Cornelius Schonnenbeck

Pavel Maryandyshev

Gwenaelle Trouve

Alain Brillard
email: alain.brillard@uha.fr

Viktor Lyubov

Jean-Francois Brilhac

Cornelius Schönnenbeck

Gwenaëlle Trouvé

Jean-François Brilhac

Combustion of hydrolysis lignin in a drop tube furnace and subsequent gaseous and particulate emissions

Keywords: Drop tube furnace, combustion, gaseous emission, particulate matter, hydrolysis lignin, woody biomass

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Coals are currently widely used for heat and electricity generation in industrial boilers and power plants due to their low cost and also because they are available in pulverized form. To decrease the world global warning, biomass and their by-products are nowadays considered as combustible in pulverized-fuel firing burners (PFFB). But whatever the solid fuels which are used as combustible for heat and electricity productions, their combustion are among the principal sources of fine particles having diameter less than 2.5 µm (PM2.5) and of gaseous compounds such as carbon monoxide or other incomplete combustion gas like nitrogen oxides or volatile organic compounds [START_REF] Nussbaumer | Overview on Technologies for Biomass Combustion and Emission Levels of Particulate Matter, Swiss Federal Office for the Environment (FOEN) as a contribution to the Expert Group on Techno-Economic Issues (EGTEI) under the Convention on Long-Range Transboundary Air Pollution[END_REF][START_REF] Herich | A 2.5 year's source apportionment study of black carbon from wood burning and fossil fuel combustion at urban and rural sites in Switzerland[END_REF].

Hydrolysis lignin is a by-product of technological cycles concerning the production of fuels and chemicals, through either a percolation (Scholler process) or a low-temperature (Bergius process) hydrolysis of wood, [START_REF] Rabinovich | Carbon adsorbents from industrial hydrolysis lignin: The USSR/Eastern European experience and its importance for modern biorefineries[END_REF]. Wood hydrolysis plants were mainly built in the former USSR, Bulgaria, China and Korea. All these plants produced substantial amounts of hydrolysis lignin, at most 1.5 million tons each year. As a consequence, the available feedstock is very large, especially in Eastern Europe. As mentioned in [START_REF] Mahmood | Hydrolytic depolymerization of hydrolysis lignin: Effects of catalysts and solvents[END_REF], hydrolysis lignin was mainly stored because no valuable valorization was possible, despite an extensive research on this available material. Compared to coal and woody biomass, hydrolysis lignin is a brittle solid and easily transformable as pulverized fuel. The present study aims at determining if hydrolysis lignin is suitable as combustible in PFFB, especially when considering the associated gaseous and particulate pollutants emitted during its combustion, which have to be as low as that occurring in the combustion of other woody biomass.

In the present study, combustion experiments were realized in a drop tube furnace which simulates the conditions prevailing in a PFFB that is pulverized fuel submitted to flash heating rate with a residence time around 1 s in the combustion chamber. An isothermal temperature ranging from 800 to 1200 °C was imposed in the isothermal zone of the reactor, which was reached under a high temperature rate (1000 to 4000 K s -1 ). The drop distance in the drop tube furnace was set between 7 and 55 cm, with a special focus at 40 cm. The drop duration ranged from 485 ms (at 800 °C) to 457 ms (at 1200 °C).

Gaseous and particulate pollutants obtained as by-products of an incomplete combustion were analyzed and ash were collected at the bottom of the drop tube furnace. The fly particles were collected using an electrical low-pressure impactor (ELPI). Methanic and non-methanic volatile organic compounds were analyzed with a flame ionization detector.

If the combustion of hydrolysis lignin was mainly considered under these conditions, that of two other biomass, spruce bark and spruce trunk, were also considered in the same experimental conditions, and also that of a South-African bituminous coal, as performed in [START_REF] Zellagui | Parametric study on the particulate matter emissions during solid fuel combustion in a drop tube furnace[END_REF], for comparison.

The influence of different parameters on the gaseous and particulate emissions was analyzed, also using the complementary results returned by different devices disposed in connection with the drop tube furnace. For an isothermal temperature of 1000 °C, the volatile yields of hydrolysis lignin proved that the devolatilization process is almost complete in these conditions. Concerning the particulate emissions, two mechanisms are proposed to explain the PM formation: the soot and tar production at low temperatures and the decomposition of the mineral fraction of the fuel at high temperatures. These hypotheses are supported by observations deduced from the mineral fractions of the fuels and on the collected ash.

Previous studies already analyzed the influence of experimental conditions on the gaseous and particulate emissions during coal and biomass combustion. Several parameters were indeed investigated, including solid fuel type (Zhang and Ninomiya, 2006;[START_REF] Wen | Emission of inorganic PM10 from included mineral matter during the combustion of pulverized coals of various ranks[END_REF][START_REF] Al-Naiema | Impacts of co-firing biomass on emissions of particulate matter to the atmosphere[END_REF][START_REF] Jiménez | Particulate matter formation and emission in the combustion of different pulverized biomass fuels[END_REF], residence time [START_REF] Tissari | A novel field measurement method for determining fine particle and gas emission from residential wood combustion[END_REF][START_REF] Zhuo | The progressive formation of submicron particulate matter in a quasi one-dimensional pulverized coal combustor[END_REF], reaction temperature (Zhang et al., 2006) and coal combustion environment (Li et al., 2013). Some authors [START_REF] Ninomiya | Transformation of mineral and emission of particulate matters during co-combustion of coal with sewage sludge[END_REF][START_REF] Jiménez | Effect of co-firing on the properties of submicron aerosols from biomass combustion[END_REF][START_REF] Zhang | Influence of woody biomass (cedar chip) addition on the emissions of PM10 from pulverised coal combustion[END_REF][START_REF] Wang | Emission behavior of particulate matter during co-combustion of coal and biomass in a drop tube furnace[END_REF] analyzed the effect of co-firing coal and biomass on PM emissions.

In their experiments, Jia and Lighty (2012) analyzed the impacts of furnace temperature, coal type and gas phase conditions on the emissions. Considering the biomass combustion, the PM formation may be classified into two distinct pathways (Zhang and Ninomiya, 2006;[START_REF] Gao | Significant contribution of organicallybound Mg, Ca, and Fe to inorganic PM10 emission during the combustion of pulverized Victorian brown coal[END_REF]. [START_REF] Obernberger | Chemical properties of solid biofuels -significance and impact[END_REF] gave a clear and detailed schematic description of the formation of ash and fly-ash during combustion. Both aerosols (0.01-0.1 µm) and coarse flyash particles (1-200 µm) are produced. On the one hand, non-volatile inorganic elements (Si, Ca, Mg, etc.) are directly transformed in coarse ash particles. On another hand, the transformations of inorganic vapors (KOH, KCl, ZnO, K2CO3, etc.) through nucleation, condensation, coagulation and agglomeration [START_REF] Sippula | Comparison of particle emissions from small heavy fuel oil and wood-fired boilers[END_REF] led to fine ash particles formation. Moreover, the incomplete biomass combustion was proved to lead to the formation of soot, tars and volatile organic compounds.

The combustion of hydrolysis lignin seems to have not yet been analyzed in the abovedescribed conditions, the available literature mainly focusing on the combustion of coals, of mixtures of coals and woody biomass or even of other woody biomass.

Material and methods

Materials

The hydrolysis lignin samples were kindly provided by the "Bionet" company which produces hydrolysis lignin pellets from the Onega lignin dump, located in the Arkhangelsk region, northwest region of the Russian Federation. The spruce (bark and trunk) samples were collected mainly from harvested forests in the Arkhangelsk region. The combustion of these samples will be compared to that of a South African bituminous coal, in the same experimental conditions. The samples were preliminary dried at ambient temperature during one week, then ground in a ball mill Retzsch PM 200 and sieved on a Retzsch AS 200 Control analyzer to a particle size distribution 200-280 micrometers.

Ash were prepared in a muffle furnace according the EN NF 14775 (2010) standards for biofuels.

The proximate analyses of the samples were performed according to EN NF 14774-2 (2010), NF M03-004 (1974) standards for coal samples and ISO 1171 (2010) and EN NF 14775 (2010) standards for biomass samples. The results are gathered in Table 1.

Table 1.

Spruce bark and trunk present a proximate analysis close to that found in [START_REF] Nussbaumer | Overview on Technologies for Biomass Combustion and Emission Levels of Particulate Matter, Swiss Federal Office for the Environment (FOEN) as a contribution to the Expert Group on Techno-Economic Issues (EGTEI) under the Convention on Long-Range Transboundary Air Pollution[END_REF].

Because the bark represents the outside part of the wood, its relative humidity is higher than that of trunk. The ash content of the bark is also higher than that of the trunk, related to the presence of minerals as alumina and silica oxides. The proximate analysis of the South-African coal was analyzed in [START_REF] Zellagui | Parametric study on the particulate matter emissions during solid fuel combustion in a drop tube furnace[END_REF] and similar results were reported in [START_REF] Li | Fine particulate formation and ash deposition during pulverized coal combustion of high-sodium lignite in a down-fired furnace[END_REF]. The fixed carbon content and ash content in hydrolysis lignin are higher than that of spruce samples.

The ultimate analyses of the different samples were determined on an analyzer EuroVector EA-300 and according to ISO 29541 (2010), ISO 19579 (2006) and ASTM 3176-09 (2009) standards. The results are gathered in Table 2. Oxygen was calculated by difference.

Table 2.

The percentage of carbon is naturally higher in coal than in the woody biomass samples. The percentages of the different constituents lie quite in the same range for the three woody biomass and are close to that of the literature [START_REF] Eom | Characterization of primary thermal degradation features of lignocellulosic biomass after removal of inorganic metals by diverse solvents[END_REF]. The percentage of sulfur is higher in coal than in the woody biomass samples. It is well known that sulfur may damage the equipment during the combustion process [START_REF] Leightner | Weather-induced changes in the trade-o¤ between SO2 and NOx at large power plants[END_REF].

The Higher Heating Values (HHV) of the four samples (which are not indicated in Table 2) have been determined according to the BS EN ISO 18125 (2017). The LHV values have then been computed from the HHV ones and the ultimate analyses of the samples. The LHV values of the three woody biomass lie in the same range but are much lower than that of coal. These LHV values are in the same order of magnitude than those found in literature for lignocellulosic fuels and coal, respectively [START_REF] Popova | Thermal degradation and combustion of wood fuels, coals and hydrolysis lignin from the Russian Federation: experiments and modeling[END_REF].

The lignocellulosic composition of hydrolysis lignin was determined according to Van Soest's protocol [START_REF] Van Soest | Methods for Dietary Fiber, Neutral Detergent Fiber, and Nonstarch Polysaccharides in Relation to Animal Nutrition[END_REF] which leads to 2.3% of hemicellulose, 15.6% of cellulose, 66.9% of lignin and 15.2% of extractives, respectively. Aromatic polymers as lignin are largely predominant in this by-product.

Combustion experiments in an equipped drop tube furnace

The samples were burnt in a drop tube furnace, which mainly consists in a reactor and a fuel feeding system and which is equipped with mass flow controllers and an Electrical Low Pressure Impactor (ELPI) device, see Fig. 1. The silica-alumina reactor is 1.7 m high and has a diameter equal to 7 cm. Different isothermal temperatures of the reaction zone were tested in the present study: 800, 900, 1000, 1100 and 1200 °C.

Figure 1.

and under a primary synthetic air (80% N2, 20% O2) flow of 40 NL/h. The pulverized material was then entrained in the drop tube furnace through a secondary synthetic air flow of 800 NL/h. The time length of an injection (corresponding to approximately 2.5 g of material) in the drop tube furnace was around 1 h. To obtain a permanent regime, only the 20 minutes in the middle of the injection time length were observed. Except for the analyses of the impact of the drop height on the production of particulate matter and of volatiles, the drop height was taken equal to 40 cm.

The ash collection stage is an impaction chamber with a 150 mm diameter inlet orifice and three outlet vent tubes. This design results in very low turbulence and allows collection of several grams of coarse particles (>10 μm) without overloading the collecting device.

An ELPI manufactured by Dekati Ltd. (Tampere, Finland) was used to collect the emitted particles from 29 to 10 μm into twelve size fractions. Within the ELPI, the particles are first electrically charged on a corona charger, according to their Stokes diameter and then impacted on twelve different plates according to their inertia related to their aerodynamic diameter. The number of particles and the mass concentrations were calculated taking into account this particularity that is using 1 g cm -3 as density value [START_REF] Marjamäki | Performance evaluation of the electrical low-pressure impactor (ELPI)[END_REF].

According to [START_REF] Gauchet | Modelling of the aerosol collection efficiency by drops influence of the distance between the drops[END_REF], the condensation of the water vapor leads to an increase of the aerosols on the higher plates of the impactor in the range 3-10 μm. For these reasons, if particulate matter was collected on the twelve plates of the ELPI (from 29 nm to 10 μm), the numbers of particles, their mass concentrations and their distributions were only calculated for PM2.5. The number and mass of the particles from 3 to 10 μm were not taken into account in the present study. Methanic and Non Methanic Volatile Organic Compounds (MVOC and NMVOC) were analyzed during the combustion in the drop tube furnace with a Flame Ionization Detector Cosmos Graphite 55 (0-10,000 ppmv). Total VOC were expressed in equivalent CH4. Carbon oxides (CO and CO2) were analyzed with a Rosemount NGA 2000 analyzer for carbon oxides and O2, respectively (carbon monoxide CO: 0-10%, carbon dioxide CO2: 0-100% and dioxygen O2: 0-100%).

Results and discussion

Particulate emissions

When observing the material collected on the twelve plates of the ELPI at different temperatures, two main features appear:

• Tars and soot are mainly formed at the lowest temperature of 800 °C and collected on a large range of diameters as observable on plates 2 to 12 (brown zones) while incompletely burnt particles as soot are collected on some other plates (dark zones).

• At the highest temperature of 1200 °C, particles are mainly minerals as ash. Grey spots can indeed be seen on plates 6 to 11, which correspond to the flight of fine ash particles during experiments. On plates 1 to 5, which collect particles with diameters lower than 0.4 µm, soot is always present. The presence of ash on plates corresponds to a more complete combustion of the material at high temperatures.

The mean values of the amounts of PM2.5 collected through repeatability experiments are gathered in Fig. 2 for hydrolysis lignin, spruce bark and spruce trunk. Figure 2 shows that the amounts of collected PM2.5 decrease from 800 to 900, or 1000 °C, then increase for the two last temperatures of 1000 and 1200 °C, except for spruce bark at 950 °C, see also below.

The ratios between the standard deviations and the mean values lie between 0.02 and 0.06 for hydrolysis lignin, between 0.00 and 0.16 for spruce bark and between 0.00 and 0.15 for spruce trunk, which allows to consider only mean values of these amounts.

The particle number concentrations lie in the same range than that obtained in other studies for both coal and biomass samples [START_REF] Moisio | Fine particle size distributions of seven different combustion power plants[END_REF][START_REF] Johansson | Particle emissions from biomass combustion in small combustors[END_REF][START_REF] Yi | Fine particle and trace element emissions from an anthracite coal-fired power plant equipped with a bag-house in China[END_REF][START_REF] Lind | Electrostatic Precipitator Collection Efficiency and Trace Element Emissions from Co-Combustion of Biomass and Recovered Fuel in Fluidized-Bed Combustion[END_REF]. For comparison, the numbers of particles emitted from the combustion of the South-African coal in the same conditions and under the temperature of 1300 °C were in p.cm -3 : 22.5×10 6 (PM2.5), 22.0×10 6 (PM0.1), .0.5×10 6 (PM0.1-1) and 1.0×10 3 (PM1-2.5), respectively, see [START_REF] Zellagui | Parametric study on the particulate matter emissions during solid fuel combustion in a drop tube furnace[END_REF]. This may be the consequence of the mineral matter present in coal, which is different from that in biomass. Consequently, it is not surprising that the particulate matters formed from coal and biomass differ (Rizvi et As exhibited in Fig. 2, the number of particles PM2.5 starts decreasing and then increases with the isothermal temperature. The minimum of such particles is reached at 900 °C for hydrolysis lignin and for spruce bark and at 1000 °C for spruce trunk. When using woody biomass as solid fuel in the current experimental conditions and considering the emissions of particulate matter, these temperatures represent the optimal ones. Increasing the temperature during biomass combustion leads to higher vaporization of ash elements such as alkali and sulfur compounds [START_REF] Dayton | Direct observation of alkali vapor release during biomass combustion and gasification. 1. Application of molecular beam/mass spectrometry to switchgrass combustion[END_REF].

Whatever the sample, the number of large particles PM1-2.5 is much smaller (100 times) than that of ultrafine particles. Nanoparticles as PM0.1 dominate in number, whatever the temperature. They represent more than 90% of the total number of particles emitted in the exhaust. The increase of the temperature largely influences the number size distribution of particles with a proportion of PM0.1 close to 99% for spruce bark and spruce trunk in the temperature range 1000-1200 °C. The part of PM0.1 also increases for hydrolysis lignin in the same temperature range but with values close to 95%. High temperature favors the biomass gasification and leads to the formation of nanoparticles mainly emitted in the gas. The effect of temperature has already been reported in [START_REF] Zellagui | Parametric study on the particulate matter emissions during solid fuel combustion in a drop tube furnace[END_REF] for a woody biomass (harvested Alsatian wood chips) but the PM2.5 was here always increasing in the temperature range 700-1300 °C.

Particulate matter formation from incomplete combustion

The large amount of particles observed at 800 °C may be explained by the incomplete combustion of the biomass. Soot, elemental carbon and tars are visually observed on the collections stage of the ELPI. The combustion of softwoods (as spruce) is well-known and numerous literature data are available to explain that they largely contribute to give tars and soot, contrary to hardwoods. The formation of products as CO and Polycyclic Aromatic Hydrocarbons (PAH) during an incomplete combustion is favored. PAH mainly constitute tars and are defined as soot precursors [START_REF] Eberle | A sectional PAH model with reversible PAH chemistry for CFD soot simulations[END_REF]. The high number of PM2.5 for hydrolysis lignin at 800 °C may be attributed to the incomplete combustion of this biofuel, mainly composed of aromatic polymers as lignin, as deduced from the lignocellulosic composition of this material. High temperatures above 800 °C and longer residence times of at least 2s are required to achieve the combustion of these aromatic molecules, as described in [START_REF] Parker | Toward the Oxidation of the Phenyl Radical and Prevention of PAH Formation in Combustion Systems[END_REF]. Moreover, inorganic and organic vapors may condense on soot particles.

To check the above-indicated hypothesis of an incomplete combustion of the biomass leading to a larger amount of particles observed at 800 °C, the gaseous emissions during the incomplete combustion in the drop tube furnace were analyzed and the results are given in Table 3.

Table 3.

For the three samples, the gaseous emissions rapidly decrease to 0 with the temperature.

The gaseous emissions for hydrolysis lignin are lower than that for spruce trunk and slightly higher than that for spruce bark.

TVOC proportions in the flue gas are very low but are in the same range than that found in the literature for lignocellulosic biomass. The increase of the temperature drastically decreases the formation of incomplete organic compounds in the flue gas, because the oxidation of these VOC becomes complete. During domestic combustion processes of biomass for heat production, methane is the lighter VOC emitted in the exhaust with proportion in the gas phase close to 60-80% (Shauer et al., 2001; [START_REF] Tissari | A novel field measurement method for determining fine particle and gas emission from residential wood combustion[END_REF]. The conversion of methane to carbon dioxide proceeds with slow rate and its total oxidation can be achieved at very high temperatures [START_REF] Yao | Evidence of two temperature regime in the slow oxidation of methane[END_REF][START_REF] Tabayashi | The early stages of pyrolysis and oxidation of Methane[END_REF]. The proportion of methane in the TVOC largely dominates when the temperature increases. For the three samples, only methane is detected at 1000 °C.

In complement to the gas measures indicated in Table 3, the CO2 and CO emissions were monitored, but they were in any case lower than the precision of the analyzer (less than 0.4%).

The gaseous emissions from the co-pyrolysis of saw dust and Shenfu coal in a drop tube furnace were measured in (Li et al., 2013) with lower amounts for saw dust than for coal.

As already discussed, PM and TVOC emissions depend on the temperature imposed in the isothermal zone of the drop tube furnace. As already discussed, soot were collected at 800 °C on ELPI collection stages for biomass combustion but not at 1200 °C. Such behaviors should be linked to the volatiles emitted from biomass during its drop and to the first step of the thermal degradation of the sample, i.e. the pyrolysis stage. The thermal degradation of hydrolysis lignin and spruce bark was then investigated through experiments carried out under pure N2 to analyze its pyrolysis in the drop tube furnace. Drop distances ranging from 7 to 55 cm were considered including the distance of 40 cm considered for the investigation of the combustion. Two temperatures were considered 800 °C and 1000 °C. Here both primary and secondary flows were pure nitrogen. The pulverized material was injected at 11.5 g h -1 , to produce more ash and volatiles. The char was collected in the ash collection step (see Fig. 1) after being quenched by a water-cooled sample probe. The reaction zone was defined by the position of the outlet of the injection probe and the inlet of the sample probe.

The collected char was analyzed using the ash tracer method, see [START_REF] Zellagui | Pyrolysis of coal and woody biomass under N2 and CO2 atmospheres using a drop tube furnace -experimental study and kinetic modeling[END_REF], to extract the fraction of volatiles emitted from the thermal degradations of hydrolysis lignin or spruce bark. The results are gathered in Fig. 3.

Figure 3.

Volatiles content ranges from 10.9 to 89.2%, depending on the drop distance and the temperature. The three components (hemicellulose, cellulose and lignin) of the lignocellulosic biomass undergo a transformation, liquefy between 200 and 400 °C and produce volatiles, gas and oil [START_REF] Nzihou | The catalytic effect of inherent and adsorbed metals on the fast/flash pyrolysis of biomass: A review[END_REF]. The maximal value for the volatile yield in the drop tube furnace (90.0% for hydrolysis lignin and 89.2% for spruce bark) is higher than that returned by the proximate analysis (69% for hydrolysis lignin and 73.0% for spruce bark). This trend was already observed in [START_REF] Zellagui | Pyrolysis of coal and woody biomass under N2 and CO2 atmospheres using a drop tube furnace -experimental study and kinetic modeling[END_REF] for woody biomass and coal. In [START_REF] Nzihou | The catalytic effect of inherent and adsorbed metals on the fast/flash pyrolysis of biomass: A review[END_REF], the authors reported that the yield of char produced by pyrolysis ranged from 5 to 31%, depending on the biomass components and heating rate. The solid fuel conversion increases in a significant way under fast pyrolysis conditions. The percentage of volatiles emitted increases with the drop height in an almost quadratic and concave way with respect to the temperature in the isothermal zone, see Fig. 3.

At temperatures of 800 °C and 1000 °C, the volatile yield reaches a maximum of 90% for hydrolysis lignin. Consequently the devolatilization process is almost complete at a distance drop equal to 40 cm. Such a behavior is not observed for the spruce bark as for the isothermal temperature equal to 800 °C and a drop distance of 40 cm, the volatile yield obtained being equal to 69.4% and much lower than that obtained at 1000 °C (89.2%). Consequently, the devolatilization process for spruce bark is not complete at 800 °C. Hence it is not surprising that unburnt hydrocarbons and soot are still produced and monitored as already observed in Fig. 3. The PM yield at 800 °C should be linked to the oil produced during the pyrolysis stage of the biomass. Oil is indeed quenched in the cooled collecting sample before being oxidized.

These complete or uncomplete devolatilization processes are also well correlated with the smaller amount of particulate matter emitted at 800 °C in the case of hydrolysis lignin (6.1×10 6 p.cm -3 ) than that of spruce bark (19.0×10 6 p.cm -3 ).

Particulate matter formation from vaporization and condensation of mineral elements

For temperatures higher than 900 °C, the mechanism of particulate matter formation is mainly due to the vaporization and the condensation of mineral elements. The mineral elements contained in the four samples and in some of their ash have been determined through a Roentgen fluorescence spectroscopy (XRF-1800). The results are gathered in Table 4.

Table 4.

The percentage of minerals is generally much higher in hydrolysis lignin than in the woody biomass (see Table 4), as a consequence of the above-described process leading to the production of hydrolysis lignin. The percentage of minerals is much higher in spruce bark than in spruce trunk, as minerals are mainly contained in barks [START_REF] Miranda | Chemical characterization of barks from Picea abies and Pinus sylvestris after fractioning into different particle sizes[END_REF]. Ash from spruce trunk contains less percentage of silica than that found in the literature because bark has been removed. For example, Rivzi et al. (2015) found 45% of silica in pine ash. The observed variations of the mineral composition of the samples could also be attributed to the different mineral composition of the soil where the tree grown.

Considering the ash chemical properties given in Table 4, the different biomass contain relatively large amounts of alkali metals. The condensation of these vapors in the cooling gas -in the collecting probe of the drop tube furnace -leads to the formation of fly ash. As already mentioned in [START_REF] Zellagui | Parametric study on the particulate matter emissions during solid fuel combustion in a drop tube furnace[END_REF], the presence of alkali metals in a woody biomass explains the high emissions of the finer particles PM0.1. This is consistent with the results obtained in the present study. The mass fractions of alkali metals (Na, Rb, K) are higher for spruce bark than for hydrolysis lignin and spruce trunk, leading to a higher level for PM1 emissions. Sulfur compounds (SO3) are higher for spruce bark and hydrolysis lignin than for spruce trunk and this is also consistent with the levels of emitted PM1. Vaporization of ash elements such as alkali vapor and sulfur compounds increases with temperature during combustion as shown in [START_REF] Dayton | Direct observation of alkali vapor release during biomass combustion and gasification. 1. Application of molecular beam/mass spectrometry to switchgrass combustion[END_REF]. The condensation of these vapors leads to the formation of fine particles when the gas is cooled down in the collecting sample probe. The number of particles emitted by spruce bark is much higher than that emitted by spruce trunk, except for 900 °C, and by hydrolysis lignin. This is well correlated with the amounts of minerals contained in the samples, as described in Table 4.

As already discussed in the previous section, the difference of the residence times of the particle in the drop tube furnace (0.5 s) and in an industrial boiler (2 s) has to be considered.

For particulate matter produced from minerals at high temperatures, [START_REF] Zellagui | Parametric study on the particulate matter emissions during solid fuel combustion in a drop tube furnace[END_REF] observed that no significant change occurred when the drop duration was increased from 0.5 s to 0.9 s with a woody biomass. Consequently, an increase of the residence time of hydrolysis lignin and spruce samples should not affect strongly the level of particulate emissions produced by minerals. But such an increase of the residence time should lower the particulate emissions at low temperatures due to incomplete combustion, as discussed in section 2.2.

Additionally, the mineral composition of ash is a point of interest during the combustion process and particularly during the cooling of the fume for heat recovery. To predict the biomass ash fusion behavior at the surface of heat exchangers of thermal facilities, some indexes based on ratios between elemental oxides and related to the chemical properties of ash were calculated. Fouling of heat exchanges have major consequences that mainly reduce the plant capacity up to 45%, favors the excess of fuel consumption, reduces service life and adds energy costs [START_REF] Kalivodová | Avifauna dubových porastov v povodí Stoličného potoka (Trnavská pahorkatina) mimohniezdnom období[END_REF]. According to [START_REF] Pronobis | Evaluation of the influence of biomass co-combustion on boiler furnace slagging by means of fusibility correlations[END_REF]Rivzi et al., 2015), Base to Acid Ratio (B/A), Slag viscosity index (Sr), Fouling index (Fu), Slagging index (Rs) and Alkali Index (AI) were calculated and given in the Table 5. The corresponding slagging or fouling tendencies have been marked as severe (S), medium (M), high (H) and low (L) when possible according to data available in the literature [START_REF] Pronobis | Evaluation of the influence of biomass co-combustion on boiler furnace slagging by means of fusibility correlations[END_REF].

Although the value of AI is quite low for hydrolysis lignin ash related to lower alkali content (K and Na), B/A, Rs, Sr and Fu tend to lean towards the high slagging and fouling tendencies compared to coal. It is interesting to note that although the predicted slagging and fouling potential depicted by these indexes are mostly based on values obtained from coals, they seem to be in good agreement with that of the biomass considered in the present study.

Finally, the level of gaseous and particulate pollutants which are emitted along the combustion of hydrolysis lignin are smaller than that obtained for spruce and for coal in similar experimental conditions.

Conclusion

The gaseous and particulate pollutants emitted during the combustion of hydrolysis lignin in a drop tube furnace were analyzed and compared to that emitted by spruce trunk and spruce bark. The volatile yields occurring during the pyrolysis of hydrolysis lignin was almost complete at 1000 °C and for a short drop distances. The number of emitted PM2.5 presented a V profile with respect to the temperature with a minimum reached at 900 °C. Considering the gaseous and PM emissions from the thermal degradation of hydrolysis lignin, one can conclude that the combustion of this by-product is cleaner than that of the two other conventional biomass.

Figure 2 .

 2 Figure 2.

  al., 2015; Nzihou and Stanmore, 2015; Zellagui et al., 2017).

Figure 1 .

 1 Figure 1. Schematic diagram of the experimental setup.

Figure 2 .

 2 Figure 2. Mean values of the amounts of collected PM2.5 for hydrolysis lignin (black

Figure 3 . 1 Figure

 31 Figure 3. The influence of the drop height on the production of volatiles for hydrolysis lignin

Figure 1 .

 1 Figure 1. Schematic diagram of the experimental setup.

Figure 2 .

 2 Figure 2. Mean values of the amounts of collected PM2.5 for hydrolysis lignin (black

Figure 3 .

 3 Figure 3. The influence of the drop height on the production of volatiles for hydrolysis lignin

Figure 1 . 3

 13 Figure 1.

Figure 2 . 4

 24 Figure 2.

Figure 3 .

 3 Figure 3.

1 TABLES Table 1 .

 TABLES1 Proximate analyses of the four samples.

		Volatile matter	Fixed carbon	Moisture	Ash
		wt%, daf	wt%, daf	wt%, ar	%, db
	Hydrolysis lignin	69.0	31.0	5.5	4.5
	Spruce bark	73.0	27.0	7.2	3.5
	Spruce trunk	81.0	18.9	5.3	0.4
	South-African coal	29.4	70.6	2.1	13.9
	daf = dry ash-free basis, ar = as received, db = dry basis

Table 2 .

 2 Ultimate analyses and Lower Heating Values (LHV) of the different samples.

	C	H	N	S		O	LHV
	(percentages on dry ash free components)			MJ. kg -1
	Hydrolysis lignin	59.5	6.6	0.2	0.0	33.7	18.6
	Spruce bark	57.1	8.4	1.0	0.0	33.5	16.4
	Spruce trunk	52.0	7.6	0.3	0.0	40.1	15.7
	South-African coal	83.2	4.7	2.1	0.7	9.3	26.4

Table 3 .

 3 Gaseous emissions from the three woody samples at different temperatures in the isothermal zone (NMVOC= Non Methanic Volatile Organic Compounds, TVOC=Total Volatile Organic Compounds).

		Temperature (°C)	NMVOC	CH4 (ppm)	TVOC (ppm)
			(ppm)
	Hydrolysis lignin	800	9.0	4.9	14.0
		900	0.5	0.9	1.5
		1000	0.0	0.7	0.7
	Spruce bark	800	21.8	6.6	28.4
		900	1.2	0.9	2.1
		1000	0.0	0.5	0.5
	Spruce trunk	800	18.3	6.2	24.5
		900	0.9	0.9	1.8
		1000	0.0	0.6	0.6

Table 4 .

 4 Mineral elements present in the raw materials (percentages on dry components) and in some ash and calculated indices.

	Mineral elements	Hydrolysis lignin	Hydrolysis lignin ash	Spruce trunk	Spruce bark	Spruce Trunk ash	Coal ash
	iron (Fe2O3)	0.191	5.842 0.048	0.032	2.233	4.78
	silicon (SiO2)	1.498	43.089 0.082	0.552	4.589	47.3
	calcium (CaO)	0.82	22.282 0.422	6.343	49.674	5.67
	potassium (K2O)	0.078	2.227 0.161	0.651	11.194	0.75
	copper (CuO)	0.024	0.315 0.137	0.01	0.045	ND
	sulfur (SO3)	0.748	11.289 0.295	0.642	5.743	2.95
	phosphorus (P2O5)	0.043	1.799	0.02	0.221	1.207	2.32
	aluminum (Al2O3)	0.339	7.535 0.017	0.104	0.959	31.6
	chlorine (Cl)	0.001	0.004	ND	0.026	0.419	ND
	lead (PbO)	ND	0.004	ND	ND	0.106	0.02
	nickel (NiO)	0.011	0.019 0.233	0.008	0.01	ND
	sodium (Na2O)	0.897	1.094 0.802	1.184	0.909	0.27
	barium (BaO)	ND	0.272	ND	ND	0.521	0.25
	zirconium (ZrO2)	ND	0.03	ND	ND	0.039	0.07
	strontium (SrO)	0.004	0.06 0.001	0.019	0.231	0.24
	rubidium (Rb2O)	ND	0.008	ND	ND	0.033	ND
	zinc (ZnO)	0.002	0.03 0.007	0.055	0.901	ND
	cobalt (Co2O3)	ND	ND	ND	ND	ND	ND
	manganese (MnO)	0.004	0.097 0.035	0.208	4.633	0.16
	chrome (Cr2O3)	0.009	0.582 0.004	0.007	0.037	0.09
	titan (TiO2)	0.02	0.988	ND	0.001	0.224	1.87
	magnesium (MgO)	0.084	2.419 0.052	0.369	5.836	1.64
	tin (SnO2)	0.02	ND 0.004	0.01	ND	ND
	The ND abbreviation denotes quantities below the detection threshold.

Table 5 .

 5 Calculated indices.

	Indices	Hydrolysis lignin ash	Spruce Trunk ash	Coal ash
	Base to Acid Ratio (B/A)	0.65 (H)	10	0.16 (L)
	Slag viscosity index (Sr)	58 (H)	7	80 (L)
	Fouling index (Fu)	2.2 (H)	146	0.16 (L)
	Slagging index (Rs)	2.9 (S)	23	0.19 (L)
	Alkali Index (AI)	0.18 (L)	0.77	0.04 (L)
	S=severe, M=medium, H=high and L=low

Acknowledgements

We thank M. C. Bailly for the experiments he performed during his training period at LGRE.

Appendix A. Supplementary data

Supplementary data to this article


Elizabeth Thomas

Robert French

Guy Alizee

Jennifer T Coull

HAVING YOUR CAKE AND EATING IT: FASTER RESPONSES WITH REDUCED MUSCULAR ACTIVATION WHILE LEARNING A TEMPORAL INTERVAL

We examined how motor responses to a stimulus evolve as individuals learn to predict when a stimulus will appear, by comparing responses to a regular versus irregular stimulus train. The study was conducted with two groups of adults -one responded to the regular appearance of a visual stimulus every 3s (R group) and the second responded to the irregular presentation of the same stimulus (IR group) at intervals varying between 2 to 4s. Participants responded to the appearance of the stimulus by bending over to press a button that was slightly out of reach. This whole body reach requires muscular activation at the ankles. Over the course of 50 consecutive responses, the response times in the R group were found to decrease more than those for participants in the IR group. The electromyographic (EMGs) of two ankle antagonist muscles, the anterior tibialis and soleus were also modified as participants progressively learnt the temporal regularity of a sequence. Tibialis onset times for the R group were found to decrease faster. A less predictable observation was the faster reduction in post stimulus activation of the tibialis muscle for the R group. Soleus muscle deactivation is an indicator movement preparation. EMG integrals for this muscle a little before stimulus onset showed a trend for greater decrease in the R group. In summary, our study shows that temporal expectations over repeated stimulus presentation permits the dynamic optimization of motor activity with progressively faster response times, muscle activation onset times and lower muscle activation amplitudes.

INTRODUCTION

In this study, we ask how the temporal organization of a stimulus train can alter responses to the stimuli. Such a question is pertinent to real life situations such as work on a factory assembly line, which might involve repetitive motor acts in response to a train of successive stimuli. This situation is in contrast to responses that would take place for a single event such as the arrival of a bus or the boiling of a kettle. The aim of this study is to look into how motor responses and muscular activation evolve over the course of repeated stimulus presentation. In particular how are the responses dynamically altered as a function of the temporal regularity of stimulus presentation?

One good reason to suspect that response dynamics would vary as a function of temporal regularity in a stimulus is a previous study in which we demonstrated that faster response times to previously unseen intervals were obtained in groups that had undergone training using temporally regular stimulus trains (Fautrelle et al, 2015). This improvement however was not obtained with groups that had instead been exposed to a temporally irregular stimulus train. The latter result especially shows that the speeding in response times was not due to neuromuscular facilitation (Fautrelle et al, 2015) and that instead, temporal stimulus regularity had led to implicit improvements in timing.

The influence of temporal stimulus properties on motor responses has also been demonstrated in a plethora of studies showing that the length of the delay between two stimuli influence response times to the second stimulus. In these studies a warning cue alerts participants to an upcoming stimulus to which they are expected to respond. The delay between this warning signal and the target stimulus is called the foreperiod. The manner in which the response time varies as a function of the foreperiod is used to study the effects of temporal expectation. In general, conditions which increase temporal expectancy reduce response times [START_REF] Woodrow | The measurement of attention. Chapter II: The effect upon reaction time of variation in the preparatory interval[END_REF][START_REF] Niemi | Foreperiod and simple reaction time[END_REF]. Some of the foreperiod studies have taken the analysis of responses a step further -to non-temporal features of the response movement such as force or muscular activation. Several investigators have reported the use of reduced force for responses occuring after foreperiod delays that permit better temporal prediction (Jaskowski and Verleger, 1993;Mattes and Ulrich, 1997;[START_REF] Van Der Lubbe | Being prepared on time: on the importance of the previous foreperiod to current preparation, as reflected in speed, force and preparation-related brain potentials[END_REF]. Delving even deeper, into the muscular level, two foreperiod studies report that the interval between EMG onset and the visible mechanical response was shorter with better temporal expectation [START_REF] Hasbroucq | Finger pairings in choice reaction time tasks: does the between-hands advantage reflect response preparation?[END_REF][START_REF] Tandonnet | The influence of time preparation on motor processes assessed by surface Laplacian estimates[END_REF].

The studies cited above show that response times, response force and muscular activation can be altered by temporal expectation. Indeed several of the neural structures important in interval timing are also very important in motor activity; especially, the basal ganglia and the supplementary motor cortex (Artieda et al, 1992;[START_REF] Meck | Neuropsychology of timing and time perception[END_REF][START_REF] Coull | Neuroanatomical and neurochemical substrates of timing[END_REF]. The aforementioned reaction-time studies however did not investigate the dynamics of learning and more importantly, they were done in the context of discrete stimulus presentation following a warning signal. It is not a foregone conclusion that results observed in the discrete reaction time paradigm would also hold for responses to a stimulus train. This is especially true as some researchers have shown that the neural circuits strongly implicated in discrete duration judgments are different from those in which temporal judgments are formed from a train of temporally regular stimuli [START_REF] Grube | Dissociation of duration-based and beat-based auditory timing in cerebellar degeneration[END_REF][START_REF] Teki | Distinct Neural Substrates of Durationbased and beat-based auditory timing[END_REF]. There is a long history of research on how perception changes as a function of temporal regularity of a stimulus train. For example, it has been shown that target discrimination in the visual [START_REF] Newhall | Effects of attention on the intensity of cutaneous pressure and on visual brightness[END_REF][START_REF] Matthewson | Rescuing stimuli from invisibility: Introducing a momentary lapse from visual masking with pre-target entrainment[END_REF][START_REF] Rohenkohl | Temporal expectation improves the quality of sensory information[END_REF] or auditory [START_REF] Jones | Time, our lost dimension: Towards a new theory of perception, attention and memory[END_REF][START_REF] Jones | Dynamic attending and response to time[END_REF] modality is best when targets appear in phase with a temporally regular stimulus train. Likewise, response times are faster when targets appear at temporally expected moments within a rhythmic or isochronous sequence [START_REF] Martin | Chronometric evidence for entrained attention[END_REF][START_REF] Bolger | Rhythm implicitly affects temporal orienting of attention across modalities[END_REF]. In this study, we ask how the temporal regularity of a stimulus sequence would affect not only speed but also muscular activation.

Our investigation on how the nature of a response would change over the course of continuous stimulus presentation was conducted using a type of motor activity called whole body pointing. This consists of leaning over with the trunk to touch or pick up a target which is slightly out of reach. We chose this movement for analysis because it provided two convenient targets for a study investigating temporal anticipation. Flexion at the ankle is an important component when reaching to a target which is slightly out of reach. Both the tibialis anterior and the soleus muscle which are the agonist and antagonist muscles at the ankle joint display changes prior to visible movement onset [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of whole-body pointing movements[END_REF][START_REF] Tolambiya | Modulation of anticipatory activity for multiple conditions of a whole-body pointing task[END_REF]. Furthermore, the soleus displays a pre-movement deactivation which precedes premovement activation by the tibialis, thereby providing an opportunity for improving upon previous temporal anticipation studies which focused only on the movement agonist [START_REF] Hasbroucq | Finger pairings in choice reaction time tasks: does the between-hands advantage reflect response preparation?[END_REF][START_REF] Hasbroucq | Preparatory inhibition of corticospinal excitability: a transcranial magnetic stimulation study in man[END_REF][START_REF] Tandonnet | The influence of time preparation on motor processes assessed by surface Laplacian estimates[END_REF]. The investigation of an agonistantagonist pair also provides us with the opportunity for looking into a distributed algorithm of motor learning. A final and non-trivial advantage of using this multijoint movement is that it has been very well studied [START_REF] Pozzo | Coordination between equilibrium and hand trajectories during whole-body pointing movements[END_REF][START_REF] Berret | Modular control of pointing beyond arm's length[END_REF][START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of whole-body pointing movements[END_REF][START_REF] Tolambiya | An ensemble analysis of electromyographic activity during whole body pointing with the use of support vector machines[END_REF], 2012;[START_REF] Casteran | Alterations with Movement Duration in the Kinematics of a Whole Body Pointing Movement[END_REF] and would hence provide points of comparison when attempting to understand the effects of temporal expectation.

The soleus and tibialis are two leg muscles which are important for forward propulsion of the body. The hypothesis of the study is that the response times and activation of these muscles, as participants respond to the appearance of a long stimulus train, will evolve differently based on whether the stimuli are presented in a temporally regular or irregular manner. In keeping with several readiness models that have been proposed in foreperiod studies (Näätänen, 1971;[START_REF] Niemi | Foreperiod and simple reaction time[END_REF]Näätänen, 1982, Mattes et al, 1997) we expect that the irregular condition will lead to slower activation times and larger activation amplitudes for the muscles.

METHOD

Thirty healthy participants (16 males and 14 females; mean age =26.9±1.5 years) volunteered for the experiment. There were 7 males and 8 females in the R group and 9 males and 6 females in the IR group. This distribution is not statically different (χ 2 =0.67, p>0.05). They had normal or corrected-to-normal vision and none had a previous history of neuromuscular or neurological disorders. All the participants were right handed. The experiment conformed to the declaration of Helsinki and informed consent was obtained from all participants according to the protocol of the local ethical committee.

General

The study was conducted by creating two groups of participants. The Regular (R) group was exposed to a temporally regular sequence of 50 consecutive dots while the Irregular (IR) group saw the same number of stimuli presented in a temporally irregular manner. Upon stimulus appearance, the participants responded by leaning over and pressing a button on a table in front of them. They were instructed to respond as soon as they saw the dot. For each participant, there was a sequence of 50 presentations of a stimulus which consisted of a dot on a screen in front of them. For each response, we recorded response times and EMG activity from the soleus and tibialis anterior muscles of the right leg. To encourage participants to maintain attention during the task and to minimize the use of counting strategies, the participants also carried out a secondary task. This consisted of counting a small proportion of the 50 dots that were green rather than white

Stimulus response protocol

All participants stood at a line marked on the floor 1.5m from the stimulus presentation screen. In order to respond to the appearance of the stimulus on the screen, the participants had to lean over and press a button, which was placed on a table 70cm from the line, while keeping their feet on the line. Stimulus response therefore required that participants involve the trunk in bending over (figure 1).

All participants went through a short familiarization phase in which the experimental protocol was explained to them and they practiced leaning over in response to seven presentations of the white dot. The familiarization phase was followed by the recorded experiment. Each recording session began with a warning cue, comprised of a small red dot, 0.5cm in diameter, presented for a duration of 0.5s on a black background. This was then followed by 50 consecutive presentations of a larger dot, 4cm in diameter, presented for a duration of 0.5s. on a black background. This dot was white on 90% of trials and green on 10% of trials. Participants were told at the start of the trial that they had to count the number of green dots.

Crucially, intervals between dots were fixed at 3s in the R group but varied randomly between 2-4 s in the IR group. The sum total of all interval durations was the same for both groups.

Equipment used

The visual stimuli were projected onto a translucent 2x2 meter screen by a CRT video projector. The spatial resolution of the visual display system was 1024x768 pixels with a vertical refresh sampling rate of 60 Hertz. Subjects responded by leaning over and pressing on a response button.

Electromyographic activity of the tibialis anterior and soleus muscles was measured with pairs of pre-gelled Ag/AgCl surface electrodes (recording diameter 10mm) placed over the muscle belly. The reference electrode was attached on the contralateral patella. EMG activity was recorded with a Biopac MP150 system at a sampling rate of 1000 Hz, bandpass filtered (10Hz to 500Hz) and stored for analysis with commercially available software (AcqKnowledge 4. For MP systems, Biopac System, Santa Barbara, CA). Synchronization of EMG signals with the timing of the visual stimuli and response button presses was also managed by the Biopac MP150 system.

Data analysis

Data analysis was conducted with custom-made programs written in Matlab.

Response time: This was defined as the duration between the onset of the visual stimulus and the moment at which participants pressed the response button (figure 2). Tibialis onset times: EMG-burst onsets were determined by first creating the cumulative distribution of the rectified, slightly (50-point) smoothed raw EMG signal (cdf(EMG)). This process helped to highlight big, rapid changes in the EMG time series. We then determined the points at which the slope of this cumulative distribution changed most rapidly from a near-zero value to a maximum value (i.e. the points at which the second derivative of cdf(EMG) is maximized). The location of each of these peaks constituted an EMG-burst onset value. We used the findpeaks function in Matlab® to find the location of all of these peaks, thereby identifying all EMG-bursts for each participant. Note that the technique relies on the fact that the differences between the EMG from baseline to abrupt burst are bigger than anywhere else. The validity of this algorithm was confirmed by a visual inspection of onset points. This technique is similar to other derivative based techniques which rely on significant abrupt changes in the time series for onset detection (Bello et al, 2005;Majumdar and Vardhar, 2011).

Muscle activation: All EMG activity was first filtered between 20 and 400 Hz, full wave rectified and then smoothed using an average moving window of 50ms [START_REF] Konrad | The abc of EMG[END_REF].

Muscle activation in all cases, was computed by using the EMG integral in a pre-defined window. In the case of the tibialis, this comprised a 200-800ms window just after stimulus onset. The window was set by using visual inspection for all participants and all trials to identify the interval over which post stimulus tibialis activation took place. For the soleus, EMG integrals were computed in a 500ms window just before stimulus onset. This window was chosen according to previous reports of intervals over which anticipatory activity prior to voluntary movement took place [START_REF] Cheron | Evidence of a preprogrammed deactivation of the hamstring muscles for triggering rapid changes of posture in humans[END_REF][START_REF] Leonard | Reaching to multiple targets when standing : The spatial organization of feedforward postural adjustments[END_REF][START_REF] Kaminski | The effects of stance configuration and target distance on reaching. I Movement preparation[END_REF][START_REF] Tolambiya | Modulation of anticipatory activity for multiple conditions of a whole-body pointing task[END_REF] as well as allowing for underestimation of interval duration This does not imply that there were responses before stimulus onset (there were none observed).

Preparatory EMG activity before movement onset however, can occur without visible movement [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of whole-body pointing movements[END_REF][START_REF] Tolambiya | Modulation of anticipatory activity for multiple conditions of a whole-body pointing task[END_REF].

Statistics: Progression of any variable over 50 stimulus presentations was done by constructing the regression lines of the variable against stimulus number. The slope of the regression line was used to quantify this evolution. The lines were constructed using Excel.

Comparisons of the resulting slopes for the R versus IR groups were conducted with independent t tests. The test was applied after ensuring a normal distribution and homogeneity of variance of the data. Normal distribution was checked using the Kolgomorov-Smirnov and Lillefors test. Homogeneity of variance was ensured using the Brown-Forsythe test. Results were considered statistically significant if p<0.05. All results are reported as mean ± standard error of the mean (SEM). Effect size was computed using the Cohen d formula.

RESULTS

Below we report the differences in the responses of subjects in the R and IR groups.

No mistakes were made in the counts of green dots amongst the presented white dots hence ensuring a maintained attention throughout the experiment for participants in both groups.

Figure 2 presents a sample recording of the stimulus appearance, participant response and the EMGs of the tibialis and soleus muscles. Below, we will analyze the manner in which these recordings changed over the course of 50 presentations for the R and IR group.

Response times

For each individual participant, reaction times (RT) were plotted for each of the 50 consecutive stimulus presentations and the value of the fitted linear regression slope characterized how RT evolved over the course of the presentations. This evolution is presented in Figure 3. Figure 3A presents the progression for two individuals in each group and in 3B we see the averages for each group. The negative slope value in Figure 3A indicates progressively faster RTs over time, while the positive slopes indicate progressively slower RTs. The slopes of the regression lines were compared between groups and were significantly more negative for the R group than the IR group (t 28 =-2.86, p=0.008, d=1.04). The mean slope value was negative at -3.01 ± 0.92 ms/presentation for the R group but positive at 0.24 ± 0.15 ms/presentation for the IR group.

Tibialis activation onset times

As for reaction times, tibialis EMG onset times were plotted across the 50 consecutive presentations for each participant. Once again, regression lines were used to characterize how onset times evolved over the experimental session. The mean slope for the R group was more negative (-3.03 ± 0.76 ms/presentation) than that for the IR group (-0.69 ± 0.57 ms/presentation) hence indicating a faster evolution towards a speed up in the onset times of the tibialis for the R group. The difference between the two means was found to be significant (t 27 =-2.86, p=0.02, d=2.75)

Tibialis activation amplitude

The way in which integrated EMG (EMG i) values of tibialis muscle activation evolved over the experimental session was measured with regression lines. EMG i values decreased over the course of 50 responses for many individuals of both groups. However, this progressive decrease (quantified by the comparison of regression line slopes) was significantly greater (t 28 =-2.33, p=0.027, d=0.83) in the R group (-0.004±0.001 mV-ms) than the IR group (-0.00013±0.001 mV-ms). Figure 4A presents the evolution with repetitive stimulus presentation for two subjects belonging to the R and IR groups. Figure 4B presents the average for each group.

Soleus activation amplitude

As was done for the tibialis muscle, we compared the evolution of soleus muscle activation EMGi values over consecutive trials for R versus IR groups. Integrals of EMG activity for this muscle were done in a 500ms window before stimulus onset. This was the window of interest as the soleus muscle is known as one that shows deactivating activities before visible movement onset. Greater preparation for stimulus onset would potentially lead to progressively greater deactivation of the muscle before stimulus onset. Once again, many participants from both groups displayed a progressive decrease in pre-stimulus activation, which was quantified by the slope of the regression line. The mean slope for the R group (-0.0033 ± 0.0015 mV-ms/presentation) was more negative than for the IR group (-0.000011 ± 0.00087 mV-ms/presentation). This difference was not statistically significant (t 28 =-1.88, p=0.069, d=0.67), but showed a tendancy for it.

DISCUSSION

The hypothesis of our study was that the dynamics of motor response to a regular stimulus train would not be the same as for an irregular stimulus train. This conjecture was investigated by analyzing how response times and muscular activations evolved with repeated stimulus presentations. Indeed we found that response movements evolved progressively and became more optimized with temporally regular (R), as compared to irregular (IR), stimuli.

Our first observation was that responses became faster more rapidly for the group exposed to temporally regular stimuli. The progression towards lower reaction times was not smooth but, ultimately, led to overall improvements. This was quantified by comparing the slopes of regression lines for response times of each individual over the repeated stimulus presentations of the experimental session (Figures 3A,B). The mean slope for the R group was more negative than for the IR group, indicating that temporal expectancy led to improvements above and beyond those that might be gained through simple motor repetition.

Indeed, for the IR group, there were in many cases, even an increase in response time over the session, as shown by a mean positive slope for the group.

The tibialis muscle is a key muscle, important for flexion towards the response button (Figure 1). As we had observed a decrease in reaction times for the R group, we would also expect to see faster onset activities in the muscles producing the response movements. As predicted, onset delay for the activation of this muscle (EMG onset delay) also decreased as response times decreased. The comparison of regression slopes between the R and IR groups showed that the decrease in tibialis onset was faster and greater in the R group, when temporal expectation was possible. This delay between stimulus onset and EMG onset has been referred to in previous studies as the 'premotor time' during which processes preceding motor execution take place. This is in contrast to the 'motor time' which follows and is thought to reflect peripheral motor execution. A previous study by Hasbroucq [START_REF] Hasbroucq | Finger pairings in choice reaction time tasks: does the between-hands advantage reflect response preparation?[END_REF] had reported that temporal predictability altered 'motor time' but did not change 'premotor time'. The previous investigation had been conducted using a discrete stimulus reaction time protocol. In contrast, as we had observed changes in the tibialis onset times with temporal predictability in the current study, our results demonstrate that 'premotor time' can also be manipulated by temporal predictability when used in a stimulus train protocol. Some of the reduction in response times with our stimulus train protocol may therefore have their origins in earlier processes, in keeping with conclusions drawn by [START_REF] Muller-Gethmann | Locus of the effect of temporal preparation: Evidence from the lateralized readiness potential[END_REF]. It should be pointed out again that both of these previous studies were conducted using the discrete stimulus reaction time paradigm.

While the progressive shift to earlier tibialis onset times with increasing temporal predictability was not unexpected, the progression towards lower tibialis activation (tibialis EMG i ) was less obvious. One would expect that faster movements are accomplished through the application of greater effort. Indeed classic motor control studies have shown that higher torques and EMG amplitudes accompany faster movements [START_REF] Hollerbach | Dynamic interaction between limb segments during planar arm movements[END_REF][START_REF] Corcos | Organizing principles for simple joint movements II A speed-sensitive strategy[END_REF][START_REF] Gottlieb | Strategies for the control of voluntary movements with one mechanical degree of freedom[END_REF]. The progression towards lower tibialis activation with consecutive muscle activation was faster in the case of the R group (Figure 4). In other words temporal predictability allowed for motor learning and better performance optimization. These results are consistent with previous observations that have also shown that the manipulation of the temporal organization of stimulus preparation can alter response force (Mattes and Ulrich, 1997;[START_REF] Van Der Lubbe | Being prepared on time: on the importance of the previous foreperiod to current preparation, as reflected in speed, force and preparation-related brain potentials[END_REF] and the nature of EMG response bursts [START_REF] Tandonnet | The influence of time preparation on motor processes assessed by surface Laplacian estimates[END_REF]. These previous studies however were conducted with discrete stimuli presented after a warned foreperiod. The focus of these previous studies was on the effect of foreperiod delays and a direct investigation of the dynamics of learning through a response-by-response analysis was missing.

The results with the antagonist soleus muscle were similar but not as striking. As the first muscle which is altered in the preparation to move, it was an interesting muscle to study in light of our interest in temporal anticipation. Previous investigations have shown that the preparation for movement can be predicted by the deactivation of this muscle [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of whole-body pointing movements[END_REF][START_REF] Tolambiya | Modulation of anticipatory activity for multiple conditions of a whole-body pointing task[END_REF]. Indeed, the integration of pre-stimulus EMGs for this muscle showed a tendency for faster reduction in the R group than the IR group, indicating a tendency for greater anticipation and preparation for movement in the case of the former group. Several researchers have reported the presence of inhibition in the agonist muscle in cases of temporal preparation [START_REF] Hasbroucq | Preparatory inhibition of corticospinal excitability: a transcranial magnetic stimulation study in man[END_REF][START_REF] Touge | Reduced excitability of the cortico-spinal system during the warning period of a reaction time task[END_REF]. This inhibition is difficult to explain in the light of improved motor performance and has been interpreted as serving to increase the sensitivity of motor structures for forthcoming movement or for preventing untimely movement. The current study shows that this inhibition may not only be restricted to the agonist but also to the antagonist. It is easier to provide an explanation for why temporal expectancy would create inhibition in the extensor soleus muscle. Deactivation in this muscle is necessary to permit forward flexion or bending forward for pressing the response button. Progressive decrements in pre-stimulus activity of this muscle would seem to indicate better preparation for movement in conditions that allow temporal expectancy.

While discussing the details of muscular activations and delays, it is easy to overlook an original aspect of this study. As opposed to previous studies on timing which take into account activities of the end effector (the hand) our investigation has positioned itself at the other end of the body -the tibialis and soleus muscles of the legs. These muscles have traditionally been viewed as having postural roles with their primary function being that of keeping the body in equilibrium under the control of lower brain structures transmitting motor commands via the ventromedial pathway. Hand function on the other hand is thought to be under the control of the motor cortex (Bear et al, 2001;Kandel, 2000). Very few studies have specifically investigated how the postural muscles are modified as a result of the temporal organization of stimuli. Our study shows that temporal expectation may have a distributed effect on the body. While the actual response took place through a hand button press, the reduction in muscular activation with increasing temporal expectation also took place at the ankles. Faster reaction times when standing may therefore be achieved through the combined mechanism of better anticipatory deactivation in the antagonist soleus muscle and faster activation in the agonist tibialis muscle.

In the next two paragraphs, we will present and discuss two models that have been presented to account for response modification as a result of temporal preparation. Both the variable-increment extension of Näätänen's readiness model (Mattes et al, 1997) and the Internal Reference Model [START_REF] Dyjas | Trial-by-trial updating of an internal reference in discrimination tasks: Evidence from effects of stimulus order and trial sequence[END_REF] were developed in the context of discrete stimulus presentation studies. Nevertheless they are interesting to study in the context of temporal readiness and we will consider how they might be modified for the current study on evolving dynamics with a stimulus train. Mattes et al (1997) proposed a model to explain how reaction force is modified as a function of temporal expectancy. These researchers extended Näätänen's readiness model (Näätänen, 1971) which was used to account for how reaction time is reduced with higher temporal expectancy. Both models consider reactions in response to a stimulus to be shaped by the distance between motor readiness levels and motor action limit. A greater level of temporal expectation and hence readiness would decrease the distance to the motor action limit and hence decrease response times. Mattes et al (1997) extended the model to provide an explanation for the fluctuations in response forces. According to these researchers, in cases of high motor readiness when a stimulus is expected, only a small force is applied, as the distance between motor readiness levels and motor action limits is also small. On the contrary, when this distance is large, a larger overshooting force is applied, hence providing a possible explanation for the larger forces applied in cases of temporally unpredictable stimuli. We propose another possible explanation for the increase of reaction force in our study using stimulus trains. We suggest that in the face of temporal unpredictability, neuromodulatory influences caused by 'stress' lead to a high level of muscular vigilance and preparation. In these conditions, cortical commands result in a higher muscular activation and contractions. Slower muscular activation times with temporal unpredictability in such a model could perhaps be explained by delayed stimulus perception. This baseline modulation mechanism can only be verified by further studies in which we monitor the evolution of muscle baseline activity levels as temporal uncertainty increases.

Delays in visual perception would have to be studied using an electroencephalogram (EEG).

Another useful model to recall at this point is the Internal Reference Model (IRM) [START_REF] Dyjas | Trial-by-trial updating of an internal reference in discrimination tasks: Evidence from effects of stimulus order and trial sequence[END_REF]. The model proposes that internal representations of time are continuously updated based on the previously seen interval. More accurately the current estimate is a weighted sum of the first and last seen interval. Our research suggests that this model can be extended in conditions of stimulus train presentation. As opposed to a fixed weight for the previously seen interval, the negative slopes of reaction times and tibialis activation onset of the current study, would suggest that the weight attributed to the last seen interval can in fact increase in time.

In the following sections, we will bring up some shortcomings in this investigation and propose some future studies that should be conducted to address them as well as provide a better understanding of the mechanisms underlying the motor control of temporal readiness.

As stated in the Results section, the differences in the activation of the soleus muscle for the R and IR groups showed a tendency for difference but did not attain the levels necessary for significance. In future studies, we will re-inspect this aspect of temporal anticipation with a protocol which should reduce response variance. Our study placed the target at the same distance for all participants irrespective of their height. This would have induced different levels of effort and anticipative delays (eg short participants may require earlier anticipation and greater effort than taller ones, for a target at the same distance). In future studies, we will place the response button at distances which vary according to participant height [START_REF] Berret | Modular control of pointing beyond arm's length[END_REF][START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of whole-body pointing movements[END_REF][START_REF] Casteran | Alterations with Movement Duration in the Kinematics of a Whole Body Pointing Movement[END_REF].

A future question to be asked with these neuromuscular modifications is -Where along the chain of neural commands do they take place? Many previous studies have shown that they begin in the motor cortex and hence early in the corticospinal circuit. The studies that established this used transcranial magnetic stimulation (TMS) and event related potentials (ERP). A good review of the conflicting results in this domain and the studies which have been conducted in attempts to resolve them can be found in [START_REF] Burle | Excitatory and inhibitory motor mechanisms of temporal preparation[END_REF]. Once again, they were all performed using the discrete stimulus warned reaction time protocol. A complete understanding of how response amplitudes are dynamically altered during learning as demonstrated in the current study will require that we also probe how the commands at the cortical level are altered using TMS and ERPs. As the latter technique may be more sensitive to the movement of the head that comes from whole body pointing, we may have to switch to responses which consist of a simple button press.

Finally, stimulus responses in this investigation were made using whole body pointing movements towards a target. As a movement that involves several joints and muscles, it provides us with the opportunity to gain insight into a key aspect of neuronal processing which is its parallel nature. It cannot be ruled out that movement optimization was obtained through a more even distribution of force generation and that a lower amplitude of muscle activation in the tibialis muscle was accompanied by greater trunk involvement for foreword movement. In other words, it is possible that the progressive decrease seen in the tibialis muscle may have been accompanied by a parallel increase in muscles like the erector spinae which would give the trunk a greater role in stimulus response. In future studies, we should place EMG electrodes on the trunk muscles in order to analyze the evolution of activation in these muscles with temporally regular or irregular stimulus sequences. Another interesting question to ask with a multijoint movement would be -how does coordination or synergy organization change in the face of temporal expectation? A multijoint movement can be performed in an infinite number of ways and the nervous system organizes synergies or correlated body segment displacements for movement [START_REF] Berret | Modular control of pointing beyond arm's length[END_REF]. How are these synergies altered when moving to a regular or irregular stimulus train?

In conclusion this investigation has shown that response times and muscular activation are more likely to decrease when responding to a train of temporally regular than irregular stimulus presentations. While previous research has shown that response forces are modified by temporal expectancy, it was primarily demonstrated using reaction time tasks with discrete stimulus presentations rather than with continuous stimulus trains. Our study with its concentration on the motor modality therefore shows along with previous studies on perception that temporal expectancy when processing information in stimulus trains can optimize the activities of the nervous system. Another original contribution of the study is the demonstration that stimulus temporal organization can alter the response characteristics of postural muscles like the tibialis and soleus muscle hence indicating that motor temporal expectation is distributed.

FIGURE CAPTIONS

Figure 1 :

 1 Figure 1: Subject response to stimulus. Participants bent over to press a button in response

Figure 2 :

 2 Figure 2: A Copy of recordings taken during experiments. The recordings were done

Figure 3 :

 3 Figure 3: Reaction times. This figure presents the reaction times (RT) of subjects in response

Figure 4 :

 4 Figure 4: Tibialis EMG i values. Progresson of tibialis EMG i values with trial. A) Figures

FIGURE CAPTIONS Figure 1 :

 CAPTIONS1 FIGURE CAPTIONS

Figure 2 :

 2 Figure 2: A Copy of recordings taken during experiments. The recordings were done

Figure 3 :

 3 Figure 3: Reaction times. This figure presents the reaction times (RT) of subjects in response

Figure 4 :

 4 Figure 4: Tibialis EMG i values. Progresson of tibialis EMG i values with trial. A) Figures

Acknowledgements

We thank Lilian Fautrelle, Yves Ballay and Cyril Sirandre for help with initial setup of the experiments.


 Jiao

Yann Klinger
email: klinger@ipgp.fr

L Scholtès

 Shear fractures, including earthquake ruptures, are spatially segmented following a pattern inherited from early fracture development  Numerical simulations show both upward and downward ack propagation when a cr brittle layer is subjected to strike slip faulting  Fault segmentation is spatially organized to maintain the material in a stable compressive state of stress through localized tensile ruptures.

Introduction

When brittle materials are sheared beyond their elastic threshold, stress is released through fractures [START_REF] Conner | Shear bands and cracking of metallic glass plates in bending[END_REF][START_REF] Taheri | Integrated approach for the prediction of crack width and spacing in flexural FRC members with hybrid reinforcement[END_REF]. In the case of the crust of the Earth it et al. et al. 19448007, 2021, This article is protected by copyright. All rights reserved.

may corresponds to earthquake ruptures that produce finite deformation. In the case of continental deformation, when the maximum compressional stress is horizontal, deformation tends to localize along strike-slip faults such as the San Andreas Fault. During medium to large            brittle crust, which thickness is 15±5km in continents [START_REF] Klinger | Relation between continental strike-slip earthquake segmentation and thickness of the crust[END_REF][START_REF] Scholz | The Mechanics of Earthquakes and Faulting[END_REF], and break the ground surface . Field studi [START_REF] Wechsler | Evolving geometrical heterogeneities of fault trace data[END_REF], space geodesy [START_REF] Wei | Surficial simplicity of the 2010 El Mayor-Cucapah earthquake of Baja California in Mexico[END_REF], and es et al. et al.

seismology [START_REF] Bilham | Sawtooth segmentation and deformation processes on the southern San Andreas fault, California[END_REF] have long brought evidence that strike-slip earthquake ruptures produce spatially segmented fracture patterns on the ground surface (Fig. 1a), with segment length scaling with the thickness of the brittle crust [START_REF] Klinger | Relation between continental strike-slip earthquake segmentation and thickness of the crust[END_REF]. These segments are usually bounded by relay zones or bends. Analogue experiments have also hinted at the correlation between the spatial distribution of fractures and the thickness of sheared brittle materials [START_REF] Cambonie | Similarities between mode III crack growth patterns and strikeslip faults[END_REF][START_REF] Lefevre | Experimental evidence for crustal control over seismic fault segmentation[END_REF].

et al. et al.
Here, we use numerical experiments to test further this correlation, explore the kinematics of fracture growth leading to this peculiar spatial pattern, and derive a universal physical process that explains the relationship between the brittle thickness and the segment length. sheared DEM models with different thickness T. Riedel shears nucleate to accommodate shear es .

The segment length L corresponds to the inter-Riedel distance L measured along the direction of shear. These segments correspond to Y-shear fractures.

Discrete element modeling of fault growth

Geological fault structures, including strike-slip fault systems, have long been studied through numerical modeling [START_REF] Lynch | Finite element models of stress orientations in well developed strike slip   fault zones: Implications for the distribution of lower crustal strain[END_REF][START_REF] Segall | Mechanics of discontinuous faults[END_REF] However, .

classical modeling approaches, like the finite element method (FEM) or the finite difference method (FDM), implement faults as pre-existing discontinuities embedded within the numerical medium, therefore hindering mechanical investigation of any spatio-temporal evolution of fault geometry. Conversely, the discrete element method (DEM) enables to simulate the nucleation and propagation of discrete structures by representing the medium as a collection of independent particles interacting one with another through predefined force-displacement laws [START_REF] Cundall | A discrete numerical model for granular assemblies[END_REF][START_REF] Potyondy | A bonded-particle model for rock[END_REF]Scholtès and Donzé, 2012). Commonly used to tackle geomechanics problems, the DEM has been successfully applied to study fault system formation or pull-apart basin, including strike-slip settings [START_REF] Fournier | Insights to slip behavior on rough faults using discrete element modeling[END_REF][START_REF] Liu | Particle Based Modeling of Transtensional Pull Apart Basins[END_REF][START_REF] Morgan | Numerical simulations of granular shear zones using the distinct element method: 2. Effects of particle size distribution and interparticle friction on mechanical behavior[END_REF][START_REF] Morgan | Numerical simulations of granular shear zones using the distinct element method: 1. Shear zone kinematics and the micromechanics of localization[END_REF].

In this study, we model the continental brittle crust using a bonded particle model implemented in the YADE DEM open-source software  et al., 2015). The particles forming the medium interact through elastic brittle inter-particle laws, which are calibrated so that the emergent bulk behavior of the simulated medium corresponds to the pressure dependent behavior of a typical elastic cohesive brittle rock (see Supplementary

Material for details of the methodology, the model formulation as well as for illustration of the emergent behavior). To study strike-slip faulting in the brittle crust, we built up three dimensional models of dimensions equal to 160 km x 40 km x T, with thicknesses T ranging from 3 km to 30 km (Fig. S2). The models are made up of spherical particles whose radii are uniformly distributed between 170 m and 320 The particle density s adjusted as function of m. wa the porosity of the particle packing so that the bulk density of the layer corresponds to the crust density (Table S1). Our synthetic crust thus consists of an initially intact and homogeneous elastic brittle layer with boundary conditions set up to mimic a strike-slip tectonic setting. The This article is protected by copyright. All rights reserved.

top surface of the layer is free, while roller type boundary conditions are defined on the three other sides (the normal displacements along the boundary walls are blocked). In the first stage of the loading sequence, internal stresses are generated by letting the layer stabilize under gravity.

Due to the boundary conditions, the maximum compressive stress at the end of this preconditioning stage is vertical and equal to the lithostatic stress, and the horizontal stresses result from the Poisson effect. Then, th pre-stressed layer is sheared horizontally by imposing is opposite and parallel constant velocities on each of its half through the lateral and bottom boundaries (Fig. S2). Thus, the only stresses considered in this study relate to the stresses induced by the initial gravitational settling and the subsequent shear loading. Also, the loading rate was chosen to ensure the model response remains quasi-static (rate independent) during the entire deformation process (Fig. S4).

During strike-slip deformation, the localization of deformation is twofold [START_REF] Naylor | Fault geometries in basement-induced wrench faulting under different initial stress states[END_REF]. In a first stage, a set of distinct Riedel-shears appears on the top free rface of the su medium, which are oblique to the shear direction. During a second stage, Y-shear fractures develop between successive Riedel-shears, parallel to the shear direction. These Y-shears in would eventually coalesce to form a through-going shear fault if the deformation is continued. In our models, the inter-Riedel Y-shears are analogue for fault segments observed in natural strikeslip systems (Fig. 1) and are thus called segments hereafter. To study the influence of the crust thickness on this localization process, we varied the thickness of our synthetic layer between T 3km and 30km (keeping the same model resolution for all cases). For -shears T would appear and a through-going shear fault formed from the beginning of the experiment. (Fig. 1b), the number of segments is 18, with an average length of 8.9 km per segment, for =10 T km (Fig. 1c), the model produces 11 segments, with an average length of 14.5 km, and for =15 T km (Fig. 1d), the model produces 10 segments, with an average length of 16 km (see Table S2 for Riedel-shears count, segment length, and uncertainties for all simulations). Therefore, our This article is protected by copyright. All rights reserved.

numerical simulations show that the segment length increases linearly with the layer thickness L T (Fig. 2).

Temporal evolution of fracture growth

Analogue experiments [START_REF] Naylor | Fault geometries in basement-induced wrench faulting under different initial stress states[END_REF]) and theoretical derivation [START_REF] Mandl | Faulting in brittle rocks: an introduction to the mechanics of tectonic faults[END_REF]) et al.

have suggested that Riedel-shears would initiate at the basal discontinuity of the brittle layer and grow upward, following an helicoidal trajectory, which corresponds to the most effective geometry for energy dissipation [START_REF] Francfort | Revisiting brittle fracture as an energy minimization problem[END_REF].

Our numerical simulation reveals that soon after the proto-Riedel shear cracks start to propagate upward from the basal shear zone (step 50 in Fig. 3), some cracks also start to nucleate at the surface (step 65 in Fig. 3). Unlike the cracks that are uniformly distributed along the basal shear zone, the cracks initiating at the surface are spatially clustered (step 70 in Fig. 3). These cracks then propagate downward (step 80 in Fig. 3) to link with the upward crack front (step 100 in Fig. 3) and to form full-grown Riedel shears (see also animation A1). Eventually, our model shows that the spatial distribution of the crack clusters at the surface of the layer controls the distance between successive Riedel-shears.

The nucleation and propagation of cracks within bonded particle models are driven by the distribution of stress within the simulated medium. Cracks develop in places where inter-particle bonds cannot bear the excess of stress due to either tensile or shear mechanisms. In order to get further insights into the mechanisms at play during the faulting process, we investigated the state of stress on an idealized plane located between two successive Riedel-shears (Fig. 4a) as a function of the ratio between thickness of the model and segment length using a purely elastic 2D model (see Supplementary Material for additional information about model setting). propagation both from top and base of crack fronts, and 3) formation of Riedel shears. L indicates the segment length.

State of stress on a plane between two Riedel-shear fractures

Under strike-slip loading conditions the local horizontal stress state at the base of the -between 2 Riedel-shears (Fig. 4a) is assumed to be primarily of tensile nature (Fig. S7). Building on previous experiments designed to study joint distribution in layered brittle materials (Taixu Bai and Pollard, 2000;T Bai , 2000;[START_REF] Yang | Fault spacing in continental strike-slip shear zones[END_REF][START_REF] Zuza | Spacing and strength of active continental strike-slip faults[END_REF], we set up a 2D elastic model to further investigate the state of stress on the plane   o between the segment length R , and the layer thickness (AB). The simplified 2D model consists of a layer with a free surface at the top, subjected to pure extensional loading at its base, in order to mimic the deformation process at play in between Riedel-equal to             zero, the tensional loading at the base induces some bending along the vertical axis that in turn ex plane in the vicinity of the vertical boundaries. the stress close to the surface is compressional (Fig. 4b and additional examples in Fig. S9).

When 1.5, however, the stress at the surface becomes tensional (Fig. 4c and4d, and Fig. S9).



The tensile strength of brittle rocks is significantly lower than the compressive strength, and ir does not exceed few tens of MPa for crustal rocks [START_REF] Cai | Practical estimates of tensile strength and Hoek Brown strength parameter m i of brittle rocks[END_REF]. Thus, when tensional stress dominates at the surface of the layer, its tensile strength is almost immediately overcome and tension cracks nucleate. These cracks then propagate downward (Fig. 3; also animation A1) to link up with the cracks originating in the vicinity of the basal shear zone, and to form a new Riedel-shear. The creation of this newly-generated Riedel-shear reduces the value of to a value R lower than ~1.5 which, in turn, brings back the stress in a compressional state. The threshold value for might vary depending on the tensile strength of the materials at play but, R nevertheless, this variation stays within a 10% range for rocks [START_REF] Cai | Practical estimates of tensile strength and Hoek Brown strength parameter m i of brittle rocks[END_REF]. A similar process has been found responsible for crack saturation in layered sedimentary rocks and has been characterized by Bai and Pollard (2000). Fig. 4e shows the variation of the horizontal stress at the point M (Table S3), located in the middle of the layer surface, as a function of the ratio R. When the thickness is significantly larger than the length (ratio R equal to 0.3 or smaller), the stress at point M is close to zero. For R between ~0.3 and ~1.5, compressional stress dominates at point M. As soon as R becomes larger than ~1.5, tensional stress dominate at point M and es the system is unstable, leading to the appearance of a new Riedel-shear and to the subsequent decrease of R to a value close to 1.5. Thus, R~1.5 corresponds to a stable configuration where no additional Riedel would form. Therefore, the thickness of the brittle layer, by controlling the state of stress along the shear plane, exerts direct control over the segment length. This article is protected by copyright. All rights reserved. [START_REF] Lefevre | Experimental evidence for crustal control over seismic fault segmentation[END_REF], and the present study (the pink polygone indicates average for thickness values generally acceped for the continental crust). In each case data are included into the compressional domain.

Comparison between field observations, analogue modeling, and numerical results

Figure 4f shows a compilation of data derived from earthquake-rupture field measurements [START_REF] Klinger | Relation between continental strike-slip earthquake segmentation and thickness of the crust[END_REF], from analogue fault segmentation experiments [START_REF] Lefevre | Experimental evidence for crustal control over seismic fault segmentation[END_REF]), and from our numerical experiments. The values of the ratio between segment length R and thickness of seismogenic crust for continental earthquakes range between 0.3 and 1.6, well within the range predicted by the 2D elastic model. The data derived from DEM models and analogue models are also within the range predicted by the 2D model. Some of the DEM model data, however, fall significantly above the maximum predicted value. This is indeed expected as in both experiments, while one tests a wide range of thickness, one also departs from the mechanical parameter self-nsistency that is needed when building a model behaving like the co Earth brittle crust. For the models that are in a reasonable range with real brittle crust thickness   T km), however, we find that the data also fall into the same range of values for the ratio R (1.1 < R < 1.5). Figure 4f demonstrates that a universal physical process controls the length of fault segments between successive Riedel-shears different materials subjected to in shear, including the crust of the Earth. Fault segmentation in earthquake ruptures is thus directly correlated to the thickness of the crust.

Figure 1 :

 1 Figure 1: a) Surface rupture for the Ridgecrest Earthquake. Individual segments (Y-shear fractures) are indicated by red arrows (after Ross et al., 2019). b) to d) Top views of left-laterally

  Fig. 1b to 1d show examples of surface fault patterns obtained for thicknesses respectively equal to T 5, 10, and 15 km, just before the appearance of the inter-Riedel Y-shears (see additional simulations for other thicknesses in Fig. S6). The associated horizontal offsets are respectively equal to 86 m, 156 m, and 174 m. The average distance between two successive Riedel-shears, distance hereafter called segment length, is determined by dividing the total number of Riedelshears by the total length of the model (160 km). Our numerical results show that for =5 km T

Figure 2 :

 2 Figure 2: Linear relationship between segment length L and thickness T observed in sheared brittle layers simulated with the DEM. Red squares indicate the range of values commonly accepted for the brittle continental crust thickness km  ).

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Figure 3 :

 3 Figure 3: Successive 2km-wide swath cross-sections along the shear direction for increasing shear deformation at the base of the DEM model. Each dot indicates an induced crack colored according to its depth. Step 65 shows nucleation of crack clusters near the layer surface, which later expand downward to form Riedel shears. Sketches to the right illustrate time evolution of cracking within the brittle layer: 1) initiating from the base and propagating upward, 2)

Figures

  Figures 4b to 4d show the horizontal stress distribution along the vertical strike plane for different values of R . By convention, compressional stresses are positive. When 1.5,  

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Figure 4 :

 4 Figure 4: a) Conceptual model where strike-slip imposed at the base induces extension on the              tension segment length  and T the thickness . Scenario d) is presented only to illustrate stress distribution  for R>>1.5, since this configuration is unrealistic as material would already have ruptured. e) Horizontal stress at the surface middle point M as a function of R. The shaded area indicates values of R for which M is in compressional state of stress. The maximum compressive stress a is observed for R~1. Surfac e strength of  the brittle layer is overcome (between 0 an 10 MPa depending on material). f) Comparison of R values measured in earthquake observations (after Klinger 2010), sandbox experiments (after

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Acknowledgments

Observational datasets used in this study are directly derived from Klinger (2010) and Lefevre et al. (2020). We thank J. McBeck, an anonymous reviewer, and the editor G. Prieto for insightful comments that helped improve this manuscript. The research was partly supported by the ANR project DISRUPT (ANR-18-CE31-0012). L.J. was funded by SIGMA-2 project.

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