Master's Thesis

MASTER'S THESIS

Placement of Thickened Tailings Adoption of a Rheology-Oriented Model for Slope Predictions

Deniz Dagli

Master of Science (120 credits) Civil Engineering

Luleå University of Technology Department of Civil, Environmental and Natural Resource Engineering Placement of Thickened Tailings Adoption of a Rheology-Oriented Model for Slope Predictions

Deniz Dagli

Lule˚aUniversity of Technology Dept. of Civil, Environmental and Natural Resources Engineering Div. of Mining and Geotechnical Engineering

2nd January 2013

ABSTRACT

Thickened tailings or “paste” disposal with deposition slopes varying from 2 to 4% results in steeper slopes compared to those of conventional placement (less than 0.5%). As a consequence, thickened tailings disposal ends up with filling more volume per storage area and thus avoids costly & frequent dam raises. Reported observations describe that the discharged slurry typically flows down the slope or “beach” in a confined, self-formed channel, in a macroscopic equilibrium between erosion and sedimentation, defining an overall slope and then spreads out & deposits on a broader area (Simms, et al., 2011). The objective of this study is to describe the slope forming elements and adopt the model for beach slope predictions by Fitton (2007) together with a discussion of simulated results and the effects of rheological & hydraulic parameters. Typical thickened tailings have average particle sizes of 25 to 75 µm with maximum particles of about 0.5 mm. To obtain a conceptually even slope with practically no segregation of particles occurring and no drainage of water taking place, the concentration by volume often needs to exceed 40% (even 45% for some cases). It is reported that these slurries show non-Newtonian behaviour and often found in a supercritical open channel flow state located in the transitional or turbulent zone. When the slurry spreads out, the flow attains a sheet-like, laminar state where particles settle out. The process repeat itself in a cyclic manner and the overall beach profiles are created as a result. Fitton’s model, based on open channel hydraulics (Darcy-Weisbach friction loss concept) and sediment transport approach, considers the self-confined open channel flow to be turbulent, based on field and large scale flume observations. The model relates the deposition velocity to maintain the channelized flow, to a Bingham rheological model parameter. The model is utilized to simulate the depositional behavior of thickened tailings slurries having a volumetric solids concentration of 46% (71% mass). This value is used to represent homogeneous (non-segregating) conditions for tailings with an average particle size of 50 µm and a solids density of 2900 kg/m3. Simulation results for slurry flow rates 3 from 25 to 400 m /h correspond to slopes of about 6 and 2%, respectively, expressing a flow rate dependence at yield stresses and Bingham viscosities of up to 30 Pa and 0.1 Pa.s, respectively. Reynolds numbers were from about 500 to 94500 for which the effect

iii of channel roughness on predicted slopes was practically negligible within values from 0.3 mm to smooth conditions at 0.05 mm. Calculated slopes were nearly insensitive to the channel shape as long as the width/depth ratio remained constant about 5.5. A rectangular cross-section was used for the calculations but a parabolic channel shape reflects field observations better. Equilibrium yield stress requirement for the flow to come to rest and the required shear strength (cohesion) to be developed upon drying for stability of slopes formed by stacked layers of various thicknesses are demonstrated in schematic examples.

iv PREFACE

This thesis report is submitted as a part of the graduation work for the fulfillment of a MSc. degree at Lule˚aUniversity of Technology, Dept. of Civil, Environmental and Natural Resources Engineering. After working on the subject of thickened tailings disposal for a considerable amount of time, I would like to use this opportunity to express my gratitudes to the people who have provided invaluable help and support. First, I wish to thank my thesis supervisor, Professor Emeritus Anders Sellgren, for his patience and guidance. Without the time he has put into this work and the effort to carefully examine the work over and over for constant improvement, I would never be able to overcome this challenge. For that, I will always be grateful. I wish to express my thanks to Mr. Thord Wennberg at LKAB for the detailed guided tour of the company’s mineral processing plant and the tailings storage facilities. I also want to thank my examiner, Professor Sven Knutsson, for his support and the encouragement to work on tailings in general. My special thanks go to Mr. Aziz Kubilay Ovacikli for the help he has provided with the coding of the MATLAB algorithm used throughout this work and also for introducing me to report writing with LATEX. Above all, I would like to express my deepest gratitudes to my family for the uncondi- tional love and for the moral, motivational & financial support they have provided during my whole life and my stay in Sweden. Without them I could have never achieved any of this and therefore, I dedicate my share of contribution in this work to them.

Deniz Da˘glı

Lule˚a, December 2012

CONTENTS

Chapter 1 – Introduction 1 1.1 Mineral Processing & Tailings ...... 1 1.2 TailingsDisposalMethods ...... 2 1.2.1 Conventional Tailings Disposal (Dams/Impoundments) ...... 2 1.2.2 Thickened Tailings Disposal ...... 5 1.2.3 PasteDisposalinUndergroundMines...... 9 1.3 ProblemDescription ...... 9 1.4 Objective&Scope ...... 10

Chapter 2 – Open Channel Flow 11 2.1 Flow Resistance & Friction Losses ...... 11 2.2 FlowRegime&ReynoldsNumber...... 13 2.3 FrictionFactor(f)...... 13 2.4 StateofFlow ...... 15 2.5 ConceptualExample1 ...... 17 2.6 Non-Newtonian Fluid & Suspension Flow ...... 19 2.6.1 Models...... 19 2.6.2 Non-NewtonianFrictionLosses ...... 23 2.6.3 ConceptualExample2 ...... 24

Chapter 3 – Transportation of Tailings Slurries 27 3.1 Solid-WaterMixtureParameters...... 27 3.1.1 Solid Content & Density ...... 27 3.1.2 Particle Size Distribution ...... 28 3.2 Classiﬁcation ...... 28 3.2.1 Settling & Non-Settling Slurries ...... 28 3.2.2 Deposition Velocity ...... 31

Chapter 4 – Placement of Tailings Slurries 33 4.1 SlurryDeposition...... 34 4.1.1 Geotechnical (Slope Stability/Equilibrium) Approach ...... 34 4.1.2 ConceptualExample3 ...... 37

Chapter 5 – Adoption of the Rheology-Oriented Model by Fitton 39 5.1 Fitton’sWork...... 39 5.1.1 ModelDevelopment...... 39 5.2 Fitton’s Semi-Empirical Beach Slope Model ...... 41 5.2.1 Segregating vs Non-Segregating Slurries ...... 42 5.2.2 Minimum Transport Velocity Equations ...... 43 5.2.3 FlowResistanceEquation ...... 45 5.2.4 Determination of the Channel Shape for the Open Channel Flow . 46 5.2.5 RunningtheModel...... 47 5.3 Validation with the Field Data ...... 48

Chapter 6 – Results & Discussion 51 6.1 ModelValidation ...... 51 6.2 Properties of the Tailings Material & Assumptions for the Simulations.. 52 6.3 Results&Discussion ...... 54 6.3.1 Results...... 54 6.3.2 StateofFlow ...... 57 6.3.3 Solid Concentration and Particle Size Distribution ...... 58 6.3.4 Sediment Transport Approach & Shield’s Diagram ...... 58

Chapter 7 – Conclusions 61

REFERENCES 62

Appendix A – Parameter Study 67 A.1 EﬀectoftheYieldStress...... 67 A.2 EﬀectofViscosity...... 68

Appendix B – Flow Simulations 71

viii List of Figures

1.1 Tailings from the mineral processing of iron ore - Schematic ﬂow chart.. 1 1.2 Conventional tailings disposal system. Slopes for deposited tailings are normallylessthan0.5%(Wennberg,2010) ...... 2 1.3 Discharging with spigots (Fell, et al., 1992) ...... 3 1.4 UpstreamMethod(Fell,etal.,1992) ...... 5 1.5 Downstream (a) and Centerline (b) construction methods (Fell, et al., 1992) 6 1.6 Schematic representation of the thickening process (Metso Minerals, 2002). Theterm“pulp”issynonymoustoslurry...... 6 1.7 Schematic representation of the thickened tailings discharge method (Fell, etal.,2005) ...... 7 1.8 Thickened discharge method on an inclined ground (Wennberg, et al., 2008) 8 1.9 Tailings disposal system with a thickener located near the deposition zone (Wennberg,2010)...... 8 1.10 Thickener location alternatives for LKAB Svappavaara mine (Wennberg, 2010)...... 9

2.1 A uniform open channel flow. The slope is normally less than 5◦ which means that φ = sin φ = tan φ and the depth perpendicular to the bottom istakenastheverticaldepth...... 12 2.2 Moodychartforpipeflows(AfterMoody,1944) ...... 14 2.3 Transition from sub-critical to supercritical flow ...... 16 2.4 Transition from supercritical to sub-critical flow ...... 16 2.5 Undular hydraulic jump taking place at Fr < 1.7 ...... 17 3 2.6 Open channel equivalent of a pipe flow with 0.15 m diameter and 80 m /h discharge...... 18 2.7 Non-Newtonian fluid models, whereγ ˙ is the shear rate (Fitton, 2007) . . 19

2.8 Transition point VT , where ﬂow regime changes from laminar to turbulent in a tailings slurry with Bingham like properties. The arrows indicate various approaches for turbulent friction losses Wennberg (2011)..... 21

2.9 Definition of the apparent viscosity. The subscript 1 relates µa to a particular rate of true shear, du/dy.Sellgren(1982)...... 22 2.10 Representation of the apparent viscosity for non-Newtonian media, Sell- gren(1982) ...... 23 3.1 Representative particle size span for tailings (Engman, et al., 2004) ... 29 3.2 Time history of settling at different concentrations (Andreasson,1989) . 30 3.3 Classification of slurries based on the particle size and the relative density (Aude,etal.,1971)...... 30 3.4 Concentration profiles for different types of slurries. (After Sellgren, 1982) 31 3.5 Graphical solution for the determination of the deposition velocity based on pipe diameter and mean particle size (Thomas, et al., 2011) ...... 32 4.1 Schematic representation of a slurry flow upon leaving the pipe (After Williams,2011) ...... 33 4.2 Angleofrepose ...... 35 4.3 Force equilibrium at angle of repose ...... 35 4.4 Sheet flow equilibrium (After Robinsky, 1999) ...... 36 4.5 Depositional behavior of the tailings in the form of a slurry and in desic- catedform...... 37 5.1 Schematic representation of the flume that is used in the field experiments forFitton’swork(Fitton,2007) ...... 40 5.2 Graphical representation of the difference between segregating and non- segregating slurries in terms of depositional behavior (After Robinsky, 1999) 43 5.3 Relationship between the flow velocity and Bingham Reynold’s number (equation5.1)(Fitton,2007)...... 44 5.4 Summary of slope predictions (Seddon & Fitton, 2011) ...... 49 6.1 Model validation with the experimental data ...... 52 6.2 Rheological representation of different slurries to be simulated ...... 53 6.3 Relationship between the yield stress and the deposition slope ...... 55 6.4 Relationship between the Bingham viscosity and the deposition slope .. 56 6.5 Shield’s diagram to predict sediment motion (Chanson, 2004) ...... 59 List of Tables

2.1 Material properties of water and a viscous liquid ...... 17 2.2 Equivalent open channel properties for water and the liquid in table 2.1 . 18 5.1 ExcerptfromFitton’sexperimentaldata ...... 41 6.1 Summary of simulation results for µB=0.05Pa.s...... 54 6.2 Summary of simulation results for µB=0.01Pa.s...... 55 6.3 Summary of simulation results for µB=0.1Pa.s ...... 56 6.4 Summary of simulation results for µB=0.05 Pa.s for a parabolic cross-section 57 A.1 Flow simulations with τy=0Pa...... 67 A.2 Flow simulations with τy=5Pa...... 67 A.3 Flow simulations with τy=10Pa ...... 68 A.4 Flow simulations with τy=20Pa ...... 68 A.5 Flow simulations with τy=30Pa ...... 68 A.6 Flow simulations with µB=0.01Pa.s ...... 69 A.7 Flow simulations with µB=0.05Pa.s ...... 69 A.8 Flow simulations with µB=0.1Pa.s ...... 69 B.1 Flow simulations with τy=5 Pa, µB=0.01Pa.s ...... 71 B.2 Flow simulations with τy=10 Pa, µB=0.01Pa.s ...... 71 B.3 Flow simulations with τy=20 Pa, µB=0.01Pa.s ...... 72 B.4 Flow simulations with τy=30 Pa, µB=0.01Pa.s ...... 72 B.5 Flow simulations with τy=5 Pa, µB=0.05Pa.s ...... 72 B.6 Flow simulations with τy=10 Pa, µB=0.05Pa.s ...... 72 B.7 Flow simulations with τy=20 Pa, µB=0.05Pa.s ...... 73 B.8 Flow simulations with τy=30 Pa, µB=0.05Pa.s ...... 73 B.9 Flow simulations with τy=5 Pa, µB=0.1Pa.s ...... 73 B.10 Flow simulations with τy=10 Pa, µB=0.1Pa.s ...... 73 B.11 Flow simulations with τy=20 Pa, µB=0.1Pa.s ...... 74 B.12 Flow simulations with τy=30 Pa, µB=0.1Pa.s ...... 74

List of Notations

A Cross-sectional area (m2)

B Width of the open channel (m)

C Solid concentration (%)

Cv Solid concentration by volume (%)

Cw Solid concentration by weight (%) d (d50) 50th percentile particle diameter (or Average particle diameter) (m) d90 90th percentile particle diameter (m)

DH Hydraulic diameter (m) f Darcy-Weisbach friction factor

Fr Froude number g Acceleration due to gravity (m/s2) hf Head loss (m) ks Surface roughness coeﬃcient (m)

L Length of the open channel ﬂow (m) n Parameter for Power-Law and Herschel-Bulkley models n Slope of the log-log plot of bottom shear stress versus pseudo shear rate

Pw Wetted perimeter (m)

3 Q Dischargerate(m /h)

Re Reynolds number

ReBP Reynolds number for Bingham plastic model (equation 5.1) RH Hydraulic Radius (m)

S Slope=sin φ

Ss Speciﬁc gravity of solids

Sc Critical Slope (%)

V Mean ﬂow velocity (m/s)

Vc Critical or deposition velocity (m/s)

VT Transition velocity from laminar to turbulent ﬂow (m/s) y Flow depth (m) yc Critical depth (m)

1 γ˙ True shear rate (s− )

µ Newtonian viscosity (P a.sn)

n µA Apparent viscosity (P a.s )

µB Bingham viscosity (P a.s)

n µH Herschel-Bulkley viscosity (P a.s )

n µP Power-Law viscosity (P a.s )

ρ Density of the slurry(kg/m3)

ρ0 Density of water (kg/m3)

kg 3 ρs Density of solids ( /m )

σg Stress due to the eﬀects of gravity (Pa)

σn Normal component of the gravitational stress (Pa)

σs Shearing component of the gravitational stress (Pa)

τ0 Mean boundary shear stress (Pa)

τ Shield’s parameter (equation 6.1) ∗

τs Shear strength (Pa)

τw Wall shear stress (Pa) τy Yield stress (Pa)

φ Slope angle (◦)

φr Angle of repose (◦) CHAPTER 1 Introduction

1.1 Mineral Processing & Tailings

Mine tailings can be defined as the by-product of mineral processing operations. During the extraction or separation of the ore in the processing plant, tailings materials are produced. A schematic flow chart of the processing of iron ore is given in figure 1.1.

Figure 1.1: Tailings from the mineral processing of iron ore - Schematic ﬂow chart

Crushed raw ore, having a particle size of about 100 mm, is fed to the processing plant (the plant is sometimes termed also as the concentrator or simply the “mill”) and the size is then reduced to less than about 0.15 mm at the end of the operation by means of milling. The valuable product is successively taken out in various separation steps resulting in an ore concentrate that will be taken for further reﬁnement and processing.

1 Introduction 2

The residual product, “tailings”, together with the water used in mineral processing forms a ﬁne-grained mixture, or tailings “slurry”. The tailings slurry is then transferred to a thickener where water is removed from the mix to be recycled; to be used again in the mineral processing plant. The slurry is then pumped to the tailings disposal facilities where it will be stored. At this stage, after in-plant thickening, the solids content in the transported slurry may correspond to 10 to 40% by mass (deﬁned as dry mass of solids over total mass of solids and water). The maximum particle sizes are often 0.5 to 1mm with an average size of 0.025 to 0.075mm depending on the type of ore that has been processed.

1.2 Tailings Disposal Methods

The basic requirement for a tailings disposal method is to store the tailings material in such a way that it remains stable without having a negative impact on the environment. Some of the most commonly used tailings disposal techniques are going to be discussed in this section. It should be noted that the methods are not limited to ones provided below and there are numerous other available techniques for tailings treatment.

1.2.1 Conventional Tailings Disposal (Dams/Impoundments) Conventional disposal here is deﬁned as the deposition of the tailings slurries at a solids concentration by mass of about 10 to 40%, which involves a large quantity of water, see ﬁgure 1.2.

Figure 1.2: Conventional tailings disposal system. Slopes for deposited tailings are normally less than 0.5% (Wennberg, 2010)

Storing tailings with an impoundment method, generally behind a dam which acts as a border, is one of the most common methods of tailings disposal. The idea is quite simple but effective. Once the site to store the tailings material has been decided, a dam embankment (or several depending on the location where the tailings material is going to be deposited) is constructed to contain the material. This is generally achieved by making use of the fine grained material which is engineered to satisfy certain criteria so that the material stored behind the dam (or embankment) is optimized and the probability of 3 1.2. Tailings Disposal Methods harming the environment (by means of seepage and/or erosion) is minimized (Fell, et al., 2005), similar to the case of earth-fill dams. The advantage of doing so is generally the fact that the mechanics, general practice and the experience gained from conventional water storage dams are often applicable in this case as well (Fell, et al., 1992). The area occupied by the deposited tailing is often referred as the “tailings beach” and the general beach slopes for conventional tailings disposal is less than 0.5%

Deposition Methods The tailings material can be deposited behind the embankment by means of either discharging from a single point or from several discharge points (spigotting). Spigotting makes use of several discharge points placed along the line of deposition as shown in ﬁgure 1.3. It also enables uniform spreading of the tailings material behind the embankment. Depending on the need, it is also possible to shift the line of discharge from one point to another on the boundaries of the embankment.

Figure 1.3: Discharging with spigots (Fell, et al., 1992)

Construction Methods Though it has been stated that the majority of the principles and practices developed in conventional water dam engineering can be applied for tailings dams, it should also be noted that not all the experience and the design philosophy from water retention dams are applicable (Fell, et al., 2005). As the mining operation will be continuing until the mine reaches the closure state, there will be a constant production of tailings throughout the life time of the mine. As a result, there is always a need for more storage space to overcome this problem. This is one of the major diﬀerences between the design philosophies of conventional water storage and tailings dams. The capacity of a water storage dam is designed for a ﬁxed volume of water and the excess water can be discharged by means of dam structures (such as spillways) Introduction 4 embedded to the dam body, when needed. In the case of tailings dams, the amount of tailings to be stored constantly increase; therefore additional storage spaces need to be provided. To address this problem, the tailings dams are designed and constructed in such way that when the capacity of the initial dam has been reached, it is possible to construct a new dam right on top of the previous one to increase the storage capacity in the impoundment. In the next sections, the construction methods to increase the capacity of a tailings dam are introduced. The descriptions of the techniques were taken from (Vick, 1990) and (ICOLD, 1982).

Upstream Method

As the name suggests, upstream method is a construction technique in which the dam is raised towards the upstream level. The initial dam (sometimes called the starter dam as well) is generally a water retention dam (can be also built from the tailings material directly if the material properties of the tailings permit). At this point, the starter dam acts like a barrier and creates a storage volume and can be considered as a simple embankment (Fell, et al., 1992). When the level of stored material reaches to its limiting values, another dam is built on the existing embankment (starter dam) to create an additional storage volume. The tailings material itself can be used for the construction of the new embankment. This procedure can be repeated when the need arises (i.e. when the capacity of the existing tailings dam has been reached). One of the greatest advantages of this method is that it requires relatively low amounts of construction material during the raising of the dam (especially when compared to the other two construction methods which will be described in the following sections). How- ever, one important drawback is that since the dam is being raised towards the upstream in stages, each stage of construction results in a decrease in the storage volume compared to the previous stage.

Downstream Method

One other method for raising the tailings dam is the downstream method. This time, the dam is raised towards the downstream instead of the upstream. The procedure is similar to the one described in the previous section. A starter dam is built ﬁrst, to act as a barrier for the tailings. When the capacity of this started dam is reached, another embankment is placed upon the old one in the downstream direction to provide additional storage space. The procedure can be repeated should the need for more storage volume arise. One of the biggest problems with this method is that the required amount of construction materials for each stage increase rapidly, rendering the method not feasible after a certain height of dam. Its major advantage, however, is the increased storage capacity 5 1.2. Tailings Disposal Methods

Figure 1.4: Upstream Method (Fell, et al., 1992) for each stage due to the fact that the dam is raised towards the downstream and the ability to construct ﬁlter layers to try to reduce the eﬀects of seepage and/or erosion.

Centerline Method

The last method that is used to raise the embankment dams is the centerline method. The raising of the dam is done along its centerline. Similar to the downstream method, the centerline method is also costly as it requires more and more amounts of construction material for each stage. It also provides the ability to construct ﬁlter and drainage layers to help improving the stability of the dam. Figure 1.5 illustrates diﬀerent methods for tailings dam construction.

1.2.2 Thickened Tailings Disposal In order to avoid the costly dam raises and to limit the operational costs of a tailings storage facility, thickened tailings disposal method can be utilized. With this kind of deposition method, the aim is to end up with a deposition slope value of 2-4% which will result in ﬁlling more volume per storage area. As a result, embankment raises will be needed less often which, in turn, will create savings in the construction costs. For thickened tailings disposal, thickening that results in solids concentration by mass of 60 to 75%, depending on the ore type and particle size distribution, is required. This means that an additional thickening is needed besides the in-plant thickening shown in Introduction 6

Figure 1.5: Downstream (a) and Centerline (b) construction methods (Fell, et al., 1992)

ﬁgure 1.1. The working principle of a thickener is schematically shown in ﬁgure 1.6.

Figure 1.6: Schematic representation of the thickening process (Metso Minerals, 2002). The term “pulp” is synonymous to slurry.

In order to achieve a discharge (“underflow”) with a solids content up to and over 70%, the circular tank of the thickener normally has a higher height/diameter ratio than it is 7 1.2. Tailings Disposal Methods shown in figure 1.6. The effectiveness is related to the extents of the compression zone. The thickener that generates the high solids content can be located at the concentrator or close to the disposal area depending on local conditions and economics. The underflow thickened slurry can be pumped for placement at the disposal area with various types of pumps based on the pressure requirement. Provided that the area where the material is being discharged is flat, resulting deposition will be cone shaped. If this area is large enough, then the need to build a dam to confine the tailings material might not be required. However, some kind of a drainage system to collect the run-off water from the boundaries is necessary to prevent the leak- age of the material to the surrounding environment. If a dam is constructed to create a pond to store the water, it might then be possible to use this collected water for recycling purposes to be used again in the processing operation (Fitton, 2007).

Figure 1.7: Schematic representation of the thickened tailings discharge method (Fell, et al., 2005)

If the deposition area for the thickened tailings disposal is rather inclined, the construction of embankments might be required to keep the tailings from spreading. An example of which can be seen in ﬁgure 1.8. This kind of thickened tailings deposition is termed as “down-valley discharge” method. The thickened tailings storage facility given in ﬁgure 1.8 is located in Norberg, in central Sweden and is being operated by Harsche AB. The deposition takes place on an inclined ground that is surrounded by tailings dams (or embankments) to contain the material. The installation has been running since mid-2011. In cases where the deposition takes place along a hill side or down a valley, it might be Introduction 8

Figure 1.8: Thickened discharge method on an inclined ground (Wennberg, et al., 2008)

favorable to locate the thickener close to the disposal area (Wennberg, 2010) as shown in ﬁgure 1.9.

Figure 1.9: Tailings disposal system with a thickener located near the deposition zone (Wennberg, 2010)

Figure 1.10 provides another tailings storage facility with two alternative locations for the thickener at Svappavaara, northern Sweden. The concept provided in ﬁgure 1.9 is marked as 2 in ﬁgure 1.10; together with another possibility where the thickener is located at the concentrator (marked as 1). For more information see Wennberg (2010). Alternative 2 was chosen and the operation will begin in the end of 2012. 9 1.3. Problem Description

Figure 1.10: Thickener location alternatives for LKAB Svappavaara mine (Wennberg, 2010)

1.2.3 Paste Disposal in Underground Mines Thickened tailings and the term “paste” are often presented in an interchangeable context in the literature. Although it is possible to assume that they loosely refer to the same type of material in many cases, it should also be noted that the true paste is generally thicker than the thickened tailings. In paste disposal, tailings can be used as a backﬁll in the underground openings at very high solids concentration by mass (about 75%). Once the underground mining operation is complete, this paste is usually mixed with cement to provide additional strength and pumped back to the openings, in order to help and improve the stability (Fell, et al., 2005). Examples in Sweden are at the Garpenberg and Zinkgruvan mines as described by Lindqvist, et al. (2006) and Tillman (2006), respectively.

1.3 Problem Description

Thickened tailings to be placed in the disposal area must possess properties that give a conceptually even slope of deposited tailings with no segregation of particles and virtually no drainage of water. Compared to an average slope of a maximum of about 0.5% for conventional placement, 2 to 4% are considered for thickened tailings. Throughout the whole process, starting with thickening & pipeline pumping and ending up with the placement stage; deposition phase, generally associated with deposition Introduction 10 slopes, is unpredictable. It has been observed that discharged slurry, at the disposal area, typically flows down the beach in a confined self-formed channel and then spreads out in a macroscopic equilibrium between erosion and sedimentation. It is indicated that the overall slope of the beach is directly related to the slope of this confined channel. The free surface open channel flow of tailings slurry forming the beach slope comprises of various flow regimes related to viscous properties and flow behavior. The particle- water mixture may attain Newtonian properties with a high viscosity value (like oil). When the viscous behavior cannot be described by a fixed viscosity, then the media may be characterized as non-Newtonian (like a tooth paste or ketchup). The corresponding rheological properties are determined through viscometric measurements and analyses. Jewell (2010) states that despite the recent advances have been made in understanding the mechanisms of slope formations of the deposited tailings; this is still an area where more work is needed to be undertaken. There is at present not a universally accepted method available for the accurate prediction of tailings beach slopes (Jewell 2012) and laboratory flume testing is not a viable method for predicting the beach slopes out on the field. In the yearly international Paste conferences 2011 and 2012, workshops and special sessions were devoted for slope predictions resulting in new and updated contributions ref. Depositional behavior of tailings can be considered as an intermediate area shared by several different disciplines, such as mineral processing, geotechnics and fluid mechanics. Due to this fact, knowledge from these different fields often needs to be combined to get a better understanding of the problem.

1.4 Objective & Scope

The objective is to describe the basic slope forming elements from the open channel ﬂow of thickened tailings slurries which show non-Newtonian behavior. A semi-empirical model for beach slope predictions by Fitton (2007) is adopted and discussed for simulating the placement of thickened tailings. Rheological measurement and evaluation procedures are not discussed in details. Basic descriptions can be found in Andreasson, (1989), Sundqvist (1994) or in textbooks. No experimental work has been carried out and details about the thickening and pipeline pumping in the system leading up to the placement are outside the scope of this study. CHAPTER 2 Open Channel Flow

An open channel flow can be defined as a channel (of any shape) in which the water flows with a free surface (Chanson, 2004). The channel in which the water flows on can be natural or artificial. Rivers or streams are examples of naturally occurring open channels whereas human built structures such as irrigation channels or flumes are artificial open channels. Man-made channels are often referred as launders in the mining industry.

2.1 Flow Resistance & Friction Losses

Open channel flows can be further classified as uniform (non-varying) or non-uniform (varying) flows. A uniform flow is defined as the type of flow in which the depth and the velocity profile remain unchanged along the direction of flow (i.e. the water depth is constant and the water surface is parallel to the channel bottom), see figure 2.1. For a fixed discharge, cross-section and slope, the water depth has a unique value at which the gravitational force component is in balance with the resisting shear force. If the control volume in figure 2.1 with a length of L is considered, the equilibrium between the resistance and the gravitational force component can be stated as

τPW L = ρgAL sin φ (2.1)

Where, ρgAL (A is the cross-sectional area) is the mass of the water and PW L (PW is the wetted perimeter) is the area on which the resisting shear stress, τ, acts. Rearranging equation 2.1, and knowing the relationship sin φ= S, where S is the channel slope, yields

τP S = W (2.2) ρgA The ratio of the cross-sectional area to the wetted perimeter is termed as hydraulic radius of the open channel ﬂow.

11 Open Channel Flow 12

Figure 2.1: A uniform open channel ﬂow. The slope is normally less than 5◦ which means that φ = sin φ = tan φ and the depth perpendicular to the bottom is taken as the vertical depth.

A RH = (2.3) PW Whether it is an open channel or a pipe flow, the energy of the system decreases continuously along the direction of flow. For a uniform open channel flow, the head loss occurring over a distance L (denoted as hf in figure 2.1) will give the slope of the channel. In other words, the slope of the free surface (or the slope of the energy grade line) is equal to the slope of the channel bed. The statement can be formulated as follows

h S = f (2.4) L This loss of energy (or often termed as the head loss) over a certain distance along the path of a pipe ﬂow can be calculated with the help of Darcy-Weisbach equation.

L V 2 hf = f (2.5) DH 2g

Where, f is the Darcy friction coefficient, DH is the hydraulic diameter, V is the mean flow velocity and g is the acceleration due to gravity. The main difference in calculating the head losses for open channels and pipe flows is in the definition of DH (hydraulic diameter). For circular pipes, the hydraulic diameter is simply the diameter of the pipe. For an open channel flow, the hydraulic diameter is given as

DH =4RH (2.6) 13 2.2. Flow Regime & Reynolds Number

The concept of DH (sometimes noted as “D”) will be used in equations related to circular closed conduits throughout this study.

2.2 Flow Regime & Reynolds Number

Depending on the cross-sectional properties of the open channel, rate of discharge as well as the material properties of the fluid flowing in the channel; the state of the flow can be classified as laminar, turbulent or transitional. The classification is based on the Reynolds number which is given as

ρV 4R Re = H (2.7) µ

Where, ρ is the density, V is the mean flow velocity, RH is the hydraulic radius and µ is the viscosity of the fluid. For open channels, the flow regime becomes turbulent for the values of Reynolds number larger than 1000. For values of Reynolds number lower than 500, the flow can be classified as laminar. The flow is in a state of transition for the values of Reynolds number in between. (Fitton, et al., 2006).

2.3 Friction Factor (f)

In section 2.1 it has been stated that the energy of the flow diminishes over the direction of the flow due to the frictional resistance caused by the channel bed. The frictional resistance of the channel bed is often associated with a friction factor, which is a function of Reynolds number and the channel (or pipe) roughness coefficient. If the Reynolds number and the channel/pipe roughness properties are known, determination of the friction factor can be carried out with the help of the Moody diagram presented in figure 2.2. An analytical solution for the Moody chart is also available in the form of equations if the state of the flow can be identified (laminar or turbulent). For laminar flows,

64 f = (2.8) Re For turbulent ﬂows,

1 k 2.51 = 2 log s + (2.9) √f − 14.8R Re√f H The equation 2.9 is also known as the Colebrook-White equation. Where, ks is the surface roughness coeﬃcient, RH is the hydraulic radius and Re is the Reynolds number. Open Channel Flow 14

Figure 2.2: Moody chart for pipe ﬂows (After Moody, 1944)

The resistance (or the boundary shear stress) caused by the channel bed is related to the friction factor in the following way

fρV 2 τ = (2.10) 8 If the equations 2.4 and 2.6 are substituted into the Darcy-Weisbach equation (equation 2.5), the relationship obtained would be

fV 2 S = (2.11) 8gRH For cross sections where the width of the channel is considerably larger than the water depth (B y) ≫ By R = (2.12) H B +2y

The hydraulic radius approaches to y. Thus, in such cases RH can be takes as the water depth (y) and the equation 2.2 becomes

τ = ρgyS (2.13) 15 2.4. State of Flow

2.4 State of Flow

The flow in closed conduits, flowing full, (e.g. pipe flows) is characterized by the laminar or turbulent regimes. In open channel flows, the flow is dominated by the effect of gravity. As a result, there are two additional regimes, termed as sub-critical and supercritical. Critical flow conditions occurring at a critical depth, yc, distinguish these two regimes which have completely different physical characterizations. The critical depth corresponds to the maximum possible flow rate for a given amount of energy in the water body. Alternatively, at the critical depth, a given flow rate is discharged at a minimum energy use. Supercritical flow takes place when the flow depth is less than yc and it is associated with steep slope values and high velocities. Supercritical flows can be observed behaving in a “fast”, “shooting” or “torrential” manner. On the other hand, sub-critical flows have a “slow”, “tranquil” or “fluvial” behavior occurring at mild slope values and low velocities at depths where the flow depth is larger than yc (Chanson, 2004). For a rectangular open channel, the critical depth can be calculated according to the formula

1 3 Q2 / y = (2.14) c gB2 The slope rate that produces the critical flow depth is defined as the critical slope and is denoted by Sc Critical depth can be observed at locations where there are variations in the channel slope. The transition from sub-critical to supercritical for uniform flow for increasing slopes is shown in figure 2.3. The classification of the state of flow for open channel flows is often based on the Froude number. The flow takes place under critical conditions when the Froude number is equal to 1. The equation to calculate Froude number for a rectangular cross-section is given as

V Fr = (2.15) √gy Where V is the mean flow velocity, y is the flow depth in the rectangular channel and g is the acceleration due to gravity. The calculation of Fr and yc for cross-sections of different shape (say, parabolic or elliptic) involves the use of concepts like the hydraulic mean depth (the ratio of area to the surface width - width of the channel section at the free surface). For more details, see the textbooks for open channel flow. The classification based on Froude’s number yields

If Fr < 1, the ﬂow is sub-critical,

If Fr > 1 then the ﬂow is supercritical. Open Channel Flow 16

Figure 2.3: Transition from sub-critical to supercritical ﬂow

The transition from supercritical to sub-critical conditions is more dramatic compared to the reversed transition in ﬁgure 2.3. The abrupt increase in depth takes place in the form of a hydraulic jump that is characterized by a high turbulence level; eddies rolling on the surface and air entrainment. The concept of hydraulic jump is illustrated in ﬁgure 2.4.

Figure 2.4: Transition from supercritical to sub-critical ﬂow

The extent of a hydraulic jump can be expressed by the preceding depth and the 17 2.5. Conceptual Example 1 corresponding Fr. For small jumps, most eddies and air entrainment disappear and the jump is merely an undulation in the liquid surface, see ﬁgure 2.5.

Figure 2.5: Undular hydraulic jump taking place at Fr < 1.7

At critical flow conditions, relationships between the flow rate, flow depth and the channel slope for typical open channels are such that different flow depths may occur for a constant discharge. In other words, the water depth (y) can vary considerably in the vicinity of yc. Due to this unstable state of flow under critical conditions, the flow is accompanied with undulating surface waves. Therefore in the design of water courses or industrial flumes, critical flow conditions are avoided due to these instabilities.

2.5 Conceptual Example 1

An example will be provided below to further illustrate the concepts introduced in the previous sections. 3 Consider a flow rate of 80 m /h discharge in a pipe of 0.15m in diameter. The equivalent uniform flow in a rectangular open channel with a water depth, y, of 0.047m and a channel width, B, of 0.378m will have the same cross-sectional area as the pipe and thus the same flow velocity (1.26 m/s) as illustrated in figure 2.6. The required slopes for uniform flow will be calculated for water and a viscous liquid with the properties given in table 2.1.

Table 2.1: Material properties of water and a viscous liquid

Water Viscous Liquid ρ (kg/m3) 1000 1950 µ (Pa.s) 0.001 1.95

The viscosity of the viscous liquid is nearly 2000 times greater than the viscosity of the Open Channel Flow 18

3 Figure 2.6: Open channel equivalent of a pipe ﬂow with 0.15 m diameter and 80 m /h discharge

water. The ﬂow parameters (such as Re, f and S) are calculated with respect to equations 2.7 - 2.11 and are summarized in table 2.2.

Table 2.2: Equivalent open channel properties for water and the liquid in table 2.1

Water Viscous Liquid Re 188323 188 f 0.025 0.34 S (%) 1.314 18.202

It follows from table 2.2 that the required channel slopes to maintain a uniform flow for the viscous liquid is about 14 times larger than that of water. For the viscous liquid with a viscosity of of 1.95 Pa.s, the corresponding slope is calculated as 18%. This difference in slopes can be attributed to the constraints (fixed flow rate, flow velocity and the cross-section of the open channel) of the example. Due to these certain limitations, the slope values to maintain a uniform flow under identical (flow depth and flow speed) conditions are different for each sample. It also follows from table 2.2 that the open channel flow for water takes place under turbulent conditions as the Reynolds number for the flow is greater than 1000. On the other hand, the uniform open channel flow of the viscous liquid takes place under laminar conditions as the Reynolds number is smaller than 500. In addition, the increase in the channel slopes, as the flow shifts from turbulent to laminar is also worth noting. Furthermore, these laminar and turbulent open channel flows are found to be super- 19 2.6. Non-Newtonian Fluid & Suspension Flow critical with Fr=1.85

V 1.26 Fr = = 1.85 √gy √9.81 0.047 ≈ × The critical depth of the ﬂow in the earlier example becomes (equation 2.14)

1 3 1 3 Q2 / 0.0222 / y = = 0.07m c gB2 9.81 0.382 ≈ × 2.6 Non-Newtonian Fluid & Suspension Flow

2.6.1 Models The non-Newtonian models of particular interest in the context of this work are the Bingham Plastic, Herschel-Bulkley and the Power Law Models. The concepts introduced in the previous sections were valid for Newtonian fluids. A non-Newtonian fluid may exhibit a yield stress which is the amount of stress required in order to get the material moving. Below this yield stress, the material behaves as solid and no flow can be initiated, or a non-linear viscosity characteristic or both (Fitton, 2007). Figure 2.7 is a graphical representation of the non-Newtonian behavior.

Figure 2.7: Non-Newtonian ﬂuid models, where γ˙ is the shear rate (Fitton, 2007) Open Channel Flow 20

As ﬁgure 2.7 implies, it is possible to further classify the non-Newtonian ﬂuids into sub-classes.

Bingham Plastic Model Bingham plastic is suitable to model the behavior of fluids with a certain yield stress and a linear viscosity characteristic. Once the yield stress is overcome and the flow is initiated, the shear stress increases linearly with µB. The mathematical model of the Bingham Plastic is given with the following equation (the equation of the line that represents Bingham plastic behavior in figure 2.7)

τ = τy + µBγ˙ (2.16)

Where, τy is the yield stress in Pa and µB is the plastic viscosity of the ﬂuid in Pa.s.

Power Law Model Power law model is appropriate to use when the fluid does not have any yield stress but has a non-linear viscosity characteristic. As a result, the rheogram (the graph in which the shear stress of the fluid is plotted against applied shear rate) of a power law fluid intersects the origin and progresses in a non-linear way. The mathematical equation of the Power law curve is as follows

n τ = µP γ˙ (2.17)

n µP is the power law consistency index (P a.s ) and n is the ﬁtting parameter.

Herschel-Bulkley Model Another Non-Newtonian model of interest is the Herschel-Bulkley model. It is suitable for the purpose of modelling the ﬂuids with an initial yield stress as well as a non-linear viscosity characteristic. This can also be treated as the combination of Bingham Plastic model and the Power Law model. The equation of the curve for Herschel-Bulkley ﬂuid is given as follows

n τ = τy + µHγ˙ (2.18)

n Where, τy is the yield stress in Pa, µH is the viscosity in P a.s and n is the ﬂow index (unit-less) of the ﬂuid.

Generally, the rheological properties are defined in terms of a yield stress and a shear rate. However, it is also possible to express the rheology of the material in terms of the operating parameters (such as the wall shear stress, flow velocity and the hydraulic diameter). The relationship between the bottom shear stress, τw, of a flow (figure 2.1) 21 2.6. Non-Newtonian Fluid & Suspension Flow and the ratio 8V/D, which defines the pseudo shear rate, can be taken as a representative of the rheological properties of a fluid. Rabinowitsch (1929) and Mooney (1931) found a technique which relates the pseudo shear rate to the true shear rate,γ ˙

1 8V γ˙ = (3n + /4n) (2.19) D

Where n is the slope of the log-log plot of bottom shear stress (τw) versus pseudo shear rate (8V/D). True rheogram representations, based on the true shear rateγ ˙ , can be transferred into operating parameters in terms of D and V through the pseudo shear rate (8V/D) which serves as a scaling parameter as shown in ﬁgure 2.8 by making use of equations 2.16 & 2.19. The relationship between the pseudo shear rate and the rheological properties for a Bingham plastic can be expressed as follows (Shook and Roco 1991).

4 8V τ 4τ 1 τ = w 1 y + y (2.20) D µ − 3τ 3 τ p " w w #

Figure 2.8: Transition point VT , where ﬂow regime changes from laminar to turbulent in a tailings slurry with Bingham like properties. The arrows indicate various approaches for turbulent friction losses Wennberg (2011)

The following relationship relates VT to the material properties, Wilson et al. (2006).

V 22.5 τy/ρ (2.21) T ≈ p Open Channel Flow 22

Where τy is yield stress and ρ the slurry density. Neglecting the higher order term in equation 2.20, the relationship for laminar ﬂows can be explained as follows

4 8V τ = τ + µ (2.22) w 3 y B D

Where 8V/D = 2V/RH is the pseudo shear rate and thus equation 2.22 becomes

4 2V τw = τy + µB (2.23) 3 RH This relationship will be used to approximate a true Bingham fluid, i.e. the yield stress is defined by a straight line back to the vertical axis, see the dashed line in figure 2.8.

Apparent Viscosity

As defined in section 2.6, a non-Newtonian fluid exhibits either yield strength or a non- linear viscosity characteristic or both. At any given instant and for a given shear rate, the apparent viscosity is defined as the slope of the line from the origin to a point on the rheogram, see figure 2.9.

Figure 2.9: Deﬁnition of the apparent viscosity. The subscript 1 relates µa to a particular rate of true shear, du/dy. Sellgren (1982)

It can be concluded from figure 2.9 that the apparent viscosity has a constant value, independent of the shear rate, for Newtonian media only. For non-Newtonian media, a constant value can only be related to a particular rate of shear. The apparent viscosity for very large shear rates can be represented by an asymptotic constant value, µR, for non-Newtonian fluids, see figure 2.10. 23 2.6. Non-Newtonian Fluid & Suspension Flow

Figure 2.10: Representation of the apparent viscosity for non-Newtonian media, Sellgren (1982)

The apparent viscosity is defined as the viscosity of a non-Newtonian fluid at a given shear rate and can be defined as the slope of the line from the origin to the representation in figure 2.9 for a given value of a pseudo shear rate. The statement can be formulated as follows τ µ = (2.24) A 2V

RH 2V Where, /RH is the pseudo shear rate (8V/D). The yield stress of a Herschel-Bulkley ﬂuid is given as (equation 2.18) Substituting equation 2.18 into equation 2.24 yields

2V n τ + µ τ τ + µγ˙ n y R µ = = y = H (2.25) A 2V 2V 2V

RH RH RH If the equation 2.25 is substituted into equation 2.7 (to take the shear rate dependent viscosity characteristic of a non-Newtonian ﬂuid into account), the modiﬁed version of the Reynolds number expression becomes

8ρV 2 Re = (2.26) 2V n τ + µ y R H Friction factor calculations of the non-Newtonian open channel ﬂows should then be carried out with the modiﬁed version of the Reynolds number provided in equation 2.26.

2.6.2 Non-Newtonian Friction Losses Reynolds number of a Newtonian ﬂuid can be expressed as (equation 2.7) Open Channel Flow 24

ρV 4R Re = H µ Due to the significant differences in the viscosity property between a Newtonian and a non-Newtonian fluid (viscosity of the Newtonian fluid is independent of applied shear rate whereas the viscosity of a non-Newtonian fluid is shear rate dependent), the above formula needs to be modified (see equation 2.26) in order to take the rheology of the non-Newtonian fluids into account.

2.6.3 Conceptual Example 2 The following example is aimed to provide more insight on the concepts like the yield stress and the modified Reynolds number. The liquid in the example of the previous section will now be treated as a non- Newtonian fluid (as Bingham plastic with a Bingham plasticity of 0.01Pa.s) and the required yield stress of these fluid will be determined to obtain the same slopes as in the case of conceptual example 1 (Newtonian open channel flow). In order to do that, the Reynolds number expressions (Newtonian & non-Newtonian) will be equated to each other and will be solved for the yield stress, τy. Recall that the Darcy-Weisbach equation is applicable for non-Newtonian fluids for the determination of head losses of a uniform open channel flow. The re-arranged version of Darcy-Weisbach equation to obtain the channel slope was as follows (equation 2.11)

fV 2 S = 8gRH In conceptual example 1, there were constraints on parameters such as the discharge and the cross-section of the channel (in order to have an open channel equivalent of a pipe flow, see section 2.5 for more details). As a result, the only parameter that is going to be affecting the channel slope is the friction factor. Knowing that the friction factor is a function of Reynolds number, in order to end up with the same slope value, one needs to equate the friction factors (or the Reynolds numbers for the flow). Equating Reynolds numbers for Newtonian and non-Newtonian versions of the viscous liquid (ρ=1950 kg/m3, µ=1.95 Pa.s) yields

8ρV 2 4ρV R Re = = H 2V n µ τ + µ y R H 8 1950 1.2552 4 1950 1.255 0.038 × × = × × × 2 1.255 1.95 τ +0.01 × y 0.038

τy = 128.14P a 25 2.6. Non-Newtonian Fluid & Suspension Flow

The calculations demonstrate that with the material properties τy=128.14 Pa and µB=0.01 Pa.s, the flow of the viscous liquid is going to have the same properties summarized in table 2.2. Therefore, for non-Newtonian fluids, it is possible to conclude that high slope rates for open channel flows can be associated with high yield stresses. The slope of the flow for the viscous liquid (with a yield stress 128.14 Pa) was found to be around around 18%.

CHAPTER 3 Transportation of Tailings Slurries

Tailings material contains solid particles in the liquid mixture. Therefore, the transportation and ﬂow characteristics of the slurry are controlled not only by the liquid portion, but also by the solid particles present in the mix. In the coming sections of this chapter, the properties of solid-water mixtures of key interest are going to be presented.

3.1 Solid-Water Mixture Parameters

3.1.1 Solid Content & Density Solid content is often deﬁned in terms of percentage and can be expressed as either concentration by weight (Cw) or concentration by volume Cv. It is possible to convert the concentration by weight to concentration by volume (and vice versa) provided that the relative density of the solids in the mix is known. Concentration by weight is given as

Ms Cw = (3.1) Mw + Ms

Where Cw is the solid concentration by weight, Ms is the mass of solids and Mw is the mass of water (or the mass of the liquid in the slurry mixture). In soil mechanics the water content is deﬁned as

M w = w (3.2) Ms Substituting equation 3.2 in equation 3.1 yields 1 C = (3.3) w 1+ w

27 Transportation of Tailings Slurries 28

The formula to convert the concentration by weight to concentration by volume is presented below

C C = w (3.4) v S C (S 1) s − w s − Where Cv is the solid concentration by volume, Ss is the relative density of solid particles and Cw is the solid concentration by weight. The density of the solid particles in a tailings mix is generally around 2700-3000 kg/m3 depending on the ore type. The density of the slurry, ρ, is related to the volumetric solids concentration in the following way

ρ = ρ0 [1 + C (S 1)] (3.5) v s − Where, ρ0 is the density of water, Cv is the solid concentration by volume and Ss is the relative density (or the speciﬁc gravity) of solid particles. The density of the slurry kg 3 with properties of Cv=48.5% and Ss=2.85, can be calculated as 1900 /m with respect to equation 3.5.

3.1.2 Particle Size Distribution The particle size distribution of the solids in the tailings slurry is of key interest. The particle size distribution curve is a simple semi-logarithmic graph where the percentage by mass which smaller than a certain size is plotted against that particular particle size (see figure 3.1). The size at which %50 of the particles are finer is denoted as d50. Similarly, the size that the 90% of the particles are finer is denoted as d90. For the discussions which will be introduced in the following chapters, d50 and d90 are of major importance. The size d50 is sometimes referred as the characteristic, the average or the median particle size as well.

3.2 Classiﬁcation

3.2.1 Settling & Non-Settling Slurries A classification based on the particle size distribution and the amount of solid particles present in the mix is significant as the presence of solid particles and their concentration play a vital role in many aspects of the slurry behavior. The rheology of the slurry, as well as the flow properties and the deposition velocity (the velocity at which the solid particles start to settle down in the channel bed instead moving along the path of flow) are highly dependent on the solids concentration. It has been stated that the solid concentration has a significant effect on whether the slurry is going to be behaving as settling or non-settling. To further demonstrate the effect of the solid concentration, consider a mixture in a transparent column that is stirred 29 3.2. Classification

Figure 3.1: Representative particle size span for tailings (Engman, et al., 2004)

to homogeneity and thereafter left to settle. The progress of the clear water interface is then recorded in time. The time history results for a tailings slurry in figure 3.2 demon- strates the strong effect of solid concentration on the homogeneity of a tailings slurry. At volumetric concentration values below about 10%, the interface quickly progresses down. The water only appears at the upper portions with relatively small layer thickness after several hours when the solid concentration approaches to 40% (Andreasson, 1989). Figure 3.3 provides regions (or intervals) for settling (heterogeneous) and non-settling (homogeneous) pipeline pumping characteristics based on the particle size distribution and the relative density of the solids in the mix (Aude, et al., 1971). Generally speaking, slurries dominated by particles larger than 40µm with maximum particles from a few hundred µm to very large sizes can be defined as settling, where large particles may slide along the bottom of the pipe (Sellgren, 2010). Truly non-settling slurries can be treated as homogeneous fluids for clay-sized particles, i.e. less than a few microns in diameter. The suspension may have Newtonian viscous properties or non-Newtonian rheological properties along with a yield stress, especially at relatively high solids concentrations (Sellgren, 2010). In most industrial applications it should be noted that it is difficult to classify the slurry as non-settling or settling. The fine particle fraction (less than about 40µm) and the liquid may form a nearly homogeneous “carrier fluid” slurry with non-settling behavior (Sellgren, 2010). Slurries in mineral processing typically have average particles sizes of 20 to 100µm with Transportation of Tailings Slurries 30

Figure 3.2: Time history of settling at diﬀerent concentrations (Andreasson, 1989)

Figure 3.3: Classiﬁcation of slurries based on the particle size and the relative density (Aude, et al., 1971)

maximum sizes of up to 500 to 1000µm. Coarser tailings products may have average sizes of 50 to 100µm. With volumetric concentrations varying from a few per cent up to and over 40%, the task of classifying the slurry becomes rather diﬃcult. Therefore, slurries having such conﬁgurations are generally termed as complex slurries because of the fact that they cover an intermediate area between homogeneous and heterogeneous (“non- settling” and “settling”, respectively) type of behavior (Sellgren, 2010). 31 3.2. Classification

In conventional tailings disposal, the solid concentration of the slurry generally ranges between 5-20%. This results in a heterogeneous (or settling) behavior of the tailings slurry if all the particles are not very fine, say less than 20µm. In order to obtain pseudo-homogeneous or homogeneous (non-settling) behavior for placement without segregation, the volumetric solid concentration should exceed 40% (often 45%) for the type of tailings considered in this work. Finally, figure 3.4 further illustrates the concept of homogeneous and heterogeneous slurries (non-settling and settling) in terms of distribution of particles and the concentration profile.

Figure 3.4: Concentration proﬁles for diﬀerent types of slurries. (After Sellgren, 1982)

3.2.2 Deposition Velocity

From a sediment transport point of view (which can be applied to the case of tailings slurries), deposition velocity is defined as the minimum velocity in pipe or open channel flows at which the solid particles start to settle in the pipe or channel bed. At velocities larger than this deposition velocity, the particles will keep moving along the direction of flow without any deposition/sedimentation occurring. Deposition velocity is also referred as the minimum transport velocity or the critical velocity in the literature. Figure 3.5 is suitable for the determination of the deposition velocity provided that the particle size and the pipe diameter values are known. There are a variety of equations available to calculate the deposition velocity for pipe flows in literature. The equation presented by (Wasp, et al., 1979) was found to be suitable for the open channel flow of tailings flows (Fitton, 2007) as will be discussed in the following chapters. Transportation of Tailings Slurries 32

Figure 3.5: Graphical solution for the determination of the deposition velocity based on pipe diameter and mean particle size (Thomas, et al., 2011)

1/6 1/2 1/4 d 2gD (ρs ρ0) Vc =3.8Cv − (3.6) D ρ0 Where, Cv is the solid concentration (% by volume), d is the mean particle size diameter (d50), D is the pipe diameter, g is the gravitational acceleration, ρs is the density of solid particles, ρ0 is the density of the carrier fluid. It should be noted that the equation 3.6 is valid for pipe flows. However, with the substitution D=4RH (RH is the hydraulic radius for an open channel) the equation can easily be converted to be applied for open channel flows. The deposition velocities for a tailings slurry with d=0.05 mm, Cv= 20% and ρs=2800 kg/m3 corresponds to 1.34 and 2.14 m/s for D=0.1 and 0.4 m, respectively. m Corresponding values at Cv=45% are, 2.61 and 1.65 /s, respectively. The calculations demonstrate that the effect of the hydraulic diameter and the volumetric concentration on deposition velocity is not strong. Even though the hydraulic diameter is reduced by 75% (from 0.4 to 0.1) the change in the deposition velocity is around 37%. Similarly, doubling the volumetric concentration does also not cause any significant differences. CHAPTER 4 Placement of Tailings Slurries

Upon discharging from a pipe or launder, the tailings slurry will be undergoing an open channel flow through cross-sections which the material forms by itself by eroding the base material of the storage area. Immediately after leaving the pool, the state of flow is normally supercritical, see figure 4.1.

Figure 4.1: Schematic representation of a slurry ﬂow upon leaving the pipe (After Williams, 2011)

As the material progresses through the naturally occurring channels, the ﬂow undergoes hydraulic jumps and the state of the ﬂow shifts to sub-critical. In the last phases of the

33 Placement of Tailings Slurries 34

flow, tailings slurry gradually spreads and moves in the form of thin flow sheets. At this stage, sheets come to a halt and the deposition takes place (Simms, et al., 2011). Deposition (or settlement of the fine particles in the mix) does not occur during the open channel phases. The open channel flow is a means to transport the material to the final stage with a minimum potential energy configuration where the solid particles settle down and start to dry out and the beach profile slowly starts to form (Williams, 2011).

4.1 Slurry Deposition

The depositional behavior of a tailings slurry can be approached in various ways. Some researchers have chosen to utilize small scale ﬂume experiments; some have tried the slope stability/equilibrium concepts from geotechnics, while others have tried to apply ﬂuid mechanics in an attempt to demonstrate the depositional behavior of slurries (Williams, 2011).

4.1.1 Geotechnical (Slope Stability/Equilibrium) Approach

Angle of Repose (φr) From a geotechnical point of view, the angle of repose is defined as the natural slope of soils. In other words, angle of repose is the steepest angle for a slope to remain static (i.e. without sliding). For slope angles those are larger than the angle of repose, the equilibrium can no longer be maintained and as a result, sliding will take place. A more practical definition of the angle of repose can be given as; when the material is slowly poured on a horizontal surface, it will come to an equilibrium forming a conical shape on the surface. The angle of repose is defined as the angle between the surface of this cone and the horizontal. Figure 4.2 illustrates the concept The angle of repose is an important parameter for soils as it can be interpreted as the critical angle before the sliding occurs. For dry sand and ordinary soil, the angles of slope are given as 31◦ and 45◦, respectively (Braja, 2010). If the stability and the equilibrium of forces acting on the soil particles are considered, it is possible to formulate the angle of repose. By definition, angle of repose is the steepest slope before sliding is initiated. Therefore at the angle of repose, the component of stress trying to move the particles along the slope surface is equal to the shear strength of the material (see figure 4.3).

σs = σg sin φr (4.1)

Where σg is the stress due to gravitational acceleration and σs is the stress trying to move the particles (or simply the shear stress). At the angle of repose

σs = τs (4.2) 35 4.1. Slurry Deposition

Figure 4.2: Angle of repose

Figure 4.3: Force equilibrium at angle of repose

If equation 4.1 is substituted in equation 4.2

τs = σg sin φr (4.3)

Where φr is the angle of repose.

Flow Equilibrium A simplified geotechnical analysis can be used to estimate the sheet flow thickness for a given deposition slope for a flow width infinite width, i.e. a depth much smaller than the width. As the flow slowly comes to rest and eventually stops moving, the force equilibrium can be established in order to determine the deposition slope. This is similar to the angle of repose concept. If the force equilibrium is established for a sheet flow with a thickness of y, the driving Placement of Tailings Slurries 36

Figure 4.4: Sheet ﬂow equilibrium (After Robinsky, 1999) component of the gravitational stress needs to be equal to the yield stress of the ﬂuid (equation 4.3).

τs = σg sin φ

The gravitational component of the stress for the sheet ﬂow can be calculated as

σg = ρgy (4.4) Where, ρ is the density of the liquid and y is the thickness of the sheet layer. Substi- tuting equation 4.4 in equation 4.3 yields

τy = ρgy sin φ (4.5) Equation 4.5 has been proposed for predicting the deposition slopes by Blight & Bentel (Blight, et al., 1983). In fact, equation 4.5 is the statement of the balance between the resistance forces and the gravitational force component of the uniform ﬂow in another form, as discussed in chapter 2 given in equation 2.2

τP τ S = w = ρgA ρgRH

Recall that for cross-sections where B y, R can be taken as the depth (y). Hence, ≫ H equation 2.2 can be rewritten in the following form (equation 2.13)

τ = ρgyS

However, the problem with the formula that Blight & Bentel proposed is the fact that the layer thickness of the sheet ﬂow (y) is not known. 37 4.1. Slurry Deposition

4.1.2 Conceptual Example 3 The following example has been provided in order to demonstrate the applicability of the angle of repose concept to the sheet flow equilibrium and the depositional behavior of the slurry. Two cases will be considered. In the first case where the sheet flow equilibrium is considered, the stability/balance is governed by the yield stress of the slurry. In the second case (once the slurry has been deposited in layers and has started to dry out), the equilibrium is governed by the shear strength (or cohesion) developed as the material desiccates.

Figure 4.5: Depositional behavior of the tailings in the form of a slurry and in desiccated form

If the sheet flow is considered, for the given configuration (a slope value of 4%, flow thickness of 0.1m and a bulk density of 1800 kg/m3) the yield stress of the slurry is calculated as (equation 2.13)

τy = ρgy sin φ

τ = 1800 9.81 0.1 sin 2.3◦ 70P a y × × × ≈ Similarly, if the equilibrium when the slurry desiccates and stacks in layers; for the given conﬁguration (a slope value of 20%, a layer thickness of 1m and solids density of 2200 kg/m3) the shear strength can be calculated by making use of the slope stability concept. Placement of Tailings Slurries 38

τ = ρgy sin φ

τ = 2200 9.81 1 sin 11.3◦ 4.23kP a × × × ≈ The assumption with the latter case is that the dried tailings stack is at the angle of repose (11.3◦ or S=20%). The example provides rough information about the shear strength development for the tailings material upon drying. Compared to the slurry form, the shear stress development of the dried tailings is signiﬁcant. The work carried out by Bohlin & Jonasson (2002) provides more details on the shear strength of the dried tailings stacks. Upon applying a direct shear test on a dried tailings sample they have determined the angle of friction to be around 23◦ - 26◦ and the shear strength to be varying in between 7-10 kPa. CHAPTER 5 Adoption of the Rheology-Oriented Model by Fitton

Fitton (2007) has important contributions for the prediction of beach slopes. In the context of his PhD work, he has carried out large scale ﬁeld experiments as well as small scale laboratory experiments in order to investigate the depositional behavior of thickened tailings. Fitton then tried to validate the majority of the available beach slope prediction methods in literature with his experiment results.

5.1 Fitton’s Work

5.1.1 Model Development Experimental Setup

Fitton performed numerous experiments in an attempt to have a better understanding of the depositional behavior of tailings slurries. His experimental procedure consists of two stages. The first stage is based on large scale experiments carried out in the field and the second stage takes place as a laboratory scale flume tests. Fitton defines the main and the secondary objectives of the large scale field experiments as; to observe the effects of the slurry concentration and the discharge on the deposition slope, to take velocity and depth measurements within the flume to identify the state of flow and to determine whether uniform flow conditions have been reached or not and finally to take rheological measurements in order to determine the non-Newtonian model parameters for the slurry (Fitton, 2007). Fitton carried out the field experiments in two different locations in Australia. The

39 Adoption of a Rheology-Oriented Model by Fitton 40

first is at the Peak Gold Mine in Cobar and the latter is at the Sunrise Dam Gold Mine. He used the following flume given in figure 5.1 for the large scale field measurements.

Figure 5.1: Schematic representation of the ﬂume that is used in the ﬁeld experiments for Fitton’s work (Fitton, 2007)

A special attention has been paid in order to come up with right dimensions for the flume so that the flow conditions in the field can be simulated as closely as possible. To this end, a flume of 10m length has been decided to be long enough for the uniform flow conditions to develop and has been constructed (see Fitton’s work for the details on the experimental set up). With the help of the apparatus, given in figure 5.1, 9 and 41 equilibrium slopes have been recorded for Cobar and Sunrise Dam experiments respectively (Fitton, 2007). The second stage of the experimental procedure took place in a laboratory environment to further investigate the effects of scaling (Fitton, 2007). Table 5.1 is a small excerpt from Fitton’s experiment results. The data have been obtained from large scale field measurements with the help of the flume given in figure 5.1 As provided in table 5.1, Fitton has experimented with two different tailings slurries. Tailings slurry from the Sunrise experiment has solids concentration by weight varying between 25-63%, mean particle diameter of 16 µm, d90 of 145 µm, solids density of 2800 kg/m3. Similarly, the slurry from Cobar experiment has a solids concentration by weight of 46-55%, a mean particle diameter of 7.8 µm, d90 of 55 µm, a solids density of 2800 kg/m3 and water as the carrier fluid. 41 5.2. Fitton’s Semi-Empirical Beach Slope Model

Table 5.1: Excerpt from Fitton’s experimental data

Flow Rate, Q (l/s) Cw (%) Flow Depth (mm) Equilibrium Slope (%) Sunrise Dam 11.94 63.4 48 4 13.405 62.3 62 2.8 13.95 63.4 53 2.8 14.12 64.2 53 3.3 15.22 63.,9 70 2.3 16.735 63 62 3.3 16.9 63.8 69 2.5 Cobar 8 57.2 43 3 11.5 54.6 54 2.6 14.5 55.5 57 2.53 15.5 55.5 57 2 16.1 57.7 67 2.32 19 55 73 1.68

After changing the discharge into the flume (ranging from 1.9-19 l/s), Fitton adjusted (tilted) the flume (for that particular value of discharge); so that a uniform channel flow can develop in the flume. Once the uniform conditions have been reached, he has recorded the depth of flow and corresponding channel slope. Fitton further used the experimental data from Cobar and Sunrise experiments to formulate his own beach slope prediction model.

5.2 Fitton’s Semi-Empirical Beach Slope Model

Based on his experimental data Fitton has formulated three beach slope prediction models of his own, each having different purposes, advantages and disadvantages. In an attempt to come up with a method which has the best prediction capability, he then decided to modify his second model (which he refers as “a-priori model” in his work) so that the relationship obtained at the end gives the best prediction (or the best fit for the experimental data). His third model namely, “a semi empirical beach slope model” will be the focus of this section. The details of how the method works under which conditions will be provided in the next parts. In his work to establish an analytical relationship to be able to predict the beach slopes, Fitton starts with an attempt to establish an equation based on the available information on flume design concepts. A flume is a custom built tank that can be used Adoption of a Rheology-Oriented Model by Fitton 42 in a laboratory environment to carry out open channel flow experiments. The idea was to come up with an expression that makes it possible to obtain a relationship which is applicable to accurately predict the slopes for his field and laboratory experimental data. After several attempts, Fitton realized that the flume design concept is not reliable enough to predict the slopes overall, especially when the amount of discharge reaches low values (Fitton, 2007). Therefore, instead of going with the flume design approach, Fitton then decided to go with the sediment transport approach. Due to the fact that the tailings material contains solid particles in suspension in the mix, the idea is to come up with a minimum flow velocity (at which the solid particles in the mix start to settle down) equation. By making use of the sediment transport approach, the idea is to try to calculate the water depth in the naturally forming open channel for the slurry flow so that the flow velocity in the channel equals to the minimum flow velocity. Right at this point, the solid particles will start to settle down, forming the beach and the depth that the equilibrium is reached is going to be used to calculate the final slope (or the equilibrium slope for the tailings beach). One of the major differences between Fitton’s a-priori model and the semi-empirical model is that the semi-empirical model allows the classification of the tailings material as segregating and non-segregating (a behavior which observed often on the field).

5.2.1 Segregating vs Non-Segregating Slurries

A segregating type of slurry is defined as a mix in which the coarse particles in the suspension start to settle before the fine particles. For non-segregating slurries, both the fine and the coarse particles are assumed to settle down at the same rate (Fitton, 2007). The classification of whether the tailings material is going to behave as segregating or non-segregating slurry depends on the solid concentration of the mix. Fitton distinguishes these two types of slurries by making use of a parameter termed as the segregation threshold. The point of transition from segregating to non-segregating behavior is known as the segregation threshold. It should be noted that the segregation threshold values of various types of tailings slurries are going to be different from one another, as it is heavily dependent on the ore type, mineral processing method, etc. Figure 5.2 is a graphical representation of the segregation threshold concept. According to this plot first introduced by Robinsky, at relatively higher solid concentrations tailings slurry has a tendency to behave in a homogeneous way. The coarse and fine particles will be depositing at the same rate resulting in a non-segregating type of behavior. At relatively lower solid concentrations however, the coarse particles will be a depositing before the fine ones. Therefore the slurry will be behaving in a heterogeneous way. As a result of this, particle sorting takes place upon deposition; which is represented by the 43 5.2. Fitton’s Semi-Empirical Beach Slope Model

Figure 5.2: Graphical representation of the difference between segregating and non-segregating slurries in terms of depositional behavior (After Robinsky, 1999) dashed curve on figure 5.2. For segregating slurries, high deposition slopes can be obtained as a result of the relatively early deposition of the coarse particles. This high slope beach profile however, cannot be maintained and will gradually decrease along the course of deposition once there are no course particles left in the mix. For non-segregating slurries, it is possible to operate with high deposition slopes due to the homogeneous nature of the slurry as explained in chapter 3. Generally speaking, thickened tailings slurries can be considered as non-segregating (homogeneous) slurries due to their higher solid concentrations.

5.2.2 Minimum Transport Velocity Equations The definition of the minimum transport velocity can be referred as the deposition velocity as defined back in section 3.2.2. To restate, the deposition velocity (or the minimum transport velocity) can be defined as the mean flow velocity at which the deposition of the solid particles present in the tailings slurry takes place. Due to the significant behavior difference based on the classification whether the tailings material is of the type segregating or non-segregating, two different minimum transport velocity equations were given for each type of material. In order to come up with the eventual formulations for the deposition velocities, Fitton have used 18 different equations available in literature and compared these equations with his large (Cobar and Sunrise Adoption of a Rheology-Oriented Model by Fitton 44

Dam) and small (laboratory) scale experiments. As a result, for segregating slurries, the minimum transport velocity equation (by Wasp et al.) is found to give the strongest correlation. The formula was given as equation 3.6 in chapter 3 and is restated below

1/6 1/2 1/4 d 2gD (ρs ρ0) Vc =3.8Cv − D ρ0 Fitton determined the minimum transport velocity equation for non-segregating slurries by fitting a curve to the parameter which showed the highest correlation (Fitton, 2007). After going through different parameters, Fitton concluded that the Reynold’s number for a Bingham plastic model representation has the strongest correlation with the mean flow velocity (Fitton, 2007). The equation of Reynold’s number for Bingham plastic is as follows

ρV RH ReBP = (5.1) µB

Figure 5.3: Relationship between the ﬂow velocity and Bingham Reynold’s number (equation 5.1) (Fitton, 2007)

The equation of the ﬁt given in ﬁgure 5.3 was found as

ρV R V =0.145ln H (5.2) c µ B 45 5.2. Fitton’s Semi-Empirical Beach Slope Model

Where, ρ is the density of the slurry, V is the flow velocity in the open channel, RH is the hydraulic radius, µB is the Bingham viscosity. Fitton suggests the use of equation 5.2 for determining the minimum transport velocity for non-segregating slurries. Equation 5.2 gives deposition velocity values within the range of 0.8 to 1.4 m/s for d50 up to about 75 µm and DH from about 0.1 to 0.4 m. Another method to determine the deposition velocity based on the graph given in figure 3.5 also yields similar results for the same slurry properties. As long as the flow remains non-segregating, the average particle size does not come in the calculations of Fitton’s model. However, the particle size distribution influences viscometric measurements and rheological results as well as the channel roughness coefficient, ks, for friction loss calculations.

5.2.3 Flow Resistance Equation For the determination of the head losses (and thus the friction coeﬃcient), Fitton proposed the use of the Darcy-Weisbach equation which has been presented in chapter 2 (equation 2.5). The Darcy-Weisbach equation can be converted to the form (equation 2.11) to obtain the channel slope.

fV 2 S = 8gRH Furthermore, the sediment transport approach dictates that if the velocity of the flow in the open channel is equal to the minimum transport velocity, Vc, (the point where the settling of the solid particles begin) the slope obtained from the Darcy-Weisbach equation for this critical value of velocity, will be the deposition slope (i.e. the equilibrium slope of the tailings material in the storage area). The determination of the friction factor, f, can be done in various ways (as described in chapter 2). One might use the Moody chart in graphical form. The other option is to use equations based on the Moody chart if the state of the flow is known (laminar or turbulent). For laminar flows, the friction factor is given as equation 2.8 in chapter 2. For the other regions (from transition to turbulent) of the Moody chart, the friction factor is given as (equation 2.9)

k 2.51 1 = 2 log s + √f − 14.8R Re√f H The first thing to note in the Colebrook-White equation is that it is not possible to obtain the friction factor directly. An iterative procedure needs to be undertaken in order to determine f. The values of ks for pipes and channels made of different types of material can be found in various sources. However when the open channel flow of the tailings slurry is Adoption of a Rheology-Oriented Model by Fitton 46

considered, the definition of ks needs to be done in terms of the grain size of the solids in the mix as these particles will be forming the channel bed for the flow of the slurry (Fitton, 2007). Different recommendations are available for the relationship between the particle size and the surface roughness in literature.

Fitton experimented with the values of ks ranging between d50

Fitton concluded that the relationship ks = 2d90 shows the strongest correlation and proposed the use of it for his model. 5 A direct solution to the Colebrook-White equation is available for the ranges of 10− < 8 ks /4RH < 2 & 4000

8ρV 2 Re = 2V n τ + µ y R H 5.2.4 Determination of the Channel Shape for the Open Channel Flow For the determination of the hydraulic radius, the channel geometry needs to be known. In the previous sections, it has been reported that upon leaving the pipe, the tailings slurry will be undergoing an open channel flow. The slurry will be eroding the base material and will be naturally creating its own open channel cross-section. It will obviously be incorrect to argue that a fixed cross section is going to be occurring at all times (as the process is heavily dependent on the bed material as well as the properties of the tailings slurry). Furthermore, even if such a cross-section exists it is also not possible to say that the cross-section will remain unchanged along the path of the flow. Regardless, an estimation needs to be done to further simplify the nature of the problem and to proceed with the remainder of the calculations. After having tried several cross-sections (rectangular, semi-circular, elliptical etc.) and different aspect ratios, Fitton concludes that a parabolic cross section, with an aspect ratio of 5.5:1 (the width of the channel is 5.5 times greater than the water depth in the channel) gives the best result (or the closest fit) for his experimental data. In the parametric study of his work, Fitton further found out that the cross-section has a little to none influence on the resultant slope. Instead, he found out that the important 47 5.2. Fitton’s Semi-Empirical Beach Slope Model parameter seems to be the aspect ratio (width to depth ratio) of the channel. In other words, as long as the aspect ratio of 5.5 is maintained there is a little difference between the beach slopes for parabolic and rectangular open channel cross-sections (Simms, et al., 2011).

5.2.5 Running the Model Brief information on how Fitton came up with his model and how it works was given in the sections above. This section will be dealing with the required input parameters to be able to use the model and the prediction sequence in order to obtain the equilibrium (the resultant) beach slope.

Input Parameters Below is a summary of the input parameters needed to be able to run the model

m3 Q, the amount of discharge ( /s),

Cv, solids concentration by volume (%),

d, median particle size diameter of solids in the tailings slurry (referred as d50 as well) (m),

d90, the 90th percentile diameter of solids in the tailings slurry (m),

kg 3 ρ0, the density of the carrier ﬂuid ( /m ),

kg 3 ρs, the density of the solid particles in the tailings mix ( /m ),

τy, µ and n, the rheological ﬁt constants for the tailings slurry to be modelled as a Herschel-Bulkley Fluid,

µB, Bingham viscosity (if the tailings slurry is non-segregating)

Prediction Sequence Once all the required parameters are established one can begin to calculate the predicted beach slope. The prediction sequence for non-segregating slurries is as follows

Start with an initial guessed value of ﬂow depth,

Assume a cross section (rectangular or parabolic with an aspect ratio of 5.5)

Based on the assumption calculate the hydraulic radius RH ,

Calculate the mean ﬂow velocity V (simply, V=Q/A), Adoption of a Rheology-Oriented Model by Fitton 48

Calculate the minimum transport velocity for non-segregating slurries with respect ρV R to V =0.145ln H c µ B

Adjust the depth of ﬂow until the condition V = Vc is satisﬁed, 8ρV 2

Calculate the Reynold’s number according to Re = 2V n τ + µ y R H

1 ks 2.51

Calculate the friction factor, f, = 2 log + √f − 14.8R Re√f H fV 2

Calculate the slope with respect to S = 8gRH

The slope value calculated in the previous step gives the equilibrium slope (the ﬁnal beach slope).

5.3 Validation with the Field Data

The slope prediction model developed by Fitton, has then been used to predict the deposition slopes for five different thickened tailings facilities and the accuracy of the model is evaluated in a recent study by Seddon & Fitton (2011). Four of these facilities (namely, Ernest Henry, Century, Peak and Sunrise) are located in Australia and one in Iran (Miduk). By using it for these five facilities each having different slurry characteristics and discharge rates, the aim was to see the prediction capabilities of the model. For example, d50 and d90 values for the Miduk facility is given as 35 µm and 120 µm, respectively. Corresponding values for Century facility is 9 and 50 µm, respectively. Similarly, the solids concentration for Miduk was given as 52-58% where as the corresponding values for Century and Ernest Henry were 51-57% and 66-73%, respectively. The performance of the model under such varying conditions was summarized in figure 5.4. 49 5.3. Validation with the Field Data

Figure 5.4: Summary of slope predictions (Seddon & Fitton, 2011)

As can be seen from ﬁgure 5.4, while the overall predictability is reasonable, some deviations also exist. Seddon & Fitton (2011) state that these deviations are mainly related to the inaccuracies for the determination of rheological parameters and conclude that in cases where the slurry characteristics are well-deﬁned, Fitton’s beach slope prediction model provides reasonable estimates.

CHAPTER 6 Results & Discussion

This chapter is devoted for the application of Fitton’s semi-empirical beach slope model and for the discussion of results. The feasibility of the thickened tailings disposal system relies on having deposition slope values of around 2-4% which, in turn, gives the opportunity to be able to fill more volume per unit storage surface area. In order to achieve this, generally volumetric solid concentrations larger than 45% is required to maintain an even slope with no segregation of particles and no drainage of water occurring (Wennberg, et al., 2008). By utilizing Fitton’s semi-empirical beach slope prediction model, the effect of different discharge rates as well as the effect of model parameters to represent slurry rheology (yield stress & viscosity) on the deposition slope will be investigated.

6.1 Model Validation

The calculation procedure of Fitton’s model is iterative. Several computational steps need to be carried out to obtain the depth of flow at which the flow velocity is equal to the minimum velocity given by Fitton’s empirical equation. To be able to experiment with a new set of data and to carry out new simulations, Fitton’s semi-empirical beach slope model has been rebuilt according to the descriptions given in Fitton’s work with the help of MATLAB software. In order to make sure that the model which has been rebuilt for the use in the context of this thesis work was operating as intended, the experimental data of Fitton’s work have been simulated and the results of the simulations were compared with the experimental data recorded by Fitton. The results are summarized in figure 6.1. From figure 6.1, it is possible to see how close the calculated slope values with the model are located around the 1 to 1 fit line. It should be noted that the simulations results have been compared with the experimental measurements on the field; not with the results obtained from Fitton’s simulations due to the fact that no information could

51 Results & Discussion 52

Figure 6.1: Model validation with the experimental data

be found related to the simulations carried out by Fitton. It is then decided that the model was working accurate enough to carry on further with the simulations.

6.2 Properties of the Tailings Material & Assumptions for the Simulations

Fitton’s model will be used to simulate the depositional behavior of thickened tailings slurries having a volumetric solids concentration of 46% (71.2% by weight). This value will be used to represent homogeneous (non-segregating) conditions for a tailings product with d50 and d90 values of 50 and 150 µm, respectively. A solids density of 2900 kg/m3 is used. Similar non-settling conditions have been noted from the work of Fitton for slurries having lower solid concentrations (about 60% by weight) with d50 being around 20 µm. In fact, the particle size does not appear explicitly in any relationship in Fitton’s slope prediction model for non-segregating slurries. In simulations which will be discussed further on, the geometry of the naturally occurring open channel for the slurry flow is assumed to be rectangular (with an aspect ratio of 5.5). This allows for simplifications in the calculation of flow parameters of particular interest. As discussed in chapter 5, the geometry of the channel section has a very small impact on the results as long as the aspect ratio of 5.5 is kept. Furthermore, friction factor calculations have been carried out by making use of the Swamee-Jain equation (equation 5.3) instead of Colebrook-White equation (equation 2.9) proposed by Fitton. The Swamee-Jain equation provides reasonable approximations 6.2. Properties of the Tailings Material & Assumptions for the 53 Simulations of the Colebrook-White equation for the geometry, roughness and Reynolds numbers considered in this study. Fitton represents the rheology of the tailings slurries by a three-parameter rheological approach, the Herschel-Bulkley model. The two-parameter Bingham model has been used here as an approximation and simplification due to the fact that Fitton considers turbulent flow only and relates the minimum velocity requirement to the Bingham viscosity for non-segregating slurries. His assumptions of turbulent conditions were based on field and large scale flume test observations and measurements. Non-Newtonian properties have less severe effects under turbulent conditions. In such cases, Newtonian methods may apply for determining the turbulent friction losses, i.e. the friction factor can be calculated by making use of the Reynolds number calculated with the Bingham viscosity, µB, and thus neglecting the yield stress. This may apply for slurries which do not have overly high solid concentrations but still behave in a non- segregating way (Thomas, 1963). The rheological representations of the thickened tailings slurries to be simulated have been given with the rheogram in figure 6.2. The yield stress of the slurries vary from 0 to 30 Pa and the Bingham plasticity values of 0.01, 0.05 and 0.1 Pa.s have been simulated in order to discuss the effects of rheological parameters.

Figure 6.2: Rheological representation of diﬀerent slurries to be simulated

Bingham model is the simplest way of representing the rheology of non-Newtonian fluids. As described in detail in chapter 2, the fluid is represented by a yield stress and a viscosity which is assumed to be constant once the flow is initiated. The intersection Results & Discussion 54

point of the graph and the vertical axis (shear stress) is deﬁned as the yield stress (τy) and the slope of the graph gives the viscosity of the ﬂuid.

6.3 Results & Discussion

6.3.1 Results Observed values of deposition slopes from thickened tailing facilities all around the world are located within the range from 1% up to 6%. Reported averages are, Kidd Creek (Canada) - 1.5%, Peak (Australia) - 1.5-2%, Warkworth (Australia) - 5% and Osborne (Australia) - 3%, respectively (Data gathered from Fitton, 2007). 3 Simulation results for slurry flow rates from 25 to 400 m /h will be presented based on kg 3 Cv=46% and ρs=2900 /m giving slopes up to about 6%. Experimented yield stress and Bingham viscosity values are up to 30 Pa and 0.1 Pa.s, respectively. Flow rates of 25 and 3 400 m /h mean capacities of about 19 and 300 dry tones of tailings per hour, respectively. The pipeline diameters to transport the slurry to the disposal area may vary from 0.075 to 0.35m. The effect of different discharge rates along with the model parameters on the deposition slope will be provided. The general trends for each parameter are summarized in figures 6.3 and 6.4. More detailed information on simulation results are given in the appendices. Table 6.1 summarizes the deposition slope values calculated for different set of operating parameters. For certain combinations, the slope values have not been calculated because the model considers only non-laminar flow cases where Re>500.

Table 6.1: Summary of simulation results for µB=0.05 Pa.s

m3 S (%) Q( /h) y (m) V (m/s) RH(m) Fr τ y =0 Pa τ y =5 Pa τ y =10 Pa τ y =20 Pa τ y =30 Pa 400 0.129 1.21 0.095 1.08 0.57 0.85 1.03 1.31 1.53 200 0.093 1.16 0.068 1.21 0.79 1.14 1.37 1.73 2.03 100 0.068 1.11 0.050 1.36 1.10 1.52 1.82 2.29 2.68 80 0.061 1.09 0.045 1.41 1.23 1.68 2.00 2.51 2.94 50 0.049 1.05 0.036 1.52 1.54 2.05 2.42 3.03 - 25 0.036 1.00 0.026 1.69 2.14 2.75 3.23 4.02 -

From table 6.1 it is possible to note that the depth of flow (at which the critical deposition velocity takes place for a specific discharge value), remains the same regardless of the changes in the yield stress. This is simply because of the fact that the yield stress is not taken into account for calculation (equation 5.2) of the deposition velocity for non-segregating slurries in Fitton’s semi-empirical beach slope prediction model. Figure 6.3 suggests that with a constant Bingham viscosity of 0.05 Pa.s, the deposition slopes increase as the yield stress increases for a constant flow rate. For example, an 55 6.3. Results & Discussion

Figure 6.3: Relationship between the yield stress and the deposition slope

m3 increase in τy from 5 to 30 Pa increases the slope from about 1.5 to 2.7% at 100 /h. At 3 400 m /h, the corresponding slope values are 0.9 and 1.5%. Additionally, it follows from figure 6.3 that the discharge rate and the deposition slope is inversely proportional i.e. for increasing discharge rates the deposition slope will be lower. The decrease in slope with increasing flow rates (Q) at a constant yield stress is approximately related to Q with an exponent of 0.5 to 0.6. The influence of the yield stress and the discharge rates have been covered for µB=0.05 Pa.s in table 6.1. Tables 6.2 & 6.3 summarize the simulation results and the effects of Bingham viscosity for 0.01 and 0.1 Pa.s while figure 6.4 expresses the slope-discharge dependence for a constant yield stress where µB varies from 0.01 to 0.1 Pa.s

Table 6.2: Summary of simulation results for µB=0.01 Pa.s

m3 S (%) Q( /h) y (m) V (m/s) RH(m) Fr τ y =0 Pa τ y =5 Pa τ y =10 Pa τ y =20 Pa τ y =30 Pa 400 0.118 1.46 0.086 1.36 0.69 1.17 1.41 1.78 2.06 200 0.085 1.41 0.062 1.54 0.97 1.56 1.89 2.37 2.75 100 0.061 1.35 0.045 1.75 1.37 2.09 2.52 3.16 3.67 80 0.055 1.34 0.040 1.82 1.53 2.30 2.76 3.46 4.03 50 0.044 1.30 0.032 1.98 1.93 2.81 3.36 4.21 4.90 25 0.032 1.25 0.023 2.23 2.71 3.79 4.50 5.61 6.53

It follows from ﬁgure 6.4 with a constant yield stress of 20Pa, the deposition slope decreases for the increasing values of Bingham viscosity (from 0.01 to 0.1 Pa.s). The Results & Discussion 56

Table 6.3: Summary of simulation results for µB=0.1 Pa.s

m3 S (%) Q( /h) y (m) V (m/s) RH(m) Fr τ y =0 Pa τ y =5 Pa τ y =10 Pa τ y =20 Pa τ y =30 Pa 400 0.135 1.11 0.099 0.96 0.53 0.75 0.90 1.14 1.33 200 0.098 1.05 0.072 1.07 0.74 1.00 1.20 1.50 1.76 100 0.071 1.00 0.052 1.19 1.03 1.35 1.59 1.99 - 80 0.064 0.98 0.047 1.24 1.15 1.48 1.74 2.18 - 50 0.052 0.94 0.038 1.32 1.44 1.81 2.12 2.63 - 25 0.038 0.89 0.028 1.46 2.00 2.45 2.83 - -

Figure 6.4: Relationship between the Bingham viscosity and the deposition slope

3 decrease at 100 m /h is from about 3 to 2%, respectively. The findings expressed in figure 6.4 is related to Fitton’s minimum velocity equation (equation 5.2) ρV R V =0.145ln H c µ B The formula is defined in terms of Bingham plasticity. An increase in µ will reduce the required velocity and thus will increase the flow depth and the cross-sectional area. When these changes have been introduced in the slope calculations, a decrease in the deposition slope will be obtained. An increase in viscosity may lead to an increase in the particle carrying capacity of the flow thus it may mechanically justify the behaviour expressed in figure 6.4. It follows from figures 6.3 and 6.4 that a lower discharge rate means a higher deposition slope. This relationship introduces some flexibility when a higher slope is required. Under such conditions when relatively higher rates of deposition is required, placement can be carried out with several discharge points, i.e. spigotting, instead of having a single point discharge scheme, as discussed in chapter 1. 57 6.3. Results & Discussion

The sensitivity of the channel roughness coefficient, ks, has also been investigated. As described in chapter 5, in Fitton’s model the channel roughness coefficient was given in terms of d90 (ks=2d90). In the simulations, d90 was equal to 150 µm and thus ks=0.3mm. Smooth channel bed conditions with ks being equal to 0.05mm yielded a reduction in the deposition slope, however the reduction can be regarded as negligible in terms of model sensitivity. In addition, the effect of the channel cross-section has also been investigated and the results are given in table 6.4. Simulations have been carried out with the exact same properties given in table 6.1 for comparison purposes and the resulting deposition slopes were found to be almost identical. For example, the deposition slope for the slurry having the properties τy=10 Pa, µB=0.05 Pa.s and Cv=46 % for a rectangular channel was found 3 to be 2% at a discharge rate of 80 m /h. The corresponding deposition slope with the same properties of the slurry and a parabolic cross-section was found as 1.96 %. A similar trend can also be noted for other combinations as a result of a comparison between tables 6.1 and 6.4.

Table 6.4: Summary of simulation results for µB=0.05 Pa.s for a parabolic cross-section

m3 S (%) Q( /h) y (m) V (m/s) RH(m) τ y =0 Pa τ y =5 Pa τ y =10 Pa τ y =20 Pa τ y =30 Pa 400 0.16 1.22 0.097 0.55 0.84 1.01 1.28 1.50 200 0.11 1.16 0.070 0.77 1.12 1.35 1.70 1.99 100 0.08 1.11 0.051 1.08 1.50 1.79 2.25 2.63 80 0.07 1.09 0.046 1.20 1.64 1.96 2.46 2.88 50 0.06 1.06 0.037 1.50 2.01 2.38 2.97 3.49 25 0.04 1.00 0.027 2.09 2.70 3.17 3.94 -

6.3.2 State of Flow It follows from the results from tables given in the appendices, that the flows were supercritical for all simulations with Froude numbers varying between 1.3 and 2. Within that range, reported observations indicate an undular (even in the form of standing waves at times) flow behavior (see figure 2.5 on page 17). The critical flow conditions at Fr=1 for water result in unstable critical depth observations where several water depths may exist for a fixed rate of discharge. Haldenwang, et al., (2004) has also found that this effect for non-Newtonian kaolin slurry flows tended to move to a higher Fr of about 1.7 which is within the span obtained here. Fitton states that the Reynolds number values around 500, correspond to the lower limit for non-laminar flow while others suggest values of up to 8000 for truly turbulent transport of highly thickened tailings. Alderman & Haldenwang (2007) discusses that the transition zone may cover a considerable span of Reynolds numbers. Results & Discussion 58

In the case of a turbulent flow, the solid particles will be kept in suspension without any settling taking place. On the other hand, if the flow is laminar, the solid particles will start to settle and eventually deposit and begin to stack up due to the low flow velocity. Equation 2.21 is an established relationship for estimating the transition point for a Bingham type of slurry

V 22.5 τy/ρ T ≈ p The simulation results in tables 6.1-6.3 have given flow velocities varying between 1-1.5 m/s. For these flows to be turbulent with Re> 500, then the yield stress needs to remain below 10 Pa according to equation 2.21. For higher values of yield stress the flow would be laminar and larger particles will start to deposit. The above discussion may reflect the complexity of the situation resulting from the open channel flow of highly concentrated tailings slurries in the laminar-turbulent transition zone including the Froude number instabilities at critical depth.

6.3.3 Solid Concentration and Particle Size Distribution

Slurries having an average particle size, d50, varying between 20 to 75 µm may show the equivalent fluid behavior when transported at Cv below 25%. Equivalent fluid behavior can be defined as when the solids have a little effect on the friction factor calculations (Wilson, et al., 2006) i.e. the slurry friction factor is identical to the friction factor for water under same conditions. For such slurries, coarse particles settle out directly at high slope rates while water and finer particles will continue flowing and deposit at a relatively low channel slope due to the lower flow resistance. This “hydraulic sorting” of particles may form a concave beach slope profile. The beach slope profile with an upward concavity, often observed on the field, is mainly associated with the particle sorting. Hydraulic (or particle) sorting is a behaviour which is generally coupled to segregating slurries and the overall beach profiles of segregating slurries have a more pronounced concavity. Beach slope profiles for non-segregating slurries are more uniform and are “less concave” compared to the ones for segregating slurries. However, the concave beach slope profiles are also observed to a certain extent even for non-segregating slurries.

6.3.4 Sediment Transport Approach & Shield’s Diagram Fitton’s semi-empirical beach slope prediction model makes use of the sediment transport approach i.e. it uses a semi-empirical equation to calculate the minimum velocity during channelized ﬂow below which sedimentation takes place. The non-segregating model by Fitton is based on the observations that no deposition (sedimentation) takes place during the self-formed channelized ﬂow phase. Overall, it can be considered as the equilibrium between dynamic sedimentation and erosive processes. 59 6.3. Results & Discussion

A widely used method to predict sediment motion is the Shield’s diagram. The diagram is provided in ﬁgure 6.5.

Figure 6.5: Shield’s diagram to predict sediment motion (Chanson, 2004)

The aim of using Shield’s diagram is to see where the majority of the simulation results are located on the graph. Ideally, one would expect the results to be located at or around the shaded zone in ﬁgure 6.5. In order to use the diagram, one needs to calculate the Shield’s parameter given with the following equation

τ0 τ = (6.1) ∗ ρ(S 1)gd s − Where τ0 is deﬁned as the mean boundary shear stress and calculated as

τ0 = ρgy sin φ (6.2) However, once the necessary calculations were carried out to calculate the Shield’s parameters it was found that most of results were located at the upper portion of the graph where the diagram predicts sediment motion. As expressed by others, the Shield’s diagram concept was not meant to be used for thickened tailings slurries (Spelay, 2007). For high concentrated slurries, it can directly be seen that the Shield’s parameter on the Results & Discussion 60 vertical axis, τ , (given in equation 6.1) will be much larger compared to that of particles ∗ in a low concentrated ﬂow. As a result, shield’s parameter will be located at the upper portion of the graph, far away from the shaded zone of erosion/sedimentation inception. CHAPTER 7 Conclusions

The desired scheme of deposition for thickened tailings disposal can be defined as placement having conceptually even slope rates of 2-4% with no segregation of particles and no drainage of water taking place. Such deposition scheme can be obtained with a tailings slurry having a solids concentration by volume greater than 45% and an average particle size of solids less than 40 µm. Fitton’s model has been used to simulate slurry flow having properties d50 as 50 µm, d90 as 150 µm, Cv=46% (70% by weight) where the rheology of the slurry is represented 3 by the Bingham plastic model and rates of discharge vary from 25 to 400 m /h. The combination of the parameters along with the slurry density of 2900 kg/m3 was used to represent non-segregating (homogeneous) conditions. Bingham model was used to represent slurry rheology for approximation and simplification purposes; due to the fact that Fitton’s model considers turbulent flow only and relates the minimum velocity requirement to the Bingham viscosity for non-segregating slurries. According to the simulation results, the configuration with the lowest rate of discharge m3 (25 /h), the highest yield stress (30 Pa) and the lowest Bingham viscosity (µB=0.01 Pa.s) corresponds to the upper limit of the predicted slopes (about 6%) for the given properties. The lowest possible values of the deposition slopes (about 0.53%) are bound 3 by the configuration with highest rate of discharge (400 m /h), no yield stress and the highest Bingham plasticity (µB=0.01 Pa.s). In the latter case, Newtonian methods may apply for determining the turbulent friction losses (by neglecting the yield stress) due to the less severe effects of non-Newtonian properties under turbulent conditions. Below this point, reductions in the beach slopes will be noticed with decreasing values of solid concentration as the slurry tends to behave in a more non-homogeneous (segregating) way. These findings can be further supplemented with the full-scale field data from different tailings disposal facilities around the world. Facilities having similar slurry characteristics such as, Miduk facility in Iran having d50 as 35 µm, d90 as 120 µm, Cw=60% and

61 Conclusions 62

τy=6-20 Pa or Ernest Henry facility in Australia having d50 as 45 µm, d90 as 170 µm, Cw=75%, τy=0-2 Pa have reported deposition slopes of 2.5% and 1.1%, respectively (Data gathered from Seddon & Fitton, 2011). In addition to these, observed deposition slopes values from other thickened tailings facilities are located within the range from 1% up to 6%. Reported average deposition slope values are, Kidd Creek (Canada) - 1.5%, Peak (Australia) - 1.5-2%, Warkworth (Australia) - 5% and Osborne (Australia) - 3%, respectively (Data gathered from Fitton, 2007). In addition to the dominating effects of the yield stress and the discharge rates, an equally important aspect of the problem might be the state of flow. The depositional behavior of the slurry is under heavy influence depending on the classification of the flow as laminar or turbulent. Fitton states that the Reynolds number values around 500, correspond to the lower-limit for non-laminar flow while Haldenwang, et al., (2004) and others suggest values of up to 8000 for truly turbulent transport of highly thickened tailings. Alderman & Haldenwang (2007) discusses that the transition zone may cover a considerable span of Reynolds numbers. Simulation results suggest that a vast majority of the flows were supercritical with Froude numbers varying between 1.3 and 2. Within that range, there might exist several water depths for the same rate of discharge due to the instabilities of the flow. For each different value of water there will be a different slope. The fact that the state of the flow has such an important effect, depending on the classification as laminar/turbulent or supercritical/subcritical, reflects the complexity of the deposition problem. Ideally, the aim of the thickened tailings disposal technique is to have an overall beach profile as uniform as possible. However, due to the fluctuations in the operating parameters (such as the yield stress and the discharge rates), deposition slope values will be varying over time. The concave beach slope profiles (instead of a perfectly uniform profile) that are observed on site are often associated with these variations in the operating parameters. However, the concavity of thickened tailings (non-segregating slurry) beach profile should not be confused with the concavity resulting from the hydraulic sorting of the particles, generally associated with the deposition of segregating slurries (Seddon & Fitton, 2011). When the problem was first introduced in chapter 1, it has been stated that the beach slope prediction can be considered as an intermediate area shared by different disciplines such as mineral processing, fluid mechanics and geotechnics. The basic slope forming elements of thickened tailings are influenced by fluid mechanics; mainly governed by the discharge rates and rheological properties. However immediately after the flow stops and desiccation starts to take place, the problem then shifts from being a deposition problem to a slope stability/equilibrium problem which is mainly governed by the shear strength developed by the dried tailings. References

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66 APPENDIX A Parameter Study

A.1 Effect of the Yield Stress

The eﬀect of the yield stress while keeping the Bingham plasticity constant at 0.01 Pa.s is investigated. Yield stress is increased from 0 Pa up to 30 Pa. The changes on deposition slopes are reported in the tables below.

Table A.1: Flow simulations with τy=0Pa

2 τ y=0 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 94451 0.022 1.36 0.14 0.69 3 Q=200 (m /h) 0.08 0.47 0.039 0.062 1.41 65564 0.024 1.54 0.11 0.97 3 Q=100 (m /h) 0.06 0.34 0.020 0.045 1.35 45476 0.026 1.75 0.09 1.37 3 Q=80 (m /h) 0.05 0.30 0.017 0.040 1.34 40419 0.027 1.82 0.08 1.53 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 31520 0.029 1.98 0.07 1.92 3 Q=25 (m /h) 0.03 0.17 0.005 0.023 1.25 21822 0.032 2.23 0.05 2.71

Table A.2: Flow simulations with τy=5Pa

2 τ y=0 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 5986 0.037 1.36 0.14 1.17 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 5443 0.038 1.54 0.11 1.56 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 4904 0.040 1.75 0.09 2.09 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 4732 0.041 1.82 0.08 2.30 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 4370 0.042 1.98 0.07 2.81 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 3845 0.045 2.23 0.05 3.79

67 Table A.3: Flow simulations with τy=10Pa

2 τ y=0 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 3091 0.045 1.36 0.14 1.41 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 2839 0.047 1.54 0.11 1.89 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 2592 0.048 1.75 0.09 2.52 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 2513 0.049 1.82 0.08 2.76 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 2348 0.050 1.98 0.07 3.36 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 2108 0.053 2.23 0.05 4.50

Table A.4: Flow simulations with τy=20Pa

2 τ y=0 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 1571 0.056 1.36 0.14 1.78 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 1451 0.058 1.54 0.11 2.37 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 1334 0.061 1.75 0.09 3.16 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 1297 0.061 1.82 0.08 3.46 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 1219 0.063 1.98 0.07 4.21 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 1107 0.066 2.23 0.05 5.61

Table A.5: Flow simulations with τy=30Pa

2 τ y=0 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 1053 0.066 1.36 0.14 2.06 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 974 0.068 1.54 0.11 2.75 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 898 0.070 1.75 0.09 3.67 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 873 0.071 1.82 0.08 4.03 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 823 0.073 1.98 0.07 4.90 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 751 0.077 2.23 0.05 6.53

A.2 Effect of Viscosity

Similarly, the eﬀect of the Bingham viscosity while keeping the yield stress constant at 5 Pa is investigated here. Bingham viscosity is increased from 0.01 Pa.s to 0.05 Pa.s up to 0.1 Pa.s. The inﬂuence of these changes on deposition slopes are summarized in the tables below.

68 Table A.6: Flow simulations with µB=0.01 Pa.s

2 τ y=5 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 5986 0.037 1.36 0.14 1.17 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 5443 0.038 1.54 0.11 1.56 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 4904 0.040 1.75 0.09 2.09 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 4732 0.041 1.82 0.08 2.30 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 4370 0.042 1.98 0.07 2.81 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 3845 0.045 2.23 0.05 3.79

Table A.7: Flow simulations with µB=0.05 Pa.s

2 τ y=5 Pa, µB=0.05 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.13 0.71 0.092 0.095 1.21 3513 0.043 1.08 0.14 0.85 3 Q=200 (m /h) 0.09 0.51 0.048 0.068 1.16 3012 0.046 1.21 0.11 1.14 3 Q=100 (m /h) 0.07 0.37 0.025 0.050 1.11 2536 0.048 1.36 0.08 1.52 3 Q=80 (m /h) 0.06 0.34 0.020 0.045 1.09 2389 0.050 1.41 0.08 1.68 3 Q=50 (m /h) 0.05 0.27 0.013 0.036 1.05 2093 0.052 1.52 0.06 2.05 3 Q=25 (m /h) 0.04 0.20 0.007 0.026 1.00 1692 0.057 1.69 0.05 2.75

Table A.8: Flow simulations with µB=0.1 Pa.s

2 τ y=5 Pa, µB=0.1 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.14 0.74 0.101 0.099 1.11 2536 0.048 0.96 0.13 0.75 3 Q=200 (m /h) 0.10 0.54 0.053 0.072 1.05 2093 0.051 1.07 0.10 1.00 3 Q=100 (m /h) 0.07 0.39 0.028 0.052 1.00 1692 0.055 1.19 0.08 1.35 3 Q=80 (m /h) 0.06 0.35 0.023 0.047 0.98 1573 0.057 1.24 0.07 1.48 3 Q=50 (m /h) 0.05 0.28 0.015 0.038 0.94 1339 0.061 1.32 0.06 1.81 3 Q=25 (m /h) 0.04 0.21 0.008 0.028 0.89 1037 0.067 1.46 0.05 2.45

APPENDIX B Flow Simulations

The following tables summarize the simulation results for diﬀerent combinations of discharge rates, yield stress and Bingham plasticity

Table B.1: Flow simulations with τy=5 Pa, µB=0.01 Pa.s

Table B.2: Flow simulations with τy=10 Pa, µB=0.01 Pa.s

2 τ y=10 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 3091 0.045 1.36 0.14 1.41 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 2839 0.047 1.54 0.11 1.89 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 2592 0.048 1.75 0.09 2.52 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 2513 0.049 1.82 0.08 2.76 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 2348 0.050 1.98 0.07 3.36 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 2108 0.053 2.23 0.05 4.50

71 Table B.3: Flow simulations with τy=20 Pa, µB=0.01 Pa.s

2 τ y=20 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 1571 0.056 1.36 0.14 1.78 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 1451 0.058 1.54 0.11 2.37 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 1334 0.061 1.75 0.09 3.16 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 1297 0.061 1.82 0.08 3.46 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 1219 0.063 1.98 0.07 4.21 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 1107 0.066 2.23 0.05 5.61

Table B.4: Flow simulations with τy=30 Pa, µB=0.01 Pa.s

2 τ y=30 Pa, µB=0.01 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.12 0.65 0.076 0.086 1.46 1053 0.066 1.36 0.14 2.06 3 Q=200 (m /h) 0.08 0.47 0.040 0.062 1.41 975 0.068 1.54 0.11 2.75 3 Q=100 (m /h) 0.06 0.34 0.021 0.045 1.35 898 0.070 1.75 0.09 3.67 3 Q=80 (m /h) 0.06 0.30 0.017 0.040 1.34 874 0.071 1.82 0.08 4.03 3 Q=50 (m /h) 0.04 0.24 0.011 0.032 1.30 824 0.073 1.98 0.07 4.90 3 Q=25 (m /h) 0.03 0.18 0.006 0.023 1.25 751 0.077 2.23 0.05 6.53

Table B.5: Flow simulations with τy=5 Pa, µB=0.05 Pa.s

Table B.6: Flow simulations with τy=10 Pa, µB=0.05 Pa.s

2 τ y=10 Pa, µB=0.05 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.13 0.71 0.092 0.095 1.21 1956 0.052 1.08 0.14 1.03 3 Q=200 (m /h) 0.09 0.51 0.048 0.068 1.16 1724 0.055 1.21 0.11 1.37 3 Q=100 (m /h) 0.07 0.37 0.025 0.050 1.11 1499 0.058 1.36 0.08 1.82 3 Q=80 (m /h) 0.06 0.34 0.020 0.045 1.09 1429 0.059 1.41 0.08 2.00 3 Q=50 (m /h) 0.05 0.27 0.013 0.036 1.05 1284 0.062 1.52 0.06 2.42 3 Q=25 (m /h) 0.04 0.20 0.007 0.026 1.00 1080 0.066 1.69 0.05 3.23

72 Table B.7: Flow simulations with τy=20 Pa, µB=0.05 Pa.s

2 τ y=20 Pa, µB=0.05 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.13 0.71 0.092 0.095 1.21 1037 0.066 1.08 0.14 1.31 3 Q=200 (m /h) 0.09 0.51 0.048 0.068 1.16 929 0.069 1.21 0.11 1.73 3 Q=100 (m /h) 0.07 0.37 0.025 0.050 1.11 825 0.073 1.36 0.08 2.29 3 Q=80 (m /h) 0.06 0.34 0.020 0.045 1.09 792 0.074 1.41 0.08 2.51 3 Q=50 (m /h) 0.05 0.27 0.013 0.036 1.05 724 0.077 1.52 0.06 3.03 3 Q=25 (m /h) 0.04 0.20 0.007 0.026 1.00 627 0.083 1.69 0.05 4.02

Table B.8: Flow simulations with τy=30 Pa, µB=0.05 Pa.s

2 τ y=30 Pa, µB=0.05 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.13 0.71 0.092 0.095 1.21 705 0.077 1.08 0.14 1.53 3 Q=200 (m /h) 0.09 0.51 0.048 0.068 1.16 636 0.081 1.21 0.11 2.03 3 Q=100 (m /h) 0.07 0.37 0.025 0.050 1.11 569 0.085 1.36 0.08 2.68 3 Q=80 (m /h) 0.06 0.34 0.020 0.045 1.09 548 0.087 1.41 0.08 2.94 3 Q=50 (m /h) 0.05 0.27 0.013 0.036 1.05 504 0.091 1.52 0.06 3.55 3 Q=25 (m /h) 0.04 0.20 0.007 0.026 1.00 441 0.145 1.69 0.05 7.05

Table B.9: Flow simulations with τy=5 Pa, µB=0.1 Pa.s

2 τ y=5 Pa, µB=0.1 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.14 0,74 0.101 0.099 1.11 2536 0.048 0.96 0.13 0.75 3 Q=200 (m /h) 0.10 0.54 0.053 0.072 1.05 2093 0.051 1.07 0.10 1.00 3 Q=100 (m /h) 0.07 0.39 0.028 0.052 1.00 1692 0.055 1.19 0.08 1.35 3 Q=80 (m /h) 0.06 0.35 0.023 0.047 0.98 1573 0.057 1.24 0.07 1.48 3 Q=50 (m /h) 0.05 0.28 0.015 0.038 0.94 1339 0.061 1.32 0.06 1.81 3 Q=25 (m /h) 0.04 0.21 0.008 0.028 0.89 1037 0.067 1.46 0.05 2.45

Table B.10: Flow simulations with τy=10 Pa, µB=0.1 Pa.s

2 τ y=10 Pa, µB=0.1 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.14 0.74 0.101 0.099 1.11 1499 0.057 0.96 0.13 0.90 3 Q=200 (m /h) 0.10 0.54 0.053 0.072 1.05 1284 0.061 1.07 0.10 1.20 3 Q=100 (m /h) 0.07 0.39 0.028 0.052 1.00 1080 0.065 1.19 0.08 1.59 3 Q=80 (m /h) 0.06 0.35 0.023 0.047 0.98 1018 0.067 1.24 0.07 1.74 3 Q=50 (m /h) 0.05 0.28 0.015 0.038 0.94 892 0.071 1.32 0.06 2.12 3 Q=25 (m /h) 0.04 0.21 0.008 0.028 0.89 721 0.078 1.46 0.05 2.83

73 Table B.11: Flow simulations with τy=20 Pa, µB=0.1 Pa.s

2 τ y=20 Pa, µB=0.1 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.14 0.74 0.101 0.099 1.11 825 0.072 0.96 0.13 1.14 3 Q=200 (m /h) 0.10 0.54 0.053 0.072 1.05 724 0.077 1.07 0.10 1.50 3 Q=100 (m /h) 0.07 0.39 0.028 0.052 1.00 627 0.082 1.19 0.08 1.99 3 Q=80 (m /h) 0.06 0.35 0.023 0.047 0.98 597 0.084 1.24 0.07 2.18 3 Q=50 (m /h) 0.05 0.28 0.015 0.038 0.94 535 0.088 1.32 0.06 2.63 3 Q=25 (m /h) 0.04 0.21 0.008 0.028 0.89 448 0.143 1.46 0.05 5.20

Table B.12: Flow simulations with τy=30 Pa, µB=0.1 Pa.s

2 τ y=30 Pa, µB=0.1 Pa.s y (m) T (m) A (m ) RH(m) v (m/s) Re f Fr yc(m) S (%) 3 Q=400 (m /h) 0.14 0.74 0.101 0.099 1.11 569 0.085 0.96 0.13 1.33 3 Q=200 (m /h) 0.10 0.54 0.053 0.072 1.05 504 0.090 1.07 0.10 1.76 3 Q=100 (m /h) 0.07 0.39 0.028 0.052 1.00 441 0.145 1.19 0.08 3.53 3 Q=80 (m /h) 0.06 0.35 0.023 0.047 0.98 422 0.152 1.24 0.07 3.95 3 Q=50 (m /h) 0.05 0.28 0.015 0.038 0.94 382 0.168 1.32 0.06 5.01 3 Q=25 (m /h) 0.04 0.21 0.008 0.028 0.89 325 0.197 1.46 0.05 7.17