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Predicting void ratio for surface paste tailings deposited in thin layers Salfate, Eduardo Raul 2011

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PREDICTI G VOID RATIO FOR SURFACE PASTE TAILI GS DEPOSITED I THI LAYERS by  Eduardo Raul Salfate  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  The Faculty of Graduate Studies (Mining)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  July, 2011  © Eduardo Raul Salfate  ABSTRACT Surface thin layer deposition of paste tailings has become an increasingly popular method of disposal. One of the reasons for its popularity is the advantages associated with the faster increase in strength and density after placement as a result of enhanced evaporation and drainage. This makes thin layer deposition particularly attractive in dry climates with high evaporation rates. Understanding how density evolves with time is an extremely relevant problem during design stages as both the overall capacity of the tailings impoundment and its stability with time depend on this parameter. Since tailings density is not readily available at early stages of planning, predictive tools are required to estimate it. Density is primarily gained through four different processes; sedimentation-self weight consolidation, drainage, evaporation and consolidation. Although consolidation will likely be the main contributor to the final density of the impoundment, the other three processes are important as the consolidation behaviour of hard rock paste tailings has been observed to depend on the initial density or state achieved during early stages of densification. The primary objective of this thesis is to provide an overview of the processes affecting the early stages of densification and to propose an approach for predicting this parameter. Laboratory testing presented as part of this work is primarily focused on determining the variables affecting the sedimentation-self weight consolidation process whereas the numerical work is focused on targeting some of the issues related to drainage and evaporation. The approach described herein has combined measured data obtained in the lab with results generated by numerical modeling to provide with density estimates as a function of time. Another important goal of this thesis is to give general guidelines for proper material characterization, which is required to overcome some of the difficulties encountered when evaluating the properties of slurries prone to large volume changes. Focus has been given to outline a method to determine hydraulic conductivity functions and soil water characteristic curves (SWCC) that account for both changes in suction and volume.  ii  TABLE OF CO TE TS  ABSTRACT ................................................................................................................................. ii TABLE OF CO TE TS...........................................................................................................iii LIST OF TABLES ..................................................................................................................... vi LIST OF FIGURES .................................................................................................................. vii ACK OWLEDGEME TS........................................................................................................ x 1  I TRODUCTIO ................................................................................................................ 1 1.1  2  Research Objectives...................................................................................................... 3  LITERATURE REVIEW A D THEORETICAL BACKGROU D ............................. 5 2.1  Paste Tailings Deposition ............................................................................................. 5  2.1.1  Potential advantages of paste tailings deposition ................................................... 6  2.1.2  Process description and influence over material properties................................... 7  2.1.3  Characteristics of thin layer deposition of paste................................................... 12  2.2  Density as One of the Key Parameter for Paste Tailings Design............................ 15  2.2.1  The process of densification in a paste tailings impoundment .............................. 16  2.2.2  The relevance of density in the estimation of liquefaction potential ..................... 19  2.2.3  Challenges for assessing liquefaction for paste tailings material......................... 27  2.3  Available Theories for Predicting Density................................................................ 28  2.3.1  Sedimentation and self-weight consolidation of slurries....................................... 29  2.3.2  Desiccation or drying ............................................................................................ 32  2.3.3  Consolidation ........................................................................................................ 35  2.3.4  Coupling between drying and consolidation......................................................... 39  2.4  Engineering Properties Relevant to the Sedimentation–Self Weight Consolidation  and Drying Stages of Densification and their Estimation .................................................. 40 2.4.1  Saturated hydraulic conductivity for slurries........................................................ 40  2.4.2  Soil water characteristic curve (SWCC) and shrinkage........................................ 43  2.4.3  Shrinkage............................................................................................................... 49  2.4.4  Unsaturated hydraulic conductivity ...................................................................... 50  2.4.5  Previous research on paste tailings sedimentation-self weight consolidation and  drying and value of the present work................................................................................... 50  iii  3  PROCEDURE DEVELOPED FOR MEASURI G THE PROPERTIES OF PASTE  TAILI GS RELEVA T TO THE SEDIME TATIO -SELF WEIGHT CO SOLIDATIO A D DRYI G STAGES OF DE SIFICATIO ............................... 53 3.1  Basic Material Properties........................................................................................... 53  3.2  Sedimentation- Self Weight Consolidation Behaviour ............................................ 54  3.2.1  4  Analysis of results.................................................................................................. 56  3.3  Saturated Hydraulic Conductivity of the Slurry Material ..................................... 60  3.4  Soil Water Characteristic Curve (SWCC) ............................................................... 61  3.5  Shrinkage..................................................................................................................... 66  3.6  Chapter Summary ...................................................................................................... 67  PROPOSED MODELI G APPROACH TO DETERMI E AVERAGE VOID  RATIO OF PASTE TAILI GS............................................................................................... 69 4.1  Determination of the Boundary between Sedimentation-Self Weight  Consolidation and Drying ..................................................................................................... 70 4.1.1  Example: application of the proposed method to different Bulyanhulu tailings  configurations ...................................................................................................................... 72 4.2  Modifying Material Properties to Obtain Appropriate Results of Density as a  Result of Drying (Shrinkage)................................................................................................ 75 4.2.1  Building the SWCC for the drying model .............................................................. 75  4.2.2  Building the hydraulic conductivity function for the drying model ....................... 78  4.2.3  Setting the initial conditions for the drying model ................................................ 80  4.2.4  Coefficient of volume change (mv)......................................................................... 81  4.3  Analysis of Results Obtained from Unsaturated Modeling .................................... 82  4.4  Method for Combining Sedimentation-Self Weight Consolidation and Drying  Results..................................................................................................................................... 83 4.5 5  Chapter Summary ...................................................................................................... 85  APPLICATIO S OF THE PROPOSED FRAMEWORK ............................................ 87 5.1  Using the Approach to Represent the Observed Behaviour under Laboratory  Conditions............................................................................................................................... 87 5.2  Evaluation of Case Scenarios..................................................................................... 91  5.2.1  Effect of paste layer thickness (no drainage) ........................................................ 92  5.2.2  Effect of climatic conditions (no drainage) ........................................................... 93  5.2.3  Effect of drainage to underlying layers of paste.................................................... 94  5.2.4  Effect of sedimentation-self weight consolidation rate over average void ratio  predictions............................................................................................................................ 95  iv  5.3  Simplified Methodologies and their Impact over Average Void Ratio Estimates  with Time................................................................................................................................ 98 5.4 6  Chapter Summary .................................................................................................... 101  CO CLUSIO S .............................................................................................................. 103 6.1  General Conclusions................................................................................................. 103  6.2  Recommendations for Future Work ....................................................................... 105  6.2.1  Sedimentation -self weight consolidation behaviour........................................... 105  6.2.2  Unsaturated properties........................................................................................ 107  6.2.3  Validation of the model results with drying tests ................................................ 108  6.2.4  Modeling approach ............................................................................................. 109  REFERE CES ........................................................................................................................ 111  v  LIST OF TABLES Table 1: Comparison of potential water savings between conventional and high density thickened tailings ......................................................................................................................................................................1 Table 2: Properties of the Bulyanhulu tailings ...........................................................................................53 Table 3: Initial conditions used for the SWCC determination....................................................................62 Table 4: Example cases analyzed for determining the boundary between sedimentation-self weight consolidation and drying ............................................................................................................................73 Table 5: Material properties at the time where drying is expected to begin (Td)........................................74 Table 6: Fitting parameters for the SWCC’s of cases A and B ..................................................................76 Table 7: Case scenarios ..............................................................................................................................92  vi  LIST OF FIGURES Figure 1: Typical variation of strength with concentration for thickened tailings........................................6 Figure 2: Typical processes involved in paste tailings production ...............................................................8 Figure 3: Comparison between paste tailings (a) and conventional tailings (b) discharge...........................8 Figure 4: Flocculation with bridging type polymers ....................................................................................9 Figure 5: Configuration of a typical paste thickener ....................................................................................9 Figure 6: Slump tests for material before (left) and after (right) transportation to tailings storage facility. ....................................................................................................................................................................10 Figure 7: Effect of pH (a) and salinity (b) over clay slurry dispersive behaviour ......................................11 Figure 8: Typical “centre stack” configuration...........................................................................................12 Figure 9: Typical “down valley discharge” configuration (advancing cones)............................................13 Figure 10: Advancement of thin layers of paste .........................................................................................14 Figure 11: Tailings depositional slope as a function of slurry density .......................................................15 Figure 12: Schematic representation of the densification process of a thin layer of paste .........................18 Figure 13: Undrained response of sands under monotonic loading............................................................20 Figure 14: Typical stress paths and zone of contractive behaviour ............................................................21 Figure 15: Region of contractive deformation............................................................................................21 Figure 16: The concept of state parameter and critical state line ...............................................................22 Figure 17: Diagram depicting the range of possible states of a sand..........................................................22 Figure 18: Effect of inclination of principal stress over maximum shear strain and stress path response of Fraser river sands........................................................................................................................................23 Figure 19: Undrained response of sands under cyclic loadings. Liquefaction (a), cyclic mobility (b) and limited liquefaction and (c) cyclic mobility................................................................................................24 Figure 20: The effect of density over the number of cycles required to achieve a target strain .................25 Figure 21: Typical sedimentation curve .....................................................................................................30 Figure 22: Typical shrinkage curve ............................................................................................................33 Figure 23: The relationship between the rate of actual evaporation and potential evaporation (AE/PE) and water availability ........................................................................................................................................34 Figure 24: Lagrangian coordinates at initial configuration (t=0) and at a given time t ..............................36 Figure 25: Relative density changes predicted and measured for mine tailings sand.................................39 Figure 26: Volume mass constitutive surface for Regina clay ...................................................................40 Figure 27: Typical SWCC showing the different stages of de-saturation ..................................................44 Figure 28: Influence of initial state on the soil water characteristic curve .................................................47 Figure 29: Soil suction versus water content for initially sluried Regina clay ...........................................48 Figure 30: Degree of saturation versus soil suction for Regina clay at two different preconsolidation pressures .....................................................................................................................................................48 Figure 31: Particle size distribution of the Bulyanhulu tailings .................................................................54 Figure 32: Settling columns prepared at material heights of 40, 30, 20 and 10 cms. .................................55 Figure 33: Verification of the repeatability of sedimentation-self weight consolidation tests ...................56  vii  Figure 34: Total settlement for columns prepared at (a) 50% GWC and (b) 40% GWC. ..........................57 Figure 35: Void ratio evolution for columns prepared at (a) 50% GWC and (b) 40% GWC.....................58 Figure 36: Void ratio evolution for columns prepared at a GWC of 40% and 50% and column heights of (a) 40 cm and (b) 20 cm .............................................................................................................................59 Figure 37: Settling velocity as a function of concentration ........................................................................60 Figure 38: Hydraulic conductivity as a function of void ratio (e) ..............................................................61 Figure 39: SWCC of Bulyanhulu tailings in terms of GWC ......................................................................64 Figure 40: SWCC of Bulyanhulu tailings in terms of VWC ......................................................................65 Figure 41: SWCC for Bulyanhulu tailings corrected and uncorrected for volume changes.......................65 Figure 42: SWCC of Bulyanhulu tailings in terms of degree of saturation ................................................66 Figure 43: Shrinkage curve for the Bulyanhulu tailings.............................................................................67 Figure 44: Representation of the simplified water balance to determine the boundary between sedimentation-self weight consolidation and drying ..................................................................................72 Figure 45: Theoretical boundary between sedimentation-self weight consolidation and shrinkage for a 40 cm layer and GWC of 40 % and 50 % .......................................................................................................73 Figure 46: SWCC depicting the possible range of GWC from slurry to settled conditions .......................76 Figure 47: Resulting SWCC for case A based on the state achieved as a result of sedimentation-self weight consolidation...................................................................................................................................77 Figure 48: Resulting SWCC for case B based on the state achieved as a result of sedimentation-self weight consolidation...................................................................................................................................77 Figure 49: Schematic representation of how the unsaturated hydraulic conductivity function was constructed (results shown in terms of relative hydraulic conductivity Kr) ...............................................79 Figure 50: Resulting SWCC for case A based on the state achieved as a result of sedimentation-self weight consolidation...................................................................................................................................80 Figure 51: Resulting SWCC for case B based on the state achieved as a result of sedimentation-self weight consolidation...................................................................................................................................80 Figure 52: Differences between modeled results for VWC (a), saturation (b) and GWC (c) and results obtained from laboratory data (accounting for volume changes) ...............................................................83 Figure 53: Unmodified (a) and modified (b) void ratio profiles from drying model..................................84 Figure 54: Void ratio of the paste layer with time......................................................................................85 Figure 55: Schematic diagram showing the configuration of the drying test (After Bryan, 2008).............88 Figure 56: Time required for pond water to evaporate ...............................................................................89 Figure 57: Modeled and measured suctions ...............................................................................................90 Figure 58: Modeled and measured actual evaporation ...............................................................................90 Figure 59: Modeled and measured average void ratios ..............................................................................91 Figure 60: Average void ratio for a 40 cm and 10 cm layer of paste subject to PE of 5 mm/d ..................93 Figure 61: Average void ratio of a 10 cm layer subject to 5 mm/d and 1 mm/d of potential evaporation .93 Figure 62: Average void ratio for different underlying conditions.............................................................95 Figure 63: Average void ratio for a 40 cm layer of paste subject to 1 mm/d of PE....................................96 Figure 64: Average void ratio for a 40 cm of paste subject to 1 mm/d of PE during the first 5 Days........96  viii  Figure 65: Sedimentation-self weight consolidation curve for a hypothetical material .............................97 Figure 66: Comparison of average void ratio for hypothetical material and Bulyanhulu tailings..............98 Figure 67: Comparison of results provided under simplified methodologies for a case with PE of 1 mm/d and layer thickness of 40cm .......................................................................................................................99 Figure 68: Comparison of results provided under simplified methodologies for a case with PE of 5 mm/d and layer thickness of 40 cm .................................................................................................................... 100 Figure 69: Comparison of results provided under simplified methodologies for the case with a rate of ED of 12 mm/d and a 40 cm layer with a smaller settling rate ....................................................................... 101  ix  ACK OWLEDGEME TS I would first like to thank my parents for their constant support and motivation throughout these years. Whether it was music, sports or engineering you were always there to provide me the tools to do what I love. I would also like to thank my brother and sister along with my friends in Vancouver and Chile. Life is much more fun having you guys around. Although I doubt you will ever read past the abstract of this thesis, if you ever end up reaching the acknowledgements I just wanted to make sure you knew I had you in mind. Of course, this would have not been possible without the help of the professors and professionals within industry, whose constant search for challenges lead to the development of this research. First and foremost, I would like to thank Ward Wilson for his constant support throughout these years. His advice in both academic and personal matters constantly reminded me of how fortunate I was to have him as a supervisor. Thank you for making my well being and professional development the top priorities of my Degree. I would also like to thank Dharma Wijewickreme and Paul Simms for their valuable feedback. Your recommendations and comments to my work were fundamental to ultimately make this a better thesis. Special thanks go to NSERC and Golder Associates for financing and supporting this research project. I owe particular thanks to all those involved in this project (Don Welch, Ken Been, Murray Grabinski, Ward Wilson, Dharma Wijewickreme and Paul Simms) for giving me the opportunity to personally present some of the findings of this thesis. Having the chance to participate in some of your meetings was a very rewarding experience. Finally and most importantly, I want to thank my wife Pachi for making these last 8 years the best of my life.  x  1  I TRODUCTIO  During the extraction and processing of ore, mines face the necessity of disposing the fraction of processed rock that no longer constitutes an economical asset. Such material is commonly referred as mine tailings, which, depending on the ore type, consist of a large fraction of the total processed rock. For a long time, tailings have been disposed as slurry, with more than 50% of the total mass being just process water. With the advances in processing technology and the increase in global demand, modern operation have significantly increase their processing rates to values sometimes above 100,000 tones per day (tpd) for some base metal mines (copper, gold, etc). Since the ore is only a small fraction of the processed rock, large volumes of tailings have to be disposed, resulting in tailings storage facilities that can easily increase in size to as much as several square kilometres. Slurry tailings are usually contained in dams, which for large operations can easily reach hundreds of meters high. These structures have failed in the past (Los Frailes (1997), Sullivan Mine (1991), Stava Mine (1985), Merriespruit (1994)), generally with catastrophic results to local economies, the environment, and occasionally loss of human life. Safety has then become a very sensitive issue, and efforts have been made in the past 30 years to develop alternatives of tailings disposal that could reduce the social, environmental and safety liabilities associated to conventional tailings storage facilities. One of the alternatives to slurry deposition that could potentially reduce the risks of catastrophic failure is surface deposition of thickened or paste tailings. Paste and thickened tailings consist of high density tailings obtained by dewatering the slurry discharged from the mill. They show minimal particle segregation and posses a yield stress allowing for gently sloped stacks to be formed. This allows for a considerable reduction in the size of the dam, which is generally reduced to small perimeter berms or in some cases no containment at all. Another important advantage of thickened and paste tailings is that the corresponding water savings obtained through dewatering can be very significant. This becomes a relevant financial factor for mines located in dry climates where the limited water availability may jeopardize the feasibility of future mine developments or expansions. Table 1 illustrates the potential differences in water savings between conventional and high density thickened tailings. Water saving also result in a reduction of the overall size of the impoundment which in turn minimizes the potential impacts over the adjacent environment as the total footprint is reduced.  Solids Content (%) 3  Water in Slurry (m /t) Assumed Recovery from Tailings Deposit (%)  Conventional  High Density Thickened  25  65  3.0  0.54  33  5  Amount of Water Returned (m3)  0.99  0.03  Total Water Loss (m3/t)  2.01  0.51  Table 1: Comparison of potential water savings between conventional and high density thickened tailings (Jewell & Fourie, 2006)  1  Regardless of the potential benefits in terms of safety, paste tailings deposits still require adequate design to ensure the long term stability of their slopes. In particular, one of the main concerns is the stability of the paste stack under undrained conditions, specifically those associated to dynamic or static liquefaction. The liquefaction of paste tailings may induce a flow slide if the slope of the stack or the slope on which the stack is built is too steep, as gravity could mobilize the liquefied material down slope. The dilemma is that on one hand steeper slopes will yield a lower factor of safety, but on the other they will increase the total capacity of the impoundment for the same surface area. The problem relies on estimating the slope that will ensure the required storage capacity at a given factor safety. Liquefaction potential is dependent on tailings density, which can be related to void ratio. One of the main problems is that the void ratio of the deposited paste tailings is not readily available during design and it is not a constant value during the life of the impoundment. The process of void ratio change in paste tailings is primarily a result of sedimentation, self weight consolidation, drainage, evaporation (which is a function of the governing climatic conditions) and consolidation caused by the loads imposed by subsequent paste layers placed throughout the life of the mine. The ability to predict the void ratio changes during each of these stages is fundamental when trying to assess the liquefaction potential of a paste tailings impoundment. The purpose of the present work is to establish a basis of the theoretical, experimental and modeling approach required to evaluate the changes in void ratio as a result of sedimentation, self weight consolidation 1 , and drying (in the form of evaporation and drainage). The present work has been developed considering the results that previous authors have presented on the subject (Wilson et al. (1994), Simms et al. (2007, 2008), Simms and Dunmola (2010), Fisseha et al. (2010), Bryan (2008)) where the concepts of unsaturated soil mechanics have been applied to the specific problem of paste tailings densification and drying. The end result is to be able to provide a framework under which reliable void ratio estimates may be obtained for a given paste tailings impoundment under any given climatic conditions.  1  The combined effect of sedimentation and self weight consolidation is sometimes referred as hindered settling or hindered  sedimentation. In this thesis, these two processes (sedimentation and self weight consolidation) will be treated together as a single parameter and will be referred to herein as sedimentation–self weight consolidation.  2  1.1  Research Objectives  The present work is part of a larger research project focused on evaluating the evolution of density and undrained response of paste tailings. The global research project involves several stages of which the most important are: 1.  Development of column tests to better characterize the sedimentation–self weight consolidation stages of paste tailings densification. Columns tests will be conducted to allow sedimentation– self weight consolidation alone and sedimentation–self weight consolidation combined with evaporation and drainage.  2.  Development of a standard to measure volume change in the water-retention curve test (soilwater characteristic curve, SWCC).  3.  Evaluation of the effect of change in void ratio (i.e. volume changes) versus hydraulic conductivity.  4.  Refinement of the existing modeling framework (as per Simms 2007, 2008, 2009) so that it properly accounts for sedimentation–self weight consolidation, volume changes and the resulting changes in material properties such as hydraulic conductivity.  5.  Development of multilayer deposition schemes to analyze the build-up of relatively deep layers of thickened tailings, and to assess the impact of combining drainage, consolidation of deeper layers and desiccation of the top layers. Multilayer tailings deposition will be developed in test pits with measurements of matric suction, moisture content, stress and strain.  6.  Fitting the data obtained from the multilayer tests with the refined model proposed in previous stages.  7.  Preliminary assessment of cyclic resistance and post-cyclic behaviour of thickened tailings using the direct simple shear apparatus. Initially, the testing work will be undertaken to assess the behaviour under limited/selected effective confining stress/density levels. The findings will serve as direct insight and input to developing a successor detailed investigation on dynamic and geotechnical stability of thickened tailings deposits.  The present thesis has been focused primarily in points 1, 2 and 4 of the above research objectives. Within these points the main goal has been to propose a consistent framework under which the sedimentation–self weight consolidation and desiccation stages can be analyzed for thin layers of paste subject to any given climate. A strong emphasis has been placed on proposing appropriate methodologies for determining the model parameters in the laboratory as well as providing a standardized methodology for combining the sedimentation–self weight consolidation and drying observations during modeling. With this in mind, the specific objectives for the present research are as follows:  3  •  Determine the key parameters affecting the process of densification in thin layers of paste during sedimentation-self weight consolidation and drying. This work is expected to provide methodologies under which the relevant properties can be obtained in the laboratory.  •  Determine appropriate unsaturated properties (SWCC and Hydraulic Conductivity Functions) that account for both changes in volume and suction. Especially, it is important to focus on providing a simplified methodology for determining hydraulic conductivities at large void ratios. This has been shown to be an important limitation when evaluating geotechnical problems for slurries prepared at low solids contents where large settlement are expected as a result of sedimentation-self weight consolidation. For such materials, conventional hydraulic conductivity testing is not possible.  •  Understand the sedimentation-self weight consolidation behaviour of thin layers of paste by performing several settling tests2 for different initial configurations. The goal is to assess the effect of material height and solids content of the slurry on the sedimentation-self weight consolidation behaviour (settling rate, final state achieved, etc).  •  Propose a modeling framework to combine the evolution of density due to sedimentation–self weight consolidation and desiccation. So far the models have provided a limited evaluation of the combined effect of these two processes.  •  Model the evolution of void ratio as a result of sedimentation–self weight consolidation and desiccation under different conditions using the proposed methodology (wet and dry climates, thick and thin layer thicknesses, etc). The objective will be to try predicting the expected densification process of a given tailings layer under different conditions. These results are expected to provide useful insight on the potential behaviours observed in the lab during future research for paste tailings sedimentation-self weight consolidation and desiccation. The modeled case scenarios will also show the potential application of the proposed methodology to paste tailings design and planning.  •  Determine the differences of using the proposed approach compared to other simplified methodologies for estimating void ratio evolution in paste tailings layers. The objective will be to illustrate the trade-off between the quality of void ratio predictions and the complexity of the approach used for their determination.  2  Settling tests refer to columns prepared in the laboratory to evaluate the combined effect of sedimentation and self weight  consolidation. The state achieved at the end of the settling test (void ratio achieved after sedimentation-self weight consolidation) will be referred to herein as “settled condition”  4  2 2.1  LITERATURE REVIEW A D THEORETICAL BACKGROU D Paste Tailings Deposition  In recent years, use of paste has evolved from an experimental backfill method with limited application to a technically viable and economically attractive alternative. This is primarily due to the development of dewatering and transportation systems that allow for controlled and consistent production and delivery of paste in a cost-effective manner (Verburg, 2001). This also arises as a response of the mining industry to sustainability issues (savings in water, reduction of land use for waste disposal, reducing environmental and safety liabilities after closure) and the “Equator Principles”, a financial industry benchmark for determining, assessing and managing social and environmental impacts of mines, including their wastes, as a requirement for obtaining debt financing (Clarke-Whistler and Welch, 2007). All these factors have motivated a change in mine waste management by developing innovative methods to dispose of tailings, conserve water, reduce risk and be more responsive to the ever increasing environmental and social concerns. The industry is responding to the pressures for change by reducing or even eliminating pond water on top of tailings, dewatering tailings to facilitate alternative disposal configurations, reducing the environmental footprint, allowing for concurrent closure and minimizing potential environmental impacts such as acid mine drainage and dust generation. The term “thickened” suggest that the tailings have been dewatered prior to deposition to the point that they exhibit a yield stress, allowing tailings to form self-supporting deposits with gentle slopes. “Paste” may be used to describe tailings thickened to the extent that no segregation of particle size occurs during transport and a relatively small amount of settling occurs after deposition (Cincilla et al. 1997). Conventional tailings typically come out of a mill at discharge slurry densities between 30% and 50% solids by mass (between 77% and 67% gravimetric water content (GWC)). For typical hard rock tailings the thickening levels beyond this are high density, non-segregated thickened tailings (60 to 65% solids 63 to 60% GWC - that can be moved with centrifugal pump), paste (>70 to 75% solids – >59 to 57% GWC – that has to be moved with a positive displacement pump as plug flow); and filtered tailings (typically >75 to 80% solids - >57 to 56% GWC - that has to be moved on a conveyor belt or by truck) (Li et al, 2009). As illustrated in Figure 1, the action of removing water from the slurry at any point in the process, and hence increasing the concentration of the solids, essentially thickens and increases the strength of the material.  5  Increasing Strength  Cake  Paste  Slurry  Increasing Concentration  Figure 1: Typical variation of strength with concentration for thickened tailings (After Jewell & Fourie, 2006) The deposition of thickened tailings on surface was pioneered at Kidd Creek by E.I. Robinsky (1975). Surface deposition of paste has been used for some time for red mud tailings in the aluminum industry, whereas the first surface deposition of hard-rock tailings as paste occurred at the Bulyanhulu mine, starting in 2001 (Theriault, 2003). Today, thickened and paste tailings deposition is gaining worldwide recognition as a method that could potentially reduce the environmental and safety liabilities associate to conventional tailings storage facilities, not only because it obviates the need for dams and reduces the risk of catastrophic failure, but also because it allows for increased water recycling within the mining operation, reduces the potential for groundwater seepage out of the tailings impoundment, and may allow for progressive closure, shortening the time of exposure of the tailings’ footprint to the environment. 2.1.1 Potential advantages of paste tailings deposition Among the benefits of paste tailings deposition, there is general agreement that the reduction of pond water and corresponding increase in stability is probably one of the greatest advantages of this method. Along with this, there are several other benefits including (Li et al., (2009), Verburg, (2001)): •  less water to manage, treat and discharge to the environment (in wet climates) as very little free water is available for generation of a leachate, thereby reducing potential impacts on receiving waters and biological receptors;  •  water conservation from thickening for reuse in the mill (in dry climates). The reduced water use may represent an important economic incentive;  •  a reduced need for large expensive dams;  6  •  more potential disposal sites to choose from as the increase in the tailings depositional slope increases the storage capacity (topographic containment is not as critical);  •  a smaller watershed for the disposal site to minimize runoff;  •  a smaller footprint to reduce the area of disturbance. The footprint of a paste facility will generally be smaller than that of a conventional impoundment designed for an equivalent amount of tailings solids;  •  flexibility to extend the life of a facility; and  •  potential for concurrent reclamation and creation of a true “walk-away” facility at closure or one that will require less long term care and maintenance.  Moreover, paste allows for production of an engineered material by modifying the paste geochemistry in such a manner that environmental benefits result. For instance, addition of Portland cement has been shown to be very effective in reducing metals mobility. In addition, acid generation in the tailings can be markedly curtailed by mixing with alkaline materials. Co-disposal of other waste materials with paste is also possible. In particular, encapsulation of acid generating waste rock in appropriately designed paste may provide significant benefits in terms of environmental control and waste management (Verburg, 2001). 2.1.2 Process description and influence over material properties The physical and chemical properties as well as the mechanical response of paste tailings are directly related to the processing stages of the ore extraction circuit. As a consequence a brief explanation of the process is required for a broad understanding on how this material could behave after deposition. Tailings can be defined as crushed rock particles that are either produced or deposited in slurry form (Vick,1990). Although the processes vary from one mine to the other, some common stages are required for processing any hard rock mineral. Most milling procedures require crushing and grinding the rock coming from the mine to a given grain size. Based on a large volume of empirical data and operational experience, it has been determined that a paste must contain at least 15% by weight finer than 20 micron to exhibit the typical paste flow properties and behave as a non-segregating mixture (Verburg, 2001). After crushing and grinding, the material passes through the beneficiation stage, where the ore is “extracted” through one or several processes that generally require the addition of water and reagents to the mixture of grinded rock. The material that no longer constitutes an economical asset is treated as tailings and is generally dewatered before being transported to the tailings storage facility (TSF). A diagram showing the typical tailings production process is shown in Figure 2.  7  Crushing  Grinding  Leaching  Concentration  Heating  Thickening Filtering * Transportation Deposition * Depending on the desired final solids content filtering may not be required for paste production  Figure 2: Typical processes involved in paste tailings production (After Vick, 1990) As mentioned previously, once the mineral of interest have been extracted from the milled and processed ore, the solids that remain (tailings) are usually at a moisture contents more consistent with a slurry than a solid. As a consequence, for paste production, thickening is required to reduce the moisture content to provide a more “solid like” material as shown in Figure 3. Thickening is the concentration by gravity settling of suspended solid particles in a feed stream and its main objective is to obtain high solids concentration in the underflow while maintaining an acceptable overflow (Jewell & Fourie, 2006).  (a)  (b) Source: www.tailings.info  Figure 3: Comparison between paste tailings (a) and conventional tailings (b) discharge Through time, thickening processes have evolved from conventional thickening to high rate thickening (high rate refers to the increase in the settling rate inside the thickener), ultra high rate thickening, and lately, ultra high density (paste) thickening. During this evolution, the thickening process has been greatly improved by the addition of synthetic flocculants. Flocculation is the aggregation of single particles, or small group of particles, into multi particle aggregates or flocs. Flocculation is sometimes preceded by coagulation which is performed to neutralize the electrical potential surrounding the particles in the slurry so that repulsion does not occur.  8  Flocculation occurs when particles begin to collide and are held together by a polymer chain which enhances sedimentation as shown in Figure 4. In general terms, solids that have been flocculated will compact at a much faster rate than solids that have not been flocculated; nevertheless, the final density is expected to be higher for un-flocculated materials (Jewell & Fourie, 2006). In the thickener, flocculated particles will pass through three different stages; free settling, where particles are far apart so they settle freely, hindered settling, where particles settle as a mass at a rate that is a function of solids concentration, and compression settling at the bottom of the thickener. Figure 5 shows the typical configuration of a paste thickener.  Dispersion  Floc Formation  Figure 4: Flocculation with bridging type polymers (After Jewell & Fourie, 2006)  Figure 5: Configuration of a typical paste thickener (From Jewell & Fourie, 2006) Filtering may be required if the moisture content of the material after thickening is still above the required amount of water for “paste like” behaviour. Generally, if conventional or high rate thickeners are used, then, filters will be required to produce paste, whereas, if ultra high density paste thickeners are used, filters may not be required. Ultra high density thickeners produce underflows of paste consistency by maximizing flocculent efficiency, using a deep tank for compression, increasing the residence times of the tailings in the thickener and by specially designed raking systems.  9  Filters are categorized into two groups, vacuum or pressure filters. Vacuum filters use negative pressure or vacuum pumps to extract the fluid from the tailings and can be separated into three groups; drum filters, disc filters and horizontal belt filters. Pressure filters on the other hand use positive pressure and can be separated into two groups; horizontal pressure systems and belt press filters. Once the tailings have been thickened and filtered to the desired extent they have to be transported to the TSF. Typically, the material is transported through pipes using centrifugal or positive displacement pumps. On some operations the tailings have been transported using trucks or conveyor belts, nevertheless, this requires for the paste to be sufficiently dewatered, almost to a filter cake consistency. When being transported in pipes either by gravity or through pumping, paste produces a plug flow, with the fine particles creating an outer annulus, thereby reducing friction. The coarse particles are forced into the center of the conduit with the finer fraction acting as the carrier. This allows for conveyance of very coarse fragments, the size of which is only limited by the pipe diameter (Verburg, 2001). It is important to mention that it has been observed that more than 90% of the structure (flocs) created in the initial thickening operation is destroyed during pumping to the TSF (Jewell & Fourie, 2006). This may result in significant changes in material properties that could lead to poor material handling characteristics for effective disposal. Figure 6 shows the potential differences in paste behaviour after transportation.  Figure 6: Slump tests for material before (left) and after (right) transportation to tailings storage facility (From Jewell & Fourie, 2006) All the processes described above will have some implication in material behaviour. Several changes in terms of grain size, chemical properties, densities and strength will occur after each of these stages and therefore appropriate material characterization is extremely important. It must be acknowledge that the product entering one stage of the process may be completely different than that coming out and entering the following stage. Within the most relevant changes in material properties, the following could be mentioned: •  Changes in mineralogy due to host rock variations during the mining process.  •  Changes in grain size distribution along the crushing, grinding and beneficiation circuit. The percentage of fines after all this processes is expected to increase.  10  •  Changes in pH and salinity due to the addition of reagents to process water. For example, in clay rich suspensions low pH has shown to help the flocculation process whereas high pH may promote dispersion. Salinity has shown to have a similar impact (Figure 7).  •  Increase in density of the slurry during thickening. Also the addition of flocculants will change the structure and “fabric” of the material formed as well as the final density of the thickened material.  •  Effects over structure and fabric of the material due to pumping and transporting. Also, during transportation “shear thinning” may occur which is the decrease in viscosity as shear rate increases.  Increase in Salinity  (a)  (b)  Figure 7: Effect of pH (a) and salinity (b) over clay slurry dispersive behaviour (After Jewell & Fourie, 2006) The high variability in material properties during the process of tailings generation (crushing, grinding, use of reagents during processing), reinforces the fact that different material characteristics may be required for analyzing different stages of the process during design. For example different material characteristics (grain size, water geochemistry) may be required to analyze the best flocculation alternative as opposed to the potential slope of a paste tailings stack after deposition. Although in geotechnical engineering the primary focus is to understand the behaviour of the tailings once they have been deposited, an understanding of the changes the material will undergo through the whole tailings production process is still required. In this sense it must be understood that it may not be the same performing a settling test using tap water as opposed to water with high salinity or low pH as this could have important consequences in the results obtained. With this in mind, it is important to always remember that laboratory testing conditions during design should resemble as close as possible the expected conditions for paste production and deposition in the field.  11  2.1.3 Characteristics of thin layer deposition of paste As mentioned previously, one of the main concerns of geotechnical engineers is the behaviour of paste tailings after the material has been deposited. Several issues become relevant after deposition among which the most important are beach geometry, achieved shear strengths, consolidation and desiccation properties, liquefaction potential, water retention ability, drainage properties (hydraulic conductivities) and geochemistry. Understanding how the material is placed on site is key to understanding how these properties will change in time. For example, different behaviours will be observed if the same material is placed in very thin layers as opposed to thick layers under the same given climate. Depending on the local topography and design criteria, paste tailings deposits can be constructed under “centre stack” or “down valley discharge” schemes. “Centre stack” tailings are generally constructed in flat areas and consist of a single discharge point at the center of the stack which forms a conical shape. Under this method, perimeter berms or dams may not be required for containing the tailings; nevertheless, these structures are often used to collect and control rainfall runoff and bleed water coming out of the tailings and usually a separate pond is required to contain this surface runoff. A typical “centre stack” configuration is shown in Figure 8. An advancing deposition point may be also used. This method has been used as part of the Bulyanhulu mine in Tanzania (Theriault et al. (2001)) and it consists of a series of deposition towers that are sequentially operated to produce a landform that is more a series of ridges than a cone.  Figure 8: Typical “centre stack” configuration (From Jewell & Fourie, 2006) “Down valley discharge” is used in sloping ground, and the tailings are usually discharged in the upper areas so they flow downhill until they come to rest. In this case, dams are required if the slope achieved by the tailings is expected to be less than the natural slope of the terrain in order to avoid paste from keeping flowing down slope. If the slope of the tailings is expected to be steeper than that of the local terrain, dams may not be necessary. The size of the containment dam will depend mainly on the volume of tailings to be deposited and the slope that can be achieved without compromising safety. Depending on the surface length of the tailings stack and the size of the project, the height of a thickened/paste tailings stack above containment toe dams can be substantial. For example, the height of the tailings stack would be 100 m for a 5% slope and a 2,000 m long tailings surface. Therefore, the physical stability of thickened/paste tailings slopes is an important consideration in design (Li et al, 2009)  12  Figure 9: Typical “down valley discharge” configuration (advancing cones) (From Theriault et al., 2001) Although there are other options for paste deposition (paste backfill of underground works and dry stacking of paste on filtered cakes) this alternatives will not be covered herein as the main focus of the present work is on the advantages of thin layer deposition of paste placed on surface. The discharge of non-segregated tailings to the surface generally forms channel flow close to discharge point and then spreads to sheet flow. Both channel flows and sheet flows are generally turbulent when the velocity is high but become laminar before coming to rest (Li et al. 2009). If the method of discharge is such that flow is in the subcritical (laminar) region, frictional resistance will be higher and the slope will be steeper. The opposite occurs for turbulent flow. Discharge rate is usually controlled to enhance frictional resistance and to create thin layers of paste (5 – 20 cm thick). In general, before the following paste lift is placed, these layers are allowed to sit for several days while deposition is ongoing at a different point in the impoundment. This process enhances evaporation and increases the strength of each deposited layer by letting the material sediment, self weight consolidate and desiccate. Thin layer deposition and desiccation are essential to increase the strength before placing the next layer. If the conditions are adequate for desiccation (drying) to the shrinkage limit, then static liquefaction can potentially be precluded. However, for wet or high production operations, drying to the shrinkage limit may not be possible (Li et al. 2009). Also, evaporation of water helps reducing the total volume of the impoundment leaving extra room for more tailings to be disposed in a given surface area.  13  (a)  (b)  Figure 10: Advancement of thin layers of paste (From Theriault et al., 2001) Eventually an equilibrium slope of the thickened tailings is developed and its final angle will depend on many factors that include density of thickened tailings, grain size distribution, ore type, discharge method, rate of rise, thickness of deposited tailings layer and climatic conditions. The slope is generally steeper closer to the discharge point and flattens slightly with distance until it comes to rest, giving the slope some degree of concavity. Predicting the slope to be achieved in the field is a critical step during design. A change in 1 % between the predicted slope and the slope achieved in the field can have tremendous implications on the footprint of the total facility, which can in turn jeopardize the continuity of a given mining project due to limited amount of space for tailings deposition. Regardless of this, there is currently no universal method to estimate the slope of the stack and this is still an area of extensive research. Since the development of thickened tailings disposal by Robinsky (1975), it has been shown that thickening allows the tailings slurry to form tailings stacks with relatively uniform beach slopes typically from 2% to 5% for thickened tailings and up to 10% for paste tailings. Evidently, steeper slopes will allow for a larger volume of dry tailings to be stored in a particular footprint but may have a negative impact on stability. Figure 11 shows a plot relating achieved slopes as a function of discharge tailings slurry densities. As can be seen, the general trend is for the slope of the stack to increase as the density of the slurry increase.  14  Figure 11: Tailings depositional slope as a function of slurry density (Li et al., 2009)  2.2  Density as One of the Key Parameter for Paste Tailings Design  Density of soil mass plays a significant role in paste tailings impoundments design and management as it is closely related to the short and long term stability of these impoundments. As mentioned in previous sections, for paste tailings, containment structures are usually small or non existent so the structural stability of these storage facilities is governed by the impounded tailings. This differs from conventional tailings deposition in that the overall stability of conventional impoundment relies primarily on the stability of the containment structure, which is only a small fraction of the impounded tailings. Containment structures are generally constructed using fill material not generally susceptible to liquefaction or with the sandy portion of the tailings that generally have good draining characteristics so the degree of saturation can be controlled to some extend during operation. Besides, if cycloned sands were to be chosen to construct the embankment, it can be argued that the liquefaction assessment can be generally performed using typical approaches developed for sandy materials. Paste tailings, on the other  15  hand, are often classified as “silty” materials for which most of the typical correlations developed for sands may not be directly applicable. This has been and it is still one of the major challenges for practising engineers during the design of paste tailings impoundments. The understanding of how these materials behave under dynamic loadings is an area that is still in its early stages of development. Density also plays a significant role in the estimation of the overall capacity of any given tailings impoundment. The ability to predict density during early stages of design allows for better estimates of the land space required for tailings deposition under a given mine plan. Several mine sites have dealt with limitations in the amount of space available for tailings deposition due to poor assessment of the in situ density of the tailings after deposition. As a consequence, mines may have to face extra environmental permitting and costs which in some cases could jeopardize the future development of the mine. Density is also relevant when determining the amount of water that could be potentially stored in the tailings material. This variable is extremely important when trying to determine the water losses or recovery of a given tailings circuit as the entrapped water could be a significant proportion of the total water balance. The following sections will present an overview of the implications of density on liquefaction and will also describe the main mechanism affecting this variable in a paste tailings impoundment. This emphasizes the relevance of the present research in the sense that predictive tools are required to obtain this parameter so proper analysis of liquefaction potential can be performed during design. 2.2.1 The process of densification in a paste tailings impoundment After deposition, tailings undergo a series of processes that generally result in an increase of the density and strength of the material. Among the processes that affect tailings density, the following are considered the most relevant: •  Sedimentation and self weight consolidation after deposition: Paste tailings often undergo some volume change immediately after deposition. This deformation is a result of the loads imposed by the weight of the material and subsequent de-watering due to minor excess pore water pressures.  •  Drying and drainage: Depending on the existing climatic conditions and depositional scheme, paste tailings will be subject to drying through evaporation and further de-watering due to downward drainage. During this stage, the tailings shrink as a result of water being extracted from the pores along with the associated increase in matric suction. The stages of sedimentationself weight consolidation, drainage and drying generally occur progressively after the tailings are exposed to the environment.  •  Consolidation: Consolidation occurs due to the loads imposed by subsequent paste tailings lifts. The rate and amount of consolidation depend on the void ratio obtained after drying and drainage. In general, for hard rock tailings, different consolidation curves are obtained for  16  different initial void ratios (Ritchie et al., 2009) and therefore, being able to predict the final void ratio after sedimentation-self weight consolidation and desiccation becomes very relevant. The process of densification of a given paste tailings layer is shown schematically in Figure 12. Each of the stages shown could be described as follows: 1.  Material is deposited at a given solids content (SC) and forms a layer of thickness “h”. It has been assumed herein that the material is fully saturated after deposition.  2.  Immediately after deposition the material will begin to settle as a result of the combined effects of sedimentation and self weight consolidation allowing part of the pore water to bleed to the surface of the tailings or to drain through the base. If the slope of the stack is sufficient bleed water will likely runoff or otherwise evaporate. Evaporation and Drainage combined will be called herein as “environmental dewatering” (ED). It is assumed that there will be no ponded water on the surface.  3.  At a given point in time the amount of “bleed” water potentially generated as a result of sedimentation-self weight consolidation will be less than the amount of water potentially taken by ED (evaporation and drainage together) during the same period of time.  4.  At this point, the layer will begin its ED process. Initially the material is assumed to be saturated and therefore evaporation from the soil mass will occur at a rate equal to the potential evaporation (PE).  5.  As more water is evaporated, the layer will begin to shrink due to a decrease in water content and an increase in suction. At this point, the evaporation rate from the soil will likely be less than the potential evaporation as higher head gradients are required to remove water from the pores.  6.  If drying continues, the layer will reach the shrinkage limit and no more volume changes will occur as a result of desiccation. Surface cracking will likely occur at this stage.  7.  Once a subsequent fresh layer of tailings is placed on top of the previously dried layer, consolidation may take place (further increasing density). The freshly deposited layer will go through processes 1 – 6 in a similar way as the previously desiccated layer. It must be noted that drainage for the fresh layer could be potentially enhanced as the suctions from the lower boundary can be very high.  17  Sedimentation–Self Weight Consolidation ED Consolidation  Evaporation (E) Runoff (R)  S=1 (1)  (2)  Bleed Water (B)  (3)  Drainage (D)  (4)  (5)  (6)  Load Imposed by New Fresh Layer  (7)  (8)  Increasing Density Figure 12: Schematic representation of the densification process of a thin layer of paste It is important to mention that the shearing process that takes place while the paste is flowing down slope (from the “out of the pipe” to the “at rest” condition) may also be an important mechanism of densification as extra water may bleed during this stage. This process is expected to occur along with sedimentation–self weight consolidation, nevertheless it has not been considered in the approach presented herein. It is assumed that shearing effects will likely enhance the densification process, and therefore not considering them may deem the presented approach to be conservative. As will be shown in the following sections, density must be determined before developing any stability assessment as this parameter will determine the overall performance of the tailings facility. The density or state of the material will impact its potential for liquefaction as well as the resistance of the material before and after liquefaction occurs. The relation between density and some of the issues relevant to the stability of these impoundments will be discussed in the following sections.  18  2.2.2 The relevance of density in the estimation of liquefaction potential The fact that the tailings have come to rest at a slope that is governed by its yield stress, and is thus in equilibrium with self weight forces, does not mean it will remain stable as the height of the stack increases. It is believed that if liquefaction is triggered in a sloping stack of paste, gravity could potentially transport the liquefied material down slope overtopping the capacity of the containment structures, thus, leading to an involuntary release of tailings to adjacent areas. It is presumed that for a flow slide to occur, first, liquefaction must be triggered and second the shear resistance of the material after it liquefies must be less than the load imposed by the sloping material under the effect of gravity (Ritchie et al. 2009) or under the effect of cyclic loads imposed by an earthquake. In other words, if the residual shear strength after the material liquefies is high enough, it will prevent a bearing capacity failure for level ground conditions, but large deformations/settlements may occur due to distortion during the earthquake and dissipation of excess pore water pressures after shaking or due to the loads imposed by the sloping stack. For sloping ground conditions, if the residual strength is sufficient, it will prevent a flow slide, but displacements commonly referred to as lateral spreading, could occur along with settlements (Greater Vancouver Liquefaction Task Force Report, 2007). Under these assumptions, two key questions must be answered during the design of a paste tailings impoundment; Is the paste going to liquefy under static or dynamic loadings? And, if the material liquefies, what slope should be targeted during deposition so that the liquefied material doesn’t flow under the effect of gravity or an earthquake? The answer for any of these two questions requires the estimation of one key parameter, density. Liquefaction refers to a sudden loss in shear stiffness and strength of soil due to static or cyclic loading. The loss arises from a tendency for soil to contract due to shear, and if such contraction is prevented or curtailed by the presence of water in the pores, it leads to a rise in pore water pressure and a resulting drop in effective stress. If the effective stress drops to zero (100% pore water pressure rise), the shear strength and stiffness also drop to zero and the soil behaves as a heavy fluid. However, unless the soil is very loose, it will likely dilate and regain some shear stiffness and strength as it strains. The postliquefaction shear strength is commonly referred to as the residual shear strength and may be 1 to 10 times lower than the static shear strength (Greater Vancouver Liquefaction Task Force Report, 2007). As mentioned above, liquefaction can be manifested under static or dynamic loading conditions. Static liquefaction is generally triggered due to monotonic loadings while dynamic liquefaction is associated to an increase in pore water pressures due to cyclic loading. The main reasons for dynamic liquefaction are associated to earthquake induced loads and could also be a result of equipment vibrations which is not particularly relevant in paste tailings deposition. Static liquefaction can be a result of slope instability alone, or can be triggered as a result of other mechanisms such as rapid rates of construction, interlayering of sandy materials with layers of fine materials that may curtail the dissipation of pore water pressures, static shear stresses in excess of the collapse surface, rapid foundation movements and episodic tailings slurry placement. Although, liquefaction is a term most often associated with seismic events (dynamic), mine tailings impoundments have demonstrated more static liquefaction events than seismic induced events (Davies et al, 2002).  19  The susceptibility of a given material to liquefaction is generally accepted to be governed by its stress and density state. In essence, the density or void ratio at which the material is under field conditions would define the response of the material to static and dynamic loadings. The following sections will provide a brief background on the implications that density could have over the response and stability assessment of a given paste tailings impoundment and will also emphasize on the relevance of reliable density estimates during design. 2.2.2.1  Impact of density on static liquefaction of sands  The susceptibility for static liquefaction in sands is closely related to its density as different behaviours will be observed between loose and dense sands. As shown in Figure 13, dense sands generally have a dilative response while loose sands have a contractive behaviour. Dilative response generally results in negative pore water pressures and an increase in effective stress while contractive behaviour generates the opposite effect. As shown in Figure 13, under monotonic loading and undrained conditions, and depending on its state, that means its relative density (Dr) or void ratio (e), sands can develop three distinct behaviours; (1) Liquefaction, (2) Limited Liquefaction or (3) Strain Hardening.  σd  (3)  n  *  n  *  n  n  *  Response  Loose  Liquefaction  (2)  Medium Dense  Limited Liquefaction  (3)  Dense  Strain Hardening  e1 > e2 > e3  Steady State  ∆u  Initial State  (1)  (2)  m  (+)  Sample  * m *  (1)  εa (1)  *  εa (2)  (−)  (3)  Figure 13: Undrained response of sands under monotonic loading (After Vaid and Chern, 1985) Similarly, the stress path of sands at any of these states is depicted in Figure 14. It is observed that at small strains sandy materials will tend to contract independent of their relative density. Dense materials will go through a phase transformation (PT), shown as points “n”, after which they will dilate to failure at the steady state line (SSL), depicted as point “n*” which is considered as the steady state (SS) following PT. On the other hand, very loose materials will just contract to failure, shown as point “m”. For a given sand both the PT and SS lines are unique and independent of relative density (Dr) and effective confining stress (σ’c) and it has been shown that PT and SS generally fall on the same line (Vaid and Chern 1985).  20  q y uit liq Ob . ) x Ma ilure (fa  *n*  n  n m  *  (2)  *  *  PT  S or S  *n* CSR  (3)  (1)  p Point m  - Liquefaction  Point n  - Phase Transformation (PT) for Dilative Samples  Point n*  - Steady State (SS) after PT  Figure 14: Typical stress paths and zone of contractive behaviour (After Vaid and Chern, 1985) Reliable determination of field densities is also relevant as the potential for liquefaction is directly related to the confining stresses at which the sand is subjected. The liquefaction potential of a given sand at a void ratio of ec has been noted to increase with increasing confining stress. Therefore, for a given void ratio there is a critical principal effective stress (σ1’) that defines the region of contractive deformation at that given state. This is shown in Figure 15 which depicts the stress path of two samples with the same void ratio but under different confining stresses. Density becomes relevant as the confining stresses in the field are generally estimated based on the density and thickness of the overlaying material at any given point. This becomes particularly relevant in a tailings impoundment where confining stresses at large depths can be substantial and enough to prevent any dilative behaviour, thus enhancing the chances of liquefaction to occur. q σ’1-crit = f (e)  y uit liq Ob . ) x Ma ilure (fa  *  (a)  *  (b)  Depth  Steady State Point  S or S PT Region of Contractive Deformation CSR  *  (b) σ’1-crit = const (a)  p’ Considering that:  ec-a = ec-b σ’1-a < σ’1-b  Figure 15: Region of contractive deformation (After Vaid and Chern, 1985) Static liquefaction potential of sandy materials has been also assessed using critical state soil mechanics (Casagrande 1975; Castro and Poulos 1977; Been et al. 1991 and Jefferies and Been 2006), which relies heavily in the ability to determine field densities. One of the main concepts of this approach is the estimation of the state parameter ψ (Been and Jefferies, 1985) which is defined as the difference between 21  the field void ratio and the critical state line (CSL) or SSL at the same mean effective stress, as shown in Figure 16. The SSL is obtained by observations of the soil behaviour at very large strains. A soil is considered to be at steady state condition if deformations are occurring at constant volume or void ratio, constant effective stress, constant shear stress or resistance and constant rate of shear strain. For sands, a plot of possible conditions during steady state flow produces a single curve (SSL) in three dimensional space of void ratio, effective stress and shear stress. If the sand is at a particular in situ effective stress and void ratio (density) below the SSL it is considered as dilative and therefore not prone to liquefaction. If it plots above the SSL it is then in the contractive zone and it is prone to liquefaction. It must be considered, that this does not mean that liquefaction failure is a certainty as a trigger mechanism is required for liquefaction to happen (Jewell & Fourie, 2006). e Loose, Contractive (Potential Liquefaction)  + ψ = e0 - ec  Dense, Dilatant (No Liquefaction)  -ψ CSL, SSL Mean Effective Stress  Figure 16: The concept of state parameter and critical state line (After Been and Jefferies, 1985) Hard rock tailings often show a similar behaviour to that observed for normally consolidated sands (Jefferies and Been 2000), where the consolidation lines are approximately parallel to each other. As a consequence, tailings may have wide ranges in its void ratio compression state and therefore there is generally not a single consolidation curve for this type of material (Li et al. 2009). This idea is depicted in Figure 17 where different initial states result in different final void ratios for the same load. With this in mind, the ability to estimate the initial void ratio before consolidation begins, becomes extremely relevant. e  Different initial states will result in different final void ratios Loose  All possible states lie within shaded zone  Dense  Log (σ σ’3c)  Figure 17: Diagram depicting the range of possible states of a sand (After Vaid and Chern, 1985)  22  In addition to density, there are also other factors that should be considered during the evaluation of static liquefaction. Several researchers have suggested that the undrained response of sands within the strain capacity of laboratory equipment is also a function of sample preparation, stress path followed during loading, and effective confining pressure (Vaid and Negussey, (1988); Vaid et al., (1999); Vaid and Chern (1985)). In this regard, it was observed that preparing water deposited sands (fluvial, hydraulic fill or tailings) by moist tamping technique may unjustifiably condemn sands as being potentially liquefiable. Uthayakumar & Vaid (1998) also explored the effects of stress path on residual strength over a wide range of stress paths defined by α, the inclination of the principal stress to the vertical axes of the sample using the hollow cylinder torsional shear device. Results suggest that different residual strengths should be assigned to different areas of the liquefied region depending on the dominant stress conditions. As observed in Figure 18, increasing α from 0 to 90° progressively promotes contractive behaviour.  Figure 18: Effect of inclination of principal stress over maximum shear strain and stress path response of Fraser river sands (from Uthayakumar and Vaid, 1998) 2.2.2.2  Impact of Density on Dynamic Liquefaction of Sands  Over the past 35 years, a methodology termed the ‘‘simplified procedure’’ has evolved as a standard of practice for evaluating the liquefaction resistance of sandy soils under cyclic loading (Idriss and Boulanger, 2008). The “simplified procedure” used to analyze liquefaction triggering for sandy materials involves comparing the Cyclic Stress Ratio (CSR) caused by the design earthquake with the Cyclic Resistance Ratio (CRR) or the capacity of the soil to resist liquefaction, which is primarily associated to its density. Seismic loading subjects elements of the soil to oscillating (or cyclic) shear stresses, typically denoted by the symbol τcyc. The CSR is defined as the ratio between the cyclic shear stresses and the vertical effective stress (σ΄vo) prior to seismic loading (CSR = τcyc/σ΄vo). On the other hand, the CRR is considered as the CSR that triggers liquefaction in a specific number of cycles (usually determined based on the magnitude of the earthquake).  23  Density becomes relevant as CRR depends mainly on this parameter as well as soil type. It can be obtained directly from tests on undisturbed samples of soil, or indirectly from field experience and in-situ testing at sites recently subjected to seismic loading. The factor of safety against liquefaction triggering is given by the ratio between CRR and CSR (FS = CRR/CSR). Accordingly, a given soil is susceptible to liquefaction if the CSR is higher than the CRR. As shown in Figure 19, the undrained response of a given material under cyclic loading can be separated into three mechanisms of strain development; (1) Liquefaction, (2) Limited Liquefaction and (3) Cyclic Mobility. Liquefaction is developed in the form of strain softening accompanied by loss of shear strength. Denser sands, when subjected to undrained cyclic shear loading, may respond with transient softening (in concurrence with transient build-up of high excess pore water pressures) and result in progressive accumulation of shear strains with increasing number of load cycles. This mechanism of strain development, which is considered to result in limited deformations under earthquake loading, is commonly described as cyclic mobility. Limited Liquefaction occurs when large deformations occur before the effective confining stress (σ’3) becomes zero.  (c)  ½(σ σ1’-σ σ 3’)  (b)  ½(σ σ 1’-σ σ 3’)  ½(σ σ1’-σ σ3’)  (a)  ½(σ σ1’+σ σ3’)  ½(σ σ1’+σ σ3’)  ½(σ σ1’+σ σ3’)  Figure 19: Undrained response of sands under cyclic loadings. Liquefaction (a), cyclic mobility (b) and limited liquefaction and (c) cyclic mobility (from Chern, 1985) Density will also determine the number of cycles required to achieve a given shear strain. As presented in Figure 20, for a given CSR dense sand will require a higher number of cycles than loose sand to achieve the same shear strains.  24  τcy/σ σ’vo  Dr 80%  40%  n for γ = γ0 n0  20%  n  Figure 20: The effect of density over the number of cycles required to achieve a target strain (After Vaid and Chern, 1985) 2.2.2.3  Density and its Relation to the Residual Strength after Liquefaction  Rapidly loaded saturated sand can have an undrained strength, and like clay this strength can be stress and strain path dependent (Davies et al., 2002). Residual shear strength refers to the shear resistance that a liquefied soil mobilizes in the field. Although residual shear strengths can be obtained in the laboratory, results should be used with care as this parameter may be affected by field mechanisms such as void redistribution and particle intermixing which cannot be represented by laboratory element testing (e.g., triaxial or simple shear test). Some of the mechanisms that are not possible to quantify using conventional laboratory testing are the effects of upward flow of pore water through loose sands that could increase the excess pore water pressure within overlaying layers of either silty or clayey materials. For overlying materials composed of silty sands the upward flow of pore water pressure may induce liquefaction of the overlying material which otherwise may have had a sufficiently large CRR to have precluded liquefaction. For clayey overlaying materials, upward flow of pore water pressure can accumulate immediately below the interface resulting in the formation of water films or water pockets under certain conditions (Idriss and Boulanger, 2008). Regardless of the limitations of determining residual shear strength using laboratory element testing the concept of expressing this parameter as a fraction of the effective confining pressure has been used in engineering practice on several water-retaining and tailings dams, including the Sardis Dam in 1989. The ratio, denoted Su/p’, ranges from very low values up to values equivalent to drained strengths. The range is dependent upon a number of factors; the most important of which is material density. The looser, more contractant, the tailings are, the lower the value of Su/p’ (Davies et al, 2002). The use of Su/p’ rather than Su is most commonly based on the fact that Su/p’ is more effective for describing undrained stress-strain behavior up to moderate strain levels in undrained monotonic laboratory element tests. In addition, the use of Su/p’ is believed to better reflect the potential effects of strength loss that is induced by void redistribution (Idriss and Boulanger, 2008).  25  Wijewickreme et al. (2005) observed that values of post-cyclic maximum shear strength ratio (Su-PC/σ′vc) for laterite and copper–gold–zinc tailings would range between 0.41 and 0.60 and 0.13 and 0.53, respectively. This range of values were larger than the liquefied strength ratios of 0.02 < Su(min)/σ′vc < 0.20 obtained by Olson and Stark (2003) from triaxial compression test data for contractive sandy soils. The Su-PC/σ′vc values were also different from the values of undrained shear strength at PT of 0.10 < SPT/σ′vc < 0.26 observed by Vaid and Sivathayalan (1996) for Fraser River sand in simple shear. Olson and Stark (2003) used the minimum strength observed in monotonic triaxial undrained testing as the liquefied shear strength Su(min); Vaid and Sivathayalan (1996) defined SPT as the mobilized shear strength at phase transformation (i.e., minimum strength) in constant-volume monotonic loading DSS tests. Castro (2003), based on triaxial tests conducted on a natural fine-grained soil of low plasticity, has also observed differences in liquefied strength ratios similar to those noted previously; Castro noted that the postcyclic ratio Su-PC/σ′vc is significantly higher than the observed value for undrained steady state strength ratio (Su-SS /σ′vc). Regardless of these differences, that could be attributed to the fact that each study had different stress – strain histories, a clear trend of increasing postcyclic maximum shear strength ratio (Su-PC/σ’vo) with decreasing void ratio (or increasing density) is generally observed. However, Wijewickreme et al. (2005) noted that measured liquefied strengths arising from laboratory specimens may not necessarily represent the in-situ conditions. Consequently, they recommended that laboratory derived post-cyclic strength data should be used in the seismic stability analyses of tailings structures with due recognition of the potential differences between the field and the laboratory. Residual undrained strength from case histories has also been correlated to cone tip resistance, which is directly related to in situ density. Idriss and Boulanger (2008) presented equations to determine Su/p’ based on the back analysis of several case histories of flow slides induced by liquefaction. Equation 1a was proposed to determine residual strengths for cases with no significant void ratio redistribution effects. This condition could include sites where stratigraphy would not impede post-earthquake dissipation of excess pore water pressure, so the dissipation of excess pore water pressure would be accompanied by densification of the soil at all depths. Equation 1b was developed for sites where void ratio redistribution could be significant. This would include sites with relatively thick layers of liquefiable soils that are overlain by lower-permeability soils that would impede the post-earthquake dissipation of earthquakeinduced excess pore water pressures. In this case, the trapping of upwardly seeping pore water beneath the lower-permeability layer could lead to localized loosening, strength loss, and possibly even the formation of water films.  q Sr q = exp c1 cs − Sr −  c1 cs − Sr  24.5 σ ' vo  61.7   2    q c1 cs − Sr  +    106  3    − 4.42  ≤ tan φ '     (Equation 1a)  26  q Sr q = exp c1 cs − Sr −  c1 cs − Sr  24.5 σ ' vo  61.7   2    q c1 cs − Sr  +    106  3    − 4.42      (Equation 1b)   q  × 1 + exp c1 cs − Sr − 9.82   ≤ tan φ ' 11 . 1    Where: Sr = Residual Strength σvo’ = Mean effective vertical stress qc1Ncs-Sr = Equivalent clean sand CPT normalized corrected cone tip resistance φ’= Effective friction angle 2.2.3 Challenges for assessing liquefaction for paste tailings material It has been clearly shown that density is a fundamental parameter in the assessment of liquefaction potential and post liquefaction behaviour of sands. In natural sandy deposits, density can be obtained through several direct or indirect methods, and commonly, “in-situ” testing (SPT, CPT, or similar) provide reliable estimations. As opposed to natural deposits, one of the major drawbacks in tailings design and planning is that density is not readily available/obtainable and must be predicted before the commencement of construction (no possibility for in-situ estimates during design). These predictions are based on previous experience, possible range of material properties and expected depositional schemes and usually rely on several assumptions that could lead to broad ranges of expected densities to be obtained in the field. Differences between predicted and actual densities after deposition can have a tremendous impacts on the stability assessment of a given tailings impoundment as the likelihood for liquefaction is closely related to this parameter. Small changes in the predicted densities could potentially result in a change of the expected mechanical response of the tailings, for example from “non-liquefiable” to potentially “liquefiable”. One of the major gaps in the prediction of liquefaction potential for tailings during design has been the inability to provide reliable estimations of void ratio before consolidation takes place. This is considered to be the void ratio after sedimentation-self weight consolidation and drying. Estimating the void ratio after these processes is extremely important as sands and tailings have shown to have a wide range of possible void ratio compression states so the void ratio or density achieved after applying a given load (consolidation) will depend on that initial state. Ultimately, this final void ratio after consolidation is the one that will define the undrained response of the material. Although the focus of the present research is to present an approach to provide reliable estimates of density after sedimentation-self weight consolidation and drying, several challenges are still remaining for an appropriate evaluation of liquefaction in paste tailings impoundments. One of the key limitations is that there is not a broad understanding of the undrained response of tailings and in most instances, the current state-of-practice for liquefaction evaluation of fine-grained soils relies on empirical criteria based on simpler soil parameters, properties, and approaches for the evaluation of liquefaction potential (Bray et al. 2004; Andrews and Martin 2000; Finn et al. 1994; Marcuson et al. 1990; Sanin and Wijewickreme 2006). Nevertheless, recent investigations have shown that these empirical approaches for seismic design 27  in silty soils have considerable drawbacks, including the potential for non-conservative liquefaction susceptibility assessments (Boulanger et al. 1998; Atukorala et al. 2000, Wijewickreme et al., 2005). Wijewickreme et al. (2005) through DSS testing suggested that the copper–gold tailings would reach a shear strain (γ) of 3.75% in 15 cycles if the specimens were subjected to a cyclic stress ratio of 0.17. This indicated that the material had the potential to develop significant strains and pore water pressure under a level of shaking commonly encountered in seismically active areas. Wijewickreme et al. (2005) also concluded that for the fine-grained tailings considered in their study, the liquefaction susceptibility predicted using commonly applied empirical criteria was not always in agreement with the liquefaction triggering determined from cyclic DSS tests. This reinforces the fact that extreme care should be undertaken when using correlations developed for other types of materials to determine the potential for liquefaction in a tailings impoundment as they may not be necessarily suitable. Although the response of sands and clays have been studied extensively to date, only limited effort has been placed to study the response of silty soils in general (Boulanger and Idriss 2004; Bray and Sancio 2006; Sanin and Wijewickreme 2006), and fine-grained tailings in particular (Moriwaki et al. 1982; Vick 1990; Poulos et al. 1985; Castro 2003; Wijewickreme et al. 2005). Paste tailings comprise predominantly silt size particles (with low plasticity, low cohesion and high angle of friction) and therefore, the knowledge of stress-strain response of silty materials under static and dynamic loadings becomes critical in the assessment of overall stability of a given paste mass. In spite of these efforts, the understanding on how these materials behave is still in its early stages of development and is currently one of the major challenges that practising engineers are facing during the stages of paste tailings design. One of the differences that have been observed as part of the behaviour of natural silty materials under cyclic loading is that, as opposed to sands, cyclic resistance is relatively insensitive to the confining pressure (and the changed initial void ratio due to consolidation) and that the response is influenced only by the mobilized shear stress ratio (Sanin and Wijewickreme, 2006). In this study the data points of CSR as a function of number of cycles plotted on a single line regardless of the confining stress applied. For sands, the cyclic resistance generally increases with increasing density and for a given relative density, the cyclic resistance has been noted to decrease with increasing confining stress. It must be noted that the results from Wijewickreme et al. (2006) were obtained for Fraser River Silts subject to cyclic loading in a DSS device and may not be necessarily applicable to silty tailings as a result of differences in material angularity. Nevertheless, this reinforces the fact that totally different responses could be obtained for materials with grain sizes in the range of silty soils.  2.3  Available Theories for Predicting Density  One of the key objectives of the present work is to provide reliable predictions of density after sedimentation-self weight consolidation and desiccation (in the form of evaporation and drainage) that could be subsequently used in the estimation of consolidation and ultimately liquefaction potential. To fulfill this goal, an understanding of the existing theories developed for describing the observed behaviour of each of the relevant stages of densification is required. The processes that contribute most to the  28  densification of a given paste tailings layer are sedimentation–self weight consolidation, evaporation, drainage and consolidation, so the following section will try to cover some of the existing theories available to fit the observed behaviour of each of these processes. 2.3.1 Sedimentation and self-weight consolidation of slurries Solids suspended in a fluid when subject to the effect of gravity will settle under their own weight until an equilibrium state has been achieved. Depending on the initial solids density of the slurry, the solids can undergo particulate sedimentation (sometimes referred to as free settling) or hindered settling where the particles move as a mass. It is generally accepted that during sedimentation there is no effective stress and the slurry behaves like a fluid, nevertheless, once a structure is formed and inter-particle effective stresses get established, the slurry becomes soil, and finite strain self-weight consolidation may be the most appropriate model to describe settlement. At this point, the amount and rate of self weight consolidation depends on material properties such as hydraulic conductivity, density of solids, and initial void ratio as well as layer thickness. One of the major drawbacks is that determining the point at which a slurry goes from a sedimenting mass to a self-weight consolidating mass is not a trivial task. The sedimentation process is represented in Figure 21, where the upper interface (suspension) is characterized by H vs t (in blue) and the sediment is characterized by L vs t (in red). A sedimenting mass will go through three different stages; a constant rate period, a first falling rate period and a second falling rate or compression zone. The constant rate period is defined by free sedimentation of the particles and generally occurs in diluted slurries. The first falling rate period is caused by upward movement of liquid as it is squeezed out of the sediment and is shown as point A in Figure 21. This point is given by a characteristic line emanating from the origin of the sedimenting mass, which can be considered as a continuity wave that propagate upwards. Along these characteristic lines concentration is constant. When the sediment meets the suspension interface (H = L), shown as point B in Figure 21, the second falling rate period begins. Further settlement will only be affected by the flow of liquid out of the compaction zone. It is important to mention that for high density paste the constant rate period may not be present and it is likely that the observed hindered sedimentation behaviour occurs somewhere between points A and B. Another important remark is that for suspensions with different particle sizes segregation is likely to happen if the initial solids concentration is low.  29  H0  Height of Interface H, L  Constant Rate Period  A  t1  t2  First Falling Rate Period  B  0  t1  t=0  Compression Zone  t2  t  H = H0 , L = 0  L = L1  H = H1  H=L  H vs t L vs t  Figure 21: Typical sedimentation curve (After Tiller, 1981) The first attempts to describe sedimentation of concentrated soil suspensions were based on Stoke’s Law, which described the idealized behaviour of a single particle by equating the fluid drag force to the gravitational force on the particle at the terminal settling velocity. This approach was extremely simplistic and not applicable to real soils as it only considered a unique particle size. It was in 1952 when Kynch proposed a new approach to assess sedimentation by assuming that the speed of fall of particles in a suspension is determined by the local density only. His theory was the first attempt to describe what was defined as hindered sedimentation and it also considered particles of uniform size. Kynch’s theory is based on the fact that density propagates as characteristics waves from the bottom to the top of a sedimenting mass. One of the reasons to this approach’s popularity is the fact that the procedures involved are graphical in nature and do not need any numerical treatment. More importantly, the properties required for analysis can be determined in a single-batch sedimentation test. The following set of equation was proposed by Kynch (1952) to analyze hindered sedimentation problems.  ∂C ∂C + V (C ) ⋅ =0 ∂t ∂x  V (C ) =  ∂ (v s ⋅ C ) ∂C  (Equation 2)  (Equation 3)  Where concentration is given by: C = (1 − n) ⋅ ρ s  (Equation 4)  30  Or in terms of void ratio (e):  C=  1 ⋅ ρs 1+ e  (Equation 5)  Where: C = mass of particles per unit volume (concentration) n = porosity ρs = density of solids vs = settling velocity Hindered sedimentation theory is considered to be valid only if the concentration is such that flocs are not in contact, as this may slower the settling rate compared to that obtained by Kynch’s theory. This suspension may be considered as a mixture of soil particles in water where the dilution is such that the soil particles are widely spaced. The particles are supported by the fluid as they settle so that the pressure in the water phase is given by the total weight of the mixture. As a consequence, the pore pressure is equal to the total stress and there are no effective stresses (Been, 1980). Also, Kynch's theory (1952) was originally meant for the sedimentation of a dispersion of similar particles; nevertheless, McRoberts and Nixon (1976) extended this to soil and defined the concentration as the mass of particles per unit volume while considering the velocity at a point rather than of a particle. Been and Sills (1981) developed a series of experiments to evaluate settlement as a result of sedimentation and self weight consolidation of slurries with uniform initial void ratios. During the experiments soil was laid down by sedimentation through water, passing through the phases of a fluid supported suspension, through a loose structure to a soft soil. During this process measurements of density (using a non destructive X-Ray technique), total stress, pore water pressure and settlement were taken at different time steps. Once the suspension starts to behave as a soil the physical behaviour is better described by large strain consolidation theory (Gibson, 1967). The governing equation for the self-weight consolidation process is then given by:  ∂e ∂ + ∂t ∂z    d  k  ∂e k dσ ' ∂e   γ s − 1  =0    +  ( 1 + e ) de ∂ z γ γ  w   w  de  1 + e  ∂z  (Equation 6)  Where: e = void ratio k = hydraulic conductivity γw = unit weight of water γs = unit weight of the solids σ’ = vertical effective stress z = reduced coordinate as will be shown in Section 2.3.3  31  In a technical note presented by Pane and Schiffman (1985) the findings of Been (1980) were extended to account for a transition zone between hindered sedimentation and consolidation. This was achieved by including an interaction coefficient (β) that depended on void ratio. The interaction coefficient was considered to be zero for void ratios greater than em (mixture behaves as a dispersion). For values of void ratio less than es it is assumed that there is full particle-to-particle contact and thus β is equal to unity. Equation 6 was expanded to:  ∂e ∂ + ∂t ∂z   k dβ de  ∂ σ' +  ( 1 + e ) de dz  ∂z γ  w    d  k  ∂e k dσ ' ∂e   γ s − 1  =0 β    +  ( 1 + e ) de ∂ z γ γ  w   w  de  1 + e  ∂z  (Equation 7)  For suspensions the coefficient β is equal to zero and the equation reduces to:  ∂e ∂e + V z (e) ⋅ = 0 ∂t ∂z  (Equation 8)  γ  d  k  V z (e) =  s − 1   γw  de  1 + e   (Equation 9)  This equation has the same form as Kynch’s equation, which governs the hindered sedimentation process. For pure consolidation, β is equal to unity and Equation 7 reduces to the Gibson-England-Hussey equation for large strain consolidation. Another important parameter that can be obtained from settling tests is the “zero effective stress void ratio” (eo). The value of eo can be determine in a simple experiment in which a small amount of the slurry is allowed to sediment in a graduated cylinder. Clearly, in this experiments the actual magnitude of the “zero” effective stress depends on how tall is the final soil column. For small columns (a couple centimetres high) this effect should be negligible. Liu (1990) investigated the void ratio corresponding to the zero effective stress and found that this is not a constant value for a soil, but that it depends on the initial water content (or void ratio) of the slurry. 2.3.2 Desiccation or drying In geotechnical engineering the increase in density due to desiccation or drying is commonly referred to as shrinkage which can be separated in three stages. First, structural shrinkage may occur as large water filled pores begin to empty. Generally, this stage is not accompanied by significant volume changes. Then, while the material is still saturated, normal shrinkage occurs and any decrease in the volume of water within the soil pores will generate an equal decrease in the volume of voids. Once the material starts to de-saturate the voids are no longer filled with water and therefore the amount of volume change is no longer equal to the amount of water being taken out of the soil mass, this stage is known as residual shrinkage. At this stage, the changes in volume will be given by the subsequent increase in suction forces.  32  Shrinkage can be described by a simple curve that relates the water content of a soil sample to its void ratio. Although the shrinkage curve may be determined for different initial degrees of saturation, the evaluation of tailings properties usually consist of slurried samples that are fully saturated or close to saturation. The typical behaviour of the drying of a slurried soil can be seen in Figure 22. As observed, the soil sample is fully saturated at the beginning of the test. As the sample dewaters, it follows the saturation line until air begins to enter the soil voids. This point is termed the General Air Entry (GAE) point. As the soil continues to dry, it reaches the minimum void ratio at which there is no further volume change. The water content at the intersection between the minimum void ratio and the saturation line is  Void Ratio (e)  called the Shrinkage Limit.  General Air Entry Void Ratio at the Shrinkage Limit  Shrinkage Limit  Line for S=1  Gravimetric Water Content (%)  Figure 22: Typical shrinkage curve (After Fredlund, 1999) The amount of shrinkage a soil experiences depends on numerous factors such as the percentage of clay in the soil, the type of clay mineral, the mode of geological deposition, the particle arrangement or structure, the overburden pressure, the degree of weathering, the exchangeable cations, the orientation of soil fabric, and the initial water content (Fredlund, 1999). Shrinkage has been shown to be independent of the rate of drying (Krisdani, 2008). Although the shrinkage of soils can be easily represented by the shrinkage curve, estimating the rate at which water will be evaporated or drained out of a given soil mass under a given soil – atmosphere boundary condition is a complex problem. The evaporation rate of porous materials is not constant but decreases as the material dries out. Initially, the actual evaporation (AE) will take place at a maximum rate known as Potential Evaporation (PE) but will then decrease as moisture within the soil mass decreases (Figure 23).  33  Figure 23: The relationship between the rate of actual evaporation and potential evaporation (AE/PE) and water availability (From Wilson, 1990) Wilson (1990) stated that there are three factors that dominate the flow of water from the soil surface to the atmosphere. These factors do not function as independent variables, but rather as a closely coupled system. The first factor is the supply of and demand for water imposed at the soil surface by atmospheric conditions such as total precipitation, net radiation, wind speed, and air temperature. The second factor is the ability of the soil to transmit water which is closely related to variables such as hydraulic conductivity and storage characteristics. The final factor involves the influence of vegetation. Wilson (1990) proposed a modified version of the Penman equation to estimate the actual evaporation rate (Equation 10).  E=  ΓQ n + ηE a Γ + ηA  (Equation 10)  Where: E = Evaporative flux (mm/day) Γ= Slope of the saturation vapour pressure versus temperature curve at the mean temperature of the air (mm Hg/°C) Qn = all net radiation at the soil surface (mm/day of water) η = psychometric constant  Ea = f (u )e a ( B − A) f (u ) = 0.35(1 + 0.146Wa )  Wa = wind speed (km/hr) ea = water vapour pressure of the air above the soil surface (mm Hg) B = inverse of relative humidity in the air A = inverse of relative humidity at the soil surface In order to obtain the estimates of actual evaporation, Wilson (1990) proposed a coupled model of heat and mass transfer equations that allows calculating the actual vapour pressure at the soil surface. The theory is based on the well known principles of Darcy's and Fick's Laws which describe the flow of liquid water and water vapour (Equation 11), and Fourier's Law to describe conductive heat flow in the soil profile below the soil/atmosphere boundary (Equation 12).  34  ∂h w ∂h  ∂P  ∂  ∂   k w w  + C w2  Dv v  = C 1w ∂t ∂y  ∂y  ∂y  ∂y   (Equation 11)  Where: hw = total head (m) t = time (s) C1w = coefficient of consolidation with respect to the liquid water phase y = position (m) kw = hydraulic conductivity (m/s) C2w = coefficient of consolidation with respect to the water vapour phase  Ch  ∂  ∂T  ∂T  P + Pv  λ  − Lv  = ∂t ∂y  ∂y   P  ∂P   ∂    Dv v  ∂y   ∂y   (Equation 12)  Where: T = temperature (°C) Ch = Volumetric specific heat of the soil as a function of water content (J/m3/0C) = Cvρs Cv = Specific heat of the soil (J/kg/0C) ρs = Mass density of the soil (kg/m3) λ = Thermal conductivity of the soil (W/m/0C) Lv = Latent heat of vaporization of water (J/kg). The equations proposed by Wilson (1990) were later included in the numerical code SoilCover (Wilson et al., 1994). SoilCover is a software widely used in engineering practice to evaluate unsaturated problems in soils and will be used herein to describe the moisture exchange between a given paste layer and the atmosphere. This model also accounts for drainage which is another important mechanism of desiccation. If the underlying layers are sufficiently dry, it is expected that this mechanism could greatly contribute to the drying process as large suctions may exist in the underlying material. Another important aspect of desiccation, which is not considered herein, is the effect of salt accumulation at the surface. Dunmola and Simms (2010) have shown that the effect of suppression of vapour pressure due to the osmotic action of salts can explain most of the reduction in evaporation. Also, the formation of a physical crust has shown to greatly reduce the evaporation potential of a soil. 2.3.3 Consolidation When a saturated soil layer is subjected to a stress increase, the pore water pressures inside the mass also increase. In fine grained soils, for which hydraulic conductivity is low, this increase in pore water pressures gradually dissipates over a potentially long period of time, along which, settlement or  35  consolidation occurs. The theory of consolidation was first developed by Terzaghi in 1925 and it was derived for saturated clay soils assuming that: 1.  The clay – water system is homogeneous  2.  Saturation is complete  3.  Compressibility of water and soil grains is negligible  4.  Strains are small in the porous media  5.  Permeability of soil remains constant during consolidation process.  Although this theory is widely used in practice it has several drawbacks for materials that undergo large deformations during the consolidation process. In particular assumptions 4 and 5 are rarely met for soft materials such as tailings. For such materials, often there will be significant strains in the media which result in a significant decrease in void ratio as a consequence of water being squeezed out of the pores. This significant decrease in void ratio means that water has less room to flow and there is a resulting decrease in the permeability of the soil. A generalized theory of consolidation was proposed by Gibson et al. (1967) for materials prone to large deformations during consolidation and has been widely used to analyze the consolidation of loose tailings materials (Li et al. 2009, Seneviratne et al. 1996). The theory considered Lagrangian instead of Eulerian coordinates, as the typically used Eulerian coordinates are inconvenient when deformations are large compared to the thickness of the compressible layer. With Eulerian coordinates material deformations are related to planes fixed in space and time, whereas with Lagrangeain coordinates deformations are related to planes that change in correspondence with material deformations (Figure 24).  Figure 24: Lagrangian coordinates at initial configuration (t=0) and at a given time t (From Gibson et al., 1981)  36  The equation for void ratio proposed by Gibson et al. was previously shown in Section 2.3.1 as Equation 6 and it was derived using a reduced coordinate (z) defined as follows:  z (a ) =  ∫  a  0  da ' 1 + e(a ' ,0)  (Equation 13)  The proposed equation is highly non-linear, nevertheless it can be rendered linear while retaining the nonlinearity of the permeability and compressibility, by examining the relationship between soil properties. Depending on the consolidation behaviour of the material under evaluation Equation 6 can be simplified by assuming that g(e) is constant. This function plays the role of a coefficient of consolidation and it is likely to be much less sensitive to changes in void ratio than are its constituent terms.  g (e ) = −  k (e) 1 dσ ' γ f 1 + e de  (Equation 14)  If the g function is assumed to be constant Equation 6 can be then transformed to:  ∂ 2e ∂z  2  (  ± γ s −γ  f  ) ded  ddeσ '  ∂∂ez = g1 ∂∂et     (Equation 15)  Another simplification to this equation can be made if the following assumption is also made:  λ (e ) = −  d  de    = Const . de  dσ '   (Equation 16)  If this is true, then the relation between void ratio and effective stress becomes:  e = (e o − e ∞ ) exp(−λσ ' ) + e∞  (Equation 17)  Where: eo = void ratio of the beginning of consolidation eoo = void ratio at the end of consolidation Finally, if parameters g and λ are assumed to be constant, the consolidation equation for void ratio can be written as: ∂ 2e ∂z  2  (  ± λ γ s −γ  f  ) ∂∂ez = 1g ∂∂et  (Equation 18)  Equations 14 to 18 were used by Gibson et al. (1981) to describe the consolidation process of a thick layer of clay under its own self weight. However, it is important to understand that its application will depend on how representative the previous assumptions are for the material under analysis.  37  Other constitutive models have been developed to represent the consolidation behaviour of soft soils. Liu and Znidarcic (1991) proposed a functional relational relationship for the compressibility in the form of:  e = A ⋅ (σ '+ Z )B  (Equation 19)  This constitutive relation has been included as part of the numerical software CONDES0 (Yao et al., 2002), which is widely used in industry for the assessment of consolidation and desiccation of soft soils. For this particular program the relation between hydraulic conductivity and void ratio is calculated based on the following relation (Somogyi, 1979):  K sat = C ⋅ e D  (Equation 20)  For this particular relations, A, B, C, D and Z can be determined based on the results of Seepage Induced Consolidation Tests. These constitutive relationships are then used to solve the Gibson et al. (1967) governing equations with the appropriate initial and boundary conditions that reflect the field conditions. In sandy soils, the drainage of the excess pore water pressures is rapidly dissipated due to the high values of hydraulic conductivity and this dissipation is accompanied by a reduction in the volume of the soil mass. As opposed to clays or fine materials this dissipation is assumed to occur very rapidly and therefore elastic settlement and consolidation are assumed to occur simultaneously. The stress densification process of sands was evaluated by Park and Byrne (2004) based on the results of one dimensional compression tests developed for eight sands. It was found that all data indicated a linear relationship between relative density (Dr) and square root of vertical effective stress (σ´v). Based on this finding, an expression for relative density in terms of initial placement relative density and subsequent applied stress was proposed.  D r = D ro + α ⋅  σ v´' Pa  (Equation 21)  Where the coefficient of stress densification, α, is given by:   1+ e   2 ⋅ (1.5 − D ro ) C  max α =  − D ro  ⋅ − e  max e min   (Equation 22)  Where: emax = maximum void ratio emax = minimum void ratio C = Sand stiffness number that is independent of void raio The application of the model proposed by Park and Byrne (2004) was shown to give appropriate results for sandy tailings (Figure 25) and could be potentially useful to estimate the void ratio obtained under a given overburden load.  38  Figure 25: Relative density changes predicted and measured for mine tailings sand (From Park and Byrne, 2004) 2.3.4 Coupling between drying and consolidation  In unsaturated soil mechanics, the volume change behaviour of a soil has been related to two stress state variables, (σ-ua) and (ua-uw) (Fredlund and Morgenstern, 1977). The combination of these variables defines a volume – mass constitutive surface that describes all possible states that a given soil may achieve as shown schematically in Figure 26. The void ratio versus net normal stress boundary constitutive relation may be formulated either from an oedometer test or an isotropic triaxial compression test. On the other hand, the relationship between void ratio and soi1 suction can be experimentally determined using the soil-water characteristic curve and the shrinkage curve. The void ratio versus soil suction boundary constitutive relationship can be calculated using a continuous mathematical relationship to represent the soil-water characteristic curve and the shrinkage curve as will be shown later in Section 2.4.3.  39  Figure 26: Volume mass constitutive surface for Regina clay (From Fredlund, 2006)  This constitutive formulation forms the basis for modeling the volume change of saturated - unsaturated soils, and may be used to describe problems such as stress/deformation, heave/shrinkage and consolidation altogether. Nevertheless, this requires for a mathematical formulation that properly defines the volume-change constitutive surface for a saturated/unsaturated soil. Fredlund (1999) developed a mathematical formulation for this surfaces based on common laboratory compression, shrinkage and soilwater characteristic curve (SWCC) tests.  2.4  Engineering  Properties  Relevant  to the  Sedimentation–Self  Weight  Consolidation and Drying Stages of Densification and their Estimation Some of the theories used to describe the observed behaviour of slurry materials during sedimentationself weight consolidation and drying have been presented in previous sections. Using any of these theories relies on the ability to determine some key material properties that are required as input parameters. From previous sections it has been determined that hydraulic conductivity (K) and its relation to void ratio (e) is one of the key parameters in sedimentation–self weight consolidation problems. On the other hand unsaturated hydraulic conductivity, shrinkage and soil-water retention properties are required for evaluating the process of drying. The following sections will briefly describe the existing methods and some important considerations that should be taken into account during the determination of these properties for slurry materials. It must be noted that the focus of the present work is on the sedimentationself weight consolidation and drying stages and therefore the estimation of other relevant parameters required to assess problems such as consolidation will not be covered herein. 2.4.1 Saturated hydraulic conductivity for slurries  The hydraulic conductivity of a slurry and its relation to void ratio is important as it defines their behaviour during sedimentation and self weight consolidation and also during the early stages of drying (while material is still saturated). When dealing with slurry materials undergoing settlement as a result of sedimentation and self weight consolidation, one should acknowledge that materials may be subject to  40  significant volume changes, even at zero normal loads, and that these changes in volume will in turn have an effect on hydraulic conductivity. This makes the use of conventional tests (constant or falling head tests), impractical for the purpose of estimating hydraulic conductivities at high void ratios as the slurry will likely change its volume as the test is being performed. Also, the application of hydraulic gradients common to constant or falling head test could potentially generate disturbances in the slurry mass that would make impossible for flows to be measured during the test. Although some relationships have been developed to determine the hydraulic conductivity of granular and cohesive soils at any given state (Hazen (1930), Kozeny (1927), Carman (1938), Chapuis (2004)), these equations are not expected to be reliable for materials at high void ratios such as those encountered for slurries. With this in mind, a different procedure must be used to measure hydraulic conductivity for slurries at high void ratios. Been (1980) proposed a relation to compute the hydraulic conductivity of a sedimenting soil based on the following set of equations (assuming incompressible fluid and solids): Continuity equations  ∂ (1 − n) ∂ (1 − n) ⋅ v s + =0 ∂t ∂x  (Equation 23)  ∂n ∂nv f + =0 ∂t ∂x  (Equation 24)  ∂σ ' ∂p + + γ s (1 − n) + γ f n = 0 ∂x ∂x  (Equation 25)  k  ∂p   +γ f  γ f  ∂x   (Equation 26)  Equation of equilibrium  Darcy´s law  n ⋅ (v f − v s ) = −  Where: n = porosity vf = velocity of the fluid vs = velocity of the solids k = hydraulic conductivity γf = unit weight of the fluid p = pore water pressure σ’ = effective stress  41  Combining Equations 23 and 24 yields:  ∂ (1 − n )⋅ v s + n ⋅ v f = 0 ∂x  [  ]  (Equation 27)  If the bottom is impermeable (as it is in a typical settling test), then, at any time at x = 0, vf = vs = 0, then solution to Equation 27 is:  (1 − n) ⋅ v s + n ⋅ v f = 0  (Equation 28)  Eliminating dp/dx from Equation 25 and 26 and rearranging gives:  γ  ∂σ '  1 n ⋅ (v f − v s ) = k ⋅ (1 − n)  s − 1 1 + γ f   (1 − n)(γ s − γ f ) ∂x      (Equation 29)  Using Equation 28, and transforming porosity (n) to void ratio (e), equation 29 becomes:  vs = −  k 1+ e  γs  (1 + e) ∂σ '   − 1 1 + γ f   (γ s − γ f ) ∂x      (Equation 30)  Been assumed that in a suspension, effective stresses are zero and therefore the Equation 30 results in Equation 31 which is the relation between the settling velocity of a slurry and hydraulic conductivity:  γ  k v s = − s − 1 ⋅ γ  w  1+ e  (Equation 31)  Tan et al. (1996) found that the behaviour of clay suspensions was also dependent on the initial conditions as this could have an impact on flocculation. A modified function to estimate the hydraulic was proposed based on the empirical fit of parameter α, as shown in Equations 32 and 33. The proposed relation is almost identical to that proposed by Been (1980) but with the only difference that hydraulic conductivity is also a function of initial state. The proposed equation require for at least two separate settling tests to be performed so α can be determined.  vs =   k (e, e o )  γ s ⋅ − 1  1 + e  γ f    1  1 k (e, e o ) = k ⋅  − 1 + e  1 + eo   (Equation 32)       α       (Equation 33)  42  A more sophisticated approach to determine hydraulic conductivities at high void ratios may be obtained if the seepage induced consolidation apparatus is used. Details of this test may be obtained in Abu-Hejleh et al., (1996). For this particular method a slurry sample is placed into the testing cell and a light piston is placed on top of the sample to prevent the formation of flow channels during the seepage induced consolidation test. A selected flow rate is then imposed across the sample by using a flow pump and the head loss is monitored by a differential pressure transducer. When the steady state is reached, the sample height and the steady state pressure difference are recorded. The sample is then loaded gradually to the maximum desired stress level and allowed to consolidate under the applied load. The sample height is recorded and the hydraulic conductivity is measured by using the flow pump again. Although this type of test does not allow for direct measurements of hydraulic conductivities at very high void ratios as those encountered during the sedimentation process, it provides a method to estimate them by extending the data of hydraulic conductivity measured at smaller void ratios. As part ongoing research at Carleton University, Manlagnit (2010) developed modified settling tests that allow for drainage to be measured at the bottom of the columns. Settlement in the tailings was measured using a non contact distance sensor that was connected to a dataloger and the tailings column were placed on top of scale so weight could be tracked daily during the test. The measurements of settlement and weight were later used to determine the water content and void ratio of the settling column. The amount of drainage coming out of the columns was related to the hydraulic conductivity based on Darcy’s Law according to the following formula:  Q=K  ∆H A L  (Equation 34)  Where: K = Hydraulic conductivity ∆H = total head, measured as the height of soil column (L) plus the height of ponded water. L = height of soil in the column It is important to mention that once the slurry have sediment and self-weight consolidated (no further volume changes) conventional permeability tests may be carried out for a more reliable estimation of Ksat at the settled condition (or settled void ratio). Comparing the measured value of Ksat obtained from conventional constant or falling head tests to that obtained from settling velocities using equation 31 may give a good indication whether the estimated values of K are within a reasonable range. 2.4.2 Soil water characteristic curve (SWCC) and shrinkage  The SWCC, also referred to as water retention curve, is a relationship between the amount of water in the soil (gravimetric, volumetric or degree of saturation) and the soil suction (negative pore water pressure). The typical shape of the SWCC in terms of volumetric water content (θ) is shown schematically in Figure 27. An initially saturated soil specimen de-saturates when it is subject to an increase in soil suction and different de-saturation stages can be identified as this process takes place. As shown in Figure 27 there  43  are three stages of de-saturation: the boundary effect stage, transition stage and residual stage of saturation. The boundary effect stage ranges from full saturation up to the air entry value. The air entry value of the soil is a soil suction value at which the largest pores in the soil begin to drain and the drained water is replaced by air that enters into the soil pores (Fredlund, 2006). When plotted in terms of volumetric water content, the slope of the SWCC in the boundary effect stage is not horizontal, as there is a slight change of water content from zero suction to the air entry value as a result of compression of the soil. It is important to mention that for slurry materials this slope can be significant as the material may compress even at very low applied suctions. If this portion of the curve is extended back into the negative suction range (positive pore water pressures) the slope would represent the coefficient of volume change mv for saturated soils (as that measured in a consolidation test). In this range (before the air entry value is reached) the volume change due to soil suction change is equal to the application of an isotropic net mean total stress. After this, the transition stage takes place and the water content in the soil declines up to the residual stage where relatively large increases in suction lead to relatively small changes in water content.  θ Air Entry Value  mv = dθ θ/duw Boundary Effect Stage  Transition Stage  Residual Stage  Residual Water Content  Pore Water Pressure (kPa)  Suction (kPa)  Figure 27: Typical SWCC showing the different stages of de-saturation (After Fredlund, 2006)  The soil-water characteristic curve is relatively easy to measure in the laboratory. Tempe cells and pressure plates are the most commonly used equipment in geotechnical practice. Tempe cells are acrylic pressure plate device with 100 kPa (1 bar) or 500 kPa (5 bar) ceramic high entry disc through which water can drain out of the sample. The soil specimen is placed inside the acrylic chamber in contact with the ceramic disk. Suction or positive air pressure is applied to the chamber and water is forced out through the porous disk. Once equilibrium is reached the cell is weighed and the amount of water that left the soil can be determined. At the end of the test the final water content of the soil sample is determined and this value is used to determine the water contents at the different suctions applied during the test. ASTM designation (Standard D-6836-02) provides a detailed description for the determination of the soil–water characteristic curves using several testing procedures.  44  2.4.2.1  Mathematical representation of the SWCC  Numerical analysis of unsaturated problems require for a mathematical representation of the SWCC. Several equations have been proposed for fitting the SWCC (Gardner (1958), Van Genuchten (1980), Mualem (1976), Burdine (1952), Fredlund and Xing (1994), Pham and Fredlund (2008)), nevertheless most of them are asymptotic to horizontal lines in both the low and high suction ranges. For materials that undergo significant changes in water content even at low suctions, which is generally the case for slurries, this can be a drawback as the fitting equation may not be able to represent the slope of the SWCC for suctions lower than the air entry value (specially if the curve is plotted in terms of gravimetric water content). The models presented by Fredlund and Xing (1994), and especially the one by Pham and Fredlund (2008) do not have this drawback and their fitting relations for gravimetric water content are presented in Equations 35 and 36. It is important to mention that, although the Pham and Fredlund (2008) relationship was developed specifically for slurries, it has the disadvantage that it is not commonly found in numerical packages developed to model unsaturated flow in soils. Fredlund and Xing (1994)       ψ      ln1 +   1  ψr   w w = w sat 1 − ⋅ 6  ln1 + 10        ψ     ln exp(1) +  ψ  r       af           nf        mf            (Equation 35)  Pham and Fredlund (2008)   w(ψ ) = (w sat     ψ     ln1 +   a  ψr   − S1 log(ψ ) − wr ) ⋅ b + wr  ⋅ 1 −   10 6   ψ +a    ln1 +  ψ   r     (Equation 36)  Where: wsat = saturated gravimetric water content at 1 kPa S1 = slope of the SWCC at low suctions wr = residual gravimetric water content af, nf, mf, a and b = fitting parameters ψr = residual suction  45  2.4.2.2  Volume change considerations  Equations 35 and 36 may also be used to fit the data of the SWCC obtained in terms of volumetric water content which has become general practice in geotechnical engineering and soi1 science. When determining the SWCC in terms of volumetric water content some challenges arise when dealing with materials that undergo significant volume change or shrinkage. Measurements of the volumetric water content are calculated based on the volume of water leaving the soil specimen as it dries. The total volume of the soil specimen is generally only measured at the start of the test and therefore the volumetric water content is determined as:  θ=  Vw Vo  (Equation 37)  Where: Vw = volume of water in the soil Vo = total volume of the specimen at the beginning of the test This laboratory method yields reasonable experimental data if the volume change of the soil specimen during drying is minimal (i.e., sands), but it becomes increasingly inaccurate for soils with reasonable fines content in which volume changes are significant during the test (Fredlund, 1999). If volumetric water content is not corrected for volume changes in the soil specimen, this can affect the interpretation of the air entry value and other parameters from experimental data. Therefore, measuring volume changes as the SWCC takes place is extremely important. Corrections for volume changes should be performed by measuring gravimetric water contents and by estimating the void ratio of the soil based on the measurements of volume. This provides the relationship between gravimetric water content and soil suction, w(ψ), and the shrinkage curve e(w). The correct volumetric water content should then be estimated according to Equation 38.  θ (ψ ) =  w(ψ ) ⋅ G s 1 + e( w(ψ ))  (Equation 38)  Volume change measurements can be difficult to perform in the laboratory and are prone to error. Usually volume changes are determined based on vertical deformations that are obtained using some sort of measuring tool (callipers, verniers, non contact displacement sensors, etc). Lateral shrinkage and volume changes associated to specimen cracking are unreliable and difficult to measure precisely without disturbing the sample.  46  2.4.2.3  Initial state considerations  The shape of the SWCC for a given material will depend on the applied total stress path and therefore different initial conditions may yield different SWCC as shown in Figure 28 (Fredlund, 2002). In this Figure, the initially slurried soil represents the maximum volume change condition and also represents the virgin compression curve up to the air entry value of the soil. It is assumed that the preconsolidation pressure of a slurry is approximately 0 kPa (i.e, 0.01 kPa) (Pham and Fredlund, 2008).  Figure 28: Influence of initial state on the soil water characteristic curve (From Pham and Fredlund, 2008)  The relation between water content and suction for an initially slurried clay specimen was compared to that of slurried specimens pre-consolidated at pressures ranging from 6.2 kPa to 400 kPa (Fredlund, 2002). As presented in Figure 29 it was observed that the pre-consolidated specimens showed gradual curvatures onto the virgin compression branch for the soil (slurry conditions) and that these curves lacked the distinct break in curvature common to specimens loaded in one dimensional compression (which was explained by the three dimensional volume changes that occur under a change in matric suction as opposed to one dimensional deformations obtained in oedometer tests). It was also noted that when large deformations occur during the test, the air entry value may not be easily determined if results are plotted in terms of gravimetric water content. Nevertheless, if results are plotted in terms of degree of saturation (Figure 30) it was observed that regardless of the applied preconsolidation stress, the soil began to desaturate at the same suction. The important consideration behind these findings is that for soils prone to large volume changes, the true air entry value can only be discerned from the plot of degree of saturation or void ratio versus suction.  47  Figure 29: Soil suction versus water content for initially sluried Regina clay (From Fredlund, 2002)  Figure 30: Degree of saturation versus soil suction for Regina clay at two different preconsolidation pressures (From Fredlund, 2002)  48  2.4.3 Shrinkage  As explained earlier in Section 2.3.2, the shrinkage curve is the property that relates void ratio to gravimetric water content. The shrinkage curve is usually determined by (ASTM Test Method for Shrinkage Factors of Soils [D 427]). In a similar way as the SWCC, the shrinkage curve also requires mathematical representation for proper numerical analysis. Fredlund (1999) proposed the following equation for fitting the shrinkage curve:  1      w csh   csh  e( w) = a sh ⋅  c + 1 sh   bsh  (Equation 39)  Where: e(w) =Void ratio as a function of gravimetric water content. w = Gravimetric water content. ash = Minimum void ratio after shrinkage. bsh = Slope of the line of tangency. csh = Curvature of the shrinkage curve. Typically, the air entry value is determined from the soil-water characteristic curve nevertheless, the shrinkage curve may also provide a measurement of the true air entry value for a soil. This becomes particularly relevant in clays and silts which undergo significant volume changes during drying as the soil-water characteristic curve may be inaccurate for this purpose. For slurries, the deviation of the shrinkage curve from the line of saturation marks the true point at which the soi1 begins to de-saturate, as was previously shown in Figure 22. Void ratio may also be related to suction as opposed to water content. Relating void ratio to suction is important as this curve represents the portion of the volume – mass constitutive surface relative to suction. This curve can be coupled with that relating volume change to total stress (consolidation) to obtain the full constitutive surface for the material. The relation between void ratio and suction may be obtained by substituting Equation 35 in Equation 39 which yields:       w e(ψ ) = a sh ⋅   sat   b sh            ψ      ln1 +   1  ψr    1 − ⋅ 6  ln1 + 10        ψ     ln exp(1) +  ψ  r      af           nf        mf                       c sh   1       csh      +1        (Equation 40)  49  2.4.4 Unsaturated hydraulic conductivity  Modeling drying requires not only the saturated hydraulic conductivity but also the unsaturated portion of this property. Water in soils flows through a series of water filled conduits. Under saturated conditions, all the pathways are available for flow and the hydraulic conductivity is at its highest, nevertheless, decreasing the water content (i.e., increasing the suction) in effect reduces the size and number of water filled conduits, which reduces the hydraulic conductivity of the soil. As the soil suction increases and the soil begins to de-saturate, the hydraulic conductivity will decrease in a non-liner fashion. Direct methods to determine unsaturated hydraulic conductivities are difficult to perform; as a result, theoretically based indirect methods have been developed. Indirect methods involve the use of the volumetric water content versus suction relationship to calculate the unsaturated hydraulic conductivity and are based on a statistical model that considers the random variation of pore sizes in a soil and the connectivity of pores at a given volumetric water content (Childs and Collis-George (1950), Mualem (1976)). If the Fredlund and Xing (1994) model is used to fit the SWCC, then the relative hydraulic conductivity function may be determined by numerically integrating the following expression: ψr  k r (ψ ) =  ∫ ψ  θ ( y ) − θ (ψ ) y  ψr  ∫ ψ  2  ⋅ θ ' ( y )dy (Equation 41)  θ ( y) − θ s y2  '  ⋅ θ ( y )dy  aev  Where: θr = volumetric water content at residual conditions θs = volumetric water content at saturation θ’ = the derivative of the soil water characteristic curve y = variable of integration representing suction ψr = suction corresponding to the residual water content ψaev = air entry value 2.4.5 Previous research on paste tailings sedimentation-self weight consolidation and drying and value of the present work  Although there are some coupled numerical models available for evaluating the consolidation and evaporation processes in soils and tailings (CONDES0 (Yao et al. (2002), MINTACO (Seneviratne et al. (1996)) these packages contain simplified methodologies to estimate the evaporative fluxes coming out of the soil mass. In particular, CONDES0 assumes a constant rate of evaporation (PE) at the surface which may be applicable only to the early stages of drying. As presented by Abu-Heileh and Znidarcic (1994, 1995) CONDES0 considers that the soft fine-grained soils remain fully saturated in one-dimensional compression and three dimensional desiccation until the void ratio reaches the void ratio at shrinkage limit, where the soil shrinkage is terminated. This constitutes a significant limitation since the actual 50  evaporation rate is expected to decrease once suctions are generated within the soil mass. MINTACO on the other hand, also requires the evaporation potential to be specified but as opposed to CONDES it accounts for the decrease in evaporation due to suction by using a simplified method which can be summarized as follows (Seneviratne et al, 1996): 1.  The program assumes that evaporation will take place at the potential rate as long as the sum of water accumulated on the surface and water flowing to the surface under self-weight consolidation gradients is sufficient to satisfy the evaporative potential.  2.  Once the evaporative potential cannot be fully satisfied from these sources, the boundary condition is changed by adjusting the hydraulic gradient at the surface so that it gives an upward flow equal to the specified potential evaporation.  3.  The surface suction required to produce this condition is allowed to increase only up to the airentry suction of the material.  4.  When the air-entry suction is reached, the boundary condition is then specified as a constant suction boundary, which persists until new material is added.  Although the simplified procedure considered in MINTACO serves the purpose of limiting the evaporation rate as the material dries, it does not provide an estimate of the real actual evaporation after the air entry value is reached. In this regard, a more thorough approach requires for a better estimation of the actual evaporation fluxes coming out of the soil. Simms et al. (2007) and Fisseha et al. (2009) have predicted desiccation and densification due to sedimentation-self weight consolidation using unsaturated flow models such as SoilCover (Wilson et al., 1994) and SVFluxTM. On one hand the models used have the advantage that they account for constant changes in suction and evaporative fluxes but on the other they have the limitation that are not built to specifically assess the problem of sedimentation–self weight consolidation (for which a code such as CONDES0 and MINTACO may be a more suitable tool than a flow model). Combining the drying and sedimentation–self weight consolidation processes has not been achieved yet so the present work is focused on extending the findings of Simms (2007) and Fisseha (2008) to properly account for some of the limitations encountered in previous research. The objective of the present work has been to improve the approach used so far to determine density as a result of sedimentation and self weight consolidation and to provide a method to combine them with results of density as a result of drying and shrinkage. As part of their research Simms et al. (2007) and Fisseha et al. (2010) modeled sedimentation–self weight consolidation by selecting an appropriate mv (coefficient of volume change as shown previously in Figure 27), as well as appropriate initial conditions, such that the flow model could generate the same amount of water as would be released during sedimentation–self weight consolidation. This appears to work well for modeling the tests undertaken by Simms et al. (2007) and Fisseha et al (2010), which, however, were done at high evaporation rates for paste tailings deposited at 40% gravimetric water content. For these conditions, any water released by 51  sedimentation–self weight consolidation is consumed by evaporation beyond the first day after deposition. However, for tailings placed at lower solids concentrations, thicker layers, or subject to lower evaporative demand, the rate of settling as a result of sedimentation-self weight consolidation cannot be modeled using unsaturated flow packages. In this sense, a new methodology must be proposed assuming that the sedimentation and self weight consolidation processes are better characterized by a model developed for hindered sedimentation or large strain consolidation and not from a model developed to estimate flow in unsaturated porous media. Another important point to note is that the hydraulic conductivity function used by Simms et al. (2007) and Fisseha et al. (2010) was obtained by fitting the Van Genuchten equation (1980) to the SWCC expressed in terms of Saturation. This was done as a way to overcome the early onset of de-saturation and the formation of a crust at the top of the model that resulted when using the Fredlund and Xing (1994) fit. The validity of this approach is questionable as the Van Genuchten – Mualem (1980) method was originally developed to use the fitting parameters determined using the SWCC expressed in terms of volumetric water content and not saturation. It is believed that some of the limitations may be related to the fact that the unsaturated hydraulic conductivity for the material was only developed as a function of suction and did not account for changes in void ratio. As mentioned in previous sections, for materials prone to large deformations, the corresponding changes in void ratio can have a big impact on hydraulic conductivity. As a result, one of the objectives of the present research is to obtain hydraulic conductivity functions that account for changes in both suction and void ratio in the numerical models. Volume changes were measured during the water retention curve testing done by Fisseha et al. (2010). This was performed by using non-contact displacement sensors to measure vertical volume change, and using callipers to characterize horizontal shrinkage. For slurry materials volume change measurements provide the real air entry value. So far the results obtained by Simms et al. (2007) and Fisseha et al. (2010) have been presented in terms of water content and suction, nevertheless these parameters may be related to void ratio if volume changes are measured. From the geotechnical perspective void ratio seems to be a better parameter to present the results as it may be directly related to density and stability. With this in mind, the present research has selected void ratio as the primary variable to present the modeled results.  52  3  PROCEDURE DEVELOPED FOR MEASURI G THE PROPERTIES OF PASTE TAILI GS  RELEVA T  TO  THE  SEDIME TATIO -SELF  WEIGHT  CO SOLIDATIO A D DRYI G STAGES OF DE SIFICATIO An approach will be presented in this thesis for predicting density during sedimentation-self weight consolidation and drying. As a result, material properties must first be determined so they can be used later during the modeling stages. Properties of the Bulyanhulu paste tailings have been used for the purpose of developing the approach presented in this thesis. Regardless of this, the proposed methodology is considered applicable to other slurry materials. Relevant material properties such as settling rates for the sedimentation–self weight consolidation process, soil water characteristics curves (SWCC), shrinkage curves and hydraulic conductivities had to be determined in the laboratory so they could be used in the models that will be presented later in Section 4. Other properties such as specific gravity of solids and Atterberg Limits were obtained from previous research developed with the same material (Simms et al. (2007), Fisseha et al. (2008)). One of the key objectives of the laboratory tests performed during this study was to complement and also confirm some existing properties as well as to explain some of the difficulties and complexities that arise in their determination in the laboratory.  3.1  Basic Material Properties  Laboratory experiments were performed using non-plastic gold tailings from the Bulyanhulu mine in Tanzania. The pumping gravimetric water content for Bulyanhulu has been reported to be between 38 – 40%. At this water content the material have shown some amount of settling as a result of sedimentation, after which a gravimetric water content of approximately 30% is generally achieved. Some of the basic properties that have been reported for this material in previous research (Simms et al. (2007), Fisseha et al. (2008)) are shown in Table 2. The particle size distribution of the percentage passing # 200 sieve (obtained from hydrometer test) is shown in Figure 31 (Fisseha, 2008). Property  Units  Value  mm  150, 40, 25, 15, 2  %  70  PL, LL, SL D90, D60, D50, D30, D10 Passing # 200 Sieve  20, 23, 23  Specific Gravity  -  2.98  Pumping gravimetric water content (w)  %  38 – 40  Gravimetric water content after sedimentation  %  Saturated hydraulic conductivity (at e~0.9) Void ratio at the shrinkage limit  30 -7  m/s  2x10 – 5x10-7  -  0.6 - 0.79  Table 2: Properties of the Bulyanhulu tailings  53  Figure 31: Particle size distribution of the Bulyanhulu tailings (From Fisseha, 2008)  3.2  Sedimentation- Self Weight Consolidation Behaviour  A series of settling tests were developed in order to measure the response of the tailings during the initial stages of densification. These settling tests were performed in 50 cm tall acrylic columns with a cross sectional area of approximately 28 cm2. Settlement was determined using a measuring scale attached to the side of each column. Tailings were prepared at the desired solids content and were thoroughly mixed in a bucket before pouring them into the columns so that material variation within the columns could be reduced (material variation within the columns was observed to result in different settling curves). The mixed tailings were poured continuously into each column using a funnel until the desired material height was obtained. Tailings in the bucket were re-mixed before preparing the next column. The settling columns were left standing still to avoid any vibrations or movement that could affect the sedimentationself weight consolidation process. Settlement was obtained by reading the height of the interface between free water and tailings at varying time intervals. Readings were performed with an accuracy of 0.5 mm. Average void ratios for each column were determined based on the settling readings, initial water content and specific gravity of the material. Figure 32 shows 4 columns prepared at the same initial solids content but with different initial material heights. There is a distinct free water – tailings interface and no apparent segregation could be observed during the settling tests.  54  Figure 32: Settling columns prepared at material heights of 40, 30, 20 and 10 cms.  One of the key objectives of the settling tests developed was to determine how parameters such as solids content and material height (considered equivalent to paste layer thickness) could affect the sedimentation-self weight consolidation behaviour. This was achieved by testing different column configurations that were used to compare and conclude on the effect of these parameters. The following column test configurations were analyzed: •  40 cm column with solids content of approximately 72% (GWC = 40%) and 67% (GWC = 50%)  •  30 cm column with solids content of approximately 72% and 67%  •  20 cm column with solids content of approximately 72% and 67%  •  10 cm column with solids content of approximately 72% and 67%  •  7 cm column with solids content of approximately 67%  In order to confirm the repeatability of the testing procedure, 4 settling tests of different material heights were initially performed using tailings prepared at approximately 47 % GWC. Once the sedimentationself weight consolidation process was over (i.e. no further settlement) the columns were mixed again and the tests were repeated to observe if there were any differences in the measured behaviour. The results of these tests are shown in Figure 33 and demonstrate that the testing procedure is consistent and repeatable.  55  9  Settlement (mm)  8  40 cm  7  30 cm  6  20 cm  5  10 cm  4  40 cm - verif  3  30 cm - verif 20 cm - verif  2  10 cm - verif  1 0 0  20  40  60  80  Time (hrs) Figure 33: Verification of the repeatability of sedimentation-self weight consolidation tests 3.2.1 Analysis of results As shown in Figure 34, results for total settlement indicate that thicker layers of tailings will have larger total settlements. Also, the time required for settlement to stop increases as layer thickness increases. These findings are confirmed when results are plotted in terms of void ratio as shown in Figure 35. From these graphs it is also observed that the settling rate (in terms of void ratio) increases as layer thickness decreases. This means that thinner layers will tend to sediment-self weight consolidate faster than thicker layers, or in other words thinner layers will require less time to achieve their final void ratio as a result of the sedimentation-self weight consolidation process. This effect could be the result of smaller layer thicknesses having a shorter drainage path, which leads to a faster release of pore water to the surface. It must be noted that the only column that did not show this trend was the 30 cm column prepared at 50% GWC (67% SC), were the settling rate was higher than that observed for the 40 cm column. This could be attributed to the creation of small channels in the settling column that displaced water to the surface through preferential paths. When these channels reached the surface of the settling column it appears as if a volcano was erupting there, with the soil deposited in a cone around the pipe outlet. This same behaviour was observed by Been (1980). Although thinner layers of tailings may sediment-self weight consolidate faster, the final void ratio achieved is generally smaller than that obtained for thicker layers of tailings. For example the final void ratio for a 40 cm column at 50% GWC (67% SC) was 0.92 whereas for the same initial solids content the final void ratio for the 10 cm column was 0.97. This is probably the result of thicker layers having a higher self weight load than thinner layers.  56  Settlement vs Time (GWC~50%) 9  Total Settlement (cm)  40 cm - 50% 8  30 cm - 50%  7  20 cm - 50% 10 cm - 50%  6  7 cm - 50%  5 4  (a)  3 2 1 0 0  10  20  30  40  50  60  70  80  Time (hrs)  Settlement vs Time (GWC~40%) Total Settlement (cm)  5 40 cm - 40%  4.5  30 cm - 40% 4  20 cm - 40%  3.5  10 cm - 40%  3 2.5  (b)  2 1.5 1 0.5 0 0  10  20  30  40  50  60  70  80  Time (hrs) Figure 34: Total settlement for columns prepared at (a) 50% GWC and (b) 40% GWC.  57  1.500 40 cm - 50% 1.400  30 cm - 50%  Void Ratio  20 cm - 50% 1.300  10 cm - 50% 7 cm - 50%  1.200 1.100  (a)  1.000 0.900 0.800 0  10  20  30  40  50  60  70  80  Time (hrs) 1.200 40 cm - 40% 1.150  30 cm - 40% 20 cm - 40%  Void Ratio  1.100  10 cm - 40% 1.050 1.000  (b)  0.950 0.900 0.850 0.800 0  10  20  30  40  50  60  70  80  Time (hrs) Figure 35: Void ratio evolution for columns prepared at (a) 50% GWC and (b) 40% GWC. The effect of initial solids content over the sedimentation-self weight consolidation behaviour was also assessed. Figure 36 shows the results for the 40 cm and 20 cm columns at a GWC of 50% and 40% (SC of 67% and 72%). Based on these results may be summarized as follows: •  Initial settling rate (in terms of void ratio) increases as solids content decreases. It must be noted that for the same material height the initial void ratio increases as initial solids content decreases.  •  Regardless of the rate of settling, void ratios for the columns at a water content of 40% are always below or equal to those measured for the columns at a water content of 50%.  •  For the same initial layer thickness, higher initial solids content lead to lower final void ratios. This could be attributed to the fact that for the same thickness of material, higher solids contents result in a higher self weight load.  58  1.500 1.400  40 cm - 40%  Void Ratio  40 cm - 50% 1.300 1.200 1.100  (a)  1.000 0.900 0.800 0  10  20  30  40  50  60  70  80  Time (hrs)  Void Ratio vs Time 1.500 1.400  20 cm - 40%  Void Ratio  20 cm - 50% 1.300 1.200 1.100  (b)  1.000 0.900 0.800 0  10  20  30  40  50  60  70  80  Time (hrs) Figure 36: Void ratio evolution for columns prepared at a GWC of 40% and 50% and column heights of (a) 40 cm and (b) 20 cm One of the basic assumptions of the theory of hindered settling is that the settling velocity is only a function of local concentration. With this in mind, settling velocities were plotted against the average density of the column to observe if there was a unique relationship between these two parameters. As shown in Figure 37, although a general trend is observed between these two parameters there is still significant data scattering. One possible explanation to this is that at such high initial solids concentration it is likely that effective stresses are forming rapidly as the material sediments–self weight consolidates. In fact, some self weight consolidation effects were observed from previous tests, as final void ratios would tend to decrease as material height (self weight load) increased. It must be noted that the hindered settling theory is considered to be valid only if the concentration is such that flocs are not in contact and therefore this limitation should be acknowledge when using this approach to analyze the sedimentationself weight consolidation data.  59  1.60 40 cm - 40% 30 cm - 40%  1.40  20 cm - 40% 1.20  Vs = 2e-39*Conc.^(-13.339)  10 cm - 40%  Vs (cm/hr)  40 cm - 50% 1.00  30 cm - 50% 20 cm - 50%  0.80  10 cm - 50% Best Fit  0.60 0.40 0.20 0.00 1.00E-03  1.10E-03  1.20E-03  1.30E-03  1.40E-03  1.50E-03  1.60E-03  1.70E-03  Concentration (Kg/cm3)  Figure 37: Settling velocity as a function of concentration  3.3  Saturated Hydraulic Conductivity of the Slurry Material  Although hydraulic conductivity for the Bulyanhulu tailings has been determined in previous research for the settled condition (condition reached once sedimentation-self weight consolidation has ended) this parameter has not been evaluated for higher void ratios while the material is still undergoing sedimentation-self weight consolidation. As mentioned in previous sections, thin layers of Bulyanhulu tailings have been observed to sediment from the pumping GWC of approximately 40% to a GWC close to 30%. This behaviour was confirmed by the settling tests performed in Section 3.2, where final void ratios ranged between 0.9 and 1.0. The objective was then to determine the hydraulic conductivity for the material between the pumping and the settled condition. As discussed in Section 2.4.1, measuring the hydraulic conductivity for slurries may not be possible using standard laboratory tests. Alternatively, the approach used herein considered using Equation 31 (Been, 1980) as presented in Section 2.4.1. It must be noted that this equation assumes that there are no effective stresses in the soil mass, which may not be the case for high density slurries as those used in this study. This is especially true during the final stages of sedimentation-self weight consolidation. As seen in Figure 38, the predicted values of Ksat using Equation 31 show a better correlation at higher void ratios. For lower void ratios data scattering is more significant as effective stresses are likely present. Regardless of this, it is observed that the trend line converges to the measured hydraulic conductivity for the settled material (shown as a large blue dot in Figure 38). This shows that Equation 31 can provide reasonable results for saturated hydraulic conductivities, and is considered appropriate for determining approximate values for this parameter at high void ratios. The data for hydraulic conductivities has been fitted using an exponential equation (as shown in Figure 38), but a power function also provides a good fit for the data. It should be acknowledged that using a power function may provide the parameters required to analyze the sedimentation-self weight consolidation process based on the constitutive model presented 60  in Section 2.3.3 (Equation 20). For the purpose of this research the exponential fit has been considered for the approach presented herein. The equation presented by Tan et al. (2006) was not used as it was specifically developed to analyze clayey materials. Also the dependence of the sedimentation-self weight consolidation behaviour to initial condition was not evident in the settling tests developed as part of this research. 1.00E-05  Ksat (m/s)  Ksat = 6e-10*exp(6.3719*e)  1.00E-06  40 cm - 40% 30 cm - 40% 20 cm - 40% 10 cm - 40% 40 cm - 48% 30 cm - 48% 20 cm - 48% 10 cm - 48% Best Fit (Exponential) Best Fit (Power) Measured Ksat (Settled Material)  Ksat = 3e-7*e^7.1057  1.00E-07  1.00E-08 0.800  0.900  1.000  1.100  1.200  1.300  1.400  1.500  Void Ratio  Figure 38: Hydraulic conductivity as a function of void ratio (e)  3.4  Soil Water Characteristic Curve (SWCC)  A series of test procedures were developed in the lab to determine the SWCC for the slurry material. Tempe cells with a maximum capacity of 100 kPa were used for this purpose. Two different approaches were used to prepare the specimens for the SWCC determination. This was done to observe the impacts of sample preparation over the results. The methods used for sample preparation are described as follows: Method 1: The material was slurried to the desired water content (between 40 – 45% gravimetric) and then placed directly in the ring inside the tempe cell for testing. The SWCC test was started right after the material was placed in the device. The most significant challenge was that the slurry material was not in equilibrium during the initial stages of the test as sedimentation-self weight consolidation would take place. As a consequence, after preparing the sample, the material would drain significant amounts of water and underwent large deformations even when subjected to zero suction (drainage due to gravity). Method 2: The material was slurried at the desired water content (between 40 – 45% gravimetric) and was then allowed to sediment-self weight consolidate outside the tempe cell. Once equilibrium was reached (settling ceased), excess (bleed) water was removed and the settled material (GWC close to 30%) was scooped gently into the ring inside the tempe cell. The SWCC test was performed immediately after placing the material inside the Tempe Cell.  61  A couple of Single Point Measurements were performed to evaluate the potential impacts of the initial condition of the slurry (GWC or SC) and the sedimentation-self weight consolidation process over the SWCC. Single Point Measurements refer to the application of a higher suction (20 and 100 kPa) immediately after sample preparation in the Tempe Cell so settlement as a result of sedimentation-self weight consolidation is somehow exceeded by the volume changes coming from the applied loads (suction) in the Tempe Cell. The slurry for these tests was prepared at higher GWC (45 – 47%) to set a different initial condition than that used for the SWCC (which were prepared at 40 – 45% GWC). The Single Point Measurements also allowed evaluating the effects of having a different stress path during the de-saturation process. For these particular tests, the specimens were prepared using Method 1 (slurry placed directly in the Tempe Cell). Table 3 shows a summary of the initial conditions used for the different SWCC performed in the laboratory. Case  Method of Preparation  Initial GWC of the Slurry  Slurry – 1  1  0.454  GWC after Sedimentation-Self Weight Consolidation (Zero Suction Condition) 0.295  Slurry – 2  1  0.410  0.326  Settled – 1  2  0.307  0.256  Settled – 2  2  0.308  0.270  Single Point Measurement - 1  1  0.445  No sedimentation-self weight consolidation allowed. Application of 20 kPa right after specimen preparation  Single Point Measurement - 2  1  0.474  No sedimentation-self weight consolidation allowed. Application of 100 kPa right after specimen preparation  Table 3: Initial conditions used for the SWCC determination Figure 39 shows the SWCC plotted as GWC versus suction that was obtained for the material under the two different methods of sample preparation and also shows the results of the Single Point Measurements. It must be noted that the initial GWC shown in this Figure corresponds to those obtained for zero suction (assumed to be 0.01 kPa). The following summarizes the observations from the measured data. 1.  Different SWCCs are obtained if Methods 1 and 2 are used for sample preparation. It was observed that samples that were prepared under Method 2 (sediment and self weight consolidated and then placed in the Tempe Cell) achieved smaller initial water content at zero suction. This is probably a result of sample disturbance as a consequence of transferring the sediment-self weight consolidated material into the ring inside the Tempe cell. It is believed that this disturbance destroys the fragile structure generated during the sedimentation-self weight consolidation process outside the Tempe Cell which may result in an increase of the pore water pressure of the slurry. This in turn allows for extra water to drain out of the sample. In this regard, sample disturbance is avoided when using Method 1 as sedimentation-self weight consolidation occurs inside the Tempe Cell. Despite of that, at suctions of 100 kPa the curves seem to be converging to a single point. Unfortunately, due to limitations of the equipment  62  capacity, higher suctions could not be achieved to confirm the unique convergence of curves to a single point. 2.  Slight differences are also observed in the water content achieved under zero suction (equilibrium water content) for both Method 1 and 2 of sample preparation. As presented in Table 3, for Method 1 equilibrium water contents ranged from 30 – 32% whereas for Method 2 the equilibrium water content ranged from 26 – 27%. Although small, these differences could be explained by the “unstable” condition of the slurry during the early stages of the test, when the material is still at a very loose state. For each Method convergence into a single SWCC was obtained at around 10 kPa. It must be noted that materials tested under Method 1 achieved an equilibrium water content similar to that obtained from the settling tests. For this reason, the SWCC obtained with Method 1 is considered to be more representative for materials that are expected to undergo pure sedimentation-self weight consolidation and then drying.  3.  All Single Point Measurements plotted along the SWCC obtained with Method 1. This confirms the idea that the sedimentation-self weight consolidation process does not affect the shape of the SWCC at higher suctions and that most likely this last process is relevant as long as pore water pressures remain positive. Once suction starts to “build up” the shrinkage process is expected to dominate the volume change process. It is important to mention that the air entry value for the material was determined to be between 20 – 30 kPa as will be shown later. This means that regardless of the rate at which suction “builds up” the resulting water content at suctions close to the AEV should be the same.  4.  A clear air entry value is not well defined and a relatively steep slope is observed even at low suction when results are plotted in terms of GWC. This is a result of volume changes at full saturation and the large quantities of water being released due to the significant compressibility of the material.  63  0.350  0.300  0.250  GWC  0.200  0.150  0.100 Method 1 (Slurry) 0.050  Method 2 (Settled) Single Point Measurements  0.000 0.01  0.1  1  10  100  1000  Suction (kPa) Figure 39: SWCC of Bulyanhulu tailings in terms of GWC Volume changes were also determined during the SWCC test by directly measuring the vertical deformations of the sample inside the ring. Axial deformations and the volume of cracks, if any, were calculated the best way possible with a vernier calliper. The method used for volume change determination is far from ideal and a more precise method for estimating this parameter would be desirable. The SWCC in terms of VWC was also obtained based on the volume change measurements and is shown in Figure 40. As mentioned in Section 2.4.2.2, volume change measurements are extremely important for proper determination of the SWCC in terms of VWC. Figure 41 shows the significant differences between the corrected and uncorrected data.  64  Volumetric Water Content (VWC)  0.600  0.500  0.400  0.300  0.200  0.100  0.000 0.01  Method 1 (Slurry) Method 2 (Settled) Single Point Measurements  0.1  1  10  100  1000  Suction (kPa)  Figure 40: SWCC of Bulyanhulu tailings in terms of VWC  Volumetric Water Content (VWC)  0.500 0.450 0.400 0.350 0.300 0.250 0.200 0.150 0.100 Corrected for Volume Change 0.050 0.000 0.01  Uncorrected  0.1  1  10  100  1000  Suction (kPa)  Figure 41: SWCC for Bulyanhulu tailings corrected and uncorrected for volume changes Although a better estimation of the approximate air entry value may be obtained from the SWCC presented in terms of VWC, as discussed in earlier sections of the present work, the best way to determine the true air entry value of the material is by using the curve in terms of Degree of Saturation (S) (Figure  65  42). As shown in Figure 42 although there is some scatter in the data, the air entry value for the material seems to be between to 20 - 30 kPa. 1.20  Degree of Saturation  1.00  0.80  0.60  0.40  0.20  Method 1 (Slurry) Method 2 (Settled) Single Point Measurements  0.00 0.01  0.1  1  10  100  1000  Suction (kPa) Figure 42: SWCC of Bulyanhulu tailings in terms of degree of saturation  3.5  Shrinkage  Shrinkage curves for the material were determined based on the results obtained during the SWCC tests and are shown in Figure 43. It must be noted that void ratios were determined based on the volume change measurements performed during the SWCC tests, which are not as precise as those obtained when using conventional methods for testing the shrinkage behaviour of a soil (wax method or similar). The void ratio at the shrinkage limit obtained for the material ranged from 0.65 to 0.7. In general, no further volume changes were observed after suctions of 20 - 30 kPa, which confirms that the AEV for the material should be within this suction range. In the SWCC this suctions result in a GWC of approximately 21 - 22%, which is close to the point at which the shrinkage curve separates from the saturation curve in Figure 43. In previous research, reported values for void ratio at the shrinkage limit range from 0.6 (Saleh-Mbemba et al., 2010) to 0.8 (Simms 2007) and the corresponding shrinkage curves are also shown in Figure 43 for comparison. It has been observed that the final void ratio achieved through drying in surface deposited silt-size tailings is often higher than the void ratio predicted from the standard ASTM shrinkage limit test. For the specific case of Bulyanhulu tailings, Fisseha et al. (2007) determined that the material would typically dry to a void ratio of 0.8 rather than the void ratio predicted by the shrinkage limit test (close to 0.6). The authors also observed that the final void ratio obtained after drying would increase with  66  decreasing initial degree of saturation. Although, this could be one of the reasons explaining the difference in the shrinkage limit obtained as part of this work, another possible explanation could be the inaccuracies of the method employed to determine volume changes. Regardless of this, the present work will use a void ratio at the shrinkage limit of 0.7. Figure 43 also shows the curve obtained by using the fitting model proposed by Fredlund 1999 (Equation 37) using fitting parameters ash = 0.7, bsh = 0.235, csh = 23. The fitted curve was obtained assuming that the material is initially saturated. A similar fit may be obtained if a different initial degree of saturation is assumed. The fitted equation will be used in subsequent sections to relate void ratio to water content and suction. 1.60  1.40  Void Ratio  1.20  1.00  0.80  0.60  Method 1 (Slurry) Method 2 (Settled) Single Point Measurements Saturation Line Simms (2007) Saleh-Mbemba (2010) Fitting Equation  0.40  0.20 0.00 0  0.1  0.2  0.3  0.4  0.5  0.6  GWC Figure 43: Shrinkage curve for the Bulyanhulu tailings  3.6  Chapter Summary  Chapter 3 has presented a methodology to determine the properties of slurry materials that are necessary to predict sedimentation-self weight consolidation and drying. One of the challenges of testing slurry materials is that volume changes can be significant even at low applied stresses and they should be carefully measured for proper material characterization. Simplified procedures like the one described in this Chapter may be used to determine reasonable volume change estimates. Based on these measurements it was determined that the AEV of the material is around 20 – 30 kPa and that the void ratio at the shrinkage limit is approximately 0.7. More sophisticated methods (non contact displacement sensors for example) may be required for a more precise determination of the AEV and the final void ratio achieved during the SWCC (which in general should be representative of the void ratio at the shrinkage limit).  67  Sedimentation-self weight consolidation behaviour was shown to depend on column height and initial GWC (or SC). As a result, to fully capture the sedimentation-self weight consolidation characteristics of the material it is recommended that settling tests are developed for different initial conditions. The number of columns to be analyzed will ultimately depend on the expected range of possible depositional characteristics (targeted layer thicknesses and pumping GWC’s during operation). Having a larger set of sedimentation curves may provide the required information to combine the processes of sedimentationself weight consolidation and drying for different conditions. This will be shown later in Section 4. It was determined that thinner layers settled faster but achieved a higher void ratio after sedimentation-self weight consolidation than thicker layers. Also, for the same layer thickness higher initial GWC’s showed faster settling rates but higher final void ratios than columns prepared at lower initial GWC’s. Sedimentation-self weight consolidation data may be also used to determine approximate values of saturated hydraulic conductivities at high void ratios. It must be acknowledge that the equation used in this thesis assumes that there are no effective stresses, which may not be the case for slurries prepared at low GWC (or high SC). Regardless of this, the values of hydraulic conductivity determined in this thesis were shown to be within reasonable range and converged to the hydraulic conductivity measured for the settled material under standard methods. A fitting equation was provided to determine hydraulic conductivities as a function of void ratio. For determining the SWCC of slurry materials it is recommended that the slurry is prepared at a GWC (or SC) close to the expected field conditions and then immediately placed in the device that will be used for testing (tempe cell, pressure plate, etc). This avoids disturbing the sample and allows the material to reach an initial state closer to that obtained after pure sedimentation (approximately 30% GWC for the case of Bulyanhulu tailings). It is recommended that a suction of 0 kPa is applied right after material preparation since this allows water to drain out of the slurry as it sediments-self weight consolidates in the device. It was also shown that sedimentation-self weight consolidation process in the SWCC device would only affect the early portion of the SWCC (low suctions) and that the curves converged at a suction of approximately 10 kPa.  68  4  PROPOSED MODELI G APPROACH TO DETERMI E AVERAGE VOID RATIO OF PASTE TAILI GS  The modeling approach presented herein has been developed as an attempt to combine the stages of sedimentation-self weight consolidation and drying. The approach is based on determining the point at which evaporation and drainage become dominant over sedimentation-self weight consolidation. This point has been determined as a function of the material properties obtained in previous sections and the expected governing climatic conditions. In summary, the approach consists of the following steps: •  First, a given layer thickness and depositional solids content are selected.  •  A sedimentation-self weight consolidation curve (void ratio vs time) is predicted or measured in the lab for the targeted depositional characteristics.  •  The amount of water potentially bleeding out of the soil due to pure sedimentation-self weight consolidation is calculated as a function of time.  •  This rate of bleed water generation is compared to the rate at which water can be potentially consumed by Environmental Dewatering (ED) (evaporation + drainage).  •  The point at which density or void ratio should be predicted using a drying model is determined as the point where ED equals the amount of water released due to sedimentation and self weight consolidation.  •  Properties for the drying model are modified to account for the point at which sedimentation-self weight consolidation is no longer the dominating process of densification.  The proposed approach has the advantage that it accounts for the rate of sedimentation-self weight consolidation during early stages of densification and should allow for predictions of density for both high and low evaporation rates. For low evaporation, the rate of densification is expected to be initially dominated by sedimentation-self weight consolidation whereas for high evaporation the role of this process may not be significant and the rate of densification will be likely dominated by shrinkage. The following sections will describe the rationale used to determine the boundary between the relevant processes of densification as well as the method to combine the resulting changes in void ratio after each of these stages have taken place.  69  4.1  Determination of the Boundary between Sedimentation-Self Weight Consolidation and Drying  Right after paste tailings have been deposited three processes act as the main contributors to densification; sedimentation-self weight consolidation, drainage and evaporation. The change in void ratio due to these processes occurs in a continuous fashion so an appropriate representation of the problem first requires understanding the contribution of each one of them to the overall increase in density. It must be acknowledged that sedimentation-self weight consolidation is governed by a different theory than that applicable to drainage and evaporation and therefore a proper evaluation of the problem requires determining which process is in fact driving the changes in void ratio. In the end, the question to answer is: at which point will the effects of evaporation and drainage exceed those of sedimentation-self weight consolidation in the overall densification process. It seems logical to think that this point is given by the time at which evaporation and drainage (ED) are capable of taking more water out of the paste pores than pure sedimentation-self weight consolidation. It is assumed that before this point void ratio will change primarily as a response of sedimentation-self weight consolidation, whereas after this point, suctions are expected to “build up” from the surface downward, progressively shrinking the paste layer as suctions increase with depth. For thin layers, suction distributions should be fairly uniform and shrinkage is expected to occur evenly through the paste layer. For thicker layers it is expected that shrinkage and drying will begin at the evaporative and draining boundaries while the other portions of the layer could still be undergoing sedimentation-self weight consolidation. Only when suctions increase with depth will the bottom portions of the layers start to shrink. This problem will be covered in Chapter 4. There are two possible cases that could be evaluated and both require a different treatment. The first considers that bleed water is allowed to pond on the surface of the tailings so de-saturation will commence after all ponded water has evaporated (cumulative approach). Although this is a common process in conventional tailings deposition, it is rarely the case for paste tailings, which are the main focus of this work. Besides, if water ponds on the surface, the material will likely settle before it starts to dry and this last stage will only begin once pond water completely evaporates or drains. With this in mind, this particular case will not be analyzed herein. The second case relates better to paste tailings deposition as it considers that the portion of water that is not allowed to evaporate or drain will runoff. In this case the drying process at the surface will commence when the amount of bleed water coming from sedimentation-self weight consolidation during a given period of time equals the amount that could be potentially taken by ED in that same time interval. This point may be determined based on the following stepped methodology. 1.  First, a numerical model should be developed in SoilCover to determine the amount of drainage (D) through the bottom of the paste layer. This model should be developed in the absence of evaporation and the material properties should correspond to the slurry conditions (before any settling has occurred as a result of sedimentation-self weight consolidation). This should  70  represent the conditions right after deposition. Initial pore water pressures may be assumed to be equal to the total stresses in the layer. The properties of the bottom boundary will depend on the type of underlying material (dry paste, saturated paste, natural ground, etc). This initial model is only developed for water balance purposes and to set the boundary between sedimentation-self weight consolidation and drying (this initial model will be called herein “water balance model”). Evidently, if no drainage is present (no flow bottom boundary), (D) is zero and ED is equal to PE. 2.  The amount of drainage (D) determined in step 1 is compared to the amount of bleed water (B) determined from pure sedimentation-self weight consolidation tests (settling tests). The amount of bleed water (B) is determined as the settling rate of a column test representative of the material under analysis and will depend on initial water content and column height.  3.  If the amount of bleed water (B) is higher than the amount of drainage (D) determined in the water balance model it is assumed that the difference will report as bleed water at the surface. The amount of bleed water will be referred to as (b). In the absence of drainage (B) = (b).  4.  The estimated amount of bleed water seeping at the surface (b) is then compared to the potential rate of evaporation (PE). If the rate of bleed water (b) is higher than PE then no water will be evaporated from the voids within the paste and runoff will occur. As long as this remains true, sedimentation-self weight consolidation will be the primary mechanism of densification for the whole layer.  5.  Evaporation of water from the paste voids at the surface is assumed to begin once the rate of bleed water (b) is less than the PE. At this point evaporation is capable of taking more water than that provided to the surface by sedimentation-self weight consolidation having discounted the amount of water draining thought the bottom. This time will be referred as Td and the void ratio achieved by sedimentation-self weight consolidation at this time will be referred as ed.  6.  The numerical model to determine void ratio due to drying begins at this point and it should account for both drainage and evaporation. Properties for this model should be modified so they start at the void ratio achieved by sedimentation-self weight consolidation (ed) after a time of Td. For this particular model, the initial suction profile for the paste layer is that obtained from the “water balance model” developed as part of step 1 after a simulation time of Td. This is to take into account that some water has already drained to the underlying layer during the sedimentation-self weight consolidation process changing the initial pore water pressure distribution within the paste layer (initially considered to be equal to the total stresses in the paste layer).  7.  Finally, it is assumed that results for average void ratio with time are given by the sedimentationself weight consolidation curves up to a time Td (final void ratio achieved at this time is ed). After this point, results for average void ratio with time are taken from the drying model  71  developed in step 6. The proposed methodology explained before is shown schematically in Figure 44.  No Drainage  With Drainage  Evaporation (E) Evaporation (E) Runoff = B-E  (B)  Runoff= b-E (b)  Bleed Water  Bleed Water  Drainage (D)  Drying model begins when:  Drying model begins when:  E=B  E=B–D=b  Figure 44: Representation of the simplified water balance to determine the boundary between sedimentation-self weight consolidation and drying 4.1.1 Example: application of the proposed method to different Bulyanhulu tailings configurations The approach presented in Section 4.1 requires an estimation of the rate of bleed water generation (B), which is equivalent to the settling rate resulting from the sedimentation-self weight consolidation process. As presented in Section 3.2, different initial GWC and layer thicknesses lead to different sedimentationself weight consolidation curves. Therefore, the rate of bleed water generation as a function of time cannot be determined if these two parameters (layer thickness and initial GWC) are not known a priori. For the purpose of presenting an example of the proposed approach, the sedimentation-self weight consolidation results obtained in Section 3.2 for the 40 cm columns at GWC of 40 % and 50 % will be used for the analysis. An equivalent analysis could be performed using some of the other configurations tested in Section 3.2. Also, for simplicity, the following examples will assume that drainage is not present and therefore ED is reduced to PE. Later sections will cover some applications assuming that drainage is present. Rates of ED or in this case PE of 5 mm/d, 3 mm/d and 1 mm/d have been used to show the effect of ED over the location of the boundary between sedimentation-self weight consolidation and drying. Table 4 shows the cases that will be evaluated in this Section.  72  Case  ED  Case A  5 mm/d  Layer Thickness  Initial GWC  Drainage  Ponding  40 cm  50%  No  No  40 cm  40%  No  No  3 mm/d 1 mm/d Case B  5 mm/d 3 mm/d 1 mm/d  Table 4: Example cases analyzed for determining the boundary between sedimentation-self weight consolidation and drying The corresponding curves for the rate of settling for Cases A and B are shown in Figure 45. In this Figure, the intersection point with the curves describing the rate of ED (or PE in this case) denotes the theoretical point at which suctions are expected to increase at the surface. This point is shown schematically for Case A and a value of ED = 5 mm/d. The proposed approach assumes that before this point (Td), void ratio will change as a result of sedimentation-self weight consolidation and the rate of change of void ratio should be determined from settling curves determined in the lab or from modeled results obtained using hindered settling or selfweight consolidation theories, similar to those presented in Section 2.3.1. After this point (Td) it is assumed that shrinkage will begin at the surface and will propagate downward (no drainage has been considered in these examples) and unsaturated models are required to model the exchange of fluxes at the surface of the paste.  Rate of Settling and ED(mm/hr)  0.400 GWC 50 GWC 40 ED = 5 ED = 3 ED = 1  0.350  0.300  0.250  Sedim entationself w eight consolidation  % (Case A) % (Case B) mm/d mm/d mm/d  Shrinkage  5 mm/d 0.200  0.150  3 mm/d  0.100  1 mm/d  0.050  Td = 15  0.000 0  10  hrs20  30  40  50  60  70  80  Time (hrs)  Figure 45: Theoretical boundary between sedimentation-self weight consolidation and shrinkage for a 40 cm layer and GWC of 40 % and 50 %  73  The void ratio achieved by sedimentation-self weight consolidation before drying begins at the surface (ed) may be determined for Cases A and B based on the settling curves obtained in the laboratory and presented in Section 3.2 (void ratio at a time Td). Table 5 summarizes the time required to achieve the theoretical point at which drying begins (Td) for Cases A and B and it also specifies the void ratio (ed) that sets the theoretical boundary between sedimentation-self weight consolidation and drying. Also, the values of Ksat at these void ratios have been determined based on the relation presented in Section 3.3.  Case Case A  Case B  5 mm/d  Theoretical time required for drying to begin (Td) 15 hrs  3 mm/d  20 hrs  0.963  0.32  0.49  2.61e-7  1 mm/d  32 hrs  0.93  0.31  0.48  2.16e-7  5 mm/d  2 hrs  1.150  0.39  0.54  9.87e-7  3 mm/d  16 hrs  0.994  0.33  0.50  3.16e-7  1 mm/d  38 hrs  0.896  0.3  0.47  1.79e-7  ED  Void Ratio (ed) *  GWC *  VWC *  Ksat * (m/s)  1.030  0.35  0.51  4.62e-7  (*) Values of GWC, VWC, Void Ratio (e) and Ksat achieved by sedimentation-self weight consolidation before drying begins (at time Td)  Table 5: Material properties at the time where drying is expected to begin (Td). As shown in Figure 45 and Table 5, as ED decreases the slurry is allowed to undergo pure sedimentationself weight consolidation for a longer period of time before water is evaporated from the voids within the paste. As a consequence, evaporation from the surface of the paste is triggered when the slurry has achieved a lower void ratio as a result of sedimentation-self weight consolidation. It is also observed that the initial characteristics of the slurry (initial water content and layer thickness) will play a significant role in the position of the theoretical boundary between sedimentation-self weight consolidation and drying. For example it is observed that for a potential rate of ED of 5 mm/d, Case A will undergo pure sedimentation-self weight consolidation for 15 hours whereas for Case B this process will last only 2 hours before evaporation from the surface of the paste layer begins. It must be noted that the present approach has been referred to as “theoretical” as the actual boundary between the two processes was not confirmed by any type of laboratory testing. Regardless of this, it is considered that the rationale used for determining this theoretical boundary should be a good representation of the actual water balance linking these two processes. It should be mentioned though that some limitations may arise for thicker layers as suction build up generally starts at the surface of the layer leaving the bottom without any noticeable increase in suction. This means that although the upper portion is drying and increasing its density due to shrinkage the lower portion of the layer may still be undergoing sedimentation-self weight consolidation. This will be shown later in Section 4.3. Regardless of this it must be kept in mind that the focus of the present research is on the deposition of thin layers of paste that allow enhancing the process of drying. For thin layers the suction distribution tends to be more uniform within the profile so the problem mentioned earlier is generally not observed. 74  4.2  Modifying Material Properties to Obtain Appropriate Results of Density as a Result of Drying (Shrinkage)  Based on the approach presented in Section 4.1, it becomes clear that densification due to drying could begin at different times depending on how long it takes for the sedimentation-self weigh consolidation process to be overtaken by evaporation and drainage. In this regard, it is expected that different initial states (densities) may be potentially achieved before drying should actually be assessed or modeled. This is a result of sedimentation-self weight consolidation being more or less important in the densification process, which depends on initial tailings properties and the expected rate of ED. The drying model can take into account the state achieved after sedimentation-self weight consolidation, if the relevant properties (SWCC, hydraulic conductivity function) are carefully modified. This approach will be presented in more detail in the following Sections. 4.2.1 Building the SWCC for the drying model The construction of the unsaturated properties for the drying model will be explained using the examples presented in Section 4.1.1 and the material properties obtained for the Bulyanhulu tailings in Chapter 3. As presented in Section 3.4, two different SWCC were obtained depending on the method used for preparing the specimen for testing. It was also mentioned that Method 1 was considered to give more representative results as the material inside the Tempe Cell would generally settle to a void ratio similar to that obtained from settling tests. For this reason, the SWCC obtained under this method will be used hereafter. For the examples developed herein, a single SWCC has been considered assuming that regardless of the initial GWC of the slurry, at zero suction (i.e. 0.01 kPa) the material will sediment to a GWC of 30%. Figure 46 shows the SWCC of the slurry material prepared using Method 1. As observed extra points have been added to show the initial condition for the slurry material before any sedimentation-self weight consolidation has occurred in the Tempe Cell. This shows the range of possible initial GWC at zero suction. It is assumed that the SWCC for the drying model can start anywhere within this range, and that the starting point will be given by the void ratio (ed) achieved by sedimentation-self weight consolidation before drying begins. This information has been provided previously in Table 5.  75  0.600 Slurry 0.500  Range of Possible Initial GWC  GWC  0.400  0.300 Settled 0.200  Lab Data - Method 1 (Slurry) Case A (Initial GWC)  0.100  Case B (Initial GWC) 0.000 0.01  0.1  1  10  100  1000  Suction (kPa) Figure 46: SWCC depicting the possible range of GWC from slurry to settled conditions Figures 47 and 48 show the resulting SWCC for Cases A and B respectively. These curves have been modified based on the GWC achieved under the different rates of ED as per the results presented in Table 5. The resulting SWCC’s have been developed assuming that the early portion of the curve (suctions up to 10 kPa) will vary depending on the initial GWC or initial state at the commencement of the drying process. After suctions of 10 kPa a unique curve was considered for all cases. This has been assumed based on the results presented in Section 3.4, were curves starting at different initial GWC were observed to converge at this particular suction. This is also supported by the results obtained from the single Point Measurements in which, regardless of the stress path and initial water content of the slurry, a unique GWC was obtained for suctions equal or higher than 20 kPa. The SWCC have been generated using the Fredlund and Xing (1994) equation (Equation 33). Table 6 shows the fitting parameters for each of the SWCC obtained. Case  ED  af  mf  nf  Case A  5 mm/d  8.67  0.44  1.13  3 mm/d  11.04  0.51  0.92  1 mm/d  14.46  0.54  0.91  5 mm/d  0.82  0.68  0.58  Case B  3 mm/d  7.35  0.5  0.89  1 mm/d  18.68  0.58  0.88  Table 6: Fitting parameters for the SWCC’s of cases A and B  76  0.600  0.500  GWC  0.400  0.300  0.200  0.100  0.000 0.01  Lab Data - Method 1 (Slurry) SWCC_ED=5 mm/d SWCC_ED=3 mm/d SWCC_ED=1 mm/d 0.1  1  10  100  1000  Suction (kPa)  Figure 47: Resulting SWCC for case A based on the state achieved as a result of sedimentation-self weight consolidation  0.450 0.400 0.350  GWC  0.300 0.250 0.200 0.150 0.100 0.050 0.000 0.01  Lab Data - Method 1 (Slurry) SWCC_ED=5 mm/d SWCC_ED=3 mm/d SWCC_ED=1 mm/d 0.1  1  10  100  1000  Suction (kPa)  Figure 48: Resulting SWCC for case B based on the state achieved as a result of sedimentation-self weight consolidation  77  4.2.2 Building the hydraulic conductivity function for the drying model The hydraulic conductivity function may be established in a similar fashion than the SWCC. As mentioned in earlier sections, this function should account for changes in both volume and suction. In the present work, the hydraulic conductivity function has been determined by combining the values of Ksat obtained from sedimentation-self weight consolidation data (as presented in Section 3.3) with the unsaturated values of K obtained by fitting the SWCC data with the Fredlund and Xing (1994) model. The saturated portion of the hydraulic conductivity function may be constructed using the following steps: 1.  Determine the mathematical relation between void ratio and suction. This can be performed by combining the fitting equations obtained for the SWCC (Equation 35) and the shrinkage curve (Equation 39). The resulting equation was previously shown in Section 2 as Equation 40.  2.  Transform void ratios to hydraulic conductivities using the fitting relation determined from settling tests using the method presented in Section 3. This provides the relation between hydraulic conductivity and suction in the saturated range. Based on the results shown in Section 3 (Figure 38) the following equation has been used herein:  Ksat = 6 ⋅ 10 −10 ⋅ exp(6.3719 ⋅ e)  (Equation 42)  It must be noted that this equation was obtained by fitting data with minimum void ratios close to 0.9, which correspond to the settled condition. In the absence of information for lower void ratios it was assumed that this equation was representative for void ratios as low as those achieved at the shrinkage limit (void ratio of 0.7). This shortcoming can be avoided by determining hydraulic conductivities at lower void ratios using large strain or seepage induced consolidation tests. 3.  The steps described above should be used for suctions up to the AEV or up to a suction above which no further volume changes occur. For the material used in this thesis, volume changes ceased at approximately 20 – 30 kPa. A suction of 20 kPa has been adopted as the last point of the saturated portion of the hydraulic conductivity function. After this point hydraulic conductivity is expected to decrease primarily as a result of de-saturation and the relation for hydraulic conductivity should be developed based on unsaturated models.  As mentioned before, the saturated and unsaturated portions of the hydraulic conductivity function should be combined to obtain a complete representation that can be subsequently used for numerical modeling. In this thesis the unsaturated portion of the hydraulic conductivity function has been determined using the following steps:  78  4.  A hydraulic conductivity function was obtained using the Fredlund and Xing (1994) model. The data used to obtain this function was the SWCC data obtained for the settled material (shown in Figure 46). The resulting function is shown in Figure 49 as a red curve.  5.  Although the Fredlund and Xing (1994) model provides a full curve it was assumed that the saturated portion (up to a suction of 20 kPa) was better represented by the curve determined previously using steps 1 to 3. For suctions higher than 20 kPa it was assumed that the slope of the hydraulic conductivity should be equal to that provided by the Fredlund and Xing (1994) model (the slope was assumed to be representative of the relative change of K as a response of relative changes in matric suction).  6.  The hydraulic conductivity function was obtained by matching the saturated and unsaturated portions at a suction of 20 kPa. For this purpose, part of the Fredlund and Xing (1994) curve had to be displaced to match the saturated portion at 20 kPa. This is shown schematically in Figure 49.  1.0E+02 1.0E+01  Fredlund and Xing (1994)  Saturated portion constructed as per steps 1 - 3.  Displaced Unsaturated Kr  1.0E+00  Saturated Portion of Kr  1.0E-01  Kr  1.0E-02 1.0E-03  Displacement of unsaturated portion for  1.0E-04  suctions above 20 kPa  1.0E-05  K function obtained using Fredlund and Xing (1994) and  1.0E-06  data for settled material  1.0E-07 1.0E-08 1.0E-09 1.0E-10 0.01  0.1  1  10  100  1000  10000  100000  1000000  Suction (kPa) Figure 49: Schematic representation of how the unsaturated hydraulic conductivity function was constructed (results shown in terms of relative hydraulic conductivity Kr) Following the examples presented in Section 4.4.1, Figures 50 and 51 show the shape of the hydraulic conductivity function for Cases A and B respectively in both the saturated and unsaturated range. As observed the initial values of Ksat for each case are equal to those shown previously in Table 5 and depend on the void ratio (ed) achieved by sedimentation-self weight consolidation before drying begins.  79  1.0E-03  Case A_ED=5 mm/d Case A_ED=3 mm/d  1.0E-04  Case A_ED=1 mm/d Unsaturated (Soil Cover)  K (cm/s)  1.0E-05 1.0E-06 1.0E-07 1.0E-08 1.0E-09 1.0E-10 1.0E-04  1.0E-02  1.0E+00  1.0E+02  1.0E+04  1.0E+06  Suction (kPa) Figure 50: Resulting SWCC for case A based on the state achieved as a result of sedimentation-self weight consolidation Case B_ED=5 mm/d  1.0E-03  Case B_ED=3 mm/d Case B_ED=1 mm/d  1.0E-04  Unsaturated (Soil Cover)  K (cm/s)  1.0E-05 1.0E-06 1.0E-07 1.0E-08 1.0E-09 1.0E-10 1.0E-04  1.0E-02  1.0E+00  1.0E+02  1.0E+04  1.0E+06  Suction (kPa) Figure 51: Resulting SWCC for case B based on the state achieved as a result of sedimentation-self weight consolidation 4.2.3 Setting the initial conditions for the drying model Pore water pressures and stress distribution within a paste tailings layer during the sedimentation-self weight consolidation process are not trivial to obtain as a function of time. Been and Sills (1981) measured the excess pore water pressures at different time steps during settling tests and they observed that the initial excess pore water pressure of slurries at low SC was very close to the total stress in the material. This means that initially, right after deposition, the material will likely be in a highly disturbed state with eventually no effective stresses. As settling took place the authors observed that pore water pressures dissipated until hydrostatic conditions were reached at the end of the sedimentation process. Although the starting and ending pore water pressure distributions may be inferred from these findings,  80  difficulties arise when trying to determine the pore water pressure distribution between these two points. As explained earlier, drying is expected to begin somewhere along the sedimentation-self weight consolidation process and therefore predictions of the initial pore water pressure distribution within the paste layer must be performed to obtain a representative initial condition for the models. It is proposed that the initial pore water pressure distribution is estimated assuming that the degree of pore water pressure dissipation is equal to the relative change in void ratio during sedimentation-self weight consolidation. With this assumption in mind the degree of pore water dissipation with time may be determined as follows:  Degree of Pore Water Pressure Dissipation (%) =  (e i − e(t )) (e i − e f )  (Equation 43)  Where: ei = average void ratio at the beginning of sedimentation-self weight consolidation e(t) = void ratio at any given time during sedimentation-self weight consolidation ef = average void ratio after sedimentation-self weight consolidation has ceased Accordingly, initial pore water pressure at the bottom of the layer can be estimated as:  PWP = γ t ⋅ h − γ t ⋅ h ⋅ % Dissipation + γ w ⋅ h ⋅ % Dissipation  (Equation 44)  This relation allows to set an approximate initial condition for the models, that will depend on the theoretical point at which drying begins. 4.2.4 Coefficient of volume change (mv)  An important issue to have in mind while modeling shrinkage is that the initial excess pore water pressures in the material may delay the “build up” of suction. This has been observed in the research performed by Simms et al. (2010) where suctions of 0 to 2 kPa were measured during the initial stages of drying. This delay in suction build-up can be effectively modeled if a proper coefficient of volume change (mv) is selected. Mv is defined as the slope of the SWCC in the positive pore water pressure region (Wilson, 1990) and is equal to the coefficient of volume change as measured in a normal consolidation test. The slope defines the volume of water taken on or released by a change in pore-water pressure. An approximated mv value for slurries was calculated based on the results obtained from SWCC tests in the low suction range. It has been assumed that the initial slope of the SWCC at the very beginning of the test should be very close to the slope in the positive PWP range. With this in mind, mv has been calculated as the difference in VWC as a response of an increase in suction from 0 to 1 kPa. An average value of mv = 2.5e-2 has been calculated using the following relation:  81  mv =  4.3  (θ i − θ f ) 1 kPa  (Equation 45)  Analysis of Results Obtained from Unsaturated Modeling  A very important consideration during the modeling stage is to be aware that commercially available unsaturated packages (SVFluxTM, SoilCover (Wilson et al., 1994), VADOZE/WTM) have limitations when addressing the results of materials prone to large volume changes. Results provided by these programs should be carefully analyzed as some of them may be determined internally by the code assuming that the initial volume (generally provided in terms of porosity) is kept unchanged during simulation. By keeping volume unchanged all the resulting variables that require this parameter for their determination (saturation for example) will not provide realistic estimates. In the case of SoilCover, the constitutive equations for the model have been developed for volumetric water contents and therefore, for the case of soils prone to large volume changes it is appropriate to input the SWCC data in terms of this parameter. When analyzing the results provided by the model it is extremely important to keep in mind that the only representative estimates are those provided in terms of suction. This parameter is obtained by solving the unsaturated flow equation and all the required volume data is provided by the SWCC in terms of VWC. In other words, no indirect calculations using the initial volume (porosity) are required to obtain this variable. In the estimation of other parameters such as GWC and saturation, SoilCover will determine the VWC at a given suction from the SWCC and will then compute either GWC or saturation by typical geotechnical relations using the given initial porosity. The problem is that in reality porosity changes significantly as suctions increase. This shortcoming of the numerical model is shown in Figure 52 (a, b, c) where the results from SoilCover in terms of VWC, GWC and saturation are compared to those obtained by analyzing the suction data separately using the SWCC and shrinkage data determined in the laboratory. As noted, the VWC results show a very good agreement with the modeled data, whereas discrepancies are encountered for both GWC and saturation. Based on the previous findings, all results have been derived combining the lab data obtained in this research with the predictions of suction obtained from SoilCover.  82  0.16  Depth (m)  0.14 0.12 0.10 0.08  (a)  0.06 0.04 0.02 0  10  20  30  40  50  60  VWC (%)  Depth (m)  0.16 0.14  Day 1 - SoilCover  0.12  Day 1 - From Lab Data  0.10  Day 5 - SoilCover Day 5 - From Lab Data  0.08  Day 12 - SoilCover  0.06  (b)  Day 12 - From Lab Data  0.04 0.02 0  20  40  60  80  100  120  Saturation (%) 0.16  Depth (m)  0.14 0.12 0.10 0.08  (c)  0.06 0.04 0.02 0  5  10  15  20  25  30  35  40  GWC (%)  Figure 52: Differences between modeled results for VWC (a), saturation (b) and GWC (c) and results obtained from laboratory data (accounting for volume changes)  4.4  Method for Combining Sedimentation-Self Weight Consolidation and Drying Results  As discussed in previous sections, once the boundary between sedimentation-self weight consolidation and drying has been determined it is possible to assume that this will be the point at which these two processes should be combined. How the results of each process are put together will be shown by taking the example presented in Figure 45, which represents a 40 cm layer of paste prepared at 50% GWC and subject to a rate of ED of 5 mm/d. The properties for this example have been determined using the methodology presented in Section 4.2 assuming that the average void ratio (ed) achieved by sedimentation-self weight consolidation before drying begins is 1.03 (as shown in Section 4.1, Table 5). It must be noted that this example considers a no flow boundary condition at the bottom and therefore ED is only given by the potential rate of evaporation at the surface (PE). 83  The curve for average void ratio with time is obtained by matching the appropriate sedimentation-self weight consolidation curve with the curve of average void ratio obtained from the drying model (SoilCover). The matching point of both curves is the theoretical void ratio at which drying begins (ed = 1.03 in this case), which is determined as described in Section 4.1. As mentioned in Section 4.1 some problems arise when modeling drying in thicker layers of paste, since suctions start increasing at the surface of the layer only, while the suctions (and void ratios) at the bottom remain unchanged (e=1.03 in this case). This is shown in Figure 53 (a). In reality, what happens is that the lower portions of the layer will not remain unchanged but will likely keep undergoing sedimentationself weight consolidation while the surface is drying. Shrinkage in the lower portion will only commence once suctions increase with depth. An equivalent analysis may be performed when drainage is present. This problem has been overcome in this thesis assuming that those points from the drying model that were not subjected to suction would continue undergoing sedimentation-self weight consolidation at the same rate than that measured in the lab for a column of similar characteristics (similar column height and initial water content). Figure 53 (a) and (b) show the void ratio profiles within the layer without and with the proposed modification. As it can be seen only the void ratios at the bottom portions of the layer are modified for the case under analysis. It must be noted that for thinner layers of paste this modification may not be required as the suction and void ratio distribution tends to be more uniform within the layer and close to the values observed at the boundaries. 0.47  Depth (m)  0.42 0.6 Days  0.37  2.6 Days  0.32  3.6 Days  0.27  5.6 Days  0.22  10.6 Days  0.17  (a)  15.6 Days  0.12  30.6 Days  0.07 0.02 0.6  0.7  0.8  0.9  1  1.1  Void Ratio Void Ratio with Depth 0.47  Depth (m)  0.42 0.6 Days  0.37  2.6 Days  0.32  3.6 Days  0.27  5.6 Days  0.22  10.6 Days  0.17  (b)  15.6 Days  0.12  30.6 Days  0.07 0.02 0.6  0.7  0.8  0.9  1  1.1  Void Ratio  Figure 53: Unmodified (a) and modified (b) void ratio profiles from drying model  84  Figure 54 shows the evolution of void ratio at the surface and in average for the column. Also, this figure shows the average void ratio when the modification discussed earlier in this section is used. As shown, this last curve lies between the other two.  Void Ratio vs Time (GWC~50%) 1.500 Sedimentation-self weight consolidation Curve_40 cm_GWC=50% Surface Void Ratio (from drying model) Average Void Ratio for the Layer (from drying model) Average Void Ratio for the Layer_Modified  1.400  Void Ratio  1.300 Results of void ratio must  1.200  be determined based on a  1.100  desiccation model  ed=1.030 1.000  0.900 0.800 0.700  Td = 15 hrs  0.600 0  2  4  6  8  10  12  14  16  18  20  Time (days)  Figure 54: Void ratio of the paste layer with time It must be mentioned that the proposed approach for modifying the void ratio of those nodes not subjected to suction has not been validated and therefore should be a subject of further analysis. If the proposed approach is not used, results are still expected to be conservative.  4.5  Chapter Summary  Chapter 4 provides a methodology to predict the average void ratio of a paste tailings layer with time. The proposed method relies on determining the point at which sedimentation-self weight consolidation and drying should be combined as both processes are governed by different constitutive models and theories. In this thesis, this boundary has been determined as the point where the amount of water generated by sedimentation-self weight consolidation on a given period of time equals the amount that could be taken by evaporation and drainage (referred in this thesis as environmental dewatering ED). This boundary depends on governing climatic conditions and has been represented as the void ratio achieved by sedimentation-self weight consolidation before drying begins (ed). Void ratio is assumed to change according to a sedimentation-self weight consolidation curve until this void ratio is reached (i.e., sedimentation-self weight consolidation ends at the average void ratio of ed). After this point, the average void ratio is expected to change as a result of shrinkage and a drying model such as SoilCover (Wilson et al., 1994) should be used for analyzing the increase in suction within the paste layer (i.e., drying begins at an average void ratio of ed). For the drying models it was assumed that those nodes that were not subjected to suction would keep undergoing sedimentation-self weight consolidation at a rate equal to that measured in the laboratory for a case similar to that under analysis (similar layer thickness and initial GWC). The results provided by the sedimentation-self weight consolidation curve and the drying model were combined by matching the curves at a void ratio of ed.  85  A method for constructing the properties for the drying model was also presented. These properties were determined for different cases based on the void ratio achieved by sedimentation-self weight consolidation before drying begins (ed) as presented in Section 4.2. Although this process is time consuming, it allows for a continuous representation of average void ratio with time. Furthermore, a method has been provided to construct hydraulic conductivity functions that account for both changes in volume and suction. The method requires determining the relation between void ratio and hydraulic conductivity as this is used to construct the saturated portion of this property. In this thesis, this relation has been obtained using sedimentation-self weight consolidation data obtained from settling tests and the equation proposed by Been (1980) (Equation 31). To determine hydraulic conductivities at void ratios less than those found after sedimentation-self weight consolidation has ended, large strain consolidation testing may be required. The unsaturated portion of the hydraulic conductivity function was determined using the Fredlund and Xing (1994) model. Both the saturated and unsaturated portions were combined at a suction of 20 kPa (equivalent to the AEV determined for the material). Recommendations were made to analyze the results provided by unsaturated models. As presented in Section 4.4 it is suggested that only the results in terms of suction should be taken from the model as other parameters such as GWC and Saturation may contain errors associated to volume change approximations developed internally by the program. Proper representation of these parameters can be obtained only by combining the suctions provided by the model with the data determined in the laboratory.  86  5  APPLICATIO S OF THE PROPOSED FRAMEWORK  The previous Chapters have covered the details involved in the framework proposed to predict void ratio of thin layers of paste subject to sedimentation-self weight consolidation and drying. Although the methodology is still in its early stages, once some of the assumptions presented in this work are confirmed, the proposed approach may be used to determine the expected rate of densification under different scenarios which can provide valuable insight during design stages. The presented framework may provide the opportunity of predicting the post depositional characteristics of the paste under different climatic, operational and site conditions and could be the starting point required to analyze consolidation and liquefaction problems more accurately. Results obtained using this approach could help evaluating the optimal depositional scheme and may be used as a decision making tool during design. Some of the questions that could be addressed with this approach are: •  How much time is required to achieve a target density, void ratio or strength under a given climate?  •  What is the optimum layer thickness that should be targeted to achieve a specific density, void ratio or strength?  •  What is the maximum theoretical slope that can be constructed under given climatic conditions without compromising the factor of safety for liquefaction?  •  How could weather conditions affect the post depositional behaviour of the paste (differences between winter and summer conditions for example)?  •  What is the contribution to shrinkage in a freshly deposited paste layer due to downward seepage to underlying layers of paste?  •  What is the most suitable void ratio versus effective stress curve to use for the evaluation of consolidation?  The potential capabilities of the framework presented in this thesis, will be shown by modeling different case scenarios. Relevant input parameters such as layer thickness, climatic conditions and drying times will be modified to show the implications over average void ratio estimates. Also, the modeling framework will be used to represent some of the measured data obtained by Simms et al. (2007) as part of previous research. This may be also used as a preliminary validation of the proposed methodology.  5.1  Using the Approach to Represent the Observed Behaviour under Laboratory Conditions  The modeling framework has been used to represent the laboratory data obtained from drying tests performed at Carleton University by Simms et al. (2007). For this purpose a model was set up to simulate the conditions under which one of these tests was developed. The drying test used for the comparison was 87  a small scale drying test set up with the following characteristics (specific details may be found in the work of Bryan (2008)): •  A 13 cm layer of paste was poured in a 5 gallon container on Day 1 at approximately 45 % GWC (reported initial void ratio of e=1.34).  •  Bleed water coming from sedimentation-self weight consolidation was allowed to accumulate at the surface and it was reported to completely evaporate by Day 3. No drainage was allowed other than that generated at the surface as bleed water (impervious bottom boundary).  •  This first layer was allowed to dry for 15 days. During this period PE, wind speed, suction at different depths and AE were measured.  •  After 15 days a second layer of approximately 12 cm was placed on top of the initially dried layer at a GWC close to 40% (reported initial void ratio of e = 1.22). Minimal bleed water was observed for this layer as it was likely absorbed by the previously dried layer.  •  Both layers were then allowed to dry for an extra 11 days (total testing time of 26 days).  This particular test was selected because it included measurements of average void ratio with time for each layer that could be compared to the final estimates of void ratio obtained with the modeling approach presented as part of this work. Also the conditions in a small scale tests were assumed to be better controlled than those in a large scale test, where other factors such as cracking could make the comparison process less reliable. Figure 55 shows a schematic representation of the drying test used for the analysis.  Sensor ID  Layer  Elevevation (cm)  tens 1  1  4.7  HD278  1  8.2  Tens3A  1  9.5  HD270  2  13.7  tens2  2  14.5  HD282  2  16.2  Tens3B  2  19.4  Figure 55: Schematic diagram showing the configuration of the drying test (After Bryan, 2008) The model developed to represent this specific test considered that the first layer must have completely sediment-self weight consolidate before drying could begin. This assumption is valid as for this particular case, bleed water was allowed to pond at the top and it only evaporated by Day 3 (Bryan, 2008). Based on the results presented in Section 3.2 of this thesis, by that time, a 10 cm column (close to the layer thickness used in the test) at around 45-50% GWC should completely settle as a result of sedimentation88  self weight consolidation. Accordingly, the properties for the drying model were determined assuming that the starting void ratio for the first layer would be equal to that obtained at the end of a 10 cm settling tests performed in the lab at a GWC of 50% (e=0.973). Also, the climatic data input to the drying model considered the values measured from Day 3 onward. Prior to Day 3 it was assumed that water was being evaporated at the potential rate from the bleed water accumulated at the surface and not from the voids within the paste layer so no shrinkage could have taken place during this time. This can be also confirmed theoretically by comparing the cumulative rate of bleed water generation of a 10 cm column to the cumulative PE measured during the first three days of testing. This comparison is shown in Figure 56. It can be observed that for initial GWC’s of 40% and 50% the cumulative potential evaporation equals the cumulative rate of bleed water generation at 66 and 98 hours respectively. Since the first layer was prepared at approximately 45% GWC it is expected that the time by which all bleed water evaporates should be between this two values. This correlates well to the 72 hours reported by Bryan (2008).  Cummulative Bleed Water and Evaporation (mm)  2.5  2  1.5  1  Cummulative PE  0.5  10 cm Settling Test at 40 % GWC 10 cm Settling Test at 50 % GWC 0 0  20  40  60  80  100  120  Time (hrs)  Figure 56: Time required for pond water to evaporate Figures 57 through 59 compare the modeled and measured results for the drying test under analysis. It must be mentioned that the measured values of suction shown correspond to the approximate range of suctions measured by the different tensiometers and Heat Dissipation Water Potential Sensors (HD sensors) used during the drying test. The location of these sensors has been shown previously on Figure 55. The measured values with the sensors were compared to the modeled suctions obtained in the middle of the layer. It can be noted that in general terms the modeled data correlates well with the actual measurements in terms of suction and average void ratio for each layer. For the purpose of comparing the measured and modeled results, the void ratio at the shrinkage limit was modified from 0.7 (value measured in this research) to 0.8 which was the value measured during the  89  drying tests performed by Simms (2007). The differences in the measured shrinkage limits may be associated to differences in initial degree of saturation as explained by Fisseha et al. (2007). 100000  Suction (kPa)  10000  Layer 2  Layer 1 1000  100  10 Modelled Suction_Mid Layer Range of Measured Suction  1  0.1 0  5  10  15  20  25  Time (days) Figure 57: Modeled and measured suctions  Evaporation (mm)  -6  PE AE AE - Measured  -5 -4 -3 -2 -1 0 1  3  5  7  9 11 13 15 17 19 21 23 25 27 29  Time (days) Figure 58: Modeled and measured actual evaporation  90  1.500  Average Void Ratio for Layer_Modeled  1.400  Average Void Ratio for Layer_Measured  Void Ratio  1.300 1.200  Layer 1  1.100  Layer 2  1.000 0.900 0.800 0.700 0.600 0  5  10  15  20  25  30  Time (days)  Figure 59: Modeled and measured average void ratios The good agreement obtained between the modeled results and the data obtained by Simms (2007) from drying tests using the same material, is a good indication that the approach is at least representative of the evolution of the average void ratio in a thin paste tailings layer.  5.2  Evaluation of Case Scenarios  Several case scenarios have been evaluated using the proposed methodology in order to show the potential capabilities of this framework. Some of these case scenarios may provide relevant insight about the expected behaviour of paste layers under different conditions and could be used to choose the optimal depositional sequences during design. Table 7 shows a summary of the Cases that will be analyzed as part of this Section. This Table also provides the information regarding the void ratio at which drying is expected to begin following the approach presented previously in Chapter 4.  91  Case  ED (mm/d)  Layer Thickness (cm)  Initial Water Content (%)  Theoretical time required for drying to begin (Td)  Void Ratio (ed)*  Ksat* m/s  Effect of Paste Layer Thickness Thickness 1  5  40  50  15.5 hrs  1.030  4.62e-7  Thickness 2  5  10  50  4.5 hrs  1.120  7.48e-7  Climatic 1  5  10  50  4.5 hrs  1.120  7.48e-7  Climatic 2  1  10  50  11 hrs  0.983  3.11e-7  Effect of Climatic Conditions  Effect of Drainage to Underlying Layer of Paste Underlying Layer at 10,000 kPa  5.66  10  40  1.5 hrs  1.070  5.12e-7  Underlying Layer at 1,000 kPa  18.2  10  40  0  1.192  1.25e-4  Underlying Layer at 100 kPa  14.6  10  40  0  1.192  1.25e-4  Underlying Layer at 10 kPa  3.2  10  40  4 hrs  1.000  Phreatic Level at the top of Underlying Layer  1.99  10  40  6 hrs  0.950  2.53e-7  Effect of Initial Water Content of the Paste GWC 1  1  40  50  32 hrs  0.930  2.35e-5  GWC 2  1  40  40  38 hrs  0.900  1.85e-5  (*) Values of GWC, VWC, Void Ratio (e) and Ksat achieved by sedimentation-self weight consolidation before drying begins  Table 7: Case scenarios 5.2.1 Effect of paste layer thickness (no drainage) The effect of having different layer thicknesses is shown in Figure 60. As expected, thicker layers will require more time to achieve the same void ratio than thinner layers subjected to the same climatic conditions. In this case there is a trade off between the depositional volumes for a given paste tailings lift and the time required to achieve a given density. On one hand thinner lifts will allow for less material to be deposited at each stage, but multiple lifts may be placed in the time frame required for a thicker lift to achieve its maximum density due to sedimentation-self weight consolidation and drying. In the specific case under evaluation it may be seen that at the specified rate of ED, at least three 10 cm thick layers could be potentially deposited in the time frame required for one 40 cm thick layer to reach its maximum density. This doesn’t consider the fact that subsequent layers will likely dry faster as the bottom boundary will enhance the drying process due to increased suction and drainage. Therefore, it is likely that the overall densification process will be enhanced if thinner layers are selected as the preferred depositional option.  92  Average Void Ratio  1.500 1.400  Thickness 1 (40 cm)  1.300  Thickness 2 (10 cm)  1.200 1.100 1.000 0.900 0.800 0.700 0.600 0  5  10  15  20  Time (days) Figure 60: Average void ratio for a 40 cm and 10 cm layer of paste subject to PE of 5 mm/d 5.2.2 Effect of climatic conditions (no drainage) A similar analysis than that presented in Section 5.2,1 may be performed by considering two different climatic conditions. This could be for example a case representative of summer and winter conditions and the implications that this could have over the depositional scheme selected for each period. As shown in Figure 61, the time required to achieve a given void ratio increases as ED (evaporation in this case) decreases. In the specific case under evaluation it may be observed that the time required to reach the void ratio at the shrinkage limit increases from approximately 4 days (for ED = 5 mm/d) to almost 14 days (ED = 1 mm/d). 1.500 Climate 1 (ED = 5 mm/d)  Average Void Ratio  1.400  Climate 2 (ED = 1 mm/d)  1.300 1.200 1.100 1.000 0.900 0.800 0.700 0.600 0  5  10  15  20  Time (days) Figure 61: Average void ratio of a 10 cm layer subject to 5 mm/d and 1 mm/d of potential evaporation  93  5.2.3 Effect of drainage to underlying layers of paste A more realistic approach requires considering drainage as an important mechanism of dewatering. As explained earlier, drainage will likely increase the amount of ED than if only evaporation is considered. Two cases will be analyzed; the first case considers a thick underlying layer of dry paste while the second case considers a thick underlying layer of saturated material (phreatic surface at the top of the bottom layer). As presented in Table 7, different suctions have been assigned to the underlying layer to observe the effect of this parameter over drainage and the rate of densification. For all cases the rate of ED has been calculated assuming that PE is 1 mm/d. It may be observed that although PE is the same for all cases, the resulting rates of ED are different as the amount of drainage to the underlying layer is variable and depends on the existing suctions at the bottom boundary. Figure 62 shows the results of all cases under evaluation as well as the case with a no flow boundary at the bottom (No Drainage). It can be seen that underlying layers subjected to suctions of 10 kPa or more will enhance the densification process compared to the case where no drainage is considered. An interesting result is that higher suctions do not necessarily imply a higher densification rate. For example, the maximum rate of densification was observed for underlying layers at 100 kPa and 1,000 kPa. When the bottom suction was increased to 10,000 the rate of densification and drainage actually decreased. This could be explained by the fact that although suction gradients between the fresh and dry paste layers are higher, hydraulic conductivity in the bottom layer has decreased so significantly as a consequence of desaturation that drainage actually decreases. Another interesting result is the fact that having a saturated underlying layer may actually decrease the densification rate compared to that obtained for the case with no drainage. As shown by the model results, a fresh paste layer placed on top of saturated material may not even reach the shrinkage limit by the end of simulation. This could be a consequence of water being evaporated not only from the fresh paste layer but also from the saturated underlying stack. This process may delay the “build up” of suction in the freshly deposited paste layer as smaller head gradients are required to fulfill the evaporation demand at the surface. It must be considered that this is only a numerical result and this particular behaviour has not been confirmed herein by any type of laboratory or field test. The results obtained suggest that determining the effect of drainage over the densification rate is not a trivial task. For example, it may be concluded that drying may be necessary up to a certain point if the densification process is to be maximized. Drying the material further (reaching higher suctions) will not yield any more gain in density and may in turn decrease the rate of densification as observed for the case with an underlying layer at 10,000 kPa. Another important consideration is that the saturated hydraulic conductivity of the bottom layer will play a significant role. For example, if the saturated hydraulic conductivity of the bottom layer is decreased for the case with a saturated underlying material, results are expected to get closer to the case were no drainage is considered at the bottom.  94  Average Void Ratio  1.3 Underlying Layer at 10,000 kPa Underlying Layer at 1,000 kPa Underlying Layer at 100 kPa Underlying Layer at 10 kPa Underlying Layer Saturated No Drainage (PE = 1 mm/d)  1.2 1.1 1 0.9  Saturated  0.8 100 kPa  10 kPa  No Drainage  10,000 kPa  0.7  1,000 kPa  0.6 0  5  10  15  20  Time (days) Figure 62: Average void ratio for different underlying conditions 5.2.4 Effect of sedimentation-self weight consolidation rate over average void ratio predictions As presented in earlier Sections, different initial conditions (water content or column heights) result in different sedimentation-self weight consolidation conditions. The following Cases have been developed to show the difference in void ratio with time when having different sedimentation-self weight consolidation curves. A low PE and a thick layer of paste were selected so that the sedimentation-self weight consolidation process would have a significant contribution to the evolution of void ratio with time. For simplicity, no drainage was considered in these cases. Figure 63 shows the results for each of the cases under evaluation. As observed, void ratios for the layer with an initial GWC of 40 % are lower than those obtained for a layer at 50 % GWC. The differences after the drying process begin (at approximately 30 hours) are relatively small, nevertheless more significant differences may be observed during the early stages of densification, while the material is settling as a result of sedimentation-self weight consolidation. This is shown in more detail in Figure 64 where only the first five days of simulation are shown.  95  1.500 GWC 1 (initial GWC = 50 %)  Average Void Ratio  1.400  GWC 2 (initial GWC = 40 %)  1.300 1.200 1.100 1.000 0.900 0.800 0.700 0.600 0  5  10  15  20  25  30  Time (days) Figure 63: Average void ratio for a 40 cm layer of paste subject to 1 mm/d of PE 1.500 GWC 1 (initial GWC = 50 %)  Average Void Ratio  1.400  GWC 2 (initial GWC = 40 %)  1.300 1.200 1.100 1.000 0.900 0.800 0.700 0.600 0  1  2  3  4  5  Time (days) Figure 64: Average void ratio for a 40 cm of paste subject to 1 mm/d of PE during the first 5 Days It should be noted that the tailings used in this research would completely settle as a result of sedimentation-self weight consolidation in just a couple of days, and thus the relevance of this process is only affecting the results during the first two days. Finer tailings are expected to settle due to sedimentation-self weight consolidate at a slower rate, and therefore for low evaporations the effects of this process is expected to be relevant for a longer period of time. To further illustrate the implications of having different sedimentation-self weight consolidation behaviours, a new simulation was developed using a hypothetical material with a sedimentation curve corresponding to that shown in Figure 65. All the other properties for this hypothetical material (SWCC, Hydraulic Conductivity, etc) were kept the same as those determined for the Bulyanhulu tailings. It  96  should be noted that this material was created only to provide an example of the potential impact that different sedimentation-self weight consolidation rates could have on the predictions of void ratio with time. By no means has the hypothetical material tried to represent the behaviour of any of the materials used as part of this research or any other type of tailings. Based on the settling curve provided in Figure 65 it was determined that for the hypothetical material the amount of bleed water generated by sedimentation-self weight consolidation would equal a PE of 1 mm/d after approximately 90 hours (as opposed to the 30 hours required by the Bulyanhulu tailings). By this time the hypothetical material would reach a void ratio of approximately 1.0. 1.500 Hypothetical Material at 50 % GWC 1.400  Measured Settling Curve for Bulyanhulu Tailings (40 cm column at 50 % GWC)  Average Void Ratio  1.300 1.200 1.100 1.000 0.900 0.800 0.700 0.600 0  50  100  150  200  250  300  350  400  Time (hrs)  Figure 65: Sedimentation-self weight consolidation curve for a hypothetical material Figure 66 compares the results obtained for the hypothetical material with those obtained using the properties of Bulyanhulu tailings. All cases consider a 40 cm layer subject to a PE of 1 mm/d. It is clearly shown that sedimentation-self weight consolidation rate for the hypothetical material has a significant contribution to void ratio evolution during the first 6 days. It is also noted that while the Bulyanhulu tailings have begun to slowly dry the hypothetical material is still undergoing significant sedimentationself weight consolidation. This illustrate that although sedimentation-self weight consolidation is not a critical process for Bulyanhulu tailings it may well be for other type of tailings.  97  1.500 GWC 1 (initial GWC = 50 %) GWC 2 (initial GWC = 40 %) Hypothetical Material  Average Void Ratio  1.400 1.300 1.200 1.100 1.000 0.900 0.800 0.700 0.600 0  5  10  15  20  25  30  Time (days) Figure 66: Comparison of average void ratio for hypothetical material and Bulyanhulu tailings  5.3  Simplified Methodologies and their Impact over Average Void Ratio Estimates with Time  Although the framework presented in this work seems to well represent the process of sedimentation-self weight consolidation and drying, it is important to assess whether the benefits of such approach are worth the extra complexity required to set the properties and boundaries. With this in mind, the results of average void ratio with time obtained under the presented approach will be compared to those obtained under the following simplified methodologies: •  Methodology 1: Determine void ratio considering only the values provided by a drying model developed with properties modified to mimic the slurry conditions (starting at a water content corresponding to the pumping water content). This methodology does not account for the rate of sedimentation-self weight consolidation.  •  Methodology 2: Determine void ratio with properties modified to mimic the slurry conditions. In this case it is assumed that those nodes not subjected to suction will continue the sedimentationself weight consolidation process at a rate equal to that measured in the corresponding settling test as presented in Section 4.4.  •  Methodology 3: Determine void ratio with time assuming that regardless of climatic conditions the material will completely sediment-self weight consolidate before drying and drainage can begin. In this case the drying model was developed using the properties corresponding to the settled condition and does not account for the early triggering of drying and shrinkage.  •  Approach Presented in this Work: Determine void ratio with properties modified to account for the void ratio (ed) and time (Td) at which drying and evaporation of water from the paste voids are expected to begin. In this case it is assumed that those nodes not subjected to suction will 98  continue the sedimentation-self weight consolidation process at a rate equal to that measured in the corresponding settling test as presented in Section 4.4. First, the case of a 40 cm layer of paste at 40 % GWC under PE of 1 mm/d and 5 mm/d was evaluated using the methodologies presented earlier. These examples were used to illustrate the potential differences of void ratio predictions obtained under the different methodologies for the material used as part of this research. As observed in Figure 67, for low rates of ED, Methodology 1 predicts higher void ratios than those predicted using the other Methodologies. In Methodology 1, void ratio predictions do not account for the sedimentation-self weight consolidation process and are only a result of shrinkage due to increases in suction. Since ED is very low there is no significant suction build up and therefore shrinkage occurs at a very slow rate. In consequence, Methodology 1 is not a good method as it does not provide appropriate results for low rates of ED. Methodology 2 provides results closer to those given by the approach proposed in this thesis. However, it can be observed that drying is having no effect over the average void ratio as it remains equal to the settled void ratio (void ratio obtained after sedimentation-self weight consolidation) during simulation. In this regard, Methodology 2 is not capturing the decrease in void ratio due to drying that is observed later when using the approach proposed in this thesis. Methodology 3 shows almost the same results as those provided by the approach presented as part of this work. Methodology 3 assumes the material will completely sediment-self weight consolidate before it starts to dry whereas the approach presented in this work assumes the material will settle up to the point where ED becomes the dominant process. For cases with low ED this point occurs at a void ratio (ed) very close to the settled conditions. This explains why for this particular case the results provided by Methodology 3 and the approach presented in this work are similar.  Average Void Ratio  1.2  1.1  1  0.9  0.8  Methodology 1 Methodology 2  0.7  Methodology 3 Approach Presented in this Work  0.6 0  5  10  15  20  25  30  Time (days) Figure 67: Comparison of results provided under simplified methodologies for a case with PE of 1 mm/d and layer thickness of 40cm 99  As shown in Figure 68, a different result is obtained when the rate of ED is increased to 5 mm/d. Methodology 1 still provides conservative results during early stages, nevertheless as the material starts to dry (increase in suction), void ratios tend to get closer to those provided by the approach presented as part of this work. Values determined under Methodology 2 are now closer to those provided by the presented approach. Methodology 2 assumes the material properties correspond to the slurry conditions whereas the approach presented in this work assumes the material will sediment-self weight consolidate up to the point where ED becomes the dominant process. For cases with high ED this point occurs at a void ratio (ed) very close to the slurry conditions. This explains why for this particular case the results provided by Methodology 2 and the approach presented in this work are similar. Methodology 3 on the other hand provides less conservative results for void ratio. This could be the consequence of having a different initial pore water pressure distribution than that considered for the models developed using the approach presented in this work. For Methodology 3 an initial PWP distribution corresponding to hydrostatic conditions was used; whereas the model developed using the approach proposed as part of this work used a PWP closer to the total stress of the material (as per assumptions presented in Section 4.2.3).  1.2  Average Void Ratio  Methodology 1 1.1  Methodology 2 Methodology 3 Approach Presented in this Work  1  0.9  0.8  0.7  0.6 0  5  10  15  20  25  30  Time (days) Figure 68: Comparison of results provided under simplified methodologies for a case with PE of 5 mm/d and layer thickness of 40 cm Finally, a set of models were developed using sedimentation-self weight consolidation curve presented earlier in Section 5.2.4 for a hypothetical material. For these cases a higher rate of ED of 12 mm/d was used. As observed in Figure 69, Methodology 1 provides conservative results during the first 5 days compared to the other Methodologies used. For this particular case Methodology 2 provides the same results than those obtained using the approach presented in this thesis. It must be kept in mind that Methodology 2 100  uses properties corresponding to the slurry conditions. For high rates of ED as the one considered in this example, drying is expected to begin immediately after deposition and therefore the properties determined using the approach presented in this thesis should almost correspond to those at the slurry conditions. In this case Methodology 3 provides more conservative results than those coming from the approach proposed in this work. This is explained by the fact that under Methodology 3 sedimentation-self weight consolidation should be completed before drying can be modeled. As a result, the effect of drying and drainage is disregarded during the early stages of densification while sedimentation-self weight consolidation is taking place. This is a significant limitation of Methodology 3. 1.5 Methodology 1  Average Void Ratio  1.4  Methodology 2  1.3  Methodology 3 Approach Presented in this Work  1.2 1.1 1 0.9 0.8 0.7 0.6 0  5  10  15  20  25  30  Time (days) Figure 69: Comparison of results provided under simplified methodologies for the case with a rate of ED of 12 mm/d and a 40 cm layer with a smaller settling rate  5.4  Chapter Summary  This Chapter has covered some applications of the methodology presented in this thesis. First, the results of the model have been compared to measured laboratory data which has also served as a preliminary validation of the approach. It was shown that understanding the conditions under which the laboratory tests are developed is fundamental to provide with reasonable void ratio estimates. For example, pond water at the surface may have a significant impact over the densification process and therefore it should be considered when developing the models. The results provided by the approach presented as part of this work showed good agreement with the data measured during drying tests performed by Simms et al. (2007). The methodology proposed in this thesis was then used to predict void ratio under different conditions. In general terms it was concluded that: •  Thicker layers will take more time to achieve the same void ratio than thinner layers subject to the same climatic conditions.  101  •  The time required to achieve the shrinkage limit will increase as ED decreases.  •  The effect of drainage to underlying layers of paste is not trivial and depends on the conditions and properties of the underlying materials. In general terms, drainage is enhanced as the suctions of the underlying material increase. This is true only up to a given point as for very high suctions (10,000 kPa for the case of Bulyanhulu tailings) it was observed that drainage in fact decreases. It was also shown that a saturated underlying material would delay the densification process due to drying. This could be a consequence of water being evaporated not only from the fresh paste layer but also from the saturated underlying stack delaying the build up of suction.  •  Sedimentation-self weight consolidation plays a more important role when ED is low and will generally affect the early stages of densification. For the specific case of Bulyanhulu tailings the effect of this process is only important in the first couple of days.  Finally, the results provided by the methodology proposed as part of this work were compared to those provided by other simplified methodologies. It was shown that there is a trade off between simplicity and representativeness. On one hand, the simplified methodologies were easier to execute, but on the other the representativeness of the results will depended on the type of problem under analysis. In this sense Methodology 2 showed to be representative in cases with low ED whereas Methodology 3 was more suitable for cases with high ED. The methodology proposed in this thesis seemed to provide representative results regardless of the case under evaluation.  102  6  CO CLUSIO S  6.1  General Conclusions  The present work has dealt with some of the problems related to the assessment of density due to sedimentation-self weight consolidation and drying. The proposed approach has been developed using the properties of Bulyanhulu tailings, and therefore, some of the assumptions and results obtained may be only limited to the behaviour of this particular material. Regardless of this, the methodology presented provides the basis necessary to apply this approach to other materials. The most important outcomes of this thesis are the following: •  A methodology to determine void ratios as a result of sedimentation-self weight consolidation and drying has been provided. The approach presented allows for the determination of average void ratio under any given climate and for different paste layer configurations (layer thickness and initial GWC). For low amounts of environmental dewatering (ED), the methodology properly accounts for the rate of settling as a result of sedimentation-self weight consolidation whereas for high ED the methodology properly represents the early onset of drying. Results using this methodology are obtained combining measured data for sedimentation-self weight consolidation with modeled data for drying using simple water balance assumptions. This is considered a clear improvement from previous attempts where all processes were tried to be represented using only unsaturated modeling.  •  Chapter 3 of this thesis provides an overview of the limitations encountered when determining the properties of slurry materials in the laboratory. Some of these limitations are associated to volume changes occurring as a result of sedimentation-self weight consolidation during laboratory testing. A simplified procedure based on settling test data has been presented to determine hydraulic conductivities at high void ratios. The proposed methodology is considered appropriate for preliminary assessment of sedimentation-self weight consolidation and drying problems. A more precise representation of hydraulic conductivity as a function of void ratio requires for the proposed procedure to be combined with large strain consolidation or seepage induced consolidation data. The trade off between extra costs and obtaining more refined properties for the model should be assessed.  •  Chapter 3 also demonstrates that the SWCC in terms of VWC, GWC and Saturation is required for proper analysis of drying in soils prone to large volume changes and shrinkage. These curves are used to analyze the results of suction provided by the numerical models. This is performed to overcome some of the limitations of unsaturated models as they usually assume that volume remains unchanged during simulation. Volume changes during the SWCC tests have been determined based on simple measurements using callipers and have provided reasonable results. In cases where lateral shrinkage or cracking is significant, this simplified procedure may not be sufficiently precise.  103  •  A good understanding of the sedimentation-self weight consolidation behaviour of Bulyanhulu tailings has been provided by the settling tests presented in Chapter 3 of this thesis. It has been shown that sedimentation-self weight consolidation behaviour depends on parameters such as column height and initial water content. As a consequence, for a proper understanding of the sedimentation-self weight consolidation behaviour the settling tests should be performed to target the range of conditions (layer thicknesses and pumping GWC) expected under field conditions. In general terms, it was shown that thinner layers would sediment-self weight consolidate at a faster rate than thicker layers; however, the final void ratio achieved by thin layers would be higher than that obtain with thick layers. Also, for the same layer thickness higher initial GWC’s showed faster settling rates but higher final void ratios than columns prepared at lower initial GWC’s. Having a large set of sedimentation-self weight consolidation data may provide a broad understanding of this process under different operational conditions.  •  Chapter 4 provides a methodology to determine unsaturated properties that account for both changes in volume and suction. The hydraulic conductivity function has been determined by constructing the saturated and unsaturated portions separately and then combining them at the AEV. The saturated portion was constructed using the relation developed to relate void ratio to hydraulic conductivity whereas the unsaturated portion was constructed using the Fredlund and Xing model (1994) with the SWCC data for the settled material.  •  A method was proposed to construct SWCC’s that would account for the void ratio achieved by sedimentation-self weight consolidation before drying begins (ed). These properties were later used in the drying models developed in SoilCover. Although manually changing the properties for the model proved to be time consuming, it allowed for continuous estimates of average void ratio and facilitated the combination of sedimentation-self weight consolidation and drying results of average void ratio.  •  Relevant applications for the modeling approach have been presented in Chapter 5. This chapter has shown the capabilities of the approach to predict densities under different climatic conditions and material properties and has also shown the ability to fit results obtained in the lab. Although some of the steps require for the presented approach are complicated in nature it was shown that simplified methodologies would not always provide representative results, and would only be suitable to assess certain scenarios. The methodology proposed in this thesis provided reasonable results for all cases and so it is considered a more general solution for the problem under evaluation.  Regarding the modeled behaviour for the Bulyanhulu paste tailings, the following may be concluded: •  Thin layers of Bulyanhulu tailings (10 – 40 cm) tend to sediment-self weight consolidate relatively fast (1 to 3 days) and therefore even at low rates of ED, this process will only affect the early portion of the void ratio curve with time. As a consequence, determining the rate at which this process occurs may not be extremely relevant for the overall evaluation of density  104  with time. For simplicity, it could be desired to assume that the material will completely settle before the onset of drying due to evaporation and therefore the properties used for the drying model would be those corresponding to the settled conditions. For some cases this would yield conservative results in terms of the time required to achieve the shrinkage limit. The trade-off between extra conservatism and using a simplified methodology should be assessed. It must be reminded that the proposed methodology has been developed so it could be applied to the deposition of thin layers of other tailings as well, for which the rate of settling as a result of sedimentation-self weight consolidation may be different to that measured for the Bulyanhulu tailings (for example the settling rates obtained for oil sand tailings). Examples were presented in Chapter 5 using a hypothetical sedimentation-self weight consolidation curve to illustrate that in some cases the rate of settling due to this process should not be disregarded. •  The sedimentation-self weight consolidation process becomes less relevant as the rate of ED increases and layer thickness decreases. For cases with very high rates of ED it was determined that all density was gained through evaporation and drainage and sedimentation-self weight consolidation had no impact in the void ratio estimates. For cases were drainage and evaporation are low, all process (sedimentation-self weight consolidation, evaporation and drainage) contribute to some extent to the densification process.  •  The amount of drainage plays a significant role and in some cases it may well be the primary mechanism of densification. Also, as long as the amount of bleed water seeping to the surface exceeds the amount of PE, evaporation is expected to have no contribution to the densification process which will only be affected by sedimentation-self weight consolidation and drainage.  •  Calibration of the modeling framework based on observed results in the laboratory or the field is essential and should be developed to validate the results provided by the model. The calibration process will also serve as a tool to fine tune some of the properties and assumptions going into the numerical models.  6.2  Recommendations for Future Work  6.2.1 Sedimentation -self weight consolidation behaviour Some important considerations have been presented in this work regarding the behaviour of sedimentation-self weight consolidation of thin layers of paste. The work performed in this thesis has also raised some important questions that could be potentially addressed in future research work. For example, although this thesis has presented some of the theories that have been used by other authors to evaluate sedimentation-self weight consolidation problems, they have not been used to fit the measured data obtained as part of this work. Moreover, some of the properties required for analyzing sedimentation-self weight consolidation problems were not obtained during this research and therefore using any consolidation model was not possible due to the lack of data for the analysis. For this reason, this thesis has only considered measured sedimentation-self weight consolidation data which has been combined  105  with drying data provided by numerical modeling. It could be argued that a more practical approach would also require for the ability to model or predict average void ratios as a result of the sedimentationself weight consolidation stages and thus this should be considered as an alternative in future work. Among the properties required for analyzing the problem of sedimentation-self weight consolidation, hydraulic conductivity as a function of void ratio and compression versus void ratio are the most important. Although this work has provided a relation between hydraulic conductivity and void ratio, this function needs to be extended for smaller void ratios than those provided by pure sedimentation-self weight consolidation of thins layers of paste. This could be performed using large strain consolidation or Seepage Induced Consolidation Tests. This has been developed successfully in the research of AbuHejleh and Znidarčić (1994, 1996), Jeeravipoolvarn (2009) and Ding et al. (2010) among others and the results obtained as part of their work could serve as a good base to extend the findings of the present thesis. Important findings have been obtained regarding the effect of variables such as initial water content and layer thickness over the sedimentation-self weight consolidation results. These finding may be used to assess the suitability of different models (CONDES0, MINTACO) with respect to their ability of predicting the behaviour of thin layers of paste during this process. The ability to predict or model sedimentation-self weight consolidation of thin layers of paste may provide a more refined void ratio distribution within the layer as opposed to the average value obtained from settling tests. Also, the rate of sedimentation-self weight consolidation may be also obtained when drainage is present at the bottom boundary condition allowing for this curve to be combined to the results provided by the drying model. For this purpose it is recommended that settling curves as a result of sedimentation-self weight consolidation are determined for cases with and without drainage at the bottom so modeled results can be compared for both cases. An important question to answer is whether in thicker layers the evaporation process at the top boundary has any implications on the sedimentation-self weight consolidation behaviour of the lower portions in the layer. It would be interesting to observe what the implications are of having a high evaporation rate at the surface of a thick layer of paste. Whether settling due to sedimentation-self weight consolidation will occur at the same rate, or if it will decrease due to the formation of a surface crust is still to be determined. It must be remembered that in this work it was assumed that for nodes not subjected to shrinkage (usually those away from the boundaries) the rate of void ratio change was equal to that measured during pure sedimentation-self weight consolidation tests (settling tests). Monitoring PWP at the bottom of the settling columns could provide a better estimate of the initial PWP distribution for columns prepared at higher SC (as those usually used for paste deposition). Although assuming that initial PWP is equal to total stress is probably a good assumption, it may be too conservative in some cases. Regardless of this, it is expected that the initial condition for the drying model will be somewhere between the total stress and hydrostatic conditions (assuming material is fully saturated). A more precise evaluation of the problem may require understanding the effect of shearing and other rheological processes that lead to the “at rest” condition of a given paste tailings layer. For this research it 106  has been assumed that the paste will instantaneously form a layer of given thickness and that the initial water content of that layer will be that corresponding to the pumping conditions. This is clearly an idealization of the problem as shearing effects will likely increase the rate of bleed water generation. Research opportunities to investigate whether it is possible to determine a water content at which a given paste layer is expected to stop flowing is required in future research work. The results of drying models similar to those presented in this work may be developed to model the water contents of a given tailings layer with time and these estimates can be used to predict the time required to reach the “at rest” conditions. Finally, understanding the effects of the pre-consolidation loads imposed by the suctions generated during the drying process should be also the focus of future research work. This apparent pre-consolidation will likely affect the consolidation process and therefore it is considered relevant for the overall densification process of paste tailings. 6.2.2 Unsaturated properties One of the most important objectives of future research related to the unsaturated properties used in the proposed approach should be to validate some of the assumptions and procedures used in this work. In particular, evaluating the effect on the SWCC of having different initial slurry conditions is important as some of the assumptions presented rely on the fact that at higher suctions the SWCC is unique regardless of initial state. It is recommended to develop a set of SWCC for different paste tailings materials starting at different initial GWC (close to those expected in the field). Results for each type of material should be compared to determine the point at which the SWCC’s start to converge. Single point measurements may provide an easy way to reach higher suctions without having to develop the full test and should also be compared to the results obtained for the complete SWCC. Suctions for the Single Point Measurements used in this work were selected to be close or higher than the AEV of the material (around 20 – 30 kPa), nevertheless, for a more thorough evaluation, it would be ideal to develop some of this measurements for lower suctions. Extending the data for hydraulic conductivity as a function of void ratio, as proposed in the previous Section would allow for a better representation of the K function in the saturated region (before the AEV). This would also help determining a more precise saturated hydraulic conductivity for a previously dried layer that has reached the shrinkage limit. It must be mentioned that hydraulic conductivity for the bottom layer is an extremely relevant parameter when drainage is considered in the simulation. Determining the expected degree of saturation of the paste upon discharge from the pipe is important as shrinkage is affected by the initial condition. Generally it is assumed that material is fully saturated, nevertheless this may be a non-conservative assumption when determining final void ratios and shrinkage limits (Fisseha et al., 2007).  107  6.2.3 Validation of the model results with drying tests The present thesis has provided a framework to combine the effects of sedimentation-self weight consolidation and drying so estimates of average void ratio for a paste tailings layer could be obtained with time. Several cases combining different layer thicknesses and initial conditions have been assessed using this approach as well as other simplified methodologies. It is important to acknowledge that some of these results have not been compared to any type of laboratory or field test yet and should therefore be considered as the “potential” behaviour of a tailings layer subject to those specific conditions. Confidence in the presented approach must be built by validating the results with laboratory tests data. For this purpose, the development of multilayer deposition is recommended as a suitable way of analyzing some of the problems evaluated in this work. To facilitate the development of future research in this specific area, some recommendations will be provided based on what is considered relevant to complement the findings provided in this thesis: •  First, it is recommended that pure sedimentation-self weight consolidation is evaluated using an approach similar to that presented in Section 3.2. The targeted column heights and initial water contents should correspond to those expected to be used in the multilayer tests.  •  Configurations having a thick saturated and thick dry underlying stack should be compared. It is recommended that both the dry and saturated underlying stacks to be prepared at the same void ratio (void ratio at the shrinkage limit for example), as this would allow having a similar saturated hydraulic conductivity in both tests. This will allow for the cases to be comparable as the only variable changing would be the underlying suction or degree of saturation. The presence of drainage was observed to have a significant impact in the evolution of modeled average void ratio with time. Based on some of the findings provided in this work, its effects are not always intuitive and therefore the previous recommendation is considered appropriate.  •  So far, behaviour is well understood for thin layers of paste at relatively high evaporation rates. It would be also interesting to observe the implications of having thicker layers (30 – 40 cm) subject to high evaporation rates (5 mm/d or more) or thin layers (10 cm) subject to low evaporation rates (1 mm/d).  •  The proposed approach has considered that bleed water will not pond on the surface but will likely runoff. This assumption makes a big difference as it may allow for drying to begin at any given point during the sedimentation-self weight consolidation process. If ponding is allowed during testing, it is expected that sedimentation-self weight consolidation will take place for a longer period of time than would be obtained if bleed water is constantly removed from the surface. Ideally, laboratory conditions should allow for water to be removed as it seeps to the surface of the tailings due to the sedimentation-self weight consolidation process. This nevertheless may prove to be work intensive and not practical. It must be acknowledged that if drainage is allowed, bleed water is expected to be minimal.  108  •  A key variable of the approach presented as part of this work is the potential rate of evaporation (PE). PE is compared to the amount of bleed water generated during sedimentation-self weight consolidation to determine the time at which this variable should be considered in the drying model. In consequence, a precise determination of PE right at the surface of the tailings is fundamental for a proper analysis and comparison of the model and measured data.  •  Measurements of suction should be complemented with measurements or estimates of void ratio with depth so a better comparison can be made between the modeled and measured data. It is acknowledge that measuring void ratio may be impractical and therefore GWC measurements may be developed alternatively. Measured suctions can provide an estimate of the degree of saturation which can be used along with the specific gravity to calculate void ratio with depth.  6.2.4 Modeling approach Once the proposed approach has been validated and refined, a series of steps should be performed to optimize it and make it a more functional tool. Some of the applications that should be included in such a model should consider the following: •  Since volume changes are important, a single curve relating water content to suction (in this case VWC) is not enough to obtain accurate estimations of other relevant parameters such as GWC and degree of Saturation. This could be modified by including in the model the SWCC in terms of VWC, GWC and Saturation so that these variables are calculated directly from the provided curves and not from typical geotechnical relations that require an initial volume. Evidently, the SWCC’s input to the model (specifically those in terms of VWC and Saturation) should account for volume changes measured during the SWCC test. In order to obtain void ratio predictions it is also required for the shrinkage curve to be input to the unsaturated model.  •  Ideally, the user should be able to analyze results at smaller times than those allowed in SoilCover (daily basis) so that some of the limitations with respect to the initial conditions used for the models when drainage is present can be reduced. Other unsaturated packages (SVFlux, Vadoze) may provide a better interface to evaluate results at smaller time frames.  •  The water balance proposed to determine the point at which Evaporation should be incorporated to the model (point at which drying begins) should be automated so that it can be performed internally during simulation. Also, if modifying the model properties based on this theoretical time proofs to be a valid assumption; this process should also be automated based on a numerical routine. This would significantly reduce human error as well as the time required to prepare the model properties and boundary conditions. Decreasing the mesh as material shrinks may also be implemented for more representative results. Whether it is possible to make these changes to a program such as SoilCover is something that should be subject of further evaluation.  109  Finally, the objective of future research should be focused on comparing the results coming from the presented approach to those obtained using other available software’s for the prediction of consolidation and desiccation of soft soils. CONDES0 and MINTACO are probably amongst the most used by industry and therefore they should be considered as the current benchmark for analyzing this type of problems. 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