Numerical Modelling of Seismic Liquefaction for Bobadil Tailings Dam

B. Ghahreman Nejad1, H. Taiebat2, M. Dillon1 and K. Seddon1 1ATC Williams Pty Ltd, Melbourne

2School of Civil and Environmental Engineering, University of New South Wales

One of the causes of tailings dam failure has been seismically induced liquefaction during earthquakes. Liquefaction, if mobilised, significantly reduces the stiffness and strength of affected soils in the embankment dam or its foundation and may lead to large deformations and dam failure. This paper reports the results of seismic liquefaction assessment and deformation analyses of Bobadil tailings dam located in Tasmania. The tailings dam consists of a perimeter rockfill starter dam which has been raised in stages using the “upstream” construction method. The embankment raises (formed by clay or coarse tailings) are constructed over a foundation of previously deposited tailings in the impoundment which is potentially susceptible to liquefaction. Extensive field and laboratory tests were carried out to assess the tailings liquefaction potential and also to determine the material properties required for seismic stability and deformation analyses. Numerical modelling of seismic liquefaction and deformation analyses were carried out to predict the magnitude and pattern of deformations that may lead to uncontrolled release of tailings. The results of these analyses are presented and compared with literature report of those observed during past earthquakes. Keywords: Numerical, modelling, earthquake, tailings dam, liquefaction analysis.

Introduction Seismic design of earth and rockfill dams often requires assessment of the earthquake induced ground and dam movements, and in particular the range of crest settlements during and after earthquake loading. In many instances, designers employ dynamic numerical analyses to evaluate the deformation of embankment dams. When the soils or rocks in a dam and its foundation are dense, the analyses can often be carried out using relatively simple elastic-plastic constitutive models. However, when saturated loose granular soils are involved, such as in tailing dams, there is a potential for soil liquefaction, and therefore the analysis becomes more complex as it requires a more complex model for the material behaviour.

A number of tailings dams have failed or suffered severe damage during earthquakes. Data of the failure of 185 dams (USCOLD, 1994) reveals that 60% of failures involved uncontrolled release of tailings, among them 20% failed due to seismic activity. A classic example is the failure of two dams in Japan in 1978 (Mochikoshi dams) due to liquefaction of the tailings materials behind the dams under a 7 magnitude earthquake with an estimated peak ground acceleration of about 0.15 to 0.25 g. One of the dams failed during the shaking and the other 24 hours after the main shock (Marcuson et al., 1979).

The contractive tendency of loose granular materials, such as those deposited as sub-aqueous tailings, under cyclic loading results in volumetric densifications under drained conditions and generation of excess pore pressures under undrained conditions. Under undrained or partially drained conditions, the effective stresses in a saturated tailings may reduce to such an extent that the soil loses its load bearing capacity and fails like a viscous liquid; this condition is termed liquefaction. The liquefaction

behaviour of a soil under cyclic loading can be experimentally evaluated in terms of pore pressure generations, volumetric compaction, or the number of cycles of load required for liquefaction. There are uncertainties related to the nonlinear behaviour of loose materials under dynamic loading and under non-conventional stress paths which are difficult to test. Therefore, the behaviour of loose materials susceptible to liquefaction is often modelled approximately using practical procedures and simplified assumptions.

The state of practice in liquefaction analysis can be generally categorised into three approaches; the traditional approach, the semi-empirical approach, and the approach based on constitutive modelling of liquefaction.

For many years, the state of design practice in liquefaction analysis has been based on the procedures developed by Seed and his co-workers (see for example Seed 1987, Seed et al. 1975). This approach cannot account for generation and dissipation of pore pressures and also cannot simulate yields or failure.

The semi-empirical approach incorporates the effects of cyclic loading, in terms of unrecoverable plastic strains or excess pore water pressures obtained from laboratory simulations, directly into constitutive formulations. This method, proposed by Martin et al. (1975) and modified later by Byrne (1991), is robust and relatively simple, and involves a level of approximation compatible with the level of accuracy expected from laboratory tests. It can also simulate the generation and dissipation of pore water pressures and the consequent settlement after consolidation of the soil (Taiebat and Carter, 2000).

The constitutive based approach is more complex as it takes into account the hysteretic non-linear behaviour of loose material under cyclic loading. This developing approach (see for example Dafalias, 1986, Zienkiewicz et al. 1990, Beaty 2001, Byrne et al. 2006, Taiebat et al.

2010) can take into account the contraction, dilation, yields, failures, and post liquefaction strength. However, application of this approach is limited mainly to special cases involving conventional stress paths.

Apart from the three general approaches, there are also other methods employed in stability analysis of tailings after earthquakes, among them is the work of Seed et al. (1984) and Castro (2003), where the post-earthquake strength of the tailings were evaluated and used in post earthquake stability analyses. However, these method cannot give any estimate of the post-failure deformation of embankments and tailings.

Both the semi-empirical and the constitutive based approaches have been implemented in FLAC 6.0 (Itasca 2008). A constitutive based model was also implemented in DIANA by Aydingun and Adalier (2003). However, the constitutive based models require comprehensive laboratory tests to be used for calibration of model parameters, and therefore are beyond the scope of this study. The semi-empirical model that has been implemented in FLAC, called Finn-Byrne’s model, requires only two model parameters that can be obtained from laboratory tests or empirical relationships. A brief description of the general framework of the semi-empirical model, which was used in the current study, is given below (Taiebat and Carter, 2000). Within the framework of the theory of plasticity, the total strain increment, ε, is decomposed into the elastic strain increment, εe, and the plastic strain increment, ε p, by a simple superposition, i.e.:

ε =ε e +ε p

The stresses can be related to the total strains by a suitable constitutive relationship. Under cyclic loading, another component of plastic strain increment, which is the direct result of cyclic loading only, εc, is added to the strains:

ε = ε e + ε p

+ ε c The general stress-strain relationship can therefore be given as:

σ′= σ – p = D(ε -εc)

where σ and σ´ are the total and effective stresses, p is pore water pressures and D is the stiffness matrix of the soil skeleton.

The additional plastic strain, εc, generated during drained cyclic loading can be obtained from experimental tests on samples of soil and used directly in the formulation.

The plastic cyclic strain can also be evaluated by empirical relationships. FLAC 6.0 used the empirical relationship given by Byrne (1991) where the cyclic volumetric strain, εvd, is related to the cyclic shear strain amplitude, γ, as:

))(exp( 21 γε

γε vdvd CC −=

∆

In the above equation C1 and C2 are constants and can be evaluated by laboratory tests. In many cases C2 can be

taken as 0.4/C1, reducing the cyclic model parameters to one independent constant.

In this work, the response of a 34 m tailing dam under the effects of an earthquake loading was analysed using the Finn-Byrne liquefaction model, as implemented in FLAC 6.0. A description of the dam and the design criteria will be given first followed by a comprehensive description of the seismic deformation analyses of the dam. The results of the seismic analyses of the tailing dam, considering both cases of liquefiable tailings and non-liquefiable tailings will be reported and compared in the following sections.

Tailings Dam Details The Bobadil tailings dam is the primary facility for the storage of tailings at Rosebery zinc-lead-silver mine. The tailings storage facility was constructed as a traditional turkeys nest dam and first commissioned in 1974. The perimeter starter embankment was constructed using a select sandy/gravelly fill and rockfill over a foundation formed by a glacial till overlying metamorphic bedrock. The starter embankment has been raised in several stages using the “upstream” construction method and the facility has been developed to a side-hill storage.

The embankment section at the highest point was chosen for the stability and deformation analyses. Figure 1 shows the tailings dam profile outlining the 34 m high embankment including the latest 2 m raise to RL 195 m. The section was simplified for the purposes of undertaking the analysis.

Design Criteria Two levels of earthquake loading were considered in the analysis and design, as recommended by ANCOLD (1998):

• Operating Basis Earthquake (OBE): OBE is for the purposes of evaluating the serviceability of a dam. It is an earthquake which could reasonably be expected to occur during the life of the dam, and should only result in minor, easily repairable damages. The dam and appurtenant structures should remain functional after the occurrence of earthquake shaking not exceeding the OBE. An annual exceedance probability (AEP) of 1 in 500 was adopted for the OBE based on ANCOLD (1998) guidelines giving a 10 percent chance of exceedance in 50 years.

• Maximum Design Earthquake (MDE): MDE will produce the maximum level of ground motion for which the dam should be designed or analysed. It is the minimum seismic load for which the impounding capacity of the dam should be maintained. Given the consequence category of Bobadil tailings dam is “High C”, a seismic event with PGA = 0.21 g and an associated magnitude of M = 6.75, was adopted as the Maximum Design Earthquake. This MDE corresponds to an event with a return period of 10,000 years. For the MDE event, a factor of safety less than 1.0 (using pseudo-static screening) is acceptable provided that a comprehensive analysis can demonstrate breach would not occur.

One earthquake time history with characteristics scaled to the site conditions was recommended by the site seismologist. The input motion was considered to be representative of the MDE event and was adopted for the seismic deformation analysis. The input motion is

presented in Figure 2a. The Fourier power spectrum of this earthquake was derived in order to identify the dominant range of frequencies as shown in Figure 2b. It can be seen that the energy of the input motion is more pronounced at frequencies of less than 10 Hz.

Figure 1: Typical Tailings Dam Section Used for Analysis

-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5

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2 )

0.0000

0.0005

0.0010

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0.0030

0 5 10 15 20

Frequency (Hz)

Four

ier P

ower

Figure 2: Acceleration Time History (a) and Fourier Power Spectrum (b) of the Design Earthquake

Seismic Deformation Analysis Background The liquefaction potential of the tailings was assessed on the basis of CPTu test results. The results indicated that only under the MDE load case the tailings may partially liquefy (i.e. the factor of safety against liquefaction < 1.1). Although the tailings are susceptible to liquefaction, post liquefaction stability analyses of the embankment section yielded a factor of safety greater than 1.7, indicating no or limited deformation of the embankment due to liquefaction after the earthquake.

Nevertheless this does not make allowance for any deformation which may occur during the shaking event. Initial pseudo static seismic analyses of the dam under the MDE loading resulted in a critical factor of safety of less than one, indicating that some deformation could be expected during the earthquake. Further analysis was subsequently carried out in order to evaluate the magnitude and the pattern of deformations which could be expected from the MDE seismic event. This was felt to be prudent practise due to the limitations of the pseudo-static approach and the adopted consequence category of “High C”. Methodology The major focus of the seismic deformation analyses was to investigate the possible displacements that could lead to the failure of the dam and uncontrolled release of tailings and water in the event of the MDE. One common failure mode is an earthquake induced crest settlement in excess of the available freeboard. The prediction of such movements is to some extent dependent on the analysis procedure used. The dynamic analysis of the embankment was conducted during the early stages of the work, using the equivalent linear analysis and the Newmark’s displacement method (Newmark, 1965), employing the computer program SHAKE (2003). Nonetheless it was concluded that due to the limitations of the Newmark’s method in prediction of the seismically induced deformations of liquefiable materials, a more rigorous deformation analysis method should be employed. A plane strain dynamic deformation analysis of the embankment was performed using the software FLAC 6.0 (ITASCA 2008) and its built-in elastic-plastic model of Mohr-Coulomb coupled with the Finn liquefaction model. The embankment materials were assumed to obey the Mohr-Coulomb failure criterion, requiring stiffness and strength parameters for all materials used in the dam and its foundation. The Finn model provides an empirical relationship between cyclic shear strain and the

(a)

(b)

incremental volumetric strains. The simplified formulation proposed by Byrne (1991) was adopted for the tailings liquefaction. Further details about these models can be found in the FLAC Manual (Itasca 2008).

The variation in stiffness of the embankment materials at different depths was considered in the modelling employing FLAC’s built-in programming language, FISH. A non-associated flow rule was assumed for different zones within the embankment, assuming the dilation angle of the material is equal to zero.

The finite difference model of the embankment was generated in two stages to better simulate the construction sequences. The initial state of stresses within the embankment and its foundation was established first, as well as the state of pore water pressures within the embankment. Water level in the pond was considered to be at a distance of approximately 10 m from the upstream edge of the embankment crest, generating a very conservative phreatic surface in the dam. The distribution of pore pressure within the embankment and in the bedrock was evaluated automatically by the software.

The earthquake motion was applied to the model base as a shear stress boundary condition in order to establish “quiet” boundaries, using a method described in the FLAC manual (Itasca 2008). To limit the minimum size of the elements/zones in the model the earthquake record was filtered to exclude the high frequency content. As quoted in FLAC manual “Numerical distortion of the propagation of wave could occur in a dynamic analysis if

the spatial element sizes are coarse as compared to the propagating wave length”.

Kuhlemeyer & Lysmer (1973) showed that an accurate prediction of displacement could be achieved if more than 4 elements per wave length are allowed. As shown previously in Figure 2b, most of the energy of the input motion was at frequencies less than 10 Hz. Therefore the seismic record was filtered to remove frequencies greater than 10 Hz, thereby a more reliable prediction could be achieved using a practically possible minimum size for the finite difference mesh.

Two cases were considered for deformation analysis including:-1) Tailings liquefaction, 2) No tailings liquefaction. Both cases were analysed for two sets of material parameters, the upper and the lower bound of the magnitudes of stiffness parameters, as described in the following section. Material Properties Overview The properties of the materials used in different zones of the dam were obtained from site investigations, laboratory tests, published literature, established correlations and previous experience. A summary of the properties used in the analyses are presented in Table 1. The discussions provided in the following sections give background information regarding the selection of some of these parameters.

Table 1: Summary of Stiffness and Damping Properties

Material c′ /Su

(kPa) φ′ ν

Gmax (MPa) ξ

Modulus Reduction &

Hysteretic Damping L.B. U.B.

Bedrock Elastic 0.4* *1,350 0.5 Shake-Rock (Schnable 1973)

Glacial Till 1 40 0.33 0.92σ’m

Min=42 22σ’m0.5 0.5 Shake-Gravel (Rollins 1998)

Select Fill 1 39 0.33 0.92σ’m

Min=42 22σ’m0.5 0.5 Shake-Gravel (Rollins 1998)

Compacted Tailings Sumin =40

Su/σ′vo = 0.38 0 0.45 4.8σ’m0.5 9.7σ’m0.5 0.5 Shake-PI=0 (Vucetic & Dorby 1991)

Clay Raise Sumin =40

Su/σ′vo = 0.35 0 0.45

0.35σ’v

Min=40

0.7σ’v

Min=80 0.5 Shake-PI=15 (Vucetic & Dorby 1991)

Rockfill στ − Function 0.26 13.2σ’m0.5

Min=80 26.4σ’m0.5 0.5 Shake-Gravel (Shibuya 1990)

Tailings Sumin = 10

Su/σ′vo = 0.2 0 0.45 4.2σ’m0.5 *8.3σ’m0.5 0.5 Shake-PI=0 (Vucetic & Dorby 1991)

c′ is cohesion, φ′ is friction angle, ν is Poisson’s ratio, Gmax is small strain shear modulus, ξ is initial damping ratio, τ is shear stress, σ is normal stress, σ′m is mean effective stress (kPa) , Su is undrained shear strength; σ′ vo is vertical effective stress, L.B. and U.B. are the lower and upper boundaries for shear modulus and PI is the Plasticity Index..

* Based on field measured shear wave velocity.

Small Strain Shear Modulus In order to check the sensitivity of the predicted deformations to the adopted shear modulus, two levels of shear moduli were used in the analysis as shown in Table 1. The small strain shear modulus and Poisson’s ratio of the foundation bed-rock and tailings were determined, using the S (shear) and P (compressional) wave velocities measured in a seismic refraction survey over the foundation and tailings beach areas.

The results of shear box tests conducted by Monash University were incorporated into a shear normal stress (τ-σ) function and used in the analyses. This is in agreement with the previous studies on the shear strength of rockfill (e.g., Leps, 1973) that shows the shear strength varies markedly as a function of the normal stress. This negates the dilation effect and therefore a dilation angle of zero was adopted for the analysis. The small strain shear modulus, Gmax, for the rockfill was taken as a function of the mean effective stress, σ′ m, using the empirical relationship reported in Kramer (1996):

5.0max2max 220 mKG σ ′=

where Gmax and σ′m are in kPa

K2max depends on the quality and relative density of the material. For gravels, K2max ranges from 80 to 180. A value of 120 was adopted for the rockfill to reflect its perceived medium quality (i.e. relatively high fines content).

The following equation has been provided by Egan and Ebeling (1985) in SHAKE (2003) to derive the small strain shear modulus of cohesive soils, such as the clay zone in the embankment profile:

uSG 2000max =

where Su is the undrained shear strength which in turn is a function of the effective overburden stress. The shear modulus function for the glacial till foundation, the selected fill embankment and the tailings raises were all derived from the results of monotonic and cyclic triaxial and simple shear tests conducted at the University of Sydney.

Shear Modulus Reduction The strain softening behaviour of material during cyclic loading is traditionally considered by reducing the shear moduli of the material as functions of shear strains. The modulus reduction curves used in the dynamic analysis are presented in Figure 3 for the different materials. These curves were obtained from the database included in the SHAKE (2003) software. The curves have been incorporated in the analyses as hysteretic damping functions to describe how the stiffness decreases at larger strains in the elastic region.

The modulus reduction function for the rockfill shown in Figure 3(a) is adopted from Shibuya et al. (1990), recommended for gravels and granular fills. Note that this

curve provides for very little strain softening during cyclic loading; a behaviour considered appropriate for the rockfill used in the embankment construction.

The modulus reduction curve for tailings and embankment raise (clay) are from Vucetic and Dobry (1991), recommended for fine grained materials with a plasticity index (PI) of 0 and 15, respectively. For glacial till and select fill materials, the adopted function is from Rollins et al. (1998), as shown in Figure 3(c).

The modulus reduction curve for bedrock is from Schnabel (1973), Figure 3(a).

Damping Damping describes the hysteretic dissipation of energy within a material when subjected to cyclic loading. The variation of damping ratios with the shear strains developed during cyclic loading were also extracted from the SHAKE (2003) database for different materials. In FLAC, the hysteretic damping was applied using the built-in default model and the dynamic characteristics of different materials represented by different curves in Figure 3. The default hysteretic model is a S-shaped curve, resembling the variation of modulus or damping ratio versus logarithm of cyclic strain, which is represented by a cubic equation, with zero gradient at both small strain and large strain. The default model requires two parameters, L1 and L2 which can be obtained by curve fitting on the variation of modulus or damping ratio with shear strain.

An initial stiffness-proportional Rayleigh damping of 0.5% was adopted for different materials as the hysteretic damping shown in Figure 3 could not completely damp the high frequency components of the dynamic inputs.

Finn-Byrne Model Liquefaction Parameters The pore pressure generation due to cyclic loading is a secondary effect resulting from the irrecoverable volumetric contraction of the soil matrix. As stated earlier, Finn’s constitutive model with Byrne’s simplified formulation (1991) was adopted for estimation of the incremental reduction in volume, ∆εvd, as follows:

))(exp( 21 γε

γε vdvd CC −=

∆

In the above equation γ is the cyclic shear strain amplitude, εvd is the accumulated irrecoverable volumetric strain, and C1 and C2 are constants.

In this analysis C1 was determined from the field density measurements of tailings, adopting a conservative relative density of 28% for tailings. C2 was calculated as C2 = 0.4/C1.

It should be noted that Finn-Byrne model was only used for the tailings zone to allow for possible tailings liquefaction.

0

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0.0001 0.001 0.01 0.1 1 10Shear Strain (%)

She

ar M

odul

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atio

G/G

max

0

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10

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25

30

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ping

(%)

G/Gmax-Clay (PI=15 Vucetic&Dobry 91) G/Gmax-Clay (Flac Default)

G/Gmax-Tailings (PI=0 Vucetic&Dobry 91) G/Gmax-Tailings (Flac Default)

Damping-Clay (PI=15 Vucetic&Dobry 91) Damping-Tailings (PI=0 Vucetic&Dobry 91)

(a)

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0.0001 0.0010 0.0100 0.1000 1.0000 10.0000Shear Strain (%)

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io G

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ax

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ping

(%)

G/Gmax-Bedrock (Schnabel 73) G/Gmax-Rockfill (Shibuya 90)G/Gmax-Bedrock (Flac Default) G/Gmax-Rockfill (Flac Default)Damping-Bedrock (Schnabel 73) Damping-Rockfill (Shibuya 90)

(b)

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0.0001 0.001 0.01 0.1 1 10Shear Strain (%)

Shea

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/Gm

ax

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ping

(%)

G/Gmax-Glacial Till&Select Fill (Gravel Rollins 98)G/Gmax-Glacial Till&Select Fill (Flac Sigma 3)Damping-Glacial Till&Select Fill (Gravel Rollins 98)

(c)

Figure 3: Modulus Reduction and Damping for (a) Clay and Tailings; (b) Bedrock and Rockfill; (c) Glacial Till and Selected Fills

Summary of Results Dynamic analyses were performed with the input time history and the material properties explained in the previous sections. The results of the analyses are summarised in Table 2 for different initial shear moduli, and cases in relation to liquefaction. Table 2 shows the maximum relative displacement of the embankment crest in both horizontal and vertical directions calculated with respect to the top of the foundation level. All displacements are downwards or towards downstream. It can be seen that application of the lower (or upper) margin of the initial shear modulus does not necessarily results in a larger movement (e.g. for Case 2), due to the complex interaction of the earthquake motion and the dynamic behaviour of the embankment.

Table 2 indicates that the liquefaction analyses, Case (1), resulted in significantly larger horizontal displacements and /or lateral spreading. The results of the analyses for Case 1, with tailings liquefaction and using the upper

bound shear moduli, are graphically presented in Figures 4 to 9. Table 2: Summary of Predicted Displacements

Case Gmax

Predicted Peak Crest

Acceleration (g)

Crest Maximum Relative

Displacement3 (mm) Horizontal¹ Vertical²

Case 1 (Liquefaction)

U.B. 0.34 675 175

L.B. 0.18 780 180

Case 2 (No Liquefaction)

U.B. 0.23 24 230

L.B. 0.15 145 260

¹ Negative horizontal displacements indicate movement in the downstream direction and vice versa.

² Negative vertical displacement indicates settlement and vice versa. 3 Relative to the top of Glacial Till.

Figure 4 shows the contours of the excess pore water pressure ratio. This is the ratio of the excess pore water pressure over the confining effective stress prior to cyclic loading. The liquefaction state is reached when the excess pore pressure ratio approaches 1. As can be seen significant excess pore pressure are generated under the decant pond area near the surface which is attenuating with the distance from the decant pond.

The general pattern of deformation and displacement vectors as a result of application of the design earthquake is shown in Figure 5. It is evident that the predicted pattern of deformation involves settlement and slumping of the upper rockfill buttress and the embankment raise (tailings), while the lower rockfill buttress generally remains upright with significant lateral deformation in the downstream direction. Figure 6 presents contours of the maximum shear strain increments illustrating the potential failure zones and the location of mass movements.

Variations of the vertical deformations of the crest as a function of time, together with the acceleration of the dam at crest level are shown in Figure 7. The predicted peak crest acceleration is about 0.34 g as compared to the peak ground acceleration of 0.21 g. This indicates an amplification factor of 1.6 which compares well with those amplifications observed for embankment dams reported for the past earthquakes, for example by Matsumoto et al. (2005).

Figure 8 and Figure 9 show the contours of the predicted vertical and horizontal displacements. It is evident that the predicted highest vertical displacement occurs at the tailings beach with a magnitude of about 600 mm, followed by settlement of the embankment crest, by 175 mm. However, the upper section of the downstream slope moved upward due probably to the flow of liquefied tailings. These displacements attenuate rapidly with depth and indicate no evidence of significant movements of concern. The maximum horizontal displacement occurs in the upper section of the downstream slope. It is evident that a great portion of the tailings and embankment moves towards the downstream side.

0.20

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0.200 0.600 1.000 1.400 1.800

x100 m

x100 m

Exaggerated Grid DistortionMagnification = 5.000E+00Max Disp = 8.844E-01

(m)

Figure 4: Exaggerated Deformed Grid and Displacement Vectors (grey)

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0.200 0.600 1.000 1.400 1.800

x100 m

x100 m

Contour interval= 2.00E-01Minimum: 0.00E+00Maximum: 1.00E+00

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0.81.0

0.8

0.60.6

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Liquefaction is mobilised when the normalised excess pore pressure ratio is around 1. 0.2

0.2

Figure 5: Contours of Normalised Excess Pore Pressure Ratio

x100 m

x100 m

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0.200 0.600 1.000 1.400 1.800

Max. shear strain 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 8.00E-02 9.00E-02

Figure 6: Contours of Maximum Shear Strain Increment

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Vertical DisplacementHorizontal Displacement

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Figure 7: Predicted Horizontal Acceleration (a) and Relative Displacement (b) of the Crest

x100 m

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Figure 8: Contours of Vertical Displacement (m)

x100 m

x100 m

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Figure 9: Contours of Horizontal Displacement (m)

Similar patterns of deformations were also predicted for the models with the lower shear moduli (L.B.) of Case (1), with slightly higher magnitudes. As shown in Table 2 the maximum crest settlement is essentially higher when the lower bound values are adopted for each cases or when tailings are subjected to liquefaction. The highest horizontal crest displacement with approximately 780 mm of movement in the downstream direction was predicted for Case 1 with L.B. shear moduli.

Some indication of the possible magnitude of crest settlement when the embankment is not subject to liquefaction (ie Case 2) can also be obtained from the results presented by Swaisgood (2003). Swaisgood analysed the observed crest settlements of embankments subjected to earthquakes and provided an empirical relationship to predict the extent of the earthquake induced settlement. This relationship only requires the earthquake magnitude and peak ground acceleration (PGA). For the purpose of comparison with Case (2) (No Liquefaction), the predicted induced deformation from Swaisgood’s relationship was calculated as around 0.056% of dam height (including the foundation gravel). This is approximately 19 mm when the embankment crest is at RL 195 m. This settlement is significantly lower than the predicted settlements for Case (2) (Table 3). Swaisgood’s relationship is based on case histories of relatively well constructed embankment dams and hence expected to underestimate the possible crest settlement of a tailings dam constructed by partial upstream raising.

Conclusions The results of dynamic deformation analyses of a tailings dam are presented here for the cases with or without liquefaction of the tailings. In summary the results of the deformation analysis indicate that the maximum deformations will occur near the crest and at the upper part of the downstream slope. The horizontal deformation of the slope is significantly larger for the case where liquefaction of the tailings was considered. The magnitude of the estimated deformations would not be sufficient to cause loss of storage under normal operating conditions and that unacceptable deformations are not predicted as a result of seismic loading.

Acknowledgement The authors would like to express their gratitude to the MMG Rosebery Mine technical office for their support and for permission to publish this paper.

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Aydingun, O. and Adalier, K. (2003) Numerical analysis of seismically induced liquefaction in earth embankment foundations, Part I. Benchmark model, Canadian Geotechnical Journal, 40, 753–765.

Beaty, M.H. 2001. A synthesized approach for estimating liquefaction-induced displacements of geotechnical structures. Ph.D. Thesis, University of British Columbia.

Byrne, P.M. 1991. A Cyclic Shear-Volume Coupling and Pore-Pressure Model for Sand, Proceedings of the 2nd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St Louis, Missouri March 1991, 47-55.

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