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Fault tree analysis of slurry and dewatered taiings management – a framework Taguchi, Genki 2014

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FAULT TREE ANALYSIS OF SLURRY AND DEWATERED TAILINGS MANAGEMENT ? A FRAMEWORK by Genki Taguchi 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) March 2014 ? Genki Taguchi, 2014  ii Abstract Fault trees are used in reliability and risk analysis to develop the probability of occurrence of the top event, or failure mode. The top event results from a logical sequence, or combination, of lower level events using ?and? and ?or? logic. Probabilities for the basic events, i.e. the lowest level events identified, are calculated or estimated in order to calculate the probability for the top event. This thesis develops a framework for fault tree analysis for failure of alternative tailings depositional schemes (slurry, thickened, paste and filtered). Failure is narrowly defined as the release of tailings to the environment. The following failure modes are evaluated for each of the depositional schemes: overtopping, static liquefaction, internal erosion, static slope instability and seismic slope instability. The fault trees are representative of potential failure sequences in the industry as a whole and not on site-specific conditions. Expert elicitation methods are used to select the likelihoods of the basic events. Not all events in the fault trees are applicable to the range of depositional schemes, e.g. overtopping as a result of a large pool on slurry deposited tailings management facilities is not an event that will occur for filtered tailings. The outcome is that some of the events and parts of fault trees ?fall away? as the tailings solids content increases. Apart from providing a visualization of the reduction in probability of occurrence of the top events for the failure modes, the results also provide a range of probabilities for the overall probability of failure for the range of tailings management options.  The framework is used to develop a site-specific likelihood of failure of the Bafokeng tailings facility. The result demonstrates that the fault tree framework can provide useful insights in both industry-wide and site-specific tailings management facility failure likelihoods.    iii Preface This thesis is original, unpublished work by the author, G. Taguchi.    iv Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Preface .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iii  Table of Contents .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv List of Tables .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vii List of Figures .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  viii Acknowledgements .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xii Dedication .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xiii 1. Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1 1.1 Research Question & Objective .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2 1.2 Thesis Outline .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3 2. Literature Review ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4 2.1 Tailings Management Options .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4  Tailings rheology ......................................................................................................................... 5 2.1.1 Slurry tailings .............................................................................................................................. 8 2.1.2 Thickened tailings ....................................................................................................................... 9 2.1.3 Paste tailings ............................................................................................................................. 11 2.1.4 Filtered tailings ......................................................................................................................... 12 2.1.52.2 Construction Method of Slurry TMF ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14  Upstream construction .............................................................................................................. 14 2.2.1 Downstream construction ......................................................................................................... 15 2.2.2 Centerline construction ............................................................................................................. 16 2.2.3 v 2.3 TMF Failures .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17 2.4 Probabilistic Analysis of Tailings Management Facilities .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21  Statistical analysis .................................................................................................................... 21 2.4.1 Event tree analysis .................................................................................................................... 23 2.4.22.5 Fault Tree Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  24  Overview .................................................................................................................................... 24 2.5.1 Procedure ................................................................................................................................... 25 2.5.22.6 Subjective Probabilities of Basic Events .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  28  Heuristics and bias .................................................................................................................... 28 2.6.1 Anchoring and adjustment ....................................................................................................... 30 2.6.2 Expert elicitation ....................................................................................................................... 31 2.6.3 Reliability modeling .................................................................................................................. 32 2.6.43. Framework, Selection of Evaluation Method and Failure Modes .. . . . . . . . . . . . . . .  36 3.1 Framework ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36 3.2 Selection of Evaluation Method ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36 3.3 Failure Modes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  38  Overtopping ............................................................................................................................... 43 3.3.1 Static liquefaction ..................................................................................................................... 44 3.3.2 Internal erosion ......................................................................................................................... 45 3.3.3 Static slope instability .............................................................................................................. 47 3.3.4 Seismic slope instability ........................................................................................................... 48 3.3.54. Fault Trees .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  51 4.1 Assigning Likelihoods for Basic Events .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  52  vi 5. Discussion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65 5.1 Overtopping .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65 5.2 Static Liquefaction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65 5.3 Internal Erosion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66 5.4 Static Slope Instability .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66 5.5 Seismic Slope Instability .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  67 5.6 Application of Fault Trees to Site-specific Conditions .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  67  Overview of Bafokeng TMF failure .......................................................................................... 67 5.6.1 Possible failure causes .............................................................................................................. 70 5.6.2 Fault trees for Bafokeng TMF failure ...................................................................................... 71 5.6.35.7 Additional Slurry Tailings Failure Modes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  77 5.8 Sources of Bias in This Thesis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  78 6. Conclusion, Contributions and Recommendations for Future Research .. . . . .  80 6.1 Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  80 6.2 Contributions .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  81 6.3 Recommendations for Future Research ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  82 References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  83     vii List of Tables Table 1 Characteristics of tailings deposition methods .................................................... 1 Table 2 Conventional graphic symbols of fault tree ........................................................ 26 Table 3 Probabilities of basic failure events .................................................................... 56 Table 4 Likelihood of failure and failure modes for slurry and dewatered TMF ......... 62 Table 5 Likelihoods of basic failure events for Bafokeng TMF failure .......................... 73 Table 6 Likelihood of failure modes for Bafokeng TMF failure ..................................... 74 Table 7 Statistics of shear strength values for stability analysis .................................. 75 Table 8 Factor of safety for 8 point estimates ................................................................. 76     viii List of Figures Fig. 1 Trends in use of dewatered tailings in mining (after Davies et al., 2010) ............ 4 Fig. 2 Typical flow behavior of Newtonian and non-Newtonian fluids (after Boger et al., 2006) ................................................................................................................................... 6 Fig. 3 Typical yield stress and solids content of tailings from metal mining ................... 7 Fig. 4 Yield stress concentration data for different industry waste streams (after Boger et al., 2006) ......................................................................................................................... 7 Fig. 5 Natural segregation of spigot-discharged tailings .................................................. 8 Fig. 6 Schematic diagram of multiple spigot disposal at the Twin Creeks Mine, Nevada (Original image is taken from Google Earth) ................................................................... 9 Fig. 7 Circular conical disposal of thickened tailings at Sunrise Dam Gold Mine, Australia (Original image is taken from Google Earth) ................................................ 10 Fig. 8 Cracked paste and fresh paste depositing over a cracked layer (after Tailings.info, 2013) ................................................................................................................................. 12 Fig. 9 Filtered tailings deposited at La Coipa Mine, Atacama, Chile (PwC, 2012) ....... 14 Fig. 10 Upstream construction method ........................................................................... 15 Fig. 11 Downstream construction method ....................................................................... 16 Fig. 12 Centerline construction method .......................................................................... 17 Fig. 13 Tailings dam incident cause comparison with dam status (after ICOLD and UNEP, 2001) .................................................................................................................... 18 Fig. 14 Tailings dam incident cause comparison with incident type for active dams ... 19 Fig. 15 Tailings dam incident cause comparison with dam type (after ICOLD and UNEP, 2001) .................................................................................................................... 19 Fig. 16 Distribution of the number of incidents according to cause in the world and in  ix Europe (after Rico et al., 2008) ....................................................................................... 20 Fig. 17 Annual probability of failure vs. factor of safety following Silva, Lambe, Marr (Silva, Lambe and Marr, 2008) ....................................................................................... 22 Fig. 18 Example event tree for internal erosion (after U.S. Department of the Interior, 2013)  ............................................................................................................................... 24 Fig. 19 Example of fault tree ............................................................................................ 25 Fig. 20 Subjectively estimated vs. actual probabilities (Data from Fischhoff et al. (1977), after Vick (1997)) ............................................................................................................. 29 Fig. 21 Subjective estimates of the compressibility of San Francisco Bay mud compared to test results for five experts (after Folayan, J., Hoeg, K. and Benjamin, J., 1970)  .............................................................................................................................. 30 Fig. 22 Fault tree for tailings embankment failure founded on paleokarst (after Van Zyl et al., 1996) ................................................................................................................ 33 Fig. 23 Conceptual model for limestone (after Van Zyl et al., 1996) .............................. 34 Fig. 24 Distribution of cavity length (left) and intact bedrock length (right) from exploratory boreholes (after Van Zyl et al., 1996) ......................................................... 34 Fig. 25 Simplified graphical representation of event tree analysis and fault tree analysis (made by the author based on RRC, 2013) ...................................................... 38 Fig. 26 Risk analysis reports provided by U.S. Bureau of Reclamation (excerpted from U.S. Department of the Interior, Bureau of Reclamation?s website) ............................ 39 Fig. 27 Relationship between failure causes, failure modes and failure ....................... 40 Fig. 28 Compilation of 8 failure causes from ICOLD and UNEP (2001) into 5 failure modes ............................................................................................................................... 41 Fig. 30 Schematic diagram of sustained overtopping and wave overtopping ................ 44 Fig. 31 Definition of state parameter, ? (after Been et al., 2012) ................................. 45 Fig. 32 Factors affecting the initiation of internal erosion (after Garner and Fannin,  x 2010)  ............................................................................................................................... 47 Fig. 33 Factor of safety relative to the piezometric height in dam (after Kealy and Busch, 1971) ..................................................................................................................... 48 Fig. 34 Schematic undrained response of a saturated, contractive sandy soil (after Olson and Stark, 2003) .................................................................................................... 49 Fig. 35 Fault tree for the release of tailings to the environment ................................... 52 Fig. 36 Fault tree for overtopping .................................................................................... 53 Fig. 37 Fault tree for static liquefaction .......................................................................... 53 Fig. 38 Fault tree for downstream surface eroded from overtopping ............................. 54 Fig. 39 Fault tree for internal erosion ............................................................................. 54 Fig. 40 Fault tree for static slope instability ................................................................... 55 Fig. 41 Fault tree for seismic slope instability ................................................................ 55 Fig. 42 Likelihood of failure and each failure mode for slurry and dewatered TMF .... 63 Fig. 43 Comparison of the results with historical values from Oboni and Oboni (2013) .   .............................................................................................................................. 63 Fig. 44 Ring dyke impoundment of Bafokeng Dam (after Caldwell, 2011) ................... 68 Fig. 45 Perimeter slimes discharge of Bafokeng Dam (after Caldwell, 2011) ............... 68 Fig. 46 Geography around Bafokeng No. 1 TMF at the time of failure (after Caldwell, 2011)  ............................................................................................................................... 69 Fig. 47 Typical foundation conditions for a TMF in the Rustenburg area (after Caldwell, 2011) ................................................................................................................ 69 Fig. 48 Fault tree for overtopping at Bafokeng TMF ...................................................... 72 Fig. 49 Fault tree for static liquefaction at Bafokeng TMF ............................................ 72 Fig. 50 Fault tree for internal erosion at Bafokeng TMF ............................................... 73  xi Fig. 51 Fault tree for static slope instability at Bafokeng TMF ..................................... 73 Fig. 52 Schematic static instability model for Bafokeng TMF ....................................... 75 Fig. 53 A sequence of failure of Bafokeng TMF (after Blight and Fourie, 2003) .......... 77 Fig. 54 Fault tree for penstock failure ............................................................................. 78     xii Acknowledgements I would like to offer my cordial gratitude to my supervisor Dr. Dirk van Zyl, who has been an exceptional mentor for me and gave me a whole new perspective on mining engineering. Meeting with you is as exciting as the first time every time. I also thank Dr. Scott Dunbar and Dr. Marek Pawlik for serving as my committee members even on a tight schedule. I owe particular thanks to Mr. Jack Caldwell for constructive advice and sharing his experience as a professional engineer to enhance the quality of my thesis. My sincere thanks also goes to Dr. Wei He who helped me with static stability analysis of Bafokeng TMF. I would also like to thank ITO Foundation, who has sponsored me financially throughout my years of education. Special thanks are owed to my family, who have continuously supported me from Japan mentally even at hardship.   xiii Dedication This thesis is dedicated to my parents who have been my constant source of inspiration and determination. Without their love and continuous support, studying abroad and writing this thesis would not have been made possible. To my parents  1 1. Introduction The US Bureau of Reclamation and US Army Corps of Engineers have made significant progress over the last two decades on the refinement and implementation of risk-based evaluations of the facilities under their jurisdiction. These evaluations are based on event tree formulations and details are available at U.S. Department of the Interior (2013). Throughout the 20th and so far, the 21st centuries, the international mining industry experienced a significant number of tailings facility failures that have impacted both human safety and health and the environment. Extensive research and implementation of dewatered tailings management techniques such as thickened, paste and filtered tailings have resulted in practices with many advantages over conventional slurry tailings, such as reduced water use. Table 1 summarizes the characteristics of slurry tailings and dewatered tailings. Solids contents listed in Table 1 are typical values for tailings from metal mining. Table 1 Characteristics of tailings deposition methods Tailings Solids content Conveyance system Beach slope Slurry < 45% Centrifugal pump 0.5% ? 2% (Vick, 1990) Thickened 45% ? 65% Centrifugal pump 2% ? 6% (ICOLD and UNEP, 2001) Paste 65% ? 70% Positive displacement pump 2% ? 10% (Theriault et al., 2003) Filtered 80% ? 85% Non-pumpable No beaches In developing conventional slurry tailings management facilities (TMFs), tailings are generally discharged from spigots installed along the embankment  2 of the facility. For surface thickened and paste storage, tailings are discharged from a central location either through risers or from specifically selected locations as determined by site topography. Filtered tailings are generally transported by a radial conveyor stacker or by truck (Davies and Rice, 2001). On a global basis, conventional slurry tailings facilities make up the majority of all existing TMFs. There are roughly the same numbers of thickened plus surface paste tailings and filtered tailings facilities worldwide (Davies et al., 2010; Davies, 2011). One of the advantages of dewatered tailings management is the reduction of failure likelihood resulting from the reduction of water in the TMF. For example, overtopping resulting from a larger volume of water in conventional slurry tailings facilities is not an event that will occur for filtered tailings.  Silva, Lambe and Marr (2008) provide historic failure rates (major accidents only) of tailings facilities. They identified four categories of structures based on operations, engineering and monitoring level ranging from I (Best) to IV (Poor). For a factor of safety of 1.5, the annual probability of slope failure varies from about 0.5 to 1?10-6 depending on the categories. Oboni and Oboni (2013) evaluate the failure of tailings facilities internationally and in the US for a number of time periods. They found that the annual failure rates (expressed per year) for the last decade of the previous century are 2?10-4 worldwide and 8?10-4 in the US. 1.1 Research Question & Objective The research question of this thesis is ?Can a methodology be developed to evaluate whether dewatered TMFs have lower likelihood of failure than conventional slurry TMFs?  The objective of this research is to develop a framework for the estimation of the likelihood of failure resulting in release of tailings for different tailings depositional alternatives: slurry, thickened, paste and filtered tailings.  3 1.2 Thesis Outline The next chapter provides the literature review compiling information from papers, books and websites regarding tailings, TMFs and analysis methods. In chapter 3, a framework is developed for the estimation of the likelihood of failure for different tailings depositional alternatives. The selection of failure modes is also discussed in chapter 3. Chapter 4 presents the results of fault tree analysis for selected failure modes. The results are further reviewed and analyzed in chapter 5. Chapter 6 provides the summary of this study, and recommendations for future research are given in chapter 7.    4 2. Literature Review 2.1 Tailings Management Options Tailings management options can be divided into four types: conventional slurry, thickened, paste and filtered tailings. For conventional slurry storage, tailings are discharged from spigots installed along the embankment of the facility. For surface thickened and paste storage, tailings are discharged from a central location either through risers or from specifically selected locations as determined by site topography. Filtered tailings are generally transported by conveyors or truck (Davies and Rice, 2001). On a global basis, conventional slurry tailings facilities make up the majority of all existing tailings facilities. In regard to dewatered tailings, there are roughly the same numbers of thickened/surface paste tailings facilities to filtered tailings facilities in worldwide operations. Fig. 1 taken from a recent evaluation of global trends in dewatered tailings practice presents a summary of the relative number of dewatered facilities on a global scale (Davies et al., 2010, Davies, 2011). $Fig. 1 Trends in use of dewatered tailings in mining (after Davies et al.,  2010) X5Y!,5%%53!2$#!-7#=#!3#Y!-#,735?548#=Z! )  5  Tailings rheology 2.1.1Rheology is the study of the flow of matter that includes liquid and soft solid materials showing plastic deformation behavior. By considering tailings rheology, it is possible to understand various tailings behaviors in a TMF. In rheology, tailings can be classified as either Newtonian or non-Newtonian fluids. Newtonian fluids exhibit a linear relationship between the applied shear stress (?) and the shear rate (?) as shown in equation (1). The viscosity of fluid (?) is the ratio of the shear stress to the shear rate. ! = ! ? ! (1) Non-Newtonian fluid starts flowing only when the applied shear stress exceeds the yield stress (?y) as expressed in equation (2). ! = 0,  ! < !!  (2) After the applied stress exceeds the yield stress, non-Newtonian fluids exhibit viscous liquid behavior where the viscosity is the function of the shear stress as shown in equation (3). ! = !! + ! ! ? ! ! > !!  (3) Fig. 2 summarizes these Newtonian and non-Newtonian fluids behavior in terms of the applied shear stress and the shear rate. Curve A shows the Newtonian fluids behavior and Curve B, C and D show the non-Newtonian fluids behavior. Curve B shows a linear relationship between the applied shear stress and the shear ratio after the yield stress is exceeded. Curve C shows shear-thinning behavior where the viscosity decreases as the shear rate increases. Curve D shows shear-thickening behavior where the viscosity increases the shear rate increases.  6 $Fig. 2 Typical flow behavior of Newtonian and non-Newtonian fluids (after Boger et al.,  2006) The main factor affecting the yield stress of tailings and thereby differentiating Newtonian and non-Newtonian fluids is the solids content of tailings. More specifically, slurry tailings are classified as Newtonian fluids and dewatered tailings are classified as non-Newtonian fluids. Fig. 3 shows how the yield stress of tailings increases with increasing solids content. The yield stresses and solids contents presented in Fig. 3 are the typical value for tailings from metal mining. 28with the rheological properties necessary for the chosen disposal method (pipeline requirements). Rheological properties sometimes change in the pipeline itself.Once the depositional and pipeline issues have been quantified and optimised on paper, it is possible to determine the thickening requirements represented by point 3 in Figure 3.3. The thickener should be designed and operated to produce the required tailings? properties via determination of thickener size and geometry, and control of flocculation and pre-treatment requirements. If the thickener requirements cannot be achieved then the process is repeated.For clarity, the design sequence is depicted in Figure 3.3 as a linear sequence. However, in reality the disposal system and thickener should be designed using an iterative approach in order to optimise the entire disposal operation.3.4 IMPORTANT RHEOLOGICAL CONCEPTSRheology is the study of the deformation and flow of matter. In terms of fluid flow, materials may be classified as either Newtonian or non-Newtonian fluids. The viscosity (?) of a fluid is defined as the ratio of the shear stress (?) to the shear rate , as shown in Equation 3.1. In many flows, the shear rate is equivalent to the gradient in velocity.  (3.1)Inelastic Newtonian fluids exhibit a linear relationship between the applied shear stress and the shear rate, as shown in Curve A in Figure 3.4. Flow is initiated as soon as a shear stress is applied. The linear relationship between the shear stress and the shear rate indicates a constant viscosity.Concentrated mineral tailings often display non-Newtonian flow behaviour in that they possess a yield stress. The yield stress (?y) is the critical shear stress that must be exceeded before irreversible deformation and flow can occur. For applied stresses below the yield stress, the particle network of the suspension deforms elastically, with complete strain recovery upon removal of the stress. Once the yield stress is exceeded, the suspension exhibits viscous liquid behaviour where the viscosity is usually a decreasing function of the shear rate. Yield stress behaviour is shown by the constitutive relationships of Equations 3.2 and 3.3.  (3.2)  (3.3)Curve B on Figure 3.4 shows a yield stress followed by a linear shear stress ? shear rate relationship, commonly known as Bingham behaviour. Although not a true viscosity according to Equation 3.1, the gradient of this line is referred to as the Bingham plastic viscosity.Table 3.1 lists typical yield stress values. The values listed for thickened tailings disposal ranging from 30 to 100 Pa are indicative of those used in the alumina industry today. There are other thickened tailings strategies where the material is discharged and flows like a river delta, where the yield stress would be greater than 0 but below 30 Pa. Mine stope fill is a true paste material where the yield stress, in our experience, can become as high as 800 Pa.TABLE 3.1 Typical yield stress valuesSubstance Yield stress (Pa)Tomato sauce 15Yoghurt 80Toothpaste 110Peanut butter 1900Thickened tailings disposal 30?100Mine stope fill 250?800In addition to yield stress behaviour, the viscosity of the material will vary with shear rate. As the shear rate is increased, pseudoplastic or shear thinning materials exhibit a decrease in the viscosity (Curve C, Figure 3.4). Dilatant or shear thickening materials exhibit an increase in viscosity with increasing shear rate (Curve D, Figure 3.4). Dilatant behaviour, although relatively rare, is sometimes observed in mineral suspensions. For the different fluid categories, various empirical flow models are used to describe the flow behaviour. The most commonly used equations are the Ostwald?De Waele model for shear thickening or shear ??i?`????i????i>?????i????i>???>?i	FIGURE 3.4 Typical flow curves. A) Newtonian;  B) Bingham (yield-constant viscosity);  C) Yield-pseudoplastic; D) Yiel -dilatantPaste and Thickened Tailings ? A Guide (Second Edition) 7 $Fig. 3 Typical yield stress and solids content of tailings from metal mining !The type of tailings mineral is also the important factor affecting the yield stress and solids content. Fig. 4 presents the yield stress of various types of tailings. The relationship displayed in Fig. 3 therefore exists for each type of tailings shown in Fig. 4. $Fig. 4 Yield stress concentration data for different industry waste streams (after Boger et al.,  2006) 32plant operators. We recommend the use of a cylinder. The equation for evaluating the yield stress from a slump height measurement is given in Equation 3.10:  (3.10)where ???y is the yield stress dimensionalised with respect to ?gh; and S' is the dimensional slump measurement, which is dimensionalised with h, the height of the slump cylinder; ? is the density of the suspension; and g is the acceleration due to gravity.A comparison of the yield stress derived from the slump measurement and the yield stress measurement with the vane is shown in Figure 3.7. Users of the slump method persist in measuring the slump in a linear dimension, centimetres of slump. This is an empirical measure and will vary from material to material depending upon its density. Table 3.2 eloquently illustrates the point that the slump is not a unique physical property measurement. Here, a coal tailings, a gold tailings, and a lead?zinc tailings, are all ????{?????n???????????{????????? ??? ??{ ??? ??n ????>?????i?V?>???>????}??>???>????}?->?`????i?V?>???>????}???->?`????i?V?>???>????}???>?}>?i?i????i??>????}? ?V?i?????i??>????}??? ?V?i?????i??>????}???,i`???`??>????}???,i`???`??>????}??????i???>????}?*>??i?v?????>???i-?i>????i?`????i????*>?-???`???>???v?>V????FIGURE 3.8 Yield stress concentration data for different industry waste streams?x?????x?????x?????x?? ?? ?? ?? {?9?i?`????i????*>?-???`???????FIGURE 3.9 Yield stress concentration data for clay waste from the phosphate industryPaste and Thickened Tailings ? A Guide (Second Edition)T?????????*-???? ? ?>???????>?i??????????? ?? ? 8 Although there is no strict boundary between slurry and dewatered tailings, one possible practical approach is to differentiate tailings in terms of the shear yield stress. For instance, if there is a bucket of unknown tailings that have the shear yield stress of 100 Pa, it can be classified as the lower range of paste tailings.  Slurry tailings 2.1.2Slurry tailings are the mixture of water and the residue after processing mined ores. Generally it has less than 45% solids content in hard rock mining and can be pumped from a mineral processing facility to a TMF using centrifugal pumps. Spigot disposal is normally utilized for slurry tailings. As the tailings deposit, they flow away from an outfall and natural segregation occurs, thereby creating a sloping beach between the embankment and the supernatant pond (Fig. 5). The degree of segregation depends on the particle size distribution of the tailings, the density of the slurry and the specific gravity of the particles. The coarser (or heavier) particles of the tailings naturally settle closer to the discharge point (spigot) with the finer (or lighter) particles settling farther away. The length of beach and its slope angle are dependent on the deposition flow rate from the spigot. Mostly, the expected beach slope angle is 0.5% ? 1.0% within the first several hundred feet. The higher the density of tailings becomes, the steeper the beach slope forms. For conventional slurry tailings, multiple spigot deposition is the most common method utilized to fill a ring dyke. Spigots are installed around the perimeter of the tailings embankment and discharge tailings (Fig. 6). $Fig. 5 Natural segregation of spigot-discharged tailings  9 $Fig. 6 Schematic diagram of multiple spigot disposal at the Twin Creeks Mine, Nevada (Original image is taken from Google Earth)  Thickened tailings 2.1.3Thickened tailings have higher solids content than slurry tailings because of the dewatering. Its solids content ranges between 45% and 65% (typical values for tailings from metal mining), and can be transported through centrifugal pumps. Compression thickeners normally carry out the dewatering process.  Thickened tailings are typically disposed in a conical shape from the center of the cone. Higher solids content allows the construction of tailings deposit with steeper beach slope (typically 1.75% ? 6%) than conventional slurry tailings, ending up with less water in the TMF. It can be dewatered to a non-segregating denser slurry that will provide for non-segregation of particles upon deposition. There is still a considerable volume of water to manage. Therefore the facilities must have an embankment at the lower end of the beach to contain bleeding water as well as surface runoff from precipitation (Fig. 7). A separate return water pond can also be established to prevent water storage on the facility.  10 $Fig. 7 Circular conical disposal of thickened tailings at Sunrise Dam Gold Mine, Australia (Original image is taken from Google Earth) There are several advantages and disadvantages of thickened tailings from the physical, economic and environmental point of view. Firstly, the dewatering cost increases the operating cost of thickened tailings compared to traditional slurry tailings. However, thickened tailings facilities are easier to reclaim than traditional tailings impoundments, which reduces the closure cost. Second, thickened tailings form a self-supporting conical pile with relatively low retaining dykes, which reduces the capital cost. Conversely, such configuration of facility favors overtopping of the facility in case of tailings liquefaction. Static and dynamic liquefaction and adequate freeboard must be carefully assessed. Thirdly, in terms of water management, water recovery during the thickening process is the most important factor. Recovering higher volumes of water results in minimizing the seepage and evaporation loss from the tailings storage. A smaller pond than for conventional slurry tailings also reduces the potential for water to transport large volumes of tailings in case of an embankment  11 failure. In addition, water recovery during the thickening process may represent a significant cost saving and be critical in arid regions.   Paste tailings 2.1.4Paste tailings have higher solids content than thickened tailings. Its solids content ranges between 65% and 70% (typical values for tailings from metal mining). Tailings material dewatering takes place in high rate and deep cone thickeners. Additives (flocculants and coagulants) are typically added to the tailings to achieve higher densities. Although it has the consistency of toothpaste and is difficult to transport by using centrifugal pumps, it can still be transported through positive displacement pumps.  Similar to thickened tailings, paste tailings are deposited from a fixed location and results in a relatively steep deposit slope (typically 2% ? 10%) or from a central deposition point to construct a circular conical deposit. Paste tailings are dewatered to a point where they do not segregate when deposited and ideally have minimal water bleeding when discharged. To contain bleeding water and surface runoff from precipitation, it must have an embankment at the lower end of the beach. When it is deposited on a surface in a sub-aerial manner, like thickened tailings, desiccation and cracking may occur after deposition, increasing evaporation and speeding up consolidation. It has also been reported that ?As the layers of paste cease to flow, desiccation can occur producing cracks. The new overlaying flow fills in the cracks and locks the layers together, forming a more stable structure.? as shown in Fig. 8 (Tailings.info, 2013). Paste tailings management also enables a smoother transition to mine closure than traditional slurry tailings.  12 $ $Fig. 8 Cracked paste and fresh paste depositing over a cracked layer (after Tailings.info, 2013)  Filtered tailings 2.1.5Filtered tailings have higher solids content than paste tailings. Its solids content ranges between 80% and 85% (typical values for tailings from metal mining). It is produced by vacuum or pressure filtration. Gradation of particles and mineralogy of the tailings should be taken into account to achieve such high solids content/low water content. For example, high percentages of clay minerals less than 74?m hinder effective filtration or residual bitumen in oil sands tailings will also affect the performance of filtration plants (Davies and Rice, 2001). Trafficability is typically the main issue for filtered tailings as stated by Davies and Rice (2001) ?The filtered tailings are generally produced at or slightly above the optimum moisture content for compaction as determined in laboratory compaction tests (Proctor Tests). This means that a construction/operating plan is required to avoid trafficability problems. This is especially true in wetter environments since trafficability drops as moisture content rises and if the tailings surface is not managed effectively it can quickly become un-trafficable resulting in significant placement problems and increased operating costs?. Filtered tailings are placed, spread and compacted to form an unsaturated,  13 dense and self-supporting tailings stack requiring no embankment for retention (Fig. 9). Thus there is no beach unlike other types of tailings and material can be treated as an earth fill. To ensure that the land mass composed of filtered tailings is stable, it is highly recommended to compact the material by roller or truck.  Surrounding groundwater, runoff and other surface water should be diverted from the filtered tailings facility by perimeter ditches, drains and groundwater cut-off. Affected groundwater and seepage from the dry stack should be collected and might be re-used in the process. In case the groundwater has been environmentally impacted, it has to be pumped to a water treatment plant (Davies and Rice, 2001). Economics of the dry stack management is critical to the project viability along with the filtering process. Dry stacking of tailings is relatively new technology with less experience available for the cost estimation, operation, water management and so on. High level of day-to-day management is required to achieve success. Dry stack reclamation and closure costs are significantly lower than that for traditional slurry tailings as a result of reduced footprint and the stable surface at the end of operations. There is also a reduction in long-term risk and liability due to the absence of the tailings retention facility and the potential to impound water.  14 $Fig. 9 Filtered tailings deposited at La Coipa Mine, Atacama, Chile (PwC, 2012) 2.2 Construction Method of Slurry TMF TMF construction is staged over the life of the mine. For slurry tailings it begins with a starter dike constructed of natural soils or borrowed materials. Raising the embankment through subsequent lifts using tailings or borrow material is the most common construction technique. The three principal methods are to construct upstream, downstream or centerline structures, which designate the direction where the embankment crest shifts in relation to the starter dyke at the base of the embankment wall (Vick 1990). Three sections below (Upstream construction, Downstream construction and Centerline construction) are based on Vick (1990), Martin and McRoberts (1999), Davies and Martin (2000), Davies et al. (2002) and Tailings.info (2013).  Upstream construction 2.2.1The upstream construction method is the most economical and popular design for a tailings impoundment, mainly due to the minimal amount of borrow or other material required for construction and raising the embankment. The upstream method is also the most common design to fail, causing significant a2=#![-.:8#=!!? +2!a58<2!183#!OH83$5==Q;!h-2,2%2;!a78?#G!Ref: CIM Mining 101 Part D - Mine Waste Disposal.   15 environmental consequences all over the world. There are reported to be more than 3500 TMFs worldwide, of which 50% are of the upstream design type (Davies and Martin, 2000). Tailings are discharged by spigots or cyclones. A series of discharge points are evenly spaced along the embankment to promote laminar flow of the tailings slurry across the beach. A sequence of construction is depicted in Fig. 10. $Fig. 10 Upstream construction method A significant amount of care should be taken when raising the embankment. If the embankment is raised rapidly and the tailings under the raised embankment is not normally consolidated, pore water pressure within tailings will increase, which makes the TMF vulnerable to failure. Likewise, the impoundment and the phreatic surface need to be managed deliberately. Most failures of upstream constructed embankments occur during or after heavy rain causing water accumulation on the impoundment, which can reduce the length of the beach. Therefore upstream construction is favored in arid regions and the location where minimal amounts of water are pumped to the TMF.  Downstream construction 2.2.2The downstream construction method is very versatile and compatible with any type of tailings. It can be used even for water storage since it can be constructed to be as robust as water-retention dams. It is therefore the most stable  16 structure of three slurry tailings deposition options. On the other hand, it requires the greatest quantity of dam fill that increases for successive raises, especially towards the end of the mine life and is often the most costly method. The construction of a downstream embankment starts with the construction of starter embankment. As the embankment is raised, the new wall is constructed and supported on top of the downstream slope of the pervious section, shifting the centerline of the top of the embankment downstream as the embankment stages are progressively raised (Fig. 11). An advantage of the downstream design is that the raised sections can be designed to be of variable porosity, in order to further control the phreatic surface of the TMF. Thus, downstream construction is particularly suited to areas of high seismicity. The installation of impervious cores and drainage layers will allow the facility to hold a substantial volume of water directly against the inner wall of the facility. $Fig. 11 Downstream construction method  Centerline construction 2.2.3Centerline construction is a hybrid between upstream and downstream construction. The material requirements are midway between those of upstream and downstream embankments. The phreatic surface is generally low depending on the materials ? careful monitoring is mandatory. The embankment has good seismic resistance and requires less fill than downstream construction.  17 As with upstream construction, centerline construction relies on the deposited tailings to form the main upstream support for the TMF.. The downstream zone may be constructed of conventional borrow materials or cycloned sand (McLeod et al., 2003). The design can incorporate internal drainage zones (Fig. 12). Therefore, the free water can be tolerated closer to the embankment crest than for upstream construction, without concerns of increasing the phreatic surface and causing a potential risk of failure. $Fig. 12 Centerline construction method 2.3 TMF Failures There are a number of failure causes of a TMF. In 2001, International Commission on Large Dams (ICOLD) performed a comprehensive study and identified 221 tailings dam incidents all over the world, which is based on the database provided by the US Commission on Large Dams (USCOLD) that collected 185 tailings dam incidents in the USA during the period 1917 ? 1989. United Nations Environmental Programme (UNEP) added 26 cases to this database in 1996, and 12 examples were added by ICOLD. After some duplications were eliminated, the total number became 221. Failure statistics are presented for the following failure modes: overtopping, slope instability, earthquake, foundation, seepage, structural, erosion, mine subsidence and unknown. Furthermore the statistics also make a differentiation between failures and accidents. If a tailings facility breaches or tailings are released to  18 the environment causing damages and troubles during operation, it is classified as a failure. Because of tailings and water existing inside of a TMF, failures generally result in catastrophic consequences. If a tailings facility breaches during or before initial filling, it is classified as an accident. Also, if some disturbances happen to a tailings facility during operation not causing any damages to the facility or being rectified before a failure occurs, it is classified as an accident. Fig. 13 presents the statistics for causes of incidents for active and inactive tailings facilities. Tailings facilities are described as ?inactive? when an impoundment is completely filled or when tailings production ceases. The most significant causes of failure of inactive tailings facilities are overtopping and earthquake. The leading causes of incidents for active tailings facilities are slope instability, overtopping and earthquake. $Fig. 13 Tailings dam incident cause comparison with dam status (after ICOLD and UNEP, 2001) The incident causes for failure of active tailings facilities are shown in Fig. 14 separating failures from accidents, where it will be seen that slope instability, overtopping, earthquake and seepage cause more than or equal to 10 failures.  19 $Fig. 14 Tailings dam incident cause comparison with incident type for active dams Fig. 15 provides the total incidents with their causes with respect to tailings facility types. This figure indicates that the leading causes for incidents are slope instability, earthquake, overtopping and seepage: particularly so for upstream-constructed tailings facilities, which are the most prevalent tailings management facilities all over the world. $Fig. 15 Tailings dam incident cause comparison with dam type (after ICOLD and UNEP, 2001)  20 Rico et al. (2008) carried out a detailed search and re-evaluation of these UNEP databases in the scope of an EU project (e-EcoRisk, a regional enterprise network decision-support system for environmental risk and disaster management of large-scale industrial spills). As a result of revision, cross checking and information updating, 147 tailings dam failures in the world were identified with accuracy and 11 failure causes are listed to cover all tailings dam failures as shown in Fig. 16. Note that the failure causes listed by Rico et al (2008) overlaps with some of those listed by ICOLD and UNEP (2001), while others are different. The failure causes listed by the former are: foundation, slope instability, overtopping/overflow, mine subsidence, unusual rain, snow melt, piping/seepage, seismic liquefaction, structural, unknown, and management operation.  $Fig. 16 Distribution of the number of incidents according to cause in the world and in Europe (after Rico et al.,  2008)  21 2.4 Probabilistic Analysis of Tailings Management Facilities Comprehensive studies on failure likelihood of TMFs have been conducted with different approaches. In this section, statistical event tree analyses are investigated as complementary approaches to fault tree analysis that is described in a later section.  Statistical analysis 2.4.1Historic failure rates (major accidents only) of tailings facilities are reviewed by Silva, Lambe and Marr (2008). They propose the presentation in Fig. 17 and identified four categories of structures based on operations, engineering and monitoring level ranging from I (Best) to IV (Poor). Silva et al. (2008) presents the following four categories as they relate to types of facilities: ?Category  ? facilities designed, built and operated with state-of-the-practice engineering. Generally these facilities have high failure consequences; Category  ? facilities designed, built and operated using standard engineering practice. Many ordinary facilities fall into this category; Category  ? facilities without site-specific design and sub-standard construction or operation. Temporary facilities and those with low failure consequences often fall into this category; and Category  ? facilities with little or no engineering.?  22 $Fig. 17 Annual probability of failure vs. factor of safety following Silva, Lambe, Marr (Silva, Lambe and Marr, 2008) Fig. 17 contains data from over 75 projects covering over 4 decades. The projects include zoned and homogeneous earth embankments, tailings embankments, natural and cut slopes, and several earth retaining structures. The authors used an iterative process to arrive at the probability of failure determinations by adopting two data points as reference points for the curves in Fig. 17. The first point is (1.5, 0.0001), which means that for the factor of safety of 1.5, the annual probability of failure is 0.0001. This is based on the historical performance of earth dams designed and constructed with conservative  23 engineering practice. The second point is (1.0, 0.5). This point is suggested by Vick (1994) and based on the theoretical fact that a normally distributed uncertainty on factor of safety gives the annual probability of failure of 0.5 at the factor of safety of 1.0. For the factor of safety of 1.5, the annual probability of slope failure varies from about 0.5 to 1?10-6 depending on the categories. (Silva, Lambe and Marr, 2008) Oboni and Oboni (2013) evaluate the failure of tailings facilities internationally and in the US for a number of time periods. By combining USCOLD (1994), UNEP (1996, 1998) and Davies & Martin (2000) data, they found that the annual failure rates for the last decade of the previous century are 2?10-4 worldwide and 8?10-4 in the US.  Event tree analysis 2.4.2As indicated before the US Bureau of Reclamation and US Army Corps of Engineers have refined the implementation of risk-based evaluations of water retaining dams. These evaluations are based on event tree formulations (U.S. Department of the Interior, 2013).  Event tree analysis as used by these agencies follows a failure from the initiating event, its propagation and development to the final consequence as shown in Fig. 18.  24 $Fig. 18 Example event tree for internal erosion (after U.S. Department of the Interior, 2013) In Fig. 18, the initiating event is internal erosion. Subsequent events are then defined using a divergent branching structure where each branch represents a unique event or state such as initiation, continuation or progression. Event tree analysis is particularly useful when conducting complete risk assessments because it can consider the likelihood of failure events and a range of consequences.  2.5 Fault Tree Analysis  Overview 2.5.1Fault tree analysis is a top down, graphical representation of the critical failures. The fault tree starts with some failure condition and then considers all possible chains of faults that could lead to that failure (Baecher and Christian, 2003). It is a useful tool to identify areas of concern for new system design or for 11-6    Figure 11-5. Sugges ed Internal E osion Potential Failure Mod  Sub Tree Potential failure mode sub trees can be used to develop system response curves that describe the probability of failure as a function of one or more loading parameters such as water surface elevation or ground acceleration.  The event tree is evaluated for multiple loading scenarios.  The number and spacing of load scenarios should be sufficient to describe the shape of the system response curve over the full spectrum of potential loads.  A curve can be fit to the resulting data so that the prob b lity of failu  can be estimated for any load condition by interpolation.  An example system response curve is presented in Figure 11-6.   Figure 11-6.  System Response Curve               Flaw ?          Initiation?          Continuation?          Progression?          Unsuccessful Intervention?          Breach?Internal ErosionNoYesNoYesNoYesNoYesNoYesNoYes01System Response ProbabilityLoad MagnitudeCurve FitAnalysis Points 25 improvement of existing facilities. It also helps identifying the best ways to reduce risk by correcting or mitigating problems. Fault tree analysis is a widely used method in the fields of reliability engineering to determine the likelihood of an accident or a particular functional failure.  Procedure 2.5.2The first step in developing a fault tree is to identify a critical failure and put it at the top of the diagram. This is the ?top level? event to be investigated. Starting with the top event, the possible intermediate causes leading to the top event are identified. Each of these failures is analyzed to identify how they could be caused. Stepwise identification of undesirable system operation is followed to successively lower system levels until further analysis becomes unproductive (ISO/IEC, 2009). When drawing a tree, Boolean logic is used to combine a series of lower-level events. An example of a fault tree and conventional logic gate symbols are depicted in Fig. 19. Note that the simplified fault tree in Fig. 19 illustrates the main concepts. Some symbols typically included in fault trees for mechanical systems are not included. $Fig. 19 Example of fault tree  26 Table 2 Conventional graphic symbols of fault tree  AND gate The higher level event occurs only if all causes occur  OR gate The higher level event occurs if any cause occurs  Top level event Intermediate event The event which needs to be explored (tree-downed) more to quantify the likelihood  Basic event or Root cause Quantifiable failures or errors in a system  Although it is recommended to use a circular shape for basic events, an elliptical shape is also used in this thesis because of space limitation. Table 2 is a summary of conventional graphic symbols used in a fault tree. When there is a higher-level event (X) which occurs only if all lower-level events (say A and B) occur, the AND gate connects these events. When event A and event B are statistically independent, the probability of higher-level event (X) is P(X)%=%P(AB)%=%P(A)%?%P(B)% % % % % (4)%When event A and event B are statistically dependent, the probability of higher-level event (X) is P(X)%=%P(AB)%=%P(A)%?%P(B|A)% % % % (5)%P(B|A) is called conditional probability. In this thesis, conditional probabilities are not assigned (refer to page 62). Thus, the calculation for AND gate will still  27 be just the multiplication. When there is a higher-level event (X) which occurs if any lower-level event (say A or B) occurs, the OR gate connects these events. Then, the probability of higher-level event (X) is P(X)%=%P(AB)%=%P(A)%+%P(B)%?%P(AB)%=%P(A)%+%P(B)%?%P(A)%?%P(B)% (6)%When the likelihood of lower-level event is small, the multiplication of those likelihoods (P(A) ? P(B)) will be negligibly small. Therefore, equation (6) is approximated as P(X)%=%P(AB)%=%P(A)%+%P(B)%?%P(A)%?%P(B)%?%P(A)%+%P(B)%% % (7)%For instance, if the probability of event A is 0.02 and the probability of event B is 0.01, the true value (equation (6)) is 0.0298 and the approximate (equation (7)) is 0.03. The difference is less than 1%, and thus there is no significant difference in using equation (7). When event A and event B are statistically dependent, equation (6) and equation (7) can be written as P(X)%=%P(AB)%=%P(A)%+%P(B)%?%P(AB)%=%P(A)%+%P(B)%?%P(A)%?%P(B|A)% (8)%P(X)%=%P(AB)%=%P(A)%+%P(B)%?%P(A)%?%P(B|A)%?%P(A)%+%P(B)% % % (9)%A rectangular shape event symbol represents a ?top level? event or an intermediate event for which the probability cannot be calculated directly, thus requiring more breakdowns until they become an aggregation of basic events. A circular shape event symbol represents a basic event or root cause for which probability must be quantified directly from other analysis, database or estimates.   28 2.6 Subjective Probabilities of Basic Events Many important uncertainties in risk analysis are not well-adapted to quantitative estimation from data. In some instances no data is available, but only the judgment of experts. The implicit knowledge of experts is based on intuition, past experience, subjective theory, and other qualitative beliefs that are not easily amenable to mathematical representation. Yet, this judgment of experts has been an important source of information in analyzing risk. (Baecher and Christian, 2003)  Heuristics and bias 2.6.1A great deal of experience has shown that subjective probabilities are often affected by biases and heuristics, such as overconfidence, anchoring and representativeness. For example, as to overconfidence, Fischhoff et al. (1977) conducted a range of experiments in which subjects provided answers to general-knowledge questions as well as the subjective probabilities of error only when their answers were correct. The results of experiments (Fig. 20) show their overconfidence that is expressed by the difference between actual and subjective error probabilities.   29 $Fig. 20 Subjectively estimated vs. actual probabilities (Data from Fischhoff et al.  (1977), after Vick (1997)) Folayan et al. (1970) obtained similar results on over-confidence effects from geotechnical engineers. Estimated distributions for compressibility parameters of San Francisco bay mud are provided by geotechnical engineers with up to 17 years of experience. Baecher (1972) further analyzed these prior distributions in comparison with those obtained from subsequent laboratory tests. As shown in Fig. 21, the estimated mean values are lower than that measured. However, the more significant and remarkable fact is that overconfidence produces distributions too narrow to encompass most of the measured data. The one exception is expert 5, a graduate student whose estimated distribution shows gross under-confidence. 504 EXPERT OPINION out to be, sometimes to a shocking extent, as reported in a well-known study by Alpert and Raiffa (1982). Figure 21.1 plots the results of experiments reported by Fischhoff e t  al. (1997) in which three groups of subjects provided answers to general-knowledge questions as well as esti- mated probabilities that their answers were correct. The estimated error probabilities were found to be reasonably well calibrated relative to the actual error frequencies only when the actual probabilities were no less than about 0.1. Their overconfidence, expressed as the difference between actual and judged error probabilities, increased dramatically at smaller values of actual error frequency. The subjects estimated a subjective probability of error as small as lop6 when the actual error frequency was slightly less than a ratio of five orders of magnitude. Moreover, the subjects showed little ability to dis- tinguish among varying degrees of extreme likelihood, with judged probabilities ranging from lo-* to despite actual error frequencies hovering near lo-?. A related and sur- prising finding is that the harder the probability estimation task, the greater the associated overconfidence. For quite easy tasks sometimes under-confidence is displayed, although this effect is poorly understood (McClelland and Bolger 1994). Neither experts in general nor geotechnical experts in particular seem immune from overconfidence. Hynes and Vanmarcke (Hynes and Vanmarcke 1976) reported on predic- tions of embankment failure height made by seven internationally-known geotechnical engineers for a test embankment on soft clay at the MIT 1-95 test site. Figure 21.2 shows each expert?s best estimate and 50% confidence interval for the amount of additional fill needed to fail the embankment, the average of the best estimates, and the actual amount required to cause failure. While the average of the seven best estimates is reasonably close to the outcome, no individual estimate had 50% error bounds large enough to encompass the actual outcome. Had the estimates been unbiased, half would have encompassed the actual failure height at the 50% confidence level, but none did so. Figure 21.3 is similar Overconfidence Bias 1 0.1 =. 0 C 0- LL % 0.01 2 L 0.001 2 k 4 0.0001 - 5 < 0.00001 0.00000 1 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 Subjective Probability of Error Figure 21.1 Subjectively estimated vs. actual probabilities. (Data from Fischhoff et al. (1997), after Vick, .  G., 1997, ?Dam s f ty risk assessment: new directions,? Water Power and Dam Construction, Vol. 49, No. 6, reproduced with permission of International Water Power and Dam Construction.)  30 $Fig. 21 Subjective estimates of the compressibility of San Francisco Bay mud compared to test results for five experts (after Folayan, J., Hoeg, K. and Benjamin, J., 1970)  As seen from the above, people including experienced geotechnical engineers are not inherently proficient at quantifying subjective probabilities, at least in the sense of providing figures that are consistent, coherent, and well calibrated. Although the effect of biases and heuristics cannot be completely removed, it could be reduced or mitigated by eliciting expert judgment (Baecher and Christian, 2003).  Anchoring and adjustment 2.6.2Anchoring and adjustment also have been a problem in the estimation of subjective probabilities. When people are asked to estimate a value, they often begin with the best estimate and then adjust the value up or down. People are apt to stick too close to the initially estimated value and cannot adjust 506 EXPERT OPINION the seminar were also invited to give their estimates and their 50% intervals ?capture[d] the true value 62% of the time.? Slovic et al. (1982) and others have cited these and similar findings in suggesting that substantive expertise, or capability within one?s specialized knowledge domain, has no necessary relationship to normative expertise or ability to provide coherent and unbiased probability judgments. On the other hand, at least some evidence with experts assess- ing probabilities about professional subjects with which they are familiar suggests that they may be more calibrated than are non-experts (viz., weather forecasters (Winkler and Murphy 1968) and auditors (Smith and Kida 1991)). Similar over-confidence effects have been shown in subjective estimates of proba- bility distributions provided by geotechnical engineers. Folayan et al. (1970) obtained estimated distributions for compressibility parameters of San Francisco bay mud from engineers with up to 17 years of experience. Baecher (1972) further analyzed these prior distributions in comparison to that obtained from subsequent laboratory tests. As shown in Figure 21.4, the estimated means were lower than that measured, but, more significantly, overconfidence produced distributions too narrow to encompass most of the measured data. The one exception was subject 5, a graduate student whose estimate showed gross under-confidence. Why over-confidence? There are many suggestions in the literature. Keren (1994) sug- gests that anchoring and adjustment may be to blame. People may anchor on a probability estimate reflecting intermediate difficulty, say 75%, and adjust up or down - but not suffi- ciently - depending of the perceived difficulty of the estimation task. Ferrell and McGoey (1980) present a similar argument, but the literature contains other attempted explanations as well (McClelland and Bolger 1994). Subjective Estimates of Compressibility of San Francisco Bay Mud - - -. Test Data - Expert 1 ---- Expert 2 Expert 3 Expert 4 Expert 5 0.1 0.2 0.3 0.4 0.5 0.6 Compression Ratio Figure 21.4 Subjective estimates of the compressibility of San Francisco Bay mud compared to test results for five experts (after Folayan, J., Hoeg, K. and Benjamin, J., 1970, ?Decision Theory Applied to Settlement Predictions,? Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 96, No. SM4, pp. 1127-1141, reproduced by permission of the American Society of Civil Engineers).  31 adequately to reflect uncertainty. This type of tendency is called ?anchoring and adjustment? that typically result in overconfidence in estimated distributions. There is one well-known way to avoid ?anchoring and adjustment?. When people are asked to estimate the undrained shear strength of soil, for example, a broader range of evaluated uncertainty and a better calibration are produced if they first state the possible largest value of the strength, then the lowest, and only afterwards focus on a central value. (Baecher and Christian, 2003)  Expert elicitation 2.6.3In discussing expert elicitation Baecher and Christian (2003) state: ?A common misconception in eliciting expert judgment is that people carry fully-formed probabilistic opinions around in their heads on almost any subject of interest and that the focus of an elicitation process is merely to access these pre-existing opinions. Actually, people do not carry fully-formed constructs around in their heads but develop them during the process of elicitation. Thus, the elicitation process needs to help experts think about uncertainty, needs to instruct and clarify common errors in how people quantify uncertainty, and needs to lay out checks and balances to improve the consistency with which probabilities are assessed.?  The steps in using expert elicitation proposed by Beacher and Chritian (2003) to quantify judgmental probabilities are:  1. Identify the general uncertainties for which the probabilities need to be assessed. 2. Select a panel of experts representing the spectrum of expertise about the identified uncertainties. 3. Decide on the specific uncertainties for which the probabilities need to be assessed.  32 4. Use a short training program on concepts, objectives, and methods as well as common errors that people make when attempting quantification of probabilities. 5. Next, elicit the judgmental probabilities of individual experts based on their expertise. 6. Facilitate the interaction of the experts in their evaluations.  7. Document the process and communicate the outcomes with the panel of experts.  Reliability modeling 2.6.4Engineering models may be available or should be developed for predicting the behavior of a structure such as components of a TMF. In reliability analysis, probabilities and uncertainties are assigned to the input parameters that determine the behavior of these engineering models. With the combined use of engineering models and reliability analysis, the problem is changed from directly estimating the likelihood of failure to estimating the probabilities and uncertainties of the input parameters (Baecher and Christian, 2003). Van Zyl et al. (1996) developed a probabilistic risk assessment for a tailings impoundment founded on paleokarst in which a fault tree and reliability models are used (Fig. 22).  33  Fig.22 Fault tree for tailings embankment failure founded on paleokarst (after Van Zyl et al.,  1996) Notes. Human Adivity Causes Vdd Failure Open Cavity Roof Mllapsos RBsuning i 1.0 -?OW LOGICAL GATE (SUM OF PROBABILITIES). (PROBABILITIES MUST BE CALCULATEDIASSIGNEO TO ALL ?BASIC EVENTS (SHOWN AS CIRCLES). SUWECTIVE PROBABlLiTlES CAN BE USE0 BASE0 ON EXPERIENCE. TAILINGS RELEASE. DUE TOTHE PRESENCE OF PALEOREST. CAN ONLY HAPPEN INTHE EVENTS OCCUR IN THE SEQUENCE SHOWN ON THiS FiGURE 2. fl -*AND? LOGICAL GATE 3. 4. Rapid u IE2.1.1 I E2.1.2 I E2.1.3 and Flows Removad by Material Liquefiers Material by internal Erosion into Mins Piping Finoe Removal b b Q Meterial Material Continuous Liquifiable Liqulfiable ConneCtion in the Cavity Over Suificient Time No Mnigation no seeiing of infiow .3.2 Existing Void Due is Size Lowerin Figure 22.6 Fault tree for Karst. (Van Zyl, D., Miller, I., Milligan, V. and Tilson, W. J., 1996, ?Probabilistic Risk Assessment for Tailings Impound- ment Founded on Paleokarst,? Uncertainty in the Geologic Environment, Madison, WI, pp. 563-585, reproduced by permission of the American Society of Civil Engineers). CJI fr!  34 Firstly, they designed a conceptual model for limestone as shown in Fig. 23. Based on this conceptual model, they also developed reliability models for some of basic events in their fault trees. The distributions of input parameters for reliability model were obtained from site characterization drilling and the probabilities of the basic events were calculated based on the reliability model. For example, a reliability model to calculate the probability of ?Cavity of sufficient size at critical location? was presented. It was assumed that the probability of the number of cavities exceeding a critical dimension over a specific length of embankment could be determined from the binominal distribution. The main input parameters were the mean length of the cavities and the mean length of intact rock segments. These two input parameters were obtained from exploratory borehole information, shown in Fig. 24. $Fig. 23 Conceptual model for limestone (after Van Zyl et al.,  1996) $Fig. 24 Distribution of cavity length (left) and intact bedrock length (right) from exploratory boreholes (after Van Zyl et al.,  1996)  35 The development of reliability models is only possible for site-specific conditions. These models are not simple to develop and also require site-specific information that, in most cases are costly and difficult to obtain.   36 3. Framework, Selection of Evaluation Method and Failure Modes 3.1 Framework The objective of this research is to develop a framework for the estimation of the likelihood of failure for different tailings depositional alternatives: slurry, thickened, paste and filtered tailings. This framework will address the following: ? Selection of representative failure modes for the depositional alternatives ? Selection and development of the evaluation method (statistical analysis, event trees or fault trees) ? Methodology to calculate the probability of failure This framework is not focused on site-specific conditions but on a broad view of international experiences with the design and performance of tailings depositional alternatives across the industry and many climatic regions. The outcomes can at best be very broad and only representative of the methodologies applied. This chapter of the thesis presents the development of the framework. 3.2 Selection of Evaluation Method In Chapter 2 three probabilistic methods are described that can potentially be used in this research, namely statistical analysis, event trees and fault trees. Statistical analysis is an attractive approach as the first reaction is that it presents a useful historic perspective on TMF failures. However, the ranges of site conditions, design and operating details are not clearly defined and the statistical numbers may provide at best a broad general estimate of the site-specific likelihood of failure of a TMF. The failure analyses described in Chapter 2 did not include any dewatered tailings facilities and therefore the  37 statistical approach will not provide any insights in probability of failure of dewatered tailings facilities.  Fig. 25 describes the difference between event tree analysis and fault tree analysis. Event tree analysis starts from the critical failure and reaches to a range of consequences. When addressing risk assessment, event tree analysis is useful because it can take into account the initial likelihood of failure and the consequences of an event. However, it does not focus on estimating the likelihood of critical failure but focuses more on how the consequences will unfold if a specific failure happens. Furthermore, the likelihood of initiating event, critical failure in this case, is often incorporated from statistical data or fault tree analysis. In contrast, fault tree analysis investigates the causes or components of the failure event. A site-specific fault tree can provide specific insights in the critical events that must be considered in design and monitoring.  In an event tree all subsequent steps are independent events effectively connecting them by ?AND? gates. Hence the likelihood of final consequence tends to be lower as the number of step increases whereas fault tree analysis can take advantage of ?AND? and ?OR? gates to evaluate the failure. Fault tree analysis fits better into the framework for this research as it provides the opportunity to include the failure causes and mechanisms based on a broad evaluation of the industry. Fault tree analysis is therefore selected to examine how the likelihood of critical failure varies among tailings depositional methods. The following are specific features of the fault trees: ? The overall structure of the fault tree provides insight in the range of failure causes and interactions that could occur ? Moving from slurry to dewatered tailings will not only impact the structure of the fault trees but will also change the overall probabilities of the top event occurring; this makes the fault tree a useful visual and analytical tool    38 ? The basic events can be considered as the ?critical? design and management aspects for each fault tree; they can become the focus for attention during the design and monitoring of a TMF $Fig. 25 Simplified graphical representation of event tree analysis and fault tree analysis (made by the author based on RRC, 2013) 3.3 Failure Modes It is recognized that on a site specific basis there can be many causes for tailings failure, which can span the range of physical, chemical, biological and human failure. In this thesis only physical failures leading to release of tailings to the environment are considered. The following 5 failure modes are proposed for this evaluation based on review of the literature and the evaluations below: overtopping, static liquefaction, internal erosion, static slope instability and seismic slope instability. U.S. Department of the Interior (2013) has very comprehensive risk analysis reports on failure modes of water retention dams. Fig. 26 shows the list of these reports excerpted from their website and failure modes they cover in these reports. They covered overtopping, internal erosion, static slope instability for various types of water retention dams. Seismic slope instability and a number of  39 structural failure causes are also evaluated. Since their focus is on water retention dams, some failure modes only true for water retention dams are covered in their reports such as trunnion friction radial gate failure. Those failure modes are generally classified as structural failure in Fig. 26 and not selected as the representative failure modes for TMFs. Although static liquefaction is not covered in their reports because water retention dams are basically well-compacted structures with high level of engineering controls, it has been a big concern for tailings facilities for a long time. Thus static liquefaction is added to the above four failure modes, and eventually 5 representative failure modes are selected for tailings management facilities $Fig. 26 Risk analysis reports provided by U.S. Bureau of Reclamation (excerpted from U.S. Department of the Interior, Bureau of Reclamation?s website) In Chapter 2 (Fig. 13 to Fig. 16) the results of the tailings failure analysis  40 provided by UNEP (2001) and Rico, et al (2008) are presented. However, they list failure causes that trigger failure modes leading to failure; this hierarchy is shown in Fig. 27. To show that those failure causes are included in the selected representative failure modes, the compilation of failure causes into failure modes is attempted. $Fig. 27 Relationship between failure causes, failure modes and failure In Fig. 28 the 8 failure causes of UNEP are represented in terms of the 5 proposed above. Mine subsidence, erosion and earthquake are considered to be failure causes triggering a sequence of events leading to failure rather than directly leading to failure. Overtopping and slope instability are considered to be failure modes since these two can directly result in the failure of a TMF. ?Foundation? and ?Structural? failure are interpreted as aggregation of failure causes, such as cracks in foundation or spillway failure, resulting in different failure modes. Seepage is interpreted as internal erosion.  41 $Fig. 28 Compilation of 8 failure causes from ICOLD and UNEP (2001) into 5 failure modes Fig. 29 shows a similar compilation for the 11 failure causes of Rico, et al (2008) are represented in terms of the 5 failure modes. Unusual rain, snow melt, mine subsidence and management operation are considered to be failure causes that initiate a string of failure. Overtopping and slope instability are considered to be failure modes that can directly result in failure. The categories ?Foundation? and ?Structural? can be various failure causes rather than failure modes. Piping/Seepage is interpreted as internal erosion, while seismic liquefaction is included in seismic slope instability.  42 $Fig. 29 Compilation of 11 failure causes from Rico et al. (2008) into 5 failure modes It is possible to select different failure modes or add/remove some failure modes from these 5 failure modes for specific site conditions. However, the purpose of this research is not to cover 100 percent of all TMF failures but to develop a framework based on an understanding of the mechanisms. These 5 failure modes are considered to have distinguishably different mechanisms that can occur and that they are collectively exhaustive enough to cover almost all of the TMF failures, thereby helping to understand how the likelihood of TMF failure will change among different tailings. The compilations in Fig. 28 and Fig. 29 confirm that the 5 failure modes selected for this research are representative of physical failures observed and previously identified and evaluated for tailings impoundments. The following sections provide further descriptions of these failure modes.   43  Overtopping 3.3.1Overtopping can be divided into two major failure modes: sustained overtopping and wave overtopping (Fig. 30). Sustained overtopping can occur due to water level increase in the TMF, and wave overtopping can occur due to waves washing over the crest. Water level increase until exceeding the dam crest can be caused by crest erosion, crest subsidence, poor pool management or major climatic events. Overtopping from waves normally results from strong wind, earth/rock slide into the reservoir or design error. In general, sustained overtopping results in more catastrophic failure than wave overtopping. Overtopping is often associated with climatic events such as heavy rainfall, rapid thaw or ice blockage of spillway. For example, Merriespruit Mine in South Africa failed because of overtopping in 1994. During the evening on Feb 22nd, heavy rainfall caused an increase in the water surface elevation on the impoundment. Although personnel from the mine tried to release water through spillways and warn people living close to the mine, the high phreatic surface led to the breach of the dam. 2.5 Mt tailings were released in this incident and traveled 2,000 meters, killing 17 people. Another example is the  Silver King Mine failure in 1974. On Jan 16th, rain on heavy snowpack caused the impoundment to fill to capacity, and emergency pumping was insufficient to prevent overtopping with the loss of 2 million gallons of water and 6,000 m3 of tailings. (ICOLD and UNEP, 2001).  44 $Fig. 30 Schematic diagram of sustained overtopping and wave overtopping  Static liquefaction 3.3.2Static liquefaction or flow liquefaction refers to the process whereby a saturated or partially saturated and contractive soil loses its strength in response to an applied static stress. Static liquefaction can undermine the stability of a TMF, thereby leading to the release of tailings to the environment.  In order for static liquefaction to happen, the static shear stress must exceed the minimum liquefied undrained shear strength as can occur in the case of undrained loading of contractive material. When undrained shear stress is applied, a contractive material undergoes strain softening during which the shear stress reduces under continuous shear strains. Thus, if a triggering event places a large enough undrained stress on a TMF containing contractive materials, the shear strength will be reduced until it falls below the static shear stress resulting in static liquefaction. Fig. 34 (described below) further clarifies the process of strain softening response during undrained loading. It is critically important to know whether materials comprising a TMF are contractive or dilative under shear stress. The critical state locus (CSL) shown in Fig. 28 can be obtained from laboratory testing while the state parameter ?  45 is a theoretically sound index of material behavior and can be readily interpreted from a cone penetration test. The state parameter depends on both the density and confining stress of the soil, since it is a measure of the void ratio difference from the CSL as depicted in Fig. 31. The CSL serves as a reference state ? representing the state where a soil will continue to shear under constant stress and constant volume conditions. When a soil is sheared, loose sands contract and dense sands dilate towards the critical state condition at large shear strains, with ? providing a measure of dilatancy (Been et al., 2012). The void ratio where the change in volume of specimen remains constant during shearing is called ?critical void ratio? represented as ec in Fig. 31. $Fig. 31 Definition of state parameter, ?  (after Been et al.,  2012)  Internal erosion 3.3.3Internal erosion is soil particle movement by water flow within a TMF. Potential failure modes for internal erosion can be classified into general categories with respect to the physical location of the internal erosion pathway continue to shear under constant stress and constant volume conditions. When a soil is sheared, loose sands contract and dense sands dilate towards the critical state condition at large shear strains, with \ providing a measure of dilatancy. Many soil behaviors are a function of \ in-cluding friction angle, penetration resistance, cyclic shear strength and undrained shear strength. In fact, the normalized CPT penetration resistance qc1Ncs is a surrogate for \(Robertson 2010), but qc1Ncs lacks the theoretical underpinning of plasticity theory and mechanics that comes with the us  of \ The ?state ?parameter ?? ?is ?the ?preferred ?measure ?of ?in ?situ ?state ?partly ?because ?it ?is ?a ?theoreti-cally sound index of material behavior, but equally important is the fact that it can be readily in-terpreted from CPT data. Characterization of tailings materials for engineering analyses can be split into two parts: (1) determining the in situ state of the material, and (2) determining the ma-terial behavior as a function of state. This paper deals with the first part of the problem. A com-panion paper (Been et al. 2012) considers the post-liquefaction residual strength of tailings as a function ?of ??. 2 CALIBRATION CHAMBERS FOR PENETRATION TESTING Penetration tests involve a complex loading of soils, in which the penetration resistance and oth-er parameters such as sleeve friction and pore w ter pressure are measured. From these meas-urements, we need to infer engineering properties or behaviors. A review of geotechnical litera-ture will reveal correlations with numerous engineering parameters, all from just three measurements made with the CPT. Clearly, more information and testing of soils is needed to determine these parameters with any accuracy, and many authors recognize that fact. However, a sensible and defensible approach is the one recommended here ? use the CPT to determine just one parameter, the in situ state, and use laboratory or field measurements to determine the engi-neering behavior as a function of the in situ state. Determination of the in situ relative density from penetration tests has been studied for many years. In the mid 1970s, several large calibration chambers were built and used for this purpose. Marcuson & Biegenowski (1977) reported SPT tests in a relatively crude testing chamber, with curves showing how penetration resistance changed as a function of stress level for three differ-ent sands. CPT calibration chambers were built at universities in the USA (Lhuer 1976, Harman 1976, Tringale 1983), at research institutions in Australia (Parkin et al. 1980), Norway (Parkin & Lunne 1982) and Italy (Baldi et al. 1982) and at a commercial laboratory in Canada (Been et al. 1987a). The approach in all calibration chamber programs is common. Material is placed in Figure 1. Definition of state parameter, \.  46 (U.S. Department of the Interior, 2013). Internal erosion can take place in an embankment, foundation or contact area between embankment and foundation. In any case, hydraulic gradient and specific material susceptibility such as plasticity, dispersiveness and particle gradation play a critical role. The process of internal erosion can be broken into 2 phases: initiation and progression. Garner and Fannin (2010) developed a Venn diagram to describe how internal erosion initiates as shown in Fig. 32 below. Initiation process starts where 1) material susceptibility; 2) critical stress condition; 3) critical hydraulic load are present. These three conditions are described by U.S. Department of the Interior (2013) as follows: ?Material susceptibility is the relative erosion resistance (plasticity) and dispersiveness of a soil. The critical hydraulic load is related to the hydraulic energy required to invoke a mechanism of internal erosion, by means of seepage flow through the dam. In other words, this factor relates to the seepage gradients and velocities present in the embankment or foundation and whether they are sufficient to induce particle movement. The critical stress condition is related to the inability to resist internal erosion due to the magnitude of effective stress, with recognition that stress varies spatially and/or temporally within the body of the dam.? Even if internal erosion initiates, it will not progress as long as a TMF has an adequate filter based on appropriate criteria. Without an adequate filter and successful intervention, the probability of progression is virtually certain. From where initiation starts, it could progress by forming a roof and concentrated leak, which could lead to breaching of a TMF.  47 $Fig. 32 Factors affecting the initiation of internal erosion (after Garner and Fannin, 2010) Thus, the fault tree for internal erosion is constructed in terms of three factors listed in Fig. 32 and where internal erosion initiates and progresses.  Static slope instability 3.3.4Static slope failure happens when the imposed stress on the embankment or foundation exceeds their effective strength. Two main factors affecting the static stability of slope are the shear strength of tailings and pore pressure. The shear strength of tailings increases as the density of the tailings increases. Higher density can be achieved by densification, natural evaporation, and consolidation after deposition. Over consolidated tailings have lower void ratio and thus show dilative behavior when sheared.. Compaction of tailings after deposition has a large influence on the stability of embankment slope. The location of the phreatic surface in a TMF is also an important factor for static slope instability, pore pressure increases as phreatic surface rises.   48 $Fig. 33 Factor of safety relative to the piezometric height in dam (after Kealy and Busch, 1971) Fig. 33 illustrates the relationship between the factor of safety and the height of dyke with the height of piezometric water surface relative to the embankment surface. The rise of piezometric head drastically reduces the factor of safety (Kealy and Busch, 1971). The compaction of tailings is readily applicable to dewatered tailings. Therefore, the likelihood of static slope stability for dewatered, especially filtered tailings, will be lower than for slurry tailings.  Seismic slope instability 3.3.5Seismic slope instability is a failure mode that occurs under cyclic loading from an earthquake or other seismic loading. Fig. 34 schematically presents the behavior of saturated, contractive, sandy soil during undrained loading (Olson and Stark, 2003). It depicts how the contractive soil loses its strength under static or cyclic loading and finally reaches the ?liquefied shear strength?  49 represented as su(LIQ) in Fig. 34. $Fig. 34 Schematic undrained response of a saturated, contractive sandy soil (after Olson and Stark, 2003) Under cyclic loads, strength decreases of a TMF and stress increases happen at the same time. The extent of strength decrease and stress increase depends on the characteristics of materials in a TMF. For example, loose soils are mostly contractive under undrained cyclic loads, which leads to pore pressure increase and finally causes seismic slope instability. Aside from the characteristics of material, size and duration of cyclic loads are also a predominant factor. Thus, it is reasonable to consider size and duration of cyclic loads and material susceptibility to seismic slope instability when analyzing the seismic reliability of a TMF. There are four sub-failure causes that can lead to seismic slope instability: seismic liquefaction, surficial deformation, slope failure and overtopping. Seismic liquefaction is caused by strain softening response of tailings under cyclic loads as explained above. Surficial deformation can happen when surface movement caused by an earthquake near a TMF exceeds the designed distance. Slope failure occurs when the total stress (cyclic loads plus static loads) imposed on a TMF exceeds the effective strength of a TMF. Overtopping results from crest subsidence and Seiche induced by an earthquake. Although TMFs are designed, constructed and operated on the assumption of probable maximum 21Figure 2.1. Schematic undrained response of a saturated, contractive sandy soil 50 earthquake (PME), seismic slope instability happens when the magnitude of earthquake exceeds PME.    51 4. Fault Trees Fault trees are developed in this chapter for each of the failure modes selected for this evaluation, i.e overtopping, static liquefaction, internal erosion, static slope instability, seismic slope instability. These fault trees are in a broad sense representative of international practices and experiences and may be considered generic in nature. They do not reflect any site-specific conditions but integrates experiences at many different sites. Project-specific conditions will result in much different fault trees, and also potentially different combinations of failure modes and pathways than selected here (Van Zyl et al., 1996).  Fig. 35 shows the fault tree combining the separate failure modes when ?top level? failure is defined as ?release of tailings to the environment?. Fault trees for each failure mode are subsequently presented in Fig. 36 to Fig. 41. Note that the fault tree in Fig. 38 is a continuation of that in Fig. 37. In this thesis, the volume of released tailings is not addressed because it is not the cause but the consequence of failure. Even though the probability of 1 m3 of tailings release and 1 million m3 of tailings release might be different, the structure of fault tree would be still the same. Thus, it should be noted that these fault trees could be used to estimate the likelihood even when dealing with the amount of released tailings, however the likelihood of the basic events may be different. However, it is not further analyzed here because that is not the purpose of this research. As the basic structures of fault trees are considered to be the same among different TMFs (upstream/centerline/downstream constructed slurry, and dewatered TMF), failure modes may have different likelihoods for different TMFs due to ?removal? of some of the failure causes and mechanisms. To visualize those differences, events that are eliminated from the fault tree for dewatered tailings management facilities are shaded. For example, all the boxes of Fig. 36 (fault tree for overtopping) are shaded indicating that these causes and mechanisms do not occur for dewatered tailings. This assumes that  52 there is not large variability of solids content delivered to the dewatered tailings facilities. In the case of large variability, the fault tree may have to be revised or the likelihoods of basic events will have to be re-evaluated. The author and his adviser, Dirk van Zyl, reviewed the structures of the fault trees and further advice was also solicited from Mr. Jack Caldwell, Robertson GeoConsultants, Vancouver, BC. 4.1 Assigning Likelihoods for Basic Events As noted above, the framework for this research is based on a broad view of international experiences with the design and performance of tailings depositional alternatives across the industry and many climatic regions. The likelihoods of occurrence of basic events cannot be ?calculated? based on probabilistic models of site-specific conditions. It was therefore decided to use a form of expert elicitation in assigning likelihoods of occurrence to these basic events. The values were discussed between the author and his adviser (Dr. Dirk van Zyl) and further advice was also solicited from Mr. Jack Caldwell, Robertson GeoConsultants, Vancouver, BC. The experience and engineering judgment of these individuals was the basis for assigning the likelihoods. Table 3 summarizes the probabilities and remarks of each basic failure event contained in the fault trees. These probabilities are considered to be for a generic slurry TMF with upstream construction representative of the international mining industry.  $Fig. 35 Fault tree for the release of tailings to the environment  53 $Fig. 36 Fault tree for overtopping $Fig. 37 Fault tree for static liquefaction  54 $Fig. 38 Fault tree for downstream surface eroded from overtopping $Fig. 39 Fault tree for internal erosion  55  Fig. 40 Fault tree for static slope instability $Fig. 41 Fault tree for seismic slope instability 56 Table 3 Probabilities of basic failure events Event&ID& Description& Remarks& Probability&Overtopping& ! &E1.1.1.1.1.1! Head!cut!advances!to!upstream!face! Unsuccessful!intervention!or!detection!of!head!cut!formation.!Assume!likelihood!is!1:100.! 0.0100!E1.1.1.1.1.2! Head!cut!formation! Tailings!are!highly!erodible!and!likelihood!of!this!event!is!estimated!as!1:50.! 0.0200!E1.1.1.1.2! Crest!deformation! Has!occurred!at!mines!or!dams.!Assume!likelihood!is!1:400.! 0.0025!E1.1.1.2! High!pool! Assume!management!control!in!place.!Likelihood!of!this!event!is!1:200.! 0.0050!E1.1.2.1.1! Slurry!inflow!exceeds!design!capacity! Dependent! on! quality! of! tailings! management.! Assume! it! is! well! done! and!therefore!the!likelihood!of!this!event!is!1:200.! 0.0050!E1.1.2.1.2! Natural!ore!variability! Dependent! on! experience! in! similar! materials! as! well! as! using! advanced!prediction!techniques.!Assume!likelihood!is!1:200.! 0.0050!E1.1.2.1.3! Design!error! Extensive!experience!in!slurry!tailings!is!available.!Assume!likelihood!is!1:200.! 0.0050!E1.1.2.1.4! Exceedance!of!design!criteria! Conditions! based! on! design! criteria! are! not! achieved! because! of! operational!error!or!lack!of!climate!change!considerations.!Assume!likelihood!is!1:100.! 0.0100!E1.1.2.2.1! Heavy!rain!exceeds!PMP! Similar!to!the!previous!event!because!climate!change!evaluations!have!not!been!included.!Assume!likelihood!is!1:100.! 0.0100!E1.1.2.2.2! Rapid!thaw! Potentially! resulting! from! climate! change! or! incomplete! climatic! information.!Assume!likelihood!is!1:100.! 0.0100!E1.1.2.3! Unsuccessful!intervention! Water! surface! elevation! is! kept! at! high! for! long! term!with! unsuccessful! or! no!intervention.!Assume!likelihood!is!1:200.! 0.0050! 57 Event&ID& Description& Remarks& Probability&E1.2.1! High!pool! Similar!to!E1.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E1.2.2.1! Strong!wind! Incomplete!climatic!information.!Assume!likelihood!is!1:100.! 0.0100!E1.2.2.2! Earth/Rock!slide! Resulting! from! surrounding! terrain! slopes! sliding! into! tailings! basin.! Assume!likelihood!is!1:100.! 0.0100!Static&liquefaction& ! !E2.1.1! Downstream!surface!eroded!from!overtopping! The!likelihood!was!derived!from!calculations!of!the!fault!tree!in!Fig.!38.! 0.0006!E2.1.2! Rapid!embankment!raise! Due! to!poor!understanding!of! excess!pore!water!pressure! resulting! from! rapid!raises.!Assume!likelihood!is!1:100.! 0.0100!E2.1.3.1.1! Slurry!inflow!exceeds!expected!amount! Similar!to!E1.1.2.1.1.!Assume!likelihood!is!1:200.! 0.0050!E2.1.3.1.2! Natural!ore!variability! Similar!to!E1.1.2.1.2.!Assume!likelihood!is!1:200.! 0.0050!E2.1.3.1.3! Design!error! Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E2.1.3.1.4! Exceedance!of!design!criteria! Similar!to!E1.1.2.1.4.!Assume!likelihood!is!1:100.! 0.0100!E2.1.3.2.1! Different!depositional!behavior! Lack! of! understanding! of! tailings! behavior,! related! to! experience! of! designer.!Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E2.1.3.2.2! Design!error! Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E2.1.3.2.3! Change!in!material!characteristics! Has! occurred! due! to! ore! body! and! processing! changes.! Assume! likelihood! is!1:100.! 0.0100!E2.1.3.3.1! Heavy!rain!exceeds!PMP! Similar!to!E1.1.2.2.1.!Assume!likelihood!is!1:100.! 0.0100!E2.1.3.3.2! Rapid!thaw! Similar!to!E1.1.2.2.2.!Assume!likelihood!is!1:100.! 0.0100! 58 Event&ID& Description& Remarks& Probability&E2.2.1! Undrained!situation! More!likely!in!finer!materials!deposited!near!discharge!points.!Assume!likelihood!is!1:20.! 0.0500!E2.2.2! Contractive!material!(?!>!Y0.05)! Most! likely! in! weather! climates! where! desiccation! does! not! occur.! Assume!likelihood!is!1:20.! 0.0500!Downstream&surface&eroded&from&overtopping& ! !E2.1.1.1.1.1! Crest!deformation! Similar!to!E1.1.1.1.2.!Assume!likelihood!is!1:400.! 0.0025!E2.1.1.1.1.2! High!pool! Similar!to!E1.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E2.1.1.1.2.1.1! Slurry!inflow!exceeds!design!capacity! Similar!to!E1.1.2.1.1.!Assume!likelihood!is!1:200.! 0.0050!E2.1.1.1.2.1.2! Natural!ore!variability! Similar!to!E1.1.2.1.2.!Assume!likelihood!is!1:200.! 0.0050!E2.1.1.1.2.1.3! Design!error! Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E2.1.1.1.2.1.4! Exceedance!of!design!criteria! Similar!to!E1.1.2.1.4.!Assume!likelihood!is!1:100.! 0.0100!E2.1.1.1.2.2.1! Heavy!rain!exceeds!PMP! Similar!to!E1.1.2.2.1.!Assume!likelihood!is!1:100.! 0.0100!E2.1.1.1.2.2.2! Rapid!thaw! Similar!to!E1.1.2.2.2.!Assume!likelihood!is!1:100.! 0.0100!E2.1.1.2.1! High!pool! Similar!to!E1.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E2.1.1.2.2.1! Strong!wind! Similar!to!E1.2.2.1.!Assume!likelihood!is!1:100.! 0.0100!E2.1.1.2.2.2! Earth/Rock!slide! Similar!to!E1.2.2.2.!Assume!likelihood!is!1:100.! 0.0100!Internal&erosion& ! !E3.1.1! Concentrated!flow!exists! Alluvial!foundation!subjected!to!continuous!recharge!from!pool!or!other!sources,!less!likely!when!experienced!designer!is!involved.!Assume!likelihood!is!1:100.! 0.0100! 59 Event&ID& Description& Remarks& Probability&E3.1.2! Unsuccessful!intervention! Concentrated!flow!in!foundation!is!undetected!or!not!treated!properly.!Assume!likelihood!is!1:200.! 0.0050!E3.2.1.1.1! High!water!pressure! High!water!pressure!can!be!tolerated!in!this!case.!Assume!likelihood!is!1:200.! 0.0050!E3.2.1.1.2! Specific!material!susceptibility! Of!similar!magnitude!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E3.2.1.2! Initiation!at! the!contact!of! the!embankment!and!foundation! Feature!in!foundation!is!not!identified!during!construction.!Assume!likelihood!is!1:100.! 0.0100!E3.2.2! Progression! With! an! adequate! filter! design,! progression! is! less! likely.! Assume! likelihood! is!1:200.! 0.0050!E3.3.1.1.1! High!water!pressure! High!water!pressure!cannot!be!tolerated!in!this!case.!Assume!likelihood!is!1:100.! 0.0100!E3.3.1.1.2! Specific!material!susceptibility! Similar!to!E3.2.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E3.3.1.2! Initiation!at! the!contact!of! the!embankment!and!foundation! Similar!to!E3.2.1.2.!Assume!likelihood!is!1:100.! 0.0100!E3.3.1.3.1! High!water!pressure! High!water!pressure!cannot!be!tolerated!in!this!case.!Assume!likelihood!is!1:100.! 0.0100!E3.3.1.3.2! Specific!material!susceptibility! Similar!to!E3.2.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E3.3.2! Progression! Without!an!adequate!filter!design,!progression!is!more!likely.!Assume!likelihood!is!1:50.! 0.0200!Static&slope&instability& ! !E4.1.1! Susceptible!features!in!foundation! Cohesionless!clay!layers!etc.!exist!in!foundation.!Assume!likelihood!is!1:100.! 0.0100!E4.1.2! Unsuccessful!detection! Similar!to!E3.1.2.!Assume!likelihood!is!1:200.! 0.0050!E4.2.1.1.1! Change!in!material!behavior!(?)! Has!occurred!due!to!ore!body!or!processing!changes.!Assume!likelihood!is!1:500.! 0.0020! 60 Event&ID& Description& Remarks& Probability&E4.2.1.1.3! Over!steepened!slope!(?)! ! Resulting!from!undetected!construction!errors.!Assume!likelihood!is!1:500.! 0.0020!E4.2.1.1.2.1.1! High!pool! Similar!to!E1.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E4.2.1.1.2.1.2! Long!term! Assume!management!control!in!place.!Likelihood!of!this!event!is!1:200.! 0.0050!E4.2.1.1.2.2.1! Runoff! from! watershed! leads! large! increase! in!water!elevation! Similar!to!E1.1.2.2.1.!Assume!likelihood!is!1:100.! 0.0100!E4.2.1.1.2.2.2! Poor!management!of!increased!pool! Similar!to!E1.1.1.2.!Assume!likelihood!is!1:200.! 0.0050!E4.2.1.2! Unsuccessful!intervention! Similar!to!E3.1.2.!Assume!likelihood!is!1:200.! 0.0050!E4.2.2! Conditions!similar!to!design! Suppose! TMF! is! constructed! with! good! engineering! practice! and! the! factor! of!safety!is!1.5.!From!the!result!of!Silva!et!al.!(2008),!assume!likelihood!is!1:10000.! 0.0001!Seismic&slope&instability& ! !E5.1.1.1! Contractive!material!(?!>!Y0.05)! Similar!to!E2.2.2.!Assume!likelihood!is!1:20.! 0.0500!E5.1.1.2! Undrained!situation! Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E5.1.2.1! Pore!pressure!increase!due!to!seismic!loading! Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!E5.1.2.2! Slope!too!steep! Similar!to!E4.2.1.1.3.!Assume!likelihood!is!1:500.! 0.0020!E5.1.3.1! Displacement!intercepts!pool! Displacement!intercepts!the!impoundment!inducing!the!release!of!tailings!water.!Likelihood!of!this!event!is!1:50.! 0.0200!E5.1.3.2! Differential!horizontal!displacement! Has!occurred!at!embankment!due!to!seismic!loading.!Assume!likelihood!is!1:100.! 0.0100!E5.1.4.1! Crest!deformation! Similar!to!E1.1.1.1.2.!Assume!likelihood!is!1:400.! 0.0025! 61 Event&ID& Description& Remarks& Probability&E5.1.4.2! Seiche! Due! to! seismic! loading,! seiche! occurs! and! generates! high!waves.! Likelihood! of!this!event!is!1:200.! 0.0050!E5.2! Ground!motion!exceeding!design!condition! Similar!to!E1.1.2.1.3.!Assume!likelihood!is!1:200.! 0.0050!  62 In Table 3, if the basic probabilities are related to ?OR? gates, then conditional probabilities are not considered. When they are related by ?AND? gates then strictly speaking conditional probabilities (equation (5)) should be used. For most of these cases it is essentially done, e.g. for a sequence of events such as initiation event (intermediate event, E3.2.1) and progression event (basic event, E3.2.2) in the fault tree for internal erosion (Fig. 39). In this case, the probability of initiation (0.01) is multiplied by the probability of progression. The probability of progression is effectively a conditional probability (P[progression | initiation]) and the magnitude of this likelihood (0.005) reflects this conditionality. Table 4 and Fig. 42 shows the likelihood of the individual failure modes as well as that for the combined failure that can result in tailings release to the environment. The likelihoods are listed for conventional tailings slurry and for dewatered tailings. Dewatered tailings have lower likelihoods of failure than conventional slurry tailings. Table 4 Likelihood of failure and failure modes for slurry and dewatered TMF Failure mode Slurry Dewatered Overtopping 1.2?10-4 0 Static liquefaction 1.9?10-4 1.3?10-4 Internal erosion 3.0?10-4 0 Static slope instability 1.7?10-4 1.6?10-4 Seismic slope instability 2.4?10-6 1.3?10-6 Release of tailings to the environment 7.8?10-4 2.9?10-4  63 $Fig. 42 Likelihood of failure and each failure mode for slurry and dewatered TMF The failure likelihoods in Table 4 resulted from the structure of the fault trees and the qualitatively assigned likelihoods for basic events. Fig. 43 shows that the likelihood of the top event (release of tailings to the environment) is the same order of magnitude as the statistical values presented by Oboni and Oboni (2013).  Fig. 43 Comparison of the results with historical values from Oboni and Oboni (2013)  64 The likelihood of slope failure (static slope instability and seismic slope instability) is encompassed in the range of values indicated by Silva, Lambe and Marr (2008). The important consideration is though that the likelihood of a tailings release from dewatered facilities is about 65% less than that for slurry tailings, even this seems like an under-estimate of the ?improvements? resulting from dewatering.    65 5. Discussion 5.1 Overtopping As contrasted with slurry tailings, the likelihood of overtopping for dewatered tailings is zero based on the fault tree shown in Fig. 36. Since there is no pond in well produced paste and filtered tailings management facilities, the likelihood of overtopping is obviously zero. Although a thickened tailings management facility could have an associated pond, in most cases it is separated from a tailings containment area. Therefore, the likelihood of overtopping in an associated pond causing the release of tailings to the environment is zero. Another possible factor that can increase the likelihood of overtopping for thickened tailings is the toe containment berm. Thickened tailings itself or bleed water from deposited thickened tailings can overtop the toe containment berm. Even if this failure mode is considered, a thickened TMF is still expected to have a lower likelihood of tailings release if overtopping occurs than for conventional slurry tailings. 5.2 Static Liquefaction The likelihood of static liquefaction for dewatered tailings is lower than for slurry tailings. This is reasonable because dewatered tailings have less water that plays a key role in strain softening response. More specifically, high phreatic surface because of poor pool management is not the event that will occur for dewatered TMFs because of the absence of a pond as stated above. The event, downstream surface eroded from overtopping, does not occur for dewatered TMFs as well for the same reason. The likelihood of static liquefaction for dewatered tailings can be lower than estimated because the likelihood of some basic events would be lower than for  66 slurry tailings. For instance, contractive material (? > -0.05) is less likely to remain in dewatered TMFs, although it requires mechanical compaction and evaporative drying and desiccation for thickened and paste tailings to achieve negative state parameter (? < 0) (Davies et al., 2002). For filtered tailings, static liquefaction is virtually impossible as long as it can be compacted well. 5.3 Internal Erosion In order for internal erosion to occur, a continuous source for water flow through the embankment or foundation is required. In dewatered TMFs, it is highly unlikely that there is continuous water flow through embankment or foundation. Thus, there is a likelihood of internal erosion for slurry tailings but not for dewatered tailings. The likelihood of internal erosion will be higher especially when there are continuous fine layers that may result in concentrated flows. Concentrated water flow would likely form between high permeability layer and low permeability layer of tailings and internal erosion may initiate. Hence the likelihood of internal erosion is highly dependent on site-specific conditions. 5.4 Static Slope Instability The likelihood of static slope instability is slightly different between slurry tailings and dewatered tailings. Tailings containment areas and water catchment ponds are separated in different locations in dewatered TMFs. Hence, pore pressure increase in the embankment because of a large amount of water in the pool is not an event that will occur for dewatered tailings. The likelihood of static slope instability for dewatered tailings can be much lower than estimated. As can be seen in Fig. 3, dewatered tailings have higher shear strength and less water content, which makes them more resistant to static slope instability.   67 5.5 Seismic Slope Instability As with the other failure modes, seismic slope instability like the other events related to an impoundment, such as wave overtopping or tailings water release from pool, is less likely to happen for dewatered TMFs. The likelihood of contractive material is lower for dewatered tailings because dewatering and increased densification of tailings is more readily available than for slurry tailings. The likelihood of pore pressure increase due to seismic loading will also be lower than for slurry tailings since dewatered TMFs will tend to be more desaturated than slurry impoundments.  5.6 Application of Fault Trees to Site-specific Conditions The framework developed above will be used to evaluate the failure of a specific tailings impoundment. The Bafokeng TMF failure of 1974 is selected as the sample case as literature and personal experience with the evaluation of this failure is available (Caldwell, 2014). Site information and the evaluation results are presented below.  Overview of Bafokeng TMF failure 5.6.1The Bafokeng mine is located near Rustenburg in South Africa where the weather is very hot and dry. The No. 1 TMF was raised through upstream construction with typical ring dyke impoundment as shown in Fig. 44. Tailings are mostly sandy silt discharged from the perimeters (Fig. 45), clayey silt materials can occur in layers due to the depositional behavior on the beach or in the pool area.  68 $Fig. 44 Ring dyke impoundment of Bafokeng Dam (after Caldwell, 2011) $Fig. 45 Perimeter slimes discharge of Bafokeng Dam (after Caldwell, 2011) According to Blight et al. (1981), on November 11th 1974, the wall of the No. 1 TMF failed. Before the failure, the TMF contained about 1.3 ? 107 m3 of tailings. About 3 ? 106 m3 of tailings flowed through the breach in the wall, engulfed a vertical shaft of the mine killing 13 miners, and flooded down the valley of the Kwa-Leragane River, causing large scale environmental impacts. Fig. 46 shows the layout of Bafokeng No. 1. TMF and flooded area. Fig. 47 is a typical soil  69 profile for the Rustenburg area. $Fig. 46 Geography around Bafokeng No. 1 TMF at the time of failure (after Caldwell, 2011)  Fig. 47 Typical foundation conditions for a TMF in the Rustenburg area (after Caldwell, 2011) Factors affecting the slope stability! Soil PropertiesTypical soil profile for the Rustenburg area.VERTICAL  70  Possible failure causes 5.6.2The detailed description at the time of failure is provided by Caldwell and Charlebois (2010) as below: ?The mine, like all mines in the area, was perpetually short of water, so they stored as much water as possible on the top of the impoundment. The day of the failure, the pool was very close to and some say lapping up against the outer dike thrown up to make a place for the discharge pipes and the next lift of tailings discharge. Then it rained. The bulldozer driver was sent to shore up a vulnerable-looking part of the outer dike. Who knows: maybe he vibrated the wet tailings and they liquefied; maybe he dug too deep or too inexpertly with his bucket as he struggled in the rain to do something unfamiliar and he just took away the freeboard; maybe some profound geotechnical occurrence happened deep in the tailings. Regardless, the water and liquid tailings flowed out, flowed far, and killed miners.? (Caldwell and Charlebois, 2010) Caldwell and Charlebois (2010) also introduce the opinion of Prof. Jennings for whom Caldwell worked to collect the data to evaluate the failure. Prof. Jennings was convinced that piping from the nearby pool to the wall initiated between two layers of low permeability slimes bordering a zone of higher permeability sand tailings. Blight who wrote about this failure in his book concludes thatIt appears at first sight that the dyke did not fail by conventional overtopping. Eyewitness accounts all point to a failure by piping erosion. However, a satisfactory explanation of how the initial hole formed in the wall was never reached?. (Blight, 2010) With knowledge of those experts opinions, Caldwell and Charlebois (2010) reach their own conclusion that ?the pool was too close to the perimeter dikes, it was raining hard, there was seepage flow in saturated sand layers between clay layers, and the bulldozer operator induced liquefaction in the confined sand  71 layer.? (Caldwell and Charlebois, 2010) Summarizing the above, there are mainly 6 possible failure causes: 1. High pool because of poor pool management allowing the impoundment to rise close to the crest of the embankment leading to overtopping. 2. Emergency construction activities on the embankment dyke that causes conditions different from design that could have resulted to static slope instability or contractive walls leading to static liquefaction. 3. Weak clay foundation susceptible to slope slide leading to static slope instability. 4. Cyclic loads from a bulldozer on confined and saturated sand layers leading to static liquefaction or crest deformation leading to overtopping. 5. Loss of freeboard by operational error leading to overtopping. 6. Layering of low permeability slimes and high permeability sand tailings make a piping-susceptible condition leading to internal erosion. Bafokeng Dam failure could be triggered by any of the above causes individually or any combinations of them.  Fault trees for Bafokeng TMF failure 5.6.3Fig. 48 to Fig. 51 are the fault trees for these failure modes. These fault trees are structured only from the components of the generic fault trees presented above. The likelihoods of basic failure event listed in Table 3 are used where appropriate otherwise they are adjusted (qualitatively) to address the site conditions on the day of the failure. Table 5 lists the basic events and likelihoods that were used in calculating the probabilities of overtopping, static liquefaction and internal erosion. Table 6 shows the numerical result of fault tree analysis.  72 $Fig. 48 Fault tree for overtopping at Bafokeng TMF $Fig. 49 Fault tree for static liquefaction at Bafokeng TMF  73 $Fig. 50 Fault tree for internal erosion at Bafokeng TMF $Fig. 51 Fault tree for static slope instability at Bafokeng TMF Table 5 Likelihoods of basic failure events for Bafokeng TMF failure Event ID Description Remarks Likelihood E1.1.1.1.2 Crest deformation Bulldozer present on the embankment to shore up the vulnerable part 0.1 E1.1.1.2 High pool Water stored as much as possible in the TMF because of water shortage in this region 0.5 E2.1.1.1.1.1 Crest deformation Same as E1.1.1.1.2. 0.1  74 Event ID Description Remarks Likelihood E2.1.1.1.1.2 High pool Same as E1.1.1.2. 0.5 E2.1.3.1.4 Exceedance of design criteria More water kept in the TMF than design capacity to resolve water shortage 0.1 E2.2.1 Undrained situation No toe drain installed into the TMF 0.1 E2.2.2 Contractive material (? > -0.05) Emergency construction of the dyke possibly without enough compaction observed 0.1 E3.3.1.1.1 High water pressure Hard rain and high pool present at the day of the failure 0.05 E3.3.1.1.2 Specific material susceptibility Permeable sand layers present between less permeable clay layers in the embankment 0.1 E3.3.2 Progression Without an adequate filter design, progression is more likely 0.02 Table 6 Likelihood of failure modes for Bafokeng TMF failure Failure mode Likelihood of failure Release of tailings to the environment 0.6721 Overtopping 0.0500 Static liquefaction 0.0015 Internal erosion 0.0001 Static slope instability 0.6200 To evaluate the static slope instability, reliability modeling of a foundation failure through the weak clay is analyzed since this is highly site-specific matter.  75  Fig. 52 Schematic static instability model for Bafokeng TMF A probabilistic slope stability analysis was performed using and cross section constructed based on information provided by Caldwell. The section is shown in Fig. 52. The statistics of the shear strength values are shown in Table 7. An adjusted phreatic surface was selected that resulted in a factor of safety against static stability failure of about 1.0 when the average shear strength values were applied. Table 7 Statistics of shear strength values for stability analysis Parameter Average Value Coefficient of Variation, % Standard Deviation ctailings 25 kPa 50% 12.5 kPa ?tailings 34 degrees 10% 3.4 degrees ?clay layer 10 degrees 20% 2 degrees The Point Estimate Method expanded by Harr (1986) was used in estimating 0 20 40 60 80 100 120 140 160 180X (m)0102030405060708090100Y (m)FOS = 1.09900.5221.0431.5652.0872.6093.133.6524.1744.6965.2175.7396.261+FOSfoundationWeakClayEmbankmentMohr CoulombMohr CoulombMohr Coulomb Unit Weight = 20 (kN/m^3) Unit Weight = 18 (kN/m^3) Unit Weight = 15 (kN/m^3) Cohesion = 25 (kPa) Cohesion = 0 (kPa) Cohesion = 37.5 (kPa) Phi = 43 (deg) Phi = 12 (deg) Phi = 30.6 (deg)MaterialsCalculation Method: Janbu SimplifiedSearch Method: Greco SearchFOS: 1.099Total Weight: 1.405E+004 kNTotal Volume: 9.265E+002 m^3Total Activating Moment: 0.000E+000 kNmTotal Resisting Moment: 0.000E+000 kNmTotal Activating Force: 2.924E+003 kNTotal Resisting Force: 3.213E+003 kNSVSlope? 76 the mean and standard deviation of the factor of safety for slope stability. The results of the stability analysis are shown in Table 8. Table 8 Factor of safety for 8 point estimates Combination Factor of Safety +++ 1.206 ++- 1.017 +-- 0.943 --- 0.748 --+ 0.898 -++ 0.908 +-+ 1.099 -+- 0.848 Note that the ?combination? in the table determines the values of the shear strength parameters used for the stability analysis; the values are in the order listed in Table 7. So that in the case of ?++-? the values used are: ctailings: average plus standard deviation ?tailings: average plus standard deviation ?clay layer: average minus standard deviation The mean value of factor of safety is obtained from: ! ! = !!!!!!!!  (10) , where the Pi s are the weights. For this calculation the weights have a constant value of 1/8, which results in the mean value of factor of safety of 0.96.  77 The variance (second moment around the mean) is calculated as follows: !"# ! = ! !! ? ! ! ! (11) which results in the standard deviation of the factor of safety of 0.14. Assuming that the factor of safety is normally distributed, the probability of factor of safety less than one (P [FS<1]) is 0.62. Admitting that the factor of safety does not physically mean anything when it is less than zero, the probability of the factor of safety less than zero is negligibly small in this case (8.310-13). It turns out that the likelihood of static slope instability is very high as a result of fault tree analysis. Although the static slope instability would be the main failure of Bafokeng TMF, it seems to be reasonable to think that not only one failure but also a string of failures triggering each other causes this disastrous failure. $Fig. 53 A sequence of failure of Bafokeng TMF (after Blight and Fourie, 2003) Fig. 53 presents the possible sequence of Bafokeng TMF failure. No matter how low the likelihood of each failure mode is, possibly all failure modes occur once one of them occurs. 5.7 Additional Slurry Tailings Failure Modes Other than the failure modes described so far in this study, there are also some other possible failure modes for slurry tailings. One such failure is that of a  78 penstock used for decanting supernatant. Fig. 54 shows the fault tree of penstock failure and it can lead to the release of tailings to the environment. However, it is not included in the fault tree for tailings release above as this form of supernatant removal is not universal for all slurry tailings TMFs. While it is still widely used in some geographic areas such as South Africa it is not a leading practice technology. $Fig. 54 Fault tree for penstock failure For site-specific analysis, additional failures not covered in this study such as cracking or failures as a result of a string of incidents that are referred to Black Swan incidents in Caldwell and Charlebois (2010) should be considered. 5.8 Sources of Bias in This Thesis There are two main sources of bias in this research. The first one is the structure of fault trees. Although the selection of failure modes is approached logically, it is based on by the author and had not been widely reviewed by  79 industry professionals, it can therefore be biased. The other and the most significant source of bias is the use of subjective probabilities for the basic events. As stated in section 2.6, there are many steps in the estimation of subjective probabilities where biases can result in countless ways. By having more experts in the panel and asking them to provide a range of probabilities, it could be avoided or at least reduced.    80 6. Conclusion, Contributions and Recommendations for Future Research 6.1 Conclusion This thesis has successfully addressed the objective that is to develop a framework for the estimation of the likelihood of failure for different tailings depositional alternatives: slurry, thickened, paste and filtered tailings. The framework was developed to deal with the following issues: selection of representative failure modes for the depositional alternatives, development of the evaluation method and methodology to calculate the probability of failure. Five failure modes (overtopping, static liquefaction, internal erosion, static slope instability and seismic slope instability) are selected based on the database established by ICOLD and UNEP (2001) to cover the majority of TMF failures. Fault tree analysis was used to calculate the probability of failure as well as to understand how failures can happen. The ?Top level? event was defined as the release of tailings to the environment and five failure modes stated above are investigated in fault trees. A form of expert elicitation was used to assign the probabilities for basic events. The structure of fault trees was reviewed by an external advisor. The probability of the release of tailings to the environment for dewatered tailings was about 65% less than for slurry tailings.  The application of the fault trees to the evaluation of actual mine site, Bafokeng TMF, was also attempted. As a result, these generic fault trees at least successfully captured possible failure causes. However, it requires a careful consideration in regards to the likelihood of basic events because it highly  81 depends on site-specific conditions. Fault trees successfully visualized how the likelihood of failure shifts with the change in water content among tailings depositional alternatives. Future-research expected to improve accuracy of fault tree analysis is presented in next chapter. 6.2 Contributions The three major contributions from this research are that: 1. the development of a framework that can be used for the estimation of the likelihood of failure for various types of TMFs, 2. the fault tree diagrams that can be used to visualize the difference of failure likelihood between slurry and dewatered TMFs, and 3. the fault tree analysis that quantified the likelihood of failure for slurry and dewatered TMFs. The framework developed in this research is useful in terms of flexibility. It can be used for the estimation of the likelihood of failure with the generic site assumptions as well as site-specific conditions if reliability modeling and adjustment of subjective probabilities are available. The fault tree analysis quantified the likelihood of failure for slurry and dewatered TMFs. The estimation of failure likelihood for dewatered TMF has not been quantitatively analyzed yet in this field. Thus the results of this research would be beneficial for that purpose. The result of fault tree analysis is quite unique in the way that it visualizes the differences of failure mechanisms and likelihoods between slurry and dewatered TMFs. It allows for a more intuitive understanding of the reliability difference between slurry and dewatered TMFs.   82 6.3 Recommendations for Future Research ? Apply framework to a number of site specific dewatered TMFs to further refine the failure causes and mechanisms ? Apply framework to downstream and centerline TMFs to further refine the failure causes and mechanisms ? Apply more complete expert elicitation of the fault trees and likelihoods of basic events ? Apply more reliability modeling approach to some basic events for further evaluation of the likelihood ? Consider development of fault trees that consider other top events, e.g. environmental impacts, operational failures, etc.     83 References Papers/Books Baecher, G.B., Pat?, M.E. and de Neufville, R. (1980) Dam failure in benefit cost analysis, Journal of the Geotechnical Engineering Division, Vol. 106(1), pp. 101?105. Baecher G.B. and Christian J.T. (2003) Reliability and Statistics in Geotechnical Engineering, Wiley, USA Been, K., Romero, S., Obermeyer, J. and Hebeler, G. (2012) Determining in situ state of sand and silt tailings from the CPT, in Proceedings Sixteenth International Conference on Tailings and Mine Waste, Keystone, Colorado, USA, pp. 217?228 Blight, G.E., Robinson, M.J. and Diering, J.A.C (1981) The flow of slurry from a breached tailing dam, Journal of South African Institution Mining and Metallurgy, January, pp. 1?8. Blight, G.E. and Fourie, A.B. (2003) A review of catastrophic flow failures of deposits of mine waste and municipal refuse, IW-FLOWS2003, Sorrento, Italy Blight, G.E. (2010) Geotechnical Engineering for Mine Waste Storage Facilities, CRC Press, USA Boger, D., Scales, P. and Sofra, F. (2006) Rheological Concepts, From: Paste and Thickened Tailings?A Guide (Second Edition), Jewell, R.J. and Fourie, A.B. (eds.), Australian Centre for Geomechanics, Perth, Australia Caldwell, J. and McPhail, G (2009) Revisit to Old South African Slimes Dams & Where We Are Today,  http://www.infomine.com/library/publications/docs/Caldwell2009c.pdf  84 Caldwell, J. and Charlebois, L. (2010) Tailings Impoundment Failures, Black Swans, Incident Avoidance, and Checklists, in Proceedings Fourteenth International Conference on Tailings and Mine Waste, Vail, Colorado, USA, pp. 33?39. Caldwell, J. (2011) Bafokeng: Failure. Flow, and Why?For?,  http://www.infomine.com/library/publications/docs/CaldwellBafokeng.pdf Christian, J.T., Ladd, C.C. and Baecher, G.B. (1992) Reliability and probability in stability analysis, in Proceedings of Stability and Performance of Slopes and Embankments ? II, ASCE, New York, Vol. 2, pp. 1071?1111. Davies, M.P. and Martin, T.E. (2000) Upstream Constructed Tailings Dams - A Review of the Basics, in Proceedings Seventh International Conference on Tailings and Mine Waste, Fort Collins, Colorado, USA, Balkema, The Netherlands, pp. 3?15. Davies, M.P. and Rice, S. (2001) An alternative to conventional tailing management ? "dry stack" filtered tailings, in Proceedings Eighth International Conference on Tailings and Mine Waste, Fort Collins, Colorado, USA, A.A. Balkema, The Netherlands, pp. 411?422. Davies, M.P., McRoberts, E.C. and Martin, T.E. (2002) Static Liquefaction of Tailings ? Fundamentals and Case Histories, in Proceedings Tailings Dams 2002, ASDSO/USCOLD, Las Vegas. 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(2003) Tailings dam versus a water dam ? what is the design difference, ICOLD Symposium on Major Challenges in Tailings Dams, Montr?al, Quebec, Canada  86 Oboni, F. and Oboni C. (2013) Factual and foreseeable reliability of tailings dams and nuclear reactors: a social acceptability perspective, in Proceedings Seventeenth International Conference on Tailings and Mine Waste, Banff, Alberta, Canada, pp. 399?407 Olson, S.M. and Stark, T.D. (2003) Yield Strength Ratio and Liquefaction Analysis of Slopes and Embankments, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 129(8), pp.727?737 Rico, M., Benito, G., Salgueiro, A.R., D?ez-Herrero, A. and Pereira, H.G. (2008) Reported tailings dam failures: A review of the European incidents in the worldwide context, Journal of Hazardous Materials, Vol. 152(2), pp. 846?852. Silva, F., Lambe, T.W. and Marr, W.A. 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