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Numerical simulation of shear-induced flow anisotropy and scale-dependent aperture and transmissivity evolution of rock fracture replicas
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
2006 (English)In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 43, no 1, 89-106 p.Article in journal (Refereed) Published
Abstract [en]

Fluid flow anisotropy in a single rock fracture during a shear process is an important issue in rock mechanics and is investigated in this paper using FEM modelling, considering evolutions of aperture and transmissivity with shear displacement history. The distributions of fracture aperture during shearing with large shear displacements were obtained by numerically manipulating relative translational movements between two digitalized surfaces of a rock fracture replica, with changing sample sizes. The scale dependence of the fluid behaviour and properties were also investigated using a fractal approach. The results show that the fracture aperture increases anisotropically during shear with a more pronounced increase in the direction perpendicular to the shear displacement, causing significant fluid flow channelling effect, as also observed by other researchers. This finding may have important impacts on the interpretation of the results of coupled hydro-mechanical experiments for measurements of hydraulic properties of rock fractures because the hydraulic properties are usually calculated from flow test results along the shear directions while ignoring the more significant anisotropic flow perpendicular to the shear direction. This finding indicates that the coupled stress-flow tests of rough rock fractures should be conducted in true three-dimensions if possible. Significant change in fracture aperture/ transmissivity in the out-of-plane direction should be properly evaluated if two-dimensional tests are conducted. Results obtained from numerical simulations also show that fluid flow through a single rough fracture changes with increasing sample size and shear displacements, indicating that representative hydro-mechanical properties of the fractures in the field can only be more reliably determined using samples of large enough sizes beyond the stationarity threshold and tested with larger shear displacements.

Place, publisher, year, edition, pages
2006. Vol. 43, no 1, 89-106 p.
Keyword [en]
Anisotropy, Computer simulation, Finite element method, Fractals, Fracture mechanics, Mathematical models, Shear flow, Shear stress, Surface roughness
National Category
Geophysical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-7465DOI: 10.1016/j.ijrmms.2005.04.006ISI: 000233798900008Scopus ID: 2-s2.0-27944459974OAI: oai:DiVA.org:kth-7465DiVA: diva2:12497
Note
QC 20100924Available from: 2007-09-10 Created: 2007-09-10 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Stress, Flow and Particle Transport in Rock Fractures
Open this publication in new window or tab >>Stress, Flow and Particle Transport in Rock Fractures
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

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.

Abstract [sv]

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.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. xiv, 196 p.
Series
Trita-LWR. PHD, ISSN 1650-8602 ; 1036
Keyword
Numerical simulation, laboratory experiments, rock fracture, coupled stress-flow-tracer test, shear displacement, fluid flow, particle transport, finite element method (FEM), particle tracking method, Navier-Stokes equation, Reynolds equation, streamline/velocity dispersion.
National Category
Geophysical Engineering
Identifiers
urn:nbn:se:kth:diva-4485 (URN)978-91-7178-746-0 (ISBN)
Public defence
2007-09-28, V2, Teknikringen 76, KTH, 13:00
Opponent
Supervisors
Note
QC 20100803Available from: 2007-09-10 Created: 2007-09-10 Last updated: 2010-08-03Bibliographically approved

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