Large-strain consolidation modeling of mine waste tailings
© Ito and Azam; licensee Springer. 2013
Received: 29 April 2013
Accepted: 15 July 2013
Published: 24 July 2013
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 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.
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.
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
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.
Results and discussion
Geotechnical index properties of selected fine-grained tailings
w L (%)
w P (%)
I P (%)
(a) Sedimentary clays
Znidarcic et al., 1986
Znidarcic et al., 1986
(b) Residual soils
Azam et al., 2009
Matyas et al., 1984
(c) Oil sand tailings
Ore A–C, RPW
Miller et al., 2010
Ore A–NC, TRW
Miller et al., 2010
Ore B–C, RPW
Miller et al., 2010
Ore B–NC, TRW
Miller et al., 2010
Ore A–NC, URW
Miller et al., 2010
Lord and Liu, 1998
Jeeravipoolvarn et al., 2009a
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.
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.
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