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3D Finite Element Analyses of a Corner at Aitik Tailings Dam in Sweden

ZARDARI, M.A.1*, MATTSSON, H.1 AND KNUTSSON, S.1

1Division of Mining and Geotechnical Engineering, Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden

The 3D finite element analyses were performed for the gradual raisings of a corner section of Aitik tailings dam, located in the north of Sweden. The purpose of the analyses was to investigate the potential risk of low compressive stresses or tensile stresses in the corner and to evaluate the slope stability of the dam for current and future raisings. The results indicate that the magnitudes of the minor effective principal stresses in the interior of the dam are sufficient to resist the development of soft zones or cracks in the dam and it is interpreted that there is no increased risk of internal erosion. The slope stability analyses show that the dam has enough safety up to a height of 76 m, if the dam is gradually strengthened with rockfill supports on the downstream side. Keywords: tailings dams, corner, cracks, internal erosion, consolidation, slope stability 1.0 Introduction

This study presents three dimensional (3D) finite element analyses of the corner between the two dam sections (E-F and G-H, shown in Figure 1) of the Aitik tailings dam, located in the north of Sweden. The purpose of the analyses is to identify zones of low compressive stresses or tensile stresses in the corner and to evaluate slope stability during sequential raising of the dam. It was suspected that low compressive stresses or tensile stresses in the corner may develop in the longitudinal direction when the lateral earth pressure, along the inside of the corner, will increase due to gradual raisings. Low compressive stresses in the corner may lead to soft zones. Hydraulic fractures (cracks) may develop in the corner, if the ground water level in the dam rises above the soft zones. The soft zones or cracks in the corner can be a potential source for initiation of internal erosion. The corner between the dam sections E-F/G-H is primarily raised with the upstream construction method (see e.g., Vick 1990). The construction work of the dam is in progress and the dam is being raised in stages. The dam is 37 m high in year 2012. It is planned to raise the dam up to a height of 76 m in year 2026. The corner was analysed previously with a two dimensional finite element model (Ormann and Bjelkevik 2009 and Ormann et al. 2011). In these studies it was suggested to perform three dimensional finite element analyses of the corner to get a better understanding of the state of stresses that can develop during sequential raising of the dam. In this paper, the corner was analysed with the finite element program PLAXIS 3D (Brinkgreve et al. 2011) to locate the zones of low compressive stresses and to find out the slope stability of the dam.

Figure 1 Satellite view of Aitik tailings dam and i 2.0 Modeling with PLAXIS 3D

A plan view of the corner is displayed in Fmodifications, has been chosen for the analyses. sensitive to the potential development of low compressive stresses or tensile stressesof the dam.

Figure 2

Satellite view of Aitik tailings dam and impoundment (Google maps

3D

of the corner is displayed in Figure 2. The region BBDD of the corners been chosen for the analyses. Geometrically, this region is considered to be

development of low compressive stresses or tensile stresses

Figure 2 Plan view of the corner E-F/G-H (Sweco 2011)

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mpoundment (Google maps 2011)

of the corner, with some is considered to be the most

development of low compressive stresses or tensile stresses than the other parts

2011)

The 3D model of the corner is material zones is illustrated in Figure 4sands according to the unified soil+390 m in year 2012. The rate of the dam will be raised 2.5 m annuallwere simulated in 19 stages. Each stage consists of a raising phase over 10 days folconsolidation phase over 355 days.

Figure 3

The constitutive behaviour of all the material zones in the dam was represented with the Mohr(MC) model. Table 1 shows the parameters of the MC model. for all the materials. The angle of dilatancy of each material is assumed to be

The 3D model of the corner is shown in Figure 3. The cross section of the corner with the different Figure 4. The material zones 2, 4, 5, 6, 7 and 8 can be classified as silty

sands according to the unified soil classification system (Wagner 1957). The existing level of the dam is. The rate of raising of the dam is 3 m per year from level +376 m to +409 m, while

the dam will be raised 2.5 m annually from level +409 m to +429 m (Figure 4). stages. Each stage consists of a raising phase over 10 days fol

consolidation phase over 355 days.

Figure 3 Three dimensional model of the corner E-F/G-

Figure 4 Cross section of the corner E-F/G-H

of all the material zones in the dam was represented with the Mohrthe parameters of the MC model. The Poisson’s ratio is assumed to be 0.33

for all the materials. The angle of dilatancy of each material is assumed to be zero.

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igure 3. The cross section of the corner with the different 7 and 8 can be classified as silty

The existing level of the dam is raising of the dam is 3 m per year from level +376 m to +409 m, while

igure 4). The raisings of the dam stages. Each stage consists of a raising phase over 10 days followed by a

-H

of all the material zones in the dam was represented with the Mohr-Coulomb The Poisson’s ratio is assumed to be 0.33

zero.

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Table 1 Parameters of the Mohr-Coulomb model (Jonasson 2007, Pousette 2007 and Jonasson 2008)

Note: γunsat is the unit weight above phreatic level, γsat is the unit weight below phreatic level, kx and ky is the hydraulic conductivity in horizontal direction, kz is the hydraulic conductivity in vertical direction, E is the Young’s modulus, c' is the effective cohesion and φ' is the effective friction angle. The following boundary conditions were used in the 3D finite element model (Brinkgreve et al. 2011):

1. The vertical model boundaries with their normal in x direction (parallel to the yz plane) are fixed in x direction and free in y and z directions.

2. The vertical model boundaries with their normal in y direction (parallel to the xz plane) are fixed in y direction and free in x and z directions.

3. The vertical model boundaries with their normal neither in x nor in y direction are fixed in x and y directions and free in z direction.

4. The model bottom boundary is fixed in all x, y and z directions. 5. All the boundaries in the finite element model of the dam are closed for water flow except the top

and outer boundary. The Young’s modulus of elasticity E of tailings is dependent on confining effective stress (Jonasson 2007). For raisings of the dam from level +409 m to +429 m, the Young’s moduli of the tailings material zones 2, 5 and 7 (cf. Figure 4) were increased to 17350 kPa, 12296 kPa and 7979 kPa, respectively. It is relevant to mention here that the downstream side of the corner has been strengthened with rockfill banks. These rockfill banks have been placed during various raising phases to increase slope stability of the dam. The details of the volume of rockfill banks utilized can be found in another study (Ormann 2012).

Material type

γunsat kN/m3

γsat

kN/m3

kx= ky

m/s

kz

m/s

E kN/m2

c' kN/m2

φ' º

Moraine (initial dike) 20 22 1×10-7 5×10-8 20000 1 35

Layered sand tailings

17 18.5 5×10-7 5×10-8 9312 9.5 22

Moraine (dikes)

20 22 5×10-8 1×10-8 20000 1 37

Compacted sand tailings 16 19 1×10-6 1×10-7 8790 13 26

Sand tailings soft at top 18 18 1×10-7 1×10-8 3048 6 18

Compacted sand tailings (dikes)

16 19 1×10-6 1×10-7 7200 13

26

Sand tailings layered at top 17 18.5 5×10-7 5×10-8 3895 9.5 22

Filter 18 20 1×10-3 1×10-3 20000 1 32

Rockfill (downstream support + external erosion protection)

18 20 1×10-1 1×10-1 40000 1 42

3.0 Results of the finite element analyses

A fully coupled deformation and consolidationraisings of the corner by allowing the raising. From this analysis, the magnitudes and directionevaluated. In addition, analysis of safety potential failure zones during successive raisings of the dam. Idenoted by a positive sign; whereas the tensile stresses are indicated with a 3.1.0 Minor effective principal stresses

Figure 5 presents the distribution raising. It is observed that minor effective principal stressesonly on the top surface of the dam. effective principal stresses from stresses seem to be sufficient (greater than zero)The minor effective principal stresses within the damdirected in the longitudinal directioneffective principal stresses in the not likely to develop at these locations in the dam. internal erosion in the dam corner.

Figure 5 Distribution of minor effective principal stresses in the dam after visibility, the height of the figure is enlarged twice the original size)

Results of the finite element analyses

A fully coupled deformation and consolidation analysis was conducted raisings of the corner by allowing the tailings material to consolidate and gain strength before the next raising. From this analysis, the magnitudes and directions of the minor effective principal stresses were

of safety was also performed to compute safety facsuccessive raisings of the dam. In this paper, the compressive stresses are

sign; whereas the tensile stresses are indicated with a negative

Minor effective principal stresses

he distribution of minor effective principal stresses in the dam after minor effective principal stresses are in tension (in the range of

top surface of the dam. As expected, there is an increase in the magnitude of the minor from the top surface to the bottom of the dam. The minor effective principal

(greater than zero) to resist the formation of soft zones or cracks he minor effective principal stresses within the dam (level +376 m to the top surface)

in the longitudinal direction, see e.g., Figure 6. Because of the high magnitude of the effective principal stresses in the interior of the dam body, transverse soft zones or transverse cracks are not likely to develop at these locations in the dam. It can be interpreted that there is no

ner.

minor effective principal stresses in the dam after 18th raisingthe height of the figure is enlarged twice the original size)

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conducted to simulate gradual tailings material to consolidate and gain strength before the next

of the minor effective principal stresses were performed to compute safety factors and to observe the

n this paper, the compressive stresses are negative sign.

effective principal stresses in the dam after the 18th in the range of 0 to -10 kPa)

As expected, there is an increase in the magnitude of the minor he minor effective principal

to resist the formation of soft zones or cracks in the dam. (level +376 m to the top surface) are mainly

, see e.g., Figure 6. Because of the high magnitude of the minor , transverse soft zones or transverse cracks are

there is no increased risk of

18th raising (for the sake of

the height of the figure is enlarged twice the original size)

Figure 6 Direction of minor effective principal stresses at a

3.2.0 Slope stability

The stability of the dam was evaluated infactors for all the raising phases and associated consolidation phases of the dam. construction stages, the factor odissipation of the excess pore pressuresof the dam is most critical immediately after a raising phase.

minor effective principal stresses at a depth of 50.5 meters (level +376 m) from the top surface of the dam after 18th raising

The stability of the dam was evaluated in terms of the factor of safety. Figure 7 shows the all the raising phases and associated consolidation phases of the dam.

the factor of safety increased gradually during the consolidation period due to dissipation of the excess pore pressures and increase in effective stresses. This suggests that the stability of the dam is most critical immediately after a raising phase.

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depth of 50.5 meters (level +376 m) from the

Figure 7 shows the safety all the raising phases and associated consolidation phases of the dam. It is seen that in all the

the consolidation period due to . This suggests that the stability

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Figure 7 Factor of safety for all the raising and consolidation phases of the dam (here the terms R and C stand for raising and consolidation phases, respectively)

The factor of safety, in all the raising phases, is greater than 1.5 (Figure 7). The stability of the dam is satisfactory according to the Swedish safety guidelines document (GruvRIDAS 2007) which recommends a minimum safety factor of 1.5 for slope stability at the end of construction and during normal operation conditions for tailings dams. The possible failure mechanism of the dam after the 18th raising is illustrated in Figure 8. The most likely slip surface occurs along the light blue shape which indicates that the slip surface is nearly symmetric in the xz and yz planes. It is seen that the failure zone is deep and wide. The corner is not exactly symmetric, therefore, more deformations are observed in the yz plane as compared to the xz plane.

Figure 8 Illustration of the most likely failure mechanism of the dam after 18th raising (crest level +428.5 m)

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4.0 Conclusions

The results of the 3D finite element analyses have shown that the magnitudes of the minor effective principal stresses in the interior of the dam are satisfactory to resist the development of soft zones or cracks in the dam. It is interpreted that internal erosion is not likely to occur in the dam. In addition, the stability analyses indicate that the dam can be raised safely up to a height of 76 m provided the dam is gradually strengthened with rockfill supports on the downstream side. 5.0 Acknowledgements

The authors would like to thank Ms. Kerstin Pousette at Luleå University of Technology, Sweden, and Mr. Fredrik Jonasson at SWECO VBB Luleå, Sweden, for performing laboratory and field tests and for help with evaluation of material parameters. The authors are grateful to Ms. Linda Ormann at Fortum, Sweden, for providing data to develop the finite element model of the dam and for valuable discussions on the subject presented in the paper. The first author would like thank Lars Erik Lundbergs Foundation, Sweden, for granting him a scholarship to conduct some part of his Ph.D research. Luleå University of Technology as well as "Swedish Hydropower Centre - SVC" are acknowledged for financial support, which made the work possible. SVC has been established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät together with Luleå University of Technology, The Royal Institute of Technology, Chalmers University of Technology and Uppsala University. Participating hydro power companies are: Andritz Hydro Inepar Sweden, Andritz Waplans, E.ON Vattenkraft Sverige, Fortum Generation, Holmen Energi, Jämtkraft, Karlstads Energi, Linde Energi, Mälarenergi, Skellefteå Kraft, Sollefteåforsens, Statkraft Sverige, Statoil Lubricants, Sweco Infrastructure, Sweco Energuide, SveMin, Umeå Energi, Vattenfall Research and Development, Vattenfall Vattenkraft, VG Power and WSP. Boliden Mining is to be acknowledged for giving access to site information. 6.0 References Brinkgreve, RBJ., Engin, E., Swolfs, WM. (2011), “PLAXIS 3D Reference manual”, PLAXIS b.v., the Netherlands. Google. (2011), “Satellite view of Aitik tailings dam near Gällivare, Sweden”, Available from http://maps.google.com [cited 15 November 2011]. GruvRIDAS. (2007), “Gruvindustrins riktlinjer för dammsäkerhet”, Svensk Energi AB/ SveMin, Stockholm. (In Swedish). Jonasson, F. (2008), “PM Förslag på materialparametrar för Övriga Material vid beräkning i Plaxis”, SWECO VBB, Luleå, Sweden. Uppdragsnummer 2166133310. (In Swedish). Jonasson, F. (2007), “Geoteknisk provtagning av anrikningssand damm EF och GH Aitik”, SWECO VBB, Luleå, Sweden. Uppdragsnummer 2473649. (In Swedish). Ormann, L. (2012), “Stabilitet damm E-F Aitik”, SWECO Infrastructure AB, Karlstad, Sweden. Uppdragsnummer 2168052. (In Swedish). Ormann, L., Zardari, MA., Mattsson, H., Bjelkevik, A., and Knutsson, S. (2011), “Numerical Analysis of Curved Embankment of an Upstream Tailings Dam”, Electronic Journal of Geotechnical Engineering, 16/I: pp. 931-944. Ormann, L., and Bjelkevik, A. (2009), “Hållfasthetsanalys av hörnet GH/EF i Aitikdammen”, SWECO Infrastructure AB, Stockholm, Sweden. Uppdragsnummer 2168007350. (In Swedish). Pousette, K. (2007), “Laboratorieförsök på anrikningssand från Aitik”, Internal working document, Luleå University of Technology, Luleå, Sweden. (In Swedish).

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SWECO, VBB. (2011), “Anslutning mellan damm G-H och E-F plan sektioner”, SWECO Infrastructure AB, Stockholm, Sweden. (In Swedish). Vick, SG. (1990), “Planning, design and analysis of tailings dams”, BiTech Publishers Ltd. Richmond, B.C. Wagner, AA. (1957), “The use of the unified soil classification system by the bureau of reclamation”, In: Proceedings of the Fourth International Conference SMFE, Vol.1, Butterworths, London. pp.125-134.

Biography of authors

Muhammad Auchar Zardari is a doctoral student in Soil Mechanics and Foundation Engineering at the Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology (LTU), Sweden. He obtained the degree of Licentiate of Engineering from LTU in 2011. His research interests include finite element modelling of embankment dams, long term stability of tailings dams, constitutive modelling of granular materials.

Dr. Hans Mattsson is an assistant professor at the Division of Mining and Geotechnical Engineering at the Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, Sweden. His research interests are: geotechnical modeling, numerical analysis, hydropower dams, tailings dams, internal erosion etc.

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Sven Knutsson is a professor at the Division of Mining and Geotechnical Engineering at the Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, Sweden. His research interests are: frost, frost action, thaw weakening, permafrost, snow mechanics, water retention dams, internal erosion, long term stability of tailings dams, mechanical properties of coarse grained material, use of industrial by-products, dredging and deposition of dredged sediments.