APPENDIX I. Deformation Analysis of the Left Abutment

Transcription

1 APPENDIX I Deformation Analysis of the Left Abutment August 25, 2016

2 Appendix I Deformation Analysis of the Left Abutment TABLE OF CONTENTS I1 INTRODUCTION... 1 I2 MODEL DEVELOPMENT... 2 I2.1 General... 2 I2.2 Model Geometry and Stratigraphy... 2 I2.3 Material Properties... 3 I2.3.1 Elastic... 3 I2.3.2 Mohr-Coulomb... 6 I2.3.3 Critical State... 7 I2.3.4 Comparison of Stress-Strain Curves... 8 I2.4 Pore-water Pressures I3 RESULTS I3.1 Element Tests I3.1.1 Drained Triaxial Compression Sand I3.1.2 Undrained Triaxial Compression I3.1.3 Collapse State Tests I3.2 2D Model of Left Abutment Section I3.2.1 Elastic Analysis I3.2.2 Mohr-Coulomb Analysis I3.2.3 Critical State Analysis I4 SUMMARY List of Tables Table I2-1 Sand-slimes mixtures strength properties... 7 Table I2-2 Critical state parameters assigned to the beached tailings sand... 8 List of Figures Figure I1-1 Deformation model cross section location... 1 Figure I2-1 Material type boundaries... 3 Figure I2-2 Sand shear modulus relationship... 4 Figure I2-3 Slimes shear modulus relationship... 5 Figure I2-4 Sand-slimes mixtures shear modulus relationship... 6 Figure I2-5 Comparison of stress-strain curves assigned to sand and slimes units... 9 August 25, 2016 Page I-i

3 TABLE OF CONTENTS (continued) Figure I2-6 Comparison of stress-strain curves for sand at different state parameters Figure I3-1 Example element test at p' = 400 kpa and ψ = void ratio close to critical state (Test ID TX-12) Figure I3-2 Example element test at p' = 300 kpa and ψ = very loose sample (Test ID TX-1) Figure I3-3 Example element test at p' = 200 kpa and ψ = very dense sample (Test ID TX-11) Figure I3-4 Example element test at p' = 200 kpa and ψ = +0.9 very loose sample (Test ID TX-2) Figure I3-5 Collapse state element test at p' = 400 kpa and ψ = (Test ID TX-28) Figure I3-6 Horizontal displacement results elastic analysis Figure I3-7 Vertical displacement results elastic analysis Figure I3-8 Comparison of horizontal displacements and crest elevation of left setback elastic analysis Figure I3-9 Regions of plastic yielding Mohr-Coulomb analysis Figure I3-10 Horizontal displacement results Mohr-Coulomb analysis Figure I3-11 Comparison of horizontal displacements and crest elevation of left setback Mohr-Coulomb analysis Figure I3-12 Horizontal displacement results base case NorSand analysis Figure I3-13 Comparison of horizontal displacements from Mohr-Coulomb and base case NorSand analyses Figure I3-14 Horizontal displacement results base case NorSand analysis Figure I3-15 Definition of the mobilized instability ratio Figure I3-16 Mobilized instability ratio and stress path Figure I3-17 Comparison of field and modeled state parameter Figure I3-18 Updated model geometry incorporating continuous interbedded slimes Figure I3-19 Horizontal displacement results continuous interbedded slimes model Figure I3-20 Comparison of displacements from NorSand base case with those from the continuous interbedded slimes sensitivity analysis Figure I3-21 Mobilized instability ratio and stress path continuous interbedded slimes model. 29 Figure I3-22 Illustration of zone of slimes strength reduction Figure I3-23 Displacements due to slimes strength reduction Figure I3-24 Mobilized instability ratio and stress path due to slimes strength reduction Figure I3-25 Figure I3-26 Figure I3-27 Updated model geometry incorporating continuous interbedded slimes with reduced strength Horizontal displacement results reduced strength continuous interbedded slimes model Mobilized instability ratio and stress path reduced strength continuous interbedded slimes model August 25, 2016 Page I-ii

4 TABLE OF CONTENTS (continued) Figure I3-28 Mobilized instability ratio development with displacement at the sand/slimes interface Figure I3-29 Mobilized instability ratio and stress path due to continuing extrusion of slimes reduced strength continuous interbedded slimes model Figure I3-30 Horizontal displacements resulting from Mohr-Coulomb analysis with mobilized shear strength ratio of 0.13 (equivalent friction angle of 7.5 ) Figure I3-31 Factor of safety results calculated using FLAC with mobilized shear strength ratio of 0.13 (equivalent friction angle of 7.5 ) Figure I3-32 Limit equilibrium analysis for comparison with FLAC analysis Figure I3-33 Comparison of trends in FLAC and limit equilibrium factor of safety analysis results 40 Figure I3-34 Comparison of displacements necessary to initiate extrusion-induced collapse and those associated with the onset of general shear failure Figure I3-35 Horizontal displacement results no slimes model Figure I3-36 Mobilized instability ratio and stress path no slimes model August 25, 2016 Page I-iii

5 I1 INTRODUCTION The purpose of this appendix is to assess the potential influence of slope deformations on liquefaction triggering at the Fundão Dam. Specific emphasis was placed on assessing the influence of deformations within the slimes layers on the stress state of the overlying tailings sand to enable comparisons with laboratory test results. The primary intent was to identify whether slope deformations on the left abutment setback could have led to a liquefaction triggering mechanism that is consistent with the observed failure on November 5, This work has included deformation analyses on a cross section through the region in which the failure initiated (Section 01 on the left abutment; see Figure I 1-1). These analyses are described throughout the remainder of this appendix. Figure I 1-1 Deformation model cross section location August 25, 2016 Page I-1

6 I2 MODEL DEVELOPMENT I2.1 General The process followed during this assessment was to complete a series of progressive analyses for Section 01, with each model iteration including either increased complexity of material behavior or a parametric difference to enable evaluation of the influence of different factors. The models were initially constructed using a relatively simple elastic parameter set for all materials to identify the elastic distribution of deformations within the dam. In the next iteration, the models were developed further to include non-associated Mohr-Coulomb properties for all materials, including a strainweakening response for the slimes layers, to demonstrate the effect of yielding within the model. The next iteration built on the Mohr-Coulomb version and included a critical state constitutive model called NorSand (after Jefferies and Been 2016) for the beached tailings sand. The purpose of the critical state analysis was to identify the influence of aspects such as density-dependent strength variation and yield in unloading. Finally, parametric sensitivity analyses were completed for the critical state model to assess the influence of the strength and continuity of the slimes layers. The sensitivity analyses concentrated on the slimes-rich layers because they represent the greatest source of uncertainty in the analysis. The deformation models were developed to simulate the staged-construction of the dam. This involved sequential activation of layers of tailings within the models in accordance with the construction history known from survey data, and the internal dike stratigraphy described in Appendix B. These layers of tailings were set to represent roughly four-month time intervals throughout the majority of the dam s operational history, starting at the end of For the final six months (June to November, 2015), this time interval was reduced to monthly to gain additional resolution on the model response close to the time of the dam failure. The models were built using version 8 of the Fast Lagrangian Analysis of Continua (FLAC) finite difference software, which was also used for running the elastic and Mohr-Coulomb versions of the models. Version 6 of this software was used for the critical state analyses, with the NorSand constitutive model implemented as a user-defined model (UDM) dll file developed for this version of FLAC. I2.2 Model Geometry and Stratigraphy The model geometry and stratigraphy was generated in accordance with the GIS compilation of survey data and interpretation of aerial photographs documented in Appendices A and B. For the purpose of these models, the soils were grouped into one of the following material types: Bedrock All materials below the stripped ground survey were assigned to this material type. Sand Tailings sand considered unlikely to be mixed or interbedded with slimes. Slimes/sand deposits of varying proportions, designated as one of: August 25, 2016 Page I-2

7 predominantly slimes; mixed sand and slimes; interbedded slimes, or isolated slimes. Compacted sand. The material boundaries used within the models are shown on Figure I 2-1. Figure I 2-1 Material type boundaries I2.3 Material Properties I2.3.1 Elastic I Sand The elastic properties for the sand were defined using data from the seismic cone penetration tests (SCPTs) completed by Fugro through the beach of the Fundão Dam in January to March, 2015, supplemented with the SCPT data collected at greater depth from the Germano Pit Dam as part of this Investigation (see Appendix C). The small-strain shear modulus (G max ) was calculated from the shear wave velocity (v s ) and density (ρ) of the tailings, which was then converted to an approximate large strain shear modulus (G) by dividing G max by a factor of three. A trend of G versus effective vertical stress (σ' v ) was then defined from these data, which was implemented in the models. The bulk modulus (K) of the tailings was defined in the models by assuming a Poisson s ratio (ν) of 0.3 and calculating K from G and ν. The relationship of G versus σ' v is shown on Figure I 2-2. August 25, 2016 Page I-3

8 Shear Modulus (G; MPa) Trend used in model CPT: GCCPT16-03 CPT: F01 CPT: F03 CPT: F04 CPT: F05 σ'v (kpa) G = 20 + (σ' v /Pa) Figure I 2-2 Sand shear modulus relationship I Slimes The elastic properties for the slimes were based on the consolidation properties derived from the one-dimensional compression testing completed as part of this Investigation supplemented with data derived from index testing completed before and after the Baia 2 loading trial completed in 2008 [4] at Germano Dam. As discussed in Appendix F, these properties were then verified against settlements observed during the Baia 2 loading trial before being used in both the consolidation modeling and the analyses outlined in this appendix. The resulting trend of G versus σ' v is shown on Figure I 2-3. August 25, 2016 Page I-4

9 0 Shear Modulus (G; MPa) Slimes Shear Modulus Trend σ'v (kpa) G = (σ' v /Pa) Figure I 2-3 Slimes shear modulus relationship Having derived elastic parameters for both the slimes and sand deposits, these properties were then blended together to create parameter sets that represented the relative proportions of these materials that we considered credible throughout the cross sections. The relative proportions of the sand and slimes properties assigned to these blended parameter sets were: predominantly slimes 100% slimes properties; mixed sand and slimes 50:50 sand and slimes properties; interbedded slimes 20% slimes properties and 80% sand properties; and isolated slimes 100% sand properties These proportions were also used for blending strength properties. The modulus relationships applied to the various regions of mixed/interbedded slimes and sand in the models are shown on Figure I 2-4. August 25, 2016 Page I-5

10 Shear Modulus (G; MPa) Predominantly Slimes Thinly Bedded Slimes Mixed Sand and Slimes Isolated Slimes σ'v (kpa) Figure I 2-4 Sand-slimes mixtures shear modulus relationship I Bedrock The bedrock was modeled as a linear elastic material within all of the analyses. This unit was modeled with a G of 170 MPa and a K of 440 MPa in order to represent a very stiff material and impose a clear stiffness contrast between the bedrock and overlying tailings. I2.3.2 Mohr-Coulomb I Sand The beached tailings sand was modeled with a friction angle of φ' = 33 and zero cohesion, which represents the critical state friction angle calculated from the triaxial compression tests completed as part of this Investigation. Mohr-Coulomb plots are shown in Appendix D on Figures D5-9 and D5-10. The compacted tailings sand was modeled with a friction angle of φ' = 35 and 5 kpa cohesion, in accordance with the values used by others during designs. August 25, 2016 Page I-6

11 I Slimes The conceptual basis for the properties assigned to slimes-rich layers was that they are expected to generate an immediate undrained response following each loading increment, but that any loadinginduced excess pore pressure will dissipate between loading increments. The assumption of dissipation between loading increments is based on the results of the consolidation modeling presented in Appendix F and observations from embankment test fills at Germano Dam in 2008 and 2013 (see Appendices C and F). This process could have been included directly within the deformation model by either alternating drained and undrained properties throughout a loading increment, or by using a coupled mechanical deformation/fluid flow approach; however, given the uncertainty in the true extent and proportions of sand and slimes within the slimes-rich layers, this added complexity was not considered appropriate. Instead, the slimes were modeled in a simplified manner with moduli representative of the drained response (see Section I2.3.1), combined with undrained strength properties. By using this approach, we are assuming that the volumetric response will be dictated by consolidation that is occurring rapidly throughout the majority of the unit, but that the strength of these regions will be dominated by the undrained response along horizons of higher slimes content. The slimes-rich regions were modeled with a strain-weakening Mohr-Coulomb relationship that included a peak friction angle of φ p = 12.4 based on field testing and the Baia 4 failure at Germano Dam on September 21, This friction angle was intended to represent an approximate undrained strength ratio, and was calculated as the arctangent of s u /σ' v = This friction angle was then assigned a linear reduction to φ r = φ p /3 at a plastic strain (ε p ) of 20% (i.e., 20% strain beyond the peak strength). This reflects an upper-bound to the sensitivity of approximately 3 that was deduced from the runout of the Baia 4 failure (see Appendix C). As for the elastic properties, the Mohr-Coulomb strength properties of the slimes were blended with those of the sand, as listed in Section I The properties assigned to the various sand/slimes mixtures are listed in Table I 2-1. Table I 2-1 Sand-slimes mixtures strength properties Material Undrained Equivalent Friction Undrained Equivalent Friction Strength Ratio Angle φ p ( ) at ε p = 0% Strength Ratio Angle φ r ( ) at ε p = 20% Predominantly Slimes Mixed Sand and Slimes Interbedded Slimes Isolated Slimes Parametric sensitivity analyses were run to assess the impact of the strength and continuity of the slimes. I2.3.3 Critical State The parameters assigned to the beached tailings sand during the critical state analyses were derived from the triaxial compression laboratory tests completed throughout this Investigation (see Appendix D). These parameters are summarized in Table I 2-2. August 25, 2016 Page I-7

12 Table I 2-2 Critical state parameters assigned to the beached tailings sand Parameter Value M tc 1.33 Γ λ e N 0.38 H 156-(756 x ψ) χ tc 7.3 All parameters other than H were obtained directly from the laboratory tests. H was calculated by completing numerical models of single elements (element tests) that represented the drained and undrained triaxial tests, and varying H within a range to obtain a trend that gave the best fit to all tests (see Section I3.1). Behavior in unloading is not specified in the NorSand model, but is calculated based on the parameters listed in Table I 2-2 and the stress history of the soil element. As part of this work, we verified that the response to unloading was significantly stiffer than the response to loading during virgin compression, consistent with the findings from 1D consolidation tests on undisturbed samples of tailings sand from Fundão Dam completed by Rezende [40], and reconstituted samples completed as part of this Investigation. It was also necessary to specify the state parameter (ψ) for the critical state analyses. Our intent was to match the 80 th percentile state parameter within the model (defined by Jefferies and Been 2016, as the characteristic state) to the combined value from the CPTs completed at the Fundão Dam in January to March, This 80 th percentile value of the field data was ψ = It should be understood that the state parameter changes in response to volumetric strain and stress changes as the model progresses; therefore, multiple trial model runs were completed with different state parameter values assigned at the time of deposition, which we have termed seed state parameters in this analysis. The seed state parameter that was required to generate an 80 th percentile in the model that was approximately equal to the characteristic state in the field in January, 2015 was ψ = The changes in state parameter within the models are discussed and illustrated in Section I3.2. I2.3.4 Comparison of Stress-Strain Curves A comparison of the stress-strain behavior assigned to the various soil units is illustrated on Figure I 2-5. It can be seen from this figure that the elastic moduli assigned to the sand in the linear elastic and Mohr-Coulomb analyses lead to a similar stress-strain response to that of the NorSand model at low strain (<~0.5%) for loose sand with a state parameter of zero. At larger strains, the NorSand model imposes a more ductile response than the linear elastic relationship. Figure I 2-5 also illustrates the greater stiffness of the sand in comparison with the slimes. August 25, 2016 Page I-8

13 Sand - Linear Elastic, Perfectly Plastic Sand - NorSand, ψ = 0 Deviator Stress (q; kpa) Interbedded Slimes - Linear Elastic, Strain Softening Mixed Sand and Slimes - Linear Elastic, Strain Softening Predominantly Slimes - Linear Elastic, Strain Softening Axial Strain (%) Figure I 2-5 Comparison of stress-strain curves assigned to sand and slimes units It can be seen from Figure I 2-6 that the response of the sand changes significantly with variations in state parameter, with the drained response becoming increasingly ductile as the state parameter increases; therefore, the linear elastic and NorSand models will differ in line with variations in state parameter. August 25, 2016 Page I-9

14 800 Sand - NorSand, ψ = Sand - Linear Elastic, Perfectly Plastic Sand - NorSand, ψ = Sand - NorSand, ψ = Deviator Stress (q; kpa) Axial Strain (%) Figure I 2-6 Comparison of stress-strain curves for sand at different state parameters I2.4 Pore-water Pressures The pore-water pressures within the models were assigned by setting phreatic surfaces for each model state based on the piezometer monitoring data, and extrapolating the data into regions and time periods without data. A hydrostatic pore pressure distribution was assigned below the phreatic surfaces. The pore pressure assumptions for these models were checked against the results of the groundwater monitoring. Full saturation was assumed below the phreatic surface, and zero saturation was assumed above it. August 25, 2016 Page I-10

15 I3 RESULTS I3.1 Element Tests I3.1.1 Drained Triaxial Compression Sand Modeling of drained triaxial compression tests was completed to verify that the NorSand constitutive model was capable of capturing the stress-strain relationship and volumetric response of the sand appropriately. These analyses were completed using a Visual Basic for Applications (VBA) program from Jefferies and Been (2016). Example analyses of the triaxial tests completed as part of this Investigation are shown on Figure I 3-1 to Figure I 3-3. These analyses show that the NorSand model is capable of closely matching the response of the tailings to shear strain at a range of confining stresses and density states. Figure I 3-1 Example element test at p' = 400 kpa and ψ = void ratio close to critical state (Test ID TX-12) August 25, 2016 Page I-11

16 Figure I 3-2 Example element test at p' = 300 kpa and ψ = very loose sample (Test ID TX-1) Lab data unreliable after 4 % axial strain due to sample distortion Figure I 3-3 Example element test at p' = 200 kpa and ψ = very dense sample (Test ID TX-11) August 25, 2016 Page I-12

17 I3.1.2 Undrained Triaxial Compression Element tests of undrained triaxial laboratory tests completed as part of this Investigation were also undertaken using the VBA software to verify that the NorSand constitutive model can capture the undrained response of the sand tailings appropriately. An example set of results is shown on Figure I 3-4, which shows that the NorSand model is capable of capturing the undrained response of the sand. Figure I 3-4 Example element test at p' = 200 kpa and ψ = +0.9 very loose sample (Test ID TX-2) I3.1.3 Collapse State Tests A final element test was completed using the NorSand constitutive model within FLAC to verify that the NorSand model is capable of identifying the collapse state identified in the stress controlled extrusion-collapse triaxial tests. This model was set up as an axisymmetric analysis with load controlled boundary conditions to mimic the conditions applied in the laboratory tests. The radial stress in the model was then reduced incrementally in 0.5 kpa load increments, following the same stress path as the laboratory test. Each unloading increment was initially modeled with a fluid bulk modulus of 2000 MPa to allow potential shear-induced pore pressure generation and emulate undrained conditions. The undrained increment was then followed by dissipation of any induced pore pressures to ensure that no pore pressures were being carried over between unloading increments. The model response compared with the laboratory test is shown on Figure I 3-5. These results show that the NorSand model is capable of replicating the response seen in the load controlled triaxial tests, with the failure stress being identified within 3% of the laboratory data. August 25, 2016 Page I-13

18 Figure I 3-5 Collapse state element test at p' = 400 kpa and ψ = (Test ID TX-28) I3.2 2D Model of Left Abutment Section 01 I3.2.1 Elastic Analysis The purpose of the elastic 2D analysis of Section 01 was to identify the pattern of displacements produced by the model without the complexity of material behavior included within the Mohr- Coulomb and critical state analyses. These results serve as a reference base against which the response of the subsequent models can be reviewed. Contours of horizontal displacement are shown on Figure I 3-6, together with graphs showing the distribution and magnitude of displacements at stages throughout the model construction. These results show two main regions of horizontal displacement. One zone is located towards the upstream end of the model and the second is located beneath the slope. The upstream zone is a result of material settling above the highly compressible zone of predominantly slimes shown on Figure I 3-7, and sliding along the interface with the bedrock. The downstream zone is a result of the dam s geometry. The abrupt break between these zones is a result of material immediately downstream of the predominantly slimes region being affected by displacement upstream due to the settlement of this layer. This is serving to offset the displacements in the downstream direction and leads to a zone of roughly zero horizontal displacement immediately downstream of the predominantly slimes region. August 25, 2016 Page I-14

19 Figure I 3-6 Horizontal displacement results elastic analysis August 25, 2016 Page I-15

20 Figure I 3-7 Vertical displacement results elastic analysis The largest horizontal displacements occur in the downstream region and concentrate in a zone that is downstream of the dike crest and centered along roughly El. 856 m. This implies compressive straining in the downstream direction and extension straining in the upstream direction. Extension strains result in a reduction of horizontal confinement consistent with a potential for liquefaction triggering from a lateral extrusion process. The maximum horizontal displacement at the end of the model construction (November, 2015) was 118 mm. Tongues of slightly increased displacement are also visible around the regions of slimes in the downstream portion of the model. The maximum horizontal displacement is shown throughout the dam construction on Figure I 3-6. This shows a consistent response to loading throughout the majority of construction. An exception to this is between August and October, 2014 when zero displacement is shown in the model. This corresponds to a time period when a berm was built on the slope and the crest was raised by only 1 m following the cracking incident in August, Figure I 3-8 compares the maximum calculated displacements with the surveyed crest of the left abutment setback. As expected, the elastic displacements correspond very closely with the rate of dike construction. August 25, 2016 Page I-16

21 Max. Horizontal Displacement Along El. 856 m (mm) Modeled Displacement Surveyed Crest Elevation - Left Setback Oct-12 Apr-13 Nov-13 May-14 Dec-14 Jun-15 Jan-16 Date Crest Elevation (m) Figure I 3-8 Comparison of horizontal displacements and crest elevation of left setback elastic analysis I3.2.2 Mohr-Coulomb Analysis The main purpose of the Mohr-Coulomb analysis was to identify the effect of shear-induced yielding for comparison with the subsequent critical state analyses, to enable responses specific to the critical state analysis to be separated from those associated with shear-induced yielding of the tailings. Zones of yielding are shown as yellow shading on Figure I 3-9. Pink shading indicates regions that have not reached the yield surface at any stage in the analysis. This figure shows that the areas experiencing the most significant yielding are those adjacent to the region of predominantly slimes material, and material at the toes of the left abutment setback and plateau. Figure I 3-9 Regions of plastic yielding Mohr-Coulomb analysis The horizontal displacements resulting from this Mohr-Coulomb analysis are shown on Figure I August 25, 2016 Page I-17

22 Figure I 3-10 Horizontal displacement results Mohr-Coulomb analysis August 25, 2016 Page I-18

23 The effect on the yielding within the model can be seen by comparing Figure I 3-10 with Figure I 3-6. From such a comparison, it is apparent that the patterns of displacement are broadly similar, in that there are two main zones of displacement in the two models, which are in roughly the same location. However, it is apparent that there is additional displacement in an upstream direction towards the predominantly slimes material in the Mohr-Coulomb analysis. This is in line with expectations given the extent of yielding in that part of the model, which is in response to the settlement associated with the highly compressible slimes. The net effect of this additional upstream displacement is to slightly reduce the maximum displacements in a downstream direction. The maximum horizontal displacement at the November, 2015 stage of this model was 106 mm, compared with 118 mm in the elastic analysis. The conflicting effects of upstream displacement due to settlement of the slimes versus downstream movements due to construction of the dam slope leads to a more complex sequence of incremental displacements than resulted from the elastic analysis. In this analysis, time periods in which the dam crest is raised by a greater amount than the beach can be seen as steps on the time displacement plot on Figure I Time periods when the beach is being raised significantly result in low displacement rates in the downstream direction due to the effects of additional settlement in the slimes. The effect of the upstream displacements can also be seen on Figure I 3-11, which shows that, unlike the elastic analysis, the trend of downstream horizontal displacements is not directly proportional to the height of the dam crest. Max. Horizontal Displacement Along El. 856 m (mm) Modeled Displacement Surveyed Crest Elevation - Left Abutment Setback Oct-12 Apr-13 Nov-13 May-14 Dec-14 Jun-15 Jan-16 Date Crest Elevation (m) Figure I 3-11 Comparison of horizontal displacements and crest elevation of left setback Mohr-Coulomb analysis As discussed previously, the purpose of the Mohr-Coulomb analysis was to form an intermediate step between the relatively simple elastic analyses and complex critical state analyses. The intent was to identify the effects of yielding due to shear only, and to aid in the later evaluation of the critical state analyses. The analyses presented meet this intent. Whilst the model shows regions of compression and extension resulting from loading, as per the elastic analyses, additional calculations are required to identify the effects of this on the stress state of the sand. This is included within the critical state analyses. August 25, 2016 Page I-19

24 I3.2.3 Critical State Analysis I Base Case Given that the Mohr-Coulomb analysis was seen to respond in line with expectations associated with the change of material behavior, this model was seen as a suitable base for further development in the critical state analyses. The first critical state analysis (base case) was set up exactly as per the Mohr-Coulomb analysis except that the beached tailings sand was modeled using the NorSand constitutive model. The intent of this analysis was to assess the effect of the displacements within the dam on the stress state of the sand tailings and to identify whether the displacements could represent a potential liquefaction trigger. We also aimed to gain insight into the difference in response between the August, 2014 cracking incident and the November, 2015 flow failure from this analysis. The horizontal displacements resulting from the base case critical state analysis are shown on Figure I August 25, 2016 Page I-20

25 Figure I 3-12 Horizontal displacement results base case NorSand analysis The horizontal displacements are compared with the results of the Mohr-Coulomb analysis on Figure I August 25, 2016 Page I-21

26 Max. Horizontal Displacement Along El. 856 m (mm) Modeled Displacements - Mohr-Coulomb Modeled Displacement - NorSand 0 Oct-12 Apr-13 Nov-13 May-14 Dec-14 Jun-15 Jan-16 Date Figure I 3-13 Comparison of horizontal displacements from Mohr-Coulomb and base case NorSand analyses When the displacement trends from this analysis are compared with those of the Mohr-Coulomb analysis, the following observations can be made: The horizontal displacements in the NorSand analysis continue to concentrate in two regions, either side of the predominantly slimes region, as per the Mohr-Coulomb and elastic analyses. The region of largest horizontal displacement continues to occur downstream of the dam crest at the November, 2015 model stage. The total horizontal displacement at the November, 2015 model stage increased from 106 mm in the Mohr-Coulomb analysis to 135 mm in the NorSand analysis. The magnitude of displacements in the NorSand analysis was initially lower than the Mohr-Coulomb analysis, but this trend reversed at roughly the stage of August, In the August, 2014 model stage, the NorSand model displacements switched from being lower than the Mohr-Coulomb model to being larger than that model. The trend of NorSand displacements being larger than the Mohr-Coulomb model continued up to the November, 2015 model stage. The observed reversal of the displacement trend from being lower than the Mohr-Coulomb model to being larger than that model at the August, 2014 model stage provides insight into a feature of the tailings behavior that may have contributed to the cracking incident occurring at that time and not sooner. To understand this trend, it is necessary to review the volumetric response of the tailings sand to loading. The variation of void ratio for an element of tailings sand located beneath the dam crest, above one of the slimes layers, is illustrated on Figure I This figure shows that as the dam is constructed, the void ratio is reducing at a lower gradient in e-log p space than the critical state line. This is having the effect of making the tailings sand increasingly contractive (increasing the state parameter). As a result, this displacement trend is understandable if the change of stress-strain behavior with state parameter, illustrated on Figure I 2-6, is considered. The explanation for this trend is that the tailings sand is initially slightly dilatant, causing the tailings to behave in a manner that is August 25, 2016 Page I-22

27 stiffer than assumed in the Mohr-Coulomb analysis. At around August, 2014, the tailings become sufficiently contractive to produce a more ductile response to loading, which leads to a consequent increase in displacements. These displacements are moderated temporarily by the construction of the reinforcement berm following the August, 2014 incident, but then continue to increase with additional dike construction up until the November, 2015 failure. Dike Figure I 3-14 Horizontal displacement results base case NorSand analysis In addition to tracking the deformations throughout this model, we have also tracked a parameter termed the mobilized instability ratio, which defines the distance of any element of soil from the critical state line in q-p' stress space, as illustrated on Figure I The reason for tracking this parameter is to enable comparison of the model response with the stress controlled extrusioncollapse laboratory tests. The laboratory tests found that as a mobilized instability ratio of 1 is approached, slightly contractant sand tailings will become highly susceptible to rapid instability under a minor increment of stress change. As a result, within this analysis the mobilized instability ratio is a criterion for the triggering for collapse. August 25, 2016 Page I-23

28 q M η/m = 1 η/m = 0.5 η/m = 0 p' η = (q/p ) Mobilized Instability Ratio = η/m Figure I 3-15 Definition of the mobilized instability ratio Contours of mobilized instability ratio are shown, together with the variation of this parameter throughout the dike construction for a sand element located beneath the November, 2015 dam crest, at the sand-slimes interface, on Figure I This figure shows that the maximum mobilized instability ratios developed within this base case NorSand model, that included peak strengths assigned to the slimes, are roughly 0.5. These values are distant from the conditions at which rapid instability occurred in our laboratory tests, and suggest that drained deformations would be unlikely to lead to rapid instability under this model scenario. This model has formed the base for examining the effect of additional displacements within the slimes that may develop under conditions of more continuous slimes, or post-peak strength mobilization in the slimes, which are discussed in the following sections. As discussed in Section I2.3.3, it was necessary in this base case NorSand analysis to define the state parameter input value (seed state parameter) that would lead to a distribution of state parameter that was roughly equivalent to that observed in the field. The reason that this is uncertain at the outset of the modeling is because the state parameter distribution within the model changes in response to loading and shearing, as discussed earlier. This issue was addressed by running multiple versions of this base case model with different seed state parameters and extracting the state parameter results in the January, 2015 model stage for comparison with the field data collected during this time period. The intent was to match the 80 th percentile of the field distribution, since this value is defined by Jefferies and Been (2016) as the characteristic state, in line with their suggestion that the loosest 20% of the soil can dominate the behavior of a deposit. A seed state parameter of was found to provide the closest match to the field data and was used in this base case analysis and subsequent variations discussed in the following sections. A comparison of the modeled distribution of state parameter with that of the field data is shown on Figure I August 25, 2016 Page I-24

29 Dike Dike Figure I 3-16 Mobilized instability ratio and stress path August 25, 2016 Page I-25

30 State Parameter - Field Frequency th percentile = State Parameter State Parameter - Model Frequency th percentile = State Parameter Figure I 3-17 Comparison of field and modeled state parameter I Parametric Sensitivity Analysis Continuity of Slimes Building on the results of the base case NorSand analysis, we completed a sensitivity analysis to identify how the results would be affected if the slimes were more continuous in the downstream direction. The model adjustment made for this analysis was to assume that the region designated as isolated slimes in the base case model was actually composed of interbedded slimes. The isolated slimes unit was merged with the interbedded slimes unit located farther upstream, leading to the model setup shown on Figure I August 25, 2016 Page I-26

31 Figure I 3-18 Updated model geometry incorporating continuous interbedded slimes As shown on Figure I 3-19 to Figure I 3-21, assuming that the interbedded slimes are continuous in the downstream direction does not change the horizontal displacement or stress state results significantly from those of the base case. The outcome of this sensitivity analysis was to increase the horizontal displacements at the November, 2015 model stage by 7 mm, from 135 mm in the base case to 142 mm. The peak instability ratio of this model was similar to that of the base case, with both models resulting in a value of roughly 0.5. Therefore, these results suggest that the presence of a relatively discontinuous mixture of sand and slimes represented by the blended sand/slimes parameter sets would not bring the stress state of the tailings to an unstable condition, and would not account for the flow failure observed on November 5, The following sections of this appendix examine whether the presence of weaker, horizontally continuous, slimes-rich layers within the interbedded slimes region, which could mobilize a much lower strength than the blended parameters, could account for the November 5, 2015 flow failure. August 25, 2016 Page I-27

32 Figure I 3-19 Horizontal displacement results continuous interbedded slimes model August 25, 2016 Page I-28

33 Max. Horizontal Displacement Along El. 856 m (mm) Modeled Displacement - NorSand - Continuous Slimes 120 Modeled Displacement - NorSand - Base Case Oct-12 Apr-13 Nov-13 May-14 Dec-14 Jun-15 Jan-16 Date Figure I 3-20 Comparison of displacements from NorSand base case with those from the continuous interbedded slimes sensitivity analysis Dike Dike Figure I 3-21 Mobilized instability ratio and stress path continuous interbedded slimes model August 25, 2016 Page I-29

34 Post-Peak Strength of Slimes Strength Reduction after Construction Having constructed the continuous interbedded slimes model to the November, 2015 model stage, this model was then used for a subsequent sensitivity analysis to assess how the strength of the slimes assigned to the interbedded slimes region was affecting the stress state of the overlying tailings sand. This analysis was completed as a separate stage to the previous model by incrementally reducing the strength of the slimes in the region shown on Figure I 3-22 and then examining the stresses and deformations within the model. As noted previously, this reflects the sensitivity of the slimes. Figure I 3-22 Illustration of zone of slimes strength reduction It was possible to reduce the strength of the slimes in this region to a friction angle of 9.5 before numerical convergence issues prevented the model from proceeding. The results shown on Figure I 3-23 illustrate how this strength reduction led to 170 mm of additional displacement (lateral extrusion) downstream of the dike crest. Figure I 3-24 shows that this lateral extrusion movement within the slimes has an effect of reducing the stress in the overlying tailings sand in a manner that is very similar to the stress path followed during the stress controlled extrusion-collapse laboratory tests (see Figure I 3-5). The maximum mobilized instability ratio calculated during this analysis was approximately 0.8, compared with 0.5 calculated in the earlier analyses. This reduced slimes strength is within the range of parameters initially considered as reasonable for the predominantly slimes layers; therefore, it would not be unreasonable to think that this strength could be mobilized anywhere within the slimes mass, should sufficient continuity exist. August 25, 2016 Page I-30

35 Figure I 3-23 Displacements due to slimes strength reduction August 25, 2016 Page I-31

36 Dike dike Dike Figure I 3-24 Mobilized instability ratio and stress path due to slimes strength reduction August 25, 2016 Page I-32

37 Post-Peak Strength of Slimes Strength Reduction throughout Construction Having identified a slimes strength that leads to a stress state in the overlying sand approaching that at which rapid instability was observed in the laboratory tests, an additional sensitivity analysis was completed to identify how the response of the dike would differ if this strength was operative throughout the entire dam construction sequence, as shown on Figure I Dike Figure I 3-25 Updated model geometry incorporating continuous interbedded slimes with reduced strength Figure I 3-26 shows that imposing a friction angle of 9.5 on the interbedded slimes region beneath and downstream of the dike crest would, as expected, lead to a marked increase in displacements downstream of the dike crest at the November, 2015 model stage compared with earlier models. The maximum horizontal displacement from this analysis was 335 mm, compared with 142 mm in the analysis with base case strength parameters. This value is similar to the cumulative displacement of the analysis in which the strength of the slimes is reduced at the end of construction: 142 mm mm = 312 mm, versus 335 mm in this analysis. The overall pattern of displacement is similar to that observed in earlier model iterations in that the maximum displacements are concentrating in the same location downstream of the crest. Figure I 3-27 shows that the additional displacements due to the reduced slimes strength throughout the dike construction would lead the stress state of the tailings sand overlying the slimes to a similar mobilized instability ratio, as was observed when the slimes strength was reduced at the end of the dike construction (0.8). This implies that whether extrusion through the slimes was occurring continuously or in isolated incidents, the effect would be to drive the stress state of the sand into a potentially unstable condition. If the volumetric response of the sand is reviewed using the e-logp' plot on Figure I 3-27, it can be seen that the model suggests a relatively consistent trend of incremental volumetric strain throughout the dike construction. Unlike the collapse tests in the published literature completed by Skopek et al. (1994), no sudden change of volumetric behavior was observed in the simulation. Therefore, the assumptions of sustained drained conditions in the sand within the analysis is supported. August 25, 2016 Page I-33

38 Figure I 3-26 Horizontal displacement results reduced strength continuous interbedded slimes model August 25, 2016 Page I-34

39 Dike dike Dike Figure I 3-27 Mobilized instability ratio and stress path reduced strength continuous interbedded slimes model August 25, 2016 Page I-35

40 It is of interest to note from Figure I 3-26 and Figure I 3-27 that if this slimes strength was operative throughout the dike construction history, the model suggests that an increase in displacement rate would be expected prior to the August, 2014 event, leading to a cumulative displacement of roughly 163 mm. However, even with this magnitude of movement, the lateral extrusion process would still not be sufficiently advanced to place the sand tailings in an unstable stress state at this stage in the dam s construction history. This, and observations from model variants discussed previously, may provide an explanation for a contributing feature to the timing of the August, 2014 event and the absence of a flowslide resulting from this incident. It is acknowledged that the strength of φ=9.5 is lower than the peak strength assumed for the slimes of φ=12.4, based on the Baia 4 failure. This implies that strain weakening of the slimes layers would need to have occurred if this, or potentially a lower, slimes strength was operative on November 5, If the strain weakening occurred at the time of the August, 2014 event, this would have compounded the mechanism for the event suggested in the paragraph above. Imposed Displacement Boundary After advancing the model with a slimes strength of φ= 9.5 throughout the construction history of the dike, we completed an additional variant on this model. In order to continue the extrusion of the slimes beyond the point at which numerical convergence issues prevented further reduction of the slimes strength, a displacement boundary condition was applied to the top of the slimes layer to force additional displacements to occur in the same pattern as they were observed during the modeled dam construction. The results shown on Figure I 3-28 and Figure I 3-29 show that additional extrusion within the slimes layer would ultimately lead the stress state of the overlying tailings to a similar condition as that at which rapid failure was observed in our laboratory tests. These figures show that a mobilized instability ratio of approximately 1 would be approached at roughly 600 mm of cumulative horizontal displacement. Therefore, this is the magnitude of displacement required to trigger liquefaction due to lateral extrusion. Mobilized Instability Ratio Dam Construction Imposed Displacement Cumulative Displacement at Sand/Slimes Interface (mm) Figure I 3-28 Mobilized instability ratio development with displacement at the sand/slimes interface August 25, 2016 Page I-36

41 Dike dike Dike Figure I 3-29 Mobilized instability ratio and stress path due to continuing extrusion of slimes reduced strength continuous interbedded slimes model August 25, 2016 Page I-37

42 Comparison with General Shear Failure As discussed in the preceding section, we have now established the magnitude of deformations in the slimes-rich layers required to initiate rapid instability and liquefaction in the overlying sand units. In order to use this deformation magnitude to evaluate the relative likelihood of the lateral extrusion mechanism triggering liquefaction versus a shear mechanism, it is necessary to compare these displacement magnitudes with those associated with the onset of a general shear failure throughout the dam. A general shear failure could potentially trigger liquefaction through a sequence of undrained yielding of the slimes-rich layers leading to uncontrolled movement of the dam, which leads to shear straining occurring more rapidly than the drainage of the sand will allow. In order to evaluate which of these mechanisms was the more probable liquefaction trigger, the following stages were completed: The Mohr-Coulomb model discussed in Section I3.2.2 was revisited and used to estimate the deformation magnitude and pattern that would develop as a condition of general shear failure through the dam, driven by displacements in the slimes-rich layers, is approached. This was achieved by running this model throughout the entire construction sequence multiple times, with each iteration using a lower strength for the slimes-rich layers. The proximity of the model to a condition of general shear failure was subsequently confirmed by completing a series of strength-reduction factor of safety analyses in FLAC, in which the reserve strength of all soil units against instability was identified. In addition, we completed a limit equilibrium stability analysis, separate from those completed in Appendix H, for comparison with the results from FLAC. Once the conditions at the onset of general shear failure were identified, the trend of displacement magnitude leading up to that condition was extracted from the Mohr-Coulomb model for comparison with the NorSand model results. The pattern of displacements resulting in November, 2015 if an undrained strength ratio of 0.13 (equivalent friction angle 7.5 ) was mobilized in the slimes is shown on Figure I The pattern of displacements is similar to that shown previously for the NorSand model analyses. Figure I 3-30 Horizontal displacements resulting from Mohr-Coulomb analysis with mobilized shear strength ratio of 0.13 (equivalent friction angle of 7.5 ) August 25, 2016 Page I-38

43 The factor of safety calculated using FLAC with an undrained strength ratio of 0.13 assigned to the slimes-rich layers is 1.07, as shown on Figure I Figure I 3-31 Factor of safety results calculated using FLAC with mobilized shear strength ratio of 0.13 (equivalent friction angle of 7.5 ) The factor of safety calculated using FLAC is similar to that calculated using limit equilibrium methods (see Figure I 3-32). The equivalence between the FLAC and limit equilibrium analyses was also checked with an undrained strength ratio of 0.12, with both methods indicating that a factor of safety of 1 would be reached at this strength (see Figure I 3-33). Strengths: Slimes-Rich Layers = s u /σ'v (0.13); Sand = φ' = 33 ; Compacted Sand = φ' = 35 & c' = 5 kpa Figure I 3-32 Limit equilibrium analysis for comparison with FLAC analysis August 25, 2016 Page I-39