Darde Benjamin

Dr Anh Minh Tang

Minh

Author

• Pereira

Roux Jean-Noël

Hydro-mechanical behaviour of high-density bentonite pellet upon partial hydration

Keywords: Partial saturation, Expansive soils, Laboratory tests

The hydro-mechanical behaviour of a high-density bentonite pellet, potential candidate for engineered barriers in high-level radioactive waste disposal, is investigated through laboratory tests. Water content and volumetric strain are first determined at various suctions (ranging from 9 MPa to 89 MPa) during partial hydration from its initial state. Afterward, compression tests allow the Young modulus and strength to be determined at various suctions. The experimental results are then interpreted by using an existing model describing the hydro-mechanical behaviour of an aggregate in compacted expansive clay. The analyses show that a single set of parameters is sufficient to predict the suction dependency of volumetric strain, Young modulus and compressive strengths. These findings would be helpful for further numerical investigations on the hydro-mechanical behaviour of granular bentonite-based engineered barriers by using both finite element and discrete element methods.

List of notations

Introduction

Bentonite-based materials are considered as candidate materials for engineered barriers in radioactive waste disposal due to their low permeability, good radionuclides retention capacity, and ability to swell upon hydration, which is an important property to fill the technological voids.

While many studies on the hydro-mechanical behaviour of bentonite-based engineered barriers have focused on compacted blocks of bentonite, bentonite pellets/powder mixtures have also been considered as an interesting alternative [START_REF] Volckaert | Thermalhydraulic-mechanical and geochemical behaviour of the clay barrier in radioactive waste repositories (model development and validation[END_REF][START_REF] Van Geet | The use of microfocus X-ray computed tomography in characterising the hydration of a clay pellet/powder mixture[END_REF][START_REF] Imbert | Hydro-mechanical response of a bentonite pellets/powder mixture upon infiltration[END_REF]Hoffman et al., 2007;[START_REF] Alonso | Hydromechanical behaviour of compacted granular expansive mixtures: experimental and constitutive study[END_REF][START_REF] Gens | Hydromechanical behaviour of a heterogeneous compacted soil: experimental observations and modelling[END_REF][START_REF] Guerra | In-depth characterisation of a mixture composed of powder/pellets MX80 bentonite[END_REF].

After [START_REF] Kröhn | New evidence for the dominance of vapour diffusion during the resaturation of compacted bentonite[END_REF], vapour diffusion plays a significantif not dominantrole in the resaturation process of bentonite-based engineered barriers. In order to study the hydromechanical behaviour of bentonite pellets mixtures upon hydration by vapour transfer, accounting for the granular nature of the material (Molinera- Guerra et al., 2018a,b), numerical simulations based on the discrete element method (DEM) [START_REF] Cundall | A discrete numerical model for granular assemblies[END_REF][START_REF] Roux | Généralités sur la simulation numérique discrète des matériaux granulaires[END_REF][START_REF] Agnolin | Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks[END_REF][START_REF] Than | Basic Mechanical Properties of Wet Granular Materials: A DEM Study[END_REF] could be an interesting way of assessing the influence of pellets swelling on the mixtures behaviour. In DEM simulations, each particle is modelled individually. A model describing the hydro-mechanical behaviour of a single pellet is therefore required. As this approach is valid for granular materials, the model has to focus on hydration state at which a pellet has not lost its initial structure.

For this purpose, the present study focuses on the hydro-mechanical behaviour of a single pellet upon partial hydration. The vapour equilibrium technique is used to hydrate the pellet. At equilibrium, the pellet volume and water content are determined, which allows determining the relationship between volumetric strain and suction. Afterward, a compression test is performed on the pellet to determine its stiffness and strength. Finally, the results are interpreted through the conceptual framework proposed by [START_REF] Alonso | Modelling the mechanical behaviour of expansive clays[END_REF].

Material

The material characterised in this study are sub-spherical MX80 bentonite pellets. MX80 is a Na-bentonite from Wyoming, with high smectite contents, which main physical properties are summarised in Table 1. Pellets are obtained through compaction of bentonite powder. They are composed of a cylinder-shaped part and two spherical ends (Figure 1). Their initial properties are shown in Table 2.

Experimental methods

Suction-controlled hydration is performed through the vapour equilibrium technique [START_REF] Tang | Controlling suction by the vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay[END_REF][START_REF] Delage | Ageing effects in a compacted bentonite: a microstructure approach[END_REF]. Pellets are placed within a desiccator containing a saturated salt solution. When equilibrium is reached (verified by pellet mass), the pellets dimensions are measured using a camera (one picture is taken from the side, Figure 1a, and pellet's height and diameter are measured with an accuracy of 0.01 mm). Axial strain ε a and radial strain ε r are determined by comparison of height and diameter with their initial values. Volumetric strain ε V is calculated as follows:

(1)

Compression tests are carried out by using a load frame (Figure 2). The displacement rate is imposed at 0.1 mm/min. Displacements are recorded by a displacement transducer and the contact force between the pellet and the frame is recorded by a force transducer (with an accuracy of 0.1 N).

Compression tests are performed in both axial and radial directions (Figure 3). In axial compression tests (Figure 3a), contact between the load frame and the pellet is sub-punctual.

Assuming isotropic linear elastic behaviour, the Hertz law is adapted to obtain Young modulus [START_REF] Johnson | Contact Mechanics[END_REF]:

(2)

Where N is the axial load; E and ν are Young modulus and Poisson's ratio, respectively; δ n is the normal displacement.

In radial compression test (Figure 3b), the contact is assumed to be linear. [START_REF] Johnson | Contact Mechanics[END_REF]'s elasticity law, relating normal displacement to normal force for a contact between an infinite plate and a cylinder, is applied to determine E.

(3) Figure 4 presents the results corresponding to s = 89 MPa. Several tests are performed and one curve is chosen to show the method for determination of E. For axial compression tests (Figure 4a), N increases with increasing displacement until failure. At failure, N decreases abruptly. The Hertz law (equation 2) is then used to fit experimental data from the start to the failure to determine E. In the present work, ν = 0.3 for the sake of simplicity. For radial compression tests (Figure 4b), N increases with increasing displacement in two distinct phases: first, a slow increase; second, a more significant and sub-linear increase. The first phase is interpreted as the consequence of an imperfect contact between the frame and the pellet at the beginning of the test. As displacement increases, the contact becomes linear and the forcedisplacement relationship is significantly modified. Considering this hypothesis, equation ( 3) is used to fit experimental data only from the start of the second phase to the failure.

In the present work, beside the initial suction, eight suctions (ranging from 9 MPa to 82 MPa) are considered. For each one, several pellets are analysed to assess the repeatability of the experimental data.

Experimental results

Figure 5 presents w versus elapsed time during the suction equilibrium phase. From its initial value (12.2%), w increases quickly during the first days and equilibrium is reached after 10 days, except for the lowest suction (9 MPa) where 30 days were necessary. The values obtained at equilibrium (Figure 5) are then plotted versus imposed suction in Figure 6a. Along the hydration path (decrease of suction from 89 MPa to 9 MPa) w increases from 12.2 % to 24.3 %. Results obtained on the same materials (MX80) in other studies are also plotted. Within the investigated suction range, w -s relationships are similar and do not depend on the initial dry density or hydration conditions. Figure 6b presents the degree of saturation (S r ) versus suction which shows that S r does not change significantly during this hydration phase.

Figure 7 presents the strains versus suction during this hydration phase. ε a is generally higher than ε r . The mean values of ε v , obtained from the mean values of ε a and ε r , are plotted. As expected, ε v keeps increasing upon hydration.

The mechanical properties (E and strength) are plotted versus suction in Figure 8. Moduli obtained for both axial and radial compression tests are similar (Figure 8a) and a single mean value is retained for both compression directions. These results confirm that the assumptions used to interpret the compression tests (isotropic linear elastic behaviour, equations 2 & 3) are appropriate. Upon hydration, the pellet modulus and strength decrease significantly.

Finally, the relationship between compressive strengths and modulus is presented in Figure 9. A linear relationship is suggested for both axial and radial directions.

Model

In the present work, the pellet initial dry density is high and its behaviour is assumed to be similar to that of an aggregate (i.e. the microstructural level) in compacted expansive clay following the model proposed by [START_REF] Alonso | Modelling the mechanical behaviour of expansive clays[END_REF].

Microstructural volumetric strain is written:

(4) (5)
Where K m is the microstructural bulk modulus, is the effective mean stress (equal to s in the present study), α m and β m are material parameters.

From compression tests results, α m = 0.024 MPa -1 and β m = 0.016 MPa -1 are obtained through basic exponential regression (Figure 8a).

Integrating ( 5) from initial suction s 0 to a given suction s leads to:

(6)

Where α m and β m values, determined from compression tests results, are found to satisfactorily model the volumetric strain upon hydration (Figure 7).

From Figure 9, it seems convenient to propose a linear relationship between pellet strengths and modulus. The following relationships are proposed:

(7) (8)
where C A and C R are material parameters relating the strength to the modulus for axial and radial compression tests, respectively. C A = 1.20610 -7 m -2 and C R = 1.81610 -7 m -2 following the fitting (Figure 9).

From ( 5), ( 7) and ( 8), the evolution of pellet strength upon hydration can be written:

(9) (10)
Model predictions are presented in dash lines in Figure 9, along experimental results for comparison.

Discussion

The experimental results show that partial hydration induces an increase in water content and pellet volume and a decrease in Young modulus and strength. These trends agree with existing results on bentonite-based materials [START_REF] Wiebe | Influence of pressure, saturation, and temperature on the behaviour of unsaturated sand-bentonite[END_REF][START_REF] Blatz | Influence of suction on the strength and stiffness of compacted sand-bentonite[END_REF][START_REF] Lloret | Mechanical behaviour of heavily compacted bentonite under high suction changes[END_REF][START_REF] Tang | Modelling the thermo-mechanical behaviour of compacted expansive clays[END_REF]Carrier et al., 2016). However, the volumetric strain obtained in the present work (50% for hydration from 89 MPa to 9 MPa) is higher than that observed on a single MX80 bentonite aggregate (25%, after Tang and Cui 2009). In addition, the Young modulus measured in the present work is generally one order of magnitude smaller than that measured by Carrier et al. ( 2016) on MX80 bentonite clay film over the same suction range. It means that the mechanical behaviour of the material is strongly dependent on the dimensions of the specimen.

In addition, it is interesting to note that the results obtained by compression tests (Figure 8a) can be used to predict the results obtained by hydration (Figure 7). The role of total stress is thus similar to that of suction as suggested by [START_REF] Alonso | Modelling the mechanical behaviour of expansive clays[END_REF] for microstructural level.

The present work contributes to a more comprehensive approach to model the behaviour of a single pellet. These results would be helpful for further numerical investigations on the hydromechanical behaviour of granular bentonite using the finite element method with double-porosity models (i.e. [START_REF] Alonso | Hydromechanical behaviour of compacted granular expansive mixtures: experimental and constitutive study[END_REF] where a single pellet corresponds to the micro-structural level.

Actually, Molinero [START_REF] Guerra | In-depth characterisation of a mixture composed of powder/pellets MX80 bentonite[END_REF] performed mercury intrusion porosimetry on a similar bentonite pellet and found that the volume of macro-pores is negligible at high suction. Besides, for numerical investigations using discrete element modelling, these results can be directly used to describe the behaviour of a single pellet under hydro-mechanical loading.

However, it is worthy to mention that the behaviour of the pellet observed in the present work doesn't correspond to all the assumptions proposed for an aggregate in the model of [START_REF] Alonso | Modelling the mechanical behaviour of expansive clays[END_REF]: (i) the pellet is not fully-saturated; (ii) its behaviour is not reversible; (iii) the volumetric behaviour of the pellet is not isotropic. In spite of these disagreements, the model would correctly predict the hydro-mechanical behaviour of a pellet during this partial hydration path (up to 9 MPa of suction). At suction lower than this value, the model would no longer be valid as the pellet would disaggregate (as suggested by [START_REF] Saiyouri | Experimental study of swelling in unsaturated compacted clays[END_REF] for bentonite particles, [START_REF] Koliji | Constitutive modeling of unsaturated aggregated soils[END_REF][START_REF] Cardoso | A constitutive model for compacted expansive and bonded marls[END_REF] for clay aggregates less reactive than bentonite).

In addition to the volumetric behaviour, the strengths of the pellet under compression can be also predicted by using the same values of α m and β m . These results can be explained by the linear correlation between the strengths and the modulus. Actually, correlations between these two properties were observed on various compacted clayey soils [START_REF] Lee | Strength and modulus of marine clay-cement mixes[END_REF][START_REF] Zeh | The tensile strength of compacted clays as affected by suction and soil structure[END_REF].

Conclusions

The behaviour of a single high-density bentonite pellet under hydration from 82 to 9 MPa of suction and the variation of its mechanical properties during this path are investigated in this study by laboratory tests. The results show an increase of pellet's volume and water content upon suction decrease. At the same time, its mechanical properties (Young modulus and strengths) decrease during hydration. When analysing the experimental result with an existing model for compacted expansive soil and assuming that the pellet behaviour is similar to that of an aggregate, a single set of parameters (α m and β m ) can be used to predict the suction dependency of volumetric strain, Young modulus and strengths.

The results from this work would be helpful for further numerical investigations (finite element and discrete element methods) on the hydro-mechanical behaviour of granular bentonite-based engineered barrier for geological radioactive waste disposal during the first years following the installation.

  ρ s : particle density ρ d : dry density e: void ratio w: water content D: pellet's diameter H: pellet's total height h: pellet's cylinder-shaped part height Rc: pellet's curvature radius s 0 : initial suction ε a : axial strain ε r : radial strain ε V : volumetric strain N: axial load E: Young modulus ν: Poisson ratio δ n : normal displacement S r : degree of saturation R R : normal force at failure during radial compression R A : normal force at failure during axial compression K m : microstructural bulk modulus : effective mean stress α m : material parameter β m : material parameter C A : material parameter relating axial strength to modulus C R : material parameter relating radial strength to modulus

Figure captions (

 captions Figure captions (images as individual files separate to your MS Word text file).

Figure 1 .

 1 Figure 1. Schematic views of a single pellet. Radial view (a) and axial view (b).

Figure 2 .Figure 3 .

 23 Figure 2. Load frame used to perform compression test. (a) Picture; (b) description

Figure 4 .Figure 5 .

 45 Figure 4. Typical results of compression tests: (a) axial compression; (b) radial compression.

Figure 8 :

 8 Figure 8: (a) Modulus versus suction for axial and radial compression tests; (b) Strength versus suction for axial and radial compression tests.

Figure 9 :

 9 Figure 9: Strength versus modulus for both axial and radial compression tests.

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Agustín Molinero Guerra

Prof Yu-Jun Cui
email: yu-jun.cui@enpc.fr

Nadia Mokni

Pierre Delage

Michel Bornert

Patrick Aimedieu

Anh Minh Tang

Frédéric Bernier

Investigation of the hydro-mechanical behaviour of a pellet/powder MX80 bentonite mixture using an infiltration column

Keywords: pellet/powder bentonite mixture, heterogeneous porosity network, mock-up test, swelling pressure, relative humidity

Non-compacted pellet/powder bentonite mixtures are considered as candidate sealing plug materials in geological disposals of radioactive waste. Due to its nature, this mixture is characterized by a heterogeneous porosity network, which is responsible for its complex hydromechanical (HM) behaviour. The French Institute of Radioprotection and Nuclear Safety (IRSN) has investigated this mixture within the SEALEX project. Both in situ large-scale and laboratory small-scale experiments were carried out. This paper presents the results of a smallscale mock-up test at 1/10 th scale of the in situ experiments, in which the pellet/powder mixture was saturated from both sides (top and bottom of the specimen). Both swelling pressure and relative humidity were monitored at several positions of the specimen. Different responses from the sensors were found, depending on the local porosity as well as the evolution of the hydration front. The HM response of the mixture is strongly conditioned by the initial pellet/powder distribution, which depends on the protocol followed for the specimen preparation. After 800day hydration, an anisotropy was found between the axial and the radial swelling pressures, due to the presence of larger void at the top of the sample and the friction at the cell wall. The sample was still heterogeneous after 800-day hydration mainly due to the initial heterogeneous porosity distribution, combined with the effect of friction and the non-saturation of the mixture.

The evolution of injected water with time revealed that the sample was not full saturated after 800-day hydration.

Introduction

Powder/pellet bentonite mixtures are considered as one of the candidate sealing materials for deep underground radioactive waste repositories thanks to their favourable properties: high swelling capacity, high radionuclide migration retardation properties and operational advantages: easy to manufacture and install (especially in vertical shafts). Once installed in the gallery, the pellet/powder bentonite mixture is initially unsaturated. Then, the saturation process starts under constrained volume condition due to the infiltration of pore water from the host rock, generating a swelling potential that allows filling the voids within the mixture. Due to its nature, these mixtures are characterized by an initial heterogeneous porosity distribution [START_REF] Molinero-Guerra | In-depth characterisation of a mixture composed of powder/pellets MX80 bentonite[END_REF], which results in a complex hydro-mechanical behaviour during the saturation process. It is therefore essential to investigate this swelling behaviour in order to validate the material for the sealing plug in the underground radioactive waste disposal.

In this context, the Institute of Radioprotection and Nuclear Safety (IRSN, France) has launched the SEALEX (SEALing performance Experiments) project, within which the work presented here was conducted. The purpose of this project is to investigate the long-term hydraulic performance of sealing systems in normal and critical scenarios, as well as different core compositions and configurations (mixture composed of bentonite pellets with bentonite powder or of sand with bentonite powder, pre-compacted or in situ compacted). Figure 1 presents the layout of the experiments.

The hydro-mechanical behaviour of different configurations of sealing plugs was investigated at both laboratory and field scales [START_REF] Wang | Experimental study on the swelling behaviour of bentonite/claystone mixture[END_REF][START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF][START_REF] Mokni | Hydro-mechanical analysis of SEALEX in situ tests -Impact of technological gaps on long term performance of repository seals[END_REF]. An important result from these investigations is the relationship between the swelling pressure and the dry density of bentonite [START_REF] Börgesson | Modelling of the physical behaviour of clay barriers close to water saturation[END_REF][START_REF] Dixon | Swelling and hydraulic properties of bentonites from Japan, Canada and the USA[END_REF][START_REF] Lloret | Mechanical behaviour of heavily compacted bentonite under high suction changes[END_REF][START_REF] Karnland | Sealing ability of Wyoming bentonite pellets foreseen as buffer material -laboratory results[END_REF][START_REF] Gens | Hydromechanical Behavior of a Heterogenous Compacted Soil: Experimental Observations and Modelling[END_REF][START_REF] Villar | Basal spacings of smectite in compacted bentonite[END_REF][START_REF] Wang | A comparative study on the hydro-mechanical behaviour of compacted bentonite/sand plug based on laboratory and field infiltration tests[END_REF][START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF][START_REF] Schanz | Swelling pressure characteristics of compacted Chinese Gaomiaozi bentonite GMZ01[END_REF]. These relationships were derived on the basis of the measured axial swelling pressure of the investigated materials. However, few investigations have been carried out on the radial swelling of the studied sealing plug [START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF]. Therefore, it is fundamental to further investigate the complex patterns governing the swelling behaviour of the initially heterogeneous mixture of pellet/powder of bentonite in order to ensure that this repository configuration design meets the performance targets.

The swelling capacity of pellet/powder bentonite mixtures was investigated by [START_REF] Imbert | Hydro-mechanical response of a bentonite pellets/powder mixture upon infiltration[END_REF] through a series of infiltration tests on a 50/50 pellet/powder FoCa bentonite compacted at different dry densities. After full saturation, the swelling pressure was found analogous to that of a specimen of powder compacted at the same dry density. [START_REF] Van Geet | The use of microfocus X-ray computed tomography in characterising the hydration of a clay pellet/powder mixture[END_REF] studied the hydration process of a 50/50 pellet/powder FoCa bentonite mixture by X-ray computed tomography. The results showed the progressive decrease of the density of pellets and the apparent homogenisation after saturation. Other sealing plug configurations were investigated by mock-up tests. [START_REF] Wang | A comparative study on the hydro-mechanical behaviour of compacted bentonite/sand plug based on laboratory and field infiltration tests[END_REF] and [START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF] studied a compacted MX80 bentonite/sand mixture (with a proportion of 70/30 in dry mass). [START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF] investigated the anisotropy of swelling pressure of compacted bentonite/sand mixture. µCT observations revealed that the material was looser in the radial direction than in the axial one. The homogenisation process of a granular material made of highly compacted bentonite pellets (granular buffer material, GBM) was investigated by [START_REF] Garcia-Siñeriz | Engineered barrier of bentonite pellets and compacted blocks: State after reaching saturation[END_REF] under the context of the EB (engineered barrier) experiment. Upon dismantling, a gradient of density and water content was found within the GBM, probably due to the initial heterogeneity of the material [START_REF] Villar | Contribution of CIEMAT to EB dismantling report. Physical state of the bentonite[END_REF].

No investigations have been carried out on the swelling of non-compacted pellet/powder bentonite mixtures. This is however crucial in the design of sealing plugs for deep radioactive waste disposal, because the initial heterogeneous distribution of porosity of these configurations might result in an anisotropy of swelling. Therefore, this study aims at investigating the HM behaviour of this kind of mixture by simulating the SEALEX in situ experiments at a small scale (1/10 th , resulting in 60 mm in diameter and 120 mm in height). Radial swelling pressure at different positions, as well as axial swelling pressure and relative humidity were monitored during hydration from both sides (top and bottom of the sample). The volume of injected water was also recorded during the test.

Investigated material

The soil studied is a mixture of pellet/powder MX80 bentonite at a proportion of 80/20 in dry mass. The bentonite investigated comes from Wyoming, USA. It was provided by the Laviosa-MPC company under the commercial name Expangel SP7 for pellets and SP30 for the powder.

The MX80 bentonite has a smectite content of 80%, other minerals being quartz, calcite and pyrite. The cation exchange capacity (CEC) is 98 meq/100g, with Na+ as major exchangeable cation (52 meq/100g). The liquid limit is 560%, the plastic limit is 62% and the unit mass is 2.77 Mg/m 3 [START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF].

Pellets of bentonite were produced by Laviosa-MPC Company by compaction of a powder of MX80 bentonite in a mould of 7 mm in diameter and 7 mm in height. Compaction was performed at a water content of 6±1% by applying instantaneous compaction effort by following the vertical axis of the pellet, resulting in a pellet dry density ρ d = 2.06±0.06 Mg/m 3 , corresponding to a void ratio e = 0.30±0.07. The pellets were stored in the laboratory in a hermetic plastic box at 20°C. The initial suction (s = 135 ± 3 MPa) was measured in the laboratory with a chilled mirror dew point tensiometer (Decagon WP4C), at an initial water content w = 7.25%, slightly higher than the fabrication one, due to further hydration after fabrication [START_REF] Molinero-Guerra | In-depth characterisation of a mixture composed of powder/pellets MX80 bentonite[END_REF].

3.17% was found in the laboratory after drying at 105°C for 24 h, corresponding to an initial suction s = 190.9 MPa (measured with a chilled mirror dew point tensiometer -Decagon WP4).

More details about the initial state of the material can be found in Molinero [START_REF] Molinero-Guerra | In-depth characterisation of a mixture composed of powder/pellets MX80 bentonite[END_REF].

The saturation water used in the test is synthetic water having the same chemical composition as the pore water of the Callovo-Oxfordian claystone from the ANDRA underground research laboratory in Bure ( Table 1). The water was obtained by mixing the chemical components with distilled water until full dissolution.

Results of mercury intrusion porosimetry (MIP) tests for a pellet of bentonite at its initial state are presented in Figure 2. A pore population with an average entrance diameter of 11.9 nm is detected, as well as a second one at diameters around 4 -5 µm that represents 6.8% of the total porosity. For the pellet/powder mixture, macro-voids existing between pellets and powder grains will play an important role in the HM behaviour. The investigated material is characterized by a multimodal porosity network with a heterogeneous distribution of the porosity within the sample. The latter was demonstrated by a qualitative analysis of a vertical slice obtained by carrying out µ-CT observations of a pellet/powder bentonite mixture prepared by following the same protocol as the investigated specimen in the mock-up test (Figure 3). This feature is crucial since it conditions the overall HM behaviour of the material.

Experimental methods

Experimental set-up

The layout of the small-scale infiltration cell (mock-up test cell) is presented in Figure 4. The dimensions correspond to 1/10 th of the in situ SEALEX experiments (60 mm in diameter and 120 mm in height). The confined saturation conditions for the pellet/powder bentonite mixture are ensured by a rigid structure that keeps a zero radial displacement (the estimated axial strain is 5 x 10 -6 ) and a piston blocked by a screw, which prevents any axial displacement. The material is saturated from both sides (top and bottom), simulating the SEALEX in situ experiments. The sample is placed between two pore stones and two filter papers. The bottom and the upper bases are equipped with a water inlet and an air outlet. The air outlet is needed to evacuate the air that is present in the base and in all the system near the inlets. Mechanical valves are mounted and sealed at the faces of both inlets, allowing the entrance of water and the evacuation of air. Flexible water hoses are connected to the valves. The side serving as a water inlet is connected to a burette and to a water tank, allowing the volume of injected water to be measured during hydration. Six total pressure sensors are installed in the cell (SP20, SP40, SP60, SP80, SP100 and SP120), which allow the measurements of the radial swelling pressures at different positions (h = 20, 40, 60, 80, 100 and 120 mm from the bottom side). Figure 3 presents the pellet/powder mixture together with the position of the radial swelling pressure sensors. A force transducer is installed under the cell base, which monitors the axial swelling pressure. In this study, the relative humidity is also recorded by five relative humidity sensors (RH31, RH51, RH71, RH91 and RH111) placed at different heights (h = 31, 51, 71, 91 and 111 mm, see Figure 4), allowing the evolution of suction to be monitored while hydration.

Sample preparation and test procedure

The sample was prepared directly into the cell that was already placed on the tray of the force transducer with the radial sensors screwed to the cell. The pellet/powder mixture was obtained by following the first protocol proposed in Molinero Guerra et al. ( 2016), which allows a relatively homogeneous sample to be obtained. However, a perfect homogeneous distribution cannot be obtained due to the nature of the mixture. It was to fill the cell by packets corresponding to one layer of pellets spread over the base of the cylinder and to add the corresponding amount of powder (taking into account the proportion 80% pellets -20% powder in dry mass). Figure 3 presents a vertical section of the pellet/powder mixture obtained by microfocus X-ray computed tomography observations on a sample at its initial state, together with the positions of the swelling pressure sensors. The global dry density is 1.49 Mg/m 3 .

Once the sample was prepared, the two stainless steel plates were fixed with three rods. The central screw was adjusted to ensure the constant volume conditions. The test was started by opening the water inlet valves. At the beginning of the test, air in the base or in the piston was evacuated by opening the air outlet valve until no air bubble was observed in the pipes. Synthetic water was injected by both the top and the bottom of the sample, as the SEALEX in situ experiments. The applied water pressure while hydration was equal to the atmospheric pressure at both top and bottom boundaries. Radial and axial swelling pressures, as well as relative humidity were recorded automatically by a data logger. The volume of injected water was also controlled while hydration by two graduated burettes connected to the hydration system. No water pressure was applied during the saturation process.

Results

Investigation of the swelling pressure

The evolution of the swelling pressure with a zoom on the first 15 days is shown in Figure 5. A different rate of increase is identified for each sensor. For sensor SP100, located at 100 mm from the bottom (and 12 mm from the top hydration front), an initial fast increase of swelling pressure is observed, reaching a peak value of 2.15 MPa, then a decrease until 1.5 MPa, and finally an increase to reach stabilisation at about 2.5 MPa. This phenomenon occurs during the first hours of hydration. For other sensors, the rates of increase are similar, being the sensor located at 20 mm from the bottom (SP20) the one who exhibits a higher swelling pressure after 15 days (1.5 MPa), because of its proximity to the front of hydration. The difference in the increase rate depends on the evolution of the hydration front as well as the local porosity of the material characterized by an initial heterogeneous distribution of macro-porosity. After a few hours, water reaches sensor SP40. This sensor presents a negative rate at the beginning of the test, which could be interpreted as a collapse of the material at this level due to the presence of larger voids. The evolution of SP60 indicates that water arrives after 4 days of hydration.

Figure 6 presents the evolution of swelling pressure during 200-day hydration. The lowest swelling pressure and increase rate are observed for sensor SP120, located at the top of the sample. This is because, at this level, the sensor is in contact with the porous stone (see Figure 3), thus the response does not correspond to the behaviour of the soil. For the sensors located at the middle position (SP40, SP60, SP80 and SP100), the increase rate and the swelling pressure depend not only on the distance to the hydration front, but also on the local porosity defined by the pellets/powder grains distribution. A common value of about 2.5 MPa of swelling pressure is reached after 60 days of hydration except for SP20. Afterwards, sensors SP40, SP60 and SP80 exhibit the same increase rate until 110 days of hydration, where a stabilized swelling pressure is reached. At 120 days, SP80 presents an increase of swelling pressure followed by a stabilization at 135 days of hydration. Sensor SP100 presents a different response: an increase of swelling pressure is observed after 60 days, with a value almost constant, and then at 93 days it increases again to reach a constant value (the same increase is observed for SP40, SP60 and SP80), lower than the swelling pressures from other radial sensors (except that at 120 mm, which value is the lowest as it was explained previously). It should be noted that the swelling pressures after 200 days are different for all the sensors. This phenomenon will be discussed later. The axial swelling pressure corresponds to the global pressure transmitted to the piston, and its value is lower than those from other sensors. However, no consistent comparison can be made with the radial rates since in the latter case the pressures are measured locally. The rate of increase of the axial swelling pressure cannot be compared to the radial rates as the force transducer measures a global force and not the local total pressure.

According to the cell design (Figure 4), the swelling pressure of the material is transmitted to the upper piston, and then the force is transmitted to the force transducer. Therefore, two phenomena should be considered to interpret the measured axial swelling pressure: (i) the local porosity at the top of the sample, which is higher due to the presence of larger voids (see Figure 3, where the porous stone is in contact with some pellets at the top of the sample but there is no powder at this level) and (ii) the effect of friction. These two combined phenomena might explain the lower value of swelling pressure.

The evolution of the swelling pressures for 845-day hydration is shown in Figure 7. Some oscillations are observed after 200 days of hydration. These oscillations could be due to laboratory temperature changes. They are not related to electrical problems because the response of the sensors was corrected with respect to the electrical voltage. After 700 days of hydration, a common value of about 4 MPa of swelling pressure is reached for sensors SP20, SP40, SP60 and SP80. Sensor SP100 still remains at a lower value, slightly higher than 3 MPa, as well as the axial pressure (2.5 MPa).

Figure 8 presents the swelling pressure profiles at a time interval of 5 days. As it was explained before, the swelling pressure at 120 mm is not representative because the sensor is in contact with the porous stone at this level. At the bottom of the sample, the increasing rate of swelling pressure is lower because there might not be preferential arrangement of pellets at this level.

After 50 days of hydration, the lowest value of swelling pressure is at 60 mm, which corresponds to the farthest position from the hydration front. These heterogeneous swelling pressure values depend on the local porosity of the material, which is controlled by the initial pellet/powder distribution within the sample. The profiles of swelling pressure every 100 days are shown in Figure 9. An increase of the swelling pressure is observed at 40 mm, 60 mm and 80 mm due to the evolution of the hydration front and the consequent swelling of the material at these levels. A heterogeneity of the final value of swelling pressure is observed after 800 days of hydration, with a mean value slightly higher than 4 MPa.

Investigation of the relative humidity

The evolution of the relative humidity with time is shown in Figure 10. Starting at 36.7% relative humidity corresponding to 138 MPa of suction, the curves show different rates for different sensors. Those located close to the front of hydration (RH31 and RH111) exhibit the highest rates, and a value of 100% is reached after 15 days for RH111 and 20 days for RH31.

Sensor RH111, located at 9 mm from the top hydration front, exhibits the highest rate because of the effect of gravity and the presence of voids at this level of the sample (Figure 3), which creates preferential paths for injected water. For sensors RH51 and RH91 the increase rate is similar, and saturation is reached after 45 days of hydration. Sensor RH71, located at 29 mm from the top hydration front, exhibits the lowest increase rate, with a value of 100% reached after almost 50-day hydration. The response of the sensors located at an intermediate position in the sample (RH51, RH71 and RH91) depends on the evolution of the hydration front.

The total volume of water injected while hydration, as well as the volume injected by the top and the bottom are presented in Figure 11. At the beginning of the test, the rate of increase is comparable for the top and bottom injection. However, a higher volume is injected by the top due to the existence of larger voids (Figure 3) combined with the gravity effect. The infiltration by the top of the specimen is controlled by the water level of the burette which hydrates the sample by the top. The volume of water injected by the top of the sample increased instantaneously after 125 days of hydration due to a manipulation of the burette connected to the hydration system; the water level was adjusted to the top of the cell. After 700 days of hydration, the volumes injected by the bottom and the top are 78.2 cm 3 and 128.2 cm 3 respectively. The total volume injected during the test is 206.4 cm 3 . As it can be observed, the rate of increasing is still positive after 700 days of hydration. This suggests that the sample is not entirely saturated after 700 days of hydration.

The profiles of relative humidity at a time interval of 5 days are presented in Figure 12. At the beginning of the test, before hydration, different values are observed for every sensor (around 40% of relative humidity). This is because the initial suction is not homogeneous within the sample, thus the results depend on the local relative humidity. Then, while wetting, an instantaneously increase is observed at 31 mm and 111 mm, due to the proximity of the hydration front. The evolution of other sensors depends on the evolution of the hydration front.

A total saturation (corresponding to a value of relative humidity of 100%) is observed after 40-day hydration. However, it was observed that the rate of injected water is still positive after 700-day hydration. This means that the measured relative humidity value of 100% after 40 days corresponds to the saturation of the large pores, and it does not represent the full saturation of the sample.

Discussion

The anisotropy of swelling pressure observed in this investigation can be interpreted based on two key features: (i) the dependence of the swelling pressure on the dry density of bentonite and (ii) the initial heterogeneous distribution of the material. The swelling pressure evolution of the sensor located at 100 mm (SP100) during the first 200 days (Figure 5) is due to the presence of larger voids at this level, as it is observed in Figure 3. A peak is observed at the beginning of the hydration process. This peak and consequent temporary drop corresponds to the reorganization of the microstructure of the soil induced by the collapse of the larger voids, so inter-pellet voids [START_REF] Alonso | Hydromechanical behaviour of compacted granular expansive mixtures: experimental and constitutive study[END_REF][START_REF] Gens | Hydromechanical Behavior of a Heterogenous Compacted Soil: Experimental Observations and Modelling[END_REF]. During hydration, pellets start swelling and filling the larger voids between them. This kind of response can be associated to the limit between two layers of pellets with powder of bentonite located in the inter-pellet voids, as it can be observed in Figure 3 at 100 mm. The heterogeneous distribution of pellets and powder within the sample plays an important role in the creation of these larger voids.

Figure 13 displays the evolution of swelling pressure with suction for sensors SP40, SP60, SP80 and SP100. As the positions of the RH sensors and SP sensors are not the same, an interpolation of the evolution of the suction is carried out in order to estimate the suction at the same level as the SP sensors. These calculations were not carried out for sensor SP20 as there is no RH sensors between the bottom hydration front and SP20. For sensor SP100, from the initial state (point A), a sudden increase of the swelling pressure is observed until a value of suction of 120 MPa. Then, a peak is observed (point B) due to the reorganization of the microstructure of the soil induced by the collapse of the macro-pores (inter-pellets voids). Then, the swelling pressure increases while wetting again until a constant value is reached (2.5 MPa) before saturation. It is worth noting that the calculated suctions using RH measurements correspond to the local macro structural suctions prevailing locally at the measured point. Unfortunately, the RH sensors do not allow the measurement of the evolution of suction at the microstructural level (micro-pores within pellets) which might experience a delay in hydration.

For other sensors (SP40, SP60 and SP80 in Figure 13) this behaviour is not observed. The shape of the wetting path depends on the local density of the material, which depends on the pellet/powder structural distribution at the corresponding position as well as the vicinity of the hydration front. The increase rate of swelling pressure of sensor SP40 is negative at the beginning of the test, which might be due to a reorganization of the macrostructure at this level.

The behaviour is different compared to sensor SP100 as no swelling is observed before the collapse. The rate of increase of swelling pressure for SP40 is the lowest for the four sensors, indicating that the material has a low dry density at this level. This response can be associated to the limit of two layers of pellets with no grains of powder between the pellets. This distribution can be observed in Figure 3 at 40 mm. For sensor SP60, a decrease in suction is observed with no swelling before 50 MPa suction. It is believed that there is concentration of bentonite powder grains in the vicinity of this sensor with no pellets (this kind of distribution can be observed in Figure 3 between SP20 and SP60). Therefore, bentonite grains swell but no pressure is recorded by the sensor until suction reaches 50 MPa due to its loose structure. For sensor SP80, swelling pressure increases with a rate higher than SP60, but no collapse of the macrostructure is observed. No constant value of swelling pressure is observed for both sensors under a certain value of suction, as it was observed for sensor SP100, indicating that the structure of the mixture is still changing at this state of the hydration process. After 700 days, a is interlayer adsorbed water, a water density of 1.316 Mg/m 3 can be estimated from the theoretical volume of injected water and the measured value. [START_REF] Marcial | A simple method to consider water density changes in the calcualtion of the degree of saturation of swelling clays[END_REF] obtained a water density of 1.02 Mg/m 3 , 1.27 Mg/m 3 and 1.57 Mg/m 3 for a sample of compacted MX80 bentonite at a dry density of 1.354 Mg/m 3 , 1.691 Mg/m 3 and 1.952 Mg/m 3 respectively. It is worth noting that the water in the interlayer zone of expansive clays has several features which are quite different from those of free water. This increase in water density, which depends on the relative humidity, could be partially associated with the predominant exchangeable cations in the clay, and the difference in the interaction mechanisms between each cation and the interlayer water [START_REF] Jacinto | Influence of water density on the waterretention curve of expansive clays[END_REF]. Possible water evaporation during the test should be considered as another reason for this difference of water intake.

Conclusions

In the context of the SEALEX project (IRSN), a small-scale test (1/10 th ) was performed in order to investigate the HM behaviour of pellet/powder MX80 bentonite mixture. The swelling pressure at different positions in the sample allowed better understanding the complex swelling behaviour of this heterogeneous material.

The evolution of the radial swelling pressure for the different positions are due to the local porosity of the material combined to the evolution of the hydration front. Local porosities depend strongly on the initial heterogeneous distribution of pellets and powder within the sample. A collapse of the material is observed at the sensor located at 100 mm due to the presence of larger voids at this level, corresponding to the limit between two layers of pellets with some bentonite powder grains between them. At 40 mm from the bottom, a collapse is found at the beginning of the test with no previous swelling, due to the reorganization of the macro structure at this level. This behaviour could be related to the limit between two layers of pellets without powder grains between them. For the rest of the sensors, no collapse is observed because there are no macrovoids in the vicinity of the sensors.

The anisotropy observed between radial and axial swelling pressure is due to the presence of larger voids at the top of the sample, where the top pore stone contacts with some pellets without no powder grains between them, as well as the friction of the material with the cell while swelling. Note that the effect of friction could be much more significant in field scale.

Moreover, it is believed that the sample is more compact radially than axially due to the fabrication process, which can greatly affect the pellet/powder distribution, and consequently the HM behaviour of the material.

The evolution of radial swelling pressure depends on the pellet/powder distribution. Different responses can be obtained even if the same protocol is followed. The final dry density profile is not entirely homogeneous at the end of test due to the initial heterogeneous distribution of porosities combined to the effect of friction and the non-saturation of the mixture.

During the saturation process, a difference was observed between the measured volume of injected water and that estimated by considering the total porosity. This difference is partially explained by changes in water density, as it was concluded by [START_REF] Jacinto | Influence of water density on the waterretention curve of expansive clays[END_REF][START_REF] Marcial | A simple method to consider water density changes in the calcualtion of the degree of saturation of swelling clays[END_REF]. The water density depends on the relative humidity, and it is associated with the predominant exchangeable cations in the clay, and the difference in the interaction mechanisms between each cation and the interlayer water. This dependence should be considered in the investigation on the performance of sealing plugs with bentonite-based materials. Table 1. Chemical composition of the synthetic water

List of Tables

List of Figures

Figure

  Figure1. Layout of the SEALEX in situ tests (after[START_REF] Mokni | Hydro-mechanical analysis of SEALEX in situ tests -Impact of technological gaps on long term performance of repository seals[END_REF] Figure2. MIP tests results for a pellet of bentonite at its initial state Figure3. Vertical section of the investigated pellet/powder bentonite mixture obtained by µ-CT observations. Resolution: 50 µm/voxel Figure 4. Layout of the mock-up test cell (a) seen from above; (b) section A-A'; (c) section B-B' (dimensions in mm) Figure 5. Evolution of the swelling pressure with time after 15 days of hydration Figure 6. Evolution of the swelling pressure with time after 200 days of hydration Figure 7. Evolution of the swelling pressure with time after 845 days of hydration Figure 8. Swelling pressure profiles at different times (every 5 days) Figure 9. Swelling pressure profiles at different times (every 100 days) Figure 10. Evolution of the relative humidity with time Figure 11. Evolution of the injected water with time during hydration Figure 12. Relative humidity profiles at different times (every 5 days) Figure 13. Suction versus swelling pressure at different positions

  Figure1. Layout of the SEALEX in situ tests (after[START_REF] Mokni | Hydro-mechanical analysis of SEALEX in situ tests -Impact of technological gaps on long term performance of repository seals[END_REF] Figure2. MIP tests results for a pellet of bentonite at its initial state Figure3. Vertical section of the investigated pellet/powder bentonite mixture obtained by µ-CT observations. Resolution: 50 µm/voxel Figure 4. Layout of the mock-up test cell (a) seen from above; (b) section A-A'; (c) section B-B' (dimensions in mm) Figure 5. Evolution of the swelling pressure with time after 15 days of hydration Figure 6. Evolution of the swelling pressure with time after 200 days of hydration Figure 7. Evolution of the swelling pressure with time after 845 days of hydration Figure 8. Swelling pressure profiles at different times (every 5 days) Figure 9. Swelling pressure profiles at different times (every 100 days) Figure 10. Evolution of the relative humidity with time Figure 11. Evolution of the injected water with time during hydration Figure 12. Relative humidity profiles at different times (every 5 days) Figure 13. Suction versus swelling pressure at different positions

Figure 2 .

 2 Figure 2. MIP tests results for a pellet of bentonite at its initial state.

Figure 3 .

 3 Figure 3. Vertical section of the investigated pellet/powder bentonite mixture obtained by µ-CT observations. Resolution: 50 µm/voxel.

Figure 4 .

 4 Figure 4. Layout of the mock-up test cell (a) seen from above; (b) section A-A'; (c) section B-B' (dimensions in mm).

Figure 5 .

 5 Figure 5. Evolution of the swelling pressure with time after 15 days of hydration.

Figure 6 .

 6 Figure 6. Evolution of the swelling pressure with time after 200 days of hydration.

Figure 7 .

 7 Figure 7. Evolution of the swelling pressure with time after 845 days of hydration.

Figure 8 .

 8 Figure 8. Swelling pressure profiles at different times (every 5 days).

Figure 9 .

 9 Figure 9. Swelling pressure profiles at different times (every 100 days).

Figure 10 .

 10 Figure 10. Evolution of the relative humidity with time.

Figure 11 .

 11 Figure 11. Evolution of the injected water with time during hydration.

Figure 12 .

 12 Figure 12. Relative humidity profiles at different times (every 5 days).

Figure 13 .

 13 Figure 13. Suction versus swelling pressure at different positions.

Table 1 .

 1 Chemical composition of the synthetic water

	Components	NaHCO 3 Na 2 SO 4 NaCl KCl CaCl 2	MgCl 2 O6H 2 O SrCl 2 6H 2 O
				2H 2 O
	Mass (g) per	0.28	2.216	0.615 0.075 1.082	1.356	0.053
	litre of solution

Figure 1. Layout of the SEALEX in situ tests (after Mokni et al., 2016).

common value of 4 MPa of swelling pressure is observed for radial sensors except SP100, which value is slightly higher than 3 MPa.

Based on the initial average dry density of the mixture (1.49 Mg/m 3 ) and the relationships between axial swelling pressure and dry density derived by [START_REF] Karnland | Sealing ability of Wyoming bentonite pellets foreseen as buffer material -laboratory results[END_REF] and [START_REF] Wang | Experimental study on the swelling behaviour of bentonite/claystone mixture[END_REF], the final value of the axial swelling pressure is estimated. It ranges from 4.15 MPa to 4.66 MPa. The lower measured value (2.5 MPa) is due to: (i) the material preparation protocol, which results in a concentration of macrovoids at the top of the sample, where the porous stone is in contact with some pellets without powder grains between them (Figure 3) and (ii) the friction of the material with the cell while swelling [START_REF] Saba | Investigation of the swelling behaviour of compacted bentonite-sand mixture by mock-up tests[END_REF], which is transmitted to the force transduced. However, it is believed that the effect of friction is not as significant as in the case of compacted bentonite/sand mixture. Therefore, the difference between the axial and radial swelling pressure in this study is mainly due to the heterogeneity of the material. Moreover, in the vicinity of the radial sensors, different pellets/powder arrangements are clearly observed (Figure 3), which is due to the sample preparation process in which the cell is filled by packets corresponding to one layer of pellets spread over the base of the sample (see for instance Molinero [START_REF] Molinero-Guerra | In-depth characterisation of a mixture composed of powder/pellets MX80 bentonite[END_REF]. This lead to different responses of the sensors. Note that other values of swelling pressure can be found in the literature for the MX80 bentonite at 1.5 Mg/m 3 of dry density. [START_REF] Komine | Predicting swelling characteristics of bentonites[END_REF] found a value of 1.5 MPa at the mentioned suction, whereas [START_REF] Agus | A method for predicting swelling pressure of compacted bentonites[END_REF] found a value of 2.5 MPa.

These values differ from the relationships found by [START_REF] Karnland | Sealing ability of Wyoming bentonite pellets foreseen as buffer material -laboratory results[END_REF] and [START_REF] Wang | Experimental study on the swelling behaviour of bentonite/claystone mixture[END_REF], showing a certain data scatter of the available data.

The total volume of injected water is 206.4 cm 3 after 700 days of hydration. However, taking into account the dry density of the material, the theoretical injected volume when the mixture is saturated should be 155 cm 3 . This difference may be partially explained by the water density changes [START_REF] Jacinto | Influence of water density on the waterretention curve of expansive clays[END_REF][START_REF] Marcial | A simple method to consider water density changes in the calcualtion of the degree of saturation of swelling clays[END_REF]. Based on the hypothesis that all water in the sample


Çərçivəsində Keçirilən Elmi

Materiallari Bakı

Jean During

"Muğam aləmi" 6-cı Beynəlxalq Musiqi Festivalı

Keywords: Tahrir, Vocal melisma, Iranian âvâz, Zəngulə, Preliminary definition

The tahrir (and its equivalent azeri zəngulə) is a melismatic form which uses a vocal technique of rapid succession of glottal strokes over a series of notes. Several articles (1974, 2016, 2019) have highlighted this effect at the level of its acoustic spectrum, but the most in-depth studies (2020) were carried out in a French laboratory, using an electro-glotto-graphic device, with the collaboration of the famous singer Mohammad-Rezâ Shajarian (d.2020). In addition to this scientific approach, the article questions the often ambiguous and vague uses of the terms tahrir, ghalt, tekye, and yodel, and proposes precise definitions based on the explanations of singing masters. These definitions are informed by the literal etymological meaning of the terms mentioned. At a musical level, the article also defines the place of tahrir in the vocal art as a melisma governed by subtle rules and aesthetic choices. It appears that the tahrir (and probably the zəngulə), is not only a decorative element appearing spontaneously in phases of expressive climax; it is an essential component of ghazal singing in all its registers, and is part of the very composition of each âvâz and gushe. This is why the tahrir formulas are also adapted to the instrumental playing of the canonical repertoire (radif), and are memorised note by note, as in singing.

The Iranian and Azerbaijani vocal repertoire comprises two main categories, as in most maqām traditions:

-measured songs (tasnif), -free singing (āvāz) not measured or pulsed, but flexibly structured in a by a poetic meter.

The particularity of this form is that it requires a vocal technique or laryngeal mechanism (Castellengo 2009) which can be defined as a glottal appoggiatura (Simms & Koushkani p. 273). It is implemented:

-in an ornament or a short embroidery that often stretches the meter over a long syllable; -or in a long melisma escaping from the text and the meter to shape an autonomous sequence within a melodic model (āvāz, gushe).

In both cases, embroidery or melisma, and even if it is only an ornament on a few notes with a glottal appoggiatura, it is generally called tahrir. In common Iranian usage, this term is therefore ambiguous, as it designates both the melodic form (embroidery or vocalisation) and the laryngeal mechanism involved.

The tahrir as a melodic sequence is assimilated to the vocal technique by which it is distinguished from an ordinary melisma.

One of the aims of this article is to clarify the usage and semantic scope of the terms applied to the vocal art.

Etymology

The ambiguous use of the term tahrir (of Arabic origin) is reflected in its polysemy. Its most common meaning is "liberation, emancipation". Musically, this makes sense, as the vocalization is freed from the meter pattern and from the verse's meaning.

Another meaning, in Arabic, Iranian and Turkic languages, is "editing" of a text, or "writing", which also makes sense, as the chant "edits" or rewrites the poem with incisions and illuminations.

The root of the word tahrir is harir, which means a light silk cloth [1], and by extension a sheet of silk paper on which one takes notes. These three meanings converge to designate, in Iran as well as in the Iraqi Maqâm (Simms 2004), a melismatic vocal form. In Azerbaijan, the equivalent of tahrir is called zəngulə (bell).

Much more than a short or elaborate embroidery, the tahrir, with its characteristic glottal mechanism, is considered "the pillar and identity marker of Persian singing" (Kazemi:15). A singer whose tahrir is not satisfactory should limit himself to measured songs (tasnif), or to religious singing (Koranic psalmody, elegies, shi'i ta'zie opera) where sobriety is required.

Faced with the lack of precision of the term tahrir in common usage and even in scholarly publications, I interviewed master Mozaffar Shafi'i, a high-level amateur from a long ancestry of singers. From the outset, he says: "we must distinguish the isolated tahrir (tak) from the chains of tahrir". And he produces a glottal blow, then two, then three in chains, and finally a longer series, which is the tahrir proper, commonly called bolboli (of the nightingale). This glottal stroke or appoggiatura is called tekye, or ghalt. In his publication of 'A. Davāmi's canonical vocal repertoire Dariush Talai does not use the term tekye at all, but he too specifies that the ghalt appears "alone or in a group" (p. 17). For his part M.-R. points that "a distinction must be made between the tahrirs that ornate a few notes and those that constitute entire phrases."

The tekye or ghalt is the minimal unit of what is called tahrir. In a singing as well as in instrumental performance, it occurs at any time, but what is meant by tahrir proper are these bursts which can be sporadic (repeating the same note or shaping a short motive) or structured in melisma.

Tekye means "support" and ghalt "rolling". In effect, notes with a tekye are highlighted, and if repeated quickly, can be said to roll. The French Chevalier de Chardin, who lived in Isfahan in the middle of the 17th century, reports that the singers "draw a great voice from the bottom of the stomach, which they roll with great force and brilliance." (T. II,p. 206).

Technical definition of the glottal jump

What is the glottal jump? In the middle register of the human vocal range, the larynx can vibrate either in a "heavy" laryngeal mechanism (M1) or in a "light" mechanism (M2). On a given note, a change of mechanism triggers a sudden jump in frequency. Western lyrical technique proscribes such melodic discontinuities but other vocal cultures, on the contrary, cultivate and refine these discontinuities. This is particularly the case in the vocal repertoire of the dastgāhs and the mughams.

Several scientific publications have analysed its acoustic characteristics, but the most advanced research has been carried out in Paris at the Laboratoire d'Acoustique Musicale of the Centre National de Recherche Scientifique. While earlier researches were based mainly on the analysis of recordings, we worked with two high-level singers: first with Mrs. Solmaz Badri, and a few years after with the late Mohammad-Reza Shajarian.

"The change in laryngeal mechanism underlying tekye has been reported by different authors [see bibliography]. It has been questioned in 2019 [

3] yet without laryngeal-behaviour assessment. To clarify laryngeal physiology in Iranian tahrir, we recorded simultaneously the acoustic and the electroglottographic signal (EGG) of these two vocalists. For both singers, tekye realization goes with a sudden decrease in glottal contact corresponding to a change in laryngeal vibratory mechanism.

The electroglottographic and glottal-contact measurements confirm our previous observations on laryngeal-mechanism jumps in tahrir. The tekye switch between Mechanism 1 and 2 can be done on ranges as large as two octaves, attesting to exceptional laryngeal control. The two singers adjust tekye parameters (duration, melodic shape, interval) to the musical context [4]." The frequency-jump musical interval is around a minor third for Mrs. Badri, which can be considered as a standard. (In instrumental renditions of the tahrir, the jump interval is also currently between 2 to 4 half tones.) For M.-R. Shajarian, tekye frequency jump can vary from a minor third (315 cents) to a major seventh (1000 cents), with a flexible and changing melodic form. The movement of the glottis is extremely rapid, of the range of 0,05 second.

In what is called tahrir, the glottal jump (tekye) is usually repeated at a rate between 4 to 6 per second. Laboratory experiments show that tekye's mechanism is different from yodeling (Tyrolean or else), the juk juk of the Turkmen bagşy or the Kurdish vocal genre hore or siaw chamani, said to be inspired by the partridge (kawk).

TWO SHORT AUDIO EXAMPLES OF JUK-JUK AND KAWK STYLE ARE GIVEN

Based on Lloyd Miller's opinion (1999: 108-9, 324), some claim that tahrir is also practised by Iraqi, Syrian, and even Flamenco singers. So far I never heard any example of it, and it is probably a confusion between sporadic ghalts and actual tahrir. In the Maqām al-'Irāqi, tahrir designates also an introductory melisma, but devoid of series of tekye. Hence, what the Iranians commonly call tahrir and the Azeris zəngulə, is specific to their music and occupies a central place in it.

As tahrir commonly designates a glottal effect and a vocal (and instrumental) melisma, for greater precision, another term may be used. A common and suggestive term is chah-chah, which also refers to the "chirping" of birds and corresponds to zəngulə (bell) in Azerbaijan. In the ancient treatises (Marāghi p. 385), tahrir was called marghule which means "gurgling", one of the dictionary definitions of which being: "to emit (a sound) in a throaty voice", or "borborygmus", as indeed tahrir only articulates syllables or onomatopoeias.

Tekye or ghalt?

Like the concept of tahrir, the use of the terms tekye and ghalt is not very clear. In Kāzemi's important work, published in 2019, tahrir and ghalt are somewhat confused (p. 22), as are tahrir and chahchah. "Vocal tahrirs, he says, are very often an arrangement (tarkibāt) of tekye and ghalt notes. A movement from one note to the other without tekye, that is, in a kind of legato, is called ghalt." (Kāzemi p. 25). Shafi'i on his side calls ghalt or tahrir-e māleshi (spread, pasty), a melisma with only a few scattered tekye but without chah-chah, without chains of tekye.

Most articles on tahrir only mention the term tekye. However, it seems that tekye applies to both voice and instrument, while ghalt, as defined by Master Shafi'i, is: "an opening and closing of the vocal cords that each one does in his/her way, for example, smoothly, or with an accent". In his analysis and transcription of 'A. Davāmi's repertoire (radif), Talai uses only the term ghalt. In transcriptions, it is customary to indicate it by a ° above the note, whether for singing or for instrumental tekye, but for singing, the reality is more subtle. Talai identifies four shades of ghalt, which he indicates by small arrowed circles: horizontal, upward tending, downward tending, and interrupted. Furthermore he provides analysis of more discreet but no less essential effects: several kinds of "allusions" (eshāre) and cuts (maqtu'), for which he designed special marks (p.18-21).

A wide variety of melismas

Let us now return to the tahrir proper, the one that includes chah-chah. Two varieties are commonly distinguished: the bolboli (nightingale) tahrir, with a fast cadence, and the hammered (chakkoshi) tahrir with a slower cadence. Yet the matter is complicated by the fact that in the literature on the subject, many qualifiers are also associated with the term tahrir, referring to nuances of timbre and style: glissando, nasal, buccal, etc. (langari, qāne'i / kheyshumi, dahāni). In addition, some have established a tahrir's classification according to their melodic profile: ascending, descending, back and forth (farāz and nashib, raft o bargasht, etc.). Thus, the Iranian Wikipedia website lists more than twenty varieties of tahrir. Moreover, connoisseurs identify tahrir styles specific to certain singers 145). For example, the tahrirs of Tāj Esfahāni were said hammered (chakkoshi), those of Banān and Adib Khānsari smooth ("from the mouth", dahāni or ghalt), in contrast to those of Zelli which are qualified as "toothed" (dandān-dār) and bolboli. As for the ordinary public, they mainly differentiate between tahrir bolboli (nightingale, up to 6 or even 9 ghalt per second), and chakkoshi (hammered, about 2 ghalt per second).

TWO MUSICAL EXAMPLES ARE GIVEN: ONE CHAKKOSHI

AND AN AMAZING BOLBOLI BY QAMAR OL MOLUK VAZIRI. All these terms, often mentioned in articles, lead to some confusion, as they belong to different registers. Nevertheless, they reflect the importance of melisma and the refinement of vocal technique.

Melisma articulation

If the tahrir or chah-chah engages acousticians as a vocal mechanism, it also deserves the attention of musicologists as a melodic form and a work on the voice.

In his abundantly documented work, Ali Kāzemi analysed and classified some fifty melisma of the great singers of the last hundred years, collected on two CDs. He also considers that the tahrir and its chah-chah is much more than an embroidery that can be added or deleted, it is part of the vocal compositions (āvāz, gushe). As a melisma, it also has an important place in instrumental performance, as does the simple tekye.

I would add that tekye and chah-chah are precision tools that allow for the clear detachment of notes in a rapid flow, which can hardly be done with a fluent vocal emission. A comparative sonogram between an Iranian tahrir and an Iraqi vocal line shows that the former is sawtooth, and the latter in gentle waves (Bahadoran p. 94). In the maqām space there are no procedures such as solmisation in India, so to meet the aesthetic need to articulate melisma, non-textual syllables were used: la, lā, dele, etc. This form, called tarannum, was common in ancient compositions that are still sung in Turkey. It has disappeared in Iran, but still existed in the beginning of the 20th century (Kazemi p.173) as we can hear.

A

MUSICAL EXAMPLE OF TARANNUM SUNG. BY SEYYED AHMAD KHĀN

Apart from tarannum, the verbal support of tahrir has three aspects that can be combined:

-stretched vowels: ā in general, ô and u, sometimes i; never a nor e; -syllables like hā----vāy, a----kh, dele; -very short filling words (jān, yār, dād, amān, 'aziz, khodā.).

Some singers and connoisseurs have reservations about the use of these terms [START_REF] Miller | Music and Song in Persia. The art of avaz[END_REF] p. 109) and recommend using them sparingly, considering that "these banal and meaningless words diminish the spiritual significance of the song" (Kāzemi p.51, quoting M. Forugh).

Behind these reservations, it's the ethos of the song that is targeted: vāy, akh, jān, dād, are expressions of a pathos that rarely has its place in the ghazals of Sa'di, Hāfez, or others. Moreover, the chahchah does not a priori have an expressive function, but rather an impressive one, especially in the high register and in the culmination of the melody; it does not communicate feelings to the listeners but is a matter of taste and mastery of the vocal art. (Similarly, according to the Turkmens, the juk juk expresses joy as well as sorrow, from which one can conclude that it expresses nothing).

In the high register, the tahrir and ghalt induce additional tension, but they also occur in the low register, where they merge into the melodic flow, as in this example of a conclusion in Rāst, sung by Mozaffar Shafi'i:

MUSICAL EXAMPLE OF SOFT TAHRIR IN THE LOW REGISTER IS GIVEN

On the proper use of melismas

The melismatic tahrir is not an ad libitum embroidery or a spontaneous flight, it obeys rules as to its place in the text, its length, and its structure. Moreover, voice inflections are not limited to a series of tekye or ghalt, as we said earlier. The famous singer Hoseyn Tāherzāde claimed that he had developed and refined this genre. He had collaborated with Nur 'Ali Borumand (an important transmitter, d.1976), who memorised his tahrirs and reproduced them on his tār. It is well known that when the young and already famous Shajarian visited Borumand, the latter pointed out to him that it was a shame to limit his tahrirs to a few clichés, since each melodic type (gushe) has its own melisma. In his view, no two tahrirs should sound the same in a performance. Shajarian later explored this path, referring to all available old recordings, so that one can say that: "the striking feature of Shajarian's tahrirs is their seemingly infinite variety. While they may share an overall contour and use similar unit configurations, no two are ever quite the same." (Simms & Koushkani, 2012 p.390).

Another aesthetic issue concerns the place of the tahrir or chah chah in the performance of an āvāz or gushe and its localisation in the cantillation of a poem. The flaw that Borumand pointed out to the young Shajarian is often found among singers who, lacking culture or taste, slip in chah-chah wherever they can, and in stereotyped forms. I remember a maqām competition where a singer was eliminated in the first round, despite her superb voice and the quality of her repertoire. The reason was that she had spoiled her performance by inserting dazzling chah-chahs at every moment, which ended up saturating the ears of the jury. Six centuries ago, Marāghi (p. 386) already recommended not to overuse tahrir, otherwise, the singing would turn out like an "overly salty dish". Though many recordings of the great singers of the first half of the 20th century could lend themselves to the same criticism, they must be seen in the context of 78 rpm records, where the performance was limited to three minutes and had to impress the audience.

While the tekye or ghalt is an obligatory ornament, the tahrir is a constitutive element of the cantillation of poems, whose compositional principle resists analysis, despite attempts at classification (Simms & Koushkani 2012, Kāzemi 2019). Its most salient features are asymmetry and avoidance of repetition. According to the masters, the model for tahrir is the song of the nightingale (hence the term bolboli), not so much because of its volubility as because its formulas are never repeated identically from one piece (gushe) to the next, which is a characteristic of the song of the nightingale.

As for asymmetry, it appears in the phrasing and in the almost random distribution of groups of 2 and 3 notes, of 3 and 4 or of 4 and 5. For example: etc. Fig. 4. In this respect, tahrir justifies the original meaning of the term: not only does it free the voice from subordination to verse and meter, but it also overflows the melodic line (āvāz, gushe). On the surface it comes in as moments of freedom where the singer can shine with his technique and eloquence, but it is often part of the composition itself, as it is taught with perfect accuracy. Hence the need to memorise formulas, some of which being standards, like tahrir-e Javād, Nāyeb Asadollāh, Abu-Atā, Samali, Hesār, Bayāt-e Kord, etc. [5].

Whatever the case, the audience enjoys these moments of intensity. Mozaffar Shafi'i reports that when he was obliged to sing in religious ceremonies, his father advised him "not to do too much tahrir". But nowadays, when he goes up to the pulpit, listeners say to him: "Do some tahrir, okay? Because, without it, it has no charm." [1] In Iran it has more the meaning of "writing".

Notes

[2] The term is mentioned three times in the Qu'ran, as the fabric of a heavenly garment.

[3] Tahamtan M. and al., 2019. There are some weaknesses in this research: -the singer (whose name is not mentioned) is not a professional; -the analysis concerns only one tasnif (Morgh-e Sahar by Mortezā Neydāvud recorded in 1927, of which an Azeri version exists); -the interpretation of a tasnif does not require tahrir mastery and may only involve a few ghalts.

[4] This paragraph is taken and adapted from a presentation given by Castellengo, During, Henrich (2020).

[5] The tahrir sung in Hesār (Chahārgāh) is almost identical in Iran and Azerbaijan.

BIBLIOGRAPHY

Fig. 1 .

 1 Fig. 1. Ostād Shajarian watching his electroglottographic signal.

Fig. 2 .

 2 Fig. 2. A short excerpt of an Arabic vocal ornament.

Fig. 3 .

 3 Fig. 3. Iranian tahrir.

  BAHADORAN Parham, 2016. Analysis of Tahreer in traditional Iranian singing . FMA Workshop Queen Mary University of London p.bahadoran@se15.qmul.ac.uk CASTELLENGO Michèle, DURING Jean, HENRICH-BERNARDONI Nathalie, 2020. "Electroglottographic assessment of tahrir, a Persian vocal technique",12th International Conference on Voice Physiology and Biomechanics, Grenoble, France.