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Structural Uncertainties of Rock Fractures and their Effect on Flow and Tracer Transport
KTH, School of Architecture and the Built Environment (ABE), Sustainable development, Environmental science and Engineering.ORCID iD: 0000-0002-1574-9044
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [sv]

Att förstå flöde och transport av lösta ämnen genom sprickorna i berggrunden är viktigt för den långsiktiga säkerheten av ett geologiskt slutförvar av farligt avfall. I en diskret spricknätverksmodell byggs flödesvägarna upp av kedjor av flödesvägar genom de enskilda sprickorna i bergmassan. Varje sådan flödesväg genom varje spricka bidrar således till bergmassans totala flödes- och transportegenskaper. Därmed är kunskap om flödes- och transportegenskaper för de enskilda sprickorna viktiga för att kunna utföra en säkerhetsanalys av ett geologiskt slutförvar av farligt avfall.Hålrummet som utgör en spricka beror av de begränsande ytornas råhet tillsammans med den normalspänning som verkar på sprickan. Därmed är uppskattningen av hålrummet beroende av noggranna mätningar av sprickans orientering i förhållande till omgivande spänningsfält samt råheten på begränsningsytorna. Eftersom alla mätningar är behäftade med osäkerheter, såsom osäkerheter i verktyg, yttre störningar och mänskliga faktorer, kommer de tolkade egenskaperna inte att beskrivas av enskilda deterministiska värden utan av sannolikhetsfördelningar. Beroende på kombinationen av använda värden från dessa fördelningar kommer flödes- och transportegenskaperna för sprickorna att variera.Syftet med denna avhandling är därför att presentera en metod att beskriva det geometriska ramverket för sprickor i kristallint berg, inklusive osäkerheter, samt att undersöka hur dessa kan påverka tolkningen av flödes- och transportegenskaper för grundvatten och lösta ämnen. Genom att beräkna sprickornas orientering och osäkerhet från sprickornas skärning med borrhål, kan ett utfallsrum för orienteringsosäkerheten beräknas. Denna osäkerhet i orientering kommer således, under antagande av ett fixt spänningstillstånd, att resultera i en fördelning av normalspänningar som kan verka på sprickan och därmed hur hoptryckt sprickan är. Råheten på sprickytorna och dess osäkerheter kan beräknas från den sprickyta som uppstår då sprickan korsar borrkärnan, givet tillräcklig upplösning på ytan samt att ytan är representativ för hela sprickan. Denna beräknade råhet påverkar korrelationsstrukturen av hålrummet mellan de två ytorna som definierar sprickan. Således kommer median och varians för tjockleken samt dess korrelationsstruktur påverkas av vilken parameterkombination som dras från utfallsrummen för normalspänning och råhet. Detta medför att flödes- och transportegenskaperna är beroende av osäkerheterna i det geometriska ramverket, dvs osäkerheterna påverkar flödesvägar, flödestider, transportmotstånd och flödesvätt yta. Typiskt kommer en högre normalspänning som verkar på sprickan att resultera i längre flödestider, längre flödesvägar, högre flödesmotstånd och större flödesvätt yta medan en råare sprickyta typiskt kommer att resultera i kortare flödestider, längre flödesvägar, lägre flödesmotstånd och mindre flödesvätt yta. Slutsatsen av arbetet är således att osäkerheterna i att bestämma det geometriska ramverket påverkar resultatet för sprickornas tolkade flödes- och transportegenskaper.

Abstract [en]

A clear understanding of solute flow and transport through the network of fractures in the rock mass is essential for accurate long-term safety assessments of geological storage of hazardous waste. In a discrete fracture network (DFN) model, flow and transport of solutes are described by chains of flow paths through single fractures, each of which contributes to the total flow and transport properties of the rock mass. Hence, knowledge of the flow and transport properties of each single fracture is essential for accurate safety assessment.The void space that forms a fracture is a derivative of the roughness of the bounding surfaces and the normal force acting on the fracture and is hence dependent on accurate measurement of these properties. As all measurements are associated with uncertainties stemming from e.g. instrument imprecision, external disturbances and human factors, the measured value of the properties will not be single values, but probability distributions. Depending on the set of values drawn from these distributions, interpretations of flow and transport properties of sheared fractures in crystalline hard rock will vary.This thesis examines how flow and transport properties through single fractures are affected by uncertainties in fracture orientation and in roughness. By inferring the orientation and its uncertainty from the fracture intercepts in boreholes, a probability space for the orientation of the fracture is obtained. For a given stress state, this uncertainty in orientation will result in a distribution of normal stresses acting on the fracture. The roughness of the fracture and its uncertainty can be inferred from the small intersecting surfaces of the rock core, if the resolution is sufficient and the surface is representative of the fracture. The inferred roughness affects the correlation structure of the void between the two surfaces defining the fracture and, together with the distribution of normal stresses, produces different flow paths and hence different properties of flow and transport of solutes. Depending on the parameter combinations, the median and variance of the aperture field will change, as will the correlation structure of apertures. Since the flow and transport properties depend on the geometrical framework, the uncertainty will affect path length, travel time, transport resistance and flow-wetted surface. Higher normal stress acting on the fracture will typically result in longer travel times, longer travel lengths, higher transport resistance and larger flow-wetted surface. A rougher fracture will typically result in shorter travel times, longer travel lengths, lower transport resistance and smaller flow-wetted surface. The conclusion is, hence, that uncertainties in the geometric framework will affect flow and tracer transport properties.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2019. , p. 96
Keywords [en]
Fracture, Flow, Transport, Orientation uncertainty, Roughness, Self-affine, Fractal, Shear, Aperture distribution.
National Category
Natural Sciences
Research subject
Land and Water Resources Engineering
Identifiers
URN: urn:nbn:se:kth:diva-260388Local ID: TRITA-ABE-DLTISBN: 978-91-7873-260-9 (print)Archive number: 1927OAI: oai:DiVA.org:kth-260388DiVA, id: diva2:1355468
Public defence
2019-11-07, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20191009

Available from: 2019-10-09 Created: 2019-09-29 Last updated: 2019-10-09Bibliographically approved
List of papers
1. A transmissivity model for deformation zones in fractured crystalline rock and its possible correlation to in situ stress at the proposed high-level nuclear waste repository site at Forsmark, Sweden
Open this publication in new window or tab >>A transmissivity model for deformation zones in fractured crystalline rock and its possible correlation to in situ stress at the proposed high-level nuclear waste repository site at Forsmark, Sweden
2014 (English)In: Hydrogeology Journal, ISSN 1431-2174, E-ISSN 1435-0157, Vol. 22, no 2, p. 299-311Article in journal (Refereed) Published
Abstract [en]

The Forsmark site was recently proposed by the Svensk Karnbranslehantering AB (SKB) to serve as the potential site for construction of a future geological repository for spent high-level nuclear fuel at about 470 m depth in fractured crystalline rock. The considerations included, among other things, distance from regionally significant deformation zones with highly strained rock, lithological homogeneity, low hydraulic conductivity, groundwater salinity with an acceptable range, and lack of potential mineral resources. This report describes the calculation of transmissivity of deduced deformation zones at Forsmark and the transmissivity model used in the regional groundwater flow modeling carried out in support of the integrated site description. Besides significant decrease with increasing depth (more than four orders of magnitude over a depth of about 1 km), the calculated transmissivity values also reveal considerable spatial variability along the strikes of the zones, i.e. lateral heterogeneity (more than two orders of magnitude). A hydro-mechanical coupling is discussed, based on presented models for the tectonic evolution and the principal stress tensor. Tentatively, laboratory-scale relationships developed from normal stress experiments on a single fracture in crystalline rock can be used to estimate the maximum values of transmissivity of deduced deformation zones at Forsmark.

Keywords
Crystalline rock, Deformation zone, Hydro-mechanical coupling, Sweden, Forsmark
National Category
Oceanography, Hydrology and Water Resources
Identifiers
urn:nbn:se:kth:diva-144377 (URN)10.1007/s10040-013-1078-9 (DOI)000332659000003 ()2-s2.0-84896725717 (Scopus ID)
Note

QC 20140422

Available from: 2014-04-22 Created: 2014-04-22 Last updated: 2019-09-29Bibliographically approved
2. Orientation uncertainty goes bananas: An algorithm to visualise the uncertainty sample space on stereonets for oriented objects measured in boreholes
Open this publication in new window or tab >>Orientation uncertainty goes bananas: An algorithm to visualise the uncertainty sample space on stereonets for oriented objects measured in boreholes
2013 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 56, p. 56-61Article in journal (Refereed) Published
Abstract [en]

Measurements of structure orientations are afflicted with uncertainties which arise from many sources. Commonly, such uncertainties involve instrument imprecision, external disturbances and human factors. The aggregated uncertainty depends on the uncertainty of each of the sources. The orientation of an object measured in a borehole (e.g. a fracture) is calculated using four parameters: the bearing and inclination of the borehole and two relative angles of the measured object to the borehole. Each parameter may be a result of one or several measurements. The aim of this paper is to develop a method to both calculate and visualize the aggregated uncertainty resulting from the uncertainty in each of the four geometrical constituents. Numerical methods were used to develop a VBA-application in Microsoft Excel to calculate the aggregated uncertainty. The code calculates two different representations of the aggregated uncertainty: a 1-parameter uncertainty, the ‘minimum dihedral angle’, denoted by Ω; and, a non-parametric visual representation of the uncertainty, denoted by χ. The simple 1-parameter uncertainty algorithm calculates the minimum dihedral angle accurately, but overestimates the probability space that plots as an ellipsoid on a lower hemisphere stereonet. The non-parametric representation plots the uncertainty probability space accurately, usually as a sector of an annulus for steeply inclined boreholes, but is difficult to express numerically. The 1-parameter uncertainty can be used for evaluating statistics of large datasets whilst the non-parametric representation is useful when scrutinizing single or a few objects.

Keywords
DrillcoreBoreholeOrientation uncertaintySample spaceStereographic projectionAlgorithm
National Category
Geotechnical Engineering
Research subject
Land and Water Resources Engineering
Identifiers
urn:nbn:se:kth:diva-248949 (URN)10.1016/j.cageo.2013.03.001 (DOI)
Funder
Swedish Nuclear Fuel and Waste Management Company, SKB
Note

QC 20190411

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-09-29Bibliographically approved
3. Orientation Uncertainty of Structures Measured in Cored Boreholes: Methodology and Case Study of Swedish Crystalline Rock
Open this publication in new window or tab >>Orientation Uncertainty of Structures Measured in Cored Boreholes: Methodology and Case Study of Swedish Crystalline Rock
2016 (English)In: Rock Mechanics and Rock Engineering, ISSN 0723-2632, E-ISSN 1434-453X, Vol. 49, p. 4273-4284Article in journal (Refereed) Published
Abstract [en]

Many engineering applications in fractured crystalline rocks use measured orientations of structures such as rock contact and fractures, and lineated objects such as foliation and rock stress, mapped in boreholes as their foundation. Despite that these measurements are afflicted with uncertainties, very few attempts to quantify their magnitudes and effects on the inferred orientations have been reported. Only relying on the specification of tool imprecision may considerably underestimate the actual uncertainty space. The present work identifies nine sources of uncertainties, develops inference models of their magnitudes, and points out possible implications for the inference on orientation models and thereby effects on downstream models. The uncertainty analysis in this work builds on a unique data set from site investigations, performed by the Swedish Nuclear Fuel and Waste Management Co. (SKB). During these investigations, more than 70 boreholes with a maximum depth of 1 km were drilled in crystalline rock with a cumulative length of more than 34 km including almost 200,000 single fracture intercepts. The work presented, hence, relies on orientation of fractures. However, the techniques to infer the magnitude of orientation uncertainty may be applied to all types of structures and lineated objects in boreholes. The uncertainties are not solely detrimental, but can be valuable, provided that the reason for their presence is properly understood and the magnitudes correctly inferred. The main findings of this work are as follows: (1) knowledge of the orientation uncertainty is crucial in order to be able to infer correct orientation model and parameters coupled to the fracture sets; (2) it is important to perform multiple measurements to be able to infer the actual uncertainty instead of relying on the theoretical uncertainty provided by the manufacturers; (3) it is important to use the most appropriate tool for the prevailing circumstances; and (4) the single most important parameter to decrease the uncertainty space is to avoid drilling steeper than about −80°.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
Orientation uncertainty Quantification Uncertainty space Uncertainty sources Fractures DFN Crystalline rock Cored borehole Stereonet
National Category
Geotechnical Engineering
Identifiers
urn:nbn:se:kth:diva-248957 (URN)10.1007/s00603-016-1038-5 (DOI)000387849400005 ()2-s2.0-84976503327 (Scopus ID)
Funder
Swedish Nuclear Fuel and Waste Management Company, SKB
Note

QC 20191002

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-10-02Bibliographically approved
4. A Novel Conceptual Approach to Objectively Determine JRC Using Fractal Dimension and Asperity Distribution of Mapped Fracture Traces
Open this publication in new window or tab >>A Novel Conceptual Approach to Objectively Determine JRC Using Fractal Dimension and Asperity Distribution of Mapped Fracture Traces
2019 (English)In: Rock Mechanics and Rock Engineering, ISSN 0723-2632, E-ISSN 1434-453X, Vol. 52, no 4, p. 1041-1054Article in journal (Refereed) Published
Abstract [en]

The understanding of fractures in hard rock is important for topics such as geomechanics, rock mechanics and groundwater flow and solute transport. One key aspect is the roughness of the fracture, often described as the joint roughness coefficient, JRC. JRC is often subjectively interpreted by one geologist comparing a fracture trace with different type traces. It has been shown that several geologists are needed to get reliable interpretations of JRC. There are numerous attempts in the literature to develop objective methods to estimate JRC from digital traces. Some methods are not applicable to fractures, which give arbitrary results while other methods are sensitive to the resolution of the digitalisation and hence need a new relationship for each resolution. Another way of describing the roughness is by the two parameters fractal dimension and magnitude distribution of the asperities. These parameters can be objectively inferred using algorithms and act as input for a model to estimate JRC. Using several evaluation methods, the uncertainty can be decreased and, hence, more robust results achieved. A multilinear model is developed, JRC = − 4.3 + 54.6σδh(1mm) + 4.3H, that estimates JRC, of the classic ten type curves by Barton and Choubey, with standard deviation ± 1 unit. Despite the simplicity of the model it explains 96.5% of the variance in JRC. The developed model is benchmarked against an ensemble of geologists, using nine synthetic fracture traces. The median difference of JRC is 0.2 units and the model shows 40% smaller spread compared to the geologists.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
JRC · Conceptual model · Fractal line · Hurst exponent · Fractal dimension · Asperity distribution
National Category
Geotechnical Engineering
Identifiers
urn:nbn:se:kth:diva-248961 (URN)10.1007/s00603-018-1651-6 (DOI)000462225400006 ()2-s2.0-85057134965 (Scopus ID)
Funder
Swedish Nuclear Fuel and Waste Management Company, SKB
Note

QC 20190426

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-09-29Bibliographically approved
5. Finally, an objective way to infer JRC from digitized fracture traces
Open this publication in new window or tab >>Finally, an objective way to infer JRC from digitized fracture traces
2018 (English)In: 52nd U.S. Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association (ARMA), 2018Conference paper, Published paper (Refereed)
Abstract [en]

The understanding of hard rock fractures is important for topics such as geomechanics, rock mechanics and ground water flow and transport. One key aspect is the geometry of the two surfaces defining a fracture, often referred to as roughness. Probably the most used measure to determine the roughness is the Joint Roughness Coefficient, JRC. The accurate way to determine JRC is to do shear tests and back calculate JRC. However, most often this procedure is neither feasible nor possible. Instead, JRC is commonly determined by a subjective comparison of the fracture and some type traces. It has been shown that at least 50 geologists are needed to get stable inferences of JRC. Lately, a model has been developed that is supposed to objectively infer JRC from the two fractal parameters H and σδh(1 mm). This model is used to predict JRC of nine synthetic traces. The results are compared to the visually interpreted JRC values by eleven geologists. The differences between the JRC, by the model, and the median value of the geologist are negligible. Hence, the model is an objective way to infer JRC from digitized fracture traces.

Place, publisher, year, edition, pages
American Rock Mechanics Association (ARMA), 2018
Keywords
Flow of water, Groundwater, Rock mechanics, Rocks, Fractal parameters, Hard rocks, Joint roughness coefficients, Median value, Shear tests, Synthetic traces, Fracture
National Category
Geophysical Engineering
Identifiers
urn:nbn:se:kth:diva-236360 (URN)2-s2.0-85053453507 (Scopus ID)
Conference
52nd U.S. Rock Mechanics/Geomechanics Symposium, 17 June 2018 through 20 June 2018
Note

QC 20181106

Available from: 2018-11-06 Created: 2018-11-06 Last updated: 2019-09-29Bibliographically approved
6. Did you forget the measurement uncertainty doing your connectivity analysis?
Open this publication in new window or tab >>Did you forget the measurement uncertainty doing your connectivity analysis?
2018 (English)In: 2nd International Discrete Fracture Network Engineering Conference, DFNE 2018, American Rock Mechanics Association (ARMA), 2018Conference paper, Published paper (Refereed)
Abstract [en]

Many engineering applications in crystalline rocks use fracture intercepts mapped in boreholes as foundation. From this mapping the distributions of intensity, spatiality and orientation can be inferred. These three distributions combined with the size distribution steer the connectivity of the fracture network and hence the nature of groundwater flow and transport of solutes. This study, however, only focuses on the impact that the orientation uncertainty has on the connectivity. The orientation of a fracture intersecting a borehole can be calculated using four angles, each afflicted with uncertainty. These uncertainties are used to distinguish between natural variability and uncertainty using a χ2 test of a contingency table of fracture poles. Two DFN models are developed, the rock mass fracture and the “measured” model, and the differences in connectivity between the models are analyzed. The rock mass fracture model have 30% more connected fractures, 60% more connected fracture area and is more elongated than the “measured” model at the connectivity level when the first fracture of the two clusters hits any boundary of the modelling cube.

Place, publisher, year, edition, pages
American Rock Mechanics Association (ARMA), 2018
National Category
Geophysical Engineering
Identifiers
urn:nbn:se:kth:diva-241876 (URN)2-s2.0-85059386910 (Scopus ID)
Conference
2nd International Discrete Fracture Network Engineering Conference, DFNE 2018, Seattle, United States, 20 June 2018 through 22 June 2018
Note

QC 20190125

Available from: 2019-01-25 Created: 2019-01-25 Last updated: 2019-09-29Bibliographically approved
7. A method to estimate flow and transport properties of sheared synthetic fractures in crystalline rock with different roughness under varying normal stress
Open this publication in new window or tab >>A method to estimate flow and transport properties of sheared synthetic fractures in crystalline rock with different roughness under varying normal stress
(English)Manuscript (preprint) (Other academic)
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-260386 (URN)
Note

QC 20191003

Available from: 2019-09-29 Created: 2019-09-29 Last updated: 2019-10-03Bibliographically approved
8. Some aspects on the applicability of peak shear strength criteria
Open this publication in new window or tab >>Some aspects on the applicability of peak shear strength criteria
(English)Manuscript (preprint) (Other academic)
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-260385 (URN)
Note

QC 20191003

Available from: 2019-09-29 Created: 2019-09-29 Last updated: 2019-10-03Bibliographically approved

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1112131415161714 of 18
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  • en-GB
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  • text
  • asciidoc
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