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Influence of data characterization process on the kinematic stability analysis of engineered rock slopes… Miyoshi, Takako 2018

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INFLUENCE OF DATA CHARACTERIZATION PROCESS ON THE KINEMATIC STABILITY ANALYSIS OF ENGINEERED ROCK SLOPES USING DISCRETE FRACTURE NETWORK MODELS AND ITS IMPLICATIONS FOR ROCK MASS CLASSIFICATION SYSTEM  by Takako Miyoshi  B.A.Sc., The University of British Columbia, 2017  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mining Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  September 2018  © Takako Miyoshi, 2018        ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled:  Influence of data characterization process on the kinematic stability analysis of engineered rock slopes using discrete fracture network models and its implications for rock mass classification system  submitted by Takako Miyoshi  in partial fulfillment of the requirements for the degree of Master of Applied Science  in Mining Engineering  Examining Committee: Davide Elmo, Mining Engineering  Supervisor  Ilija Miskovic, Mining Engineering Supervisory Committee Member   Supervisory Committee Member  Additional Examiner          iii  Abstract  The thesis investigates the influence of data characterization process on kinematic slope stability analysis using a Discrete Fracture Network (DFN) approach. The first aspect of the data characterization process considered in this thesis is the influence of separate statistical procedure to define fracture set (aggregate vs disaggregate approach). The DFN models generated using aggregate and disaggregate approaches are compared in terms of simulated fracture properties and the kinematic slope stability analysis. The results showed the aggregate approach either overestimates or underestimates the important fracture properties such as fracture intensity and length. Accordingly, the number and volume of blocks formed on the slope would not be truly representative of field condition.  The second aspect of data characterization process is the influence of conditioning (incorporation of mapped fractures) to DFN models. The unconditioned and conditioned DFN model are compared in terms of kinematic slope stability analysis, with emphasis on the locations of potential block formations. The results showed that the conditioned DFN model would allow for a better consideration of spatial locations of potentially unstable blocks.  Lastly, the thesis presents the application of DFN approach to study the variability of Geological Strength Index (GSI). The Particle Size Distribution (PSD) plots obtained from DFN models are combined with the quantification method of GSI to estimate the GSI rating. Additionally, the implication of two-dimensional (2D) versus three-dimensional (3D) data to characterize rock mass blockiness is examined. The results showed that the range of GSI rating for a rock mass could be as large as ±10. This suggests the limitation on using a unique value of GSI rating, when the GSI rating is variable due to the inherent uncertainty of the rock mass in reality. The comparison between 2D and 3D blockiness showed that the blockiness observed on a 2D plane does not necessarily correspond to the true 3D blockiness of the rock mass. In these contexts, DFN models offer the opportunity to characterize this variability and provide better estimates of rock mass blockiness.    iv  Lay Summary The applications of Discrete Fracture Network (DFN) has been widened significantly in the past decades due to its ability to realistically simulate natural fracture network in three-dimension. Despite that, little attention has been given in literature to study the influence of data characterization process in the development of DFN models. This thesis investigates the influence of two aspects of data characterization process on kinematic slope stability analysis. A new approach to estimate the variability of GSI using DFN models is also presented.  The research identified important considerations of data characterization process required for the generation of realistic DFN models, and accordingly the kinematic stability analysis that is truly representative of field condition. The study of variability of GSI suggested that GSI should be expressed as a range rather than a point estimate to better reflect the inherent variability of rock mass.                     v  Preface  The thesis is original and independent work done by the author. The author was the lead author of two published conference papers and one journal paper based on the work of this these. The co-author of these papers was the thesis supervisor.  The paper “Influence of Data Characterization Process on the Kinematic Stability Analysis of Engineered Slopes using Discrete Fracture Network Models” published in the proceedings of the 2017 15th International Associations for Computer Methods and Advances in Geomechanics in Wuhan, China is based on Chapter 4 and 5 in this thesis.  The paper “A Discrete Fracture Network approach to study the Variability of the Geological Strength Index” published in the proceedings of the 2018 International Discrete Fracture Network Conference in Seattle, United States is based on Chapter 6 of this thesis.  The paper “Influence of data analysis when exploiting DFN model representation in the application of rock mass classification systems” published in the Journal of Rock Mechanics and Geotechnical Engineering (in press) is based on Chapter 4,5, and 6 in this thesis.      vi  Table of Contents Abstract ........................................................................................................................................................ iii Lay Summary ............................................................................................................................................... iv Preface .......................................................................................................................................................... v Table of Contents ......................................................................................................................................... vi List of Tables ............................................................................................................................................... ix List of Figures ............................................................................................................................................... x Acknowledgements .................................................................................................................................... xiii Chapter 1 Introduction .................................................................................................................................. 1 1.1 Project statement ................................................................................................................................. 1 1.2 Research objectives ............................................................................................................................. 2 1.3 Thesis organization ............................................................................................................................. 2 Chapter 2 Literature Review ......................................................................................................................... 4 2.1 Introduction ......................................................................................................................................... 4 2.2 Principles of DFN modelling .............................................................................................................. 4 2.2.1 Data collection for DFN models .................................................................................................. 5 2.2.2 Data characterization.................................................................................................................... 7 2.2.3 DFN model generation ............................................................................................................... 11 2.2.4 DFN model validation ................................................................................................................ 12 2.3 Kinematic slope stability analysis ..................................................................................................... 12 2.3.1 Stereographic analysis................................................................................................................ 13 2.3.2 Limit equilibrium analysis ......................................................................................................... 14 2.3.3 SiroModel block model analysis ................................................................................................ 15 2.3.4 FracMan rock wedge analysis .................................................................................................... 15 2.3.5 Discrete element methods .......................................................................................................... 16 2.3.6 Comparison between DFN rock wedge analysis and limit equilibrium/stereographic analysis 16 2.4 Geological Strength Index (GSI) ...................................................................................................... 18 2.4.1 Estimation of GSI in the field .................................................................................................... 18 2.4.2 Quantification of GSI ................................................................................................................. 20 2.4.3 In-Situ Block Size Distribution (IBSD) ..................................................................................... 22 Chapter 3 DFN Model Generation and Validation ..................................................................................... 24 3.1 Introduction ....................................................................................................................................... 24 3.2 Case Study 1: Open pit mine model .................................................................................................. 24 3.2.1 DFN model generation ............................................................................................................... 24 vii  3.2.2 Model validation ........................................................................................................................ 26 3.3 Case Study 2: Brunswick model ....................................................................................................... 27 3.3.1 Model generation ....................................................................................................................... 27 3.3.2 Model validation ........................................................................................................................ 29 3.4 Case Study 3: Mountain model ......................................................................................................... 31 3.5 Case Study 4: Middleton mine model ............................................................................................... 32 3.5.1 Model generation ....................................................................................................................... 33 3.5.2 Model validation ........................................................................................................................ 36 Chapter 4 Influence of DFN Modelling Approach on Kinematic Stability Analysis ................................. 40 4.1 Introduction ....................................................................................................................................... 40 4.2 Influence on simulated intensity and orientations ............................................................................. 40 4.3 Influence on block forming potential ................................................................................................ 43 4.4 Chapter summary .............................................................................................................................. 48 Chapter 5 Kinematic Stability Analysis using a Conditioned DFN model ................................................. 50 5.1 Preliminary analysis .......................................................................................................................... 50 5.1.1 Methodology .............................................................................................................................. 51 5.1.2 Generation and validation of conditioned DFN model .............................................................. 51 5.1.3 Kinematic slope stability analysis .............................................................................................. 52 5.1.4 Discussion and conclusions (preliminary analysis) ................................................................... 54 5.2 Large-scale conditioned DFN model ................................................................................................ 55 5.2.1 Methodology .............................................................................................................................. 55 5.2.2 Generation and validation of conditioned DFN model .............................................................. 56 5.2.3 Kinematic slope stability analysis .............................................................................................. 57 5.2.4 Discussion .................................................................................................................................. 62 5.3 Chapter summary .............................................................................................................................. 63 Chapter 6 A DFN Approach to Quantify the Variability of GSI ................................................................ 65 6.1 Introduction ....................................................................................................................................... 65 6.2 Methodology ..................................................................................................................................... 66 6.3 Model setup ....................................................................................................................................... 67 6.4 Results of the rock wedge analysis ................................................................................................... 68 6.5 Characterization of GSI variability ................................................................................................... 72 6.6 Limitations of 2D surveys to determine rock mass blockiness ......................................................... 77 6.7 Comments on quantifying GSI from block analysis ......................................................................... 78 6.7.1 Definition of IBSD and GSI blockiness parameter .................................................................... 78 6.7.2 Influences of bin sizes on IBSD curves ..................................................................................... 78 viii  6.8 Chapter summary .............................................................................................................................. 80 Chapter 7 Conclusions and Recommendations ........................................................................................... 81 7.1 Research conclusions ........................................................................................................................ 81 7.2 Recommendations for future work ................................................................................................... 82 References ................................................................................................................................................... 84                         ix  List of Tables  Table 1: Primary and secondary fracture properties required for DFN model generation ............................ 5 Table 2: Classification of blocks in rock wedge analysis option in FracMan ............................................. 16 Table 3: Summary of case studies............................................................................................................... 24 Table 4: Input parameters for the Open pit mine model ............................................................................. 25 Table 5: Input parameter for the Brunswick DFN model ........................................................................... 29 Table 6: Input parameters for the Mountain DFN model ........................................................................... 32 Table 7: Input parameters for the Middleton DFN model .......................................................................... 36 Table 8: Comparison of input parameters between aggregate and disaggregate model (Case Study 1)..... 40 Table 9:  Comparison of input parameters between aggregate and disaggregate model (Case Study 3).... 41 Table 10: Comparison of P10 intensity between aggregate and disaggregate approach (Case Study 1) ..... 42 Table 11: Quantitative comparison of number of blocks and block volume .............................................. 48 Table 12: Comparison of number and size of blocks between unconditioned and conditioned Brunswick DFN model.................................................................................................................................................. 52 Table 13: Input parameters for the unconditioned and conditioned Mountain DFN model ....................... 56 Table 14: Comparison of number of blocks, block volume between for Models 1 to 3, South and North wall .............................................................................................................................................................. 60 Table 15: Comparison of P21 intensity between the models, South wall, and North wall .......................... 62 Table 16: Input parameters for the Middleton model (aggregate and disaggregate approach) ................... 68 Table 17: Comparison of GSI ranges corresponding to P20, P30, P50, P70 and P80 passing size for the Middleton mine case study ......................................................................................................................... 73 Table 18: Comparison of GSI ranges corresponding to P20, P30, P50, P70 and P80 size passing for the slope model described in Section 5.1.3 (South wall and North wall) ......................................................... 75 Table 19: Classification scheme of block volume suggested by Palmstrøm (1995) ................................... 78 Table 20: Bin sizes used for each method (All units are in m3) .................................................................. 79            x  List of Figures Figure 1: Example showing the limitations of ISRM suggested methods (Elmo et al., 2015) ..................... 6 Figure 2: Pij Intensity (Elmo, 2006) ............................................................................................................. 9 Figure 3: Common termination types (Elmo, 2006) ................................................................................... 11 Figure 4: Schematic diagram of plane failure, wedge failure and toppling (from left to right) (Wyllie and Mah, 2004) .................................................................................................................................................. 13 Figure 5: Example of stereographic analysis of structure-controlled failures (Wyllie and Mah, 2004) ..... 14 Figure 6: Example of limit equilibrium analysis of plane failure (Wyllie and Mah, 2004). W represents the weight of the block, U and V are forces related to pore pressure, H is the height of slope, b is the distance of tension crack from the crest, and Zw is the depth of water in the tension crack. ................................... 14 Figure 7: Comparison of limit equilibrium analysis (left) and DFN modeling approach (right) ................ 17 Figure 8: GSI chart (Marinos and Hoek, 2000) .......................................................................................... 19 Figure 9:  Examples of excavated slopes and natural outcrops .................................................................. 20 Figure 10: Determination of SR from Jv (Sonmez and Ulusay, 1999) ........................................................ 21 Figure 11: Quantification of GSI. Cai et al. (2004): left, Hoek et al. (2013): right .................................... 22 Figure 12: Stereonet plots of the orientation for the Open pit mine model (raw data) ............................... 25 Figure 13: Selected example of the DFN model for the Open pit mine case study .................................... 25 Figure 14:  Comparison of stereonet plots of the Open pit mine model between mapped orientations (left), simulated orientations (middle), simulated orientations of all fractures in the model (right) ..................... 26 Figure 15: Comparison between the mapped and simulated trace length (Case Study 1) .......................... 27 Figure 16:  Scanline mapping on the rock outcrop at Brunswick Prospect Point (left) and Google map image of the study area (right) .................................................................................................................... 28 Figure 17: Stereonet plot of fractures for the Brusnwick model (raw data) ............................................... 28 Figure 18: Selected example of the DFN model for the Brunswick case study .......................................... 29 Figure 19: Comparison of stereonet plots of the Brunswick model between actual orientations (left), simulated orientations (middle), simulated orientations of all fractures in the model (right) ..................... 30 Figure 20: Comparison between the mapped and simulated trace length (Case Study 2) .......................... 30 Figure 21: Stereonet plots of fracture orientation of the Mountain model. Mapped data (left) and simulated orientations (right) (Schlotfeldt et al., 2017) .............................................................................. 31 Figure 22: Example of DFN realizations for the Mountain model (figure on the right shows the simulated traces equivalent to the mapped exposure) ................................................................................................. 32 Figure 23: Location of mapped pillar faces (modified from Elmo (2006)) ................................................ 33 Figure 24: Simulated fracture orientations for the Middleton model.......................................................... 33 Figure 25: Comparison of simulated trace length and mapped trace length (Case Study 4) ...................... 35 Figure 26: Selected example of the DFN model for the Middleton mine case study ................................. 36 Figure 27: Comparison of simulated P21 intensity and mapped P21 intensity (Case Study 4) ..................... 37 Figure 28: Comparison between simulated and mapped tracemaps for Panel 1 and 2 ............................... 38 Figure 29: Comparison between simulated and mapped tracemaps for Panel 3 and 4 ............................... 39 Figure 30: Comparison of simulated orientations (Case Study 1) .............................................................. 42 Figure 31:  Comparison of simulated orientations (Case Study 3) ............................................................. 42 Figure 32: Location and geometry of the slopes used for rock wedge analysis in Case Study 1 (left) and Case Study 3 (right). ................................................................................................................................... 44 Figure 33: Comparison of tracemaps between aggregate and disaggregate approach (Case Study 1) ....... 45 Figure 34: Comparison of tracemaps on the North wall between aggregate and disaggregate approach (Case Study 3) ............................................................................................................................................. 45 xi  Figure 35: CDF plots of equivalent radius of simulated fractures between aggregate and disaggregate approach (Case Study 1) ............................................................................................................................. 46 Figure 36: PSD curves for aggregate and disaggregate approach and the blocks formed on the slope (Case Study 1) ....................................................................................................................................................... 47 Figure 37: PSD curves for aggregate and disaggregate approach and the blocks formed on the North wall (Case Study 3) ............................................................................................................................................. 47 Figure 38: PSD curves for aggregate and disaggregate approach and the blocks formed on the South wall (Case Study 3) ............................................................................................................................................. 48 Figure 39: Generation of the Brunswick conditioned DFN model ............................................................. 51 Figure 40: Comparison of mapped and re-generated fractures for the Brunswick DFN model ................. 52 Figure 41: Comparison of tracemaps between unconditioned and conditioned Brunswick DFN model ... 52 Figure 42: Comparison of block locations between unconditioned and conditioned Brunswick DFN model .................................................................................................................................................................... 53 Figure 43: Comparison of tracemap and block formations of unconditioned Brunswick DFN model (Black: Stochastic fractures, Red: Deterministic Fractures, Blue: Faults) .................................................. 54 Figure 44: Selected example of unconditioned (left) and conditioned (right) Mountain DFN model (Blue: Stochastic fractures, Red: Deterministic fractures) ..................................................................................... 57 Figure 45: Visual comparison of mapped traces and DFN model traces (Schlotfeldt et al., 2017) ............ 57 Figure 46: Comparison between the PSD for Models 1, South and North wall ......................................... 58 Figure 47: Comparison between the PSD for Models 2, South and North wall ......................................... 59 Figure 48: Comparison between the PSD for Models 3, South and North wall ......................................... 59 Figure 49: Comparison between the PSD for Models 1 to 3, South and North wall .................................. 60 Figure 50: Model 1; tracemaps for DFN realization (a) and outlines of blocks formed on South wall for DFN realization (a), (b) and (c) .................................................................................................................. 61 Figure 51: Model 2; tracemaps for DFN realization (a) and outlines of blocks formed on South wall for DFN realization (a), (b) and (c) .................................................................................................................. 61 Figure 52: Model 3; tracemaps for DFN realization (a) and outlines of blocks formed on South wall for DFN realization (a), (b) and (c). Thick red lines represent deterministic trace maps ................................. 62 Figure 53: Estimating a 3D rock mass classification rating requires access to 3D information. ................ 65 Figure 54: Sampling planes used for rock wedge analysis ......................................................................... 67 Figure 55: Examples of generated DFN models. From left to right: Model 1 (aggregate), Model 2 (aggregate with bedding features), Model 3 (disaggregate), and Model 4 (disaggregate with bedding features) ...................................................................................................................................................... 68 Figure 56: PSD plots of block volume for Model 1 to 4, all vertical and horizontal sampling planes combined ..................................................................................................................................................... 69 Figure 57: PSD plots of block volume for Model 1 (aggregate, no bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes ............................................................................................................. 70 Figure 58: PSD plots of block volume for Model 2 (aggregate, with bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes ............................................................................................................. 70 Figure 59: PSD plots of block volume for Model 3 (disaggregate, no bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes ............................................................................................................. 70 Figure 60: PSD plots of block volume for Model 4 (disaggregate, with bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes ............................................................................................................. 71 Figure 61: Block formations on the vertical walls (Surface 1 to 4) in Model 2 (top row) and Model 4 (bottom row) ............................................................................................................................................... 71 Figure 62: Block formations on the horizontal walls (Surface 5 and 6) in Model 1 (top row) and Model 2 (bottom row) ............................................................................................................................................... 72 xii  Figure 63: Comparison of variation of GSI ranges for the 4 DFN models generated for Middleton mine (Vertical wall: left, Horizontal wall: right). Green dot represents P50, the thick orange line and the thin black line represents the P30-P70 and P20-P80 size passing range, respectively. Results for Models 2 and 4 are given with respects to the modified GSI charts by Cai et al. (2004) .................................................. 74 Figure 64: Variation of estimated GSI for Case Study 3 (South wall: left, North wall : right). Green dot represents P50, the thick orange line and the thin black line represents the P30-P70 and P20-P80 size passing range, respectively. ........................................................................................................................ 76 Figure 65: Comparison between 2D perceived blocks and actual 3D blocks formed across Surfaces 1 to 4 (see Figure 58 and Figure 60) for Models 2 (top) and 4 (bottom) .............................................................. 77 Figure 66: PSD curves produced with three different bin sizes (Model 2: left, Model 4: right) ................ 79                       xiii  Acknowledgements I would like to express my sincere gratitude to my supervisor, Prof. Davide Elmo for sharing his extensive knowledge and experience in rock mechanics and discrete fracture networks with me and for providing important guidance in my research.  Financial support was provided by NSERC (Natural Sciences and Engineering Research Council of Canada) through a Collaborative Research Development grant (Grant No. 11R74149; Mine-to-Mill Integration for Block Cave Mines).  I would also like to express thanks to Golder Associates for providing an academic license for the code FracMan.  1  Chapter 1 Introduction 1.1 Project statement  With the advancements in remote sensing techniques such as laser scanning and digital photogrammetry, our ability to remotely acquire high quality, and larger amount of fracture data has significantly improved. Despite the improvements in fracture data collection, the current practice of kinematic stability analysis remains dependent on limit equilibrium and stereographic analysis, which assume infinite and ubiquitous fractures.  When considering the stability of engineered and natural slopes, the size and shape of potential wedges in the rock mass is a function of the orientation, size and frequency of the significant discontinuity sets. While limit equilibrium and stereographic analysis are appropriate for preliminary design, their unrealistic assumption of ubiquitous and infinite fractures overestimates the block forming potential of rock mass. In this context, Discrete Fracture Network (DFN) has been increasingly identified as a useful tool for its ability to realistically represent natural fracture network in three-dimension using statistical distributions.  The quality of DFN model is largely dependent on the quality of input data and their interpretation. For instance, several authors (e.g. Hadjigeorgiou, 2012; Elmo et al., 2015) have demonstrated that inadequate care in collecting the necessary structural data at the required engineering scale would strongly limit the quality of any DFN model. However, in the literature little attention has been given to the study of the influence that data analysis plays in developing DFN models.  One application of DFN that has been given only partial recognition is the assessment of rock mass quality using a DFN approach. Although several authors including Elmo (2006; 2012), Pierce et al. (2007) and Mas Ivars et al. (2008) have applied DFN to Synthetic Rock Mass (SRM) modelling to estimate rock mass strength and deformability, they did not establish a relation between connectivity of fractures and the rock mass classification system.   The earlier attempt to establish this relation was performed by Cai et al. (2004), where they presented a quantification method of Geological Strength Index (GSI) by supplementing the blockiness parameter in GSI with a measure of block volume. However, this analysis was limited to a simple conceptual block mass and did not account for the complex configurations of fracture network in naturally fractured rock mass. It is argued that a DFN approach could provide a more sophisticated insight on the block forming potential to predict GSI rating.   2  1.2 Research objectives  In this thesis, two aspects of data characterization processes are explored to examine the influence of them on kinematic slope stability analysis. This is followed by the introduction of the new DFN approach to estimate the GSI rating that better reflects variability of rock mass blockiness. Fundamental questions related to the estimation of GSI are also addressed using DFN models.  The primary objectives of this thesis are:  • To investigate the influence of modelling approach that relates to the separate statistical procedure to define fracture set (aggregate vs disaggregate approach) on kinematic slope stability analysis; • To investigate the influence of conditioning (incorporating the mapped fractures deterministically) on kinematic slope stability analysis; • To propose a new DFN approach to quantify the variability of GSI, and; • To address fundamental questions related to the estimation of GSI using DFN models.  In order to address the primary objectives, following secondary objectives are proposed:  • Generation and validation of DFN models for four case studies;  • Comparison between aggregate and disaggregate approach in terms of intensity and orientation of generated DFN models, and block dimensions;  • Comparison between unconditioned and conditioned DFN model in terms of block dimensions and locations; • Estimation of the range of GSI by combining the Particle Size Distribution (PSD) curves obtained from DFN model and the quantification method proposed by Cai et al. (2004), and; • Comparison between the largest area formed by connected fractures in two-dimension and actual block formations in three-dimension.  1.3 Thesis organization  The thesis consists of seven chapters. This Chapter is followed by Chapter 2 (Literature Review) and Chapter 3 (DFN Model Generation and Validation), where generation and validation processes of DFN models for four case studies are presented. The final chapter summarizes key findings of the research and outlines the recommendations for future work. The descriptions for three chapters in between are following;  Chapter 4 (Influence of DFN Modelling Approach on Kinematic Stability Analysis) covers the first aspect of the two data characterization processes considered in this thesis. The input parameters of the models for 3  aggregate and disaggregate approach, generated DFN models, and the results of kinematic slope stability analysis are presented.  Chapter 5 (Kinematic Stability Analysis using a Conditioned DFN model) covers the second aspect of the characterization processes. The Chapter presents the generation process of conditioned DFN model, and comparison between unconditioned and conditioned DFN model in terms of the results of kinematic slope stability analysis. The focus is also given on the comparison of the locations and shapes of potential blocks.  Chapter 6 (A DFN Approach to Quantify the Variability of GSI) presents a new DFN based approach to quantify the variability of GSI. The methodology describing the quantification process, and the obtained GSI rating are presented along the discussion. The comparison between 2D and 3D blockiness is included. The Chapter also presents the limitations associated with the proposed quantification method of GSI.                 4  Chapter 2 Literature Review   2.1 Introduction  Chapter 2 provides a literature review describing the current practice of data collection and characterization process of discontinuity data for Discrete Fracture Network (DFN) modeling and the application of DFN models to engineering problems, with emphasis on kinematic slope stability analysis and quantification of rock mass classification system.  2.2 Principles of DFN modelling  DFN modelling is used for the three-dimensional (3D) stochastic representation of discrete fractures. DFN models were first introduced in the late 1970s to study fluid flow in fractured rock mass through connected fractures (Dershowitz et al., 2004). Since then, the DFN approach has been developed continuously, and its applications widened to various engineering situations. In recent years, DFN models have been increasingly used as an effective tool in mining and civil geomechanics. Some examples of mining and civil geomechanics applications include (Lorig et al., 2015):  Mining geomechanics  • Synthetic Rock Mass (SRM) models to estimate the rock mass strength, deformability, etc.  • Kinematic analysis to study block stability in open pit mines and underground excavations  • Large scale slope stability  • Determination of equivalent porous media for flow estimates  Civil geomechanics  • Flow studies (nuclear waste repositories) • Excavation stability (Lin et al., 2007)  There are various DFN software packages commercially available. Some examples are FracMan (Dershowitz and Einstein, 1988; Golder Associates, 2017), SiroModel (CSIRO, 2017), FracSim 3D (Xu and Dowd, 2010), and MoFrac (MIRARCO, 2013). Some DFN packages have specific applications such as hydrological simulation or geomechanical analysis. For example, SiroModel was originally developed as part of an open pit mine project, and as such is most appropriate for mining geomechanics.  Primary and secondary fracture properties required to generate discrete fractures are listed in Table 1 below. Primary fractures are necessary to generate discrete fractures while secondary fractures may be necessary 5  depending on the applications of the DFN model. For example, the fracture aperture and transmissivity should be defined when applying DFN models to flow simulations.  Table 1: Primary and secondary fracture properties required for DFN model generation Primary Properties Secondary Properties Orientation distribution Aperture distribution Fracture length distribution Fracture shear strength properties Fracture intensity distribution Fracture stiffness properties Termination percentage Transmissivity distribution Spatial variation Storativity distribution  Termination percentage The steps to generate simple DFN models include:  1. Data collection  2. Discontinuity data characterization  3. DFN model construction  4. DFN model validation  Additional steps may be included depending on the complexity and applications of DFN models. Each of these steps are described in the following sections.  2.2.1 Data collection for DFN models  Data collection is the process of collecting primary fracture properties and secondary fracture properties (if necessary) in the field. Since the direct measurement of primary fracture properties in three-dimension is not possible, the data collection has to rely on 1D or 2D methods.  Conventional methods of discontinuity data collection include boreholes and surface mapping (scanline and window mapping). Scanline mapping is when fractures intersecting a horizontal tape placed on the rock mass are measured whereas window mapping is when fractures within a rectangle or circular area on the rock mass are measured. It is important to note that ISRM suggested methods of data collection may not be best appropriate for DFN modeling. Elmo et al. (2015) outlined important considerations required when collecting discontinuity data for DFN modeling.  For instance, ISRM (1981) recommends the use of bins to measure fracture size. Fractures with length of less than 1 m, 1 to 3 m, 3 to 10 m, 10 to 20 m, and greater than 20 m long are described as very low persistence, low persistence, medium persistence, high persistence, and very high persistence fractures respectively. This method adds subjectivity in the data characterization process, which may result in inaccurate estimation of statistical distribution of fracture length (Figure 1).  6   Figure 1: Example showing the limitations of ISRM suggested methods (Elmo et al., 2015) 2D mapping (surface mapping) is generally preferred over 1D mapping (boreholes) because 1D mapping cannot provide a measure of fracture length. However, conventional mapping techniques suffer four types of biases (Brady and Brown, 2007):  • Orientation bias  • Size bias  • Truncation bias  • Censoring bias  Orientation bias is associated with the orientation of sampling geometry with respect to the discontinuities. In case of scanline mapping, the frequency of sampled discontinuities is the highest when the scanline is oriented perpendicular to the discontinuities and the lowest when the scanline is oriented parallel to the discontinuities. Size bias is related to the size of discontinuities. Larger discontinuities have higher chance to be sampled than smaller discontinuities. Truncation bias is when fractures shorter than a certain size are not measured; for example, discontinuities less than 1 m may be ignored. It has been proved that truncation bias impact the analysis of the rock mass’ in-situ block size distribution (Brady and Brown, 2007). Censoring bias is when the observed discontinuity size is limited by the sampling geometry imposed on the rock mass. Censored trace length provides the lower-bound of true trace length. This bias is of particular importance when the collected discontinuity data are eventually used for DFN model generation (Read and Stacey, 2007). If a large portion of sampled discontinuities were censored, the estimation of accurate statistical distribution of fracture size would be difficult.  Some of these biases can be reduced using remote sensing techniques such as photogrammetry and Light detection and ranging (LiDAR). The application of remote sensing to discontinuity characterization has 7  been increasingly recognized. Some examples include the work by Sturzenegger et al. (2011) and Tuckey (2012) who applied photogrammetry and laser scanning techniques to discontinuity characterization at open pit mines. Havaej et al. (2016) also used photogrammetry and laser scanning to characterize discontinuities and to reproduce realistic 3D slope surface. The remotely sensed data were then incorporated into numerical simulation to study the stability of the slope. Salvini et al. (2016) used Unmanned Aerial Vehicle (UAV) to collect the discontinuity data within a marble quarry to generate DFN models.  One of the major advantages of remote sensing over conventional mapping methods (scanline and window mapping) is indirect measurement. This is of importance when the slope of interest is inaccessible by conventional mapping method. The volume of data that can be obtained by remote sensing techniques is larger than conventional methods both in terms of areal extent and the magnitude (Fekete and Diedrichs, 2013). The other advantages include improvements in accuracy of characterization of discontinuity characteristics; especially, discontinuity location, persistence, and curvature. For instance, persistence above a bench height (5 to 10 m) is difficult to accurately estimate with conventional techniques, but this can be significantly improved by the use of remote sensing techniques. Also, remote sensing techniques allow more realistic measurements of discontinuity orientation. This is because conventional mapping methods focus on small-part of discontinuity while remote sensing techniques average measurements at number of points along a discontinuity (Sturzenegger and Stead, 2009b).  However, there are several limitations in the applications of remote sensing to discontinuity characterization (Sturzenegger et al., 2007; Sturzenegger and Stead, 2009a; Sturzenegger and Stead, 2009b). One of the major limitations is occlusion and orientation bias. Occlusion refers to the phenomena where certain parts of rock outcrops are not remotely sensed due to the orientation of rock outcrops relative to the location of the sensor. Remote sensing techniques also have trouble with capturing discontinuity characteristics if the rock mass exhibits varying reflectivity or texture.  Regardless of these limitations, remote sensing techniques are irreplaceable tools considering the advantages they offer over conventional mapping techniques. The use of remote sensing techniques to discontinuity characterization is expected to increase further in the future.  2.2.2 Data characterization  In the context of this thesis, data characterization refers to the process of defining statistical distributions or values of primary fracture properties from field data. In DFN models, discrete fractures are generated either stochastically (using statistical distributions) or deterministically (at exact locations). Typically, large-scale fractures (bedding planes and faults) that likely impact the stability of the rock mass are modelled 8  deterministically, while the small-scale joints that are not captured deterministically are modelled stochastically.  Data characterization process in this context applies for stochastic fractures. Deterministic fractures do not require data characterization process since modelled fractures have exact same properties as mapped fractures. Stochastic fractures require primary fracture properties to be represented as statistical distributions or averaged values to model a family of discrete fractures.  The detailed process of data characterization for each primary fracture property is presented in the following paragraphs.  Fracture Spatial Model  Fracture spatial model governs the way discrete fractures are distributed in three-dimension. A detailed review of spatial DFN models can be found in (Dershowitz and Einstein, 1988; Staub et al., 2002). The spatial DFN models available with the code FracMan are Enhanced Baecher, Nearest-Neighbour, and Fractal Levy-Lee. A majority of spatial models typically have similar law governing the fracture length, shape and termination. The main difference exists in fracture orientation and location. Generally, the Enhanced-Baecher model provides appropriate solutions, especially when the model is small-scale. In Enhanced Baecher model, the fractures are assumed to be randomly located according to Poisson process. This can be verified with an exponential distribution of fracture spacing along a sampling line. The Nearest-Neighbor is effective to simulate the fracture system where fractures have tendency to cluster around major points and faults by forming new fractures near earlier fractures (Dershowitz et al., 1998). The Levy-Lee model is a fractal model and effective to represent a layered system. The fracture centers are modelled sequentially by the Levy flight process and the size of fractures depends on the distance from previous fractures (Staub et al., 2002).  Fracture Intensity  Fracture intensity in the context of DFN modelling is typically expressed as Pij Intensity (Dershowitz and Herda, 1992), where i refers to the dimensions of feature, and j refers to the dimensions of sampling region (Figure 2).  9   Figure 2: Pij Intensity (Elmo, 2006) For example, fracture count per unit length (1/m) is expressed as P10 intensity, fracture length per unit area (m/m2) is expressed as P21 intensity (areal fracture intensity), and fracture area per unit volume (m2/m3) is expressed as P32 intensity (volumetric fracture intensity). P10 intensity and P21 intensity are typical forms of intensity measured in the field. However, these are orientation-dependent feature, and influenced by the orientation of fractures relative to the orientation of sampling planes or lines.  In contrast, P32 is an intrinsic rock mass property but cannot be directly measured in the field.  Commonly, P10 intensity and P21 intensity are used to infer P32 intensity by assuming a linear relation between P10 intensity or P21 intensity and P32 intensity as shown below (Equation 1 and 2). The constants 𝐶𝐶32 and 𝐶𝐶31depend on the orientation of fractures relative to the orientation of sampling region and the fracture radius.                                                                             𝑃𝑃32 = 𝐶𝐶32                                                                                   (1)                                                                                                                                                   𝑃𝑃32 = 𝐶𝐶31𝑃𝑃10                                                                            (2)  10  One example of estimating P32 intensity from orientation-biased P10 or P21 intensity is by DFN model simulation (Elmo et al., 2014a). The first step is the estimation of P32 intensity in 3D DFN model at a range of values of P10 or P21 intensity. In this process, the P10 or P21 intensity that act as input parameter, need to be correctly input at actual sampling plane or line orientation. The results are plotted on P10 or P21 intensity vs P32 intensity plot to estimate the linear correlation. This correlation is then applied to actual P10 or P21 intensity to estimate the corresponding P32 intensity.  Alternatively, a DFN model can be generated with P10 conditioning. P10 conditioning allows direct replication of P10 intensity measured along sampling line in the field to the modelled sampling line.  An acquisition of true fracture intensity of rock mass requires collection of full extent of fracture length. However, the range of fracture length measured in the field is limited by truncation and censoring bias. Therefore, the measured fracture intensity is effectively reduced from true fracture intensity.  Fracture Orientation  DFN models can be generated either by applying separate statistical distributions for each fracture set and combining later to obtain the overall representation of the model or by applying same statistical distribution for all fractures, independently of their orientation. The latter approach is called aggregate approach while the former approach is called disaggregate approach. In disaggregate approach, the fractures that do not belong to any of the fracture sets are normally discarded.  The fracture pole distributions are commonly expressed as Fisher, Bingham, bivariate Fisher, or bivariate Bingham. A bootstrap approach is used when the data do not conform to a straight-forward statistical distribution. This approach allows the generation of a pseudo-replication sample of fracture orientations based on multiple random sampling (Elmo et al., 2014a).  Fracture Length  Fracture size in the context of DFN modelling is typically expressed as equivalent radius. Equivalent radius is defined as the radius of a circle of equivalent area to a polygonal fracture. This should be distinguished from trace length, which is the intersecting length of the fracture on the sampling plane.  Although it is not possible to directly measure equivalent radius in three-dimension, trace length can be measured with 2D mapping such as surface mapping and remote sensing techniques. One example of the methods used to estimate equivalent radius from trace length is analytical method.  A comprehensive description of analytical methods of estimating equivalent radius can be found in (Mauldon, 1998; Zhang and Einstein, 2000). This method is appropriate when using trace length 11  distribution as an input parameter to derive equivalent radius distribution. The method was developed based on the fracture data collected using circular window mapping as this has advantages over scanline and rectangular mapping of automatically eliminating orientation bias.  The distribution of equivalent radius is commonly expressed as log normal distribution or negative exponential function. Power law is also used when correlating small scale fractures to intermediate and large scale discontinuities (e.g. faults).  Fracture Termination  Fracture termination is one of the parameters that is generally overlooked during data collection. Fracture termination is directly correlated to fracture connectivity, which is an important factor when considering fragmentation of rock mass. Also, fracture termination could be useful to understand structural character of rock mass and to validate the model. An important type of fracture termination is T-type as shown in Figure 3 below. This can be related to the order of fracture formation. In the code FracMan, fracture termination is expressed as termination %, which refers to the percentage of T-type termination out of all observed ends.   Figure 3: Common termination types (Elmo, 2006) 2.2.3 DFN model generation  Generation of a DFN model depends on whether the fractures are defined as stochastic or deterministic. If the fractures are stochastic, the process of fracture generation differs based on the approaches used (aggregate vs disaggregate). Deterministic fractures are modelled with exact same primary fracture properties as the mapped fractures. Stochastic fractures can be modelled either with aggregate approach or disaggregate approach. In disaggregate approach, separate DFN models are generated for each fracture set and combined later. Aggregate approach involves all fractures to be treated as one fracture set; therefore, all fractures are generated with a single set of definitions of primary fracture properties.  One important aspect of DFN methods involves the stochastic nature of DFN models. DFN models with same input parameters would yield equi-probable realizations with different fracture geometry. Therefore, 12  a probabilistic approach using multiple realizations is recommended when performing analyses with DFN models. 2.2.4 DFN model validation  Model validation is an important step to ensure the generated DFN model captures the reality with an adequate level of accuracy. Validation is performed by comparing the primary fracture properties (intensity, length and orientation) of the fractures intersecting sampling line or plane in the model with the mapped fractures. For 2D mapping, P21 intensity and tracemaps of fractures on the surface exposure are typically compared. For 1D mapping, P10 intensity and orientations of the fractures intersecting the sampling line are compared. In the process of DFN model validation, it is important to ensure that DFN models are capturing not only the statistical description of the observed fractures, but also the underlying geology governing the fracture distributions.  2.3 Kinematic slope stability analysis  The purpose of this section is to provide a review on the application of DFN methods to kinematic slope stability analyses of engineered slope. Kinematic slope stability analyses concern structure-controlled failures i.e. failures controlled due to block formations by excavation surface and discontinuities. Kinematic slope stability analyses have applications to both civil engineering (highway and railway road cut design) and mining engineering (open pit mine design). The civil engineering design typically requires higher factor of safety as the consequences of failure may end up in infrastructure damage and human life loss while minor failures at the bench scale may be tolerated in open pit mine design.  Although structure-controlled failures due to large-scale structures (such as faults) are not impossible, structure-controlled failures in large-scale slope are more commonly controlled by step path failure i.e. failure where several shorter fractures are connected to form a failure surface. Step-path failure requires sliding along discontinuities as well as the breakage of intact rock in between the fractures. In this thesis, the focus is given on structure-controlled failures due to sliding along discontinuities, and not the step-path failures. Also, the consideration is not given to groundwater condition or external loads.  Kinematic slope stability analysis is performed by checking whether a block forms from the fractures and the excavation surface, and if so, whether the block satisfies the stability criteria.  The three types of structure-controlled failures are; plane failure, wedge failure and toppling (Figure 4). Toppling includes different types such as block toppling and flexural toppling. Block toppling involves the movement of blocks formed by a set of discontinuities steeply dipping into the slope and another set of discontinuities orthogonal to that. Flexural toppling occurs by the bending of rock columns separated by a 13  set of continuous, steeply dipping discontinuities. A comprehensive review on the types of structure-controlled failures are provided in (Sjoberg, 1996; Wyllie and Mah, 2004).   Figure 4: Schematic diagram of plane failure, wedge failure and toppling (from left to right) (Wyllie and Mah, 2004)  The kinematic stability analysis can be 2D or 3D; the latter is preferred when the direction of key geological feature (geologic structures, material anisotropy etc.) does not strike nearly parallel (within ±20-30°) of the slope or the complex geometry of the slope cannot be represented by 2D analysis.  In this section, stereographic analysis, limit equilibrium analysis, discrete element methods, and discrete fracture network modelling are reviewed as a tool to analyze structure-controlled failures. Since, the focus is given on the identification of blocks on the excavation surface and its stability, more advanced options such as hybrid FEM-DEM are not considered.  2.3.1 Stereographic analysis  Stereographic analysis uses joint orientations, shear strength of fractures and slope orientation to analyze the potential of structure-controlled failure. Stereographic analysis is the simplest method amongst kinematic slope stability analyses, and typically used in the preliminary stage of the project. This method allows representation of 3D fracture orientations in two-dimension. The geometrical conditions of structure-controlled failure are imposed on the stereonet plot as an envelope (Figure 5). However, it is important to note that not all geometrical conditions can be represented on a stereonet plot. If the pole of a plane (for plane and toppling failures) or the pole of line of intersections (for wedge failure) fall within the envelope, the corresponding planes are classified as potentially unstable. The number of fractures that fall within the envelope indicates the likeliness of the failure.  14   Figure 5: Example of stereographic analysis of structure-controlled failures (Wyllie and Mah, 2004) 2.3.2 Limit equilibrium analysis  A more advanced option is limit equilibrium analysis. Limit equilibrium analysis calculates the factor of safety (FOS) by comparing resisting forces to driving forces. Many of the limit equilibrium packages have the ability to consider 2D and 3D geometries, and to incorporate pore water pressure and external loading into the analysis. An example of limit equilibrium analysis for 2D plane failure is shown in Figure 6 below.   Figure 6: Example of limit equilibrium analysis of plane failure (Wyllie and Mah, 2004). W represents the weight of the block, U and V are forces related to pore pressure, H is the height of slope, b is the distance of tension crack from the crest, and Zw is the depth of water in the tension crack.  15  2.3.3 SiroModel block model analysis  SiroModel (CSIRO, 2017), also known as Open Pit Simulator (OPS) was originally developed for the slope stability analysis in the large open pit mine. The model incorporates DFN generator and allows a batch of simulations using Monte Carlo analysis.  Block model analysis in SiroModel utilizes a polyhedral modelling where vertices, edges and therefore the faces formed from the intersections of finite-persistence fractures are defined. Subsequently, the rock blocks formed from these faces can be computed. The generation of rock blocks using this method is not limited by the number of faces and shapes. The polyhedral modelling algorithm incorporated into SiroModel has been documented in Elmouttie et al. (2010).  The stability analysis of defined rock blocks is performed using a limit equilibrium analysis. The rock block geometry is analyzed using Warburton vector analysis (Warburton, 1981) to determine if the block is removable. The surface conditions are then considered to categorize the rock blocks according to Goodman and Shi (1985) classification scheme (Type 1: Stable, Type 2: Unstable with friction, Type 3: Unstable with no friction). 2.3.4 FracMan rock wedge analysis With specific reference to the proprietary DFN code used as part of this research (FracMan, Golder Associates 2017), the two types of block search algorithm available are an implicit block search algorithm (block size analysis) and an explicit block search algorithm (rock wedge analysis).  Block size analysis looks for all the blocks within a defined DFN model. It works by mapping the fractures on the grid cells overlaid on the DFN model. The block volume is then determined by assembling the connected grid cells (Elmo et al., 2014b).  In contrast, rock wedge analysis searches for the blocks formed from intersecting fractures and a given free surface. This approach is more appropriate for kinematic stability analysis on slopes and roads tunnel. A detailed algorithm can be found in Dershowitz and Carvalho (1996). A rock wedge analysis starts with the generation of a tracemap of fractures on a given free surface, then 2D closed blocks are identified in the tracemap. This process is repeated until all fractures participate in one or more blocks. The identified 2D blocks are then processed with “unfolding algorithm” to generate the minimum volume polyhedron. In this process, the generated polyhedrons are ensured to be closed.  The stability analysis in rock wedge analysis is based on limit equilibrium assumptions. The first step is to identify the force vectors acting on the wedge. This includes weight of the wedge, bolt force, seismic force etc. The resultant active and passive force vectors are calculated. The next step is the determination of the 16  sliding direction of the wedge. Subsequently, the determined sliding direction is used for the calculation of the normal forces on each plane, and the resisting forces due to the assumed fracture shear strength. Lastly, the stability of the wedge is assessed by comparing driving and resisting forces. The wedges are categorized following the scheme shown below in Table 2. FracMan has a post-processing option to visualize the composite blocks. This option allows contiguous blocks to be treated as a single block volume.  Table 2: Classification of blocks in rock wedge analysis option in FracMan FOS Category FOS=100 Kinematically Inadmissible blocks FOS>1 Stable Blocks FOS<1 Unstable Blocks FOS=0 Free Fall Blocks  2.3.5 Discrete element methods  Discrete element modelling codes such as Universal distinct element code (UDEC) and 3DEC (Itasca, 2014) have been extensively applied to slope stability analysis. UDEC can model in two-dimension and 3DEC in three-dimension. These programs allow discretization of rock mass into joint-bounded blocks and can simulate the movement of blocks along discontinuities. The programs also allow simulation of brittle fracturing of intact rock using methods such as Voronoi and Trigon tessellation (Gao and Stead, 2014).  It is increasingly becoming a common practice to use DFN models in combination with UDEC/3DEC. DFN models can also be incorporated within a Voronoi or Trigon mesh to simulate rock slope failure involving rock bridges. However, it is important to note that careful calibration is required to define the contact properties of Voronoi or Trigon. The size of the mesh needs to be chosen with caution as this may affect the kinematics of movement.  In the context of kinematic slope stability analysis, DEM offers the opportunity to identify the blocks formed from the interesting discontinuities within the rock mass (Kim et al., 2007). However, not all fractures can be modelled as non-persistent joints in 3DEC. At least one of the fracture set has to be persistent throughout the volume, and other fracture have to be terminated against each other.  2.3.6 Comparison between DFN rock wedge analysis and limit equilibrium/stereographic analysis  Although the use of DFN models has been increasing, limit equilibrium analysis and stereographic analysis remain the mainstream tool for kinematic stability analysis.  The major advantage of limit equilibrium and stereographic analysis is the ease to use. The software packages of limit equilibrium and stereographic analysis do not require heavy computational power, and 17  the analysis results can be obtained instantaneously. The packages are also easy to learn compared to DFN, which requires extensive knowledge of fracture mechanics to generate a model. The whole process of analysis is quick, as there is no need to build a complex model. However, there are some issues in limit equilibrium/stereographic analysis, which can be overcome by the use of DFN modeling approach.  One of the limitations of limit equilibrium analysis is the assumption of infinitely continuous fractures. This assumption does not allow consideration of rock bridges and may result in less conservative design (Rogers et al., 2007). Some of the packages allow inclusion of rock bridges, but the amount of rock bridges needs to be defined by users. Also, limit equilibrium analysis does not consider fractures locations. For example, it is common to test all possible combination of fractures for the wedge failure in limit equilibrium analysis and stereographic analysis, even though the fractures are not intersecting, or the intersection line is not daylighting. The other limitation is its incapability of modelling complex failure mode. Most of the packages do not have ability to model blocks formed by more than two fractures, in addition to the excavation free surface (Rogers et al., 2006).  In contrast, rock wedge analysis using DFN methods has ability to generate blocks that are more realistic. For instance, this approach can indirectly incorporate rock bridges into the model as a function of fracture size. Also, the approach makes no limitations on the number of fractures forming the blocks or the failure mode. Thus, failures involving complex geometries can be modelled. An example is illustrated in Figure 7. In fully stochastic DFN model, the location of the potentially unstable blocks should be treated in a probabilistic manner.    Figure 7: Comparison of limit equilibrium analysis (left) and DFN modeling approach (right) 18  2.4 Geological Strength Index (GSI) This section is dedicated to review current methods of estimation and quantification of GSI. A review of In-situ Block Size Distribution (IBSD), which is closely correlated to kinematic slope stability analysis and rock mass blockiness is also presented.    GSI is a qualitative assessment of rock mass quality, developed to assist in the use of Hoek-Brown criterion (Hoek and Brown, 1980; Hoek et al., 2002). Since 1970s, with the increasing use of numerical modelling for rock engineering design, researchers started to recognize the need of estimating rock mass properties from intact rock properties and discontinuity properties. This led to the development of a failure criterion for rock mass, “Hoek-Brown failure criterion” by Hoek and Brown (Marinos et al. 2005). GSI (Hoek et al., 1995) was developed in response to the need of classification system for rock mass that could be easily applied to the failure criterion from the field observation. The main assumption of the GSI is that the deformation and peak strength of rock mass is controlled by rotation and sliding of rock blocks defined by intersecting discontinuities. Therefore, this assumption requires rock mass to be homogeneous and isotropic in order for GSI to be applied.  2.4.1 Estimation of GSI in the field  GSI classifies a rock mass based on two descriptive parameters; joint condition and blockiness of the rock mass (Figure 8). The downward direction of the vertical axis represents decreasing interlocking of rock pieces. The qualitative description of the degree of blockiness ranges from massive or intact, blocky, very blocky, disturbed, disintegrated to laminated rock mass. The horizontal axis represents decreasing surface quality towards right. This is expressed as very good, good, fair, and poor to very poor.   19   Figure 8: GSI chart (Marinos and Hoek, 2000)  The blockiness parameter in GSI is estimated by considering the intersections that the fractures produce with rock exposures (e.g. rock outcrops, excavated slope or tunnel faces). GSI estimated using 1D data (boreholes) may be questionable due to the lack of consideration for fracture length. Some examples of rock mass exposures used for blockiness estimation are shown in Figure 9.  20    Figure 9:  Examples of excavated slopes and natural outcrops 2.4.2 Quantification of GSI  The estimation of GSI requires careful description of engineering geology of rock mass, including lithology, structure and condition of discontinuity surfaces (Marinos et al., 2007). Although GSI has been proven to work well when used by experienced geologists or engineering geologists, assigning GSI value could be a difficult task when the user is not familiar with qualitative assessment of geological conditions. To overcome this issue, several attempts were made in the past to “quantify” the GSI.  Sonmez and Ulusay (1999) proposed Surface Condition Rating (SCR) and Surface Rating (SR) to express surface condition of discontinuity and blockiness of the rock mass, respectively. SCR is expressed as the sum of RMR 89 rating (Bieniawski, 1989) for roughness, weathering and infilling. SR is a scale from 0 to 100 based on volumetric joint count (Jv) (Figure 10). Jv is defined as a measure of the degree of jointing or the inter block size (Palmstron, 2005). The range of Jv and corresponding descriptions of blockiness were adopted from ISRM suggested methods of rock characterization (ISRM, 1981)  21    Figure 10: Determination of SR from Jv (Sonmez and Ulusay, 1999) Cai et al. (2004) expressed the blockiness parameter in GSI as a function of equivalent block volume and surface condition of discontinuities as joint condition factor (Jc). Equivalent block volume can be obtained from spacing (𝑆𝑆𝑖𝑖) and angle between the fracture sets (𝛾𝛾𝑖𝑖) and joint persistence factor (𝑝𝑝1) using Equation (3). Joint persistence factor represents a degree of interlocking of rock pieces and expressed as Equation (4) where L represents characteristic length of rock mass, and 𝑙𝑙𝚤𝚤� refers to the accumulated length of Set 𝑖𝑖 on a sampling plane. These equations account for the observation that the shorter fractures have insignificant influences on block formations compared to persistent fractures. Cai et al. (2004) demonstrated that if the joints are only 20 % of the reference length, the apparent block is five times larger than the block formed by persistent fractures. Joint condition factor accounts for joint roughness, alteration and infill. The proposed GSI chart is reproduced in Figure 11.                                                                        𝑉𝑉𝑏𝑏 = 𝑆𝑆1𝑆𝑆2𝑆𝑆3�𝑝𝑝1𝑝𝑝2𝑝𝑝33 𝑠𝑠𝑖𝑖𝑠𝑠𝛾𝛾1𝑠𝑠𝑖𝑖𝑠𝑠𝛾𝛾2𝑠𝑠𝑖𝑖𝑠𝑠𝛾𝛾3                                                                   (3)                                                                                                                                                   (4)           Russo (2007, 2009) recognized that the correlation factor between intact rock and rock mass can be described by the joint parameter (JP) in Rock mass index (RMi) system (Palmstrøm, 1996) and by constants s and a in Hoek-Brown failure criterion. The authors then derived the correlation between the GSI and JP.   22  Hoek et al. (2013) proposed the quantification of discontinuity surface conditions and blockiness of the rock mass by joint condition rating from RMR 89 (Bieniawski, 1989) and Rock Quality Designation (RQD) defined by Deere (1963), respectively (Figure 11). The relation is expressed as following;                                                                    𝐺𝐺𝑆𝑆𝐺𝐺 = 1.5𝐽𝐽𝐶𝐶𝐽𝐽𝐽𝐽𝐽𝐽89 + 𝑅𝑅𝑅𝑅𝑅𝑅2                                                                     (5)     Figure 11: Quantification of GSI. Cai et al. (2004): left, Hoek et al. (2013): right  2.4.3 In-Situ Block Size Distribution (IBSD) IBSD has been an important aspect of civil and mining rock engineering design where block forming potential of rock mass is of interest. IBSD is defined as the range of sizes of blocks formed by the intersecting discontinuities. The formation of blocks in naturally fractured rock mass is a function of discontinuity properties such as persistence, spacing, and frequency. Several modelling techniques were developed in the literature to characterize IBSD of rock mass. For example, Wang et al. (2003) developed a software which predicts IBSD through random sampling of discontinuities from database and considering the persistence of fractures indirectly from the spacing. Kim et al. (2007) presented the method to predict 23  the volumes of blocks formed by non-persistent discontinuities using polyhedral modeler tool available in discrete element code UDEC and 3DEC.  The previous attempts to predict IBSD using a DFN approach include the work by Rogers et al. (2007), Elmouttie and Poropat (2012) and Kim et al. (2015). Rogers et al. (2007) employed a rock wedge analysis option in FracMan using horizontal surface as a sampling plane to estimate the block volumes. The results demonstrated that the rock mass is dominated by a super block (the block with the block volume almost equivalent to the rock mass) for rock masses with high intensity of low-persistent fractures. This supports the observation by Cai et al. (2004) that apparent block volume is larger for rock masses with non-persistent joints. Elmouttie and Poropat (2012) used a combination of realistic DFN model, polyhedral modelling and Monte-Carlo simulation to predict IBSD of rock mass. Their results demonstrated that previous methods of IBSD prediction (Wang et al., 2003; Kim et al., 2007) overestimate the fragmentation of rock mass, especially for the rock masses with relatively small fracture size. Kim et al. (2015) used stochastically simulated DFN models in combination with 3D discrete element code to predict IBSD.  In their approach, the method proposed by Kim et al. (2007) was incorporated to obtain volume of all blocks formed from intersecting discontinuities within the DFN model. However, this method requires at least one of the fracture sets to be fully persistent through the domain, and other fracture sets need to be terminated against the fractures. This is incorporated in Kim et al. (2015) work by making the fracture size large enough to be fully persistent through sample domain. In this process, the size of the domain was adjusted so that the fracture intensity of the model is constrained to the field data collected from boreholes. In Chapter 6 of this thesis, the IBSD is also obtained from DFN model, but the model is generated with data collected from surface mapping; therefore, involving realistic consideration for fracture length. Also, the approach in Kim et al. (2015) considers all blocks within the model to generate IBSD while this thesis considers the blocks formed on 2D free-surface to produce IBSD.          24  Chapter 3 DFN Model Generation and Validation  3.1 Introduction  The first step of any analysis involving DFN methods is the generation and validation of DFN model. This is an important step to ensure that the DFN model is capturing the reality with reasonable accuracy in terms of both statistical analysis and geological characterization. This Chapter presents the generation and validation processes of DFN models for four case studies that will be used for specific analyses in the following Chapters. Only the DFN models using disaggregate approach are presented in this Chapter as aggregate models use subsets or averaged data generated for the disaggregate model. Table 3 summarizes the information of four case studies. Based on the industry practice, 5 to 10 realizations are typically used (Elmo, 2018 personal communication).   Table 3: Summary of case studies ID Name Location Mapping Method Analysis 1 Open pit mine model Sandstone mine in British Columbia Scanline Chapter 4 2 Brunswick model Andesitic rock outcrop along Highway 99 in British Columbia, Canada Scanline Chapter 5 3 Mountain model Location cannot be disclosed for confidentiality reasons Scanline & Photogrammetry Chapter 4 Chapter 5 Chapter 6 4 Middleton mine model Room and pillar mining operation in bedded limestone in Derbyshire, UK Scanline & Window Chapter 6  3.2 Case Study 1: Open pit mine model  The DFN model for this case Study is generated using field data collected along the slopes of a sandstone open pit mine located in British Columbia, Canada.  The name and location of the mine cannot be disclosed for confidentiality reasons. Field mapping was undertaken using scanline methods. The traverse length of the scanline is 100 m with azimuth of 340°.  3.2.1 DFN model generation  A total of five fracture sets were identified, together with their primary fracture properties (Table 4). The orientations of each fracture sets are shown (Figure 12). In addition to the five fracture sets, two faults were modelled deterministically as continuous fractures. The intensity of each fracture sets is modelled using the P10 conditioning based on the number of fractures measured along the scanline for each set. Although there is a difference in the distribution type, the mean trace lengths are in the range of 2 – 3 m for all sets. The 25  fracture sets were stochastically generated within a volume with dimensions of 100 m × 100 m × 25 m. An example of a DFN models generated for the slope under the consideration is shown in Figure 13.  Table 4: Input parameters for the Open pit mine model Fracture set # 1 2 3 4 5 Spatial model Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Orientation Bootstrap Bootstrap Bootstrap Bootstrap Bootstrap P10 (m-1) 0.1 0.19 0.1 0.34 0.17 Fracture Size Distribution Exponential  Log Normal Exponential Exponential Log Normal Mean (m) 9.6 8 8.7 7.94 7.24 S.D. 2.1 2.4 2.1 2.8 3.0  Figure 12: Stereonet plots of the orientation for the Open pit mine model (raw data)  Figure 13: Selected example of the DFN model for the Open pit mine case study 26  3.2.2 Model validation  For 1D mapping, model validation is performed by comparing intensity, orientation and trace length (if available) between mapped and simulated fractures along a simulated scanline in the model. However, only fracture orientation and trace length can be compared in this case because fracture intensity was conditioned to the mapped intensity along the scanline, and therefore the assumed P10 intensity is directly constrained to field data. Figure 14 shows the comparison of stereonet plots between mapped orientations along the scanline, modelled orientations along the scanline, and modelled orientations of all generated fractures. Although there is a difference in the spread of pole orientations, the overall similarity of the clusters locations is considered satisfactory.   Figure 14:  Comparison of stereonet plots of the Open pit mine model between mapped orientations (left), simulated orientations (middle), simulated orientations of all fractures in the model (right) The validation of DFN is also performed by comparing the mapped and simulated trace length (Figure 15). The simulated trace length is truncated at the minimum trace length mapped in the field for comparison purpose. The cumulative density function (CDF) plots of mapped trace length is derived from scanline data while the distribution of simulated trace length is derived from the 2D slope face. As shown in Figure 15, the simulated model contains a larger percentage of persistent fractures. For instance, the fracture with trace length above 12 m is 10 % for mapped fractures and 40 % for simulated fractures. This can be explained by the limitation of using 1D method to collect fracture length data. When collecting trace length data using scanline, only the fractures intersecting the scanline are mapped; therefore, the derived CDF plots of trace length may not be truly representative of field condition. Also, the mapped trace length is subjective to censoring biases due to the limited height of rock exposure. This may limit the accurate measurement of persistent fractures, resulted in lower percentage of large trace length for mapped fractures.  27   Figure 15: Comparison between the mapped and simulated trace length (Case Study 1) 3.3 Case Study 2: Brunswick model  Brunswick model is a small-scale DFN model generated from the data collected at Brunswick Prospect Point in the Southern Coast Mountains in British Columbia. The study area is located along the Sea to Sky Highway (Highway 99), approximately 10 km north of Brunswick beach, British Columbia, Canada. The geology consists of a heavily jointed andesitic rock mass associated with a coastal plutonic complex intruded between 140 and 90 million years ago (Armstrong, 1990). The rock outcrop is approximately 50 m-wide and 20 m-high (Figure 16). During the construction of the highway between 1959 and 1966, the outcrop had been blasted with explosives, which resulted in heavy blasting damage of the rock mass. The characterization of blasting damage on the rock outcrop was previously studied by Lupogo (2016).  The google map image showing the location of scanline mapping can be found in Figure 16. Scanline mapping was performed at two locations on the west face of the outcrop, each with the traverse length of approximately 10 m. The scanlines were placed horizontally on the outcrop with the azimuth of 114˚ and 116˚. Primary fracture properties as well as other basic fracture properties (joint roughness coefficient (JRC), shape and joint condition) were collected.  3.3.1 Model generation  Two continuous local faults and two fracture sets were identified based on field mapping. The stereonet plot showing the orientations of the fracture sets is shown in Figure 17. Set 1 is shallow dipping towards the West with mean dip/dip direction of 35˚/272˚. Set 2 is a NW-SE steeply dipping set with a mean dip/dip direction of 73˚/341˚. This set slightly rotates dip direction over the length of the scanline.  28             Figure 16:  Scanline mapping on the rock outcrop at Brunswick Prospect Point (left) and Google map image of the study area (right)  Figure 17: Stereonet plot of fractures for the Brusnwick model (raw data) The input parameters for the Brunswick DFN model are summarized in Table 5. The intensity of the fractures is modelled using P10 conditioning, therefore the fractures count along the scanline in the model matches the one for the mapped fractures. Two local faults were deterministically modelled as continuous fractures. The fractures are generated within a volume with the dimensions of 20 m × 20 m × 10 m, and an example is shown in Figure 18.   29  Table 5: Input parameter for the Brunswick DFN model Fracture set # 1 2 Spatial model Enhanced Baecher Enhanced Baecher Orientation Bootstrap Bootstrap P10 (m-1) 1.45 0.35 Fracture Size Distribution Log Normal Log Normal Mean (m) 4.03 2.47 S.D. 1.90 1.12   Figure 18: Selected example of the DFN model for the Brunswick case study 3.3.2 Model validation  Similar to Case Study 1, model validation is performed by comparing the orientation of the fractures along the sampling line and the trace length distribution. Figure 19 shows the comparison of the stereonet plot of mapped orientations along the scanline, simulated orientations along the scanline, and simulated orientations of all fractures in the model. Pole clusters are observed at the same locations in all stereonet plots, which suggests that the mapped fracture orientations are correctly reflected in the model. However, it is important to note that the verification for this DFN model is limited due to the amounts of collected data, and further verification may be required.  30   Figure 19: Comparison of stereonet plots of the Brunswick model between actual orientations (left), simulated orientations (middle), simulated orientations of all fractures in the model (right) The comparison between the mapped and simulated trace length is shown in Figure 20. The difference could be explained taking into consideration the series of 4.5 m long fractures mapped in the field as part of a closely set of parallel fractures.  Also, the same biases as Case Study 1 has been introduced by using scanline method to collect trace length data, resulted in lower percentage of mapped fractures with high persistence.   Figure 20: Comparison between the mapped and simulated trace length (Case Study 2)  31  3.4 Case Study 3: Mountain model    The so-called Mountain DFN model was based on data collected from a large-scale slope, whose location cannot be disclosed for confidentiality reasons. An extensive field mapping program was undertaken to collect fracture properties for more than one thousand fractures. Field mapping consisted of vertical scanline mapping and areal mapping using photogrammetry; the latter was used to obtain fracture length data. Further details about the data collection process, DFN model generation and validation are documented in Schlotfeldt et al. (2017). This Section presents the primary fracture properties used as input parameters for the generation of the DFN model.  A total of five fracture sets were identified, denoted as J0, J1, J2, J3 and J4 (Table 6). The orientations of fracture sets are shown in Figure 21. All fracture sets follow a similar fracture length distribution except J0, which is more persistent. The fracture radius distribution was initially assumed to be equivalent to the trace length distribution, and then adjusted by the process of simulation. The resulting simulated trace length distributions are in good agreement with mapped trace length distribution (Schlotfeldt et al., 2017). The P32 intensity is used to define the intensity of the stochastic fractures. A selected realization of the resulting DFN model is shown in Figure 22.  Figure 21: Stereonet plots of fracture orientation of the Mountain model. Mapped data (left) and simulated orientations (right) (Schlotfeldt et al., 2017)     32  Table 6: Input parameters for the Mountain DFN model Fracture set # J0 J1 J2 J3 J4 Spatial model Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Orientation Bootstrap Bootstrap Bootstrap Bootstrap Bootstrap P32 (m-1) 0.36 0.40 0.43 0.71 0.28 Fracture Size Distribution Negative Exponential Negative Exponential Negative Exponential Negative Exponential Negative Exponential Mean (m) 7.50 1.62 1.87 1.61 1.62   Figure 22: Example of DFN realizations for the Mountain model (figure on the right shows the simulated traces equivalent to the mapped exposure) 3.5 Case Study 4: Middleton mine model  The data used for this model were collected at Middleton mine in Derbyshire, UK. Middleton mine is a room and pillar mining operation in bedded limestone. Scanline mapping program was completed on four faces of the pillar (denoted as Panel 1 to 4), each of them is 7 m-high and 14 m-wide. Additionally, a detailed window mapping program was performed at the base of the pillar faces. The faces are oriented approximately perpendicular to each other (Figure 23). The detail of the data collection is documented in Elmo (2006). A revised version of the DFN model initially build by Elmo (2006) is presented in this Section.  Despite the data being collected from underground mine, the data analysis is applicable for both surface and underground engineering problems.  33   Figure 23: Location of mapped pillar faces (modified from Elmo (2006)) 3.5.1 Model generation  For simplicity, the pillar region in the DFN model was oriented along the X-Y axes. To account for the local orientation of the pillars in the field, the mapped data set was rotated counter-clock wise. A total of six fracture sets were identified. The orientations of fracture sets are shown in Figure 24. Despite not being included in Figure 24, mapped bedding planes (forming a continuous, shallow dipping set) were later added to the DFN model.   An Enhanced Baecher model was selected as a spatial model governing the location and orientation distribution of the fractures. This was justified considering the mapped negative exponential distribution of fracture (Elmo, 2006).   Figure 24: Simulated fracture orientations for the Middleton model 34  The fracture radius distribution was assumed to be equivalent to the distribution of the mapped trace lengths, and the parameters of the radius distribution were adjusted in an iterative process until a good match was obtained with the field data.  A minimum cut-off of 0.25 m is used for the equivalent radius distribution, since no fractures less than 0.5 m long were mapped in the field. The comparison between the mapped and simulated trace length is shown in Figure 25. There is some discrepancy between the mapped and simulated trace length data for Set 1a. Set 1 was subdivided in Set 1a and Set 1b based on the bimodal distribution of mapped trace length for the combined data. However, field mapping of the longer fractures belong to combined Set 1 was carried out by remote estimation, and outside of the mapped windows only the longer fractures could be visually traced.  The P32 intensity used in the model was determined from the mapped P21 intensity by simulation. It should be noted that the process is performed using different sampling panels for each set depending on the relative mean orientation of the fracture set with respect to the orientation of the sampling panel. For example, a fracture set dipping parallel to the strike of the sampling plane would be under-sampled due to orientation bias. In this case, other sampling planes (preferably the sampling plane striking perpendicular to the dip direction of the fracture set) should be used for simulation.         35     Figure 25: Comparison of simulated trace length and mapped trace length (Case Study 4) 36  The primary fracture properties are summarized in Table 7. Set 1a and 1b share very similar orientation, but they are distinguished by different size distribution. Set 3a and 3b are likely originated from same geological event as they share similar fracture length distribution, and oriented approximately orthogonal to each other. The generated model is shown in Figure 26. The model is first generated in a box with the dimension of 100 m × 100 m × 100 m and then cropped to a smaller box of 15 m × 15 m × 15 m to reduce boundary effects. The bedding planes are modelled as horizontal, persistent fractures with an average spacing of 3 m.  Table 7: Input parameters for the Middleton DFN model Fracture set # 1a 1b 2a 2b 3a 3b Spatial model Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Enhanced Baecher Orientation Bootstrap Bootstrap Bootstrap Bootstrap Bootstrap Bootstrap P32 (m-1) 0.78 0.63 0.64 0.46 0.35 0.26 Termination (%) 0.15 0.50 0.34 0.50 0.43 0.54 Fracture Size Distribution Log Normal Log Normal Log Normal Log Normal Log Normal Log Normal Mean (m) 8.17 2.46 4.48 4.06 2.59 3.32  S.D. (m) 1.11 1.65 1.82 1.65 1.92 2.23   Figure 26: Selected example of the DFN model for the Middleton mine case study 3.5.2 Model validation  Model validation is performed by comparing the orientation, intensity and size distribution of the mapped and simulated fractures. Since the fracture size distribution is already validated (i.e. constrained) during the DFN generation process, the validation is limited to comparing P21 intensities and trace maps. For instance, Figure 27 shows the comparison between the simulated P21 intensity the mapped P21 intensity.   37      Figure 27: Comparison of simulated P21 intensity and mapped P21 intensity (Case Study 4) 38  Although the simulated fracture intensities show a trend comparable with field data across the pillar faces, the actual simulated P21 values differ (though not significant) from the mapped P21 values. This could be interpreted as a good example in which data uncertainty (i.e. limited data) impacts data characterization and the ability to capture the true variability of the parameters being mapped.   The second step of model validation is the comparison of the mapped 2D tracemaps within the sampling region (14 m × 2 m window). Due to the stochastic nature of the DFN model the purpose is not to compare the location of every fracture, but rather to compare the overall spatial distribution of the fractures (Figure 28 and Figure 29).  Note that the simulated tracemaps were not filtered to exclude fractures shorter than 0.5m (field cut-off value). The results include 3 DFN realizations; qualitatively, it is possible to conclude that the modelling results are in good agreement with field observations.   Figure 28: Comparison between simulated and mapped tracemaps for Panel 1 and 2 39   Figure 29: Comparison between simulated and mapped tracemaps for Panel 3 and 4                40  Chapter 4 Influence of DFN Modelling Approach on Kinematic Stability Analysis  4.1 Introduction  This Chapter is dedicated to the study of how the data characterization process may influence the generation of a DFN model and the resulting analysis. In Chapter 3 all DFN models were generated using a disaggregate approach, in which the properties of each fracture set are independently defined. In this Chapter, the same DFN models are regenerated using an aggregate approach (no distinction between fracture sets), and the resulting models are then compared using kinematic stability analysis tools and measurements of rock mass fragmentation. Two case studies form Chapter 3 are considered in the analysis: i) Case Study 1 (Open pit mine); and ii) Case Study 3 (Mountain model).   4.2 Influence on simulated intensity and orientations    The input parameters for the DFN models are compared between aggregate and disaggregate approach in terms of fracture intensity and fracture length distribution (Table 8 and Table 9).  Linear P10 intensity and volumetric P32 intensity are used for Case Study 1, and Case Study 3 respectively due to the difference in the data collection methods. The total fracture intensity using a disaggregate approach is less than the aggregate approach in both case studies. This is because the random fractures that do not belong to any of the fracture sets are discarded in the disaggregate approach, as these fractures are assumed to not significantly influence slope stability.  As shown in Table 8, the mean fracture lengths among the sets in disaggregate approach are similar in Case Study 1. Essentially, the difference between the mean fracture lengths between disaggregate approach and aggregate approach is minor. In contrast, Case Study 3 contains one set of persistent fractures (J0), while the rest of the fractures are relatively low persistence. This resulted in the mean fracture length in aggregate approach to be higher than most of the sets in disaggregate approach. Table 8: Comparison of input parameters between aggregate and disaggregate model (Case Study 1) Set # Disaggregate Aggregate Fracture Size (Mean (m) /S.D. (m)) P10 (m-1) Fracture Size (Mean (m) /S.D. (m)) P10 (m-1) 1 Negative Exponential (9.6/2.1) 0.1 Log Normal (7.9 / 2.6) 1 2 Log Normal (8/2.4) 0.19 3 Negative Exponential (8.7/2.1) 0.1 4 Negative Exponential (7.9/2.8) 0.34 5 Log Normal (7.2/3.0) 0.17   41  Table 9:  Comparison of input parameters between aggregate and disaggregate model (Case Study 3) Set # Disaggregate Aggregate Fracture Size (Mean (m)) P32 (m-1) Fracture Size (Mean (m)) P32 (m-1) 0 Negative Exponential (7.50) 0.36 Negative Exponential (3.00) 2.19 1 Negative Exponential (1.62) 0.40 2 Negative Exponential (1.87) 0.43 3 Negative Exponential (1.61) 0.71 4 Negative Exponential (1.62) 0.28  The difference in fracture lengths becomes of particular importance when comparing the simulated intensity of the DFN models between aggregate and disaggregate approach (Figure 30 and Figure 31). For Case Study 1, the intensity by set are also compared quantitatively between the approaches (Table 10). The intensity by set in aggregate approach is estimated from the stereonet plot by counting the fracture poles that fall within the range of orientations of the set defined in disaggregate approach. The minimum, maximum, and average of the P10 intensity are obtained from five realizations. The P10 intensity in disaggregate approach is conditioned along scanline and is equivalent to target intensity.  The quantitative measurement of P10 intensity, combined with the qualitative comparison of stereonet plots in Case Study 1 indicate differences in simulated fracture intensity for particular sets. The intensity of Sets 1 and 3 generated using aggregate approach are considerably lower than the target intensity. In contrast, the fracture intensity of Set 5 in aggregate approach is more than double the target intensity. One of the reasons of this could be orientation bias due to the relative orientation of scanline with respect to the orientation of fracture sets. A dashed line in Figure 30 represents scanline orientation. Sets 1 and 3, which resulted in lower intensity in aggregate approach, are oriented parallel to the sampling line (i.e. strike of the sets is parallel to the trend of sampling plane). In contrast, Set 5, which resulted in higher intensity in aggregate approach, is oriented perpendicular to the sampling line (i.e. strike of the set is perpendicular to the trend of sampling line). As discussed in Section 2.2.1, fractures are sampled at the highest frequency when oriented perpendicular to sampling line, and it is possible that same bias is introduced when bootstrapping the orientations using aggregate approach.  42   Figure 30: Comparison of simulated orientations (Case Study 1)  Figure 31:  Comparison of simulated orientations (Case Study 3) Table 10: Comparison of P10 intensity between aggregate and disaggregate approach (Case Study 1)  Aggregate Disaggregate (Target Intensity) Set # Average P10 Min P10 Max P10 1 0.02 0 0.04 0.10 2 0.17 0.11 0.22 0.19 3 0.04 0.01 0.05 0.10 4 0.29 0.24 0.31 0.34 5 0.43 0.41 0.46 0.17 43  The difference in the stereonet plots between two approaches is more obvious in Case Study 3. It is clear that J0 resulted in a higher intensity using an aggregate approach while the intensity of the other sets was underestimated. This is most likely originated from the difference in fracture length among the sets.  Unlike Case Study 1, where simulated intensity is defined by P10 intensity, Case Study 3uses P32 intensity. While P10 intensity is directly related to the number of poles on the stereonet plots, P32 intensity is defined by the combination of number of fractures and the persistence of fractures. For example, in disaggregate approach, J0 and J1 have similar intensity and orientations but very different fracture lengths (Table 9). J0, which is more persistent set, achieves similar intensity as J1 by having less number of fractures. In contrast, J1 achieves similar intensity as J0 by having shorter, but more fractures.  However, an aggregate approach does not consider fracture length, intensity and orientation of individual fracture sets. The aggregate approach takes the stereonet plot of raw data, averaged fractured length, and total P32 intensity as input parameters. When generating a DFN model, aggregate approach achieves the specified fracture length distribution and total P32 intensity by adjusting the number of fractures. Therefore, when there is a variation in fracture length within a rock mass, aggregate approach tends to under-sample the shorter fracture sets and over-sample the longer fracture sets.   Another difference in the stereonet plot between aggregate and disaggregate approach is the amount of random fractures. In Case Study 1, there is a concentration of poles on the 80°-90° line on the west portion of the stereonet plot in aggregate approach. This concentration is not observed in disaggregate approach, indicating the concentration is populated from random fractures.  4.3 Influence on block forming potential  The block forming potential between the models are compared in terms of the number of blocks and Particle Size Distribution (PSD) plots of block volume obtained from the rock wedge analysis performed on slopes. Passing size of PSD is expressed as P#, where P stands for passing and # stands for the cumulative percentage. The number of blocks that fall within the defined range of block volume are counted to produce PSD curves. In order to account for the stochastic nature of the model, five realizations are generated for each approach.  In this section, the block forming potentials of the DFN models are compared between aggregate and disaggregate approach. The geometry and location of the slopes is shown in Figure 32. In Case Study 1, a slope is simulated with the same orientation as the mapped slope while two vertical planes opposite to each other are simulated in Case Study 3. The tracemap of fractures on the slope are compared between aggregate and disaggregate approach (Figure 33and Figure 34).  44  In Case Study 1 modelled using a disaggregate approach, 39 % of fractures have mean fracture length above 7.9 m. However, this is not captured in the model with aggregate approach using the log normal distribution with the mean fracture length of 7.9 m, resulted in lower number of persistent fractures, and subsequently a lower P21 intensity. This is also evident from the average CDF plots of equivalent length distribution showing that 10% of fractures are above 10 m in disaggregate approach in comparison to 5 % in aggregate approach (Figure 35). Another key observation is regarding fracture orientation. Figure 33 shows that the dominant fracture orientation in aggregate approach is a set of steeply dipping fractures (Set 5) while horizontal fractures are more dominant in disaggregate approach (Set 1 and 2). This is consistent with low intensity of fractures parallel to scanline orientation in aggregate approach as previously shown.   Figure 32: Location and geometry of the slopes used for rock wedge analysis in Case Study 1 (left) and Case Study 3 (right).  45   Figure 33: Comparison of tracemaps between aggregate and disaggregate approach (Case Study 1)  Figure 34: Comparison of tracemaps on the North wall between aggregate and disaggregate approach (Case Study 3) 46    Figure 35: CDF plots of equivalent radius of simulated fractures between aggregate and disaggregate approach (Case Study 1) In Case Study 3, P21 intensities for aggregate and disaggregate approach are very similar. The main difference between aggregate and disaggregate approach involves fracture length distribution. Fracture length is similar in any orientations in aggregate approach while in disaggregate approach, the persistence of fractures clearly depends on orientations.  The results of rock wedge analysis are shown in Figure 36, Figure 37, and Figure 38 for Case Study 1, Case Study 3 (North wall) and Case study 3 (South wall), respectively. The results include a visual example of block formations on the slope and PSD curves of block volume for aggregate and disaggregate approach. The number of blocks, and P50 and P90 of block volume are summarized in Table 11.  Figure 36 and Table 11 show that for Case Study 1 fewer but larger blocks are formed in aggregate. The differences in block forming potential between the aggregate and disaggregate approach can be explained as follows:  • As previously shown in Figure 28, Set 3, which forms critical wedges on the slope when combined with Set 4, is under-sampled in aggregate approach. This effectively reduced the number of blocks on the slope in aggregate approach.  • Disaggregate approach contains a larger number of persistent fractures compared to aggregate approach. The persistent fractures likely increased the block forming potential, resulted in more, but smaller blocks in disaggregate approach.  • High intensity of Sets 1 and 2 that are dipping out of the slope may be another factor of block formations in disaggregate approach. These fractures solely may not be a problem as long as fractures that act as lateral release do not exist in the rock mass. However, Sets 3 and 4 may have played a role as a lateral release in this case, forming a wedge when combined with Sets 1 and 2.   47       Figure 36: PSD curves for aggregate and disaggregate approach and the blocks formed on the slope (Case Study 1)      Figure 37: PSD curves for aggregate and disaggregate approach and the blocks formed on the North wall (Case Study 3) 48    Figure 38: PSD curves for aggregate and disaggregate approach and the blocks formed on the South wall (Case Study 3) Table 11: Quantitative comparison of number of blocks and block volume   Case Study 1 Case Study 3   South Wall North Wall   Aggregate Disaggregate Aggregate Disaggregate Aggregate Disaggregate Number of Blocks Total 594 1118 209 92 402 203 Stable 561 1091 205 89 386 187 Unstable 37 44 4 3 16 16 Block Volume P50 0.42 0.29 0.36 0.07 0.32 0.06 P90 9.30 6.13 9.43 2.69 8.55 2.17  The difference in block forming potential between aggregate and disaggregate approach can be more clearly observed in Case Study 3. In this case, aggregate approach results in more, and larger blocks because of the high block forming potential due to the averaged fracture lengths (~3 m). In contrast, block formation is more difficult in disaggregate approach due to high intensity of low-persistent fractures (<2 m). This suggests the importance of considering the difference in fracture lengths exists among the sets.  4.4 Chapter summary  The influence of the selection of approaches on the kinematic stability analysis was examined in terms of simulated intensity and orientations, and the block forming potential.  The comparison of the simulated orientations and intensity between the approaches demonstrated that an orientation bias might be introduced when applying aggregate approach in combination with bootstrapping from the 1D sampling data. When this bias is introduced, fracture sets parallel to the sampling line are under-sampled and fracture sets perpendicular to the sampling line are over-sampled.  49  Case Study 3 demonstrated the risk of treating all fractures as a single set in terms of fracture lengths. The variation of fracture length among different sets would not be captured in aggregate approach. By applying the same fracture length distribution to all sets, the sets with persistent fractures are under-sampled, and the sets with low-persistent fractures are over-sampled.  Lastly, the influence of the selection of approach on the block forming potential is closely related to the simulated fracture length and orientation of fractures. Although different trends were observed between case studies, it is clear that the number and size of blocks are significantly influenced by whether the aggregate or disaggregate approach is used.                  50  Chapter 5 Kinematic Stability Analysis using a Conditioned DFN model  This Chapter presents another aspect of data characterization process, which is also a fundamental question in DFN modelling that is: which discontinuities should be treated deterministically: which ones should be treated stochastically? To answer this question, the study considers conditioned DFN models which incorporates tracemaps obtained from field mapping. The author believes that in the context of kinematic slope stability analysis using DFN modeling, large-scale fractures (e.g. faults and very persistent fractures, longer than 20 meters according to ISRM definition) that are likely to impact the stability of the slope should be modelled deterministically, while low to high persistent fractures (persistence less than 20 m) should be modelled stochastically.   As discussed in Section 2.2.1, recent developments in remote sensing techniques (LiDAR and photogrammetry) have improved the efficiency of fracture data collection drastically. With these techniques, it is now possible to map all fractures within the sampling area deterministically (the truncation value would depend on the LiDAR and photogrammetry resolution, but mapping could potentially include low to high persistent fractures). This means that mapping methods no longer limits the way fractures are treated, but it rather depends on users to decide which fractures should be incorporated into the model stochastically or deterministically.  In this context, the purpose of this chapter is twofold:  • To examine the methodology for the generation of conditioned DFN model, and;  • To examine the influence of deterministic fractures (that incorporated into conditioned DFN model) on kinematic slope stability analysis.  Two case studies are considered in this Chapter: Case Study 2, Brunswick model and Case Study3, Mountain model. Case Study 2 is used as a preliminary analysis to examine the methodology of generating a conditioned DFN model. The lessons learned from Case Study 2 are then applied to Case Study 3 to assess the influence of deterministic fractures on kinematic slope stability analysis.  5.1 Preliminary analysis  Preliminary analysis is performed with Case Study 2: Brunswick DFN model. Brunswick conditioned DFN models are generated from the scanline data. This is then compared with unconditioned DFN model in terms of kinematic stability analysis. Only DFN models generated with a disaggregate approach are considered in this Section.   51  5.1.1 Methodology  The generation of the Brunswick conditioned DFN model consists of fours steps: 1. Generate unconditioned DFN model using disaggregate approach; 2. Remove the stochastic fractures that are 1) intersecting the scanline and 2) in the range of trace length mapped in the field; 3. Import tracemap obtained from scanline mapping, and; 4. Re-generate stochastic fractures from the tracemap, assuming the trace length on the tracemap corresponds to the equivalent diameter of simulated fracture.  The conditioned DFN models are validated by visually comparing the tracemap of re-generated stochastic fractures to the mapped tracemap.  P21 intensities for both conditioned and unconditioned DFN model are compared to ensure consistency in fracture intensity between the two.  Once the conditioned DFN models are validated, a comparison is made in terms of kinematic slope stability analysis. Ten realizations are generated for both conditioned and unconditioned DFN models. The number, size and location of blocks are compared between conditioned and unconditioned DFN model.  5.1.2 Generation and validation of conditioned DFN model   The generation process of conditioned DFN model is illustrated in Figure 39, where each model corresponds to the 4 steps described above. In Step 2, the pink-colored fractures represent all stochastic fractures intersecting the scanline. The fractures with a size equivalent to the mapped trace lengths are removed and substituted with determinist fractures mapped in the field (as shown in red color in Step 4).   Figure 39: Generation of the Brunswick conditioned DFN model 52  The validation of the conditioned DFN model is performed by comparing the tracemap of re-generated stochastic fractures and the mapped tracemap, as shown in Figure 40. Although the algorithm had difficulty simulating the fractures at exact same locations especially for the closely-spaced fractures, the overall similarity is considered satisfactory.   Figure 40: Comparison of mapped and re-generated fractures for the Brunswick DFN model  The tracemap of all fractures on the slope are also compared between conditioned and unconditioned DFN model (Figure 41). Although the fractures look highly concentrated in conditioned DFN model due to the closely-spaced fractures, average P21 intensity of conditioned model is measured to be 1.49 and in good agreement with P21 intensity of the unconditioned model, that is 1.38.   Figure 41: Comparison of tracemaps between unconditioned and conditioned Brunswick DFN model 5.1.3 Kinematic slope stability analysis  The results of rock wedge analysis are compared in terms of location, number, and size of blocks. Table 12 summarizes the number of blocks and P50/P90 passing size. Generally, the conditioned models resulted in slightly higher number of blocks with smaller P50/P90 passing size. However, it is argued that the difference is minor, and beyond the statistical uncertainty of the model.  Table 12: Comparison of number and size of blocks between unconditioned and conditioned Brunswick DFN model  Total No. of blocks P50 (m3) P90 (m3) Conditioned 41 0.069 1.6 Unconditioned 38 0.084 1.7  53  In the context of kinematic slope stability analysis, DFN models are typically not used to locate blocks formed on the slope, but rather used to obtain statistical information of the size, factor of safety, and number of blocks. This is simply because the geometry of fractures is different for each realization, thus the location of blocks. However, in conditioned DFN model, the geometry of fractures intersecting the slope is similar across realizations due to the incorporation of deterministic fractures. Therefore, the locations of blocks are compared to assess the impact of deterministic fractures on the distribution of blocks on the slope.  Figure 42 shows the visual examples of blocks formed on the slope in conditioned and unconditioned DFN model. Regardless of the efforts of conditioning, the locations of blocks remain consistent in both unconditioned and conditioned DFN models. This means that the incorporation of deterministic fractures in the DFN model does not have significant impact on the block formations. However, it is noticed that the blocks are formed at similar locations across different realizations, which may suggest the ability of stochastic DFN model to better account for blocks locations.   Figure 42: Comparison of block locations between unconditioned and conditioned Brunswick DFN model  54  5.1.4 Discussion and conclusions (preliminary analysis)  It is recognized that most blocks are formed from the intersection of stochastic fractures, rather than the deterministic fractures. This is also evident from the comparison of the tracemap of fractures and the block formations on the slope (Figure 43). Although some of the deterministic fractures participate in block formations, it is clear that stochastic fractures played a major role.    Figure 43: Comparison of tracemap and block formations of unconditioned Brunswick DFN model (Black: Stochastic fractures, Red: Deterministic Fractures, Blue: Faults)  In the process of generating the conditioned DFN model, the fractures that were 1) intersecting the scanline and 2) in the range of trace length mapped in the field, were removed. However, Figure 43 shows that several of the stochastic fractures are outside (larger) the range of mapped trace length, therefore they are not removed; however, they can play a major role in block formations. This suggests the importance of removing large fractures that do not match with the field observations when conditioning the fractures. Only the fractures that match the field observations, and shorter than the truncation cut-off should be kept.  The results also imply the difficulty of generating a conditioned DFN model from limited amount of field data. Unlike window mapping where all fractures within certain areal extent of the 2D exposure are recorded, scanline data only provides information of fractures along a 1D sampling line. Using scanline mapping data, the conditioning can only be applied along the sampling line, and this has to be combined 55  with stochastic fractures. This may result in ineffective conditioning depending on the scale, and the amount of deterministic fractures incorporated into the conditioned DFN model.  The key lessons learned included:  • In step 2 of the generation process (where stochastic fractures on the sampling line/plane are removed), it is important to ensure that large fractures that do not match with the field observation are removed, except the fractures that are shorter than truncation cut-off, and;  • Conditioned DFN model should not be generated with limited amount of data as this likely results in ineffective conditioning.  5.2 Large-scale conditioned DFN model  Case Study 3 has an advantage over Case Study 2 that makes it more appropriate for conditioned DFN model. One of the advantages is the quantity and quality of the fractures mapped in the field; additionally, the deterministic fractures are generated from 2D tracemaps. Extensive field mapping (vertical scanline mapping and photogrammetry) was undertaken for Case Study 3 to obtain tracemaps of fractures on two faces of the rock mass, allowing the generation of more than one thousand deterministic fractures. This removes the risk of ineffective conditioning due to the limited amount of deterministic fractures.  Similar to the preliminary analysis, the section consists of the generation and validation of conditioned DFN model, and the comparison between the conditioned and unconditioned DFN model in terms of kinematic stability analysis.  5.2.1 Methodology  The input parameters and the generation process of a conditioned DFN model are adopted from the work by Schlotfeldt et al. (2017). The generation of a new and improved Mountain DFN model consists of four steps:  1. Generate stochastic fractures within a box with volumetric intensity (P32S) determined from the mapped data;  2. Import the deterministic fractures into the model and measure the volumetric intensity of those fractures (P32D);  3. Remove all stochastic fractures, and; 4. Re-generate stochastic fractures using a new volumetric intensity adjusted to account for the contribution of the deterministic fractures (P32S - P32D) and remove large stochastic fractures yielding larger traces that would not correspond to field observations.   56  The basic flow of the generation is similar to the preliminary analysis, except a larger effort is put in to ensure a match between conditioned fractures and the field observation. For instance, the undulation profile of fractures that observed in the field is incorporated into deterministic fractures. Also, the P32 intensity of stochastic fractures is adjusted in Step 4 to balance the overall P32 intensity.  Model validation is performed by comparing the simulated tracemap to the mapped traces. Similar to preliminary analysis, the unconditioned and conditioned DFN models are compared in terms of kinematic analysis results. Rock wedge analysis is performed on two vertical faces, which correspond to the faces where data are collected. Five realizations are generated for each of unconditioned and conditioned DFN model.  5.2.2 Generation and validation of conditioned DFN model  The P32 intensities of the input parameters are compared between unconditioned and conditioned DFN model (Table 13). The same fracture size distributions are used for both models.  Table 13: Input parameters for the unconditioned and conditioned Mountain DFN model Set ID    Fracture Size (Mean (m)) P32 Intensity (m-1) Unconditioned Conditioned Stochastic  Deterministic J0 Negative Exponential (7.50) 0.36 0.01 0.36 J1 Negative Exponential  (1.62) 0.40 0.38 0.02 J2 Negative Exponential (1.87) 0.43 0.28 0.15  J3 Negative Exponential (1.61) 0.71 0.62 0.07 J4 Negative Exponential  (1.62) 0.28 0.27 0.01 All five fracture sets follow similar fracture length distribution except J0, which is the most abundant mapped fracture set. In contrast, most of the fractures in J1, J3 and J4 were not mapped in the field, therefore less deterministic fractures are incorporated into the conditioned DFN model. The P32 intensity is approximately the same for all fracture sets except J3. Figure 44 shows the examples of unconditioned and conditioned DFN model. In conditioned DFN model, the stochastic fractures are shown in shades of blues, where each shade representing the sets, and the 57  deterministic fractures are shown in red. The conditioned DFN model was validated by comparing tracemap of the final model to the mapped fractures as shown in Figure 45.   Figure 44: Selected example of unconditioned (left) and conditioned (right) Mountain DFN model (Blue: Stochastic fractures, Red: Deterministic fractures)  Figure 45: Visual comparison of mapped traces and DFN model traces (Schlotfeldt et al., 2017) 5.2.3 Kinematic slope stability analysis  The results of the rock wedge analysis are compared between unconditioned and conditioned DFN model in terms of number, size, and location of blocks. In addition to the conditioned DFN model, and the unconditioned DFN model generated using disaggregate approach, the unconditioned DFN model generated using aggregate approach is included in the analysis. In this section, these are referred as Model 1, Model 2, and Model 3 as following:  58  • Model 1: Unconditioned model generated using disaggregate approach.  • Model 2: Unconditioned model generated using aggregate approach. • Model 3: Conditioned model generated using disaggregate approach. Figure 46 - Figure 48 show the PSD curves of the block formed on the North wall and South wall of all realizations for each model.  These five realizations are combined to produce an average PSD curve for each model (Figure 49). As discussed in Section 4.3, Model 2 resulted in more, and larger block sizes due to averaged fracture length (~3 m) while block formation is more difficult due to variable fracture length between the sets in disaggregate approach (most of the fractures are < 2 m except J0).  The role of deterministic fracture is evident when comparing block volume between Model 1 and 3 (Table 14). Although the number of block is similar between Model 1 and Model 3, Model 3 yielded in larger size of blocks. For instance, the P50 block volume of North wall for Model 1 and 3 is 0.06 m3 and 0.16 m3 respectively.   South Wall North Wall Figure 46: Comparison between the PSD for Models 1, South and North wall 59   South Wall North Wall Figure 47: Comparison between the PSD for Models 2, South and North wall  South Wall North Wall Figure 48: Comparison between the PSD for Models 3, South and North wall 60   South Wall North Wall Figure 49: Comparison between the PSD for Models 1 to 3, South and North wall Table 14: Comparison of number of blocks, block volume between for Models 1 to 3, South and North wall  South Wall North Wall Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Number of Blocks Total 209 92 90 402 203 230 Block Volume (m3) P50 0.36 0.07 0.096 0.32 0.06 0.16 P90 9.43 2.69 3.69 8.55 2.17 5.80  Another important observation from PSD curves is the variation across realizations. For Model 1, this originates from the stochastic nature of the DFN model. Therefore, the block locations and properties would be different depending on which realization is used.  In contrast, less variation is observed in Model 3 compared to Model 1. This is because block formation of the walls is controlled by deterministic fractures due to conditioning, resulting in better consistency of block volume across realizations than fully stochastic models.  The consistency in Model 3 is observed not only in the block volume, but also in the location and shape of blocks. Figure 50 - Figure 52 show the tracemap of fractures on South wall and the examples of block locations for each model. In terms of spatial locations, the blocks are concentrated on the lower left corner of the wall in Model 3, while the block locations are widely distributed across realizations in Model 1 and 2. More specifically, tabular blocks in the lower-middle, and larger polygonal blocks in the upper-left are observed in all examples in Model 3 (Figure 52). The locations of blocks formed in Model 3 corresponds to where the traces of fractures are concentrated. This suggests that block forming potential of rock mass corresponds to the degree of concentration of fractures as seen in trace map. However, it is important to note that the fractures forming an enclosed area in 2D space does not necessary imply the block formations in 3D.  61  Table 15 compares the P21 intensity between the models for both of North and South walls. Model 3 yields the least P21 intensity at 1.4 m-1. The P21 intensities for Model 1 and 2 are 1.57 m-1 and 1.62 m-1 respectively (South wall). Field estimates of P21 for an equivalent slope region as the one simulated in the current models were in the range of 1.2 to 1.5 m-1 (Elmo, 2018 personal communication). Model 3 shows the best match with field estimates while Model 2 resulted in the least agreement with field observations, due to the process of combining all fractures into one single set.    Figure 50: Model 1; tracemaps for DFN realization (a) and outlines of blocks formed on South wall for DFN realization (a), (b) and (c)   Figure 51: Model 2; tracemaps for DFN realization (a) and outlines of blocks formed on South wall for DFN realization (a), (b) and (c)  62   Figure 52: Model 3; tracemaps for DFN realization (a) and outlines of blocks formed on South wall for DFN realization (a), (b) and (c). Thick red lines represent deterministic trace maps Table 15: Comparison of P21 intensity between the models, South wall, and North wall  P21 (South Wall) (m-1) P21 (North Wall) (m-1)  Deterministic Stochastic Total Deterministic Stochastic Total Model 1 (disaggregate) 0 1.57 1.57 0 1.72 1.72 Model 2 (aggregate) 0 1.62 1.62 0 1.87 1.87 Model 3 (conditioned disaggregate) 1.04 0.36 1.40 1.06 0.49 1.55  5.2.4 Discussion  The results demonstrate the advantages of incorporating deterministic fractures into the DFN model over fully stochastic models. This includes the following: 1) Increasing consistency of block properties (number and shape of blocks and block volume) across realizations;  2) Ability to predict the location and shape of blocks, and;   3) Ability to incorporate anisotropic distribution of fractures.  One of the advantages is increasing consistency of block dimensions across realizations. The variation across realizations due to the stochastic nature of the model is reduced by the use of deterministic fractures. The results of rock wedge analysis are typically obtained probabilistically from multiple realizations. Although a DFN approach allows the generation of an infinite number of realizations, performing rock wedge analysis on a large number of realizations would be difficult, especially for a large-scale model, due 63  to the limitation in computing efficiency. In this context, conditioned DFN model could potentially provide more precise results with fewer number of realizations.  Secondly, locations of blocks are typically not considered important in rock wedge analysis using DFN approach, because the locations of blocks depend on which realization is used. However, the results presented above suggests that blocks locations are generally consistent across realization when deterministic fractures are incorporated. This has a clear implication to kinematic slope stability analysis, specifically in civil engineering applications whereby identification of potential failure is critical to engineering design.  Another advantage of conditioned DFN model is the ability to incorporate anisotropic distribution of fractures. The anisotropic distribution of fractures is difficult to model with fully stochastic DFN models, as the fracture pattern is typically not captured by the available inputs of spatial pattern. However, this approach may fail to recognize the potential failure location. In this Case Study, Set J0 (persistent fractures) is evenly distributed in Model 1 (Figure 50), while in reality, it is concentrated in lower portion of the wall (which shown as deterministic fractures in Figure 52). The difference in the concentration of fractures between the models resulted in different locations of blocks.   Although the advantages the conditioned DFN model would offer, the generation of conditioned DFN model requires sufficient care in data collection.  The major issue encountered in the preliminary analysis was ineffective conditioning due to limited amount of deterministic fractures. This could be largely improved by integrating remote sensing techniques with conventional mapping method.  As shown by the comparison between aggregate and disaggregate approach, fracture length is an important factor controlling the block formations in the context of kinematic slope stability analysis. However, this is one of the difficult properties to measure in the field due to the biases, and due to the limited exposures of rock surfaces. It is important that the engineers are aware of these limitations when mapping fracture length in the field.  5.3 Chapter summary  In this Chapter, the concept of conditioned DFN model, which incorporates tracemaps obtained from field mapping, was introduced. The generation process of a conditioned DFN model and its impacts on the kinematic analysis results were examined using two case studies.  64  The results of preliminary analysis performed with Case Study 2 demonstrated the importance of using sufficient amount of deterministic fractures in order for conditioning to be effective and ensuing a good match between the conditioned fractures and the field observations.  The analysis was repeated with Case Study 3, a large-scale Mountain model, which incorporated a larger number of deterministic fractures. The results showed that the conditioned DFN model effectively increased the consistency of block properties across realizations. The results also demonstrated the conditioned DFN model’s ability to predict location of blocks and to incorporate anisotropic distribution of fracture into the model.                 65  Chapter 6 A DFN Approach to Quantify the Variability of GSI  6.1 Introduction This Chapter is dedicated to the study of a new approach to quantify the variation of GSI, whereby realistic representation of fracture network and IBSD are combined with the GSI quantification method proposed by Cai et al. (2004) to obtain the variation of GSI ratings. The emphasis is given on the limitations of assigning a single rating of GSI in rock engineering design.  GSI is a rock mass classification system based on qualitative description of joint condition and blockiness of rock mass. The blockiness parameter in GSI is directly related to IBSD, which is defined as the range of sizes of blocks formed from the intersecting discontinuities.  An earlier attempt to apply the block size analysis to quantify the GSI was performed by Cai et al. (2004). In this work, the authors supplemented the blockiness parameter in GSI with a measure of block volume by introducing the concept of equivalent block volume and considering the fracture persistence. However, the analysis is limited to a simple conceptual rock mass and did not account for complex configurations of fracture network that would arise when considering naturally fractured rock mass. In this context, a DFN approach could potentially provide a better tool by realistically representing 3D fracture network.  One of the challenges of estimating GSI in the field is the fact that field observations are limited to 1D (core) or 2D (rock exposures), while the true blockiness parameter in GSI is a 3D parameter (Figure 53). In this context, the focus is also given on the limitations of estimating GSI from lower-dimensional exposure of rock mass.   Figure 53: Estimating a 3D rock mass classification rating requires access to 3D information.  66  Two case studies are considered in this Chapter; Case Study 3 Mountain model and Case Study 4 Middleton mine model. Most of the sections in this Chapter focus on Case Study 4, and Case Study 3 is used as a supplementary case study to test the proposed quantification method.  6.2 Methodology  The process to characterize the variability of GSI consists of three steps;  1) Generate a DFN model;   2) Obtain a PSD curve of from a rock wedge analysis using 2D surfaces as a free-surface, and;  3) Obtain P20 and P80 of the PSD curve to find the corresponding range of GSI.  For Case Study 4, a total of four models are generated, and the work will be described in detail in Section 6.3. The differences between the models are whether the bedding planes are included, and the approach used to generate the model (aggregate vs disaggregate approach). The bedding planes are excluded for some of the models to examine how critical the bedding planes are with respect to blocks formations and GSI.  It should be noted that the use of GSI is generally not recommended for anisotropic rock masses. However, GSI can still be applied (with caution) to anisotropic rock masses if the failure of such rock masses is not controlled by structure-controlled failure (Marinos et al., 2005). For Case Study 3, the three types of models generated in Chapter 5 (aggregate, disaggregate, and disaggregate conditioned) are used for the analysis.  Once the models are generated, a rock wedge analysis is performed to identify potential blocks intersecting a series of sampling planes oriented vertically and horizontally (Figure 54). The vertical sampling planes are spaced 5 m apart. When considering the horizontal sampling planes (5, 6, and 7), the rock wedge analysis is performed with respect to the top side of the surface. For surfaces 2 and 3, the rock wedge analysis is performed with respect to the west side of the surface (left sides of vertical surfaces on Figure 54), while for surfaces 1 and 4, it is performed such that the blocks would be contained inside the pillar region. Multiple sampling surfaces oriented both horizontally and vertically are used for the analysis to examine the variations of block formation with respect to the locations and orientations of sampling plane. For Case Study 3, the PSD curves generated from the rock wedge analysis performed on two vertical walls in Section 5.2.3 are used to obtain corresponding GSI. In this analysis, the PSD curves are obtained from the blocks formed on the 2D surfaces. This is not a true representation of IBSD in strict sense as this approach does not consider all blocks formed in the rock mass. Notwithstanding, this approach is chosen to simulate the actual situation of estimating GSI in the field from 2D rock exposure.  67  The final step of the process is to estimate the corresponding GSI rating using the quantification method proposed by Cai et al. (2004). P20 and P80 of the PSD curves are used as key indicators of finer and coarser sizes, respectively. The corresponding GSI of P30, P50 and P70 are also included to examine how GSI is distributed along the PSD curves. Additionally, trace maps generated for surfaces 1 to 4 are used to study the difference between apparent 2D block formations (fracture traces forming closed polygons) and the actual block formations associated with the creation of 3D blocks.  Figure 54: Sampling planes used for rock wedge analysis 6.3 Model setup  The complete list of four models generated for Case Study 4 are following;  • Model 1: DFN model without bedding planes generated using aggregate approach.  • Model 2: DFN model with bedding planes generated using aggregate approach. • Model 3: DFN model without bedding planes generated using disaggregate approach. • Model 4: DFN model with bedding planes generated using disaggregate approach. The input parameters of fracture length and P32 intensity used for the generation of DFN model are compared between aggregate and disaggregate approach (Table 16). Similar to Case Study 3, the rock contains one set of persistent fractures, while the rest of fracture sets have similar fracture length. In aggregate approach, these differences in the fracture length are average out to the mean fracture length of 3.67 m. The dimension of the model used for the analysis is 15 m × 15 m × 15 m. Five generations are generated for each model and examples are shown in Figure 55.   68  Table 16: Input parameters for the Middleton model (aggregate and disaggregate approach)   Figure 55: Examples of generated DFN models. From left to right: Model 1 (aggregate), Model 2 (aggregate with bedding features), Model 3 (disaggregate), and Model 4 (disaggregate with bedding features) 6.4 Results of the rock wedge analysis  The PSD curves in Figure 56 represent the average block volume for all vertical surfaces combined (Surface 1, 2, 3, and 4) and all horizontal surfaces combined (Surface 5, 6, and 7). Figure 57 to Figure 60 show the variations of block volume for each model for one of the realizations. The PSD plots are separated with respect to the orientation of sampling planes since the results for the latter are strongly influenced by the location of the bedding features.  It is clear that block forming potentials depend on the modelling approach (aggregate vs disaggregate approach) and the orientation of the free surface (horizontal or vertical). Figure 56 shows that the models using aggregate approach resulted in larger blocks. This is because the averaged fracture length in aggregate approach made block formations easier, while the block forming potential is less in disaggregate approach  Disaggregate Approach Aggregate Approach Set ID Equivalent Radius Distribution mean (m) /S.D. (m) P32 intensity (m-1) Equivalent Radius Distribution mean (m) /S.D. (m) P32 intensity (m-1) 1a Log Normal (8.17 / 1.11) 0.78 Log Normal (3.67 / 2.22) 3.61 1b Log Normal (2.46 / 1.65) 0.63 2a Log Normal (4.48 / 1.82) 0.64 2b Log Normal (4.06 / 1.65) 0.46 3a Log Normal (2.59 / 1.92) 0.35 3b Log Normal (3.32 / 2.23) 0.26 69  with higher intensity of low persistence fractures. The difference in block formations between the approaches can also be seen from Figure 61, showing the block formations on Surfaces 1 to 4 for Model 2 and 4.  Although no major difference is observed in the PSD curves between the models generated with aggregate approach (Model 1 and Model 2) when vertical wall is used, it is clear that persistent bedding planes increased the formation of blocks in disaggregate approach, resulted in more, and larger blocks in Model 4 compared to Model 3 (Figure 56). The bedding planes and the orientations of sampling planes have inter-related effects on the block forming potential. When horizontal surfaces are used as a free-surface, the volume of blocks formed on top side of the surface is a function of relative locations of the bedding planes and the sampling surface (Figure 62). This effect is combined with the stochastic nature of DFN model to produce different PSD curves for horizontal surfaces in the models with bedding planes (Figure 57 vs Figure 58).  Although minor, the variation displayed by PSD curves is also observed when a vertical surface is used as a free-surface. This suggests the variation of block forming potential with respect to the locations of sampling planes.    Vertical Horizontal  Figure 56: PSD plots of block volume for Model 1 to 4, all vertical and horizontal sampling planes combined  70   Figure 57: PSD plots of block volume for Model 1 (aggregate, no bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes  Figure 58: PSD plots of block volume for Model 2 (aggregate, with bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes  Figure 59: PSD plots of block volume for Model 3 (disaggregate, no bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes 71   Figure 60: PSD plots of block volume for Model 4 (disaggregate, with bedding), vertical (1 to 4) and horizontal (5 to 7) sampling planes  Figure 61: Block formations on the vertical walls (Surface 1 to 4) in Model 2 (top row) and Model 4 (bottom row) 72   Figure 62: Block formations on the horizontal walls (Surface 5 and 6) in Model 1 (top row) and Model 2 (bottom row) 6.5 Characterization of GSI variability Case Study 4  The blockiness parameter in GSI is obtained using P20, P30, P50, P70 and P80 passing sizes of the average PSD curves of all DFN realizations (Figure 56). The joint condition is given a rating of fair to good based on the observation that the joints are smooth to rough (average joint roughness coefficient, JRC, of 10) and slightly weathered (Elmo, 2006). The obtained GSI ratings are summarized in Table 17 and Figure 63.   Due to its definition, Model 4 (disaggregate approach with bedding) is the one that most accurately reflects the field condition of the pillars at Middleton mine. According to field observations (Pine and Harrison, 2003; Elmo, 2006), the GSI for the pillars at Middleton mine was in the range of 60 to 70, which is not exactly in good agreement with the GSI range obtained from Model 4 (GSI range of 50 to 65). However, it should be noted that those field estimates were based on a qualitative assessment of rock mass blockiness from the rock exposure and may be biased towards the larger block size due to the inherent propensity of a person that collects data to focus on the largest visible structures. The models generated using aggregate approach (Model 1 and 2) result in slightly higher GSI than Model 4, reflecting larger block sizes. The GSI rating for the model generated using an aggregate approach corresponds to more massive rock mass compared to disaggregate approach. Model 3 is the least close to 73  Model 4, due to the underestimation of block volume with the absence of bedding planes. Therefore, the results suggest the importance to recognize the differences that exist between the fracture sets.  Another important finding is the orientation dependency and associated variation of GSI rating. The PSD curves presented above demonstrated the variation of block volume depends on whether the vertical or horizontal surface is used, and on the location of sampling plane. These are directly correlated to the variation of GSI, suggesting the importance of not relying on a single sampling plane or rock exposure for the estimation of GSI.  Although the differences in GSI ratings between the models may seem minor, this could be because of the model uncertainty inherently associated with the quality of the input data. To further investigate this topic, the proposed quantification method of GSI is applied to Case Study 3, which relies on better quality field data.  Table 17: Comparison of GSI ranges corresponding to P20, P30, P50, P70 and P80 passing size for the Middleton mine case study  Model  P20-P80 P30-P70 P50 1 Vertical 53 - 68 55 - 66 60 Horizontal 55 - 70 58 - 67 62 2 Vertical 55 - 68 58 - 66 61 Horizontal 52 - 66 55 - 64 60 3 Vertical 43 - 60 47 - 55 50 Horizontal 45 - 60 48 - 58 53 4 Vertical 50 - 65 53 - 62 58 Horizontal 50 - 64 53 - 60 58  74   Figure 63: Comparison of variation of GSI ranges for the 4 DFN models generated for Middleton mine (Vertical wall: left, Horizontal wall: right). Green dot represents P50, the thick orange line and the thin black line represents the P30-P70 and P20-P80 size passing range, respectively. Results for Models 2 and 4 are given with respects to the modified GSI charts by Cai et al. (2004)      75  Case Study 3  Similar to Case Study 4, the GSI rating is estimated using the P20, P30, P50, P70 and P80 of the average PSD curves of all realizations (Table 18 and Figure 64). The joint condition is given a rating of fair to good based on the field mapping data (Elmo, 2018 personal communication). Three models are considered in this section, Model 1: disaggregate approach, Model 2: aggregate approach, and Model 3: conditioned disaggregate approach. The difference in GSI rating between Model 1(disaggregate) and Model 2 (aggregate) is quite evident for this Case Study. Model 2 corresponds to the GSI rating of massive to blocky rock mass while Model 1 corresponds to blocky rock mass. Thus, in this case, Model 2 (aggregate) would overestimate rock mass quality compared to Model 1(disaggregate). Model 1 (disaggregate) and Model 3 (disaggregate conditioned) are in good agreement (South wall sampling plane) while only slightly differs in terms of GSI rating when considering the North wall sampling plane. This would suggest a larger influence of deterministic fractures on block forming potential along the North wall compared to the South wall.  Table 18: Comparison of GSI ranges corresponding to P20, P30, P50, P70 and P80 size passing for the slope model described in Section 5.1.3 (South wall and North wall)  Model Wall P20-P80 P30-P70 P50 1 South 54-70 57-67 61 2 South 58-77 62-73 67 3 South 53-72 57-67 62 1 North  52-68 55-66 60 2 North  58-77 60-73 66 3 North 55-75 58-70 64       76    Figure 64: Variation of estimated GSI for Case Study 3 (South wall: left, North wall : right). Green dot represents P50, the thick orange line and the thin black line represents the P30-P70 and P20-P80 size passing range, respectively.    77  6.6 Limitations of 2D surveys to determine rock mass blockiness  The blockiness parameter in GSI is commonly estimated by visually inspecting the closed polygons formed by the intersecting fractures on 2D planes. Using Case Study 4, the trace maps of fractures are compared with the traces of blocks formed on the surfaces (Figure 65). By visually connecting the traces of fractures, it is possible to draw the areal extent of largest possible 2D block. This is compared with the actual area of blocks formed in three-dimension to qualitatively assess the difference between 2D and 3D.  Two models are considered in the analysis; Model 2, aggregate approach with bedding planes and Model 4, disaggregate approach with bedding planes. In Model 2, more and larger blocks are formed due to the fracture length assumption based on aggregate approach. As a result, the difference between the enclosed area and the actual area is relatively small. In contrast, the difference is relatively large for Model 4, because of less, and smaller block formation using disaggregate approach. The results suggest that the enclosed area formed on a 2D plane does not necessarily correspond to the actual block formations in three-dimension. In other words, the blocks formed in two-dimension may not be forming actual blocks. The results also show the variation in block forming potential depending on the location of sampling planes. For instance, the actual area of blocks is smaller on Surface 1 compared to the actual area on Surface 2 to 4. This emphasizes the importance of using multiple sampling planes to estimate the GSI.    Figure 65: Comparison between 2D perceived blocks and actual 3D blocks formed across Surfaces 1 to 4 (see Figure 58 and Figure 60) for Models 2 (top) and 4 (bottom)  78  6.7 Comments on quantifying GSI from block analysis  6.7.1 Definition of IBSD and GSI blockiness parameter  Although the GSI rating obtained from the proposed approach yielded satisfactory results, the approach has a limitation that makes it difficult to apply for massive rock mass with abundant low-persistence fractures. Such rock mass comprises of a single large block with the volume almost equivalent to the volume of rock mass (Rogers et al. 2007; Cai et al. 2004). In this case, the overall block forming potential is very low, corresponding to high value of GSI rating (massive to intact rock mass). However, when simply applying the proposed approach to this rock mass, it would not be possible to capture the formation of the larger (apparent) block; rather the simulation would only show small blocks being formed by the intersection of the free-surface with short discontinuities, resulting in low value of GSI rating. In order to avoid this situation, it is important to ensure that a sufficient number of blocks are formed on the surfaces before proceeding with the estimation of GSI ratings.  6.7.2 Influences of bin sizes on IBSD curves  Another issue is regarding the fundamental question related to producing a CDF plot of block volume from identified blocks. Unlike soil mechanics, where bin sizes are clearly defined by sieve sizes, the lack of standards for rock mass block volume constitutes a source of uncertainty when estimating percentages passings (e.g. P20). For instance, Palmstrøm (1995) suggests block volume to be classified as Table 19 while others (Rogers et al., 2007; Kim et al., 2015) prefer bin sizes to be defined as one order of magnitude. In mining-related researches, the block fragmentation is commonly expressed by maximum distance between two vertices participated in a block rather than by volumes (Wang et al. 2003; Elmouttie and Poropat, 2012).  Table 19: Classification scheme of block volume suggested by Palmstrøm (1995) Very Small Vb = 10-200 cm3 Small Vb = 0.2-10 dm3 Moderate Vb = 10-200 dm3 Large Vb = 0.2-10 m3 Very large Vb >10 m3  In order to analyze the influence of the bin sizes on passing size, the PSD curves for Model 2 vertical wall and Model 4 horizontal wall in Case Study 4 (Figure 58 and Figure 60) are reproduced in Figure 66 using three bin sizes as shown in Table 20.  Method 3 uses the smallest bin sizes, therefore most accurately captures the increment of cumulative percentages with increasing volume. In contrast, Method 1 uses the largest bin size of two orders of 79  magnitude. The use of large bin sizes in Method 1 oversimplifies the PSD curve, resulting in major differences in percentage passing size with other methods. For instance, Method 1 yields P20 of 0.007 m3 while Method 2 and 3 yield P20 of 0.01 m3. Although Method 2 and Method 3 are generally in good agreement, minor difference is observed in the range of P80 to P100. The results demonstrate that the choice of bin sizes influences the resulting PSD curves, therefore the passing sizes. This suggests the need of standardization of bin sizes to allow effective communication between researchers on the topic of block analysis of rock mass.  Table 20: Bin sizes used for each method (All units are in m3) Method 1 Method 2 Method 3 < 0.0001 <0.0001 0.0001 – 0.0002 0.0001 - 0.01 0.0001 – 0.001 0.0002 – 0.0005 0.01 - 1 0.001 – 0.01 0.0005 – 0.002 1 – 100 0.01 – 0.1 0.001 – 0.002  0.1 - 1 0.002 – 0.005  1 - 10 0.005 – 0.01  10 - 100 0.01 – 0.02   0.02 – 0.05   0.05 – 0.1   0.1-0.2   0.2 – 0.5   0.5 -1   1 – 2   2 - 5   5 – 10   10 – 20   20 – 50   50 – 100   Figure 66: PSD curves produced with three different bin sizes (Model 2: left, Model 4: right) 80  6.8 Chapter summary  In this Chapter, the variability of GSI was quantified by combining the quantification method proposed by Cai et al. (2004) and the PSD curve obtained from the DFN models. This approach has the advantage of considering complex configurations of fracture network by realistic representation of fractures in three-dimension.  The range of GSI corresponding to P20 and P80 block volume of PSD curves is as large as ±6 in Case Study 3 and ±10 for Case Study 4. This has a clear implication for engineering design scenario, as it shows the limitations of using a unique value of GSI to characterize rock mass quality. The results also demonstrated that the variation of GSI depends on the orientations and the locations of sampling plane. This suggests the importance of not relying on a single plane of rock exposure to estimate the GSI, especially when the rock mass comprises of orientation-dependent feature.  The second part of the analyses compared the enclosed area in 2D with the actual block formations in 3D. The results demonstrated the difference between the inferred blockiness and actual blockiness, implying the risk of estimating the blockiness parameter in GSI by visually inspecting the pattern that the fractures would make with 2D surface.            81  Chapter 7 Conclusions and Recommendations  7.1 Research conclusions  DFN methods have been increasingly identified as a useful tool in civil and mining engineering design involving fractured rock mass. In the context of kinematic slope stability analysis, DFNs offer the advantage of realistically represent a natural fracture network by describing fracture properties with appropriate statistical distribution. This automatically removes the unrealistic assumption of ubiquitous and infinite discontinuities in limit equilibrium and stereographic analysis, avoiding overly-conservative design. Despite the significant improvements in data collection method in the past decades, little attention has been given in the literature on the process to characterize them in the development of DFN models. In response to this, two aspects of data characterization process were examined in this thesis i) influence of generating a DFN model using either an aggregate or a disaggregate approach; and ii) influence of incorporation of deterministic fractures into the DFN model. In Chapter 4, the influence of the selection of modelling approach (aggregate vs disaggregate approach) on the kinematic stability analysis was examined. The comparison between aggregate and disaggregate approach revealed that the important input parameters such as fracture intensity and fracture size could be either overestimated or underestimated using aggregate approach. Accordingly, the number and size of blocks may not be truly representative of field conditions. The degree of overestimation or underestimation of fracture properties when using aggregate approach would depend on the data collection method and the fracture properties. For instance, the fractures bootstrapped from 1D mapping data are subject to orientation bias when using aggregate approach.   It is not a rare practice to use aggregate approach, especially at the preliminary stage of the project where enough data are not available to define fracture sets. However, the findings suggested the importance to incorporate the differences between the sets into DFN model as more data become available to identify sets.  In Chapter 5, the influence of the conditioning on the kinematic slope stability analysis was examined. The results clearly showed the ability of conditioned DFN model to better considerate the spatial location of potentially unstable block.  The results also showed that a conditioned model would not be as effective if based on a limited amount of deterministic fractures. Conditioning requires fractures to be mapped deterministically, and the quantity of mapped fractures needs to be large enough comparative to the scale of the model. The use of remote sensing techniques is recommended for this purpose over conventional mapping methods as it can cover larger areal extent and accurately capture the spatial distributions of fracture.  82  Chapter 6 addresses the fundamental questions related to the estimation of GSI from rock block analysis using DFN models. Three key aspects have been examined: i) estimation of GSI ratings for rock masses that contain well defined bedding features; ii) determination of GSI ratings to better reflect the variability of rock mass blockiness; and iii) implication of using 2D versus 3D data to characterise rock mass blockiness. The results showed that the variation of GSI could be as large as ±10. This has clear implications for design scenario since it shows the limitations of using a single point estimate of GSI to establish rock mass behaviour.  Another key finding is regarding the comparison between 2D and 3D blockiness. The results suggested that the blockiness inferred from connected fractures on 2D exposure may actually be different from the true blockiness in three-dimension. Therefore, estimates of GSI based on perceived 2D blockiness may yield overly either conservative or non-conservative ratings for smaller and larger 2D blocks respectively Likewise, there could be a high variation in block forming potential depending on the location of the sampling plane. In this context, DFN models offer the opportunity to characterize this variability and provide better estimates of rock mass blockiness.  7.2 Recommendations for future work  The research on the influence of data characterization process on kinematic slope stability analysis could be further extended using numerical simulation program such as discrete element program and hybrid finite-discrete element program. These programs simulate not only the block formation but also how these blocks are displaced; therefore, the influence of data characterization process can be compared in terms of deformation and displacement of slopes.  The results from Chapter 6 offered a new perspective of rock mass classifications system. Because of the inherent variability of the underlying rock mass fabric, classification ratings are not supposed to provide exact measurements of rock mass quality. The results suggest that there may be the need to develop classification methods that are more sensitive to data uncertainty and use a unique set of rock mass properties directly instead of assigning a rating based on the value of a measured rock mass property (e.g. measurements of fracture frequency and fracture spacing). As shown in Chapter 6, the ability to predict realistic block forming potential considering the natural fracture network is an important advantage that DFN offers and the author believes this has applications to other rock mass classifications systems. One example of this is Q index (Barton et al. 1974) proposed for the determination of rock mass characteristics and tunnel support requirements. A part of Q index represents structure of rock mass (block size) which is closely related to block forming potential of rock mass.  However, one of the concerns regarding the application of IBSD obtained from DFN models is the lack of standards defining the bin sizes to produce a CDF Plot of block volume. This could result in different 83  interpretations of passing sizes depending on which bin size is used; therefore, there is a need to establish a standard of bin sizes of IBSD to allow effective communications between the researchers on this topic.  Another quantification method of GSI that DFN could potentially be applied is the method proposed by Hoek et al. (2013). In this quantification method, the blockiness and joint condition parameter are supplemented by RQD and joint condition rating from RMR 89 (Bieniawski, 1989) respectively. Previously, Wang (2017) showed the orientation and scale dependency of RQD using a DFN approach. This could be correlated to GSI using the method by Hoek et al. (2013) to study the GSI rating at varying scale.                    84  References 1 Armstrong J.E. 1990. 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