Fractured Rock Masses as Equivalent Continua – A Numerical Study Ki-Bok Min April 2004 TRITA-LWR PHD 1011 ISSN 1650-8602 ISRN KTH/LWR/PHD 1011-SE ISBN 91-7283-757-8 To my father and mother in Korea and my lovely wife, Mi-Suk Lee Fractured Rock Masses as Equivalent Continua – A Numerical Study ACKNOWLEDGEMENT It is my great pleasure to be able to thank the people who have helped and supported me in various ways. First of all, I would like to express my deepest gratitude to my main supervisor, Dr. Lanru Jing of the Royal Institute of Technology (KTH) for his academic guidance throughout the duration of the study. I am greatly indebted to his advice, suggestion and all the support for my research work. I also would like to express my sincere gratitude to my co- supervisor, Prof. Ove Stephansson of GeoForschungsZentrum (GFZ), Germany for the trust on my work and endless encouragement, which led me to come to this stage with confidence. I also thank Dr. Jonny Rutqvist of Lawrence Berkeley National Laboratory (LBNL), USA as my third supervisor for his enlightening advice and discussion, through my two visits to Berkeley and numerous email and telephone correspondences. Main financial support for the study was given by European Commission and additional support was provided by the Swedish Nuclear Inspective (SKI) and the French National Radioactive Waste Management Agency (ANDRA). I would like to thank Dr. Henning von Maravic of EC, Dr. Fritz Kautsky of SKI and Dr. Kun Su of ANDRA for their en- gagements. I was very fortunate to be involved in the prestigious international projects, DECO- VALEX and BENCHPAR. I would like to thank the colleagues in the projects for their comments, fruitful discussion and cooperation during the course of workshops. In particu- lar, I would like thank Prof. John Hudson of Imperial College, UK for his insightful com- ments and especially encouragement. I would like to extend my sincere gratitude to Dr. Chin-Fu Tsang of LBNL for suggesting many ideas on my research, collaboration on the two papers and hospitality during my visits to Berkeley. I also would like to thank Philipp Blum of then Univ. of Birmingham, Johan Öhman of Uppsala Univ., Dr. Johan Anderson of JA Streamflow, Dr. Leslie Knight of Nirex, Dr. Auli Niemi of Uppsala Univ. for very fruitful interactions. I am grateful to the former and current colleagues at Engineering Geology and Geophysics (EGG) group at KTH for all the comments, discussion and cooperations. Ms. Ulla Eng- berg is specially thanked for having been supportive of many aspect of my life in Stock- holm, especially my early days. Diego Mas of Itasca Geomekanik is acknowledged for our collaborations and fruitful discussions. I greatly appreciate the expert review of the sum- mary of the thesis by Tomofumi Koyama and I wish him the best of luck in both profes- sional and private life in Stockholm. I would like to thank Britt Chow for effective and kind help with all administrative matters. I would like to thank my ex-supervisor, Prof. Chung-In Lee of Seoul National University, for giving me enormous moral support and advice for my PhD study through many email correspondences. Prof. Jae-Dong Kim of Kangwon National University is acknowledged for the help in finding this wonderful place and encouragement. I would like to convey my special thanks to a number of seniors in rock mechanics community in Korea, including Dr. Hee-Suk Lee of SK E & C, for their encouragement for the initiation and continuation of my PhD study. i Ki-Bok Min TRITA-LWR PHD 1011 Contribution by my wife, Mi-Suk Lee, is immeasurable if invisible in this thesis. Her ex- ceptional support and understanding during my thesis work have been essential and it made me to complete the thesis successfully. Also I would like to share much of this pleasure with Mi-Suk’s family in Korea, especially new-born nephew and nieces. I am deeply grateful to my parents for their exceptional moral support on my study and I would like to thank my sisters and brother for encouraging my study. I am excited and so happy to give this thesis to my parents who have been extremely enthusiastic for the higher education of their four children. Tack så mycket!! Ki-Bok Min, Stockholm, April 2004 ii Fractured Rock Masses as Equivalent Continua – A Numerical Study ABSTRACT In this thesis, fractured rock masses are treated as equivalent continua for large-scale analyses of rock engineering projects. Systematic developments are made for the determi- nation of equivalent mechanical and hydraulic properties of fractured rock masses using a hybrid discrete fracture network - distinct element method (DFN-DEM) approach. The determined equivalent properties are then used for a far-field finite element analysis of the thermo-mechanical impacts on the stress, deformation and permeability of fractured rocks surrounding a hypothetical geological repository of nuclear waste. The geological data were extracted from the results of an extensive site investigation programme at Sellafield, UK, conducted by Nirex UK Ltd. The scale dependencies of the hydraulic and mechanical properties were investigated by using multiple realizations of the fracture system geometry with increasing model sizes until properly defined hydraulic and mechanical representative elementary volumes (REVs) were reached. The validity of the second order permeability tensor and the fourth- order mechanical compliance tensor were tested for continuum analyses at larger scales. The REV was determined to be around 5 m for mechanical and hydraulic data in this study. Analysis of the stress-dependent mechanical and hydraulic properties shows that the effect of rock stresses is crucial. The elastic moduli increase significantly with the increase of stress and an empirical equation of stress-dependent elastic modulus is suggested based on results of numerical experiments. Calculations of the Poisson’s ratios suggest greater val- ues than are normally assumed in practice. Depending on the state of stress, permeability decreases or increases with increasing compressive stress. Stress-induced flow channeling effect is captured by numerical modeling for the first time and detailed mechanisms of shear dilation of fractures are provided. Based on the numerical experiments, a set of em- pirical equations was suggested for the stress-dependent permeability, considering both normal deformation and shear dilation of fractures. Thermo-mechanical impact on the performance of a hypothetical repository at a far-field scale (5 km by 1 km) was investigated with the stress-dependent equivalent properties de- termined at the REV scale. This analysis shows that mechanical responses vary signifi- cantly depending on how the mechanical properties were determined. The change of per- meability due to the thermal loading is, however, not significant in this particular case. The thesis provides a framework for systematic analysis of large-scale engineering appli- cations in fractured rock masses, such as geological repositories of nuclear wastes. Keyword: Fractured rock masses, Equivalent Continuum, Discrete Fracture Network (DFN), Distinct Element Method (DEM), Finite Element Method (FEM), Nuclear Waste Disposal, Coupled Thermo-Hydro-Mechanical Processes iii Ki-Bok Min TRITA-LWR PHD 1011 iv Fractured Rock Masses as Equivalent Continua – A Numerical Study SAMMANFATTNING I denna avhandling behandlas metoder för analys av spruckna bergmassor som kontinuer- liga material. En systematisk utveckling av metoder för ekvivalenta mekaniska och hyd- rauliska egenskaper hos spruckna bergmassor har skett med användninga av diskreta spricknätsmodeller och distinkt elementmetod (DFN-DEM). De ekvivalenta materialmo- dellerna har sedan tillämpats på storskaliga analyser av ett hypotetiskt slutförvar för kärn- avfall med hjälp av finit elementmetod. Spänningar, deformationer, flöden och termome- kanisk respons hos bergmassan har analyserats. Geologiska data för studien baseras på resultaten av platsundersökningarna vid Sellafield i Storbritannien, som genomfört av Ni- rex UK Ltd. Skalberoendet hos de hydrauliska och mekaniska egenskaperna har undersökts genom an- vändande av upprepade analyser av spricksystem med samma statistiska egenskaper men med ökande modellstorlek tills representativa hydrauliska och mekaniska elementarvoly- mer (REV) uppnåddes. Skalan för den fastställda elementarvolymen REV för den testade bergmassan är ungefär 5m för konstanta mekaniska och hydrauliska egenskaper. Studien av spänningsberoende mekaniska och hydrauliska egenskaper visar att effekten av bergspänningarna är kritisk. Elasticitetsmodulen ökar signifikant med ökad spänning och ett empiriskt samband för elasticitetsmodulens spänningsberoende presenteras. Det beräk- nade Poissonsförhållandet är mycket högre för bergmassorna än de typiska värden som används i praktiken. Permeabiliteten hos bergmassan minskar eller ökar med ökad spän- ning och är beroende av spänningstillståndet. Effekter av spänningsinducerad kanalström- ning i sprickorna fångas upp genom numerisk modellering och redovisas för första gången och mekanismerna bakom dilatation av sprickorna i samband med skjuvning redovisas. Baserat på numeriska experiment föreslås en uppsättning av empiriska ekvationer för spänningsberoende permeabilitet i samband med normalbelastning och skjuvning av sprickorna och bergmassan. Den termomekaniska responsen hos bergmassan från ett hypotetisk slutförvar för radioak- tivt avfall i skalan 5km x 1 km har studerats med den utvecklade DFN-DEM tekniken för ekvivalenta