Christophe Dano

Pierre-Yves Hicher

S Tailliez

P.-Y Hicher

Engineering Properties of Grouted Sands

Keywords: Grouting, Elastic properties, Experimental data, Sand

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Introduction

The construction of underground structures on soft ground often requires the soil to be improved in order to ensure the safety and the stability of surrounding buildings. Grout permeation is an efficient technique for reducing permeability and for increasing stiffness and strength of coarse-to-medium grained soils with low initial mechanical properties.

Traditional organic grouts, such as silicate gels, have proved to be hazardous for groundwater such that organic grouts have been prohibited over the years. New grouts, therefore, such as very fine cement suspensions and mineral grouts, have been developed for about the past 20 years ͑Zebovitz et [START_REF] Zebovitz | Injection of fine sands with very fine cement grout[END_REF][START_REF] Benhamou | Comportement rhe ´ologique des coulis de liants hydrauliques ultrafins destine ´s a `l'injection[END_REF]. These new grouts present similar groutability performance as do previous chemical solutions. Their considerable advantage is that they prove to be stable with time.

This paper reports the results of an evaluation of the mechanical behavior of sands improved with these new grouts. Some grouted sands were prepared in the laboratory, others were sampled from in situ impregnated soils.

Behavior of Laboratory Grouted Sands

An extensive review of published experimental results relative to grouted sands reveals a large discrepancy of the results due to a wide variety of parameters relative to ͑Zebovitz et [START_REF] Zebovitz | Injection of fine sands with very fine cement grout[END_REF][START_REF] Schwarz | Effect of preparation technique on permeability and strength of cement-grouted sand[END_REF][START_REF] Tailliez | Etude expe ´rimentale du comportement me ´canique des sols granulaires injecte ´s[END_REF][START_REF] Schillinger | Injection of micro-cement in fine-grained soil: theory, modelling and laboratory testing[END_REF] • The soil ͑grain-size distribution, mineralogy, soil density, specific area͒; • The grout ͑nature, cementitious material-to-water ratio, particle-size distribution͒; and • The injection conditions ͑rate of discharge, grout pressure, injection procedure͒. Even if trends are drawn from studies inevitably restricted to some of these parameters, and key factors are pointed out in the case of naturally or artificially cemented sands, these reported results still would not allow one to propose standard design rules.

As a result, experimental observations from the literature based on cement-treated sands are supported by mechanical tests performed using grouted sands in this study. These tests are performed either by conventional laboratory testing ͑unconfined uniaxial compression tests, tensile tests, triaxial tests͒ or by innovative experiments for the determination of elastic properties in a small-strain domain.

Materials

Four natural uncemented sands, namely the Fontainebleau NE34 sand ͑termed FS͒ and three alluvial deposits of the Seine River ͓Seine River Sand ͑SRS͒, medium alluvial deposit ͑ADM͒ and coarse alluvial deposit ͑ADC͔͒, were improved with three patented grouts. The characteristics of the tested soils are indicated in Table 1. The Fontainebleau sand ͑FS͒ is a standard fine siliceous uniform sand, whereas the SRS and the alluvial deposits ͑ADM, ADC͒ are silico-calcareous gravelly sands. Fig. 1 shows their respective grain-size distribution curves. The natural gradation of the SRS and of the alluvial deposits ͑ADM, ADC͒ were reduced to a particle size of 2.5 and of 10 mm, respectively. The largest particles contained within the test specimens were therefore smaller than one tenth of the specimen diameter. Particles of the tested sands present a subrounded or subangular shape.

Three mix designs of an initial very fine cement grout ͑CG͒ ͑i.e., CG1, CG2, and CG3͒, three mix designs of a mineral solu-tion ͑i.e., MG1, MG2, MG3͒ ͑Gouvenot 1995͒ and six mix designs of a subsequent very fine cement grout ͑i.e., IJ1, IJ2, IJ3, IJ4, IJ5, and IJ6͒ were proposed, as shown in Table 2. The dry material-to-water ratio is (M /W); the cement-to-water ratio is (C/W) ͑Table 2͒. The particle sizes of the cementitious grouts are less than 12 m, as shown in Fig. 1. Their rheological properties, including a low plastic viscosity and a low yield shear stress, are maintained at essentially constant values during the injection phase by the use of dispersing agents, superplasticizer admixtures, and high-speed mixers. The grout stability ensured an effective permeation of the grouts through the sands.

Laboratory Preparation of Grouted Sands

The preparation of the grouted sands in the laboratory follows a systematic procedure inspired by previously published injection devices ͑Zebovitz et [START_REF] Zebovitz | Injection of fine sands with very fine cement grout[END_REF][START_REF] Benhamou | Comportement rhe ´ologique des coulis de liants hydrauliques ultrafins destine ´s a `l'injection[END_REF][START_REF] Schwarz | Effect of preparation technique on permeability and strength of cement-grouted sand[END_REF][START_REF] Tailliez | Etude expe ´rimentale du comportement me ´canique des sols granulaires injecte ´s[END_REF]. Improvements in the permeation grouting process and in checking the grouted samples have been made. A detailed description of the procedure can be found in Dano and Derache ͑2001͒. Briefly, the sand was placed with a zero fall height in a transparent and rigid cylindrical column made of polyvinyl chloride ͑PVC͒. The diameter of the tube was 80 or 100 mm, and its height was 900 mm. As the inner tube was being pulled up, as illustrated in Fig. 2, a few simultaneous hammer strokes on the PVC tube compacted the soil. This method induced a satisfactory homogeneity for the soil. This procedure was also found to be repeatable for high relative densities of the granular skeleton, where the relative density D r is defined as follows:

D r ϭ ␥ max ␥ ϫ ␥Ϫ␥ min ␥ max Ϫ␥ min (1)
where ␥ϭdry unit weight of the soil; ␥ min ϭits minimum dry unit weight ͑ASTM D 4254-91͒; and ␥ max ϭits maximum dry unit weight ͑ASTM D 4253-93͒. The relative density of the samples subsequently tested was always greater than 90%.

After the column was completely filled, some of the columns were saturated with water, while others were left dry. A fixed volume of grout equal to 1.2 times the initial volume of voids of the granular skeleton was then injected from the base to the top of the column at a constant volumetric flow rate of 3 cm 3 /s. Grout permeation occurred without any significant pressure rise. Gradually the grout completely filled the intergranular voids without visible fabric change of the granular skeleton. The void ratio of the granular skeleton deposited in a dense state was not significantly changed, as evidenced by dry density measurements of grouted specimens.

Columns were kept in a humidity and temperature-controlled room for a period of 28 days. After this period, the mechanical properties of grouted samples became constant. Four samples with a height-to-diameter ratio equal to 2 were cut from each column. Their faces were made parallel and smooth by straightening, and they were subsequently subjected to mechanical tests.

Unconfined Uniaxial Compression Strength

Unconfined uniaxial compression tests ͑ASTM D 2166-91͒ are routinely performed to assess the effect of the previously men- tioned parameters on the strength of the grouted sands. For most soil-cement mixtures, the strength depends mainly on the cement content of the grout and on the grain-size distribution, the mineralogy, and the relative density of the granular skeleton, regardless of the manufacturing process e.g., hand mixing, grout injection ͑Clough and Sitar 1981; [START_REF] Zebovitz | Injection of fine sands with very fine cement grout[END_REF][START_REF] Airey | Triaxial testing of naturally cemented carbonate soil[END_REF][START_REF] Tailliez | Etude expe ´rimentale du comportement me ´canique des sols granulaires injecte ´s[END_REF]. Some published results of the unconfined compressive strength, R c , for sands injected with microfine cement grouts or mineral grouts as a function of the C/W are reported in Fig. 3͑a͒ ͑Zebovitz et [START_REF] Zebovitz | Injection of fine sands with very fine cement grout[END_REF][START_REF] Schwarz | Effect of preparation technique on permeability and strength of cement-grouted sand[END_REF][START_REF] Kutzner | Grouting of rock and soil[END_REF]Tailliez 1998͒. Fig. 3͑b͒ shows the evolution of R c as a function of D r for three soils tested in this study ͑FS, ADM, ADC͒ for a similar cement-to-water ratio (C/Wϭ0.172), without saturation before grout injection. Three samples are tested for each relative density. The apparent scatter in the data is mainly due to the imperfect parallelism of the sample faces and to the injection process; i.e., the unconfined compressive strength of the three samples extracted from the same PVC column depends slightly on location from which the sample was extracted from the column. On the other hand, the scatter was small among samples from columns prepared under the same conditions. The unconfined compressive strength tends to increase with higher relative densities. Similar tendency was also found by Clough and Sitar ͑1981͒ and Huang and Airey ͑1998͒ for cemented sands. One possible explanation is that cementation is more effective in denser specimens because the particles are closer together.

The effect of the gradation is also highlighted in Fig. 3͑b͒. The grouted FS shows greater unconfined compressive strengths than the alluvial deposits ͑ADM or ADC͒. However, further work will be necessary to disconnect the effect of the mean size (d 50 ) of the particles ͑Saxena and Lastrico 1978; [START_REF] Zebovitz | Injection of fine sands with very fine cement grout[END_REF], the effect of the specific area of the sand grains ͑Kaga and Yonekura 1991͒, and the effect of the coefficient of uniformity (U c ).

Fig. 3͑c͒ represents the evolution of the unconfined compressive strength, R c,PG , of the pure microfine cement grout ͑IJ͒ and the evolution of the unconfined compressive strength, R c , of the FS at D r ϭ78%, injected with the microfine cement grout IJ without initial water saturation. As previously mentioned, the unconfined compressive strength of the grouted sands increases as the cement-to-water ratio of the grout increases.

Kaga and Yonekura ͑1991͒ suggested that the unconfined compressive strength of the cemented sands, R c , is related to the unconfined compressive strength of the cement paste, R c,PG , as follows:

R c ϭBϩA soil ϫ͑R c,PG ͒ n (2)
where the parameters A soil , B, and n depend mainly on the soil relative density and on the specific area of the sand grains. Kaga and Yonekura ͑1991͒ also stated that the power n depends linearly on the relative density D r as follows:

nϭn 0 Ϫn 1 ϫD r (3)
where n 0 and n 1 ϭconstants.

The parameter B represents the unconfined compressive strength of the granular skeleton without any cement paste. Consequently, its value here is assumed to be equal to zero. Finally, the compressive strength of the grouted sand, R c , is related to the compressive strength of the pure grout, R c,PG , as follows:

R c ϭA soil ͑ D r ͒ϫ͑ R c,PG ͒ n 0 Ϫn 1 ϫD r (4)
Based on results presented in Fig. 3͑c͒ and in Table 2, R c,PG is related to the cement-to-water ratio, C/W as follows:

R c,PG ϭA 0 ϫ ͩ C W ͪ N (5)
The values of the two parameters A 0 and N are determined by matching the experimental data ͓Fig. 3͑c͒, Table 2͔. In the case of the microfine cement grout ͑IJ͒, A 0 is equal to 45.3 MPa and N is close to 2.2. By combining Eqs. ͑4͒ and ͑5͒, R c of the grouted sand is related to the cement-to-water ratio

C/W R c ϭA soil ͑ D r ͒ϫA 0 n 0 Ϫn 1 ϫD r ϫ ͩ C W ͪ Nϫ͑n 0 Ϫn 1 ϫD r ͒ (6)
Matching the experimental data corresponding to the Fontainebleau sand (D r ϭ78%) injected by the microfine cement grout ͑IJ͒ leads to the following equation:

R c ϭ40.0ϫ ͩ C W ͪ 2.0 (7)
Further work will be necessary to determine the mathematical expression for the function A soil (D r ), which depends on the relative density and on the nature of the soil, and to clarify the effect of each soil characteristic ͑for example, specific area, grain size, and mineralogy͒.

Unconfined compression tests were also performed to assess the effect of the shear rate on the strength of grouted sands. These tests were required because silicate-grouted sands generally show Fig. 4 shows that the viscous effect in sands grouted by either pure microfine cements or mineral grouts can be disregarded for shear rates between 1.25ϫ10 Ϫ2 and 12.5 %/min.

Tensile Strength

The bonds produced by the hydration and the setting of the cement also provide a tensile strength for the soil-cement mixture. For example, Airey ͑1993͒ and Huang and Airey ͑1998͒ showed that the tensile strength of artificially cemented carbonate In the case of grouted sands, the tensile strength was experimentally evaluated from both splitting tensile tests ͑ASTM D 3967-92͒ and direct tensile tests ͑ASTM D 2936-84͒. In the latter case, the 80-mm-diameter by 160-mm-height samples were glued to PVC pedestals with an epoxy resin ͑Araldite glue, Ciba Specialty Chemicals, U.K.͒. A clear failure surface perpendicular to the extension axis was observed in the upper part of the grouted samples, slightly above mid-height.

Values of the tensile strength measured by splitting tensile tests, R TB,exp , and the tensile strength determined by direct tensile tests, R TD,exp , for Fontainebleau sand samples first saturated, then injected with the microfine cement grouts ͑i.e., CG1, CG2, CG3͒ and the mineral grouts ͑i.e., MG1, MG2, MG3͒ are reported in Table 3. The splitting tensile strength was found to be approximately 18% of the unconfined compression strength for the microfine cement grout and approximately 7% for the mineral grout. The ratio between the direct tensile strength and the unconfined compression strength, R TD,exp /R c , was even lower, about 1-2%. For comparison, Clough and Sitar ͑1981͒ indicated that the strength obtained by splitting tensile tests corresponded to 9-12% of the unconfined compression strength for cemented sands (0.09рR TB,exp /R c р0.12). Also, for cemented carbonate sands, Huang and Airey ͑1998͒ reported ratios of tensile to compressive strengths, R TB,exp /R c , between 10 and 30%.

If a Mohr-Coulomb yield criterion F() is assumed for the grouted sand (Ͻ0 in compression͒:

F͑Ј͒ϭ͑ 3 ЈϪ 1 Ј͒ϩ͑ 3 Јϩ 1 Ј͒ϫsin ЈϪ2cЈϫcos Ј (8)
where Јϭstress tensor; 1 Ј and 3 Јϭminor principal stress and major principal stress, respectively

( 1 Јр 3 Ј);

cЈϭeffective-stress cohesion; and Јϭeffective-stress friction angle. The unconfined compression strength, R c , and the direct tensile strength, R TD,the , are related to cЈ and Ј as follows:

R TD,the ϭ 2cЈϫcos Ј 1ϩsin Ј (9a)

R c ϭ 2cЈϫcos Ј 1Ϫsin Ј (9b)
and R TD,the /R c Ϸ20% for standard values of the friction angle.

The large difference between R c and R TD,exp found in this study means that the failure envelope is probably curved in the tensile stress domain. In other words, the relationship between the major and the minor principal stresses is not linear over a large domain of stresses as predicted by Griffith's crack theory ͑Hoek and Brown 1980; Kutzner 1996͒. However, the tensile strength is usually not taken into account in numerical computations for geotechnical design. Therefore, a linear failure envelope in the compressive domain will be assumed later.

Triaxial Tests

Although many studies have pointed out that the linear failure envelope, described by a friction angle and an intercept cohesion, does not exactly represent the actual failure envelope of soils and rocks ͑Bishop 1966; Baligh 1976͒, these parameters remain widely used in current geotechnical design. They can be determined by means of conventional consolidated-drained triaxial tests ͑French Standard NF P 94-074͒ which were carried out on saturated uncemented sands ͑with B values always greater than 96%͒ and on grouted sands prepared in the laboratory. Free water in grouted samples, due to the water saturation before grout injection, was smoothly removed by drying at room temperature.

The effect of the drying procedure was not investigated but was assumed to be negligible. The axial strain rate was 1.25ϫ10 Ϫ1 %/min. Confining pressures were between 0.1 and 0.4 MPa representing the vertical stress domain for tunnel works in urban areas ͑Bouvard-Lecoanet et al. 1992͒. The height-todiameter ratio of the samples was close to 2. No lubrication was applied to the end platens. The results are presented in terms of deviator stress q and volumetric strain v versus axial strain 1 . The axial strain 1 was calculated from the sample shortening measured on an external micrometer, which induces an experimental uncertainty due to bedding and compliance errors. This uncertainty is more pronounced in the case of stiff grouted sands. An internal load cell was used to determine the axial stress 1 . Finally, sample volume changes were recorded either by measuring pore water exchanges ͑water expulsion in the contracting domain or water absorption in the dilating phase͒ in a burette for saturated uncemented samples, or by measuring volume changes of the cell fluid on the pressure-volume controller from which the confining pressure c was applied, provided that these volume changes were corrected from the load cell penetration, for grouted samples. Previous calibration tests showed that these two measurements were equivalent.

As shown in Figs. 5 and6, the results of these tests illustrate the beneficial effect that the grout injection has on the strength and on the stiffness of the soil. They also confirm the following general trends for the cement-treated soils:

• Stiffness and strength increase as the binder content increases; • The volumetric behavior is typically contractive-dilatant; and • The postpeak behavior is more brittle for cementitious grouts, for low confining pressures, and for high cement contents. Failure occurs with visible vertical cracks for high cement-towater ratios and low confining pressures, whereas strain localization with inclined shear bands occurs for low cement-to-water ratios and high confining pressures.

The cohesion cЈ due to cemented intergranular bonds and the friction angle Ј due to interparticle contacts were determined by plotting the failure envelope in the Mohr-Coulomb diagram. For uncemented granular soils, a straight-line failure envelope with zero cohesion is apparent, as shown in Fig. 7. For grouted sands ͑Fig. 7͒, a straight-line failure envelope that is almost parallel to that for the uncemented granular soil is apparent. In other words, the value of the friction angle is approximately the same, probably since permeation grouting with low injection pressures does not cause any disturbance of particle assembly ͑Cambefort 1967͒. Similar results have been found by Dupas and Pecker ͑1979͒ on mortars, and by Clough and Sitar ͑1981͒ on natural weakly cemented sands.

The values obtained for the cohesion cЈ ͑Table 4͒ confirmed the influences of the sand characteristics, the binder, and the cement content. These effects can be formally introduced by the following equation, obtained by combining Eqs. ͑6͒ and Eq. ͑9b͒:

cЈϭ 1Ϫsin Ј 2ϫcos Ј ϫA soil ͑ D r ͒ϫA 0 1Ϫn 1 ϫD r ϫ ͩ C W ͪ N͑1Ϫn 1 ϫD r ͒
(10) Volume measurements indicate that grouted sands have a contractive-dilatant behavior ͑Figs. 5 and 6͒. However, when compared with uncemented sands, the contractancy domain is slightly reduced and the slope in the volumetric strain in the dilatancy stage increases ͑Table 5͒. Poisson's ratio is deduced from the initial slope of the curve in the contractancy domain ͓Eq. ͑11͔͒, whereas the dilation angle is conventionally related to the maximum slope of the v -1 curve ͓Eq. ͑12͔͒, at the inflection point in the dilatant stage, as follows:

ͩ ⌬ v ⌬ 1 ͪ ϭ1Ϫ2 (11) ͩ ⌬ v ⌬ 1 ͪ max ϭ ͩ Ϫ2ϫsin 1Ϫsin ͪ (12)
However, the values of have to be considered only in a qualitative way insofar as the grouted sands are concerned, at least for the lower confining pressures. Indeed, as previously mentioned, the grouted soils showed a brittle behavior under low confining pressures ͑vertical cracks͒ and more ductile behavior as the confining pressure increased ͑strain localization͒. The postpeak behavior is no longer representative, since failure systematically occurred in a localized mode.

The prefailure behavior and the pseudoelastic properties were, therefore, investigated further. The stress-strain curves ͑Figs. 5 and 6͒ show an almost linear initial part that extends over a large range of strains, but ends slightly before reaching the peak stress. Nevertheless, the pseudolinear elastic behavior provides a rough estimate. Also, the value of the secant modulus E determined at the beginning of the stress-strain curve in the strain range close to 0.1% ͓Eq. ͑13͔͒, as well as the maximum value of the deviator stress q, depend on the cement content, the nature and density of the granular material, the nature of the grout ͑Table 5͒, and the effective stress 3 Ј

Eϭ ⌬q ⌬ 1 (13)
The value of E is overestimated because of bedding errors during triaxial tests, as described later. The secant modulus E, for a strain level equal to 0.1%, increases linearly with the effective stress 3 Ј for uncemented sands. The dependency of the secant modulus on the effective stress, for a strain level also equal to 0.1%, is less pronounced for grouted sands, especially for high cement contents. Secant moduli for grouted sands are thus improved by a ratio of 2:5, depending on the mean stress value and on the nature and cement content of the grout, compared to secant moduli for uncemented sands, for the same strain level. Nevertheless, these improvement ratios of the secant modulus probably underestimate the improvement of the real elastic properties obtained for a strain level below 0.001% because of nonlinearity ͑Shibuya et al. 1992͒.

GrindoSonic Tests

Some more accurate measurements of the elastic properties have been completed in the very small-strain range (0.0001%р р0.001%). Such an investigation requires specific devices generally based on wave propagation. Devoted originally to tests on hardened concrete with values of the Young's modulus between 100 MPa and 840 GPa, the nondestructive GrindoSonic method consists of measuring the fundamental resonant frequency of the samples ͑RILEM 1983; Allison 1988͒ and French Standard NF P 18-414. A mathematical application based on Spinner and Tefft ͑1961͒ is therefore used to identify two independent parameters describing an isotropic-linear-elastic material, among the following three parameters: the Young's modulus (E max ), the shear modulus (G max ) and the Poisson's ratio ͑͒. The Grindo-Sonic measurements on concrete samples were found to agree with conventional static measurements by local extensometry ͑Valette 1992͒.

The cylindrical 100-mm-diameter by 200-mm-height samples lie on an absorbent cover to avoid any worktop interference effects. The sample is excited by a mechanical impulse caused by one slight plastic hammer stroke. The resulting propagating complex wave is detected by a piezoelectric detector held in contact in a point with the tested sample. The wave is therefore converted into an electronic signal. The fundamental resonant frequency is automatically deduced by the analysis of this signal. Two pulse modes ͑torsion and bending͒ are required to determine the aforementioned elastic parameters, which are obtained by different positions of the hammer stroke and the detector. Finally, the results for individual samples can be corroborated by repeated analysis under constant conditions.

Allison ͑1988͒ indicated that the elastic parameters dynamically identified depend on the water content of the tested material. Therefore, the grouted sand samples were gently dried in the open air before they were tested.

Experimental results are provided in Table 6. Young's moduli in the very small-strain domain are 1 order of magnitude greater than the secant moduli statically determined from the stressstrain curve in triaxial testing, whereas the values for the Poisson's ratios were typically between 0.15 and 0.30. This means that the behavior is nonlinear, with a progressive decrease of the secant modulus as the strain level increases. The behavior is assumed to be linear with a constant modulus for strains below about 0.001%, as shown by many writers ͑Shibuya et al. 1992; [START_REF] Baig | Low strain shear moduli of cemented sands[END_REF], for instance͒.

Summary of Experimental Results

The experimental results show that the behavior of grouted sands presents the same features as other cement-treated soils, namely a contractive-dilatant and mean stress-dependent behavior. Also, the stress-strain behavior of grouted sands is nonlinear, and stiffness and strength are greatly improved by grouting. Finally, a Mohr-Coulomb failure envelope seems to represent reasonably well the failure envelope for compressive stresses. These experimental observations were supported by triaxial tests on samples of uncemented Dunkerque sand ͑Fig. 1, Table 1͒ and the same Dunkerque sand injected in situ or in the laboratory by a mineral grout. Although the results are not presented here, the strength of the grouted sands prepared in the laboratory was systematically lower than that obtained from the field samples. Since the friction angle was found to be equal in both cases, the strength decrease means that the different preparation processes affected the cohesion. The decrease in cohesion for laboratory prepared samples can be attributed to the injection process. For the field conditions, an initially high pressure is required to break down the sleeve grout. This breakdown extends also to the soil, creating some zones with a greater quantity of grout than the quantity necessary to impregnate the sand. On the other hand, the laboratory conditions are well controlled and induce a homogeneous permeation of the grout through the sand.

Recommendations for Design

A simple linear elastic-perfectly plastic Mohr-Coulomb model is often used for design in sandy soils. Even if it only roughly represents the soil behavior, its simplicity makes it popular among geotechnical engineers. The triaxial test results give qualitatively similar results for grouted sands as for natural sands of medium to high relative density, i.e., a contractive-dilatant behavior as well as frictional and cohesive characteristics in the plastic domain. Therefore, the Mohr-Coulomb model was extended to grouted sands. This model is defined by the yield surface F ͓Eq. ͑8͔͒ and by a nonassociated flow rule that allows the dilatant behavior of a densely compacted granular soil to be represented more precisely. The plastic potential function, G(Ј), is expressed as follows:

G͑Ј͒ϭ͑ 3 ЈϪ 1 Ј͒ϩ͑ 3 Јϩ 1 Ј͒ϫsin (14) d i j p ϭϫ ץG ץ i j (15)
A nonassociated flow rule was chosen because the measured dilation angles were systematically lower than the friction angle.

Based on the previous experimental work, improvement ratios X* will be defined as the ratio between a property obtained after injection, X p , and the same property before any treatment, X b , or X*ϭX p /X b . These ratios have been integrated into the technical specifications for underground construction works in Paris. Geotechnical investigations are commonly carried out to assess the soil characteristics before treatment. Depending on the objective of the grout injection ͑soil mechanical reinforcement or permeability reduction͒, characteristics of the grout will be defined, particularly its cement-to-water ratio. For design purposes, mechanical properties of the grouted soil can be calculated using the improvement ratios adapted to the chosen grout. The following improvement ratios are proposed: 1. The value of the Poisson's ratio, for uncemented sands as well as for grouted sands, is between 0.15 and 0.30. No distinct correlation was found between the two materials and the Poisson's ratio for the grouted sand can be considered as equal to the Poisson's ratio of the uncemented sand, i.e., *ϭ1. 2. Experiments have also shown that the value of the friction angle was hardly changed by permeation grouting. Consequently, it can be determined by carrying out conventional triaxial tests on the uncemented sand with a density close to the in situ one, such that Ј*ϭ1. 3. It is difficult to propose a clear improvement ratio for the dilation angle since mechanisms responsible for dilation are probably not similar, due to irreversible grain displacements and rotations in the case of uncemented sands, and damage crack opening in the case of grouted sands, at least for low mean stresses and high cement-to-water ratios. Therefore, the dilation angle for grouted sands is at least equal to the dilation angle of the uncemented sands: 1р*р1.5. 4. The improvement ratio for the pseudoelastic properties ͑secant modulus in particular͒ not only depends on the cementto-water ratio, the mean stress and the soil characteristics, but also on the strain level. For secant moduli at a strain level of 0.1%, E* is set to a value greater than 2 for a consolidation grouting, for the same mean effective stress. But failure can occur not far from such a strain level. Consequently it is more advisable to compare the Young's moduli in the very small-strain range where E max * can reach a value close to 10. Further investigations are planned to correlate the elastic modulus of the grouted sand to the elastic modulus of both the grout and the uncemented sand. 5. Assuming that the cohesion of the uncemented soil is 0, the increase of the cohesion depends on the cement-to-water ratio of the grout and the relative density of the soil, as stated by Eq. ͑10͒. It can be calculated from unconfined compression tests on the pure grout and on the grouted sand and from conventional triaxial tests on the uncemented sand. The effect of the initial saturation of soil voids was not discussed here, but pore water generally induces a slight decrease of the cohesion due to the dilution of the grout in the water ͑Perret et al. 2000͒.

Conclusions

Grouted sands present the general characteristics of cemented soils and can be considered as an intermediate material between soil and concrete. Based on the results of triaxial tests, when a given sand is impregnated by a cementitious grout, the evolution of its mechanical behavior is as follows: 1. The friction angle is almost unchanged by the injection treatment. 2. The Mohr-Coulomb cohesion varies between 0.1 and 0.5 MPa depending on the cement content of the grout and the relative density of the soil and increases in proportion with the cement-to-water ratio. 3. The secant modulus, measured at an axial strain of 0.1%, is increased by a factor equal at least to 2, referring to the experimental data of this work. This ratio should be greater for a reinforcement ground treatment and can reach 4 -5, depending on the mean effective stress. In the very smallstrain domain, the increase of real elastic properties leads to higher values of improvement ratios. 4. The grouted sands show a contractive-dilatant response along a deviatoric stress path and Poisson's ratio is between 0.15 and 0.3. The dilation angle of the grouted sand is at least equal to and usually higher than the dilation angle of the uncemented sand at the same dry density.

Notations

The following symbols are used in this paper: A 0 ,A soil ,B ϭ parameters describing evolution of unconfined compression of pure grouts or grouted sands; C/W ϭ cement to water ratio; cЈ ϭ Mohr-Coulomb effective stress cohesion; D r ϭ relative density; d x ϭ grain size at which x% of particles by weight are smaller; d 50 ϭ mean grain size of sand particles; E ϭ secant modulus; E max ϭ Young's modulus in small-strain domain; F() ϭ yield criterion; G max ϭ shear modulus in small-strain domain; M /W ϭ dry material to water ratio; n,N,n 0 ,n 1 ϭ parameters describing evolution of unconfined compression of pure grouts or grouted sands; q ϭ deviator stress; R c ϭ unconfined compressive strength; R c,PG ϭ unconfined compressive strength of pure grout; R TB,exp ϭ tensile strength measured by splitting tensile test; R TD,exp ϭ tensile strength measured by direct tensile test; R TD,the ϭ tensile strength obtained with Mohr-Coulomb yield criterion; U c ϭ coefficient of uniformity (U c ϭd 60 /d 10 ); ␥ ϭ weight per unit of volume; ␥ max ϭ maximum dry weight per unit of volume; ␥ min ϭ minimum dry weight per unit of volume; , 1 , V ϭ strain level, axial strain, and volumetric strain during triaxial tests, respectively; ϭ Poisson's ratio;

Ј, 1 Ј , 3 Ј ϭ stress tensor, minor principal effective stress, major effective principal stress; c ϭ confining pressure; Ј ϭ Mohr-Coulomb effective stress friction angle; and ϭ dilation angle.

Fig. 1 .

 1 Fig. 1. Gradation curves of tested sands

Fig. 2 .

 2 Fig. 2. Laboratory preparation of grouted sands

Fig. 3 .

 3 Fig. 3. Effect of cement to water, ratio and relative density D r on unconfined compressive strength R c of grouted sands ͑ASTM D 2166-91͒: ͑a͒ effect of cement to water ratio of cementitious grouts; ͑b͒ effect of relative density D r ; and ͑c͒ evolution of unconfined compressive strength R c with cement to water ratio

Fig. 4 .

 4 Fig. 4. Effect of strain rate on unconfined compressive strength R c of grout and grouted sands ͑ASTM D 2166-91͒

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Drained triaxial tests on Fontainebleau sand prepared in laboratory ͑AFNOR P 94-074͒ ( 3 Јϭconstant effective lateral stress during triaxial tests͒

Table 1 .

 1 Characteristics of Sands d 10 , d 60 is grain size at which 10 and 60% of particles by weight, respectively, are smaller. d 50 is mean grain size. c ␥ min is minimum dry unit weight. d ␥ max is maximum dry unit weight.

	Sand

d

Table 2. Grouts and Grouted Sands Unconfined Compressive strengths ͑ASTM D 2166-91͒

		Dry material	Cement to	R c,PG a	R c	b
	Grout	to water ratio	water ratio	͑MPa͒	͑MPa͒
	Cementitious grout ͑CG1͒	0.2	0.07	-	0.9
	Cementitious grout ͑CG2͒	0.2	0.11	-	1.1
	Cementitious grout ͑CG3͒	0.2	0.15	-	1.9
	Mineral grout ͑MG1͒	0.3	0.056	-	0.6
	Mineral grout ͑MG2͒	0.3	0.078	-	0.9
	Mineral grout ͑MG3͒	0.26	0.123	-	1.9
	Cementitious grout IJ1	-	0.17	0.8	1.1
	Cementitious grout IJ2	-	0.23	1.9	2.5
	Cementitious grout IJ3	-	0.29	-	3.2
	Cementitious grout IJ4	-	0.34	4.2	5.1
	Cementitious grout IJ5	-	0.40	5.6	6.4
	Cementitious grout IJ6	-	0.46	7.7	8.5
	a R c,PG is unconfined compressive strength of the pure grout.

b R c is unconfined compressive strength of the grouted sand.

Table 3 .

 3 Tensile Strength of Grouted Fontainebleau Sand

			Fontainebleau sandϩcementitious grout ͑CG͒	Fontainebleau sandϩmineral grout ͑MG͒
			CG1	CG2	CG3	MG1	MG2	MG3
	R c	MPa	0.9	1.1	1.9	0.6	0.9	1.9
	R TB,exp /R c	%	17	23	16	8.3	7.8	6.8
	R TD,exp /R c	%	-	1-1.25	-	-	1.7-2	-
	R TD,the /R c	%	-	20-25	-	-	20-25	-

Note: R c is unconfined compressive strength; R TB,exp is tensile strength measured by splitting tensile test ͑ASTM D 3967-92͒; R TD,exp is tensile strength measured by direct tensile test ͑ASTM D 2936-84͒; R TD,the is tensile strength obtained with the Mohr-Coulomb yield criterion.

Table 4 .

 4 Values of Effective Stress Cohesion cЈ and Effective StressFriction Angle Ј

		Fontainebleau	Seine River
		sand ͑FS͒	sand ͑SRS͒
		Ј	cЈ	Ј	cЈ
	Elements	͑degrees͒	͑MPa͒	͑degrees͒	͑MPa͒
	Natural sand	39	0	40	0
	Sandϩcementitious grout ͑CG1͒	42	0.2	42	0.18
	Sandϩcementitious grout ͑CG2͒	43	0.3	43	0.25
	Sandϩcementitious grout ͑CG3͒	44	0.5	44	0.35
	Sandϩmineral grout ͑MG1͒	42	0.125	43	0.1
	Sandϩmineral grout ͑MG2͒	42	0.2	43	0.125
	Sandϩmineral grout ͑MG3͒	40	0.45	42	0.4

Table 5 .

 5 Values of Secant Modulus E, Poisson's Ratio , and Dila-

	tion Angle
		3 Ј a	E
	Sand	͑MPa͒	͑MPa͒		͑degrees͒
	Fontainebleau sand ͑FS͒	0.1	63		15.2
		0.2	117	0.3	14.0
		0.4	252		13.1
	Fontainebleau sand ͑FS͒ϩ	0.1	332	-	27.0
	cementitious grout ͑CG1͒	0.2	406		24.0
		0.4	790		22.0
	Fontainebleau sand ͑FS͒ϩ	0.1	-	-	-
	cementitious grout ͑CG2͒	0.2	630		-
		0.4	630		-
	Seine River sand ͑SRS͒	0.1	-	0.31	9.7
		0.2	74		8.4
		0.4	97		5.9
	Seine River sand ͑SRS͒ϩ	0.1	112	-	27.0
	cementitious grout ͑CG1͒	0.2	180		21.4
		0.4	-		19.6
	Seine River sand ͑SRS͒ϩ	0	180	-	-
	mineral grout ͑MG2͒	0.1	187		29.8
		0.4	240		21.1
	a 3 Ј is major principal effective stress (ЈϽ0 in compression͒ applied
	during triaxial test.

Table 6 .

 6 Elastic Properties Determined by Use of GrindoSonic Apparatus ͑AFNOR NF P 18-414-1993͒ E max is Young's modulus ͑measured in the small-strain domain͒. b G max is shear modulus in the small-strain domain. c is Poisson's ratio.

		E max a	G max
	Sand	͑GPa͒	͑GPa͒
	Fontainebleau sand ͑FS͒ϩ	9.1	3.9	0.18
	cementitious grout IJ1
	Fontainebleau sand ͑FS͒ϩ	12.4	5.2	0.18
	cementitious grout IJ2
	Fontainebleau sand ͑FS͒ϩ	15.7	6.1	0.22
	cementitious grout IJ3
	Medium alluvial deposits ͑ADM͒ϩ	11.1	4.4	0.20
	cementitious grout IJ1
	Coarse alluvial deposits ͑ADC͒	11.9	5.2	0.14
	ϩcementitious grout IJ1
	Pure cementitious grout IJ1	1.4	0.5	0.40

a


Vinod Kasam
email: kasam@clermont.in2p3.fr

Jean Salzemann
email: salzemann@clermont.in2p3.fr

Nicolas Jacq

Astrid Mass

Vincent Breton

Large Scale Deployment of Molecular Docking Application on Computational Grid infrastructures for Combating Malaria

Computational grids are solutions for several biological applications like virtual screening or molecular dynamics where large amounts of computing power and storage are required. The WISDOM project successfully deployed virtual screening at large scale on EGEE grid infrastructures in the summer 2005 and achieved 46 million dockings in 45 days, which is equivalent to 80 CPU years. WISDOM is one good example of a successful deployment of an embarrassingly parallel application. In this paper, we describe the improvements in our deployment. We screened ZINC database against four targets implicated in malaria. During more than 2 months and a half, we have achieved 140 million dockings, representing an average throughput of almost 80,000 dockings per hour. This was made possible by the availability of thousands of CPUs through different infrastructures worldwide. Through the acquired experience, the WISDOM production environment is evolving to enable an easy and faulttolerant deployment of biological tools.

Introduction

WISDOM stands for World-wide In Silico Docking On Malaria. Malaria together with many other tropical and protozoan diseases is one of the most neglected diseases by the developed countries as well as by the pharmaceutical industries. Plasmodium is the protozoan genus causing malaria. Due to very high costs associated to the drug discovery process as well as due to late stage attrition rates, novel and cost effective strategies are absolutely needed for combating the neglected diseases, especially malaria [START_REF] Breman | Conquering the intolerable burden of malaria: what's new, what's needed: a summary[END_REF].

In silico screening of chemical compounds against a particular target is termed as virtual screening. The costs associated to the virtual screening of chemical compounds are significantly low when compared to screening of compounds in experimental laboratory. Beside the costs, virtual screening is fast and reliable [START_REF] Bleicher | Hit And Lead Generation: Beyond High-Throughput Screening[END_REF][START_REF] Boehm | Virtual Screening For Bioactive Molecules. Chapter 1, High Throughput Screening and Virtual Screening Entry Points To Drug Discovery[END_REF]. However, it is computationally intensive; docking a single compound within the active site of a given receptor requires about 1 minute CPU. With the development of combinatorial chemistry technology, millions of different chemical compounds are now available in electronic databases [START_REF] Spencer | High throughput virtual screening of historic collections on the file size, biological targets, and file diversity[END_REF]. To screen all these compounds and store the results is a real data challenge. To address this problem, computational grid infrastructures are used. WISDOM-I [START_REF] Jacq | Grid enabled virtual screening against malaria[END_REF] is the first large scale deployment of molecular docking application on EGEE grid infrastructure. It took place from August 2005 to September 2005 and achieved 41 million dockings which is equivalent to 80 years of CPU. The docking was performed on Plasmepsins, a aspartic protease involved in haemoglobin degradation. On the biological front, three scaffolds were identified, of them one is guanidino scaffold which is likely to be novel as it was not known as a plasmepsin inhibitor before [START_REF] Kasam | Design of Plasmepsin Inhibitors: A Virtual High Throughput Screening Approach on the EGEE Grid[END_REF]. With the success achieved by the WISDOM-I project both on the computation and biological sides, several scientific groups around the world proposed targets implicated in malaria which led to the second assault on malaria. WISDOM-II project deals with several targets which are both X-ray crystal models and homology models. Targets from different classes of proteins are also being tested.

Materials and methods

Virtual screening by molecular docking requires target structure, chemical compound database and docking software. Several targets are used in the current project and are described in the table 1: Dihydrofolate reductase (DHFR), Glutatione-Strasferase (GST) and Tubulin. The chemical compound database used is ZINC and the docking software used is FlexX [START_REF] Rarey | Predicting Receptor-Ligand interactions by an incremental construction algorithm[END_REF]8].

Procedure

The goal of WISDOM II is two folds, the biological goal is to find the best hits against the targets implicated in malaria and the computational goal is to keep improving the relevance of computational grids in drug discovery applications. We are going to discuss in details the virtual screening experimental set up and the grid architecture and deployment.

Virtual screening experimental setup

The structural features of all the targets screened are given in table 1. The complete virtual screening experiment is segmented into five different phases. i: Target preparation, ii: Compound database, iii: Validation of the docking experiment, iv: Screening, v: Result analysis.

Target preparation.

A standard protocol is used while preparing the target structures. The initial coordinates for all the target structures are obtained from Brookhaven protein database (http://www.pdb.org). Depending upon the inclusion of the significant residues, active site is defined as 8.0 Å for GST, 10.0 Å for PfDHFR and PvDHFR around the co-crystallized ligand. X-ray crystal models for tubulin are not available; hence a homology model had to be built. Tubulin will be discussed in detail in another paper. Structural details on the first three targets used for screening in WISDOM-II are described in table 1.

Compound database.

The compound library used for WISDOM was obtained from the ZINC database [START_REF]A Free database for virtual screening[END_REF]. The ZINC database is a collection of 4.3 million chemical compounds ready for virtual screening from different vendors. We have chosen to use the ZINC library because ZINC is an open source database and the structures have already been filtered according to the Lipinski rules. Moreover the data are available in different file formats (Sybyl mol2 format, sdf and smiles). A total of 4.3 million compounds were downloaded from the ZINC database and screened against 4 different targets (table 1).

Validation of the docking experiment.

Redocking against the co-crystallized compound is performed to check and tune the docking experiment requirements. Re-docking serves as a control for finally selecting the parameters for target structure.

Grid infrastructure and Deployment

Grid Infrastructures.

The deployments were achieved on several grid infrastructures: Auvergrid [START_REF] Auvergrid | auvergrid[END_REF], EELA [START_REF] Eela | [END_REF], EGEE [START_REF] Gagliardi | Building an infrastructure for scientific Grid computing: status and goals of the EGEE project[END_REF], EUChinaGrid [17] and EUMedGrid [18]. All these infrastructures are actually using the same middleware, gLite. While EGEE is the main infrastructure offering the largest resources, they are all interconnected with EGEE. In the case of Auvergrid, it is even more evident as all the resources available through the Auvergrid Virtual Organization (VO) are also shared with several EGEE VOs.

WISDOM production Environment.

WISDOM environment has been used two times in previous large-scale experiments, WISDOM-I in the summer 2005 and a second deployment against avian flu in the spring 2006 [START_REF] Jacq | Virtual Screening on Large Scale Grids[END_REF]. WISDOM environment keeps evolving in order to make it more user friendly and easier to use by non grid experts. The environment was initially using scripts that took care of submitting the jobs and following up their respective status on the grid, giving feedback to the end user. These scripts were reorganized in two different and independent tasks: the submission of the jobs, the follow-up of the jobs, and eventually their resubmission, as well as the collection of the job status and their publication on a web site. These two processes can be started and run simultaneously, the second one being fed from the information provided by the first one.

With the gained experience from the previous deployments [START_REF] Lee | Grid-Enabled High-Throughput In Silico Screening Against Influenza A Neuraminidase[END_REF], the environment was continuously maintained to improve the fault-tolerance of the system, in implementing, for instance, a persistent environment, that can be stopped and restarted at any time without risking of loosing important information. The user can also manage jobs finely, for instance force the cancellation and resubmission of a scheduled job. Along with this, we tried to minimize the cost of the environment in terms of disk space and CPU consumption for the User Interface: for example, we are generating dynamically the job files which also allow the user to modify on the fly the configuration of the resource brokers and the jobs requirements while saving disk space. This way, the user is sure that the next submissions will take these modifications into account. The figure 1 shows the overall architecture of the environment.

The jobs are submitted directly to the grid Workload Management System (WMS), and are executed on the grid Computing Elements (CEs) and Worker Nodes (WNs). As soon as it is running, a job transfers all the files stored on the Storage Elements (SEs) via the Data Management System (DMS) of the grid with the gridFTP protocol. Then the FlexX software can start to process the dockings. During the job lifetime the status is retrieved from the User Interface and some statistics are generated and collected to a remote server which hosts a relational database and outputs these statistics through a web site. Once the job is finished, the outputs are stored back on the grid Storage Elements (SEs) and the useful docking results are inserted directly into a relational database.

Data Challenge Deployment.

The three groups of targets (GST, PvDHFR and PfDHFR) were docked against the whole ZINC database (4.3 millions of compounds) which was cut into 2,422 chunks of 1,800 compounds each. This splitting was chosen because we wanted to have an approximated processing time ranging from 20 to 30 hours for each job (one docking process takes from 40s to 1min depending on the CPU power and the data). The subsets had to be stored on the involved grid infrastructures. They were basically copied on a SE and were replicated on several locations whenever possible to improve fault-tolerance.

We define a WISDOM instance as being a target structure docked against the whole ZINC database, with a given parameter set. During the experiment a total number of 32 instances were deployed, corresponding to an overall workload of 77,504 jobs, and up to 140,000,000 docking operations. On this total 32 instances, 29 were docked on EGEE, and 3 were run on Auvergrid, EELA and EuChinaGrid.

The job repartition was quite similar to the previous deployments, but here the United Kingdom and Ireland federation played an even bigger part. For instance, one of the British sites offered for quite a long period of time more than 1,000 free CPUs, which is half of the average used CPUs. The repartition of the jobs on the Auvergrid, EUChinaGrid and EELA infrastructures corresponds to 3% of the total 32 instances.

Results

Grid results analysis.

Table 2 shows the overall statistics of the deployment. The number of jobs was actually the number of awaited results, but far more jobs were actually submitted on the grid because of the resubmissions and failing jobs.

Anyhow the average docking throughput is coherent with the crunching factor, which basically represents the average number of CPUs used simultaneously all along the data challenge. If we consider 80,000 dockings per hour for 2,000 CPUs (the crunching factor) it means 40 dockings for one CPU per hour, which is coherent with the empiric observation of one docking process lasting approximately 1 minute on a 3.06 Intel Xeon processor. In the same logic, we can estimate that the instantaneous throughput peak would be obtained when the max number of CPUs were used (i.e.: 5,000), giving a throughput of approximately 200,000 dockings per hour.

In the table 2, the estimated grid success rate is the ratio between successful grid jobs on the total of submitted jobs. The success rate after output checking will consider just the jobs that succeeded in producing the good results; this score is thus lower. There are several explanations for these small values. Actually at the beginning of the data challenge, the observed grid success rate was about 80 to 90%, but it decreased constantly because of overload. The available disk space has also decreased dramatically on some WMS machines, the Resources Brokers, up to a point where some of the job data could not reach the CE. The Resource Brokers failed again to balance reasonably the jobs on the CEs, and some of them ended up with more than 500 jobs in queue. Actually, because of the automatic resubmission, this information should not be taken as an overall significant way to evaluate the efficiency of the grid, because the automatic resubmission guaranteed a successful job, and the aborted jobs are not staying a long time on the grid consuming useful resources. So one must keep in mind that the grid is a very dynamic system, and errors can occur at the last minute.

Preliminary docking results.

All the results are stored on the SEs of the Grid. Three different types of results are stored for each docking:

• Docking scores (free energy) of the ten best compound conformations after clustering.

• Interaction information between protein and compound for ten best conformations. • 3D co-ordinates of the ten best conformations in MOL2 format. As the result analysis of all the instances is under process, preliminary results of one instance, GST A chain score distribution is shown in figure 2. Approximately 100,000 compounds scored more than its co-crystallized ligand (GTX) and these compounds will be given further focus.

Issues

As pointed out in the previous section and in the previous experiences of large scale deployment, the scheduling efficiency of the grid is still a major issue. The Resource Broker is still the main bottleneck, and even if used in high number (>15), is always a source of trouble. The sometimes unreliable and incomplete information provided by the Information System, which does not publish the available slots and VO limitations that would be mandatory to perform an efficient scheduling, is another point of failure. This deployment also shows that it is not possible to do a naive blacklisting of the failing resources, for the simple fact that virtually all the grid resources have produced aborted jobs, and this blacklisting should also take care of the site scheduled downtimes.

Another issue was that to be able to store and treat the data in a relational database. The machine hosting the database must have good performances to avoid its overloading by the number of queries coming from the grid. In this deployment we used a MySQL database and planned to put all the produced result in the same table, but finally we had to spit this database in several ones (one per target), because MySQL would not have been able to withstand the total number of records.

All these elements demonstrate clearly that even if the grid can show very good result in comparison to very simple architecture it is still missing robustness and reliability, and can indeed be improved performance-wise.

Conclusions

We have demonstrated the role and significance of computational grids in the life science applications such as structure based drug design. Large scale virtual screening on four different targets of malaria was performed in search for potential hits on several grid infrastructures:

Auvergrid, EELA, EGEE, EUChinaGrid and EUMedGrid. One of our goals was to further demonstrate the impact of computational grids in life science applications like virtual screening where large amounts of computing power is required; we have achieved it by successfully screening the whole ZINC database for three malaria targets in 76 days instead of 413 years. We have reached during this ten-week period an average docking throughput of 78,400 dockings. MySQL databases are used for the analysis of the docking results, which will ease the final analysis of the virtual screening data. On the biological front, 1,738 Terabytes of valuable data has been produced. Analysis of the results (identification of the best hits) is under way: the best hits will be post processed by molecular dynamic simulations and tested in the experimental laboratories.

Figure 1 .

 1 Figure 1. Schema of the production environment.

Figure 2 .

 2 Figure 2. The repartition of docking energies of the ZINC database against GST A structure. (The red column represents a score of -24kj/Mol, which is the docking score of a co-crystallized ligand (GTX) of GST A chain).

Table 1 . Structural features of all the targets used in WISDOM II. * Target preparation and Screening are under process.

 1

	Target	Activity	Structure PDB id	Resolution Ligand	Co-factor
	GST [9]	Detoxification Dimer	1Q4J	2.2	GTX	NO
	P. falciparum	DNA	Polymer	1J3I	2.33	WR99210	NADPH
	DHFR	synthesis
	Wild type
	P. falciparum	DNA	Polymer	1J3K	2.10	WR99210	NADPH
	DHFR [11]	synthesis
	Quadruple mutant
	P. vivax	DNA	Polymer	2BL9	1.90	Pyrimethamine	NADPH
	DHFR [10]	synthesis
	Wild type
	P. falciparum	DNA	Polymer	2BLC	2.25	Des-	NADPH
	DHFR	synthesis				Chloropyrimethamine
	Double mutant
	Plasmodium	Cell division	Monomer	Homology	-	-	GTP
	Tubulin [12]*			model

Table 2 . Overall statistics of the deployment.

 2

	Number of Jobs

Maximum number of loaded licences (concurrent running jobs) 5,000 Number of used computing elements 98 Average duration of a job

		41 hours
	Average crunching factor	1,986
	Volume of output results	1,738 TB
	Estimated distribution efficiency	39%
	Estimated grid success rate	49%
	Estimated success rate after output checking	37%


Robert Riemann
email: robert.riemann@inria.fr

Stéphane Grumbach
email: stephane.grumbach@inria.fr

Distributed Protocols at the Rescue for Trustworthy Online Voting

Keywords: distributed online voting, trust, distributed protocols, Bitcoin

While online services emerge in all areas of life, the voting procedure in many democracies remains paper-based as the security of current online voting technology is highly disputed. We address the issue of trustworthy online voting protocols and recall therefore their security concepts with its trust assumptions. Inspired by the Bitcoin protocol, the prospects of distributed online voting protocols are analysed. No trusted authority is assumed to ensure ballot secrecy. Further, the integrity of the voting is enforced by all voters themselves and without a weakest link, the protocol becomes more robust. We introduce a taxonomy of notions of distribution in online voting protocols that we apply on selected online voting protocols. Accordingly, blockchain-based protocols seem to be promising for online voting due to their similarity with paper-based protocols.

VOTING IN THE DIGITAL AGE

Online services have emerged during the last decade in most areas of every day life. Online banking, online auctions, online shopping, online learning and online dating, to name a few, have become serious alternatives to their offline counterparts for the additional convenience they provide. Most online services are available 24 hours a day 7 days a week and can be accessed from any place with an internet connection. In particular, online social networks gained a lot of momentum. Many people are permanently connected to communicate with friends and colleagues. The social network Facebook, for instance, reports on 1.71 billion monthly active users as of June 2016 which is more than 20 % of the world population. The adoption of online services increases further with the global dissemination of internet-enabled devices.

In these circumstances of pervasive online services, the paper-based voting procedure used to carry out elections in many democracies appears like a legacy from the past. This is even more the case for the generation of Digital Natives that is used to the convenience offered by online services.

Paper-based voting requires voters to cast their ballot within a given time frame at a particular location. In contrast, remote electronic voting, in short online voting, allows voters to cast their ballot from home or any other place. The time and effort to vote decreases. Consequently, the overall voter turnout is expected to increase [START_REF] Carter | Internet Voting and Political Participation: An Empirical Comparison of Technological and Political Factors[END_REF]. Moreover, the ballot casting is carried out using a special software which improves the voter convenience as the ballot presentation considers for instance the voter's spoken language and possible disabilities.

The voter convenience is especially important if voters are often asked to vote, e.g. for elements of direct democracy such as referenda. Not only doubts in the integrity of the voting outcome, but also a low voter turnout can negatively impact the legitimacy of the result.

Despite the advantages, only few countries employ online voting for general elections, e.g. Estonia [START_REF] Ülle | E-voting in Estonia 2005. The first practice of country-wide binding Internet voting in the world[END_REF], Canada [START_REF] Goodman | Internet Voting in a Local Election in Canada[END_REF]) and Australia [START_REF] Brightwell | An overview of the iVote 2015 voting system[END_REF], and for those, security concerns have been addressed repeatedly by the scientific community [START_REF] Springall | Security Analysis of the Estonian Internet Voting System[END_REF][START_REF] Halderman | The New South Wales iVote System: Security Failures and Verification Flaws in a Live Online Election[END_REF]. Other countries have abandoned online voting trials or banned online voting for their insufficient security, as it happened in Germany. In fact, the provision of the same set of security properties as known from paper-based voting for online voting proves to be challenging with no universal solution, but with different potential concessions.

In this paper, we address the issue of trustworthy online voting protocols with regard to the potential of distributed protocols. Starting from paper-based voting with its broadly accepted trustworthiness (Sec. 2), we give a high-level review of the principle security concepts of online voting protocols and deliver an over-view of their trust assumptions (Sec. 3). The capacity of authorities and of the voters defined by the protocols are hereby of primary concern. We show that the trustworthiness in those approaches is limited due to the concentration of power and argue hereinafter that distributed protocols are promising to increase the trustworthiness due to their similarity with paper-based protocols. Bitcoin, an electronic currency with no trusted authority, is introduced in Sec. 4. Moreover, the development towards online voting is compared with those to Bitcoin and BitTorrent. Sec. 5 is dedicated to the prospects of distributed protocols for trustworthy online voting. Then in Sec. 6, different notions of distribution are introduced in order to analyse a selection of existing online voting protocols for their degree of distribution. Our conclusion follows in Sec. 7.

Our findings motivate our ongoing research on distributed online voting protocols with a novel distributed protocol currently in preparation for publication.

PAPER-BASED VOTING

The paper-based voting protocol used today in many democracies is the result of a development rooted in Ancient Greece where pebbles were casted in an urn for votings. Since then, many provisions have been added to ensure the voting outcome reflects indeed the aggregated choice of all eligible voters. Neglecting local particularities, we give a sketch of a paper-based voting protocol to recall afterwards how basic security properties are implemented.

Preparation Phase

The voting station is the dedicated location to receive voters on voting day and is run by volunteering voters that become thus occasionally voting officers. For large numbers of voters, the voters are partitioned by locality to a reasonable number of voting districts with each one voting station. Every station is provided with undistinguishable voting ballots and a list of eligible voters issued by the central voter registry.

Casting Phase On arrival at the voting station, voters have to present a proof of identity in order to proceed to the casting. Once the voter is confirmed to be eligible, a blank ballot is handed out and the voter list is annotated accordingly to prevent that voters can get more than one ballot. Under public supervision, the voter enters alone the voting booth to fill and fold in secret the paper ballot. Again under public supervision, the filled ballot is thrown into a transparent ballot box.

Aggregation and Evaluation Phase Once, the casting phase is terminated, ballot boxes are opened and ballots are tabulated to determine the tally that is published independently along with the derived voting outcome, e.g. using the majority rule.

Verification Phase Every voter is allowed to attend all phases to supervise the compliance with the voting protocol.

Conflicting Security Properties Paper-based voting resolves the dilemma of voting protocols to ensure secrecy of the ballot and voter eligibility at the same time [START_REF] Lambrinoudakis | Secure electronic voting: The current landscape[END_REF]) in a straightforward way. Voting officers and voters control that only eligible voters get one single paper ballot and that every voter puts only one ballot into the ballot box. Secrecy of the ballot is provided, because every voter fills and folds its ballot alone and once deposited in the ballot box, all ballots are indistinguishable and cannot be linked back to the voter. By eye-sight, ballots can be followed from its distribution, through its casting into the transparent ballot box until the tallying of all ballots. Verifiability is realised by the observation of the physical ballot transport, which is called chain of custody. This verification does not require any special knowledge. Hence, neither trust in the authority carrying out the voting, nor in employed technology is imposed.

ONLINE VOTING CONCEPTS

The development of online voting protocols, that preserve the security properties known from paper-based voting, is proven to be difficult. Electronic ballots can be cloned with no effort and their physical transport via wire cannot be observed. That is why special cautions must be taken to prevent the casting of illegitimate ballots, e.g. of ineligible voters or voters that seek to cast more than one ballot. Various concepts have been considered to ensure secrecy, eligibility and verifiability of online voting. Nonetheless, the overwhelming majority of current online voting protocols, as we detail hereafter, are either lacking properties, so that trust in authorities to carry out essential tasks must be assumed, or use advanced cryptography, which imposes trust in technology as expert knowledge cannot be implied.

One can distinguish online voting protocols by the following concepts to ensure both secrecy of the ballot and eligibility [START_REF] Lambrinoudakis | Secure electronic voting: The current landscape[END_REF]

):

Trusted Authorities A very basic approach is to assume trust in all or a subset of the authorities. Voters transmit their ballot to the authorities using an authenticated channel that allows to verify the eligibility. Authorities are trusted to keep ballots confidential and to produce the correct tally.

Anonymous Voting Using an authenticated channel, voters acquire from one authority an eligibility token, e.g. using blind signatures (D. [START_REF] Chaum | Blind Signatures for Untraceable Payments[END_REF], that cannot be linked to the voter's identity, but allows to verify its eligibility. Then, voters send both ballot and token through an anonymous channel to the authority. Technological trust is assumed in the secrecy ensured by the token. Authorities are trusted to produce the correct tally.

Random Perturbation Voters send encrypted ballots to a group of authorities that shuffle one after each other the set of all ballots. Shuffling can be realised using a secure multi-party computation called Mix-Nets (D. L. Chaum 1981). This way, ballots cannot be linked to voters if at least one authority is honest. Afterwards, ballots are decrypted to compute the tally. Technological trust and trust in at least one authority is assumed.

Homomorphic Encryption With homomorphic encryption, encrypted ballots are tallied and decrypted only afterwards [START_REF] Benaloh | Verifiable secret-ballot elections[END_REF]. To prevent early decryption, (k, n)-threshold cryptography [START_REF] Pedersen | A threshold cryptosystem without a trusted party[END_REF]) is used, which requires the cooperation of k out of n authorities. The use of cryptography implies technological trust and trust in authorities to the extent that less than k out of n authorities are dishonest.

Balancing Verifiability and Secrecy of the Ballot Online voting protocols offering end-to-end verifiability [START_REF] Benaloh | End-to-end verifiability[END_REF]) allow voters to verify the online voting outcome using cryptographic proofs. However, the very nature of the mentioned cryptographic protocols prevents to have both universal verifiability of the voting outcome and unconditional secrecy of the ballot (Chevallier-Mames et al. 2010). Eventually, authorities have to be trusted to either respect the secrecy of the ballot or deliver the correct voting outcome. For a trustworthy voting, it is reasonable to let all voters choose their trusted authorities. Hence, the number of authorities is in the order of voters, which is infeasible for large scale elections with protocols based on the presented cryptographic concepts, because of an amount of required resources polynomial (or worse) in the number of authorities. As the distribution of powers in retrospect seems to be problematic, we consider in the next sections dedicated distributed protocols.

DISTRIBUTED PROTOCOLS

Without consensus on trusted authorities, it is reasonable to omit authorities altogether if possible and assume instead equipotency of all voters.

Bitcoin [START_REF] Nakamoto | Bitcoin: A Peer-to-Peer Electronic Cash System[END_REF] demonstrates the feasibility to find such protocols without trusted authority. It establishes an electronic currency without inherent value, prevents its duplication, thus, double spending, and allows for fast online transactions between peers from many internet-enabled devices. Therefore, the protocol assumes that the majority of computing resources is controlled by honest peers. Technically, Bitcoin can be interpreted as an approach to the situation in the past, when traders used mostly currencies of inherent value such as gold, and no trust in online banking systems or authorities like central banks were assumed (Perez-Marco 2016). Hence, after technological progress allowed a shift from distributed offline to centralised online systems, Bitcoin presents a distributed online alternative, c.f. Fig. 1 (c). A similar analogy is given with BitTorrent [START_REF] Cohen | The BitTorrent Protocol Specification[END_REF]) that allows its peers to share their resources to provide information (files) online, when before central online servers had to be used. The notion of peer empowerment/democracy in both Bitcoin and BitTorrent offers inspiration for the development of novel online voting protocols and is further detailed in the following section. In his essay 'Authoritarian and Democratic Technics', [START_REF] Mumford | Authoritarian and Democratic Technics[END_REF] explained the arising conflict if technology for democratic purposes is based on authorities. Indeed, protocols that omit distinct authorities and instead make provisions for equally privileged, equipotent voters sharing the same responsibilities, seem to better reflect the basic democratic concept of equally powerful voters. We assume further a distributed online voting protocol in which voters are represented as equipotent peers.

In BitTorrent and Bitcoin, peers cooperate, because they share a common goal. Peers are providers and consumers at the same time. Applied to online voting, we find a constellation similar to paper-based voting where voters serve as voting officers to run the voting station and carry out the supervision.

Even though not all tasks can be carried out by everyone at the same time, equipotent peers can replace each other easily. All peers are responsible to enforce the protocol policy, while byzantine peers with inconsistent behaviour are often tolerated to a certain degree. These properties contribute to the robustness of the protocol as there is no weakest link or bottleneck. Therefore, distributed protocols offer great potential for resilience against Distributed Denial of Service (DDoS) attacks.

The peers joining a distributed system, contribute with their own resources, e.g. communication capacity, memory and computation power. The global resources grow and diminish with peers joining or leaving the system offering potential for great scalability. Further, distributed protocols allow for ephemeral databases that vanishes entirely when all peers have left the system, offering new avenues for applications with sensitive data such as voting. In the case of centralised online voting protocols, ballots are most often encrypted, but there might be potential for a malicious decryption at some point in the future, if the implementation of cryptographic routines turns out to be flawed, secret keys leak or computing power got sufficiently cheap to brute-force the encryption.

As every peer has only partial knowledge of the global information, any unintentional or intentional disclosure is locally bounded. The impact of an attack, and thus its incentive, is reduced. In contrast, a disclosure by the authorities of centralised online voting can impact the secrecy of all casted ballots.

TOWARDS ONLINE VOTING WITHOUT AUTHORITIES

As presented in Sec. 3, cryptographic algorithms allow to limit the power of authorities in online voting protocols. Note, that there is a trade-off. Less trust in authorities is assumed if authorities are less powerful, but as the protocol complexity increases, more technological trust is required. Using Anonymous Voting for example, voters do not have to present their ballot in clear, but have to trust in the properties of the eligibility token. Further, online voting protocols employing many authorities might assign authorities either equal roles like in Random Perturbation or Homomorphic Encryption where authorities carry out the same tasks, or different roles. In Anonymous Voting, one authority ensures the eligibility of voters while the other aggregates all ballots and produces the tally. If all authorities are equipotent and their number can match the number of voters allowing for an identification between authorities and voters, the protocol becomes essentially distributed. In between, there is room for different kinds of partially distributed protocols that we want to characterise as follows. Note, that the registration phase shall not be considered in this paper.

Degree of Specialisation ranging from equipotent voters with no specialisation to authorities with dedicated powers

Topology ranging from centralised over decentralised to distributed topologies, c.f. Fig. 1 Phase Authorities can intervene either not at all, only in few or in all phases (not distributed).

A protocol shall be called fully distributed if the topology is distributed and voters are equipotent during all phases but the registration.

Note, that we consider large scale elections for our analysis. First, we want to qualify paper-based voting as presented in Sec. 2. There are responsible voting officers, who can principally exchanged as no special knowledge is required. If we accept that every voter can become spontaneously voting officer, the protocol is actually fully distributed during all phases.

Helios One of the few published, well-studied online voting protocols with unconditional end-to-end verifiability is Helios [START_REF] Adida | Helios: Web-based Open-Audit Voting[END_REF]. While the original version is based on Random Pertubation (Mix-Nets), the version available online 1 uses Homomorphic Encryption. In both cases trusted authorities are assumed for threshold decryption requiring communication costs polynomial in the number of authorities. Hence, the number of authorities must be small. During the aggregation, ballots are sent to the authorities for tallying, which corresponds to a centralised topology. The final step of end-to-end verification is the only distributed phase, because it can be carried out independently by all voters once the authorities have published the required material.

While Helios is as such an online voting protocol employing a central web server to receive ballots and produce the tally, other protocols do not require such a server as they omit an authority. A selection is presented hereafter.

Secure Multiparty Computations

The aim of Secure Multiparty Computations (SMC) is to compute collectively a joint function over the private inputs of all participants. The correctness and secrecy properties rely on cryptography [START_REF] Yao | Protocols for secure computations[END_REF]. It seems to be an appropriate technique to compute the tally from the individual, secret ballots. However, several issues render an implementation of a decentralised voting protocol based on this scheme difficult. As [START_REF] Gambs | Scalable and Secure Aggregation in Distributed Networks[END_REF]) points out, the communication complexity for n participants is O n 2 , or in the case of the existence of a trusted party, O (n). Both render the scheme impractical for large-scale distributed online voting. Though, SMC is suited for boardroom voting protocols with only few voters.

Furthermore, the employed cryptography is computationally extensive and provides often only computational instead of information-theoretic security.

Scalable and Secure Aggregation Protocol An intermediate solution between a centralised online voting protocol based on cryptography and an aggregation by the voters is given with Scalable and Secure Aggregation (SPP) [START_REF] Gambs | Scalable and Secure Aggregation in Distributed Networks[END_REF]. Voters are grouped using a chord overlay into clusters of equal size in order to partition potential dishonest voters. The clusters are then arranged in a binary tree structure (Fig. 2 (b)). Voters assigned to the root cluster have to create a key pair for homomorphic public-key cryptography. Thus, a (k, n)-threshold decryption key pair is jointly created using a distributed key generation protocol. While the private key parts are distributed among the members of the root cluster, the public key is communicated to all child clusters in the tree.

Every voter encrypts its ballot and adds a noninteractive zero-knowledge-proof to back the validity of its vote. Encrypted ballots are gathered from voters in the same cluster to compute an intermediate aggregate for the cluster. From the tree leaves, aggregates are passed to all members of the parent cluster, who com- pute first the sub-tree aggregate taking into account the own aggregate and those of its child, and pass the result to all members of the parent cluster. By majority rule, voters decide in case of diverging results which aggregate has to be used for the computation. At some point, the root cluster will possess the encrypted final tally of all ballots. A union of k voters will carry out the joint decryption algorithm to compute the final tally that is subsequently propagated down the tree to all voters.

Even though all voters are involved in the aggregation procedure, the parity of knowledge is not given. The voters in the root cluster correspond effectively to randomly determined, trusted voting officers in a centralised protocol, that cannot be flexibly exchanged after the key pair generation.

Decentralised Polling

Another technique to realise distributed online voting is based on secret sharing schemes. A corresponding protocol known as Decentralised Polling (DPol) is described in [START_REF] Guerraoui | Decentralized polling with respectable participants[END_REF]. n voters are grouped to clusters of size √ n. The clusters form a ring, so that each cluster has one preceding and one succeeding cluster (Fig. 2 (a)). Every voter gets accorded 2k + 1 recipient voters from the succeeding cluster and is itself recipient to 2k + 1 voters from the preceding cluster. k is a privacy parameter. A ballot for a particular option from a set of size d is represented by a vector in {0, 1} d . The voter issues then 2k + 1 vectors, k + 1 towards its choice and k for others. The vectors are distributed among the receivers. In the next step, received vectors are summed up and the result is exchanged with other voters of the same cluster in order to compute the tally for the preceding cluster. The tallies are then communicated to the succeeding clusters in the ring until every cluster is in possession of all the cluster tallies such that the final tally can be computed by every voter.

It is remarkable, that this scheme provides secrecy [START_REF] Hoang | Efficient and Decentralized Polling Protocol for General Social Networks[END_REF], that generalises the DPol voting system in such a manner, that the actual social graph structure (with some assumptions) can be used and a ring social net overlay and a perfect square voter number is not a prerequisite anymore.

Both DPol and EPol provide for equipotent voters. The aggregation is a joint effort in which all voters are involved. Every voter computes the final tally and then the voting result. Similar to the SPP protocol, intermediate aggregates are employed to keep the information on individual ballots local in the overlay.

Blockchain-based Voting Systems Online voting based on Bitcoin technology, namely the global consensus algorithm given by its blockchain, is eagerly anticipated by some groups. Various prototypes and commercial solutions are or have been developed2 . However, the actual protocols are either lacking essential properties or remain obscure. Scientific results are very sparse. [START_REF] Zhao | How to Vote Privately Using Bitcoin[END_REF] present a protocol for a binary vote that requires a monetary deposit and a funding of the winner by all voters. Transactions to the winner and voter payback is controlled due to contracts enforced by the distributed network which limits the flexibility of the ballot.

To the author's knowledge, most other approaches to online voting using Bitcoin are based on so-called coloured coins that allow to associate digital assets to Bitcoin addresses. Consequently, asset ownership can be traded like the Bitcoin currency and (pseudonymous) ownership is publicly verifiable by following the previous asset transactions.

To construct an online voting protocol, every voter must initially own a coloured coin representing its eligibility. Those coins are then transferred to a destin-ation that corresponds to e.g. a candidate. Transactions are publicly verifiable, so that aggregation and evaluation can be carried out by every voter. Though, the publicity of all transactions endangers the secrecy of the ballot, because coins can be linked back to the voter that has been identified during the registration phase to receive its coin.

Different protocols have been proposed to provide anonymous Bitcoin transactions [START_REF] Miers | Zerocoin: Anonymous distributed ecash from bitcoin[END_REF][START_REF] Ibrahim | SecureCoin: A Robust Secure and Efficient Protocol for Anonymous Bitcoin Ecosystem[END_REF]) that are considered to ensure secrecy of the ballot in blockchain-based online voting. Also blind signatures may permit to distribute coins anonymously to voters. In that case, the protocol approaches the Anonymous Voting concept (c.f. Sec. 3). The authority carrying out the aggregation is hereby replaced by the distributed blockchain that serves as a public add-only bulletin board to log casted ballots. Consequently, tallying and verification can be carried out by every voter. The distributed topology is inherited from Bitcoin which uses gossiping to spread transactions (Fig. 2 (d)). Transactions are then gathered into blocks by voters or third parties that seek to confirm transactions. Every voter can as its own discretion engage in the confirmation procedure. There is no specialisation of voters.

It turns out that blockchain-based and paper-based voting are on par with respect to the notions of distribution and qualify both as fully distributed, c.f. Tab. 1.

CONCLUSION

Major votings in 2016, e.g. the Brexit referendum or the US presidential elections, demonstrated the importance of a high voter turnout for the legitimacy of the outcome, especially in the case of tight outcomes.

While online voting is generally considered with much hesitation, advances in technology are eroding the security of paper-based voting. Coercion-freeness, in the past a major argument for on-site ballot casting, is at stake due to omnipresent smart phone cameras. Exit polls on social media allow voters casting their ballot very late a more informed choice, which harms the fairness. More and more voters use early postal voting sacrificing thus their means of verification and the potential to change their vote last minute. Meanwhile, many online voting protocols seek to achieve those security properties that paper-based voting with optional postal voting can ensure less and less.

In this situation, distributed online voting offers a promising perspective. It does not assume a trusted authority and the integrity of the voting is enforced by the voters themselves. Without a weakest link, votings are difficult to interrupt. The damage in case of security breaches is locally bounded thanks to the distribution of data. Like in all online voting protocols, voting becomes more convenient, especially as ballots can be casted from remote. We acknowledge that still trust in technology or expert knowledge is assumed and leave it as an open issue.

So far, only few distributed online voting protocols have been proposed and even less are fully distributed. We hope to see more proposals in the future and plan to contribute to this subject with a novel fully distributed protocol. This work in progress follows the Anonymous Voting concept and uses techniques from BitTorrent to create a voter overlay network and from Bitcoin to ensure verifiability. Similar to DPol, secrecy is provided by a particular sharing scheme instead of cryptography. To achieve logarithmique complexity, it is based like SPP on a tree overlay network. Unlike in SPP, no decryption step is needed. Hence, all voters are equipotent.

Figure 1 :

 1 Figure 1: (a) centralised, (b) decentralised, (c) distributed systems. Points represent peers and lines interaction between peers. In (a), strong specialisation and hierarchy is depicted as one sole peer carries out a distinct role. The hierarchy becomes more flat in (b) as more peers serves as intermediaries. In (c), peers are equipotent and interact with any set of peers, e.g. within a given distance.

Figure 2 :

 2 Figure 2: Topology of distributed voting protocols. (a) DPol and (b) SPP have a higher degree of hierarchy than (c) SMC and (d) blockchain-based protocols due to partition of voters in clusters. This way, the number of exchanged messages can be reduced at the cost of less equipotent voters with less flexible roles. Unstructured SMC-and blockchain-based protocols use a distributed topology allowing for equipotent voters.

Table 1 :

 1 Quality of distribution of selected online voting protocols.

	Protocol	Degree of Specialisation Topology	Distributed Phases
	Paper-based Voting	none (flexible)	distributed	all
	Helios, Adida 2008	selected authorities	centralised	verification
	SPP, Gambs et al. 2011	random authorities	structured, tree aggregation
	DPol, Guerraoui et al. 2012 none	structured, ring all
	Blockchain-based Voting	none (flexible)	distributed	all
	of the ballot without the employment of cryptography.
	The protocol authors describe means to determine
	dishonest voters with high probability without false-
	positives and tag them accordingly, e.g. in a public
	social network profile.
	Few extensions have been proposed, among them
	EPol

https://vote.heliosvoting.org/faq

https://github.com/domschiener/publicvotes, http://votem.com, http://www.bitcongress.org, http://followmyvote.com, http://cryptovoter.com, http://votosocial.github.io

ACKNOWLEDGEMENTS

The authors wish to thank Stéphane Frénot, Damien Reimert and Aurélien Faravelon for fruitful discussions on distributed voting protocols.