Fraj

Jean-François Barthélémy

Camille Chateau

Denis Garnier

Experimental and micromechanical investigation on the mechanical and durability properties of recycled aggregates concrete

Keywords: Recycled aggregates concrete, elasticity, chloride diffusion, indentation, micromechanics

In this work, we conducted an experimental and micromechanical investigation on the mechanical and chloride diffusion properties of recycled aggregates concrete (RAC). Due to the composite aspect of the recycled concrete aggregates (RCA), their impact on the properties of concretes is first evaluated by conducting an experimental campaign and further numerically modeled using micromechanical tools. Local mechanical properties of phases such as the attached mortar, the interfacial transition zones (ITZ) and the aggregates are also investigated by means of indentation tests at nano and microscale. Finally, experimentally informed multi scale model is established and the overall elastic modulus and chloride diffusion coefficient of concretes (with different rates of RCA) are computed and compared to experimental results at macroscopic scale for discussion. The established model provides a predictive tool for the mechanical and chloride diffusion properties of RAC.

Introduction

The increasing and unsustainable consumption of natural resources as well as the excessive production of waste from construction and demolition are an environmental and economical challenges. Indeed, as the rate of demolition is still increasing and the supply of suitable natural aggregates is rapidly dwindling due to their over-exploitation, it is essential to effectively reuse demolition waste in order to conserve natural resources. Moreover, the use of recycled aggregates (as an alternative Email address: ayodele.adessina@cerema.fr (Ayodele Adessina) for natural aggregates) is known to be environmentally friendly, since it decreases the delivery distance of aggregates [START_REF] Fraj | Concrete based on recycled aggregates -recycling and environmental analysis: A case study of paris' region[END_REF]. First, most of the studies on the mechanical properties of concretes containing RCA point out the fact that, the recycled aggregate concretes exhibits weakened mechanical properties compared to the conventional concretes [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF][START_REF] De Juan | Study on the influence of attached mortar content on the properties of recycled concrete aggregate[END_REF][START_REF] Padmini | Influence of parent concrete on the properties of recycled aggregate concrete[END_REF][START_REF] Abbas | Durability of recycled aggregate concrete designed with equivalent volume method[END_REF]. Accordingly, mechanical properties such as the compressive strength, the elastic moduli and the tensile strength of recycled concretes (RAC) are found to depend on the amount of RCA in the microstructure [START_REF] Padmini | Influence of parent concrete on the properties of recycled aggregate concrete[END_REF], apart from other mixing parameters such the water to binder ratio. Indeed, the numerous interfacial transition zones denoted ITZ (with high level of porosity [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF]) and the weakened properties of the attached mortar are known as the main factors justifying the reduced mechanical properties of the RAC. Furthermore, Padmini et al. [START_REF] Padmini | Influence of parent concrete on the properties of recycled aggregate concrete[END_REF], when investigating the relationship between the quality of the 'parent concrete' (from which the recycled aggregates are extracted) and the mechanical properties of the resulting RAC, show that the properties of the latter are entirely related to parameters such as the physical and mechanical properties of the parent concrete and the mixing proportions of the concrete content (water to binder ratio for instance). As for the mechanical properties of the individual phases such as the cement paste and the ITZ, nanoindentation tests are successfully conducted on this phases as reported in recent works [START_REF] Xiao | Properties of interfacial transition zones in recycled aggregate concrete tested by nanoindentation[END_REF][START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF].

On the other hand, the durability properties of concretes are also affected by the replacement of natural aggregates by the RCA. Therefore, the chloride diffusion coefficient of RAC is found to be higher than that of the conventional concretes [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF]. This aspect is explained by the high porosity of RCA leading the resulting recycled concretes to be more permeable than natural concretes with the same water to binder ratio. This argument is also used to explain the important carbonation depth measured in RAC [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF][START_REF] Abbas | Durability of recycled aggregate concrete designed with equivalent volume method[END_REF]. However, in a recent work, Thomas et al. [START_REF] Thomas | Durability of recycled aggregate concrete[END_REF] show that, durability properties of recycled concretes can be improved by the adjustment of the water/cement ratio since for relatively reduced water/cement ratio, the matrix (herein the mortar) is less porous and therefore compensates the high porosity of the RCA.

In the framework of micromechanical investigation of the properties of cement based materials, concretes are generally considered as three phase materials at mesoscale [START_REF] Nilsen | Concrete: A three phase material[END_REF][START_REF] Ghorbanbeigi | A micromechanics-based model for concrete materials subjected to carbonation[END_REF][START_REF] Shen | A micromechanical study of drying and carbonation effects in cement-based materials[END_REF]. Therefore, the microstructure of the latter is assumed to be made up of matrix (mortar) embedding inclusions with interfaces (aggregates surrounded by interfacial transition zones (ITZ)) at mesoscale. Consequently, the effective properties (mechanical and durability) of concretes are derived from the available information on the microstructure at each specific level (volume fraction, properties of phases, size,...) [START_REF] Ungar | Multiscale Modeling of Concrete. From Mesoscale to Macroscale[END_REF]. The particular case of RAC introduces additional parameters to be considered. In fact, recycled aggregates are composite materials containing coarse aggregates, old and new ITZ, associated with the old or attached mortar [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF][START_REF] Padmini | Influence of parent concrete on the properties of recycled aggregate concrete[END_REF] (Fig. 1). Although intensive works have been conducted in last decades to understand and to predict the properties of RAC, questions still arise about how does the microstructure of RAC influences the observed macroscopic behavior. This works seeks to investigate, at different scales, the properties of high-performance recycled aggregate concretes, in order to establish a predictive micromechanical model for macroscopic effective properties. For this purpose, the adopted procedure is organized into three parts :

• The first part is devoted to the quantification of the impact of a progressive replacement of NA by RCA, on the mechanical and durability properties of RAC. In this part, specimen of recycled concretes are fabricated, submitted to mechanical and durability tests (compressive strength, elastic moduli, carbonation, chloride migration) and the results are presented for discussion.

• The second part deals with the relationship between the macroscopic behavior of RAC and the microstructural properties of individual phases (aggregates, interfacial transition zones, attached mortar). For this purpose, local mechanical properties of the phases (hardness, elastic modulus, volume fractions and distribution) are characterized using indentation tests at nano and micro scale, combined with optical and Atomique Force Microscopy observations .

• The third part addresses the modeling of the macroscopic behavior of RAC using multi scale approach. Results collected on the microstructure of the RAC (in section 3) are used as input information for the micromechanical based models. Effective elastic modulus and chloride diffusion coefficient are predicted for different replacement rates and the results are compared to those obtained at macroscopic scale (in section 2). The purpose of this part is to establish predictive models efficient to estimate the macroscopic behavior of RAC.

The paper is organized as follow : the section 2 is devoted to the experimental campaign at macroscopic scale (method, material, tests and results) whereas section 3 deals with the characterization of the microstructure (the indentation test at nano and microscale for different phases (aggregates, attached mortar, ITZ)). Finally, section 4 and 5 present the modeling of the elastic modulus and the chloride diffusion problem of RAC with different volume fractions of RCA.

Results of the models are compared to experimental data for discussion.

Experimental study of the mechanical and durability properties of recycled aggregates concrete

Materials

For the preparation of the concretes, ordinary portland cement (CEM I 52.5N PM ES) from Leteil plant is used for the study. The natural aggregates are calcareous aggregates (grading 4/20 mm) associated with the fine aggregates (sand 0/4 mm). The recycled aggregates used in the experimental campaign are extracted from the demolishing process of a pile [START_REF] Fraj | Concrete based on recycled aggregates -recycling and environmental analysis: A case study of paris' region[END_REF] and are classified as aggregates of type 1 according to the standard NF EN 933-1 [START_REF]Tests for geometrical properties of aggregates -Part 11 : Classification test for the constituents of coarse recycled aggregate[END_REF]. The physical and mechanical properties of the aggregates are resumed in

Mix proportion

Due to the high water absorption of the RCAs, and in order to avoid any disturbance in the hydration process, the recycled coarse aggregates were presoaked 24 hours before mixing.

Consequently, when substituting the natural aggregates by the recycled ones, some adjustments in concrete dosage are necessary as regards the volume compensation and presoaking water for recycled aggregates. Therefore, the necessary volume of water is calculated by taking into account the water absorption coefficient of the RCAs and the volume of super-plasticizer as reported in

Preparation of the specimens

The preparation of all the mixes was conducted with concrete mixer of 80 litres. The sand, the cement, and the coarse aggregates were placed and dry mixed for about 2 min before water was added. After 5 min of mixing, the slump test was run in order to determine the workability of the obtained concrete (Table (3)). Thereafter, the mixture was casted in cylindrical specimens 110 mm × 220 mm and vibrated. Finally, the specimens were demoulded after 24 hours and were cured in water at 20˚C until the different testing days (at 28 and 90 days).

Tests and results

The following section presents the results of the tests conducted on the concretes with different replacement rates of RCA at fresh and hardened states. It helps to quantify the impact of the RCA on the mechanical and durability properties of RC.

Workability and density

The slump of the fresh concrete is measured according to the standard the decrease of the concrete density with increasing volume of RCA. This reflects the impact of the density of the recycled aggregates on that of RCs especially when their volume fractions increases.

Compressive strength and elastic modulus

On the test days (28 and 90 days), the specimens were removed from water and their surfaces get prepared (in order to obtain perfectly smooth and parallel surfaces). Thus, tests are conducted according to the standards NF EN 12390 -3 [START_REF]Testing hardened concrete -Part 3 : Compressive strength of test specimens[END_REF], NF EN 12390 -13 [START_REF]Testing hardened concrete -Part 13 : Elastic modulus of test specimens[END_REF] in order to evaluate,respectively, the compressive strength and the elastic modulus of concretes with different replacement rates. For each formula, the results are obtained by averaging results of at least three tests. First, as shown in Fig. 2, the compressive strength decreases for increasing replacement rates of natural aggregates by the recycled ones. According to the results, the total replacement of the NA par RCA reduces the compressive strength up to respectively 16% and 12% at 28 and 90 days. This reduction of the compressive strength is quite consistent with other reports in the literature [START_REF] Fraj | Concrete based on recycled aggregates -recycling and environmental analysis: A case study of paris' region[END_REF][START_REF] Wagih | Recycled construction and demolition concrete waste as aggregate for structural concrete[END_REF] and may be explained by the poor mechanical properties of the attached mortar in recycled aggregates [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF]. In addition, since the recycled aggregates are porous materials, they influence the porosity of the recycled concretes and consequently the compressive strength of the formulas. Moreover, the angular shape of the recycled aggregates can also explain this loss in the compressive strength since this aspect disables optimum packing of aggregates and consequently induces large amount of voids in the concretes [START_REF] Agamuthu | Challenges in sustainable management of construction and demolition waste[END_REF]. However, results presented in Fig. 2 show that, up to the replacement rate of 20%, the compressive strength does not exhibit significant variation.

This aspect is probably due to the fact that, the 20% of volume replacement rate corresponds to a small mass substitution rate of NA by RCA and the latter is insufficient to induce significant weak zones in the microstructure.

On the other hand, a decrease of 20% and 22% in the elastic moduli is observed for a total replacement of the NA by the RCA (Fig. 3) at 28 and 90 days. These results are in accordance with those reported in the literature [START_REF] Wagih | Recycled construction and demolition concrete waste as aggregate for structural concrete[END_REF][START_REF] Silva | Establishing a relationship between modulus of elasticity and compressive strength of recycled aggregate concrete[END_REF]. The decrease in the elastic modulus of concrete is intrinsically associated to parameters such as the volumetric fractions, the density, and the Young modulus of the recycled aggregates and the interfacial transition zones. These latter are known as porous zones with poor mechanical properties [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF]. Consequently, the presence of many interfacial transition zones in RC compared to conventional concretes may explain the difference in the elastic modulus of recycled aggregates concrete. Furthermore, these results may be explained by the aggregates deformations as reported in [START_REF] Agamuthu | Challenges in sustainable management of construction and demolition waste[END_REF][START_REF] Mehta | Concrete : Structure, properties and materials[END_REF]. Deformation of aggregates are mainly related to their porosity and in a lesser degree to their grading, texture and mineralogical composition.

Durability properties

This part resumes the results of the durability tests conducted on the specimen under study at 90 days (when the microstructure is relatively stable). Water accessible porosity, rapid chloride diffusion and carbonation tests are carried out on the different formulas, according to the associated standards.

Water accessible porosity

For this test, cylindrical specimens (diameter : 110 mm and 50 mm thick) were submitted to test according to the standard NF P18 -459 [START_REF]Testing hardened concrete -Testing porosity and density[END_REF]. Two specimens are tested for each replacement rate and the average of the results considered as the corresponding property. The results (Fig. 4)

show the variation of the water accessible porosity versus the replacement rate. Obviously, the porosity increases with the quantity of the recycled aggregates included in the microstructure.

This aspect is first related to the porosity of the recycled aggregates (since these latter exhibit

Carbonation

Similarly to the case of water accessible porosity, the 50 mm thick cylindrical specimen are submitted to carbonation test according to the slightly modified standard recommendations with 50% of carbon dioxide instead. The results (Fig. 5) show the increase of the carbonation depth with quantity of the recycled aggregates in the content. This observation is explained by the porosity of the recycled aggregates associated with the fact that the introduced recycled aggregates are most of the time already carbonated.

Chloride penetration

After 90 days when the microstructure is almost stable, the 50 mm thick specimen are submitted to chloride penetration test according to standard NF EN 12390-11 [START_REF]Testing hardened concrete-Determination of the chloride resistance of concrete ; unidirectional diffusion[END_REF]. The results shown in Fig. 6 represent the temporal variation of the chloride cumulative concentration. Obviously, the 4 indicate that the new mortar presents a diffusion coefficient greater than that of the reconstructed attached mortar. This result is first related to the content of the reconstructed attached mortar (made up of CEM III cement) and further due to the fact that the reconstructed mortar is not damaged contrary to the real attached mortar in the RCA. Indeed, as shown in Fig. 8, the crushing process induces micro-cracks in the microstructure between the diffusion coefficients of respectively the new mortar and the reconstructed attached mortar (Table 4). Nevertheless, it is worth noticing that the real chloride diffusion coefficient of the attached mortar is expected to be greater than that of the reconstructed attached mortar due to the aforementioned effects (presence of the micro-cracks and interface effects). .

Phases New mortar Reconstructed attached mortar

Diffusion coefficient ×10 -12 (m 2 /s) 2.66 0.0164

Investigation on the local mechanical properties

In this part, multi scale indentation technique is used to investigate the mechanical properties of the phases in the microstructure of the RAC. The obtained results are first discussed and further used as input information of the multi scale models developed in the last part. Phases in the cement paste inside the interfacial transition zone are analyzed thanks to statistical indentation technique whereas a direct measurement is used to capture the overall properties of the aggregates and the attached mortar. The indentation depths will be discussed for each considered phase.

Sample preparation

For indentation tests, samples (20 mm × 20 mm × 10 mm) were cut with a diamond saw and embedded in ethanol solution for 48 hours in order to stop the hydration process of unhydrated clinker. Thereafter, the slices were molded in epoxy resin for 24 hours (when the epoxy gets hardened : see Fig. 12). In order to avoid any tilt or wobbling during the test, the faces of the enrobed samples were made parallel by grinding before the polishing. The latter was realized by using dry SiC abrasive papers (1200, 2000 and 4000 grit sizes) followed by the use of alcoholbased diamond suspensions of 3µm and 1µm grain sizes combined with an alcohol-based lubricant.

Similarly to [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF], a long polishing at 1 µm (6 hours) was necessary to get a smooth enough surface in the ITZ (see section 3.5). The studied samples were taken from two formulas, which were chosen according to the presence of the phase of interest (aggregates, ITZ and the old mortar). Therefore, C[60] was chosen because of the presence of the aforementioned zones within the microstructure (Fig. 11) whereas C[100] provided sufficient area for large indentation tests (micro indentation) with a reduced disturbance between neighbouring indents.

Indentation test

Indentation test consists of making contact between a sample (herein sample under study)

and an indenter tip of known geometry and mechanical properties. The experimental process is based on two phases : the loading phase (when the indenter is pressed against a specimen with increasing load ) and the unloading phase (characterized by a progressive decrease of the load over the sample).The exploitation of the recorded force-displacement curve (P-h) during the two phases helps to derive the mechanical properties of the specimen, which are related to parameters such as the projected contact area between the indenter and the sample surface and the maximum load.

M = √ π 2 S √ A c ; H = P max A c ( 1
)
where S = dP dh is the measured initial slope of the unloading branch of the P-h curve. Furthermore, A c , which accounts for the projected contact area of the indenter (on the sample surface), is expressed as function of the indentation depth and depends on the geometry of the indenter tip.

Using Oliver and Pharr model [START_REF] Oliver | An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[END_REF], the projected area reads : A c = 24.5h 2 c for perfect Berkovich tip, with h c accounting for the contact depth (Fig. 10). In the case of cylindrical tip, the projected area remains constant since the latter is not related to the contact depth : A c = πD 2 /4 (D is the diameter of the disc in contact with the sample).

Elastic modulus of the aggregates

Indentation of heterogeneous materials requires two different approaches according to the size and the distribution of the phases. The scale separation principle between the indentation depth and the typical size of the heterogeneities governs the measured response. As shown in Fig. 13.b, large indentation depth, compared to the heterogeneities length scale, is required to evaluate the effective behavior of a composite whereas indentation length is expected to be small (respecting scale separation principle [START_REF] Constantinides | Grid indentation analysis of composite microstructure and mechanics: Principles and validation[END_REF], Fig. 13.a) compared to the heterogeneities when investigating individual properties of the phases.

Constantinides et al. [START_REF] Constantinides | Grid indentation analysis of composite microstructure and mechanics: Principles and validation[END_REF] established the separation scale relation between the indentation depth and the characteristic size of the heterogeneities inside a composite through continuum indentation analysis :

d << h max ≤ D 10 ( 2
)
where d is the characteristic length scale of the heterogeneities within a phase, D is the typical In practice, a reduced number of indentation (typically 50 points) is necessary to stabilize the average indentation modulus (as shown by the standard deviation of the indentation modulus Fig. 18,19). In addition, lower indentation depths were tested and confirm that the chosen depth h max = 1000 nm is enough to capture the composite indentation modulus of the aggregates : its distribution is narrower and the mean value become independent from the maximum depth.

Finally, the found indentation modulus are in a good accordance with results presented in literature for calcareous and siliceous aggregates [START_REF] Chalhoub | Massifs rocheux : Homogénéisation et classification numériques[END_REF][START_REF] Mavko | The rock physics handbook. Tools for seismic analysis in porous media[END_REF].

Elastic properties of the attached mortar

The old or the attached mortar is part of the original concrete from which the RCAs are extracted. This phase is usually presented as one of the most damaged zone in the microstructure of RAC [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF][START_REF] Abbas | Durability of recycled aggregate concrete designed with equivalent volume method[END_REF][START_REF] Thomas | Modeling and simulation of cement hydration kinetics and microstructure development[END_REF]. In this approach, the old mortar is viewed as an heterogeneous medium which comprises matrix (cement paste) embedding fine aggregates (sand). The typical size of the latter is around D=500µm (Fig. [START_REF] Silva | Establishing a relationship between modulus of elasticity and compressive strength of recycled aggregate concrete[END_REF]). For indentation purpose, a microindenter with 6kN of maximum load provided with cylindrical tip (diameter of the contact disc : 1 mm) is used for the indentation sand grains in this zone (Fig. 21). A grid of ten indents is realized on each specimen (Fig. 20)

and the indentation modulus is obtained by averaging the results of tests conducted on the grid.

The choice of the number of indents is guided by the small dispersion of the results. Finally, the average of the realized indentation tests on the two specimens under study leads to the indentation modulus of 16.99 ± 2.85 GPa for the attached mortar. By assuming a Poisson's ratio of 0. test gives access to an estimation of the elastic modulus of the old mortar which is difficult to measure due to the configuration of the material under study.

Elastic properties of the interfacial transition zones (ITZ)

The ITZ plays the role of bridge between the aggregates and the mortar within the microstructure of concretes in general. As described in [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF][START_REF] Königsberger | Micromechanics of itz-aggregate interaction in concrete part i: Stress concentration[END_REF][START_REF] Scrivener | The percolation of pore space in the cement paste/aggregate interfacial zone of concrete[END_REF], this phase is made up of highly hydrated cement paste and is consequently more porous than other phases in the microstructure. Topics related to the precise mechanism of formation of this zone are still under studies [START_REF] Barnes | The contact zone between portland cement paste and glass "aggregate" surfaces[END_REF][START_REF] Hashin | An inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste[END_REF][START_REF] Zimbelmann | A contribution to the problem of cement-aggregate bond[END_REF].

As for the typical thickness of this zone, it is reported to be around 50µm by Xiao et al. [START_REF] Xiao | Properties of interfacial transition zones in recycled aggregate concrete tested by nanoindentation[END_REF]. In this study, for the sake of simplicity and for modeling convenience, one assumed the ITZ as a cement paste made zone surrounding the aggregates with a constant thickness (50µm, Fig. 22) and without any gradient of property. In order to measure the homogenized properties of the cement paste, a typical indentation depth of at least 10µm should be necessary [START_REF] Liang | Multiscale modeling elastic properties of cement-based materials considering imperfect interface effect[END_REF]. However, the size of the imprint corresponding to that indentation depth is too large (l 7h = 70µm) compared to the thickness of the ITZ and the results could be perturbed by the neighbouring phases (aggregates and mortar). Consequently, nanoindentation test (implying small indentation depth) is conducted on the cement paste of the ITZ (from concrete specimen of 28 and 90 days) in order to investigate the mechanical properties of the hydrate phases. The typical range covered by the nanoindentation test is between 6 nm and 2µm [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF][START_REF] Constantinides | Grid indentation analysis of composite microstructure and mechanics: Principles and validation[END_REF]. This range covers the characteristic length of the encountered phases in the cement paste at nanoscale. Furthermore, considering Constantinides rule [START_REF] Constantinides | Grid indentation analysis of composite microstructure and mechanics: Principles and validation[END_REF] (equation 2), the corresponding indentation depth is set to h max = 200 nm similarly to nanoindentation tests conducted on cement paste by Vandamme et al. [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF]. The expected phases are : LD CSH, HD CSH, UHD CSH, and unhydrated cement. Statistical grid indentation technique is used to extract the mechanical properties of the aforementioned phases similarly to [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF]. Since significant contrast is not expected between HD CSH and UHD CSH phases, we associated these two phases in one denoted HD(UHD) CSH. Before the test, the roughness at the surface of the specimen under study are reduced thanks to specific polishing process described in [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF][START_REF] Miller | Surface roughness criteria for cement paste nanoindentation[END_REF]. The typical roughness obtained at the surface of the specimen is around 40 nm in average (Fig. 23) fulfilling Miller criteria [START_REF] Miller | Surface roughness criteria for cement paste nanoindentation[END_REF]. Finally, the specimen of 28 and 90 days are submitted to tests and the properties of the phases in the ITZ found at different ages through deconvolution technique [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF][START_REF] Sorelli | The nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques[END_REF][START_REF] Constantinides | The nanogranular nature of C S H[END_REF][START_REF] Constantinides | Invariant mechanical properties of calcium-silicate-hydrates (c-s-h) in cement-based materials : instrumented nanoindentation and microporomechanical modeling[END_REF]

Results and discussion

Given the multiphase nature of the cement paste within the ITZ, a large array of nanoindentation test is carried out and the results are analyzed statistically. In the process, each indentation point is considered as an independent event for which the corresponding mechanical property is viewed as random variable. Therefore, grids of typically 400 points are analyzed and the results carried out thanks to deconvolution technique. Indeed, the latter consists in fitting the experimental cumulative distribution functions (of indentation modulus and hardness both), by a sum of n theoretical Gaussian distributions. A detailed description of this technique is presented in [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF][START_REF] Sorelli | The nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques[END_REF]. After the deconvolution, one gets access to the mechanical properties of each phases (herein indentation modulus and hardness) with their volume fractions and attributed standard deviations as resumed in Fig. 24,25,26,27 and Table 5.

• Phase 1 : this phase is the less rigid among all the identified phases. Compared to data available in the literature, it can be assimilated to low density hydrates phase (LD CSH). The latter is reported in [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF][START_REF] Sorelli | The nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques[END_REF] with the following mechanical properties (M= 22.5 ± 5.0 GPa ; H= 0.61 ± 0.17 GPa). Additionally, the results indicate that the volume fraction associated to this phase is around 0.63 at 28 days and 0.34 at 90 days. This variation of the volume fraction is probably related to the densification of the hydrate phases transforming the low density hydrates to more densified ones.

• Phase 2 : mechanical properties of this phase are between that of HD CSH (M= 30.4 ± 2.09

GPa ; H= 0.92 ± 0.10 GPa) and UHD CSH (M= 40, 9 ± 7, 7 GPa ; H= 1, 46 ± 0, 46 GPa) [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF]. In a recent work, Chen et al. [START_REF] Chen | A coupled nanoindentation/SEM-EDS study on low water/cement ratio Portland cement paste: Evidence for C-S-H/Ca(OH)2 nanocomposites[END_REF] described the UHD CSH phase as a nanocomposite phase made with hydrates foam and portlandite cristals. Even though, the nature of this phase is still under discussion in the literature, we assume that, the measured values correspond to the mechanical properties of composite phase (which comprises the two types of hydrates HD and UHD CSH).

Consequently, this phase is denoted HD(UHD) CSH with a volume fraction of 0. • Phase 3 : this phase represents the most rigid phase identified and corresponds (according to available data in the literature M= 93.4 ± 44.8 GPa ; H= 6.13 ± 4.22 GPa [START_REF] Vandamme | Nanogranular packing of c-s-h at substochiometric conditions[END_REF]) to unhydrated cement. The latter is also found to represent 14 and 13% at respectively 28 and 90 days.

Micromechanical modeling

In this part, we provide a predicting model accounting for the elastic modulus and the chloride diffusion properties of recycled aggregate concretes, based on the available information on the microstructure (collected in sections 2 and 3). For this purpose, the adopted micromechanical approach is based on the multi-scale characterization of heterogeneous materials (case of cementitious materials). Therefore, a Representative Elementary Volume (REV) is defined and a simplified description of the microstructure is proposed in Fig. 28. Finally, the homogenized elastic modulus and the chloride diffusion coefficient are estimated and the results compared to experimental data for discussion.

Simplified representation of the microstructure

The representation associated to the recycled concrete microstructure comprises at the first scale, the mortar and the different aggregates. For the sake of simplicity and for modeling convenience, all the aggregates are considered as spherical inclusions surrounded by uniform layers of 50µm [START_REF] Xiao | Properties of interfacial transition zones in recycled aggregate concrete tested by nanoindentation[END_REF] thick representing the ITZs. The choice of this configuration is based on previous results on complex configurations representing the recycled aggregates [START_REF] Adessina | Effective elastic properties of materials with inclusions of complex structure[END_REF]. These results indicate that, due to the relatively weak contrast between the involved phases, the impact of the distribution of phases within the recycled aggregate is of rather minor importance. Furthermore, the typical ratio of size between the aggregates and the ITZs thickness is set to e/R ∼ 1/100 where e accounts for the thickness of the interphase and R represents the radius of the spherical inclusion (section 2) . In the same frame, we assume a perfect bonding between the attached mortar and the old aggregates and the detailed description of the microstructure in study is assumed to be made up of three scales as presented in the Fig. 28. Moreover, the mechanical properties of phases described in the different scales are extracted from indentation and macroscopic tests.

• Scale I : (10 -2 m∼ 10 -1 m)

This level concerns the first step in the multi scale description of the microstructure of RAC.

The latter is assumed to be made up of natural and recycled aggregates (represented respectively by homogeneous and composite inclusions) embedded in homogeneous matrix (herein the mortar which mechanical properties are obtained through macroscopic tests). Moreover, for the sake of Therefore, considering the REV at scale I (Fig. 28), made up of N morphological representative patterns (MRP) [START_REF] Zaoui | Structural Morphology and Constitutive Behaviour of Microheterogeneous Materials[END_REF], the effective stiffness tensor reads :

C ef f =   p f p B p   :   p f p A p   -1 (3)
where f p accounts for the volume fraction of the morphological representative pattern 'p' and A p and B p are fourth order tensors obtained thanks to the Eshelby problem with E ∞ as the imposed macroscopic strain at infinity. Consequently, A p and B p satisfy the relations :

< ε > p = A p : E ∞ ; < σ > p = B p : E ∞ (4)
• Scale II (10 -6 m∼ 10 -4 m)

This scale refers to the cement paste matrix inside the ITZ as shown in Fig. 28. The ITZ is assumed to be made up of low density hydrates foam embedding spherical composite inclusions which consists of unhydrated clinker surrounded by high density hydrates. Due to the matrixinclusion aspect of the microstructure at this specific level, Mori-Tanaka estimate is used to derive the homogeneous elastic properties of the ITZ. The effective stiffness tensor of the REV at this scale is derived according to the equation 3.

• Scale III (10 -7 m∼ 10 -6 m)

In this step, the low density hydrates foam of scale II is regarded as porous media made up of low density hydrates (represented as needle-shape phase exhibiting isotropically distributed orientations [START_REF] Pichler | Upscaling quasi-brittle strength of cement paste and mortar : A multi-scale engineering mechanics model[END_REF] ) and capillary pores considered as spherical inclusions. Furthermore, as suggested in [START_REF] Oh | Prediction of diffusivity of concrete based on simple analytic equations[END_REF][START_REF] Gao | The itz microstructure, thickness and porosity in blended cementitious composite: Effects of curing age, water to binder ratio and aggregate content[END_REF][START_REF] Patel | Diffusivity of saturated ordinary portland cement-based materials: A critical review of experimental and analytical modelling approaches[END_REF] one considers the hypothesis of a ratio 3/2 between the porosity of the ITZ and that of the neighbouring cement paste. Consequently, by using Powers model [START_REF] Powers | Studies of the physical properties of hardened portland cement paste[END_REF] one writes :

f IT Z cp = 3(e/c -0.36α) 2(e/c + 0.32) (5)
Considering the mutual interaction of the considered phases (as in polycristal), the use the selfconsistent scheme is appropriate for the effective stiffness tensor of the REV at this specific scale.

Therefore one writes :

C ef f =   f hyd C hyd : 2π 0 π 0   I + P hyd (θ, ϕ) : (C hyd -C ef f )   -1 sinθdθdϕ 4π   :   f cp   I -P cp : C ef f   -1 + f hyd 2π 0 π 0   I + P hyd (θ, ϕ) : (C hyd -C ef f )   -1 sinθdθdϕ 4π   -1 (6)
where f hyd is the volume of the low density hydrates considered at scale III (Fig. 28) ; C hyd accounts for the fourth order stiffness tensor of LD CSH (Table 5) and P cp , P hyd are Hill tensors of respectively the spherical capillary pores and the needle shape low density hydrates expressed in [START_REF] Pichler | Spherical and acicular representation of hydrates in a micromechanical model for cement paste: prediction of early-age elasticity and strength[END_REF].

The elastic properties of the ITZ are obtained considering the multi scale behavior of the phases present in the microstructure. Furthermore, in order to evaluate the efficiency of the approach, first, additional experiments are performed on a sample of pure cement paste. Secondly, nanoindentation results are combined with parameters such as the w/c ratio and the degree of hydration (obtained through thermogravimetric analysis TGA [START_REF] Byfors | Plain concrete at early ages[END_REF]) and used as input parameter for the multiscale model. Results presented in Table 6, show that the model provides a good estimate of the elastic modulus of the cement paste. Based on these results, the predicted elastic modulus of the ITZ can be considered as reliable results concerning the mechanical properties of the ITZ.

Homogenized properties of the REV

Considering the described microstructure associated to the REV of RAC (Fig. 28 : scale I), the effective elastic properties are deduced from the solution of the following problem posed on the representative volume element :

                       div σ(x) = 0 (V ) (a) σ(x) = C(x) : ε(x) (V ) (b) ε = 1 2 (grad ξ + t grad ξ) (V ) (c) ξ(x) = E.x (∂V ) (d) (7)
where (7.a) stands for the equilibrium equation at the microscopic scale (σ(x) is the stress field),(7.b) accounts for the linear elastic behavior of the phases (C is the fourth order rigidity tensor) and ε is the strain field. The latter is related to the displacement ξ(x) field by the relation expressed in the (7.c). Finally, the homogeneous macroscopic strain E imposed at the boundary of the REV is expressed in (7.d). The latter implies the average rule < ε > V = E. Considering the relation 3, the effective stiffness tensor of the REV is rewritten in the form :

C =   (1 -f )C m + f (1 -λ)B GN + f λB GR   :   (1 -f )I + f (1 -λ)A GN + f λA GR   -1
B GN , B GR are related respectively to the natural aggregates and the recycled aggregates(deduced from the generalized Eshelby problem [START_REF] Herve | n-layered inclusion-based micromechanical modelling[END_REF]) ; C m is the stiffness tensor of the mortar. As regards parameters λ and f , they account for the volume fractions of respectively the recycled and natural aggregates. [START_REF] Thomas | Durability of recycled aggregate concrete[END_REF] Considering the absorption coefficients of the listed phases (Table 1)

Input information of the model

w recy.aggreg. = 5.3%, w aggreg = 1.7%, w old mortar = 9.5 -11%

one founds :

0.53 ≤ ϕ ≤ 0.61 (10)
Therefore, the volume fraction of the attached mortar is to be around 39 and 47% and is in good accordance with data available in the literature ( [START_REF] De Juan | Study on the influence of attached mortar content on the properties of recycled concrete aggregate[END_REF][START_REF] Braymand | Separation and quantification of attached mortar in recycled concrete aggregates[END_REF][START_REF] Etxeberria | Influence of amount of recycled coarse aggregates and production process on properties of recycled aggregate concrete[END_REF]).

Results and discussion

We compute the effective Young modulus with respect to the replacement rate of natural aggregates by the recycled ones. The properties attributed to each phase is extracted from the available information on the microstructure and resumed in the above paragraphs. Fig. 29 shows the compa- rison of the results between the model and the experimental data. Obviously, the predictions of the established models are in the general trend of the experimental results for different replacement rate NA by RCA. Indeed, the decreasing behavior of the effective elastic modulus (for increasing content of RCA) is probably due to the degraded properties of the old mortar associated to the high number of interfacial transition zones (ITZ). This aspect is also shown in the modeling thanks to the contrast between phases in the composite inclusions representing the recycled aggregates.

Consequently, the increase of the volume fraction of the latter inclusions affects the effective elastic modulus of the REV and confirms experimental observations.

On the other hand, the time dependency of the elastic modulus is also predicted by the model at 28 and 90 days. Although macroscopic tests on the mortar (at 28 and 90 days) are directly used as input information in the model, the latter expresses a clear difference between the elastic modulus of the recycled concretes at 28 and 90 days. This particular aspect demonstrates the impact of an evolving elastic properties of individual phases (herein the new mortar) on the overall behavior of the REV as predicted by the model and confirmed by the experimental data.

Effective chloride diffusion properties

In this part, the effective chloride diffusion coefficient of the REV (Fig. 28) is computed thanks to a multi scale approach. Macroscopic tests are first conducted on the different concretes and the new mortar similarly to the elastic part. As regard the diffusion properties of the attached mortar and the ITZ, they are approximated through optimization process. The typical representation of the microstructure is identical to that presented in Fig. 28 with the new and old aggregates herein considered as no diffusive medium (D = 0). Only the scale I is considered in the homogenization process. Mori-Tanaka scheme is also used to derive the homogenized diffusion properties of the RVE [START_REF] Dormieux | Microporomechanics[END_REF]. The problem posed on the REV is written in the form :

               divj(x) = 0 (V ) (a) j(x) = -D(x) • gradρ(x) (V ) (b) ρ(x) = H • x (∂V ) (c) (11)
where relations (a), (b) and (c) are respectively related to the mass balance equation, the Fick law and the uniform density gradient boundary condition (similarly to elasticity) [START_REF] Dormieux | Microporomechanics[END_REF] with ρ, j, H, D(x) accounting for respectively the solute concentration, the diffusion flux, the macro-scopic concentration gradient and the diffusion tensor. For the sake of simplicity, one denotes D 2 ,D IT Z , the diffusion tensor of respectively the attached or old mortar and ITZ ; all assumed as isotropic. The effective diffusion tensor is proportional to the second order unit tensor since the medium is considered as an isotropic material. Thus one writes

D hom =   p f p B p   •   p f p A p   -1 = D hom 1 (12)
with

< gradρ(x) > p = A p • H ∞ ; < j > p = -B p • H ∞ (13)
where H ∞ is the imposed macroscopic gradient at infinity (in the generalized Eshelby problem in diffusion) [START_REF] Dormieux | Microporomechanics[END_REF] and 1 is the second order unit tensor. In the particular case of coated inclusions, the expressions of the concentration tensors are computed thanks to the approaches developed in [START_REF] Caré | Application of a n-phase model to the diffusion coefficient of chloride in mortar[END_REF][START_REF] Herve | Thermal and thermoelastic behaviour of multiply coated inclusion-reinforced composites[END_REF].

Input information

The input data for this part concerns the chloride diffusion coefficient of the new mortar as resumed in table 4. Additionally, chloride penetration test carried out on a reconstructed attached mortar is considered for further analysis (Table .4). An optimized algorithm based on a least square method is performed in order to identify the chloride diffusion coefficient of the attached mortar and the ITZ.

Results and discussion

As shown in Fig. 30, the Mori-Tanaka based model predicts with an acceptable accuracy, the increase of the chloride diffusion coefficient for different replacement rates. The best fit of the experimental results is obtained for D 2 = 4.43 × 10 -12 m 2 /s,D ITZ = 3.9 × 10 -11 m 2 /s. This results confirm the fact that the interfacial transition zone is probably the most diffusive phase inside the microstructure of RAC. This particular property is surely due to the important porosity of the ITZ as reported in the literature [START_REF] Otsuki | Influence of recycled aggregate on interfacial transition zone, strength,choride penetration and carbonatation of concrete[END_REF][START_REF] Oh | Prediction of diffusivity of concrete based on simple analytic equations[END_REF]. Moreover, the attached mortar exhibits higher chloride diffusion coefficient compare to the reconstructed mortar. This aspect is probably related to the presence of connected microcracks in the microstructure (induced by the crushing process). Indeed, the microcracks play the role of facilitating the transport of the chloride agent throughout the microstructure and consequently increase the chloride diffusion coefficient of this phase.

Fig. 1 :

 1 Fig. 1: Different phases in the microstructure of RAC

Fig. 2 :Fig. 3 :

 23 Fig. 2: Compressive strength for different replacement rates

Fig. 4 :

 4 Fig. 4: Water accessible porosity with different replacement rates

Fig. 5 :

 5 Fig. 5: Carbonation depth with different replacement rates

Fig. 6 : 7 :

 67 Fig. 6: Chloride cumulative concentration Fig. 7: Evolution of the chloride diffusion coefficient for different formulas of recycled concretes

Fig. 8 :

 8 Fig. 8: Typical example of micro-crack observed in the attached mortar

Fig. 9 :

 9 Fig. 9: Load and unloading profile

Fig. 11 :

 11 Fig. 11: Microstructure of a section of C[60] concrete with phases of interest.

Fig. 12 :

 12 Fig. 12: epoxy enrobed slice.

Fig. 13 :Fig. 14 :Fig. 15 :

 131415 Fig. 13: (a) :scale separation principle ; (b) : Direct measurement principle

Fig. 16 :Fig. 17 :

 1617 Fig. 16: An atomic resolution scanning probe microscopy image of a residual indent on a calcareous aggregate (natural) for different indentation depths h = 200, 500, 1000nm

Fig. 18 :Fig. 19 :Fig. 20 :

 181920 Fig. 18: Distribution (pdf) of the measured indentation modulus for calcareous aggregates

Fig. 21 :

 21 Fig. 21: Microstructure of the attached mortar showing the typical size of the sand grains and the imprint of the largest indentation depth (h=0.42 mm)

Fig. 22 :

 22 Fig. 22: Delimitation of the interfacial transition zone Fig. 23: Evolution of the roughness of the ITZ at 28 and 90 days (during the last time of the polishing process)

Fig. 24 :Fig. 25 :Fig. 26 :Fig. 27 :

 24252627 Fig. 24: Probability Density Function (PDF) of the indentation modulus (curves represented in blue are for individual phases)

Fig. 28 :

 28 Fig. 28: Simplified representation of the microstructure of RAC

Fig. 29 :

 29 Fig. 29: Evolution of the effective young modulus of concrete with different replacement rates at 28 and 90 days.

Fig. 30 : 6 Conclusion

 306 Fig. 30: Diffusion coefficient of RAC with different replacement rates (Obtained results for D 2 = 4.43 × 10 -12 m 2 /s,D ITZ = 3.9 × 10 -11 m 2

Table

Table 1 :

 1 . The parent concrete (from which the recycled

	Aggregates	Natural aggregates Recycled aggregates
	Grading(mm)	4/12	12/20	4/10	10/20
	Unit weight (g/cm 3 ) 2.65	2.72	2.26	2.5
	Water absorption(%) 0.7	0.6	5.3	5.5
	LA	23	22	32	35
	MDE	16	11	36	27

Physical and mechanical properties of the aggregates of interest (according to the standards NF EN 1097 -1, 2, 6

[START_REF]EN 1097-6 : Tests for mechanical and physical properties of aggregates -Part 6 : Determination of particle density and water absorption[END_REF][START_REF]EN 1097-2, Tests for mechanical and physical properties of aggregates -Part 2 : Methods for determination of resistance to fragmentation[END_REF]

). LA : Los Angeles coefficient, MDE : Micro Deval coefficient aggregates are extracted) is made with a CEM III 52.5L cement with a water/cement ratio of 0.43 and characterized by a compressive strength and elastic modulus of respectively 50.5 ± 1 MPa and 51 ± 1 GPa at 90 days (measured in laboratory on reconstructed concrete).

Table (

 (

	for different
	formulas of concretes. Apart from the natural concrete C[0] (without recycled aggregates), five other
	formulas of concretes were fabricated corresponding to 20, 40, 60, 80 and 100% of replacement rate
	in volume. The mixing proportions are summarized in Table 2.

[START_REF] Fraj | Concrete based on recycled aggregates -recycling and environmental analysis: A case study of paris' region[END_REF]

. The targeted concretes are high performance concretes made with recycled aggregates with a good workability (160-210 mm). The water / cement ratio was set to 0.42 for all the different formulas of concretes. The changing parameter was the replacement rate of natural aggregates by recycled ones. For the sake of simplicity, we adopted the notation C[replacement rate]

Table 2 :

 2 Mix proportion of the concrete (kg/m 3 ). NA : Natural aggregates.The super plasticizer used is the Master

	Mixture	C[0]	C[20]	C[40]	C[60]	C[80] C[100]
	Replacement rate (%)	0	20	40	60	80	100
	Cement			380
	Sand			867.8
	NA (4-12mm)	432	345.6 259.20 172.80 86.40	0
	RCA (4-12mm)	0	77.02 154.03 231.05 308.52 385.08
	NA (12-20mm)	561.2 448.96 336.72 224.48 112.24	0
	RCA (12-20mm)	0	99.63 199.26 298.89 398.52 498.14
	Effective water/cement ratio			0.42
	Super-plasticizer			2
	Glenium 671.

Table 3 :

 3 Physical properties of the studied concretes. Density (g/cm 3 ).

Table 4 :

 4 Diffusion coefficient of the new and the reconstructed attached mortar.

Table 5 :

 5 Mechanical properties of the hydrate phases identified in the ITZ at 28 and 90 days.

Table 6 :

 6 Elastic modulus of the cement paste and the ITZ (α is the degree of hydration of the cement paste and f cp accounts for the volume fraction of the capillary pores).

	Phases	Age (days)	α	f cp E(GPa) Model E(GPa) Macroscopic test
		28	0.85 0.15	20.57	21.98±1.56
	Cement paste
		90	0.94 0.11	24.01	22.54 ±1.4
		28	-	0.22	16.08	-
	ITZ
		90	-	0.16	19.95	-

Table 7

 7 summarizes the necessary data concerning the properties of the phases in the microstructure. The elastic modulus of the new mortar at 28 and 90 days are obtained through macroscopic tests . As regards the elastic properties of the attached mortar, the obtained results come from micro indentation test presented in the section 3 of the work. Furthermore, the average of the

	Phases	Elastic modulus (GPa)	Poisson ratio [30, 31]
	New Mortar (28 days)	31.7	0.2
	ITZ (28 days)	16.08	0.23
	New Mortar (90 days)	36	0.2
	ITZ (90 days)	19.95	0.23
	Attached mortar	16.31	0.2
	Old Aggregate(siliceous)	92.9	0.08
	New Aggregate(Calcareous)	68.81	0.32

Table 7 :

 7 Input information concerning the mechanical properties of phases in the microstructure volume fraction of the attached mortar (within the recycled aggregate) is found experimentally using the water absorption coefficients of respectively the recycled aggregates, the old aggregates and the recycled sand. Indeed, the latter is supposed to represent the attached mortar. Considering the aforementioned hypothesis, one writes the volumetric relationship between different parts in the recycled aggregate (with ϕ accounting for the volume fraction of the 'old natural' aggregate inside the recycled aggregate). w recy.aggreg. = ϕ × w aggreg + (1 -ϕ) × w old mortar

the model prediction so as the temporal variation of the elastic modulus (at 28 and 90 days). The chloride diffusion properties is also investigated in this work and the results show that optimization approach is efficient to evaluate parameter such as the diffusion coefficient of the ITZ and that of the attached mortar ; information which is difficult to obtain through experimental setup.

Acknowledgment

The authors gratefully thank Pr Jian-Fu Shao, Dr Xie Shouyi from LaMCube laboratory (at Lille), Jerôme Carriat and Florencio Thalardiere (From Cerema IdF) and Jean-Marc Plessier from Navier Laboratory for their helpful collaboration.


Frederic C Do

Venceslas A Goudiaby

Olivier Gimenez

Amadou L Diagne

Mayecor Diouf

Alain Rocheteau

Leonard E Akpo

ENVIRONMENTAL INFLUENCE ON CANOPY PHENOLOGY IN THE DRY TROPICS 2

Keywords: Sahelian Africa, Acacia tortilis, canopy fullness, leaf flushing, leaf fall, vapour pressure deficit, soil water availability

In the dry tropics, leaf activity of dominant woody species in the dry season is fundamental for ecosystem vitality. Prediction of the potential impact of climate change on leaf phenology of these species is a major challenge in Tropical Ecology. However, the environmental controls of inter-annual variation of leaf flushing and leaf fall are poorly understood. We focused on a comparison between the two major drivers considered in the dry tropics: soil water availability and atmospheric conditions. We performed a 5 year phenological study of 39 individual trees of Acacia tortilis ssp. raddiana in the northern Sahelian zone. Our data show that a significant inter-annual variation, up to 2.0 months, affects both the timing of the peaks of leaf flush and leaf fall. The full canopy stage lasted between 5 and 8 months, broadly including the rainy season and the "cool" dry season, the timing of leaf flush peak varying from one month before the first rains to one month after. The trees have access to a deep water table (31 m) which had no significant inter-annual variation. Predictions of canopy fullness from upper soil water availability (SWA), temperature, relative humidity and vapor pressure deficit (VPD), were compared applying polynomial logistic regressions pooling all the years. We found that atmospheric conditions and particularly VPDmax (midday value) were far better predictors than SWA.

Simulations based on VPDmax, significantly predicted the inter-annual variations both in the timing of leaf flush peak (RMSE = 0.5 month) and in the timing of leaf fall peak (RMSE = 0.6 month). We conclude that the inter-annual variation of canopy phenology is mainly a fine tuning to atmospheric conditions.

INTRODUCTION

In dry tropical regions such as Sahelian Africa, leaf activity of dominant woody species in the dry season is a keystone resource for domestic herbivores, wildlife and ecosystems as a whole (Le [START_REF] Houérou | The grazing land ecosystems of the African Sahel[END_REF]). Prediction of the potential impact of climate change on the timing of leaf flushing and leaf fall, i.e. leaf phenology, is a new and major challenge in Tropical Ecology.

Authors are in agreement on a primary genetic control and an influence of day length on leaf phenology [START_REF] Halevy | Ecological studies on Acacia species in the Negev and Sinai: II. Phenology of Acacia raddiana, A. tortilis and A. Gerrardii negevensis[END_REF][START_REF] Reich | Water stress and tree phenology in tropical dry forest in the lowlands of Costa Rica[END_REF]Borchert 1994 a&b;[START_REF] Reich | Phenology of tropical forest: patterns, causes, and consequences[END_REF][START_REF] Williams | Leaf phenology of woody species in a north Australian tropical savanna[END_REF][START_REF] Morellato | Phenology of atlantic forest trees: A comparative study[END_REF]. The controversy is over precisely which environmental control can best explain inter-annual and inter-site variations in the timings of leaf flush and leaf fall.

The hypothesis that has gained most support is that of control by soil water availability through tree water status (Borchert 1994 a,b,c;[START_REF] Eamus | Ecophysiology of trees of seasonally dry tropics: Comparisons among phenologies[END_REF]. However, several irrigation experiments in the field have shown little impact of soil water availability on leaf phenology and a number of authors have suggested that evaporative demand may also be an important driver [START_REF] Wright | Seasonal drought and leaf fall in a tropical forest[END_REF][START_REF] Duff | Seasonal patterns in soil moisture, vapour pressure deficit, tree canopy cover and predawn water potential in a northern Australian savanna[END_REF][START_REF] Myers | Does irrigation affect leaf phenology in deciduous and evergreen trees of the savannas of northern Australia ?[END_REF].

In conducting a five and a half years study on 39 individuals of Acacia tortilis in the Sahelian zone, we have chosen to investigate the issue by using an inter-annual analysis, which is rare in the bibliography (Poupon 1979, Corlett and[START_REF] Corlett | Potential impacts of climate change on tropical asian forest through influence on phenology[END_REF]. The Sahelian zone sensu stricto represents one of the driest savannas with 200-400 mm y -1 of rainfall and with high inter-annual variability (C.V. = 37%), potential evaporation is in excess of 2000 mm y -1 and groundwater is usually located deeper than 30 m (Le Houerou 1989). Acacia tortilis (Forsk.) Hayne ssp. raddiana (Savi) Brenan, is a dominant tree of the area which is classified as semi-evergreen or semi-deciduous [START_REF] Breman | Woody plants in Agro-Ecosystems of Semi-Arid Regions, with Emphasis on the Sahelian Countries[END_REF]Kessler 1995, Le Floc'h and[START_REF] Floc | Acacia raddiana, un arbre des zones arides à usages multiples[END_REF], i.e. the loss of leaves which takes place in the late dry season is and its rate varies with years, sites and individuals. The tree regularly exhibits leaf flush before the onset of rains.

It is known that its roots can reach the deep water table [START_REF] Lhote | Au sujet de l'arbre du Ténéré[END_REF][START_REF] Deans | Nitrogen in interstitial waters in the Sahel: Natural Baseline, Pollutant or resource ? Plant and Soil[END_REF]) in common with numerous woody species of low-rainfall areas. However, high seasonal fluctuations of predawn leaf water potential attest to the influence of soil water availability near the soil surface on tree water status [START_REF] Berger | The water status of six woody species coexisting in the Sahel (Ferlo, Senegal)[END_REF]. In this study, we focused on the annual attainment and maintenance of the full canopy stage in the tree population. The full canopy stage of a tree is assessed when the proportion of the branches supporting green expanded leaves represents more than 50 % of those in the canopy.

Such simple phenological assessment at a monthly interval is a good indicator of the seasonal transpiration and activity of the tree [START_REF] Do | Cycle annuel de transpiration d'Acacia raddiana par la mesure des flux de sève brute (Nord-Sénégal)[END_REF]. The timings when foliation rose above or fell beneath the 50 % value defined the timings of leaf flushing and leaf fall peaks, respectively. These timings allow the calculation of full canopy stage duration. Using concurrent measurements of climatic conditions and soil water availability, the study had two objectives. The first objective was to assess the inter-annual variation in the timings of leaf flushing and leaf fall and by consequence the changes in the full canopy stage duration and period in the year. The second objective was to determine which environmental variable can best explain inter-annual change in the timings of leaf flushing and leaf fall peaks. In this water-controlled biome, we focused on a comparison between soil water availability and the following atmospheric variables: temperature, relative humidity and vapour pressure deficit which is a combination of the former variables and the driving force of water loss.

METHODS

Location, climate and vegetation

The study was carried out in northern Senegal, near Souilene Village (16°20' N, 15°25' W) located 20 km south of Dagana in the grazing land ecosystem of the sandy Ferlo. Annual rainfall averages 280 mm, mean annual temperature is 28.7°C and average maximum and minimum temperatures are, respectively: 41 and 22 °C for the hottest month (May) and 31 and 14 °C for the coldest month (January). The sparse woody community is dominated by three species: Acacia tortilis and Balanites aegyptiaca (L.) Del, for the tree layer (90 individuals ha -1 ) and Boscia senegalensis (Pers.) Lam for the shrub layer (50 individuals ha -1 ). The soil is very deep and sandy (90 % sand).

Population and measurements

The studied population included 39 mature individuals located in a 1 ha area that has been protected since 1989. Trunk diameter, which was measured 30 cm above the soil, varied from 5 to 45 cm, with 70 % of the population having diameters between 15 and 30 cm. Tree height ranged from 5 to 10 m.

Assessment of phenological stages

For each tree, a phenological stage for the foliage was allocated according to the 6 following categories taking into account the proportion of branches bearing green expanded leaves in the canopy [START_REF] Grouzis | A method for the phenological study of browse populations in the Sahel: the influence of some ecological factors[END_REF]): 0, leafless, 0%; 1, leaf buds opening, <10 %; 2, start of leaf expansion, 10-50 % of the branches; 3, full canopy, > 50 %; 4, start of leaf senescence, changing colour, <50 %; 5, full leaf senescence or fall, <10 %.

Data analysis

To express canopy fullness, the phenological stages were converted to their midrange percentage value of branches bearing green expanded leaves in the canopy: 0, 0 %; 1, 5 %; 2, 30 %; 3, 75 %; 4, 30 %; 5, 5%. Thus the maximum value of canopy fullness is 75 by definition.

The timings of leaf flush or leaf fall peaks were calculated for each tree by linear interpolation such as the time when the canopy fullness rose above or fell below the 50 % value in the long term (> 1 month). Time is expressed in numerical values of months (mo.), e.g. 6.5 for the middle of June.

Because phenological cycles are displayed across two years, we use for simplicity's sake, the year of the rainy season to name the phenological cycle, e.g. 1998 for 1998/99. Timings of leaf fall peak located at the beginning of the second year are expressed as greater than month 12, e.g. 13.5 for the middle of January. The duration of full canopy was calculated for each tree by difference between the timings of leaf fall peak and leaf flush peak.

Year effects on the duration of full canopy and the timings of leaf flush peak and leaf fall peak were tested using a repeated-measures analysis of variance (SAS proc. Mixed, SAS Institute Inc.

1999). Potential influence of environmental variables (edaphic or atmospheric) on changes in canopy fullness, were investigated by regression analysis between values of canopy fullness and each variable, considering all trees and pooling data for all of the years. For atmospheric variables (temperature, relative humidity and vapour pressure deficit), the average value for the 15 days preceding phenological observations was considered. For soil water availability, the actual SWA and the amount of rainfall were used. Since at the tree level, canopy fullness values were qualitative and ordinal response variables, classified as 0, 5, 30 and 75, we specifically performed ordered polynomial logistic regressions with a cumulative logit link (SAS proc. Genmod, SAS Institute Inc. 1999). This model relates the cumulative log of odds of the response variable to the explanatory variable in a linear form [START_REF] Agresti | Analysis of ordinal categorical data[END_REF]. We assessed the validity of the regression by computing the significance of each variable using Wald tests [START_REF] Agresti | Analysis of ordinal categorical data[END_REF]). Because we wanted to compare the predictive power of environmental variables, the c statistic was computed (Hosmer and Lesmehow 2000). It measures the degree to which predicted probabilities agree with actual outcomes. The c statistic ranges from 0.5 to 1. A 0.5 value means that the model is no better than assigning observations randomly into outcome categories. Variables with c statistic value greater than 80 % were therefore selected as having high predictive power. The analysis gives the values of the explanatory variable (environmental variable) corresponding to the selected probability of each response (0, 5, 30, 75). For environmental variables having good predictive power, regressions were used to predict for each year, the times of leaf flush and leaf fall peaks such as the day when the probability of full canopy (response 75) rose above or fell below the 50 % value in the long term (> 1 month). Inputs were climatic data for the 15 days preceding each day. Quality of prediction was evaluated by the root mean square error:

n m s RMSE n i i    1 2 ) ( , i
s is the model prediction, i m the corresponding observation, i the year and n the total number of years.

RESULTS

During the study period (1995)(1996)(1997)(1998)(1999)(2000), annual precipitation averaged 230 mm with minima of 146 and 153 mm in 1997 and 1996, and a maximum of 367 mm in 1999 (Table 1, Fig. 1a). It is noteworthy that inter-annual variability over the six year period (C.V. = 37%) was similar to the long-term variability for the area. Rains occurred mainly between July and September. The dates for onset of the rains were variable, i.e. about the start of June in 1996 and 1997, but the end of July in 1998. August and September were the wettest months. On average, 70 % of the total annual precipitation fell during these 2 months. SWA in the upper layer (0-100 cm) was closely correlated with annual rainfall (Fig. 1b). In the wet season, SWA increased proportionally with rainfall and reached 80% for the wettest year 1999. However, by January, SWA decreased to similar values between years, (from 7 to 9 %).

Subsequently, SWA declined to small values of 3 to 5%, before the start of the rains.

Atmospheric conditions in the rainy season were characterized by highest relative humidities (RH), above 50 %, with mean temperatures around 30°C (Fig. 1a). This was the time of the lowest evaporative demand: daily means of vapor pressure deficit (VPD) were less than 2 kPa (Fig. 1b). RH increased between May and June, from one to two months before the start of the rains. This is a common phenomenon induced by the northerly movement of the Inter-Tropical Convergence Zone but there were notable differences between years (Fig. 1a). RH decreased sharply after the rainy season, then it fluctuated, from 10 to 50 %, with notable differences between years. In the dry season, two climatic seasons are usually distinguished according to air temperature: the "cool" dry season lasting from December until February and the hot dry season lasting from March until June (Fig. 1b, month 15 to 17). The hot dry season with low RH and increasing temperatures is characterized by the highest evaporative demand: mean VPD generally exceeds 2 kPa and maximum VPD regularly exceeds 5 kPa.

Evolution of Canopy fullness showed an annual cycle with both similarities and differences between years (Fig. 1b, Table 1). The defoliation phase was centred around the hot dry season.

Defoliation was never complete at population scale as shown by Canopy fullness which never reached a zero value (Fig. 1b). The point closest to zero occurred in April 2000 (Fig. 1a: point at 16 mo. in "1999" or 4 mo. in "2000"), which corresponded to 63 % of fully defoliated trees. The full canopy stage lasted an average 7 months (Table 1), from mid-July to the start of February, broadly including the rainy and cool dry seasons (Fig. 1). The inter-annual variation of full canopy stage duration was large, e.g. more than two months between the extreme years: 5.2 mo. in 1996 and 7.5 mo. in 1998 or 1999 (Table 1). The repeated-measures analysis of variance revealed a highly significant (P<0.001) effect of year on canopy duration. The observation interval which was at the best biweekly and more often monthly, precludes discussion of differences or equalities at less than 0.5 months. The magnitude of differences clearly distinguishes two groups, the group of the years 1996 and 1997 where duration was shortened by 25 % in comparison with the group of the years 1995, 1998 and 1999. The duration differences resulted from variation in a two month range both in the timings of peaks for leaf flush and leaf fall (Table 1). The timing of leaf flush peak varied from the start of June (years 2000, 1999), more than one month before the first rains (Fig. 1), to the end of July in the rainy season (years 1995,1996,1997). The situation in 1998 was intermediate: the start of leaf flushing was early, in May as in 1999 and 2000, but was followed by a defoliation before leaf flush peaked in July (Fig. 1). The timing of leaf fall peak varied from the start of January (year 1996) to the start of March (year 1995). The years 1996 and 1997 had intermediate defoliation in December. The inter-individual variation was large and variable depending upon year (standard deviation in Table 1). For example, for the same average timing of leaf flush peak, the inter-individual variation was fourfold larger in 1999 than in 2000. Similar results occurred between 1995 and 1996 for the timing of leaf fall peak. At the individual level, the time between the onset of flushing and full foliation was approximately 1 to 1.5 mo (data not shown). Figure 1b shows the average of canopy fullness in the population, so durations were increased by an averaging effect in the case of large inter-individual variation.

The influence of SWA on the inter-annual variation of canopy phenology could involve ground water and/or upper soil water. The top of the water table was found at 31 m depth, consistent with the water level found in village wells in the study area. Between the upper layer of soil and the water table, SWA for plants was very limited because the actual moisture contents were equivalent to a water potential of -1.5 MPa. Living root fragments of A. tortilis, which can be identified from their very special smell, were collected at 25 m depth. These confirmed that the trees have access to the water table. However no fluctuations of the deep water table which could explain inter-seasonal variability of leaf phenology, are known in the area [START_REF] Gaye | Groundwater recharge estimation using chloride, stable isotopes and tritium profiles in the sands of north-western Senegal[END_REF].

Results of regression analysis between canopy fullness and environmental variables over all years are summarized in Table 2. For upper SWA, two variables were considered: the actual SWA and the amount of rainfall in the 15 days preceding phenological observations. In the completely dry season (timing of leaf fall), changes of SWA were slow and actual SWA, measured at monthly intervals, was a good integrator of soil conditions for the 15 day period of time. By contrast, during the transition between dry and rainy seasons (timing of leaf flush), due to the effect of rainfall, measured SWA was a poor predictor and rainfall amount (hourly recording) was used as a surrogate (see Fig. 1).

Whatever the analysis, there was a significant relationship (P < 0.05) with all environmental variables. This was due to the fact that during the considered periods, soil water and atmospheric variables were all moving broadly at the same seasonal time as canopy fullness (See Fig. 1). The key point is the comparison between predictive powers of variables (c values in Table 2). For the whole time of deciduousness (mainly from January to August), VPDmax is from far a higher predictive variable than SWA or rainfall (Table 2). VPDmax is the value measured around midday, which defines the maximum evaporative demand during the day. The value of VPDmax corresponding to a prediction of 50% of canopy fullness was 4.8 kPa.

When the time of deciduousness was divided between times of leaf flush and leaf fall, there was a remarkable switch between the predictive powers of relative humidity (RH) and temperature (Ta), which are combined in VPD (Table 2). During the time of leaf flush, RH and VPD are the variables which best predicted canopy fullness. During the time of leaf fall, temperature and VPD are the variables which best predicted canopy fullness. The same analysis considering a period of 30 days before phenological observations gave similar results (data not shown).

Regression analyses were performed pooling all of the years. For environmental variables having a high predictive power, regressions were used to predict for each year, the timings of leaf flush and leaf fall peaks. Inputs were climatic data for the 15 days preceding each date. The day when the probability of full canopy rose above (leaf flush) or fell below (leaf fall) the 50 % value in the long term (> 1 month) was retained. The precision of "long term" is particularly important for the prediction of the date of leaf fall peak because the dynamics of climatic variables fluctuated strongly at this time (see Fig. 1). Root mean square errors of predictions are given in Table 2 anddetailed results for VPDmax are shown in Figure 2. Atmospheric conditions explained a large part of interannual variation in both the timing of leaf flush peak (RMSE = 0.4-0.5 month) and the timing of leaf fall peak (RMSE = 0.6 -0.7 month, Table 2). Finally, combination of Figures 2a and2b illustrates that VPDmax can explain a part of the duration and period of canopy fullness for the 5 complete years of the study (RMSE = 0.8). The period containing October and November was not considered in the regression-prediction analysis, however, simulations based on atmospheric conditions also predict defoliation for this period, which was not systematically observed (Fig. 1).

DISCUSSION

The full canopy stage of A. tortilis sp. raddiana lasts between 5 and 8 months, broadly including the rainy season and the "cool" dry season. The seasonal period and duration of full canopy stage is in agreement with general description of its leaf phenology in Sahelian Africa (Grouzis andSicot 1980, Diouf and[START_REF] Diouf | Phénologie comparée d'Acacia raddiana au nord et au sud du Sahara[END_REF]. As with the majority of species in the seasonally dry tropics, the defoliation phase was centered around the hot dry season.

The first main result of this study was large inter-annual variation in the start and end of the full canopy stage on the same site, more than 2 months in each case. One consequence was a 25 % shortfall of the stage duration for two of the years (1996 and 1997). Such variation confirms that genetics and day length cannot be the unique controlling factors of canopy phenology and that other factors have complementary influence on the timings of leaf flush and leaf fall peaks. We should insist that here we deal with the major timing of leaf flush and not initial leaf flush which is often discussed in the literature (Borchert 1994c). Initial leaf flush was generally observed between April and May.

Finally we discuss which factors influence the timing of the massive leaf flush which follows the initial leaf flush.

The second main result was that atmospheric conditions and particularly VPDmax could explain inter-annual change of canopy fullness better than upper or deep SWA. The influence of annual rainfall on canopy phenology through upper SWA is a current hypothesis in the Sahelian zone : higher rainfall would induce a larger residual upper soil water availability in the dry season which could delay the timing of defoliation and would advance the time of leaf flushing peak. Our results do not support this hypothesis despite a large inter-annual variation in rainfall (from 146 mm in 1997 to 367 mm in 1999). It was particularly notable that three month after rainy season, upper SWA reached similar and very small values in all years. How was this possible? The phenological stage or canopy fullness percentage does not describe leaf number or area which were two times higher for the wettest years, 1998 and 1999 than for 1997 [START_REF] Goudiaby | Impact d'un déficit pluviométrique sur la feuillaison d'Acacia tortilis[END_REF]. Biomass of grass was also greater at the end of the wettest rainy seasons. These two factors involve greater water uptake, which can explain how SWA reached similar small values.

The third main result was that atmospheric conditions and particularly VPDmax predicted a significant part of the inter-annual variations in both the timing of leaf flush peak and of leaf fall peak.

We conclude that these inter-annual variations of canopy phenology were mainly controlled by atmospheric conditions. Comparable data on this point are scarce in the literature although the possible influence of relative humidity on leaf flush was often hypothesized. One reason may be that phenological studies on the same individuals, which last for more than one or two years, are rare in the tropics. Another reason could be that until now, VPD was not always considered as a climatic variable influencing savanna tree phenology [START_REF] De Bie | Woody plant phenology in the West Africa savanna[END_REF][START_REF] Chidumayo | Climate and phenology of savanna vegetation in southern Africa[END_REF]. Moreover, the conditions of water constraint (rainfall amount, evaporative demand and depth to the water table) in the ecosystem studied here were more extreme than in savanna situations detailed elsewhere in the literature [START_REF] Eamus | Ecophysiology of trees of seasonally dry tropics: Comparisons among phenologies[END_REF]. However, an inter-annual analysis with "only" 5 to 6 years cannot definitively demonstrate that VPD is a major proximal cue of canopy phenology in the dry tropics.

Nevertheless, the results give a new and clear insight on the influence of atmospheric conditions.

What would be the adaptative significance of such response to atmospheric conditions? This behaviour leads to maximization of the duration of canopy fullness below a VPD threshold between 4.5 and 4.9 kPa. Such behaviour maximizes the duration of photosynthetic activity under a threshold of evaporative demand and does not reduce water loss. Field observation at the terminal branch scale in 1997 and 1998 showed, that the annual phenological pattern corresponds to three main cohorts of leaves [START_REF] Goudiaby | Impact d'un déficit pluviométrique sur la feuillaison d'Acacia tortilis[END_REF]. The first cohort begins between April and May, the second cohort begins in July and the last begins between December and January. The cohort of July expressed the longest leaf life span around 6-7 months. The life span of the initial and final cohorts was very short and variable depending upon the year. Leaf stomata are known to be very sensitive to VPD. We hypothesize that the response of the two extreme cohorts of leaves to climatic conditions could explain inter-annual variation of canopy phenology. Do these results mean that soil water availability has no influence on leaf phenology of Acacia tortilis?

We do not support this. Firstly, leaf activity of trees during large periods of the dry season is only possible because trees have access to extra-annual water in the deep soil. Secondly, the existence of large spatial variation in canopy deciduousness at the landscape scale suggests a strong effect of SWA.

It was particularly notable at the border of the Senegal river, near Dagana city, where the water table is close to the top soil that the tree population behaves like an evergreen species. Finally, we believe that the average phenological pattern fits the prevailing local SWA's, annual rainfall amount and depth to the water table. While the inter-annual variation of canopy phenology is a fine tuning to atmospheric conditions.

In conclusion, if such large inter-annual variation of canopy phenology is common to other dominant species of the seasonally dry tropics, which is fairly possible, the consequences for the potential impact of climate change are important and not only rainfall should be considered. corresponding to 50 % of Canopy Fullness. RMSE is root mean square error of predicted timings of leaf fall and leaf flush peaks against observed timings.

ACKNOWLEDGEMENTS

We thank Youm Mbaye, Hyacinthe Tendeng and Baïdi Li for technical assistance. We are grateful to Michel Grouzis for initiating the research program. The research was partly funded by the European

LIST OF FIGURES

LIST OF TABLES

Table 1: Mean values of timing of leaf flush peak, timing of leaf fall peak, and duration of full canopy stage expressed in months for 39 individuals of Acacia tortilis growing at Souilène in North Senegal. Repeated-measures ANOVA revealed highly significant effects of year (P < 0.001) on the three variables. The study ended in August 2000 before observation of the timing of leaf fall for the phenological cycle 2000-01.

Table 2. Parameters of regression-prediction analysis testing which environmental variable can best explains inter-annual changes in canopy fullness (CF) and the timings of leaf fall and leaf flush peaks (50% of CF). Variables were upper soil water availability (SWA), rainfall and daily mean, minimum and maximum air temperatures (T), relative humidity (RH) and vapour pressure deficit (VPD). Polynomial logistic regressions were performed (see methods). C is the predictive power, which is high when (*) is added. 50% CF indicates the value of variables