E Charkaluk*'*

A Constantinescu

A Bignonnet

K Dang Van

ON A FAILURE CRITERION FOR THERMOMECHANICAL MULTIAXIAL LOW CYCLE FATIGUE AND ITS INDUSTRIAL APPLICATION

Keywords: Low cycle fatigue criterion, dissipated energy, constitutive law, thermal fatigue, structure computation

The purpose of this paper is to assess the fatigue strength of complex structures submitted to low cycle thermomechanical fatigue. In a fi rst step, the behaviour of the material in a high range of temperatures has been modelled using a simple elastoviscoplastic constitutive law. In a second step, a criterion based on the dissipated energy per cycle derived from the results of the numerical computations, allows the prediction of the fatigue strength of the structure.

Strain controlled isothermal low cycle fatigue tests were carried out on cast iron specimens for the identification of the constitutive and the fatigue laws. Temperature controlled tests on specimens and structures permitted the evaluation of the precision of the numerical computation under anisothermal loading. The lifetime prediction is showed to agree with the experiments both on specimens and structures.

INTRODUCTION

The prediction of fatigue and failure of structures submitted to thermal loading is one of the important problems in mechanical engineering. One can recognize two research directions in this field : one concentrated on the understanding and modelling of the physical phenomena underlying fatigue of materials and one concentrated on finding a robust prediction criterion to evaluate the fatigue strength of components from a structural computation. The prediction criterion should correspond to the expectation of the design engineer, i.e. to be identified from simple mechanical experiments on specimens and to be applicable on actual structures of complex geometry and complex thermomechanical loadings.

In spite of major advances in the understanding of fatigue phenomena at a local microscopic level and a large amount of experiments on specimens, robust criteria at a global macroscopic level to predict low cycle thermomechanical fatigue failure on structures are still missing. There are essentially two difficulties to attain this objective : a formulation of the material behaviour which gives access to an accurate description of the mechanical values which control the fatigue 1 phenomenon in a structure and a failure criterion, derived from simple tests, which provides a reasonable estimation of the lifetime of the structure.

The constitutive law should permit computer simulations in a acceptably small computation time of elastoviscoplastic structure subjected to complex thermomechanical loadings. The fatigue criterion should be capable of explaining isothermal and anisothermal LCF failure for a large range of temperatures and for multiaxial loadings.

From a material point of view , one can identifY different steps in the fatigue life time (initiation of a crack, propagation, failure of a representative elementary volume, .. . ). The interpretation of these steps from the point of view of applications to industrial structure permits a distinction between different situations, for example :

• in the security assessment of a cracked structure, one can directly concentrate on the crack propagation rate and the critical size of the crack [1].

• in a particular design process, where no control is done after the delivery of the product to the customer, one can not accept crack growth leading to component disfunctionment before the targeted lifetime. Therefore one can consider in the design analysis the time to failure of a representative elementary volume (REV) as a failure criterion of the whole structure [2].

These considerations have suggested a certain number of assumptions in the present study :

• the material behaviour can be modeled by a simple elastoviscoplastic constitutive law, which permits the representation of the cyclic response of the structure under thermomechanical loading,

• the fatigue criterion can be based on an intrinsic quantity permitting the prediction of failure under isothermal and anisothermal multiaxial loading. The dissipated energy per cycle, seem to give good results. This paper presents in a first section the identification of the constitutive law and in a second section the fatigue criterion and its applications to the fatigue assessment of actual structures using isothermal and anisothermal LCF experiments.

EXPERIMENTS AND COMPUTATIONS

The material studied is a spheroidal graphite cast-iron with silicium and molybden additions.

Three types of test have been carried out on specimens and actual exhaust pipes of automotive engines :

• Isothermal strain controlled tests (TRV) were carried out in order to caracterize the mechanical behaviour of the material. The experiments have been done at different constant temperatures between 20°C and 800°C. The applied cycle corresponds to a tension relaxation-recovery (TRV) test, with total strain rates applied to the specimen between 10 -4 s-1 and 10-2 s-1 and maximal strain ranges between 2% and 5%.

• Fully reversed isothermal low cycle fatigue tests (LCF) (R.: = -1) were carried out under strain control of the material. The experiments have been done at different constant temperatures between 200°C and 700°C, with a total strain rate of I o-3 s-1 and three different strain ranges:± 0,25 %, ± 0,5 % and± 1 %. Using this elastoviscoplastic constitutive law, FEM computation using the ABAQUS code has been performed in order to simulate the anisothermal fatigue tests. A typical result of computed axial stress in the specimen versus temperature is presented in Figure 3.

The observed difference between the experimental and the computed first cycle is actually due to the constitutive parameters of the elastoviscoplastic law. However one can remark that the stabilized cycle has been evaluated both in term of residual stress at room temperature and amplitude difference between loading and unloading. The dwell temperature has been considered constant during the computation, which differs from the experiment where a 20°C difference due to the thermal regulation can be observed.

The irregularities at 500°C are due to variations of the elastoviscoplastic parameters at this temperature, corresponding to a dynamic strain ageing phenomenon. A better control of the numerical convergence of the code can be achieved and is part of the study not reported here.

The anisothermal tests on components were also simulated using the same elastoviscoplastic constitutive law. A typical FEM model for an exhaust pipe containing about 20000 hexaedric volume elements is represented in Figure 4. The temperature computed distribution on the components has been checked with experimental values obtained by infrared thermography. The thermomechanical loading has been given by the temperature variation described before and stresses and strains distribution were obtained in all the structure. SWT interpretation of the anisothermal experiments are difficult as the choice of Omax is impossible in an anisothermal case ( SWT function = JE. a max. !:.e ). One can remark that for cast-iron, a maximum stress for the same strain can vary from 30 to 300 MPa depending on the temperature.

The principal criticism of the previously discussed criteria is their inapplicability for all types of loading case. A possible way to overcome this difficulty is an energy criterion. Different forms of energy criteria have already been proposed and discussed for example by Ostergren [8],

Ellyin et a\. [9] or Halford [10]. These papers present different expressions of macroscopic deformation energy including or excluding its elastic, plastic or work-hardening part [START_REF] Lemaitre | Mecanique des materiaux so/ides[END_REF].

An interesting interpretation of the cyclic behaviour of the material is presented in Skelton [START_REF] Skelton | [END_REF].

These results [START_REF] Skelton | [END_REF] suggest that the cumulated dissipated energy to the cyclic response stabilization can be used as a crack initiation criterion in low cycle fatigue. Denoting by Ns the number of cycles to stabilization, assumed to correspond to crack initiation, Skelton showed that the cumulated dissipated energy to stabilization: Ns x t:.W, is relatively constant for a given material, between 1 J.mm" 3 and 10 J.mm• 3 .

Our basic assumption is that the failure of the representative elementary volume corresponds to the failure criterion and in the case of a specimen, the failure of the representative elementary volume implies the complete failure. Using the ideas developed by Skelton, the present LCF and TMF tests on cast iron were analysed with a dissipated energy on the stabilized cycle.

The experimental versus predicted lifetime is presented in log-log plot in Figure 5. The cumulated energy to failure on components and specimens was showed to be of the same order of magnitude as reported by Skelton [START_REF] Skelton | [END_REF], i.e. between I J.mm• 3 and 10 J.mm• 3

CONCLUSION

The aim of this paper was to investigate a possible low-cycle fatigue criterion and its applications to industrial structures subjected to thermomechanical loading.

It has been shown that a relatively simple elastoviscoplastic constitutive law can describe the mechanical behaviour of the structure in a large range of temperatures. The temperature dependance of the parameters permitted the emphasis on a plastic behaviour at low temperatures (20°C -400°C) and a viscous behaviour at high temperatures (400°C -800°C).

The dissipated energy per cycle, obtained directly from the computed stresses and strains demonstrated a robust fatigue criterion for the lifetime prediction of industrial structures.

Moreover the total dissipated energy to failure has been found to be of the same order of magnitude as reported earlier by Skelton [START_REF] Skelton | [END_REF]. The applicability of an energy criteria to the lifetime prediction of structures subjected to complex low-cycle fatigue loadings has thus been proved.

However further efforts are necessary to improve the accuracy of life estimations of structures submitted to thermomechanical fatigue. A better quantitative understanding of the dissipation mechanisms and their relation to different types of failure will fi nd a logical place in low-cycle fatigue lifetime predictions.

•

  Thermal fatigue tests (TMF) were conducted on clamped specimens heaten by the Joule effect. Maximum temperatures have been varied between 40 oc and 700 °C with an heating rate of 20°C/s. The maximum temperature has been obtained in a region of approximatively 10 mm in the center of the specimen. The maximum temperature gradient was 30-40°C/mm. The parameters of the test are the clamp value (183000 N/mm and 227000 N/mm) and the dwell time at 700 oc (60 seconds and 900 seconds).• Thermomechanica/ tests were carried out on engine components. Maximum temperatures have been varied between 20°C and 700°C. It is important to remark that temperatures have not been distributed uniformly over the component. Some points never exceeded 200°C. The heating rate was approximately 10°C/s.An elastoviscoplastic constitutive law with five temperature depending parameters has been identified for each temperature on the stabilized cycle obtained with the isothermal TRY. The rheological representation is shown in Figure1. A comparison between computation and experimentation is given in the Figure2and it can be observed that relaxation is reasonnably well represented with a 1 0 % error on stresses. A difference of stress hardening was observed between compression and traction and similar behaviour for cast-iron has already been reported by Josefson et al.[3]. In the model an average of the two values of stress hardening has been used to minimize the error in tension and compression, which explains the differences between the computed and experimental curves of Figure2.

Figure I :Figure 2 :

 2 Figure I : a representation of the constitutive law

Figure 3 :

 3 Figure 3 : comparison between the thermal fatigue test curve and the corresponding computation for a 40°C-700°C test with a 227000 N/mm clamp and a 60 s dwell time.

Figure 4 :

 4 Figure 4 : FEM model of the exhaust pipe.

  10COOO ,-----------------------------------------------------� �� �

Figure 5 :

 5 Figure 5 : comparison between estimated lifetime and predicted lifetime for LCF tests and thermal tests on specimens and anisothermal tests on real structures.


J.-C Sangleboeuf

T Bretheau

Sudre

D Caldemaison

A Quantitative Mesoscale Characterization of the Mechanical Behavior of Ceramic Matrix Composites

Keywords: CMC, In Situ Tension Tests, Mi crom echanics, Matrix Cracking

An experimental micro-macro kinematic description of matrix cracking in unidirectionnal ceramic matrix composites is proposed. It has been enlighted by observations performed during an in situ tensile test in a Scanning Electron Microscope. The characterization of matrix crack nucleation, propagation and coalescence has been done with new parameters and related to the macroscopic behaviour.

INTRODUCTION.

The different damage and failure mechanisms in ceramic matrix composites are now well known, and the critical role of interfaces has bee n demonstrated by numerous authors. Two classes of theoretical models have been proposed to predict the macroscopic mechanical behaviour of such materials but no model can encompass the complexity of the problem.

The first class of models combines a phenomenological description of the different matrix damage modes with a global approach by damage mechanics. For any given composite and after a relatively straightforward phase of parameter identification, these models find some use in structural designing [1]. However, the parameters in the models have seldom relation with physical composite characteristics [START_REF] Guillaumat | 11Microfissuration des CMC : relation avec la microstructure et le comportement mecanique[END_REF]. Thus, no feed-back information is given to the material designer for further improvement of the composite properties.

The second starts with a fracture mechanics description of the physical events that have been well identified and characterised at the fibre scale and is pursued by extending this analytical or semi analytical micromechanical model to a more macroscopic description [START_REF] Vagaggini | Relationships between Hysteresis Measurements and the Constituent Properties of Ceramics Matrix Composites : I, Theory[END_REF]. This approach is meaningful for the material designer but gets useless for the structural designer due to the complexity induced by multidirectional fibre architectures and multiaxial loading.

In the present study we try to bridge the gap between these two descriptions by performing experiments at a mesoscale to quantify damage kinetics in the composite and identify some physical parameters meaningful for both classes of models. The mechanical testing technique consists in insitu tensile tests in a Scanning Electron Microscope (SEM). Some new parameters have been defined so as to explain the matrix cracking evolution.

EXPERIMENTAL PROCEDURE.

Material.

All experiments were conducted on a unidirectional laminate of SIC:MAS provided by ONERA. This material is made of 27% Nicalon NLM202 fibre in a MLAS matrix (ref : l\1LAS SG-P2 Saint-Gobain Recherche).

Specimens.

Tensile specimens 100 x 2 x4,8 mm3 were prepared by machining 100 x 100 x 4,8 mm3 plates with a diamond blade. The matrix layer at the plate faces was removed by polishing; the two other faces were as well polished .. An Au/Pd thin layer was sputtered on the gauge to facilitate SEM observations.

Testing.

Ex situ tensile tests. monotonous and repeated, were performed on a servomechanic machine at a 2.4.10'5s•1 nominal strain rate. Special attention was given to avoid any bending. The specimens were directly glued and clamped into the grips what leaves an effective 20mm gauge length for testing. Strain was measured by means of an extensometer attached to the gauge section for accuracy. Stress/strain curves allow to identify macroscopic parameters such as : initial modulus E0, tangent modulus E" permanent strain e P , maximum opening of hysteresis loop emax• (fig 1 ). The choice of these parameters will be enlightened during meso/macro correlation.

In situ tensile test under in the SEM were performed at a nominal strain rate of 2,5.10 . 5s•1• Ex situ and in situ strain rates are very close so as to ensure a time independent interpretation. Panoramas of the whole sample surface, 2x20 mm2, and enlargement of some typical areas were worked out at several stress level so as to study the onset and the evolution of matrix cracks, and also to get the evolution of the crack opening in connection with its neighbourhood. Mesoscopic observations can be related to macroscopic informations with reference to the corresponding stress level.

EXPERIMENTAL RESULTS.

This study exhibits three scales : -macroscale : the Representative Volume Element (RVE), characterised by the evolution of global parameters such as the tangent modulus.

-mesoscale : several fibres inside the matrix, characterised by matrix cracking.

-microscale : a single fibre inside the matrix, characterised by interfacial decohesion, friction, and fibre failure .

A central point for the correlation between two scales, is the choice of an indicator at a scale that is representative of the kinetic of evolution of the pertinent mechanisms active at a lower scale. The evolution of several parameters will be studied in the following.

Macroscale.

The composite presents a non-linear behaviour before failure, with a "plateau" at the beginning of the non linear stage. Permanent strains and quite large hysteresis loops characteristic of dissipation phenomena can be noted. (fig 2). ,-.. The behaviour is highly reproducible either under monotonous or repeated tensile conditions; nevertheless the strain to failure is always higher for repeated tests. This particular shape has already been reported by Spearing ant Zok [4J.

•-••-r••• •-•• .. •• •••••••)•••••••••--••••••••• r• ••••••••-••••••- .. -••• ...... •••••••••-�--............. •••••••t• ....... •••••••••••••-�---••• ...... ••-... .

Rep�ated tensil� test

The behaviour can be divided in fou r stages : a rapid decrease between 0 and 180Mpa, then a minimum between 180 and 240MPa, an increase passing by a max i mum between 240 and 380MPa and a slower decrease between 380 and 520MPa.

These stages can also be observed in the evolution of two other macroscopic parameters ; the maximum opening of hysteresis loops. (Emax ) for tlhe dissipative aspect of the behaviour, and the permanent strain (EP) for the irreversible aspect (fig 4).

- Matrix cracks can be observed at low magnification; they are quite tortuous due to microstructural heterogeneities (variation in the local fibre volume fraction) and cracks interaction. This interaction shows two characteristic distances: the first one is lower than tortuousness (short range screen effect); the second one has a magnitude equivalent to the average distance between cracks (large range screen effect).

� - c •- eo: .... - � 0, 3.2. Mesoscale. • •••••••••••••••••-� .. ..
11 Large range screen effect It is very important to take into account these screen effect phenomena if we want to define what is the dimension of a crack at such a scale. When cracks are not in the same plane, their identification is easy. But, when cracks are roughly in the same plane and show a short range screen effect, we will consider that two cracks coalesce when they are physically connected (when there is a real crack path) and when secondary branches are disactivated. For example, on figure 5, the two cracks presenting a short range screen effect have not coalesced; they are connected but the secondary branch is still open (otherwise it could not be observed). These three curves (fig 6) show unambiguously that the matrix crack JnJtJatlon stress is about 150Mpa; the stress corresponding to the sat uration of Dlin can be considered as the matrix crack saturation stress and evaluated at 400Mpa; D ri n increases monotonously with the applied stress; this evolution has induced some authors [5][START_REF] Budiansky | Matrix fracture in fiber-reinforced ceramics[END_REF][START_REF] Budiansky | Matrix fracture in fiber-reinforced ceramics[END_REF] to propose that matrix cracking develops in two phases: first the unstable creation of cracks gives rise to a regula r pattern; then, these cracks propagate in a stable manner throughout the entire section of the specimen.

With this definition of a crack

Nevertheless, the evolution of D,0, leads to moderate the previous interpretation, by acco unt ing with the oscillatory behaviour of matrix cracking. The rapid evolution of the number of cracks for stresses between 150 and 240MPa corresponds to the nucleation of the first generation of cracks, just followed by a coalescence stage; then the evolution is made of nucleation and coalescence steps with a lower amp li tude compared to the initial burst. This decrease in amplitude occurs because less and less defects can nucleate new cracks due to the stress relaxation induced by the cracks already present in the composite. Moreover, the evolution rate decreases too; this could be a consequence, at a local scale, of the short range screen effects (fig 7). Thus, for a particular crack, the plot of the crack opening displacement vs. stress shows the effect of its neighbourhood on its propagation: a secondary crack, nucleated around 180Mpa, induces a deceleration of the principal crack; the arr est Moreover, this oscillatory behaviour of matrix cracking is confinned by the evolution of Lav (fig 6). This parameter decreases with the creation of new short cracks, and increases during coalescence.

(,J f u 0 r-r --T ooooooooo looo•oooooooooo•oooooooo0oo0t0"0"'"' ""O OOOO Ooooooo{ooo O•O • •••••••••••••••�••••••'•''"'0'00000Hoooo tooooooo" i i.., i ------ ! r r -i r
Therefore it can be concluded that matrix cracking begins by a nucleation stage (150 -250MPa), followed by coalescence/nucleation stages until the applied stress reaches 400MPa. The control mechanism is crack propagation, but nucleation and coalescence disturb the regularity of the evolution.

4. MESOMACRO CORRELATIONS.

The decrease of E/E0 between 180 and 240MPa (fig 3) seems to be clearly due to the initial nucleation stage ranging from 150 and 240MPa. The rapid nucleation of cracks bridged by fibres leads jointly to increase the friction surface at fibre/matrix interfaces; this is confinned by the increase of emax between 190 and 260Mpa (fig 4). The inflexion point at 240MPa corresponds to the transition between monotonous and oscillatory regimes in the evolution of the total density.

The increase of E/Eo in the range 240 -380MPa is correlated with the oscillatory regime where matrix cracking is controlled by crack propagation. Moreover, the evolution of e max between 280 and 400MPa seems to indicate that matrix cracking reaches saturation on a stable manner. For applied stress ranging from 340 to 380MPa, the curve representing the evolution of E/Eo is under VfE/E0, which corresponds to the stiffness of the only fibres of the composite (fig 3). In that stress range, matrix cracking is near saturation andit can be considered that Joad is supported by fibres only. Under the reasonable hypothesis of a total fibre/matrix decohesion of a weak interfacial shear stress, the proximity between the residual stiffness and the theoretical one induces that only a few fibres have failed at that stage.

The decreasing stage of E/Eo between 380 and SOOMPa seems to be correlated with fibre failure: this failure causes a decrease in the elastic energy stored in the bridged cracks; during unloading they consequently close less allowing an increasing pennanent strain emax (fig 4 ). All these correlations are confinned by acoustic emission during tensile tests; it begins to be very active around 350Mpa.

The increase in strain to failure under repeated loading, compared to monotonous one, can be interpreted owing to the observation of the fibre/matrix interphase (fig 9); it shows, after only a few cycles, a damaged aspect with debris; that damage can weaken the interfacial shear stress and promote the extension of the interfacial cracks and then diffuse the stress concentrations associated with matrix cracks; a more homogeneous stress state could delay the specimen failure.

fig 1 :

 1 fig 1 :Typical stress/strain curve and definition of macroscopic parameters.

fig 2 :

 2 fig 2 : Stress/strain curves.

Afig 3 :

 3 fig 3 : Evolution of E/Eo vs. the applied stress.

5 :

 5 fig 5: Matrix cracks observed at mesoscale (x55)under 255MPa stress.

  , it is interesting to follow the evolution, in relation with the applied stress, of three parameters representative of matrix cracking (fig 6) :-the linear density D1in• measured by the intercept method and classically used, -the total density D101 (total number of cracks/specimen length), -the average length of crack, L.v•

  fig 6 :Evolution of Dli n ' D,01 and Lav•

  fig 7 : a) Local screen effect (x650). b) Crack opening (x 17000).

  fig 8 : Evolution of the crack opening displacement for the principal crack of figure 7.

:

  ............... .. �C. .. . P. . .......... : .. ... . .. ....... r .. ........... .. T .. .... . • ; .... � ... -.. ...... .. .... ... ......... . ... ................... ...... .. .. .. l ..... ............... t .. .. . .. �, . . . . . . : .. . .. ... .... ..... . .. •• -\ .. .. .. ............ 1 ... ............ �L�-�-�� .. . ............ � ...... ? ........... � .... . Evolution of Ep and Emax.

.. ............. . ! ••• • • • • .......... .. . i ... ...... ............ t. . . . . .. . . .. .. . . .. . .; ... .... . ...... .. . . : : : : . ie max --�-.� ; � : . : . l fig 4


domain: shs sde

text:
Julie Trottier
email: julie.trottier@cnrs.fr

Anaïs Rondier
email: anais.rondier@sciencespo.fr

Jeanne Perrier
email: jeanne.perrier@sciencespo.fr

Palestinians and Donors Playing with Fire: 25 Years of Water Projects in the West Bank

Keywords: water projects, Palestinian water, water governance, territorial change, water infrastructure

This article explores how Palestinian led, donor supported water projects have transformed societal interactions concerning water since 1994. It distinguishes spatial, institutional and sectoral trajectories of water and explores the impacts on each type of trajectory. It demonstrates that the overall impact of these projects is more than the sum total of the individual projects. All together, they entail territorial change. Wastewater and reuse projects transform the largest flows and have the greatest impact on water trajectories. Overall, the recharge of the upper unconfined aquifer is compromised, with the effect that grass-root farmer institutions managing it are negatively affected.

Introduction

What happens when a small territory such as the West Bank becomes the focus of donor funding in an unprecedented manner? Since 1994, donors have been supporting the Palestinian Authority (PA), ultimately making it far more accountable to them than to its constituency [START_REF] Brynen | A Very Political Economy: Peacebuilding and Foreign Aid in the West Bank and Gaza[END_REF] [START_REF] Keating | Aid, diplomacy and facts on the ground : the case of Palestine[END_REF] (Le More, 2008) [START_REF] Nakhleh | Globalized Palestine[END_REF]. The case of development projects concerning water is especially salient. In a semi-arid environment, a society necessarily devises rules to manage its interactions with water. Infrastructure projects, no matter how well intentioned, unavoidably alter these interactions, often inadvertently undermining many actors and processes they sought to support [START_REF] Harvey | Infrastructures and Social Complexity[END_REF]. Since 1994, donors supported over 2000 projects concerning water in the West Bank. This article explores the overall transformations they have entailed.

Research in the political ecology of water often reiterates that the flow of water connects all socio-spatial relations. It pays great attention to the production of the hydro-social cycle as a metabolic circulation whereby actors, actants and water enrol each other to coproduce their discourse and action [START_REF] Swyngedouw | Liquid Power. Contested Hydrol-Modernities in Twentieth -Century Spain[END_REF]. Such research paid little attention to native people's interactions with water because it tended to follow an orthodox marxist framework which considers that their interactions with water are necessarily doomed. This framework posits a development of history whereby Capital unavoidably disempowers small, native peasants. The interactions with water that were considered important in this literature were those involving the state and private companies [START_REF] Castro | Neoliberal water and sanitation policies as a failed development strategy: lessons from developing countries[END_REF]. It focused on urban areas and the plight of the urban poor [START_REF] Kaika | Constructing scarcity and sensationalising water politics: 170 days that shook Athens[END_REF] [START_REF] Gandy | Landscapes of disaster: water, modernity, and urban fragmentation in Mumbai[END_REF]. This theoretical framework leads this research to consider appropriation of water bodies rather than to consider the successive users interacting along a multiplicity of water flows.

Whether it explores the conflicts concerning dam construction [START_REF] Espeland | The Struggle for Water, Politics, Rationality and Identity in the American Southwest[END_REF], hydro-justice [START_REF] Boelens | Water, Power and Identity. The cultural politics of water in the Andes[END_REF] or water privatisation [START_REF] Bakker | Neoliberalizing nature? Market environmentalism in water supply in England and Wales[END_REF], research in the political ecology of water emphasises the discursive constructions of the actors when considering water. Part of this literature has explored the water rights of native people and legal pluralism. It has explored issues of environmental justice and the difficulties involved in integrating the grass-root water law elaborated by native people into national legislation. However, it has paid surprisingly little attention to the actual, material flow of water itself unless large scale projects such as inter river transfers were considered. Barnes (2012) and [START_REF] Brooks | Changing the nature of transboundary water agreements: the Israeli-Palestinian case[END_REF] pioneered a flow approach where the various actors interacting successively with the same flow of water were studied in spite of the fact each of these actors acted over a different scalar level. [START_REF] Lankford | Resource Efficiency Complexity & the Commons[END_REF] developed a reflection on water efficiency that also took the multiplicity of actual water flows in consideration. [START_REF] Trottier | Challenging the Coproduction of Virtual Water and Palestinian Agriculture[END_REF] harnessed his theoretical framework to examine actual flows of water. This article proposes to focus on the myriad trajectories of water flows in the West Bank, and the manner they have been affected by this massive donor intervention, to understand the territorial transformation that has occurred. A scientific discourse relies on the silence of its object [START_REF] Foucault | L'archeologie du savoir[END_REF].

Examining the multiple manners water flows have been altered sheds some light on the transformation of the hydro-social cycle in a manner that is independent from the discourses of those that brought it about.

The article starts by discussing the type of impacts water projects have on trajectories of water. It distinguishes spatial, institutional and sectoral trajectories and demonstrates that the usual considerations of annual stocks of water fail to shed light on many transformations entailed by development projects concerning water. The article then details our methodology to analyse the great number of projects concerning water carried out thanks to donors in the West Bank since 1994. In a third section, the article discusses the changes brought overall to each type of water trajectories and their consequences on Palestinian society. It concludes with a consideration of the territorial change that these projects induced. Clearly, the overall impact of all donor supported water projects is more than the sum total of these individual projects.

When space or a resource in this space is appropriated by a social actor, it becomes a territory. The objective of this article is to understand the territorial change entailed by the interactions between donors and the PA regarding water development. It proposes a methodology to explore the manner a great number of projects may entail territorial change because they alter societal interactions with water flows. Such a methodology can be useful to understand territorial change in any situation, elsewhere in the world, where a great number of water projects are carried out by the state, with or without close interaction with donors.

This study in no way denies the fact that Israel still occupies and still abstracts water from wells located in the West Bank. The article does not study such Israeli activity, which has been the focus of most articles on Palestinian water development.

The overwhelming attention paid to the role of Israel, as an occupying power, in shaping water development in the West Bank has led to a prolific literature discussed in the following section. This corpus stops short of exploring the internal Palestinian political processes that also contribute to the present water situation. Palestinians have been mostly portrayed as objects of Israeli action. Indeed, their degree of freedom is extremely limited. But they remain social and political actors. The PA and the donors use their degree of freedom and so do other Palestinian actors, such as farmers or business leaders. Our focus is to explore how Palestinian led, donor supported water projects have transformed Palestinian societal interactions concerning water. Such intra-Palestinian mechanisms are important. Their interactions with donors are significant.

The reality of Israeli occupation should not deter researchers from studying such Palestinian political developments.

The Impact of Water Projects on Trajectories of Water

Research has long portrayed water in Palestinian Territories as a competition between Israel and the PA for quantities of water. [START_REF] Brooks | Changing the nature of transboundary water agreements: the Israeli-Palestinian case[END_REF] showed this literature has focused on the yearly recharge of the aquifers as if it was a pie that needed to be divided between two parties. Research has emphasised the unequal distribution of water among the two populations [START_REF] Frederiksen | Water: Israeli Strategy, Implications for Peace and the Viability of Palestine[END_REF] [START_REF] Zeitoun | Water policy for sustainable development[END_REF]. This matches the approach of the Oslo agreements (1995) that proceeded with a quantitative allocation of water for Recent research explored the impact of the flow reversal entailed by the largescale desalination undertaken by Israel since the 2000s. Water used to flow from the land to the sea. This has now been largely reversed in Israel. Some explored the changes this entails for power relations within Israel and at the international level [START_REF] Feitelson | Desalination, space and power: The ramifications of Israel's changing water geography[END_REF]. However, the manner water flows within Palestinian territories involve power relations among Palestinian and foreign actors has hardly been studied.

Analysing water as a complex series of flows rather than as national stocks sheds light on stakes and power relations that remain otherwise undetected. When water flows, it follows a trajectory. Interacting with this flow, such as happens within a water development project, usually alters this trajectory. Several actors located on the previous trajectory may find themselves dispossessed from all or part of the water they used to access. Elsewhere, the degradation of water quality makes former uses impossible once this alteration is carried out. Often, new actors, previously unrelated to water uses, benefit from the new trajectory.

The trajectories water follows may be  Spatial, because water flows through space,  Institutional, as water flows successively through different human institutions managing it from the moment it emerges from the earth, or from the desalinating plant, to the point where it evaporates, is transpired by a plant or an animal, or reaches the sea,  Sectoral, as water is used successively by different sectors of activity such as agriculture, domestic use or industrial use.

Each of these three types of trajectories needs to be examined in turn.

Spatial trajectories of water flows refer to the paths water travels through whether as surface flow or underground. The Jordan River is no longer accessible to Palestinian farmers who used to divert its flow for irrigation before 1967, when the Israeli occupation began. So, for the purpose of this research on the West Bank, the only surface flows considered are springs. Their trajectory can change naturally. For instance, sudden floods may cause reflux phenomena underground that lead a spring to disappear. The trajectory and the flow of springs can also be altered artificially. For instance, wastewater released in the environment can swell the water of a naturally flowing spring. Underground flows are inextricably linked to surface flows. The karstic soil of the West Bank means that the complex trajectories of water underground are extremely difficult to map or model. Underground water trajectories can change naturally, such as in the example of refluxes cited above. They can also be altered artificially. For instance, the wells in Kufr Adam, close to Jenin, stopped being dry since the treated wastewater reuse scheme was put in place. This scheme brings treated wastewater from Jenin's treatment plant to irrigate fields and orchards. Enough water percolated from this irrigation to replenish these wells, an inadvertent result of the reuse scheme.

Infrastructure can transform spatial trajectories of water radically. For example, Los Angeles redirected the Owen River through several hundred kilometres to reach its drinking water network. [START_REF] Reisner | Cadillac Desert. The American West and its Disappearing Water[END_REF] Elsewhere, the Amu Darya and Sy Daria rivers were redirected by the Soviet Union to cotton fields for irrigation, thus causing the disappearance of the Aral Sea [START_REF] Karimov | The problems of fishermen in the southern Aral Sea region. Mitigation and Adaptation Strategies for Global Change[END_REF]. On a smaller scale, when treated wastewater is directed towards irrigation, this reuse is usually depicted as a 'creation of a new resource' [START_REF] Alfarra | A Framework for Wastewater Reuse in Jordan: Utilizing a Modified Wastewater Ruse Index[END_REF]. This is inaccurate. Reuse of treated wastewater in irrigation results from deviating water from a previous trajectory into a new trajectory.

Considering spatial trajectories of water, before and after projects are carried out, allows discerning the impacts of their alteration on the actors interacting with these flows and on the uses they made of this water. [START_REF] Fischendler | The Politics of Unilateral Environmentalism: Cooperation and Conflict over Water Management along the Israeli-Palestinian Border[END_REF]. This Israeli policy largely drives the present Palestinian reuse projects as discussed in the third section of this article. This large-scale depiction of spatial flows of water doesn't account for the many changes that occurred in recent years. Ein Far'a spring has dried out [START_REF] Tomeizeh | Water Rights[END_REF]. So did Ein Shibli, Ein Mishka and Ein Auja springs. All flowed abundantly until numerous, mostly unlicenced, wells started being drilled after 1994. These wells redirected the spatial trajectories of water. This caused the springs to dry. Elsewhere, new surface streams became perennial as cities and villages increasingly generated untreated wastewater.

These new trajectories of surface and groundwater have yet to be mapped. The changes in these trajectories have had a huge impact on Palestinian's interactions with water.

Institutional trajectories of water refer to the course of water through different forms of management from the moment it emerges either from the ground, or from the desalination plant, up to the point it evaporates or is transpired by a plant or an animal as illustrated in Figure 1. Tenure designates the relationship, either legally or customarily defined, between people, as individuals or groups, with respect to a resource [START_REF] Hodgson | Exploring the Concept of Water Tenure[END_REF]. Tenure is a social construction. It can be formal or informal, individual or collective. In the West Bank, when spring water is directed to a field, it is usually managed by farmers according to a common property regime. When a portion of this water seeps into the ground and recharges a well, it becomes managed by another institution. If the well is an agricultural well, the water might now be managed by a "shirket al bir", literally a 'well company' in dialectal Arabic. Such an institution is made up of farmers and deploys a common property regime over the water and the well, which is described in written statutes. The well might also be privately owned, in which case a private property regime now applies to the water. Once this water is abstracted from that well and directed to a field or an orchard, it may seep again into the ground and reappear in a well that is managed either by Israel or by the Palestinian Water Authority (PWA). In this case, it becomes managed by a public property regime [START_REF] Trottier | Challenging the Coproduction of Virtual Water and Palestinian Agriculture[END_REF].

Considering institutional trajectories allows understanding how various forms of water tenure are embedded within each other. It also allows understanding which forms of social organisation destined to manage water are strengthened or undermined whenever spatial trajectories are altered.

Sectoral trajectories refer to the course of water, as it is used successively in different sectors such as domestic use, industrial use or agriculture. Most domestic water is not consumed when it is used. Water becomes consumed when it evaporates, when it is transpired by an animal or a plant, or when it reaches the sea. The water that flows out of a household, after a bath for example, has been used but has not been consumed. Considering sectoral trajectories of water allows understanding the overall impact resulting from changes in either spatial or institutional trajectories. For instance, a project that refurbishes a reticulation network eliminates many of the leaks along this network. This changes the spatial trajectory of water because the flow of this leaked water to neighboring agricultural wells is decreased. It also changes the institutional trajectory. The flow of water through a farmer managed common property regime used for the well is reduced while the flow of water through a WWTP according to a public property regime is increased. Finally, the sectoral trajectory of this water is also altered if the water from the leaks that previously flowed to the farmer managed well was previously used in irrigation while the WWTP sells its treated wastewater to an industry, for instance. In this case, a change in spatial trajectory occasioned an institutional change from a common property regime to a public property regime and a sectoral change from irrigation to industry.

These three types of trajectories are subsets of each other. Spatial trajectories don't necessarily entail institutional trajectories. For instance, water in a river flowing through a desert island follows a spatial trajectory but doesn't follow an institutional or a sectoral trajectory. But institutional trajectories necessarily entail a spatial trajectory.

And sectoral trajectories necessarily entail an institutional trajectory. Changes in these three types of trajectories, taken all together, effectuate territorial transformation. This is examined in the last part of this article.

Since 1994, over 2000 projects concerning water were proposed for donor funding in the West Bank. Almost half of them were actually funded and 90% of the funded projects were implemented or ongoing in 2016. These projects were systematically planned and implemented in a piecemeal fashion, with consideration of their impact only in a very limited manner and over a small scale. The West Bank is a small place: 5,655 km 2 (OCHA, 2015). Research has also long shown the large sums that donors have invested in water development projects in the West Bank [START_REF] Le More | International assistance to the Palestinians after Oslo : political guilt, wasted money[END_REF]. So many water projects in such a small area have massively impacted spatial, institutional and sectoral water trajectories. The manner this impacts territorial

transformation has yet to be studied. Yet, research has long demonstrated that a piecemeal approach to development projects can have huge, overall, unwanted negative effects on a country [START_REF] Ferguson | The anti-politics machine : "'development,'" depoliticization, and bureaucratic power in Lesotho[END_REF]. Uvin (1998) demonstrated, for instance, the manner the many development projects in Rwanda contributed unintentionally to conditions that brought about the 1994 genocide. The overall impact of all donor supported water projects is more than the sum total of these projects. Understanding this overall impact requires us to understand how these projects alter the many trajectories of water and thus how they alter the manner Palestinian society structures its interactions with water. This allows understanding the path dependency and the territorial transformation entailed by this massive aid concerning water that poured into the West Bank since 1994.

Methodology

Our methodology combined several years of extensive fieldwork, deploying qualitative research methods, with quantitative methods and geographical information system analysis. We used three databases of water projects that were proposed by the PA for donor funding. 2009, listing 200 projects (World Bank, 2009). These three databases overlapped in part as some projects appeared in several bases. Moreover, large projects sometimes appeared as a series of distinct slices, each of which might be funded by a different donor or by the same donor but over different periods of time.

These databases were elaborated for political reasons. [START_REF] Espeland | The Struggle for Water, Politics, Rationality and Identity in the American Southwest[END_REF] Databases may still prove useful to researchers providing they are used carefully.

All databases distinguished between « inactive » projects that had not yet received either a permit from the Joint Water Committee (JWC) or a commitment from a donor, from « active » projects where donors had pledged funding but may not yet be undertaken. For a project to exist in these databases, someone, usually a donor, had to fund drafting the proposal. As a result, the projects are simultaneously Palestinian led and donor driven as well as donor supported. So, we studied all the projects, whether ongoing or unfunded. Indeed, these projects reflect the vision donors have for Palestinian water.

The maps, graphs and tables this study produces on the basis of these databases specify systematically whether they illustrate (1) both funded and unfunded projects or

(2) only funded projects. Projects that were neither funded nor implemented could not effectuate territorial transformation. Nevertheless, they are also worth being studied because their not being funded testifies to a development that wasn't pursued by donors.

Their being funded but not implemented testifies to a development that was pursued by donors but met with resistance from either Palestinian or Israeli actors.

The PWA databases were gathered in order to provide an overview of all water projects in the West Bank. The World Bank's database was part of its Movement and Access study series. It sought to allow a balanced analysis and create awareness of the factors restricting Palestinian water sector development. Table 1 summarises the type of information each database provided.

The information provided in these databases was combined with results from fieldwork on these projects' interactions with water trajectories carried out from 2016 through 2018 in the West Bank. This included field observations such as visits to farmers, their lands and their wells, semi-structured interviews and participant observation in meetings involving donors, the PWA and local contractors. This allowed identifying some inaccuracies in the databases, which are discussed at the end of appendix 2. A detailed description of our methodology appears in appendix 1. The information was spatialized to understand which transformations predominated over which areas of the West Bank.

Wastewater treatment projects and projects of reuse of treated wastewater required specific attention. They emerged as the type of projects that interacts with the biggest flows overall. They also redirect the spatial, institutional and sectoral trajectories of water flows far more than the other types of projects. A detailed description of our methodology to assess wastewater treatment and reuse projects appears in appendix 2.

The shortcomings of this methodology are discussed at the end of appendix 2.

Nevertheless, this methodology had some usefulness. Using this data cannot provide absolute values in terms of quantities and flows. This methodology allows identifying trends whereby spatial, institutional and sectoral flows are altered. This allows us to understand which categories of actors previously interacting with a water flow are dispossessed and which categories of actors that were not previously interacting with a water flow now start doing so. In so doing, we understand the transformations of societal interactions concerning water brought about by donors, whether these were intentional or not. 2 shows the number of each type of projects that appear in the databases. 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Nu mber of projects in the West Bank 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 These projects included the construction, rehabilitation or extension of domestic water networks, well drilling and rainwater harvesting. Between 1994 and 2016, 43% of domestic water projects that were proposed were funded (see Table 3). The construction and rehabilitation of domestic water networks made up 73% of the projects that obtained funding. With 593 funded projects, domestic water projects were the type most implemented. Map 3 shows most were located over the western aquifer. This matches the pre-existing demographic distribution and contributed to its perpetuation. Overall, three trends emerged concerning the impacts of domestic water projects on spatial trajectories of water since 1994:

The Changes in Water Trajectories

(1) They decreased the flow of water travelling towards the unconfined aquifer close to the networks.

(2) They increased a flow of desalinated water traveling from the coast to populated areas of the West Bank.

(3) They increased a flow of wastewater leaving the inhabitations and returning to the environment whether treated or untreated.

Agricultural water projects were least favored by donors (see Figure 3

(a)(b)(c)
and Table 2 and3). Even including treated wastewater reuse projects, only 197 agricultural water projects were proposed, of which only 33% were funded. These projects included irrigation network rehabilitation or improvement that accounted for 26% of the funded projects. They also included storm water sewerage projects which accounted for 42% of the funded projects. More recently, they also included wastewater reuse. Rehabilitation projects may transform open-air irrigation systems into piped systems. They may consist of lining dirt irrigation channels with cement or repairing the leaks in an existing piped system. Irrigation improvement usually means switching to drip irrigation. In each case, a greater proportion of the irrigation water flow is directed to plants to be transpired and less water percolates into the ground. This means less water flows towards uncultivated plants such as khubbeza, a highly nutritious weed which people pick free of charge in cultivated fields. Such weeds constitute a staple food for the poor [START_REF] Trottier | Challenging the Coproduction of Virtual Water and Palestinian Agriculture[END_REF]. Less water percolating through the soil means less water recharging the unconfined aquifer and percolating towards the neighboring village's well.

As of 2016, agricultural water projects, both proposed and funded, have been mostly located in the eastern aquifer (see Figure 3 (b), Table 4 andMap 3). The eastern aquifer hosts the highest number and the highest proportion of proposed agricultural projects.

Palestinian irrigation, up to the advent of reuse projects, relied on farmer managed wells or springsboth tapping the unconfined aquifer -the water of which was channeled to neighbouring lands [START_REF] Trottier | Water driven Palestinian agricultural frontiers: the global ramifications of transforming local irrigation[END_REF]. Before 1999, most irrigation from wells was located in the northwest of the West Bank over the western and northeastern aquifers. Most spring irrigation was located in the Jordan Valley over the eastern Overall, four trends emerged concerning the impacts of agricultural water projects since 1994 on spatial trajectories of water:

(1) A greater proportion of the irrigation water is directed to cultivated plants to be transpired.

(2) A lesser proportion of the irrigation water is directed to nourishing weeds and to crops cultivated within polyculture for subsistence purposes.

(3) A lesser proportion of the irrigation water recharges the upper, unconfined aquifer that supplies neighbouring fields and the wells of neighbouring villages with water.

(4) A new flow of water is brought to previously unirrigated land.

By 2016, wastewater projects totaled 222, of which 50% were funded (see Table 3). The construction and rehabilitation of wastewater networks made up 74% of the funded projects. The construction of WWTPs made up 10% of the funded projects.

WWTPs and reuse projects emerge in the early 2000s and multiply in the 2010s. The distribution of WWTPs doesn't depend only on the space available for building such large infrastructure. It also depends on land tenure, on Israeli permits from the civil administration for area C, and on politically motivated reasons from municipalities in some cases.

Reuse projects account for 64% of the projects that remain unfunded. This high rate is logical because most of them were proposed very recently. Appendix 2 details our methodology to calculate the flows involved in WWTPs and reuse projects. They entail the most significant changes in spatial trajectories of water (see Table 5). This is unsurprising because WWTPs usually collect the flow generated by several reticulation networks. Table 5 shows the outflow of the existing WWTPs is already important. It shows this outflow will increase significantly in the near future. Domestic water projects had predominated in the initial years of donors' involvement. WWTPs and reuse projects now constitute the next wave of donor led water development.

Up till donor intervention, nearly all wastewater seeped into the aquifer through domestic cesspits or was channeled into a nearby wadi, i.e. into a valley, ravine, or channel that is dry except in the rainy season. The many trajectories of these flows led simultaneously to a recharge and a contamination of the upper unconfined aquifer. The wastewater eventually gathered in wadis and, in the western and northeastern aquifer, Field work reveals that Jenin shows the most advanced case of reuse and illustrates this trend. The WWTP provides secondary treatment. Its outflow is channeled to formerly rainfed fields growing fodder north of the plant, through an underground drip irrigation system, and to orchards through an above ground drip irrigation system.

Here, sheep raising enticed farmers to invest in irrigating fodder. Previously, rainfed fodder only generated one crop a year. Now, the same plot provides ten crops a year.

What used to be a surface flow of wastewater into Israel has now been directed to Overall, four trends emerge concerning the impacts of wastewater and reuse projects since 1994 on spatial trajectories of water:

(1) The treatment of wastewater and reuse of treated wastewater aims to eliminate surface wastewater flow through the six entry points into Israel that causes a sizeable bill for the PWA.

(2) The projects aim to direct treated wastewater to previously rainfed land or, in the case of the Jordan Valley, to previously uncultivated land.

(3) The projects may inadvertently replenish dried up wells, but none of them aim to recharge the upper unconfined aquifer.

(4) Their alterations of spatial trajectories involve greater flows than those involved in other sectors.

Changes in Institutional Trajectories of Water

The changes in spatial trajectories of water detailed above have induced drastic changes in the institutional trajectories of water. They created, in theory, a new institutional trajectory whereby water would be controlled and managed entirely by the PWA through a public property regime. Extensive field work carried out over several years in the West Bank reveals that reality has differed significantly from this plan.

Municipalities still manage their wells and their WWTPs. The changes in spatial trajectories wiped out many preexisting institutional trajectories whereby grassroot organisations managed part of the spatial trajectory of water through common property regimes. They reduced the flows through other preexisting institutional trajectories.

These transformations also inadvertently led to the emergence of new actors, such as unlicenced well owners deploying private property regimes over water, and new, unforeseen institutional trajectories. Recently, some donors have switched to working with municipalities rather than the PWA, transforming the institutional trajectories initially set up by the donors.

The Oslo agreements created the PWA which, for many years, became donors' only interlocutor and main partner. Drilling wells in the deep, confined aquifer allowed supplying the PWA with the only water it controlled at a time when Palestinian well water was overwhelmingly managed by farmer organisations, even when these wells supplied municipalities [START_REF] Trottier | Hydropolitics in the West Bank and Gaza Strip[END_REF]. Building WWTPs managed by PA institutions and later reuse projects built by the PWA amounted in theory to a vertical integration of water management by the PA. In principle, such development places the institutional trajectory of water entirely in its hands. Water purchased from Mekorot by the PA or abstracted from a PA operated well is distributed to domestic networks. It is then collected as wastewater and channeled to a WWTP which in turns, sells it to farmers.

These are chosen according to criteria set by the PA at a price set by municipalities within a range determined by the tariff bylaw of 2013 for growing crops specified by the PA in a location chosen by the PA. A new tariff bylaw of 2018 exists but has yet to be approved (World Bank Group, 2018, p. 22). In practice, such a vertical integration did not occur because municipalities kept the control of domestic and wastewater management. Simultaneously, donor projects increased the PA's dependence on Israel since they contributed to its purchasing an increasing amount of water from Mekorot over the years. Thus, donors participated in increasing an institutional flow whereby water was first managed by Israel before being managed by the PWA. 'prior rights from springs or licenced quantity of water extracted from wells' but stops short of listing or detailing them [START_REF] Trottier | Water driven Palestinian agricultural frontiers: the global ramifications of transforming local irrigation[END_REF]. This law and decree do not foresee either a private property regime over water, yet many unlicenced private wells managing water according to a private property regime were legalised by the PWA after they started operating. A legal framework was thus created, with the support of donors, which made these changes in institutional trajectories invisible. Donors didn't plan the demise of existing, sustainable forms of local water management. They usually weren't aware of the impact of their projects over these institutions.

Since 2015, some donors such as French Development Agency and German Kreditanstalt für Wiederaufbau Development Bank have turned to partnering directly with municipalities for large water projects. This now transforms the institutional trajectories of water flows further. But nowhere is the upheaval in institutional trajectories more visible than in the new reuse projects. As irrigation water is directed to previously rainfed or uncultivated land, new actors emerge. Some are agribusinesses [START_REF] Trottier | Water driven Palestinian agricultural frontiers: the global ramifications of transforming local irrigation[END_REF]. This transformation of agriculture matches what has been described as a neoliberal conflict resolution and state building in the West Bank [START_REF] Haddad | Palestine Ltd. Neoliberalism and Nationalism in the Occupied Territory[END_REF]. This is explored further in the last section of this article.

Changes in sectoral trajectories

In 1994, upon the arrival of donors in the West Bank, irrigation accounted for the majority of water consumed by Palestinians even though only about 6% of cultivated land was irrigated. Open air, dirt irrigation channels were common and flood irrigation was still widespread. This meant that a sizeable proportion of spring and well water directed towards irrigation contributed to replenishing the upper, unconfined aquifer and the neighbouring wells that tapped into it. The sectoral trajectory of water thus often entailed being channeled first to an irrigated field before reappearing in a well and being directed to domestic use. Projects targeting irrigation systematically aimed to increase its efficiency at the field level. They reduced the flow of water along any trajectory other than that leading to the cultivated plant. Lankford demonstrated the usefulness of the many other trajectories "wasted" water followed in systems deemed inefficient [START_REF] Lankford | Resource Efficiency Complexity & the Commons[END_REF]. Considering the transformation to these many trajectories shows that, while, overall, donor led projects didn't aim to transform a sectoral allocation of water among Palestinians, they did transform the sectoral trajectories water followed.

The dominant sectoral trajectory emerging from the sum of donor projects is one whereby water first travels through a domestic use, then reaches a WWTP before being directed to reuse either in irrigation or in industry. This matches the hegemonic representation supporting the "right to water" promoted by the United Nations and brings about territorial change.

Territorial Changes Resulting from 25 Years of Water Aid

The overall impact of all donor supported water projects is more than the sum total of these projects. This emerges clearly when considering the manner transforming the spatial, institutional and sectoral trajectories of water flows results in territorial transformation. Elden defined territory as a political technology that includes techniques to measure land and to control the terrain [START_REF] Elden | Land, terrain, territory[END_REF]. Our work shows that this political technology also includes techniques to interact with water flows. Altering the spatial trajectory of water flows entails a transformation of their institutional and sectoral flows. This alters the control actors previously exerted on water, favours some, eliminates others and introduces new ones. In short, while every water project aimed to increase the efficiency of one system over a small scale, it transformed the territory overall by changing the manner Palestinian society interacts with water.

The overwhelming focus on the international scale within the literature on Palestinian water [START_REF] Elmusa | Negotiating Water: Israel and the Palestinians[END_REF] [START_REF] Selby | Water, Power & Politics in the Middle East The Other Israeli-Palestinian Conflict[END_REF] [START_REF] Schlütter | Water Rights in the West Bank and in Gaza[END_REF] The global literature on water has long recognised the importance of a public participatory approach to illuminate the distribution of the gains and losses of a project across different social groups, before a project is undertaken [START_REF] Beekman | Social Change and Water Resource Planning and Development[END_REF]. But examining the environmental and social impact assessments of water projects carried out in the West Bank show that they tended to consult token groups of concerned parties outside of those asking for a project. Participation can never constitute a silver bullet, in any case, because so called stakeholders usually exclude the views of segments of the population [START_REF] Tortajada | Water infrastructure as an essential element for human development[END_REF]. Field work showed that few donors became aware of the role of local Palestinian actors, such as farmers. This is a common occurrence wherever communities are heterogeneous and dominated by a local elite whose preference doesn't match that of the grassroots [START_REF] Platteau | Elite capture through information distortion: A theoretical essay[END_REF]. The 'water flow The funded projects systematically fitted that vision. This led to the rise of alliances between the PA and private actors on the basis of a neoliberal understanding of efficiency. New actors include small farmers interested in cultivating land, within reuse schemes, which they intend to rent, one hectare at a time, from their owners who used to practice rainfed agriculture and polyactivity. New actors also include agribusinesses that rent large tracts of desert land in the Jordan Valley, 60 hectares at a time, intending to develop irrigation of medjoul dates destined for exportation. Irrigated agriculture in the Jordan Valley is ancient. But for the past hundred years, it was carried out on the basis of water turns from Ein Sultan, Ein Auja and Fassayil springs, or from the 16 springs that used to flow in Ein El Beida, Bardala or Kardala [START_REF] Trottier | The social construction of water management at the intersection of international conflict The Case of Al Auja[END_REF] [START_REF] Trottier | Le rapport à l'eau et à la terre dans la construction de territoires multisitués: le cas palestinien[END_REF].

These water turns were not monetised. The changes brought to water tenure have transformed the sort of actors who can access water and the purposes for which they access it. Overall, the changes entailed by the water projects undermined the livelihoods that depended on a water tenure that was not monetised. They also increased the dependence of the PWA on water delivered by Mekorot.

Conclusion

Whether or not the projects concerning water have contributed to the emergence of a Palestinian state is debatable. Overall, they have undermined the grassroot organisations that had developed sustainable water management locally. The main advantage of the methodology developed here is that it leads to conclusions that are not foreclosed by the underlying theoretical framework. It can be used elsewhere in the world wherever a great number of water projects are carried out within a relatively small space. The evolution of a water sector fuelled by foreign aid is intertwined with the changing nature of a state [START_REF] Sharma | Foreign Aid and Institutional Plurality: The Domestic Water Sector in Nepal[END_REF]. This methodology provides a tool to explore such transformation.

  Israel and the PA from each of the three main aquifers lying in the West Bank detailed in Annex 10, Paragraph 20, Article 40 of the Protocol Concerning Civil Affairs. This focus on 'national' quantities has obfuscated many aspects of water politics among Palestinian actors.

  Currently, spatial trajectories of water in the West Bank are mapped very roughly, over a large scale. Three main aquifers lie under the West Bank. The most plentiful flows towards the west, into Israel. The northeastern aquifer flows northward into Israel and the eastern aquifer flows mostly towards the Jordan River as illustrated by Map 1. Israel has built a series of wastewater treatment plants (WWTPs), inside Israel, along the Green Line, to treat the wastewater reaching it as surface flow from the West Bank through six entry points (see Map 2). Maps 2, 3 and 4 locate all information within the zoning of the West Bank into A, B and C areas. For a discussion of these areasTransboundary wastewater and Israeli wastewater treatment plants Israel charges the PA both for the building costs and the running costs of these plants. It then supplies the outcoming treated wastewater to Israeli farmers inside Israel

Figure 1 -

 1 Figure 1 -Example of institutional trajectories of water flows

  noted that numbers are the tools of the weak when they face powerful outsiders. The West Bank water databases are no exception. The 2009 databases were gathered to support the "Palestinian Reform and Development plan" led by Prime Minister Fayyad starting in 2007. State institutions always have political objectives when they gather data.

  Emerging from 25 years of Donor Supported Water Development Donors funded, in part, the type of projects Israel had been developing in the West Bank, in the sector of domestic water, after its occupation in 1967. They also funded irrigation water and wastewater projects, a type of project initially introduced during the first intifada by Palestinian non-governmental organisations (NGOs) such as the Palestinian Agricultural Relief Committees (PARC) or the Union of Agricultural Work Committee (UAWC). Donor intervention increased the dimensions and number of such projects significantly after 1994. Table

  Figure 2 shows the number of projects along a timeline according to the year they were proposed. The number grew up till the outbreak of the second intifada at the end of 2000. It then decreased to a low in 2007 before reaching a peak in 2010. This matches the local historical landmarks. During the intifada (2000-2004), the security situation prevented the emergence of new projects. The 2006 elections led Hamas to victory, which did not please donors. The latter threw their support behind the government of Salam Fayyad who became prime minister in 2007. Elaborating a water project takes time and the 2010 peak corresponds to the lag time between the advent of the Fayyad government and the completion of the proposals.

  Figure2

Figure 2 :

 2 Figure 2: Number of water projects according to the year they were proposed from 1994 to 2016 (PWA, 2016)

  Figure 3 (a)

Map 3 .

 3 Status of the water projects in the West Bank from 1994 to 2016 (PWA 2016) The construction or extension of domestic water network or the drilling of a well creates a new spatial trajectory for water. The new, donor funded wells drilled in the West Bank reached depths over 600 meters. They tapped the lower, confined aquifer, a novelty for Palestinians whose wells, up to 1994, had mostly tapped the upper, unconfined aquifer. The rehabilitation of domestic water networks changes the proportion of flows along two different trajectories. More water flows to the designated destination and less water leaks out of the reticulation network. Consequently, the leaked flow along the trajectory leading water to the neighboring wells tapping into the unconfined aquifer, or to neighboring fields decreases. A brand new, or newly rehabilitated reticulation network typically leaks 20% of its water. Older, badly maintained networks could leak 0 of the water they carried. The difference in the flow to the neighboring unconfined aquifer is significant. Rainwater harvesting projects least altered the spatial trajectory of water. They mostly delayed the percolation of rainwater through the soil because they tended to occur where houses were unconnected to a sewage system. However, 88% of rainwater harvesting projects appearing in the databases were never funded. The significant development of domestic networks contributed to an increasing dependence of the PWA upon Mekorot. By 2011, the PWA purchased 53 million m 3 /year from the Israeli national water company, Mekorot (Palestinian Water Authority, 2011). Overall, that year, its domestic networks received 88.3 million m 3 /year and « consumed » [sic] 62.3 million m 3 /year. Already, 60% of domestic water managed by the PWA was purchased from Israel. In 2016, the PWA purchased 69 million m 3 from Mekorot, i.e. 59% of the 117 million m 3 it was directing to domestic networks (World Bank Group, 2018). Mekorot uses a variety of sources, including wells located in Israel as well as in the West Bank, but the large-scale desalination Israel undertook in the 2000s has led to a steady increase in the share of desalinated water within the portion of water it supplies to the PWA.

  fodder and trees for transpiration for 8 months of the year. Farmers don't irrigate for the remaining 4 months because rainfall spares them the cost of treated wastewater. During those months, the outflow of the wastewater plant keeps reaching Israel. A waiting list of farmers exists, ready to purchase any additional treated wastewater once more houses are connected to the plant. Neighbouring farmers, with water rights to local wells that are now dry, are not participating in this project.Many wells tapping the upper unconfined aquifer in villages located between Jenin and the northern limit with Israel have become dry since 2006. Yet, as in the rest of the West Bank, no project aimed to recharge the aquifer to supply them with water once again. An unintended consequence of the reuse project in Jenin was the replenishment of wells in the neighbouring village of Kufr Adam. The reuse project directed the flow of treated wastewater in part, as planned, to plants for transpiration and, in part, unwittingly, to these agricultural wells.Reuse projects in the West Bank aim to irrigate previously rainfed or uncultivated land. None aim to direct water to farmers who irrigated previously or to recharge their wells or springs. Thus, reuse projects are creating new trajectories for water. Map 4 and Table5illustrate these changes in spatial trajectories and the flows this represents once the reuse projects are implemented. Reuse from Nuba WWTP Nursery Reuse from Al Arrub Camp WWTP Reuse from Al Tireh WWTP 1000 m3/d for Ramallah city service Reuse from Al Bireh WWTP 5750 m3/d to irrigate 26900 dunums in Al Auja Reuse from Ramallah WWTP Reuse from Biddya WWTP 11 m3/d for fodder and fruit trees Reuse from Hajja WWTP 40 m/d for olive trees Reuse from Nablus West WWTP 8850 m3/d for fodder and fruit trees Reuse from Attil WWTP 30 m3/d for 13 dunums of agriculture Reuse from Zeita WWTP 4.5 dunums of almond trees Reuse from Jenin WWTP 600 dunums of fodder and almond trees Reuse from Mysillia WWTP 50 m3/d for agriculture Reuse from Anza WWTP 100 m3/d for 20 dunums of agriculture WWTP 9889 m3/d for date palm treesThe 2016 database shows wastewater projects are mostly located in the eastern aquifer as illustrated in Figure3(c) and Map 3.The 2013 PWA strategy aims to direct most of the reused water to the Jordan Valley in order to irrigate date palm trees(Palestinian Water Authority, 2013). This could entail a trunk line carrying treated wastewater from Al Bireh to Al Auja, bringing water 40 km away to land never previously irrigated. This project has yet to obtain funding but its feasibility study was completed thanks to European Union funding (Environmental and Social Impact Assessment for Al-Bireh Reuse Trunk Line toAl-Auja Area, 2016). Such expensive projects could be avoided if the treated wastewater was instead used to recharge the upper unconfined aquifer supplying existing agricultural wells and springs with water. Altering the spatial trajectories of wastewater to develop reuse on previously rainfed land or on previously uncultivated land entails a deep alteration of institutional trajectories of water, which is examined in the following section.

Farmer

  organisations deploying common property regimes to manage wells and springs tapping the upper, unconfined aquifer have faced drastically reduced flows, often a complete disappearance of the resource[START_REF] Trottier | Water driven Palestinian agricultural frontiers: the global ramifications of transforming local irrigation[END_REF] [START_REF] De Donato | Spring Water : the Lifeblood of the Village of Wādī Fūkīn (West Bank)[END_REF]. Storm water sewerage, spring rehabilitation, irrigation network improvement and rehabilitation projects didn't overtly alter the institutional trajectories of the water they managed. But, overall, water projects contributed to reduce the flows replenishing their water source, as detailed in the previous section on spatial trajectories. The treated wastewater generated by WWTP could have been directed to replenish the aquifer feeding wells and springs devoted to irrigation. Instead, it is directed to previously unirrigated land. This has contributed to the demise of many farmer organisations that deployed grassroot common property regimes over springs or wells. Other reasons also contribute to explain the reduction in flows managed by the grassroot organisations predating the PWA. Growing urbanisation, whether in Israeli settlements or in Palestinian towns, increases impermeable surfaces, which interferes with the recharge of the upper unconfined aquifer. Numerous unlicenced wells deploying private property regimes have contributed to drying previously abundant springs. Israeli wells in the West Bank also have an impact. But the changes in spatial trajectories detailed above have undeniably contributed to the demise of many institutional trajectories whereby farmer organisations managed wells and springs for irrigation purposes. The 2002 Palestinian Water Law (2002) did not even mention farmer organisations managing water locally. Article 31 of the 2014 decree on water mentions

  [START_REF] Abu-Eid | Water as a Human Right: The Palestinian Occupied Territories as an Example[END_REF])[START_REF] Gasteyer | Water Grabbing in Colonial Perspective: Land and Water in Israel/Palestine[END_REF] contributed to painting a situation where Palestinians had no control over their water, as if local institutions didn't exert any management on any portion of the spatial trajectories of water since the beginning of the Israeli occupation in 1967. Donors' representation of existing water management stemmed from this literature.

  analysis' followed in this article shows a territorial change largely unintended by donors. Donors always proceed with impact assessments before they carry out a project and with an evaluation post-project. The epistemology driving these impact assessments and evaluations embeds the preferences of the donors. What is considered costeffective, environmentally sustainable or in the interest of the public good is determined by the vision of what constitutes development within the donor culture. The vision of what constitutes development is a social construction. It generates many blind spots within these impact assessments and evaluations. Many societal interactions with water are not considered. And every project is considered in a piecemeal fashion, which prevents these assessments and evaluations from including the overall impact on the actors interacting successively with the many flows generated by the one flow under study within one project. A careful examination of the types of changes in trajectories shows that those brought about by Palestinian NGOs before 1994 differed significantly from those now brought about by donors, while those brought about by the Israeli Civil Administration were furthered and magnified by donor supported projects. After 1967, Israel introduced reticulation networks to bring domestic water to several Palestinian villages. This work was pursued by donors after 1994. During the first intifada, Palestinian NGOs introduced small, low cost, domestic greywater treatment units. These filtered the greywater from one household to irrigate a few fruit trees next to the house. Such small scale systems were managed by individual households. Such work was less supported by donors after 1994. The global economic crisis in 2008 occasioned an unexpected, steep spike in the price of food commodities. It fuelled a drastic increase of export oriented contract farming around the world. This affected Palestinian development projects as well. For instance, the Food and Agriculture Organisation of the United Nations developed the Global Gap certification in Palestinian farms. Such certification allows a farmer to export his produce because it ensures the production process follows recognized standards (Liu, Casey, Cadilhon, Hoejskov, & Morgan, 2007). Agricultural water projects multiplied (see Figure 3) because irrigation stabilises production and allows a farmer to meet the calendars set by contract farming. The Kerry Plan gathered the tools deemed valid by the existing scientific discourse and policies to construct economic development in a future, independent state of Palestine. As far as agriculture is concerned, important components of this discourse and policies were constructed between 2008 and 2012. This includes a priority given to the development of contract farming for export oriented crops.The Kerry Plan integrated such processes into an economic development plan. The political part of the Kerry Plan collapsed but the agricultural component of its economic component matches many aspects of what now unfolds in the West Bank. What sort of territory arises from 25 years of water development in the West Bank? Projects purportedly aimed at supporting the PWA to develop a state that would manage water according to a public property regime. Created by the Oslo agreements in 1994, the PWA emerged in a context where a specific understanding prevailed concerning what constitutes an « efficient » economic management of the environment.

  They have simultaneously contributed to integrating Palestinian society into globalisation. They have introduced a monetised interaction with water where none existed before. They have introduced foreign engineering firms that showcase their technology in the wastewater plants they build. They have participated in reducing subsistence agriculture. They have introduced agribusiness led irrigated agriculture in otherwise desert land. The preference of irrigation and reuse projects for the eastern aquifer, where rainfall is lowest, shows the priority given to develop commercial agriculture in the desert in a fashion that mirrors the development of American agriculture. The preference of domestic water projects for the western aquifer contributes to the perpetuation of the existing demographic distribution in the West Bank. Finally, the clustering of these projects close to B and A areas has left a large track of C area undeveloped, open to the development of Israeli settler agriculture and development.

Figure 1 -Figure 3 Figure 3

 133 Figure 1 -Example of institutional trajectories of water flows

Table 1 .

 1 Information on the three databases

		Number of projects	I nformation abou t the projects provided
			Short description of project
			Donor (if funded)
			Implementing agency (if active)
	PWA database of 2009	1135	Location of project
			Distinguishes between
			proposed or active projects
			Costs (if project is active)
			Short description of project
			Donor (if funded)
			Implementing agency (if active)
	PWA database of 2016	1978	Location of project Year of proposal
			Distinguishes between
			unfunded or submitted or
			implemented or ongoing
			Costs (if project is active)
			Short description of project
			Donor (if funded)
			Location of project
			Estimated Cost
	World Bank database 2009	200	Planned number of beneficiaries of projects
			Date of submittal to JWC
			Date of approval of JWC
			Distinguishes between pending
			approval or approved by JWC

Table 2 .

 2 Number of domestic, agricultural water and wastewater projects according to the different databases.

			Number of projects
	Database	Domestic water projects Agr icultural water Wastewater Others TOTAL
	PWA 2016	1378	197	222	181	1978
	PWA 2009	553	4	468	110	1135
	World Bank 2010	175	12	13	0	200

Table 3 .

 3 Type and proportion of funded and undunded domestic, agricultural water and wastewater projects(PWA 2016)

		Number of projects	Pro p o r tio n of funded projects	Funded projects	Pro p o r tio n of the funded projects	Unfunded projects	Pro p o r tio n of unfunded projects
						Construction and
				Construction of domestic water network	45%	rehabilitation of domestic water	70%
	projects Domestic water	1378	43%			networks
				Rehabilitation of domestic water network	28%	Rainwater harvesting	19%
				Storm Water sewerage	42%
	Ag r icultural water projects	197	33%	Irrigation network rehabilitation / improvement	26%	Wastewater reuse in agriculture	64%
	Wastewater projects	222	50%	Construction and rehabilitation of wastewater network Construction of wastewater treatment plant	74% 10%	Construction of wastewater network Construction of plant wastewater treatment	56% 19%

Table 4 .

 4 Number of agricultural water projects per aquifer(PWA 2016) to a lesser extent, south of Jerusalem over the western aquifer. The springs either dried out or have seen their flows drastically reduced in recent years. Agricultural water projects tended to neglect the northwest of the West Bank. They often targeted users and land in the Jordan Valley that was not previously irrigated. Spring rehabilitation was funded in the late nineties. This is now superseded by new projects to reuse treated wastewater generated by the newly built WWTPs. Such projects are examined in the following section, dealing with wastewater.

	Aquifer	Number of projects	Number of total water projects (when know n)
	Western	51	785
	Northeastern	42	441
	Eastern	103	685

Table 5 .

 5 Present and planned treated wastewater outflow and treated wastewater reuse flows for existing WWTPs and WWTPs under construction. flowed into Israel through the Green Line, mainly through the six entry points illustrated on Map 2. In 2017, 21.4 million m 3 of wastewater flowed into Israel which billed the PA 31 million$ for treating it(World Bank Group, 2018). The PA counts on WWTPs and reuse projects to eliminate this outflow of surface wastewater into Israel, thereby eliminating this sizeable expense.

	Wastewater treatment pl ant	2019	Futur e

Table 3 -

 3 Type and proportion of funded and unfunded domestic, agricultural water and wastewater projects (PWA 2016) Map 3 -Status of the water projects in the West Bank from 1994 to 2016 (PWA 2016)

Table 4 -

 4 Number of agricultural water projects per aquifer(PWA 2016)

Table 5 -

 5 Present and planned treated wastewater outflow and treated wastewater reuse flows for existing WWTPs and WWTPs under construction Map 4 -Existing wastewater treatment plants and proposed or active treated wastewater reuse projects in the West Bank

Appendix 1 -Detailed methodology Appendix 2 -Methodology for wastewater treatment projects

Constructed