# Large-strain consolidation modeling of mine waste tailings

- Maki Ito
^{1}and - Shahid Azam
^{1}Email author

**2**:7

**DOI: **10.1186/2193-2697-2-7

© Ito and Azam; licensee Springer. 2013

**Received: **29 April 2013

**Accepted: **15 July 2013

**Published: **24 July 2013

## Abstract

### Background

Sustainable management of mine waste tailings during operation, closure, and reclamation requires a clear understanding of modeling the large-strain consolidation behaviour of these loose and toxic slurries. A state-of-the-art was presented focusing on process phenomenology and coordinate systems for tailings dewatering thereby devising a simple constitutive equation with a small number of input parameters. A one-dimensional self-weight consolidation model for quiescent conditions was developed using the finite element method. Test data on oil sand fine tailings were used for model training and predictions were made for an upper bound and a lower bound of various tailings types using a 1 m high hypothetical column.

### Results

Results indicated that hydraulic conductivity along with specific gravity dictated pore water pressure dissipation and effective stress development with respect to both time and depth. Likewise, volume compressibility and initial solids was found to govern the void ratio reduction and solids content increase with respect to both time and depth.

### Conclusions

The developed model requires a small numbers of input parameters and is capable of capturing the behaviour of a wide range of tailings. Depending on field conditions, the model can predict multiple filling conditions and various types of drainage systems in tailings containment facilities by incorporating appropriate boundary conditions.

### Keywords

Large-strain consolidation Mine waste tailings Numerical modeling## Background

Large volumes of mine tailings (solid minerals suspended in chemical-rich liquids) are generated worldwide as by-products of ore beneficiation. Conventionally, these loose slurries are deposited on ground with perimeter dykes constructed from their relatively coarser fraction. Such facilities are notorious for a high failure rate and the resulting economic, social, health, and environmental issues (Azam and Li, 2010). To reduce tailings footprint, next-generation containment strategies include waste disposal in mined-out pits or in thickening vessels. The storage capacity of these facilities depends on the dewatering behaviour of the deposited material under self weight. The settling process (rate and amount) is influenced by complex physicochemical phenomena at solid-liquid interfaces. Whereas field monitoring and laboratory testing are routinely carried out to understand the consolidation behaviour of the placed tailings, these methods are quite expensive, time consuming, and material specific. Sustainable waste management during operation, closure, and reclamation requires a general understanding of tailings consolidation.

The numerical prediction of large-strain consolidation properties of slurries has evolved over the years. Non-linear consolidation equations were independently formulated by Mikasa (1965) and Gibson et al. (1967) and were subsequently modified by Koppla (1970) and Somogyi (1980) to facilitate mathematical solution. Various deposition conditions such as quiescent, staged filling, surcharge loading, and initial solids content were analyzed by Townsend and McVay (1990) and Priestley (2011). Likewise, different forms of the constitutive relationships were employed (Caldwell et al., 1984; Jeeravipoolvarn et al., 2009a) and consolidation models were extended to include sedimentation (Azam et al., 2009; Jeeravipoolvarn et al., 2009b). The main problems with such models are the large number of input parameters and the complexity in solving the constitutive equations. Furthermore, most of the models were developed for material specific consolidation properties and a general purpose large-strain model is currently non-existent (Bartholomeeusen et al., 2002; Priestley et al., 2011).

The main objective of this paper was to study the large-strain consolidation modeling of mine waste tailings. Initially, a stat-of-the-art was established focusing on process phenomenology and coordinate systems for tailings dewatering thereby devising a simple constitutive equation with a small number of input parameters. Next, a one-dimensional self-weight consolidation model was developed for quiescent conditions because of negligible lateral drainage, absence of surcharge loading, and diminishing effect of filling on underlying sediments in the containment facilities. Finite element analysis was chosen for model development because of its robustness in capturing the changes in material coordinates during large strain tailings consolidation. The model was applied to capture the behaviour of a wide range of tailings using the tailings classification scheme of Paul and Azam (2013) that captures physicochemical interactions arising from ore geology and mill processing. Finally, test data on oil sand fine tailings were used for model calibration and predictions were made for an upper bound and a lower bound of various tailings types using a 1 m high hypothetical column.

## State of the art

*e*–

*σ'*) and hydraulic conductivity (

*k*–

*e*), as shown in Figure 1b and 1c, respectively. These relationships explain the void ratio (

*e*) decrease with an increase in effective stress (

*σ'*) along with a corresponding decrease in hydraulic conductivity (

*k*). Generally, these relationships are best described using power law functions and the fit parameters (A, B, C, D) are used for numerical modeling.

*t*, depth with respect to datum by

*x*, excess pore water pressure by

*u*, and coefficient of consolidation by

*C*

_{ v }, the governing equation for infinitesimal deformation in clays can be written as follows (Terzaghi et al., 1996):

This theory assumes a linear stress-strain relationship, a constant hydraulic conductivity, and infinitesimal strain. The low compressibility of clays allows the use of Eulerian reference frame in which material deformation is related to a fixed plane in space. Because of significant volume changes, the use of Eulerian coordinate system (in which flux rate and soil movement are measured with respect to a fixed reference plane) is not valid for tailings consolidation.

*X*from a datum (

*X*= 0) located at the tailings upper surface at time

*t*= 0. The datum (ξ = 0) shifts downward during consolidation such that the particle’s new position (ξ at time,

*t*) can be represented by the convective coordinate system (Figure 2b). This system focuses on the space occupied by the particle instead of on the particle itself. To solve the governing equation (written in the material coordinate system), the geometry needs to be updated for each time step thereby increasing the computation time. The reduced coordinate system (Figure 2c) focuses on the solid volume (

*z*) occupied between the fixed datum (

*z*= 0) and the point of interest at time,

*t*. It simplifies numerical implementation because this system does not require updated geometry at each time step. The datum settlement can be obtained by converting the solution of the reduced coordinate system to the appropriate coordinate system, that is, material coordinate system for

*t*= 0 and convective coordinate system for

*t*> 0. The coordinate transformation among the three systems uses the following conversions (McNabb, 1960):

*G*

_{ s }and the coordinate difference between the surface and the point in question by

*Δz*, Somogyi (1980) updated the above equation using the following time dependent effective stress:

## Model development

## Results and discussion

*G*

_{ s }= 2.28; initial solids content of 31%) in a 10 m standpipe. Figures 4 and 5 give the volume compressibility and the hydraulic conductivity relationships for the investigated tailings. Power law fits were applied to handle the nonlinearity in both relationships. A detailed description of material behaviour was provided by Jeervipoolvarn et al. (2009a).

*G*

_{ s }) of sedimentary clays ranged from 2.6 to 2.77, which is the typical range for such materials (Wesley, 2010). Conversely, residual soils showed higher

*G*

_{ s }values due to the presence of ferrous minerals such as goethite and hematite in laterite (Azam, 2005), and gibbsite and hematite in bauxite (Newson et al., 2006); the higher

*G*

_{ s }(in comparison with sedimentary clays) of uranium tailings was attributed to the high amount of muscovite (Paul and Azam, 2013). The low

*G*

_{ s }(2.55 ± 0.1) for oil sand tailings was due to the presence of bitumen (

*G*

_{ b }= 1.03) with variations attributable to the variable amount of bitumen in the different samples (Miller et al., 2010). The consistency limits varied over a wide range due to the presence of different types and amounts of clay minerals. Although the consistency limits are influenced greatly by the type of process water, data on the chemical composition of water was not readily available.

**Geotechnical index properties of selected fine-grained tailings**

Slurry type |
G
| w | w | I | USCS Symbol | Reference |
---|---|---|---|---|---|---|

(a) Sedimentary clays | ||||||

China clay | 2.66 | 53 | 32 | 21 | MH | Znidarcic et al., 1986 |

Georgia Kaolin | 2.6 | 44 | 25 | 19 | CL | Znidarcic et al., 1986 |

Phosphate Slime | 2.77 | 100 | 40 | 60 | CH | Roma, 1976 |

(b) Residual soils | ||||||

Laterite | 3.16 | 83 | 42 | 41 | MH | Azam et al., 2009 |

Bauxite | 3.05 | 54 | 40 | 14 | MH | Cooling,1985 |

Uranium | 2.81 | 32 | 27 | 5 | ML | Matyas et al., 1984 |

(c) Oil sand tailings | ||||||

Ore A–C, RPW | 2.55 | 50 | 26 | 24 | CH | Miller et al., 2010 |

Ore A–NC, TRW | 2.51 | 60 | 31 | 29 | CH | Miller et al., 2010 |

Ore B–C, RPW | 2.48 | 52 | 27 | 25 | CH | Miller et al., 2010 |

Ore B–NC, TRW | 2.45 | 58 | 28 | 30 | CH | Miller et al., 2010 |

Ore A–NC, URW | 2.5 | 55 | 28 | 27 | CH | Miller et al., 2010 |

Desanded | 2.65 | 57 | 25 | 32 | CH | Lord and Liu, 1998 |

Cyclone overflow | 2.53 | 50 | 21 | 29 | CH | Jeeravipoolvarn et al., 2009a |

## Conclusions

A one-dimensional self weight consolidation model for quiescent conditions was developed in a finite element code. The model was calibrated using oil sand fine tailings and validated through a wide range of tailings. The one dimensional model captured the dewatering behaviour because of the homogeneous nature of fine grained tailings. The developed model requires a small numbers of input parameters and capable of capturing the behaviour of a wide range of tailings. Depending on field conditions, the model can predict multiple filling conditions and various types of drainage systems in tailings containment facilities by incorporating appropriate boundary conditions. The general purpose model can be improved to include heterogamous tailings using a multi-dimensional approach. Results indicated that hydraulic conductivity (Figure 8) along with specific gravity (Table 1) dictated the rate of consolidation with respect to both time and depth, as evident from pore water pressure dissipation (Figure 9) and effective stress development (Figure 10), Likewise, volume compressibility (Figure 7) and initial solids was found to govern the amount of consolidation with respect to both time and depth, as given by void ratio reduction (Figure 11) and solids content increase (Figure 12). The model captured the self-weight consolidation behaviour for a wide range of tailings. The load-deformation based model can be extended to include the sedimentation part of slurry settling thereby incorporating the effect of physiochemical interactions.

## Declarations

### Acknowledgements

The authors acknowledge the financial support provided by the Natural Science and Engineering Research Council of Canada and the computation facilities provided by the University of Regina.

## Authors’ Affiliations

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