Abrasive waterjet (AWJ) cutting is a versatile technique which has been effectively applied to rock cutting since the late 1980s. The complexity of the interaction between the waterjet and the rocks complicates the thorough understanding of the phenomena involved in AWJ rock cutting. On one hand, rocks are complex materials which are generated through different processes in an uncontrolled environment without human interference. On the other hand, the AWJ acts with high velocity and turbulence, complicating direct observation and the perception of details. In this respect, the present research aims to contribute to the study of AWJ cutting applied to rocks, including the analysis of qualitative and quantitative information, both of great importance regarding the study of complex materials. Concerning quantitative data, special attention is given to the investigation of the cutting efficiency, which can be analyzed by observing conditions in which the higher cutting rate is associated with the minimum energy provided by the AWJ machine per removed volume of rock. Moreover, the real efficiency can be analyzed through the investigation of the conditions in which the major part of the energy provided by the AWJ machine is used effectively for rock cutting, deducting dissipation losses. The effects of varying traverse velocity and pump pressure on cutting parameters were also investigated, in addition to the influence of rock properties on the effective energy of cutting. The effective energy was calculated based both on the specific energy and specific destruction work of the materials. With respect to the qualitative investigation, petrographic and scanning electron microscopy (SEM) analyses were conducted in order to visualize and better understand the different effects of cutting on the studied rocks. Cutting tests with a traverse velocity of 200 mm/min and a pump pressure of 400 MPa presented the most efficient rock cutting regarding both methods of efficiency analysis. Dry density and tensile strength presented fair correlations with the effective cutting energy, while the modulus ratio presented the best correlations. It was observed that brittleness plays a key role in the understanding of the phenomena involved in AWJ rock cutting. / O jato d\'água abrasivo (AWJ) é uma técnica versátil que tem sido efetivamente aplicada ao corte de rochas desde o fim da década de 1980. A complexidade da interação entre o jato e as rochas dificulta a compreensão detalhada dos fenômenos envolvidos no corte de rochas com AWJ. Por um lado, rochas são materiais complexos gerados em ambientes sem interferência humana. Por outro lado, o AWJ age com alta velocidade e turbulência, dificultando a observação direta do procedimento. Assim, a presente tese de doutorado visa a contribuir com o estudo do corte de rochas com AWJ, incluindo análises de dados qualitativos e quantitativos, ambos de grande importância em estudos de materiais complexos. A análise quantitativa possui foco na investigação da eficiência de corte, a qual pode ser analisada por meio da observação das condições em que há a maior taxa de corte associada à mínima energia fornecida pelo AWJ por volume de rocha removido. Além disso, a eficiência real do corte pode ser analisada a partir da investigação das condições em que a maior parte da energia fornecida pelo AWJ é usada para efetivamente cortar a rocha, descontando perdas por dissipação. Os efeitos da variação da velocidade transversal de corte e da pressão da bomba nos parâmetros de corte também foram investigados, além da influência das propriedades das rochas na energia efetiva de corte. A energia efetiva de corte, denominada energia relativa de formação da ranhura (EKR), foi calculada com base na energia específica e no trabalho de destruição específico dos materiais. Análises de microscopia eletrônica de varredura (SEM) e petrografia foram conduzidas para visualizar e compreender melhor os diferentes efeitos do corte nas rochas estudadas. Os testes de corte realizados com velocidade transversal do bocal de 200 mm/min e pressão da bomba de 400 MPa apresentaram as melhores eficiências de corte considerando-se ambos os métodos de análise de eficiência. Dentre as propriedades das rochas investigadas, a massa específica e a resistência à tração por compressão diametral apresentaram correlações razoáveis com EKR, enquanto que o modulus ratio apresentou as melhores correlações. Observou-se que a ruptibilidade possui papel fundamental na compreensão dos fenômenos envolvidos no corte de rochas com AWJ.

This thesis is dedicated to the study of the turbulent fluid flow in rough-walled rock fractures. Fracture models were generated from 3D scans of fractured rock samples, while fluid flow was simulated numerically by means of FVM-based open-source CFD toolbox OpenFOAM, employing the high-performance computing cluster for the more demanding 3D models. First part of the thesis addresses the issue of fracture geometry. Realistic 2D and 3D fracture models were constructed from 3D scans of upper and lower halves of a fractured rock sample, taking both shear displacement and contact spots into account. Furthermore, we discuss the shortcomings of the available fracture aperture metrics and propose a new aperture metric based on the Hausdorff distance; imaging performance of the new metric is shown to be superior to the conventional vertical aperture, especially for rough fracture surfaces with abundant ridges and troughs. In the second part of the thesis we focus on the fluid flow through the rock fracture for both 2D and 3D cases. While previous studies were largely limited to the fully viscous Darcy or inertial Forchheimer laminar flow regimes, we chose to investigate across the widest possible range of Reynolds numbers from 0.1 to 10^6, covering both laminar and turbulent regimes, which called for a thorough investigation of suitable turbulence modeling techniques. Due to narrow mean aperture and high aspect ratio of the typical fracture geometry, meshing posed a particularly challenging problem. Taking into account limited computational resources and a sheer number of model geometries, we developed a highly-optimised workflow, employing the steady-state RANS simulation approach to obtain time-averaged flow fields. Our findings show that while flow fields remain mostly stationary and undisturbed for simpler contactless geometries, emergence of contact spots immediately triggers a transition to non-stationary flow starting from Re ∼ 10^2, which is reflected by the streamline tortuosity data. This transition disrupts the flow pattern across the fracture plane, causing strong channeling and large separation bubbles, with area of the latter being much larger than the generating contact spots. Adverse influence of the contact spots on the overall permeability is strong enough to override any benefits of aperture increase during shear and dilation. Contactless 3D models can to a certain degree be approximated by their 2D counterparts. Lastly, we investigate the influence of both shearing and contact spots on the overall permeability and friction factor of the fracture, drawing a parallel to the well-studied area of turbulent flow in rough-walled pipes and ducts. Unlike the latter, 3D curvilinear fracture geometries exhibit a gapless laminar–turbulent transition, behaving as a hydraulically rough channel in the turbulent range as the shear displacement increases.

The fluid flow and tracer transport in a single rock fracture during shear processes has been an important issue in rock mechanics and is investigated in this thesis using Finite Element Method (FEM) and streamline particle tracking method, considering evolutions of aperture and transmissivity with shear displacement histories under different normal stresses, based on laboratory tests. The distributions of fracture aperture and its evolution during shear were calculated from the initial aperture fields, based on the laser-scanned surface roughness features of replicas of rock fracture specimens, and shear dilations measured during the coupled shear-flow-tracer tests in laboratory performed using a newly developed testing apparatus in Nagasaki University, Nagasaki, Japan. Three rock fractures of granite with different roughness characteristics were used as parent samples from which nine plaster replicas were made and coupled shear-flow tests was performed under three normal loading conditions (two levels of constant normal loading (CNL) and one constant normal stiffness (CNS) conditions). In order to visualize the tracer transport, transparent acrylic upper parts and plaster lower parts of the fracture specimens were manufactured from an artificially created tensile fracture of sandstone and the coupled shear-flow tests with fluid visualization was performed using a dye tracer injected from upstream and a CCD camera to record the dye movement. A special algorithm for treating the contact areas as zero-aperture elements was used to produce more accurate flow field simulations by using FEM, which is important for continued simulations of particle transport, but was often not properly treated in literature. The simulation results agreed well with the flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow channels with changing normal stresses and increasing shear displacements, which were also captured by the coupled shear-flow tests of fracture specimens with visualization of the fluid flow. From the obtained flow velocity fields, the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Péclet number, Pe, respectively. The fluid flow in the vertical 2-D cross-sections of a rock fracture was also simulated by solving both Navier-Stokes (NS) and Reynolds equations, and the particle transport was predicted by streamline particle tracking method. The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for large scale problems. The flow simulation results show that the total flow rate and the flow velocity predicted by NS equations are quite different from that as predicted by the Reynolds equation. The results show that a roughly 5-10 % overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Péclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear. The scientific findings from these studies provided new insights to the physical behavior of fluid flow and mass transport in rock fractures which is the scientific basis for many rock mechanics problems at the fundamental level, and with special importance to rock engineering problems such as geothermal energy extraction (where flow rate in fractures dominates the productivity of a geothermal energy reservoir) and nuclear waste repositories (where radioactive nuclides transport through fractures dominates the final safety evaluations) in fractured rocks. / Vätskeflödet och spårämnestransporten i en enskild bergsspricka under skjuvningsprocesser har varit ett viktigt ämne inom bergmekanik. I denna avhandling undersöks ämnet med hjälp av finita element metoden (FEM) och en strömlinjebaserad partikelspårningsmetod. Hänsyn tas till utveckling av öppningar och transmissivitet med skjuvningens förflyttningshistoria under olika normala belastningar baserat på laboratorietester. Fördelningen av spricköppningar och deras utveckling under skjuvning beräknades från de initiala öppningsfälten baserat på det laserscannade provets ytas grovhetskännetecken sam tskjuvningsöppningar uppmätta under de kopplade skjuvning-flöde-spårämneslaboratorietesterna som utförts med nyutvecklad testapparatur i Nagasaki Universitet i Nagasaki, Japan. Tre bergssprickor i granit med olika grovhetskarakteristika användes som utgångsprover från vilka nio gipskopior gjordes. Kopplade skjuvning-flödes tester utfördes sedan under tre normala belastningstillstånd (två nivåer med konstant normal last (KNL) och en konstant normal styvhetstillstånd (KNS). För att visualisera spårämnestransporten tillverkades en transparent övre del av sprickproverna av akryl och en nedre del av gipsbaserat på en kostgjord spänningsspricka i sandsten och de kopplade skjuvning-flödes testerna med vätskevisualisering utfördes med färgspårämne injekterat uppströms och en CCD kamera monterad ovanför för att registrera färgens rörelse. En särskild algoritm användes för att behandla kontaktytorna som nollöppningsämnen användes för att åstadkomma mer exakta flödesfältssimuleringar med FEM. Detta är viktigt för kontinuerliga simuleringar av partikelflöden men uppmärksammas oftast inte tillräckligt i litteraturen. Simuleringsresultaten överensstämde väl med de flödesnivådata som erhölls från laboratorietesterna vilket visade att komplexa historier av spricköppningar och invecklade flöden överensstämde med ändrade normala belastningar och ökande skjuvningsförflyttningar, vilket även fångades av de kopplade skjuvning-flödestesterna av sprickproverna genom visualisering av vätskeflödet. Från de erhållna flödesfälten förutsågs partikeltransporten genom en strömlinjebaserad partikelspårningsmetod med kalkylerade flödeshastighetsfält (vektorer) från flödessimuleringarna genom vilka resultat som flödeshastighetsprofiler, totala flödesnivåer,partikeltransporttid, genombrottskurvor samt Pécletnumret, Pe, erhölls. Vätskeflödet i det vertikala tvådimensionella tvärsnittet av en bergsspricka simulerades även genom att både Navier-Stokes (NS) och Reynoldsekvationerna löstes och partikeltransporten förutsågs genom den strömlinjebaserade partikelspårningsmetoden. Resultaten som erhöllsmed NS och Reynoldsekvationerna jämfördes för att illustrera graden av tillförlitlighet för Reynoldsekvationen för allmänna tillämpningar i praktiken då den senare är betydligt mer beräkningseffektiv för storskaliga problem. Resultaten från flödessimuleringarna visar att den totala flödesnivån och den totala flödeshastigheten förutsedda med NS ekvationer är helt annorlunda motsvarande värden som förutsågs med Reynoldsekvationen. Resultaten visar att en ca 5-10 % för hög uppskattning av flödesnivån erhålls då Reynoldsekvationen används och de ideala parabola hastighetsprofilerna, som definieras av den lokala kubiklagen när Reynoldsekvationen används, inte längre är giltiga särskilt när sprickytornas grovhetskarakteristika ändras med skjuvning. De här avvikelserna i flödesnivå och flödeshastighetsprofiler längs med spricköppningen har en betydande påverkan på partikeltransportuppträdande och de tillhörande egenskaperna såsom rörelsetid och Pécletnummer. Avvikelserna ökar med ökande flödeshastighet och blir mer signifikanta när spricköppningarnas geometri ändras med skjuvning. Forskningsresultaten från dessa studier gav nya insikter i de fysiska uppträdandet av vätskeflöde och masstransporter i bergssprickor vilket är den vetenskapliga basen för många bergmekanikproblem på grundläggande nivå och som har särskild vikt för bergstekniksproblem såsom geotermisk energiutvinning (där flödesnivå i sprickor dominerar produktiviteten för en geotermisk energikälla) och kärnavfallsförvaringsplatser (där transporten av radioaktiva nuklider genom sprickor dominerar den slutgiltigasäkerhetsutvärderingen) i sprickigt berg. / QC 20100803