This article was downloaded by: [University of Haifa Library] On: 05 September 2013, At: 16:50 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK International Journal of Mining, Reclamation and Environment Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/nsme20 Staged construction analysis of surface tailings disposal facilities Bassam Saad a & Hani Mitri b a Parsons Brinckerhoff Inc, 2777 N Stemmons Freeway, Suite 1333, Dallas, Texas, 75207 b Department of Mining and Materials Engineering, McGill University, Montreal, Quebec, Canada Published online: 01 Mar 2010. To cite this article: Bassam Saad & Hani Mitri (2010) Staged construction analysis of surface tailings disposal facilities, International Journal of Mining, Reclamation and Environment, 24:1, 44-63, DOI: 10.1080/17480930902951293 To link to this article: http://dx.doi.org/10.1080/17480930902951293 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions
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This article was downloaded by: [University of Haifa Library]On: 05 September 2013, At: 16:50Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
International Journal of Mining,Reclamation and EnvironmentPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/nsme20
Staged construction analysis of surfacetailings disposal facilitiesBassam Saad a & Hani Mitri ba Parsons Brinckerhoff Inc, 2777 N Stemmons Freeway, Suite 1333,Dallas, Texas, 75207b Department of Mining and Materials Engineering, McGillUniversity, Montreal, Quebec, CanadaPublished online: 01 Mar 2010.
To cite this article: Bassam Saad & Hani Mitri (2010) Staged construction analysis of surface tailingsdisposal facilities, International Journal of Mining, Reclamation and Environment, 24:1, 44-63, DOI:10.1080/17480930902951293
To link to this article: http://dx.doi.org/10.1080/17480930902951293
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Staged construction analysis of surface tailings disposal facilities
Bassam Saada and Hani Mitrib*
aParsons Brinckerhoff Inc, 2777 N Stemmons Freeway, Suite 1333, Dallas, Texas 75207;bDepartment of Mining and Materials Engineering, McGill University, Montreal, Quebec,
Canada
(Received 19 January 2009; final version received 7 April 2009)
One of the major challenges that faces the mining industry is the stability ofsurface tailings disposal facilities (STDF) particularly when they are raised withthe more economical upstream method whereby the embankments are partiallybuilt on previously deposited soft tailing materials. Whether the effective or totalstress analysis should be used to evaluate the stability of STDFs underconstruction/operation has been a controversial issue among the respectiveresearchers. Although both analyses cannot compete with the coupled deforma-tion approach, the latter is still grossly underused in the geotechnical evaluationprocess of STDFs. The goal of this article is to develop a numerical model thatcan more genuinely assess the stability of STDFs during staged construction usingthe coupled deformation approach. A number of simulation techniques arepresented and discussed using actual data for an upstream coal wash STDF.
In recent years, structural and environmental safety of surface tailings disposalfacilities (STDFs) have become a major concern for mining and environmentalagencies. This is mainly because of the increasing number of reported failureaccidents. It has become well recognised that one of the contributory factors forcatastrophic failures of STDF’s is that the design is based on inadequate stabilityanalysis [1,2]. In particular, unforeseen failure was mainly because of miscalculationof the pore pressure regime and the manner in which it influences the stabilityresponse of the facility [3,4] particularly in the staged construction analysis, which isconsidered the most complex stability analysis conducted on the STDFs [5].
This article concerns itself with the upstream STDF, which is the most commonamong STDFs [6]. It is also the oldest, simplest, and most cost-effective constructionmethod [7]. The staged construction of an STDF built with the upstream methodrepresents a situation in which excess pore pressure may develop and cause failuredue to the contractive nature of the deposited tailings being the foundation, and insome situations the components, of the retaining embankment [3,8,9]. According to
International Journal of Mining, Reclamation and Environment
Vol. 24, No. 1, March 2010, 44–63
ISSN 1748-0930 print/ISSN 1748-0949 online
� 2010 Taylor & Francis
DOI: 10.1080/17480930902951293
http://www.informaworld.com
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ICOLD [2], the upstream method recorded the largest number of failure eventsamong STDFs.
The goal of this article is to develop a numerical model based on thedeformation-pore pressure full coupled response [10] that can more rationallypredict the pore pressure regime and thus more accurately evaluate the stability ofSTDFs during staged construction. First, classical stability analyses are brieflyreviewed. Techniques for numerical modelling of embankment construction withemphasis on staged construction loading are then presented. Finally, a numericalmodel is developed for a geometric and material nonlinear finite element coupledanalysis of an upstream coal wash STDF.
2. Classical stability analyses
Three types of analyses are traditionally performed for investigating the stability ofSTDFs during their staged construction. The shear strength determined by theseanalyses is used in the stability calculations which are commonly performed by thelimit equilibrium method to obtain the factor of safety of the facility.
2.1. Effective stress analysis
This analysis implies that failure occurs under the fully drained condition and thus itimplements the effective strength parameters in the stability calculations. The porepressure regime required by the effective stress analysis (ESA) is obtained from fieldmeasurements for in-operation facilities. In the design analyses, however, theequilibrium pore pressure regime can be predicted from a steady state seepageanalysis while the pore pressure developed due to an applied external load can beestimated using the pore pressure parameters approach; e.g. A and B Skempton’sparameters [11,12]. However, accurate estimation of the excess pore water pressuresvia the available parameters-based approach is very unlikely; refer for example toRefs. [3] and [13]. Moreover, other researchers [3,4,14,15] concluded that an ESAgenerally leads to unsafe factors of safety since most failure events during the stagedconstruction occur under the undrained condition.
2.2. Total stress analysis
According to this analysis, failure occurs under the undrained case. Hence,noncohesive materials are represented by the peak undrained shear strength (atthe inception of liquefaction) or the steady state/residual undrained shear strength(post liquefaction) [16]. In general, analyses in terms of the total strength angle, f, [5]are more common. Also, soft cohesive soils and tailings are represented by theundrained shear strength obtained from a consolidated undrained shear test [15], orby the undrained shear strength obtained from an unconsolidated undrained sheartest with f ¼ 08. On the basis of f ¼ 08 analysis, the undrained shear strengthexisting before construction will control the strength during the staged construction.The validity of the total stress analysis (TSA) was argued by a number ofinvestigators; see e.g. [13], based on the fact that the mechanical response of the soilshould be dictated by the effective stresses [17]. Wood [18] pointed out that the TSAis sometimes performed for cases involving undrained phenomena because of thedifficulty of predicting the pore pressure regime required by the ESA. Nonetheless,
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the manner according to which the undrained shear strength is in reality dependenton sample disturbance, direction of the principal stresses, and strain rate, should beaccurately determined was another debatable issue among researchers. For example,Ladd and Foott [19] criticised the field Vane shear test as a tool to predict theundrained shear strength in the embankment stability calculations, and supportedevaluating such strength from consolidated undrained triaxial compression,extension, and simple shear tests under what [20] called SHANSEP approach. Onthe other hand, Trak et al. [20], and Tavenas and Leroueil [21] did not recommendthe SHANSEP approach, which requires a large number of tests, indicating that byreconsolidating a normally consolidated sample to its in-situ stress condition thevirgin state existing in field cannot be unmissed and thus the undrained strengthobtained from such an approach may not be accurate.
2.3. Undrained strength analysis
The undrained strength analysis (USA) can be seen as an intermediate approachbetween ESA and TSA; it assumes that failure occurs under the undrained case but,unlike the TSA, the USA does consider the gain in strength due to the consolidationprocess during construction. This is done by updating the effective stress profile dueto consolidation at a chosen time and computing the corresponding undrained shearstrength. Therefore, the accuracy of the USA is not only dependent on the manner inwhich the undrained shear strength is assessed, but also on the accuracy of theupdated effective stress profiles obtained. Because the updated effective stresses arecommonly predicted based on one dimensional consolidation theories, which cannotaccount for the shear pore pressure and drainage in the horizontal direction [8], thestability results obtained from a classical USA are not based on precise pore pressureprediction.
3. Biot’s theory-based analysis
The above discussion implies that classical stability analyses are limited in theirability to realistically predict pore pressure evolution in the upstream tailingsdisposal facility (UTDFs) during staged construction. However, pore pressure canbe assessed with greater accuracy if a coupled deformation-based analysis is made,particularly with the use of appropriate mechanical constitutive laws, so that the fullinteraction between pore pressure evolution and deformation induced by theconstruction process is accounted for.
3.1. Historical background
Biot’s formulations [10] for analysing three dimensional consolidation of porousmedia entail that deformation of the soil skeleton causes flow and an imposed flowcauses soil skeleton deformation. Such formulations were derived for fully saturatedlinear isotropic media with incompressible fluid phases governed by Darcy flow. [22]were the earliest to use Biot’s formulations to solve initial boundary value problems.Later, Ghaboussi and Wilson [23] developed a variational formulation of Biot’sdynamic field equations for saturated porous elastic media allowing for thecompressibility of both the fluid and solid phases. Lewis and Schrefler [24] managedto account for partial saturation in the development of coupled finite element
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formulations. Kohgo and Yamashita [25] used the coupled theory for investigatingfill type dams during their construction accounting for the partially saturated state.More recent studies have further extended Biot’s theory to accommodate a numberof advanced non-linear constitutive laws; see for example [26]. With the rapidadvancements in computer technology and numerical simulation techniques, it hasbecome possible to implement coupled formulations in numerical modelling codesfor the analysis of porous media.
3.2. Consolidation of a partially saturated soil
Zienkiewicz et al. [26] presented the coupled formulations of soil mixtures in a simplifiedform which made it easier to understand the physical realm underlying theseformulations. Neglecting the weight of air and its pressure within the partially saturatedsoil mixture, this form is represented by three equations: the linear momentumconservation equation of the mixture, as well as the mass and the linear momentumconservation equations of the fluid. Further, Zienkiewicz et al. [26] proposed that whenthemedium isunder slow tomoderate phenomena, the last two equations canbe reducedto one equation. Assuming that the water flow is governed by the Darcy law andneglecting the thermal effect, the equations governing the coupled response of a partiallysaturated soil mixture continuum point subjected to a static loading can be expressed inthe indicial notation in the Cartesian coordinates system as follows:
sij:j þ rBi ¼ 0 ð1Þ
ðkeijð�pw;j þ SrwBjÞÞ;i þ a eii� þ p
�w=Q ¼ 0 ð2Þ
In the above equations, sij is the stress tensor, r is the mass density of the soilmixture, Bi is the body force vector, keij is the effective permeability tensor given bykeij ¼ kij=ðrwgÞ, where kij (length/time) is the permeability tensor and g is themagnitude of the gravity acceleration, S is the degree of saturation, pw is the porewater pressure, rw is the mass density of the water in the mixture, a is Biot’s effectivestress parameter which is unity for an incompressible soil skeleton, eii is thevolumetric strain (first invariant of the strain tensor), Q is the storage capacity givenby Q ¼ (1/n)(@pw/@S) assuming water and soil skeleton incompressible, and n is themedium porosity. The dot overlying eii and pw in Equation (2) above impliesderivative with respect to time whereas the subscripts i and j are notations used torepresent the tensors in an indicial form. Given a mechanical constitutive responseand hydraulic and mechanical boundary conditions, the Galerkin method is used todevelop the coupled finite element formulations from the above equations whichformulations are then truncated with the appropriate algorithms for the pore waterpressure and displacement fields.
3.3. Implications of the drained and undrained cases on the consolidationformulations
It is interesting to see how the assumptions of the ideal drained and undrainedconditions influence the response of the partially drained medium by inspectingEquations (1) and (2). More specifically, as the drained condition assumption impliesindependence of time, the last two terms in Equation (2) will drop and thus the two
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equations become time-independent and uncoupled. However, under the undrainedcondition where no water flow is permitted, only the last two terms of Equation (2)will survive and if the hydraulic and mechanical conditions coincide, which is acommon situation; the above equations become time-independent but remaincoupled. However, if under a case in which the medium becomes fully saturated,only the term aeii remains in Equation (2), and therefore one is encountered with aconstrained problem, which can be handled by a Lagrange multiplier-basedtechnique; refer for example to [27]. More elaborate discussions on the fate of thecoupled formulations that could emerge from imposing various boundary andloading scenarios can be found in Refs. [26,28].
4. Numerical modelling of embankments construction
4.1. Simulation scheme of the construction process
Construction of embankments including theUTDFswith time ismodelled by adding anumber of construction stages to the existing foundation. The number of theconstruction stages and the height of each stage depend on the construction schedule.This number should not be too large to avoidmodelling complexity and it should not betoo small so that a gradual facility build-up with time is simulated. Customarily, aconstruction stage addition is simulated either by adding elements to the existing meshor by applying pressure equivalent to this stage at the boundaries of the existing mesh.The latter approach gives a satisfactory solution provided the layer being added is notexpected to undergo shear deformations. Therefore, the former technique (addingelements to the mesh) will be used herein so that the shear deformation of each layerbeing constructed and the influence of its hydromechanical response on the facilityperformance as a whole are accounted for during the construction period. Simulationof the facility construction is firstmade by creating amesh representing the facility at itsultimate height.An initial analysis is then conducted inwhich themesh representing theimpoundment above the foundation is removed (deactivated) and only the foundationis analysed under the in-situ loading and boundary conditions. The analysis will ensurethat the foundation under the existing in-situ stress condition is undeformed beforeplacing the impoundment. The first construction stage is activated in themodel and theproper hydraulic and mechanical boundary conditions are invoked. The change of thetransient system response because of the construction of the first stage is examined in aconsolidation analysis spanning the construction time of such stage. The nextconstruction stage is then constructed in the same manner and the transient systemresponse due to its construction is analysed in a new consolidation analysis. The stagedconstruction simulation procedure continues until the ultimate height of the facility isattained.
4.2. Idealisation of staged construction loading
Classical modelling of the embankment construction involves an instantaneousapplication of each construction stage (an undrained loading application) followedby a partial dissipation period as shown in Figure 1a; refer for example to [29,30]. Inreality, however, the facility height increases gradually with time according to a set-up construction schedule, as shown in Figure 1b, during which the systemdemonstrates partial drainage with time. The assumption that a layer is builtinstantaneously will provoke a fictitious undrained state produced at the moment of
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placement of such layer. This drawback is commonly mitigated by increasing thenumber of layers simulating the embankment construction process; refer for exampleto Ref. 31.
In present work, the load of each construction stage is considered to increaseuniformly over the construction time of this stage. To show the merit of this rampedloading application scheme, the vertical stress induced within an embankment layerhaving a thicknessHand constructed uniformly over timeT, is computed for the simpleone dimensional loading condition under: the true (sv
True), ramped (svRamped), and
sudden (svSudden) loading applications; refer to Table 1. As can be seen fromTable 1, if
at time t a layer portionwith thickness h is realistically built, the stress field produced bythe ramped application more closely simulates the field loading case than the suddenloading application. For example, it is noticed from the table that although the stressobtained by both the ramped and instantaneous cases overestimate the realisticconstruction stress induced within the layer, the overestimation is significantly smallerunder the ramped load application case and it further tends to decrease by movingtowards the bottom of the layer until it vanishes at its base.
4.3. Numerical modelling techniques
The coupled analysis was carried out with the following points taken intoconsideration:
(1) Simulation of porous media consolidation requires that the initial time stepbe greater than a minimum value in order to avoid oscillations and non
Table 1. The vertical stress produced by an embankment layer with g unit weight consideredat time t for the true (sv
True ), ramped (svRamped) and sudden (sv
Sudden) loading applications ofthe self-weight of the layer.
Height svTrue sv
Ramped svSudden
svRamped 7sv
Truesv
Sudden 7sv
True
y ¼ 0 gh ¼ g H (t/T) gH (t/T) gH 0 g(H 7 h)0 5 y 5 h g[H (t/T) 7 y] g(t/T) (H 7 y) g(H 7 y) gy (1 7 t/T) gH (1 7 t/T)h 5 y 5 H 0 g(t/T) (H 7 y) g(H 7 y) g(t/T) (H 7 y) g(H 7 y)
Figure 1. Simulation of staged construction loading.
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convergence; refer to the work of Vermeer and Verruijt [32] for the formulagiving such minimum values;
(2) The total water pore pressure should be considered in the coupling processcomputations so that the gravity-induced pore water pressure is accountedfor;
(3) Appropriate boundary conditions should be applied on the face of theembankment downstream slope to permit drainage on the part of the surfacehaving positive pore pressures and prevent drainage on the part of the surfacehaving negative pore pressures; and
(4) Low permeability-materials should be simulated by finite elements with shapefunctions order of the displacement field higher than shape functions order ofthe pore pressure field. This is to avoid numerical instability and divergencethat can arise due to volumetric locking in some poorly drained numericalpoints; refer to [26] for more discussion on this issue.
5. Finite element study
A two-dimensional (2D) nonlinear coupled finite element model is created toinvestigate the performance of a UTDF during the staged construction. The UTDFanalysed is of a coal wash type whose mill tailings are adopted from [33,44]. The coalwash tailings considered contain 40% sand and 22.5% clay with plasticity index of16% and liquidity limit of 40%. Along with these tailings the model uses a typicalcross section that is set up to encompass average operational and geometric features,as derived from the relevant literature. The finite element model is created and thecomputations are performed with the general purpose coder ABAQUSTM [34]. Thefeatures of the numerical model developed are summarised in the following section.
5.1. Section configuration and impoundment zoning
The section modelled is shown in Figure 2, which demonstrates the principalcomponents of a UTDF, namely:
(1) The impoundment tailings: based on tailings coarseness variation and formodelling purposes the impoundment tailings is considered to include three
Figure 2. The cross section modelled; the points 1, 2, 3, 4, 5, and 6 represent locations atwhich drainage conditions are inspected and discussed in detail.
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zones [35–38]: (a) the embankment dykes which contain the coarse fraction ofthe mill tailings (materials retained on the sieve: d ¼ 0.063 mm according tothe USCS). The downstream and upstream slopes of the dykes are assumedto be 3.5 H:1V and 3.0 H:1V, respectively, in this work; (b) the beach whichcontains the mill tailings. For this study the beach is considered to form a 2 mfreeboard with the neighbouring dykes at the commencement of theconstruction and slope at 1% inclination towards the centre of theimpoundment; and (c) the slime zone which embraces the fine fraction ofthe mill tailings;
(2) The starter dam: it is built from waste rock materials to 15 m height abovethe ground surface to retain the impoundment tailings in the early productionperiod;
(3) The internal drainage layer : it is 1.75 m-thick gravel medium with very largepermeability built under the starter dam; and
(4) The foundation strata: it is postulated to have two layers, namely, the upperfoundation taken as a very stiff clayey glacial till material and the deepfoundation layer which is assumed to be limestone bedrock. The materialproperties of the section components are discussed in section 5.4. As can beseen from Figure 2, the model extends to a depth of 100 m below the groundsurface and 80 m away from the external perimeter of the facility in thehorizontal direction to ensure minimal or negligible edge errors. It is importantto mention that in most practical situations, a filter medium preventingpossible erosion of fine particles of a zone into another neighbouring zonehaving significantly coarser particles should be incorporated. However, thesection proposed herein does not account for the existence of a filter, asmodelling the erosion phenomenon is beyond the scope of this article.
5.2. Operational measures and boundary conditions
The impoundment tailing is raised at a uniform rate of 5.25 m per year over fourconstruction stages following the technique explained in the previous section.Concerning the boundary conditions (BCs), the model is fixed along its bottom edgeand constrained in the horizontal direction along its vertical edges. Also, uponbuilding each stage, a new set of boundary conditions is invoked so that zero pore
Figure 3. Illustration of pore pressure (pw ) and displacement (ui) BCs at the end ofconstruction: pw ¼ 0 along 1–2 and 4–5, drainage-only BC along 3–4, ux ¼ uy ¼ 0 along 6–7,ux ¼ 0 along 5–6 and 7–1.
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water pressure (drainage is allowed) is maintained on the slime surface and groundopen (construction-free) surface and a drainage only-BC is imposed on the face ofthe impoundment downstream slope; refer to section 4.3. Figure 3 illustrates the BCsfor the last construction stage at which the facility is at its full height.
5.3. Model truncation
The model is truncated with the pore fluid/stress eight-node quadrilateral continuumplane strain element. This element is formulated in terms of the biquadraticdisplacement and bilinear pore pressure shape functions with the full Gaussintegration rule. Figure 4 shows the mesh used in the simulations. This mesh consistsof 2904 elements which are distributed as follows: 630 elements of bedrockfoundation, 459 elements of the upper foundation layer, 138 elements of drainage,168 elements of the starter dam, 344 elements of the embankment dykes, 714elements of the beach, and 451 elements of slime. As can be seen from Figure 4, themesh is made finer in the areas where high hydraulic and deformation gradients areexpected; e.g. the interface between beach and slime zones, to avoid divergence inthese areas. Also, the model is finely truncated in the embankment dykes and theadjacent beach portion being critical for the stability of the facility so that results canbe obtained with greater accuracy in these regions.
5.4. Constitutive laws and materials properties
The constitutive laws considered for the materials of the UTDF model are presentedin Table 2 along with their respective mechanical properties. The materialsmechanical properties and the hydraulic data are determined as follows.
5.4.1. Beach and slime tailings
The slime and beach zones are idealised by the elastoplastic strain hardening/softeningDrucker Prager Cap model (DPCM) with porous elasticity response [34]. While thecompression index of the beach tailings is taken from Refs. 33,44, the compressionindex of the slime tailings zone is assumed based on Ref. 5 considering thecorresponding compression index of the underlying mill tailings. For both the slimeand beach tailings, the recompression index is assumed to be 0.10 of the correspondingcompression index; refer toRef. 39. Further, the hardening curve of the beach tailings isobtained from the large consolidation test results reported by Qiu and Sego [33].Whereas the hardening curve of the slime is predicted based on the assumed
Figure 4. Finite element mesh used in the analyses.
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compression and recompression indices and a reference consolidation point taken fromthe consolidation test data performed on the underlying mill tailings as a void ratio of1.57 corresponding to an effective pressure of 0.5 kPa [33]. With respect to the modelfailure parameters, the model strength angle, fDP, and cohesion, cDP, are found fromthe Mohr Coulomb strength angle, f, and cohesion, c, reported by Qiu and Sego [33].To account for possible static liquefaction in the beach zone having relatively lowplasticity index (refer to [40] for more details on liquefaction of soils having plasticfines) the tailings strength in this zone is marked by the instability friction angle [41],which is estimated from the corresponding failure angle in light of the work of Olsonand Stark [42]. However, the strength of the tailings in the slime zone is marked by anormalised undrained shear strength of 0.08. Also, the tailings in the slime zone aregiven cohesion that is slightly higher than the cohesion of themill tailings existing in thebeach based on the observations made by Abadjiev [43].
Regarding the hydraulic parameters, the void ratio-vertical permeability functionof the mill tailings contained in the beach zone is obtained from Qiu and Sego [44]who show that such function can best be expressed by an exponential relationship:k ¼ AeB, where k is the permeability, e is the void ratio, A ¼ 0.000002 andB ¼ 4.0686. The permeability of slime tailings is assumed to be one order ofmagnitude lower than the underlying beach mill tailings permeability; refer forexample to Refs. [5,45] for detailed discussions on the variations of permeabilitybetween the sand and slime zones within a tailings impoundment. Also, the initialpermeability of the tailings is assumed to correspond to an initial void ratio of 0.9and 1.0 for the beach and slime zones, respectively; refer to Refs. [5,46]. As thepermeability of the tailings in the beach and slime zones is considerably anisotropicdue to the inter-layering of fine and coarse tailings particles [47], the vertical tohorizontal permeability ratio for slime and beach tailings is assumed 0.1 in thisstudy; refer to Refs. [5,45]. In terms of the unsaturated parameters, the soil watercharacteristic curve (SWCC) data of the initial mill tailings is obtained from Qiu andSego [44] while the unsaturated hydraulic conductivity functions of these tailings arepredicted using Mualem-van Genuchten approach [48]. For this purpose, theparameters of the van Genuchten SWCC curve equation are first optimised from thedata of the SWCC reported by Qiu and Sego [44] using RETC open source code [49]and then such data is used along with the saturated permeability function to predictthe unsaturated hydraulic conductivity function using RETC code.
5.4.2. Starter dam and embankment dykes
The sands and gravels waste rock materials of the starter dam which are adopted from[50] and the sand materials of the embankment dykes zone are assumed to becompacted to a dense state and thus they are modelled by the elastic perfectly plasticDrucker-Pragermodel. Although themodel mechanical parameters of the starter dykeare assumedby the authors, the embankment dykes zone is given the same elasticity andstrength parameters as the underlying mill tailings in addition to zero dilation angle.Also, the vertical permeability-void ratio functions of the embankment dyke andstarter dam zones are predicted from the formula proposed by Chapuis [51]:k ¼ 2.4622 [d10
2e3/1 þ e]0.7825 (where k is in cm/s and d10 is in mm), where d10 is0.12 mm for the embankment dykes materials being obtained from the gradation ofthese materials which is extracted, by normalisation, from the gradation of theunderlyingmill tailings reported byQiu and Sego [33] and d10 is 0.18 mm for the starter
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dam materials [50]. Thus, the starter dyke initial permeability of 0.0241 cm/scorresponding to the considered initial void ratio of 0.5 [50] is obtained. But the initialpermeability of embankment dykes (0.0109 cm/s) is computed based on an initial voidratio of 0.7, which is calculated for a relative density of 60% and minimum andmaximum void ratios of 0.5 and 1; refer to [52]. In addition, the permeability of thestarter dyke materials is considered isotropic, whereas the embankment dykes zone isassumed slightly anisotropic with vertical to horizontal permeability ratio of 0.8; referfor example to [47]. Regarding the unsaturated characteristics, the SWCC of theembankment dykes zone is assumed to be governed by the formula proposed by VanGenuchten [48] while the SWCC of the starter dam materials is obtained from thelaboratory tests results reported byHerasymuik et al. [50]. In addition, the unsaturatedhydraulic permeability functions of the materials in both zones are found from theequation of Irmay [53]: kus/k ¼ Se
C with kus and k being the unsaturated and saturatedpermeability values, respectively, Se is the effective degree of saturation, and C is afitting constant. In this work, C is assigned the value 3, which leads to accurate resultsfor soils with uniform pore size distribution [54].
5.4.3. Drainage layer and bedrock foundation
The response of these zones is considered linear isotropic elastic. The physicalparameters of the limestone bedrock considered including the void ratio, density,and permeability are adopted from [55] while its elastic parameters are taken from[56]. On the other hand, the parameters required for modelling the drainage layer arepostulated by the authors.
5.4.4. Upper foundation layer
The parameters of the upper foundation layer being very stiff clayey glacial tillmaterials are obtained from [57]. These materials represent a typical foundationunderlying the Tar Island tailing dyke, as investigated by Morsy et al. [57]. Theresponse of these materials is idealised by the Modified Cam Clay model; refer toRef. 34 for more details on this model. With respect to the permeability-void ratiofunction, the equation k(e) ¼ cv krc gw/[P0(1 þ e)] [18] (where P0 is the effectivepressure, e is the void ratio, cv is the coefficient of consolidation, kr is therecompression index) is used considering cv ¼ 1 6 1077m2/s, kr ¼ 0.013, andconsolidation points (P0, e) obtained from consolidation data [57]. Thus, based onthe above equation, an initial permeability of 6.89351E-07 cm/s corresponding to aninitial void ratio of 1 [57] is obtained.
6. Results and discussions
The response of the system is assessed by the deformation and pore water pressure,which are the primary fields obtained from the coupled analysis.
6.1. Pore pressure
Figure 5 shows the contours of the pore pressure evolution plotted at the end of eachimpoundment construction stage. The results show that the beach becomes fullysaturated after the first impoundment stage with a phreatic surface level being
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coincident with the internal boundaries of the embankment dykes. Although the porepressure decreases moving towards the embankment dykes and starter dam possessingrelatively large permeability, most of the beach underneath the embankment dykesremains largely underconsolidated (the total pore pressure is much larger than thehydrostatic pore pressure) during the staged construction. The low permeability ofslime and beach tailings seems to limit the flow of water in these zones leaving themunder poorly drained conditions. Further, as noticed in Figure 5, the low permeability-foundation of the facility results in producing a large pore pressure domainwith a bulb-like shape at the impoundment-foundation interface; such observation is consistentwith the results reported in [58] and [59]. As shown in Figure 6, the drainage conditions
Figure 5. Evolution of pore pressure during staged construction.
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in the system impoundment are inspected closely byplotting the timehistory of the porewater pressure against the corresponding effective confining pressure at various points,namely, points 1, 2, 3, 4, 5 and 6 (refer to Figure 2 for the locations of these points). Itcan be observed from Figure 6 that at both points 1 and 2, which represent the bottomportions of the slime and the beach half neighbouring the slime, respectively, that theeffective pressures increase negligibly compared to the corresponding pore pressures inthe first 1000 days of construction.Hereafter, the construction loading at these points iscarried almost solely by the pore pressure marking a semi-undrained response at thesepoints. However, point 3 in the lower portion of the beach under the upperembankments shows a partial drainage state but with a remarkably greater rate ofincrease in pore pressure than the rate of increase of the effective pressure during the
Figure 6. Time history of pore pressure (pw) and effective confining pressure (P0) at variouspoints in the impoundment; refer to Figure 2 for the points locations.
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deposition of the impoundments. Point 4 on the other hand, which is relatively close tothe internal drainage medium, shows a different drainage trend. It demonstrates verylow pore pressures at the early construction stage in which the point has not yet taken aconsiderable construction load that generates significant excess pore pressure. Withprogress of construction (after 750 days) the pore pressure starts to increase with ahigher rate than the effective pressure and the construction loading is continued to becarried by both the pore and effective pressures until reaching a phase (after 2000 days)where the pore pressure rate almost vanishes while the effective stress continuesincreasing: hydraulic equilibrium is reached. Similar to the response of point 3, points 5and 6 in themiddle portion of the beach part adjacent to the embankment dykes exhibitpartial drainage conditions but with relatively low pore pressure dissipation rates oncethey start to feel the loading of the disposed tailings; i.e. after almost 1330 days.Consequently, the results and discussion above indicate that the slime zone and beachhalf portion adjacent to this zone seem to operate under semi-undrained states. Also,the beach portion adjacent to the embankment dykes exhibits a partial drainage statebut with low pore pressure dissipation rates except in the vicinity of the drainage; asseen when inspecting the drainage response of point 4. This implies that, under theoperational conditions considered, the shear strength represented by the instabilitystrength angle given to the beach zone (refer to Table 2) is unsafe shear strength, i.e. itoverestimates its shear strength,which should by represented by the residual undrainedshear strength implying post instability response. On the other hand, the compactedembankment dykes zone exists under an unsaturated state during the stagedconstruction, and therefore the effective failure strength angle is appropriate. Further,the results demonstrate the transient seepage state dominating the facility under itsstaged construction and thus they confirm that traditional seepage analyses cannotaccount for the transient flow induced by the consolidation of tailings.
6.2. Horizontal movement
The behaviour of the horizontal displacement can directly reflect the stability of theembankment staged construction; refer for example to [60]. Thus, in this study, thehorizontal displacement response of the impoundment is considered as an indicationof its stability. Figure 7, showing the contours of the evolution of the maximumhorizontal movement during the staged construction, indicates that the largesthorizontal movement is developed in the middle portion of the tailings beachimmediately beneath the embankment dykes. Because of the deformation compat-ibility between the embankment dykes and beach, the large horizontal movementexperienced by the beach tailings being contractive materials operating under poorlydrained states, as seen above, results in considerable horizontal displacements in theadjacent upstream portion of the embankment dykes. Clearly, such deformationcompatibility cannot be simulated with the 1D consolidation analyses routinelycarried out on the embankments; refer for example to Ref. 61. It is also noticed fromFigure 7 that the maximum lateral movement starts to become tangible in the thirdconstruction stage; i.e. when the impoundment reaches a considerable height. Morespecifically, during the last construction stage (last 2.2 years of construction) themaximum lateral movement increases by 100% (from*0.4 m to 0.8 m). Such lateraldisplacement with this remarkable rate indicates that the stability of the beachtailings forming the foundation of the upstream portion of the embankment dykes,and thus the stability of these dykes, is at risk. This lateral deformation response can
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be expected in light of the field observations reported by Leroueil et al. [62], whoindicated that the lateral movement increases quickly once the undrained conditionstarts to operate with a profile, being compatible with the time history of the inducedpore pressure. Moreover, Figure 7 shows that at the end of construction anappreciable differential horizontal displacement (almost 0.3 m) at the dykes-beachinterface in the middle portion of the facility occurs. This large differential movementwill result in longitudinal cracking and thus will increase the hydraulic fracturingpotential at this location.
6.3. Settlement
The stability of the embankment dykes is also dictated by the differential settlementof such dykes and therefore the vertical settlement is plotted along the bases of these
Figure 7. Evolution of the maximum horizontal movement during the staged construction.
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dykes at the end of construction. As noted in Figure 8, there is an appreciablesettlement between the part of the first dyke resting on the starter dam and its otherpart founded on the tailings beach. The settlement profiles for the upperembankment dykes which rest on relatively weak beached tailings show smoothsettlement curves with peaks that vary (in terms of the location and magnitude) withthe height of the embankment. Also, it is obvious that the bottom three embankmentdykes experience higher values of the differential settlements. More specifically, thesecond dyke located almost in the middle portion of the facility undergoes the largestvalue of differential settlement. The differential settlements along the bases of thesedykes will result in vertical cracks breaking up the dykes into blocks; refer to the fieldobservations made by Mittal and Hardy [63], and hence increasing the erosionpotential.
Although the operation of the dykes is mainly dictated by the differentialsettlement, the total settlement must also be accounted for, particularly for afreeboard requirement purpose. It is noticed that at the facility’s ultimate height,the embankment dykes zone will experience remarkable settlements which couldincrease the overtopping potential. Such excessive settlement should be consideredin the design process by accounting for additional freeboard, for example,through heightening the crest of the embankment dyke by an amountproportional to the anticipated settlement of the embankment dykes at theconsidered height.
7. Conclusion
Rational prediction of pore water pressures is fundamental to the correctness ofstability analyses of STDF during staged construction. The appreciation of porepressure by classical stability approaches is questionable not only because they do
Figure 8. Vertical settlement response recorded along the bases of embankment dykes at theend of construction; refer to Figure 2.
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not address deformations but also because they neglect the inextricable interactionbetween the hydraulic and mechanical responses of tailings, porous media.Following appropriate numerical modelling techniques, efficient coupled-deforma-tion analysis simulating staged construction process in a more pragmatic fashion canbe achieved. It is shown in this article that the staged construction loading can bemodelled more closely using a smooth time function instead of an abrupt loadingapplication as done in the traditional modelling of embankments construction. Thenonlinear finite element study made herein for a UTDF demonstrates the power of acoupled analysis-based approach in providing valuable information on the systemperformance for the final design stage. For instance, the response data obtained fromthe study, which in general was verified qualitatively with the relevant majorobservations reported in literature, reveals the time history of the drainageconditions exhibited by each zone in the facility. In addition to exploring the shearstrength operating in each zone in the facility, a major advantage of this revelation isenabling the designer to prepare more effective pore pressures monitoring planduring staged construction. To conclude, in combination with good judgment andrelevant history-based experience data on the stability of STDFs, a coupleddeformation analysis can be a powerful method toward ensuring efficient and safeoperation of the these facilities.
Acknowledgements
The research work is partially supported by Natural Sciences and Engineering ResearchCouncil of Canada, Canada (NSERC) and McGill University, Canada. The authors aregrateful for their generous support.
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