R Branka

G Marlair

J P Bertrand

H Biteau

Characterisation of Sparklers and Bengal Flames using the Fire Propagation Apparatus

Understanding the decomposition mechanism of fireworks is essential to improve the safety related to their storage (CHAF project). A study has been carried out on sparklers and Bengal flames to identify the nature of the combustion gases produced and investigate the potency of toxic emissions. Tests have been realised using the Fire Propagation Apparatus (FPA). It has become a widely used device for materials characterisation in fire research. It allows to directly measure the CO 2 , CO, NOx and THC productions. The emission of soot, the concentrations of HCl, SO 2 and HCN can also been obtained. From the experiments, it appears that the major gases produced were CO 2 , CO and SO 2 .

Pyrotechnics also present the peculiarity to carry an oxidiser and do not require O 2 from the air to burn. To explore this specificity, combustion experiments have been carried out in air as well as in nitrogen atmosphere. Results have been compared to underline the variations in the production of combustion gases depending on the reacting atmosphere. Under N 2 atmosphere, it emerges that the emission of CO 2 decreases while the CO increases.

In the future, other tests will be realised coupling FPA and FTIR to better characterise the emission of toxics.

Introduction

The two major stages where the risk related to the production and the use of fireworks become critical appear during storage and transport [START_REF] Chapman | CHAF project report[END_REF]. In the last few years, an increase in serious accidents involving fireworks has been observed. They often led to casualties and major damage to a large area where the event took place. One of the reasons suggested to explain this growth is that fireworks transport marking appeared to be inappropriate [START_REF] Chapman | CHAF project report[END_REF]. Several tests applied for material classification did not allow identifying a potential explosion hazard associated with the storage of fireworks in large quantities. The Quantification and Control of the Hazards Associated with the Transport and Bulk Storage of Fireworks project (CHAF project) was a recent initiative to develop a better understanding of fireworks behaviour in fires when large quantities are involved. The aim was then to provide methods allowing to identify fireworks likely to pose a mass explosion risk which would not be identified by current UN tests. Encouraged by results obtained, a larger consortium of laboratories, including INERIS, has decided to go further (CHAF2 Project), to suppress still remaining gaps in appropriate knowledge on those fireworks that may also lead to soil contamination and present acute or chronic toxicity issues at the work place level or the display stage for the workers [START_REF] Marlair | Toxicity Issues Pertaining to Burning Pyrotechnics[END_REF]. Thus learning more on intermediate or final decomposition products is deemed essential for progressing towards more sustainable fireworks industry. In order to be able to quantify the propagation of a reaction involving fireworks, the dominant parameters driving the phenomenon have to be recognized. In this perspective, understanding the decomposition mechanism of fireworks is essential to improve the safety related to their storage [START_REF] Marlair | Energetic Materials and the fire problem[END_REF]. This characterisation requires adequate diagnostic instrumentation. This work will investigate the ability of the FM-Global Fire Propagation Apparatus (FPA) [START_REF]Standard Test Method for Measurement of Synthetic Polymer Material Flammability Using a Fire Propagation Apparatus[END_REF] to provide appropriate data to determine the reaction process involved in the burning of fireworks. The FPA is a small scale calorimeter which became a widely used device in the field of fire research. It has proven it is efficiency to characterise flammability parameters, related to the propensity of a material to support fire propagation [START_REF]Standard Test Method for Measurement of Synthetic Polymer Material Flammability Using a Fire Propagation Apparatus[END_REF]. Thermal and chemical characteristics the FPA is qualified to measure or estimate are time to ignition, mass loss rate, chemical, convective and effective heat release rate, combustion gases generation rates (CO 2 , CO, Total Hydrocarbons (THC), soot...), O 2 consumption, the transient response to prescribed heat flux in a specified inert or oxidizing environment.

In the present work, an experimental study has been carried out on the ignition and the combustion of sparklers and Bengal flames to identify the nature of the major combustion gases produced and investigate the potency of toxic emissions. Atmospheres of the reaction area have been modified. In order to investigate the peculiarity of pyrotechnics mixtures to incorporate a fuel and an oxidizer in the same material, experiments have been performed under air and N 2 atmosphere. It will be of importance to analyse the influence of the O 2 concentration on the fireworks behaviour.

Experimental Approach

The experimental device used to perform the different tests is the FM-Global Fire Propagation Apparatus (FPA). It is a fire calorimeter (cf. Figure 1) which has been designed by Tewarson [5] in his early configuration in the middle of the 70's. During the last thirty years, the instrumentation received valuable improvement. Because it embodied several novel design concepts, it has been internationally recognised by standard organisation [START_REF]Standard Test Method for Measurement of Synthetic Polymer Material Flammability Using a Fire Propagation Apparatus[END_REF].

It comprises two main sections: the combustion line and the exhaust products (combustion gases, soot…) collecting and measurement line. The material submitted to a test is placed on a sample holder mounted on a load cell enclosed in a quartz tube delimiting the combustion area. Four infrared heaters fixed at the exterior of the quartz tube allows for applying a given external heat flux onto the sample. The heating system is both air and water cooled due to the high temperatures developed by the lamps. When self ignition is not expected, ignition of the material usually occurs by use of an ethylene/air pilot flame. When tests have to be performed under low O 2 or N 2 atmospheres, the usual ignition procedure could not maintain a flame. The ignition source is usually replaced by a sparks system. Air, O 2 and N 2 concentrations are introduced at the base of the apparatus (i.e. from the bottom of the sample holder). A hood system topped the "reaction zone". It has been dimensioned so that all the combustion gases are sucked up. From the hood, the system narrows to an exhaust duct to ensure gases mixing. Further down, volumetric flow rate is measured by a Pitot tube and gas sampling is operated. Gases pass through a soot filter and a cold trap. They are continuously distributed to a set of different analysers enabling to measure combustion gases concentrations. The O 2 concentration is estimated through a paramagnetic analyser while CO/CO 2 concentrations are determined using an infrared technology. A Flame Ionization Detector (FID) device is used to estimate THC level. A laser beam at λ = 632 nm is projected along the exhaust duct in order to evaluate the extinction and the smoke molar fraction. Additional measurement procedures have been implemented to obtain the concentrations of HCl, SO 2 and HCN. This device is adapted to the calorimetric methodology. It allows estimating the heat release rate (HRR) using oxygen consumption (OC) or carbon dioxide generation (CDG) calorimetry [START_REF] Janssens | Oxygen Consumption Calorimetry[END_REF]. Data are acquired every two seconds for the duration of the experiments. Two types of fireworks have been tested, sparklers and Bengal flames. They are relatively common pyrotechnic materials. The compositions of the different samples are presented on Table 1. In order to obtain long combustion times and verify the homogeneity of the compounds, experiments were performed by coupling several samples together. For each test of sparklers and Bengal flames, respectively, 10 and 3 specimens were ignited. Samples were positioned in a way that they would burn one after the other allowing a reaction time long enough to be captured by the different measurement instrumentations. The Bengal flames were prepared in tubes with a diameter of about 5 mm. They were ignited by the top using a pilot flame or sparks.

Experimental Results

CO 2 , CO, THC (Total Hydrocarbons), NO and HCl generation rates have been estimated from measured molar fraction. Mass loss was also recorded directly. Heat release rates were obtained from OC and CDG calorimetry. For the red Bengal flames, the CO 2 yield is significantly decreased by more than half while the CO generation substantially increases. On the other hand, combustion time decreases under N 2 atmosphere. The blue Bengal flame sees a slight decline of the CO 2 yield, combined with a low rise of the CO generation. As the blue Bengal flame seems to contain less fuel, the change from air to N 2 atmosphere in the reaction zone causes minor variation in the combustion gases concentrations. The yellow Bengal flame would represent an intermediate behaviour between the one observed with the red and blue compounds. The productions of THC, NO and soot do not seem to be affected when reaction takes place into a N 2 atmosphere rather than in air. No significant differences are measured regarding the combustion times.

Table 2 and Table 3 present mass losses, combustion times and generation yields obtained for combustion under air and N 2 atmosphere. Considering the combustion of sparklers, the percentage of mass burnt is relatively similar whether the reactive atmosphere was air or N 2 . However, the combustion time is increased when the reacting atmosphere is changed from air to N 2 . Generation rates diverge from one test conditions to another. CO 2 yield is decreased by more than half while the CO yield is multiplied by four when the atmosphere within the tube is changed from air to N 2 . Higher level of THC is also observed.

Blue, yellow and red tested Bengal flames contained the same oxidizer, potassium chlorate (KClO 3 ). White contained potassium nitrate (KNO 3 ) but will not be studied in the present work. The compositions also differ by the colour producing components and the amount of resin. The combustion of red Bengal flames under air atmosphere produces the highest level of CO 2 yield. It is easily explained by the composition of the firework which contains more carbon than blue and yellow ones. Moreover, it also appears that Blue Bengal flames present the lowest emissions of CO 2 in case of well-ventilated combustion. One more time, it can be related with the composition of the material where carbon will be mainly present in the resin. The emissions of CO, THC, NO, HCl and soot remain very low during the reaction under air atmosphere. When the reacting medium is changed to N 2 , fireworks chemical behaviour differs. For the red Bengal flames, the CO 2 yield is significantly decreased by more than half while the CO generation substantially increases. On the other hand, combustion time decreases under N 2 atmosphere. The blue Bengal flame sees a slight decline of the CO 2 yield, combined with a low rise of the CO generation. As the blue Bengal flame seems to contain less fuel, the change from air to N 2 atmosphere in the reaction zone causes minor variation in the combustion gases concentrations. The yellow Bengal flame would represent an intermediate behaviour between the one observed with the red and blue compounds. The productions of THC, NO and soot do not seem to be affected when reaction takes place into a N 2 atmosphere rather than in air. No significant differences are measured regarding the combustion times. 3 represent the molar fractions of the major gases produced during the combustion respectively for sparklers and yellow Bengal flames. Sparklers seem to show a different kinetic depending on the reacting atmosphere. Varying the O 2 concentration seems to slow down the reaction. Under air atmosphere, apart for NO 2 , combustion gases begin to be produced simultaneously (about 26s). A first slop between 26 and 40s is then followed by a plateau between during about 4s. Afterwards, CO2 and NO rise again, while CO stays relatively constant and THC decrease. At 76s, a maximum is recorded for CO 2 and NO which then begin to drop off as does CO. At the same time, the molar fraction of NO 2 begins to increase to reach a maximum peak at 86s which corresponds to a sharper decrease of CO molar fraction. For the reaction under N 2 atmosphere, the dynamics are relatively similar between the combustion gases, apart again for NO 2 which starts every time to be produced during the fall of production of the other species. Figure 3.a. presents the production of gases from the combustion of yellow Bengal flames. At ignition, the considered species start to be generated. However, different dynamics are observed. CO 2 , CO, THC and SO 2 show plateaux which correspond to constant reaction rates. Magnitudes illustrate variations (as observed for CO 2 and CO molar fractions) that are due to the experimental setup. Three fireworks were positioned so that they were supposed to ignite one after the other. However, in the present experiment, two ignited simultaneously creating the divergence observed in the plateaux levels but this has no influence for interpreting the results. NO and NO 2 present peaks at the ignition of each Bengal flame which are followed by fast decrease of the concentration of these two species. Reaction last for about 2 minutes.

Under N 2 atmosphere, the combustion reaction time is relatively similar to the one under air. Same dynamics were noticed but of different magnitudes. The CO 2 production decreases while more incomplete combustion products (CO, THC and SO2) are generated. Concerning nitrogen oxides, peaks appear again for a lapse of time after ignition with the same order of magnitude as for the tests carried under air.

From the previous experiments, it emerges that the major combustion gases produced are CO 2 and CO. Reducing the O 2 concentration leads to a less complete combustion. CO but also THC or SO 2 become more increasingly generated while the CO 2 concentration decreases. However, burning still occurs. For the Bengal flames, it seems that constant generation rates are observed for CO 2 , CO, THC and SO 2 . On the other hand, peaks of NO and NO 2 are observed at ignition for the yellow flames.

Discussion

Pyrotechnics present the peculiarity to carry an oxidizer and do not require O 2 from the air to burn. The possibility of a fire even in low O 2 concentration conditions is not negligible. They can be found during a hazard, for example in a vitiated atmosphere. To explore this specificity, combustion experiments have been carried out in air as well as in N 2 atmosphere. Results have been compared to underline the variations in the production of combustion gases depending on the reacting atmosphere. Ignition occurred for every tested. The results initially expected would be similar to the ones that would be observed for conventional fires in under ventilated conditions (i.e. fuel-rich). The combustion tends to be largely incomplete; the CO 2 generation significantly decreases while the opposite effect is observed for the CO, THC productions.

If discrepancies appeared when the reacting medium is changed, the variations in terms of production of combustion gases are not always significant. If CO 2 yields are divided by 2 and 2.5 respectively for sparklers and red Bengal Flames, they only slightly decrease for yellow and blue Bengal flames. Similar comments can be done for the CO generation. In the case of the Bengal flames, they all enclose the same oxidizer, potassium chlorate. It highlights a critical dependency on the composition of the firework. The fuel, the binder and quantities of each compound are as dominant factors as the oxidizer to understand the material behaviour.

First consider the sparklers. When KNO 3 decomposes, it releases O 2 . Freeman [START_REF] Freeman | The Kinetics of Thermal Decomposition of Potassium Nitrate and of the Reaction between Potassium Nitrite and Oxygen[END_REF] suggested the following reaction:

(

At the same time, the fuel decomposes into volatizes which will first form CO by reacting with radicals and in a second time, CO will be oxidized into CO 2 [START_REF] Pitts | Reactivity of product gases generated in idealized enclosure fire environments[END_REF]. We first observe an increase in the generation of CO 2 , CO and THC. Then, the CO and CO 2 reach a plateau. This instant correspond to the start of decrease of THC which present after a different dynamics. A hypothesis can be that hydrocarbons are oxidized to produce CO. The more O 2 is released from the oxidizer or present in the air, the faster goes the reaction HC + free radicals → CO. As CO is produced, it will be oxidized into CO 2 if enough O 2 is present in the medium. If the reactions HC + free radicals → CO and CO+ ½ O 2 → CO 2 have close reaction rates, it can explain the constant level of CO and the increase of CO 2 .

Moreover, as HC are more consumed, there concentration decreases. Under N 2 , the only O 2 supply comes from the oxidizer. HC will react with radicals to form CO. Because less O 2 is available, less CO will be oxidized into CO 2 .

Under air or N 2 , CO 2 and NO seem following the same dynamics. An assumption is to relate this behaviour with the decomposition of the oxidizer. Blackwood and Bowden [START_REF] Blackwood | The Initiation, Burning and Thermal Decomposition of Gunpowder[END_REF] [10] assume the following reaction to explain the formation of NO during the combustion of black powder:

(

) 2
Sparklers composition is very similar to the one of black powder. To verify this hypothesis, it could be interesting to measure in the future the production of K 2 SO 4 . Nevertheless, the formation of CO 2 is mainly dependent on the O 2 supply from the oxidizer. The production of CO 2 is related to the reaction rate of the KNO 3 decomposition. The similarity of both dynamics tends to the assumption developed previously.

The combustion time is almost doubled when changing the reacting medium from air to N 2 .

Temperature measurements in the quartz tube are lower in the N 2 medium. Then, reaction rates are then lesser. It has been previously noticed that the same percentage of mass was burnt, which explains the longer duration of the reaction.

Independently of the reacting atmosphere, the production of NO 2 starts once, the generation of CO 2 , CO and NO decreases. A possible explanation is to consider that NO 2 is produced by the oxidation of NO when remaining O 2 is present. Several assumptions have been introduced in order to try to understand the decomposition of sparklers. Additional tests would be necessary to verify them.

Moving to Bengal flames, mass losses and combustion time are relatively constant under air or N 2 atmosphere. Temperature in the tube does not vary significantly, so reaction rates may be considered constant. CO 2 and CO generation rates are sensibly constant. The specimens are contained in paper tubes. Their main aim is to burn with the same intensity for a given time then, once ignited, the spread rate of the reaction front needs to be constant. It can be achieved if its area is fixed. Moreover, the oxidizer allows mixing of volatizes and O 2 in the medium while air is only in contact at the surface. This can explain the small variation in CO 2 generation when changing the reacting atmosphere. The oxidizer is the main supply in O 2 but the O 2 concentration has clearly an effect on the rates of combustion gases generated.

Peaks of NO and NO 2 are observed for every ignition of a yellow Bengal flame. The formation of NO and NO 2 can only be due to oxidation of N 2 , as the mixture does not contain nitrogen. This reaction occurs for high temperatures. Nevertheless, measurements of the temperature above the flames show consequent peaks at ignition. The hypothesis is that high energy is released at ignition inducing high temperatures allowing the formation of NO and NO 2 following the reactions [START_REF] Hussain | FTIR -Spectra of Gaseous Products from the Combustion of Pyrotechnic Mixtures containing Carbon[END_REF],

Reactions ( 3) and ( 4) also imply that O 2 is available for N 2 oxidation. It could be another reason explaining the decrease of NO and NO 2 after ignition. The assumption of a large release of energy at ignition could be verified by estimating the heat release rate (HRR). As previously mentioned, the FPA is equipped to allow calculating the HRR based on OC or CDG calorimetry. The estimations realised show significant discrepancies between the methods. Because of the presence of the oxidizer in the material, the OC calorimetry does not appear to be relevant in the current study because based on the measure of the consumption of O 2 . Applying this technique would suppose introducing a correction in the calculation accounting for the internal supply of O 2 . On the other hand, the CDG calorimetry relies on energy constants with large uncertainties. No accurate estimation of the HRR can be obtained. A solution would be to measure the heat of combustion of the material by means of a bomb calorimeter.

Conclusion

Lessons from the past have demonstrated that hazards related to the storage and the transport of pyrotechnics were real. It is of great importance to be able to identify and quantify the risks associated with these materials that will have to fulfil in a near future more stringent sustainability criteria. To achieve these objectives, relevant tests have to be defined. The FPA (developed primarily for the fire science community needs) has already shown its ability to characterise the flammability of materials in case of "conventional" fires. Pyrotechnics present the singularity to carry an oxidizer and are then able to sustain flaming even without O 2 from the air. Conditions of low level of O 2 concentration can be encountered during a fire and it is critical to be able to understand how behave pyrotechnics in these circumstances. The advantage of the FPA is that experiments can be carried under variable O 2 concentration levels.

Tests have been carried out with two different types of pyrotechnics: sparklers and Bengal flames.

The reacting medium has been varied from air to N 2 atmosphere to observe the effect on the combustion gases generation. Ignition occurred for every test, highlighting the role of the oxidizer as the main reaction partner. Under N 2 atmosphere, it emerges that the emission of CO 2 decreases while the CO increases. However, the magnitude of this behaviour is dependent on the nature of the mixture. If it was significant for sparklers and red Bengal flames, it was noticeably lower for blue and yellow Bengal flames. Moreover, tests showed that independently of the atmosphere, generation rates of the major species were relatively constant. Different reactions have been underlined for the formation of nitrogen oxides. It is essential to be able to identify such compounds given the pollutant nature of NO 2 .

The FPA was able to access information about the chemical and thermal characteristic of a material. It is able to identify the major species generated during the combustion and their evolution with the O 2 concentration. However studying in depth the combustion toxicity related to pyrotechnics is a complex issue given the diversity in the chemical processes involved. Being able to estimate the HRR and identify more species taking place in the combustion reaction will be a next step in order to better quantify the toxic potency of fireworks. In the future, other tests will be realised coupling FPA and FTIR to better characterise emissions of toxics. First, black powder will be inerted with alumina to slow down the combustion and allow a chemical and thermal characterisation. Results will be compared to previous studies ones. In a second time, other pyrotechnics materials, such as pyrotechnic stars, comet flares or smoke powders, will be tested based on a similar procedure in order to attempt defining relevant test methods.

Figure 1 .

 1 Figure 1. Scheme of the FM-Global Fire Propagation Apparatus.

Figure 2

 2 Figure2and Figure3represent the molar fractions of the major gases produced during the combustion respectively for sparklers and yellow Bengal flames. Sparklers seem to show a different kinetic depending on the reacting atmosphere. Varying the O 2 concentration seems to slow down the reaction. Under air atmosphere, apart for NO 2 , combustion gases begin to be produced simultaneously (about 26s). A first slop between 26 and 40s is then followed by a plateau between during about 4s. Afterwards, CO2 and NO rise again, while CO stays relatively constant and THC decrease. At 76s, a maximum is recorded for CO 2 and NO which then begin to drop off as does CO. At the same time, the molar fraction of NO 2 begins to increase to reach a maximum peak at 86s which corresponds to a sharper decrease of CO molar fraction. For the reaction under N 2 atmosphere, the dynamics are relatively similar between the combustion gases, apart again for NO 2 which starts every time to be produced during the fall of production of the other species.

2 Figure 2 .Figure 3 .

 223 Figure 2. Combustion of sparklers under Air (a) and N 2 Atmosphere (b).

Table 1 .

 1 Compositions of the different tested fireworks.

	Material	Colour Composition
				100% KNO 3	21% Sulphur
	Sparkler	White
				21% Charcoal	14% Aluminium
				100% KNO 3	35% Sulphur	25% M 1 *
		White	12.5% Antimony Sulphur 6.3% Aluminium
				100% KClO 3	18.8% Sodium Oxalate	15.6% Shellac
	Bengal Flames	Yellow	3.1% Acroides Gums
				100% KClO 3	25% Strontium Carbonate	15% Resin
		Red		5% Acroides Gums
		Blue		100% KClO 3	40% Copper Oxychloride	8.7% Resin
	*M 1 :	100% KNO 3	22% Charcoal	16% Sulphur

Table 2 .

 2 Yield of various combustion products from burning of sparkles and Bengal Flames (BFl) under air atmosphere.

	Sample	Sparklers	Blue BFl	Yellow BFl	Red BFl
	Atmosphere	Air	air	air	air
	Initial Mass (g)	15.88	16.32	14.91	15.13
	Total Mass Loss (g)	3.73	13.52	12.55	12.1
	% Mass Lost	23.5	82.84	84.17	79.97
	Combustion Time (s)	74	232	122	220

Table 3 .

 3 Yield of various combustion products from burning of sparkles and Bengal Flames (BFl) under N2 atmosphere.

	Sample	Sparklers	Blue BFl	Yellow BFl	Red BFl
	Atmosphere	N2	N2	N2	N2
	Initial Mass (g)	12.48	16.69	14.7	15.45
	Total Mass Loss (g)	2.61	14	12.13	12.93
	% Mass Lost	20.91	83.88	82.52	83.69
	Combustion Time (s)	134	210	120	188
	Combustion Products		Yield (g/g of fuel)
	CO2	0.242	0.336	0.387	0.258
	CO	0.164	0.019	0.056	0.178
	soot	0.004	0.04	0.023	0.016
	THC	0.016	0.003	0.002	0.006
	NO	0.121	0.002	0.003	0.002
	HCl	nm	nm	nm	nm
	*nm: non measured


N Prime

Fabrice Emeriault

Matthieu Caudron

Marwan Al Heib

Efficiency of mitigation measures for structures subjected to ground movement

Surface subsidence resulting from the collapse of underground cavities, whether natural or man-made can interact with existing buildings on the surface. One of the mitigation measures used is to dig a peripheral trench at a certain distance from the structure, filled with a soft material, like peat, or artificial material. This is thought to reduce the horizontal strain applied to the structure. The 3D numerical analysis presented in this paper is a first step towards evaluating the efficiency of this type of mitigation technique. The numerical model developed using Abaqus allows the effect of various parameters such as the width or depth of the peripheral trench, its distance from the building and/or the stiffness and strength of the filling material to be clearly determined. 0.6 % : Greenfield case 0.6 % : Greenfield case 0.6 % : Greenfield case Greenfield case

INTRODUCTION

The collapse of underground cavities, both natural and man-made, causes many accidents at the surface. This can cause human and material damage. Various types of ground movement can be observed, such as subsidence and sinkholes.

INERIS 1 is in charge of a research project aimed at assessing the consequences of this type of ground movement on buildings and infrastructures, proposing and evaluating mitigation measures and defining design recommendations. The most affected zones in France are the Lorraine iron-ore basin, the Northern coal field and the Paris basin. The latter is particularly vulnerable due to its dense urbanization.

The present study is a contribution to this research project and deals with 3D numerical modelling of the effect of ground movement on buildings protected by a peripheral trench. This mitigation method has been proposed, for example in France, by CSTB (Deck, 2002, CSTB 2 2004) and already implemented in some planning documents (PPRM 3 at Auboué, 2007 andHayange 2005). [START_REF] Caudron | Etude expérimentale et numérique de l'interaction sol-structure lors de l'occurrence d'un fontis[END_REF] studied the effect of the collapse of underground cavities using physical and numerical modeling without any mitigation measures. The first 2D numerical model was developed by Al Heib (2008) to evaluate the effect of structure and trenches. In this paper, we use a 3D numerical model to evaluate the mechanical response and to propose design recommendations. In particular, the influence of the different geometrical and mechanical characteristics of the trench must be assessed: stiffness and strength of the filling material of the trench (one of possible materials is peat), distance to the building, depth and width of the trench.

Ground movement induced by the collapse of an underground cavity is generally complex. A combination of horizontal and vertical displacement is observed at ground level under greenfield conditions (i.e. with no existing buildings or structures). It is alternatively described through horizontal strains (compression and extension), curvature (sagging and hogging) and slope (Al Heib, 2008). The consequences on the structures embedded in the subsurface can therefore be of various types: translation, tilt, horizontal strain (compression or extension) and bending; the structures are generally impacted by a combination of these different types. Unfortunately, the numerical of displacement fields in soil requires an explicit description of the cavity and its failure process. The resulting computing cost is excessive and not acceptable in the proposed parametric study which focuses on the building and surrounding trench.

According to many observations and back-analyzed case studies [START_REF] Deck | Etude des conséquences des affaissements miniers sur le bâti. Proposition pour une méthodologie d'évaluation de la vulnérabilité du bâti[END_REF], horizontal strains appear to be the most important source of damage in buildings: it generates cracks in the corners of apertures, friction in the lower parts of the structure, bending the embedded walls and other complex reactions of the building. Therefore, the proposed numerical model focuses on this loading process alone. The problem can thus be split: the horizontal stress field generated by underground cavity failure can be directly calculated (with reference to the greenfield case) and applied to a 3D model that explicitly includes the structure, trench and volume of soil necessary to avoid boundary effects.

THE PROPOSED NUMERICAL MODEL

The numerical model described in Figure 1

ÅSlab ÅTrench

Compressional horizontal displacement U o =0.30 m is applied at boundary 1 of the model (Fig. 1). This displacement value was chosen with reference to the greenfield case to induce 0.6 % compressive stress in the ground and, with the soil strength parameters under consideration, to produce plastic deformation in the vicinity of the ground surface. According to [START_REF] Burland | Assessment of risk of damage to buildings due to tunnelling and excavation[END_REF], horizontal stress İ xx of this magnitude in a building can be responsible for Category 4 or 5 ('severe' or 'very severe') damage due to hogging, whatever the deflection ratio. In addition to the soil-structure interaction resulting from the difference in stiffness, the proposed numerical model will consider frictional interfaces between soil and slab. Therefore stresses transferred to the slab will be less than 0.6 % but will still correspond to possibly severe damage.

On boundaries 2, 3, 4 and 5, rotational displacement is restrained in the direction perpendicular to the boundaries. Boundary 6 is considered free.

Linear elastic isotropic is considered for the structure, with stiffness parameters corresponding to reinforced concrete (Table 1). Soil and trench material is linear elasticperfectly plastic materials using the Mohr-Coulomb criterion and non-associated flow rule. Reference values for the trench material correspond to peat soil (Table 1). The density of the virtual slab is actually used to represent the weight of a concrete structure with four walls and a 0.25 m thick roof. The soil characteristics considered correspond to compact cohesive soil. The difference in soil-structure stiffness can be estimated, according to [START_REF] Potts | A structure's influence on tunneling induced ground movements[END_REF], by relative bending stiffness ȡ*=EI/E s H 4 and relative axial stiffness D*=EA/E s H, with EA and EI axial and bending stiffness of the structure, E s soil Young's modulus and H half the length of the building. In the present case, ȡ*= 6.25x10 -4 m -1 and D*=15. [START_REF] Potts | A structure's influence on tunneling induced ground movements[END_REF] showed that in the case of a tunnel excavation beneath a centered building, for these values of ȡ* and D*, the behavior (in particular horizontal displacements and strains) at the ground surface is affected by the presence of the slab. Although they also showed that for D* greater than 4.86 and any value of ȡ*, there is approximately no horizontal displacement in the soil under the slab (with rough interaction between soil and slab), the proposed numerical model will consider frictional interfaces between soil and slab.

For the trench, CSTB ( 2004) recommended the use of peat soil for filling the trench, therefore the mechanical parameters considered, listed in Table 1, correspond to this type of material. In the PPRM for Auboué (2007) and Hayange (2005), it is proposed to use an alternative material with Young's modulus E less than 10 MPa.

The interface between the soil and the slab or the trench uses a simplified normal interaction (hard contact option in Abaqus) and a frictional tangential interaction ("penalty" type in Abaqus) with the parameters given in Table 2. The mesh corresponds to 4 node tetrahedral elements for the soil and 8 node hexahedral elements for the slab (Fig. 2). Due to the symmetry, only half of the problem is shown.

ANALYSIS OF THE REFERENCE CASE WITH TRENCH

The reference case considers a peripheral trench with distance to the slab D=1 m, depth H=0.5 m and width W=0.5 m. It is compared to the greenfield case and the case with the slab but no peripheral trench. The results are analyzed along three profiles (Figure 3): profile 1 in the direction of ground level loading (longitudinal direction), profile 2 in the transverse direction at ground level and corresponding to the edge of the slab, and profile 3 is a vertical profile in the plane of symmetry. The horizontal strains İ xx and stresses V xx are considered as well as horizontal displacements U x . Figure 4a shows that, in the longitudinal direction, horizontal strains at ground surface are modified by the presence of the slab compared to the greenfield case. Without the peripheral trench, horizontal strains decrease under the edge of the structure and are greater than the strains in the greenfield case. With the trench, a drastic decrease of İ xx is observed under the slab, in particular at its edge, and in the vicinity of the trench (on both sides of the trench). On the other hand, strain concentration is observed within the trench on each side of the building: İ xx reaches average values of 4.3 % and 4.2 % respectively in the left and right trench (Fig. 4a), i.e. 7 times the greenfield strain value.

Horizontal strain İ xx determined along section A (along the slab) which coincides with section 1 but refers to the slab, are very small in both cases with or without trench (approximately 10 -3 %) due to the axial stiffness of the slab and to the soil-slab interface that experiences slippage along most of its length. Nevertheless, the presence of the trench reduces the value of the maximum relative horizontal longitudinal displacement from 26.0 to 21.0 mm

To evaluate the efficiency of the trench, an average horizontal strain İ xx can be determined on the part of section 1 limited by the left and right trenches (i.e. between x=-6 and x=6 m). With the trench, İ xx = 0.41 % whereas without the trench, İ xx = 0.56% (the effect of the slab can also be evaluated by comparing this latter value to the greenfield 0.6 % constant strain. The presence of the trench thus reduces the average strain by 27%. Horizontal stress distribution V xx is also modified by the presence of the trench (Fig. 4b): in particular a decrease of V xx is noticeable in the soil close to the trench. However, this decrease of stress from 351 kPa to 250 kPa is very local and in particular the stress distribution under the slab is quite similar with or without the peripheral trench. Under the slab, an average value V xx = 397 kPa is obtained whereas it is 408kPa without any mitigation measures. The horizontal stress transferred to the slab is smaller due to the slippage occurring at the soil-slab interface (Fig. 4b).

In the transverse and vertical directions, strain profiles are also modified. For example, in section 2, horizontal strain is almost uniformly decreased under the slab (Fig. 4d): İ xx falls from 0.53 % without the trench to 0.28 % with the use of this mitigation measure. It is also noteworthy that the trench induces an increase of İ xx on the outer boundary of the trench whereas without the trench, strains in this area are very close to the greenfield values. In a vertical direction (for example section 3, see Fig. 4c), İ xx is also reduced in the close vicinity of the structure's base (between 0 and 0.78 m below ground level). A corresponding sharp increase of İ xx is observed between -0.78 m and -2.1 m. A clear effect of the trench can be noticed up to -6 m.

INFLUENCE OF THE TRENCH ON MECHANICAL PARAMETERS

Influence of cohesion c

In the reference case, the trench fill materia has cohesion c = 40 kPa. In this part, in order to analyze the effect of material strength, a cohesionless material is considered by introducing c = 0.01 kPa (for computational reasons). The resulting horizontal strains in sections 1 and 2 are reported in Figure 5. Only a slight change is observed, confirming that the trench material remains essentially in an elastic regime during loading (whereas this part of the ground surface would experience plastic behavior without the trench). İ xx is 0.38 % compared with 0.41 % with c = 40 kPa and 0.56 % without the trench. The average strains in the trench are nevertheless more affected: 5.7% and 4.7% respectively in the left and right trench (compared to 4.3 and 4.2 %).

Considering horizontal stress variation along section 1, although V xx close to the trenches is reduced to 80 kPa, the influence of this reduction is only local. Horizontal stress below the slab retains almost constant values.

In the transverse and vertical directions, very slight differences are reported between the two cases of material cohesion (see for example Fig. 5b).

Influence of Young's modulus E

The influence of the stiffness of the trench filling material is analyzed by considering E = 10 MPa instead of 5 MPa in the reference case (note that 10 MPa is the value recommended by Auboué and Hayange PPRM), cohesion is kept constant at c=40 kPa. It appears that the efficiency of the trench is directly related to the elastic modulus of the filling material: the average strain within the trench is reduced to 2.9 and 2.7% respectively in SLAB POSITION

Greenfield case

Greenfield case

İxx in the trench = 5.7 to 4.7 % a) b)

the left and right trenches. In the meantime, the average horizontal strain İ xx below the slab is equal to 0.46 %, thus representing 18 % of reduction compared to the case without trench. The same phenomenon is observed along section 2, where the computed average horizontal strain is 0.35 % beneath the slab (compared to 0.27% in the reference case). The same conclusion can be drawn from the analysis of results in section 3 in the first layer of soil below the slab. The extent of this layer is slightly increased by the stiffening of Young's modulus (-0.95m instead of -0.78m). Between -0.95 m and -2 m deep, the strain is still greater than the greenfield value but smaller than that computed for the reference case.

Stresses V xx are not affected by the change in elastic modulus.

The results of this parametric study are summarized in Table 3. The case of an empty trench has also been analyzed. Trench efficiency is increased when its stiffness and strength are reduced (within the considered range of values). It also appears that for an empty trench, the efficiency of the surrounding trench is greater than for any combination of material properties considered , but in practice, the trench must be filled. *without any trench, the average İ xx between the trenches is 0.56 %. H xx : horizontal strain L : left, R right

INFLUENCE OF THE GEOMETRICAL PARAMETERS OF THE TRENCH

Influence of distance D from trench to structure

In the reference case, the distance D between the trench and the structure is 1.0 m. To determine the influence of this distance on strain and stress distribution, the case of D=1.5 m is analyzed (all other parameters remaining constant, in particular c=40 kPa and E=5 MPa).

Along section 1, the average horizontal strain İ xx between the trenches is 0.43%. Without the peripheral trench, İ xx is slightly higher than that of the reference case at 0.57 % (the average is calculated between x=-6.5 and 6.5 m). Thus the presence of the trench is responsible for a 25% reduction in strain. The distance D does not therefore have a great impact on this reduction, even though in the reference case, this value was slightly higher (27%).

In the transverse direction (section 2), increasing the distance between the trench and the structure induces a noticeable increase in average strain, İ xx increases from 0.28% with D=1m under the slab to 0.36 %. Finally in the vertical direction (section 3), it can be concluded from Figure 6 that an increase in D leads to a deepening of the zone where strains less than the greenfield values are experienced (from -0.78 m to -1 m) and also of the zone where higher values are observed (from -2 m to -2.8 m). In addition, in each of these zones the difference in strain between the greenfield case and the case without a trench is reduced.

Influence of the depth of the trench

Based on the geometry of the reference case, the depth of the trench is now decreased to H=0.5 m. It appears that the average horizontal strain İ xx, along section 1 between the trenches, is greater than that observed with a deeper trench (0.46 % compared to 0.41 % with H = 1.0 m and 0.56 % without the trench). In the transverse direction (Fig. 7), the horizontal strain under the slab is uniformly reduced compared to the deeper trench: İ xx is approximately equal to 0.42% instead of 0.28% with H = 1.0 m. Along section 3, the influence of the trench is qualitatively the same as for deeper trenches but the thickness of the fringe of soil concerned by strain reduction is now reduced to 0.40 m instead of 0.78 m when H = 1 m.

Influence of the width of the trench

All others parameters remaining identical to the reference case, when trench width W is increased from 0.5 m to 0.8 m, it is observed that the average strain İ xx along section 1 between the trenches is reduced to 0.37 % compared to 0.41 % with W = 0.5 m and 0.56 % without the trench. Simultaneously, the average strain along section 2, below the slab,

Greenfield case

Greenfield case decreases from 0.28 % to 0.23 % and the thickness of the soil layer experiencing strain reduction below the slab increases to 0.9 m from 0.78 m.

The results of this parametric study are summarized in Table 4. The case of an empty trench with D = 1 m, H = 1 m and W = 0.5 m has also been analyzed. The efficiency of the trench is increased when its depth and width are increased and/or its distance from the structure reduced (within the considered range of values). It also appears that for an empty trench, the efficiency is greater than for any considered geometry of a trench filled with a material where E = 5 MPa. *as a percentage of the average strain obtained without any trench (i.e. İ xx between the trenches is 0.56% between -6 m and +6 m and 0.57% between -6.5 m and +6.5 m).

CONCLUSION

The main objective of this study is to analyse the efficiency of mitigation measures in the case of ground movement induced by the collapse of underground cavities. The peripheral trench was considered using simplified numerical modeling. The proposed 3D, numerical model, taking soil-structure interaction into account, is used to analyze the effect of a peripheral trench around buildings qualitatively and quantitatively, in order to reduce possible damage caused by ground movement (for example due to failure of underground cavities).

Only compression horizontal strains have been studied. From these preliminary numerical results, it appears that the main effect of the trench is to reduce the horizontal strain transferred to the structure. This parametric study focused on the impact of mechanical properties (both strength and stiffness) of the material used to fill the trench and the geometry of the trench, mainly its width, depth and distance from the structure.

It appears that most of the horizontal strain is absorbed by the trench and that its efficiency as a mitigation measure mainly depends on the stiffness of the material used to fill it. In that sense, maximum efficiency seems to be obtained for the limiting case of an empty trench, but in practice, the trench must be filled.

In addition, the efficiency is increased when the trench is wider, deeper and closer to the structure.

The main limitation of the proposed analysis is that it considers a plain slab as representing an entire structure. Only the total weight of a true structure was included. The actual stiffness and heterogeneity of the structure was neglected.

  1 INERIS : Institut National de l'Environnement industriel et des Risques 2 CSTB : Centre Scientifique et Technique des Bâtiments 3 PPRM stands for Plan for the Prevention of Mining Risks.

  has been implemented in Abaqus v6.7: a virtual square slab (10 m wide and 0.25 m thick) installed on a 50 m x 50 m wide, 10 m thick volume of soil. The surrounding trench is further introduced at a distance D from the structure, with depth H and width W. Reference values are first considered: D=1 m, H=1 m and W=0.5 m.

Fig. 1 .

 1 Fig. 1. Geometry of the model, U 0 is the uniform horizontal displacement applied to the left boundary of the model

Fig. 3 .

 3 Fig. 3. Profiles localization used for the analysis

  Origin of the X, Y and Z axis 1: profile in the ground A: profile in the structure base Slab maximum element size :0.125 m Soil maximum element size :2.5 m

Fig. 4 .

 4 Fig. 4. Horizontal strain and stress profiles along sections 1, 2 and 3: greenfield case, without and with the trench (trenches appear as grayed areas)

Fig. 5 .

 5 Fig. 5. Strain İ xx in section 1 and 2 with different levels of cohesion c (trenches appear in grayed areas)

Fig. 6 .

 6 Fig.6. Effect of the distance D on the distribution of İxx in a vertical direction (section 3)

Fig. 7 .

 7 Fig.7. Effect of depth H on the distribution of İ xx in the transverse direction

Table 1 . Properties of the ground and structure Density (kg/m 3 ) Young's modulus E (MPa) Poisson's modulus Ȟ Friction angle M Ҟ (°)җ Dilatation angle \ ҏ Ҟ (°) Cohesion c (MPa)

 1

	Ground	2000	100	0.3	30°	15°	0.1
	Slab	10,000	30,000	0.3	-	-	-
	Trench
	filling	1500	5	0.4	35°	15°	0.04
	material

Table 2 .

 2 Properties of the ground/ trench and ground/slab interfaces Fig.2. Mesh used in the numerical simulations

Table 3 .

 3 Comparison of the efficiency of the filling material

		Empty trench	c=40 kPa E=5 MPa	c=0.01 kPa E=5 MPa	c=40 kPa E=10 MPa
		Left Trench	Right Trench	L	R	L	R	L	R
	Trench closure (cm)	3.75	3.60	2.13	2.08	2.86	2.36	1.45	1.35
	Average strain within the trench (%)	7.5	7.2	4.3	4.2	5.7	4.7	2.9	2.7
	Average İ xx in section 1 between trenches (%)	0.28		0.41		0.38		0.46
	Reduction of İ xx (x=-6 m
	and +6 m) due to the	50 %		27 %		32 %		18 %
	trench*

Table 4 .

 4 Comparison of the different trench configurations

					D=1 m		D=1.5 m	D=1 m		D=1 m
			Empty trench	H=1 m		H=1 m		H=0.5 m	H=1 m
					W=0.5 m	W=0.5 m	W=0.5 m	W=0.8 m
			Left Trench	Right Trench	L	R	L	R	L	R	L	R
	Closure (cm)	3.75	3.60	2.13	2.08	2.12	2.15	1.59	1.69	2.79	2.80
	Average strain
	within	the	7.5	7.2	4.3	4.2	4.25	4.3	3.2	3.4	3.5	3.5
	trench (%)
	Average İ xx in
	section between	1	0.28		0.41		0.43		0.46		0.37
	trenches (%)
	Reduction of
	İ xx due to the	50 %		27 %		25%		18%		34%
	trench*

Further analysis will consider a more detailed model of a simple structure (with walls, roof and apertures) resting on shallow foundations (square or strip foundations) embedded in the soil (the depth of the trench being in that case based on the depth of the foundation).


Farid Laouafa

Gilles Armand

Jean-Bernard B Kazmierczak

Tatiana Maison

Finite element analysis of the Meuse Haute-Marne underground research laboratory

INTRODUCTION

The Meuse/Haute-Marne Underground Research Laboratory (URL) is located on the eastern boundary of the Paris basin, at the border of the Champagne-Ardenne and Lorraine regions, at Bure. The French national radioactive waste management agency (Andra) (Andra 2005a,b) started to build this URL in the year 2000 in order to demonstrate the feasibility of a radioactive waste repository in claystone formation [START_REF] Piguet | French Underground Research Laboratory -Construction and experimental programme[END_REF]. The host formation consists of claystone (Callovo-Oxfordian argillaceous stone) layer, 130 m thick lying at a depth of approximately 500 meters (middle of the layer) [START_REF] Maison | Dossier 2005, synthesis, Evaluation of the feasibility of a geological disposal in an argillaceous formation[END_REF]. The Callovo-Oxfordian clays are overlain and underlain by poorly permeable carbonate formations. The objectives of the URL during the 2000 -2006 period were mainly in-situ characterization of the physical and chemical properties of this rock. This involved achieving a level of knowledge that may be used to develop disposal designs and perform safety studies. The confining properties of the clay were studied through in-situ hydrogeological experiments, chemical measurements and diffusion analyses. An understanding of the fundamental physical and chemical properties and processes that govern geological isolation in clay-rich ABSTRACT: The Meuse/Haute-Marne Underground Research Laboratory (ANDRA) has been excavated to study the feasibility of a deep underground repository in the Callovo-Oxfordian argillite. The laboratory, lying at depth between 420 m and 550 m, has a complex structure due to the shape and location of various shafts and drifts. The purpose of this study is to analyse the mechanical behaviour of rock due to the excavation process, and the mechanical interaction between drifts and shafts during the excavation steps. Numerical analysis, which considers the geometry and excavation sequence of the Underground Research Laboratory (URL), is carried out using a finite element model having 2.5 million degrees of freedom with relatively simple constitutive equations describing the argillite's behaviour. The main interest of such large-scale modelling is to analyse the evolution of various mechanical fields during excavation progress. Indeed, comparisons between 2D and 3D analysis are performed and show that the 2D-plane strains assumption is no longer fulfilled in some areas of the laboratory. The results of the analysis are used to highlight areas where interaction between drifts and/or shafts is important. It is helpful to restrict the field of the analyses using some relevant criterion or appropriate boundary conditions, to perform the numerical simulations based on a more realistic elasto-visco-plastic constitutive model for rocks.

rocks has been acquired (Delay et al 2007a). This knowledge includes both the host rocks at the laboratory site and the regional geological context.

Another aspect of the research program was to demonstrate that the construction and operation of a geological disposal will not create pathways which allow radionuclide migration. This study involved a deep understanding of the hydro-mechanical behavior and of building impacts (the excavation-damaged zone, for instance). That is why the construction of the laboratory itself serves a research purpose by way of in situ monitoring of the excavation effects and for the optimization of construction technology.

The underground components of the laboratory consist of two shafts and several drifts constructed for scientific and technical purposes. As the in situ stress field is anisotropic, the drift network has been excavated in order to investigate hydromechanical drift behavior in the direction of both principal stresses. This means that, in order to meet the geomechanical issues, experiments are performed in drift parallel and/or perpendicular to the major horizontal stress. The whole of the laboratory is mainly located in a volume of several million cubic meters in the Callovo-Oxfordian layer.

Several numerical modeling has already been done in order to predict and analyze the insitu measurements, mainly the time evolution of strains and pore pressures. However, most of the numerical models usually focused on the specific area where instrumented boreholes have been located. The following two questions could be asked: Is it relevant or necessary to understand the effect of this drift network on stress distribution and accurately evaluate the stress state at the URL main level? And secondly: during a stage-by-stage construction of the different drifts, can we measure the mechanical interaction between drifts and their intensity? Andra started a new research program which requires an expanse of the URL drifts. New drifts will be excavated for new scientific analyses [START_REF] Delay | The Meuse Haute Marne underground research laboratory: seven years of scientific investigations[END_REF]. What effect will these new excavations have on the existing drifts? On the other hand, is it possible to situate experiments in areas where we are sure that the stress field has not been disturbed by the previous excavation works? Nowadays computers with larger memory and faster processors, make it feasible to study larger computational models.

This paper presents, in the first part, some modeling results of a 3D study performed to analyze the mechanical behavior of all of the drifts in the Callovo-Oxfodien layer by using a chronological evolution (time stepping) of the excavations, close to what was realized in reality. In the second part, we performed a comparison of some fields arising from the 3D computations to those resulting from a 2D plane strain assumption. These comparisons are performed for several vertical planes of the URL. We clearly show that the 2D assumption is no longer valid. Let us emphasize that this comparison is performed in a purely mechanical framework (no thermal or hydraulic coupling).

The 3D elastic or elastoplastic modeling is, in our opinion, interesting, because as it is commonly performed in monitored in situ field, the numerical results provide information on the more disrupted area and one can then conduct a more accurate analysis, involving more realistic physical laws, in restricted areas which noticeably reduce computation times.

Considering the size and the complex geometry of the problem, the analyses are carried out by finite elements with relatively simple constitutive models describing the argillites' mechanical behavior. Finally, we discuss the scientific contribution of such huge computations and provide some recommendations for future work.

GENERAL DESIGN

The underground installations consist of two shafts and drift networks (Delay et al (2007 b). The main shaft, 5 meters in diameter after lining, grants access to a 445 meter deep drift network and to the 490 meter deep main drift network. The auxiliary shaft, 4 meters in diameter after lining, is also connected to the URL's main level. Drifts have a "horse shoe" cross section. The drift network at 445 m is 45-meter long and T-shaped. This experimental zone has been equipped to perform monitoring of a mine by testing during shaft sinking. These drifts are 17 m 2 in section. At the main level located at 490 m, the network consists of experimental and technical drifts. By mid 2007, this network was 485 meter-long, out of which 80 meters are dedicated to experiments. The orientation of the scientific drifts has been determined according to the orientation of in situ stress fields (Wileveau et al., 2007a). The current section of the drifts is 17 m 2 ; however, some technical zones have been excavated in different diameters, up to 40 m 2 .

Drift excavation methods depended on the nature of the rock mass they passed through. A drill-and-blast technique was used to excavate the 445 meter-deep drift. Rock bolts were set in place after blasting. Support consists of rock bolts and sliding arches. A concrete raft was installed to facilitate displacements.

At the main level, a stone crushing technique was used for excavation. Bolts and sliding arches were set in place immediately following a two-meter maximum progression. At minimum, a 10 cm-thick layer of concrete was applied on all of the drift walls to limit the spalling induced by drift convergence.

Construction of the underground installations started in August 2000 with the sinking of the main shaft and was completed on 27 April 2006, when it linked up with the southern drift of the laboratory. Equipment of the laboratory was completed in July 2007 with the installation of the hydraulic and electrical networks. This sums up the main stages of the laboratory construction.

The geometrical model takes the drift and shafts in the Callovo-Oxfordien layer into account. In order to take the excavation evolution versus time into account, the numerical excavation was performed in 26 steps based on monthly excavation rates actually performed in situ. In the experimental area, formed by GLE, GKE, GMR and GEX drifts (Fig. 1), the time stepping was reduced to weeks to better analyze interference between those drifts in the area where sensors have been placed.

Scientific actions were carried out concurrently with the sinking and excavating. They consisted of a systematic geological mapping, closure measurements and drilling of boreholes to measure pore pressure and displacement [START_REF] Delay | The Meuse Haute Marne underground research laboratory: seven years of scientific investigations[END_REF].

3D FINITE ELEMENT COMPUTATIONS

Assumptions

The main difficulties of the 3D and time stepping analysis lie in the construction of the complex geometry of the network of galleries and the associated mesh. The entirety of the galleries and wells of the URL is shown at the level of the Callovo-Oxfordien (Fig. 2). One of the main difficulties of this 3D and time stepping analysis lies in the construction of the geometry of the network of galleries and the associated mesh. The geometric shape of the different galleries, the wells, as well as their arrangement and their intersection generates an extremely complex geometry. The entirety of the galleries and wells of the URL is shown at the level of the Callovo-Oxfordien (Fig. 2). The exact geometry is defined in the section above. The finite element mesh is made up of 603,325 quadratic tetrahedrons, which leads to a number of degree of freedom equal to 2,452,635. The kinematical boundary conditions are imposed on all vertical boundaries and on the bottom of the model as follows: 0 U n . This defines five planes of symmetry (n is the outward unit normal to these boundaries). The only boundary tractions are applied on the top of the model and are equal to ( , , 150 ) ( , , ) (0, 0, 9.95 MPa)

x y z t x y z m t t t t { , assuming a constant density J of 25 kN/m 3 . In terms of initial conditions, three assumptions are made: (i) the initial stress is principal in the reference frame: 0, ij i j V z , (ii) at any point of the domain, the initial stress state is anisotropic and characterized by two coefficients Kox and Koy and (iii) at any point of the domain, the vertical stress zz V is equal to the weight of the overburden soil. Thus the initial anisotropic stress field is defined as follows:

9.95-150

xx zz yy zz zz Z Kox Koy V V V V V Ju u ° u ® ° ¯where (0) 1.3 (0) yy zz Koy V V and (0) 1 (0) yy zz Kox V V (1)

Constitutive models

The analysis of the 3D study was performed by successively using two constitutive models. The first assumes linear isotropic elastic models for the different soil layers. The second analysis was performed using a simple elastic-perfectly plastic model. In this case we adopted a modified Drucker-Prager yield surface ( ) F V . This yield surface passed through the inner vertex of the Mohr-Coulomb yield surface and is stated as follows [START_REF] Lubliner | Plasticity Theory[END_REF]: At this stage we may observes that for the purely elastic problems (linear problems), there was no risk of loss of ellipticity (Marsden, 1983) because the analysis is performed under the small strains hypothesis, and that the constitutive operator is positive definite in all material points of the domain. In light of the structures of the different networks of galleries, and of the "massive" structure of the model, all bifurcation problems, such buckling or others, can be excluded [START_REF] Hill | A general theory of uniqueness and stability in elastic plastic solids[END_REF][START_REF] Rudnicki | Conditions for localization of deformation in pressure sensitive dilatant material[END_REF]). However, one can expect stress concentrations with very high intensity, and unrealistic, notably at the level of the corners and of some intersections. These singularities have no effect on the solution in the elastic computation because their influence decreased very quickly, as soon as one moves away from it. This is not the case for the nonlinear analysis, for which precautions are taken in the results analysis. Let us stress that in light of the number of degrees of freedom, we choose an iterative algorithm to resolve the linear or linearized problem. We utilized the preconditioned GMRES algorithm [START_REF] Saad | GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems[END_REF] that showed itself to be more robust than the preconditioned conjugate gradient. As soon as the initial and boundary conditions were assigned, 26 excavation steps were performed inside the different layers, where each one corresponds roughly to a monthly excavation step.

3D numerical results

Figures 4, 5 and 6 depict the disrupted area in terms of displacement. As we can see, the disrupted zone remains close to drifts and wells. The greater displacements (amplitude varying from 5 mm to 4 cm) are measured on the boundaries of the galleries. In Figure 7, we show an example of the time (excavation step) evolution of stress and displacement components of point A (Fig. 3). It is interesting to note that no component remains constant and that the stress and displacement norms at the (y-z) plane (plane for plane strain analysis) evolve non-uniformly. This point will be discussed in the next section. In Figure 8 we show, on the left, the monitoring of relative vertical displacement between the drift located at a depth equal to 447 meters and five points distributed vertically above in the soil within the limit of 20 meters. The measured relative displacement is from 0.51 mm to 1.05 mm. The computational relative displacement obtained from the graph of Figure 12 (right) gives a relative displacement from 0.5 mm to 1 mm, thus in very good agreement with the measured variable. Just note that this agreement is observed far away from the drift in an area where the rock behavior is nearly elastic. In the vicinity of the drift, those calculations cannot provide an accurate estimate of relative displacement. At the main level of the URL, geological mapping of the front faces and structural analysis on the drill core exhibit a fracture pattern around the drift showing the occurrence of non-elastic deformations.

3D VS. PLANE STRAIN FINITE ELEMENT COMPUTATIONS

The figure below indicates the different planes of the 2D analyses. Five planes passing through lines 1, 2 , 3, 4 and 6 are considered. We observe that the component of the stress tensor and displacement vector can be significantly different, which confirms that the plane strain assumption can be a strong hypothesis. Furthermore, we observe the mechanical influence of the shafts which disrupt the two mechanical fields. In Figure 9 we have depicted the location of different points and lines where a more accurate analysis was performed, in particular in term of stress, strain and displacement distribution and "time-excavation step" evolution. While the evolution of vertical displacement for the different points seems smooth and quite similar, the evolution of the vertical stress clearly shows the influence or contribution of the two orthogonal excavations. Indeed, points and E are the closest to the drift intersection, and are both subjected to mechanical perturbations. The fact that this perturbation is less significant in the displacement field is linked to the fact that the stress or strain distribution is in 0 2 2 ( / ) O r r and then, the decreasing rate is of the order of 2, which means the stress or the stress perturbation decreases more quickly and affects a more restricted area.

Note that the same observations are made for the all of the points. The question of the usefulness of such purely mechanical 3D computations may be posed. Are plane strain or plane stress assumptions acceptable? The answer is clearly no, in some obvious zones, where the problem is locally really 3D. Elsewhere these assumptions could perhaps be accurate enough, in comparison with the many uncertainties. In order to answer to the question posed above, we analyze the results depicted in Figure 14. The red circles correspond to the last step, while the blue ones correspond to the first step of excavation. This line is chosen because it is far enough from its parallel drift and it is orthogonal to two excavated zones. In terms of x U , we observe no constant distribution, except at the beginning of the excavation phase (the excavated zones are too far from this line). This graph demonstrates the "non-validity" of a plane strain assumption. The same remarks are made in terms of stress. We also observe no constant distribution, except at the beginning of the excavation phase (the excavated zones are too far from this line). This graph demonstrates the "non-validity" of a plane stress assumption. The sentence "non-validity" is between quotes to put our conclusion into context.

CONCLUDING REMARKS

We have briefly presented the 3D mechanical analysis of the Andra laboratory composed of several drifts and shafts and a comparison with computations based on a plane strain assumption. The mechanical behavior of such an underground structure has been investigated by the way of step-by-step, "huge" finite element computations. The aim of this work is to analyze the various mechanical interactions between the different components of the laboratory and to analyze their "time" evolution during the excavation. The relevance of such huge three-dimensional modeling is twofold. The first aspect of this relevance is that the adopted approach provides several of information, namely on the spatial distribution and time evolution of the different mechanical fields (stress, strain and displacement).

Secondly, we have some measurements on the extension of perturbations induced by the different excavations, and the eventual interaction between the components of the laboratory. Such an analysis is difficult to circumvent, since the development of the laboratory evolves without any spatial or mechanical symmetry. This fact is demonstrated by several comparisons with purely mechanical 2D analyses. Although the constitutive models are relatively simple, such analysis provides interesting information and could be useful for a more accurate future analysis (coupling processes, creep model for instance). Let us underline that with such a simple model, the numerical results provide the correct trend observed in situ in terms of displacement.

Fig. 1 .

 1 Fig. 1. General view of the Meuse Haute Marne Underground research laboratory (mid to late 2006)

Fig. 2 .

 2 Fig. 2. From left to right: part of geometrical model, mesh of the domain and detail of gallery and wells

Fig. 3 .

 3 Fig. 3. Reference frame (left) and lines (planes) and points of analysis (right)

J

  first invariant of the stress tensor while ' 2 is the second invariant of the deviatoric stress tensor. The parameters C and I are the cohesion and the internal friction angle, respectively. Our geometric model contains three rocks layers. The different parameters are provided in the following tables 1 and 2.

Fig. 4 .

 4 Fig. 4. 3D view of the disrupted area in terms of displacement at the end of excavation process

Fig. 6 .

 6 Fig. 6. Example of isovalues of the Euclidean displacement norm in the horizontal plane passing through the middle of the laboratory on the left. Isovalues of the Euclidean displacement norm in the boundaries of the different shafts and drifts.

Fig. 7 .

 7 Fig. 7. Example of evolution of stress and displacement components during excavation process

Fig. 8 .

 8 Fig. 8. Relative displacement monitoring in situ (left) during two months and computational total displacement for the 26 steps.

Fig. 9 .

 9 Fig. 9. Spatial location of the plane used in plane strains analyses

Fig. 13 :

 13 Fig.13: Evolution of vertical displacement (left) and vertical stress (right) at different material points.

Fig 14 .

 14 Fig 14. "Time" evolution and space distribution of horizontal x U displacement (left) and horizontal stress xx V

Table 1 .

 1 Elastic parameters for the three rock layers

	Parameter		Value
	Layer 1 -Young modulus E 1	5400 MPa
	Layer 2 -Young modulus E 2	4500 MPa
	Layer 3 -Young modulus E3	4500 MPa
	Poisson coefficient Q		0.3
	Table 2. Plastic parameters for the three rock layers
	Parameter	Layer 1	Layer 2	Layer 3
	Cohesion C (MPa)	4	4	4
	Cutting traction strength (MPa) 2.6	2.6	2.6
	Friction angle (°)	23	23


INERIS Christophe Didier

N Van Der Merwe

M Betournay

Mark Mainz

O Aydan

A Kotyrba

W K Song

Jean-Pierre Josien

Nielen Van Der Merwe

Marc Bétournay

Presentation of the ISRM mine closure state of the art report

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

INTRODUCTION

Commission constitution and objectives

The mine closure Commission has been appointed with two main objectives. The first one was to facilitate contacts between experts in rock mechanics from different countries concerned with post mining management in order to create opportunities to exchange experiences, case studies and scientific data.

The second objective of the commission was to produce a reference document, presenting the international "state-of-the-art" for existing techniques and methods enabling identification, characterisation and management of geotechnical hazards related to mine closure processes [START_REF] Didier | Mine Closure and Post-Mining Management[END_REF].

An expert panel has thus been constituted to produce the document. All the members that joined the commission got involved on a strictly voluntary basis and gave considerably of their time and their expertise to the benefit of the commission work. They are listed below:

The document contains 7 sections and 3 appendices. After a brief presentation of the mine closure context, at an international scale, the document describes precisely the most frequent geomechanical hazards that may develop above an abandoned mine. In addition to the description of consequences and potential effects on people and surface structures, the basic mechanisms that may initiate the failure are discussed.

The commonly used hazard assessment methods are then described, with particular attention to the key factors that have to be taken into account in the assessment process. Classical post-mining risk management methods are then discussed: voids treatment, monitoring methods and land use management. Specific references are included at the end of each section and a large recommended additional literature is also given.

Numerous figures/photographs illustrate the document to make it clear and understandable, for both mining experts and non specialists.

NATURE OF GEOMECHANICAL HAZARDS

Many kinds of disorders may affect an abandoned mine, some of them specific to underground mine workings, others to abandoned open pit mines. The report describes all those phenomena, describing for each one, which kind of mechanism may be the generator one (depending on the geological and mining context). As an illustration, three typical phenomena that can develop above underground mine workings are presented below.

Continuous subsidence

Continuous subsidence is characterised by a usually slow, smooth and flexible re-adjustment of surface. In most cases, the maximum amplitudes observed in the centre of the depression are decimetric to metric [START_REF] Kratzsch | Mining Subsidence Engineering[END_REF][START_REF] Peng | Surface Subsidence Engineering[END_REF].

Generally, it is not so much vertical displacements which affect surface buildings and infrastructures, but ground deformation (NCB, 1975). Depending on its position in the subsidence depression (Figure 1), differential horizontal displacement may take the form of shortening (compression zone -inside depression) or extension (tensile zones -outside depression).

Maximum vertical movement

Extensive area

Compressive area

Maximal dip effect

Figure 1: Effects of continuous subsidence on structures.

Continuous subsidence classically develops during mining extraction above panels mined by total extraction methods (e.g. longwall methods). It may also affect areas mined by partial extraction methods (e.g. room and abandoned pillars), when the mine workings fail after closure.

Sinkholes

A sinkhole is characterised by a sudden appearance of a collapse crater at surface [START_REF] Piggott | Ground movements arising from the presence of shallow abandoned mine workings[END_REF]. The instability extent varies usually from a few metres to several tens of metres in diameter.

The dimensions of the crater and suddenness of its development on surface make sinkholes potentially dangerous events, particularly when they develop in or close to urban sectors or infrastructures (Figure 2). Sinkholes result in the progressive failure of the hanging-wall, a dome-shape propagating towards the surface if there are no resistant layers to stop the mechanism.

Massive discontinuous subsidence

Massive discontinuous subsidence events are caused by dynamic failure of all or part of the mine workings. They may affect surface stability over several hectares. On the opposite of continuous subsidence, in a discontinuous event, the central trough is edged with open, sub-vertical cracks, marking out "steps", which can generate severe damage to people and property Those kinds of events (Figure 3) denote a general instability of the mining works, usually due to an excessive extraction. Fortunately, these events are very rare but the consequences are potentially serious.

Contrary to sinkholes, massive discontinuous subsidence events may concern relatively deep mines. Their occurrence also requires adequate horizontal extension relative to their depth.

HAZARD ASSESSMENT METHODS

A hazard is defined by the probability of occurrence and foreseeable magnitude of an event at a specific location. The probability of occurrence, reflecting the site's sensitivity subject to an instability, is generally more difficult to quantify than the magnitude. No matter what type of events are feared, the complexity of the mechanisms involved, the heterogeneous environment and the incomplete available data often make it very difficult to assess quantitative probabilities.

Priority is therefore often given to qualitative "predisposition" of a site subject to a particular damage. Evaluation of this predisposition depends on the combination of different factors, which are favourable or unfavourable to the initiation and development of a given mechanism.

Some mine closure context specifies may strongly influence the choice of the best adapted hazard assessment method. Experts have to face the "collective memory loss syndrome" which contributes to the difficulty of data collection and to the choice of assessment methods adapted to very partial knowledge of the mining context as well as the environment (e.g. geology, hydrogeology).

Selection of adapted hazard assessment methods

A large variety of methods can contribute to evaluate, characterise and describe post-mining hazards [START_REF] Bétournay | Canadian Manual for Metal Mine Shallow Stope Decommissioning[END_REF][START_REF] Ineris | L'élaboration des Plans de Prévention des Risques Miniers[END_REF]Deutsche Gesellschaft für Geotechnik, 2004). Some of them are explicit, others implicit; some combine qualitative data, others require qualitative values. The choice of the best adapted method will depend on several parameters, some of them being discussed below.

Economic consideration

The future surface utilisation is usually the most important parameter in the choice of the assessment method. Important investments to collect data (investigation) and use precise quantitative assessment method (e.g. numerical modelling) are generally restricted to dense surface occupation areas.

Typology of phenomenon The type of suspected phenomenon may influence the assessment method. For sinkhole prediction, simple analytical approaches are recommended. For risk evaluation of massive collapses, large scale numerical models are, on the contrary, often needed.

Amount of available data When few data are available, qualitative methods may be used, taking benefit of expert judgement. On the contrary, when lot of data are available (very large mining field with different mining methods and contexts), one will consider the application of the decision-making aid methods.

Principal stages of a hazard assessment process

The first (if not the only) stage of the assessment is a desk study. This step aims to gather existing data and applicable knowledge from which pertinent engineering information can be extracted and used in order to identify and evaluate the hazard. The aim is to locate and review, in detail, potential impacts of the abandoned mine, to identify the potential hazards. At this stage the information that are required but missing should be identified.

Complementary to the desk study, a detailed inspection of the mining site is generally strongly recommended. Whatever the accessibility of the mine workings, the knowledge and understanding of the site and its history provide to experts a satisfactory degree of accuracy for the hazard assessment process.

In the case of very old mine workings (serious lack of data), if the surface occupation is very sensitive to potential disorders (urban environment, important infrastructure), complementary information may be necessary. Field complementary investigation works have then to be performed. Numerous investigation techniques exist; the most suitable ones will depend on the objectives, the kind of requested data as well as the time and budget available.

Among the most classical investigation techniques used, one may quote: drilling (diamond or destructive, with possible geophysical survey) and geophysical methods (gravimetric, seismic, electro-resistivity, electromagnetic).

A specific appendix of the report is dedicated to the main geophysical methods adapted to locate disused mine workings (Figure 4).

Factors influencing hazard predisposition

The rock mass failure that induces instabilities on surface may be affected by several influences. Influence of time Time is a fundamental factor, which must be integrated in the hazard assessment process (Van der Merwe, 2003). The phenomena observed nowadays often occur for mine workings having several tens of years of existence, and sometimes more than one century. Several mechanisms must thus be taken into account to evaluate the effect of time on mechanical stability (creep effect, ageing effect, long term evolution of fracturing).

Influence of water Mine closure is very frequently accompanied by a progressive flooding of underground mine workings. The effect of water on rock mass is difficult to quantify because there are plausible arguments for both beneficial and damaging effects. The balance of these effects determines whether flooding is stabilising or detrimental in a given condition (e.g. nature of rocks, mining methods). Among those effects, one may quote: strength drop (water sensitive rocks) and stress modification (effect of water pressure).

Influence of geology and mining methods Geological configuration of the deposit (e.g. sedimentary flat layers, vein deposits) as well as rock mass properties may strongly influence the nature and the magnitude of the potential surface disorders. The presence of a "stiff" horizon in the hanging-wall may for example contribute to increased risk of violent collapse of the overburden [START_REF] Didier | Importance of failure mechanisms for management of surface instability risk above abandoned mines. 10 th Congress of the ISRM[END_REF].

The nature of potential disorders is also strongly related to the mining configuration. Mining methods ensuring a systematic treatment of the mining voids and mining methods leaving behind large residual voids will evolve very differently in time, the most severe disorders being specific to the partial extraction methods.

HAZARD MANAGEMENT METHODS

When hazard has been assessed and located, depending on the type of surface occupation, several kinds of management methods may be considered. Among the numerous ones developed in the ISRM report, three of them will be briefly presented below.

Backfilling

Quite often, where harmful consequences of subsidence are expected on surface in inhabited areas, the most efficient and sustainable protection is assured by backfilling of underground works (Figure 5). Different backfilling methods may be used (Hydraulic, Pneumatic, hand packing, both from underground or from the surface). The choice of the most adapted process will depend on the site context.

Land use Management and Regulation

When, for technical or economical reasons, it appears irrelevant to treat existing mine workings by backfilling or grouting, it is of major importance to properly manage land use of undermined sectors. Two approaches may then be complementary: a preventive one that consists in defining regulatory measures to avoid or reduce risky situations and a curative approach that consists in managing existing goods subjected to high risk (evacuation, reinforcement).

As an example of land use regulation procedure, the ISRM report presents an overview of the French "Mining Risk Prevention Plans". The scope of MRPP is to identify post-mining risk exposed zones and to elaborate instructions to be applied for existing and future property and activities in those areas [START_REF] Didier | MRPP -The French Prevention Procedure to Manage Post-Mining Hazards[END_REF].

Monitoring

When serious hazards have been identified in areas where sensitive structures are already located on surface, if voids treatment is technically difficult and/or too expensive, monitoring may be an interesting alternative.

Monitoring does not eliminate risk. It is designed and implemented to manage the risk in collecting "earlywarning data" that enables one to take decisions before the mine workings failure. The main objective is thus to avoid accidents in taking appropriate measures in advance (treatment, evacuation).

There are many kinds of monitoring processes; the best adopted one depending on the site characteristics. The most simple and classical monitoring consists in regular visual monitoring performed by experts visiting accessible mine workings. To collect more quantitative data (including kinetics evolution), one may use instrumental monitoring. This consists in installing sensors (e.g. extensometers, inclinometers) in potentially unstable mining sectors in order to monitor ground movements and their evolution in time.

Some innovative monitoring techniques have been developed to enable "large scale" monitoring. The objective is to allow detection of early-warning signals within a large rock mass volume and a limited number of sensors. Among those promising techniques, one may quote: micro-seismic monitoring (Figure 6), Time Domain Reflectometry (TDR) monitoring, Interferometric Synthetic Aperture Radar (InSAR) Technique.

PERSPECTIVES

The mine closure and post-mining management state-ofthe-art report concludes the first step of on-going work of the mine closure commission. The "version 1" of the report is now available through the ISRM website (www.isrm.net). The document will be completed. The ISRM members are thus strongly encouraged to download the report and transmit to the president or members of the commission, their suggestions to improve the document. The contributions will be welcome (e.g. complementary references, technical modifications, illustrations) and will be considered in a further edition of the document.

The members of the mine closure commission are motivated to continue and finalise the work already accomplished. The commission will thus probably be reappointed for a second mandate. The objective is to prepare a reference publication that will enlarge and complete the report available.

This will notably consist in the extension of the international post mining context to major mining countries that have not yet been represented in the commission (e.g. Australia, China, India, United States; Russia, Brasil). It will also include a compilation of several well documented "case studies" of successful mine closure examples, properly managed in different contexts (e.g. countries, type of mining methods, treatment or monitoring).

An enlargement of the commission to the previously listed countries is thus envisaged in the coming months. The commission plans to finalise the publication for the XII th International Congress of the ISRM that will be held in 2011 in Beijing.

Figure 2 :

 2 Figure 2: Sinkhole having caused a fatality within a French urban area (source CETE/MEEDDAT).. Sinkholes develop above mining sectors where residual voids are present underground. This phenomenon is generally restricted to shallow mine workings (often less than 50 m deep even if there are exceptions).Sinkholes result in the progressive failure of the hanging-wall, a dome-shape propagating towards the surface if there are no resistant layers to stop the mechanism.

Figure 3 :

 3 Figure 3: Massive discontinuous subsidence associated with vertical cracks above a French chalk mine.

Figure 4 :

 4 Figure 4: Models of resistivity distribution over abandoned silver mine galleries in Poland.

Figure 5 :

 5 Figure 5: Injected paste in an abandoned Slovenian Mercury mine (By courtesy of Bojan Rezùn).

Figure 6 .

 6 Figure 6. Illustration of a microseismic monitoring network managed by INERIS above an abandoned mine.