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Seismic analyses of Wappapello Dam Ahlfield, Kay 1994

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SEISMIC ANALYSES OF WAPPAPELLO DAM by KAY AHLFIELD B.A.Sc. (Honours), University of British Columbia A THESIS STJBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE M.A.Sc. in THE FACULTY OF GRADUATE STUDIES (Department of Civil Engineering) We accept this thesis as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA May 1994 © Kay Ahlfield, 1994 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of £ > V > U Z ^ N G / A J a ^ i H ^ The University of British Columbia Vancouver, Canada Date Ape z*i/<?4-DE-6 (2/88) Li ABSTRACT Wappapello Dam is a rolled-fill, earth dam located on the St. Francis River, approximately 15 miles north of Poplar Bluff, in Missouri, USA. The dam is currently owned and operated by the US Army Corps of Engineers, St. Louis District (USACE-CELMS). The dam was constructed between 1938 to 1941 for flood control purposes. The dam is approximately 73 ft high and the crest is 30 ft wide at El. 419.74 ft (NGVD). The dam is approximately 2,700 ft long. The dam is founded on approximately 120 ft of alluvium underlain by bedrock material identified as dolomite. The upper 40 ft of the alluvial deposits consist of loose, fine sands and silts, less than 500 years old, identified as the Young Point Bar Deposits. This deposit has been identified as potentially liquefiable, and the USACE have initiated a number of studies over the years to determine the dynamic behaviour of Wappapello Dam. The first phase of the seismic study was carried out in 1982 by the USACE-Memphis District and consisted of a one-dimensional liquefaction assessment of Wappapello Dam and the underlying foundation soils. The main conclusions resulting from this work indicated that the Young Point Bar Deposits were indeed susceptible to liquefaction under the design earthquake loads. The second phase of the seismic study was carried out in 1988 b> the USACE-St. Louis District and consisted of limit equilibrium stability analyses, assigning post-liquefaction residual strength values to the liquefied deposits. The residual strength values were determined using an empirically-based correlation relationship with field measured penetration values. The post-earthquake limit equilibrium factor of safety was about 1.0 for the estimated residual strength, and Cut. therefore, the main conclusion from the phase 2 studies was that the likelihood of an earthquake-induced embankment slide causing a reservoir release was low. Since 1988, further advances have been made in the liquefaction assessment procedures, the assessment of residual strength and the evaluation of post-liquefaction deformation analyses. Therefore, the USACE initiated the third phase of the seismic study of Wappapello Dam. This phase included a critical review of the phases 1 and 2 work, to ensure that advances made in the liquefaction assessment techniques and the residual strength evaluations since 1988 have not changed the previous conclusions, and a more rigorous evaluation of the post-earthquake deformation analyses, to ensure that the magnitude of the movements are within acceptable limits. The post-earthquake deformation analyses was carried out using the finite element computer programs, TARA-3 and TARA-3FL, developed by Dr. W.D.L. Finn of the University of British Columbia, Canada. The phase 3 work deformation analyses indicated that the magnitude of the post-earthquake movements were in the order of 25 ft vertically and greater than 200 ft horizontally, if the same design parameters as used in the phase 2 work were assumed. The discrepancy between the results of the finite element analyses and the limit equilibrium slope stability analyses was attributed to the different failure mechanisms assumed in each analysis. In the finite element analysis, failure was a result of the squeezing out of the liquefied foundation deposits due to the high gravity loads of the dam and the sliding on the softened material as a result of reservoir loading. In the limit equilibrium slope stability model, the failure is modelled by a circular slip surface cutting through both the embankment having a high strength of 3,000 psf and the Young Ui/ Point Bar Deposit with a low, post-liquefied strength of 115 psf. The seismic stability of structures with extensive zones of liquefiable materials in the foundation should not be assessed using limited equilibrium slope stability analyses as the conclusions resulting from this type of analysis may be misleading. Additional deformation analyses were carried out in the phase 3 work using more realistic field-measured penetration test values for the Young Point Bar Deposit. Parametric analyses were carried out by assuming different residual strength correlation relationships and varying ( N ^ values for the Young Point Bar Deposits located downstream of the dam toe (which was unknown during the phase 3 work). The deformation values ranged from less than about 3 ft of vertical and horizontal deformations to greater than 20 ft vertically and 250 ft horizontally for the varying strength assumptions. Therefore, the seismic stability of Wappapello Dam depends on two critical input parameters: the penetration test values of the Young Point Bar Deposits located downstream of the dam toe; and the evaluation of residual strength. The following recommendations are made following the phase 3 studies: further field investigations should be carried out to determine the (Nj)^ values of the Young Point Bar Deposits located downstream of the dam toe; further studies should be carried out to determine the residual strength of the Young Point Bar Deposits. Additional laboratory testing and review of the empirically-derived residual strength vs (N,)^ database should be carried out to establish appropriate Sur values for this site; after the ( N ^ values of the Young Point Bar Deposit have been established and the appropriate design Sur values have been assigned, further deformation analyses should be carried out to determine the post-earthquake deformations of Wappapello Dam. The maximum acceptable post-earthquake deformation limits to ensure seismic stability of V Wappapello Dam should be established by the USACE. If the estimated deformations are not acceptable, potential remedial measures should be assessed and implemented. vL T A B L E O F C O N T E N T S Page A B S T R A C T u T A B L E O F C O N T E N T S »L LIST O F T A B L E S ix LIST OF FIGURES xL 1. INTRODUCTION 1 1.1 Background 1 1.2 Scope of Thesis ' 7 2. SITE DESCRIPTION 9 2.1 Foundation Stratigraphy 9 2.2 Ground Motion Evaluation 10 2.2.1 Design Earthquake Motions 13 3. SITE INVESTIGATIONS 16 3.1 Previous Geotechnical Investigations 16 3.3.1 Drilling and Geophysical Explorations 16 3.1.1.1 Pre-Construction Investigations 16 3.1.1.2 Phase 1 Field Investigations 16 3.1.1.3 Phase 2 Field Investigations 19 3.2 Monitoring Instruments 19 4. GEOTECHNICAL CHARACTERIZATION OF WAPPAPELLO DAM AND FOUNDATION SOILS 21 4.1 Standard Penetration Test (SPT) Data 21 4.2 Shear Wave Velocities 21 4.2.1 Soil Properties 24 5. REVIEW OF USACE PHASES 1 AND 2 WORK - LIQUEFACTION ASSESSMENT AND POST-EARTHQUAKE STABILITY 31 5.1 Background 31 5.2 Phase 1 Work 33 5.2.1 One-dimensional Dynamic Analysis 33 5.2.1.1 SHAKE Input 35 5.2.1.2 Computation of Equivalent Number of yii'i. Cycles of Stress 43 5.2.1.3 Determination of the Dynamic Shear Strength of the Foundation Soils 45 5.2.2 Dynamic Factors of Safety Against Liquefaction 54 5.3 Phase 2 Work 58 5.3.1 Post-earthquake Limit Equilibrium Slope Stability Analyses 58 5.4 Conclusions Based from the USACE Phases 1 and 2 Work 61 6. TARA-3 AND TARA-3FL PROGRAM DESCRIPTION 62 6.1 General Background 62 6.2 TARA-3 Program Description 62 6.2.1 Finite Element Representation ,63 6.2.2 Stress-Strain Behaviour in Shear 64 6.2.3 Stress-Strain Behaviour in Hydrostatic Compression . . . 70 6.2.4 Dynamic Analysis 73 6.2.4.1 Dynamic Stress-Strain Behaviour in Shear 75 6.2.5 Residual Pore Pressure Model 78 6.2.5.1 Martin-Finn-Seed Pore Water Pressure Model 79 6.2.5.2 Determination of Pore Water Pressure Constants in Practice 81 6.2.6 Special Features of Analysis by TARA-3 82 6.3 TARA-3FL Program Description 83 6.4 Evaluation of Undrained Residual Strength 85 7. TARA-3 MODELLING OF WAPPAPELLO DAM 90 7.1 Material Properties 90 7.1.1 Strength Properties 90 7.1.2 Shear Stress-Shear Strain Parameters for Wappapello Dam 90 7.1.3 Bulk Modulus Parameters Selected for Wappapello Dam 92 7.2 Pore Water Pressure Constant Values Selected for Wappapello Dam 94 7.3 Finite Element Modelling 98 7.3.1 General 98 7.3.2 Water Loads . 103 \!iil> 8. DYNAMIC ANALYSES RESULTS OF WAPPAPELLO DAM BY TARA-3 104 8.1 General 104 8.2 Dynamic Analyses on Original Geometry of Wappapello Dam 104 8.3 Dynamic Analyses on Deformed Shape of Wappapello Dam 110 9. POST-LIQUEFACTION FLOW DEFORMATION RESULTS BY TARA-3FL 113 9.1 General 113 9.2 Constant ( N ^ Values in the Young Point Bar Deposits 113 9.2.1 Comparison Between the Results of the Flow » Deformation and Slope Stability Analyses 114 9.3 Relationship Between Dam Displacements and S^ in the Young Point Bar Deposit 117 9.4 Varying (Ni)60 Values in the Young Point Bar Deposit 119 10. CONCLUSIONS AND RECOMMENDATIONS 135 REFERENCES 140 APPENDIX I )x LIST OF TABLES Page Table 1 - Earthquake Ground Motion Parameters at Wappapello Dam Site 13 Table 2 - Earthquake Time Histories Recommended for Wappapello Dam . 14 Table 3 - Instrumentation Location 20 Table 4 - Strength Properties of Wappapello Dam Site 26 Table 5 - Shear Test Results 29 Table 6 - SHAKE Parameters, Free Field Profile 36 Table 7 - SHAKE Parameters, Centreline Profile 37 Table 8 - a ^ Results from SHAKE 38 Table 9 - Post-earthquake Stability Analyses Results 60 Table 10 - Suggested Bulk Modulus Parameters Correlated to Dr and Nj (Byrne and Cheung, 1984) 72 Table 11 - Recommended Fines Correction for S^ Evaluation Using SPT Data 87 Table 12 - K2 or Kclay Values 92 Table 13 - kb and n Values for Wappapello Dam 93 Table 14 - Pore Pressure Constants for Reservoir Level at El. 360 ft (NGVD) 97 Table 15 - Pore Pressure Constants for Reservoir Level at El. 390 ft (NGVD) 98 Table 16 - Water Loads on Upstream Face 103 Table 17 - Relationship Between S^ Values and (N,)^ Values used at Station 14+00 at Wappapello Dam 122 X Table 18 - Upstream Crest Displacements with (Nj)60 Values Variable Across Station 14+00 with the Upstream Reservoir Water Level at El. 390 ft (NGVD) 132 Table 19 - Upstream Crest Displacements with ( N ^ Values Variable Across Station 14+00 with the Upstream Reservoir Water Level at El. 360 ft (NGVD) 133 *l< LIST OF FIGURES Page Figure 1 - Site Location of Wappapello Dam (Wahl and Deer, 1982) 2 Figure 2 - Plan View of Wappapello Dam (Wahl and Deer, 1982) 3 Figure 3 - Cross-section of Wappapello Dam at Station 14+00 (Wahl and Deer, 1982) 3 Figure 4 - History of Seismic Studies of Wappapello Dam 5 Figure 5 - Assumed Extent of the Young Point Bar Deposit , (Wahl and Deer, 1982) 11 Figure 6 - Acceleration-Time Plots for Design Earthquakes (Wahl and Deer, 1982) 15 Figure 7 - Test Layout of Geophysical Investigation of Wappapello Dam (Wahl and Deer, 1982) 18 Figure 8 - Plan View of Wappapello Dam Showing the Areal Extent of Soils with Low Blow Counts (Wahl and Deer, 1982) 22 Figure 9 (a) - Average Contours of Nx Betweem El. 300 ft to El. 319 ft (NGVD) 23 Figure 9 (b) - Average Contours of ^ Between El. 320 ft to El. 329 ft (NGVD) 23 Figure 9 (c) - Average Contours of Nj Between El. 330 ft to El. 360 ft (NGVD) 24 Figure 10 - S-wave Zonal Interpretation for Cross-section through Station 14+00 (Wahl and Deer, 1982) 25 Figure 11 - Relationship Between the Ratio of Undrained Shear Strength to Effective Overburden Pressure and Plasticity Index for Normally-consolidated (Holtz and Kovacs, 1981) 27 Figure 12 - UU Test and Pressurement Test Results (USACE, 1988) 30 Figure 13 - SHAKE Results, Maximum Acceleration vs Depth for Centreline Profile (Wahl and Deer, 1982) 39 YXL Figure 14 - SHAKE Results, Maximum Acceleration vs Depth for Free Field Profile (Wahl and Deer, 1982) 40 Figure 15 - SHAKE Results, Maximum Stress vs Depth for Centreline Profile (Wahl and Deer, 1982) 41 Figure 16 - SHAKE Results, Maximum Stress vs Depth for Free Field Profile (Wahl and Deer, 1982) 42 Figure 17 - Equivalent Number of Uniform Stress Cycles as a Function of Earthquake Magnitude (Wahl and Deer, 1982) 44 Figure 18 - Cyclic Stress Ratio vs the Number of Cycles to Failure, Effective Confining Pressure at 10 psi (Wahl and Deer, 1982). . . ,47 Figure 19 - Cyclic Stress Ratio vs the Number of Cycles to Failure, Effective Confining Pressure at 35 psi (Wahl and Deer, 1982)... 47 Figure 20 - Dynamic Shear Strength versus Normal Effective Stress for the Foundation Soils at Wappapello Dam (Wahl and Defer, 1982). 49 Figure 21 - Correlation Curve Between Stress Ratio Causing Liquefaction Penetration Resistance for Sands Having D50 > 0.25 mm (Seed and Idriss, 1981) 51 Figure 22 - Recommended Curves for the Determination of CN (Seed and Idriss, 1981) 52 Figure 23 - Factors of Safety Against Liquefaction, Free and Centreline Profiles (Wahl and Deer, 1982) 55 Figure 24 - Plan View of Wappapello Dam showing the Areal Extent of the Zone of Potentially Unstable Material (Wahl and Deer, 1982) 57 Figure 25 - Relationship Betweem Residual Strength and (N^,, Values for Clean Sands (Seed, 1987) 59 Figure 26 - Stress-Strain Relationship During Loading, Unloading and Reloading Phases . 65 vjuil Figure 27 - Shear Moduli of Sands at Different Relative Densities (Seed et al, 1984) 68 Figure 28 - Comparison of Shear Moduli for Gravelly Soils and Sands at a Relative Density of 95% (Seed et al, 1984) 69 Figure 29 - In-situ Moduli for Saturated Clays (Seed and Idriss, 1970) 71 Figure 30 - Nonlinear Hysteretic Loading Paths 76 Figure 31 - Adjusting Stress-Strain State to Post-liquefaction Conditions . . . . 84 Figure 32 - Relationship Between Corrected Clean Sand Blowcount (Nj)60^ and Residual Strength, Sr From Case Studies , (Seed and Harder, 1990) 88 Figure 33 - Variation in Residual Strength with (N,)^ (USBR, 1989) 89 Figure 34 - Liquefaction Resistance Curves for Various Earthquake Magnitudes (Koester and Franklin, 1985) 95 Figure 35 - Fit of Pore Pressure Constants to Liquefaction Resistance Curve at ( N ^ of 11 blows/ft 96 Figure 36 - Finite Element Numbering for Wappapello Dam 100 Figure 37 - Node Number for Wappapello Dam 101 Figure 38 - Finite Element Soil Characterization of Wappapello Dam 102 Figure 39 - Stress-Strain and Pore Pressure Plots for Element 285 -Upstream Toe 106 Figure 40 - Stress-Strain and Pore Pressure Plots for Element 296 -Under Centre of Dam 107 Figure 41 - Stress-Strain and Pore Pressure Plots for Element 310 -Downstream Toe 108 Figure 42 - Shear Stress Time History for Element 342, Located in Young Point Bar Deposit under the Centre of the Dam I l l Xt-V Figure 43 - Acceleration Time History Recorded at the Crest of Wappapello Dam I l l Figure 44 - Displacement Time History Recorded at the Crest of Wappapello Dam 112 Figure 45 - Flow Deformation of Wappapello Dam when Residual Strength in Young Point Bar Deposits is Equivalent to 115 psi, (Nj)60 = 9 blows/ft 115 Figure 46 - Variation in Horizontal and Vertical Displacement of the Dam Crest with Residual Strength Values in the Young Point Bar Deposit . . 118 Figure 47 - Variation in Dam Freeboard with Residual Strenths in the Young ( Point Bar Deposit 119 Figure 48 - Distribution of ( N ^ Values in the Young Point Bar Deposit for TARA-3FL Analysis 121 Figure 49 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at (Nj)^ of 4 blows/ft, Seed's Lower Bound Curve 124 Figure 50 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at (N,)60 of 8 blows/ft, Seed's Lower Bound Curve 125 Figure 51 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at ( N ^ of 4 blows/ft, US Bureau of Reclamation Curve. 126 Figure 52 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at (N,)^ of 8 blows/ft, US Bureau of Reclamation Curve. 127 Figure 53 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (N,)^ of 4 blows/ft, Seed's Lower Bound Curve 128 Figure 54 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at ( N , ^ of 8 blows/ft, Seed's Lower Bound Curve 129 Figure 55 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (N,)^ of 4 blows/ft, US Bureau of Reclamation Curve. 130 Figure 56 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (Nj)^ of 8 blows/ft, US Bureau of Reclamation Curve. 131 - 1 - Chapter 1 INTRODUCTION Background Wappapello Dam is a rolled-fill, earth dam located on the St. Francis River, approximately 15 miles north of Poplar Bluff, in Missouri, USA (Figure 1). The dam is currently owned and operated by the US Army Corps of Engineers, St. Louis District (USACE-CELMS). The dam was constructed between 1938 and 1941 for flood control purposes. Currently, the dam is approximately 73 ft high and the crest is 30 ft wide at El. 419.74 ft above the National Geographic Vertical Datum (NGVD). The dam is approximately 2,700 ft long. The slopes of the dam are protected by rip rap and a drain is installed at the downstream toe. Plan and cross-section views of the dam are shown in Figures 2 and 3. The dam is founded on approximately 120 ft of alluvium underlain by bedrock material identified as dolomite. The alluvial soils consist of deposits from the St. Francis River with isolated alluvial and colluvial deposits from Redman Creek and Peoples Creek. The foundation soils have been categorized into three major depositional units, as shown in Figure 3, as follows: Older Alluvium; Recent Alluvium; and Young Point Bar Deposit The Young Point Bar Deposit consists of loose, fine sands and silts, less than 500 years old. Wappapello Dam was designed before the development of adequate analytical - 2 - Chapter 1 O 60 100 1S0 SCALE, mU >T . LOUIS •PRINOFIELDY WAPPAPELLO i l " * . _ 'us eo LAKE ) [ y ^ • c * m o 1 - 6 6 i m » i NASHVILLE O SO 1 0 0 1 6 0 2 0 0 SCALE, <nl. Figure 1 - Site Location of Wappapello Dam (Wahl and Deer, 1982) -3- Chapter 1 Figure 2 - Plan View of Wappapello Dam (Wahl and Deer, 1982) NORMAL POOL IS • !. 360 3 2 0 2 8 0 2 0 0 L-HORIZONTAL SCALE. I t 0 100 200 SANOS ANO SILTY SANDS (YOUNG POINT BAR DEPOSIT.) LEAN CLAY (RECENT ALLUVIUM) CRAVELS ANO SANOS (RECENT ALLUVIUM) FAT CLAY fOLOER ALLUVIUM) GRAVELS ANO SANOS (OLDER ALLUVIUM) " ^ «*»-OOLOMITE -**&&&• *vw&,q Figure 3 - Cross-section of Wappapello Dam at Station 14+00 (Wahl and Deer, 1982) - 4 - Chapter 1 procedures to assess the effects of earthquake loading on the structure; therefore, no rigorous analyses was carried out prior to dam construction. However, the original designers recognized that the Young Point Bar Deposit could present a problem for dynamic stability and constructed the dam with relatively flat embankment slopes of 2.5H.1V, 4.5H:1V and 8H:1V, with an average slope of 4.5H:1V. Since the 1940's, considerable advancements have been made in the field of earthquake engineering and numerical modelling. As a result, the USACE have initiated a number of studies over the years to determine the dynamic behaviour of Wappapello Dam. The history of the seismic studies carried out to assess the dynamic behaviour of Wappapello Dam is presented in Figure 4. The first phase of the seismic study was carried out in 1982 by the USACE-Memphis District (Wahl and Deer, 1982). This study consisted of a liquefaction assessment of the Wappapello Dam site to determine the susceptibility of the dam and foundation soils, particularly the Young Point Bar Deposit, to triggering of liquefaction under the earthquake loads. A one-dimensional dynamic analyses of two soil profiles, one modelling the dam centreline profile and the second modelling the free field conditions, was carried out to estimate the cyclic stresses. The soil cyclic strengths were evaluated by two methods, as follows: laboratory cyclic triaxial testing carried out on "undisturbed" soil samples; and in situ Standard Penetration Testing (SPT) values. These values measured at Wappapello Dam were compared to other sites whose performance (where either liquefaction did or did not occur) during an earthquake was known (Seed and Idriss, 1982). - 5 - Chapter 1 CONSTRUCTION OF WAPPAPELLO DAM constructed in 1938 - 1 9 4 0 no foundation densffication no seismic assessment PHASE 1 INITIAL SEISMIC ASSESSMENT -1982 USACE-Memphis District (Wahl and Deer. 1982) - liquefaction assessment of dam and foundation soils SHAKE analyses field and laboratory testing CONCLUSIONS: -liquefaction would be triggered in Young Point Bar Deposit > PHASE 2 POST-EARTHQUAKE STABILITY ASSESSMENT -1988 USACE - St. Louis District (USACE. 1988} limit equilibrium stability analyses use of Seed, 1987 lower bound residual strength CONCLUSIONS: liquefaction induced embankment slide causing a reservoir release unlikely Advances in Liquefaction Assessment Methodology PHASE 3 CRITICAL REVIEW OF PHASE 1 AND PHASE 2 AND POST-EARTHQUAKE FLOW DEFORMATION ANALYSES -1991 UBC-1991 quantify magnitude of post-earthquake deformations to ensure seismic stability of Wappapello Dam Advances in 1. Liquefaction Assessment Methodology 2. Residual Strength Evaluation 3. Flow Deformation Analyses Figure 4 History of Seismic Studies of Wappapello Dam -6- Chapter 1 Factors of safety against the triggering of liquefaction were computed. The results of this seismic assessment indicated that liquefaction would be triggered in the Young Point Bar Deposit under the earthquake loads. The triggering of liquefaction required that an evaluation of the post-earthquake stability of the dam be carried out. The second phase of the seismic study was carried out in 1988 by the USACE-St. Louis District (USACE, 1988). The study consisted of limit equilibrium stability analyses, assigning post-liquefaction residual strength values to the liquefied deposits. The residual strength values were determined using an empirically-based correlation relationship with field-measured ( N ^ values (Seed, 1987). The post-earthquake limit equilibrium factor of safety was about 1.0 for the estimated residual strengths, and therefore the conclusion of the second phase of the study was that the likelihood of an earthquake-induced embankment slide causing a reservoir release was low. Since that time, however, further advances have been made in the liquefaction assessment procedures, the assessment of residual strength (Seed and Harder, 1990, and USBR, 1989) and the evaluation of post-liquefaction deformation analyses (Finn et al, 1986 and Finn and Yogendrakumar, 1989). Therefore, the USACE initiated the third phase of the seismic study of Wappapello Dam. This phase included the following work: a critical review of phases 1 and 2, to ensure that the changes that have occurred in the methodology of liquefaction assessment since 1988 and the updated correlation relationships between residual strength and dynamic shear strength have not changed the previous conclusions; and a post-earthquake deformation analyses to ensure that the magnitude of the movements are within acceptable limits. - 7 - Chapter 1 The third phase of the seismic study of Wappapello Dam was conducted at the University of British Columbia (UBC) in 1991 and is the subject matter of this thesis. Scope of Thesis This thesis summarizes the dynamic seismic stability review of Wappapello Dam and the results of the post-earthquake deformation analyses. The data obtained from the previous field investigation work, the laboratory testing program carried out on the Young Point Bar Deposits, and a critical review of the past seismic assessment of the dam are detailed in the following sections: Chapter 2 - Site Description; Chapter 3 - Site Investigations; Chapter 4 - Geotechnical Characterization of the Wappapello Dam and Foundation Soils; and Chapter 5 - Review of the USACE Phases 1 and 2 Work -Liquefaction Assessment and Post-earthquake Analyses. The post-earthquake deformation analyses were completed using two-dimensional finite element computer programs, TARA-3 and TARA-3FL (Finn et al, 1986, and Finn and Yogendrakumar, 1989). This work consisted of both dynamic analyses and post-liquefaction flow deformation analyses, detailed in the following sections: Chapter 6 - TARA-3 and TARA-3FL Program Description; Chapter 7 - TARA-3 Modelling of Wappapello Dam; Chapter 8 - Dynamic Analyses Results of Wappapello Dam by TARA-3; and - 8 - Chapter 1 Chapter 9 - Post-liquefaction Flow Deformation Results by TARA-3FL; and Chapter 10 - Conclusions and Recommendations. - 9 - Chapter 2 SITE DESCRIPTION Foundation Stratigraphy Wappapello Dam is founded on approximately 120 ft of alluvial deposits underlain by bedrock. The bedrock has been identified as dolomite; the bedrock, however, does not represent a critical deposit for dynamic stability analyses and will be not be discussed further in the following sections. The foundation soils consist of the Older Alluvium, the Recent Alluvium and the YoUng Point Bar Deposit (Figure 3). The Older Alluvium deposit consists primarily of sand and gravel from El. 230 ft to El. 252 ft (NGVD), 22 ft in thickness, overlain by a continuous layer of overconsolidated brown silty clays and silts from El. 252 ft to El. 268 ft (NGVD), 16 ft in thickness. The Older Alluvium probably represents aggradation of the St. Francis River's bedrock valley following the Pleistocene period. The overlying clay layer probably represents a backswamp deposit The clay layer is considered to be overconsolidated. The Recent Alluvium deposit consists of sands and gravels in the centre of the valley from El. 268 ft to between El. 280 ft to El. 300 ft (NGVD), varying from 12 ft to 32 ft in thickness, grading upwards to silts and overconsolidated clays approximately 26 ft thick. This deposit may have formed as bars and chutes deposited as the St Francis River aggraded its bed in response to decreasing gradients of rising base levels. - 10 - Chapter 2 The Young Point Bar Deposit consists of approximately 40 ft of loose, fine sands and silts, indicating point-bar deposition by the modern day SL Francis River prior to reservoir filling. The assumed extent of the Young Point Bar Deposit is shown in Figure 5. Ground Motion Evaluation In order to determine earthquake ground motion parameters for use in evaluating Wappapello Dam under seismic loading, a seismic hazard evaluation was carried out by the US ACE in 1988. The design ground motion parameters were selected using the probabilistic seismic hazard evaluation. In order to carry out a probabilistic seismic hazard evaluation, the following input is required: the seismic sources in which future potential earthquakes are likely to occur; the earthquake magnitude and frequency of the earthquakes within each source; and the attenuation relationships for seismic parameters, such as absolute acceleration and velocity and spectral acceleration, velocity and displacements. There are several potential earthquake sources that may contribute to ground motions at the Wappapelio Dam site. The source zones, maximum credible earthquakes and magnitude-recurrence relations were obtained from US Army Engineering District (USAED)-St. Louis (1981). -11 - Chapter 2 % , Po/A/r-BAK. i :;&>&& 'APPiPlLLO \ o \ ^ v ^ i90;v'-. < s-i," !«" rJS^c £r^? 3 9 0 -^iiililliiliP1^^1 — St* ] « « 0 0 t ISO 370 'H!!:n:«::i:::::::I::n' -«"lo" o a O O 400 6 0 0 GRAPHIC SCALE IN I I *\ o- I, o '•• » / / it —-t::::::s«!i:j::ji!Hiy jc:!:i:s:-:=j{::::n::7'" » * « ^ \ ::?' I 5*° ri Vll / / 1 \ III lO'A in K\\ V« lf\ \> Figure 5 •, Assumed Extent of the Young Point Bar Deposit (Wahl and Deer, 1982) -12- Chapter 2 Wappapello Dam is situated within the Ozark Random Seismotectonic Zone, which exhibits moderate seismicity not correlated to any known geologic structure. The closest mapped fault to Wappapello Dam is the NE-SW trending Greenville Fault which lies approximately 16 miles northwest of the dam site. Another structural feature, the N-S trending Roselle Lineament is about 15 miles west of the dam. These features, however, are not considered active, earthquake-producing faults. The dam may be affected more severely by events within two other source zones; the West Embayment and the New Madrid Seismotectonic Zones. The West Embayment source area is about 3 miles southwest of the dam site and has a relatively high random seismicity unrelated to known geologic structure. The shortest distance to the New Madrid Seismic zone is approximately 30 miles southwest from the dam site. This zone is the major source of earthquake activity in the central US. The largest earthquakes that have occurred in the New Madrid Zone were the largest events known to have occurred east of the Rocky Mountains. The energy released by the New Madrid series of events that occurred in 1811-1812 exceed the energy of all US earthquakes since that time. These earthquakes are related to the New Madrid Fault, the nearest active fault to the dam site. At its closest, the fault lies about 30 miles southeast of the dam. The attenuation relationships used in the probabilistic model were obtained from Nuttli and Hermann (1984) and Krinitzsky and Marcuson (1983), appropriate for the eastern US. - 13 - Chapter 2 An epicentral distance of 30 miles was selected, as this distance represents the closest distance of the dam to the New Madrid Fault of the New Madrid Seismic Zone. The probabilistic seismic hazard evaluation was carried out by Teledyne Geotech Consultants of Alexandria, Virginia, using the computer program EQRISK (McGuire, 1976). The ground motion parameters for the 1,000 year event, selected as the appropriate level by the client, are summarized in Table 1. Table 1 - Earthquake Ground Motion Parameters at Wappapello Dam Site ACCELERATION (maximum) VELOCITY (maximum) DISPLACEMENT (maximum) DURATION 0.4g 40cm/s 1.3'fl/s 30cm 1.0 ft 20 seconds Design Earthquake Motions The design earthquake for Wappapello Dam was specified to have a body wave magnitude, Mb, of 7.5 (Richter magnitude, M, of 8.3), based on historical evidence from the New Madrid earthquakes of 1811 -1812. Acceleration time histories were required for input into the dynamic analyses. Time histories were selected such that the velocity (maximum) and the duration of the earthquake matched the design values, listed in Table 1. In addition, the response spectra - 14 - Chapter 2 of the time histories were checked for sufficient energy near the predominant period of the structure, approximately 0.2 second. Table 2 summarizes the recommended earthquake acceleration time histories for Wappapello Dam for use in the dynamic analyses. Figure 6 presents the acceleration-time plots of the design earthquakes. Table 2 - Earthquake Time Histories Recommended for Wappapello Dam EARTHQUAKE Imperial Valley, CA Kern County, CA DATE 15 OCT 1979 13 JUL 1952 RICHTER MAGNITUDE 6.6 7.7 ^mtx 0.19g 0.18g RECORDING STATION Superstition Mountain Tafr-Lincoln School COMPONENT 1351 degrees S69E These time histories were considered appropriate for the phase 3, 1991 work. - 15- Chapter 2 z o < o < 0.2 0.0 z o • • < s u u u < ACCELERATION RECORD FOR KERN COUNTY. CALIFORNIA EARTHQUAKE OF 31 JULY 1»»J RECORDED AT TAFT LINCOLN SCHOOL TUNNEL COMPONENT: S • • " E ,yi\^^Wu«y^ • ( » • > . ) SCALEO TO 0.4 • ' • • («<>.) 15.4 l»« TIME, sec 2 1 28 — I — as — I — 4 2 4 9 —I 5 6 ACCELERATION RECORO FOR IMPERIAL VALLEY. CALIFORNIA EARTHQUAKE OF IS OCT l l l l V RECORDED AT SUPERSTITION MOUNTAIN. CALIFORNIA COMPONENT: 135° flj^NlflgfllrW '•*> i . i f ' • (ma*.) SCALED TO 0.4 « ' • «<m«>.) = 7.2 lp* — I — 1 0 — I — I S TIME, sec 1 20 - 1 — 3 0 — I — 35 Figure 6 - Acceleration-Time Plots for Design Earthquakes (Wahl and Deer, 1982) - 16- Chapter 3 3. SITE INVESTIGATIONS 3.1 Previous Geotechnical Investigations Geotechnical investigations have been carried out by the USACE during the original dam design phase in the 1930's and subsequently since then by the UCACE - Memphis District (CELMM) in the late 1970's to early 1980's and by the USACE- St. Louis District (CELMS) in the 1980's. The following sections summarize the scope of the field investigations. 3.1.1 Drilling and Geophysical Explorations 3.1.1.1 Pre-construction Investigations A large number of foundation borings were carried out at the dam site prior to construction in the late 1930's. This work consisted of drilling 34 auger borings, 23 "core borings", trenches, pits and 6 "undisturbed" borings. The "core borings" were drilled by the wash-boring method and continuously sampled by a split spoon sampler. Information on soil densities is limited since this work was completed before the development of the standardized penetration test. Differences between the 1930's sampling and classification methods and current methods make it difficult to estimate the in situ soil densities from the field data obtained from the 1930's. 3.1.1.2 Phase 1 Field Investigations USACE - Memphis District (CELMM) performed additional foundation explorations as part of the phase 1 seismic study program between August 1977 and June 1979. This - 17- Chapter 3 field work consisted of 24 borings carried out by both government (CELMM) and contracted (ATEC Associates) personnel. ATEC borings were carried out by rotary drill rigs using 4" diameter casings, wire-line retrieved rock bits and clear water. The CELMM borings were carried out using rotary drills advancing 4" fishtail bits with bentonite mud. Boreholes were sampled by 2" and 3" (OD) split spoon samplers using 140 and 300 pound hammers respectively. In most cases, the standard penetration test (SPT) procedures were followed in the dam foundation soils. A review of the field logs indicated that the ATEC rigs used "A" rods to drive their SPT's whereas "N" rods were used by the CELMM rigs. The samples obtained in the field were classified according to the Unified Soil Classification System. "Undisturbed" samples were obtained from the Young Point Bar Deposit during the field work by CELMM using a Hvorslev fixed-piston sampler. This technique consisted of pushing a three inch diameter thin-walled tube into the soil with a hydraulic system. Each sample was X-rayed to check for disturbance, and the samples showing the least amount of disturbance were subsequently selected for laboratory testing. In the summer of 1981, a geophysical field program, including seismic refraction, crosshole P and S wave tests and downhole P and S wave tests, was carried out. The test layout of the geophysical investigations is shown in Figure 7. These seismic surveys were conducted to determine the foundation conditions and dynamic soil properties of the embankment and foundation. - 18- Chapter 3 Figure 7 - Test Layout of Geophysical Investigation of Wappapello Dam (Wahl and Deer, 1982) - 19 - Chapter 3 Phase 2 Field Investigations USACE - St. Louis District (CELMS) conducted an investigation consisting of drilling 20 additional borings, sampling and standard penetration testing (SPT) at the dam site. Particular care was taken during this field investigation program to follow the recommended standard penetration test procedure (as outlined by Seed et al., 1984), since blow count data (N,^ were to be used for input into the liquefaction assessment. Appendix I describes the recommended standard penetration test procedure. Boreholes were 4 7/8" in diameter, drilled with bentonite mud using a tricone roller bit. Standard penetration testing (SPT) was carried using 2" OD, 1 1/2 inch ID split spoon samplers and "N" rods. The energy delivered to the sampler was measured using the stress wave energy method. Results from this analysis indicated that the CELMS operators conducted the SPT at an average energy ratio of about 54% (percent of theoretical free fall energy). In addition, borehole electrical and gamma ray logging, Menard pressuremeter testing down 4 holes and an electrical resistivity survey of the area immediately downstream of the embankment were carried out. Monitoring Instruments During the summer of 1989, CELMS drilled holes to install piezometer and seismic instruments near Station 14+00. The instruments are clustered at three locations on the cross-section, offset at approximately 25 ft, 150 ft and 300 ft downstream from the centreline of the dam. The piezometer tips were installed to record pore pressures in the - 20 - Chapter 3 potentially liquefiable Young Point Bar Deposits. The accelerometers were located near the centreline of the dam axis, at the toe of the dam in the upper young point bar deposits, and at the mid-slope of the dam in the bedrock. Table 3 details the depths and stations of the instruments. "P" represents piezometer holes approximately 11 inches in diameter and "S" represents seismic holes approximately 9 inches in diameter. Table 3 - Instrumentation Location TYPE P P S P P S P P S STATION 14+40 14+65 14+75 14+70 14+65 14+75 14+70 14+65 14+75 OFFSET D/S (ft) 19.2 27.9 27.9 144.2 152.9 152.9 294.2 302.9 302.9 GROUND EL. (ft) 417.3 414.1 413.8 381.7 379.5 379.4 355.8 355.7 355.1 INSTRUMENT > DEPTH (ft) 340 313.5 342 340 345 210 340 315 . 342 The piezometers and seismic instrumentation are read by remote monitoring units (RMU) controlled by a central computer located in the Administration building. The RMU can be programmed to record the data at predetermined time intervals, as required, and supply intermediate data storage for the instrumentation. The data can then be transferred to the central computer for permanent storage and processing. - 21 - Chapter 4 GEOTECHNICAL CHARACTERIZATION OF WAPPAPELLO DAM AND FOUNDATION SOILS Standard Penetration Test (SPT) Data Results from the SPTs carried out in boreholes PE-5, PE-6, PE-7, PE-26, PE-23, PE-8, and PE-24 indicated that the Young Point Bar Deposits exhibited low resistance to penetratioa CELMM defined low blow count materials as those materials which had blow counts, N values, of 10 blows/ft or less. The interpretation by CELMM of the areal and vertical extent of this potentially liquefiable zone lay between Station 11+00 to 16+60 and extended from 100 ft upstream of the dam centreline to approximately 1,000 ft downstream of the dam centreline, as shown in Figure 8. This, zone has a thickness of approximately 30 ft, with its upper surface at the original ground level prior to dam construction at EI. 347 ft (NGVD). The materials of this zone have been classified by CELMM as fine sands, silty sands and silts. N value contour plots for the Young Point Bar Deposit were interpolated from the field test holes. They are segregated into 3 different elevation zones - El. 300 ft to 319 ft, El. 320 ft to 329 ft, and El. 330 ft to 360 ft (NGVD) - and are presented in Figure 9. Shear Wave Velocities The dynamic properties of the materials at the Wappapello Dam site are characterized from the shear wave velocities, vs, measured during the geophysical investigations. The shear wave velocity profiles with depth, measured by both cross hole and dOwnhole seismic tests, were obtained at the centreline and downstream free field locations at - 22 - Chapter 4 Figure 8 - Plan View of Wappapello Dam Showing the Areal Extent of Soils With Low Blow Counts (Wahl and Deer, 1982) -23- Chapter 4 o 5; too so 12+00 I 4 f 0 0 16*00 DAM STATIONING (ft) 18 tOO Figure 9 (a) - Average Contours of Nt Between El. 300 ft to El. 319 ft'(NGVD) 2SO 200 Uj ISO 2 a o M IOO £< 9 -so j j . a <o O w -IOO •*•-.» - 2 0 0 - 2 3 0 - 3 0 0 \-- 3 S O - 4 0 0 '2*O0 14-foo 16+00 DAM STATIONING ( f t ) 18+00 Figure 9 (b) - Average Contours of Nt between El. 320 ft to El. 329 ft (NGVD) - 24 - Chapter 4 i 1 1 r OAM 12+00 14+00 OAM STATIONING (ft) 16-tOO Figure 9 (c) - Average Contours of N, between El. 330 ft to El. 360 ft (NGVD) Station 14+00 and included the low blow count material. Figure 10 presents the vs values vs depth. 4.2.1 Soil Properties The soil properties of the materials at Wappapello Dam site are obtained from the field investigations conducted by the USACE. The unit weight, y the undrained cohesion value, cu, the drained cohesion value, c', and friction angle, <j)' values are summarized in Table 4. -25- Chapier 4 *S * A ? ' NOTE: ALL VELOCITIES ARE IN «p( . OOLOMITE • ESTIMATED ANO NOT MEASURED Figure 10 - S-wave Zonal Interpretation for Cross-section through Station 14+40 (Wahl and Deer, 1982) - 26 - Chapter 4 Table 4 - Strength Properties of Wappapello Dam Site Materials DESCRIPTION SAND/GRAVEL in Older Alluvium CLAY in Older Alluvium SAND/GRAVEL in Recent Alluvium CLAY in Recent Alluvium SAND/SILT in Young Point Bar Deposit EMBANKMENT CLAY y (psf) 125 125 125 125 125 125 (psf) -3,050 -1,650 -3,000 c' -(psf) 0 -0 -0 -4 > ' (degrees) 35 -35 -28 -No shear testing was carried out on the Recent and Older Alluvium materials. Therefore, the shear strengths of these materials were estimated using correlations between the undrained shear strength and Atterberg limits for the clays and between shear strength parameters and SPT N values for the sands. Values of undrained shear strength, cu, for the clays were obtained from correlations between plasticity index and undrained shear strength from a geotechnical database derived by several studies (Bjerrum, 1972, Skempton, 1957, andKenney, 1976), as shown on Figure 11 (Holtz and Kovacs, 1981). The field investigations indicated that the clays were overconsolidated, and therefore Bjeruum's "aged" curve on Figure 11 was selected as the appropriate relationship. No field test data were available for these materials. Since these materials are not considered to be potentially liquefiable, these values are therefore not critical in the dynamic analyses, and approximate estimates of c' values are probably adequate. - 27 - Chapter 4 0.8 -i 1 1 r -l r Bjcrrum (1972) "ag«d' Sk«mpton (1957) BJ«rrum ( 1 9 7 2 ) "young' K«nn«y(1976) -i l I L 100 Plasticity Ind«x 2 0 0 Figure 11 - Relationship Between the Ratio of Undrained Shear Strength to Effective Overburden Pressure and Plasticity Index for Normally-consolidated (Holtz and Kovacs, 1981) The in situ shear strengths of the embankment materials were obtained from the field in situ testing and laboratory testing of "undisturbed" samples. The field work consisted of Menard pressuremeter tests. The undrained strengths ranged from 0.62 tsf to 2.3 tsf, and averaged 1.63 tsf or 3260 psf, as shown in Figure 12. Many of the "undisturbed" samples obtained for the laboratory tests were disturbed and untestable. The laboratory program consisted of 5 unconfined compression (UC) tests and 2 unconsolidated undrained (UU) tests, carried out on testable portions of the samples. - 28 - Chapter 4 In addition, three UU tests were carried out on "combined" samples, reconstituted from three disturbed samples. The results from the shear strength tests are summarized in Table 5, with the results of the UU tests plotted in Figure 12. The cu values measured from the 5 UC tests appeared unreasonably low, probably due to disturbance of the samples. The UU tests showed better results, but also appeared low for a compacted earth embankment. The UU tests measured increasing shear strength values with increasing confining stresses, indicating that the cu values are stress-level dependent. Due to the disturbance of the laboratory samples, more reliance was placed on the pressuremeter test results. A design strength of 3,000 psf was selected for the embankment material based on an average of the pressuremeter results. -29- Chapter 4 Table 5 - Shear Test Results DEPTH BELOW DAM CREST (ft) 60.0 TO 60.5 72.0 TO 73.0 52.8 TO 53.5 57.5 TO 58.0 8.5 TO 9.7 19.0 TO 19.5 12.9 TO 14.0 ---TEST UC UC UC UC UU UC UU UU UU UU CONHMNG PRESSURE (tsf) 0 0 0 0 6.9 0 10.4 1.0 3.0 5.0 (tsf) 0.19 0.22 0.15 0.14 0.60 0.44 1.65 0.34 0.48 0.53 For the phase 3 work, these soil strength parameters were considered appropriate. -30- Chapter 4 6 1 3-C (tsf) 2 1-f UNORAINED PRE88UREMETEH 8TRENOTH8 ~> 2 , 3 0 1.83 • — 1.78.4 1.78 . 1.41 1 1.10 0.88 0.82 P. r\ (^ ( \ i 1 — • — i i i 0 1 2 3 ;4 6 0 7 8 - 8 10 11 12 13 14 16 <T"(t8f) Figure 12 - UU Test and Pressuremeter Test Results (USACE, 1988) -31 - Chapter 5 REVIEW OF USACE PHASES 1 AND 2 WORK -LIQUEFACTION ASSESSMENT AND POST-EARTHQUAKE STABILITY Background The procedures for evaluating the seismic performance of dams comprised of, or founded on, potentially liquefiable soils were originally developed in the early 1970's (Seed, 1987, Seed, 1979, Seed, 1976, Seed et al, 1985, and Seed et. al 1981). The recommended procedures for the evaluation of the liquefaction potential and seismic performance of dams is summarized, as follows: 1. Determine the appropriate cross-sections of the dam to be studied; 2. Determine, with the input of geologists and seismologists, an appropriate design earthquake and acceleration time histories for the dam site; 3. Determine the static stresses in the design cross-sections prior to the earthquake loading. This step is particularly important because the dynamic soil properties vary nonlinearly with the effective confining stresses, and both the effective vertical stress and the shear stress affect the liquefaction resistance of the soil; 4. Determine the dynamic properties of the soils. These may include: damping; shear modulus, G; bulk modulus, B; Young's modulus, E; and Poisson's ratio, u. Since these properties are dependent on strain level, it is necessary to model their variation with strain. 5. Using an appropriate dynamic finite element computer program, compute the acceleration and/or dynamic shear stresses induced in various locations in the cross-section by the design earthquake. Note that a one-dimensional program is not recommended for embankments. A two--32- Chapter 5 dimensional finite element program is not appropriate when the ratio of the crest length to the maximum dam height is less than 3 or 4 to 1 because of three-dimensional effects on dam response; 6. Determine if liquefaction can be triggered in the materials of the dam or foundation by computing the factor of safety against liquefaction (the factor of safety against liquefaction is defined as the ratio of the liquefaction resistance of the material to the cyclic stress induced by the earthquake); 7. Compute either the seismic pore pressure or shear strain within the dam and foundation; 8. If the pore pressure generation is significant, determine the undrained residual strength S,,,, of the materials and evaluate the post-liquefaction behaviour of the dam and foundation; 9. If liquefaction is triggered, evaluate the magnitude of the post-liquefaction deformations due to both static and dynamic loads; and 10. Note that steps 1 to 9 require a great deal of engineering judgement and knowledge in selecting the appropriate soil properties and soil models. The appropriate computer program, whether it be one-dimensional, two-dimensional, or three-dimensional, must be selected so that it can model the soil properties accurately to account for changes due to seismic pore water pressures and large strains. In step 6, the liquefaction resistance of the materials within the dam and foundation must be evaluated. The liquefaction resistance may currently best be evaluated using correlations with the SPT data, or cone penetration test (CPT) data appropriately correlated to SPT data. Appendix I details the procedures for evaluating the liquefaction resistance. The US Army Engineer Waterway Experiment Station (WES) carried out a seismic safety evaluation of Wappapello Dam in 1982 (phase 1 seismic studies) at the request of the USACE, Memphis District (CELMM), who were, at that time, responsible for operating -33- Chapter 5 and maintaining the dam. Procedures 1 to 6, outlined above, were carried out in the phase 1 work. The results of this study are summarized in Wahl and Deer, 1982. Although a two-dimensional analyses was recommended for embankments, only a one-dimensional analyses was carried out in this study. The validity of the results using a one-dimensional model will be checked in the phase 3 work. Procedures 7 and 8, listed above, were carried out by the USACE in the phase 2 seismic study. Procedure 9, evaluating the magnitude of the post-liquefaction deformations, was not carried out by the USACE as part of the phase 2 work. The need for this work was identified by the USACE, and therefore was included as part of the phase 3 work carried out by UBC. 5.2 Phase 1 Work 5.2.1 One-dimensional Dynamic Analysis WES investigated the liquefaction potential of the foundation materials underlying Wappapello Dam by conducting a one-dimensional dynamic analyses on two soil columns at Station 14+00 - one at the centreline of the darn and the second in the free field downstream of the dam. The soil stratigraphy and material properties from the ground surface to bedrock for the two soil columns were obtained from the field work. -34- Chapter 5 The one-dimensional computer program SHAKE (Schnabel, Lysmer, and Seed, 1972) was used in this analysis to evaluate the dynamic response of both of the idealized soil profiles to the design earthquake motions. The nonlinearity of the shear modulus and damping is accounted for by the use of equivalent linear soil properties using an iterative procedure to obtain values for modulus and damping compatible with the effective strains. The following assumptions are inherent in the SHAKE program: all layers in the soil profile are horizontal and of infinite lateral extent, and the ground surface is level; therefore, before the earthquake, there are no shbar stresses on horizontal planes; each soil layer in the profile is completely defined by the following properties; shear modulus, critical damping ratio, density, and thickness; the response of the soil profile is caused by horizontally polarized shear waves (which originate at bedrock) propagating vertically upward through the layers of the soil system; and the equivalent linear procedures satisfactorily model nonlinear soil response and the hysteretic damping. The reservoir level of El. 370 ft (NGVD) was used in this analysis. This value was obtained by averaging the maximum pool level attained each year from 1941 to 1978. This level, therefore, represents the average annual maximum over that time period. The standard deviation of the annual maximum pool levels is 7.5 ft. All piezometer readings used in this study to compute effective stresses were from the March 14, 1979 readings when the reservoir level was at El. 370 ft (NGVD). - 35 - Chapter 5 5.2.1.1 SHAKE Input The required input to SHAKE was shear wave velocity, vs, unit weight, ytot, and thickness for each sublayer. The initial damping ratio for each sublayer was assumed to be 5%. The SHAKE input parameters are summarized in Table 6 (free field profile) and Table 7 (centreline profile). The acceleration time histories, listed in Table 2, scaled to 0.4g were input into the SHAKE runs. Each profile was excited by the scaled Superstition Mountain and Kern County records. Four computer runs were performed as follows: RUN 1 2 3 4 PROFILE USED Free field Centreline Free field Centreline ACCELERATION RECORD Kern County Kern County Superstition Mountain Superstition Mountain -36- Chapter 5 Table 6 - SHAKE Parameters, Free Field Profile SUBLAYER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 DESCRIPTION silty clayey sand (Young Point Bar) gravelly sand (Recent Alluvium) sandy silty clay (Recent Alluvium) fine sand (Recent Alluvium) sands and gravels (Recent Alluvium) fat clay (Older Alluvium) sands and gravels (Older Alluvium) clayey sand (Older Alluvium) bedrock THICKNESS (ft) 4.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 4.1 8.2 9.7 17.3 19.4 15.8 17.5 6.1 -SUBLAYER MID-DEPTH (ft) 2.05 5.65 8.75 11.85 14.95 18.05 21.15 24.25 27.85 34.0 42.95 56.45 74.8 92.4 109.05 120.85 -SHEAR-WAVE VELOCITY (ft/s) 475 475 475 475 475 475 475 475 475 625 625 625 1350 850 1175 1175 7500 UNIT WEIGHT (pcf) 118 118 118 118 118 118 118 118 118 125 125 125 125 125 125 125 170 -37- Chapter 5 Table 7 - SHAKE Parameters, Centreline Profile SUBLAYER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 DESCRIPTION clayey gravel (embankment) lean clay (embankment) clayey sands and gravels lenses of silt and clay (embankment) clayey sand (embankment) silty sand (Young Point Bar) fine sand (Young Point Bar) medium sand (Young Point Bar) silty, sandy clay (Recent Alluvium) sandy gravel (Recent Alluvium) fat clay (Older Alluvium) sands and gravels (Older Alluvium) 20 bedrock THICKNESS (ft) 5.0 8.5 4.7 20.0 10.5 11.5 4.7 4.2 5.5 3.1 5.7 11.5 8.5 13.1 13.5 14.5 14.5 12.5 7.8 -SUBLAYER MID-DEPTH (ft) 2.5 9.25 15.85 28.2 43.45 54.45 62.55 67.0 71.85 76.12 80.52 89.12 99.12 109.92 123.22 137.22 151.72 165.22 175.37 -SHEAR-WAVE VELOCITY (ft/s) 900 1350 1350 1350 1050 1375 1375 1375 675 675 675 850 850 850 850 1475 1100 1400 1100 7500 UNIT WEIGHT (pcf) 110 110 110 110 110 t 125 125 125 120 120 120 125 125 125-125 125 125 125 125 170 - 38 - Chapter 5 The following output was obtained from each SHAKE run: maximum acceleration at the top of each sublayer, maximum shear stress at the centre of each sublayer, shear stress history for the top of user-specified sublayers. The maximum base rock and surface accelerations from the computer runs are presented in Table 8. Table 8 - a ^ Results from SHAKE Kern County Superstition Mountain FREE FIELD Base Rock 0.38g 0.36g FREE FIELD Surface 0.29g 0.19g CENTRELINE Base Rock 039g 0.37g CENTRELINE Surface 0.16g 0.19g Maximum accelerations at the top of the sublayers in each soil column for both input acceleration histories are shown in Figures 13 and 14. The Kem County earthquake record resulted in higher surface accelerations in the free field by 50%, but the Superstition Mountain earthquake record resulted in a higher surface acceleration by 20%. Maximum shear stress vs depth in both the free field and centre line soil columns for both the Kern County and Superstition Mountain acceleration rec-ords are presented on Figures 15 and 16. All values were calculated by SHAKE at the -39- Chapter 5 MAXIMUM A C C E L E R A T I O N , g ' s Figure 13 - SHAKE Results, Maximum Acceleration vs Depth For Centreline Profile (Wahl and Deer, 1982) -40- Chapter 5 MAXIMUM A C C E L E R A T I O N , a'-. e . i B.-Z Z.A B . S a .6 0.7 6.8 1 2 . 2 % - SUPERSTIT ION MOUNTAIN EO Figure 14 - SHAKE Results, Maximum Acceleration vs Depth for Free Field Profile (Wahl and Deer, 1982) -41 - Chapter 5 MAXIMUM S T R E S S , p s f seo icca = 38 2080 "I 1 !— WAPPAPELLO CENTER L IHE PROFILE A KERN COUNTY EQ Q SUPERSTIT ION MOUNTAIN EO 252a BEDROCK Figure 15 - SHAKE Results, Maximum Stress vs Depth for Centreline Profile (Wahl and Deer, 1982) -42- Chapter 5 M A X I M U M S T R E S S , p s f sse is?a 1EC8 zaee W A P P A P E L L O F R E E F I E L D P R O F I L E . A . K E R N C O U N T Y EQ E l S U P E R S T I T I O N M O U N T A I N EQ Figure 16 - SHAKE Results - Maximum Stress vs Depth for Free Field Profile (Wahl and Deer, 1982) -43- Chapters centres of the constituent sublayers. Higher values of the maximum shear stress, tmax were generated by the Kern County record than by the Superstition Mountain record by 1.5 to 2.0 times. The Kern County earthquake record was therefore assumed to be the design earthquake. 5.2.1.2 Computation of Equivalent Number of Cycles of Stress The actual stress histories at selected soil layers are obtained from the computer program SHAKE. These stress histories are nonuniform and irregular in nature with respect to both amplitude and frequency. For liquefaction analyses, it is common to convert the irregular cyclic shear stress time history output by SHAKE to a uniform cyclic stress series at an equivalent number of uniform cycles (Seed, 1976). "Equivalent", for this case, means that the soil will experience either liquefaction or the same cyclic strain under either the computed stress history or the uniform periodic stress history. A computer program, EQCYCLE, (Lee and Chan, 1972) converts any shear stress time history from SHAKE to the appropriate number of equivalent uniform cycles (i.e. 15 cycles for M 7.5) using the weighting procedures of Seed (1976), and then calculates the corresponding uniform cyclic shear stress. The number of equivalent cycles, N^, of 15 was selected using the mean curve from the plot of earthquake magnitude, M vs equivalent number of cycles at xav = 0.65 xmax developed by Seed et al (1975) and shown in Figure 17. AM 7.5 - 44 - Chapter 5 was used. The uniform cyclic shear stresses computed from EQCYCLE, xm will be compared to soil strengths to determine the dynamic factor of safety against liquefaction. 4 0 i r W A P P A P E L L O DAM M E A N + 1 SD Figure 17 - Equivalent Number of Uniform Stress Cycles as a Function of Earthquake Magnitude (Wahl and Deer, 1982) - 45 - Chapter 5 5.2.1.3 Determination of the Dynamic Shear Strength of the Foundation Soils The dynamic shear strength or liquefaction resistance of the foundation soils were determined by two methods: cyclic triaxial tests performed on isotropically consolidated undisturbed specimens in the laboratory. These strength values will be called the LAB strengths; and empirical procedure correlating SPT results with liquefaction resistance (Seed and Idriss, 1981). These strength values will be referred to as the SPT-derived strengths. Note that these procedures have been updated since the phase 1 study (Seed and Idriss, 1982, and Seed and Harder, 1990). The strengths determined by both methods were then compared with the seismically induced shear stresses computed by SHAKE and EQCYCLE for the design earthquake. The factors of safety against liquefaction, defined as the ratio of shear strength to shear stress, were then computed for each of the two strength determination methods. Cyclic Triaxial Tests Ten stress-controlled cyclic triaxial tests were carried out at two confining pressures ( five at each confining pressure) on "undisturbed" samples obtained from the Young Point Bar Deposit only. Radiographs were used as an aid in determining the least disturbed samples. All samples were isotropically consolidated at two confining pressures - 10 psi (1.44 ksf) and 35 psi (5.04 ksf). Ideally, the confining pressures selected for the - 46 - Chapter 5 test program should bracket the range of effective vertical overburden stresses present in the field in the soil strata being evaluated. The confining pressures agree with those stresses present in the free field soil column, but are lower than the stresses present in the centre line soil column. It was, therefore, necessary to extrapolate the cyclic strength of the low blow count material present in the centreline soil column from the laboratory data. The results from the laboratory testing program are presented in Figures 18 and 19, shown as plots of cyclic stress ratio {GJ2<5^ VS the number of cycles, where adc is the cyclic deviator stress and ca is the effective confining stress. Three different failure criteria were studied for comparison. These failure criteria were as follows: • J 00% pore pressure response; • 5% double amplitude strain; and • 10% double amplitude strain; at confining stresses of 10 psi and 35 psi. Curves were fit to each of the three test group of points. The failure criterion finally selected for this study was the 10% double amplitude strain. For this study, however, the differences between the 3 failure criteria were small and for any given stress ratio, all 3 failure criteria were reached at about the same number of cycles. The isotropically consolidated cyclic triaxial test data must be adjusted by a correction factor, Cr, to make them representative of the anisotropic field conditions. The Cr used for this study was 0.57 and was based on empirical -47 - Chapter 5 0 .2 10 s o NUMBER OF C Y C L E S . N Figure 18 - Cyclic Stress Ratio vs the Number of Cycles to Failure, Effective Confining Pressure at 10 psi (Wahl and Deer, 1982) NUMBER OF CYCLES, N Figure 19 - Cyclic Stress Ratio vs the Number of Cycles to Failure, Effective Confining Pressure at 35 psi (Wahl and Deer, 1982) - 48 - Chapter 5 relationships developed by Seed, 1979. Figure 20 shows a plot of dynamic shear strength vs effective normal stress at 15 equivalent cycles. Both the laboratory-generated isotropic curve and the curve corrected to anisotropic field conditions are shown. The field line was used to evaluate the dynamic shear strength of the Young Point Bar Deposit. Liquefaction Resistance from the SPT The second method of evaluating the cyclic shear strength of the Young Point Bar Deposit is through empirical correlations which make use of the field-measured SPT N values. In this case, the strengths of soil deposits of Wappapello Dam were determined by comparing their SPT N values with the SPT N values of other sites whose liquefaction performance during earthquakes of known magnitudes is knowa This approach to the determination of cyclic strength was developed by Seed and Idriss (1971). They have modified their original procedures in light of new data provided by more recent earthquakes and data from China (Seed and Idriss, 1982). This procedure includes methods of evaluating liquefaction characteristics of clay soils, sands with a mean grain size, D50 greater than 0.25mm, and silts and silty sands having a D50 less than 0.15mm. Since the time of the phase 1 work, the procedures have since been updated (Seed and Harder, 1990), as presented in Appendix I. Materials classified as clay soils are considered as liquefiable materials if they meet all of the following criteria (Wang, 1979): : less than 15% of the particles are less than 0.005mm; -49- Chapter 5 Figure 20 - Dynamic Shear Strength versus Normal Effective Stress for the Foundation Soils at Wappapello Dam (Wahl and Deer, 1982) the liquid limit is less than 35%; the moisture content is more than 90% of the liquid limit; and the liquidity index is less than 0.75. The cyclic strength of a material meeting all the criteria should be deteraiined by laboratory testing. If a clay does not meet all of the above criteria, it may be considered nonliquefiable. -50- Chapter 5 For sands having a Dso > 0.25mm, the correlation between the liquefaction resistance and penetration resistance (as measured by blow counts of the SPT) is presented in Figure 21. In this plot, the penetration resistance is given in terms of Nj values, where N2 is the measured penetration, N, corrected to an effective overburden pressure of 1 tsf by the following equation: NUCN x N (1) where CN = an empirically derived coefficient whose value, is dependent upon the effective overburden pressure and relative density at the depth where the measured blow count, N, was obtained. The curve used in this analysis is shown in Figure 22. The curve plotted in Figure 21 represents the lower boundary of average cyclic shear strengths for an earthquake with a magnitude of M7.5 for sites where liquefaction has occurred. To obtain the cyclic strength of materials having D50 < 0.15mm, a correction of 7.5 blows/ft was added to the N^  value before using the relationship for sands with D50 > 0.25mm. This adjustment, which accounts for the higher liquefaction resistance of silts and silty sands when compared with sands having the same N,, will be referred to as the silt correction. For silts and silty sands having D50 < 0.15mm, therefore, the N, is determined by the following equation: - 51 - Chapter 5 * o o ^ u. o I I I cc 3 10 e> Ul s Ul cc o o z to 3 < U •• o t -< ecto CO Ul cc t -te o _ J o > u u. to ^ o s o u. _l < t -z Ul h-O 0 . z «t cc H co o u t-T ^ z =B a6 0.5 -0.4 0.3 -0 .2 0 .1 1 1 1 1 -• S I T E S W I T H L I O U E F A C T I O N D S I T E S W I T H N O A P P A R E N T L I Q U E F A C T I O N • M = 7 .5 . «" " • / B "SB ^ J3ul_ / / / e 0 / DATA 1 1 I i 1 / / * f e l 2 1 <* I °7 // • * / « * / / 7*5 / A ' / Q / i D POINTS AFTER / TOKIMATSU AND YOSHIMI, 1981 / ' . • • • i i 10 2 0 3 0 4 0 5 0 MODIFIED PENETRATION RESISTANCE N - BLOWS/ft Figure 21 - Correlation Curve Between Stress Ratio Causing Liquefaction and Penetration Resistance for Sands Having DJO > 0.25 mm (Seed and Idriss, 1981) - 52 - Chapter 5 0 0 .2 0 . 4 0 .6 0 .8 1.0 1.2 1.4 1.6 i r i r Ul c 03 m ui cc a. z u a c 3 ffi C Ul Ul > u Ul — Df = 4 0 TO 6 0 * 1 0 O R I G I N A L D A T A P R E S E N T E D IN M A R C U S O N AND B I E G A N O U S K Y . 1 9 7 7 . Figure 22 - Recommended Curves for the Determination of CN (Seed and Idriss, 1981) - 53 - Chapter 5 N1=(CNx N)+ 7.5 (2) The suggested method at the time the phase 1 1982 report was written (Wahl and Deer, 1982), is as follows: 1. If the soil is at a depth less than 10 ft, multiply the measured SPT blow count, N, by 0.75 to account for the energy loss in the drive rods. 2. Determine Nj for: a) Sands having D50 > 0.25mm by the following , relationship: NUCN x N (1) b) Silty sands and silts having D50 < 0.15mm by the following relationship: (2) NUCN xN + 7.5 where 7.5 blows/ft represents the silt correction factor in 1982. c) Soils having 0.15mm < D50 < 0.25mm by the following relationship: Air r M A far °-15> 7* ( 3 ) N1=CN x N + —— x 7.5 N 0.15 3. Determine the dynamic shear strength expressed as a stress" ratio, isJo\, from the correlation curve for sands having D50 > 0.25mm shown in Figure 21. Enter this chart using the Nj value obtained in Step 2. -54- Chapter 5 4. Determine the SPT derived strength, dynamic shear strength, x, by multiplying the ratio Tsd/a'v by the effective vertical stress a'v. Dynamic Factors of Safety Against Liquefaction Safety factors against liquefaction are defined by: SAFETY FACTOR = (DYNAMIC SHEAR STRENGTHJflAMPLITUDE OF CYCUC SHEAR STRESS AT THE EQUIVALENT NUMBER OF CYCLES) These safety factors were obtained by two methods, using the two different methods of determining dynamic shear strength. The dynamic shear strengths were obtained by both the laboratory cyclic triaxial tests and by empirical correlation procedures using SPT results. The dynamic shear stresses were obtained from the results of SHAKE. Factors of safety against liquefaction of less than 1 imply that sufficient pore pressures have been generated in the soil or that a specified strain has occurred and that liquefaction has been triggered by the design earthquake. The factors of safety against liquefaction computed at the centreline and the free field for both laboratory-derived and SPT-derived shear strengths are shown in Figure 23. Chapter 5 ELEV.. DEPTH. f t . I t . j — 418 r— o —398 —378 - 4 0 CENTERLINE SUBLAYERS - 6 0 LABORATORY SAFETY FACTORS 1.08-i.oe— EMBANKMENT •FT SAFETY FACTORS 3:!? L >• J." t 17 A 7 ALLUVIAL FOUNOATION MATERIALS FREE FIELD SUBLAYERS LABORATORY " SAFETY FACTORS • FT SAFETY FACTORS \ DEPTH. ELEV.. I I I I—1 1 I I I—I I I J I BEDROCK 100 -Figure 23 - Factors of Safety Against Liquefaction, Free Field and Centreline Profiles (Wahl and Deer, 1982) -56- Chapter 5 There was very good agreement between the factors of safety computed by the laboratory and the SPT results. Factors of safety computed for the Young Point Bar Deposits located under the centreline of the dam ranged from 1.1 to 0.7, indicating that this material is susceptible to liquefaction. The factors of safety computed for the Young Point Deposits located in the free field ranged from 0.4 at the surface increasing to 0.7 at depth, indicating that this material is also susceptible to liquefactioa The extent of the potentially liquefiable deposits was determined by computing the factor of safety against liquefaction using the SPT values measured at other locations of the dam site and the SHAKE results. The area of potentially liquefiable material is identified as the shaded area in Figure 24. This potentially liquefiable zone covers the area between Station 10+50 to 20+00 and at least as far as 250 ft upstream of the dam's centre line and as far as 1,000 ft downstream of the dam's centre line. Note that the upstream extent was estimated from Boring G located on upstream face. No other test holes providing SPT data upstream from Boring G were available to establish the upstream extent of the potentially liquefiable zone. Although the procedures for computing SPT-derived shear strengths have been modified and updated since 1982 (the time of the phase 1 report), these changes in the methodology do not affect the conclusions of the 1982 report. The Young Point Bar Deposits are still considered to be potentially liquefiable under the design earthquake. -57 - Chapter 5 LAKE WAPPAPELLO re-to •;••.;.• re-« :-:.;•"-:-:-:• E-*o .;.;.;. re-« .-.v.-.v.v-.'.-.-J-.y.-.*. v.- : j |vp ••• > rc-» jyV*-iv«-' Figure 24 - Plan View of Wappapello Dam showing the Areal Extent of the Zone of Potentially Unstable Material (Wahl and Deer, 1982) - 58 - Chapter 5 Phase 2 Work Post-earthquake Limit Equilibrium Slope Stability Analyses -The post-earthquake stability of Wappapello Dam was determined by CELMS (USACE, 1988) in the phase 2 work by conducting a limit equilibrium slope stability analyses. A post-earthquake limit equilibrium slope stability analysis involves the use of the residual or steady state strengths Sw for the materials in the dam and/or the foundation identified to liquefy. For Wappapello Dam, the sand/silt materials of the Young Point Bar Deposit, both upstream and downstream, as identified in the phase 1 work, were assumed, to liquefy. The residual strengths were obtained by the SPT correlation method developed by Seed (1987), where SPT (N,^ values (corrected for silt content) are empirically correlated to Sm values from sites where the S,,, values are known. The lower bound of this chart was used for all strength values. This correlation relationship is shown in Figure 25. The N values at the dam site were reviewed by CELMS. They determined that the average of the ( N ^ values of the Young Point Bar Deposit was 16 blows/ft, with a standard deviation of 8 blows/ft. The slope stability analysis was therefore carried out using (N g^o values of 16 blows/ft corresponding to a Sur of 660 psf and 8 blows/ft (average N minus one standard deviation) corresponding to 60 psf. In addition, the residual strength required to give a factor of safety of 1 was determined. -59- Chapter 5 2000 <n 1600 CO ^ 1200 X CD UJ £ : 8 0 0 CO < Q 4 0 0 CO UJ or LOWER SAN FERNANDO OAM 4 a 12 16 20 EQUIVALENT CLEAN SAND (Ni)6o 24 Figure 25 - Relationship Between Residual Strength and (N,)^ Values for Clean Sands (Seed, 1987) -60- Chapter 5 Limit equilibrium slope stability analyses were carried out assuming circular slip surfaces. The reservoir water level was assumed to be at El. 390 ft (NGVD). The results from the stability analysis are summarized in Table 9. Table 9 - Post-earthquake Stability Analyses Results (blows/ft) 16 8 9 RESIDUAL STRENGTH (psf) 660 60 115 UPSTREAM FACTOR OF SAFETY 1.93 1.16 -DOWNSTREAM FACTOR OF SAFETY 1.38 0.91 0.95 The results from the stability analysis indicate that, even assuming the entire Young Point Bar Deposit, extending both upstream and downstream of the dam centreline, liquefied with the materials reaching their residual strengths, there would be no chance of the upstream slope failing and only a slight chance that the downstream slope will fail. A factor of safety close to 1.0 was achieved by assuming a residual strength of 115 psf. It was therefore concluded that the dam would only suffer minimal deformations because the post-earthquake limit equilibrium slope stability factor of safety was only marginally less than 1. Since the phase 2 work was completed in 1988, several changes have occurred in the Sur vs (N,)^ relationship (Seed and Harder, 1990). The S^ values at (N,)^ values less than about 8 blows/ft have decreased considerably. More studies should be carried out in the phase 3 work to re-examine the assessment of residual strengths. In addition, assessing -61 - Chapter 5 the post-earthquake deformations by computing limit equilibrium factors of safety is an indirect, and possibly unreliable, method. The scope for the phase 3 work includes a more rigorous, more direct method of estimating the post-earthquake deformations. Conclusions Based From the USACE Phases 1 and 2 Work The following conclusions were drawn from the phases 1 and 2 work by the USACE: 1. The sand/silt materials comprising the Young Point Bar Deposit are potentially liquefiable from Sta 10+00 to 20+00 along the dam axis and from at least 1,000 ft downstream of the dam and 250 ft upstream of the t dam. 2. Slope failures are likely if the residual strengths are as low as 115 psf. As the post-earthquake limit equilibrium factors of safety are just marginally less than 1, the USACE considered that the predicted post-earthquake deformations would likely be minimal. However, the requirement for additional, more detailed deformation analyses was identified. 3. The likelihood of an earthquake-induced embankment slide causing a reservoir release is low. In 1991, CELMS requested Dr. Finn of the University of British Columbia to carry out an additional study of the seismic stability of Wappapello Dam, with emphasis on the post-liquefaction behaviour of the dam. This study was carried out using the dynamic effective stress program TARA-3 (Finn et al., 1986) to check the triggering of liquefaction and the development of seismic displacements and the program TARA-3FL (Finn and Yogendrakumar, 1989) for estimating post-liquefaction flow deformations. The analyses were based on the soils data and seismic parameters established in the previous phases 1 and 2 studies. The following sections describe the phase 3 study carried out at UBC. - 62 - Chapter 6 TARA-3 AND TARA-3FL PROGRAM DESCRIPTION General Background The results of the one-dimensional dynamic analysis carried out by WES (phase 1) indicated that the foundation materials of the Young Point Bar Deposit at the Wappapello site were found to be potentially liquefiable. A post-liquefaction limit equilibrium slope stability analysis carried out in phase 2, however, computed limit equilibrium factors of safety that were only marginally less than 1, suggesting that even if the Young Point Bar Deposit liquefied, only minimal deformations of the dam and foundation should occur. The USAGE, however, decided to initiate a study to compute the potential pore pressure generation during the design level earthquake and the potential post earthquake deformations using the TARA-3 series of computer programs developed by Dr. W.D.L. Finn at the University of British Columbia, Canada. The TARA-3 series of programs include the dynamic program TARA-3 (Finn and Yogendrakumar, 1989) which is capable of modelling the pore pressure generation and the static program TARA-3FL which is capable of modelling the flow deformations of the earth structure and the foundation after liquefaction has occurred. Some key factors in the TARA-3 and TARA-3FL programs, essential for understanding the analysis carried out on Wappapello Dam, will be explained in the following sections. TARA-3 Program Description The finite element computer TARA-3 can be used to model nonlinear hysteretic effective stress response of 2-D structures. This program has been the subject of detailed verification using data from simulated earthquake tests on centrifuge models (Finn, 1988). - 63 - Chapter 6 It is capable of modelling both the total stress method where no pore pressures are computed and the effective stress method where pore pressures are computed and the material properties are subsequently updated to account for the change in effective stress. This program consists of two basic analyses - static analysis and dynamic analysis. TARA-3FL derived from the static part of TARA-3 and is explained in more detail in section 6.3. 6.2.1 Finite Element Representation r The cross-section of interest is approximated by a number of finite elements that are connected by nodal points. TARA-3 elements are represented by four-noded, isoparametric quadrilateral elements with eight degrees of freedom. Triangular elements can also be modelled by repeating the third node twice in the input. The unknowns are the vertical and horizontal displacements at each node in the element. The stresses and strains in the elements are interpolated linearly with strain within the element. The incremental equations governing the static response of the system is: [/q (A} = {Aft - [K'\ - iAU} (4) where: [KJ = global tangent stiffness matrix {A} = incremental nodal displacement vector {AP} = increment nodal force vector [K*} = matrix associated with pore water pressures {AU} = incremental pore water pressure vector -64- Chapter 6 The stiffness matrix is a function of the current tangent moduli during loading or unloading. The use of shear and bulk moduli allows the elasticity matrix [D] to be expressed as: [PI = Bt [Q,\ + Gt [G2] (5) where: [QJ and [Q2] = B, G, constant matrices for the plane strain conditions usually considered in analysis tangent bulk modulus matrix tangent shear modulus matrix This formulation reduces the computation time for updating [D] whenever B, and G, change in magnitude because of straining or pore water changes. Stress-Strain Behaviour in Shear The shear stress, x, vs shear strain, y, relationship in soils is assumed in TARA-3 to be nonlinear, hysteretic and to exhibit Masing behaviour (Masing, 1926) during unloading and reloading. Masing behaviour provides hysteretic damping. To model this nonlinear relationship in TARA-3, the x-y relationship, under undrained and drained conditions, is assumed to follow a hyperbolic path as shown in Figure 26. The relationship between x and y can be expressed by two hyperbolic parameters, Gmax and imax, by: Gmi*Y (1 Yl, (6) "max - 65 - Chapter 6 where: Gmax = maximum shear modulus at y —> 0 "W = appropriate ultimate shear strength as y —» « Figure 26 shows the x-y relationship during loading, unloading and reloading phases. V-I — — ~ =»-Shear Strain 7 Figure 26 - Stress-Strain Relationship During Loading, Unloading and Reloading Phases The objective during analysis is to follow the stress-strain curve of the soil in both loading and unloading. Checks are built into the program to determine whether or not a calculated stress-strain point is on the stress-strain curve, and correction forces are applied to bring the point back on the stress-strain curve, if necessary. The use of the hyperbolic model is very popular in practice because the shape provides a good fit to most experimental or field stress-strain curves and its parameters, Gmax and xmax, can be obtained Reloading Gmax 7 * 'truix ' - 66 - Chapter 6 using conventional laboratory testing or insitu testing. These parameters are dependent on many factors and the method incorporated in TARA-3 reflects the most important of these factors. In TARA-3, all materials must be classified as either a sand/silt/clay type material exhibiting $' and c' properties or a clay type material exhibiting undrained properties. The method for computing Gmax varies with material type. For <()'-c' materials, Gmax is a function of the mean normal effective stress, o'm, relative density, Dr, and previous stress history given in terms of the overconsolidation ratio, OCR. (The OCR is defined as the ratio of the maximum past stress to the existing overburden stress.) Gmia is computed in TARA-3 by one of two possible methods. The first method is based on the relationship developed by Hardin and Drnevich (1972) where: / G^ = KG Pa (.octf i-j^2 where: K^ = shear modulus constant for a given soil OCR = overconsolidation ratio k = constant dependent on the plasticity of the soil Pa = atmospheric pressure (7) In TARA-3, equation 7 has been modified to reflect the void ratio, in the form astbllows: - 67 - Chapter 6 C? = 320.8 Pa ( 3 9 7 3 e ) (OCR)" (^-5)^ W " " (1+c) Pa where: e = void ratio The second method of computing Gmax is based on the relationship developed by Seed and Idriss (1970) where: < W = 1000 JCj ( o ' j 1 ^ (OC^)* (9) where: a'm = mean effective overburden stress in psf units K2 = constant dependent on the soil type and relative density. Equation 9 can be modified to allow its usage in any consistent set of units by: a' m < W = 21-7 *2 P<* (<~) <PC®k ( 1 0 ) The variation of K2 with shear strain and relative density for sands is given in Figure 27, and for gravelly soils in Figure 28, obtained from Seed and Idriss, 1970. To compute Gm„, the K2 value at small shear strains should be used in equation 10. The following relationship may be used as a guide for the selection of K2 (Byrne et al, 1987): - 68 - Chapter 6 icr* Sneor Siroin -percent Figure 27 - Shear Moduli of Sands at Different Relative Densities (Seed et al, 1984) -69- Chapter 6 140 10"° 3 ICT^ 3 I 0 H Cyclic Shear Strain ± y % Figure 28 - Comparison of Shear Moduli for Gravelly Soils and Sands at a Relative Density of 95% (Seed et al, 1984) -70- Chapters *2 = 15 + 0.61 Dr _ (11) where: Dr = relative density expressed in percentage. For clay materials, Gmax is computed by: max — clay u where: K ^ = constant for a given clay Su = undrained shear strength of the clay The variation of G/Su with shear strain for saturated clays is shown in Figure 29 (Seed and Idriss, 1970). Typical values of K ^ vary between 1,000 and 2,000. The program has the option to incorporate field values of the moduli from geophysical investigations. 6.2.3 Stress-Strain Behaviour in Hydrostatic Compression The response of the soil to uniform all-round pressure is assumed to be nonlinearly elastic and dependent on the mean normal stress, o'm. This volume change behaviour of soils is given in terms of the bulk modulus, B,, and the mean normal effective stress, a'm using the hyperbolic model defined by two constants, K,, and n. This relationship is given by: (12) - 71 - Chapter 6 30 .000 10.000 3 0 0 0 IOOO 3 0 0 100 A Wilson and Oielrlch ( I960) • Thiers (1965) A Idriss (1966) • Zeevoerl (1967) • Shannon and Wilson (1967) ZEShannon and Wilson (19671 v Thiers and Seed (19681 O Kovacs((960) a Itordin and Olock 0966 ) i—TAisiris and Torshonslir (1968) fflmseed and Idriss (19701 S S T i o i ond llousner (1970) Slieor Slroin - percent Figure 29 - In-situ Shear Moduli for Saturated Clays (Seed and Idriss, 1970) - 72 - Chapter 6 i Bt = Kh Pa (—5)" <13> ' P a where: K,, = bulk modulus number n = bulk modulus exponent Pa = atmospheric pressure The parameters of K,, and n can be determined using conventional triaxial test d>ta following procedures developed by Duncan et al (1978, 1980), or from isotropic consolidation testing. The values of F^ for sand/silt type materials depend on the relative density of the soil and soil type, with typical values ranging from 300 to 1000. The bulk modulus exponent, n, is typically 0.25 for sandy or silty materials. Tables of K^  and n are given in Table 10, developed by Byrne and Cheung (1984). Table 10 - Suggested Bulk Modulus Parameters Correlated to Dr and Nx (Byrne and Cheung, 1984) Dr 25 50 75 100 N, 4 10 23 >50 K* 150 - 300 270 - 540 450 - 900 900 - 1800 n 0.25 0.25 0.25 0.25" - 73 - Chapter 6 For fully saturated deposits, Bt is assigned a very high value to simulate undrained conditions in dynamic analysis. 6.2.4 Dynamic Analysis The dynamic portion of the TARA-3 program simulates the input of a dynamic earthquake motion on the cross-section in question. TARA-3 attempts to take into account the key effects of the input earthquake load on the earth structure. The major factors included are: insitu stress states of the earth structure and foundation and corresponding moduli values; ' stress-strain variation during phases of initial loading, unloading and reloading of the earthquake load; seismically induced pore water pressure; effective stress changes in the elements due to the pore water pressure generation; viscous and hysteretic damping; and volume changes induced by shear. - 74 - Chapter 6 The incremental dynamic equilibrium forces {AP} are given by the following equation: [M]{ Ax) + [C]{ Ax) + [K\{ Ax} = { AP} <14) where: [M] = mass matrix [C] = damping matrix [K] = stiffness matrix {x} = acceleration matrix {x} = velocity matrix ' {x} = displacement matrix {AP} = inertia force vector = - [M] {1} {Ab} where: {1} = column vector of 1 {Ab} = base acceleration vector The base acceleration is assumed to be identical at every nodal point along the base of the cross section. {AP}, therefore, is a function of time only. The viscous damping is of the Rayleigh type, and its use is optional. Very small amounts of viscous damping are used, typically equivalent to less then 1% of critical damping in the dominant response mode. Its primary function is to control any high frequency oscillations that may arise from numerical integration. Damping is primarily hysteretic and is automatically included as the hysteretic stress-strain loops are executed during analysis. ~ - 75 - Chapter 6 6.2.4.1 Dynamic Stress-Strain Behaviour in Shear The incremental elastic approach has been used in TARA-3 to model the nonlinear behaviour of the soil system. In this approach, the soil is assumed to behave isotropically and linearly in the increment of load, and can thus be modelled by a pair of elastic constants, the shear modulus, G„ and the bulk modulus, B,. In the dynamic analysis, the seismic load is input as a series of irregular loads based from historical earthquake records. This irregular load consists of loading, unloading and reloading, and the soil behaves in a different manner in each of the loading phases. The shear stress-shear strain relationship during the initial loading phase under either drained or undrained conditions, is assumed to follow a hyperbolic curve given by: G v T = O " T I ( ,5) (1+ m " ' T ' ) max or T = f(y) (16) - 76 - Chapter 6 where G„ maximum shear modulus at y —> 0 appropriate ultimate shear strength as y -» • The initial loading or skeleton curve is shown on Figure 30 (a). <W,1 (c) Figure 30 - Nonlinear Hysteretic Loading Paths (d)<-^~ The unloading and reloading phases are assumed to exhibit Masing (1926) behaviour. This relationship is defined by the following equation: _ -77 - Chapter 6 T~T r _ 2 max o (i j . max Y"Yr ) / ( 1 7 ) or -LJLE = f( Y Y^) (18) 2 2 where (ir.Y,.) = stress-strain point at which loading reverses direction The shape of the unloading-reloading curve is shown in Figure 30 (b). The Masing behaviour implies that the unloading and reloading curves of the hysteretic loop are the same skeleton curve with the origin translated to the reversal point, and the scales for the stress and strain are increased by a factor of 2. Lee (1975) and Finn and Byrne (1976) proposed rules for extending the Masing behaviour to account for irregular loading. They suggested that the unloading and reloading curves should follow the previous skeleton loading curves when the magnitude of the previous maximum shear strain is exceeded (Figure 30 (c)). When the current loading curve intersects the previous loading curve, the stress-strain curve then follows the previous loading curve (Figure 30 (d)). - 78 - Chapter 6 The tangent shear modulus, Gt is the value of the tangent slope of the stress-strain curve at the strain point. The Gt value, given in terms of strain, y, is given by the following equation: (-, _ °inax ( 1 + _max M ) T max G, given in terms of shear stress, T, given by the following equation: Gt = GLx d - - ^ ) . (20) ""max An additional feature incorporated into TARA-3 is the ability to start the stress-strain analysis at any point along the stress-stress curve. This allows the program to include the effects of the static insitu stress-strain condition of the soil into the dynamic analysis, predicting a more realistic soil response, especially in earth structures or foundations with slopes with insitu x, „ values. 6.2.5 Residual Pore Pressure Model During irregular loading, such as for seismic loads in undrained conditions, two types of pore pressures are generated by the sand/silt type materials in the saturated state. These pore pressures are: - 79 - Chapter 6 transient pore pressures; and residual pore pressures. Transient pore pressures are developed due to changes in the applied mean normal stress due to the load. For saturated sands, the transient pore pressures are equal to changes in the mean normal stresses. Since the transient pore pressures and the applied load are equal, the effective stress of the soil does not change and hence the behaviour of the soil is not affected by these transient pore pressures. TARA-3 does not compute these transient pore pressures. The residual pore pressures are developed due to the plastic deformation in the sand/silt material skeleton. These pore pressures remain in the system until they have dissipated by internal drainage or internal diffusion. The effective stress of the soil system changes as a result of the residual pore pressures, and thus the pore pressures must be computed and the changes on the shear and bulk moduli values due to the change in effective stress must be evaluated. TARA-3 models the residual pore water pressures using the Martin-Finn-Seed model (Martin et al, 1975). 6.2.5.1 Martin-Finn-Seed Pore Water Pressure Model In the Martin-Finn-Seed pore water pressure model, the increments in pore water pressures, AU, that develop in a saturated sand under cyclic shear strains, are related to the volumetric strain increments, AE^, that - 80 - Chapter 6 occur in the same sand under drained conditions with the same shear strain history. During a drained cyclic simple shear test, a cycle of shear strain, y, causes an increment of volumetric compaction strain, Ae^, due to slippage of the grains. During an undrained cyclic test, starting with the same effective stress system, the same cycle of shear strain, y, causes an increase in incremental pore water pressure, Au. In the Martin-Finn-Seed model for fully saturated sands, assuming that water is incompressible, this increase in incremental pore water pressure, Au is modelled as: Au = Ez A e ^ (21) where Er = one-dimensional rebound modulus at an effective stress of a'v Under drained simple shear conditions, the volumetric strain increment, Ae^, is a function of the total accumulated volumetric strain, E^, and the amplitude of the current shear strain, y, and is given by the following equation: A £ v d = cx y e x p ( - c 2 i s ? ) (22) where C, and Q = volume change constants that depend on the sand type and relative density -- 81 - Chapter 6 The volume change constants, C, and C2, may be determined directly by means of drained cyclic simple shear tests on dry or saturated samples. In practice, simpler procedures have been implemented, as described in the next section. The one-dimensional rebound modulus, Er, at any vertical effective stress level, a'v, can be expressed by: Ez = —^-4 (23') where: m, n, and K2 = experimental rebound constants derived from rebound tests in a consolidation ring 6.2.5.2 Determination of Pore Water Pressure Constants in Practice The volume change constants Q and C2 and the rebound constants m, n, and K2 can be determined either by experiments, previous experience or by regression analyses from the liquefaction resistance curve. The liquefaction curve may be determined from cyclic triaxial or simple shear tests, or derived from standard penetration test data (Seed, 1983). In the latter case, the constants are derived by a regression process to ensure that the predicted liquefaction curve compares satisfactorily with the field liquefaction curve using the program SIMCYC2 (Yogendrakumar and Finn, 1986a). If the liquefaction curve has been derived by laboratory - 82 - Chapter 6 tests, the rate of pore water pressure increase is known as well. A regression analysis is then used to select constants that match both the rate of pore water pressure generation and the liquefaction curve using the program C-PRO (Yogendrakumar and Finn, 1986b). Special Features of Analysis by TARA-3 Dynamic analyses are carried out in current engineering practice without including the effects of gravity or previous strains. Initial static analyses are usually carried out only to determine the initial stress conditions so that appropriate initial moduli may be selected. However, as strength and stiffness degrade during seismic excitation because of increasing pore water pressures, the structure deforms under the gravitational forces. This effect is taken into account in TARA-3. TARA-3 also has the capability to begin the dynamic analysis from a zero-strain conditions, as in current practice, or from the initial state of strain under static loading. The latter procedure leads to the best modelling of plastic deformations. For analysis involving soil-structure interaction, it is important to model slippage between the structure and soil. Slip may occur during very strong shaking or even between the structure. TARA-3 contains slip elements of the Goodman type (Goodman et al, 1968) to allow for relative movement between soil and structure in both sliding and rocking modes of response during earthquake excitation. -83- Chapter 6 The three components of permanent deformation in a soil structure system as a result of earthquake loading are computed by TARA-3. The first component is the dynamic residual deformation that occurs as a result of the hysteretic stress-strain response. The second component is the deformation under gravity loading when increasing pore water pressures during the earthquake reduce the stiffness of the dam. The third component is the deformation of the system that occurs due to consolidation as the seismically induced residual pore water pressures dissipate. The final post earthquake deformation field computed by TARA-3 is the sum of all three deformation components. TARA-3FL Program Description TARA-3FL is a modified version of TARA-3 which incorporated features related to the triggering of liquefaction and residual strength, and the tracking of the subsequent deformations. The first requirement is a triggering criterion to switch the strength of any liquefiable element in the dam to the steady state strength at the proper time during the dynamic analyses. Two liquefaction triggering criteria are available, as follows: the peak strain criterion of Castro et al., (1989); and the stress ratio criterion of Vaid and Chern (1985). The dynamic analyses can be bypassed if it is assumed that the residual strength will be triggered in all elements that will liquefy according to the criteria developed by Seed (1983) and Seed et al, (1985), and then concentrate on post-liquefaction behaviour only. This is the procedure that has been followed in TARA-3FL analyses. -'84- Chapter 6 In a particular element in the earth structure, the shear stress-shear strain state which reflects the pre-earthquake conditions is represented by point P„ on the stress-strain curve shown in Figure 31. When liquefaction is triggered, the strength will drop to the steady state value. The post-liquefaction stress-strain curve cannot now sustain the pre-earthquake stress-strain condition, represented by point P, on the curve, and the unbalanced shear stresses are redistributed throughout the dam. In the liquefied elements, the stresses are adjusted by the following equation: dv = _ df da' do' m df dy dy ( 2 4 ) where: x f(a'm,Y). 2 0 0 0 T T 5 10 SHEAR STRAIN, % Figure 31 - Adjusting Stress-Strain State to Post-liquefaction Conditions -85- Chapter 6 This process leads to progressive deformation of the earth structure until equilibrium is reached at the state represented by point P2 on the curve. Since the deformations may become large, it is necessary to progressively update the finite element mesh. Each calculation of incremental deformation is based on the current shape of the dam, not the initial shape as in conventional finite element analysis. Evaluation of Undrained Residual Strength When the soil is strained beyond peak strength, the undrained strength eventually drops to a value that remains constant over a large range in strain. This value is referred to as undrained residual strength, S^, or steady state strength. To calculate the post-earthquake deformations, the undrained residual strength, S^ for the liquefied elements is required for analysis. Over the years, there have been 2 basic approaches for evaluating the residual strength. One method evaluates the residual strength by obtaining high quality samples with minimal disturbance, and testing these samples in the laboratory. Using specifically developed techniques, the laboratory results are corrected to account for the effects of void ratio changes due to the sampling, handling, and test set-up disturbances, to obtain estimates of the field S .^ The residual strengths, however, are very sensitive to the void ratio, and small changes in the void ratio can significantly affect the S^. - 86 - Chapter 6 The second approach to computing the S^ is based on correlation relationships of S^ to SPT N values. Back-analyses were carried out on a number of liquefaction failures to evaluate the S,,, values for soil zones where SPT data were available. From these results, a correlation between S,,, and ( N ^ values have been developed (Seed, 1987). The correlation between Sur and ( N ^ first involved correcting the field N values to 1 tsf of overburden stress to get (NJ values, then correcting this value for a standard of 60% energy efficiency to obtain ( N ^ values, as described in Appendix I. An additional > correction due to the fines content (material passing the #200 sieve or material finer than 0.075 mm) is required. The fines correction is applied by: Wso-« = Wso + Kerr < 2 5 > N value corrected for overburden stress, energy efficiency and fines content N value correct for overburden stress and energy efficiency fines content correction factor obtained from Table 11 where: (Ni)60<s (N,)6o N 1 corr - 87 - Chapter 6 Table 11 - Recommended Fines Correction for Sur Evaluation Using SPT Data PERCENT FINES 10% 20% 50% 75% N ^ (blows/ft) 1 2 4 5 The fines correction factor for computing Sm is different from the fines correction factor used in the liquefaction resistance evaluation. , Figure 32 shows the most current correlation between S^ and (N^^^, based on values back-calculated from a number of case studies. Many of the S,,, values presented are slightly different from those presented by Seed (1987). Due to the scatter of points and limited number of case histories studied thus far, the lower bound or near lower bound relationship between S^ and (N1)60^s is recommended. The US Bureau of Reclamation has reviewed many of the case histories studied by Seed, 1987. By placing more reliance on certain case histories, they have established a slightly higher lower bound curve, presented in Figure 33 (USBR, 1989). This curve will be referred to as the US Bureau residual strength curve, or the US Burec curve. -88- Chapter 6 2000 "' 1600 x* t~ o UJ H 1200 v> a: < UJ X to o z < tr o ID o Ul (T 800 400 0 EARTHQUAKE - INDUCED LIOUEFACTION AN0 SLIDING CASE HISTORIES WHERE SPT DATA AND RESIOUAL STRENGTH PARAMETERS HAVE BEEN MEASURED. D EARTHOUAKE-INOUCEO L10UEFACTI0N AND SUOING CASE HISTORIES WHERE SPT DATA AND RESIOUAL STRENGTH PARAMETERS HAVE SEEN ESTIMATED. CONSTRUCTION - INOUCEO LIQUEFACTION ANO SLIDING CASE HISTORIES. LOWER SAN FERNANDO DAM 4 8 12 16 20 24 EQUIVALENT CLEAN SAND SPT BLOWCOUNT. (N,}60_cs Figure 32 - Relationship Between Corrected Clean Sand Blowcount ( N j ) ^ and Residual Strength, Sr From Case Studies (Seed and Harder, 1990) -89- K Chapter 6 2000 co 1600 en x \-iD LLI CC h-CO 1200 800 < ID Q 400 CO UJ rr US BUREC BEST ESTIMATE LOWER SAN FERNANDO DAM 4 8 12 16 20 EQUIVALENT CLEAN SAND (Ni)eo 24 Figure 33 - Variation in Residual Strength with (N,)^ (USBR, 1989) - 90 - Chapter / 7. TARA-3 MODELLING OF WAPPAPELLO DAM 7.1 Material Properties 7.1.1 Strength Properties The strength parameters of the materials at the Wappapello Dam site were obtained from the field investigations carried out by USACE for the phases 1 and 2 work, and detailed in sections 3 and 4. The strength parameters are summarized in Table 4. 7.1.2 Shear Stress-Shear Strain Parameters for Wappapello Dam The hyperbolic parameters for Wappapello Dam were obtained primarily by in-situ testing carried out by the USACE. The in situ shear wave velocities, vs, presented in Figure 10, were used to compute Gmax directly by: G = o(v ) 2 (26) "max r v vs' where: p = total mass density of the soil material The Seed and Idriss (1970) equations for computing Gmax are used in TARA-3. The equations are: - 91 - Chapter 7 G^ = 1000 iq ( < 0 1 / 2 (OCR)k (27) to model materials exhibiting drained behaviour and ^max = KclaySu * 2 8 ) to model materials exhibiting undrained behaviour. > To comply with the TARA-3 input format, the constants Kj for c'-<(>' materials or Kday for Su material types were backcalculated from the Gmax values computed from shear wave velocities for each material type. Since vs varied across the profile for the Young Point Bar Deposit and the embankment clay, different K^ or Kclay values were used for the same material type. For the materials of the Older and Recent Alluvium, average values of Kj and K,., were used. The K2 or Kc, values are listed on Table 12. - 92 - Chapter 7 Table 12 - K2 or K£lay Values Description SAND/GRAVEL in Older Alluvium CLAY in Older Alluvium SAND/GRAVEL in Recent Alluvium CLAY in Recent Alluvium SAND/SILT in Young Point Bar Deposit (Bottom) SAND/SILT in Young Point Bar Deposit (Top) EMBANKMENT CLAY (Bottom) EMBANKMENT CLAY (Middle) EMBANKMENT CLAY (Top) RIPRAP Y (pcf) 125 125 125 125 125 125 125 125 125 125 c' (psf) 0 -0 -0 0 ---0 4 > ' (deg) 35 -35 -28 28 ---45 (psf) -3050 -1650 --3000 3000 3000 -(ft/s) 1175-1225 850-1100 1350-1475 625-850 850 475-675 1375 1050 1350 '-K2 KtUy 70 1500 100 1700 40 26 i 2450 1430 2360 70 Bulk Modulus Parameters Selected for Wappapello Dam The hyperbolic bulk modulus parameters kb and n of the Young Point Bar Deposit, the Old and Recent Alluvium at station 14+00 were selected on the basis of experimentally established relationships between relative density and the bulk modulus parameters (Byrne and Cheung, 1984) for the materials exhibiting drained behaviour, as well as the relationship established between G, B and u (Poisson's ratio). The relative densities were inferred from the (N,)^, values. The following assumptions were made in selecting k,, and n: 1) The hyperbolic exponent parameter, n, is usually equal to 0.25 for sand and silt type materials and equal to 0 for clay materials. -93- Chapter 7 2) p is initially approximately equal to 0.3 for sand and silt type materials and is approximately equal to 0.4 for clay type materials. 3) G = E/(2*[l-u]) and B=E/(3*[l-2u]); therefore G/B = [3(l-2u)]/[2(l+u)]. Assuming (2), the following relationship between G and B was developed; B = 2 .167 x G for sands; (29) and B = 4 .667 x G for clays. (30) Using the Gmax values computed from the vs values, B and k,, were obtained. Table 13 summarizes the k,, and n values used in the TARA-3 analysis. Table 13 - kb and n Values for Wappapello Dam Description SAND/GRAVEL of Older Alluvium CLAY of Older Alluvium SAND/GRAVEL of Recent Alluvium CLAY of Recent Alluvium SAND/SILT of Young Point Bar Deposit EMBANKMENT CLAY (Bottom) EMBANKMENT CLAY (Middle) EMBANKMENT CLAY (Top) RIP RAP 7 (pcf) 125 125 125 125 125 125 125 125 130 K 4300 9000 4000 5525 1960 13900 8400 14500 2000 n 0.25 0 0.25 ' 0 0.25 0 0 0 0.25 - 94 - Chapter 7 Pore Water Pressure Constant Values Selected for Wappapello Dam The Martin-Finn-Seed pore pressure model, consisting of constants Q, C2, m, n, and K2, is selected for use in the analysis of Wappapello Dam. The regression analysis was carried out to obtain the pore pressure constants required for this model. The pore pressure constants were determined to match the liquefaction resistance curves derived from the in situ (N,)^ data using Seed's liquefaction resistance chart (Figure 34 (Koester and Franklin, 1985)). The curves were adjusted, where appropriate, to include the effects of overburden pressures greater than 1 tsf using the K^ correction factors (refer to Appendix I for an explanation of K„). The K„ correction factors, to correct for the effects of initial static shear stress, were not applied as the Young Point Bar Deposits were treated as contractive materials. This assumption of ignoring K„ is conservative. Figure 35 shows the fit of the pore pressure constants obtained from the regression analyses to the liquefaction resistance curve for a (N,^ of 11 blows/ft. Pore pressure constants for Wappapello Dam were determined for groups of elements that were similarly stressed. Tables 14 and 15 summarizes the pore pressure constants, together with other TARA-3 parameters, for reservoir levels at El. 360 ft and El. 390 ft (NGVD). -95- Chapter 7 0 . 6 <",>«, Figure 34 - Liquefaction Resistance Curves for Various Earthquake Magnitudes (Koester and Franklin, 1985) -96- Chapter 7 O ^ 0 . 2 0 T CO (N1)60 = 11 BLOWS/FT Ksigma=1.0 0 0 0 15 1 UJ 0.10 00 0.05 -3 o SIMCYC2 CONSTANTS c l -1 .0 . C2-0.4 Kr=0.0092. m=0.42. n=0.62 O > - 0 . 0 0 i i i i i i u i o 0 I l | l l l l I I I I l | I I I I I I I 10 15 TTTTT 20 I I i | i i I I i i I I i 25 30 NL cycles to liquefaction Figure 35 - Fit of Pore Pressure Constants to Liquefaction Resistance Curve at (N,), of 11 blows/ft -97- Chapter 7 Table 14 - Pore Pressure Constants for Reservoir Level at El. 360 ft (NGVD) ELEMENT # 231 to 238 239 to 241 242 to 244 245 to 247 248 to 252 253 to 257 258 to 264 265 to 276 277 to 285 286 to 293 294 to 298 299 to 305 306 to 322 323 to 331 332 to 339 340 to 344 345 to 351 352 to 368 352 to 368 394 to 405 394 to 405 (N,)«, (blows/ft) 22 22 22 16 11 11 14 14 14 14 11 8 8 12 12 8 8 8 4 8 4 (psf) 2003 1789 3277 7720 7828 5422 1908 2127 1188 3837 7421 3800 1500 406 3063 6770 3031 717 717 156 156 T vmax (psf) 708 723 1540 2823 2824 2211 760 781 422 1585 2696 1604 566 145 1276 2417 1282 292 292 68 68 (psf) 1.5E6 1.5E6 2.2E6 3.0E6 3.0E6 2.7E6 1.5E6 1.6E6 7.3E5 1.5E6 1.9E6 1.5E6 8.6E5 4.3E5 1.3E6 1.8E6 1.3E6 6.3E5 6.3E5 3.1E5 3.1E5 c, 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 c2 0.1 0.1 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 K2 0.16 0.078 0.03 0.005 0.00225 0.0026 0.0094 0.011 0.02 0.0082 0.0038 0.0025 0.0052 0.0145 0.0068 0.00275 0.00335 0.005 0.0017 0.0035 0.002 m 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 , 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 n 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 K 1.0 1.0 0.9 0.7 0.65 0.75 1.0 1.0 1.0'. 0.85 0.7 0.75 1.0 1.0 0.9 0.75 0.9 1.0 1.0 1.0 1.0 NOTE: Refer to Figure 36 for location of element numbers. - 98 - Chapter 7 Table 15 - Pore Pressure Constants for Reservoir Level at El. 390 ft (NGVD) ELEMENT # 231 to 238 239 to 241 242 to 244 245 to 247 248 to 252 253 to 257 258 to 264 265 to 276 277 to 285 286 to 293 294 to 298 299 to 305 306 to 322 323 to 331 332 to 339 340 to 344 345 to 351 352 to 368 352 to 368 394 to 405 394 to 405 (N,)«, (blows/ft) 22 22 22 16 11 11 14 14 14 14 11 8 8 12 12 8 8 8 4 8 4 <7',„ (psf) 2003 1734 3585 6214 7641 5078 2127 2315 1189 3623 6494 3441 1499 406 1996 6091 2070 717 717 156 156 T (psf) 708 683 1461 2389 2765 2089 835 849 421 1501 2401 4674 567 145 860 2284 1146 292 292 68 68 (psf) 1.5E6 1.4E6 2.2E6 2.8E6 3.0E6 2.6E6 1.6E6 1.6E6 7.3E5 1.4E6 1.8E6 1.4E6 8.6E5 4.3E5 1.1E6 1.8E6 1.3E6 6.3E5 6.3E5 3.1E5 3.1E5 c, 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 c2 0.1 0.1 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 K2 0.16 0.085 0.045 0.006 0.0026 0.0019 0.0094 0.011 0.02 0.0093 0.0038 0.0033 0.0052 0.015 0.0085 0.0026 0.00334 0.005 0.0017 0.0055 0.0018 m 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 . 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 n 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 K 1.0 1.0 0.9 0.75 0.7 0.75 1.0 1.0 1.0 < 0.9 0.7 0.9 1.0 1.0 1.0 0.75 0.9 1.0 1.0 -1.0 1.0 NOTE: Refer to Figure 36 for location of element numbers. 7.3 Finite Element Modelling 7.3.1 General The cross-section of Wappapello Dam at Station 14+00 was selected for analysis because it represented the thickest deposit (approximately 40 ft) of the potentially liquefiable Young Point Bar Deposit, and hence represented the worst case scenario. Station 14+00 - 99 - Chapter 7 was modelled as 545 elements and 608 nodes, as shown in Figures 36 and 37. All elements are isoparametric quadrilateral elements. The nodes along the foundation-bedrock interface were modelled to be fixed in both the x and y directions. The nodes bordering the sides of the foundation materials were modelled to be fixed in the x direction and free in the y direction in the static analysis and fixed in the y direction and free in the x direction in the dynamic analysis. All other nodes were considered to be free in both the x and y directions. The foundation materials above the dolomite bedrock at Station 14+00 were divided mto 5 different material types - the sands and gravels of the Older Alluvium, the clay of the Older Alluvium, the sand and gravels of the Recent Alluvium, the clay of the Recent Alluvium, and the silts and sands of the Young Point Bar Deposits, as shown in Figure 38. The rolled clay embankment was modelled as a clay-type material. The foundation materials consisting of the Older Alluvium, the Recent Alluvium and the Young Point Bar Deposit were modelled in TARA-3 as pre-existing elements. The clay embankment dam was modelled in a staged construction sequence consisting of 8 layers. The elements located below the water line were assigned buoyant unit weights; the elements located above the water line were assigned total unit weights. As the flow lines across the dam are very flat, the seepage forces were taken into account by applying water pressures against the upstream slope. Some elements in the Young Point Bar Deposit were assigned excess pore pressures to account for artesian water conditions. - 100- Chapter 7 5 2 6 / 1 u \ 5 4 3 5.06/! A-Q&/MKH 4 6 6 fii'l'ii T faljfc' • w\ft< ,4?U7J476 4 i , ! M 3 \ \ W 323 324 325 326 327 328 J2S m 331 m 313 53+JSS33C >/44?//45l 4SJ 45fi «»46H6flV Jw/nu fill imvfr 4 2 6/3274294JI 433415 U7 439 441 443 \ \445 />'<<? .••' , ' / I ||T i i \ '• '• \ \ /4074O94II 4I34I54I74I9 421 4 2 3 \ \ 4 2 5 / / • • / • ' / / I IIII \ \ \ \ \ \ ~ , 372 374 376370380 332 304 3 8 6 V JSSj! 4 0 6 3 6 9 / 3 7 0 372 374 376370 34l| 537S58.J3* 540 Wst 341 344 1345 54( 54! HI I {55 355 }49JI54>15J 154, 556J5? 80 39030?l94 |J95 306 jo? }I0 I M» 307109|5l l ! j l2 M * I I I I 396 358 559 397 360 398 599 361 562 4oo 56J 401 564 402 365 4 0 3 366 4 0 4 367 4 0 5 368 277 278 279 2 8 0 261 282 281 284285 28E 717 288 28!29( 791 29i 29: Win 29t 29' Ml 102)0) am- m 313 314 315 516 317 318 519 3 2 0 321 322 *rm%; 231 232 233 234 233 23G 237 236239, 185 186 187 188 189 190 191 192193 139 140 141 142 143 144 145 I4GI47 24C 241 24} 24324W45 t I 194 mm 197 190799,200 148 14! ISO ISI15? 15315< !4( 24' 2411250 201 . ' 2 0 3 ?04 202 205 is: 1S6 2S2 IJJ 25-H55 254 !5? 151 25 I ts ,.w mux toi 20! 210 211 157 io |l». 160 161 162 163 164 rrn 266 267 <6«269 270 271 272 273 274 275 276 220 221 222 223 224 225 226 227 228 229 230 173 174 175 176 177 176 179 ISO 181 182 183 184 93 94 95 96 97 98 99 IOC 101 102103 10'105.106107KK109110 III 112 114 113 115 IIC in 118 119 122 124 1)6 120,121 123 125 127 128 129 130 131 132 133 134 135 136 137 133 47 48 49 50 51 52 53 54 55 56, 57 58 591 6061 62 63 64 6?l 66 67 68 69 70 71 72 73 7J76 n 7« 00 79 81 82 83 84 85 86 87 88 89 9 0 91 92 19 10 12 13 14 15 16 17 18 20 22 LUL 23 32 24 25 26|27 88 •29 30 M 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Figure 36 - Finite Element Numbering for Wappapello Dam HOR.: o 200 4l.O H. SCALES: / o i TO - C O j £ •o 9 CD O CD £ *-c 1 e 1 = 1 ~ 1 $ 1 S 1 c 1 s 3 8 5 4 T 4 0 *-. 1 * * 3 ~ 0 to O in O 10 «o 4 0 rfj «0 * £ 1 s 0 1 4S» I 5 i £ fc S 1/1 s ; 4 » \ 4 C |T» »*» 1 S £ 2 03 CD ? ? 4 0 t O 4 T •E s = I 2 4 0 s ? • 0 0 • 0 t \ » I N I ^ m = * I s s 1 0 s 5 • 1 O i > ( 2?: S| Si 0 OJ 0 c s s «0 f O e 2 0 o o C I O C-f O-] IM I IS O W 2 > w UJ < o p 00 Pi •g i z O I - 102 - Chapter 7 CLAY EMBANKMENT BEDROCK ( H O R I Z O N T A L . SCALES < ° VERTICAL; I l_ 200 400 f t I I t___l_ 1600 3200 ft Figure 38 - Finite Element Soil Characterization of Wappapello Dam -103- Chapter 7 7.3.2 Water Loads The loads resulting from the reservoir water acting on the upstream face were modelled in TARA-3 as externally applied loads acting on the nodes on the upstream face. The seepage paths through the dam are strongly horizontal and the horizontal components of the loads were used. Table 16 table summarizes these loads. Table 16 - Water Load on Upstream Face NODE* 90 91 92 93 94 95 LOAD AT WATER LEVEL El. 360 ft (NGVD) (lbs) 2,770 3,600 700 ---LOAD AT WATER LEVEL , El. 390 ft (NGVD) (lbs) 8,957 17,542 15,068 10,739 9,229 1,758 - 104 - Chapter 8 8. DYNAMIC ANALYSES RESULTS OF WAPPAPELLO DAM BY TARA-3 8.1 General Dynamic analyses were carried out on Wappapello Dam, using TARA-3. The purposes of the dynamic analyses were: to determine the dam and foundation materials of Wappapello Dam that would liquefy under the design earthquake; and to determine the impact of the seismic forces on the final displacements of the dam after liquefaction has been triggered. The Kern County, CA earthquake of July 13, 1952 recorded at Taft-Lincoln School Tunnel (component S69E), scaled to a peak horizontal ground acceleration of 0.4g, was selected as the design earthquake for all the dynamic analyses. Dynamic effective stress analyses were carried out on Wappapello Dam using TARA-3. Two reservoir levels were considered, as follows: water level at El. 360 ft (NGVD), the normal operating reservoir level; and water level at El. 390 ft (NGVD), the maximum operating water level. 8.2 Dynamic Analyses on Original Geometry of Wappapello Dam To determine the dam and foundation materials of Wappapello Dam that would liquefy under the design earthquake, TARA-3 analyses were carried out on the original geometry of the dam. - 105- Chapter 8 The results of the dynamic analyses showed that, for the elements modelling the Young Point Bar Deposit, liquefaction was generally triggered (i.e. pore pressure ratios of 1 were reached) after about 5 seconds to 10 seconds of earthquake shaking, with the exception of some elements located directly beneath the crest of the dam. The maximum pore pressure ratios for the elements located beneath the crest of the dam generally reached about 0.4 to 0.6. The dynamic results were similar for both reservoir water levels. Typical pore pressure generation and stress and strain behaviour are plotted in Figures 39 > to 41. The pore pressure generation behaviour is plotted in terms of pore pressure ratios vs time plots. The stress-strain behaviour is plotted in terms of shear stress vs time and shear stress vs shear strain. The plots represent the following elements: element 285 in the Young Point Bar Deposit at the upstream toe (Figure 39); element 296 in the Young Point Bar Deposit under the centre of the dam (Figure 40); and element 310 in the Young Point Bar Deposit at the downstream toe (Figure 41); for the reservoir at El. 360 ft (NGVD). Figure 39 shows that liquefaction has been reached in this element at about 7.6 seconds (i.e. pore pressure ratio reaches 1). The corresponding shear stress vs time plot shows that the magnitude of the shear stress has dropped off after 7.6 seconds, indicating that there is a reduction in shear stresses transmitted to the soil after liquefaction has been triggered. By comparison, Figure 40 shows an element located beneath the centre of the dam where the pore pressure ratio after 8 seconds of earthquake shaking is only about 0.25. The - 106- Chapfer 8 OQ Pi CO 03 W CO s W W CO m Pi CO CO pa CO s w « CO TIME (seconds) o — —*-r ^ J ! ' — / r / / / / -Figure 39 TIME ( s e c o n d s ) Stress-Strain and Pore Presure Plots for Element 285 - Upstream Toe -107- Chapter 8 a ft CQ CQ >d CQ G ft » CQ O .a Si pa x CQ * J - « STRAIN (%) a ft^ CQ CQ >d CQ Pi W a) ft to CQ O Si w s CQ TIME ( seconds ) Figure 40 - ^ r — Stress Dam TIME (seconds) Strain and Pore Pressure Plots for Element 296 - Under Centre of - 108 - Chapter 8 TO Pi CQ CO H CQ a w CO to Pi CO CO pa E H CQ 9 « CO /I o 1 - i r j —££*-•— U-_ , — OJO-2. OJ32 CO« O.I STRAIN (%) TIME ( s e c o n d s ) 1.1 -o -r 2 4. V TIME ( s e c o n d s ) Figure 41 - Stress-Strain and Pore Pressure Plots for Element 310 - Downstream Toe - 109 - Chapter 8 strain vs time plot shows that the magnitude of the shear stresses is still increasing, common behaviour for an element where liquefaction has not been triggered. The hysteretic behaviour of the elements can be seen by the stress-strain plots. Figure 41 shows the behaviour of an element located in the Young Point Bar Deposit at the downstream toe of the dam where low ( N , ^ values (as low as 4 blows/ft) were recorded in the field investigations. Liquefaction was triggered in this element after about 6.8 seconds. The shear stress vs time plot (Figure 41) shows a dramatic reduction in shear stress being transmitted to this element. The shear stress vs shear strain plot shows much higher shear strains being generated in this element after liquefaction had been triggered, as compared to Figure 39 where the ( N ^ values were much higher (about 12 blows/ft). No liquefaction was triggered in the elements modelling the Older and Recent Alluvium deposits. The TARA-3 dynamic analyses results of the phase 3 work confirm the conclusions obtained from the phase 1 work, where one-dimensional SHAKE analyses were carried out to assess the shear stresses induced by the design earthquake and the liquefaction resistance of the material had been assessed using both ( N ^ values and laboratory results. - 7 7 0 - Chapter 8 Dynamic Analyses on Deformed Shape of Wappapello Dam Dynamic analyses were also carried out on the deformed shape of Wappapello Dam to determine the impact of seismic forces on the final displacements of the dam after liquefaction had been triggered in the Young Point Bar Deposit. The deformed shape of the dam, as a result of liquefaction being triggered in the Young Point Bar Deposit, was determined using TARA-3FL analyses, discussed in the next section. For these analyses, the residual strengths of the Young Point Bar Deposits were estimated using a correlation curve published by the U.S. Bureau of Reclamation (1989) (Figure 33). These strengths ranged from about 10 psf for the very loose materials located at the downstream toe of the dam, increasing to 400 psf beneath the centre of the dam. The results from the dynamic analyses show that the liquefied Young Point Bar Deposits were unable to transmit the large peak accelerations from the foundation to the dam. The low cyclic shear stresses generated in the liquefied Young Point Bar Deposit under the dam are shown on Figure 42. The peak acceleration at the crest of the dam after liquefaction had been triggered in the Young Point Bar Deposits was approximately 0. lg, indicating a reduction factor in peak acceleration of about 4. Figure 43 shows a time history plot of the peak accelerations recorded at the crest of the dam. -111- Chapter 8 CO a. CO CO 111 cc I -co cc s X CO 400 300 -200 -100 --100 -200 -300 --400 TIME (sec) Figure 42 - Shear Stress Time History for Element 342, Located in Young Point Bar Deposit under the Centre of the Dam TIME (sec) Figure 43 - Acceleration Time History Recorded at the Crest of Wappapelio Dam - 112- Chapter 8 The main conclusion obtained from the dynamic analyses of the phase 3 work is that the accelerations felt by the dam after liquefaction had been triggered in the Young Point Bar Deposit have little impact on the final deformations of the dam because of the greatly reduced inertial forces. The displacements recorded at the crest of the dam due to the post-liquefaction seismic shaking are shown on Figure 44. The main factor contributing to the final post-liquefaction deformations is the action of gravity and water pressures from the reservoir. TIME (sec) Figure 44 - Displacement Time History Recorded at the Crest of Wappapello Dam - 1 1 3 - Chapter 9 POST-LIQUEFACTION FLOW DEFORMATION RESULTS BY TARA-3FL General Post-liquefaction stability of Wappapello Dam had been investigated by the USACE (1988) using conventional limit equilibrium analyses assuming circular slip surfaces (phase 2 work). Results of these analyses suggested factors of safety only marginally less than 1 assuming a uniform (N^o value of 9 blows/ft for the Young Point Bar Deposit. This blow count value corresponds to a residual strength of about 115 psf, using the Seed (1987) lower bound correlation relationship between ( N ^ and residual strength. Very small post-liquefaction deformations were therefore anticipated. This very critical conclusion was checked in the phase 3 work using TARA-3FL. Constant ( N ^ Values in the Young Point Bar Deposits The post-liquefaction deformations of Wappapello Dam were estimated first by assuming a constant (Ni)60 value of 9 blows/ft for the entire Young Point Bar Deposit, as modelled in the phase 2 work. This analysis attempts to estimate the post-liquefaction deformations of the dam by modelling the same conditions as those used in the phase 2 post-liquefaction static slope stability analyses (USACE (1988)). As part of the phase 3 work, a relationship between the post-earthquake deformations and residual shear strengths in the Young Point Bar Deposits (assumed constant for the entire deposit) was established. For the analyses, the reservoir water level of El. 390 ft(-NGVD) was selected, as assumed in the phase 2 work. - 1 1 4 - Chapter 9 9.2.1 Comparison Between the Results of the Flow Deformation and Slope Stability Analyses The results from the phase 2, post-earthquake static limit equilibrium slope stability analysis carried out by USACE (1988), indicated that the dam was marginally stable (i.e. factors of safety are approximately equal to 1) if the potentially liquefiable materials of the Young Point Bar Deposits had a ( N ^ value of at least 9 blows/ft, corresponding to a residual strength, Sur, of 115 psf (using Seed, 1987 lower bound curve) at a reservoir level of El. 390 ft NGVD. In the flow deformation analyses, the Young Point Bar Deposits are assumed to liquefy upstream, below and downstream of the dam during the design level earthquake. Sufficient pore pressures have been generated by the design earthquake to cause the undrained shear strength to drop from its initial value to its S .^ Constant Sm values are assumed for the entire Young Point Bar Deposits. TARA-3FL tracks the deformation as a result of this loss in shear strength from its initial value to the final value Sm. In the TARA-3FL analyses, the strength in each potentially liquefiable element was reduced in 5% increments by multiplying the current shear strength by the factor 0.95. After n increments, the shear strength Su was reduced to (0.95)n times its original value. The progress of deformation during the strength reduction process is shown by the deformation plots in Figure 45. As the shear strength approaches its residual Sur value of 115 psf, the crest of the dam moves about 230 ft downstream and settles 25 ft, leaving a freeboard of only 3 ft. - 115- Chapter 9 Iteration number = 1, Reduction Factor = 0.95 Iteration number = 25, Reduction Factor = 0.28 Iteration number = 30, Reduction Factor = 0.22 i i t i « t t I I 4 I i I | | I I I I 1 I I I I i I < I 'HI I I I I ( M l I i l i j I I I I 1 < 1 I I l" I t e ra t ion number = 40, Reduction Factor = - .13 1 * < « < i i ' < • • • <  < < • " i i « • • • < • i i i i i T T I i . ,1 iI . i I 1 r I ' ' I I I M I 1 I I I I i I l MM I I I I I i I I I I I I I I | | j j j | ) ( j | | Reduction Factor = 0 (i.e. all potentially liquefiabl< elements have reached their residual iquetiabK strengths) GEO.SCRLE „ •—j^o—— SCALE 2 V : 1 H DISPLACEMENT 0 ' ^ 5 -— Figure 45 - Flow Deformation of Wappapello Dam when Residual Strength in Young . Point Bar Deposits is Equivalent to 115 psf, (N,)^ = 9 blows/ft - 1 1 6 - Chapter 9 The deformation plots clearly show that failure occurs as a result of squeezing out of the soft liquefied Young Point Bar Deposit from beneath the dam due to the gravity forces of the dam itself (where the elements were most highly stressed in the cx and the ay directions) towards the toe, causing the crest to settle 25 ft. The large horizontal load applied on the upstream face by the El. 390 ft (NGVD) reservoir causes the large horizontal movement of the deformed dam. The discrepancy between the results of the limit equilibrium stability analyses and the TARA-3FL analyses may be explained by observing the failure mechanism causing the deformations. In the limit equilibrium slope stability analyses, the failure plane is modelled by a circular slip surface cutting through both the embankment having a Su of 3,000 psf and the Young Point Bar Deposits having a S^ of 115 psf. The TARA-3FL deformation plots, however, show the failure mechanism is a squeezing out of the weak foundation materials due to high gravity loads of the dam and sliding on the softened material due to the high reservoir loads. The high undrained strength of the embankment materials does not contribute any resistance to this failure mode. A comparison between the TARA-3FL deformation analysis and the static post earthquake limit equilibrium slope stability method raises an important point. If the results of an analyses are to be considered reliable, the analysis or simulation must model the appropriate failure mechanism. In this case, the failure surface does not follow a circular slip surface through the embankment; thus, the slope stability analyses, which assumes that the failure surface follows a circular path, overestimated the resistance to failure. - 117- Chapter 9 Relationship Between Dam Displacements and Sur in the Young Point Bar Deposit Additional flow deformation analyses were carried out on Wappapello Dam using varying constant residual strengths in the Young Point Bar Deposit to establish a deformation vs residual strength relationship. The results of the analyses are presented in Figure 46 in terms of horizontal and vertical displacement of the crest with varying residual strengths. This figure shows that only minimal horizontal displacement of the crest occurs if Sm values in the Young Point Bar Deposits are greater than about 300 psf. If the constant S^ in the Young Point Bar Deposit falls below 300 psf, the stability of the entire dam structure is in jeopardy as the horizontal displacements increase dramatically. Displacements of about 230 ft were obtained for the low S^ of 115 psf. Figure 47 shows the relationship between the loss of the freeboard of the dam with the water table at El. 390 ft (NGVD) with decreasing S^ values. Only minimal loss of freeboard occurs if the residual strength in the Young Point Bar Deposits is greater than 600 psf, equivalent to an ( N ^ greater than 17 blows/ft. In order to ensure that the post-earthquake stability of Wappapello Dam is maintained and limit vertical and horizontal displacements to acceptable limits, the Sm must be greater than 600 psf, corresponding to a ( N ^ value of greater than 17 blow/ft (assuming a lower bound relationship, Seed and Harder, (1990)). Since the field data indicate that portions of the Young Point Bar Deposits have (NJ^ values less than 17 blows/ft, additional - 118 - Chapter 9 250.0 200.0 £ 150.0 100.0 -E 50.0 i 0.0 - 5 0 . 0 -_ DISPLACEMENT OF THE UPSTREAM CREST WITH REDUCTION IN RESIDUAL SHEAR STRENGTH OF THE YOUNG POINT BAR DEPOSIT » * *<• HORIZONTAL DISPLACEMENT - positive downstream » » » * « VERTICAL DISPLACEMENT - positive upwards 1 0 0 . 0 - | i i i i r i i T i [ i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | 2000 1500 1000 500 0 RESIDUAL SHEAR STRENGTH (psf) Figure 47 - Variation in Horizontal and Vertical Displacement of the Dam Crest with Residual Strength Values in the Young Point Bar Deposit - 1 1 9 - Chapter 9 40.0 30.0 -_ Q <20.0 m QJ LU LL. 10.0 0.0 2000 LOSS OF FREEBOARD WITH REDUCTION IN RESIDUAL SHEAR STRENGTH OF THE -YOUNG POINT BAR DEPOSIT -i i i i i i i i i l i i i i i i i i i l i i i i i i i i i I i i i i i i i i i 1500 1000 500 0 RESIDUAL SHEAR STRENGTH (psf) Figure 48 - Variation in Dam Freeboard with Residual Strengths in the Young Point Bar Deposit deformation analyses were carried out to evaluate the actual post-earthquake stability of the dam, as detailed in the next section. Varying ( N ^ Values in the Young Point Bar Deposit The seismic work carried out to date (phases 1, 2 and 3) indicates that the seismic stability of Wappapello Dam is governed by the magnitude of the post-earthquake deformations. To evaluate more realistic post-earthquake deformations of Wappapello Dam, additional studies were required to address the following items: - 120 - Chapter 9 (N.L, values in the Young Point Bar Deposit: Modelling the Young Point Bar Deposit using a constant (Nj)60 value is an oversimplification of the field conditions. Additional flow deformation analyses, using the actual, field-measured (N,)^ values for the Young Point Bar Deposit, were required; and Correlation relationship between (N,)ftn and residual strength The residual strength values are a critical input for the prediction of post-liquefaction deformations analyses. If field-measured (N^ values are used to model the Young Point Bar Deposit, additional studies of the correlation relationship between (N,)60 and residual strengths were required. A review of the (N,)^ value distribution throughout the cross-section of the Young Point Bar Deposits indicated that the penetration resistance generally decreased in the downstream direction and increased with depth. The lowest ( N ^ values of less than 4 blows/ft were recorded in the material directly downstream of the dam at Station 14+00. The review by CELMS of the (Ni)^ database of the foundation material of Wappapello Dam produced the (N,)^ distribution shown in Figure 48. Note that the ( N ^ values of the top 15 ft of the Young Point Bar Deposit located downstream of the dam are still not established definitely at this time. The (N,)^ values listed in Figure 48 were correlated to S^ values using the following relationships: lower bound curve on the correlation relationship proposed by Seed and. Harder (1990), shown in Figure 32; and - 121 - Chapter 9 Table 17 lists the residual strengths, Sm, associated with (Nj)^ values using Seed's lower bound and the US Bureau line. j » HOR.: 0 SCALES: VERT.: 0 400 3200 800 ft. 6400 ft. Figure 48 - Distribution of ( N ^ Values in the Young Point Bar Deposit for TARA-3FL Analysis - 122 - Chapter 9 Table 17 - Relationship Between Sur Values and (Nj)60 Values Used at Station 14+00 of Wappapello Dam (blows/ft) 22 16 14 12 11 8 4 (psf) Seed's Lower Bound 1150 550 375 200 150 30 10 (psf) US Burec 1350 700 530 400 350 190 10 Ratio of US Burec to Seed's Lower Bound 1.17 1.27 1.41 2.00 2.33 6.33 1.0 The S^ values obtained from the curve labelled US Burec are higher than the values obtained from Seed's lower bound curve, for all (N,)60 values. Although both the US Burec line and Seed's lower bound line indicate that Sm is equal to 0 psf for (Nj)60 values less than 4 blows/ft and 6 blows/ft, respectively, a minimum S^ . value of 10 psf is assigned to the ( N ^ value of 4 blows/ft in all the TARA-3FL analyses. This assumption will not affect the conclusions resulting from this work. The flow deformation assessment was carried out using the (N,^ distribution shown in Figure 48 and the corresponding Sur values summarized in Table 17 for the following conditions: 1. Upstream reservoir water levels at: El. 390 ft (NGVD); and El. 360 ft (NGVD). - 123 - Chapter 9 2- (Ni)eo values in the top 15 ft of the downstream Young Point Bar Deposit ranging from 4 blows/ft to 12 blows/ft, to account for the uncertainty of values at this location; 3. Residual strengths determined by: Seed's lower bound curve (Seed and Harder, 1990), shown in Figure 33; and US Burec curve (U.S. Bureau of Reclamation, 1989), shown in Figure 34. Figures 49 to 56 plot the flow deformations for the various cases. The iteration numbers, n, and the reduction factors are shown with each plot. Tables 18 and 19 summarize ithe upstream crest displacements when all liquefiable elements have reached S,,,. - 124 - Chapter 9 \ \ ^ 5 ^ * £> * T <T_ • -H~-i t-~ 1 i , ; -. Iteration number = 1, Reduction Factor = 0.95 ^L^L^^^//^ ,^ SIWrtTTlUWi v / ^ ^..•.. '_,\,i^.<-t.^_ tyrr Iteration number = 28, Reduction Factor = 0.24 (~1 * T r. fff • x > *-P^ " ^ •^"•**?vT -*— — Iteration number = 32, Reduction Factor = 0.19 •^f^mTfrWB Iteration number = 36, Reduction Factor = 0.16 "*5 f --L -- - i _i ! ^ 1* P* 1 -l / i — Iteration number = 40, Reduction Factor = 0.13 GE0.SCRLE o 200 3oo SCRLE 2V :1H (DISPLACEMENT 0 '—sir- '—«o Figure 49 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at ( N ^ of 4 blows/ft, Seed's Lower Bound Curve - 125- Chapter 9 *0m /'l' .' / - ] i\\^ ^ * . Iteration number = 1, Reduction Factor = 0.95 — ((((((\(C4 S»^W : = = = = = _ . . . ± Wfi Iteration number = 24, Reduction Factor = 0.29 Iteration number = 34, Reduction Factor = 0.17 ' ^ J ? 2 fff^>&• -£*S£7JT '—7 3 3 Iteration number = 40, Reduction Factor = 0.13 >- §§S&^: ji If 31 •M r ^ ^ f-T " 1 Iteration number = 49, Reduction Factor = 0.08 SCALE 2V:1H GEO. SCALE o ^ — z o o " DISPLACEMENT 0 ' jjg- 400 Figure 50 - Deformation Plots, Water Level at EI. 390 ft (NGVD), Downstream Strength at ( N ^ of 8 blows/ft, Seed's Lower Bound Curve - 126- Chapter 9 ** <*./ S 1 / — I I \ \ S V < « - ^ V I I I I I i i i I i i 1 j -Iteration number = 1, Reduction Factor = 0.95 111 rffufi''/I/, E-i ji n ^ YVT^fT "L?iY~i Iteration number = 30, Reduction Factor = 0.21 z^gfipslfe i====!=!y!i / ^™m< ("f 1 1 1 1 1 1 I Iteration number = 40, Reduction Factor = 0.13 Iteration number = 50, Reduction Factor = 0.08 1 .. p^asajpi _. 7~f -f=F Iteration number = 69, Reduction Factor = 0.03 SCALE 2V:1H GE0.SCRLE o~ DISPLACEMENT f 200 400 200 400 Figure 51 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at (N,)^ of 4 blows/ft, US Bureau of Reclamation Curve - 127- Chapter 9 * * • I t e r a t i o n number = 1 , R e d u c t i o n F a c t o r = 0 .95 — T 1 t | I t e r a t i o n number = 2 4 , R e d u c t i o n F a c t o r = 0 .29 --r=^gy•?••'.•''/ / / j -v-'i \ \ -EEEEEEEEEEEEEE iEEE, / j:=ii:!:ii=iiiiii= I t e r a t i o n number = 3 4 , R e d u c t i o n F a c t o r = 0 .17 - ^ ==MpB¥:=":E: EEEEEE|EEEEE™E;:;EE I t e r a t i o n number = 4 0 , R e d u c t i o n F a c t o r = 0 . 1 3 ===^lwmm felH^iiiiliiil^ I t e r a t i o n number = 4 9 , R e d u c t i o n F a c t o r = 0 .08 SCALE 2V:1H GEO.SCRLE o 200 -wo DISPLACEMENT o " 260 ' *6o Figure 52 - Deformation Plots, Water Level at El. 390 ft (NGVD), Downstream Strength at (N,)^ of 8 blows/ft, US Bureau of Reclamation Curve - 128 - Chapter 9 i—i "'r^ T r^ r r 7 r — t 1 i T i Y i 1 — Iteration number = 1, Reduction Factor = 0.95 = :p^| l | 1 Iteration number = 30, Reduction Factor = 0.21 r—'-£ ffn^MTT _ i _ $smm i ~ i — Iteration number = 40, Reduction Factor = 0.13 / / iS? ^—rr Iteration number = 50, Reduction Factor = 0.08 s Iteration number = 60, Reduction Factor = 0.05 —I— P^£p5»^* 1 ^ j 11 Iteration number = 86, Reduction Factor = 0.01 GEO. SCALE ^—J j j j ' sj0 SCALE 2V:1H OISPLRCEMENT i • j& r • '—5j0 Figure 53- Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (N,)^ of 4 blows/ft, Seed's Lower Bound Curve - 129- Chapter 9 Iteration number = 1, Reduction Factor - 0.95 2 = 2 Iteration number = 30, Reduction Factor = 0.21 Iteration number = 40, Reduction Factor = 0.13 Iteration number = 50, Reduction Factor = 0.08 Iteration number = 60, Reduction Factor = 0.05 Iteration number = 86, Reduction Factor = 0.01 r« 1 fi s \ is^s . i i> '-/ i ± T " 1 1 J 1 ^ * "T 1 1 | I K ^ T T T x •"7 "•/ / A- I— ^ A , fif-h J L M i l j i j 1 1 1 1 1 £; 1 1 | 1 j 1 1 glllSI " i * ' \ ' , i / - (—i-— M SCALE 2 V : 1 H GEO. SCALE o ' to ' 5oo DISPLACEMENT I ' jfo • jfo Figure 54 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (N,^ of 8 blows/ft, Seed's Lower Bound Curve - 130- C h a p t e r 9 • I Yf (I i >L>^\^^S^T^T\ 11 M I i i i i i i i I t e r a t i o n numb e r 1 9 R e d u o t i o n L- TJ I F a c t o r = 0 9f Iteration number = 24, Reduction Factor = 0.29 i — i i i i i r T n C f / ' /V -W-yv ||;;:;::======iii-^ Iteration number = 34, Reduction Factor = 0.17 Iteration number = 40, Reduction Factor = 0.13 ~* > f— r^-i r^-| * Iteration number = 50, Reduction Factor = 0.0J SCALE 2V:1H GEO. SCALE 0 ' & • «j0 DISPLACEMENT i ' aft, • ^ Figure 55 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (N,)^ of 4 blows/ft, US Bureau of Reclamation Curve - 131 - Chapter 9 ^=^^^y"r^y-T{ i i i VS 1 r^ T1! II 111 T T""I~l I I I I I ' I ~T 1 Iteration number = 1, Reduction Factor = 0.95 + 1 1 Iteration number = 24, Reduction Factor = 0.29 -*-. *^f? y'?' .< J J J • \V'>'\ n ^ i j in / J I I I I I 1 i I I Iteration number = 34, Reduction Factor = 0.17 ~ — — — — ~ x j^ V / {'.,*' / - - -Iteration number = 40, Reduction Factor = 0.13 — 1 ... .. - / / ss)f\ -_ Iteration number = 50, Reduction Factor = 0.08 SCALE 2V:1H GEO. SCALE o ' 200 ' 5oo 01SPIRCEMENT 0 ' ^ 5 ' ^ 0 Figure 56 - Deformation Plots, Water Level at El. 360 ft (NGVD), Downstream Strength at (N,)60 of 8 blows/ft, US Bureau of Reclamation Curve • - 132 - Chapter 9 Table 18 - Summary of Displacements Computed at the Upstream Edge of the Crest with (N,)60 Values Variable Across Station 14+00 with the Upstream Reservoir Water Level at EI. 390 ft (NGVD) D/S (NJso Value Variable Zone (Figure 48) (blows/ft) SEED'S LOWER BOUND CURVE 4 8 12 US BUREC CURVE 4 8 (psf) 10 30 200 10 190 Horizontal Displacement (ft) 271.5 262.8 243.5 34.1 2.2 Vertical Displacement (ft) -20.8 -20.7 -19.9 -5.3 -3.2 NOTE: Positive horizontal direction is in the downstream direction Positive vertical direction is in the upward direction - 133 - Chapter 9 Table 19 - Summary of Displacement Computed at the Upstream Edge of the Crest with (N^,, Values Variable Across Station 14+00 with the Upstream Reservoir Water Level at El. 360 ft (NGVD) D/S (N,)*,, Value Variable Zone (Figure 48) (blows/ft) SEED'S LOWER BOUND CURVE 4 8 12 US BUREC CURVE 4 8 (psf) 10 30 200 10 190 Horizontal Displacement (ft) 17.8 18.9 18.4 1.3 0.8 Vertical Displacement (ft) -22.6 -22.6 -20.8 i -3.4 -3.2 NOTE: Positive horizontal direction is in the downstream direction Positive vertical direction is in the upward direction Displacement trends in the horizontal and vertical directions were evident by plotting the TARA-3FL results. The large horizontal displacements predicted in the downstream direction for the reservoir at El. 390 ft cases, but not for the reservoir at El. 360 ft cases, indicate that the post-earthquake horizontal displacements of Wappapello Dam are a result of the horizontal force applied by the reservoir on the dam, rather than the result of the liquefaction triggering in the Young Point Bar Deposits located downstream of the dam toe. Improving the properties of the Young Point Bar Deposit located downstream of the dam toe will reduce the magnitude of the horizontal displacements for the reservoir at El. 390 ft. However, the horizontal displacements predicted for the El. 360 ft loading case are relatively insensitive to the (N,)60 values of the Young Point Bar Deposit located - 134 - Chapter 9 downstream of the dam toe. The magnitude of the vertical displacements remain relatively consistent for both reservoir loading cases and for varying (Ni)^ values of the Young Point Bar Deposits located downstream of the dam toe, indicating that the vertical displacement are mainly a result of the gravity loads of the dam imposed on the liquefiable deposits located directly beneath the dam. Improving the properties of the Young Point Bar Deposit located downstream of the dam toe will not reduce the vertical displacements of the dam significantly, unless the properties of the deposits of located directly beneath the dam are also improved. - 735 - Chapter 10 CONCLUSIONS AND RECOMMENDATIONS Seismic assessments of Wappapello Dam have been carried out by USACE in three phases. Phase 1 work included a liquefaction assessment of the Wappapello Dam site by the USACE-Memphis District to determine the susceptibility of the dam and foundation soils to triggering of liquefaction under the earthquake loads. This analysis was carried out by performing a one-dimensional dynamic analysis at two soil profiles, one modelling the dam centreline profile and the second modelling the free field conditions. The main conclusion obtained from the phase 1 study was that the Young Point Bar Deposit was potentially liquefiable under the design earthquake loads. The conclusions of the phase 1 study led to an assessment of the post-earthquake stability analyses of the dam by the USACE-St. Louis District in the phase 2 seismic study. This soidy consisted of a limit equilibrium stability analyses, assigning post-liquefaction residual strength values to the liquefied deposits. The stability analyses indicated that, since the post-earthquake static factors of safety were about 1, slope failures were unlikely for the assumed residual strength values in the Young Point Bar Deposits. Since the phase 2 work, however, further advances have been made in the area of liquefaction assessment, the evaluation of residual strengths, and the modelling of post-earthquake flow deformation analyses. The third phase of the seismic study of Wappapello Dam was carried out at UBC. This phase included the critical review of phases 1 and 2, to ensure that the changes that have occurred in the liquefaction assessment procedures and the evaluation of residual strengths did not change the - 136- Chapter 10 conclusions obtained from the phases 1 and 2 seismic studies. In addition, a more rigorous post-liquefaction deformation behaviour of the dam was carried out. This study was performed using the two-dimensional finite element computer program TARA-3, to check the triggering of liquefaction and the development of seismic displacements, and the program TARA-3FL for estimating post-liquefaction flow deformations. Dynamic effective stress analyses were carried for two reservoir water levels, as follows: water level at El. 360 ft (NGVD), the normal operating reservoir level; and > water level at El. 390 ft (NGVD), the maximum operating water level. Dynamic analyses were carried out on the original geometry of Wappapello Dam. The result showed that, for both reservoir levels, liquefaction was triggered in the Young Point Bar Deposit, with the exception of some elements located directly beneath the crest of the dam. No liquefaction was triggered in the Older and Recent Alluvium deposits. Generally, liquefaction was triggered in the Young Point Bar Deposits between 5 seconds to 10 seconds of earthquake shaking. These results are in agreement with the phase 1 USACE study. Post-liquefaction stability of Wappapello Dam was investigated using TARA-3FL for the following cases: 1. Constant (Ni)60 values in the Young Point Bar Deposits This analyses modelled the Young Point Bar Deposit properties by a constant (Ni)eo value of 9 blows/ft, corresponding to a residual strength of 115 psf (Seed, 1987 lower bound curve). The water level was modelled at El. 390 ft (NGVD). This analysis was carried out to model the phase 2 post-earthquake limit equilibrium slope stability analyses, for comparison purposes. - 137 - Chapter 10 As the shear strength in the Young Point Bar Deposits decreased from its initial value to its post-earthquake residual value, the crest of the dam moved about 230 ft downstream and settled 25 ft, leaving a freeboard of only 3 ft. The TARA-3FL deformation plots clearly showed that failure occurred by squeezing out of the soft liquefied Young Point Bar Deposit from beneath the dam (due to the weight of the non-liquefied, intact dam) towards the toe, causing the crest to settle 25 ft. The large horizontal load applied on the upstream face by the reservoir water caused the large horizontal movement of the deformed dam. The discrepancy between the results of the finite element TARA-3FL analyses and the limit equilibrium slope stability analyses is attributed to the different failure mechanisms assumed in the analyses. In the TARA-3FL model, failure is a result of the squeezing out of the weak (liquefied) foundation materials due to the high gravity loads of the dam and sliding on the softened material as a result of reservoir loading. In the limit equilibrium slope stability model, the failure is modelled by a circular slip surface cutting through both the embankment having a strength of 3,000 psf and the Young Point Bar Deposit with a strength ofll5psf. The seismic stability of structures with extensive zones of liquefiable materials in the foundation may not always be adequately assessed by assumed sliding along well defined slip surfaces. Post-earthquake limit equilibrium slope stability analyses should not be used to assess the post-liquefied behaviour of the structures for these cases. 2. Varying (Ni)60 values in the Young Point Bar Deposit A more realistic post-earthquake flow deformation analysis was carried out. The field in situ data indicated that the Young Point Bar Deposit generally decreased in penetration resistance in the downstream direction and increased in resistance with depth. The Young Point Bar Deposit was therefore divided into 10 sub-units and assigned varying field-measured ( N ^ values in the TARA-3FL model. However, there is insufficient in situ data available for the top 15 ft of the Young Point Bar Deposit located downstream of the dam toe, and therefore the (Ni)^ values for this sub-unit was varied from 4 blows/ft to 12 blows/ft in the TARA-3FL analyses. The TARA-3FL results indicated that the crest movements are very sensitive to the residual strengths values; hence, the correlation relationship between ( N ^ values and residual strength became more critical. Two correlation relationships were studied: -138- Chapter 10 Seed's lower bound relationship (Seed and Harder, 1990); and US Bureau of Reclamation curve (USBR, 1989). The TARA-3FL results indicated that Wappapello Dam would undergo post-liquefaction vertical displacements greater than 20 ft and horizontal displacements greater than 270 ft (downstream (Nj)^ value of 4 blows/ft) to about 245 ft (downstream ( N ^ value of 12 blows/ft) for the reservoir level at El. 390 ft (NGVD) if Seed's lower bound residual strength correlation relationship was assumed. If Seed's lower bound residual strength correlation relationship is assumed, the predicted post-liquefaction deformations would be too large to ensure seismic stability of the dam. If the USBR relationship was assumed, the deformations decreased considerably with vertical displacements of about 3 ft and horizontal deformations of about 2 ft estimated for the case where the downstream (Nj)^ values for the Young Point Bar Deposit are equal to 8 blows/ft The TARA-3FL results indicate that if the USBR residual strength correlation relationship is assumed, the predicted post-liquefaction deformations may be tolerated by this dam if the downstream ( N ^ values in the Young Point Bar Deposit are greater than 8 blows/ft. For the reservoir level at El. 360 ft (NGVD), the estimated post-liquefaction deformations are about 23 ft vertically and about 15 ft to 20 ft in the downstream direction if Seed's lower bound relationship was assumed. If the USBR relationship was assumed, the deformations decreased to about 3 ft in the vertical direction and about 1.5 ft in the downstream direction. The selection of the residual strength correlation relationship is a critical input in determining the seismic stability of Wappapello Dam. Dynamic analyses were also carried out on the deformed shape of Wappapello Dam to determine the impact of seismic forces on the final displacements of the dam after liquefaction had occurred in the Young Point Bar Deposit. The results show that the liquefied Young Point Bar Deposits were unable to transmit the large accelerations from the foundation to the dam. The accelerations felt by the dam after liquefaction has been triggered have little impact on the final deformations of the dam. The main factor contributing to the final post-liquefaction deformations is the action of gravity bfthe dam and the water pressures from the reservoir. 139 - Chapter 10 To determine the post-earthquake deformations and to assess the seismic stability of Wappapello Dam, the following recommendations are made: further field investigations should be carried out to determine the ( N ^ values of the Young Point Bar Deposits located downstream of the dam toe; further studies should be carried out to determine the residual strength of the Young Point Bar Deposits. Additional laboratory testing and review of the empirically-derived residual strength vs (N^ database should be carried out to establish appropriate Sw values for this site; after the (N,^ values of the Young Point Bar Deposit have been established and the appropriate design Sur values have been assigned, further deformation analyses should be carried out to determine the post-earthquake deformations of Wappapello Dam. The maximum acceptable post-earthquake deformation limits to ensure seismic stability of Wappapello Dam should be established by the USACE. If the estimated deformations are not acceptable, potential remedial measures should be assessed and implemented. - 140 - References REFERENCES Byrne, P.M., H. Cheung, and L. Yan (1987). "Soil Parameters for Deformation Analysis of Sand Masses", Canadian Geotechnical Journal, Volume 24, Number 3, pp 366-376. Byrne, P.M. and H. Cheung (1984). "Soil Parameters for Deformation Analysis of Sand Masses", Soil Mechanics Series No. 81, Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada. Castro, G., T.O. Keller and S.S. Boynton (1989). "Re-evaluation of the Lower San Fernando Dam", Report No. 1, USACE, Waterways Experiment Station, Vicksburg, Mississippi, September. Clough, R.W. and J. Penzien (1975). "Dynamics of Structures", McGraw Hill Book Company, New York, U.S.A. Duncan, J.M., P.M. Byrne, K.S. Wong and P. Mabry (1980). "Strength, Stress-strain and Bulk Modulus Parameters for Finite Element Analyses of Stresses and Movement in Soil Masses", Report No. UCB/GT/80-01, University of California, Berkeley, CA. Finn, W.D.L. (1988). "Dynamic Analysis in Geotechnical Engineering, Earthquake Engineering and Soil Dynamics II - Recent Advances in Ground Motion Evaluation", Geotechnical Special Publication No. 20, ASCE, August, pp. 523-591. Finn, W.D.L. and M. Yogendrakumar (1989). "TARA-3FL - Program for Analysis of Liquefaction Induced Flow Deformations", Department of Civil Engineering, University of British Columbia, Vancouver, British Columbia, Canada. Finn, W.D.L., M. Yogendrakumar, N. Yoshida, and H. Yoshida (1986). "TARA-3: A Program for Nonlinear Static and Dynamic Effective Stress Analysis", Soil Dynamic Group, University of British Columbia, Vancouver, British Columbia, Canada. Finn, W.D.L. and P.M. Byrne (1976). "Estimating Settlements in Dry Sands During Earthquakes", Canadian Geotechnical Journal, Volume 13, No. 4, pp 355-363. Finn, W.D.L., W.K. Lee, and G.R. Martin (1976). "An Effective Stress Model for Liquefaction", Journal of the Geotechnical Division, ASCE, Volume 103, No. GT6, Proc. Paper 13008, pp 517-533. Goodman, R.B., R.L. Taylor and T.L. Brekke (1968). "A Model for the Mechanics of Jointed Rock", Journal of the Soil Mechanics and Foundation Engineering Division, ASCE, May, pp. 637-659. Hardin, B.O. and V.P. Drenevich (1972). "Shear Modulus and Damping in Soils;Design Equations and Curves", Journal of the Soil Mechanics and Foundation Division, ASCE, Volume 98, SM7, Proceedings papers 9006, July, pp 667-692. - 141 - References Holtz, R.D. and W.D. Kovacs, (1981). "An Introduction to Geotechnical Engineering", Prentice-Hall, New Jersey, U.S.A. Koester, J.P. and A.G. Franklin (1985). "Current Methodologies for Assessing the Potential for Earthquake-induced Liquefaction in Soils", NUREG/CR-430, US Nuclear Regulatory Commission, Washington, DC. Krinitzsky, E.L. and W.F. Marcuson (1983). "Principles for Selecting Earthquake Motions in Engineering Design", AEG, Bulletin, Volume XX, No. 3, pp 253-266. Lee, K.W. (1975). "Mechanical Model for the Analysis of Liquefaction of Horizontal Soil Deposits", Ph. D. Thesis, Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada Lee, K.L. and K. Chan (1972). "Number of Equivalent Cycles in Strong-Motion Earthquakes", Proceedings, International Conference on Microzonation, Seattle, WA, Volume II, pp 609-627. Martin, G.R., W.D.L. Finn and H.B. Seed (1975). "Fundamentals of Liquefaction Under Cyclic Loadings", Proc. Paper 11284, Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, No. GTS, pp. 324-438. Masing, G. (1926). "Eigenspannunung und Verfestigung beim Messing", Proceedings, 2nd International Congress of Applied Mechanics, Zurich, Switzerland. McGuire, R.F. (1976). "FORTRAN Computer Program for Seismic Risk Analysis", USGS, Open-File Report 76-67, Washington, DC. Nuttli, O.W. and R.B. Hermann (1978). "State-of-the-Art for Assessing Earthquake Hazards in the United States, Report 12, Credible Earthquakes for the Central United States," Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Schnabel, P.B., J. Lysmer, and H.B. Seed (1972). "SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites", Earthquake Engineering Research Centre, University of California, Berkeley, CA. Seed, H.B. (1987). "Design Problems in Soil Liquefaction", Journal of Geotechnical Engineering, ASCE, Vol. 113, No. 7, August, pp. 827-845. Seed, H.B. (1983). "Earthquake-resistant Design of Earth Dams", in Seismic Design of Embankments and Caverns, Terry R. Howard, Editor, ASCE, pp 41-64. Seed, H.B. (1979). "Soil Liquefaction and Cyclic Mobility Evaluation for LeveTGround During Earthquake", Journal of Geotechnical Engineering Division, ASCE, Volume 105, No. GT2, Proceedings Paper 14380, pp 201-255. - 142- References Seed, H.B. (1976). "Evaluation of Soil Liquefaction Effects on Level Ground During Earthquakes", ASCE Annual Convention and Exposition Liquefaction Problems in Geotechnical Engineering, Philadelphia, pp 1-104, September 27 - October 1. Seed, H.B., R.B. Seed, L.F. Harder and H.L. Jong (1988). "Re-evaluation of the Slide in the Lower San Fernando Dam in the Earthquake of February 9, 1971", Report No. UCB/EERC-88/04, University of California, Berkeley, CA. Seed, H.B., K. Tokimatsu, L.F. Harder and R.M. Chung (1985). "Influence of SPT Procedures in Soil Liquefaction Resistance Evaluations", Journal of the Geotechnical Engineering Division, ASCE, Vol. 3, No. 12, December. Seed, H.B., R.T. Wong, I.M. Idriss and T. Tokimatsu (1984). "Moduli and Damping Factors for Dynamic Analyses of Cohesionless Soils", Report No. UCB/EERC-84/14, Earthquake Engineering Research Centre, University of California, Berkeley, CA, September. » Seed, H.B. and I.M. Idriss (1982). "Ground Motions and Soil Liquefaction During Earthquakes", EERI Monograph No. 5, Earthquake Engineering Research Institute. Seed, H.B. and I.M. Idriss (1982). "Evaluation of Liquefaction Potential using Field Performance Data", Journal of Geotechnical Engineering, ASCE, Vol. ,-No. . Seed., H.B., I.M. Idriss and I. Arango (1981). "Evaluation of Liquefaction Potential using Field Performance Data", ASCE, Convention presentation and Journal of GED, Volume 109, No. 3, pp 458-482. Seed, H.B., I.M. Idriss, F. Makdisi, and N. Banerjee (1975). "Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in Liquefaction Analysis", Report No. EERC 75-29, Earthquake Engineering Research Centre, University of California, Berkeley, CA. Seed, H.B. and I.M. Idriss (1971). "Simplified Procedure for Evaluating Soil Liquefaction Potential", Journal, Soil Mechanics and Foundation Engineering, ASCE, Volume 97, No. SM9, pp 1249-1273. Seed, H.B. and I.M. Idriss (1970). "Soil Modulus and Damping Factors for Dynamic Response Analyses", Report No. EERC 70-10, Earthquake Engineering Research Centre, University of California, Berkeley, California, December. Seed, R.B. and L.F. Harder (1990). "SPT-based Analysis of Cyclic Pore Pressure Generation and Undrained Residual Strength"; Proc. H. Bolton Seed Memorial Symposium, Berkeley, California, pp. 351-377. Sun, J.I., R. Golesorkhi, and H.B. Seed (1988). "Dynamic Moduli and Damping Ratios for Cohesive Soils", Report No. UCB/EERC-88/15, Earthquake Engineering Research Centre, University of California, Berkeley, CA, August. - 143- References U.S. Bureau of Reclamation (1989). "Design Standards: Embankment Dams No. 13, Chapter 13, Seismic Design and Analysis", U.S. Bureau of Reclamation, Denver Office, Denver, Colorado. U.S. Army Corps of Engineers (USACE) St. Louis District, 1988. "Earthquake Study for Wappapello Dam, Missouri", September, 29. U.S. Army Engineering District (USAED)-St. Louis, 1981. "Earthquake Potential of St. Louis District". St. Louis, Missouri. Vaid, Y.P. and J.C. Chem (1985). "Cyclic and Monotonic Undrained Response of Saturated Sands", ASCE National Convention, Session - Advances in the Art of Testing Soils Under Cyclic Loading, Detroit, October 21-25, pp. 120-147. Wahl, R.E. and G.W. Deer, 1982. "One-dimensional Dynamic Analysis of the Liquefaction Potential of the Foundation Materials of Wappapello Dam", report prepared for the U.S. Army Engineer District, Memphis, Term., U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Report Number GL-82, November. Wang, W. (1979). "Some Findings in Soil Liquefaction", Water Conservancy and Hydroelectric Power Scientific Research Institute, Beijing, China, August. Yogendrakumar, M. and W.D.L. Finn (1986a). "SIMCYC2: A Program for Simulating Cyclic Simple Shear Tests on Dry or Saturated Sands", Report, Soil Dynamics Group, Department of Civil Engineering, University of British Columbia, Vancouver, Canada, November. Yogendrakumar, M. and W.D.L. Finn (1986b). "C-PRO: A Program for Evaluating the Constants in the Martin-Finn-Seed Pore Water Pressure Model", Soil Dynamics Group, Department of Civil Engineering, University of British Columbia, Vancouver, Canada, November. (4+ APPENDIX I CURRENT DESIGN PROCEDURES FOR THE EVALUATION OF LIQUEFACTION RESISTANCE FOR SATURATED COHESIONLESS SOILS /4f -1-2 - Appendix I EVALUATION OF LIQUEFACTION RESISTANCE One of the most widely used methods of evaluating the liquefaction resistance of cohesionless soils is to compare the cyclic shear stresses induced by an earthquake with those materials which, on the basis of field experience for soils of known penetration resistance, have or have not liquefied during earthquakes. The liquefaction resistance, expressed in terms of the cyclic stress resistance, CSR, is best evaluated, at present, by correlation relationships of CSR to standard penetration test, SPT, N data or cone penetration test, CPT, data. The following sections outline the procedures for determining the liquefaction resistance of saturated cohesionless soils. 1 SPT Procedure and Equipment In order to use reliable SPT N data for comparison with the established database, however, the SPT procedure and equipment must first be well defined as variations in either the SPT testing procedures or SPT equipment result in different N values for the same type and density of soil. Table 1-1 summarizes the standard equipment and procedures recommended by Seed, et al (1984). Hfc 1-2- Appendix I Table 1-1 - Recommended Standardized SPT Equipment and Procedures (Seed et al, 1984) Sampler Drill Rods Energy Delivered to Sampler Blow Count Rate Penetration Resistance Count Standard sampler with : a) OD = 2.00 inches; and b) ID = 1.375 inches (constant - i.e. no room for liner in the barrel). A or AW for depths less than 50 feet N or NW for greater depths 2520 inches-lbs (60% of theoretical free fall maximum) Note: The usual hammer weight is 140 lbs, and the usual free fall height is 30 inches. 30 to 40 blows per minute Measured over a range of 6 to 18 inches of penetration into the ground Typically, the rope and cathead system with two turns of the rope about the cathead combined with the standardized SPT procedures in Table 1-1 deliver approximately 60% of the theoretical "freefall" hammer energy to the system. Different types of hammer (eg. donut) or different types of drop mechanisms (eg. automatic, mechanical "trip" hammers, or "free fall" hammers) can impart different energy levels to the top of the drill stem. The energy ratio, ER, which is defined as the percent ratio of the energy imparted to the drill stem to the theoretical free fall energy (i.e. efficiency), must be known or measured for each system. The ER can be measured directly using a pile analyzer. The recorded blow counts, N, must be therefore corrected to the standardized blow count (N)^, where the ER of the standard system is assumed to be 60%, by the following equation: N^N ER 60% (1-1) An additional correction may be required if an internal sample liner or tube is included in the ASTM standard sampler. This liner causes a reduction in the frictional drag inside ( 4 T -1-3- Appendix I the sampler, thus lowering the N values recorded by 10 to 30% ( with increasing percentage change with increasing blow counts). 1-1.2 Computation of the CSR from SPT N Data The Nfn values obtained from the SPT must be further corrected to account for the effect of overburden stress. The standardized penetration resistance, N^, is normalized to an effective overburden stress of 1 tsf (1 kg/cm2) and expressed as (Nj)^ by the following equation: (Ndeo " ^60 x CN (I-2) where CN = overburden correction factor shown in Figure 1-1 for sandy soils; or 1/CO"2 (Liao and Whitman, 1985) where a'a = effective overburden pressure (in tsf) Figure 1-1 - Chart of CN Values (Seed and Harder, 1990) -1-4 - Appendix I After computing the (N,)^ value, the liquefaction resistance is evaluated by using the empirically derived correlation relationship developed by Seed and his colleagues, shown in Figure 1-2. The liquefaction resistance is represented by the equivalent uniform cyclic stress ratio, CSR, required to trigger liquefaction during an earthquake with a duration (or number of loading cycles) representative of a typical earthquake with a M of 7.5. The CSR if defined as: CSR = - ^ (1-3) a'o where Thvc = cyclic shear stress acting on a horizontal plane <?'0 = effective overburden stress The relationship shown in Figure 1-2 has different plots to account for the influence of different fines content on the (N,^ values. If earthquake magnitudes, M, other than 7.5 are used, the CSR obtained from Figure 1-2, must be corrected. This correction is based on the assumption that earthquakes of larger magnitudes tend to produce a longer duration of shaking or greater number of cycles of loading. Seed et al (1975) and Seed and Idriss (1982) developed a correlation between the typical or average number of equivalent uniform loading cycles for different magnitude events. This correlation is summarized in Table 1-2. m -1-5- Appendix i (N,)60 Figure 1-2 - Relationship Between Cyclic Stress Ratio Causing Liquefaction and re-values for M=7 1/2 Earthquakes (Seed et al, 1984) Table 1-2 - Relationship Between Magnitude, Number of Equivalent Uniform Loading Cycles, and Liquefaction Resistance Factor CM EARTHQUAKE MAGNITUDE 8.5 7.5 6.75 6 5.25 # OF REPRESENTATIVE CYCLES AT 0 . 6 5 1 ^ ™ 26 15 10 5 TO 6 2 TO 3 MAGNITUDE OR DURATION CORRECTION FACTOR, CM 0.89 1.0 1.13 1.32 1.5 fro -1-6 - Appendix I For earthquakes of magnitudes other than 7.5, the value of CSR, obtained from Figure 1-2 can be corrected to the appropriate C S R , ^ ^ by: CSRt(t/hMj = CSR,(M=7S) CM (> where C S R , ^ , ^ = CSR at the appropriate magnitude, M CSRJ(M=7 5) = CSR at M = 7.5 obtained from Figure 1-2 CM = Magnitude or duration correction factor obtained from Table 1-2 While soils generally develop higher cyclic load resistances with increasing confining pressures, the normalized resistance expressed in terms of CSR, usually decreases with increasing confinement. An additional correction factor, K„, must be applied to the CSR, obtained from Figure 1-2, if the initial effective overburden stresses are greater than 1 tsf. CSR, is corrected by the following equation: CSR..J „A = CSR.., 1W1 K (1-6) where CSR,(a.0=o.) = CSR corrected for overburden stress, a0, greater than 1 tsf CSR|(„.0) = CSR for o ' 0 less than 1 tsf obtained from Figure 1-2 K„ = overburden correction factor obtained from Figure 1-3 ( T i -1-7 • Appendix I i.2°riy-i° 2.0 3.0 4.0 5.0 6 .0 70 8.0 I.O 0.8 0.6 0.4 0.2 \ \ . \ 8 O i - 2 • (««MMN| 6AM # ( « « ( A#NKH»Mf*0^O*4l ^r v « r r < « o C * M 1*1*11 Q © U*4-f« SAN 4IAWONO 0«« SffCLl V t<H*** SAM «««MAMOO M « SHCtt A t * # f « SAW f(«*tA«tOO ©*W SMCLl A «OS AMCClCSOM* SMfiL T « • • « * 0 * « S M C L L . « C « M . I 0 0 % O 5*«04S CAM SM<l.l O i*«ots OAM roi*to*t*o« • |Mf MWAillO AflCKCA* OAM fOUMOAIfON • lM««niAttfO fO*C«AT 0 * « fOUMOAftOK Q * * » i f i o n OAW ****** v»Ou$ MAfCMtAl O foftt rtc* CMW S M C I I O S«C«AM| WtO NtvCM 1**0, O* « M . «0. M . iOO% • ttONttfltY O S**C. O* * M % U HtlO MO<0«f> S*«0. O* * 4 0 , « 0 % f-1.0 . 2.0 3.0 4.0 5.0 6.0 EFFECTIVE CONFINING PRESSURE t lsf ) or (kscl 7.0 8.0 Figure 1-3 - Relationship Between Effective Vertical Stress and K^ (Seed and Harder, 1990) The presence of initial static shear stresses in the soil decreases the resistance of the soil to pore pressure generation and increases the accumulation of shear strains in the soil under cyclic loading. Since most of the data in Figure 1-2 had no initial static shear stresses, the cyclic stress ratio obtained from that correlation must be corrected by K^  if initial static shear stresses are present CSR, is corrected by: OSRl{a^a) - CS/? / ( a=0 ) Ka (1-6) where CSR,(a=a) = CSR where static shear stresses are present -1-8 - Appendix I ^SRt(a=0) = CSR obtained from Figure 1-2 where no static stresses are present K,, = correction factor for the presence of static shear stresses obtained from Figure 1-4 a = ratio of \Jo\ Figure 1-4 shows that K„ could both increase the CSRj (for K„ > 1) as well as decrease the CSR, (for K^ < 1). Early studies by Seed indicated that the presence of static shear on a horizontal plane significantly increased the resistance to liquefaction. However, this is only true for soils that act dilatively under unidirectional shearing. Other studies, conversely, have shown that for contractive soils under unidirectional shearing, the presence of static shear decreases the liquefaction resistance. A knowledge of the contractive or dilative nature of the soil is required in establishing the effect of K„. Generally, relatively dense soils are considered dilative and loose soils are contractive. 2.0, , 1 - ; . , , , , • , . . , , , . , , . I.! I.I 0.5 I Q^'jg3tsf O' 1 1 i i I O 0.1 0.2 0.3 0.4 0 5 oC Figure 1-4 - Relationship Between a and K^  (Seed and Harder, 1990) 0, = 55-70%V A / / - - ' y - -4 >'W y y ,-' ix s^ — • ^ ^ • ""^F s^ \ v^ v \ " ^ ^ 0, « 45-50% X X V s. \ X \ \ \ X \ ^ Df =? 35% s ^ \ ^ \ -^ o ?». oc o: (S3 -1-9 - Appendix I In summary, in order to find the correct CSR^ the following soil parameters must be known: 1- ( N , ) ^ 2. fines content; 3. earthquake magnitude or number of equivalent loading cycles; 4. initial effective overburden stress, a'0; 5. initial static shear stresses, xhv; and the CSR, obtained from Figure 1-2 must be corrected by: CSRIJMd = CSR, Cu Ka Ka (1-7) where CSR, fieM = CSR corrected for the site conditions CSR, = CSR obtained from Figure 1-2 CM = earthquake magnitude correction factor Ka = correction factor for effective overburden stress > 1 tsf K„ = correction factor for presence of static shear stress (54 -1-10 - Appendix I REFERENCES Liao, S.C. and R.V. Whitman (1985). "Overburden Correction Factors for SPT in Sand", JGED, ASCE, Volume 112, No. 3, pp 373-377. Seed, H.B., K. Tokimatsu, L.F. Harder and R. Chung (1984). "The Influence of SPT Procedures in Soil Liquefaction Resistance Evaluations", Report No. UCB/EERC-84/15, University of California, Berkeley, U.S.A. Seed, H.B. and I.M. Idriss (1982). "Ground Motions and Soil Liquefaction During Earthquakes", EERI Monograph, Earthquake Engineering Research Institute. Seed, H.B., I.M. Idriss, F. Makdisi, and N. Banerjee (1975). "Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in Liquefaction Analyses", Report No. UCB/EERC-75/29, University of California, Berkeley, U.S.A. 

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