APPENDIX J. Dynamic Response Analysis

APPENDIX J Dynamic Response Analysis August 25, 216

Appendix J Dynamic Response Analysis TABLE OF CONTENTS J1 INTRODUCTION... 1 J2 EARTHQUAKE TIME HISTORIES... 1 J3 MODEL AND INPUT DATA FOR SITE RESPONSE ANALYSIS... 4 J3.1 General... 4 J3.2 Shear Wave Velocity... 6 J3.3 Modulus Reduction and Damping... 9 J4 RESULTS OF SITE RESPONSE ANALYSES... 1 J4.1 Weathered Rock Profile at Samarco Office Site... 1 J4.2 Tailings Dam Profiles at Fundão Dam Site... 12 J5 CYCLIC LIQUEFACTION TRIGGERING... 14 J6 SEISMIC DISPLACEMENTS... 16 List of Tables Table J2-1 Summary of time histories provided for analysis by Atkinson (216)... 2 Table J2-2 PGA values in bedrock of estimated November 5, 215 time histories at Samarco... 3 Table J4-1 Computed amplification factors from SHAKE analyses... 12 List of Figures Figure J2-1 Estimated time histories of November 5, 215 earthquakes from Atkinson (216). (BC1 median-level motions on left; BC2 median-level motions on right)... 3 Figure J2-2 Response spectra of BC1 (mainshock) and BC2 ground motions provided by Atkinson (216)... 4 Figure J3-1 Aerial image showing locations of Samarco office and Fundão Dam... 5 Figure J3-2 Shear wave velocity data in weathered phyllite at Samarco office site... 6 Figure J3-3 Selected soil columns at Fundão Dam for 1D site response analysis... 7 Figure J3-4 Shear wave velocity data in tailings at Fundão and Germano... 8 Figure J3-5 Shear wave velocity data in compacted sand... 9 Figure J3-6 Three soil columns used in SHAKE2 analyses... 9 Figure J3-7 Modulus reduction and damping curves for tailings sands, slimes and soft rock... 1 Figure J4-1 Computed peak accelerations from SHAKE2 analyses of weathered rock column. 11 Figure J4-2 Comparison of output and input response spectra from SHAKE2 analyses... 11 Figure J4-3 Results of SHAKE analyses for crest and toe soil columns at Fundão Dam... 13 Figure J4-4 Comparison of cyclic stress ratios induced by CD1 and CD2 ground motions... 14 August 25, 216 Page J-i

Appendix J - Dynamic Response Analysis TABLE OF CONTENTS (continued) Figure J5-1 Pore pressure development in laboratory test following lateral extrusion mechanism and then cyclic loading (test ID TX-31) very loose sample (ψ=+.5)... 15 Figure J5-2 Laboratory test following lateral extrusion mechanism and then cyclic loading (test ID TX-31) very loose sample (ψ=+.5)... 16 Figure J6-1 Calculation of yield acceleration for Newmark-type displacement analysis... 17 Figure J6-2 Estimated displacements... 18 List of Attachments Attachment J1 Ground Motion Time Histories used in Newmark Displacement Analysis August 25, 216 Page J-ii

J1 INTRODUCTION This appendix presents the results of dynamic response analyses of the November 5, 215 earthquakes at Samarco, using the one-dimensional ground response analysis software SHAKE2. The November 5, 215 earthquake time histories were estimated by seismologist Dr. Gail Atkinson (Atkinson 216) and used as input ground motions in our site response analyses. The analyses were performed at two locations, namely: 1. at the Samarco office site to evaluate potential amplification of ground motions through the weathered rock profile; and 2. at the Fundão Dam site to estimate the likely earthquake-induced shear stresses in the tailings dam profile. Section J2 summarizes the input earthquake time histories. Section J3 describes the soil models and input data used in our site response analyses. Section J4 presents the results of the SHAKE2 analyses. Finally, Sections J5 and J6 present the results of assessments to identify whether pore pressures or displacements significant to the triggering of liquefaction could result from the computed ground motions. J2 EARTHQUAKE TIME HISTORIES Atkinson (216) analyzed the ground motions from the November 5, 215 earthquake sequence near Fundão Dam. The analysis considered data from the following sources: seismographic data obtained from the regional Brazilian network (www.rsbr.gov.br); felt (intensity) reports of the November 5 earthquakes at the Samarco office site; data collected on a local accelerometer that was installed on November 11, 215 following the dam failure, and ground motion data collected to May 2, 216 on a six-station local broadband array installed by Nanometrics Inc. at the end of April, 216. Note that the nearest Brazilian regional seismographic stations that recorded the November 5, 215 earthquakes near Fundão Dam were more than 15 km away from the dam, hence ground motion prediction equations were used by Atkinson (216) to estimate the likely ground motions at Samarco. Atkinson (216) used the above data to develop a time history of motions that represents those that likely occurred at the Samarco site on November 5, 215 prior to the dam failure at approximately 15:45 (local time). The time history sequence includes three earthquakes closely spaced in time: M 2.2 at 14:12:15 (foreshock) M 2.6 at 14:13:51 (mainshock) M 1.8 at 14:16:3 (aftershock) where M is moment magnitude, estimated from local magnitudes reported by RSBR, and all times noted are local Brazilian time. August 25, 216 Page J-1

As a result of the ground motions analysis, Atkinson (216) provided time histories on rock that can be used to evaluate the response of the structures at Samarco due to the November 5, 215 earthquake. The time histories provided are summarized in Table J 2-1. Table J 2-1 Summary of time histories provided for analysis by Atkinson (216) Time History Sequence Name BC1 (18 individual event time histories) BC2 (6 time histories) Confidence Interval Median 84 th Percentile Median Events Represented Mainshock Foreshock Aftershock Mainshock Foreshock Aftershock Composite 84 th Percentile Composite Directional Components 2 x Horizontal (H1 & H2) 1 x Vertical (V) 2 x Horizontal (H1 & H2) 1 x Vertical (V) 2 x Horizontal (H1 & H2) 1 x Vertical (V) 2 x Horizontal (H1 & H2) 1 x Vertical (V) NEHRP Site Classification B/C v s3 = 76 m/s The time histories were provided for three directional components, i.e. two horizontal and a vertical, and for a reference NEHRP B/C site condition (soft rock) with near-surface average shear wave velocity, v s3, of 76 m/s. Since the v s3 values of the weathered rock at Samarco are lower, at about 34 m/s to 4 m/s based on Multichannel Analysis of Surface Waves (MASW) measurements (Appendix C), which corresponds to NEHRP site class C/D (stiff soil), Atkinson (216) proposes an amplification factor of 1.4 (multiplication factor) to convert the site class B/C ground motions to site class C/D ground motions. To account for both aleatory and epistemic uncertainties, Atkinson (216) used a factor of 3.2 times the median (5 th percentile) ground motions to obtain the 84 th percentile confidence-level (mean plus one standard deviation) ground motions. Figure J 2-1 shows the two sets of median-level time histories provided by Atkinson (216). The BC1 time histories contained the estimated foreshock, mainshock and aftershock sequence of November 5, 215, whereas the alternative BC2 time histories were scaled up from a M3 earthquake that occurred about 7 km west of Samarco on May 2, 216, and was recorded on the Nanometrics local array. Note the very long duration of the BC2 ground motion due to its original recording at 7 km distance from Samarco. As noted by Atkinson (216), the BC2 time history sequence was intended to represent a composite of the foreshock-mainshock-aftershock events of November 5. Even so, the duration of the BC2 record is expected to be longer than the combined duration expected of the November 5, 215 earthquake sequence. August 25, 216 Page J-2

Figure J 2-1 Estimated time histories of November 5, 215 earthquakes from Atkinson (216). (BC1 median-level motions on left; BC2 median-level motions on right) Table J 2-2 summarizes the peak ground acceleration (PGA) values of the two sets of records, i.e. BC1 and alternative BC2, for both median-level and 84 th percentile horizontal ground motions, as well as the corresponding ground motions for C/D site conditions using the amplification factor of 1.4 proposed by Atkinson (216). Note: only the horizontal component time histories are used in the dynamic response analyses. Table J 2-2 PGA values in bedrock of estimated November 5, 215 time histories at Samarco Horizontal Components M w used in Scaling by Atkinson (216) B/C PGA (%g) Median Equivalent C/D PGA (%g) Median B/C PGA (%g) 84 th % Equivalent C/D PGA (%g) 84 th % BC1-H1 Foreshock 2.2 2. 2.8 8.4 9. BC1-H2 Foreshock 2.2 1.9 2.7 6.1 8.5 BC1-H1 Mainshock 2.5 2.5 3.5 8. 11.2 BC1-H2 Mainshock 2.5 2.4 3.4 7.7 1.8 BC1-H1 Aftershock 1.8 1.2 1.7 3.8 5.4 BC1-H2 Aftershock 1.8 1.7 2.4 5.4 7.6 BC2-East 2.5 2.4 3.4 7.9 11.1 BC2-North 2.5 2.2 3.1 7.1 9.9 August 25, 216 Page J-3

Figure J 2-2 shows the response spectra of the BC1 (mainshock) and alternative BC2 median ground motions, for both horizontal components. As shown, the BC2 records are generally larger in amplitudes across most of the periods of interest (or frequencies) than the BC1 records. Figure J 2-2 Response spectra of BC1 (mainshock) and BC2 ground motions provided by Atkinson (216) J3 MODEL AND INPUT DATA FOR SITE RESPONSE ANALYSIS J3.1 General We used the computer program SHAKE2 to perform one-dimensional equivalent-linear site response analyses at the following two sites in Samarco: 1. weathered rock profile at Samarco office site. 2. tailings dam profiles at Fundão Dam site. Figure J 3-1 shows the plan locations of these two sites. August 25, 216 Page J-4

Figure J 3-1 Aerial image showing locations of Samarco office and Fundão Dam The key inputs needed for one-dimensional dynamic response analysis of a site profile, or soil column, in addition to the input earthquake time histories, are: shear wave velocity profile of the ground; and shear modulus and damping variations with shear strain. These input data for SHAKE2 analyses are described in the following subsections. August 25, 216 Page J-5

J3.2 Shear Wave Velocity Figure J 3-2 shows our estimated shear wave velocity (v s ) profile for the residual soil/weathered phyllite rock at the Samarco office. The v s profile was estimated based on v s measurements in the top 36 m depth from a geophysical survey (MASW survey conducted by AFC Geofisica Ltda., see June, 216 report in Appendix C Attachment C3) and extrapolated to 18 m depth by gradually increasing v s to a value of 76 m/s, based on a typical weathered rock profile in California for which extensive v s measurements were available. The v s value of 76 m/s at the base of the model corresponds to site class B/C soft rock conditions, for which the November 5, 215 earthquake ground motions were developed by Atkinson (216). The v s value of the top 3 m (v s3 ) of the weathered rock profile is about 35 m/s, which corresponds to site class C/D stiff soil condition near the surface. Shear Wave Velocity (m/s)) 2 4 6 8 2 4 6 8 1 12 14 16 18 2 Vs= 15*.17D.21 Vs-Section 3 - MASW Survey Vs-Depth Relationship Figure J 3-2 Shear wave velocity data in weathered phyllite at Samarco office site At the Fundão tailings dam, we modeled a typical soil profile at the crest of the dam and one at the toe. Figure J 3-3 illustrates these two soil columns relative to a cross-section of the dam. The crest soil column is 88 m deep, consisting of a surface layer of compacted sand, overlying uncompacted tailings sands and slimes. The toe soil column is 17 m deep and comprises compacted sand overlying only sand tailings. Both soil columns overlie weathered phyllite (C/D soft rock condition) at the original ground surface. August 25, 216 Page J-6

Figure J 3-3 Selected soil columns at Fundão Dam for 1D site response analysis For characterizing the tailings, we compiled the v s data measured by Fugro in 215 at Fundão (see Appendix C), and recent measurements carried out by ConeTec (see Appendix C, Attachment C2) at the Germano Dam and Germano Pit Dam tailings sites. Figure J 3-4 shows the compiled v s data from various test locations at Fundão and Germano, and the average v s trend line used to characterize the tailings deposit for our dynamic response analyses. Note the narrow band of data from the various sets of v s measurements in the tailings at Samarco. August 25, 216 Page J-7

. 1. Shear Wave Velocity, Vs (m/s) 2 4 6 8 Germano Pit Dam- GCCP16-3-Sand Fundao Dam - F1-Sand Fundao Dam - F3 - Sand 2. Fundao Dam - F4 - Sand 3. 4. 5. Vs= 41 + (D/1).36 Fundao Dam - F5 - Sand Germano Dam - GSCPT16-2-Sand Germano Dam - GSCPT16-2B - Interbedded Sand and Slimes Germano Dam- GSCPT16-5-Slimes 6. Figure J 3-4 Shear wave velocity data in tailings at Fundão and Germano An average v s of 265 m/s was estimated for the compacted tailings sand at the crest, based on measurements in test hole GSCPT16-6 by ConeTec (Appendix C, Attachment C2) at the Germano Buttress, as shown on Figure J 3-5. For the residual soil/soft rock that underlies the tailings deposit, an average v s of 4 m/s was estimated based on measurements in GSCPT16-3 by ConeTec (Appendix C, Attachment C2) at the Germano Pit Dam. August 25, 216 Page J-8

Shear Wave Velocity, Vs (m/s) - Compacted Sand 2 4 6 8 5 1 15 GSCPT16-6 - Compacted Sand 2 25 3 Figure J 3-5 Shear wave velocity data in compacted sand Figure J 3-6 shows the three soil columns and corresponding input shear wave velocity profiles used in our dynamic response analyses. Figure J 3-6 Three soil columns used in SHAKE2 analyses J3.3 Modulus Reduction and Damping The shear modulus reduction and damping curves used in the dynamic response analyses are shown on Figure J 3-7 for tailings sands, slimes and weathered rock. These curves were adopted based on the following data sources: For tailings sands, relationships proposed by Winckler et al. (214) that vary with effective stress and are based on laboratory test data on tailings. August 25, 216 Page J-9

For tailings slimes, with measured plasticity index values between about 7 and 11, relationships proposed by Vucetic and Dobry (1991). For weathered rock, relationships proposed by Silva et al. (1997). A total unit weight of 22 kn/m 3 was used for all tailings and soft rock in the dynamic response analyses. Figure J 3-7 Modulus reduction and damping curves for tailings sands, slimes and soft rock J4 RESULTS OF SITE RESPONSE ANALYSES J4.1 Weathered Rock Profile at Samarco Office Site We used the two horizontal components of the BC1 median-level and BC1 84 th percentile mainshock records as outcrop input ground motions in the site response analyses of the weathered rock profile at the Samarco office site, in order to evaluate potential site amplification. Figure J 4-1 shows the depth profiles of the computed PGAs from the SHAKE2 analyses of the November 5, 215 mainshock ground motions. The results indicate some amplification in PGAs in the top 1 m to 2 m of the ground profile. The maximum shear strains generated in the ground vary between approximately.2% and.7%. August 25, 216 Page J-1

Weathered Bedrock Peak Ground Accelleration (g).5.1.15-5 -25-45 -65-85 -15-125 -145-165 -185 BC1-H1-MS-Median BC1-H2-MS-Median BC1-H1-MS-84th-Percentile BC1-H2-MS-84th Percentile Figure J 4-1 Computed peak accelerations from SHAKE2 analyses of weathered rock column Figure J 4-2 compares the response spectra of the input BC1 ground motions and the output or computed motions at ground surface (labeled as -surface layer 1 on Figure J 4-2) from the site response analyses, for both median and 84 th percentile mainshock events. Note the site period of the 18 m deep soft rock column computed from the SHAKE2 analyses is approximately 1.14 sec..3 Pseudo Acceleration Response Spectra - Weathered Bedrock -BC1- H1-Mainshock.3 Pseudo Acceleration Response Spectra - Weathered Bedrock -BC1- H2-Mainshock.25.25.2 H1-MS-Median.2 H2-MS-Median H1-MS-Median-Surface Layer 1 H2-MS-Median-Surface Layer 1 SA(g).15 H1-MS-84th SA(g).15 H2-MS-84th.1 H1-MS-84th - Surafce Layer 1.1 H2-MS-84th - Surafce Layer 1.5.5..2.4.6.8 1 Period (s)..2.4.6.8 1 Period (s) Figure J 4-2 Comparison of output and input response spectra from SHAKE2 analyses August 25, 216 Page J-11

Table J 4-1 summarizes the range in amplification factors, defined as the ratio of the output motion (i.e. computed surface response spectrum) to input motion (i.e. BC1 response spectrum), across all periods for the two horizontal components (H1 and H2) of the mainshock. As shown in Table J 4-1, the SHAKE2 results compare well with Atkinson s proposed amplification factor of 1.4 to convert site class B/C ground motions to site class C/D ground motions. Table J 4-1 Computed amplification factors from SHAKE analyses Ratio of Output to Input Motion Response Spectra Minimum Median Maximum BC1-H1 Median.83 1.25 1.59 BC1-H2 Median.9 1.25 1.67 BC1-H1 84 th Percentile.97 1.34 1.64 BC1-H2 84 th Percentile.96 1.28 1.5 Sensitivity analyses were performed with different modulus reduction and damping curves, and the results were very similar to the above. The B/C ground motions amplified by a factor of 1.4 were carried forward into the dynamic response analyses of the Fundão Dam. The amplified versions of the BC1 and BC2 time history sequences are termed CD1 and CD2, respectively. J4.2 Tailings Dam Profiles at Fundão Dam Site We used the two horizontal components of the CD1 median-level and CD1 84 th percentile records as outcrop input ground motions in the site response analyses of both the crest and toe soil columns at Fundão Dam. Figure J 4-3 presents the results of the SHAKE2 analyses for the CD1 mainshock analyses of the crest and toe soil columns. The figure shows the input v s profile, computed PGA, maximum shear stresses, and cyclic stress ratios (CSR), defined as.65 times maximum shear stress divided by vertical effective stress at the depth of interest. The site period of the 88 m deep crest soil column is 1.15 sec, and the site period of the 17 m deep toe soil column is.42 sec. The maximum shear strains developed in the mainshock analyses of the crest soil column vary from.5% to.2% for the median motions and from.2% to.11% for the 84 th percentile motions. At the toe soil column, the maximum shear strains vary from.2% to.9% for median motions and from.5% to.34% for 84 th percentile motions. As shown on Figure J 4-3 for the crest soil column, the estimated CSR in the sand near the top of the slimes deposit at 58 m depth is about.14 for the median ground motion and.4 for the 84 th percentile ground motion. The estimated number of equivalent uniform cycles of the irregular shear stress time histories extracted at the sand-slimes interface is about 6 to 8. This information was used for the laboratory cyclic testing described in Appendix D, and discussed further in Section J5. August 25, 216 Page J-12

-1 CREST Compacted Sand -1 Vs (m/s) 2 4 6-1 PGA (g).5.1.15-1 Max. Shear Stress (kpa) 2 4 6 8 1-1 CSR.5.1.15-2 -2-2 -2-2 -3-4 -5-6 Sand -3-4 -5-6 -3-4 -5-6 -3-4 -5-6 -3-4 -5-6 Range CSR.139 -.14 CD1- Median Range CSR.41 -.42 CD1-84th -7-8 Slimes -7-8 -7-8 -7-8 -7-8 -9-1 Soft Rock Vs=4 m/s -9-1 Compacted Sand Sand Slimes Water Table Original ground -9-1 CD1-H1-MS-Median CD1-H2-MS-Median CD1-H1-MS-84th Percentile CD1-H2-MS 84th Percentile -9-1 CD1-H1-MS-Median CD1-H2-MS-Median CD1-H1-MS 84th Percentile CD1-H2-MS-84thPercentile -9-1 CD1-H1-MS-Median CD1-H2-MS-Median CD1-H1-MS 84th Percentile CD1-H2-MS-84thPercentile -2-4 -6-8 -1-12 -14-16 -18-2 TOE Compacted Sand Sand -2-4 -6-8 -1-12 -14-16 -18-2 Vs (m/s) 2 4 6 Water Table Sand Compacted Sand Original ground -2-4 -6-8 -1-12 -14-16 -18-2 PGA (g).5.1.15 CD1-H1-MS-Median CD1-H2-MS-Median CD1-H1- MS 84th Percentile CD1-H2-MS 84th Percentile Max. Shear Stress (kpa) 2 4 6 8 1-2 -4-6 -8-1 -12-14 -16-18 -2 CD1-H1-MS-Median CD1-H2-MS-Median CD1-H1-MS - 84th Percentile CD1-H2-MS 84th Percentile -2-4 -6-8 -1-12 -14-16 -18-2 CSR.5.1.15 CD1-H1-MS-Median CD1-H2-MS-Median CD1-H1-MS - 84th Percentile CD1-H2-MS 84th Percentile Figure J 4-3 Results of SHAKE analyses for crest and toe soil columns at Fundão Dam For the crest and toe soil columns at Fundão Dam, we also ran SHAKE2 analyses using the alternative CD2 input ground motions. The cyclic stress ratios induced by the CD2 time histories are compared to those from the CD1 time histories on Figure J 4-4, for both median and 84 th percentile horizontal ground motions. In general, the higher-amplitude alternative CD2 ground motions generated CSRs about 4% higher than those of the CD1 ground motions. Also, the earthquakeinduced cyclic stresses at the toe soil column are higher than at the crest soil column, due to amplification of ground motions. August 25, 216 Page J-13

-1 CREST Compacted Sand -1 CSR.5.1.15-1 CSR.5.1.15-2 -2-2 -3-4 -5-6 Sand -3-4 -5-6 -3-4 -5-6 -7-8 Slimes -7-8 -7-8 -9-1 Soft Rock Vs=4m/s -9-1 CD1-H1-MS-Median -9-1 CD1-H1-MS 84th Percentile CD1-H2-MS-Median CD1-H2-MS-84thPercentile CD2-East-Median CD2-East-84th Percentile CD2-North-Median CD2-North-84th Percentile -2-4 -6-8 -1-12 -14-16 -18-2 CREST TOE Compacted Sand Sand Soft Rock Vs=4 m/s -2-4 -6-8 -1-12 -14-16 -18-2 CSR.5.1.15 CD1-H1-MS-Median CD1-H2-MS-Median CD2- East - Median CD2-North-Median -2-4 -6-8 -1-12 -14-16 -18-2 CSR.5.1.15 CD1-H1-MS - 84th Percentile CD1-H2-MS 84th Percentile CD2-East-84th Percentile CD2-North-84th Percentile Figure J 4-4 Comparison of cyclic stress ratios induced by CD1 and CD2 ground motions J5 CYCLIC LIQUEFACTION TRIGGERING The calculated ground motions are not sufficient to trigger seismic liquefaction under ordinary conditions; however, in light of the collapse behavior observed in the laboratory tests (see Appendix D), and the likelihood of similar stress conditions having developed in the field (see Appendix I), it was deemed necessary to assess whether these motions could induce collapse in an already fragile sample. This was investigated by completing an additional stress controlled extrusion collapse triaxial test. In this test (TX-31), a very loose sample (ψ=+.5) was brought to a condition of incipient failure, identified by the axial strain response to an increment of unloading, before closing the drainage valves and then subjecting the sample to cyclic loading. We intended to apply the CSR August 25, 216 Page J-14

calculated at the sand/slimes interface beneath the crest, since that is the region of the dam cross section where the lateral extrusion mechanism would initiate static liquefaction. The cyclic loading calculated for the sand slimes interface beneath the crest is a CSR of.1 to.4. It was not practical to apply such a low load in the laboratory testing; therefore, a CSR of.1 was applied. The sample did not fail under this load after applying 525 cycles. The load was increased to a CSR of.2 and cycled for a further 521 cycles. The sample still did not fail, so the CSR was increased to.3 and the sample failed after a further 29 cycles. Very little pore pressure was developed during the cyclic loading. This shows that the loading from the earthquake would be insufficient to induce liquefaction in even a very fragile sample. The results from this test are shown on Figure J 5-1 and Figure J 5-2. Refer to the cyclic direct simple shear tests shown in Appendix D for further examples of the insignificant effect that this level of shaking would have on pore pressure development in other samples of sand tested along an alternate stress path. The higher cyclic loads calculated close to the surface occur (Figure J 4-3) in compacted material that would not be susceptible to liquefaction. CSR =.3 CSR =.2 CSR =.1 Figure J 5-1 Pore pressure development in laboratory test following lateral extrusion mechanism and then cyclic loading (test ID TX-31) very loose sample (ψ=+.5) August 25, 216 Page J-15

Start of cyclic loading 525 cycles at CSR=.1, followed by 521 cycles at CSR=.2 then 29 cycles at CSR=.3 then collapse Figure J 5-2 Laboratory test following lateral extrusion mechanism and then cyclic loading (test ID TX-31) very loose sample (ψ=+.5) J6 SEISMIC DISPLACEMENTS Having established that the seismic loading on November 5, 215 would be insufficient to trigger liquefaction through development of cyclic pore pressure, an analysis was completed to identify whether the seismic loading could have contributed to the lateral extrusion triggering mechanism by generating lateral displacements. We assessed this by completing Newmark-type displacement calculations using acceleration time histories extracted from the sand/slimes interface in the SHAKE2 models. The displacement calculations were made using the software SLAMMER. August 25, 216 Page J-16

The displacement calculations involve the identification of a seismic yield acceleration (ay) from limit equilibrium analyses. The calculation within SLAMMER then identifies portions of the acceleration time histories that exceed the yield acceleration. The displacements are then calculated by double integration of the accelerations > ay, and then summation of the displacements resulting from the integration. The yield acceleration was calculated in this analysis for the cross section used in the deformation and stability analyses (Section 1 - see Appendices H and I) assuming that the dam was on the verge of collapse due to lateral extrusion. Consistent with this assumption, an s u /σ'v strength ratio of.14 was used in the calculations because this is the mobilized strength necessary to initiate liquefaction due to lateral extrusion (see Appendix I). The ay value calculated in this analysis was.1 g. Strengths: Slimes-Rich Layers = s u /σ'v (.13); Sand = φ' = 33 ; Compacted Sand = φ' = 35 & c' = 5 kpa Horizontal seismic coefficient =.1 g Figure J 6-1 Calculation of yield acceleration for Newmark-type displacement analysis The displacement analyses were run using the 84 th percentile time histories in order to understand the upper-bound of potential displacements. Analyses were run for both the crest and toe columns, and using both the CD1 and CD2 time history sequences. For the CD1 time history sequence, the displacements were calculated as the sum of those from the foreshock, mainshock and aftershock. The results shown on Figure J 6-2 indicate small displacements, ranging from 2 mm to 8 mm, with an average of 5 mm. Time histories extracted from the SHAKE2 models, used in this analysis, are shown in Attachment J1. August 25, 216 Page J-17

9 Calculated Displacements Sliding Displacement (mm) 8 7 6 5 4 3 2 Ay =.1 1 CD1-H1-ALL-84th Percentile - Crest Column CD1-H2-ALL-84th Percentile - Crest Column CD1-H1-ALL-84th Percentile - Toe Column CD1-H2-ALL-84th Percentile - Toe Column CD2-H1-84th Percentile - Crest Column CD2-H2-84th Percentile - Crest Column Figure J 6-2 Estimated displacements August 25, 216 Page J-18