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This thesis presents numerical and analytical investigation of the geomechanics underlying longwall mining. It was tried out to study the disturbances induced by longwall mining in nearby rocks and their influence on the stability of the gates, pillars and main tunnels of longwall mines. The thesis consists of two major parts: numerical and analytical investigations. The study site is the Svea Nord coalmine, Svalbard, Norway. A novel algorithm was proposed for numerical simulation of the longwall mining process. In the proposed algorithm progressive cave-in and fracturing of the roof strata, consolidation of the cave-in materials and stress changes are simulated in detail. In order to outline the caved-in roof rocks a criterion based on maximum principal strain (in tension) was used. The critical tensile strain of roof cave-in was determined through back-calculation of the surface subsidence above a longwall panel at the mine. The results of the simulations were then used to analyse stress changes induced by longwall mining and the stability of gates. The simulations revealed that the stability of the gates and the loading to the rock bolts are closely related to the width of the chain pillars. With slender pillars, shear displacements along weak interlayers and bedding planes result in heavy loading to the rock bolts. Therefore, the locations of weakness zones should be taken into account in rock bolt design. The developed algorithm was implemented to study the loading and stability of the barrier pillar of the mine. The barrier pillars protect the main tunnels and border area of the mine from disturbances induced by longwall mining in the panels. The simulations show that the stresses in the barrier pillars fluctuate up and down during mining because of periodic cave-in events behind the longwall face. A failure zone of about 12 m exists in the wall of the barrier pillars. A large portion of the barrier pillar is still intact and is, thus, capable of protecting the border area. The results of the detailed simulations of longwall mining via the developed algorithm were, also, implemented in a large-scale numerical model. The model consists of all of the longwall panels and the border area of the mine. It is intended that the coal in the border area on the other side of the longwall panels will be mined after completion of the longwall mining. There is concern about how the longwall mining affects the stress state in the border area and how stress changes would affect future mining in the border area. A failure zone of about 20 m developed in the wall of the main tunnels on the side of the border area after all the longwall panels were mined out. The stress state in the remaining portion of the border area remains unchanged. Therefore, it will be possible to mine the border area in the future. In order to investigate the roof strata cave-in mechanism in detail a discontinuous numerical simulation of roof cave-in process was conducted by UDEC code. The block size in the roof strata and the mechanical parameters of the discontinuities were obtained through back-calculations. The back-calculations were conducted with a statistical method, Design of Experiment (DOE). Numerical simulations revealed that jointed voussoir beams formed in the roof strata before the first cave-in. Beam bending results in stress fluctuations in the roof strata. The maximum deflection of a roof stratum at the study site before the first cave-in is about 70% of the stratum thickness. The simulations and field measurements show no periodic weighting on the longwall shields in this mine. Numerical sensitivity analyses show, however, that periodic weighting may occur in strong roof strata. Roof strata with a high Young’s modulus and large joint spacing are not suitable for longwall mining. The maximum sustainable deflection of the roof strata before cave-in depends upon the horizontal in-situ stress state. It slightly increases with the in-situ horizontal stress in the stratum beams, but the horizontal stress would increase the possibility of rock-crushing in deflected roof beams. The implemented numerical method would be useful in assessment of the cavability of the roof strata and in selection of longwall shields with adequate load capacity. As shown through discontinuous numerical simulations, the roof strata above the underground opening constructed in the stratified rocks form voussoir beams. The stability of those beams is the major concern in the study of the gate stability and roof cave-in assessment in the longwall panels. Two different analytical methods were developed for cases with and without the in-situ horizontal stress acting along the beams. In the analytical model for the beams without horizontal stress a bilinear shape was assumed for the compression arch generated within the voussoir beams. The stability of the compression arch is governed by the energy method. The model requires an iterative procedure for convergence, and an algorithm was proposed for it. The analytical method was verified with numerical simulations by means of a discrete element code, UDEC. For the beams subjected to in-situ horizontal stress, the classic beam theory was employed to drive the analytical solution for it. The superposition method was used to obtain bending/deflection equations of the beam. The validity of both the assumptions and the developed method were, also, investigated by numerical simulations. The developed analytical method revealed that high Young’s modulus of a beam rock increases the stability of the beams against buckling but it causes higher stress within the compression arch which increases the probability of crushing failures in the beam abutments and midspan. In-situ horizontal stress along beams increases their stability against buckling and abutment sliding failure, but it raises the possibility of crushing failure at the abutments and the midspan.

Travail sur un point important de la construction des ponts : le comportement des bossages d'ancrage de câbles de précontrainte. Le travail théorique prend comme point de départ une recherche très poussée du LCPC du point de vue du calcul élastique, qui comportait une étude expérimentale d'un ancrage par bossage centré dans une plaque appuyée sur la tranche à un about. La thèse se limite à la sollicitation du hourdis par suite de l'application d'une force de précontrainte au moyen d'un bossage (ou de plusieurs). Utilisation de la méthode des coupures modifiée pour une analyse élastique et mise au point d'un programme aux éléments finis non linéaires pour l'analyse non linéaire du comportement à la rupture. Étude expérimentale du groupement des bossages.

L’Agence nationale pour la gestion des déchets radioactifs (l’Andra) en France propose un nouveau type de voussoirs de tunnel pour les ouvrages très profonds. Pour éviter des segments de tunnel trop épais, ils proposent d’intégrer une couche de matériau granulaire sur l’extrados d’un voussoir moins épais. Cette approche prétend utiliser la grande compressilibité de la couche granulaire constituée de particules broyables et les transferts de charge interne au matériau granulaire pour réduire l’épaisseur du voussoir tout en gardant des performances mécaniques importantes. Un segment de tunnel avec une telle conception est appelé un VMC monobloc compressible (brevet en instance de l’Andra & CMC). Il s’agit d’un nouveau type de revêtement de tunnel particulièrement innovant.Cette thèse est consacrée à la création d’un modèle numérique capable de reproduire le comportement mécanique d’un couche granulaire très compressible à l’aide de la méthode aux éléments discrets (DEM) en 3D. Le milieu granulaire est constitué de particules d’argile cylindriques creuses appelées textitcoques. Chaque coque est un tube de 2 cm de long avec un diamètre de 2 cm. La faible épaisseur de la coque cylindrique la rend essentiellement constituée de vide entourée d’une fine couche d’argile. Dans le modèle, un cluster sécable (la coque) est généré à l’aide de clumps sphéro-polyédriques allon- gées . Ces clumps, appelés secteurs, sont associés entre eux en utilisant deux lois de contact adhésives. Si la combinaison des forces de contact normales et tangentielles satisfait un critère de charge spécifique, la coque se casse au niveau de l’interface entre les deux secteurs. L’outil DEM Rockable mis au point pour cette recherche peut fonctionner sur ces particules fragiles. Les propriétés mécaniques des coques, composé de 12 à 24 secteurs, sont ajustées à l’aide d’essais de compression radiale uniaxiale (verticale). Les expériences à l’échelle du grain sur les coques en argile cuite ont servi de référence. Nous avons déterminé la plage réelle de rupture et sa distribution statistique (Weibull). Les paramètres numériques et mécanique ainsi obtenus ont été validés avec succès dans le cas de la compression radiale d’une coque contrainte latéralement.Dans un premier temps, l’étude des assemblages de coques porte sur la caractérisation expérimen- tale des échantillons avec un controle sur les variables d’état initiales telles que la densité et l’orienta- tions des coques. La reconstruction 3D à partir de tomographies à rayons X d’échantillons de coques carottés dans l’extrados d’un voussoir nous a permis de caractériser l’anisotropie de l’orientation des particules. Il s’agit là d’une information précieuse pour la génération d’échantillons numériques ayant les caractéristiques initiales pertinentes. Deuxièmement, des simulations DEM de compressions oedo- métriques sur des échantillons de ⟨2 000⟩ coques sont réalisées. Une étude paramétrique permet de mettre en évidence le rôle des variables d’état initiales. Un ensemble bien choisi de variables initiales et des paramètres DEM correctement adaptés permettent d’obtenir des simulations prédictives pertinentes pour une comparaison avec les expériences de laboratoire. Une analyse micro-mécanique de l’effet de la proportion des grains cassés sur les contraintes locales exercées sur les coques (et les fragments) est effectuée. Il est observé que la rupture des coques entraîné une compressibilité élevée du matériau. Par conséquent, la réponse mécanique en déformation est considérée comme une conséquence directe de l’évolution de la rupture des particules. Pour finir, un modèle analytique de prédiction de la re- lation Contrainte↔Déformation est proposé dans le cas de la compression oedométrique. Ce modèle prédictif tient compte des variables internes du milieu granulaire comme la résistance mécanique en compression des coques. / The National Agency for Radioactive Waste Management (FR Andra) in France suggested a new way to design a tunnel lining, especially, beneficial in the case of very deep tunnels. To avoid very thick tunnel segments, they propose to integrate a layer of granular material on the extrados of the thinner lining. This approach takes the advantages of the compressible capacity of the crushable particles and the load transfer in the granular material. A tunnel segment with such design is called a Mono-block Compressible Arch-segment VMC (Andra’s & CMC’s pending patent) and is an innovative new type of tunnel linings.This PhD dissertation is dedicated to the creation of a numerical model capable of reproducing the mechanical behaviour of this compressible granular layer using 3D Discrete Element Method (DEM). The granular packing is made of the brittle hollow coarse-size cylindrical particles, called shells. Each shell is a 2 cm long tube with a diameter of 2 cm. Its small thickness makes the cylindrical shell mainly made of void surrounded by a thin layer of clay. In the model, a breakable cluster (shell) is generated using sphero-polyhedral elongated clumps. These clumps, called sectors, are glued together using two adhesive contact force laws. If the combination of the normal and tangential contact forces exceeds a suitable failure criterion, a de-clustering of the shell (breakage) occurs. The DEM tool Rockable devel- oped for this research can operate on such crushable particles. The mechanical properties of the shell model, composed of 12 to 24 sectors, are adjusted in the case of a uniaxial (vertical) radial compres- sion of shells. The preceding grain-scale experiments on the true shells made of baked clay serve as a reference. We determine the true range of the failure tensile load and its statistical Weibull distribu- tion. The user-specified parameters is then successfully validated in the case of radial compression of a horizontally constrained shell.Firstly, the macroscopic study of shell assemblies focuses on the experimental characterisation of the samples with a control of the initial state variables like a number density and a spatial arrangement of shells (shells orientations). 3D reconstruction from X-ray tomographies of the original coated shells samples extracted from the extrados of a tunnel segment help us to characterise the anisotropy of the shells orientation. This is a piece of valuable information to the generation the numerical samples of shells with relevant initial features. Secondly, a series of DEM oedometric tests on ⟨1 000 : 2 000⟩ shells is simulated. A parametric study successfully leads to the understanding of each internal state variable role. A well-chosen set of initial variables with properly adapted DEM parameters give the relevant predictive simulations for a final comparison with the experimental oedometer tests. Thanks to a discrete insight into the micromechanics, the evolutions of the breakage level, the orientation anisotropy and the local stresses exerted on the shells (and/or the fragments) are quantified during the compression. The breakage of the shells result in high compressibility of the material. Therefore, the mechanical response is seen as a consequence of the breakage evolution. Finally, an analytical model is suggested in order to predict the Stress↔Void ratio relationship knowing the initial state of the sample and the tensile strength of the constituents: the shells.