Mécanique des roches, phénomènes de rupture avec la prise en compte des fissures existantes et l’écoulement du fluide interne à travers les fissures : thèse de doctorat

This thesis deals with the problem of localized failure in rocks, which occurs often in civil engineering practice like in dam failure, foundation collapse, stability of excavations, slopes and tunnels, landslides and rock falls. The risk of localized failure should be better understood in order to be prevented. The localized failure in rocks is usually characterized by a sudden and brittle failure without warning in a sense of larger and visible deformations prior to failure. This happens also under the strong influence of material heterogeneities, pre-existing cracks and other defects. The three novel numerical models, incorporating the localized failure mechanisms, heterogeneity of rock and pre-existing cracks and other defects, are presented in this thesis. First model deals with 2D plane strain two-phase rock composite, where stronger phase represents the intact rock and weaker phase initial defects. Second model represents the extension of the previous model towards the 3D space, where full set of 3D failure mechanisms is considered. Heterogeneous properties are taken here through the random distribution and Gauss statistical variation of material properties. The latter model is also used for the analysis of intact rock core specimens geometrical shape deviations influencing the uniaxial compressive strength. Third model is a 2D, dealing with volumetric fluid-structure interaction and localized failure under the influence of fluid flow through the porous rock medium. The discrete beam lattice approach is chosen for general framework for three models, where Voronoi cells represent the rock grains kept together by Timoshenko beams as cohesive links. The enhanced kinematics characterized for embedded discontinuity approach is added upon standard kinematics of cohesive links. This serves for the macrocrack propagation in all failure modes and their combinations, between the rock grains. The fracture process zone formation followed by micro-cracks coalescence, preceding the localized failure, is considered as well. Fluid flow is governed by a Darcy law, while coupling conditions obey Biot’s theory of poroplasticity. The results of the numerical models were verified by the benchmarks available from literature in 2D case. The 3D model was validated against the experimental results conducted on 90 rock specimens, where even slight geometrical deviations of specimens are considered. Presentation of these models, as well as their implementation aspects are given in full detail. Embedded discontinuity concept and the local nature of enhancements required to capture the displacement discontinuities leads to the very efficient approach with static condensation of enhanced degrees of freedom and technique that can be efficiently incorporated into finite element code architecture.Ova doktorska disertacija bavi se problemom lokaliziranog sloma u stijenama koji se često pojavljuje u različitima zadaćama u inženjerskoj praksi kod otkazivanja nosivosti brana, sloma temelja, stabilnosti iskopa, klizišta i tunela ili stijenskih odrona. Bolje razumijevanje ovog fenomena je nužno zbog prevencije rizika od lokaliziranog sloma. Lokalizirani slom u stijenama karakteriziran je iznenadnim i krtim slomom bez upozorenja u obliku velikih i vidljivih deformacija, a uvjetovan je materijalnim heterogenostima, postojećim pukotinama i oslabljenjima. U ovome radu prezentirana su tri nova numerička modela koja uključuju mehanizme lokaliziranog sloma, materijalnu heterogenost stijene s postojećim pukotinama i drugim oslabljenjima. Prvi je 2D model za analizu ravninskog stanja deformacija dvofazne kompozitne stijene, kod koje čvršća faza predstavlja intaktnu stijenu, a slabija faza početne nepravilnosti (oslabljenja) u stijeni. Drugi model predstavlja proširenje opisanog 2D modela u 3D područje, gdje su uključeni 3D mehanizmi sloma. Heterogenost je uzeta u obzir pomoću slučajne raspodjele i Gaussove statističke varijacije materijalnih karakteristika. Ovaj model je upotrijebljen u analizi utjecaja geometrijskih nepravilnosti oblika stijenskih uzoraka na jednoosnu tlačnu čvrstoću. Treći numerički model je dvodimenzionalni, a bavi se volumenskom interakcijom tekućine i konstrukcije i lokaliziranim slomom pod utjecajem protoka tekućine kroz poroznu stijensku sredinu. Osnova sva tri numerička modela je pristup zasnovan na diskretnoj rešetkastoj mreži greda u kojem su Voronoi ćelije kao diskretne čestice stijene međusobno povezane kohezivnim vezama modeliranima pomoću Timoshenkovih greda. Poboljšana kinematika, karakteristična za metodu konačnih elemenata s ugrađenim diskontinuitetima, dodana je standardnoj kinematici kohezivnih veza što omogućuje nastanak i širenje makropukotina između mineralnih zrna stijene u svim mehanizmima sloma i njihovim kombinacijama. Proces nastanka mikropukotina koji prethodi lokaliziranom slomu stijene je također uzet u obzir u modelu. Protok tekućine definiran je Darcijevim zakonom dok je volumenska interakcija tekućine i stijene zasnovana na Biotovoj teoriji poroplastičnosti. Rezultati razvijenih numeričkih 2D modela su verificirani na primjerima iz literature. Validacija 3D modela provedena je usporedbom s eksperimentalnim rezultatima dobivenima ispitivanjem 90 stijenskih uzoraka, gdje su razmatrane i geometrijske nepravilnosti stijenskih uzoraka. U ovoj doktorskoj disertaciji detaljno su prezentirani svi razvijeni numerički modeli, kao i njihova matematička i numerička implementacija. Pristup s ugrađenim diskontinuitetima i lokalnim poboljšanjima za simulaciju diskontinuiteta u polja pomaka te statičkom kondenzacijom dodatnih stupnjeva slobode je na vrlo efikasan način ugrađen u program za analizu konstrukcija metodom konačnih elemenata.Cette thèse aborde le problème de la rupture localisée dans les roches, qui charcterise un grand nombre d’applications dans le domaine du génie civil, tels que la rupture du barrage, effondrement desfondations, la stabilité des excavations ou les tunnels, les glissements de terrain et éboulements. Le risque de rupture localisée devrait être mieux apprehendé pour mieux l’évitér. La rupture localisée dans les roches est généralement caractérisé par une une rupture soudaine et quasi-fragile sans avertissement dans un sens de plus grandes déformations et visibles avant l’échec. Cela se produit également sous l’influence des hétérogénéités matériels, influencé par des fissures existantes et d’autres défauts initaux. Les trois nouveaux modèles numériques, intégrant les mécanismes de rupture localisées, l’hétérogénéité de la roche et de fissures existantes et d’autres défauts, sont présentés dans cette thèse. Premier modèle propose une représentation 2D de roche composite à deux phases, où la phase solide représente la roche intacte et les plus faibles en phase défauts initiaux. Deuxième modèle représente l’extension du modèle précédent vers l’espace 3D, où un ensemble complet de mécanismes de défaillance 3D est considéré. Propriétés hétérogènes sont prises ici par la distribution aléatoire en accord avec la variation statistique Gaussienne des propriétés des matériaux. Ce dernier modèle est également utilisé pour l’analyse de la roche intacte spécimens écarts de forme géométriques qui influencent la résistance à la compression uniaxiale. Troisième modèle est un modèle 2D, traitant interaction volumétrique entre fluide et structure et la rupture localisée sous l’influence de l’écoulement du fluide à travers le milieu de la roche poreuse. L’approche de lattice discret est choisi pour construire le cadre général pour trois modèles, où les cellules de Voronoi représentent les grains de roche gardés ensemble par Timoshenko poutres que des liens de cohésion. La cinématique améliorées caractérisées pour l’approche intégrée de discontinuité est ajouté sur la cinématique standard de liens cohérents. Cela sert pour la propagation de la fissure macro dans tous les modes de défaillance et de leurs combinaisons, entre les grains de la roche. La formation de la zone de processus de rupture suivie par des micro-fissures coalescence, précédant la rupture localisée, est considéré comme bien. Écoulement de fluide est régie par une loi de Darcy, tandis que les conditions de couplage obéissent à la théorie de Biot de poroélasticité. Les résultats des modèles numériques ont été vérifiées par les repères de la littérature dans le cas 2D. Le modèle 3D a été validé contre les résultats expérimentaux effectués 12 sur 90 échantillons de roches, où de légères déviations géométriques de spécimens sont considérés. Présentation de ces modèles, ainsi que leurs aspects de mise en oeuvre sont présentés en détail. Notion de discontinuité intrinsèque et le caractère local des améliorations nécessaires pour capturer les discontinuités de déplacement conduit à l’approche très efficace avec condensation statique des degrés améliorés de liberté et de technique qui peut être efficacement intégrés dans architecture standarde d’un logiciel élément finis

DISCRETE LATTICE ELEMENT APPROACH FOR ROCK FAILURE MODELING

This paper presents the ‘discrete lattice model’, or, simply, the ‘lattice model’, developed for rock failure modeling. The main difficulties in numerical modeling, namely, those related to complex crack initiations and multiple crack propagations, their coalescence under the influence of natural disorder, and heterogeneities, are overcome using the approach presented in this paper. The lattice model is constructed as an assembly of Timoshenko beams, representing the cohesive links between the grains of the material, which are described by Voronoi polygons. The kinematics of the Timoshenko beams are enhanced by the embedded strong discontinuities in their axial and transversal directions so as to provide failure modes I, II, and III. The model presented is suitable for meso-scale rock simulations. The representative numerical simulations, in both 2D and 3D settings, are provided in order to illustrate the model’s capabilities

Overview of the numerical methods for the modelling of rock mechanics problems

Počeci numeričkih metoda sežu u rane 1960-e. Već tada je bilo jasno da numeričke metode mogu biti uspješno upotrijebljene za različita inženjerska i znanstvena područja, uključujući i primjenu u mehanici stijena. Ubrzan razvoj računala je omogućavao razvoj numeričkih metoda i rješavanje računalno zahtjevnijih sustava. Takav razvoj doveo je do velikog broja različitih metoda i pristupa koji se mogu svrstati u dvije skupine: metode kontinuuma i metode diskontinuuma. Određene zadaće zahtijevaju prednosti oba pristupa, što je dovelo do razvoja kombiniranih konačno-diskretnih metoda. Prvi cilj ovog rada je predstavljanje numeričkih metoda i pristupa koji se koriste za rješavanje zadaća u mehanici stijena, kao i kratko objašnjenje osnovnih teorijskih postavki svake od metoda. Drugi cilj je osvrt na primjenjivost pojedine metode u mehanici stijena.The numerical methods have their origin in the early 1960s and even at that time it was noted that numerical methods can be successfully applied in various engineering and scientific fields, including the rock mechanics. Moreover, the rapid development of computers was a necessary background for solving computationally more demanding problems and the development process of the methods in general. Thus, we have many different methods presently, which can be separated into two main branches: continuum and discontinuum-based numerical methods. Some problems require the strengths of both main approaches which brought the hybrid continuum/discontinuum methods. The first goal of this paper is to present the state of the art numerical methods and approaches for solving the rock mechanics problems, as well as to give the brief explanation about the theoretical background of each method. The second goal is to emphasise the area of applicability of the methods in rock mechanics

Numerical Simulation of Saturated and Unsaturated Consolidation Behaviour of Marl Residual Soil

Consolidation tests were performed on reconstituted marl samples under saturated and unsaturated conditions in the geomechanical laboratory at the Faculty of Civil Engineering, Architecture and Geodesy (FCEAG). Reconstituted marl samples were used to simulate the behaviour of marl residual soil as a final product of weathering. The experimental results were implemented in the Plaxis 2D finite element software, and saturated and unsaturated consolidation tests were simulated using hydro-mechanical coupling analysis. Material parameters for the Mohr-Coulomb and Hardening Soil models were calculated from the obtained experimental results. The validity of above mentioned constitutive models for marl residual soil was evaluated using the consolidation tests results and considering the values of axial displacement and void ratio as deformation indicators for saturated and unsaturated conditions. The validity of the input parameters for unsaturated analysis (i.e. the obtained SWCC fitting parameters) and the applied boundary conditions were evaluated considering the achieved degree of saturation value for each calculation phase

LABORATORY INVESTIGATION OF EMBANKMENT SETTLEMENT CAUSED BYMARL GRAINS DETERIORATION

Nasip izrađen od zrna dobivenih drobljenjem meke stijene može biti podložan dodanom slijeganju uzrokovanim raspucavanjem zrna unutar strukture nasipa. Ovo dodatno slijeganje nije uzrokovano promjenom stanja naprezanja unutar nasipa i ne može biti procijenjeno standardnim metodama proračuna na osnovi modula stišljivosti izmjerenog nakon zbijanja nasipa. Raspucavanje zrna je uzrokovano procesom rastrošbe, koji je u mekim stijenama kao što je lapor, uglavnom uzrokovan procesom sušenja i vlaženja. Ako su zrna u strukturi nasipa podvrgnuta sušenju i vlaženju, rezultat je usitnjavanje zrna do razine raspada u materijal koji se može opisati kao tlo. Usitnjeni materijal odvaja se od zrna i popunjava makro pore u strukturi nasipa što za posljedicu ima dodatno slijeganje nasipa. Uzorci za ispitivanje su izrađeni od drobljenog lapora u laboratorijskim uvjetima. Ispitivanje je provedeno sa modificiranim edometarskim uređajem. Izmjerene veličine se mogu iskoristiti u svrhu procjene dodatnog slijeganja nasipa uzrokovanog rastrošbom.Embankments made of crushed soft rock grains can be susceptible to additional settlement caused by deterioration of the grains inside the embankment. This additional settlement is not caused by the change of the stress state inside embankment and cannot be predicted by standard calculating methods with the embankment modulus of deformability measured after compaction of the embankment. The deterioration of the grains is mainly caused by the weathering process which is, in soft rocks such as marl, mainly induced by the wetting and drying processes. If marl grains in an embankment are subjected to the wetting and drying process, the result is breakage of the grains, as well as decomposition into soil material. Disintegrated material then fills the macropores of the embankment grain structure and gradually causes additional settlement. The samples were made of crushed marl in laboratory conditions. A test was conducted with modified oedometer apparatus. Measured values can be used for estimating the additional settlement caused by the weathering

LABORATORY INVESTIGATION OF EMBANKMENT SETTLEMENT CAUSED BYMARL GRAINS DETERIORATION

Nasip izrađen od zrna dobivenih drobljenjem meke stijene može biti podložan dodanom slijeganju uzrokovanim raspucavanjem zrna unutar strukture nasipa. Ovo dodatno slijeganje nije uzrokovano promjenom stanja naprezanja unutar nasipa i ne može biti procijenjeno standardnim metodama proračuna na osnovi modula stišljivosti izmjerenog nakon zbijanja nasipa. Raspucavanje zrna je uzrokovano procesom rastrošbe, koji je u mekim stijenama kao što je lapor, uglavnom uzrokovan procesom sušenja i vlaženja. Ako su zrna u strukturi nasipa podvrgnuta sušenju i vlaženju, rezultat je usitnjavanje zrna do razine raspada u materijal koji se može opisati kao tlo. Usitnjeni materijal odvaja se od zrna i popunjava makro pore u strukturi nasipa što za posljedicu ima dodatno slijeganje nasipa. Uzorci za ispitivanje su izrađeni od drobljenog lapora u laboratorijskim uvjetima. Ispitivanje je provedeno sa modificiranim edometarskim uređajem. Izmjerene veličine se mogu iskoristiti u svrhu procjene dodatnog slijeganja nasipa uzrokovanog rastrošbom.Embankments made of crushed soft rock grains can be susceptible to additional settlement caused by deterioration of the grains inside the embankment. This additional settlement is not caused by the change of the stress state inside embankment and cannot be predicted by standard calculating methods with the embankment modulus of deformability measured after compaction of the embankment. The deterioration of the grains is mainly caused by the weathering process which is, in soft rocks such as marl, mainly induced by the wetting and drying processes. If marl grains in an embankment are subjected to the wetting and drying process, the result is breakage of the grains, as well as decomposition into soil material. Disintegrated material then fills the macropores of the embankment grain structure and gradually causes additional settlement. The samples were made of crushed marl in laboratory conditions. A test was conducted with modified oedometer apparatus. Measured values can be used for estimating the additional settlement caused by the weathering

A Voronoi Based Discrete Numerical Approach for Modelling Reinforcement in Concrete Structures

In this paper, we present a novel discrete lattice numerical model for modelling reinforcement in concrete structures. Concrete behaviour is represented here by Voronoi cells and Timoshenko beams as cohesive links between them. Reinforcement bars are explicitly implemented as separate beam elements, while the connection between the concrete and reinforcement is established through the bond elements. Each bond element is positioned between the concrete node and reinforcement node inside the Voronoi cell that crosses the reinforcement bar. Numerical tests are performed to demonstrate the capabilities of the discrete model to predict the response of reinforced concrete structures in the linear elastic stage. The paper also covers the review of different numerical models for modelling reinforced concrete. The overview of research areas in the development of numerical models for reinforced concrete is divided with regards to the manner of modelling cracks, discretisation of the concrete domain and modelling of reinforcement

Data-driven multiscale modeling using lattice model on the lower scale

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Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

International audienceIn this work we propose and compare the two models for crack propagation in dynamics. Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms. The first one is based on discrete lattice approach, where the domain is discretized with Voronoi cells held together prior to crack occurrence by cohesive links represented in terms of Timoshenko beams. The second one is based on constant strain triangular solid element. In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities. The latter remain localized inside the element, regulated by the localized traction separation behavior defined through exponential softening law. Thus, the both models provide the result that remain mesh-independent, with fracture energy as the model parameter. We show that implementation in dynamics framework can be obtained by adding inertial effects without modifying the existing quasi-statics models. In order to provide reliable results, classical implicit Newmark algorithm can be used for time integration. The two presented models are subjected to dynamic crack propagation benchmarks, where detailed analysis on strain, kinetic, plastic free and dissipated energy during simulation is verified by comparison to the amount of total work which is introduced into the system. The main strength of the proposed approach is that cracks initiation, propagation, their coalescence, merging and branching are automatically obtained without any tracking algorithms. In addition, since the discontinuities remain localized inside elements, accurate results can be obtained even with coarser grids, leading to efficient methodology capable of capturing complex crack patterns in dynamics