Static and Dynamic behaviour of joints in schistose rock
Transcription
Static and Dynamic behaviour of joints in schistose rock
VERÖFFENTLICHUNGEN des Instituts für Geotechnik der Technischen Universität Bergakademie Freiberg Herausgeber: H. Konietzky Heft 2013-3 Static and Dynamic behaviour of joints in schistose rock: Lab testing and Numerical simulation von Van Manh Nguyen Freiberg 2013 Veröffentlichungen des Instituts für Geotechnik der TU Bergakademie Freiberg Herausgeber: Prof. Dr.-Ing. habil. Heinz Konietzky Anschrift: TU Bergakademie Freiberg Institut für Geotechnik Gustav-Zeuner-Straße 1 09596 Freiberg Telefon: 03731 39-2458 Fax: 03731 39-3638 E-Mail: [email protected] Internet: http://tu-freiberg.de/fakult3/gt/ Herstellung: Druckerei Wagner Verlag und Werbung GmbH Printed in Germany Ohne ausdrückliche Genehmigung der Herausgeber ist es nicht gestattet, das Werk oder Teile daraus nachzudrucken oder auf fotomechanischem oder elektronischem W ege zu vervielfältigen. Für den Inhalt ist der Autor allein verantwortlich. © Institut für Geotechnik - TU Bergakademie Freiberg - 2013 ISSN 1611-1605 Static and Dynamic behaviour of joints in schistose rock: Lab testing and Numerical simulation To the Faculty of Geosciences, Geoengineering and Mining of the Technische Universität Bergakademie Freiberg approved THESIS to attain the academic degree of Doctor of Engineering Dr.-Ing. by Dipl.-Ing. Nguyen, Van Manh born on the May.12, 1976 in Hanoi, Vietnam Reviewers: Prof. Dr.-Ing. habil. Heinz Konietzky, Freiberg Prof. Dr.-Ing. Christof Lempp, Halle Prof. Dr.-Ing. Quang Phich Nguyen, Hanoi Date of the award: 14.10.2013 ii Acknowledgments The work described within this thesis was conducted at the Chair for Rock Mechanics, Geotechnical Institute (IFGT), TU Bergakademie Freiberg (TU BAF), Germany, from September 2009 to September 2013. Foremost, I wish to express my sincere gratitude to Prof. Dr. habil. Heinz Konietzky, my major supervisor, for all his constant support and instructive guidance on the development of my dissertation. I would like also to thank him for being an open person to ideas and for encouraging and helping me to complete my work. I would like to thank the Vietnam International Education Development (VIED), Ministry of Education and Training (MOET), for financially supporting this research. I would like to thank also the “Deutscher Akademischer Austausch Dienst - DAAD” for assistance and the additional financial contribution. They gave me the chance to understand more about Germany through the German language course. In addition, I am greatly thankful to all the colleagues at the Chair for Rock Mechanics for their support. They gave me many helpful advices during my stay in Freiberg. Specifically, I would like to thank Dr. Thomas Frühwirt, Tom Weichmann and Gerd Münzberger from the Rockmechanical Laboratory (IFGT) for all the support in sample preparation and conducting the experiments. I would like to thank also Angela Griebsch for kind help since I came to Freiberg. My greatest appreciation and friendship goes to all my friends at TU Freiberg. They always shared with me the good times while living and studying in Freiberg. Thank you for your good comments and suggestions which helped me to improve my understanding in quite different fields. Finally, I would like to thank my parents for their understanding and support. I am deeply indebted to my wife, Nguyen Thanh Thuy, and my son, Nguyen Manh Vu, for their patience, love and support in taking care of my family, without which would not have been able to complete my work while I stayed in Germany. iii iv Abstract The shear behaviour of rough rock joints was investigated by both laboratory testing and numerical simulations. The most powerful servo-controlled direct shear box apparatus in the world with normal forces up to 1000 kN, shear loading up to 800 kN and frequencies up to 40 Hz under full load was used to investigate the shear strength of schistose rock blocks with dimensions of up to 350 x 200 x 160 mm in length, width and height, respectively. The experiments were performed to study the behaviour of rough rock joints under constant normal load, constant normal stiffness and dynamic boundary conditions. The joint surface of rock specimen was scanned 3-dimensional at the initial stage before shearing by new 3D optical-scanning equipment. The 3D-scanner data were used to estimate the joint roughness coefficient (JRC) and to reconstruct rough surface of rock discontinuities in numerical models. Three dimensional numerical models were developed using FLAC3D to study the macro and micromechanical shear behaviour of the joints. Numerical simulation results were compared to experimental results. Three dimensional characteristics of the joint surface including micro-slope angle, aperture, contact area and normal stress distribution were determined and analyzed in detail. Finally, a methodology is proposed to combine shear box experiments in the laboratory with corresponding numerical simulations to get maximum information about joint behaviour. v vi Table of Contents List of Figures .................................................................................................................. ix List of Tables................................................................................................................... xv 1 2 3 Introduction ............................................................................................................... 1 1.1 Problem statement ............................................................................................. 1 1.2 Objective of this work ....................................................................................... 1 1.3 Structure of the dissertation .............................................................................. 2 1.4 Major contributions of the thesis....................................................................... 3 Literature review ....................................................................................................... 5 2.1 Introduction ....................................................................................................... 5 2.2 Shear strength of rock joint under static loading .............................................. 5 2.2.1 Shear strength of rock joints under CNL boundary conditions................. 7 2.2.2 Shear strength of rock joints under CNS boundary conditions ............... 17 2.3 Shear strength of rock joints under dynamic loading...................................... 19 2.4 Rock joint surface roughness measurements .................................................. 24 2.4.1 Contact methods ...................................................................................... 25 2.4.2 Non-Contact methods.............................................................................. 26 2.4.3 Roughness scale-dependency .................................................................. 27 2.4.4 Joint roughness coefficient (JRC) ........................................................... 28 2.5 Overview about shear box test devices ........................................................... 31 2.6 Direct shear box testing methods .................................................................... 32 Shear box device GS-1000 ...................................................................................... 35 3.1 Introduction ..................................................................................................... 35 3.2 Shear box test apparatus GS-1000 .................................................................. 36 3.2.1 Hardware ................................................................................................. 36 3.2.2 Software .................................................................................................. 38 3.2.3 Test modes .............................................................................................. 41 3.3 3.3.1 Description of scanner device zSnapper ................................................. 42 3.3.2 Measurement of the rock joint surfaces by scanner zSnapper ................ 44 3.4 4 zSnapper: scanner for rock joint roughness measurement .............................. 42 Sample preparation.......................................................................................... 47 Laboratory shear box tests ...................................................................................... 49 4.1 Static tests ....................................................................................................... 49 vii 4.1.1 Constant Normal Load (CNL) tests ........................................................ 49 4.1.2 Constant Normal Stiffness (CNS) tests ................................................... 68 4.2 5 Dynamic shear tests......................................................................................... 77 4.2.1 Dynamic shear test set-up ....................................................................... 77 4.2.2 Dynamic shear test results....................................................................... 78 Numerical simulation of direct shear box tests - comparison with laboratory tests 89 5.1 Overview of FLAC3D ...................................................................................... 89 5.2 Numerical model set-up .................................................................................. 90 5.2.1 Surface roughness simulation ................................................................. 90 5.2.2 Constitutive model .................................................................................. 92 5.2.3 Rock mechanical model calibration ........................................................ 98 5.2.4 Simulation of direct shear tests under CNL conditions ........................ 100 5.2.5 Simulation of direct shear tests under CNS conditions......................... 101 5.3 Micro-slope angle distribution ...................................................................... 102 5.4 Numerical simulations of quasi-static shear tests ......................................... 109 5.4.1 CNL simulation results ......................................................................... 109 5.4.2 CNS simulation results.......................................................................... 136 5.4.3 Plasticity state ....................................................................................... 151 5.5 Numerical simulations of dynamic shear tests .............................................. 153 5.5.1 Micro-slope angle distribution .............................................................. 155 5.5.2 Dynamic simulation results ................................................................... 157 6 Parameter set for Mayen-Koblenz schist .............................................................. 167 7 Conclusions and recommendations ....................................................................... 169 7.1 Conclusions ................................................................................................... 169 7.2 Recommendations ......................................................................................... 172 References ..................................................................................................................... 173 viii List of Figures Figure 2.1. Rock block sliding along existing joints at slope and excavation .................. 6 Figure 2.2. Patton’s experiment on the shear strength of saw-tooth specimens ............... 7 Figure 2.3. Roughness profiles and corresponding JRC values [Barton, 1976] ............... 8 Figure 2.4. Alternative method for estimating JRC from measurements of surface roughness amplitude from a straight edge [Barton and Bandis, 1982]............................. 9 Figure 2.5. Estimation of joint wall compressive strength (JCS) from Schmidt hardness [Deere and Miller, 1996] ................................................................................................ 11 Figure 2.6. Definition scheme of joint matching: (a) matched joint; (b) mismatched joint ......................................................................................................................................... 12 Figure 2.7. Simple profilograph for measurement of joint roughness ............................ 25 Figure 2.8. Example of contact methods for measurement of joint surface roughness .. 26 Figure 2.9. Principle of photogrammetry [Birch, 2006; Gaich, et al., 2006] ................. 27 Figure 2.10. Scale dependency of shear strength of rock joints...................................... 28 Figure 2.11. Simulation of the in-situ boundary conditions in the direct shear test ....... 33 Figure 3.1. Overview of direct shear test apparatus GS-1000 ........................................ 35 Figure 3.2. Loading system of shear box device GS-1000 ............................................. 36 Figure 3.3. Shear box of the GS-1000 apparatus ............................................................ 37 Figure 3.4. Water tanks for cooling system [Luge, 2011; Konietzky, et al., 2012] ......... 38 Figure 3.5. LVDT’s for the normal and shear displacement measurement .................... 38 Figure 3.6. Simplified flowchart of electronically control unit ...................................... 40 Figure 3.7. The data logging unit AM8 [Luge, 2011; Konietzky, et al., 2012] ............... 41 Figure 3.8. 3D-scanner zSnapper [ViALUX., 2010] ........................................................ 42 Figure 3.9. Measuring volume (red) of the zSnapper [ViALUX., 2010] ......................... 43 Figure 3.10. Calibration gauge with reference points [ViALUX., 2010] ......................... 43 Figure 3.11. Example of using zSnapper for capturing surface features ........................ 46 Figure 3.12. Intact rock specimen preparation for shear testing ..................................... 47 Figure 4.1. CNL test set-up for intact (a) and jointed (b) sample ................................... 50 Figure 4.2. LVDT’s for the horizontal and vertical displacement measurement ............ 51 Figure 4.3. Shear stress versus shear displacement under different normal stress (3.6; 5.0 and 10.0 MPa) for intact rock specimens ........................................................................ 53 Figure 4.4. Mohr-Coulomb failure envelope for peak and residual state for initial intact rock samples .................................................................................................................... 53 ix Figure 4.5. Shear stress versus shear displacement of the CNL01 specimen under ....... 56 Figure 4.6. Shear stress versus shear displacement of the CNL02 specimen under ....... 56 Figure 4.7. Shear stress versus shear displacement of the CNL03 specimen under ....... 56 Figure 4.8. Shear stress versus shear displacement of the CNL04 specimen under ....... 57 Figure 4.9. Ratio of shear to normal stress versus shear displacement of CNL01 specimen ......................................................................................................................................... 58 Figure 4.10. Ratio of shear to normal stress versus shear displacement of CNL02 specimen ......................................................................................................................................... 58 Figure 4.11. Ratio of shear to normal stress versus shear displacement of CNL03 specimen ......................................................................................................................................... 59 Figure 4.12. Ratio of shear to normal stress versus shear displacement of CNL04 specimen ......................................................................................................................................... 59 Figure 4.13. Peak shear stress versus normal stress for different shear velocities and JRC .................................................................................................................................. 59 Figure 4.14. Shear stress versus shear displacement at different shear velocities .......... 61 Figure 4.15. Mohr-Coulomb failure envelope for individual samples under CNL tests 62 Figure 4.16. Mohr-Coulomb failure envelope in general under CNL tests .................... 63 Figure 4.17. Normal stress versus shear displacement for CNL tests ............................. 63 Figure 4.18. The relationship between shear direction and slope direction of interface 64 Figure 4.19. Normal displacement versus shear displacement of CNL01 specimen ...... 65 Figure 4.20. Normal displacement versus shear displacement of CNL02 specimen ...... 65 Figure 4.21. Normal displacement versus shear displacement of CNL03 specimen ...... 65 Figure 4.22. Normal displacement versus shear displacement of CNL04 specimen ...... 66 Figure 4.23. Dilation angle versus normal stress under CNL conditions ....................... 67 Figure 4.24. Constant normal stiffness test set-up for intact (a) and jointed (b) sample 69 Figure 4.25. Shear stress versus shear displacement of CNS01 specimen ..................... 71 Figure 4.26. Shear stress versus shear displacement of CNS02 specimen ..................... 71 Figure 4.27. Shear stress versus shear displacement of CNS03 specimen ..................... 71 Figure 4.28. Peak shear stress versus normal stiffness at different shear velocities and JRC .................................................................................................................................. 73 Figure 4.29. Effective normal stress versus shear displacement of CNS01 specimen ... 74 Figure 4.30. Effective normal stress versus shear displacement of CNS02 specimen ... 74 Figure 4.31. Effective normal stress versus shear displacement of CNS03 specimen ... 74 Figure 4.32. Normal displacement versus shear displacement of CNS01 specimen ...... 75 x Figure 4.33. Normal displacement versus shear displacement of CNS02 specimen ...... 76 Figure 4.34. Normal displacement versus shear displacement of CNS03 specimen ...... 76 Figure 4.35. Dilation angle versus normal stiffness under CNS conditions ................... 77 Figure 4.36. Dynamic shear test set-up for jointed rock sample..................................... 77 Figure 4.37. Shear displacement versus time of DT01 specimen ................................... 79 Figure 4.38. Shear displacement versus time of DT02 specimen ................................... 79 Figure 4.39. Shear displacement versus time of DT03 specimen ................................... 79 Figure 4.40. Shear stress versus time of DT01 specimen ............................................... 80 Figure 4.41. Shear stress versus time of DT02 specimen ............................................... 80 Figure 4.42. Shear stress versus time of DT03 specimen ............................................... 81 Figure 4.43. Shear stress and shear displacement versus time of DT01 specimen ......... 82 Figure 4.44. Shear stress and shear displacement versus time of DT02 specimen ......... 82 Figure 4.45. Shear stress and shear displacement versus time of DT03 specimen ......... 83 Figure 4.46. Shear stress versus shear displacement after shearing of 10 cycles of the DT01 specimen ............................................................................................................... 83 Figure 4.47. Shear stress versus shear displacement after shearing of 10 cycles of the DT02 specimen ............................................................................................................... 84 Figure 4.48. Shear stress versus shear displacement after shearing of 10 cycles of the DT03 specimen ............................................................................................................... 84 Figure 4.49. Normal stress versus time of DT01 specimen ............................................ 85 Figure 4.50. Normal stress versus time of DT02 specimen ............................................ 85 Figure 4.51. Normal stress versus time of DT03 specimen ............................................ 86 Figure 4.52. Normal displacement versus time of DT01 specimen ................................ 86 Figure 4.53. Normal displacement versus time of DT02 specimen ................................ 86 Figure 4.54. Normal displacement versus time of DT03 specimen ................................ 87 Figure 4.55. Shear displacement and normal displacement versus time for one cycle of DT01 specimen ............................................................................................................... 87 Figure 5.1. Distribution of representative areas to interface nodes [Itasca., 2012] ........ 89 Figure 5.2. Simulation of surface roughness using FLAC3D .......................................... 91 Figure 5.3. General model for simulating the direct shear test in FLAC3D .................... 92 Figure 5.4. Components of the bonded interface constitutive model [Itasca., 2012] ..... 93 Figure 5.5. Mohr-Coulomb failure criterion [Itasca., 2012] ........................................... 96 Figure 5.6. Mohr-Coulomb model - domains used in the definition of the flow rule ..... 98 Figure 5.7. Model calibration procedure ......................................................................... 99 xi Figure 5.8. Conceptual model for CNL direct shear tests ............................................. 100 Figure 5.9. Conceptual model for CNS direct shear tests ............................................. 102 Figure 5.10. Triangle elements on the joint surface ...................................................... 103 Figure 5.11. Definition of positive and negative micro-slope angle ............................. 104 Figure 5.12. Surface mesh of CNL01 and CNL04 specimen ....................................... 104 Figure 5.13. Areal distribution of the micro-slope angles for CNL specimens ............ 105 Figure 5.14. Areal distribution of the micro-slope angles for CNS specimens ............ 105 Figure 5.15. Contour plot of the micro-slope angles with respect to relative shear direction for CNL specimens ........................................................................................ 107 Figure 5.16. Contour plot of the micro-slope angles with respect to relative shear direction for CNS specimens ........................................................................................ 108 Figure 5.17. The 3D model simulation results for CNL tests ....................................... 110 Figure 5.18. Shear stress versus shear displacement for different normal stress levels for CNL01 specimen........................................................................................................... 111 Figure 5.19. Shear stress versus shear displacement for different normal stress levels for CNL04 specimen........................................................................................................... 111 Figure 5.20. Normal stress versus shear displacement for different normal stress levels for CNL tests ................................................................................................................. 111 Figure 5.21. Contact area at interface surface for CNL01 specimen at different shear displacements under normal stress of 5 MPa ................................................................ 113 Figure 5.22. Contact area at interface surface for CNL04 specimen at different shear displacements under normal stress of 1 MPa ................................................................ 115 Figure 5.23. Contact area versus shear displacement under different normal stress for CNL01 specimen........................................................................................................... 115 Figure 5.24. Contact area versus shear displacement under different normal stress for CNL04 specimen........................................................................................................... 115 Figure 5.25. Definition of aperture size ........................................................................ 117 Figure 5.26. Aperture size distribution of CNL01 specimen under different normal stresses after shearing of 10 mm ................................................................................... 119 Figure 5.27. Aperture size distribution of CNL04 specimen under different normal stresses after shearing of 5 mm ..................................................................................... 120 Figure 5.28. Aperture size distribution of CNL01 specimen at different shear displacements under normal stress of 5 MPa ................................................................ 122 Figure 5.29. Definition of the dilation during the shearing process.............................. 123 xii Figure 5.30. Normal displacement versus shear displacement under CNL conditions for CNL01 and CNL04 samples ......................................................................................... 126 Figure 5.31. Normalized “real” dilation angle as a function of normal stress and JRC 127 Figure 5.32. Distribution of normal stress [Pa] across the joint surface for CNL01 specimen under initial normal stresses of 5 MPa and different shear displacements ... 129 Figure 5.33. Distribution of normal stress [Pa] across the joint surface for CNL01 specimen under initial normal stresses of 10 MPa and different shear displacements . 131 Figure 5.34. Distribution of normal stress [Pa] across the joint surface for CNL01 specimen under initial normal stresses of 15 MPa and different shear displacements . 133 Figure 5.35. Ratio of maximum to initial normal stress for CNL01 specimen............. 134 Figure 5.36. Distribution of local normal stress at the joint for different specimens ... 135 Figure 5.37. Ratio of maximum to initial normal stress for different specimens ......... 136 Figure 5.38. Numerical 3D model for CNS tests .......................................................... 137 Figure 5.39. Shear stress versus shear displacement under different normal stiffness for CNS specimens ............................................................................................................. 138 Figure 5.40. Normal stress versus shear displacement for CNS01 specimen under different normal stiffness levels .................................................................................... 139 Figure 5.41. Variation of contact area under CNS testing for different initial normal stiffness and specimens ................................................................................................. 140 Figure 5.42. Aperture size distribution of CNS01 specimen under different initial normal stiffness at shear displacement of 10 mm ......................................................... 142 Figure 5.43. Aperture size distribution of CNS02 specimen under different initial normal stiffness at shear displacement of 10 mm ......................................................... 143 Figure 5.44. Aperture size distribution of CNS03 specimen under different initial normal stiffness at shear displacement of 10 mm ......................................................... 144 Figure 5.45. Normal stress [Pa] distribution for CNS01 specimen under different normal stiffness at shear displacement of 10 mm ..................................................................... 147 Figure 5.46. Normal stress [Pa] distribution for CNS02 specimen under different normal stiffness at shear displacement of 10 mm ..................................................................... 149 Figure 5.47. Normal stress [Pa] distribution for CNS03 specimen under different normal stiffness at shear displacement of 10 mm ..................................................................... 150 Figure 5.48. Failure envelope for rock matrix and bedding and local stresses at interface (FLAC3D simulations) for sample CNL01 at 10 mm shear displacement. ................... 151 xiii Figure 5.49. Plasticity state inside lower part of sample CNL01 under different initial normal stress at shear displacement of 10 mm.............................................................. 152 Figure 5.50. Cracking inside the rock blocks after shear testing .................................. 153 Figure 5.51. Numerical 3D model for dynamic tests .................................................... 154 Figure 5.52. Areal distribution of the micro-slope angles for DT specimens ............... 155 Figure 5.53. Contour plot of the micro-slope angle with respect to relative shear direction for DT specimens ........................................................................................... 157 Figure 5.54. Shear displacement versus time for DT specimens .................................. 158 Figure 5.55. Shear stress versus time for DT specimens .............................................. 159 Figure 5.56. Shear stress and shear displacement versus time for DT03 specimen...... 160 Figure 5.57. Shear stress versus shear displacement for DT samples ........................... 161 Figure 5.58. Normal stress versus time for DT specimens ........................................... 162 Figure 5.59. Normal displacement versus time for DT specimens ............................... 164 Figure 5.60. Plastic states on lower block of DT03 sample for different number of cycles ............................................................................................................................. 166 Figure 5.61. Joint damage behaviour of DT03 sample ................................................. 166 Figure 7.1. Algorithm for combination of the direct shear tests and numerical simulations .................................................................................................................... 171 xiv List of Tables Table 2-1. Main technical data of some direct shear box devices .................................. 31 Table 3-1. Technical data of the GS-1000 apparatus ...................................................... 41 Table 3-2. zSnapper technical data ................................................................................. 45 Table 4-1. Rock mechanical matrix properties ............................................................... 49 Table 4-2. Set-up for CNL testing (multi-stage tests) ..................................................... 50 Table 4-3. JRC values for different rock specimens ....................................................... 52 Table 4-4. Peak and residual shear stresses for initial intact rock samples..................... 54 Table 4-5. Peak shear stress under different normal stress for the CNL tests ................ 57 Table 4-6. JRC, peak shear stress (τp) and shear velocity (v) data ................................. 60 Table 4-7. Peak shear stress at different shear velocities ................................................ 60 Table 4-8. Normal and shear displacements for various normal stresses ....................... 66 Table 4-9. Dilation angle (ψ), JRC and applied normal stress (σno) ............................... 67 Table 4-10. Rock joint mechanical parameters of CNL tests ......................................... 68 Table 4-11. Set-up for CNS testing (multi-stage tests) ................................................... 69 Table 4-12. JRC, normal stiffness (Kn) and peak shear stress (τp) ................................. 73 Table 4-13. Normal stresses and shear displacements under CNS conditions ............... 75 Table 4-14. Dilation angle (ψ), JRC, normal stiffness (Kn) and shear velocity (v) ........ 76 Table 4-15. Rock joint mechanical parameters of the CNS specimens .......................... 77 Table 4-16. Parameters for dynamic shear testing .......................................................... 78 Table 4-17. Absolute maximum shear stresses ............................................................... 81 Table 4-18. Average peak dynamic friction angle and JRC ........................................... 85 Table 5-1. Rock mechanical matrix properties ............................................................... 99 Table 5-2. Rock mechanical joint properties ................................................................ 100 Table 5-3. Micro-slope angle data for different specimens .......................................... 106 Table 5-4. Contact area data for different specimens under CNL conditions ............... 116 Table 5-5. Aperture size data for different specimens under CNL conditions ............. 121 Table 5-6. Coefficients (a, b, c) and joint surface slope angle (α) for CNL samples ... 125 Table 5-7. Dilation data for CNL tests .......................................................................... 126 Table 5-8. Stress amplification ratios for joint surface of CNL01 specimen under different applied normal stresses ................................................................................... 133 Table 5-9. Contact area for different specimens under CNS conditions....................... 141 xv Table 5-10. The aperture size for different specimens under CNS conditions ............. 141 Table 5-11. Coefficients (a,b,c) and joint surface slope angle (α) for CNS samples ... 145 Table 5-12. Dilation data for CNS tests ........................................................................ 145 Table 5-13. Stress amplification ratios for joint surface under different normal stiffness ....................................................................................................................................... 150 Table 5-14. Micro-slope angle and JRC for different DT specimens ........................... 156 Table 6-1. Mechanical parameters for Mayen-Koblenz schist (σno = 0 ÷ 15 MPa)...... 167 xvi 1 Introduction 1.1 Problem statement In geotechnical engineering, the shear strength of rock joints is one of the most important parameters used for stability analysis and design of excavations, slopes and foundations in rock masses. The behaviour of jointed rock can be investigated in the insitu or laboratory by using direct shear apparatus. The shear behaviour of rock joints has been investigated by many researchers under both constant normal load [Patton, 1966; Ladanyi and Archambault, 1970; Barton, 1976; Gentier, et al., 2000; Grasselli and Egger, 2003; Belem, et al., 2004; Jiang, et al., 2006; Kim and Lee, 2007; Asadi and Rasouli, 2012] and constant normal stiffness [Lam and Johnston, 1982; Ohnishi and Dharmaratne, 1990; Kodikara and Johnston, 1994; Haberfield and Seidel, 1999; Haque, 1999; Jiang, et al., 2004]. However, most of them were performed on small artificial specimens at low normal load. The joint surface was usually saw-tooth shaped. Rock structures such as rock slopes, tunnels, power plants, dams, mines and underground storage caverns must resist dynamic loads caused by blasting or earthquakes. Therefore, dynamic shear strength of rock joints becomes more important for design of rock structures. Unfortunately, until now the dynamic behaviour of rock discontinuities is still not very well investigated. This dissertation presents results obtained by a large new servo-controlled direct shear apparatus designed for rock mechanical testing with normal forces up to 1000 kN, shear loading up to 800 kN and frequencies up to 40 Hz under full load. 1.2 Objective of this work Shear behaviour of rock joints was investigated under Constant Normal Load (CNL), Constant Normal Stiffness (CNS) and dynamic (DT) boundary conditions. The experiments are conducted on rough joints in schist rock. Effects of various parameters such as normal stress, normal stiffness, joint roughness coefficient (JRC) and shear velocity on the shear behaviour of rock joints were also investigated. 1 Based on the experiment results, numerical simulations have been carried out to model the shear behaviour of rough rock joints at the micro-scale using FLAC3D [Itasca., 2012]. Finally, the numerical simulation results were analyzed and compared with laboratory results. Within this thesis a new methodology is proposed, which combines different shear experiments in the laboratory with corresponding numerical simulations at the microscale. Due to the combination of these two methods, a much more detailed insight into the joint behaviour under different boundary conditions can be obtained. 1.3 Structure of the dissertation This dissertation documents the experimental results of the shear behaviour of rough rock joints under CNL, CNS and dynamic boundary conditions. The dissertation presents also a procedure to simulate the behaviour of rough rock joints at the microscale. The dissertation is subdivided into seven chapters as follows: The first chapter (current chapter) introduces the topic, outlines the goals of the work and provides an overview. The second chapter introduces the theoretical background of shear strength of rock joints. It gives a literature review about the shear strength of rock joints under different boundary conditions such as constant normal load, constant normal stiffness and dynamic conditions. It also presents the measurement methods for estimating rock joint roughness coefficient (JRC). Finally, recently developed direct shear box apparatuses are mentioned and compared. The third chapter describes the new developed shear box tests apparatus GS-1000 and the 3D scanner, which were used to perform and analyze the direct shear tests. It also deals with sample preparation for direct shear tests and rock mechanical properties obtained from literature. The forth chapter presents the laboratory experiments and discusses the obtained results. The direct shear tests were firstly conducted on intact schistose rock blocks to 2 create the shear joint surface. After that they were sheared on the shear joint surfaces to investigate the shear behaviour of rock joints. The laboratory direct shear tests were performed under constant normal load, constant normal stiffness and dynamic boundary conditions. The fifth chapter deals with numerical simulations of the direct shear tests. The rough surface of the samples was reconstructed using FLAC3D program. The shearing process was also simulated to investigate the shear behaviour of rough rock joint surfaces. The simulation results are compared with the experimental results. The distributions of micro-slope angles and apertures on the joint surfaces were determined. Also, the normal stress acting on the joint surface during the shearing process is presented in this chapter. Finally, the joint behaviour under dynamic loading was investigated by laboratory tests and corresponding numerical simulations. The sixth chapter summarizes the intact and joint surface mechanical parameters for Mayen-Koblenz schist obtained from laboratory experiments. The seventh chapter provides a discussion of the obtained results. An outline of the proposed methodology combining laboratory tests and numerical simulations is presented. Conclusions are drawn, achievements and new finding are summarized and recommendations for future possible research work are given. 1.4 Major contributions of the thesis This thesis focus on experiments using a new developed shear box device GS-1000 and corresponding numerical simulations for direct shear tests on rough rock surfaces under quasi-static and dynamic conditions. The main contributions of the dissertation are: Conduction of direct shear tests under constant normal load (CNL), constant normal stiffness (CNS) and dynamic (DT) conditions using the new servocontrolled direct shear box device GS-1000. Development of a procedure of combined use of shear box tests and corresponding numerical simulations to get detailed knowledge about joint behaviour. 3 Application of the new 3D-scanner (zSnapper) to scan the joint surfaces. Development of routines to calculate JRC from 3D-scanner data and transfer to set-up corresponding numerical models. Proposal for a method to estimate shear strength of jointed rock for different shear velocities. Adaption of a numerical calculation scheme to simulate direct shear tests on rough joint surface under CNL, CNS and dynamic conditions at the micro-scale. Detailed analysis of dilation angle for rough and inclined joint surfaces (negative and positive dilation) and development of a method to determine the ‘real’ dilation angle for joints of any kind of roughness and orientation. Programming of routines to estimate the micro-slope angles for rough rock joint surfaces under consideration of the shear direction. Developed the routines to calculate the aperture size distribution of the joint interfaces after shearing. Developed the routines to determine the contact area for rough joint surfaces. Programming of routines to determine the normal stress distribution on the rough joint surfaces. Deduction of a complete data set for rough joints for Mayen-Koblenz schist rock. Generation of large rough joints inside intact schist samples by using the new shear box device GS-1000. 4 2 Literature review 2.1 Introduction Natural rock masses always contain discontinuities such as joints, fractures, faults, bedding planes and other geological structures. The discontinuity surfaces can be smooth or rough; in good contact or poor contact; filled or not. The presence of discontinuities in a rock mass may have a significant influence on its shear strength. Rock mass behaviour under low stress conditions is mostly controlled by sliding along existing discontinuities rather than failure of the intact rock mass [Hoek, 2007]. This means that the shear strength of a discontinuity in rock mass may have a strong impact on the mechanical behaviour of rock joints in engineering structures (slopes, foundations, tunnels, mine openings etc.). The behaviour of rock discontinuities is still not very well investigated and understood in general and especially under dynamic loads. Large-size underground structures such as storage cavern and radioactive waste repositories or dams require a high standard of resistance against blasting and earthquake loads. Therefore, the dynamic shear behaviour of rock joints becomes more important for designers and engineers. The most popular method currently used to determine the joint shear strength is a direct shear test which can be performed in the field and in the laboratory using a direct shear apparatus. The shear behaviour of rock joints is studied in laboratory under CNL, CNS and dynamic boundary conditions. 2.2 Shear strength of rock joint under static loading Shear strength is the maximum resistance to deformation by continuous shear displacement upon the action of shear stress. Shear strength of a rock is the sum of surface frictional resistance to sliding, interlocking effect between the individual rock grains and natural apparent cohesion. 5 Peak shear strength: The peak shear strength is the highest stress sustainable just prior to complete failure of sample under shear load; after this, stress cannot be maintained and major strains usually occur by displacement along failure surfaces [Allaby, 2008]. The peak shear strength of a rock joint undergoing shear displacement is dependent on the normal load applied across the interface, surface characteristics such as roughness and joint wall strength, and the boundary conditions. Residual shear strength: The residual shear strength is the ultimate strength along a surface or parting in rock after shearing has occurred [Allaby, 2008]. The residual shear strength typically depends on the applied normal pressure. Shear behaviour of rock joints is one of most important factors that must be considered in rock mechanical engineering. In fact, rock blocks can slide along existing joints or faults at slopes or underground openings as shown in Figure 2.1. W Figure 2.1. Rock block sliding along existing joints at slope and excavation [Brady and Brown, 2005] Shear strength of rock joints is controlled by constant normal load (CNL) generated by the weight of the block in the case of unreinforced rock slope; while in deep underground structures and rock slopes reinforced by bolts, shear strength of jointed rock is controlled by constant normal stiffness (CNS) due to constraints of lateral displacement as shown in Figure 2.1. Consequently, depending on the actual problem, the shear strength of rock joints should be investigated under constant normal load or constant normal stiffness boundary conditions. 6 2.2.1 Shear strength of rock joints under CNL boundary conditions Several researchers have studied the shear strength of rock joints (artificial and natural joints) under CNL boundary conditions. The relationship between the peak shear stress and the normal stress can be expressed by the Mohr-Coulomb equation: τ p = σ no tan φb + c where (2-1) τp is the peak shear stress, σno is the normal stress, φb is the basic friction angle, and c is the cohesion of rock. Patton (1966) carried out shear tests on 'saw-tooth' specimens such as the one illustrated in Figure 2.2. Shear displacement in these specimens occurs as a result of the surfaces moving up the inclined faces, causing dilation (increase in volume). shear stress τ normal stress σno i shear stress τ failure of intact rock shearing on sawtooth surfaces (φb + i) Normal stress σno Figure 2.2. Patton’s experiment on the shear strength of saw-tooth specimens The shear strength of Patton's saw-tooth specimens can be represented by τ p = σ no tan (φb + i ) where (2-2) i is the angle of the saw-tooth face. 7 Ladanyi and Archambault (1970) have suggested a new method to define shear strength of the material adjacent to the discontinuity surfaces as follows: τ= where σ no (1 − a s )(V + tan φ ) + a s .τ r 1 − (1 − a s )V tan φb (2-3) τ is joint shear strength, as is the proportion of the discontinuity surface which is sheared through projections of intact material, V is the dilation rate (dv/du) at peak shear strength, and τr is the shear strength of the intact material. Figure 2.3. Roughness profiles and corresponding JRC values [Barton, 1976] 8 The surface roughness of natural rock joints is an extremely important parameter, which has influence on the shear strength of joints, especially in the case of unfilled joints. Generally, the shear strength of the joint surface increases with increasing surface roughness. Barton (1976) has proposed a joint roughness coefficient (JRC) to take care of the strength of discontinuities in rock mass (Q - system). Figure 2.3 shows typical roughness profiles for the entire JRC range. Figure 2.4. Alternative method for estimating JRC from measurements of surface roughness amplitude from a straight edge [Barton and Bandis, 1982] 9 JRC is determined by the direct profiling method or by an indirect method as illustrated in Figure 2.4. The International Society for Rock Mechanics [ISRM., 1978] suggests that in general terms the roughness of the discontinuity walls can be characterized by “waviness” (large-scale undulations which, if interlocked and in contact, cause dilation during shear displacement since they are too large to be sheared off) and by “unevenness” (small-scale roughness that tends to be damaged during shear displacement unless the discontinuity walls are of high strength and/or the stress levels are low, so that dilation can also occur on these small scale features). Many researchers [Barton, 1973; Barton, 1976; Barton and Choubey, 1977; Zhao and Zhou, 1992; Maksimovic, 1996; Kulatilake and Um, 1997; Zhao, 1997a; Zhao, 1997b; Fox, et al., 1998; Yang and Chiang, 2000; Lee, et al., 2001; Grasselli, et al., 2002; Seidel and Haberfield, 2002] have investigated the roughness in two dimensions. The joint roughness coefficient (JRC) is a measure of the texture of a surface. It is quantified by the vertical deviations of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small the surface is smooth. Based upon the results of experimental investigation, Barton (1973, 1976) suggests the relationship between the shear strength of rough rock joint and JRC as follows: JCS σ no τ = σ no tan φb + JRC log10 where (2-4) JRC is the joint roughness coefficient, JCS is the joint wall compressive strength. On the basic of direct shear test results for 130 samples of variably weathered rock joints, Barton and Choubey (1977) revised this equation to: JCS σ no τ = σ no tan φ r + JRC log10 where φr is the residual friction angle, which is defined as: 10 (2-5) φ r = (φb − 20) + 20 r R (2-6) with r is the Schmidt rebound number for wet and weathered fracture surfaces and R is the Schmidt rebound number on dry unweathered sawn surfaces. Joint wall compressive strength (JCS) is an extremely important component of shear strength and deformation of rock joints. Deere and Miller (1966) have suggested the technique for estimating JCS by Schmidt Rebound Hammer test. The technique considers the unit weight of rock, hammer orientation, and Schmidt hardness as shown in Figure 2.5. Figure 2.5. Estimation of joint wall compressive strength (JCS) from Schmidt hardness [Deere and Miller, 1996] 11 Barton and Bandis (1982) have studied the scale effects of JRC and proposed JRC values for joints of large scale. The results show that joint wall compressive strength decreases with increasing sample size. They also proposed a scale correction for JRC defined by the following relationship: L JRC n = JRC o n Lo −0.02 JRCo (2-7) where JRCo and Lo (length) refer to 100 mm laboratory scale sample and JRCn and Ln refer to in-situ block size. The average joint wall compressive strength decreases with increasing scale. Barton and Bandis (1982) proposed a scale correction for JCS defined by L JCS n = JCS o n Lo −0.03 JRCo (2-8) where JCSo and Lo (length) refer to 100 mm laboratory scale sample and JCSn and Ln refer to in-situ block size. Zhao (1997a) and Zhao and Zhou (1992) have suggested a new parameter - the joint matching coefficient - JMC. This roughness index is based on the percentage of joint surface in contact. When the two surfaces completely fit together, the joint is totally matched. The degree of matching is therefore represented by the degree of fitness of the joint surfaces. a) b) Figure 2.6. Definition scheme of joint matching: (a) matched joint; (b) mismatched joint 12 A new shear strength criterion proposed by Zhao (1997b) includes the effects of both joints surface roughness and joint matching as follows: JCS σ no τ = σ no tan JRC × JMC × log10 + φ r (2-9) where JMC is the joint matching coefficient and JMC ≥ 0.3, for any measured JMC < 0.3, JMC should be set to 0.3 [Zhao, 1997b]. Maksimovic (1992) suggested a non-linear failure envelop of hyperbolic type to deduce the angle of shear resistance of rock joints. New shear strength envelop for rough rock joints is proposed as follows: ∆φ τ p = σ no tan φb + σ 1 + no PN where (2-10) ∆φ is the joint roughness angle which is the angle of maximum dilatancy, PN is the “median angle pressure” which is equal to the normal stress when the contribution is equal to one half of the angle of dilatancy for zero normal stress. Several researchers [Kulatilake, et al., 1995; Roko, et al., 1997; Re and Scavia, 1999; Belem, et al., 2000; Gentier, et al., 2000; Grasselli, 2001; Grasselli, et al., 2002; Grasselli and Egger, 2003; Belem, et al., 2004; Hong, et al., 2006; Jiang, et al., 2006] have studied 3-dimensional characterization of joint surfaces. They found some relationship between joint surface and the shear behaviour of rock joints. Re and Scavia (1999) used X-ray computer tomography to determine contact area in rock joints subjected to normal loads. Kulatilake et al. (1995) conducted direct shear tests on artificial anisotropic joints under constant normal stress and observed the average inclination angle along the direction of 13 the joint surface. Based on experimental results, they proposed a new peak shear strength criterion for rock joints: where σJ + I σ no d τ p = σ no tan φb + a( SRP) c log10 (2-11) SRP is the stationary roughness parameter, I is the average inclination angle along the direction of the joint surface, a, c and d are coefficients to be determined by performing regression analysis on experimental shear strength data, σJ is the joint compressive strength. Gentier et al. (2000) performed a series of shear tests on replicas of natural granite joints and found that there is a strong relationship between the fracture geometry and the mechanical behaviour. They analysed images of damaged zones on joint surfaces after shearing and suggested that the size, shape and spatial distribution of the damaged areas depend on the shear direction and shear displacement. Grasselli et al. (2001) have investigated the size and distribution of contact areas of rough surfaces in a 3-dimensional manner during shearing and concluded that damaged area increases with increasing stress and displacement. Based on the results of more than 50 constant normal load direct shear tests, Grasselli and Egger (2003) developed a new constitutive criterion for peak shear strength of rock joints under constant normal load conditions: θ ∗ τ p = σ no tan φb + max C where 1.18 cos α σ θ − max no 9A C σ 1 + e 0 t ∗ (2-12) θ∗max is the maximum apparent dip angle of the surface with respect to the shear direction, C is the roughness parameter, calculated using a best-fit regression function, which characterises the distribution of the apparent dip angles over the surface, 14 α is the angle between the schistosity plane and the normal to the joint, if the rock does not exhibit schistosity, α is assumed to be equal to zero, A0 is the maximum possible contact area in the shear direction, and σt is the tensile strength of the intact rock. Belem et al. (2004) suggested a new peak shear strength criterion taking into account anisotropy of surface morphology to predict the shear behaviour of irregular and regular joint surfaces under constant normal load and constant normal stiffness: τ p = σ no tan (φb + id ) + K n [u so tan (i p )]tan (φb + id ) where (2-13) Kn is the normal stiffness, ip is the peak dilation angle, id is dilatancy-degradation angle and can be expressed as 2 σ u o u so 2 (k a ) id = 2θ so exp − no s max + o 3 DRr σ c a o u s where (2-14) θ0s is the initial surface angularity, σc is the compressive strength of rock, u so is the shear displacement in 1st quadrant of cyclic shear curve, ao is the maximum amplitude of surface, usmax is the cumulated maximum shear displacement in 1st quadrant for n cycles of shearing, ka is the degree of surface apparent anisotropy, DR0r is the initial degree of surface roughness. Jiang et al. (2006) carried out direct shear tests on rock joints under low initial normal stress and measured the surface of rock joints before and after shearing by using a 3D laser scanning profilometer system. They found that the residual shear strength under constant normal stiffness boundary condition is higher than residual shear strength under constant normal load boundary condition. They also suggested a relation between shear stress and 3D fractal dimensions as follows: 15 JCS + φb σ no τ = σ no tan 500(Ds − 2) log where (2-15) Ds is the real fractal dimension of a rough surface. Hong et al. (2006) proposed a new method for rock joint surface roughness measurement by use of a camera-type 3D-scanner and showed that the new method is faster, more precise and more accurate than the current methods. The camera-type 3Dscanner method also produced 10% larger roughness values than current methods. Kim and Lee (2007) conducted direct shear tests on the joint models under constant normal stress and free dilatancy condition. Based on the experimental results, a new peak shear strength criterion for anisotropic rock joints was proposed: JCS + φ I σ no τ p = σ no φb + NRP log where (2-16) φI is the average non-stationary slope of the entire joint, NRP is a new roughness parameter, which is given by NRP = where dn JCS log10 σ no (2-17) dn is the peak dilation angle. Asadi and Rasouli (2012) investigated the effects of joint surface roughness on asperity contact degradation of synthetic and real rock samples and concluded that by increasing the normal stress, asperity degradation increases. The shear strength is reduced when the surface roughness is decreased. 16 2.2.2 Shear strength of rock joints under CNS boundary conditions The shear behaviour of rock joints under CNS boundary conditions is relevant for many practical situations such as rock socketed piles, grouted rock bolts and rock joints in deep underground openings. Several researchers have reported that the peak shear stress of rock joints under CNS boundary conditions is larger than that under CNL boundary conditions. Lam and Johnston (1982) conducted CNS tests on concrete/rock interfaces which were made from a synthetic rock material and concrete. They developed an analytical method for the peak shear stress: τ = (σ no + ∆σ n ) tan (θ + φ ) + where cos 2 c tan (i )η ( θ tan i + tan θ )(1 − tan θ tan φ ) (2-18) τ is the average shear stress, ∆σn is the change in normal stress due to dilation, θ is the inclination of shear plane, φ is the peak friction angle, c is the cohesion, i is the initial asperity angle, and η is the interlocking factor. Benmokrane and Ballivy (1989) performed CNS tests with regular and irregular interface surfaces and reported that the normal stiffness can have a large influence on the shear strength of the joints. A normal stiffness increase will increase the peak shear strength, decrease the peak dilation and increase the normal stress. Ohnishi and Dharmaratne (1990) performed CNS tests on artificial joint surfaces which were created by mortar, and observed that the shear strength increases with increasing initial normal stress and shear strength obtained under CNS was greater than that under CNL boundary conditions. Van Sint Jan (1990) carried out tests on several regularly shaped joints under low constant normal stiffness of 0.39 MPa/cm, and observed that the peak shear stress of 17 joints increases with increasing normal stiffness and that peak shear stress is always attained before the maximum normal stress has developed. Kodikara and Johnston (1994) conducted a series of direct shear tests on regular and irregular triangular asperities (rock-concrete joint samples) and concluded that regular joints have higher shear strength than irregular joints. Haberfield and Seiden (1999) carried out direct shear tests under CNS conditions and found that the peak shear strength is significantly lower than peak shear strength of concrete/rock joints with same roughness geometry and rock strength. Based on experimental results, a theoretical model was developed for sliding between rough surfaces of essentially elastic materials, asperity shearing and post-peak behaviour as follows: τ= where 1 n ∑ a jσ nj tan (φb + i j ) A j =1 (2-19) A is the total joint contact area, aj is the contact area of the individual asperities, σnj is normal stress acting on the individual asperities, ij is the asperity inclination, and n is number of asperities. Haque (1999) investigated shear strength of unfilled and infilled joints under CNL and CNS boundary conditions. The experimental results indicated that the peak shear strength obtained under CNS conditions is significantly lower than that under CNS conditions. The dilation of the joints under CNL conditions is greater than that under CNS conditions. Based on the Fourier transform method, new shear strength model was proposed to predict the shear behaviour of joints under CNS conditions as follows: τ p = σ no + where kn A 2πhτp a0 + a1 cos T 2 kn is the external normal stiffness, A is the joint surface area, 18 tan(φb ) + tan(i ) 1 − tan(φb ) tan(iτp ) (2-20) a0 and a1 are the Fourier coefficients, hτp and iτp are horizontal displacement and dilation angle corresponding to peak shear stress, T is the period, i is the initial asperity angle. 2.3 Shear strength of rock joints under dynamic loading In situ, the deformation of jointed rock mass surrounding an excavation may result from dynamic loadings due to blasting or earthquake excitation. Therefore, the dynamic effects on jointed rock need to be considered. The shear behaviour of joints under dynamic conditions have been studied by many researchers [Crawford and Curran, 1981; Gillette, et al., 1983; Bakhtar and Barton, 1984; Barla, et al., 1990; Hobbs, et al., 1990; Hutson and Dowding, 1990; Jing, et al., 1993; Qiu, et al., 1993; Kana, et al., 1996; Divoux, et al., 1997; Belem, et al., 2007; Ferrero, et al., 2010; Konietzky, et al., 2012]. Crawford and Curran (1981) conducted tests on many rock types such as syenite, dolomite, sandstone and granite. The tests were performed at constant rates of shear displacement varying from 0.05 to 200 mm/sec at normal loads of up to 100 kN. The results indicate that the shear strength of rock joints is dependent on the rate of shear velocity. In general, for harder rocks, the shear strength was found to decrease with increasing shear velocity. Conversely, the shear strength of softer jointed rocks increased with increasing shear velocity. Dynamic direct shear experiments were conducted on fresh artificial rock joints under drained and undrained conditions by Gillette, et al. (1983). The tests were carried out at frequencies ranging from 0 to 10 Hz and normal loads ranging from 69 to 3,448 kPa. They found that the shear strength of dry rock joints is velocity dependent and shear strength of rock joints increase with increasing shear velocity. Dynamic tests on undrained rock joints revealed that the interstitial water pressure in a joint subjected to dynamic shear displacements stabilizes early in the process and does not continue to increase with increasing number of cycles. They also found that the shear strength of the 19 joint closely follows the effective stress law even during the highly fluctuating water pressures. Bakhtar and Barton (1984) conducted a series of shear tests on artificially fractured blocks of sandstone, tuff, granite, hydro-stone, and concrete with surface areas of approximately 1 m2. The tests were performed under dynamic loading with shear velocities in the range of 400 to 4,000 mm/sec and the maximum load up to 2,700 kN. They used modified stress transformation equations developed by Barton and Choubey (1977) to predict the measured rock joint strengths with an accuracy of ±15%. The average predicted shear strengths were approximately 5% lower than measured under pseudo-static conditions and 10% lower than measured under dynamic conditions. Thus, the dynamic strength may be approximately 5% higher than the static strength if shear displacement velocities of approximately 0.001 to 0.1 mm/sec (pseudo-static) are compared with velocities of approximately 400 to 4,000 mm/sec. Barla et al. (1990) have also conducted direct shear tests on single joints under dynamic loading. The tests were performed on saw-cut surfaces of dry sandstone. Dynamic tests were conducted at loading velocities ranging from 1.0 to 10.0 MPa/sec and normal stresses of 0.5, 1.0 and 1.5 MPa. The experimental results indicate that the dynamic shear strength is greater than the corresponding static one and increases with increasing shear stress rate. The normal stress decreases with increasing shear loading rate. Hobbs et al. (1990) also studied the dynamic behaviour of rock joints and observed the frictional response to a perturbation in sliding velocity. The frictional shear stress behaviour is explained in terms of cohesion and friction angle evolution laws (softening character). Hutson and Dowding (1990) performed some cyclic tests on granite and limestone joints. The results indicate that asperity degradation is a function of joint roughness, normal stress and unconfined compressive strength of the joint walls. Kana et al. (1992) performed several types of dynamic shear tests simulating earthquake motions. Based on the experimental data, they pointed out the importance of second- 20 order asperities during cyclic loading and proposed an interlock-friction model for dynamic shear response. Jing et al. (1993) investigated the behaviour of rock joints during cyclic shear under constant normal load on regular surface concrete replicas. Based on the experimental results, they have developed a 2-dimensional constitutive model for rock joints under cyclic loading conditions: a1 k t2 a3 k t k n du t − dσ t = k t − du n a1 k t + a 2 k n + mQ a1 k t + a 2 k n + mQ dσ n = − where a4 kt k n a 2 k n2 du n du t + k n − a1 k t + a 2 k n + mQ a1 k t + a 2 k n + mQ (2-21) dσt is the increment of shear stress σt, dσn is the increment of the normal stress σn, dut is the increment of the shear displacement ut, dun is the increment of the normal displacement un, m is a scalar representing hardening or softening effects, kt is the shear stiffness of rock joints, kn is the normal stiffness of rock joints, Q = σ tc = σ t cos α + σ n sin α a1 = cos2α - µsgn(σtc)sinαcosα a2 = sin2α - µsgn(σtc)sinαcosα a3 = sinαcosα + µsgn(σtc)cos2α a4 = sinαcosα + µsgn(σtc)sin2α where α is the asperity angle of rock joints, µ = tanφr for the forward shear stage (φr = residual friction angle), µ = tanφb for the reversal shear stage (φb = basic friction angle), and sgn(σtc) is the sign of contact shear stress σtc. Huang et al. (1993) and Qui et al. (1993) also conducted cyclic direct shear tests on artificial and natural joints with normal stress ranging from 0.5 to 6.0 MPa. Experimental results show that at low normal stresses, surface damage was primarily 21 caused by wear which is a gradual process of asperity degradation. At high normal stresses, damage occurs more rapid and catastrophic (asperities are sheared). At moderate normal stresses, the mode of damage is wear. They also developed a quantitative theory for joint behaviour under cyclic loading. Ahola et al. (1996) have studied the dynamic behaviour of natural and artificial rock joints. The dynamic lab tests were performed under both harmonic and earthquake loading conditions with frequencies ranging from 1.4 to 3.5 Hz. They observed that the shear resistance could be quite different for the forward and reverse shear directions depending on the joint roughness and interlocking nature of the joint surfaces. The joint dilation response during dynamic tests showed very little hysteresis between the forward and reverse shear directions. Divoux et al. (1997) introduced a mechanical constitutive model based on experimental results of cyclic shear tests. Fox et al. (1998) investigated the influence of interface roughness on dynamic shear behaviour in jointed rock. An interlock/friction model was developed and used to predict the behaviour of natural jointed rock specimens subjected to dynamic shear load. Homand-Etienne et al. (1999) have carried out many cyclic direct shear tests on artificial joints of mortar under both constant normal stiffness and constant normal stress conditions. They have also proposed two constitutive models to predict the degradation of the anisotropic joints according to loading conditions and shear mode. Lee et al. (2001) studied the influence of asperity degradation on the mechanical behaviour of rough rock joints (granite and marble) under cyclic shear loading. Laboratory test results indicated that degradation of asperities under cyclic shear loading follows the exponential degradation laws for asperity angle and the mechanism for asperity degradation would be different depending upon the shear direction and the type of asperities. Jafari et al. (2003) also studied the influence of the cyclic shear tests on the degradation of an undulated artificial joint of mortar and found that during cyclic shear displacement, degradation will occur, depending on the cyclic displacement magnitude 22 and normal stress applied. During small earthquakes and low amplitude dynamic loadings, asperities will be slightly affected, but during strong earthquakes and under high amplitude dynamic loadings, asperities may be totally damaged. The shear strength of joint replicas is decreasing during small repetitive cyclic loadings. The number of load cycles and stress amplitude are two main parameters controlling the shear behaviour of rock joints during cyclic loading. Dilation angle, degradation of asperities and wearing are three main factors which affect the shear strength of rock joints during large cyclic displacement. The shear behaviour of rock joints during sliding is in direct relation to the normal stress level and may change from sliding to breaking during cyclic displacement. Based on the experimental results, mathematical models were developed to evaluate the shear strength of the rock joints under cyclic shear loading. In the case of low amplitude cyclic loading (shear velocity from 0.05 to 0.4 mm/sec and maximum shear displacement of 0.1 mm), the following relation is proposed: a( NC s ) (ω n An ) τ = σ no 1 + a(NC s )m (ω n An )n m where n (2-22) NCs is the number of stress cycles, ωn is the normalized shear velocity, An is the normalized stress amplitude, a = 0.3; m = -0.045; n = -0.17. In the case of large cyclic shear displacement (maximum shear displacement of 15 mm), the following relation is proposed: b( NC d ) (in ) + c τ = σ no 1 + b(NC d ) p (Dn )q p where q (2-23) NCd is the number of displacement cycles, in is the normalized dilation angle, Dn is the normalized degradation (normalized by maximum value of asperity amplitude), B = -0.33; c = 1.44; p = 0.12; 23 q = 0.3. Belem et al. (2007) conducted tests on three different specimens with different shapes (hammered, corrugated and rough) under monotonic and cyclic shear test conditions. Surface topographical data were measured before and after each shear test using a laser sensor profilometer. Based on the experimental results and previously proposed surface roughness description parameters, they have proposed two rock joint surface roughness degradation models to predict the variation of joint surface degradation during monotonic and cyclic shearing. Ferrero et al. (2010) have developed a new apparatus for monotonic cyclic shear tests. The lab cyclic tests were performed with frequencies ranging from 0.013 to 3.9 Hz and maximum displacements between 1.0 and 4.0 mm. The experimental results show that the strength decrease is strongly conditioned by the amplitude since, for equal global displacement, smaller amplitudes determine the damage of asperities in a smaller range with a consequent lower global degradation when compared with cycles of larger size. Konietzky et al. (2012) have developed a new large dynamic rockmechanical direct shear box device for both quasi-static and dynamic tests. Dynamic tests were conducted on shalestone samples with dynamic normal load (earthquake signal) of about 550 kN and a shear load of about 300 kN. The experimental results show that the shear strength deceases with ongoing shear displacement and the dynamic input also leads to a further settlement of the sample. Static and dynamic tests were also performed on MayenKoblenz schist. 2.4 Rock joint surface roughness measurements A joint inside a rock mass is an interface between two contacting surfaces. The joints can be smooth or rough, in good contact or poor contact. The shear strength of the rock joints is strongly dependent on the surface roughness. Therefore, it is important to estimate the roughness of discontinuity surface accurately. Roughness can be subdivided into small scale surface irregularities and large scale undulations of the discontinuity surface. Several methods have been developed and used to measure rock joint surface roughness in-situ and in the laboratory. These methods can be divided into two categories: 24 requiring contact with the rock joint surface termed “Contact methods” and not requiring contact with the rock joint surface termed “Non-Contact methods” [Maerz, et al., 1990]. 2.4.1 Contact methods Several instruments and methods, respectively, have been developed to measure the surface roughness of rock discontinuities: • the linear profiling method [Fecker and Rengers, 1971; Weissbach, 1978; Shigui, et al., 2009]. • the compass and disc-clinometer method [Fecker and Rengers, 1971]. • the profile combs method [Barton and Choubey, 1977; Stimpson, 1982]. • the straight edge and rulers method [Piteau, 1970; Milne, et al., 1991]. • the shadow profilometry method [Maerz, et al., 1990]. • the tangent plane and connected pin sampling method [Rasouli and Harrison, 2004]. Balance block Drawing pen Fixed board Drawing paper Trace-fixed balance axis Feeler Joint sample Benchmark base Figure 2.7. Simple profilograph for measurement of joint roughness [Shigui, et al., 2009] The contact methods have the advantage to be cheap, accurate, easy and suitable to obtain large scale roughness in the field [Fecker and Rengers, 1971; Maerz, et al., 1990; Schmittbuhl, et al., 1993; Rasouli and Harrison, 2004] or small scale roughness in the 25 laboratory [Weissbach, 1978; Kulatilake, et al., 1995]. However, contact methods also have some disadvantages: they are time-consuming when used to measure large areas and they do not allow for data recording at dangerous and inaccessible locations [Feng, et al., 2003]. These drawbacks can be overcome by using non-contact methods to measure discontinuity surface topography. (a) (b) (a) use of a profile comb to measure discontinuity roughness profiles (b) use of straight edge method to measure the waviness of rock discontinuity. Figure 2.8. Example of contact methods for measurement of joint surface roughness [Milne, et al., 1991] 2.4.2 Non-Contact methods There are several non-contact measurement instruments and methods, respectively, available to obtain 2D and 3D rock joint surface topography, for example: • the photogrammetry method [Wickens and Barton, 1971; ISRM., 1978]. • the image processing method [Galante, et al., 1991]. • the advanced topometric sensor method [Grasselli and Egger, 2003]. • the laser scanning [Fardin, et al., 2004; Hong, et al., 2006; Rahman, et al., 2006]. Application of photogrammetry for measurement of rock joint surface roughness was first proposed by Wickens and Barton (1971) and ISRM (1978). In recent years, several researchers have developed close-range photogrammetry to measure discontinuity surface roughness in the laboratory [Jessell, et al., 1995; Lee and Ahn, 2004; Nilsson, et al., 2012] and in-situ [Baker, et al., 2008; Haneberg, 2008; Poropat, 2009]. 26 The advanced topometric sensor method has been developed and manufactured by GOM mbH and is intensively used to digitize rock discontinuity surfaces [Grasselli and Egger, 2003; Grasselli, 2006; Hong, et al., 2008; Nasseri, et al., 2009; Tatone and Grasselli, 2009]. (a) (b) Lens Image Sensor Unique 3D location (a) simplified scheme showing the process of finding the unique 3D location of the intersection of rays projected from two 2D images and (b) concept illustrated via two 2D photographs of a rock mass. Figure 2.9. Principle of photogrammetry [Birch, 2006; Gaich, et al., 2006] 3D laser scanning is a sophisticated active remote sensing technique that has been used recently to measure more accurate discontinuity surface roughness in the field [Fardin, et al., 2001; Chae, et al., 2004; Fardin, et al., 2004; Hong, et al., 2006; Rahman, et al., 2006; Poropat, 2009; Tatone and Grasselli, 2012]. These methods greatly improved the speed and accuracy of roughness measurements. However, many of these methods can only be used in the laboratory for measuring small specimens [Poropat, 2006; Tonon and Kottenstette, 2006]. 2.4.3 Roughness scale-dependency The roughness of rock joints is scale dependent. Bandis et al. (1981) investigated scale effects in the laboratory using plaster models. They found that the peak shear strength of rock joints decrease with increasing size of the specimen as presented in Figure 2.10. Fardin et al. (2001) have studied the scale dependence of rock surface roughness with sampling windows ranging in size from 100 mm x 100 mm to 1000 mm x 1000 mm and concluded that, for surface roughness to be accurately characterized at the laboratory 27 scale or in the field, samples need to be equal to or larger than the stationarity limit. To investigate the effect of scale on the large size surface roughness, Fardin et al. (2004) used sampling windows of different sizes from 1 m x 1m to 4 m x 4 m. The experimental results indicate that the surface roughness of rock joints is scale dependent at small scales and reaches stationarity at a size of about 3 m. Asperity failure component 1 Shear stress, τ 2 3 2 4 3 4 Basic frictional component Roughness components Geometrical component Total frictional component Displacement, δ Figure 2.10. Scale dependency of shear strength of rock joints [Bandis, et al., 1981] Rahman et al. (2006) used 3D terrestrial laser scanning to investigate the fractal parameters of rock joints. The results show that the roughness of joint surfaces increases with increasing sample size. They concluded that the roughness of rock joints has a significant scale effect. Tatone and Grasselli (2012) investigated joint roughness scale dependency using highresolution surface measurement tool ATOS II. Large scale (2 m x 6 m) fracture surfaces in-situ and small scale (100 mm x 100 mm) samples in the laboratory were digitized. The experimental results indicate that roughness of joint surface increases with increasing the sampling window size. However, the resolution of surface measurements has greater influence on roughness determination than sampling window size. Therefore, the observation that suggested that the roughness of rock joint surface often decrease with increasing sample size may be attributed to inconsistent measurement resolution. 2.4.4 Joint roughness coefficient (JRC) The JRC is a commonly used measure of joint roughness in rock engineering practice. The JRC value of a rock joint can be estimated visibly by comparing it with the ten standard JRC profiles [Barton and Choubey, 1977]. However, it may be difficult to 28 determine the proper JRC number in practice, because of the scale effect. At present, many researchers [Tse and Cruden, 1979; Belem, et al., 2000; Yang, et al., 2001; Tatone and Grasselli, 2009] have proposed methods to calculate the JRC value from the profile geometry. Tse and Cruden (1979) determined an empirical relationship between JRC and statistical parameter Z2 (with a correlation coefficient R = 0.986 and sampling interval of 1.27 mm) as follows: JRC = 32.2 + 32.47 log10 (Z 2 ) (2-24) with Z2 (the root mean square of the first derivative of the profile) given as: ∆y 1 Z 2 = RMS = ∆x L where L dy ∫ dx 2 = 0 1 m ∑ (y m(∆x ) 2 i =1 i +1 − yi ) 2 (2-25) L is the total joint length, ∆x is the sampling interval along the x-axis, ∆y is the sampling interval along the y-axis, ∆y/∆x is the asperity slope, m is the number of sampling intervals. Yang et al. (2001) have reconstructed the standard JRC profiles by using Fourier transform method and found a relationship between JRC and Z2 with a higher correlation coefficient R = 0.99326 (sampling interval of 1.27 mm): JRC = 32.69 + 32.98 log10 (Z 2 ) (2-26) Tatone and Grasselli (2009) analyzed 2D roughness profiles in the shearing direction with sampling intervals of 0.5 mm and 1.0 mm. Using the new experimental results, new empirical equations were proposed to estimate JRC from Z2: JRC = 51.85(Z 2 ) 0.60 − 10.37 (0.5 mm sampling interval) (2-27) JRC = 55.03(Z 2 ) 0.74 − 6.10 (1.0 mm sampling interval) (2-28) 29 The resulting equations to estimate JRC from θ*max/(C+1)2D value for sampling intervals of 0.5 mm and 1.0 mm can be expressed as: ∗ θ max JRC = 3.95 (C + 1)2 D 0.7 ∗ θ max JRC = 2.40 (C + 1)2 D 0.85 − 7.98 (0.5 mm sampling interval) − 4.42 (1.0 mm sampling interval) (2-29) (2-30) where θ*max is the maximum inclination of the profile in the chosen analysis direction and C is the roughness parameter, calculated using a best-fit regression function, which characterises the distribution of the apparent dip angles of the surface. In order to define the 3-dimensional equivalent of Z2, noted Z2S, Belem et al. (2000) have replaced the slope by the gradient norm of the surface heights. By assuming that the surface is continuous and differentiating, let S be the actual area of the surface of the joint wall defined by the points M(x, y, z) so that x ∈ [0, Lx], y ∈ [0, Ly] and z = z(x, y). The heights are defined in respect to the reference plane XOY. The Z2S parameter can be estimated according to Belem et al. (2000): Z 2S = 1 N x −1 N y −1(z i +1, j +1 − z i , j +1 )2 + (z i +1, j − z i , j )2 + ∑ ∆x 2 ∑ 2 1 i =1 j =1 (2-31) 2 2 N 1 − N 1 − (N x − 1)(N y − 1) 1 y x (z i +1, j +1 − z i +1, j ) + (z i , j +1 − z i , j ) + 2 ∑ ∑ 2 ∆y j =1 i =1 Z2 ≈ where Z 2 S + 0.0002 1.5656 (2-32) Nx is the number of points along the x-axis, Ny is the number of points along the y-axis, ∆x is the sampling interval along the x-axis, ∆y is the sampling interval along the y-axis, Lx is the nominal length along the x-axis, 30 Ly is the nominal length along the y-axis, Lx = (Nx – 1) ∆x ; Ly = (Ny – 1) ∆y ; zi,j = z(xi, yj). 2.5 Overview about shear box test devices Shear box tests are widely used to estimate shear strength of rock joints in geotechnical engineering. In recent years, several commercial producers have developed shear box devices for rock mechanical testing [e.g. MTS-816, GCTS-RDS-500, TerraTek-DS4250, LO-50100 and HR72.340]. The technical data show maximum normal forces between 500 kN and 1500 kN, maximum shear forces between 250 kN and 750 kN and maximum shear box dimensions between 100 mm and 350 mm. A summary of technical data for several direct shear box devices is presented in Table 2-1. Table 2-1. Main technical data of some direct shear box devices Technical data Direct shear apparatus Normal Force [kN] Shear Force [kN] Max. shear displacement [mm] Shear box dimensions [mm] Dynamic testing MTS-816 500 250 100 200 x 200 x 340 No GCTS-RDS-500 1500 300 50 100 x 100 x 150 No TerraTek-DS-4250 1000 300 50 150 x 150 x 300 No HR72.340 500 750 - 350 x 350 x 450 No LO-50100 500 500 50 150 x 250 Yes Huang (1993) 500 500 7 200 x 150 Yes Barbero (1996) 9.51 17.2 20 100 x 100 0 ÷3.5Hz Kana (1996) 333.6 222.4 - 203 x 203 x 101 Yes Boulon (1995) 100 100 - 100 x 100 No Gehle (2002) 150 150 20 250 x 50 x 150 No Hans (2003) 100 100 - 100 x 100 Yes Jiang (2004) 400 400 - 500 x 100 No Kim (2006) 150 150 25 140 x 75 No Gomez (2008) 200 200 305 711 x 406 No Barla (2010) 100 100 18 φ100 No Konietzky (2012) 1000 800 50 400 x 200 x 160 0÷40Hz 31 Besides that, several researchers have designed and constructed their own shear box devices with maximum load capacity of 500 kN [Huang, et al., 1993; Kana, et al., 1996; Geertsema, 2002; Gehle, 2002; Seidel and Haberfield, 2002; Jiang, et al., 2004; Kim, et al., 2006; Gomez, et al., 2008; Barla, et al., 2010]. These apparatuses can perform tests under CNL or CNS or both CNL and CNS boundary conditions. Dynamic shear box testing was reported by several researchers [Huang, et al., 1993; Ahola, et al., 1996; Barbero, et al., 1996; Kana, et al., 1996; Fox, et al., 1998; HomandEtienne, et al., 1999; Lee, et al., 2001; Jafari, et al., 2003; Wang, et al., 2007; Buzzi, et al., 2008]. However, these dynamic shear box devices were developed for tests on significant smaller samples and they are of quite different types. Barbero et al. (1996) have designed and constructed a direct shear testing machine with the purpose to test rock joints under both static and dynamic conditions. Loading capacity of this apparatus in dynamic condition is 10 kN, and the frequency range covers 0.01 ÷ 3.5 Hz. Kana et al. (1996); Ahola et al. (1996) and Fox et al. (1998) developed direct shear testing devices with higher load capacity up to 222 kN and frequencies up to 1.4 Hz. Lee et al. (2001) have designed a servo-controlled direct shear testing machine and attached it to a MTS-815 loading frame. The loading capacity of the testing system is 250 kN and allows cyclic shear motion of up to ± 60 mm displacement. Jafari et al. (2003) used the shear apparatus BCR-3D developed by Boulon (1995) to investigate the effect of cyclic displacements on shear strength of rock joints. Barla et al. (2010) have designed and developed a new direct shear testing apparatus for either soil or soft rock. The maximum loading capacity in the axial and in the shear direction is 100 kN and the maximum shear displacement is 18 mm. Ferrero et al. (2010) developed of a new apparatus based on MTS-810 to investigate the behaviour of a rock discontinuity under monotonic and cyclic loads. 2.6 Direct shear box testing methods There are two main methods usually used in the laboratory to investigate the shear behaviour of rock joints. They are called constant normal load (CNL) and constant normal stiffness (CNS) tests. 32 CNL means that the normal load is maintained constant during the shearing process. Shear testing under CNL boundary condition is only suitable for cases such as nonreinforced rock slopes, where the surrounding rock mass freely allows the joint to shear without restricting the dilation, therefore, the normal load on the shear plane is constant during shear process as shown in Figure 2.11a. W N = constant (a) (b) S K S Figure 2.11. Simulation of the in-situ boundary conditions in the direct shear test [Brady and Brown, 2005] CNS means that the normal stiffness is maintained constant during the shearing process (Figure 2.11b). Shear testing under CNS boundary condition is usually suitable to investigate the behaviour in deep underground openings or in rock bolt reinforced slopes, where the surrounding rock mass is unable to deform sufficiently and the normal stress acting on the shear plane is not kept constant during the shearing process. In this case, the dilation is controlled by the normal stiffness of the surrounding rock mass. Therefore, the normal stresses on the shear plane increase or decrease with increasing or decreasing dilation, respectively. 33 34 3 Shear box device GS-1000 3.1 Introduction Many shear box devices have been developed by professional companies and researchers for rock testing under both static and dynamic conditions as mentioned already. Almost all of these shear box devices are designed for maximum loads of less than 500 kN and shear box dimensions smaller than 200 mm in length and width. A new direct shear device (GS-1000) was developed and installed at the rockmechanical laboratory at the Geotechnical Institute of the TU Bergakademie Freiberg to perform direct shear tests under static, dynamic and hydro-mechanical coupled conditions with extreme high loads (up to 1000 kN), big shear box dimensions (up to 400 x 200 mm2) and dynamic loads up to 40 Hz with force amplitudes of up to ± 500 kN in both normal and shear directions. ◄ Dynamic control unit Hydraulic aggregate ► Shear box ▼ LVDTs ▼ ▲ Shear box test device GS-1000 SPS-control unit ▼ Data logging unit AM8 ▼ Figure 3.1. Overview of direct shear test apparatus GS-1000 [Luge, 2011; Konietzky, et al., 2012] 35 3.2 Shear box test apparatus GS-1000 The GS-1000 apparatus (Figure 3.1) consists of two parts: hydraulic and mechanical part (including loading system, shear box, water cooling system and loading aggregate) and control and measurement part (including measuring system, control unit and data acquisition system). 3.2.1 Hardware The hardware of the GS-1000 apparatus consists of the vertical and horizontal servocontrolled loading aggregate, the shear box and the water cooling system. The loading system: Vertical frame Upper shear frame Piston for normal load 15o Lower shear frame Piston for shear load Figure 3.2. Loading system of shear box device GS-1000 [Luge, 2011; Konietzky, et al., 2012] The loading is applied to the specimen by two load pistons: the vertical piston is used to create the normal load and a horizontal one is used to create the shear load as shown in Figure 3.2. The normal load capacity ranges from 0 up to 1000 kN and the shear loading from -300 kN up to +800 kN. The hydraulic piston for the shear movement is spherically seated. The degrees of freedom for the upper shear frame are given by ballbearing mounts with predefined clearance. If the reactive forces within the shear plane are too high, the upper shear frame can move upwards. After the shear experiment the 36 shear gap can be widely opened to investigate the shear planes. Also, lower and upper shear frame can be moved vertically to allow comfortable placement of the sample into the shear box. Shear velocities applied range from 1e-7 mm/sec up to 70 mm/sec. The maximum shear displacement is 50 mm. Several small and bigger air pressure accumulators are installed to provide energy for the seismic loading. For the vertical loading plate special friction bearing with maintenance-free material CA.S30 (DIN ISO 3547-4 Typ P1) is used. This special material avoids stick-slip, has extremely low friction (friction coefficient between 0.02 and 0.08) and is water resistant. The shear box: Figure 3.3 shows the shear box of the testing equipment GS-1000. The shear box was built of stainless steel and divided into two different parts, a lower shear box part and upper shear box part. The upper shear box is fixed and accommodates one half of the specimen. The lower shear box is in direct contact with the mechanism which provides the force necessary for shearing. The joint is sheared by moving the lower shear box. Figure 3.3. Shear box of the GS-1000 apparatus The box has sufficient wall thickness to minimise deformations caused by loads acting on them. Rectangular specimen dimension up to L x W x H = 400 x 200 x 160 mm can be used in this apparatus. Water cooling system: In case of dynamic tests, special cooling will be necessary, if high dynamic loads will be superimposed for a longer time. A special water cooling system with 3 underground 37 water tanks, each with 10.000 litres, was erected (Figure 3.4). The water will circulate through the cooling system of the aggregate, a 100 m long buried water pipe and the 3 buried water tanks. Cooling through heat transfer to the ground will mainly take part along the buried water pipes. This cooling system needs minimal energy only for the water pump and works without any noise. Figure 3.4. Water tanks for cooling system [Luge, 2011; Konietzky, et al., 2012] 3.2.2 Software Software of the GS-1000 apparatus comprises the measuring system, the control units and the data acquisition. The measurement system: Figure 3.5. LVDT’s for the normal and shear displacement measurement The apparatus is equipped with a number of transducers that allows continuous electronical measurement of all load and displacement components. The normal load is 38 measured by a load-cell integrated into the vertical load piston. The shear load is measured by another load-cell connected to the horizontal load piston. Horizontal and vertical displacements are measured by LVDT’s (Linear Variable Differential Transformer). Vertical displacement is measured at the four corners at the upper shear frame. Horizontal displacement is measured by a LVDT fixed to the lower shear box part as shown in Figure 3.5. Accuracy in displacement measurements is smaller than 1 µm. Test control units: A simplified flowchart of the test control and data acquisition system of the shear box device GS-1000 is given in Figure 3.6. Central part is the PC-based software GBSS, which controls and supervises the control unit SPS-S7, the dual board NET16LU and the data logging system AM8. Through GBSS the control unit SPS-S7 gets target values, e.g. for normal and shear forces. The actual values of the displacement and force sensors were given to the GBSS through the SPS-S7. Two separate control units are used by the SPS-S7 to operate the servo valves for normal and shear forces. The SPS-S7 delivers the target values for the static shear experiments. For the dynamic tests up to 40 Hz under full load or higher frequencies at reduced loads a special designed generator (GSG) on the basis of two coupled dual-boards NET16LU was developed. The NET16LU unit comes with 2 TCP/IP interfaces for fast communication with GBSS software. The GSG works on the basis of a 16 bit digital signal synthesis with synchronous and separate gate for normal and shear force. Standard signals (sinus, rectangle, ramps etc.) as wells as arbitrary signals, e.g. from earthquake recordings, can be used. A sampling rate between 1 and 10.000 Hz can be chosen. The dilatancy controlled testing can be performed independently from the PC with 16 bit accuracy using the dual board NET16LU unit [Luge, 2011; Konietzky, et al., 2012]. 39 Figure 3.6. Simplified flowchart of electronically control unit [Luge, 2011; Konietzky, et al., 2012] 40 IP 1 Switch IP 2 Ethernet TCP/IP Software Data logging System with 8 (16) channels and data storage as well as TCP/IP Network interface to PC acquisition of displacement (4), shear movement (1) shear and AM8 – measuring system IP 3 Signal for stiffness control DA/ AD Shear displacement Water pressure Shear force Water pressure sensor Shear force control system Normal force control system LVDT – Shear displacement 4 x LVDT – normal displacement extern desired shear force extern desired normal force Saferty funstions SPS -S7- Normal displacement RS232 NET16LU – binarily computer core and GSG Generator 2 x microcomputer board‘s with AD/DA converter for digital signal synthesis and stiffness controlled shearing and application software TCP/IP Software AM8 PC – Software GBSS Shear force piston Load cell for shear force Load cell for normal force Servo valve for shear load Displacement signal Displacement signal Normal force piston Servo valve for normal load Data acquisition system: Figure 3.7 shows the data acquisition system AM8. The data logging unit AM8 with 8 channels is used for registration of displacements and forces in vertical and shear direction. AM8 is connected to the PC via USB interface. Periodically the GBSS software recalls the data and stores them into a data base. All data are available in binary, XLS- and ASCII-format for subsequent evaluation. Figure 3.7. The data logging unit AM8 [Luge, 2011; Konietzky, et al., 2012] The main technical data of the new direct shear box device GS-1000 are summarized in Table 3-1. Table 3-1. Technical data of the GS-1000 apparatus Unit Value Maximum shear displacement Parameter mm 50 Shear force kN -200 ÷ +800 Normal force kN 0 ÷ 1000 Shear box size (L x W x H) mm 200 x 400 x 160 Frequency Hz 0 ÷ 40 (>40) kN ± 500 MPa 10 Dynamic loading Water pressure (hydro-mechanical coupling) 3.2.3 Test modes The GS-1000 equipment with the servo-controlled system can be used to perform both static and dynamic tests. Testing under CNL boundary conditions is carried out by applying the normal stress at the upper shear box and a shear velocity to the lower shear box to create shear displacement. Testing under CNS boundary conditions is managed 41 by controlling the normal displacement through P-factor in the control system of the equipment. For example, if input value of P-factor equals 1, the device produces a stiffness of 100 kN/mm. That means that the normal stiffness is reduced (or increased) by 100 kN when normal displacement is decreased (or increased) by 1 mm. The GS-1000 device can also be used to carry out dynamic tests with superimposed dynamic loading of up to ± 500 kN and frequency up to 40 Hz with maximum load capacity in both normal and shear directions. The input signals for dynamic tests are loaded as ASCII-files or CSV-format (Excel format). 3.3 zSnapper: scanner for rock joint roughness measurement In recent years, many methods to determine rock joint surface roughness (JRC) with high accuracy in the laboratory and in-situ such as laser profilometry [Milne, et al., 2009], digital photogrammetric systems [Nilsson, et al., 2012], and stereo-topometric scanners [Tatone and Grasselli, 2009] were developed. All these methods provide “cloud points” that need to be mathematically treated to describe the surface in a synthetic way [Haneberg, 2007]. In this study, 3D-scanner was used to measure the joints surface roughness of jointed rock specimen. The 3D-scanning results were used to determine JRC and to set-up numerical models. 3.3.1 Description of scanner device zSnapper projector camera Figure 3.8. 3D-scanner zSnapper [ViALUX., 2010] The joint surface roughness of the samples was measured by using the 3-dimensional scanner zSnapper from ViALUX [ViALUX., 2010]. The apparatus consists of an optical 42 monochromatic projector and separately digital camera which are mounted on a horizontal bar and placed on a tripod as shown in Figure 3.8. Figure 3.9. Measuring volume (red) of the zSnapper [ViALUX., 2010] The zSnapper operation is based on the phase encoded photogrammetry which is a version of full-field triangulation and represents technology advancement for the wellknown and precise white light scanners. The device use blue LED light which is a significant practical improvement, e.g. for the suppression of ambient light influence. The measuring volume of the zSnapper is limited by the intersection of the two beam envelopes of camera and projector as shown in Figure 3.9. Figure 3.10. Calibration gauge with reference points [ViALUX., 2010] 43 As shown in Figure 3.9, the blue beam represents the projector, the grey one the camera and the measuring volume is highlighted red. 3D surface data can be measured for all surface points that are visible in the camera image and are illuminated by the projector at the same time. The 3D reconstruction software calculates independent coordinates (x, y, z) for each single pixel of the camera. The 3D scanner software determines these parameters quickly and fully automated using a calibration plate with reference targets as shown in Figure 3.10. 3.3.2 Measurement of the rock joint surfaces by scanner zSnapper The measurement procedure using zSnapper comprises the following steps: zSnapper hardware preparation: Projector and digital camera should be mounted on a very stable horizontal bar and placed on a tripod. The distance between projector and camera is adjusted to match the size of the sample. A suitable calibration gauge will be used for calibration. A computer with the installed ViALUX-3D software is connected with the apparatus to control the operations of the equipment. Calibration with SnapCal software: • Start the program SnapCal and make sure that other zSnapper applications were terminated. • Select the calibration gauge by selecting the entry from the menu: File → Load Reference Coordinates • A dialog will appear where the calibration data for used gauge have to be selected. • Adjust the camera brightness: for optimum calibration results make sure that the photogrammetry targets are of high contrast but not yet saturated. • Take at least 5 records of the calibration gauge in different positions. • Calculate the calibration: if enough measurements are taken, click on calculate the calibration button to get the result of the calibration. 44 3D scanning with SinglezSn software: • After starting SinglezSn program, the application window appears. The mode of operation can be selected by the menu: Scanner → Mode of Operation → With Reference. • Scanning with references requires the presence of reference coordinates. Load the coordinates of reference targets from the device file: File → Load Reference Coordinates. • Place the coordinates of reference targets in a way that the scanning object and reference targets can be seen from various viewing directions. • Measurement of angle between reference target plane and horizontal plane to convert coordinates. • Start the scanning loop and add the current 3D point cloud to the entire model. The scanning loop will stop when the entire surface of the sample was scanned. • Save the scanned data and export (x, y, z) coordinates to specified data format. • Check calibration: put the calibration gauge in front of the zSnapper and select from menu: Tools → Check Calibration. This test visualizes the status of sensor calibration by projecting a cross on each recognized photogrammetry target. The calibration status is OK if each cross is exactly located in the centre of a target. Table 3-2. zSnapper technical data Parameters Unit Value Field of views mm 180 ÷ 1100 Recording time ms 22 ÷ 220 Point cloud standard (x, y, z) - 300,000 High resolution option (x, y, z) - 4,200,000 µm 20 ÷ 125 Accuracy Data output Dimensions (L x W x H) Weight - ASCII, AOP, VLX3D mm 230 x 130 x 115 g 2300 The main technical data of the scanner equipment are listed in Table 3-2. An example of 3D scanning result of the rock surface is shown in Figure 3.11. 45 a) set-up apparatus b) reference target and sample c) surface of sample d) zSnapper scanning result Figure 3.11. Example of using zSnapper for capturing surface features 46 3.4 Sample preparation The sample preparation and the direct shear tests were conducted according to the recommendation of the International Society for Rock Mechanics [ISRM., 1974] and the American Society for Testing and Materials [ASTM, 2002]. a) Intact sample b) Shear box c) Sample in the shear box d) Grouted sample e) Grout drying f) LVDTs for displacement measurement Figure 3.12. Intact rock specimen preparation for shear testing 47 The rectangular specimens were cut to fit the dimensions of around 3 300 x 150 x 150 mm (length x width x height). The sample was grouted into a steel shear box. The fixing material is made from a mixture of sand, cement and water. The strength of the fixing material should be larger than that of intact material of the sample. The sample is then left for at least 48 hours to let the grout drying. Figure 3.12 shows the procedure of the sample preparation. 48 4 Laboratory shear box tests 4.1 Static tests Direct shear box tests are carried out in the laboratory to determine shear strength of intact rock and jointed rock under static boundary conditions. The static tests were conducted under CNL and CNS conditions. The tests were performed at the Rock Mechanical Laboratory at the Geotechnical Institute of the TU Bergakademie Freiberg using the direct shear box test apparatus GS-1000. The tests were performed on MayenKoblenz schistose rock. Many different laboratory tests were already performed on Mayen-Koblenz schistose rock [Walter and Konietzky, 2009; Dinh, 2011] to determine their mechanical matrix properties. General rock mechanical data for Mayen-Koblenz schist rock are summarized in Table 4-1. Table 4-1. Rock mechanical matrix properties Matrix parameters Unit weight Young’s modulus Min. ÷ Max. value Unit kg/m 3 GPa Friction angle Uniaxial compressive strength ⊥ 2780 2780 71 ÷ 75 40 ÷ 43 0.25 ÷ 0.3 0.23 ÷ 0.3 MPa 0.33 ÷ 3.7 0.93 ÷ 5.7 degree 17.7 ÷ 43.7 17.7 ÷ 41.5 MPa 98 ÷ 117 152 ÷ 216 Poisson’s ratio Cohesion // (//: parallel to bedding; ⊥: perpendicular to bedding) 4.1.1 Constant Normal Load (CNL) tests 4.1.1.1 CNL test set-up The set-up for constant normal load (CNL) tests for intact and jointed rock specimens is illustrated in Figure 4.1. In general, the dilation angle (ψ) is negative in compression 49 and positive in dilation. In other words, the normal displacement (un) is positive in dilation and negative in compression. un + σno = constant + (a) Shear velocity + σno = constant (b) + un Shear velocity us us Figure 4.1. CNL test set-up for intact (a) and jointed (b) sample Table 4-2. Set-up for CNL testing (multi-stage tests) Input parameters Sample Stage LxWxH [mm3] intact CNL01 CNL02 CNL03 CNL04 1 σno [MPa] v [mm/min] us_max [mm] 10 3.0 10 5 3.0 10 10 3.0 10 3 15 3.0 10 intact 3.6 3.0 5 1 3.6 3.0 10 2 2 300 x 160 x 160 323 x 153 x 150 7.2 3.0 10 3 10.8 3.0 5 intact 5 4.5 10 1 5 4.5 5 10 4.5 5 3 15 4.5 5 intact 5 3.0 5 1 3.0 5 4 3.0 5 2 1 318 x 164 x 166 335 x 165 x 150 2 (L: length; W: width; H: height) The CNL tests are conducted as multi-stage tests for every sample. The tests were carried out at three different normal stress values. The first specimen (CNL01) and second specimen (CNL02) were tested with the same shear velocity equal to 50 3.0 mm/min. The CNL03 specimen was tested at the shear velocity of 4.5 mm/min. Table 4-2 gives an overview of the lab tests performed under CNL boundary conditions. The applied normal stress for each stage is constant as shown in Table 4-2. The shear velocity is applied at the lower half of the shear box. Normal and shear load are measured by load-cells integrated into the vertical and horizontal loading pistons. The shear displacement is measured by one horizontal LVDT which is attached to the lower part of the shear box. The normal displacement is measured by four vertical LVDT’s which are positioned at the four corners of the upper part of shear box as shown in Figure 4.2. 4th LVDT for vertical displacement measurement 1st LVDT for vertical displacement measurement 3th LVDT for vertical displacement measurement 2nd LVDT for vertical displacement measurement LVDT for horizontal displacement measurement Figure 4.2. LVDT’s for the horizontal and vertical displacement measurement First, shear box tests were performed with the intact rock sample and shear direction is parallel to the schistosity planes of sample until peak shear strength and maximum shear displacement were reached. The vertical load is maintained constant during shear process in the case of CNL tests. At the second stage, each test of the already fractured (jointed) sample was performed at three levels of normal stresses as shown in Table 4-2. At each normal stress level each sample was sheared first until peak shear stress was reached and further until residual shear stress was reached. 51 Joint roughness coefficient (JRC) measurement: The Joint Roughness Coefficient proposed by Barton (1973) is a commonly used measure of rock joints surface in rock engineering practice. The geometry of the joints was scanned after each shear test using the scanner zSnapper. Results of scanning were used to calculate JRC value according to equation (2-26), (2-31) and (2-32) and later on used to simulate the joint surface in FLAC3D. Based on equations (2-26), (2-31) and (2-32), a FISH (FISH is a programming language embedded within FLAC3D) routine was developed for calculating the JRC value from 3D-scanner data. Results of JRC determination are summarized in Table 4-3. Table 4-3. JRC values for different rock specimens Sample JRC CNL01 CNL02 CNL03 CNL04 CNS01 CNS02 CNS03 8 6 7 4 17 6 5 4.1.1.2 CNL test results Shear strength of intact rock: Normal and shear stresses are calculated by the following equations: σ no = τh = where N0 W ×L (4-1) Sh W ×L (4-2) N0 is the normal load, Sh is the shear load, W is the width of specimen, L is the length of specimen. The shear stresses of intact rock obtained throughout the direct shear tests under various normal stresses are shown in Figure 4.3. 52 9 3.6 MPa Shear stress [MPa] 8 5 MPa 10 MPa 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.3. Shear stress versus shear displacement under different normal stress (3.6; 5.0 and 10.0 MPa) for intact rock specimens Figure 4.3 shows that shear stress of intact rock increases linearly (elastic behaviour) with increasing shear displacement until peak shear strength is reached. After that the shear stress decreases until the residual shear strength (plastic behavior) is reached. Peak and residual shear strength of intact rock increase also with increasing normal load. The peak shear strength was obtained at higher shear displacement when normal stress increases, as follows: 0.938, 1.374 and 2.366 mm at 3.6, 5.0 and 10.0 MPa normal stress, respectively. Peak and residual shear stress of intact rock obtained from laboratory tests under various normal stresses are summarized in Table 4-4. Shear stress [MPa] 9 8 7 6 5 4 y = 0.568x + 2.4616 2 R = 0.9129 Peak y = 0.5106x + 0.1676 Residual 3 2 1 0 2 R = 0.9959 0 1 2 3 4 5 6 7 8 9 10 11 Normal stress [MPa] Figure 4.4. Mohr-Coulomb failure envelope for peak and residual state for initial intact rock samples 53 Table 4-4. Peak and residual shear stresses for initial intact rock samples Normal stress σno [MPa] Peak shear stress τp [MPa] Residual shear stress τres [MPa] CNL01 10 8.0 5.3 CNL02 3.6 4.0 2.1 CNL03 5 5.95 2.6 Sample Based on the peak and residual shear stresses of intact rock samples, the Mohr-Coulomb envelope is constructed for both peak and residual states as shown in Figure 4.4: peak state: τ p = σ no tan (φ p ) + c p (4-3) τ res = σ no tan (φ res ) + c res (4-4) residual state: where τp is the peak shear strength, τres is the residual shear strength, σno is the normal stress, φp is the peak internal friction angle, φres is the residual internal friction angle, cp is the peak cohesion, and cres is the residual cohesion. The Mohr-Coulomb failure envelope for the peak state was obtained from Figure 4.4: τ p = 0.568σ no + 2.4616 (4-5) Cohesion and internal friction angle according to equation (4-5) are: cp = 2.4616 MPa; φp = atan(0.568) = 29.60 54 The Mohr-Coulomb failure envelope for the residual state was also obtained from Figure 4.4 as follows: τ res = 0.5106σ no + 0.1676 (4-6) Residual cohesion and residual internal friction angle according to equation (4-6) are: cres = 0.1676 MPa; φres = atan(0.5106) = 270 Shear strength of jointed rock: Figures 4.5 to 4.8 show the shear stress versus shear displacement graphs for four samples under CNL test conditions. The experimental results show that the direct shear behaviour can be divided into 3 stages as follows: Stage 1: begin of shear movement; when slipping occurs on the rock joint surface, the relationship between shear stress and shear displacement is linear; shear displacement increases slowly while shear stress increases rapidly. Stage 2: relationship between shear stress and shear displacement is nonlinear and tends to reach the peak shear stress value; shear stress increases slowly while shear displacement increases stronger. Stage 3: shear stress reaches peak value; shear failure happens on the joint surface and shear stress varies little or keeps constant during movement. 55 Shear stress [MPa] 6 5 CNL01 4 5 MPa 3 10 MPa 15 MPa 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Shear displacement [mm] Figure 4.5. Shear stress versus shear displacement of the CNL01 specimen under different normal stress (5, 10, 15 MPa) Shear stress [MPa] 5 4 CNL02 3 3.6 MPa 2 7.2 MPa 10.8 MPa 1 0 0 1 2 3 4 5 6 7 8 9 10 Shear displacement [mm] Figure 4.6. Shear stress versus shear displacement of the CNL02 specimen under different normal stress (3.6, 7.2, 10.8 MPa) 8 Shear stress [MPa] 7 6 CNL03 5 4 5 MPa 3 10 MPa 15 MPa 2 1 0 0 1 2 3 Shear displacement [mm] 4 5 Figure 4.7. Shear stress versus shear displacement of the CNL03 specimen under different normal stress (5, 10, 15 MPa) 56 Shear stress [MPa] 3 2.5 CNL04 2 1 MPa 4 MPa 1.5 1 0.5 0 0 1 2 3 Shear displacement [mm] 4 5 Figure 4.8. Shear stress versus shear displacement of the CNL04 specimen under different normal stress (1, 4 MPa) Peak and residual shear strength of jointed rock: One of the most important factors influencing the shear strength of rock joints is the normal stress acting on the joint surface. Data obtained from previous studies [Indraratna and Haque, 2000; Huang, et al., 2002; Grasselli, 2006] indicate that the shear stress increases with the increase in normal stress. Table 4-5. Peak shear stress under different normal stress for the CNL tests Sample JRC σno [MPa] τp [MPa] 5 2.2 CNL01 8 10 4.0 15 5.5 3.6 2.0 7.2 3.2 10.8 4.0 5 3.0 10 5.2 CNL02 CNL03 CNL04 6 7 4 15 7.4 1 0.73 4 2.56 Figures 4.5 to 4.8 show the relationship between shear stress and shear displacement obtained by own measurements. As can be seen in these figures the peak shear stress 57 increases with the increase of the applied normal stress. The mean values for the peak shear stress under various normal stresses are given in Table 4-5. Figures 4.5 to 4.8 indicate also that the residual shear strength is only slightly lower than the peak shear strength in all cases. This is typical behavior of ductile rock joints [Grasselli, 2001]. However, with increasing applied normal stress (σno) the ratio of peak shear stress to applied normal stress (τp/σno) tends to decrease (Figures 4.9 to 4.12). This result is similar to the observation by Grasselli (2006). The data for JRC, peak shear stress and shear velocity for the different specimens under different normal stresses are listed in Table 4-6. Shear/Normal stress 0.5 0.4 0.3 CNL01 0.2 5 MPa 10 MPa 15 MPa 0.1 0 0 1 2 3 7 4 5 6 Shear displacement [mm] 8 9 10 Figure 4.9. Ratio of shear to normal stress versus shear displacement of CNL01 specimen Shear/Normal stress 0.6 0.5 0.4 CNL02 0.3 3.6 MPa 0.2 7.2 MPa 10.8 MPa 0.1 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.10. Ratio of shear to normal stress versus shear displacement of CNL02 specimen 58 0.7 Shear/Normal stress 0.6 0.5 0.4 CNL03 0.3 5 MPa 10 MPa 15 MPa 0.2 0.1 0 0 1 2 3 Shear displacement [mm] 4 5 Figure 4.11. Ratio of shear to normal stress versus shear displacement of CNL03 specimen 0.8 Shear/Normal stress 0.7 0.6 0.5 CNL04 0.4 1 MPa 0.3 4 MPa 0.2 0.1 0 0 1 2 3 Shear displacement [mm] 4 5 Figure 4.12. Ratio of shear to normal stress versus shear displacement of CNL04 specimen Peak shear stress [MPa] 8 JRC=8,v=3mm/min JRC=6,v=3mm/min JRC=7,v=4.5mm/min 7 6 5 JRC=4,v=3mm/min 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Normal stress [MPa] Figure 4.13. Peak shear stress versus normal stress for different shear velocities and JRC 59 Peak shear strength value for different normal stresses and different shear velocities are shown in Figure 4.13. It can be seen that the shear velocity has a significant effect on the peak shear strength of rock joints. With increasing shear velocity, the peak shear strength of rock joints increases although the value of JRC is smaller. This result is similar to the results reported by Haque (1999) and Crawford and Curran (1981). Table 4-6. JRC, peak shear stress (τp) and shear velocity (v) data Sample CNL01 CNL02 CNL03 CNL04 JRC σno [MPa] v [mm/min] τp [MPa] 5 3.0 2.2 10 3.0 4.0 15 3.0 5.5 3.6 3.0 2.0 7.2 3.0 3.2 10.8 3.0 4.0 5 4.5 3.0 10 4.5 5.2 15 4.5 7.4 1 3.0 0.73 4 3.0 2.56 8 6 7 4 Effects of shear velocity: To examine the effects of the shear velocity on the peak shear stress value, CNL tests were performed at normal stress of 2.5 MPa and shear velocity of 1 mm/min, 10 mm/min and 50 mm/min (Figure 4.14). The peak shear stresses obtained from laboratory experiments are listed in Table 4-7. Table 4-7. Peak shear stress at different shear velocities v [mm/min] σno [MPa] τp [MPa] 1 2.5 1.20 10 2.5 1.30 50 2.5 1.35 60 1.6 Shear stress [MPa] 1.4 1.2 1 1 mm/min 10 mm/min 0.8 0.6 50 mm/min 0.4 0.2 0 0 1 2 3 4 Shear displacement [mm] 5 6 Figure 4.14. Shear stress versus shear displacement at different shear velocities With increasing shear velocity an increase in peak shear stress was observed. The peak shear stress increases about 8.3% and 12.5% when shear velocity increases from 1 to 10 mm/min and 1 to 50 mm/min, respectively. Based on the own experimental results and Barton’s (1976) suggestion, a mathematical model was parameterized to evaluate the peak shear strength of the rock joints at different shear velocities: v n JCS τ p = 1 σ no tan φb + JRC log10 v2 σ no where (4-7) v1 and v2 are the shear velocities, σno is the normal stress, φb is the basic friction angle of the surface, JRC is the joint roughness coefficient, JCS is the joint wall compressive strength, n is the coefficient, which was determined by performing regression analysis using own experimental results (n = 0.02944). Substitute n = 0.02944 into equation (4-7) the peak shear strength can be predicted for any shear velocity: 61 v 0.02944 JCS σ no σ no tan φb + JRC log10 τ p = 1 v2 (4-8) Mohr-Coulomb failure envelope for joint surface: The relationship between shear stress and normal stress at failure according to the Mohr-Coulomb envelope can be expressed as follows: τ j = σ j tan (φ j ) + c j (4-9) τj is the shear stress on the joint surface at failure, where σj is the normal stress on the joint surface at failure, φj is the internal friction angle of the joint surface, cj is the cohesion of the joint surface. Peak shear stress [MPa] 8 y = 0.44x + 0.8 CNL01 CNL02 CNL03 CNL04 7 6 5 4 R2 = 1 y = 0.33x + 0.6 R2 = 0.9973 3 y = 0.61x + 0.12 2 R2 = 1 y = 0.2778x + 1.0667 R2 = 0.9868 1 0 0 2 4 10 6 8 Normal stress [MPa] 12 14 16 Figure 4.15. Mohr-Coulomb failure envelope for individual samples under CNL tests The peak shear stresses according to the applied normal stress obtained from experiments are presented in Table 4-6. Based on these values, Mohr-Coulomb envelopes were constructed for individual samples (Figure 4.15) and in general (Figure 4.16). Friction angle and cohesion of the joint surfaces are given by the Mohr-Coulomb failure envelope for different samples as follows: 62 CNL01: cj = 0.6 MPa; φj = atan(0.33) = 18.30 CNL02: cj = 1.0667 MPa; φj = atan(0.2778) = 15.50 CNL03: cj = 0.8 MPa; φj = atan(0.44) = 23.70 CNL04: cj = 0.12 MPa; φj = atan(0.61) = 31.40 Peak shear stress [MPa] 8 y = 0.4407x 7 R2 = 0.8653 6 y = 0.3815x + 0.6139 5 2 R = 0.8936 4 3 2 1 0 0 1 3 2 4 5 6 7 8 9 10 11 12 13 14 15 16 Normal stress [MPa] Figure 4.16. Mohr-Coulomb failure envelope in general under CNL tests If all data are considered together (Figure 4.16), the following values were obtained: cj = 0.6139 MPa; φj = atan(0.3815) = 20.90 cj = 0 MPa; φj = atan(0.4407) = 23.80 As Figure 4.17 documents, the normal stress level was kept constant with high accuracy during all experiments. 16 Normal stress [MPa] 14 CNL01 CNL03 CNL02 CNL04 12 10 8 6 4 2 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.17. Normal stress versus shear displacement for CNL tests 63 Determination of dilation: In general the dilation angle (ψ) is defined as the ratio of incremental normal displacement to incremental shear displacement as follows: tanψ = where ∆u n ∆u s (4-10) ∆un is the increment of normal displacement, ∆us is the increment of shear displacement. Results obtained from previous studies [Vásárhelyi, 1998; Homand, et al., 2001; Pötsch, et al., 2007; Ghazvinian, et al., 2009; Muralha, 2012] have shown that the dilation potential of rock joints decreases with the increase of the applied normal stress. Depending on the relationship between shear direction and slope direction of interface as shown in Figure 4.18, the dilation angle can be positive or negative. Z σno ∆un < 0 Slope direction σno Slope direction Shear direction Slope direction θ (positive) O Initial position Shear direction ∆us X a) angle (θ) is positive (negative dilation, ∆un < 0) Z σno σno ∆un > 0 Slope direction Slope direction θ (negative) Shear direction Slope direction O Shear direction ∆us Initial position X b) angle (θ) is negative (positive dilation, ∆un > 0) Figure 4.18. The relationship between shear direction and slope direction of interface 64 Normal displacement [mm] 0.2 Shear displacement [mm] 0 -0.2 0 1 2 3 4 5 6 7 8 9 10 -0.4 -0.6 CNL01 -0.8 5 MPa -1 10 MPa Shear direction 15 MPa -1.2 Figure 4.19. Normal displacement versus shear displacement of CNL01 specimen 0.1 Shear displacement [mm] Normal displacement [mm] 0 -0.1 0 1 2 3 4 5 6 -0.2 7 8 10 3.6 MPa CNL02 -0.3 9 7.2 MPa 10.8 MPa -0.4 -0.5 -0.6 Shear direction -0.7 Figure 4.20. Normal displacement versus shear displacement of CNL02 specimen Normal displacement [mm] 0.1 Shear displacement [mm] 0 -0.1 -0.2 0 1 2 3 5 CNL03 -0.3 05 MPa 10 MPa 15 MPa -0.4 -0.5 4 Shear direction Figure 4.21. Normal displacement versus shear displacement of CNL03 specimen 65 Normal displacement [mm] 0.4 0.3 CNL04 0.2 Shear direction 1 MPa 4 MPa 0.1 0 0 1 2 -0.1 3 4 5 6 Shear displacement [mm] Figure 4.22. Normal displacement versus shear displacement of CNL04 specimen Experimental results are shown in Figures 4.19 to 4.22. Negative normal displacement behaviour was observed for samples CNL01, CNL02 and CNL03 (Figures 4.19 to 4.21). Positive dilation was observed for sample CNL04 (Figure 4.22). Dilation related parameters are given in Table 4-8 and Table 4-9. Table 4-8. Normal and shear displacements for various normal stresses Sample σno [MPa] us [mm] un [mm] 5 10 -0.36 CNL01 10 10 -0.76 CNL02 CNL03 CNL04 15 10 -1.10 3.6 10 -0.17 7.2 10 -0.59 10.8 5 -0.45 5 5 -0.16 10 5 -0.33 15 5 -0.44 1 5 0.38 4 5 0.22 The dilation angle depends on the level of applied normal stress. The experimental results show that increasing applied normal stress leads to a decrease of the dilation angle as shown in Figure 4.23. 66 Table 4-9. Dilation angle (ψ), JRC and applied normal stress (σno) Sample JRC CNL01 8 σno [MPa] ψ [o] 5 -2.0 10 -4.3 15 -6.3 3.6 -1.0 7.2 -3.4 10.8 -5.1 6 CNL02 7 CNL03 5 -1.8 10 -3.8 15 -5.0 1 4.3 4 2.5 4 CNL04 Dilation angle [degree] 6 CNL01: JRC=8 4 CNL02: JRC=6 2 CNL03: JRC=7 CNL04: JRC=4 0 -2 0 2 4 6 8 10 12 14 16 -4 -6 -8 Normal stress [MPa] Figure 4.23. Dilation angle versus normal stress under CNL conditions From all above mentioned experimental results, one can conclude that the shear stress and strength on the rock joints do not only depend on the applied normal stress and JRC but also on the shear velocity and the relationship between shear direction and slope direction of joint. Determination of normal and shear stiffness for joint surface: Rock joint parameters normal stiffness (kn) and shear stiffness (ks) can be determined from direct shear tests [Vallier, et al., 2010]. 67 The normal stiffness (kn) of the rock joints is the parameter relating the normal stress and the normal relative displacement in the elastic state and is given by kn = σn δn (4-11) σn is the normal stress value, where δn is the corresponding normal displacement. The shear stiffness (ks) is the slope of the shear stress versus shear displacement curve in the elastic state and is given by ks = τ δs (4-12) τ is the shear stress, where δs is the related shear displacement measured in the elastic state. Rock joint mechanical parameters were calculated for all the CNL tests and are summarized in Table 4-10. Table 4-10. Rock joint mechanical parameters of CNL tests Sample kn [GPa/m] ks [GPa/m] φjoint [degree] cjoint [MPa] CNL01 3.33 4.98 18.26 0.60 CNL02 4.09 9.99 15.52 1.07 CNL03 2.68 5.93 23.75 0.80 CNL04 5.55 3.23 31.38 0.12 4.1.2 Constant Normal Stiffness (CNS) tests 4.1.2.1 CNS test set-up Test set-up for constant normal stiffness (CNS) boundary conditions is illustrated in Figure 4.24. All CNS tests were also conducted as multi-stage tests. The tests were 68 carried out at three different normal stiffnesses (Kn values of 3, 5 and 9 GPa/m) for each specimen. Direct shear tests with 1.0, 1.8 and 2.4 mm/min shear velocities were performed on CNS01, CNS02 and CNS03 specimens, respectively. Table 4-11 gives an overview of the lab tests performed under CNS boundary conditions. un un K = constant Shear velocity (b) + + (a) K = constant Shear velocity us us Figure 4.24. Constant normal stiffness test set-up for intact (a) and jointed (b) sample Before shearing under CNS boundary conditions, the normal load was applied on the upper shear box to reach the prescribed values. The initial applied normal stress for each stage was a constant value of 5 MPa for CNS01 and CNS02 specimens and 6.6 MPa for CNS03 specimen. All forces (normal force and shear force) were measured by loadcells. The horizontal displacement and vertical displacements were measured by LVDT’s in the same way as for the CNL tests. Table 4-11. Set-up for CNS testing (multi-stage tests) Parameters Sample Stage LxWxH [mm3] σno [MPa] v [mm/min] Kn [GPa/m] us_max [mm] 5.0 1.0 3 10 5.0 1.0 5 10 3 5.0 1.0 9 10 1 5.0 1.8 3 10 1 CNS01 CNS02 CNS03 2 2 348 x 156 x 160 5.0 1.8 5 10 3 5.0 1.8 9 10 1 6.6 2.4 3 10 6.6 2.4 5 10 6.6 2.4 9 10 2 3 350 x 155 x 150 355 x 164 x 160 69 The CNS shear box tests were performed first with intact rock samples and shear direction parallel to the schistosity planes until the peak shear strength and maximum shear displacement were reached. The normal stiffness was maintained constant during shear process. After finishing the shear test with the intact rock sample a jointed sample was obtained. The geometry of the joint was scanned before and after each multi-stage shear test by using the zSnapper scanner. Results of scanning were used to calculate JRC of the rock surface. Each specimen was tested at three levels of normal stiffness as indicated in Table 4-11. Each sample was sheared first at initial normal stiffness level to reach peak shear strength and maximum shear displacement value, after that normal stiffness was increased and shear test was continued until next peak shear strength level and maximum shear displacement were reached. Finally the normal stiffness was changed again to the third normal stiffness level and shear test was continued to reach peak shear strength and maximum shear displacement in this step. At the end of each test, the shear box was moved back to its initial position by reversing the shear direction. 4.1.2.2 CNS test results Peak and residual shear strength of rock joints: Shear behaviour of rock joints under constant normal stiffness boundary conditions has been investigated by several researchers [Ohnishi and Dharmaratne, 1990; Van Sint Jan, 1990; Haque, 1999]. These previous studies have shown that the peak shear stress under constant normal stiffness boundary conditions is increased when normal stiffness is increased. Own experimental results for rock joints under constant normal stiffness boundary conditions are illustrated in Figures 4.25 to 4.27. 70 3 CNS01 Shear stress [MPa] 2.5 2 1.5 3 GPa/m 5 GPa/m 9 GPa/m 1 0.5 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.25. Shear stress versus shear displacement of CNS01 specimen 3 CNS02 Shear stress [MPa] 2.5 2 1.5 3 GPa/m 5 GPa/m 1 0.5 9 GPa/m 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.26. Shear stress versus shear displacement of CNS02 specimen 3 CNS03 Shear stress [MPa] 2.5 2 1.5 3 GPa/m 1 5 GPa/m 9 GPa/m 0.5 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.27. Shear stress versus shear displacement of CNS03 specimen 71 The shear stress was observed to increase until peak shear strength was reached at about 2 mm shear displacement for the CNS01 and CNS03 samples. The peak shear stress of the CNS02 sample was obtained at about 1 mm shear displacement. However, no reduction in shear stress with ongoing shear displacements was observed. The experimental results show that normal stiffness has a significant influence on shear stress of rock joints. The peak shear stress decreased with an increase in normal stiffness. This means that our experimental results differ from previous studies. This can be explained by following equation: σ n (h ) = σ no + K n ∆u n (h ) where (4-13) σ n (h ) is the effective normal stress, σ no is the initial normal stress, Kn is the normal stiffness, ∆u n (h ) is the normal displacement (or dilatancy). It is easily seen that the effective normal stress ( σ n (h ) ) increases when normal stiffness (Kn) increases and dilation of specimen is positive ( ∆u n (h ) > 0). However, when the dilation is negative ( ∆u n (h ) < 0) then the effective normal stress decreases with increasing normal stiffness. The peak shear stress is directly proportional to effective normal stress. Therefore, the peak shear stress decreased with an increase in normal stiffness during our experiments. The peak shear stress obtained under variation of JRC and normal stiffness conditions are summarized in Table 4-12. Figure 4.28 shows peak shear stress versus normal stiffness for different JRC and shear velocities. It can be seen that increasing normal stiffness leads to a pronounced decrease of peak shear stress. Furthermore, one can observe that the peak shear stress versus normal stiffness envelops for CNS02 and CNS03 specimens have the same slope (red and green line in Figure 4.28). But the red line lies above the green line. This means that the peak stress of the CNS03 sample is higher than that of CNS02 sample because the initial applied normal stress of CNS03 and CNS02 samples are 6.6 and 5.0 MPa, respectively. 72 Table 4-12. JRC, normal stiffness (Kn) and peak shear stress (τp) v σno [MPa] [mm/min] Sample JRC CNS01 17 5.0 CNS02 6 5.0 CNS03 5 6.6 Peak shear stress - τp [MPa] Kn = 3GPa/m Kn = 5GPa/m Kn = 9GPa/m 1.0 2.30 2.10 1.70 1.8 2.24 1.88 1.40 2.4 2.6 2.24 1.70 Peak shear stress [MPa] 3 2.5 2 1.5 1 JRC=17, v=1mm/min JRC=6, v=1.8mm/min 0.5 JRC=5, v=2.4mm/min 0 0 1 2 3 4 5 6 7 Normal stiffness [GPa/m] 8 9 10 Figure 4.28. Peak shear stress versus normal stiffness at different shear velocities and JRC Variation of normal stress: The relationship between effective normal stress and shear displacement under constant normal stiffness boundary conditions is illustrated in Figures 4.29 to 4.31 for CNS01, CNS02 and CNS03 specimens, respectively. These Figures indicate that magnitude of change of effective normal stress is affected by normal stiffness. Furthermore, it is observed that the effective normal stress on the joints decreased during the shearing process. Normal stress decreased when normal stiffness is increased. The effective normal stress is changed very little when normal stiffness is small (3 GPa/m) during the shearing process. But the change in effective normal stress is higher when normal stiffness is increased. Experimental results are summarized in Table 4-13. The normal stresses (σn) were measured at maximum shear displacement (us_max). 73 Effective normal stress [MPa] 6 CNS01 5 4 3 3 GPa/m 5 GPa/m 9 GPa/m 2 1 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.29. Effective normal stress versus shear displacement of CNS01 specimen Effective normal stress [MPa] 6 CNS02 5 4 3 3 GPa/m 5 GPa/m 9 GPa/m 2 1 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.30. Effective normal stress versus shear displacement of CNS02 specimen Effective normal stress [MPa] 8 CNS03 7 6 5 3 GPa/m 5 GPa/m 9 GPa/m 4 3 2 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 4.31. Effective normal stress versus shear displacement of CNS03 specimen 74 Table 4-13. Normal stresses and shear displacements under CNS conditions Sample σno [MPa] Kn [GPa/m] us_max [mm] σn [MPa] 5 3 10 4.8 5 5 10 4.4 5 9 10 3.5 5 3 10 4.7 5 5 10 4.3 CNS01 CNS02 CNS03 5 9 10 3.3 6.6 3 10 6.3 6.6 5 10 5.7 6.6 9 10 4.4 Variation of normal displacement: Normal displacement versus shear displacement curves for rock joints at various normal stiffness values are shown in Figures 4.32 to 4.34. During the shearing process, the dilation of the rock joints is controlled by the joint asperities, normal stiffness levels, applied initial normal stress and joint angle. As shown in Figures 4.32 to 4.34 normal displacement of rock joints decreases with increasing normal stiffness. The dilation angles for different specimens under different constant normal stiffness were calculated according to the equation (4-10) and are listed in Table 4-14. Normal displacement [mm] 0.1 Shear displacement [mm] 0 -0.1 0 1 2 3 4 5 6 CNS01 7 8 9 10 3 GPa/m -0.2 5 GPa/m -0.3 9 GPa/m -0.4 -0.5 -0.6 Shear direction Figure 4.32. Normal displacement versus shear displacement of CNS01 specimen 75 Normal displacement [mm] 0.1 CNS02 Shear displacement [mm] 0 -0.1 0 1 2 3 4 5 6 7 8 9 10 -0.2 -0.3 -0.4 -0.5 3 GPa/m -0.6 5 GPa/m -0.7 9 GPa/m Shear direction -0.8 Figure 4.33. Normal displacement versus shear displacement of CNS02 specimen Normal displacement [mm] 0.2 -0.2 CNS03 Shear displacement [mm] 0 0 1 2 3 4 5 6 7 8 9 10 -0.4 -0.6 -0.8 3 GPa/m 5 GPa/m -1 9 GPa/m Shear direction -1.2 Figure 4.34. Normal displacement versus shear displacement of CNS03 specimen Table 4-14. Dilation angle (ψ), JRC, normal stiffness (Kn) and shear velocity (v) Sample CNS01 CNS02 CNS03 JRC 17 6 5 σno [MPa] 5 5 6.6 v [mm/min] 1.0 1.8 2.4 76 Kn [GPa/m] ψ [o] 3 -0.8 5 -2.3 9 -3.3 3 -1.9 5 -3.1 9 -4.3 3 -2.8 5 -4.2 9 -5.7 Normal stiffness [GPa/m] Dilation angle [degree] 0 -1 0 1 2 3 4 5 6 7 8 9 10 -2 -3 CNS01 CNS02 CNS03 -4 -5 -6 Figure 4.35. Dilation angle versus normal stiffness under CNS conditions The relation between dilation angle versus normal stiffness under different shear velocities and JRC are presented in Figure 4.35. The results indicate that the dilation angle depends on both JRC and shear rates. Rock joints mechanical parameters are summarized in Table 4-15. Table 4-15. Rock joint mechanical parameters of the CNS specimens Sample kn [GPa/m] ks [GPa/m] φjoint [0] CNS01 3.58 1.45 19.4 CNS02 3.11 4.04 20.5 CNS03 4.59 2.40 19.3 4.2 Dynamic shear tests 4.2.1 Dynamic shear test set-up un σno = constant Shear velocity us Figure 4.36. Dynamic shear test set-up for jointed rock sample 77 As mentioned previously in chapter 3, the GS-1000 apparatus can also be used to study the dynamic shear behaviour of rock joints. The set-up for dynamic tests (DT) is illustrated in Figure 4.36. The applied normal stress was maintained constant at 5 MPa and applied at the upper half of the specimen. The amplitude of shear displacement was maintained close to ± 4.5 mm. Each specimen is subjected to 10 cycles of shear displacement. Parameters for dynamic shear testing are given in Table 4-16. The shear displacement controlled sinusoidal excitation was applied horizontally to lower half of specimen as follows: u s = u max sin (2πft ) (4-14) us is the shear displacement, where umax is the maximum amplitude of shear displacement, f is the frequency, t is the time. Table 4-16. Parameters for dynamic shear testing Sample Parameters 3 L x W x H [mm ] σno [MPa] f [Hz] umax [mm] Num. of cycle DT01 318 x 164 x 166 5.0 1.0 4.5 10 DT02 318 x 164 x 166 5.0 0.5 4.5 10 DT03 246 x 156 x 150 5.0 1.0 4.5 10 Normal and shear load were measured by load-cells integrated in the vertical and horizontal loading pistons of the direct shear box device. The shear displacement was measured by a horizontal LVDT which is attached to the bottom part of shear box. The normal displacement is also measured by four vertical LVDTs which are positioned at the four corners of the upper part of shear box as already mentioned in previous chapter. 4.2.2 Dynamic shear test results The measured shear displacements versus time (10 cycles) for the three tested specimens are illustrated in Figure 4.37 to 4.39. 78 Shear displacement [mm] 6 4 DT01 2 0 723 724 725 726 727 728 729 730 731 732 733 734 735 736 -2 -4 -6 Time [sec] Figure 4.37. Shear displacement versus time of DT01 specimen Shear displacement [mm] 6 4 DT02 2 0 -2 518 520 522 524 526 528 530 532 534 536 538 540 542 -4 -6 Time [sec] Figure 4.38. Shear displacement versus time of DT02 specimen Shear displacement [mm] ] 6 4 DT03 2 0 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 -2 -4 -6 Time [sec] Figure 4.39. Shear displacement versus time of DT03 specimen 79 The measured shear stresses versus time for different specimens are shown in Figures 4.40 to 4.42. The measured peak shear stresses increase with increasing time and number of cycles, respectively, as shown in Figures 4.40 to 4.42. This behaviour of the rock joints under dynamic loading is similar to the reported results by Homand-Etienne Shear stress [MPa] et al. (1999). 5 4 3 2 1 0 DT01 -1723 724 725 726 727 728 729 730 731 732 733 734 735 736 -2 -3 -4 -5 Time [sec] Figure 4.40. Shear stress versus time of DT01 specimen 4 DT02 Shear stress [MPa] 3 2 1 0 -1518 520 522 524 526 528 530 532 534 536 538 -2 -3 -4 -5 Time [sec] Figure 4.41. Shear stress versus time of DT02 specimen 80 540 542 4 DT03 Shear stress [MPa] 3 2 1 0 -1531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 -2 -3 -4 -5 Time [sec] Figure 4.42. Shear stress versus time of DT03 specimen Experimental results show that the absolute peak shear stress in the negative phases is higher than peak shear stress in the positive phases for all the three specimens. However, the peak shear stress in positive phases of the DT03 specimen is slightly higher than absolute peak shear stress in the negative phases. The reason for such different peak shear stress behaviour is the relationship between shear direction and slope direction of the rock joint surface as explained in previous chapter. The DT01 and DT02 specimens were compressed when shear displacement was forward (positive shear displacement), and these were dilated while shear displacement was backward (negative shear displacement). In contrast, DT03 specimen was dilated when shear displacement was positive, but it was compressed when shear displacement was negative. The maximum shear stresses in the positive and negative phases are given in Table 4-17. Table 4-17. Absolute maximum shear stresses Sample DT01 DT02 DT03 Absolute maximum shear stress [MPa] Cycle number positive phase 3.76 1 negative phase 4.33 10 positive phase 3.13 10 negative phase 4.46 10 positive phase 3.46 10 negative phase 3.31 10 81 Figures 4.43 to 4.45 show the measured shear stresses and shear displacements versus time for the three dynamic tests. These Figures reveal a phase shift between shear displacement and shear stress. The shear displacement is phase lagging in comparison with the shear stress. This behaviour of rock joints under dynamic loading was observed during all experiments. These observed results are similar to the results reported by Ahola et al. (1996). The reason for the phase shift between shear stress and shear displacement is associated with chatter of the joint surface and vibrations of the apparatus as reported already by Ahola et al. (1996). DT01 6 4 4 2 2 0 723 724 725 726 727 728 729 730 731 732 733 734 735 -2 -2 0 -4 -4 -6 Shear stress [MPa] Shear displacement [mm] 6 Stress Displacement Time [sec] -6 Figure 4.43. Shear stress and shear displacement versus time of DT01 specimen DT02 6 4 4 2 2 0 0 518 520 522 524 526 528 530 532 534 536 538 540 542 -2 -2 -4 -4 -6 Shear stress [MPa] Shear displacement [mm] 6 Displacement Stress Time [sec] -6 Figure 4.44. Shear stress and shear displacement versus time of DT02 specimen 82 6 DT03 4 4 2 2 0 0 532 533 534 535 536 537 538 539 540 541 542 543 544 -2 -2 -4 Shear stress [MPa] Shear displacement [mm] ] 6 -4 Displacement -6 Stress -6 Time [sec] Figure 4.45. Shear stress and shear displacement versus time of DT03 specimen Figures 4.46 to 4.48 show the shear stress versus shear displacement curves (10 cycles) for the three different specimens. The JRC of DT01 and DT02 specimens are the same and equal to 5. Hence, the maximum shear stresses of DT01 and DT02 specimens were nearly the same, and reached around 3 MPa and -4 MPa, respectively, under applied normal load of 5 MPa. The absolute maximum shear stress of DT03 specimen (JRC equal to 1) for positive shear displacement phase is similar to that for negative shear displacement phase and reached around 3 MPa. Shear stress [MPa] DT01 4 3 2 1 0 -5 -4 -3 -2 -1 -1 0 1 2 3 4 5 6 -2 -3 -4 -5 Shear displacement [mm] Figure 4.46. Shear stress versus shear displacement after shearing of 10 cycles of the DT01 specimen 83 Shear stress [MPa] DT02 4 3 2 1 -5 -4 -3 -2 -1 0 -1 0 1 2 3 4 5 -2 -3 -4 -5 Shear displacement [mm] Figure 4.47. Shear stress versus shear displacement after shearing of 10 cycles of the DT02 specimen 4 Shear stress [MPa] DT03 3 2 1 0 -6 -5 -4 -3 -2 -1 -1 0 1 2 3 4 5 -2 -3 -4 -5 Shear displacement [mm] Figure 4.48. Shear stress versus shear displacement after shearing of 10 cycles of the DT03 specimen The peak dynamic friction angle corresponding to each specimen was computed on the basis of the ratio between peak shear and normal stresses. The peak dynamic friction angle averaged after 10 cycles is given in Table 4-18. Comparisons of the peak shear stresses for different frequencies (DT01 and DT02 specimen) do not reveal any significant differences. However, the peak shear stress under dynamic conditions was 30% higher than that under static conditions. 84 Table 4-18. Average peak dynamic friction angle and JRC Sample JRC σno [MPa] τp [MPa] φ [o] DT01 5 5 3.70 36.5 DT02 5 5 3.51 35.0 DT03 1 5 3.03 31.2 Normal stress: As Figures 4.49 to 4.51 document, the applied normal stress was kept nearly constant at 5 MPa during the entire tests. Normal stress [MPa] 6 5 4 DT01 3 2 1 0 723 724 725 726 727 728 729 730 731 732 733 734 735 736 Time [sec] Figure 4.49. Normal stress versus time of DT01 specimen Normal stress [MPa] 6 5 4 DT02 3 2 1 0 518 520 522 524 526 528 530 532 534 Time [sec] 536 538 540 Figure 4.50. Normal stress versus time of DT02 specimen 85 542 Normal stress [MPa] 6 5 4 DT03 3 2 1 0 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 Time [sec] Figure 4.51. Normal stress versus time of DT03 specimen Normal displacement: Normal displacement [mm] 0 Time [sec] 723 724 725 726 727 728 729 730 731 732 733 734 735 736 -0.3 -0.6 DT01 -0.9 -1.2 -1.5 -1.8 -2.1 Figure 4.52. Normal displacement versus time of DT01 specimen Normal displacement [mm] 0.2 0 Time [sec] -0.2518 520 522 524 526 528 530 532 534 536 538 540 542 -0.4 DT02 -0.6 -0.8 -1 -1.2 -1.4 Figure 4.53. Normal displacement versus time of DT02 specimen 86 Normal displacement [mm] 0.5 Time [sec] 0 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 -0.5 -1 DT03 -1.5 -2 -2.5 -3 Figure 4.54. Normal displacement versus time of DT03 specimen The variations in normal displacement with time for DT01, DT02 and DT03 specimens are shown in Figures 4.52 to 4.54, respectively. The normal displacements behave like a harmonic function and continue to decrease with increasing time and number of cycles, respectively. The reason for increasing negative displacements (settlements) during the cyclic shearing is the ongoing degradation of the joint surface. However, the shear movement of one cycle can be subdivided into four different phases: forward advance, forward return, backward advance and backward return phase. Exemplary, the shear and normal displacements for DT01 specimen are illustrated in Figure 4.55 for one cycle. forward advance B 0 DT01 Shear displacement 4 Normal displacement 2 A forward return E -0.2 -0.4 C 0 -0.6 725.1 725.2 725.3 725.4 725.5 725.6 725.7 725.8 725.9 726 726.1 726.2 726.3 -2 -0.8 -4 -6 backward advance D Time [sec] backward return -1 Normal displacement [mm] Shear displacement [mm] 6 -1.2 Figure 4.55. Shear displacement and normal displacement versus time for one cycle of DT01 specimen The four phases can be characterized as follows: 87 Phase I (A to B): lower block is moved forward and due to slope direction dilation is negative (compression). Phase II (B to C): lower block is moving into the opposite direction and due to slope direction dilation is positive (dilation). At point C the sample has reached again the original position. Phase III (C to D): lower block is still moving into the opposite direction and dilation is still positive (dilation). Phase IV (D to E): direction of lower block movement is returned and has the same direction as in phase I, due to slope direction dilation becomes negative (compression). 88 5 Numerical simulation of direct shear box tests comparison with laboratory tests 5.1 Overview of FLAC3D FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) is developed by ITASCA and is based on an explicit finite-difference scheme [Itasca., 2012]. FLAC3D software is a numerical modelling code for advanced geotechnical analysis of soil, rock and structural support in three dimensions and was used to simulate the direct shear tests. Joint surface between top and bottom part of the specimen in direct shear tests is modelled with interfaces elements in FLAC3D. Interface elements are represented by a collection of triangular elements, each of which is defined by three nodes (interface nodes). Each interface element distributes its area to its nodes in a weighted fashion. Each interface node has an associated representative area. The entire interface is thus divided into active interface nodes representing the total area of the interface. Figure 5.1 illustrates the relation between interface elements and interface nodes, and the representative area associated with an individual node [Itasca., 2012]. Interface node Interface element Node’s representative area Figure 5.1. Distribution of representative areas to interface nodes [Itasca., 2012] Interfaces in FLAC3D are simulated by Coulomb sliding and/or tensile and shear bonding. Interfaces have the properties of friction, cohesion, dilation, normal stiffness, shear stiffness, tensile and shear bond strength. 89 5.2 Numerical model set-up Numerical simulation methods have been used to simulate direct shear tests by several researchers [Haque, 1999; Park and Song, 2009; Zhou, et al., 2009; Iragorre, 2010; Shrivastava and Rao, 2010; Bacas, et al., 2011; Lin, et al., 2012; Park and Song, 2013]. FLAC3D has been successfully used to investigate the shear behaviour of rock joints under CNL boundary conditions [Itasca., 2012; Lin, et al., 2012]. However, they have used FLAC3D to simulate the shear strength of smooth and regular saw-tooth rock joints not considering the joint roughness in detail. In this study the behaviour of rough rock joint surfaces under different boundary conditions and considering the joint roughness at the microscopic scale was simulated using FLAC3D. 5.2.1 Surface roughness simulation Surface roughness is one of the most important parameters, which influences the shear behaviour of rock joints. Therefore, special attention was paid to a very detailed simulation of the joint surfaces. Surface roughness of a sample was simulated in FLAC3D by using the 3D-scanner data. The 3D-scanner data were converted into ASCII format and finally used to manipulate the mesh in FLAC3D, so that the joint topography was duplicated. We assume that the upper joint and lower joint surfaces are completely matched at the initial stage. Geometry and size of the models are identical to the laboratory samples. The surface mesh is generated by 50 x 100 elements. This means that each mesh element has area of around 3 mm x 3 mm. The surface roughness was generated by manipulation of the Z elevation of the grid points of the flat surface according to the 3D-scanner data. FISH code was developed to perform these manipulations. Figure 5.2 illustrates the procedure. 90 a) Rock sample b) 3D-scanner data c) FLAC3D flat surface mesh d) FLAC3D manipulated surface mesh Figure 5.2. Simulation of surface roughness using FLAC3D 91 The geometry of the model is divided into two parts: the upper part and lower part. The interface is assigned on the joint face of the lower part. A uniform mesh with about 50.000 elements is generated for each part on the model (X x Y x Z = 100 x 50 x 10). The whole model is divided into about 100.000 zones as shown in Figure 5.3. Figure 5.3. General model for simulating the direct shear test in FLAC3D 5.2.2 Constitutive model 5.2.2.1 Constitutive model for rock joint interface The fundamental contact relation is defined between the interface node and a zone surface face, also known as the target face. The normal direction of the interface force is determined by the orientation of target face. During each time step, the absolute normal penetration and the relative shear velocity are calculated for each interface node and its contacting target face. Both of these values are then used by the interface constitutive model to calculate a normal force and a shear force vector. The constitutive model is defined by a linear Coulomb shear-strength criterion that limits the shear force acting at an interface node, normal stiffness, shear stiffness, tensile and shear bond strengths, and a dilation angle that causes an increase in effective normal force on the target face after the shear-strength limit is reached. Figure 5.4 illustrates the components of the constitutive model acting at interface node P [Itasca., 2012]. 92 Target face Ss S ks Ts Ss = shear strength S = slider D ks = shear stiffness Ts = tensile strength D = dilation kn kn = normal stiffness P = interface node P Figure 5.4. Components of the bonded interface constitutive model [Itasca., 2012] The normal and shear forces that describe the elastic interface response are determined at calculation time (t + ∆t) using the following relations: Where Fn(t + ∆t ) = k n u n A + σ n A (5-1) Fsi(t + ∆t ) = Fsi(t ) + k s ∆u si(t + 0.5 ∆t ) A + σ si A (5-2) Fn(t + ∆t) is the normal force at time (t + ∆t), Fsi(t + ∆t) is the shear force vector at time (t + ∆t), n is the absolute normal penetration of the interface node into to target face, ∆usi is the incremental relative shear displacement vector, A is the representative area associated with the interface node, σn is the additional normal stress added due to interface stress initialization, kn is the normal stiffness, ks is the shear stiffness, σsi is the additional shear stress vector due to interface stress initialization. The inelastic interface logic works in the following way: 93 • Bonded interface: the interface remains elastic if stresses remain below bond strengths: there is shear bond strength, as well as tensile bond strength. The bond breaks if either the shear stress exceeds the shear strength, or the tensile effective normal stress exceeds the normal strength. • Slip while bonded: An intact bond, by default, prevents all yield behaviour (slip and separation). • Coulomb sliding: a bond is either intact or broken. If it is broken, then the behaviour of the interface segment is determined by the friction and cohesion (and of course the stiffness). A broken bond segment cannot take effective tensile stress (which may occur under compressive normal force, if the pore pressure is greater). The shear force is zero (for a non-bonded segment) if the effective normal force is tensile or zero. The Coulomb shear strength criterion limits the shear force by the following relation: Fs max = cA + (Fn − pA) tan φ where (5-3) Fsmax is the normal force at time, c is the cohesion along the interface, φ is the friction angle of the interface surface, p is pore pressure (interpolated from the target face). If the criterion is satisfied (i.e., if Fs ≥ Fs max ), then sliding is assumed to occur, and Fs = Fs max , with the direction of shear force preserved. During sliding, shear displacement may cause an increase in the effective normal stress on the joint, according to the relation: σn =σn + where Fs 0 − Fs max Ak s tan ψk n (5-4) ψ is the dilation angle of the interface surface, Fs 0 is the magnitude of shear force before the correction is made. 94 5.2.2.2 Constitutive model for rock matrix Many constitutive models for the rock matrix are available in FLAC3D. Each model is developed to represent a specific type of constitutive behaviour commonly associated with specific geologic materials. Among them the most popular model and commonly used for simulating behaviour of rock is the so-called Mohr-Coulomb model. Mohr-Coulomb model: The three components of the generalized stress vector of the Mohr-Coulomb model are expressed in terms of the principal stresses σ1, σ2 and σ3; and three components of the corresponding principal strains ε1, ε2 and ε3. The relationship between incremental stress and strain according to Hooke’s law can be expressed as follows: ( + α (∆ε + α (∆ε ∆σ 1 = α 1 ∆ε 1e + α 2 ∆ε 2e + ∆ε 3e ∆σ 2 = α 1 ∆ε e 2 ∆σ 3 = α 1 ∆ε 3e 2 e 1 + ∆ε 2 e 1 + ∆ε 2e e 3 ) ) ) (5-5) where α1 and α2 are material constants and defined as 4 3 (5-6) 2 3 (5-7) α1 = K + G α2 = K − G where K is the bulk modulus, G is the shear modulus. Failure criterion: The failure criterion used in the FLAC3D model is a composite Mohr-Coulomb criterion with tension cutoff. The three principal stress components must satisfy the following condition: 95 σ1 ≤ σ 2 ≤ σ 3 (5-8) The Mohr-Coulomb failure criterion may be represented in the plane (σ1, σ3) as illustrated in Figure 5.5 (compressive stresses are negative). The failure envelope f(σ1, σ3) = 0 is defined from point A to point B by the Mohr-Coulomb failure criterion f s = 0 with f s = σ 1 − σ 3 N φ + 2c N φ (5-9) and from point B to point C by a tension failure criterion of the form f t = 0 with f t = σ3 −σ t where (5-10) φ is the friction angle, c is the cohesion, σt is the tensile strength and Nφ = 1 + sin φ 1 − sin φ (5-11) σ3 B fs=0 ft=0 C σt A 2c Nφ c tan φ σ1 + σ3 - σ1 = 0 Figure 5.5. Mohr-Coulomb failure criterion [Itasca., 2012] 96 Note that the tensile strength of the material cannot exceed the value of σ3 corresponding to the intersection point of the straight lines (f s = 0) and (σ3 - σ1 = 0) in the f(σ1, σ3) plane (point C in Figure 5.5). This maximum value is given by t σ max = c tan φ (5-12) The potential function is described by means of two functions, gs and gt, used to define shear plastic flow and tensile plastic flow, respectively. The function gs corresponds to a non-associated law and has the form g s = σ 1 − σ 3 Nψ (5-13) 1 + sinψ 1 − sinψ with Nψ = where ψ is the dilation angle. The function gt corresponds to an associated flow rule and is written by g t = −σ 3 (5-14) The flow rule is given a unique definition by application of the following technique. A function h(σ1, σ3) = 0, which is represented by the diagonal between the representation of f s = 0 and f t = 0 in the (σ1, σ3)-plane is defined as illustrated in Figure 5.6. The function is selected with its positive and negative domains, as shown in Figure 5.6, and has the form ( h = σ 3 − σ t + aP σ1 − σ P where ) (5-15) aP and σP are constants defined as a P = 1 + N φ2 + N φ (5-16) 97 σ P = σ t N φ − 2c N φ (5-17) σ3 h=0 - + + domain 1 fs=0 + domain 2 ft=0 σ1 Figure 5.6. Mohr-Coulomb model - domains used in the definition of the flow rule [Itasca., 2012] An elastic guess violating the composite yield function is represented by a point in the (σ1, σ3)-plane, located either in domain 1 or 2, corresponding to negative or positive domain of h = 0, respectively (see Figure 5.6). If the stress point falls within domain 1, shear failure is declared, and the stress point is placed on the curve f s = 0 using a flow rule derived using the potential function gs. If the point falls within domain 2, tensile failure takes place, and the new stress point conforms to f t = 0 using a flow rule derived using gt. 5.2.3 Rock mechanical model calibration Calibration is the task of adjusting the mechanical input parameters (matrix and interface properties) so that the numerical simulation results match well with the laboratory results. The general calibration procedure is illustrated in Figure 5.7. 98 FLAC3D Shear test model Lab test parameters C, φ, E, σno, σt τ, ψ, us, un, ν No Shear Lab tests τ, σno, us, un Yes Mechanical parameters C, φ, E, σno, σt, ψ, ν Figure 5.7. Model calibration procedure The mechanical properties for rock matrix and joint were derived from direct shear laboratory tests performed by the author under consideration of additional values from previous studies [Dinh, 2011; Dinh, et al., 2013]. The final mechanical properties for rock matrix and joint obtained from the calibration procedure are listed in Tables 5-1 and 5-2. Table 5-1. Rock mechanical matrix properties Matrix parameters Symbol Unit 3 Value Unit weight γ kg/m Young’s modulus E GPa 2780 45.0 Poisson’s ratio ν - 0.3 Cohesion c MPa 2.46 Friction angle φ degree 29.6 Tensile strength σt MPa 1.0 Dilation angle ψ degree 0 99 Table 5-2. Rock mechanical joint properties Joint properties Sample Cohesion [MPa] Friction angle [degree] Normal stiffness [GPa/m] Shear stiffness [GPa/m] CNL01 0.6 18.3 3.33 4.98 CNL02 1.06 15.5 4.09 10.0 CNL03 0.8 23.7 2.68 5.93 CNL04 0.12 31.4 5.55 3.23 CNS01 0.2 19.4 3.58 1.45 CNS02 0.2 20.5 3.11 4.04 CNS03 0.2 19.3 4.59 2.40 5.2.4 Simulation of direct shear tests under CNL conditions Upper part Interface Lower part Figure 5.8. Conceptual model for CNL direct shear tests Figure 5.8 shows the geometry of a model under CNL boundary conditions. The geometry of the model is divided into two parts: the upper part and lower part. The lower part of model is fixed in the vertical direction at the bottom face (z-axis). The upper part of model is fixed in the horizontal direction (x-axis) at two faces: left and right boundary. The initial normal stress is applied at the upper boundary of the model and calculation is performed until equilibrium is reached. After that, a horizontal velocity is applied to the lower part of specimen to produce the required shear displacement compatible with laboratory shear rate. The shear and normal stresses along the joint were calculated via FISH functions. The peak shear stress for the applied 100 normal stress can be determined from the shear stress versus shear displacement plot. The normal displacement is measured at the 4 points on the upper part of model in the same way as in the laboratory. The shear displacement was determined by multiplying the shear velocity with time steps. 5.2.5 Simulation of direct shear tests under CNS conditions FLAC3D can be also used to simulate the direct shear tests under CNS boundary conditions. The conceptual CNS shear model is shown in Figure 5.9. The external constant normal stiffness applied was simulated by a spring block on top of the model. The external normal stiffness was determined according to following equation [Johnston, et al., 1987]: Kn = where E r (1 + ν ) (5-18) Kn is the external normal stiffness, r is the socket radius, ν is the Poisson ratio. The socket radius (r) can be replaced by the equivalent radius (req) of specimen: req = where WH (5-19) π W is the width of specimen, H is the height of specimen. Therefore, the elastic bulk modulus (K) and elastic shear modulus (G) of the spring material can be determined by following equations: K= K n req (1 + ν ) (5-20) 3(1 − 2ν ) 101 G= K n req (1 + ν ) 2(1 + ν ) = K n req (5-21) 2 Top part Upper part Interface Lower part Figure 5.9. Conceptual model for CNS direct shear tests The geometry of the model under CNS boundary condition is divided into three parts: lower part, upper part and top part. The lower part of the model is fixed in the zdirection at the bottom face. The upper and top parts of the model are fixed in the xdirection at two faces: left and right boundary. The top part is fixed in the z-direction at the top face. 5.3 Micro-slope angle distribution The angle between joint surface and shear direction is very important for the shear behaviour of rock joints as indicated in previous study of Grasselli (2001). In this study, the joint surfaces were reconstructed from three-dimensional scanning point cloud data by a triangulation algorithm. The accuracy of the reconstruction depends on the density of point clouds. The joint surface was discretized into a finite number of triangles as shown in Figure 5.10, whose geometric orientations are easy to estimate based on the orientation of the normal vector of the triangle plane [Grasselli, 2001]. Each element of the joint surface was established by three points in space, which has only true dip angle. The apparent dip angle is angle between two lines, one is intersection of the joint surface element and shear direction plane and other one is 102 projected of it on the vertical plane [Grasselli, 2001]. This means that the apparent dip angle depend on the shear direction. In other words, the apparent dip angle varies with the shear direction. In this study the term “micro-slope angle” is used, which is an extension of the apparent dip angle concept proposed by Park and Song (2013), to estimate the apparent dip angle of the joint surface elements. The micro-slope angles were calculated with respect to the shear direction for every element of the joint surface. C A B Shear direction o Figure 5.10. Triangle elements on the joint surface The specimen is sheared by moving the lower part in a direction parallel to the X-axis; this means that the XOZ plane is the shear direction plane. The shear plane indicates the plane that includes X-axis and Y-axis. The triangle ABC has coordinates A(xi,j, yi,j, zi,j), B(xi+1,j, yi+1,j, zi+1,j), C(xi,j+1, yi,j+1, zi,j+1) as indicated in Figure 5.10. The true dip angle (α) of the ABC plane in space is the angle between ABC plane and XOY plane and it is calculated as follows: cos(α ) = where n ABC • n XOY (5-22) n ABC n XOY n ABC is the normal vector of the ABC plane, n XOY is the normal vector of the XOY plane. The apparent dip angle or micro-slope angle (θ) is angle between two vectors ( AB and OX ) and it is calculated as follows: 103 cos(θ ) = AB • OX (5-23) AB OX Normal load positive angle θpos θneg negative angle shear direction Figure 5.11. Definition of positive and negative micro-slope angle The micro-slope angle is positive (θpos) and varies from 00 to 900 if the joint surface element may come into contact during the shearing. The micro-slope angle is negative (θneg) and ranging between -900 to 00 if the joint surface element may be detached causing void in space during the shearing process. The definition of positive and negative micro-slope angle is shown in Figure 5.11. CNL01 Shear direction CNL04 Shear direction Figure 5.12. Surface mesh of CNL01 and CNL04 specimen Exemplary joint surface of the samples CNL01 and CNL04 are shown in Figure 5.12. The joint surface is modeled by a grid of 100 and 50 elements along to x-axis and y104 axis, respectively. Therefore, the grid point distance is around 3 mm. Each element is 2 Area [cm ] subdivided into two smaller triangle elements. Total area of CNL01: 495 cm2 40 35 30 CNL01 CNL02 CNL03 25 CNL02: 505 cm2 2 20 CNL04: 561 cm2 15 CNL03: 534 cm CNL04 10 5 0 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 Micro-slope angle [degree] Figure 5.13. Areal distribution of the micro-slope angles for CNL specimens The micro-slope angles were calculated for all of the interface elements on the joint surface under consideration of the shear direction. The areal distribution of the microslope angles on samples CNL01, CNL02, CNL03 and CNL04 are illustrated in Figure 5.13. The areal distribution is bell-shaped as can be observed in Figure 5.13. The distributions are nearly symmetric at about -6.50, -3.40, -6.70 and 3.50, which indicate that the joint surface has upward inclination in respect to the shear direction for CNL01, 2 Area [cm ] CNL02, and CNL03 and downward inclination for sample CNL04. Total area of 2 CNS01: 571 cm CNS02: 553 cm2 2 CNS03: 594 cm 35 30 25 20 15 CNS01 CNS02 CNS03 10 5 0 -70 -60 -50 -40 -30 -20 -10 0 10 Micro-slope angle [degree] 20 30 40 50 Figure 5.14. Areal distribution of the micro-slope angles for CNS specimens 105 The areal distribution of the micro-slope angles for CNS01, CNS02 and CNS03 samples are illustrated in Figure 5.14. The micro-slope angles are nearly symmetric with center values at -5.10, -3.00 and -6.00 for CNS01, CNS02 and CNS03 samples, respectively, as can be seen from Figure 5.14. Detailed data for micro-slope angles for different specimens are summarized in Table 5-3. Table 5-3. Micro-slope angle data for different specimens Sample Micro-slope angle [0] Maximum Minimum Mean CNL01 41 -46 -6.5 CNL02 37 -53 -3.4 CNL03 17 -63 -6.7 CNL04 47 -34 3.5 CNS01 55 -77 -5.1 CNS02 31 -44 -3.0 CNS03 36 -44 -6.0 Figures 5.15 and 5.16 show the distribution of the micro-slope angles with respect to the relative shear direction for CNL and CNS specimens. (continued) 106 Figure 5.15. Contour plot of the micro-slope angles with respect to relative shear direction for CNL specimens 107 Figure 5.16. Contour plot of the micro-slope angles with respect to relative shear direction for CNS specimens 108 5.4 Numerical simulations of quasi-static shear tests 5.4.1 CNL simulation results Figure 5.17 shows the 3-dimensional numerical models used to simulate the quasi-static CNL shear tests. Model size and shape of each specimen are identical to those used in the laboratory. The CNL01, CNL02 and CNL03 specimens were sheared in the negative x-direction under three different normal stress levels. The joint surfaces inclination is directed upwards with respect to the shear direction. The CNL04 specimen was sheared in the positive x-direction and the joint surface inclination is directed downwards with respect to the shear direction. (continued) 109 Figure 5.17. The 3D model simulation results for CNL tests 5.4.1.1 Stress - displacement relations In order to compare numerical simulation results with laboratory results, both results are plotted together in the same graphs. The relation between shear stress and shear displacement for two samples under CNL boundary conditions at difference normal stress levels are plotted in Figures 5.18 and 5.19 together with corresponding experimental results. It can be observed that the shear stresses versus shear displacements curves obtained from numerical simulations are in good agreement with laboratory data. In numerical simulations the peak shear stress increases also with increasing applied normal stress as observed in laboratory experiments. 110 7 Shear stress [MPa] Lab CNL01 6 FLAC3D FLAC3D 5 15 MPa 4 10 MPa 3 05 MPa 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Shear displacement [mm] Figure 5.18. Shear stress versus shear displacement for different normal stress levels for CNL01 specimen Shear stress [MPa] 3 CNL04 2.5 4 MPa 2 Lab 1.5 3D 1 FLAC 1 1 MPa 0.5 0 0 1 2 3 Shear displacement [mm] 4 5 Figure 5.19. Shear stress versus shear displacement for different normal stress levels for CNL04 specimen 16 Normal stress [MPa] 14 12 10 Lab FLAC-3D FLAC3D 8 6 4 2 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 5.20. Normal stress versus shear displacement for different normal stress levels for CNL tests 111 Figure 5.20 documents that normal stress was kept constant during lab testing as well as during the numerical simulations. It is evident to note that the numerical simulation results obtained here are in exceptionally good agreement with experimental data. 5.4.1.2 Joint surface contact area The true area of contact between upper and lower parts of the joint surface during the shearing is always smaller than the total nominal contact area. In FLAC3D, the contact relation is defined by the interface node and the zone surface face. a) shear displacement = 0 mm b) shear displacement = 4 mm (continued) 112 c) shear displacement = 8 mm d) shear displacement = 10 mm Figure 5.21. Contact area at interface surface for CNL01 specimen at different shear displacements under normal stress of 5 MPa Figure 5.21 shows the contact area distribution at the interface of CNL01 specimen under applied normal stress of 5 MPa after shearing of 0, 4, 8 and 10 mm. Figure 5.22 shows the contact area distribution at the interface of CNL04 specimen under initial normal stress of 1 MPa after shearing of 0, 1, 3 and 5 mm. The blue colour denotes contact area and the green colour specifies area with no contact. Most of the contact areas occur in regions which have asperities with flatter slopes. The contact area decreases with increasing shear displacement. 113 a) shear displacement = 0 mm b) shear displacement = 1 mm c) shear displacement = 3 mm (continued) 114 d) shear displacement = 5 mm Figure 5.22. Contact area at interface surface for CNL04 specimen at different shear displacements under normal stress of 1 MPa 110 CNL01 Contact area [%] 100 90 80 2 MPa 70 5 MPa 10 MPa 60 15 MPa 50 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 5.23. Contact area versus shear displacement under different normal stress for CNL01 specimen Contact area [%] 110 CNL04 100 90 80 1 MPa 4 MPa 70 60 0 1 2 3 Shear displacement [mm] 4 5 Figure 5.24. Contact area versus shear displacement under different normal stress for CNL04 specimen 115 Figures 5.23 and 5.24 show the change in contact area during the shearing process under different applied normal stresses for CNL01 and CNL04 specimens. The variation of contact area under different applied normal stresses for different specimens is illustrated in Table 5-4. The contact area is increasing with increasing normal stress [Johansson, 2009]. However, with increasing applied normal stress (σno > 5 MPa) the change in contact area is becoming much smaller. As observed in Figure 5.23, the contact area under normal stress of 5, 10 and 15 MPa is nearly the same during the shearing process. But at normal stress of only 2 MPa, the contact area is significantly reduced (Figure 5.23). The reduction of contact area can be observed even more clearly for CNL04 specimen as illustrated in Figure 5.24. The contact area is nearly 98% under normal stress of 4 MPa, but it is reduced to 64% under normal stress of 1 MPa after shearing of 5 mm. Table 5-4. Contact area data for different specimens under CNL conditions Sample JRC CNL01 CNL02 CNL03 CNL04 8 6 7 4 σno [MPa] us [mm] Contact area [%] 2 10 55.06 5 10 70.80 10 10 74.61 15 10 74.88 3.6 10 79.53 7.2 10 88.87 10.8 5 96.37 5 5 77.73 10 5 85.91 15 5 89.77 1 5 64.38 4 5 98.15 The results shown in Table 5-4 indicate that the contact area of joint surface is proportional to the initial normal stress. These results are similar to those observed by Johansson (2009). 116 5.4.1.3 Aperture size distribution The aperture of a joint is an important parameter to investigate fluid flow and transport in rock mass. The aperture size is the distance between the upper and lower joint surfaces when they satisfy the non-contact condition. Three dimensional joint surface data are digitized on a XY grid. Therefore, the elevation (Z) of each point on joint surface is a function of x and y coordinates, Z(x, y). We assume that the elevations of points (x, y) on the lower and upper joint surfaces in the same coordinate system are Zlow(x, y) and Zup(x, y), respectively, as shown in Figure 5.25. The aperture is estimated by the difference of the two z-coordinates at the upper and lower part. Consequently, the aperture size at any point can be calculated as follows: A( x, y ) = Z up ( x, y ) − Z low ( x, y ) ≥ 0 where (5-24) A(x,y) is the aperture at the point (x,y), Zup(x,y) is the elevation at the point (x,y) of the upper joint surface, Zlow(x,y) is the elevation at the point (x,y) of the lower joint surface. z Zup(x,y) Zlow(x,y) shear direction x x Figure 5.25. Definition of aperture size The aperture size of the specimen after shearing was determined by equation (5-24) for every grid point on the joint surface. Figure 5.26 shows contour plots of aperture size which were determined at shear displacement of 10 mm for CNL01 specimen under normal stress of 2, 5, 10 and 15 MPa. The aperture size of CNL04 specimen under initial normal stress of 1 and 4 MPa after shearing of 5 mm is shown in Figure 5.27. The maximum aperture size is dependent upon the asperities of the joint surface, normal stress and shear displacement. The aperture size is reduced with increasing normal 117 stress as shown in Figures 5.26 and 5.27. However, the maximum aperture size is only slightly influenced by the normal stress. (continued) 118 250 2 Area [cm ] 200 2 MPa 5 MPa 10 MPa 150 100 15 MPa 50 0 0 1 2 3 Aperture [mm] 4 5 6 Figure 5.26. Aperture size distribution of CNL01 specimen under different normal stresses after shearing of 10 mm The aperture sizes distributions for CNL01 specimen presented in Figure 5.26 show that the aperture size concentrate at around 0.6 and 0.8 mm under high (5, 10, 15 MPa) and low (2 MPa) normal stress, respectively. The aperture size distribution of CNL04 specimen shows concentrations at 0.09 and 0.13 mm under initial normal stress of 4 and 1 MPa, respectively, as illustrated in Figure 5.27. The maximum aperture size for different specimens was estimated under different applied normal stress conditions and listed in Table 5-5. It can be seen from this table that maximum and mean aperture size decrease with increasing normal stress for all specimens. 119 2 Area [cm ] 1800 1600 1400 1200 1000 800 600 400 200 0 1 MPa 4 MPa 0 0.5 1 1.5 Aperture [mm] 2 2.5 Figure 5.27. Aperture size distribution of CNL04 specimen under different normal stresses after shearing of 5 mm 120 Table 5-5. Aperture size data for different specimens under CNL conditions Sample CNL01 CNL02 CNL03 CNL04 σno [MPa] us [mm] Aave [mm] Amax [mm] 2 10 0.85 6.19 5 10 0.65 5.86 10 10 0.62 5.79 15 10 0.58 5.70 3.6 10 0.46 8.14 7.2 10 0.41 7.48 10.8 5 0.23 4.50 5 5 0.31 6.60 10 5 0.30 6.46 15 5 0.29 6.28 1 5 0.13 2.33 4 5 0.09 2.22 (Aave: mean aperture size; Amax: maximum aperture size) The change of aperture at different shear displacements for CNL01 specimen is presented in Figure 5.28. Comparison of aperture size distribution at different shear displacements shows that with ongoing sliding some asperities leave contact and consequently aperture is increasing. The maximum aperture size varies from 1.94 mm to 5.86 mm at shear displacement of 2 mm and 10 mm, respectively. The mean value of aperture varies from 0.18 mm to 0.65 mm when shear displacement increases from 2 mm to 10 mm. (continued) 121 Figure 5.28. Aperture size distribution of CNL01 specimen at different shear displacements under normal stress of 5 MPa 5.4.1.4 Dilation of the joint surface When a specimen with rough surface is sheared, different dilation behaviour like illustrated in Figure 5.29 can be observed. The sliding of the lower part over the upper 122 part takes place along an area which is characterized by deformable asperities. This area or plane can be considered as mean plane of the micro-slopes of the joint surface. Therefore, the total dilation includes two components: dilation caused by mean plane of the micro-slope angles and dilation caused by the asperity of joint surface. un z α us Shear direction o ∆z x us a) positive dilation, un > 0 z α us Shear direction o ∆z x us b) no dilation, un = 0 z un α Shear direction o ∆z us x us c) negative dilation, un < 0 Figure 5.29. Definition of the dilation during the shearing process Assuming that (α) and (β) are defined as the angle between average joint plane and horizontal plane with respect to the shear direction and the mean value of micro-slope angle, respectively. The “real” dilation can be calculated by subtraction of joint surface slope angle (α) or mean value of micro-slope angle (β) from measured dilation (ψlab): ψ1real = ψlab - α (5-25) 123 ψ2real = ψlab - β (5-26) An average plane can be defined as follows: Z = a + bX + cY (5-27) Where a, b and c are the variables of the plane equation. These variables are equivalent to the components of the normal vector of the plane. These three unknown variables could be calculated, if three equations are available. Therefore, if coordinates of three points are known, the planar formula could be defined. However, natural surfaces are not completely planar and best fitting plane must be defined from least-square method. Suppose (X1, Y1, Z1), (X2, Y2, Z2),…, (Xn, Yn, Zn) are the coordinates of the n points on the surface. The best fitting curve f(x,y) has the least square error: n Π = ∑ [Z i − f ( xi , y i )] =∑ [Z i − (a + bX i + cYi )] = Minimum 2 2 (5-28) i =1 Please note that a, b and c are unknown coefficients while all Xi, Yi and Zi are given. To obtain least square error, the unknown coefficients (a, b, c) must yield to zero for the first derivative equations: ⇔ n ∂Π ∂a = 2∑ [Z i − (a + bX i + cYi )] = 0 i =1 n ∂Π = 2∑ X i [Z i − (a + bX i + cYi )] = 0 ∂ b i =1 n ∂Π = 2∑ Yi [Z i − (a + bX i + cYi )] = 0 i =1 ∂c (5-29) n n n n ∑ Z i = a ∑1 + b∑ X i + c ∑ Yi i =1 i =1 i =1 i =1 n n n n 2 ∑ X i Z i = a ∑ X i + b∑ X i + c ∑ X i Yi i =1 i =1 i =1 i =1 n n n n 2 ∑ Yi Z i = a ∑ Yi + b∑ X i Yi + c ∑ Yi i =1 i =1 i =1 i =1 (5-30) 124 Equation (5-30) can be rewritten as follows: N n X i ∑ i =1 n ∑ Yi i =1 n i ∑X 2 i i =1 n i =1 n ∑X Y i =1 n ∑ Zi i =1 i =1 a n n X i Yi b = ∑ X i Z i ∑ i =1 i =1 n c n 2 ∑ Yi Z i Yi ∑ i =1 i =1 n ∑X i i ∑Y i (5-31) The unknown coefficients (a, b, c) can be obtained by solving the equation (5-31). The angles between average plane and horizontal plane with respect to the shear direction for different CNL samples are listed in Table 5-6. Table 5-6. Coefficients (a, b, c) and joint surface slope angle (α) for CNL samples Parameters CNL01 CNL02 CNL03 CNL04 a 1.01e-1 7.92e-2 9.91e-2 8.27e-2 b -1.27e-1 -2.67e-2 -1.00e-1 -6.62e-2 2.51e-2 6.22e-2 1.10e-3 2.18e-2 -7.2 -1.5 -5.7 3.8 c 0 α[ ] Depending on applied normal stress and asperity strength, the asperity can be damaged or not during shearing, therefore, the dilation may be negative or positive. The “real” dilation was calculated according to equations (5-25) and (5-26) for all specimens under CNL boundary conditions. The results are presented in Table 5-7. Because the two surfaces are not completely matched and damaged material can be released during the shearing process, the “real” dilation can be negative or positive. As mentioned previously, the dilation is also measured by averaging values obtained from 4 points at the upper part of the numerical model. The variation of normal displacement under CNL tests for different normal stresses and samples are shown in Figure 5.30. 125 Normal displacement [mm] 0.2 -0.2 CNL01 Shear displacement [mm] 0 0 1 2 3 4 5 6 7 8 9 10 5 MPa -0.4 -0.6 Lab 3D FLAC3D FLAC -0.8 10 MPa 15 MPa -1 5 MPa 10 MPa 15 MPa -1.2 0.4 Normal displacement [mm] 11 1 MPa CNL04 0.3 1 MPa Lab FLAC3D 0.2 4 MPa 4 MPa 0.1 0 0 1 2 -0.1 3 4 5 6 Shear displacement [mm] Figure 5.30. Normal displacement versus shear displacement under CNL conditions for CNL01 and CNL04 samples Table 5-7. Dilation data for CNL tests Sample σno [MPa] ψlab [o] ψsimulation [o] α [o] β [o] CNL01 (JRC = 8) 5 -2.0 -5.6 -7.2 -6.5 5.2 4.5 10 -4.3 -6.0 -7.2 -6.5 2.9 2.2 CNL02 (JRC = 6) CNL03 (JRC = 7) CNL04 (JRC = 4) ψ1real [o] ψ2real [o] 15 -6.3 -6.5 -7.2 -6.5 0.9 0.2 3.6 -1.0 -3.6 -1.5 -3.4 0.5 2.4 7.2 -3.4 -4.4 -1.5 -3.4 -1.9 0.0 10.8 -5.1 -4.6 -1.5 -3.4 -3.6 -1.7 5 -1.8 -5.5 -5.7 -6.7 3.9 4.9 10 -3.8 -6.4 -5.7 -6.7 1.9 2.9 15 -5.0 -8.9 -5.7 -6.7 0.7 1.7 1 4.3 3.0 3.8 3.5 0.5 0.8 4 2.5 1.7 3.8 3.5 -1.3 -1.0 126 Figure 5.30 shows that the numerical simulation results for dilation are somewhat different from experimental results because FLAC3D is not suitable for simulation of asperity degradation. However, the numerical simulation results show the same trends and indicate that the dilation is decreasing with increasing normal stress. The numerical simulation results for dilation under CNL test conditions for different specimens are given in Table 5-7. The “real” dilation angle was used to assess the effect of applied normal stress and JRC on dilation potential. The “real” dilation angle was normalized as a function of applied Dilation angle [0] normal stress and JRC as shown in Figure 5.31. 8 6 4 2 0 -2 -4 -6 -8 15 10 5 Normal stress [MPa] 0 4 5 7 6 8 JRC Figure 5.31. Normalized “real” dilation angle as a function of normal stress and JRC The “real” dilation potential is predicted by regression analysis data with respect to applied normal stress and JRC as follows: ψ real ≈ 1.95( JRC ) − 0.4σ no − 8.64 (5-32) with coefficient of multiple determination R2 = 0.741906 and σno in MPa. 5.4.1.5 Normal stress distribution on joint surface The normal load applied on the sample is constant during the CNL tests. However, there is only a part of the lower joint surface area in contact to the opposite joint surface 127 during the shearing process. As a consequence, the normal stresses at these contact areas can be much higher than applied normal stress. The normal stress concentrations at different points on the joint surface are not constant because of the asperities. Therefore, the normal stress concentration at contact areas, especially at the tips of asperities will be very high in comparison to initial normal stress, and can lead to failure of these parts [Barton and Choubey, 1977]. The local normal stresses under different initial normal stresses are recorded at shear displacements of 2, 4, 8 and 10 mm. The normal stress distributions on the joint surface under different applied normal stresses of 5, 10 and 15 MPa for CNL01 specimen are illustrated in Figures 5.32 to 5.34, respectively. (continued) 128 160 CNL01 140 2 Total area: 495 cm Initial normal stress: 5 MPa 2 Area [cm ] 120 100 2 mm 4 mm 80 60 8 mm 10 mm 40 20 0 0 2 4 6 8 10 12 14 16 Normal stress [MPa] 18 20 22 24 Figure 5.32. Distribution of normal stress [Pa] across the joint surface for CNL01 specimen under initial normal stresses of 5 MPa and different shear displacements 129 (continued) 130 80 CNL01 70 Total area: 495 cm2 Initial normal stress: 10 MPa 2 Area [cm ] 60 50 2 mm 40 30 4 mm 8 mm 10 mm 20 10 0 0 5 10 15 20 25 30 Normal stress [MPa] 35 40 45 50 Figure 5.33. Distribution of normal stress [Pa] across the joint surface for CNL01 specimen under initial normal stresses of 10 MPa and different shear displacements (continued) 131 (continued) 132 60 CNL01 2 Area [cm ] 50 Total area: 495 cm2 Initial normal stress: 15 MPa 40 2 mm 4 mm 30 20 8 mm 10 mm 10 0 0 5 10 15 20 25 30 35 40 Normal stress [MPa] 45 50 55 60 65 Figure 5.34. Distribution of normal stress [Pa] across the joint surface for CNL01 specimen under initial normal stresses of 15 MPa and different shear displacements Table 5-8. Stress amplification ratios for joint surface of CNL01 specimen under different applied normal stresses σno [MPa] 5 10 15 us [mm] σmax [MPa] σmax/σno 2 8.71 1.74 4 13.71 2.74 8 20.14 4.03 10 21.48 4.30 2 17.69 1.77 4 27.29 2.73 8 40.21 4.02 10 43.10 4.31 2 25.18 1.69 4 38.14 2.54 8 54.84 3.65 10 60.17 4.01 An initial normal stress of 5 MPa is applied to the specimen. When the specimen is sheared the normal stress is redistributed on the joint surface as shown in Figure 5.32. The local normal stress distribution on the joint surface varies in wide range. However, the distribution is still centered at the initial normal stress. For example, the initial normal stress of 5 MPa was applied to the specimen, after shearing of 2 mm, most of the joint surface area is still subjected to a normal stress of around 5 MPa (Figure 5.32). This behaviour is also observed for different initial normal stresses and specimens as 133 illustrated in Figures 5.33 and 5.34. The ratio of maximum normal stress to applied normal stress (local stress amplification factor) on the joint surface of CNL01 specimen at different shear displacements is given in Table 5-8. It can be seen from Figures 5.32 to 5.34 that the non-contact area (area of 0 MPa normal stress) increases with increasing shear displacement. Consequently, the contact area decreases with increasing shear displacement, which leads to higher local normal stresses. Figure 5.35 shows the ratio of maximum normal stress to initial normal stress as a function of shear displacement. This ratio increases when shear displacement increases. However, it is slightly reduced when initial normal stress is increased. It can be identified from Figure 5.35 that the maximum normal stress at 2 mm shear displacement is greater than initial normal stress by a factor of approximately 1.7 and it increases further to 4.3, 4.31 and 4.01 times the applied normal stress at shear displacement of 10 mm under initial normal stress of 5, 10 and 15 MPa, respectively. Max. / initial normal stress 5 4 3 5 MPa 2 10 MPa 15 MPa 1 0 0 2 4 6 8 Shear displacement [mm] 10 12 Figure 5.35. Ratio of maximum to initial normal stress for CNL01 specimen 60 2 Area [cm ] 50 CNL01 40 5 MPa 30 10 MPa 20 15 MPa 10 0 0 5 10 15 20 25 30 35 40 Normal stress [MPa] 134 45 50 55 60 65 (continued) 80 CNL02 70 2 Area [cm ] 60 50 3.6 MPa 40 7.2 MPa 10.8 MPa 30 20 10 0 0 2 4 8 6 10 12 14 16 18 Normal stress [MPa] 70 2 22 24 26 CNL03 60 Area [cm ] 20 5 MPa 50 10 MPa 15 MPa 40 30 20 10 0 0 2 4 6 8 10 12 14 16 18 20 22 Normal stress [MPa] 24 26 28 30 120 CNL04 2 Area [cm ] 100 80 1 MPa 4 MPa 60 40 20 0 0 2 4 6 8 10 12 14 16 18 20 22 Normal stress [MPa] Figure 5.36. Distribution of local normal stress at the joint for different specimens The distributions of local normal stress for different specimens under variation of initial normal stress are shown in Figure 5.36. This Figure indicates that local normal stress can vary quite strongly, but distribution is centered more or less at the value of the applied normal stress. 135 Max./Initial normal stress 25 CNL01 20 CNL02 CNL03 15 CNL04 10 5 0 0 2 4 6 8 10 Initial normal stress [MPa] 12 14 16 Figure 5.37. Ratio of maximum to initial normal stress for different specimens Ratio of maximum normal stress to initial normal stress for different specimens under CNL testing is presented in Figure 5.37. The results show that maximum normal stress has not exceeded five times the applied normal stress for specimens CNL01, CNL02 and CNL03 (all specimens with negative dilation) during the shearing. However, the maximum to initial normal stress ratio is very high (up to twenty) for the CNL04 specimen (specimen with positive dilation) as shown in Figure 5.37. It is also observed that the ratio of maximum to initial normal stress is decreasing with increasing initial normal stress. 5.4.2 CNS simulation results Figure 5.38 shows the 3D models used for simulations under CNS boundary conditions. The three specimens (CNS01, CNS02 and CNS03) were sheared in the negative xdirection under three normal stiffness levels identical to the laboratory experiments. The joint surfaces are upward inclined in respect to the shear direction for all three specimens as shown in Figure 5.38. 5.4.2.1 Stress - displacement relations The relation between shear stress and shear displacement under different conditions of normal stiffness is illustrated in Figure 5.39 for both the numerical simulations and the corresponding laboratory tests. 136 Figure 5.38. Numerical 3D model for CNS tests 137 Shear stress [MPa] 2.5 3 GPa/m 2 5 GPa/m 1.5 9 GPa/m 1 Lab 3D FLAC-3D FLAC CNS01 0.5 0 0 1 2 3 7 4 5 6 Shear displacement [mm] 9 8 10 11 Shear stress [MPa] 2.5 3GPa/m 2 5GPa/m 1.5 9GPa/m 1 Lab 3D FLAC FLAC-3D CNS02 0.5 0 0 1 2 3 6 7 5 4 Shear displacement [mm] 8 9 10 11 3 3 GPa/m Shear stress [MPa] 2.5 5 GPa/m 2 9 GPa/m 1.5 1 CNS03 0.5 Lab FLAC3D FLAC-3D 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 11 Figure 5.39. Shear stress versus shear displacement under different normal stiffness for CNS specimens As Figure 5.39 shows, the shear stress versus shear displacement curves obtained from numerical simulation are similar to laboratory data. The peak shear stress in numerical simulations decreases also with increasing initial normal stiffness as observed in laboratory experiments. However, after reaching the peak value, the shear stress is 138 slightly decreasing with increasing shear displacement. In all cases the dilation is negative. Thus, the normal stress acting on the joint surface is decreasing with increasing shear displacement (Figure 5.40). Normal stress [MPa] 6 CNS01 5 3GPa/m 5GPa/m 4 9GPa/m 3 Lab 3D FLAC FLAC-3D 2 1 0 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 5.40. Normal stress versus shear displacement for CNS01 specimen under different normal stiffness levels Experimental results under CNS conditions show that normal and shear stresses decrease during shearing. The asperities of the joint surface are degraded if the current local stresses exceed the strength of asperities. As the asperities degradation of the joint surface cannot be modelled by FLAC3D, the corresponding normal stress is slightly over-predicted and numerical models do not show the stiffness depending change in normal stress with ongoing shear displacement. 5.4.2.2 Joint surface contact area The variations of interface contact area during the shearing process under CNS boundary conditions are shown in Figure 5.41. The joint surface contact area is reduced with increasing shear displacement, but nearly independent on the initial normal stiffness. This is because the initial normal stress is equal to 5 MPa for all cases. Therefore, the contact area is almost unchanged. However, the contact area depends on asperities of the joint surface. The JRC of CNS01, CNS02 and CNS03 samples is 17, 6 and 5, respectively. Higher JRC leads to stronger decrease of contact area with increasing shear displacement. The simulation results in respect to contact area under different initial normal stiffness and specimens are summarized in Table 5-9. 139 Comparison of the contact area for CNS02 and CNS03 shows that the contact area increases with increasing initial normal stress. Contact area [%] 105 CNS01 100 95 3 GPa/m 90 5 GPa/m 9 GPa/m 85 80 0 1 2 3 Contact area [%] 102 4 5 6 7 Shear displacement [mm] 8 9 10 CNS02 100 98 3 GPa/m 5 GPa/m 96 9 GPa/m 94 0 1 2 3 4 5 6 Shear displacement [mm] 7 8 9 10 102 Contact area [%] CNS03 100 98 3 GPa/m 5 GPa/m 9 GPa/m 96 94 0 1 2 3 4 5 6 7 Shear displacement [mm] 8 9 10 Figure 5.41. Variation of contact area under CNS testing for different initial normal stiffness and specimens 140 Table 5-9. Contact area for different specimens under CNS conditions Sample JRC σno [MPa] us [mm] CNS01 17 5 10 CNS02 CNS03 6 5 5 Kn [GPa/m] Contact area [%] 3 85.34 5 85.58 9 85.83 3 96.66 5 96.45 9 96.51 3 97.43 5 97.44 9 97.06 10 6.6 10 5.4.2.3 Aperture size distribution To obtain the aperture distribution, calculations according to equation (5-24) for every grid points on the joint surface were performed. The changes of aperture with respect to initial normal stiffness for CNS01, CNS02 and CNS03 specimens are shown in Figures 5.42 to 5.44. Table 5-10. The aperture size for different specimens under CNS conditions Sample CNS01 CNS02 CNS03 σno [MPa] 5.0 5.0 6.6 Kn [GPa/m] us [mm] Aave [mm] Amax [mm] 3 10 1.00 18.17 5 10 1.00 18.16 9 10 1.01 18.17 3 10 0.47 5.89 5 10 0.49 7.50 9 10 0.49 5.37 3 10 0.65 5.20 5 10 0.67 5.33 9 10 1.21 6.13 (Aave: mean aperture size; Amax: maximum aperture size) 141 CNS01 2 Area [cm ] 100 80 3 GPa/m 5 GPa/m 9 GPa/m 60 40 20 0 0 2 4 6 8 10 12 Aperture size [mm] 14 16 18 20 Figure 5.42. Aperture size distribution of CNS01 specimen under different initial normal stiffness at shear displacement of 10 mm 142 Area [cm2] 240 CNS02 200 160 3 GPa/m 120 5 GPa/m 9 GPa/m 80 40 0 0 1 2 3 4 5 Aperture size [mm] 6 7 8 Figure 5.43. Aperture size distribution of CNS02 specimen under different initial normal stiffness at shear displacement of 10 mm 143 CNS03 2 Area [cm ] 300 250 200 3 GPa/m 150 5 GPa/m 9 GPa/m 100 50 0 0 1 2 3 4 Aperture size [mm] 5 6 7 Figure 5.44. Aperture size distribution of CNS03 specimen under different initial normal stiffness at shear displacement of 10 mm 144 During CNS testing, the initially applied normal stresses for CNS01 and CNS02 specimens was 5 MPa and 6.6 MPa for CNS03 specimen, while the initial normal stiffness was different. The aperture size is nearly unchanged under different normal stiffness for CNS01 and CNS02 specimens. However, the aperture size of CNS03 specimen is increasing with increasing normal stiffness. The mean aperture of CNS01 specimen is about 1 mm for normal stiffness ranging from 3 to 9 GPa/m. For CNS03 specimen, the mean aperture is increasing from 0.65 to 1.21 mm when normal stiffness is increasing from 3 to 9 GPa/m as indicated in Table 5-10. 5.4.2.4 Dilation of the joint surface The dilation angle under CNS conditions is determined in the same way as under CNL conditions. The coefficients (a, b, c) and joint slope angle (α) for CNS samples are presented in Table 5-11. Table 5-11. Coefficients (a,b,c) and joint surface slope angle (α) for CNS samples Parameters CNS01 CNS02 CNS03 a 9.24e-2 7.71e-2 1.06e-1 b -1.43e-1 -5.96e-2 -1.08e-1 6.97e-3 -1.30e-3 -4.68e-2 -8.2 -3.4 6.2 c 0 α[ ] Table 5-12. Dilation data for CNS tests Sample CNS01 (JRC = 17) σno [MPa] 5.0 CNS02 (JRC = 6) 5.0 CNS03 (JRC = 5) 6.6 Kn [GPa/m] ψlab [o] ψsimulation [o] α [o] β [o] ψ1real [o] ψ2real [o] 3 -0.8 -2.9 -8.2 -5.1 7.4 4.3 5 -2.3 -2.7 -8.2 -5.1 5.9 2.8 9 -3.3 -2.4 -8.2 -5.1 4.9 1.8 3 -1.9 -2.1 -3.4 -3.0 1.5 1.1 5 -3.1 -1.5 -3.4 -3.0 0.3 -0.1 9 -4.3 -1.4 -3.4 -3.0 -0.9 -1.3 3 -2.8 -4.1 -6.2 -6.0 3.4 3.2 5 -4.2 -3.8 -6.2 -6.0 2.0 1.8 9 -5.7 -3.3 -6.2 -6.0 0.5 0.3 145 The asperities of rough joint surfaces may be damaged under high normal stress during shearing. That is the main process controlling the dilation of joint surfaces. As mentioned previously the numerical simulation results for dilation differ somewhat from the experimental data because FLAC3D cannot simulate asperity degradation of joint surfaces. The average planes of joints are determined similar way in the case of CNL conditions and results are presented in Table 5-11. The “real” dilation was calculated according to equations (5-25) and (5-26) for all CNS specimens and is listed in Table 5-12. The numerical simulation results indicate that dilation is slightly increased with increasing initial normal stiffness. 5.4.2.5 Normal stress distribution The variations of local normal stresses due to shearing under CNS boundary conditions depend on shear displacement. Because the area of contact between two rough surfaces is reduced during the shearing process, the local normal stresses at contact areas are much higher than the applied normal stress. The normal stress distribution on the joint surface under different initial normal stiffness for CNS01, CNS02 and CNS03 specimens is shown in Figures 5.45 to 5.47. (continued) 146 140 CNS01 2 Area [cm ] 120 100 80 3 GPa/m 60 5 GPa/m 9 GPa/m 40 20 0 0 1 2 3 4 5 Normal stress [MPa] 6 7 8 Figure 5.45. Normal stress [Pa] distribution for CNS01 specimen under different normal stiffness at shear displacement of 10 mm 147 (continued) 148 200 CNS02 2 Area [cm ] 150 100 3 GPa/m 5 GPa/m 50 9 GPa/m 0 0 1 2 3 4 5 Normal stress [MPa] 6 7 8 Figure 5.46. Normal stress [Pa] distribution for CNS02 specimen under different normal stiffness at shear displacement of 10 mm 149 (continued) 200 CNS03 2 Area [cm ] 150 100 3 GPa/m 5 GPa/m 9 GPa/m 50 0 0 1 2 3 4 5 6 Normal stress [MPa] 7 8 9 10 Figure 5.47. Normal stress [Pa] distribution for CNS03 specimen under different normal stiffness at shear displacement of 10 mm Table 5-13. Stress amplification ratios for joint surface under different normal stiffness Sample CNS01 CNS02 CNS03 Kn [GPa/m] us [mm] σno [MPa] σmax [MPa] σmax/σno 3 10 5 6.78 1.35 5 10 5 6.75 1.35 9 10 5 6.76 1.35 3 10 5 6.89 1.38 5 10 5 6.92 1.38 9 10 5 7.35 1.47 3 10 6.6 9.03 1.37 5 10 6.6 9.07 1.37 9 10 6.6 8.59 1.30 150 The maximum normal stress under CNS conditions is not much higher than the initial normal stress. The ratio of maximum to initial normal stress for different specimens is presented in Table 5-13. The results in this table show that the ratio of maximum to initial normal stress is approximately 1.3 for all of three specimens under normal stiffness varying from 3 to 9 GPa/m. Furthermore, it is indicated that the normal stress distribution is nearly unchanged when normal stiffness increases. 5.4.3 Plasticity state The Mohr-Coulomb failure envelopes were constructed based on data obtained from own direct shear tests, Walter et al. (2009) and Dinh (2011) as shown in Figure 5.48. The normal and shear stresses at the interface obtained from numerical simulation for CNL01 sample under different applied normal stresses were also plotted in this Figure. 40 35 Shear stress [MPa] 0 τmatrix = σno tan(41.5 ) + 3.3 "matrix" Series1 σno = 15 MPa Series4 σno = 10 MPa σno = 5 MPa Series5 30 25 "bedding" 0 τbedding = σno tan(29.5 ) + 2.5 "joint" 20 0 τjoint = σno tan(18.0 ) + 0.73 15 10 5 0 0 10 20 30 40 50 60 70 Normal stress [MPa] Figure 5.48. Failure envelope for rock matrix and bedding and local stresses at interface (FLAC3D simulations) for sample CNL01 at 10 mm shear displacement. As Figure 5.48 shows, most local stress states at the interface (joint) have reached the failure envelope for the joint. That means that contact areas and especially asperities at the interface are highly damaged (broken). Furthermore, as Figure 5.49 reveals, also the rock itself is partly damaged. This is confirmed by visual inspection (broken asperities and cracking inside the rock sample mainly parallel to bedding) as shown in Figure 5.50. 151 CNL01: σno = 5 MPa CNL01: σno = 10 MPa CNL01: σno = 15 MPa Figure 5.49. Plasticity state inside lower part of sample CNL01 under different initial normal stress at shear displacement of 10 mm 152 Figure 5.50. Cracking inside the rock blocks after shear testing 5.5 Numerical simulations of dynamic shear tests Figure 5.51 shows the geometry of the numerical models used for dynamic simulations. To reduce calculation time in dynamic simulations, only a coarse mesh (231 grid points on surface) was generated. A shear displacement controlled sinusoidal excitation was applied to the lower shear frame. 153 Figure 5.51. Numerical 3D model for dynamic tests 154 The 3D-scanner data were used to simulate rough surface of the rock joints. The lower part of the model is fixed in the vertical direction at the bottom face. The upper part of the model is fixed in the horizontal direction (x-axis) at two faces: left and right boundary. At first the initial normal stress is applied at the top of the model and calculation is performed until equilibrium is reached. Then a shear velocity is applied to the lower part of specimen to produce the desired shear displacement. The average normal stresses, shear stresses, normal displacements and shear displacements versus time were calculated via FISH functions and stored. JRC of the three specimens was determined according to equation (2-26), (2-31) and (2-32) and is listed in Table 5-14. 5.5.1 Micro-slope angle distribution The micro-slope angles were estimated on the joint surfaces with respect to the relative shear direction for the three specimens and are presented in Figure 5.52 and Table 5-14. The micro-slope angles (Table 5-14) of the three specimens vary within a wide range (from -290 to 270), but the distributions are symmetric at about -3.10, -3.30 and 1.40 for DT01, DT02 and DT03 specimens, respectively. Also, with exception of a few very local high values, nearly all values are within a range of ± 200. The results indicate that the joint surface has upward inclination in respect to the shear direction for DT01 and Area [cm2] DT02 and downward inclination for DT03 sample. 40 35 30 DT01 25 Total area of 2 DT01: 521 cm 2 DT02: 521 cm 2 DT03: 384 cm DT02 20 DT03 15 10 5 0 -35 -30 -25 -20 -15 -10 -5 0 5 10 Micro-slope angle [degree] 15 20 25 30 Figure 5.52. Areal distribution of the micro-slope angles for DT specimens 155 Table 5-14. Micro-slope angle and JRC for different DT specimens Micro-slope angle [0] Sample JRC Maximum Minimum Mean DT01 5 27 -29 -3.1 DT02 5 20 -23 -3.3 DT03 1 17 -12 1.4 Figure 5.53 shows the distribution of the micro-slope angles with respect to the relative shear direction for DT01, DT02 and DT03 specimens. (continued) 156 Figure 5.53. Contour plot of the micro-slope angle with respect to relative shear direction for DT specimens 5.5.2 Dynamic simulation results 5.5.2.1 Shear displacements Numerical simulation results of shear displacement versus time of the dynamic tests are presented in Figure 5.54. The shear displacement varies as a sinusoidal function in both, the numerical simulations and experiments. The numerical simulation results are in good agreement with laboratory experiments as documented by this Figure. Shear displacement [mm] 6 DT01 4 2 0 -2 0 1 2 3 4 5 6 7 8 9 10 11 -4 -6 FLAC3D FLAC Lab Time [sec] (continued) 157 Shear displacement [mm] 6 DT02 4 2 0 -2 0 2 4 6 8 12 14 16 18 20 22 -4 FLAC Lab -6 3D Time [sec] 6 Shear displacement [mm] 10 Lab FLAC3D DT03 4 2 0 -2 0 1 2 3 4 5 6 7 8 9 10 11 -4 -6 Time [sec] Figure 5.54. Shear displacement versus time for DT specimens 5.5.2.2 Shear stresses Figure 5.55 shows the variation of shear stress versus time for three specimens in comparison with experimental data. The phases are in good agreement. However, the numerical simulation shows constant amplitude while the laboratory tests show slightly increasing shear stress with ongoing cycles. Degradation of asperities is ignored in numerical simulations, therefore, the amplitude of shear stress is unchanged during cycling. 158 5 DT01 4 FLAC3D Lab Shear stress [MPa] 3 2 1 0 -1 0 1 2 3 4 5 6 7 8 9 10 11 14 16 18 20 9 10 11 -2 -3 -4 -5 Time [sec] 4 DT02 3 Shear stress [MPa] 2 1 0 -1 0 2 4 6 8 10 12 -2 -3 -4 FLAC 3D Lab -5 Time [sec] 4 DT03 Shear stress [MPa] 3 2 1 0 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 Lab FLAC 3D Time [sec] Figure 5.55. Shear stress versus time for DT specimens The typical shear behaviour of rough rock joint surface under dynamic load is illustrated in detail in Figure 5.56. A sinusoidal input signal with frequency of 1 Hz is applied as 159 shear velocity to perform dynamic tests. The behavior within one cycle can be characterized as follows: Shear stress [MPa] 5 Displacement Stress DT03 4 4 3 3 2 2 1 1 0 -1 0 -2 0.25 0.5 0.75 1 1.25 1.5 1.75 0 2 -1 -2 -3 -3 -4 -4 -5 Time [sec] Shear displacement [mm] 5 -5 Figure 5.56. Shear stress and shear displacement versus time for DT03 specimen • Phase I (dynamic time: 0 to 0.25 seconds): the lower part of the specimen moves from initial position to a positive maximum value. The shear stress increases with time and peak shear stress is reached. • Phase II (dynamic time: 0.25 to 0.50 seconds): the shearing direction is reversed and sample comes back to initial position. The shear stress decreases and reaches to peak negative value. • Phase III (dynamic time: 0.50 to 0.75 seconds): the specimen is sheared from initial position until reaching the negative maximum value. Because the shear direction is not changed within phase II and III, the shear stress is kept constant at the peak value in both phases. • Phase IV (dynamic time: 0.75 to 1.0 seconds): the shearing direction is reversed and sample moves back into initial position. The shear stress increases from negative peak to positive peak when shearing direction is changed. Figure 5.57 shows the shear stress versus shear displacement curves for DT specimens under dynamic conditions. The numerical simulation results show that the shear stress is nearly unchanged with increasing number of cycles. The reason for this behaviour is that degradation of the joint surfaces is not considered in numerical simulations. 160 5 Shear stress [MPa] DT01 4 3 2 Lab 1 FLAC3D FLAC 0 -5 -4 -3 -2 -1 -1 0 1 2 3 4 5 2 3 4 5 -2 -3 -4 -5 Shear displacement [mm] 4 DT02 3 Shear stress [MPa] 2 1 0 -5 -4 -3 -1 -2 -1 0 1 -2 -3 -4 -5 Shear displacement [mm] FLAC FLAC3D Lab 4 Shear stress [MPa] DT03 3 Lab FLAC3D FLAC -6 -5 -4 -3 -2 2 1 0 -1 -1 0 1 2 3 4 5 -2 -3 -4 -5 Shear displacement [mm] Figure 5.57. Shear stress versus shear displacement for DT samples 5.5.2.3 Normal stresses The behaviour of normal stresses versus time observed during numerical simulations and laboratory experiments under dynamic conditions are presented in Figure 5.58. The 161 results show that normal stresses vary slightly in both, the experiments and the numerical simulations. Normal stress [MPa] 5.6 DT01 5.4 Lab FLAC3D FLAC 5.2 5 4.8 4.6 0 1 2 3 4 5 6 Time [sec] Normal stress [MPa] 5.4 7 8 9 10 11 18 20 22 9 10 11 DT02 5.3 Lab FLAC 3D 5.2 5.1 5 4.9 4.8 4.7 0 2 4 6 8 10 12 Time [sec] Normal stress [MPa] 5.2 14 16 DT03 5.1 5 Lab FLAC3D FLAC 4.9 4.8 0 1 2 3 4 5 6 Time [sec] 7 8 Figure 5.58. Normal stress versus time for DT specimens 162 The diagrams in Figure 5.58 show the normal stresses measured with the load cell during the laboratory experiments and the average normal stresses at the interface during the numerical simulations. The fluctuations are caused by the joint roughness and inclination and the fact that a servo-mechanism like that working inside GS-1000 always show some fluctuations due to the loop and correction process. The fluctuations observed during the numerical simulations are caused by some inaccuracies for the local interface stress calculations. For both cases, the fluctuations are smaller than 10% and therefore acceptable. 5.5.2.4 Dilation The horizontal movement of the specimen is repeated several times. Consequently, significant surface roughness degradation of rock joint has to be expected. Thus, asperities of the joint surface are highly degraded when the numbers of cycles increase. Therefore, normal displacement becomes negative (settlement) with increasing dynamic time as explained in the previous chapter. Figure 5.59 shows normal displacement versus time for laboratory tests and numerical simulations. The comparison reveals that the amplitudes of normal displacements are quite similar, but the experiments show a clear tendency of increasing settlement (negative normal displacement) with increasing number of cycles. The later can be explained by ongoing damage of asperities, which is not included in the modeling. Figure 5.59 shows that dilation decreases slightly when specimen is compressed and increases when specimen is dilated. Normal displacement [mm] 0.6 DT01 0.3 Time [sec] 0 -0.3 0 1 2 3 4 5 -0.6 6 7 8 9 10 Lab FLAC3D FLAC -0.9 -1.2 -1.5 -1.8 163 (continued) Normal displacement [mm] 0.6 DT02 0.3 FLAC 3D Time [sec] 0 -0.3 Lab 0 2 4 6 10 8 14 12 16 18 20 8 9 22 -0.6 -0.9 -1.2 -1.5 Normal displacement [mm] 0.5 Time [sec] 0 -0.5 0 1 2 3 4 5 6 7 10 DT03 -1 Lab 3D FLAC -1.5 -2 -2.5 -3 Figure 5.59. Normal displacement versus time for DT specimens Figure 5.60 shows the plasticity state of the DT03 samples for different points in time. As can be seen in Figure 5.60, the volume of damage increases with increasing dynamic time. Asperity degradation is increasing with increasing number of cycles. In other words, the dilation angle decreases with increasing dynamic time. Figure 5.61 shows the joint surface before and after the dynamic laboratory test for DT03 specimen. After 10 cycles, the joint surface is highly damaged. Also, extensive micro-cracking is observed within the entire sample as also indicated by the numerical simulations. 164 (continued) 165 Figure 5.60. Plastic states on lower block of DT03 sample for different number of cycles Lower surface of DT03 sample before dynamic test Lower surface of DT03 sample after 10 cycles Figure 5.61. Joint damage behaviour of DT03 sample 166 6 Parameter set for Mayen-Koblenz schist The mechanical parameters for Mayen-Koblenz schist obtained from laboratory experiments are summarized in Table 6-1. These parameters are valid for normal stresses from 0 to 15 MPa. Table 6-1. Mechanical parameters for Mayen-Koblenz schist (σno = 0 ÷ 15 MPa) Mechanical parameters Symbol Unit Min. ÷ Max. value MPa 2.46 Intact sample Peak cohesion cp Residual cohesion cres MPa 0.16 Peak friction angle φp degree 29.60 Residual friction angle φres degree 27.04 Mohr-Coulomb failure envelope (peak): τp = 0.568σno + 2.4616 Mohr-Coulomb failure envelope (residual): τres = 0.5106σno + 0.1676 Joint (natural fracture) Cohesion cj MPa 0.12 ÷ 1.07 Friction angle φj degree 15.52 ÷ 31.38 Normal stiffness knj GPa/m 2.68 ÷ 5.55 Shear stiffness ksj GPa/m 1.45 ÷ 9.99 Dilation angle ψj degree -3.6 ÷ 7.4 Joint roughness coefficient JRC 1 ÷ 17 Mohr-Coulomb failure envelope: τj = 0.3815σno + 0.6139 τj = 0.4407σno Dilation angle prediction (JRC = 4 ÷ 8; σno = 0 ÷ 15 MPa) ψ real ≈ 1.95( JRC ) − 0.4σ no − 8.64 167 168 7 Conclusions and recommendations 7.1 Conclusions Shear strength controls the failure in rock masses. Therefore, shear strength of jointed rock is one of the most important parameters in geotechnical engineering. The shear behaviour of rock joint is a complex problem related to normal stress, dilation, asperity characteristics, contact area and stiffness of the surrounding rock mass. Direct shear tests were performed on rough joint surfaces under static and dynamic boundary conditions in the laboratory. In parallel, numerical simulations were performed to understand the shear behaviour of rock joints in detail. Intact schistose rock blocks from Mayen-Koblenz, Germany, were used to perform the direct shear tests. The intact rock blocks were sheared to create rough joint surfaces, which were tested later on under static and dynamic boundary conditions. The shear strength characteristics of rough joints of Mayen-Koblenz schist were investigated considering various initial normal stresses, normal stiffnesses, shear velocities and JRC under CNL, CNS and dynamic boundary conditions. The direct shear tests were performed up to 15 MPa normal stress equivalent to more than 500 m in depth. Based on the experimental and numerical simulation results, the following conclusions can be drawn: 1) Lab test results: Shear behaviour of jointed rock under CNL conditions: The shear strength of rough joints under CNL boundary conditions increases with increase in applied normal stress and shear velocity. The peak shear stress is increasing by approximately 10% under normal stress of 2.5 MPa when shear velocity increases from 1 to 10 mm/min. However, the ratio of peak shear stress to initial normal stress (τp/σno) tends to decrease with increasing applied normal stress. The dilation decreases when applied normal stress is increasing. The “real” dilation is positive for low applied normal stress and negative for high applied normal stress. 169 Shear behaviour of jointed rock under CNS conditions: Peak shear strength and normal stress of rough joints under CNS boundary conditions tends to decreases with increasing normal stiffness in case of negative dilation. Peak shear stress increases when shear velocity increases. Normal stress and dilation decrease also with increasing normal stiffness in case of negative dilation. Shear behaviour of jointed rock under dynamic conditions: Peak shear stress of the jointed rock under dynamic loading shows tendency to increase with time. Depending on the joint orientation the peak shear stresses are higher or lower in the positive or negative shear direction. The peak shear stress under dynamic loading is approximately 30% higher than that under static loading. The normal stress was nearly constant at the level of applied normal stress during cyclic shearing. However, the normal displacements show a sinusoidal decrease with increasing time because of degradation of asperities. 2) Numerical simulation results: New methodology was proposed to analyse shear behaviour of rock joints by combination of direct shear tests and numerical simulations (Figure 7.1). Based on high resolution scanning of joint surfaces and set-up of numerical models considering the interface (joint) topography in detail numerical simulations equivalent to the CNL, CNS and dynamic tests were conducted. The micro-mechanical analysis has given the following results: • Micro-slope angle distributions of the joints indicate that specimen is compressed or dilated with respect to the relative shear direction. • Aperture sizes increase with decreasing applied normal stress. However, these values are nearly constant with increasing normal stiffness. • The variation of shear stress with shear displacement is in good agreement comparing experimental and numerical simulation results. 170 • Development of a method to determine the “real” dilation angle for joints of any kind of roughness and orientation. • The regression analyses enable a prediction of the “real” dilation angle with respect to JRC (JRC = 4 ÷ 8) and applied normal stress (σno = 0 ÷ 15 MPa) as follows: ψ real ≈ 1.95( JRC ) − 0.4σ no − 8.64 • Contact area decreases with increasing shear displacement, but it increases when applied normal stress is increasing. • Local normal stresses vary within a wide range, but concentrate at the initial applied value. The local normal stresses can reach values up to 20 times the initial value. Generation of natural joint by shearing of intact sample Joint roughness determination by optical 3D-scanner Direct shear box tests Numerical simulation: on rock joints 3D model set-up Measured values: • • • Shear stress Normal stress Shear displacement • Normal displacement Mechanical parameter calibration Micro-mechanical analysis: Deduced parameters: • • • • • • Peak shear strength Residual shear strength Cohesion, Friction angle Dilation Normal stiffness Shear stiffness • • • • Micro-slope angle distribution Local normal stress distribution Contact area “Real” dilation • Aperture size distribution Figure 7.1. Algorithm for combination of the direct shear tests and numerical simulations 171 7.2 Recommendations Static and dynamic tests have been conducted to better understand shear and dilatancy behaviour of rough joint surfaces. Results were obtained under different boundary conditions. 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