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HomeMy WebLinkAboutBradley Lake Final Supporting Design Report Vol 3 1988Alaska Power Authority FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT BRADLEY LAKE HYDROELECTRIC PROJECT FEDERAL ENERGY REGULATORY COMMISSION PROJECT NO. P-8221-000 VOLUME 3 DAM AND SPILLWAY STABILITY ANALYSIS Prepared By STONE & WEBSTER ENGINEERING CORPORATION MARCH 1988 TABLE OF CONTENTS TABLE OF CONTENTS FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 1 -REPORT VOLUME 2 -DESIGN CRITERIA VOLUME 3 -DAM AND SPILLWAY STABILITY ANALYSIS VOLUME 4 -CALCULATIONS VOLUME 5 -CALCULATIONS VOLUME 6 -CALCULATIONS VOLUME 7 -CALCULATIONS VOLUME 8 -CALCULATIONS VOLUME 9 -CALCULATIONS 0216R-4460R/CG 1 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 1 REPORT 1.0 INTRODUCTION 2.0 DESIGN AND GENERAL TECHNICAL DATA 2.1 DESIGN 2.2 DESIGN LOADS 2.3 STABILITY CRITERIA 2.4 MATERIAL PROPERTIES 2.5 GENERAL TECHNICAL DATA 3.0 SUITABILITY ASSESSMENT 3.1 SPECIFIC ASSESSMENTS 4.0 GEOTECHNICAL INVESTIGATIONS 4.1 CHRONOLOGY OF INVESTIGATIONS 4.2 BORING LOGS, GEOLOGICAL REPORTS AND LABORATORY TEST RESULTS 5.0 BORROW AREAS AND QUARRY SITES 5.1 BORROW AND QUARRY AREAS 5. 2 OTHER MATERIAL SOURCES 6.0 STABILITY AND STRESS ANALYSIS 6.1 GENERAL 6.2 DIVERSION TUNNEL INCLUDING INTAKE STRUCTURE 6. 3 MAIN DAM 6.4 SPILLWAY 6.5 POWER TUNNEL AND PENSTOCKS 6.6 POWERHOUSE/SUBSTATION EXCAVATION, COFFERDAM AND TAILRACE CHANNEL 6.7 POWERHOUSE 6.8 REFERENCES 7.0 BASIS FOR SEISMIC LOADING 7.1 GENERAL 7.2 SEISMOTECTONIC SETTING 7.3 SEISMIC DESIGN 0216R-4460R/CG 11 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 1 REPORT 8.0 SPILLWAY DESIGN FLOOD BASIS 8.1 STUDY METHODOLOGY 8.2 WATERSHED MODEL CALIBRATION 8.3 PROBABLE MAXIMUM FLOOD 8.4 SPILLWAY DESIGN FLOOD 8.5 MODEL TEST 9.0 BOARD OF CONSULTANTS 9.1 INDEPENDENT BOARD OF CONSULTANTS 9.2 FERC BOARD OF CONSULTANTS APPENDIX A Plates Exhibit F 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 Figures F.6.2-5 F.6.2-6 DRAWINGS Title General Plan General Arrangement -Dam, Spillway and Flow Structures Concrete Faced Rockfill Dam -Sections and Details Spillway -Plan, Elevations and Sections Power Conduit Profile and Details Intake Channel and Power Tunnel Gate Shaft -Sections and Details Civil Construction Excavation at Powerhouse -Plan Civil Construction Excavation at Powerhouse -Elevations 90 MW Pelton Powerhouse Construction Diversion -Sections and Details Main Dam Diversion -Channel Improvements General Arrangement -Permanent Camp and Powerhouse Barge Dock Powerhouse Substation and Bradley Junction Main One Line Diagram Martin River Borrow Area Waterfowl Nesting Area Powerhouse Access Roads Mean Horizontal Response Spectrum Design Accelerogram 0216R-4460R/CG 111 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 1 REPORT APPENDIX B ATTACHMENTS B.l Construction Schedule Contract Dates B.2 Meetings of the Independent Board of Consultants Meeting No. 1 Meeting No. 2 Meeting No. 3 Meeting No. 4 Meeting No. 5 Meeting No. 6 Meeting No. 7 Meeting No. 8 Meeting No. 9 Meeting No. 10 May 12 and 13, 1983 July 11 to 15, 1983 September 25 to 27, 1984 November 4 and 5, 1985 with response of November 25, 1985 January 28, 1986 May 6 to 8, 1986 with response dated May 21, 1986 August 12 to 14, 1986 with response dated October 20, 1986 December 8 to 10, 1986 Site Visit by Mr. A. Merritt on December 11, 1986 May 5 to 1, 1987 December 17 and 18, 1987 B.3 Meetings of the FERC Board of Consultants Meeting No. 1 Meeting No. 2 March 6 and 7, 1986 May 28 and 29, 1986 with response dated July 11, 1986 Hydraulic Model Test of Spillway July 9, 1986 Meeting No. 3 August 18 to 20, 1986 with response dated October 28, 1986 Meeting No. 4 Meeting No. 5 Meeting No. 6 0216R-4460R/CG Hydraulic Model Test Spillway and Diversion Tunnel August 29 and September 25, 1986 January 27, 1987 with response dated January 29, 1987 May 26 to 28, 1987 with response December 7 and 8, 1987 with response lV TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 2 DESIGN CRITERIA 1.0 Civil Design Criteria 2.0 Geotechnical Design Criteria 3.0 Structural Design Criteria Part A General Design Criteria Part B Special Requirements for Major Structures Section 1. Section 2. Section 3. Section 4. Section 5. Section 7. Main Dam Diversion Main Dam Spillway Power Tunnel Lining, Intake and Gate Shaft Steel Liner and Penstock Tailrace 4.0 Hydraulic Design Criteria 1. Main Dam Diversion 2. Tailrace 3. Hydraulic Turbines, Governors and Spherical Valves 4. Spillway 5. Power Intake, Tunnel and Penstock 5.0 Architectural Design Criteria 0216R-4460/CG v TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 3 DAM AND SPILLWAY STABILITY ANALYSIS DAM STABILITY REPORT Section Section Title 1.0 INTRODUCTION 1.1 PURPOSE 1.2 SCOPE 1.3 DAM SAFETY CRITERIA 2.0 DESCRIPTION OF PROJECT FEATURES 2.1 GENERAL 2.2 MAIN DAM 2.3 UPSTREAM COFFERDAM 3.0 DESIGN EARTHQUAKE REGIME 3.1 SEISMOTECTONIC SETTING 3.2 DESIGN RESPONSE SPECTRA 3.3 ACCELEROGRAM DEVELOPMENT 4.0 ALTERNATIVE METHODS OF ANALYSIS 4.1 GENERAL STABILITY CRITERIA 4.2 PSEUDOSTATIC METHOD 4.3 SARMA/NEWMARK METHOD 4.4 FINITE ELEMENT METHOD 4.5 SELECTION OF SARMA METHOD 5.0 SARMA ANALYSIS METHODOLOGY 5.1 MATERIALS PROPERTIES AND EARTHQUAKE SELECTION 5.2 LEASE II ANALYSIS 5.2.1 Static Analysis 5.2.2 Critical Circles and Accelerations 5.3 SARMA ANALYSIS 5.3.1 Data Requirements 5.3.2 Processing 5.3.3 Analytical Output 5.3.4 Significance of Results 6.0 BRADLEY LAKE EMBANKMENT ANALYSES 6.1 EARTHQUAKE RECORDS 6.2 INPUT PARAMETERS 6.3 DESIGN CASES 6.4 LEASE II ANALYSES 6.5 SARMA ANALYSES 6.6 INTERPRETATION OF RESULTS 0216R-4460R/CG Vl TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 3 DAM AND SPILLWAY STABILITY ANALYSIS Section Section Title 7.0 8.0 6.7 6.7.1 6.7.2 6.7.3 6.7.4 6.7.5 6.7.6 6.7.7 6.7.8 6.8 7.1 7.2 7.3 7.4 SPECIAL STUDIES Megathrust (a = .55g) DBE (ah = .375g) Influence of Downstream Berm Failed Concrete Face Varying Embankment Height Planar Slip Surfaces La Union Accelerogram Parametric Analyses COFFERDAM CONCLUSION CRITICAL CASES SUMMARY OF CRITICAL FAILURE SURFACES PREDICTED DISPLACEMENTS RESPONSE TO VARIOUS EVENTS BIBLIOGRAPHY LIST OF FIGURES Figure Title 1 Project Location Map 2 Main Dam Area -General Arrangment 3 Main Dam Sections 4 (Not Used) 5 MCE Response Spectra -Mean and Chosen 6 Rockfill Friction Angles 7 Intermediate av/ah Ratio 8 Selected Sliding Surfaces -Main Dam 9 Critical Acceleration Plots 10 Permanent Deformation Plots 11 MCE Response/Displacement Plots 12 Megathrust Response/Displacement Plots 13 DBE Response/Displacement Plots 14 Flow Through Dam Without Face 15 Dam Height vs. Acceleration and Displacement 16 Wedge Stability: Sloped Sliding Planes 17 Wedge Stability: Horizontal Sliding Planes 18 La Union Response/Displacement Plots 19 Response Spectrum -La Union E-W Record 20 Response Spectrum -Taft Record 21 Arias Intensity 22 Taft Response/Displacement Plot 0216R-4460R/CG Vll TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 3 DAM AND SPILLWAY STABILITY ANALYSIS SPILLWAY STABILITY REPORT Section 1.0 INTRODUCTION 1.1 PURPOSE 1.2 SCOPE 1.3 SPILLWAY SAFETY CRITERIA 2.0 DESCRIPTION OF PROJECT FEATURES 2.1 GENERAL 2.2 OGEE SECTION 2.3 NON-OVERFLOW SECTIONS 2.4 GEOLOGIC CONDITIONS 3.0 DESIGN EARTHQUAKE REGIME 3.1 SEISMOTECTONIC SETTING 3.2 DESIGN RESPONSE SPECTRA 3.3 ACCELEROGRAM DEVELOPMENT 4.0 STABILITY CRITERIA 4.1 GENERAL 4.2 LOADS 4.2.1 Deadweight 4.2.2 Ice 4.2.3 Hydrostatic 4.2.4 Earthquake 4.2.5 Wind 4.2.6 Up1 ift 4.2.7 Temperature 4.3 LOADING CONDITIONS 4.4 ACCEPTANCE CRITERIA 4.4.1 Stability Requirements 4.4.2 Minimum Allowable Stress 4.4.3 Shear-Friction Factor of Safety 5.0 METHODS OF ANALYSIS 5.1 STATIC METHOD 5.2 FINITE ELEMENT METHOD 5.3 SARMA METHOD 6.0 STATIC ANALYSIS 6.1 STABILITY ANALYSIS 6.2 RESULTS 7.0 FINITE ELEMENT ANALYSIS 7.1 STRESS ANALYSIS 7.2 RESULTS 0216R-4460R/CG Vlll Section 8.0 8.1 8.2 9.0 9.1 9.2 10.0 Figure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0216R-4460R/CG TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 3 DAM AND SPILLWAY STABILITY ANALYSIS Section Title SARMA ANALYSIS STABILITY ANALYSIS RESULTS CONCLUSIONS CRITICAL CASES SUMMARY OF STABILITY CONDITIONS BIBLIOGRAPHY LIST OF FIGURES Title Project Layout Map General Arrangement -Main Dam Area General Arrangement -Spillway Project Response Spectra Hybrid Accelerogram Static Spillway Model Case I -Static Analysis-Base El 1124 Case II -Static Analysis-Base El 1124 Case IV -Static Analysis-Base El 1124 Finite Element Model -Base El 1160 Finite Element Model -Base El 1150 Finite Element Model -Base El 1124 Finite Element Analysis: Case III -Max. Tensile Stresses -Base El 1160 Finite Element Analysis: Case III -Max. Compressive Stresses -Base El 1160 Finite Element Analysis: Case V -Max. Tensile Stresses - Base El 1160 Finite Element Analysis: Stresses -Base El 1160 Finite Element Analysis: -Base El 1150 Finite Element Analysis: Stresses -Base El 1150 Finite Element Analysis: Base El 1150 Finite Element Stresses -Base Finite Element -Base El 1124 Analysis: El 1150 Analysis: lX Case V Max. Compressive Case III -Max. Tensile Stresses Case III -Max. Compressive Case V -Max. Tensile Stresses - Case V -Max. Compressive Case III -Max. Tensile Stresses Figure 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 0216R-4460R/CG TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 3 DAM AND SPILLWAY STABILITY ANALYSIS LIST OF FIGURES Title Finite Element Analysis: Case III Max. Compressive Stresses -Base El 1124 Finite Element Analysis: Case V -Max. Tensile Stresses - Base El 1124 Finite Element Analysis: Case V Max. Compressive Stresses -Base El 1124 SARMA Analysis Model, Ogee Sections-Sheet 1 SARMA Analysis Model, Ogee Sections -Sheet 2 SARMA Analysis Model, Non-Overflow Sections SARMA Analysis: Base El 1160 -Ogee SARMA Analysis: Base El 1150 -Ogee SARMA Analysis: Base El 1130 -Ogee SARMA Analysis: Base El 1124 -Ogee SARMA Analysis: Base El 1160 -Left Abutment SARMA Analysis: Base El 1124 -Right Abutment Spillway Stability Analysis Summary -Sheet 1 Spillway Stability Analysis Summary -Sheet 2 Spillway Stability Analysis Summary -Sheet 3 X HYDRAULIC TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 4 CALCULATIONS Calculation Title No. SPILLWAY CREST SHAPE H-027 FLOOD ROUTING -P.M.F. THROUGH SPILLWAY H-028 FLOOD ROUTING -FLOOD OF RECORD THROUGH H-033 BRADLEY LAKE & DIVERSION TUNNEL DESIGN THRUSTS -POWER PENSTOCK NEAR H-036 MANIFOLD SIMPLIFIED DAM BREAK ANALYSES AND WATER H-046 SURFACES PROFILES WAVE RUNUP AND FORCE ON DAM PARAPET H-048 TAILRACE CHANNEL SLOPE PROTECTION H-050 PROTECTION AGAINST WAVES FOR THE H-066 UPSTREAM COFFERDAM & POWER TUNNEL INTAKE ROCK PLUG ICE FORCE ON DAM PARAPET H-068 INVESTIGATION OF NEED FOR AERATION OF SPILLWAY FLOW H-077 RIPRAP DESIGN H-079 FILLING BRADLEY LAKE RESERVOIR H-081 0216R-4460R/CG Xl TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 5 CALCULATIONS GEOTECHNICAL Title ROCK STRESS IN CIRCULAR TUNNEL LININGS AND SELECTION OF EXTERNAL WATER PRESSURE CRITERIA GROUND WATER SEEPAGE LOADS ON DIVERSION TUNNEL LINER VERIFICATION OF INTAKE GEOMETRY FOR THE POWER AND DIVERSION INTAKES AT THE BRADLEY LAKE RESERVOIR EXTERNAL ROCK & GROUND WATER LOADS ON POWER INTAKE AND GATE SHAFT STRUCTURES FINAL STABILITY ANALYSIS: BRADLEY LAKE MAIN DAM PENSTOCK -MANIFOLD THRUST BLOCK EMBEDMENT LENGTH AND STABILITY ANALYSIS ROCK MODULI FOR POWER TUNNEL TRANSIENT STUDY DESIGN OF ROCK SUPPORT FOR THE MAIN POWER INTAKE STRUCTURE PLINTH AND TOE SLAB GEOMETRY -MAIN DAM 0216R-4460R/CG Xll Calculation No. G(Ak)-04 G(Ak)-08 G(Ak)-10 G(Ak)-22 G(D)-24 G(Ak)-29 G(Ak)-31 G(Ak)-35 G(D)-38 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 6 CALCULATIONS GEOTECHNICAL Calculation Title No. GROUNDWATER INFLOW & LEAKAGE INTO POWER TUNNEL G(Ak)-41 EVALUATION OF SHEAR STRENGTH OF ROCK MASSES AT THE BRADLEY LAKE SITE G(Ak)-47 EVALUATION OF EXTERNAL LOADS ON POWER TUNNEL LINER G(Ak)-48 VERIFICATION OF CONFINEMENT TO PREVENT HYDRAULIC JACKING OF THE POWER TUNNEL G(Ak)-49 TAILRACE SLOPE STABILITY & PROTECTION G(A)-50 DESIGN OF ROCK BOLTS FOR DIVERSION G(A)-58 TUNNEL & GATE SHAFTS DAM TOE PLINTH LOADS G(A)-60 POWER TUNNEL INTAKE EXCAVATION DESIGN MANIFOLD & PENSTOCK THRUSTBLOCK STABILITY CONSIDERING SHEAR ZONE FEATURE POWERHOUSE CELLULAR SHEETPILE COFFERDAM STABILITY ANALYSIS EVALUATION OF CONCRETE LINER REQUIREMENTS FOR THE MAIN POWER TUNNEL MAIN DAM FACE SLAB DESIGN SPILLWAY: SARMA DISPLACEMENT ANALYSIS SPILLWAY OF THE UPSTREAM COFFERDAM TOE AND ABUTMENT PLINTH DOWEL EMBED. LENGTHS AND QUANTITIES 0216R-4460R/CG Xlll G -70 G -86 G(Ak)-89 G(Ak)-90 G(Ak)-93 G -98 G -104 G -106 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 7 CALCULATIONS STRUCTURAL Title WIND LOADS FOR DESIGN CRITERIA SNOW & ICE LOADS FOR DESIGN CRITERIA SEISMIC DESIGN DATA MAIN DAM DIVERSION TUNNEL LINING AND GATE CHAMBER ANALYSIS POWER TUNNEL INTAKE POWER TUNNEL GATE CHAMBER AND LINING DESIGN AND ANALYSIS GATEHOUSE CONCRETE STRUCTURE 0216R-4460R/CG XlV Calculation No. SDC.l SDC.2 SDC.3 SC-133-3 SC-151-16 SC-152-21 SC-152-32 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 8 CALCULATIONS STRUCTURAL Title DAM PARAPET MAIN DAM TOE PLINTH DESIGN SEGMENTS A, B, C, D ABUTMENT DESIGN SPILLWAY STABILITY ANALYSIS - STATIC ANALYSIS FINITE ELEMENT ANALYSIS OF SPILLWAY FOR SEISMIC LOAD COMBINED WITH DEAD WEIGHT, ICE THRUST, AND WATER LOADS SPILLWAY TRAINING WALLS 0216R-4460R/CG XV Calculation SC-191-26 SC-191-27 SC-191-29 SC-201-8A SC-201-34 SC-205-23 TABLE OF CONTENTS (Continued) FINAL SUPPORTING DESIGN REPORT GENERAL CIVIL CONSTRUCTION CONTRACT VOLUME 9 CALCULATIONS STRUCTURAL PENSTOCK AND MANIFOLD ANCHOR BLOCKS MAIN DIVERSION & MAIN INTAKE BULKHEADS MAIN DAM DIVERSION PENSTOCK DESIGN POWER TUNNEL INTAKE TRASH RACKS POWER PENSTOCK THRUST RINGS AND MISC. COMPONENTS REQUIRED THICKNESS OF STEEL LINER UNDER INTERNAL AND EXTERNAL PRESSURE STRESS ANALYSIS OF FLANGE WITH 108" INSIDE DIAMETER LOCAL STRESSES DUE TO GEOMETRY DISCONTINUITY AT REDUCERS AND MITERED ELBOWS REQUIRED THICKNESS OF ELLIPSOIDAL HEADS FOR PENSTOCK STRESS ANALYSIS OF POWER PENSTOCK WYE BRANCH PENSTOCK ACCESS FLANGE BOLTS 0216R-4460R/CG xvi Calculation No. SC-261-25 SS-132-2 SS-134-12 SS-153-10 SS-261-16A SS-261-17A SS-261-178 SS-261-17C SS-261-17D SS-261-17F SS-261-18 DAM STABILITY REPORT DAM STABILITY REPORT BRADLEY LAKE HYDROELECTRIC PROJECT Prepared for ALASKA POWER AUTHORITY March 1988 STONE & WEBSTER ENGINEERING CORPORATION DENVER, COLORADO 80111 PROJECT NO. P-8221-000 BRADLEY LAKE HYDROELECTRIC PROJECT ALASKA POWER AUTHORITY DAM STABILITY REPORT TABLE OF CONTENTS Section Section Title 1.0 INTRODUCTION 1.1 PURPOSE 1.2 SCOPE 1.3 DAM SAFETY CRITERIA 2.0 DESCRIPTION OF PROJECT FEATURES 2.1 GENERAL 2.2 MAIN DAM 2.3 UPSTREAM COFFERDAM 3.0 DESIGN EARTHQUAKE REGIME 3.1 SEISMOTECTONIC SETTING 3.2 DESIGN RESPONSE SPECTRA 3.3 ACCELEROGRAM DEVELOPMENT 4.0 ALTERNATIVE METHODS OF ANALYSIS 4.1 GENERAL STABILITY CRITERIA 4.2 PSEUDOSTATIC METHOD 4.3 SARMA/NEWMARK METHOD 4.4 FINITE ELEMENT METHOD 4.5 SELECTION OF SARMA METHOD 5.0 SARMA ANALYSIS METHODOLOGY 5.1 MATERIALS PROPERTIES AND EARTHQUAKE SELECTION 5.2 LEASE II ANALYSIS 5.2.1 Static Analysis 5.2.2 Critical Circles and Accelerations 5.3 SARMA ANALYSIS 5.3.1 Data Requirements 5.3.2 Processing 5.3.3 Analytical Output 5.3.4 Significance of Results 4329R/CG Page 1-1 1-1 1-1 1-2 2-1 2-1 2-1 2-2 3-1 3-1 3-3 3-5 4-1 4-1 4-2 4-3 4-4 4-5 5-1 5-1 S-5 S-5 S-6 5-7 S-7 5-9 5-10 5-11 TABLE OF CONTENTS (Cont'd) Section Section Title Page 6.0 BRADLEY LAKE EMBANKMENT ANALYSES 6-1 6.1 EARTHQUAKE RECORDS 6-1 6.2 INPUT PARAMETERS 6-1 6.3 DESIGN CASES 6-3 6.4 LEASE II ANALYSES 6-6 6.5 SARMA ANALYSES 6-8 6.6 INTERPRETATION OF RESULTS 6-8 6.7 SPECIAL STUDIES 6-10 6.7.1 Mega thrust (ah = .SSg) 6-10 6.7.2 DBE (ah = .375g) 6-11 6.7.3 Influence of Downstream Berm 6-12 6.7.4 Failed Concrete Face 6-12 6.7.5 Varying Embankment Height 6-13 6.7.6 Planar Slip Surfaces 6-14 6.7.7 La Union Accelerogram 6-16 6.7.8 Parametric Analyses 6-18 6.8 COFFERDAM 6-20 7.0 CONCLUSIONS 7-1 7.1 CRITICAL CASES 7-1 7.2 SUMMARY OF CRITICAL FAILURE SURFACES 7-2 7.3 PREDICTED DISPLACEMENTS 7-3 7.4 RESPONSE TO VARIOUS EVENTS 7-6 8.0 BIBLIOGRAPHY 8-1 4329R/CG Table 1 2 3 4 5 6 7 8 4329R/CG LIST OF TABLES Title Main Dam Characteristics Main Dam Cofferdam Characteristics Historic Seismic Events Summary Design Factors of Safety Input Parameters Main Dam Static Stability Summary Main Dam SARMA Results SARMA Results-Old Geometry Figure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 4329R/CG LIST OF FIGURES Title Project Location Map Main Dam Area -General Arrangement Main Dam Sections (Not Used) MCE Response Spectra -Mean and Chosen Rockfill Friction Angles Intermediate av/ah Ratio Selected Sliding Surfaces -Main Dam Critical Acceleration Plots Permanent Deformation Plots MCE Response/Displacement Plots Megathrust Response/Displacement Plots DBE Response/Displacement Plots Flow Through Dam Without Face Dam Height vs. Acceleration and Displacement Wedge Stability: Sloped Sliding Planes Wedge Stability: Horizontal Sliding Planes La Union Response/Displacement Plots Response Spectrum -La Union E-W Record Response Spectrum -Taft Record Arias Intensity Taft Response/Displacement Plot 1.0 INTRODUCTION 1.1 PURPOSE The purpose of this stability analysis is to document that the designs of the Bradley Lake Project main darn and cofferdam meet stability criteria established for the site. Figure 1 shows the site location and relationship of the darnsite to other project features. 1.2 SCOPE This report presents results of stability analyses of the Bradley Lake main embankment and the associated upstream cofferdam. The darnsite general arrangement is shown on Figure 2. The Bradley Lake darn embankment was analyzed to determine its factor of safety under various static loading conditions, and to predict its potential deformation under seismic loading conditions. Static cases analyzed include maximum and minimum normal headwater levels, Probable Maximum Flood (PMF), and end of construction conditions. The seismic analyses include estimates of maximum anticipated permanent deformation expected to result from the Maximum Credible Earthquake (MCE), the Design Basis Earthquake (DBE), and an intermediate sized mega thrust event. In addition, parametric studies were performed to determine the sensitivity of the analysis to the relevant variables. 4329R/CG 1-1 1 • 3 DAM SAFETY CRITERIA The basic requirement which must be met by the embankment design is that the reservoir must be retained under all conditions evaluated. Dam safety criteria were established for this analysis to aid in evaluating embankment performance. For static loading conditions, factors of safety were calculated and compared with design criteria minimum safety factors. These minimum safety factors were based on current industry standard practice. The calculated factors of safety were greater than or equal to the recommended minima. For dynamic loading conditions, the safety criteria were in the form of deformation limits since a safety factor is often not relevant to fill structures under dynamic loading. The limit on vertical deformation was loss of one half of the freeboard for permanent structures. The normal maximum headwater level on the main dam leaves 10 ft. of freeboard (not including wave parapet), so the greatest allowable vertical deformation was 5 ft. The limit on horizontal deformation was based on the need to keep the bedding layer beneath the concrete face sufficiently intact in order to limit seepage through the embankment after a major earthquake. 4329R/CG 1-2 2.0 DESCRIPTION OF PROJECT FEATURES 2.1 GENERAL The main dam wi 11 be built at the outlet of Bradley Lake in a rock gorge and will be constructed on an excavated bedrock foundation. The upstream cofferdam will be permanent, providing for future low reservoir level access to the diversion tunnel inlet and providing for potential dam face dewatering. 2.2 MAIN DAM The main dam included in the Bradley Lake Project design is a concrete faced rockfill dam with a design crest length of 602.5 ft. and a maxi-mum height of approximately 120 ft. (Fig. 3). The slopes of the embankment will be 1.6H:lV. The embankment crest width is 18ft plus the wave parapet wall. The concrete face will rest on a bedding layer at least 12 ft. thick (horizontally) composed of angular gravel. The concrete face is topped by a parapet wall four feet high at the upstream edge of the dam crest. The location chosen for the main dam has a relatively steep (near vertical in places) right abutment and a generally more gently sloped left abutment. Table 1 provides a summary of main dam characteristics. 4329R/CG 2-1 2.3 UPSTREAM COFFERDAM The upstream cofferdam (Fig. 4) will not be incorporated into the main dam, but will remain in place to facilitate dewatering of the full concrete face and toe plinth of the main dam. Its slopes will be 2H: lV. It will be approximately 30 ft. high and 200 ft. long. See Table 2 for a sunnnary of cofferdam characteristics. 4329R/CG 2-2 3.0 DESIGN EARTHQUAKE REGIME 3.1 SEISMOTECTONIC SETTING The detailed project seismic design studies and parameters are provided in two reports by Woodward-Clyde Consultants (Ref. 1 and 2). Southern Alaska is one of the world's most seismically active regions. The primary cause of seismic activity in southern Alaska, including the site area, is the stress imposed on the region by the relative motion of the Pacific and the North American tectonic plates at their common boundary. The Pacific plate is moving northward relative to the North American plate at a rate of about 2-1/2 in/yr., causing the underthrusting of the Pacific plate. This underthrusting results primarily in compressional deformation, which causes folds, high-angle reverse faults, and thrust faults to develop in the overlying crust. A counterclockwise rotational effect also induces strike-slip faulting parallel to the plate boundary. The boundary between the plates where the underthrusting occurs is a northwestward-dipping megathrust fault or subduction· zone. The Aleutian Trench marks the surface expression of this subduction zone and is located on the ocean floor approximately 185 miles southeast of Bradley Lake. The orientation of the subduction zone is inferred along a broad inclined band of seismicity, referred to as the Benioff Zone, that dips northwest from 4329R/CG 3-1 the Aleutian Trench, and is approximately 30 miles beneath the surface at the Bradley Lake site. Great earthquakes (Richter magnitude M =8 or s greater) and large earthquakes (M =7 or greater) s have occurred historically throughout the region and can be expected to occur in the future. Historically (1899 to date), eight earthquakes ranging between M =7.4 and M =8.5 have occurred within 500 miles of the site (Ref. 2). s s Table 3 provides a representative summary of significant historic seismic events in the project area. Bradley Lake is situated on the overriding crustal block above the subduction zone and between the Castle Mountain fault to the northwest and the Patton Bay-Hanning faults to the southeast. All of these faults have documented Holocene or historic surface ruptures. Because of the active tectonic environment, activity is conceivable on other faults, such as those found near or on the project site between the known active faults mentioned above. Two faults of regional extent exist at or near the site. The Border Ranges Fault trends southwest beneath Kachemak Bay to the west of the project, and the Eagle River fault crosses the southeastern end of Bradley Lake at about the same trend. While no evidence of recent activity along these faults has been found in the site area, recently defined data indicates recent activity on the Eagle River Fault near Eklutna (125 mi NE of the site). Given the tectonic setting, it is reasonable to consider these faults as potentially active. 4329R/CG 3-2 In addition to the nearby regional faults, the site is crossed by two large local faults, called the Bradley River Fault and the Bull Moose Fault, and a number of probable smaller faults. The dominant trend is northeasterly, paralleling the regional trend. The larger local faults, particularly the Bradley River, are considered as potentially capable of independent earthquake generation, while any of the local faults could possibly move in sympathetic response to earthquakes occurring on the regional faults. It is therefore concluded that the site will probably experience at least one moderate to large earthquake during the life of the proposed project. The possibility of significant ground rupture exists but is much less subject to prediction and is considered to have a much lower probability. 3.2 DESIGN RESPONSE SPECTRA The response spectra considered for this analysis were taken from a report prepared by Woodward-Clyde Consultants (WCC) for the Army Corps of Engineers (Ref. 1). The report documents the work performed by WCC to develop parameters for what the Corps terms the "design maximum earthquake" and the "ope.rational base earthquake", henceforth called Maximum Credible Earthquake and Design Basis Earthquake, respectively. The Maximum Credible Earthquake (MCE) is defined as the most severe earthquake believed to be probable that could affect the site. The Design Basis Earthquake (DBE) is less severe, and it is defined as the seismic level that is considered likely to occur during the life of the project. Maximum Credible Earthquakes are normally used as a basis for determining whether or not 4329R/CG 3-3 certain structures can withstand extreme events having remote probabilities of occurring, regardless of damage level. Design Basis Earthquakes are used as a basis for estimating the maintenance and other costs resulting from events expected to occur, and for design of non-critical structures where severe damage and loss of function in a seismic event is considered an acceptable risk. The response spectra for both the DBE AND MeE will be used in the seismic stability analysis to estimate vertical and horizontal displacements of the dam. Based on their work on the seismicity of the site, wee proposed two possible response spectra for the "design maximum earthquake", the equivalent of the MeE. The one that was expected to control was based on rupture of one of the faults nearest the site. The resulting earthquake would have a magnitude of M =7.5, peak ground acceleration of 0.75g at s the site, and a significant ground motion duration of 25 seconds. This event would have a response spectrum roughly corresponding to the upper smooth curve on Figure 5. The other possible MeE was an event tied to the Benioff Zone roughly 30 miles beneath the site. This event would have a magnitude of M =8. 5, s peak ground acceleration of 0.55g at the site, and a significant ground motion duration of 45 seconds. It was not expected to be the controlling event unless the faults in the immediate vicinity of the site could be shown to be inactive. 4329R/eG 3-4 A third response spectrum proposed by WCC was an event with a peak ground acceleration approximately one half that of the MCE. This was used for the DBE with a peak ground acceleration of 0.35g (Fig. 5). 3.3 ACCELEROGRAM DEVELOPMENT Because the near field crustal M =7.5 s event is more severe than the megathrust M =8.5 event, in terms of both peak parameters and spectral s accelerations throughout the frequency range of interest, an accelerogram for the crustal event is of primary interest. The megathrust event is considered in detail in the WCC reports, but was utilized in design only for parametric comparative purposes. Since all critical structures of the Bradley Lake Project are founded on bedrock, it is desirable to perform seismic analyses based on actual accelerograms recorded on rock from large magnitude earthquakes having similar parameters to those for the crustal event. More importantly, the response spectra of any accelerograms used should match, in an average sense, the curve shown in Figure 5. At the time the analysis was being performed, no accelerograms recorded on rock in the near field of large magnitude earthquakes (M 7.5+) were available anywhere in the United s States, including Alaska. Furthermore, no such comparable record was known to be available from elsewhere in the world. Consequently, available accelerograms from historical earthquakes having appropriate peak and spectral characteristics over a broad period range, even when scaled, were not available for use. 4329R/CG 3-5 To provide the appropriate accelerograms to the COE, WCC developed synthetic accelerograms (Ref. 1). The synthetic accelerograms were developed by taking an existing "real event" accelerogram and modifying its spectral ordinates using a trial-and-error frequency-domain technique. This approach and the resulting accelerograms are valid when the response of the structure analyzed is essentially linear and elastic; as is usually the case for concrete dams, spillways, intake towers, power plant structures, etc. However, for the rockfill dam designed for Bradley Lake by Stone & Webster, WCC' s accelerograms may not be appropriate. The reason is that synthetic accelerograms developed from interactive frequency domain techniques are usually "frequency-rich". That is, this type of synthetic accelerogram is normally characterized by well-ordered frequency components which exist uniformly throughout the record. This is never the case with accelerograms obtained from actual earthquakes, and it may lead to an over-estimation of nonlinear phenomena, such as accumulated displacements in a rockfill dam. To avoid this over-estimation, a composite hybrid accelerogram consisting of historical accelerograms from two earthquakes, having appropriate characteristics, was developed and used for the Bradley Lake Main Dam analyses in lieu of wee's synthetic accelerogram. This approach has been previously used for other studies including those performed by the California Department of Water Resources for Oroville Dam and is considered an appropriate state-of-the-art method for simulation of strong motion events. 4329R/CG 3-6 After examining the response spectra for recorded accelerograms from a number of earthquakes in the United States and abroad, it was cone! uded that a suitable accelerogram for the M =7.5 crustal event could be s obtained by combining the S69°E component of the Taft record from the 1952 Kern County, California earthquake and the East-West component of the San Rocco record from the September 15, 1976 Friuli, Italy earthquake. The Taft record was scaled by a factor of 3. 5 and was used to represent the hybrid earthquake from time 0. 00 to 2. 32 seconds and from 4. 32 seconds to the end. The portion of the Friuli record from time 2.14 to 4.10 seconds was scaled by a factor of 3.2 and inserted into the scaled Taft record, replacing the portion of the Taft record from time 2.34 through 4.30 seconds in the hybrid record. In effect, the portion of the Friuli record with the highest accelerations was spliced into the high-acceleration portion of the Taft record, resulting in a record with greater duration and a greater proportion of relatively high acceleration peaks. The resulting accelerogram, called the Hybrid record, is shown on the displacement plots starting with Figure 11, and its response spectrum is compared to the spectrum recommended by wee in Figure 5. The significant duration of the Hybrid record, defined as the time to reach 95% of the Arias Intensity (Ref. 16), is 28.8 seconds. This is slightly longer than the 25 second MCE proposed by wee. This longer event duration, when combined with the greater density of high acceleration peaks from the combined records, results in a design record which is felt to be conservatively intense and definitely on the "safe" side when used to simulate the project MeE. As 4329R/CG 3-7 will be explained later in the discussion of results, it was not necessary to develop a separate record for the mega thrust event since the magnitude 7.5 crustal earthquake has been demonstrated to be more severe to project structures. 4329R/CG 3-8 4.0 ALTERNATIVE METHODS OF ANALYSIS 4.1 GENERAL STABILITY CRITERIA Stability analysis of an embankment dam is intended to allow prediction of how the embankment will behave under anticipated loading conditions. Generally, the behavior of interest is any movement of the embankment material that might lead to failure of the dam, or secondarily, any change that might cause excessive leakage through the dam. An analysis commonly results either in factors of safety or in estimates of permanent deformation. For static and pseudostatic analyses, stability criteria are most appropriately given in terms of minimum factors of safety acceptable under various loading conditions. The criteria for minimum factors of safety used in the static portion of this analysis are found in Table 4, as modified for the project from Wilson and Marsal, 1979 (Ref. 3). For dynamic analyses, the stability criteria are most appropriately stated as maximum allowable deformations. In the operating case, vertical deformations were limited to one half the normal freeboard, which would be 5 ft. on the main dam. Horizontal deformations that would produce movement in the bedding layer were limited to roughly one half the width of the layer. 4329R/CG 4-1 4.2 PSEUDOSTATIC METHOD For purposes of simplicity, dynamic stability analyses are sometimes done by the pseudostatic method. Dynamic loads are modeled as static forces and a normal static analysis is performed. The dynamic load due to an earthquake. is included as the static force which would result from a steady horizontal acceleration equal to the peak ground acceleration expected from the earthquake. This method is useful in situations where only relatively small peak ground accelerations are expected. In other cases it has some limitations as described below. Perhaps the most obvious limitation of 'the pseudostatic method is that it gives results 1n terms of factors of safety. Thus, its results are readily useable only if no permanent deformation is expected; that is, when the factor of safety is one or greater. Factors of safety less than one are meaningless in this method, and give an indication of total failure. This interpretation is overly conservative for massive structures which can be designed to accommodate movement. The other limitation of the method is that it does not take into account the frequency characteristics of the earthquake or the natural frequency and response of the darn. This is particularly important for earth embankments since their natural frequencies are generally significantly lower than the frequencies associated with the highest accelerations in earthquake accelerograrns. This causes the pseudostatic method to be overly 4329R/CG 4-2 conservative for sites where large peak accelerations are expected. For this reason, the pseudostatic method is not recommended for use with peak ground accelerations greater than 0.2g (Ref. 4). 4.3 SARMA/NEWMARK METHOD This is one of the methods often used to model the response of darns to earthquakes when the pseudostatic method is inappropriate. It is commonly used by the Army Corps of Engineers in modeling for darn design or analysis of existing darns. The Sarma method starts with the calculation of resonant frequencies and response shapes of the embankment for each frequency. The next step is calculation of participation factors for a given potential failure wedge or block. These factors describe how much effect each of the modes of oscillation will have on the potential failure wedge. Once this is accomplished, the accelerations of the wedge in each mode in response to the earthquake accelerograrn are calculated, and the modes are combined. The result is a time-history of the accelerations the wedge would experience as a result of the chosen earthquake. Once the time-history of acceleration of the individual wedge is known, the cumulative displacement is calculated by Newmark's sliding block procedure (Ref. 5). In this procedure, the wedge is assumed to remain fully attached to the rest of the dam as long as the average acceleration of the wedge is less than a specified critical (or break-free) acceleration. When the 4329R/CG 4-3 acceleration exceeds the critical acceleration, the wedge slides relative to the darn until it comes to rest during a subsequent reversal of the acceleration. The total movement of the wedge is the sum of all the increments of movement that occur during a particular earthquake record. Wedges most appropriate for analysis and their respective critical accelerations are calculated using static and pseudostatic analyses. Aside from basic simplifying assumptions such as homogeneity and symmetry of the darn and elastic behavior of the material, a significant limitation of this method is that permanent deformations are assumed to occur along a well-defined failure surface rather than along multiple surfaces. Thus, some care must be used in interpreting the resulting deformations. For example, while movement along a single surface might result in predict ion of a discrete offset of several feet in the concrete face, the same amount of deformation distributed over a significant area of the face along innumerable sliding surfaces would result in a curvature of the face and limited cracking, without large discrete offsets. The latter type of movement is more typical of granular fill structures in earthquakes. Therefore, it is advantageous to analyze a series of different wedges to see how the tendency to deform varies with location in the dam. 4.4 FINITE ELEMENT METHOD The Finite Element Method (FEM) is a widely known computer modeling method that is sometimes applied to embankment dams. It allows somewhat more detailed modeling of the embankment configuration and variations in material 4329R/CG 4-4 properties than the Sarma method. The FEM also generally models stress distributions and transmission of vibrations well, but it does not readily model permanent deformations. As with other methods, the results obtained are dependent on the values chosen for different material properties. With the FEM, the results are dependent to a significant degree on how the structure is modeled. For example, whether the mass is modeled at nodes or distributed through the elements has a significant impact on how the model responds to vibration. For these reasons it is desirable to make numerous runs varying material properties and some other properties of the model to improve the reliability of, or confidence in, the resulting stresses and strains. Since the FEM does not model permanent deformations, another step must be taken in the analysis to compute them. This can take the form of the Newmark sliding block analysis (Ref. 5) or one of a few other methods (Ref. 6). 4.5 SELECTION OF SARMA METHOD The three methods of seismic embankment analysis mentioned above were considered for use in this analysis. The pseudostatic method was quickly eliminated because, with a peak ground acceleration of 0.75g, it would result in a excessively conservative design. After evaluation of the remaining two methods, the Sarma method was chosen based on a number of factors. 4329R/CG 4-5 While the FEM could potentially provide a better approximation of the final shape of the embankment, the magnitude of the deformation is more important than the approximate final shape of the embankment slopes. Permanent deformation magnitudes calculated by the Sarma method are thought to be as realistic as those produced by the FEM, though the Sarma method is thought to be the more conservative. Also the ability of the FEM to model zones within an embankment in some detail is not needed for the largely homogeneous embankment used at Bradley Lake. Thus the FEM, which is markedly more expensive, has little advantage over the Sarma method. Permanent deformation analysis by the FEM requires many of the same simplifying assumptions used by the Sarma method. Both the methods are dependent on a number of variables, some of which are difficult to pick with precision. For instance, the Sarma analysis requires the assumption that the shear wave velocity is constant throughout the embankment. The FEM is dependent to a significant degree on modeling aspects, such as how the mass is distributed in the model, that are easy to overlook or oversimplify. All of the above factors make it desirable to make multiple calculations with whatever method is used, varying the inputs through a reasonable range and trying various potential failure surfaces or modes. In this area the Sarma method has a clear advantage because it is significantly easier and cheaper to use. 4329R/CG 4-6 The Sarma method is widely used and accepted, e.g., by the Army Corps of Engineers, and is considered to be relatively conservative in the way it models and amplifies earthquake accelerograms. Also, deformations calculated using the Sarma method are considered to be as realistic as, and perhaps more conservative than, those predicted by the FEM. Finally, the Sarma method lends itself to parametric studies which would probably not be feasible with the FEM due to constraints of time and expense. For these reasons it was concluded that the Sarma method was the more appropriate method for use in the Bradley Lake main dam analysis. 4320R/CG 4-7 5.0 SARMA ANALYSIS METHODOLOGY 5.1 MATERIAL PROPERTIES AND EARTHQUAKE SELECTION Aside from the geometry of the embankment, several parameters must be chosen to describe the mechanical properties of the fill materials. For static and pseudostatic analyses using the Slope Stability Analysis LEASE II program (Ref. 7), the internal friction angle (0) and the unit weight must be picked for each material. For seismic analyses using the SARMA program (Ref. 8), an average damping ratio (D.R.) and shear wave velocity (V ) must be picked for the embankment. s Values for the four parameters mentioned above can be obtained from laboratory tests or from a review of published values. For rockfill, as opposed to soil, tests to measure 0 are very difficult and expensive and are rarely representative of coarse materials. However, a review of available test results has been published (Ref. 9) which allows a reasonable estimate of 0 to be made. The friction angle varies with several factors. Higher values are associated with more angular, hard, strong particles in a well graded rockfill. Higher values of 0 are also associated with lower confining pressures. These factors and Figure 6 can be used to estimate an appropriate friction angle. The rockfill unit weight can be estimated directly from published values, or based on the unit weight of the source rock and reasonable values of void 4329R/CG 5-l ratio. Using both these approaches increases confidence in the resulting estimate. Shear wave velocity of rockfills can be most readily estimated based on published values and empirical equations (Ref. 10). V is dependent on s confining stress, degree of compaction and the level of strain associated with the wave. Rockfill is significantly stiffer at lower strain levels and experiences strain softening as strain levels increase and as the shaking continues (i.e., the number of cycles of displacement increases). The level of strain must first be estimated and used to choose V . This s V is then used in the calculation to find the level of strain. s Thus, the process is iterative. The damping ratio, similar to V , is most readily obtained from s literature. It is also strain dependent and so must be chosen by an iterative process. The remaining input to the analysis, 1n addition to the darn geometry, is the earthquake record to be used. For the pseudostatic part of the analysis performed by the LEASE II program, the required input is the ratio between vertical and horizontal accelerations. Neglecting vertical acceleration is considered unconservative for sites with fairly large earthquakes, though the Army Corps of Engineers does generally omit the vertical component in their analyses. On the other end of the spectrum, using an av/~ of 2/3 (which is cited as a common ratio of peak a/~) is overly conservative since it assumes a relatively large vertical component occurring simultaneously with the peak horizontal 4329R/CG S-2 component of the earthquake. A compromise between these two extremes, illustrated by Figure 7, was suggested by Dr. A. J. Hendron. The intent of this approach is to find the av/~ ratio which yields the smallest possible resultant acceleration that will be critical for a given wedge. For the purposes of the SARMA program, an accelerogram with appropriate characteristics must be used. Characteristics of the earthquake are site specific and depend on such factors as whether the dam is founded on bedrock, and proximity, length, and geologic type of capable faults. The characteristics of the record which should be examined include significant duration, earthquake magnitude, peak ground acceleration, response spectrum, and source. Significant duration in the current case was quantified as the time between reaching 5% and 95% of the Arias Intensity (Ref. 11). Response spectrum and source are related, since a record of bedrock acceleration generally will have a different frequency content than one recorded on soil or on a foundation not in intimate contact with bedrock. The importance of the above factors is more obvious in some cases than in others. Significant duration is loosely related to the amount of damage an earthquake might be expected to cause. Magnitude affects the amount of energy that an earthquake might be expected to put into a structure and also the distribution of that energy across the range of frequencies. Peak ground acceleration is a parameter widely used to scale the magnitude of records to appropriate levels. The response spectrum of a record is of 4329R/CG 5-3 great significance to the current analysis because the typical earthquake transmits most of its energy at frequencies higher than the natural frequency of an earth or rockfill dam. The dam cannot respond to this higher frequency portion of the record and therefore is not significantly affected by it. Ideally, for a dynamic stability analysis, one would be able to select one or more recorded accelerograms that fit the above parameters. Failing that, a record with an appropriately shaped response spectrum and duration could be scaled up or down to achieve the right peak ground acceleration. If no record is available with the proper duration, existing records can be shortened by removing parts of the accelerogram, or lengthened by repeating some parts or inserting parts of similar accelerograms. In the current analysis, this method of combining accelerograms was used to manufacture the Hybrid accelerogram. The resulting accelerogram fits the mean response spectrum developed by wee significantly better than any of the available natural records. If no earthquake records are available that can be adjusted to be suitable, artificial records (pseudoseismograms) can be generated by filtering white noise to fit a specified duration and response spectrum. These may result in an overly conservative design when inelastic response is expected, as in the case of earth or rockfill dams. 4329R/eG S-4 To illustrate, a response spectrum from an actual earthquake record may show a peak acceleration of 0.4g at a period of 1 second. The actual earthquake may reach that acceleration level at that period only once while the rest of the record does not come close to it. By contrast, a synthetic record created to fit that response spectrum by filtering white noise would contain a continuous component with a 1 second period and 0.4g acceleration. This would make little difference while all motion is elastic, but when permanent deformation is calculated, the synthetic record would most likely result in significantly more pulses of inelastic movement. Thus, this approach to earthquake record generation is overly conservative for the type of analysis under consideration. 5.2 LEASE II ANALYSIS 5.2.1 Static Analysis Once material properties (0, unit weight) have been selected, static stability analysis can be performed using the LEASE II program. This program calculates stability of masses defined by circular arcs using the Simplified Bishop's method or, for non-circular failure surfaces, the Morgenstern-Price method. Rotation centers can be tried individually or can be selected automatically following a grid entered with the data. For each center of rotation the program calculates factors of safety for circles of various size, starting with the largest radius selected and ending with the smallest radius selected. 4329R/CG 5-5 The program allows consideration to be limited to circles of significance. For example, circles through bedrock can be excluded and circles of less than a certain depth, such as 5 or 10 feet, can also be excluded. Embankment geometry, water levels and phreatic surfaces can be entered and handled by the program in as much detail as is necessary to provide the desired results. For each static loading condition of interest, the geometry, water levels and any other loads are entered and a grid of center points is picked and tried. Ideally, the grid is expanded as necessary so that the center point with the smallest minimum safety factor is bracketed. If further refinement is needed, a finer grid can be used around this most critical center point. At the end of this process, the most critical circle for the given condition has been defined and its factor of safety calculated. This procedure is repeated for each of the relevant static loading conditions. 5.2.2 Critical Circles and Accelerations The first step in the seismic analysis is examination of the results of the static analysis. Seismic analyses generally assume normal operating conditions exist, so the relevant part of the static analysis consist of the results from the normal operating case. One or more circles from each face of the embankment are picked for use in the SARMA program. These selected circles have the lowest factors of safety of those analyzed, have overall geometry which is critical to the overall stability of the dam and 4329R/CG 5-6 represent a variety of potential failure modes or configurations. As an example of the last requirement, one circle may be picked that is entirely within the upper half of the dam while another may reach nearly to the toe of the embankment. Since it is not known beforehand what configuration will be most critical in terms of permanent deformation, it is best to try a variety of conditions. The LEASE II program is used to determine the critical acceleration for each of the circles chosen. This is done by inputting the same geometry and loads used in the static analysis together with the chosen center point, radius and horizontal and vertical accelerations based on the a/~ ratio picked earlier. A range of seismic accelerations are used and the resulting factors of safety are plotted versus horizontal acceleration. The critical acceleration (~c) is the acceleration corresponding to a factor of safety of 1.0. For each circle, the critical acceleration must be recalculated for each new value of 0, unit weight, or av/~. 5.3 SARMA ANALYSIS 5.3.1 Data Requirements The SARMA program calculates the seismic response of a predefined wedge of the dam by the Sarma method and integrates to obtain a predicted permanent displacement of the wedge by the Newmark method, described in Section 4.3. 4329R/CG 5-7 The data required to do this include embankment geometry, wedge geometry, fill density, a , V , damping ratio and the earthquake accelerogram. nc s The embankment is treated as a symmetrical wedge with a pointed top and must be composed of a single material. The data are entered as an embankment height and a ratio between height and width. This requires some simplification of the input, but is a very close approximation of the Bradley Lake main dam, thereby making the use of the program viable. It also requires that average values of the material properties be used. The circle radius and center point are entered with the ~c from the LEASE II analysis. The ~c includes the effects of 0, density, av/~, and the more detailed geometry. The unit weight, in the form of density, and the average values of V s and damping calculation of the embankment response. ratio are entered to allow If a foundation layer is appropriate, its thickness (assumed uniform), density and V are entered. The damping ratio is assumed to be the same s as that of the embankment. In this instance, since the dam is founded on bedrock, the intermediate foundation layer was not used. The earthquake accelerogram is read as a series of ground acceleration values at constant short time increments. The peak ground acceleration can be specified, and the earthquake record scaled up or down to this point to match the design peak acceleration. 4329R/CG 5-8 5.3.2 Processing The SARMA program uses the embankment shape, density, and V to calculate s the natural or resonant frequency of the embankment in various modes of vi brat ion. It also calculates what the shapes of the various modes would be. Since the potential failure wedge or arc is well defined, it is possible to calculate how much the potential failure mass would be influenced by each mode of vi brat ion. This is done by calculating an average participation factor for the sliding mass as a whole for each mode of vibration. Using these participation factors and the damping ratio it is possible to determine how the wedge will respond to oscillations of a given input frequency at the base of the dam. Next, the ground accelerations based on the accelerogram are applied to the base of the dam (or foundation layer if there is one). The resulting accelerations experienced by the wedge are then calculated. This is called the time-history of wedge acceleration. The process is repeated with the time record reversed to obtain a second time history. The time-history of acceleration and the critical acceleration of the wedge are used together to calculate cumulative displacement along the sliding surface. The wedge is assumed to move with the rest of the dam as long as the average acceleration of the wedge is less than ~c· When the average acceleration exceeds ~c, the wedge slides relative to the remainder of the dam until coming to rest during a subsequent reversal of the acceleration. The resulting increments of movement are summed to yield the 4329R/CG S-9 total anticipated movement. As mentioned above, this is performed with the earthquake record applied in each direction consecutively. This yields a net greatest displacement which accommodates any asymmetry of the record. 5.3.3 Analytical Output The information available from the SARMA program includes the fundamental resonant frequency and frequencies of other vibration modes for up to 20 modes, modal shapes, participation factors for each mode, the earthquake accelerograrn, the wedge's time-history of acceleration, peak ground acceleration, peak wedge acceleration, number of pulses of movement, and total movement. The program produces a plot (such as Fig. 11) which includes a graph of the accelerograrn and wedge acceleration response and a parallel graph of cumulative displacement of the wedge. Much of the output is optional and can be suppressed if not needed. The fundamental resonant frequency can be used with the earthquake response spectrum to see whether the embankment is responding to an outstanding peak or valley in the spectrum. Participation factors indicate how many modes have a significant effect on the wedge so the cost of runs can be cut by cutting out unnecessary modes. Peak wedge acceleration can be compared to peak ground acceleration to give an indication of how the earthquake is amplified in the dam. The output number of greatest interest is the predicted permanent displacement of the wedge. 4329R/CG 5-10 5.3.4 Significance of Results As mentioned previously, bulging and settling of the embankment is a much more likely response to an earthquake than movement along a single surface as modeled by the SARMA program. For this reason, some thought must be devoted to the meaning of the displacements predicted by the program. Since the Sarma method is considered to be relatively conservative with respect to calculated displacements, it seems reasonable that vertical movement should not exceed movement predicted by this method, even if it actually occurs by general settlement rather than by movement on a single surface. Thus, the vertical component of the movement calculated by the SARMA program is treated as the actual maximum predicted vertical settlement .of the embankment crest. On the other hand, if the actual mode of deformation is general settling and bulging, the horizontal component of the predicted movement should not be viewed as a single offset of the concrete face. Bulging would produce curves and cracks in the face, but presumably not offsets of several feet. Viewed as a potential discrete offset in the concrete face, the horizontal component of the SARMA result is extremely conservative. To make the results as representative as possible of the embankment as a whole, it is helpful to analyze circles or other shapes of various sizes in various parts of the dam. This provides information on where greatest deformation might take place and provides greater assurance that the worst case has been found. 4329R/CG 5-11 A final step that has been taken to increase confidence in the results of the analysis is to use a range of values for the relevant variables rather than a single number. The importance of doing this depends on the level of precision with which the variables can be specified. If one or more parameters cannot be specified with much precision it is helpful to vary those parameters over a reasonable range to determine the possible range of resulting movements. Performing the Sarma analysis with a range of values for a parameter is probably most significant in the case of V . This is because the shear s wave velocity is difficult to define precisely in the first place and because it changes as a result of "softening" of the embankment during an earthquake. The amount and time-history of the change is also hard to define. Another reason for varying V is to allow the unique individual s characteristics of an accelerogram to be taken into account. If only one V is used, the SARMA program results can be skewed by a large spike or s trough in the response spectrum. The effect can be evaluated by varying v . s 4329R/CG 5-12 6.0 BRADLEY LAKE EMBANKMENT ANALYSES 6.1 EARTHQUAKE RECORDS During the conceptual design phase, an accelerogram was developed to meet the criteria proposed by Woodward-Clyde (Ref. 1). The accelerogram used was the Hybrid record explained in Section 3.3. This record is still considered the most appropriate for the current analysis. Two additional records were also tried. One was the Taft Lincoln School Tunnel S69E component and the other was the La Union E-W record of the Michoacan, Mexico earthquake of September 19, 1985. 6. 2 INPUT PARAMETERS The input parameters which must be chosen for the analysis are the material properties of the embankment and foundation. These include the friction angle (0) and unit weight for the rockfill and semi-pervious bedding material, as well as the shear wave velocity (V ) and the damping ratio s for the embankment as a whole. The rockfill and the bedding material are assumed to be cohesionless as is anticipated to generally be the case for hard blasted rock. The rockfill material that will form the major portion of the embankment is anticipated to be derived from blasted rock with a moderately high compressive strength of at least 10 to 15 KSI. It will be specified to be made up of angular particles of predominantly medium to coarse gravel size and larger, with a specified maximum percentage passing 1 inch and #200 sieves. The particles are expected to be relatively dense 4329R/CG 6-1 and the fill should be well compacted. The semi-pervious bedding material, used beneath the concrete face, is expected to be like the rockfill except in its grain size distribution. Its gradation will be that of a well graded sandy gravel, of minus 3 inch size. The embankment is founded on bedrock, so use of a foundation layer in the analysis was not necessary. The choice of the unit weight of the rockfill was based on laboratory test values of a specific gravity of 2.7 for the particles. By assuming different porosities for the rock a reasonable range of moist unit weight of 125 to 150 pcf was determined. A moist unit weight of 135 pcf was chosen for the analysis. The unit weight of the bedding layer might be slightly different due to differences in gradation or compaction. The unit weights are assumed to be the same for purposes of this analysis. This assumption is necessary for the Sarma analysis and is considered reasonable. The above values of the unit weight are within the range of applicable published data. The choice of the friction angle for the rockfill was accomplished using an article containing collected triaxial data (Ref. 9). A rockfill composed of material as described could have a friction angle of 48 to 53 degrees at depths in the embankment of about 10 to SO feet (Fig. 6). Since most failure surfaces of interest are relatively shallow, a friction angle of 48 degrees with an analytical range from 45 to SO degrees was chosen as suitably conservative. In the case of the semi-pervious bedding material, the same friction angles could be justified, but because of less certainty as to the exact characteristics of the material, slightly lower values will be used. 4329R/CG 6-2 A friction angle of 46 degrees was chosen with an evaluated range of 44 to 48. The shear wave velocity, V , was calculated using the relationship s between V and the shear modulus, G, and the density: s V = (G/density)112 s The shear modulus was calculated as shown in Seed, et. al, (Ref. 10), and Seed & Idriss, (Ref. 12), and the density was computed for the range of unit weights previously described. It was determined that a range of shear wave velocities of 700 to 1000 fps was appropriate, with a most likely value of 800 fps. The damping ratio was determined using relationships developed for sands (Ref. 12). Assuming a strain level of 0.1% results in a damping ratio of 15%. A range of 12 to 20% was chosen to bracket the damping ratio. The summary of input parameters is provided in Table 5. 6.3 DESIGN CASES Several typical loading conditions were examined to document the static stability of the dam and to define the cases to be used in seismic analyses. The cases of the highest and the lowest headwater elevations (1180 feet and 1090 feet, respectively) during normal operating conditions were designated the maximum and minimum normal operating conditions. The minimum normal headwater elevation at the dam is assumed to be 1090 feet, 4329R/CG 6-3 rather than the usual 1080 feet, because of the effect of the upstream cofferdam. The condition after completion of construction and prior to filling of the reservoir was designated the end of construction case. The probable maximum flood results in the condition of the reservoir reaching its peak elevation, 1190.6 feet. The condition of rapidly dropping the headwater elevation is the rapid drawdown case. Steady state seepage flow will not be significant within the embankment due to the inherent nature of a rockfill dam. Therefore, in all loading cases the analyses are performed with an internally dry embankment above tailwater level. Table 6 presents a summary of static cases and minimum calculated safety factors. In the maximum normal operating condition (headwater elevation 1180 feet and tail water elevation 1065 feet) the upstream slope is supported by the water of the reservoir and the downstream slope becomes the more critical part of the embankment. A factor of safety of 1. 78 for the downstream slope was determined using an "infinite slope" analysis. This analysis results in the minimum static factor of safety for the downstream slope. In the minimum normal operating conditions (headwater elevation 1090 feet and tail water elevation 1065 feet) the stability of the downstream slope will not be changed and the factor of safety will be 1.78 because the toe is essentially dry. The upstream slope without the concrete face or support from the water (i.e., dewatered case) would have a minimum factor of safety of 1.66 based on an "infinite slope" analysis. 4329R/CG 6-4 The end of construction case is not relevant for a concrete faced rockfill dam because there is no opportunity for consolidation pore pressures to build up. This case then reduces to the minimum normal operating level case above. The probable maximum flood, headwater elevation 1190.6 feet, makes the upstream slope more stable by adding more water to support it. This case does not affect the downstream slope since seepage does not develop through the embankment of a rockfill dam to a significant degree, so the minimum factor of safety remains 1.78. In the rapid drawdown case the stability of the rockfill will not be affected because it is free draining and there is no build up of excess pore water pressure. Because of the semi-pervious nature of the bedding layer and the fact that it is well drained on its lower side, it is reasonable to assume that pore pressures in this layer will also dissipate as rapidly as the reservoir can be drawn down. This will leave the bedding layer temporarily at a saturated unit weight. As the LEASE analysis shows, the unit weight of the material makes very little difference in the factor of safety. This case would also be very similar to the minimum normal operating case. Based on the static analysis, the embankment is stable in all design cases. For the seismic analysis, the normal cases will be used since it is highly unlikely for an abnormal high water condition and an earthquake to happen simultaneously. Three cases will be considered for the seismic analysis. 4329R/CG 6-5 The maximum credible earthquake (MCE) is the condition caused by nearby crustal faulting having a peak ground acceleration o-f 0. 75g. The design basis earthquake (DBE) uses a peak ground acceleration of 0.375g. This is slightly higher than the final selected project criterion of 0.35g, but was retained throughout analysis in order to avoid two variants in the same analysis. The megathrust condition, which simulates a large earthquake at a great distance, uses a peak ground acceleration of O.SSg. 6.4 LEASE II ANALYSES A static stability analysis was conducted using the LEASE II program to determine the critical potential slip surfaces and their critical accelerations. The analysis was conducted for both the upstream and downstream slopes for the two normal cases; normal maximum and normal minimum operating levels. Two embankment geometries were used 1n the initial LEASE II analyses. The old geometry which was based on the conceptual cross-section did not include a downstream berm. The final embankment geometry which was selected during the analyses, included the downstream berm. Large, coarse grids of circle center points were used to locate the areas of low factors o£ sa-fety on the original embankment. Smaller finer grids were then used on the final geometry to determine the slip circles with the lowest factors of safety. In this manner, six slip circles of various types in various parts of the dam were selected for further analysis. The circles on the downstream slope are designated A, B, and C and the circles on the upstream slope are designated D, E, and F. These slip circles are shown on Figure 8. The circles were chosen because of their low factors of safety and because they are distributed over the 2-1223-JJ 6-6 height of the dam. The shallow "infinite-slope" cases were not included because they are not critical to water retention or structural stability, because they would result only in loss of dam crest width. If multiple regressive surface slumps occurred, they would eventually regress to one of the sloped sliding planes, illustrated on Figure 16. The critical accelerations of the six slip circles were next determined for use in the SARMA program. The LEASE II program was used with a 0 value of 48° and a unit weight of 135 pcf. The program also requires input of a vertical and horizontal seismic acceleration, so the ratio of vertical to horizontal acceleration, a/~· was determined. Three values of a/~ were used for each circle. The first is given by the equation a/~ = tan (0-8) where 0 is the friction angle and e is the slope of the slip surface (Fig. 7). The other two values assumed are a/~ = 2/3 and a/~ = 0. Horizontal and vertical accelerations were input according to which av/~ was used, and factors of safety were determined. Plots were made of the factor of safety versus horizontal acceleration. By entering the graphs at a factor of safety of 1, the critical horizontal acceleration can be read off the acceleration axis. Critical horizontal accelerations were then determined for a range of values of friction angle, unit weight and the ratio of av/~. For these determinations each of the design parameters were varied independently while the other two parameters were held constant (Table 7). The variation of critical acceleration for the main dam with each variable is illustrated by Figure 9. 4329R/CG 6-7 6.5 SARMA ANALYSIS The dynamic stability analysis was conducted using the SARMA computer program on the six slip circles chosen by the LEASE II analysis. The circles were subjected to the Hybrid and Taft earthquake records described previously. The analysis was run with the range of values given previously (Table S) for each of the input parameters. The case using the average, or most likely values, of all the input parameters was designated the "normal" case. Also, a "worst case" condition, containing the value of each input parameter which resulted in the greatest deformation, was run. The results of the analysis are presented in Table 7, along with data from the Taft earthquake (scaled up) for comparison. The influence of the various input parameters on the critical accelerations and vertical displacements of the various slip circles is shown graphically in Figures 9 and 10. For circles B, D, and E, representative critical case plots of displacement and wedge response versus time for various cases are shown in Figure 11. The plots indicate progressive slip-displacement cycles of each wedge. These circles were selected as the critical modes which could result in loss of freeboard or rupture of the concrete face. 6.6 INTERPRETATION OF RESULTS The LEASE II analysis of the embankment showed a lowest minimum static factor of safety of 1. 7, for circle C, a shallow circle through the downstream berm. It should be noted that the embankment geometry used in 4329R/CG 6-8 the original berm. The analysis ("old geometry") did not include the downstream larger, more safety of 1.8 or higher. under static conditions. significant circles showed minimum factors of The analysis shows that the embankment is stable The maximum displacement calculated from the Sarma analysis for the MCE in the normal case was 3.2 feet vertical and 5.7 feet horizontal. Even the "worst case", with low 0 angle, low density and vertical acceleration equal to 2/3 of the horizontal acceleration yielded total vertical and horizontal displacements of only 4.7 and 8.4 feet respectively. The design criterion requires that half of the available 10 feet of freeboard be maintained, so the calculated vertical displacement is acceptable. The 5.7 feet of estimated horizontal movement is also acceptable because even if it is considered to be the offset of the upstream face, it would leave a signifi-cant part of the minimum 12 foot bedding layer intact. It should be noted that the analysis assumes that the movement will occur along one slip surface, while in an actual earthquake-induced movement, this type of dam is more likely to experience settlement and bulging. For this reason the horizontal displacement should be considered only a very rough approxima-tion, with the actual horizontal movement being less. The analyses show that the embankment will respond satisfactorily to earthquake loadings produced by the MCE or any lesser event. 4329R/CG 6-9 6.7 SPECIAL STUDIES A number of special studies were performed to see how the embankment responded to smaller or different earthquakes, post-earthquake conditions, or changes in slip surface or embankment geometry. These studies and their results are explained below. 6.7.1 Megathrust (~ = O.SSg) To simulate the effects of a large earthquake in the Benioff Zone, (the megathrust event), a Sarma analysis was conducted using the Hybrid and Taft earthquake records normalized to a peak acceleration of O.SSg. The analysis used the same circles as the analyses conducted with a peak ground acceleration of 0. 75g. The maximum loss of freeboard (vertical displace- ment) was 1.4 feet, which is well within the criteria and approaching insignificant damage for this type of darn. The results are presented in Table 7 and plots of the displacement versus time curve and the earthquake accelerograrn for the selected design cases are shown in Figure 12 for circles B, D, and E. These plots are presented as the "design" estimates of response of the circles which could be critical to darn safety. It can be seen by inspection that the displacement is limited to about 30 "pulses" of motion. The number of pulses of motion is illustrated on the displace- ment/elapsed time plot. Each displacement is in response to an acceleration on the accelerograrn plot where wedge acceleration exceeds the dashed line representing critical acceleration. 4329R/CG 6-10 The records, as used, do not completely match the criteria suggested by wee since the significant length is about 25% short. However, even if the records were doubled in length, the deformation would not equal that resulting from the nearby crustal faulting (peak ~ = .75g). Therefore, it is reasonable to conclude that the peak ~ = .75g event is the critical case. On that basis, the megathrust event will not be examined further. 6.7.2 DBE (~ = .375g) In order to determine the response of the embankment when subjected to the Design Basis Earthquake (DBE), a Sarma analysis was conducted using the Hybrid and Taft earthquake records normalized to a peak ground acceleration of 0.375g. The analysis used the same critical circles as the analysis conducted with a peak ground acceleration of 0. 75g. The maximum loss of freeboard (vertical displacement) was 0.4 feet. Subjected to the design basis earthquake, the embankment, and particularly the concrete face, would probably need some repairs, but it would remain safely operational. The results are shown in Table 7 and plots of the displacement versus time curve and the earthquake accelerogram for circles B, D, and E are shown on Figure 13. It should be noted that the design criteria specify a DBE peak ground acceleration of .35g. The 0.375g peak ground acceleration (which reflects a preliminary criterion value) used should result in movements only slightly greater than the .35g acceleration; therefore, it was decided not to redo the computer runs. 4329R/CG 6-11 6.7.3 Influence of Downstream Berm The effect of the downstream berm on the stability of the embankment was evaluated using the LEASE II program. In order to directly compare the factors of safety of the embankment with and without the berm, two computer runs were made, one with the berm and one without, with all other parameters being constant. This analysis was performed with a slope on the berm of 1.25H:lV. The slope was changed to 1.6V:lH in the final design, but that should not change the conclusions below. In the LEASE II analysis, the downstream berm was shown to have a very small effect on the stability of the embankment. For most of the potential slip circles the factor of safety is essentially unchanged. The factor of safety of the critical circle having the lowest factor of safety did not change without the berm. This is an indication that a dynamic analysis of the embankment without the berm would not change significantly from the embankment with the berm. Based on this reasoning, a dynamic analysis was not performed on the embankment without the berm. In the final design, the berm has the same slope and same composition as the rest of the dam and so is not expected to behave any differently. 6.7.4 Failed Concrete Face A special study was performed to estimate the effects on the stability of the downstream slope, of seepage through the embankment caused by a hypothetically completely failed concrete face. A flow net was drawn, 4329R/CG 6-12 assuming no concrete face, to determine the effect of seepage on circles A and B, described previously. In modeling the embankment, the effective height was taken as 130 ft., the bedding layer was 12 ft. horizontal and the downstream berm was ignored. It was felt to be appropriate to ignore the downstream berm based on the study of the effect of the berm on the stability of the downstream slope. The downstream berm should have little effect on the flow-net since it is composed of oversized rock fill. Two assumptions made in drawing the flow net were that the coefficient of permeability of the rockfill is 10 times that of the bedding layer, and the horizontal permeability of the fill is 10 times the vertical permeability. The flow net was drawn following the transformed section construction techniques outlined by Cedergren (Ref. 13) and by Casagrande (Ref. 14). Figure 14 shows the final flow net including circles A and B. From the figure it can be seen that seepage would not affect circle A at all and would affect circle B only slightly. The seepage would result in pore pressure along a small part of circle B. Since driving and resisting forces would both be affected it would have a minimal effect on the factor of safety. Under these conditions seepage would not adversely affect the stability of the embankment. 6.7.5 Varying Embankment Height In order to illustrate the effect of the embankment height on the slip circle displacement, a series of SARMA runs was made using different heights of the embankment. Only circle D remained within the embankment 4329R/CG 6-13 through the whole range of heights, so it was the only circle considered. The vertical displacement of circle D went from 1.20 feet at a height of 145.6 feet to .03 feet at a height of 30 feet, showing that the slip circle displacement decreases as the embankment height decreases, as might be expected due to lower seismic amplification in the fill. Similarly, peak acceleration generally decreased with embankment height, but not in as consistent a manner due to modal effects which result in amplification variations over the range of fill height (Fig. 15). 6.7.6 Planar Slip Surfaces The variation in results of the Sarma method at different levels within the embankment was investigated. Two approaches were taken. To estimate maximum potential offset of the dam upstream face at various levels, sloped planes through the toe of the downstream slope were first analyzed (Fig. 16). These slip surfaces through the downstream toe should give approximately the greatest deformations that would be expected to result from movement of various portions of the embankment. To provide information on maximum accelerations at various levels within the embankment, horizontal slip surfaces were also analyzed (Fig. 17). Statics analysis was used to determine the static factor of safety of each of the wedges, as well as the critical horizontal acceleration. The SARMA program was used to model the seismic response of the wedges. The Hybrid earthquake record was the only earthquake used in this analysis. 4329R/CG 6-14 The analysis of the sloping planes through the downstream toe showed a maximum displacement of 2.3 feet vertically and 3.9 feet horizontally. Data presented (Fig. 16) includes the variation of static factor of safety, critical horizontal acceleration, and vertical and horizontal displacement for each case. The static factor of safety decreased as elevation increased, as would be expected due to the steeper overall slopes of the slip surfaces. The critical horizontal acceleration also decreased with increasing elevation, leading to the increasing displacements. The face offset due to earthquake loading approximated by this type of analysis might cause cracking of the concrete face but the bedding layer would not be breached. It should be noted that below elevation 1180 (normal maximum operating level) the displacements rapidly decrease 1n magnitude, indicating that while measurable crest movements can be expected, deep-seated instability is not a concern. The analysis of the horizontal slip surfaces showed a maximum wedge acceleration at the top of the embankment. The maximum wedge acceleration increases with elevation (Fig. 17). This figure also shows the variation of factor of safety, critical acceleration and displacement with elevation. The static factor of safety for horizontal planes above the water level is infinity because there is no driving force. It should be noted for this case that the ratio of vertical to horizontal acceleration is 2/3, resulting in very high relative seismic driving force. Again, below elevation 1180 the net displacement drops off rapidly. 4329R/CG 6-15 The Sarma method generally does not take into account any dynamic water load. The effect of dynamic water load was checked using Zangar' s method and horizontal sliding planes. It was found that, due to the slope of the impervious face, the seismic water load has a slight stabilizing influence rather than causing a reduction of stability. On this basis, it was neglected in the remainder of the analysis. 6.7.7 La Union Accelerogram A special effort was made to utilize a record from the Michoacan, Mexico earthquake of September 19, 1985 (Ref. 15) for comparison. This was reported as a magnitude 8.1 event, and is one of the few great earthquakes with good bedrock seismograms. The available records were scanned and the one chosen was the La Union E-W accelerogram, which has a significant duration of 26.4 seconds and a peak ground acceleration of O.lSg. The recording station is about 52 miles from the epicenter. The La Union record was scaled up to have a peak ground acceleration of 0.75g and applied to circle B. As shown in Fig. 18, the total movement predicted was 4.9 ft. with a predicted loss of freeboard of 2.0 ft. This is about 78% more movement than predicted using the Hybrid record, so the results require some explanation. There are some key differences between the La Union and Hybrid accelerograms which account for the increase in the amount of predicted movement and make the Hybrid record more appropriate for the current analysis. 4329R/CG 6-16 One key difference is that the magnitude of the Michoacan event was 8.1, which is significantly larger than the magnitude 7.5 event specified as the MCE. Among other effects, this results in a much greater number of relatively large acceleration spikes in the La Union record. The difference is obvious upon comparison of the accelerograms (Figs. 11 and 18, note difference in time scales). A related effect is that the Arias Intensity (Ref. 16) of the La Union record is 21.7 when it is amplified to a peak ground acceleration of 0.7Sg. The Hybrid record has an Arias Intensity of only 8.8 at the same ground acceleration level. This indicates that the potential for damage which could occur from an earthquake with the La Union accelerogram was almost two and a half times that which the Bradley Lake project design earthquake could produce. Another key difference is in the epicentral distance of the two records. The Bradley Lake MCE is supposed to be caused by rupture of one of the faults on or very near the site. Thus, the Hybrid record, constructed to approximate near field accelerograms, is more appropriate than the La Union record, which was made 52 miles from the epicenter. The difference can be seen in the response spectra (Figs. 5 and 19). At greater distances, proportionately more of the high frequency content of the earthquake is damped out. Thus, scaling a record from some significant distance up to the same ground acceleration as a near field record results in a disproportionate amplification of the lower frequency portion of the record. This is the reason the La Union record is below the mean response 4329R/CG 6-17 spectrum at very short periods and significantly above it at most periods of significance. The Taft record, which was utilized in unmodified form for parametric analysis has the same problem to a slight extent. Its res- ponse spectrum appears in Figure 20. A plot of the Arias Intensity of these three records is shown in Figure 21. This figure illustrates the difference among the three records which result from sealing low acceleration records to high accelerations. The object of this analysis was not to find the worst imaginable case, but rather to find the worst appropriate case. The results based on the Hybrid record are considered to be the best indication of the maximum deformations which could be anticipated because this accelerogram has been produced to fit the site conditions. 6.7.8 Parametric Analyses As a part of this analysis, input parameters were varied over the range considered reasonable for each parameter. This allowed examination of the sensitivity of the analysis to changes in the input data. Most of the resulting information of significance is contained in Figures 9 and 10 in the form of graphs. These graphs visually present the information effectively so the writeup of these analyses will be abbreviated. Friction angle, av/~ and damping ratio all tion in the way that would normally be expected. affect permanent deforma- Their effects appear to be minor to moderate in magnitude. Unit weight of the fill within reasonable limits generally does not have a significant influence. Shear 4329R/CG 6-18 wave velocity has what appears at first to be an odd effect on displacement. However, it should be noted that changes in V have the s effect of changing the natural period of the dam. This causes the natural period to fall on different parts of the response spectrum as the velocity is changed. The V versus movement curves are simply a reflection of the s shape of the response spectrum for the Hybrid record. Circle C is not affected in the same way since it is near the bottom of the dam and responds at different frequencies than the other circles. Table 8 includes the results of the SARMA runs based on a previous dam geometry ("old geometry") without a downstream berm. It includes results from varying V over a wider range than was utilized in the final design runs. s As expected, the parameter that has the greatest effect on the amount of deformation is the peak ground acceleration. As the peak acceleration decreases by a factor of 2, the displacement drops by a factor of 7 or more. Input not covered by the above graphs includes the earthquake accelerogram and the embankment slope. Three accelerograms were used in the current study. Of these the La Union record is the least appropriate, as discussed in Sect ion 6. 7. 7. The Taft and Hybrid records are related to each other. The Taft record has responses significantly above the mean response spectrum throughout the period range of interest. It was modified by insertion of a small segment from a similar record (Friuli) which had a slightly higher peak acceleration. The resulting record (the Hybrid) has a response spectrum that matches the mean curve fairly well, with the exception of one prominent spike in the period range of interest. 4329R/CG 6-19 The results obtained using the Hybrid and Taft records are very similar, as can be seen by examination of Tables 7 and 8, and by comparing Sheet 1 of Figure 11 (Hybrid MCE for circle B) to Figure 22 (Taft MCE). The Hybrid record is considered a better representation of the MCE, and was used for design analyses. The remaining input parameter, slope angle, was picked by engineering judgement based on a number of factors, including infinite slope stability factor of safety, site seismicity, precedents provided by other similar dams and constraints created by the configuration of the site. 6 • 8 COFFERDAM A static and dynamic stability analysis was conducted on the upstream cofferdam. The general geometry of the cofferdam is shown on Figure 4. The stabi 1i ty analyses were based on an "infinite slope" approach. The static factor of safety was 1.35 and the factor of safety for the construction earthquake was 1.1. The stability and effectiveness of this cofferdam will be increased by the placement of waste fill on its upstream side. 4329R/CG 6-20 7.0 CONCLUSIONS 7.1 CRITICAL CASES In an analysis such as this there are numerous modes of movement that can be considered. At tent ion must be directed toward the modes that are most 1 ikely to occur and the ones with the greatest potential consequences. Some of the more relevant modes are sliding of the whole dam on its base, surficial ravelling or slumping of slopes, general settling and bulging of the dam, and movement on one or more well defined planar or circular surfaces. Of these various modes of movement, sliding of the whole dam on its base is of little interest because it is extremely unlikely, being far from a critical failure surface. In fact, part of the analysis showed that even the MCE would produce no permanent deformation at the base of the dam due to the overlying fill. At the other extreme, surficial raveling or minor slumping of faces is much more likely, but it is of little interest because it poses no threat to the integrity of the embankment as a whole. Since only modes that have a significant connection to the overall integrity of the dam or loss of freeboard are of interest, the remaining two modes deserved the most consideration. Settling and bulging of slopes is the more likely of the two. 4329R/CG 7-1 This would result in some loss of freeboard and in bending and cracking of the concrete face. Movement along a well defined surface is significantly less likely but would result in at least as much loss of freeboard and probably a great deal more damage to the concrete face. For these reasons, this last mode of movement was given the most attention with the assumption that it would serve as a limiting or extreme case as far as effect on the embankment, hence resulting in a more conservative design. 7.2 SUMMARY OF CRITICAL FAILURE SURFACES Of the various types of surfaces along which movements could occur, only certain ones are of interest. Planes or arcs that intersect the concrete face below headwater level, and those that could remove all freeboard with sufficient movement are· of the greatest concern. Six circular arcs and numerous planes were considered in the present analysis. Circles and planes that slope downstream and intersect the upstream face below the water level were given considerable at tent ion. Of these, circle B (Fig. 8) was considered most critical, since it intersects the concrete face slightly below elevation 1180 feet and has one of the steepest inclinations possible within the embankment. Planar surfaces 2 and 3 on Figure 16 are similar to it but were not analyzed as extensively. Some attention was also devoted to upstream sloping surfaces. Because of the supporting effects of the reservoir water, only circles almost completely above headwater level were predicted to move significantly at 4329R/CG 7-2 full reservoir. Of the upstream-sloping surfaces, circle E was considered most critical since it showed the highest amount of movement. Circle E assumes the minimum normal operating level, el. 1090 ft., so the circle is mostly above headwater level and receives little support from it. Therefore, for the retained pool case, which is critical for dam safety, the upstream face is more stable than the downstream. In the low-pool case, the upstream slope is similar to the higher and identical downstream slope, with the primary difference being in the lower 0 angle of the bedding material, which will contribute to slightly greater surficial slip surface motions. 7.3 PREDICTED DISPLACEMENTS Each of the circular arcs chosen for analysis was analyzed with a range of values for each input parameter, as previously explained. The calculated permanent displacements, as well as the input values used, are given in Table 7 and illustrated in Figures 10 through 13. For the Maximum Credible Earthquake, circle B shows a maximum loss of freeboard of 1.8 feet and total movement of 4.64 feet. Using the expected values, rather than worst values, of the previous parameters results in vertical and total movements of 1.1 and 2.76 ft., respectively. This is comparable to the results calculated for planes 2 and 3, Figure 16. With a peak ground acceleration of O.SSg, comparable to the megathrust event, circle B moved 0.4 ft. vertically and 1.0 ft. total. This is a reduction by a factor of about 2.7 from the MCE. Movement with a peak 4329R/CG 7-3 ground acceleration of 0.375g, slightly above the DBE, was 0.1 ft. vertical and 0.22 ft. total. The movement is less than that caused by the MCE by a factor of about 12.5 and is considered essentially insignificant and unlikely to result in structural damage. The other circles and planes on the downstream slope of the dam were examined, but more steeply sloped surfaces failed to intersect headwater, and the less steep surfaces did not move as much according to the calculation. On the upstream slope of the dam, circle E was predicted to have a maximum vertical movement of 4.8 ft. and total movement of 9.6 ft. as a result of the MCE. Using the. expected values of input parameters resulted in movements of 3.2 ft. vertical and 6.5 ft. total. The 0.5Sg event produced vertical movement of 1.4 ft. and total movement of 2.9 ft. These are about a factor of 2.2 less than resulted from the MCE. The 0.375g event produced vertical movement of 0.4 ft. and total movement of 0.9 ft. These are about a factor of 7.1 less than resulted from the MCE. Other surfaces on the upstream slope did not exhibit as much predicted movement as circle E. One major factor causing circle E to show more movement than other surfaces, including downstream-sloping ones, is the influence of the lower friction angle used for the bedding layer. However, considering the dependence of circle E on headwater level, the most likely critical surface is circle B on the downstream slope of the dam for retained pool cases. 4329R/CG 7-4 From the above information it can be seen that the amount of movement, and therefore damage, drops off sharply with a decrease in peak ground acceleration from 0. 75g. This knowledge is useful when considering the relative probability of occurrence of the three seismic events used in the calculation. It should also be noted that the greatest vertical movement predicted would result in a loss of less than one half the freeboard, without considering the added height of the parapet wall. In addition to calculating maximum displacements and examining how they vary with different parameters, some effort was devoted to evaluating how peak acceleration and displacement vary with height above the base of the dam. Analysis of horizontal surfaces (Fig. 17) within the dam showed that peak acceleration varied from 0.75g at the base to a maximum of 2.7g at the crest of the dam. Similarly, permanent displacement varied from 0 to 2.2 ft. in the downstream direction. It can be concluded that the response of the dam to any seismic event will be minimal near the base and most severe at the crest. This would also suggest that following a large earthquake, some reshaping of the crest may be required. Parapet displacement may result in the need for concrete repair, but the parapet is designed to remain upright, with only translational motion of an estimated 2 - 3 ft. Another area of interest is the probable effect of an earthquake on the concrete face of the dam. First, it should be noted that even if dam displacements were restricted to a single surface, the maximum predicted movement would not breach the integrity of the bedding layer beneath the concrete face. This is significant because the bedding layer is intended to restrict flow through the embankment in the event of damage to the 4329R/CG 7-5 concrete face. For this reason it is graded to have a lower permeability than the rockfill and to avoid piping into the rockfill. Thus, even the most extreme horizontal movement predicted would not produce enough leakage to affect the stability of the dam. Further, as has been pointed out previously, it is much more 1 ikely that deformation of the dam would take the form of movement distributed over numerous surfaces or of general settling and bulging of slopes. The effect of these more likely modes of deformation on the concrete face would be bending and cracking rather than large discrete offsets. Thus, the more likely modes of deformation would result in even less leakage and in more readily repairable damage to the face. In addition, the dam face joints have been designed to accommodate, without damage, movements up to those predicted for the DBE. The joints are expected to survive in functional, if not intact form, movements several times that severity. 7.4 RESPONSE TO VARIOUS EVENTS It has been shown that the embankment will remain stable, meeting the design criteria, even in the case of the 0.75g MCE. Most of the response of the dam was shown to take place in the upper part of the embankment. This would remain true regardless of the magnitude of the earthquake. For the DBE it was shown that the resulting deformation was relatively minor, dropping off by a factor of roughly 7 to 12 from deformations caused by the 2-1223-JJ 7-6 MCE. This was based on use of 0.375g rather than 0.3Sg, and a longer accelerogram than should be necessary for the DBE, so these values are conservative. With respect to the MCE, it should be remembered that the . 75g crustal fault event is extremely unlikely compared to the . SSg mega thrust event. The . 75g event is based on movement on existing faults at the site, but there is no evidence that these faults are active and the microseismic stations in the area have indicated no activity attributable to them. Thus, it is likely that the most severe earthquake the project will experience over any length project life is the mega thrust event with peak ground acceleration of .SSg. This would produce only about one quarter the amount of deformation predicted for the MCE so the maximum loss of freeboard expected would be 0.4 ft. and 1.4 ft. for circles B and E, respectively. These levels of movement would not be likely to cause damage other than cracking and minor leakage. The leakage and loss of freeboard should not be significant to stability of the dam. It is therefore concluded the dam and cofferdam can readily serve their intended purpose through events up to the DBE and construction case earthquake, respectively, and will remain structurally intact (though potentially aesthetically and functionally damaged) up to the MCE event. 4329R/CG 7-7 8.0 BIBLIOGRAPHY 1) Woodward-Clyde Consultants, Report on the Bradley Lake Hydroelectric Project, Design Earthquake Study, submitted to Alaska District, Corps of Engineers, 10 Nov 1981. 2) Woodward-Clyde Consultants, Seismicity Study, Bradley Lake Hydroelectric Project, submitted to Alaska District, Corps of Engineers, 28 March 1980. 3) Wilson, S.D. and R.J. Marsal ed., Current Trends in Design and Construction of Embankment Darns, ASCE, 1979. 4) Hausner, G.W. et al, Safety of Darns: Flood and Earthquake Criteria, National Academy Press, 1985. 5) Newmark, N.M., Effects of Earthquake on Darns and Embankments, Fifth Rankine Lecture in Geotechnique Vol X'J No. 2, Institution of Civil Engineers, 1965. 6) Bureau, Gilles et al, "Seismic Analysis of Concrete Face Rockfill Darns" 1n Concrete Faced Rockfill Dams-Design, Construction, and Performance, edited by J.B. Cooke and J.L. Sherard, ASCE, 10/21/85. 7) "Slope Stability Analysis, LEASE II," SWEC Program GT018, Version 01 Level 00, August 1980. 4329R/CG 8-1 8) "Seismic Amplification Response by Modal Analysis, SARMA," SWEC program GTOSS Version 01 Level 00, September 1986. 9) Lepps, Thomas, M., "Review of Shearing Strength of Rockfill, Journal of the Soil Mechanics and Foundations Division ASCE Vol. 96, No. SM4, July, 1970. 10) Seed, H. B. et. al, "Seismic Design of Concrete Faced Rockfill Dams" in Concrete Faced Rockfill Dams Design, Construction, and Performance, edited by J. B. Cooke and J. L. Sherard, ASCE, 10/21/85. 11) Arias, A., "A Measure of Earthquake Intensity" in Seismic Design for Nuclear Power Plants, edited by R. J. Hansen, MIT Press, 1970. 12) Seed, H. B. and Idriss, I.M., "Soil Moduli and Damping Factors for the Dynamic Response Analysis", Report No. EERC 70-10, EERC, Berkley, CA., 1970. 13) Cedergren, H., Seepage, Drainage and Flow Nets, 2nd edition, Wiley & Sons, 1977. 14) Casagrande, A., Seepage Through Dams, Journal of the New England Water Works Association, Vol. LI., June 1937. 4329R/CG 8-2 15) Anderson, J.G., Bodin, P., Brune, J. N., Prince, J., Singh, S. K., Quaas, R., and Onate, M., "Strong Ground Motion from the Michoacan, Mexico, Earthquake," Science, Vol. 233. 16) National Oceanic and Atmospheric Administration, Earthquake History of the United States, Publication 41-1, Reprinted 1982. 4329R/CG 8-3 Crest Elevation Crest Length: Crest Width: Maximum Height: Slopes: Materials: 4329R/CG TABLE 1 MAIN DAM CHARACTERISTICS 1190.0 feet 602.5 feet 18.0 feet (Inside of Parapet to edge of dam) 120 feet 1.6H: lV U/S Concrete face, 1 ft. thick, reinforced both ways Bedding layer beneath face (Zone 1) 12 ft. horizontal thickness minus 3" well-graded, angular gravel Remainder of dam-blasted rockfill (4 Zones) Zone 2 Coarse base drain, 36 inch max. size Zone 3 Upstream shell, approx. 36 inch max. size Zone 4 Downstream shell, approx. 36 inch max. size Zone 5 Downstream face slope protection, 48 inch max. size TABLE 2 MAIN DAM COFFERDAM CHARACTERISTICS U/S Cofferdam Crest Elevation: 1090 ft. min. Crest Length: 200 ft. Crest Width: 18 ft. Maximum Height: 32 ft. Slopes: U/S 2H = lV DIS 2H = lV Materials: Random fill with geomembrane and geotextile protection 4329R/CG Date Aug. 24, 1898 July 11, 1899 Oct. 7, 1900 Oct. 9, 1900 Dec. 30 and Dec. 31 , 1901 Sept. 19, 1909 Sept. 21, 1911 Jan. 31, 1912 June 6 and June 10, 1912 June 21, 1928 TABLE 3 (REF 16) HISTORIC SEISMIC EVENTS SUMMARY (SUMMARY OF LARGER EARTHQUAKES OCCURRING WITHIN A FEW HUNDRED MILES OF THE HOMER AREA IN THE PERIOD 1788-1980) Local time 0228 1000 1901 1012 2356 0606 0627 Approximate location (lat. N.; long. W.) Valdez (61°, 146°) Tyonek ( 61 °, 151 o) do Chugach Mountains Area (60 ' 142°) Kenai, on Cook Inlet (60.5°, 151°) Kenai Peninsula Prince William Sound and Kenai Peninsula (60.5°, 149°) Prince William Sound (61°, 147.5°) Cook Inlet ( 59°, 15 3°) South-central Alaska (60°, 146.5°) Estimated Richter magnitude (Msl 8.3 7.4 6.9 7.25 6.4 & 7.0 7.0 Page 1 of 3 Remarks Heavy. Severe. Severe. Probably is same as following one Severe, felt from Southwestern Yukon Territory, Canada to Kodiak Volcanic eruption and several sea waves. Strong at Seward. Severe, felt at Kenai Lake. Strong at Valdez. Severe. Ground waves at Seward. TABLE 3 Page 2 of 3 Estimated Richter Local Approximate location magnitude Date time ( 1 at. N . ; 1 ong . w. ) (Msl Remarks Mar. 25, 1932 1359 South-central Alaska 6.9 Water main burst at (62.5°, 152.5°) Seward. Sept. 13, 1932 2243 Prince William Sound 6.25 Stopped clocks in and Kenai Peninsula Homer, Valdez and ( 61°. 1480) Wasilla. Oct. 6, 1932 0705 Homer --------------Awakened all. (59.5°, 151.5°) Apr. 26, 1933 1703 Homer 7.0 At Homer, worst shock (59.5°, 151.50) in 15 years. June 13, 1933 0219 Old Tyonek 6.25 Severe shock with (61°, 151°) some damage. June 17, 1934 2314 South-central Alaska 6.75 Damage at Anchorage. (60.5°, 151°) July 29, 1941 1551 Kenai Pensinsu1a Area (61°, 151°) 6.25 Damage at Anchorage. Sept. 27, 1949 0531 South-Central Alaska 7.00 Strong aftershock (59.750, 1490) also. Damage at Seward and Anchorage. June 25, 1951 0613 Chickaloon Bay (61°, 150°) 6.25 Damage at Anchorage. Oct. 3, 1954 0119 Kenai Peninsula 6.75 Damage at Homer. ( 60. 5°. 151°) TABLE 3 Page 3 of 3 Estimated Richter Local Approximate location magnitude Date time {lat. N.; long. w.) (Msl Remarks Sept. 5, 1961 0135 Kenai Peninsula 6-6.25 Felt. Anchorage (600, 150.6°) rocked. June 23, 1963 1827 Cook Inlet 6.75 Damage at Homer, (59.5°. 151. 70) Barbara Point and Seldovia. March 27, 1964 1736 Prince William Sound 8.5 Loss of life, severe ( 61°. 14 7. 70) damage. April 14, 1964 1256 Kodiak Island Region 4.5-4.75 Damage at Kodiak. (580, 152.6°) Aug. 30, 1966 1021 South-central Alaska 5.75-6.0 Damage at Anchorage. 1023 (61.3°, 1476.50) Dec . 17, 1968 0202 Southern Alaska 6.5 Slight damage at (60.2°, 152.8°) Kenai and Ninilchik. Jan. 15, 1970 2206 Southern Alaska 6.1 Shocks felt on Cook (60.3°, 152.7°) Inlet and Kenai Peninsula. TABLE 4 DESIGN FACTORS OF SAFETY Load Case Normal Pool Level: Dead + Live + (Wind or ice) Dead + Construction Dead + MCE Earthquake PMF Pool Level: Dead + Live Seismic Loss of Freeboard (Max Loss/Total Freeboard) Infinite Slope Stability Static Operational Drawdown Emergency Drawdown 4329R/CG Main Dam 1.5 1.2 N/A 1.5 < 50% (MCE) 1.5 1.2 1.0 Cofferdam 1.2 1.05 N/A N/A N/A 1.2 N.A. N/A Variable Name Friction angle (0) rockfill bedding layer Unit weight, moist saturated Shear wave velocity, Vs Damping ratio, D.R. TABLE 5 INPUT PARAMETERS 125-150 pcf 138-154 pcf 700-1000 fps 12%-20% 0-2/3 * e = slope angle of sliding surface 4329R/CG Most Likely Value 135 pcf 145 pcf 800 fps 15% tan (0-9)* TABLE 6 MAIN DAM STATIC STABILITY SUMMARY Loading Condition Definition Normal Maximum Operating H.W. el. 1180 T. W. el. 1065 Normal Minimum Operating H.W. el. 1090 T.W. el. 1065 Design Flood-PMF H.W. el. 1190 T.W. el. 1082 Safety U/S 1.66 1.66 1.66 Factors DIS 1. 78 1. 78 1. 78 Criteria Minimum 1.5 1.5 1.5 End of Construction] Rapid Drawdown ] These cases reduce to Normal Minimum oper- ating case due to features of the upstream cofferdam which result in headwater retention at El 1090 even if lake level drops lower. Factors of safety calculated by "infinite slope" analysis. Failures of significance to the integrity of the dam (i.e., penetrating water retention zone) have higher safety factors . as shown on subsequent figures (e.g., Figure 16). U/S analysis neglects support from concrete face slab and headwater. H.W. = Reservoir Headwater Level T.W. = Dam Toe Tailwater Level 4329R/CG TABLE 7 page 1 of 6 Main Dam SARMA Results CIRCLE A, DOWNSTREAM, H.W. El. = 1180 ft., T.W. El. = 1061 ft. CENTER POINT (596.0, 1450.0), RADIUS 347.13 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Case/Para-0 (Degrees) Density Static D.R. Vs Peak v h v h meter Varied Rockf111/Bedding (pcf) F.S. av/ah a he % (fps) Ah• (ft) ( ft) ( ft) (ft) Normal Case 48/46 135 2.0 0.335 0.31 15 800 1. 78 2.8 5.0 3.0 5.4 " 45/44 135 1.8 0.277 0.275 15 800 1. 78 3.4 6.0 3.6 6.3 " 50/48 135 2. 1 0.374 0.345 15 800 I. 78 2.4 4.2 2.5 4.5 Density 48/46 125 2.0 0.335 0.31 15 800 1. 78 2.8 5.0 3.0 5.4 Density 48/46 150 2.0 0.335 0.31 15 800 1. 78 2.8 5.0 3.0 5.4 av/ah 48/46 135 2.0 0 0.355 15 800 1. 78 2.2 4.0 2.4 4.3 avlah 48/46 135 2.0 2/3 0.285 15 800 1. 78 3.2 5.7 3.4 6. 1 D.R. 48/46 135 2.0 0.335 0.31 12 700 1.58 2.5 4.5 3.3 5.9 D.R. 48/46 135 2.0 0.335 0.31 20 700 1.16 1.3 2.3 1.7 3.0 Vs 48/46 135 2.0 0.335 0.31 15 700 1.40 1.9 3.4 2.5 4.4 vs 48/46 135 2.0 0.335 0.31 15 900 1.90 3.2 5.7 3.4 6. 1 Vs 48/46 135 2.0 0.335 0.31 15 1000 1. 73 2.7 4.8 3.8 5.7 Worst Case 45/44 125 1.8 2/3 0.245 15 900 1.90 4.3 7.6 4.5 7.9 Megathrust .55g 48/46 135 2.0 0.335 0.31 15 800 1. 31 1.2 2.2 1.4 2.4 DBE .375g 48/46 135 2.0 0.335 0.31 15 800 0.89 0.4 0.7 0.5 0.8 .. Peak horizontal acceleration of the failure circle. TABLl page 2 of 6 Main Dam SARMA Results CIRCLE B, DOWNSTREAM, H.W. El. = 1180 ft., T.W. El. = 1061 ft. CENTER POINT (596.0, 1450.0}, RADIUS= 366.51 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Case/Para-foJ (Degrees) Density Static D.R. Vs Peak v h v h meter Var'led Rockfill/Bedding (pcf> F.S. av/ah ahc % (fps) Ah'" ( ft) (ft) (ft) ( ft) 48/46 135 2.34 0.456 0.375 15 800 1. 35 1.1 2.5 1.2 2.7 foJ 45/44 135 2.11 0.394 0.340 15 800 1. 35 1.3 3.0 1.4 3.3 0 50/48 135 2.52 0.499 0.400 15 800 1. 35 1.0 2.2 1.1 2.5 Density 48/46 125 2.34 0.456 0.375 15 800 1. 35 1.1 2.5 1.2 2.7 Denslty 48/46 150 2.34 0.456 0.375 15 800 1. 35 1.1 2.5 1.2 2.7 av/ah 48/46 135 2.34 0 0.435 15 800 1. 35 0.8 1.9 1.0 2. 1 av/ah 48/46 135 2. 34 2/3 0.345 15 800 1. 35 1.3 2.9 1.4 3.2 D.R. 48/46 135 2.34 0.456 0.375 12 700 1. 10 0.8 1.8 1.1 2.6 D.R. 48/46 135 2.34 0.456 0.375 20 700 0.89 0.4 1.0 0.5 1.3 Vs 48/46 135 2.34 0.456 0.375 15 700 1. 00 0.6 1.4 0.9 2.0 vs 48/46 135 2.34 0.456 0.375 15 900 1.50 1.3 3.0 1.5 3.5 Vs 48/46 135 2.34 0.456 0.375 15 1000 1.39 1.2 2.6 1.4 3.2 Worst Case 45/44 125 2.12 2/3 0.305 15 900 1.50 1.8 4.2 2.1 4.7 Megathrust .55g 48/46 135 2.34 0.456 0.375 15 800 0.99 0.4 1.0 0.4 1.1 DBE .375g 48/46 135 2.34 0.456 0.375 15 800 0.67 0. 1 0.2 0. 1 0.2 ,. Peak horizontal acceleration of the failure circle. TABLt.. page 3 of 6 Main Dam SARMA Results CIRCLE C, DOWNSTREAM, H.W. El. ~ 1180 ft., T.W. El. : 1061 ft. CENTER POINT (696.67, 1249.33), RADIUS 213.8 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Case/Para-9 (Degrees) Dens1ty Static D.R. Vs Peak v h v h meter Varied Rockf111/Bedd1ng (pcf) F.S. av/ah a he % ( fps) Ah * ( ft) (ftl (ft) (ft) Normal Case 48/46 135 1.89 0.374 0.239 15 800 0.567 0.3 0.6 0.6 1.1 g 45/44 135 1. 71 0.315 0.202 15 800 0.567 0.5 0.9 0.8 1.6 0 50/48 135 2.03 0.414 0.265 15 800 0.567 0.2 0.4 0.4 0.9 Density 48/46 125 1.89 0.374 0.234 15 800 0.567 0.3 0.6 0.5 1.2 Density 48/46 150 1.89 0.374 0.242 15 800 0.567 0.3 0.5 0.6 1.1 avlah 48/46 135 1.89 0 0.265 15 800 0.567 0.2 0.4 0.4 0.9 av/ah 48/46 135 1.89 2/3 0.215 15 800 0.567 0.4 0.8 0.7 1.4 D.R. 48/46 135 1.89 0.374 0.239 1 2 700 0.626 0.3 0.6 0.7 1.3 D.R. 48/46 135 1.89 0.374 0.239 20 700 0.573 0.2 0.4 0.5 0.8 Vs 48/46 135 1.89 0.374 0.239 15 700 0.597 0.3 0.5 0.6 1.0 Vs 48/46 135 1.89 0.374 0.239 15 900 o. 728 0.5 0.9 0.5 1.2 Vs 48/46 135 1.89 0.374 0.239 15 1000 0.897 0.8 1.5 0.8 1.6 Worst Case 45/44 125 1. 71 2/3 0.180 15 900 0. 728 0.8 1.6 1.0 2.0 Megathrust .55g 48/46 135 1.89 0.374 0.239 15 800 0.423 0. 1 0. 1 0.2 0.4 DBE .375g 48/46 135 1.89 0.374 0.239 15 800 0.288 0.0 0.0 0.0 0.0 .. Peak hor1zontal acceleration of the failure circle . TABL~ page 4 of 6 Main Dam SARMA Results CIRCLED, UPSTREAM, H.W. El. = 1180 ft., T.W. El. = 1061 ft. CENTER POINT (24.5, 2056.5), RADIUS= 938.17 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Case/Para-~ (Degrees) Density Static D.R. Vs Peak v h v h meter Varied Rockfill/Bedding (pcf) F.S. avlah ahc % (fps) Ah" ( ft) ( ft) ( ft) (ft) MCE 0.75g Nonnal Case 48/46 135 3.47 0.515 0.504 15 800 2.48 1.2 3.2 1.3 3.5 ~ 45/44 135 3.24 0.450 0.475 15 800 2.63 1.4 3.7 1.6 4. 1 ~ 50/48 135 3. 72 0.560 0.539 15 800 2.63 1.1 3.0 1.3 3.3 Density 48/46 125 3.54 0.515 0.506 15 800 2.48 1.2 3.2 1.3 3.5 Density 48/46 150 3.38 0.515 0.487 15 800 2.63 1.4 3.6 1.5 3.9 avlah 48/46 135 3.47 0 0.620 15 800 2.63 0.9 2.3 1.0 2.6 av/ah 48/46 135 3.47 2/3 0.486 15 800 2.63 1.4 3.6 1.5 4.0 D.R. 48/46 135 3.47 0.515 0.504 12 700 2.33 1.2 3.2 1.6 4.2 D.R. 48/46 135 3.47 0.515 0.504 20 700 1.63 0.5 1.4 0.7 1.9 Vs 48/46 135 3.47 0.515 0.504 15 700 2.03 0.9 2.3 1.2 3.0 Vs 48/46 135 3.47 0.515 0.504 15 900 2.53 1.4 3.6 1.5 3.9 Vs 48/46 135 3.47 0.515 0.504 15 1000 2.24 1.0 2.8 1.4 3.6 Worst Case 45/44 125 3.30 2/3 0.455 15 900 2.65 1.7 4.5 1.9 4.9 Megathrust .55g 48/46 135 3.47 0.515 0.504 15 800 1.82 0.5 1.2 0.5 1.4 DBE .375g 48/46 135 3.47 0.515 0.504 15 800 1. 24 0.1 0.3 0. 1 0.3 ,. Peak horizontal acceleration of the failure circle. TABL, page 5 of 6 Main Dam SARMA Results CIRCLE E. UPSTREAM, H.W. El. = 1190 ft., T.W. El. = 1061 ft. CENTER POINT (71.5, 1609.33), RADIUS= 522.97 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Case/Para-lit (Degrees) Density Static D.R. Vs Peak v h v h meter Varied Rockfill/Bedding (pcf) F.S. a 11 /ah ahc % (fps) Ah" ( ft) ( ft) (ft) (ft) .75g Normal Case 48/46 135 1.95 0.335 0.299 15 800 1.90 3.2 5.7 3.4 6. 1 " 45/44 135 1.77 0.277 0.215 15 800 1. 93 4.0 7.0 4.2 7.4 " 50/48 135 2.09 0.374 0.330 15 800 1.90 2.8 4.9 3.0 5.3 Density 48/46 125 1. 95 0.335 0.299 15 800 1.90 3.2 5.7 3.4 6. 1 Density 48/46 150 1.95 0.335 0.299 15 800 1.90 3.2 5.7 3.4 6. 1 a 11 /ah 48/46 135 1. 95 0 0.335 15 800 1.90 2.7 4.8 2.9 5. 1 a 11 /ah 48/46 135 1. 95 2/3 0.270 15 800 1.90 3.7 6.6 3.9 6.9 O.R. 48/46 135 1. 95 0.335 0.299 12 700 1. 71 2.9 5.2 3.8 6.8 O.R. 48/46 135 1.95 0.335 0.299 20 700 1. 25 1.5 2.7 2.0 3.4 Vs 48/46 135 1.95 0.335 0.299 15 700 1. 52 2.2 3.9 2.9 5.1 vs 48/46 135 1. 95 0.335 0.299 15 900 2.01 3.6 6.4 3.8 6.7 Vs 48/46 135 1.95 0.335 0.299 15 1000 1.82 3.0 5.2 3.6 6.3 Worst Case 45/44 125 1.77 2/3 0.235 15 900 2.01 4.8 8.4 5.0 8.6 Megathrust .55g 48/46 135 1.95 0.335 0.299 15 800 1.40 1.4 2.5 1.6 2.7 DBE .375g 48/46 135 1.95 0.335 0.299 15 800 0.95 0.4 0.8 0.6 0.9 "' Peak horizontal acceleration of the failure circle. TABLE page 6 of 6 Main Dam SARMA Results CIRCLE F, UPSTREAM, H.W. El. 1190 ft., T.W. El. = 1061 ft. CENTER POINT (71.5, 1609.33), RADIUS= 550.07 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Case/Para-1.1 (Degrees) Density Static D.R. Vs Peak v h v h meter Varied Rockfill/Bedding (pcf) F.S. av/ah ahc % (fps) Ah* (ft) ( ft) (ft) (ft) MCE 0.75g Normal Case 48/46 135 2.48 0.445 0.396 15 800 2.63 0.8 1.9 1.0 2. 1 0 45/44 135 2.24 0.384 0.359 15 800 1.20 1.0 2.3 1.1 2.5 " 50/48 135 2.67 0.488 0.425 15 800 1. 20 0.8 1.6 0.8 1.8 Density 48/46 125 2.50 ' 0.445 0.404 15 800 1.35 0.9 2. 1 1.1 2.4 Density 48/46 150 2.47 0.445 0.390 15 800 1.20 0.9 2.0 1.0 2.2 av/ah 48/46 135 2.48 0 0.479 15 800 1. 20 0.6 1.2 0.7 1.4 av/ah 48/46 135 2.48 2/3 0.370 15 800 1. 20 1.0 2.2 1.1 2.4 O.R. 48/46 135 2.48 0.445 0.396 12 700 1. 71 0.5 1.2 0.8 1.7 O.R. 48/46 135 2.48 0.445 0.396 20 700 1. 25 0.3 0.6 0.4 1.0 Vs 48/46 135 2.48 0.445 0.396 15 700 2.23 0.4 0.9 0.7 1.4 vs 48/46 135 2.48 0.445 0.396 15 900 2.65 1.1 2.4 1.2 2.7 Vs 48/46 135 2.48 0.445 0.396 15 1000 1. 29 0.9 2.0 1.1 2.5 Worst Case 45/44 125 2.25 2/3 0.330 15 900 1. 37 1.4 3.2 1.6 3.6 Hegathrust .55g 48/46 135 2.48 0.445 0.396 15 800 0.88 0.3 0.7 0.3 0.8 DBE ,375g 48/46 135 2.48 0.445 0.396 15 800 0.60 0.0 0. 1 0. 1 0. 1 .. Peak horizontal acceleration of the failure circle. TABU:. -page 1 of 4 SARMA Results-Old Geometry CIRCLED, UPSTREAM, H.W. El. = 1180 ., T.W. El. = CENTER POINT (640.33, 1900.0), RADIUS 770.87 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Varied 0 (Degrees) Density Static D.R. Peak v h v h v5 (fps) Rockfill/Bedding (pcf) F.S. av/ah ahc % A * h (ft) (ft) ( ft) ( ft) 700 48 1 35 4.4 0.52 0.585 15 2.29 0.90 1.95 l. 32 2.43 800 48 135 4.4 0.52 0.585 15 2.57 1.24 2.65 1.36 2.91 950 48 135 4.4 0.52 0.585 15 2.22 0.92 1.96 l. 25 2.67 1100 48 135 4.4 0.52 0.585 15 1.83 0.67 1.45 l. 01 2.18 1250 48 135 4.4 0.52 0.585 15 1.84 0.43 0.93 o. 70 1.49 1350 48 135 4.4 0.52 0.585 15 1.95 0.42 0.90 0.60 1. 28 1500 48 135 4.4 0.52 0.585 15 2.09 0.40 0.85 0.52 1.11 "' Peak horizontal acceleration of the failure circle. TABLt. page 2 of 4 SARMA Results-Old Geometry CIRCLE A, DOWNSTREAM, H.W. El. = 1190 ft., T.W. El. CENTER POINT (497.8, 1386.86), RADIUS 246.17 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Varied 0 (Degrees) Density Stat'ic D.R. Peak v h v h v5 (fps) Rockfi 11/Bedding (pcf) F.S. ay/ah a he % Ah,. ( ft l (ft) (ft) (ft) 700 48 135 2.2 0.38 0.345 15 2.03 2. 10 4.49 2.45 5.26 800 48 135 2.2 0.38 0.345 15 2.32 2.91 6.24 2.93 6.30 850 48 135 2.2 0.38 0.345 15 2.30 2.82 6.07 2.99 6.41 950 48 135 2.2 0.38 0.345 15 2.04 2.24 4.80 2.76 5.91 1100 48 135 2.2 0.38 0.345 15 1.68 1. 74 3.75 2.32 4.97 1250 48 135 2.2 0.38 0.345 15 I. 71 I. 37 2.94 1. 81 3.88 1350 48 135 2.2 0.38 0.345 15 1.84 1.29 2.76 1.60 3.43 1500 48 135 2.2 0.38 0.345 15 1.99 1. 15 2.45 1. 41 3.03 " Peak horizontal acceleration of the failure circle. TABLt. . page 3 of 4 SARMA Results-Old Geometry CIRCLE G, DOWNSTREAM, H.W. El. = 1190 ft., T.W. El. CENTER POINT (557.8, 1353.53), RADIUS 204.43 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT HYBRID TAFT Varied 0 !Degrees) Density Static O.R. Peak v h v h Vs (fps) Rockfill/Bedding (pcf) f.S. avlah a he % A " h (ft) (ft) (ft) ( ft) 700 48 1 35 2.04 0.31 0.348 15 1 .034 0.99 1. 82 1. 21 2.23 800 48 135 2.04 0.31 0.348 15 1. 33 1.63 3.00 1 76 3.24 850 48 135 2.04 0.31 0.348 15 1. 38 1.67 3.08 1.88 3.47 950 48 135 2.04 0.31 0.348 15 1. 28 1.41 2.60 1. 76 3.24 1100 48 1 35 2.04 0. 31 0.348 15 1. 10 1. 14 2. 10 1.57 2.89 1250 48 135 2.04 0.31 0.348 15 1. 10 0.86 1.59 1.24 2.29 1350 48 135 2.04 0.31 0.348 15 1.24 0.83 1.53 1. 13 2.07 1500 48 135 2.04 0.31 0.348 15 1.44 0.79 1.45 1.04 1.90 " Peak horizontal acceleration of the failure circle. Varied v5 (fps) 800 TABU:. w page 4 of 4 SARMA Results-Old Geometry CIRCLED, UPSTREAM, H.W. El. = 1190 ft., T.W. El. CENTER POINT (625.6, 1523.73), RADIUS= 432.82 INPUT PARAMETERS/INTERMEDIATE RESULTS DISPLACEMENT II {Degrees) Rockf111/Bedding 48 Density {pcf) 135 Static F.S. 1.98 av/ah 0.32 HYBRID TAFT D.R. Peak v h v h ahc % Ahw (ft) (ft) (ft) (ft) 0. 305 15 1.75 2.84 5.34 2.90 5.45 * Peak horizontal acceleration of the failure circle. g "' ~ 2.115.000 ~4/ V/u 1 KACHEMAK BAY ~s I ~'" ~~~ y.O -.,o d .... l ...... . .... - 2.110 ;· 2.100,000 -) c MUD FLAT '!.1 ·~-1 '-1'" A~ /<:>oO I 1 1 1 r=.........._ C>~ l 1 r--""" <@f? :::;::s:) T 1 , n 1 n ''' 1 ) i11~'\(" ~' EXISTING SITE PREP CONTRACTOR CAMP ~ NOTES I I• IIILl FEA~ ltCMIII ME. EllSTU. £JCI:f'TI A. MLN5 DEil..,.TED M -slTE" 8. I'IIIUN IWt C. SI'ILLIMY D. ..a.EI T\.NEL urr Met 0 1000 2000 (\ ~ I SCALE • 1"•1000' PROJECT LOCATION MAP FIGURE 1 I ACCESS OOAO-j I / /~ASTE DISPOSAL AREA B • lL 1\00.0'MAX ~~~ '0 --~ 't 'b ( \ \ WASTE DISPOSAL AREA ~7 EL 1090,0' MA':f \ ', "-, ', .......... , ', \ ', ~ \ "' \ 0 \ ( I t \ r, 1 l \J .......... \ \ \ \ I ' / , __ • I MAXIMUM NORMAL I 1 OPERATiNG WATER • C3~1 1 SURF!>CE EL\1800' I ' ' I \ I I 1 WASTE DISPOSALl--ll ~ AREA F J \ rt EL 10900' \M~AA ~ ,: / \ ~ / I I I I f I I I \ I \ t \ \ \ \ \ \ \ I I J I I -\ \ \ ' \ \ \ ' ............... ~ ........... ~ ........ , '.._, ', ',, ',:,;, ',, ', ', ',, ', ', ',',,o ', ',~,, ',,>·, ', ', <>o, ' ......... , ',' 'n"'' ......... ..... .... ' .... ',_'1:> ..... .... ..... - tiJ SYMBOLS KEY E) SURVEY MONUMENT • SEISMOGRAPH INSTALLATION G) WCRK POINT ..... ' .... ' ......... ' '-b~ ....... ' .... , ......... , ..... ~ ..... ' .... .... ........ , ,...., <~-G~~~E~~c::. ~ ..... ::----........ .:: ....... , ... __ ...... __ ' .... .... --........ , ... , ........ ............. : ......... : ......... ..... ....... ...... , .... ,, ', ', ', ................ , ' ......... .......... ...... ..... 1:>, 0~~ STAGtNG ~ EL 11 ~· 0 !'1'1£A ..,c?. ~.7 "'..,•"' ' ' ... ,,,\ \ \ \ /' \,.. .-' ....... __ _ GENERAL ARRANGEMENT MAIN DAM AREA FIGURE 2 3' PROCES!>ED CRUSHED STONE 39MAX ROCK FILL· GAP GRADED DRAIN 36°MAX ROCK FILL 36'MA)( ROCK FILL B!> I 48"MAX ROCK F"LL (OIIERSIZE) B1l I GRAIIEL ROAD SUIFACING ZONE TYPE 91 CONC FACE SLAB 1'·0' THICK GROJT CURTAIN ZONE 2 TYPE 62 FILL El. 119_4'_1..__ ZONE J TYPE 93 FILL ZONE 4 TYPE 94 FILL II MAXIMUM DAM PROFILE ... ICAl.t•nn 581f·6· AO.RAPET EXP JT IT'IP) PARAPET WALL !10'·0• ~~~ 11 I \ " " " " - SEGMENT A TRANSfTKlN .DINT W/WATERSTOP 3-3 .. ~ IC.U.I'. "IT .......... -._ .......__ --- REINFORCED /'CONCRETE .t' FI>C£ SLABS ,.J 21 2 SEGMENT D VIEW LOOKING DOWNSTREAM--------- ~ ~ b ,! . -· .. !!'liiil"'"<ii I &4UllfUU DISTANCE A L, 6\.7• T Jl.()' Lz 4'·10f SEGMENT B c 0 .4•-7f 8'-1-f' e•.oo 2•~-4t• 2t.)• 2'-3' !>'·!Of !>'·3r ~-3f I. - ZONE 2 TYPE 62 FILL RIGHT AEilJTMENT PLINTH I I J 'i:"'-/--GROut I CURTAIN / / -.. ·-. ·~ . ~ '. :\ '· "'" .I. . .. ::!·'j 2-2 , r •' I"Siie; I "' ~ b tOi FLOW- MEMBRANE LINER FILTER MINUS 3' MARTIN RIIIER BORROW MATERIAL UPSTREAM COFFERDAM PROFILE o• 10• '2d w I SCAL[ lflj Jl'f;(T 10'·0' PARAPET WALL SL1190t .· ...... ·F-'·0::·~ .· · ..... ~-<~~- <!'·91 1 -1 '. ~ ~ e---Q I .C&Lt: * rUI' MAIN DAM SECTIONS FIGURE 3 2.25 ...-.... 01 ..._, ns (/) 1.88 z 0 ~1.50 0:: w _j w u 1.13 ~ _J <{ 0.75 0:: 1-w 0.. 0.38 (j) 0.00 RESPONSE SPECTRUM FOR HYBRID EARTHQUAKE BRADLEY LAKE HYDROELECTRIC PROJECT MEAN RESPONSE SPECTRUM FOR M C E (NEARBY SHALLOW CRUSTAL FAULT) REF: WOODWARD-CLYDE CONSULT REPORT1 "DESIGN EARlliQUAKE STUDY' NOV 10,1981 -- SPECTRUM --~- 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 PERIOD (SEC) MCE RESPONSE SPECTRA..., MEAN AND CHOSEN ~------------------------FIGURE 5 - LOW DENSITY, POORLY GRADED# -+----+ WEAK ROUNDED PARTICLES ANTICIPATED RANGE- BRADLEY LAKE MAIN DAM HIGH DENSITY 1 WELL GRADED I STRONG ANGULAR PARTICLES ROCK FILL 304---~----+---+---~----r---+-----+---~ 1 2 5 10 20 50 100 200 500 NORMAL PRESSURE (PSI) FROM LEPS ,1970 ROCKFILL FRICTION ANGLES ~-----------------------------FIGURE 6 ELEMENT OF DAM FACE A RESULTANT OF FORCES ACTING ON THE ELEMENT WHICH FALLS ON ONE OF THE 11 CRITICAL LINES" GIVES A FACTOR OF SAFTY OF 1.0 AGAINST SLIDING. IF RESULTANT IS OUTSIDE THE CRITICAL LINEJ THEN ELEMENT IS UNSTABLE. THE PRIMARY FORCE IS THE ELEMENT WEIGHT (w). THE MIN SEISMIC FORCE (amm) NEEDED TO REACH THE CRITICAL LINE WILL BE PERPENDICULAR TO THE CRITICAL LINE. THE RATIO BETWEEN av & aH WHICH GIVES THAT MINIMUM SEISMIC FORCE IS 0YciH = t~n (;-e) FOR MOST VALUES OF ¢ & e J THIS GIVES A RATIO BETWEEN 0 AND~. IN THE CASE OF CIRCULAR ARCS RATHER THAN PLANES: THE SLOPE ANGLE FROM pt. A TO pt. B WAS USED TO APPROXIMATE e. INTERMEDIATE 0 %H RATIO ----------------------------------FIGURE 7----~ CIRCLE SLIP SURFACES USED IN THE DETAILED ANALYSIS 1250 1200 1150 1100 1050 NORMAL MAX OPER LEVEL EL 1180.0' \7 (PMF) EL 1190.0' \7 ~DAM SHELL~ CIRCLE X CENTER Y CENTER A B c D E F ---..::::.::=:; s >.. B " < POINT POINT 596.0 1450.0 596.0 1450.0 696.67 1249.33 24.50 2056.50 71.50 1609.33 71 .50 1609.33 MAX TAILWATER (PMF) EL 1077.01 '\7 ----- 1000;-------~----~------~------,-------~-----.------~------~------.-------.------.------~ 100 150 200 250 300 350 400 450 500 550 600 650 700 SELECTED SLIDING SURFACES -MAIN DAM ~----------------------------------------------------------------------------------FIGURE 8 . RADIUS 347.13 366.51 213.80 938.17 522.97 550.07 NORMAL TAILWATER EL 1061.o' \7 0.6 ___.,~-or---.--. D 0.5 I I :J.tC I I u I: 0.4 I I I ~ :31 I 0 0.31 I ~ Q2 ' II"" I t I ~· 50• 44• 49 6 ¢-ROCKFILL I BEDDING 0.6 0.5 D u J0.4 -F 0.3 0.2 1 20 - I 140 B A E- c 1tJ 0 lROCKFILL ~ MOIST ( PCF) ~ c 0.7 ~-----,----, 0.6 --Pr-------1---~ Q5 t ~D I 04 I -.. """"" I I • -.:c:: -..:::: F B 0.31~ A I E c 0.2 I I I 0 0.5 1.0 Oy/OH ?_) s CIRCLE LOCATIONS SHOWN ON FIGURE 8 CRITICAL ACCELERATION PLOTS ----------------------------------------------------FIGURE 9 ---- 4 ~ ~ w u 3 <! ...J n. Vl 0 -~~2 --~ <! ~ ....J :::> 1 u _, <! u i= a::: 0 w. w 45° 0 > 44• .¢'-ROCKFILL I BEDDING 4 3 2 1 0 120 - E A ~ D __.. 8 F c 140 160 ROCKFILL ~ MOIST ( PCF) HYBRID RECORD PERMANENT DEFORMATION PLOTS 4------~------~ E A 3 1 " ...,. I ,.-:ir 2 -1------+--------1 g 1 (;;,,............-__............. l::::;;....o-F I c 0 -+------t-----i 0 0.5 1.0 av/aH CIRCLE LOCATIONS SHOWN ON FIGURE 8 L------------------------------FIGURE 10 _ ___. SHEET 1 OF 4 ffi ~ w u ~ (/) B w >-~~ ~ L: :::> u _J <{ u 1-- 0:: w > 4 __ ___,.. __ ...,......, J I ., " I E 2 'A 1 'D 0 I I I I I I 600 1000 SHEARWAVE VELOCITY ( FPS) 4~-r-----t-___,..--, 3,E 2 I I ,._ t. I I 1 I I ..,._ I I I c ' I ~ I I I 0 I 20 12 DAMPING RATIO ( Ofo) HYBRID RECORD .55 g MEGATHRUST 4------~~~~-- I g~ "a M 3 j I I 2 I I I II I I 1 I I Ill lA-I 0 I I 16<)' 11 I 0 OH PEAK (0/o OF g) PERMANENT DEFORMATION PLOTS .___---------------------------FIGURE 10 ---4 SHEET 2 OF 4 ~ 4 }: w u ·~ ... 31 EC 3~ I -- t/) 0 w >-~t j ._ 2 T1T 1 -------'1 ~ I I }: }: a ..J <{ u -...._ 1 I I...,__ 1-1 0: w > Ql I I I I 45° 44° 50° 48° .¢-ROCKFIL L I BEDDING 4 E 3 A- 2 ~ D -----8 1 ...._ F - .....,. c 0 I' {') 1 ..1("\ H 0 ROCKFILL ~ MOIST (PCF) TAFT RECORD PERMANENT DEFORMATION PLOTS 4 E A 3 I I -I I .-1- 2~----~~----~ 1 I~ ==-~· I c o~---+-------1 1.0 Oy/OH ~-------------------------------------------------------FIGURE 10 --~ SHEET 3 OF 4 ..... z ~ w u <( ...J a.. Vl -0 ~- 4 -r-----r----r_, E 3 ~ I I I I Eit: 21 I II ...J- ::> ~ :::> U 1~ lA I _j <( u ..... a:: w > 0 t I I I I I 600 1000 SHEARWAVE VELOCITY ( FPS) 4 -r-r----,----r-, E 3 ~ 1\ '.r I I I 2 I I I ~ ~ I 1 I -1"-""= I I 0 I I I I I I I 12 20 DAMPING RATIO ( o/o ) TAFT RECORD .75g-MCE 4 w ~ tn I :::> ~ rn~ JE ,......_ l!H- 3 I ~ Ll1 ~ JJA UJ ~ 2. I Ill I I 1---1 I II I /II 0 t I ...,...-l 1 11 I 0 50 100 aH PEAK (0 /o OF g) PERMANENT DEFORMATION PLOTS ~-----------------------------------------------------------------------FIGURE 10----~ SHEET 4 OF 4 1-0 .... w. WN lL. V,)o ~--~ z-w :c w u cz:o ....I~ a._o V,) ,_.. 0 o.oo s.oo TIME-HISTORY CIRCLE B,Vs= .oo 25.00 OF· WEDGE MOTIONS 800 FPS "NORMAL .. Earthquake accelerogram and acceleration plotted Wedge acceleration is of larger 60.00 magnitude and is more prominent U _of .tbe._tv.cLcu.:r:ves~ -------------------------~ --INDICIITCi [11-I"QU~kfl "YIIIIIO llttCI..f~OOAM 1 kt•N to. 111ft IUtfl ~ flliULI HIILl '~N •otco lfWI ----INDICIUU Clllflti!L IICCfLCilllrlON. Q.JU D'l --INOitiiTU llfODC oarLACC"fH" ~ IICt[LUIITIOMI. 0 II) 0 -I 0 .... N 0 (j) 0 II) 0 0 0 0 0 . . s.oo 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 ss.oo 60.00 ° TIME -SECONDS MCE RESPONSE I DISPLACEMENT PLOTS ~------------------------------------------------------FIGURE11 SHEET 1 OF 6 TIME-HISTORY OF WEDGE MOTIONS CIRCLE B~Vs= 11 000 FPS o.oo 5.00 .oo 55.00 60.00 0 U)~ ~0 1-0 "'# w. W"' LL U)o I-"? z-w L: w u a:o _J~ (LO U) ~ 0 u, -------------------------------------------------------------------------- Jf\AAJ.It~~-------- --------------------------------------------------------------------------U, --J"OICAIU CAAIHIIUAKCI HUAID ACCCLCAOOIIAn 1 KCA" CD. TArT IIIICI ~ rAJULI JIALY 'A" AOCCD 1(~1 DATA AAC CDCHICIC"U or D--f7S7 rDI"" •I • D.D%0 HCD"D' ----I"DICAIU CAlli CAL ACCCLCAAIJDM. o.,S D'' I"DICAIC' ~COD( DllrLACCn£"" ~ ACCCLCUIJD"'· 0 CD 0 0 0 0 0 CD 0 I 0 10 -I 0 "'# N 0 10 0 CD 0 0 0 0 0 . . 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 ss.oo 60.00 ° TIME -SECONDS MCE RESPONSE/ DISPLACEMENT PLOTS FIGURE 11-----~ SHEET 2 OF 6 TIME-HISTORY OF WEDGE MOTIONS CIRCLE B, Vs = 900 FPS o.oo s.oo .oo 0 (f.)~ ._o I.U~ LLJI"l u.. (f.)o .... ~ ZN l.LJ I: I.U u a:o ...Jo a....: (f.) ...... Cl ~ -------~----------------------------------------------------~-------------- 0 CD 0 0 0 WJU~~~~~~~~.~~w~~~~~~~~~~~~~~----------+~ ----------~---·----------------------------------------------------------------------~ I~ --IIIOICIITU CIUITIIQUM[I HYII.IIIO AttC~UOOAAII 1 KUII tO. tArT UIUI ~ fltiULI ITA~Y IIIII ltOCCO I [Ill ---IIIOICIIIU CltltiCA~ IICCCLCIUHIOII. O.SU 0'1 DATA AU tOC,ICICHU Of 0--ll5l rOINU •T • Q.OtO UCOHOI IIIOICIITU 11[00( Ollrl~t!ft[llfl ~ IICCllCUTIONI • ~~F=~~~======~========~ 0 ID -I 0 0 ..... 0 0 N 0 0 ~I I I I I I I I 1 I I I I I I~ u.oo s.oo to.oo ts.oo zo.oo 25.oo 3o.oo 35.oo ~o.oo 45.oo 5o.oo 55.oo Go.oo TIME -SECONDS MCE RESPONSE/ DISPLACEMENT PLOTS L-------------------------------------------------------FIGURE11----- SHEET 3 OF 6 TIME-HISTORY OF WEDGE MOTIONS CIRCLE B J V5 = 700 FPS o.oo s.oo 0 V,)IJ) cc;; 0 1-N w· w- u... v:lo ~--~ zo w :c w u a:o ...J~ Q..o V) -0 0 0 ------------------------------------------------------------------------------------~ 0 IJ) 0 0 0 ~MI~~·Iwl-'\fl\o~.MJI'I'\'lAA.M.IMjW""""~-----+c;; 0 -------------------------------------------------------------------------------------:u--11J) < --IIIDICAJU (IUIJ"OUM(I lllUID ACtCLfltOOI!M 1 lUll CO. Iliff IIUU l UIULI ITALY ,1111 aGCCO Ifill DlliR Rill: COUflCJ[IIU Of 0--flU rOIIIU •J: Q.OZO UCOHOI ----INOICAIU CltlriCAL ACCILUAJIOII, o·.nl 0'1 IIIOICIIIU 11(00( DIII'LACinCIIII 4 ACC(L(UJIOIIf, 0 1:'1 0 <I) 0 0 .... 0 0 0 •I II I j ' I 9J.oo s.oo to.oo t5.oo 2o.oo 2s.oo 3o.oo 3s.oo ~------~r--------r--------,---------r--~ . 4o.oo -4S.oo sb.oo ss.oo sb.oo o TIME -SECONDS MCE RESPONSE/ Dl SPLAC EM ENT PLOTS ~--------------------------------------------------------FIGURE11----~ SHEET 4 OF 6 TIME-HISTORY OFWEDGE MOTIONS Cl RCL E D J Vs = 800 FPS ~" NORMAL" 0 .QQ 5.00 10.00 IS .00 20.00 ZS .00 30.00 35.00 ~0 .Otr ~5 .00 50.00 55.00 60.00 ~-------L------~~------1 0 (.1')0 d~ VJo 0 0 N zo o~~Jamt~.' !Jl84Jv-\l.ftl.)l\1(Uillli.lm-~, irh-.-.;'~•I.~-~~T.:::~~------------------------------------~ 1 g 1 ur'Y~ _r~r:~r~-~-v: --------~ · >--- a: et: wo ..J~ WN u' u a: ---------------------------0 --------------------------------------:u-- ' --llfOICIII(I UA!!<IIIJUC1 "lUIO •ttCLUOO«M 1 HU co. T~fl IUUI 'riiULI IIAlf ~<• JOC<O 4(wl o•U Uf CDCfriCIUU or 0--t?n IOI•U •I • O.QtO Hto•DI 0 0 N I ----llfDICA!£1 tJ<IIICAi. ~CCC\.C.AIIO•, 0.101 0'1 g I --lifO I caru wcooc DllfLacc•nu ' ~cccLC•AT 10"'. 0 0 -.: I ,___g uJ • tu"" u... (/)0 --~ ZN w r w a...: (/) _, 0 s.oo 10.00 MCE .. I 0 0 1'1 0 0 N 0 0 0 0 ,.----,--------·--.-------.-----.---.----.--------1. . \5.00 20.00 25.00 30.00 35.00 40.00 45.00 so.oo ss.oo 60.00 ° T I tiE -SECONDS RESPONSE/DISPLACEMENT PLOTS Fl GURE 11------~ SHEET 50F 6 o.oo 0 (/)0 . . (!)- s.oo 10.00 TIME-HISTORY OF WEDGE MOTIONS CIRCLE E , Vs = 800 FPS >"NORMAL" ts.oo zo.oo zs.oo '3o.oo 3S.oo •o.oo-•s.oo so.oo ss.oo 1 1 1 ___________ L __ ____L L.. _ _____.__._1_ ___ _._. 60.00 Cl 0 (f)o zo oc;;~• u ~~----------------------------------------------~ ~~ ...... t- cr: 0:::0 Wo _J • -------------------------------------------------------:u-- ' w- u' u cr: 0 0 ~---I~Oitl'UI fAA!l10V~M[I •UUO ~ttClUOGUII I MU• tO. T~ff llUCI ~ f~IUll ll~ll ~~~OttO I[Wl ---I•Oitl!IU CAI!ltftl AttCl[~~IID•, a.Ut 0'1 .,_o 0 W• w10 lL. U)o ~--~ z~'"~ w I: w 0 --IMDitl!IU WCO!K OUrLAtCoC•II ~ /ltC(lUA!I O•l, OA!A ~A[ COCfrltlC•U Of ~--nn tOI•U •I • O.Oto UtO•GI Cl 0 -I 0 0 !:'ol I 0 0 ID .::;, 0 "' 0 0 0 0 . . ~ "' 10.oo s.oo to.oo ts.oo zo.oo zs.oo 3o.oo 3s.oo 4u.oo 4S.oo so.oo ss.oo so.oo 1 TIME -SECONDS MCE RESPONSE/DISPLACEMENT PLOTS L--------------------------------------------------------FIGURE11 SHEET 6 OF 6 TIME-HISTORY OF WEDGE MOTIONS CIRCLE 8, aH = 0.55G o.oo 50.00 55.00 so.oo 0 U)IJ) de;; 1-0 wO? wo LL. U)o ~--~ zo w :1:: w u a:o _jeri lLc;; <n ...... 0 ~ 0 Ill ------------------~------------------------------~------------------------------------------ 0 0 IIIWINIIJIIMit'WIMR'\AI\IVW'\Jidfo\liMitn~ ... l\j.\6;/~J~Aw-e-· ------1-c:;; --INDICJIJ[f fiiiJ"IIUIIII[t 11lUID IICCfU:It08111111 t Kfllll CO. JAn IIIIKI 4 fRIULI ITIILY filii lottO 1[111 ----INDitiiTfS tltiJ I tilL IICCfL[IIIIUDII. 0 ,,IJ O'S --IIIOICIITU 11[118( PIII'LIItfllfiiTI 4 IICtfLfiUITJDIIIJ. 0 -r-lln c OATil Ill[ COf,ltlfiiTI Of 0--Ulrl I'OIIITI •T • O.OU UtONOS 0 (I) 0 0 II) . 0 0 crl 0 0 0 0 0 . . 5.00 10.00 I .00 20.00 2 .00 30.00 3 .00 40.00 4 .00 50.00 55.00 60.00 ° TIME SECONDS MEGATHRUST RESPONSE/ DISPLACEMENT PLOTS L-------------------------------------------------------FIGURE12----~ SHEET 1 OF 3 TIME-HISTORY OF WEDGE MOTIONS CIRCLE D 1 OH = 0.55 G o.oo 5.00 lO.OO 15.00 20.00 25.00 30.00 35.00 0 U)O 0 1-c.~ w. w- ll... wo ~--~ zo w r w u a:o _, .... Q._~ U) ..... 0 0 0 u ------------------------------------- ------------~ 0 0 0 0 0 ----------------------------------::ij I o --t 0 JIIOICIITU fiiiiT"IlWIIIft "YIIIIID ACCflfiOIIIIAII : !!fill CO. TArT 1688fl ~ raJULI ITAU 6AII IOCCO Ifill ----IIIDICIITU CIITICfll flttflf:IIHJDII. o.S04 0'6 --IIIOICfiTfi llfDOf Ol6rlfltfllf11Ti ~ ACULUfiHDIIi· DATA AI[ CO[frltlfiHi Or 0--t757 rOIHTll •T : o.ao I[COH06 -I 0 0 0 N 0 liD 0 0 .... 0 +---~--~------~------,-------.-~.00 5.00 10.00 .-------------y 25.00 30.00 35.00 40.00 45.00 55.00 50.00 LS.OO 20.00 TIME -SECONDS MEGATHRUST RESPONSE/ DISPLACEMENT PLOTS FIGURE 12----' SH T 2 OF 3 TIME-HISTORY OF WEDGE MOTIONS CIRCLE o.oo 5.00 0 Ul"! 1-0 .. W• WN LJ... U)o ~--~ z-w :E w u a:o _JCIO a...~ U) ....... D ------------------------~ 0 CD 0 0 0 lll.l!tiMVII~'Wli!Mh\W~IINWPA~6ll~J\.Aw~ ... ·~-I~ -------------------------------------------------------------------------=u-- c --INDICIITfl fll~THUUilKfl HTIIIID llttfLfiiDOIIIln 1 KfiiN to. TllP'T llllfl ' P'~IULI ITIILT IRII ~DCCD IfNI ----INDICilTfl ~ITICIIL llCC[L[~IlTIDN. D.UI D"l --INDICIITfl WfDDf DllrLiltfllfiiTI 'llttfLUilTIDIII. ( rP Dlllll llllf COfP'P'ICI[IITI OP' D--!757 roiNTI •T 2 o.oto lfCDNDI 0 CD 0 ID -I ~ ~0 ---.. N 0 ID 0 CD 0 0 0 0 0 . . 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 ° TIME -SECONDS MEGATHRUST RESPONSE I DISPLACEMENT PLOTS FIGURE 12-----~ SHEET 3 OF 3 TIME-HISTORY OF WEDGE MOTIONS CIRCLE = 0.375G o.oo s.oo .oo 0 U) .... de;; I-liD w-:' wo l.i.. U)N 1--:' zo w l:: w u a:"" _Jc; CLo U) ....... 0 0 --------------------------------------------------------~ I.,.. ------------------------------------------:u-- c IIIOICIITU (llllfiiQUAII[o IIYUID IICCfLlllOOIIIIII o l!.fllll CO. ffl(f 1&18[1 <f. riiiULI ITIILT SAil I!DttO lUI ----IIIOICIITU tltiUCfll IICC:flfi!ATIOII. O.US D'S IIIOICIITU MfOOf Ol&tlfiUIIfNT6 <f. RCUU~RTIOII&. J ORTR lilt[ tKrntlfllf& Of 0 •• t751 tOIIITS at : D.otO &ftOIIO& 0 0 0 0 .... liD - 0 N - 0 (I) 0 0 0 0 0 0 . . s.oo 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 so.oo 55.00 60.00 ° TIME -SECONDS DBE RESPONSE /DISPLACEMENT PLOTS ~--------------------------------------------------------FIGURE13----~ SHEET 1 OF 3 TIME-HISTORY OF WEDGE MOTIONS CIRCLE D ,aH = 0.375 G o.oo 0 U)ll'l d~ ~--· w~ wa lL. U)<O t-': :z:a w ::c w (J a:"' _.~o a...~ (/) ...... 0 u, --------------------~--------------------------------·· -------------~----.......,_ 0 "' 0 a 0 a ------r 1 ~ ' --INOICIITfi flll!THIIOMft HlUIO IICCfl[IIOO«A" 1 IIUN Co. TIII'T 1618[1 ~ Fllllll.l JTIIll &liN UCCO Ifill ----lNOICIITfi CIIJT I CAl IICCflfiiiiTIOH. 0.504 0'1 INOICIITU II£0Gf: 0161'lACf"fNrli ~ IICCflfiiiiTION6. UIITA flftf C(l[f"f"ICifHf' Of 0--t757 I'OINT6 •f = O.O'lO UCOII06 .... cv a <0 - 0 (I) a a a a o a . . s.oo to.oo 15.00 20.00 2 .oo 30.00 35.00 40.00 45.00 50.00 55.00 60.00 a TIME -SECONDS DBE RESPONSE/DISPLACEMENT PLOTS ~-------------------------------------------------------FIGURE13----~ SHEET 2 OF 3 TIME HISTORY OF WEDGE MOTIONS CIRCLE E 0.375 G o.oo s.oo .oo 45.00 .oo 60.00 0 ([JII) ~~ t-:i LIJ • LIJO lL. (J)o t-~ z:o LIJ I:: LIJ u a:o _J(\') a...~ (fJ ._ 0 -----------------------------------------------------------------~ --L·-----------------------------------------------------------~ --IMOICIIfU fllltfH8lllllf1 "YUIO llttfl.fiiOGIIIIft 1 11011 CO. flirT 1&18[1 ~ rlUUI.I UIII.T &liM liOCCO Ifill 011111 ur c«P'P'Itlfiiiii or G·-ns, reuna .r = o.oto arcoHG& --INDICIIff& ClllfiCIIl lltCfLfliiiUOM. o.raa 0'1 --IMDJCIIJfl llfOIN' DJfjrLIICfftfNfl ~ IICC[L[~IITIOMti. 0 II) 0 0 0 0 0'1 0 0 CD 0 0 (\') 0 0 0 0 0 . . s.oo to.oo t5.oo 2o.oo 2s.oo 3o.oo 35.oo 40.oo 4S.oo 5o.oo 55.oo so.oo o TIME -SECONDS DBE RESPONSE/DISPLACEMENT PLOTS Fl GURE 13 __ __. SHEET 3 OF 3 EL 1180 CONDITIONS : Kv = 1b K H K BEDDING = Tb K ROCKFlLL BEDDING LAYER = 12FT HORIZONTAL DIS BERM IGNORED FLOW THROUGH DAM WITHOUT FACE MAX BEL 1066 \! ~--------------------------------------------------FIGURE14 I- I <.9 -....-... 20 15 ~~ 10 ~ L: ~ 5 )~--~--~--~~--~--~--- ) -+--+--+--t I -t-----t.rfiL----f-----t- 1~---+----~--+---~---+--~ 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 VERTICAL DISPLACEMENT ( FT MCE CASE) 1- I <.9 -.......... WI- IIJ... ....__. L: <( 0 200~------~-----.-------r------. 150 ---+-----·----+···-~-----·---+--···--------1 • 100 ~-+------------·-----+-·----·· -------~- • 50 • 04-------~-----+-------r----~ 1.0 1.5 2.0 2,5 MAX WEDGE ACCELERATION (G) 3.0 DAM HEIGHT VS. ACCELERATION AND DISPLACEMENT ~--------------------------------------------------FIGURE15 ---~ FOR PLANAR SLIDING SURFACES ILLUSTRATED BELOW I 1200 End Pt. F.S. <XV \ledge I (Left} Slope 8 Static o( H 366,1190 30.05° 1.92 .324 2 350,1180 26.74° 2.20 .389 334,1170 23.65° 2.51 • 453 318,1160 20.77° 2.83 .515 5 302,1150 18.10° 3.19 .575 6 286,1140 15.62° 3.59 .634 270,1130 13.32° 4.04 2/3 254,1120 11.19° 4.55 2/3 9 238,1110 9.21° 5.14 2/3 10 222,1100 7.38° 5.81 2/3 11 206,1090 5.68° 6.59 2/3 12 190,1080 4.11° 7 .so 2/3 13 174,1070 2.64° 8.57 2/3 14 158,1060 1.27° 9.86 213 15 142,1050 0.0° 11.41 213 o<.v < 2 ---<XH 3 1200-, t ......... 1- !::S 11 50~ z 0 ~ Gj 1100~ _j w 1050 Vert. Horiz. c< HC 6...fh_ 6rt. .293 2. 3 3. 9 I .338 1. 5 2.9 .375 1.0 2. 3 .405 .6 1. 8 .431 .5 1. 5 .453 .3 1.1 .476 .2 .9 .506 .1 • 7 . 534 .1 .s .561 o.o .3 .588 0.0 .2 .614 o.o .1 .640 0.0 0.0 .665 o.o o.o .690 o.o 0.0 1180 z 1150 0 -!-....-... ~~ W'-' _j w 1100 1150 6 5 . 10 15 STATIC FACTOR OF SAFETY 1 E L 1180 - -;<.__ -------- ~ - I~ -------------- 0 0.2 0.5 0 Hc ~~ 0.7 0 1.0 2.0 3.0 0 6 VERTICAL (FT) ~ 15~------~------~------~------~------~------~----~--~~~~~--~ 150 200 250 300 350 400 450 500 550 600 WEDGE STABILITY: SLOPED SLIDING PLANES 1.0 2.0 3.0 4.0 6 HORIZONTAL ( FT) r 1200 ~ 1150 l-1100 1050 ~--------------------------------------------------------------------------------------FIGURE16 Wedge I Elevation Static F .S. <?< HC Top 1190 oO .638 1170 49.83 .648 2 1150 19.29 • 666 3 1130 14.92 • 676 4 1110 13.23 .682 5 1090 12.34 .685 6 1070 11.78 .688 7 1050 11.4 1 .690 el.y - 2 o<H -3 1200 ......... 1- lL .......... 1150~ z 0 -1-:g; ~ 1100-1 w 1050. 1200 Ha.x. Accel. 6H I 1180 2.724 2.2 ......... 2.4563 t: 1150 2.1598 1.5 .......... .9 • z 0 1. 6219 .5 -1-1.2578 1.0566 .2 :g; 1100 .92 97 • 1 ,w _j 0 .w 1050 o 1o 20 30. 40 ·5o .62 STATIC FACTOR OF SAFETY 2 / .65 o(HC 0.7 1.0 2.0 3.0 0 MAX. ACCELERATION (G) "" 1 2 6 HORIZONTAL (FT) 1200 l-1150 l-11 00 7~------~------~------~----~------~------~------~-----.:-----~~ 1050 150 200 250 300 350 400 450 500 550 600 WEDGE STABILITY: HORIZONTAL SLIDING PLANES ~---------------------------------------------------------------------------------------FIGURE 17--~ o.oo 0 (1)10 ~.; ....... 1- a: a::: wo _Jo:; we u' u a: 0 "' s.oo \2.00 TIME-HISTORY OF WEDGE MOTIONS CIRCLE B ,aH = 0.75 G, LA UNION E-w 16.00 2 4. 00 30.00 60.00 66.00 .oo I 1 ~~ u I ------- ----------------~-----~ 1 ------------u, 0 0 0 0 (0 0 I 0 "' --lHOICRTES EARTHQUAKE• RffORTE DEL ARCHIVO: UNI0850S19AI.l 616nQ: 8509190A E61ACION: UNIO N90E• EVEN TO: OA HOftA: 13 ;J1 :<9 OUftRClOH: e2 .7 7 ~--~ w. ww lL UJo 0 1-. z..t ILl :L w CLN (j) 0 62H fOINI6 •1 0.010 SECOHD6 INDICATES CRITICAL ACCELERATION, 0.375 0'6 INDICATE& WEOOE Ol6FLACEnfHI6 < RCCELERATJOH6. ~========================================~ 0 0 ------,------.-9Jj.._o_o __ __,6 '. o-o---, r-2 ~.:-o o 1 B • oo 2 4 . o o T I ME LA UNION RESPONSE I DISPLACEMENT PLOTS 0 0 "' 0 0 ... 0 0 N 0 0 FIGURE 18 3.38 3.00 ........... rn2.63 - z 0 2.25 t- <( 0:: w _J 1.88 w u u <( 1.50 _j <( 0:: 1. 13 t-w a_ If) 0.75 0.38 0.00 \ -\ " ~ " 1\VV J \ /'JI -----------· \ v\ r/ / v ~ -- --r---- --------- I --- , ---------- / LA UNION -·----~~ -~---~--·--- ~PROJECT DESIGN MCE RESPONSE ~SPECTRUM ~ ---·---··-------------------- ....... ~::-:r-::-r--------- ~ --......... 1---~ -------1------~------L. .. -- 0.00 0.25 0.50 075 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 PERIOD (SEC) RESPONSE SPECTRUM -LA UNION E-W RECORD ~-------------------------------------------------------FIGURE19----~ 2.63 -2.25 m ........ z 1.88 0 1-- ~ 1.50 w _J w u 1.13 u <! _J <! 0.75 0:: 1--u w 0.38 Q_ l/) 0.00 --- j ( ~M ~v ~ 1--u ---------------------------------- __ ,.,., .. _______ ~_ 1-------------- I/ ~-PROJECT DESIGN MCE RESPONSE SPECTRUM ~ (\ ----f---~t--TAFT .. __ ~~ -----· ~ ~t--~ -r---- -----~---. ----------------~ -------------------· ----------'----------------- 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 PERIOD (SEC) RESPONSE SPECTRUM -TAFT RECORD ~-------------------------------------------------FIGURE20 ----~ 25 20 >-15 r- l/) z w r-z -10 l/) <! 0::: <! 5 o. 0 10 20 LA UNION - HYBRID NOTE : PLOTS OF ARIAS INTENSITY FOR THREE ACCELEROGRAMS USED 1 SCALED TO 0.75g PEAK GROUND ACCELERATION. 30 40 TIME (SEC) ARIAS INTENSITY 50 60 70 ~--------------------------------------------------FIGURE 21 0 U)<D d~ •I 1-0 • W• W"" lL U)o 1-"':: z-w :E w u a:o ...Ja:> (L~ U) D .oo 5.00 TIME-HISTORY OF WEDGE MOTIONS CIRCL B JOH = 0.75 G 15.00 20.00 25.00 I I .oo 55.00 .oo 0 (D 0 u -----------------~· -----------------------__:._ 0 -::u:-I o (D 0 <.0 ------INDICATES EARTHQUAKE: IIA004 52.002.0 TAFT LINCOLN SCHOOL TUNNEL COMP S69E --2720 POINTS •T : 0.020 SECONDS I -----INDICATES CRITICAL ACCELERATION, 0.375 G'S -------INDICATES HEDGE OJSI'LACEMENTS «. ACCELERATIONS. ...-----.------------·-··-·-····-·······--·-·--~ -----y--------, 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 TIME SECONDS TAFT RESPONSE /DISPLACEMENT PLOT 55.00 0 • "" 0 <.0 0 co 0 L-----------------------------------------------------FIGURE22--~ SPILLWAY STABILITY REPORT SPILLWAY STABILITY REPORT BRADLEY LAKE HYDROELECTRIC PROJECT Prepared for ALASKA POWER AUTHORITY March 1988 STONE & WEBSTER ENGINEERING CORPORATION DENVER, COLORADO 80111 FERC PROJECT NO. P8221-000 BRADLEY LAKE HYDROELECTRIC PROJECT ALASKA POWER AUTHORITY SPILLWAY STABILITY REPORT TABLE OF CONTENTS Section Section Title Page 1.0 INTRODUCTION 1-1 1.1 PURPOSE 1-1 1.2 SCOPE 1-1 1.3 SPILLWAY SAFETY CRITERIA 1-1 2.0 DESCRIPTION OF PROJECT FEATURES 2-1 2.1 GENERAL 2-1 2.2 OGEE SECTION 2-2 2.3 NON-OVERFLOW SECTIONS 2-3 2.4 GEOLOGIC CONDITIONS 2-4 3.0 DESIGN EARTHQUAKE REGIME 3-1 3.1 SEISMOTECTONIC SETTING 3-1 3.2 DESIGN RESPONSE SPECTRA 3-3 3.3 ACCELEROGRAM DEVELOPMENT 3-4 4.0 STABILITY CRITERIA 4-1 4.1 GENERAL 4-1 4.2 LOADS 4-1 4.2.1 Deadweight 4-1 4.2.2 Ice 4-2 4.2.3 Hydrostatic 4-2 4.2.4 Earthquake 4-2 4.2.5 Wind 4-3 4.2.6 Uplift 4-3 4.2.7 Temperature 4-4 4.3 LOADING CONDITIONS 4-4 4.4 ACCEPTANCE CRITERIA 4-5 4.4.1 Stability Requirements 4-5 4.4.2 Minimum Allowable Stress 4-7 4.4.3 Shear-Friction Factor of Safety 4-8 5.0 METHODS OF ANALYSIS 5-l 5.1 STATIC METHOD 5-1 5.2 FINITE ELEMENT METHOD 5-l 5.3 SARMA METHOD 5-2 6.0 STATIC ANALYSIS 6-1 6.1 STABILITY ANALYSIS 6-1 6.2 RESULTS 6-2 7.0 FINITE ELEMENT ANALYSIS 7-1 7.1 STRESS ANALYSIS 7-1 7.2 RESULTS 7-3 TABLE OF CONTENTS (Cont'd) Section Section Title Page 8.0 SARMA ANALYSIS 8-1 8.1 STABILITY ANALYSIS 8-1 8.2 RESULTS 8-2 9.0 CONCLUSIONS 9-1 9.1 CRITICAL CASES 9-1 9.2 SUMMARY OF STABILITY CONDITIONS 9-1 10.0 BIBLIOGRAPHY 10-1 Figure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 LIST OF FIGURES Title Project Layout Map Main Dam Area -General Arrangement General Arrangement -Spillway Project Response Spectra Hybrid Accelerogram Static Spillway Model Case I -Static Analysis-Base El 1124 Case II -Static Analysis-Base El 1124 Case IV -Static Analysis-Base El 1124 Finite Element Model -Base El 1160 Finite Element Model -Base El 1150 Finite Element Model -Base EL 1124 Finite Element Analysis: Case III -Max Tensile Stresses -Base EL 1160 Finite Element Analysis: Case III -Max. Compressive Stresses - Base EL 1160 Finite Element Analysis: Case V -Max. Tensile Stresses -Base EL 1160 16 Finite Element Analysis: Case V -Max. Compressive Stresses - Base EL 1160 17 Finite Element Analysis: Case III -Max. Tensile Stresses -Base EL 1150 18 Finite Element Analysis: Case III -Max. Compressive Stresses - Base EL 1150 19 Finite Element Analysis: Case V -Max. Tensile Stresses -Base EL 1150 20 Finite Element Analysis: Case V -Max. Compressive Stresses - Base El 1150 21 Finite Element Analysis: Case III -Max. Tensile Stresses -Base EL 1124 22 Finite Element Analysis: Case III -Max. Compressive Stresses - Base EL 1124 23 Finite Element Analysis: Case V -Max. Tensile Stresses -Base EL 1124 24 Finite Element Analysis: Case V -Max. Compressive Stresses - Base EL 1124 25 SARMA Analysis Model, Ogee Sections -Sheet 1 26 SARMA Analysis Model, Ogee Sections -Sheet 2 27 SARMA Analysis Model, Non-Overflow Sections 28 SARMA Analysis: Base EL 1160 -Ogee 29 SARMA Analysis: Base EL 1150 -Ogee 30 SARMA Analysis: Base EL 1130 -Ogee 31 SARMA Analysis: Base EL 1124 -Ogee 32 SARMA Analysis: Base EL 1160 -Left Abutment 33 SARMA Analysis: Base EL 1124 -Right Abutment 34 Spillway Stability Analysis Summary -Sheet 1 35 Spillway Stability Analysis Summary -Sheet 2 36 Spillway Stability Analysis Summary -Sheet 3 SPILLWAY STABILITY REPORT 1.0 INTRODUCTION 1.1 PURPOSE The purpose of the stability analysis reported herein is to document that the design of the Bradley Lake Hydroelectric Project spillway meets the required stability criteria as defined for the Project. 1.2 SCOPE This report presents the analysis methods and results for stability analysis of the spillway located adjacent to the main dam at Bradley Lake. The spillway was analyzed to determine stresses and factors of safety under various static and dynamic loading conditions. The spillway was also analyzed to predict maximum potential movement under seismic loading conditions. Static loading conditions included normal maximum reservoir operating level and Probable Maximum Flood (PMF). Dynamic loading conditions included analysis of the Maximum Credible Earthquake (MCE) with normal maximum reservoir level and with a low reservoir level, as well as a pseudostatic analysis of a lower intensity earthquake during construction. A Design Basis Earthquake (DBE) was also evaluated to predict potential movement in order to provide a comparison of MCE and DBE results. 1.3 SPILLWAY SAFETY CRITERIA The basic requirement which must be met by the spillway design is that the reservoir must be retained under all conditions evaluated. Spillway safety criteria were established to aid in evaluating spillway stability and performance. These criteria established limiting allowable stresses and minimum factors of safety. Each loading condition was classified as either a Usual, Unusual, or Extreme Condition, and the acceptance criteria were based on currently accepted recommended minimum factors of safety for the applicable loading condition (Ref. 1). 3777R/20SR/LS 1-1 2.0 DESCRIPTION OF PROJECT FEATURES 2.1 GENERAL The Bradley Lake Hydroelectric Project is located on the Kenai Peninsula in southcentral Alaska. The project will develop the hydroelectric energy potential of Bradley Lake, a natural lake at El 1080, and will have an initial (2 unit) nominal generating capacity of 90MW. The Project consists of water diversion facilities, a concrete-faced rockfill dam, a spillway and an underground power conduit leading to a surface powerhouse with tailrace discharging into Kachemak Bay. See Figure 1 for the general Project layout. The spillway included for reservoir discharge is a mass concrete ungated ogee crest spillway with the crest at El 1180. The spillway was designed to accommodate flows within the range from zero flow up to and including the Probable Maximum Flood (PMF) flow of 23,800 cfs. See Figures 2 and 3 for the location and general arrangement of the spillway. The spillway will be constructed in the low saddle area to the right of the main dam (looking downstream) and will be in line with the main dam baseline. This saddle is formed by a steep rock cliff on the right side of the spillway and a knob of rock on the left that constitutes both the right dam abutment and left spillway abutment. Non-overflow concrete sections will connect the ogee section with the rock abutments on each side. Although the neglecting any structure, that is spillway is designed as a gravity load transfer to the abutments, keys are provided at and to provide better contraction joints seismic stability. to allow some load transfer The spillway will be founded on bedrock. A grout curtain will be developed upstream of the spillway baseline to a depth of 2/3 of the design head at the foundation level. A line of foundation drains will be provided downstream of the grout curtain. 3777R/205R/LS 2-1 The spillway will be provided with an 8 ft wide by 8 ft high drainage gallery generally at the rock surface to allow for inspection and maintenance of the foundation drains. A V-notch measuring weir is provided at the discharge of the drainage gallery to allow measurement of foundation drain seepage rates. The vertical rock cuts adjacent to the spillway aprons will be lined with concrete training walls to prevent erosion and undercutting of the rock. These walls will be tied to the rock with rock bolts. The wall along the west side of the spillway channel will be extended beyond the end of the rock cut to control flow near the diversion tunnel outlet structure and to prevent damage from lateral flow. The agee and non-overflow sections will be constructed of a lower strength mass concrete core (3,000 psi compressive strength at 28 days) and a shell approximately three feet thick of a higher strength concrete (4,000 psi compressive strength at 28 days). The core concrete mix is designed to limit heat of hydration on the mass sections of the pour, whereas the shell concrete mix is designed to provide durability. The shell concrete will be placed concurrently with the core concrete to assure a monolithic structure. For the purpose of establishing allowable stresses, the effect of the higher strength of the shell concrete is neglected in the analysis. 2.2 OGEE SECTION The agee section will have a 175 foot crest length (E1 1180). A 5 foot long concrete apron at the end of the reverse curve on the downstream slope will be cast against rock. The drainage gallery will be provided for the full length of the agee section. In order to minimize rock excavation and concrete quantities, the spillway is designed to discharge to two different downstream elevations. The spillway apron will discharge at approximately El 1135 for a 105 foot length and at approximately El ll65 for a 70 foot length. The corresponding ogee section base elevations on natural rock contours at the 3777R/205R/LS 2-2 upstream edge of the cross section range from approximately El 1120 to 1140 at the lower section and El 1140 to 1160 at the upper section. The natural and excavated rock contours at the downstream edge vary from approximately El 1125 to 1135 at the lower section and El 1160 to 1165 at the upper section. The agee section at each discharge elevation will consist of two blocks separated by a contraction joint. Although keys are provided at these joints, the spillway was analyzed using a unit-width gravity neglecting any load transfer between blocks and to the abutments. method, Static stability analyses were performed for the agee section with base elevations at El 1124, 1135, 1150, and 1160. The spillway is founded on the varying existing rock surface. The above range of assumed base elevations appropriately brackets actual foundation elevations. Finite element analyses were performed for base elevations 1124, 1150, and 1160. 2.3 NON-OVERFLOW SECTIONS Non-overflow sections, extending up to El ll95, will be provided at both ends of the agee section to provide the transition to the adjacent rock. The left non-overflow section (looking downstream) will be approximately 72 feet long and have a foundation on natural and excavated rock contours varying from approximately El 1160 to 1190. The right non-overflow section will be approximately 30 feet long and contain an emergency exit and ventilation shaft for the drainage gallery. Its base will be founded at elevation 1145 and keyed into an inclined rock cut over its entire height. The keying of the right non-overflow section into rock and to the adjacent agee section will provide added stability. To verify stability of the left non-overflow section, sections with bases at El 1160 and El 1180 were evaluated by the static method neglecting the additional restraint provided by keys and varying cantilever heights. The overturning and 3777R/205R/LS 2-3 sliding stability of the right non-overflow section with base El ll45 was deemed not to be critical in the upstream-downstream direction and was not analyzed separately for this condition. However, due to its short length relative to its height, the right non-overflow sect ion was evaluated for seismic stability in the east-west direction. 2.4 GEOLOGIC CONDITIONS The crest of the main dam structure is located approximately 500 ft downstream of the existing Bradley Lake outlet and will dam the Bradley River between two bedrock knobs. The right dam abutment, spillway, and diversion tunnel/gate shaft are founded predominantly in massive graywacke that is generally slightly weathered and hard with occasional deep open joints and fractures, with weathering generally limited to joints. Jointing is well developed, widely to very widely spaced and cross-oriented, giving the exposed rock a large-scale blocky appearance. The spillway lies east of the main dam in a low saddle. Bedrock in the spillway saddle, exposed during excavation performed under the Site Preparation Contract, displays glacial striations and chatter marks left by glacial ice that once occupied the spillway saddle and Bradley River channel. The bedrock also exhibits a smooth polished finish, caused by ice scouring or by glacial meltwater flowing through the spillway saddle. The east cliff has continuous bedrock exposure, and the west abutment knob has numerous outcrops near the crest elevation of the spillway. These outcrops are mapped as graywacke (98%) with very minor argillite (2%). The rock appears fresh and is hard to very hard. The bottom of the saddle has bedrock outcrops and the rock appears identical to the high cliff and rock knob. Hence, the saddle does not appear to have been formed in weaker lithology. This implies a structural influence for the formation of the spillway saddle. 3777R/205R/LS 2-4 A 20-foot-wide, rubble-filled notch (Lineament 3 in the Geotechnical Interpretive Report, Ref. 13) was located, prior to Site Preparation work, at the base of the steep cliffs that form the eastern edge of the spillway site. The lineament is oriented approximately Nl0° W with a near vertical dip. Borings intersected limited zones of highly fractured rock and clayey gouge, and encountered loss of circulation water and high flows during pressure testing. There is no apparent change in lithology across this feature in outcrop or in the boreholes. From aerial photographs, a lineament can be projected through the area and is suspected to be a minor fault or a swarm of closely spaced joints. A small gouge zone is visible at the lake edge, roughly projecting along the cliff face and perpendicular to the spillway baseline. The saddle represents a minor fault or shear zone that has been eroded by glaciation and partially obscured by subsequent glacial and post-glacial deposition. Trenching exposed a 1 to 3 ft wide shear zone, paralleling the base of the cliff. Borings throughout the spillway area show a preponderance of graywacke. Two boreholes, RM43 and DH7EX, were drilled at an angle across the spillway from west to east. Neither boring penetrated all the way to the plane of the cliff east of the spillway. However, these two borings, and others drilled near to the east cliff, showed evidence of highly to intensely fractured rock with some gouge present in one area. In several borings, circulation water returns were lost and not recovered. Several small groundwater seeps, which originate from bedrock fractures, flow from the high ground to the east and were noted on the face of the east cliff. Major joints in and adjacent to the spillway trend and dip N84° W, 84° S and N25° E, 72° SE. Where trenching exposed joints, they often made small amounts of water (up to 0.5 gpm) for periods of less than 12 hours. Overburden depths in the area of the spillway are quite variable, originally ranging from 2 ft on the west flank to an estimated 17 ft near the east cliff. As a result of excavation during Site Preparation, very little overburden remains on the crest of the saddle. Throughout the spi 11 way area, the soil materials consist of till and alluvium with cobbles and boulders (greater than 5 ft in dimension) in a silty, sandy gravel matrix. Very coarse and bouldery graywacke talus lies below the eastern cliff and extends from the saddle to the bottom of the spillway. 3777R/205R/LS 2-5 All overburden from the upstream edge of the spillway to the downstream pool (to El 1060) will be removed to the bedrock surface. Overburden varies in thickness from 2 ft near the crest to greater than 60 ft (locally) near the downstream pool. Due to the presence of geologic structure through the saddle and the proximity of steep cliffs to the east, the overburden is expected to contain talus in addition to the glacial till. The bedrock surface is expected to be locally somewhat fractured and weathered. This will require some grouting and limited dental concrete for foundation improvement. Some ripping and limited blasting will be necessary to meet design grade and flow path requirements in the apron area, in addition to the specified controlled blasting in the concrete foundation area. A grout curtain is designed to transect upstream base of the spillway structure. The curtain extends eastward about 80 ft from the cliff face. This will be done to seal a series of joints, which are oriented approximately N48° W. These fractures may connect the reservoir with the downstream pool, so they will be grouted to reduce potential leakage. More detailed geologic data is provided and referenced in the Geotechnical Interpretive Report, contained in the General Civil Construction Contract as Volume 6 and in the report entitled 1987 Geotechnical Exploration Program (Ref 12). 3377R/205R/LS 2-6 3.0 DESIGN EARTHQUAKE REGIME 3.1 SEISMOTECTONIC SETTING The detailed project seismic design studies and parameters are provided in two reports by Woodward-Clyde Consultants (Ref. 2 and 3). Southern Alaska is one of the world's more seismically active regions. The primary cause of seismic activity in southern Alaska, including the site area, is the stress imposed on the region by the relative motion of the Pacific and the North American tectonic plates at their common boundary. The Pacific plate is moving northward relative to the North American plate at a rate of about 2-1/2 inches/year causing underthrusting of the Pacific plate. This underthrusting results primarily in compressional stresses which cause folds, high-angle reverse faults, and thrust faults to develop in the overlying crust. A counterclockwise rotational effect also induces strike-slip faulting parallel to the plate boundary. The boundary between the plates where the underthrusting occurs is a northwestward-dipping megathrust fault or subduction zone. The Aleutian Trench marks the surface expression of this subduction zone and is located on the ocean floor approximately 185 miles southeast of Bradley Lake. The orientation of the subduction zone is inferred along a broad inclined band of seismicity, referred to as the Benioff Zone, that dips northwest from the Aleutian Trench, and is approximately 30 miles beneath the surface at the Bradley Lake site. Great earthquakes (Richter magnitude M =8 or s greater) and large earthquakes (M =7 or greater) have occurred s historically throughout the region and can be expected to occur in the future. Historically (1899 to date), eight earthquakes ranging between M =7.4 and M =8.5 have occurred within 500 miles of the site. (Table 3 s s in the Dam Stability Report provides a representative sunnnary of historic seismic events within 100 miles of the area.) 3777R/205R/LS 3-1 Bradley Lake is situated on the overriding crustal block above the subduction zone and between the Castle Mountain fault to the northwest and the Patton Bay-Harming faults to the southeast. All of these faults have documented Holocene or historic surface ruptures. Because of the active tectonic environment, activity is conceivable on other faults, such as those found near or at the project site between the known active faults mentioned above. Two faults of regional extent exist at or near the site. Fault trends southwest beneath Kachemak Bay to the The Border Ranges northwest of the project, and the Eagle River fault crosses the southeastern end of Bradley Lake at about the same trend. While no evidence of recent activity along these faults has been found in the site area, recently reported data indicates recent activity on the Eagle River Fault near Eklutna (125 mi NE of the site). Given the tectonic setting, it is reasonable to consider these faults as potentially active. In addition to the nearby regional faults, the site is crossed by two large local faults, the Bradley River Fault and the Bull Moose Fault, and a number of confirmed and probable smaller faults. The dominant trend is northeasterly, paralleling the regional trend. The larger local faults, particularly the Bradley River, are considered as potentially capable of independent earthquake generation, while any of the local faults could possibly move in sympathetic response to earthquakes occurring on the regional faults. It is therefore concluded that the site will probably experience at least one moderate to large earthquake during the life of the proposed project. The possibility of significant ground rupture exists but is much less subject to prediction and is considered to have a much lower probability. 3777R/205R/LS 3-2 3.2 DESIGN RESPONSE SPECTRA The response spectra utilized for this analysis were taken from a report prepared by Woodward-Clyde Consultants (WCC) for the Army Corps of Engineers (Ref. 2). The report documents the work performed by WCC to develop parameters for what the Corps terms the "design maximum earthquake" and the "operational base earthquake" , henceforth called Maximum Credible Earthquake and Design Basis Earthquake, respectively. The Maximum Credible Earthquake (MCE) is defined as the most severe earthquake believed to be probable which could affect the site. The Design Basis Earthquake (DBE) is less severe, and is defined as the seismic level which is considered as likely to occur during the life of the project. Maximum Credible Earthquakes are normally used as a basis for determining whether or not certain structures can structurally withstand extreme events having remote probabilities of occurring, regardless of damage level. Design Basis Earthquakes are used as a basis for estimating the maintenance and other costs resulting from events expected to occur, and for design of non-critical structures where severe damage and loss of .function in a major seismic event are considered an acceptable risk. The response spectra for the MCE will be used in the seismic stability analysis of the spillway. Based on their work on the seismicity of the site, wee proposed two possible response spectra for the "design maximum earthquake", the equivalent of the MCE. The one which was expected to control was based on rupture of one of the faults nearest the site. The resulting earthquake would have a magnitude of M =7. 5, peak ground acceleration of 0. 75g at s the site, and a significant ground motion duration of 25 seconds. This event would have a response spectrum roughly corresponding to the upper smooth curve on Figure 4. The other possible MCE was an event tied to the Benioff Zone roughly 30 miles beneath the site. This event would have a magnitude of M =8.5, s peak ground acceleration of O.S5g at the site, and a significant ground motion duration of 45 seconds. It was not expected to be the controlling event unless the faults in the innnediate vicinity of the site could be shown to be inactive. 3777R/205R/LS 3-3 A third response spectrum proposed by wee was an event with a peak ground acceleration approximately one half that of the MCE. This was used for the DBE, resulting in a peak ground acceleration of 0.35g (Fig. 4). 3.3 ACCELEROGRAM DEVELOPMENT Because the near field mega thrust M =8. 5 event, s crustal M =7.5 event is more severe than the s in terms of both peak parameters and spectral accelerations throughout the frequency range of interest, an accelerogram for the crustal event is of primary interest. The mega thrust event is considered in detail in the wee reports, but was utilized in design only for parametric comparative purposes. Since all critical structures of the Bradley Lake Project are founded on bedrock, accelerograms recorded on rock from large magnitude earthquakes having similar parameters to those listed above for the crustal event would ideally be used for the required analyses. More importantly, the response spectra of any accelerograms used for design should match, in an average sense, the curve shown in Figure 4. At the time the analysis was being performed, no accelerograms recorded on rock in the near field of large magnitude earthquakes (M =7. 5) were available from anywhere in the world, s including Alaska. Consequently, available accelerograms from historical earthquakes having appropriate peak and spectral characteristics over a broad period range, even when scaled, were not available for use. Since no actual accelerogram was available, a composite hybrid accelerogram was derived for the dam and spillway stability analyses from the historical accelerograms of two earthquakes having appropriate characteristics. This approach has been previously used for other studies, including those performed by the California Department of Water Resources for Oroville Dam, and is considered an appropriate state-of-the-art method for simulation of strong motion events. 3777R/ 205R/ LS 3-4 After examining the response spectra for recorded accelerograms from a number of earthquakes in the United States and abroad, it was concluded that a suitable accelerogram for the M =7.5 crustal event could be s obtained by combining the S69° E component of the Taft record from the 1952 Kern County, California earthquake and the East-West component of the San Rocco record from the September 15, 1976 Friuli, Italy earthquake. The Taft record was scaled by a factor of 3.5 and was used to represent the hybrid earthquake from time 0.00 to 2.32 seconds and from 4.32 seconds to the end. The portion of the Friuli record from time 2.14 to 4.10 seconds was scaled by a factor of 3.2 and inserted into the scaled Taft record, replacing the port ion of the Taft record from time 2. 34 through 4. 30 seconds in the hybrid record. In effect, the portion of the Friuli record with the highest accelerations was spliced into the high-acceleration portion of the Taft record, resulting in a record with greater duration and a greater proportion of relatively high acceleration peaks. The resulting accelerogram, called the Hybrid record, is shown on Figure 5, and its response spectrum is compared to the spectrum recommended by WCC in Figure 4. The significant duration of the Hybrid record is 28.8 seconds, which is slightly longer than the 25 second MCE proposed by WCC. This longer event duration, when combined with the greater density of high acceleration peaks from the combined records, results in a design record which is conservatively intense and definitely on the safe side when used to simulate the project MCE. 3777R/205R/LS 3-5 4.0 STABILITY CRITERIA 4.1 GENERAL The spillway was evaluated for sliding stability, for maximum compressive and tensile stresses, and for the maximum permanent deformation under dynamic loading. The evaluation of the sliding stability and stresses was performed in general agreement with the gravity method as presented in "Engineering Guidelines for the Evaluation of Hydropower Projects", FERC 0119-1 (Ref. 11). The gravity method was used in both the static and finite element analyses. Permanent dynamic deformations were evaluated using the Sarma method of analysis. The maximum stresses were evaluated for loading Cases I, II, and IV by the static method and for Cases III and V (MCE) by the finite element method. For these analyses, uplift in an uncracked section was not included as an active external force (i.e., uplift does not contribute to overturning) since it is an internal pressure resisted by the structure until cracking occurs. The calculated stress was combined with the uplift pressure by superposition to determine the effective stress. For static loading conditions, uplift in a cracked section was considered as an active force (i.e., uplift in a crack acts as an external hydrostatic force). The sliding stability was evaluated for loading Cases I, II, and IV by calculating the shear-friction factor of safety in the static analysis. The sliding stability for dynamic loading conditions (Cases III and V) was evaluated by determination of the maximum permanent dynamic deformation using the Sarma method of analysis. 4.2 LOADS 4.2.1 Dead Weight The weight of the spillway was evaluated using a concrete unit weight of 145 lbs/cu ft. 3777R/205R/LS 4-1 4.2.2 Ice An ice load of 12,000 lbs/lin ft was applied at El 1179. This was based on an assumed ice thickness of 28 inches. 4.2.3 Hydrostatic Hydrostatic pressures were calculated based on a unit weight of water of 62.4 lbs/cu ft. For the Probable Maximum Flood (PMF) condition, the hydrostatic forces downstream of the crest were considered negligible. While the horizontal hydrostatic force on the upstream face was based on the PMF reservoir level, the vertical hydrostatic force on the upstream face was reduced by five feet to account for drawdown at the spillway crest. Due to the spillway elevation relative to lake bottom, forces due to accumulated sediment were determined to be negligible. 4.2.4 Earthquake Two earthquakes were evaluated for the stress analyses: the Maximum Credible Earthquake (MCE) with a peak horizontal ground acceleration of 0.75g, and a Construction Condition Earthquake with a peak horizontal ground acceleration of O.lOg. The Sarma analysis also evaluated the Design Basis Earthquake (DBE) with a peak horizontal ground acceleration of 0.35g. Vertical ground accelerations in all cases were assumed equal to 2/3 the horizontal accelerations. The pseudostatic and finite element analyses considered horizontal and vertical seismic forces to act simultaneously. The acting alone after Sarma analysis both components evaluated horizontal seismic forces of acceleration were utilized to calculate the critical horizontal acceleration. Static analysis assumed an acceleration equal to the peak ground acceleration. Finite element analysis was based on the Project Response Spectra (Figure 4) and the Sarma analysis was based on the developed Hybrid Accelerogram (Figure 5). 3777R/205R/LS 4-2 The hydrodynamic earthquake pressure was based on the Westergaard added mass approach (Ref. 7 & 8) for the finite element method and based on the Zangar formula (Ref. 1 & 6) for the static and Sarma methods. The difference in magnitude of these forces utilizing the two differing methods is not significant to the results. 4.2.5 Wind A wind loading of 90 psf was evaluated as an alternate loading to the Construction Condition Earthquake but was found to be a less critical case. This loading is equivalent to Uniform Building Code (UBC) Exposure C with a 120 mph wind speed and a 1.15 Importance Factor. 4.2.6 Uplift The uplift pressure at all lift lines above the foundation was assumed to vary linearly from the full headwater pressure at the upstream face to zero at the downstream face. The PMF headwater pressure at the upstream face was based on 50% headrise above normal headwater pressure. Uplift pressures at the downstream face were assumed as negligible for the PMF case. At the rock-concrete interface the foundation drains were considered SO% effective, so the uplift was assumed to vary linearly from full headwater pressure at the upstream face to 50% of headwater pressure at the foundation drains, then decreasing linearly to zero at the downstream face, (Ref. 4). The drainage gallery will permit inspection, monitoring, and maintenance of drains. For static cracked sections, the uplift was assumed at full headwater pressure for the length of the crack then decreasing linearly to zero at the downstream face. Uplift for the dynamic analysis was not revised from that developed for the Normal Condition. Uplift was assumed to act over 100 percent of the base area. 3777R/205R/LS 4-3 4.2.7 Temperature Loadings from volumetric changes due to temperature change were not considered in the analysis since the joints are not grouted. While the loadings were not evaluated, consideration was given to temperature effects in location of contraction joints and in material selection. 4.3 LOADING CONDITIONS Five loading combinations were considered, as follows: Case I Normal Reservoir -Usual Condition 1. Normal Max. Reservoir El 1180 2. Uplift and seepage forces 3. Dead loads 4. Ice at El 1179.0 Case II Probable Maximum Flood (PMF) -Unusual Condition 1. Max. Reservoir El 1191 2. Uplift and seepage forces 3. Dead loads Case III Earthquake -Extreme Condition 1. Normal Max. Reservoir El 1180 2. Uplift and seepage forces 3. Dead loads 4. Ice at El 1179.0 5. Maximum Credible Earthquake (0.75g) Case IV Construction Case -Unusual Condition 3777R/205R/LS 1. Reservoir water surface at El 1065 2. Dead loads 3. Construction Condition Earthquake (O.lg) or wind load 4-4 Case V Low Reservoir with Earthquake -Extreme Condition 1. Reservoir below El 1124 (no hydrostatic) 2. Dead 1 oads 3. Maximum Credible Earthquake (0.75g) Ice loads were not included in the SARMA analysis. 4.4 ACCEPTANCE CRITERIA 4.4.1 Stability Requirements Maximum allowable stresses and minimum required factors of safety are as specified in Table 4-1. These values are based on factors of safety as recommended in Design of Gravity Dams (Ref. 1) for Usual Loadings, Unusual Loadings, and Extreme Loadings and factors of safety specified in project design criteria. TABLE 4-1 Case I Case II Case III Case IV Case V Normal PMF Earthguake Construction Low Res. Stresses: Concrete (f'c = 3000 psi) Assumed Safety factor 3.0 2.0 1.0 2.0 1.0 Compression, psi 1000 1500 3000 1500 3000 Tension, psi ;'r 60 90 270 90 270 Rock (40 ksf = 280 psi )~·r:r:r Assumed Safety factor 2.0 1.5 1.1 1.5 1.1 Compression, psi 140 185 250 185 250 Tension, psi -:c 0 0 ..,•c 0 0 Sliding: Shear -Friction in Concrete Safety factor 3.0 2.0 1.0 2.0 1.0 (in Concrete and at Rock/Concrete Interface) On Rock Foundation Joints and Faults Safety factor 4.0 3.0 1 • 2-lrlr 3.0 1. 2-lr:r 3777R/205R/LS 4-5 *For Usual and Unusual Conditions, tensile resistance is allowed only above the rock-concrete interface. For dynamic stress analysis by the finite element method, the tensile stress at the rock-concrete interface shall not exceed the allowable tensile capacity of the concrete. Tensile capacity of concrete is increased 50 percent above static tensile capacity for dynamic loading conditions. ~rlcSafety factors are not relevant to the SARMA analysis. ~rlrlcSafety factors for rock bearing capacity are applied against the allowable bearing capacity, which already includes a minimum factor of safety of two relative to ultimate bearing capacity. Thus actual factors of safety are at least double those shown and exceed the recommended factors of safety given in References 1 and 11. The structure may be considered stable against overturning when the minimum calculated stress, without uplift, meets the requirements of paragraph 4.4.2 and when the maximum compressive stresses are 1 ess than those specified above. The structure may be considered stable against sliding when the shear-friction factor of safety, as given in paragraph 4.4.3, is greater than the value specified above. 3777R/205R/LS 4-6 4.4.2 Minimum Allowable Stress The evaluation of stresses assumes that the concrete has tensile strength. In order not to exceed the allowable tensile stress, the minimum allowable stress without uplift (assuming compression is positive and tension is negative) is determined by: where: Minimum allowable stress = WH -ft w = H = unit weight of water depth below reservoir surface ft = allowable concrete tensile strength at lift surfaces which includes the safety factor as given in Table 4-1 for concrete; zero at rock-concrete interface. For static cases, tensile strength = 61 x compressive strength For dynamic cases, tensile strength = 1501 x static tensile strength If the calculated minimum stress (without uplift) is less than the minimum allowable stress given above then cracking is assumed to occur. If the minimum stress for a Usual or Unusual case is less than zero, i.e., tension present, then reinforcing steel is required to limit crack development. 3777R/205R/LS 4-7 4.4.3 Shear-Friction Factor of Safety The shear-friction factor of safety is the ratio of resisting to driving forces as computed by: where: Q Q c A N 0 H = = = = CA + N Tan 0 H shear-friction factor of safety unit cohesion 300 psi at concrete on concrete (10% f'c) = 160 psi at concrete on rock = = = area of base in contact (uncracked section) summation of normal loads including uplift forces internal friction angle = 45° at concrete lift lines = 45° at concrete on rock = summation of horizontal driving forces The passive resistance of the vertical rock against which the spillway apron is cast was not included in the resisting forces, due to potential water scouring and sloping of the bedrock contour surface away from the spillway apron. 3777R/20SR/LS 4-8 5.0 METHODS OF ANALYSIS 5.1 STATIC METHOD The static method analyzes the spillway using the gravity method by solving for the summation of forces and moments acting on a theoretical one foot vertical strip of the structure. The effects of load transfer across the keyed joints and the effects of transversely sloping foundations were conservatively omitted. Seismic loads for Case IV, Construction Case, were included as pseudostatic forces. This analysis calculates the maximum compressive and tensile stresses, shear friction factors of safety, summation of vertical and horizontal forces, location of resultant force and, if present, the crack length. This is the simplest of the methods of analysis used and is useful in evaluating the overall stability for various loading conditions. It does, however, possess a number of limitations. A significant limitation is that it does not take into account the frequency characteristics of a dynamic loading or the natural frequency of the structure. Where large peak accelerations are expected, as for Cases III and V, a pseudostatic analysis is considered to be inappropriate for analysis of dynamic stability. For this reason, a dynamic analysis has been performed. 5.2 FINITE ELEMENT METHOD Due to the potential seismic risk and the magnitude of the seismic design accelerations, with capable faults near the spillway site and located in a seismic Zone 4 region as specified in "Engineering Guide! ines" (Ref. 11), the spillway was dynamically analyzed. In order to take into account the frequency characteristics of the structure and the seismic loading, a two-dimensional finite element analysis was performed on the concrete ogee sections. The non-overflow sections were not analyzed for dynamic stresses for Cases III and V, but are considered adequate for seismic stresses by comparison of cross sections and loadings with the ogee sections analyzed. 3777R/205R/LS 5-1 STARDYNE (Ref. S) was used to perform two-dimensional linear elastic analyses to obtain the stresses in the spillway and the reactions at the base for the loading conditions considered. The STAR program of STARDYNE was used to do the static analysis for water load, ice thrust force, and dead weight of spillway and to perform the frequency and modal shape analysis. The seismic analysis was done by the DYNRE4 program of STARDYNE. 5.3 SARMA METHOD In order to predict the maximum potential permanent deformation of the spillway under seismic loading conditions, the spillway sections were analyzed by the SARMA (Seismic Amplification Response by Modal Analysis) computer program (Ref. 9). This program has been developed by Stone & Webster Engineering Corporation and qualified for the Nuclear Regulatory Commission to evaluate potential deformations utilizing the methods of S. K. Sarma and N. N. Ambraseys for seismic amplification in fill structures and N. M. Newmark for the cumulative displacement under dynamic excitation. This program was used to evaluate potential movement of the various spillway sections, conservatively neglecting cohesion at the rock-concrete interface. This method is one that is often used to model the response of dams to earthquakes when the pseudostatic method is inappropriate. It is commonly used by the Army Corps of Engineers in modeling for new dam design and for analysis of existing dams. The Sarma method starts with the calculation of resonant frequencies and modal response shapes of the structure. The next step is calculation of participation factors for a given potential failure wedge or block. These factors describe how much effect each of the modes of oscillation will have on the potential failure wedge. Once this is accomplished, the accelerations of the wedge in each mode in response to the earthquake accelerogram are calculated and the displacements from the various modes 3777R/205R/LS S-2 due to each pulse are combined. The result is a time-history of the accelerations the earthquake if it foundation. wedge would experience as remained attached to the a result of the chosen rest of the structure or Once the time-history of acceleration pulses of the individual wedge is known, the cumulative displacement is calculated by Newmark's sliding block procedure (Ref. 10). In this procedure, the wedge is assumed to remain fully attached as long as the average acceleration of the wedge is less than a specified critical (or break-free) acceleration. When the acceleration exceeds the critical acceleration, the wedge slides relative to its support until it comes to rest during a subsequent reversal of the acceleration. The total displacement of the wedge is taken as the sum of all the increments of movement that occur during a particular earthquake record. In this case, the entire spillway was taken as a single wedge supported by the foundation for analytic purposes. 3777R/205R/LS 5-3 6.0 STATIC ANALYSIS 6.1 STABILITY ANALYSIS Load Cases I, II and IV were evaluated by the static method. Seismic loads in Case IV were included as pseudostatic forces. Due to the relative flexibility of the spillway apron with respect to the remaining structure, the apron area was neglected in calculations and assumed to be detached. The toe was assumed at a hypothetical extension of the downstream face slope, as shown in Figure 6. Since the apron deadweight exceeds the uplift in that region, uplift under the apron was also neglected. Uplift was also conservatively assumed to act across the gallery width. Any Usual or Unusual case where the minimum stress, without uplift, at the upstream face is less than that required by paragraph 4.4.2, will require reinforcing steel. The concrete and reinforcing steel stresses for such cases have been evaluated based on concrete working stress methods with all concrete tensile capacity neglected. Shear-friction factors of safety were calculated based on net uncracked areas. It should be noted that the effective stress, including uplift, may be tensile without assuming cracking provided that the tension is caused solely by the uplift pressure. The spillway agee section was evaluated at base elevations of El 1124, 1135, 1150 and 1160, and for lift lines at El 1140, 1150, 1160 and 1170. Due to tension on the upstream face at El 1170 in the Usual Condition, evaluations of additional lift lines at El 1165 and El 1175 were added. The remaining lift lines were evaluated by interpolation. Non-overflow sections at the left spillway abutment were evaluated with base elevations at El 1160 and El 1180. The non-overflow section at the right spillway abutment is keyed into rock along its base and sloping east face, with most of its 15 foot base width keyed horizontally into rock and a minimum of 3 feet keyed horizontally into rock above the base. 3777R/205R/LS 6-1 A summary of sliding factors of safety and maximum effective tension and compression stresses within the agee section is given in Table 6-1. Detailed information for each case and elevation, with agee base El 1124, is provided in Figures 7 to 9. TABLE 6-1 STATIC RESULTS-OGEE SECTION Case I Case II Case IV Usual Unusual Unusual Shear-Friction F.S. Min Calculated 5.2 13.6 61.0 Allowable 3 2 2 Concrete Compression (psi): Max Calculated 45 34 48 Allowable 1000 1500 1500 Concrete Tension, Incl. uplift (psi): Max Calculated 3.6* (No Tension) (No Tension) Allowable 60 90 90 Rock compression (psi): Max Calculated 32 34 48 Allowable 140 185 185 '" Maximum tensile stress due to uplift without cracking assumed is 3. 6 psi. Maximum tensile stress including ice load and uplift is 7. 3 psi, neglecting reinforcement. Section is reinforced in all tensile zones. 3777R/205R/LS 6-3 Cohesion and shear-friction along the rock cut will assist in resisting overturning in the north-south direction. Based on these facts and evaluation of the non-overflow section with base El 1160, the right non-overflow section was deemed acceptable for stability in the north-south direction, but required further evaluation for seismic loading in the east-west direction. 6.2 RESULTS The static analysis indicates that the ice loading in the Usual Condition results in tension (5 psi) on the upstream face of the spillway agee section at El 1170 and El 1175. However, stresses for the Usual Condition without ice load or uplift remained compressive. Reinforcing was added to control cracking due to the ice load, with very low resulting steel stresses (f = 3. 4 ksi). Since some reinforcing was being added in the s upstream face near the crest due to tension, it was extended down the upstream face to the base elevation and over the crest to the point of inflection to limit thermal and shrinkage cracking and to improve overall stability. It should also be noted that if the reservoir level were at El 1178 with the corresponding iceload applied at El ll77. the static analysis for the Usual Condition, without uplift, indicates no concrete tension or cracking. As ice will occur primarily during winter months when the reservoir is lower, the potential for cracking due to ice load is very small. All remaining cases and levels were found to meet the stability criteria without additional reinforcing. The effective stress, including uplift, for El ll60 and El ll65 in the normal reservoir case was tensile, but these tensile stresses were due to uplift so cracking was not assumed. With the exception of those levels requiring reinforcing due to ice load (El 1170 and El ll75), the resultant for all Usual and Unusual Conditions (Case I, II, and IV) is located within the middle third of the section. No tension was indicated at the rock-concrete interface for any of the static analyses. 3777R/205R/LS 6-2 The non-overflow sections analyzed with bases at El 1160 and El 1180 were found to be statically stable in all cases. For Cases I & II the stresses at El 1160 without uplift were always compressive at 23 psi to 40 psi. The minimum shear-friction factor of safety for these cases was in excess of 22. Case IV indicated stresses of 1 psi to 72 psi and a shear-friction factor of safety over 56. The right non-overflow section was evaluated for seismic stability in the east-west direction using pseudostatically applied accelerations at 0.35 g and 0.75 g. In order to improve the stability of the right non-overflow section, the concrete section will be tied back into the rock abutment using rock bolts. 3777R/205R/LS 6-4 7.0 FINITE ELEMENT ANALYSIS 7.1 STRESS ANALYSIS Required inputs for the finite element analysis are as follows: (1) Physical geometry of the ogee sections. (2) Elastic modulus and Poisson's ratio of concrete. (3) Deformation modulus and Poisson's ratio of rock. (4) Density of concrete. (5) Hydrostatic loads, corresponding to reservoir EL 1180. (6) Ice thrust force, equal to 12000 lb/lin ft at EL 1179. (7) Ground response spectra. (8) Uplift and seepage forces. (Combined with finite element results by superposition.) In addition, to account for the hydrodynamic effects of reservoir water during the earthquake, the Westergaard added mass approach was used to calculate the additional mass (Ref. 7 and 8). Two types of concrete m1x were selected for the spillway construction. The mass concrete core will be constructed with a specified concrete compressive strength of 3000 psi and the outer 3 foot shell will be constructed with a specified concrete compressive strength of 4000 psi. The spillway was evaluated with properties for 3000 psi concrete. The moduli of elasticity and Poisson's ratio used in the finite element analysis are given in Table 7-1. 3777R/205R/LS 7-1 TABLE 7-1 ASSUMED CONCRETE PROPERTIES f' = 3000 psi c Modulus of Elasticity: (psi) Static Dynamic Poisson's Ratio 0.2 The assumed rock foundation deformation modulus was taken as 4xl0 6 psi. Poisson's ratio for the rock was taken as 0.27 for static conditions and 0.35 for dynamic conditions. These values were based on Beiniawski's Rock Mass rating method for moderately fractured rock. The spillway was designed for an earthquake with the response spectrum shown on Fig. 4, Mean Horizontal Response Spectrum, with a normalized peak acceleration of 0. 75g and 5 percent damping. Vertical earthquake ground motions were assumed equal to 2/3 the horizontal motions. The spillway may be considered to have the so-called "plane strain" state of stress. Therefore, a finite element model with two-dimensional elements was adopted for this analysis. These elements can be either quadrilateral or triangular in shape. To account for the contribution from the stiffness of the rock foundation, the foundation was included in the model. The model included a foundation with its depth equal to the height of the concrete spillway and extending a distance equal to the height of the spillway upstream and downstream from the spillway. The seismic stress was obtained by response spectra modal analysis. In each direction of earthquake, the contribution from each mode was combined by square root of the sum of the squares (SRSS) of all modes considered. The results from each direction (vertical and horizontal) were then combined by vector sum. 3777R/205R/LS 7-2 Three finite element models were prepared. Models were for ogee sect ions at base El 1160, 1150, and 1124 (Figures 10,11, and 12, respectively). 7.2 RESULTS The stresses for the ogee sect ions for Cases III and V are presented in Figures 13 to 24. All stresses at each of the sections of spillway analyzed under the extreme loading conditions were within the allowable stresses based on 3000 psi concrete. Uplift pressures were combined by superposition with the computer analysis results for Case III to obtain maximum concrete tensions. For Case V the section was analyzed without hydrostatic loads but for simplicity included the Westergaard. added mass in the seismic analysis. This approach resulted in slightly conservative seismic stresses but well within allowable values. A summary of maximum stresses for Case III and Case V is given in Table 7-2. The shear-friction factor of safety was not calculated using the finite element method. Sliding stability was evaluated using the Sarma method of analysis. TABLE 7-2 FINITE ELEMENT RESULTS CASE III CASE V Base at: El ll24 El ll50 El ll60 El ll24 El 1150 El ll60 Concrete Compression (psi) Max Calculated 155.7 77.9 52.3 165.5 86.3 48.8 Allowable 3000 3000 3000 3000 3000 3000 Concrete Tension (psi) Max Calculated: W/o uplift 87.3 32.1 45.4 77.5 18.3 22.5 Incl. uplift 111.6 45.1 54.1 Allowable 270 270 270 270 270 270 Rock Compression (psi) Max Calculated 155.7 77.9 52.3 165.5 86.3 48.8 Allowable 250 250 250 250 250 250 3777R/205R/LS 7-3 8.0 SARMA ANALYSIS 8.1 STABILITY ANALYSIS The sliding stability of the spillway was evaluated by dynamic analysis. The analysis utilized the SARMA computer program (Ref. 9) to model the response of the spillway under earthquake loading. In order to use the SARMA program the following assumptions were made: the concrete spillway sections act as an intact failure wedge, the failure plane is the contact between the spillway sections and the foundation rock or a horizontal approximation of same, and the spillway sect ions will remain intact. All downstream rock restraint was ignored in the analysis, resulting in significant conservatism in the final sliding stability. The shear wave velocity, the mass density, and the critical accelerations of the spillway are needed as input to the program. The shear wave velocity (V ) was calculated using the following relationship between the s modulus of deformation (G) and the mass density: V = (G/mass density)112 s The mass density was calculated assuming the unit weight of the concrete was 145 lb/ft 3 . The critical acceleration of a wedge section is the horizontal earthquake acceleration necessary to initiate sliding. The critical acceleration depends on the assumed loading conditions and is found by statics. Six spillway cross sections were evaluated in the analysis, including four spillway ogee sections and two non-overflow sections. The SARMA program requires that the section to be analyzed be modeled as a symmetrical triangle. To model the spillway sections most accurately, the model triangle was configured to have the same center of gravity, base elevation, and area as the spillway section being modeled, as shown in Figures 25 to 27. 3777R/205R/LS 8-1 Several loading cases and special conditions were considered. It was assumed in all cases that the reservoir was at El 1180, as this was more critical than the low water reservoir condition. In the first case, the static head was included and the only resisting force considered was the friction (45 degree friction angle) between the concrete and the rock. The uplift pressure was assumed to be the full head at the upstream face, decreasing linearly to 1/2 the head at the drainage gallery, and then decreasing linearly to zero at the downstream toe. The vertical earthquake acceleration, 2/3 of the horizontal acceleration, was used in the static analysis to determine the critical horizontal acceleration. In the second case, the inertial force of the water created by the earthquake was also included by using Zangar's formula, (Ref. 6). In the third case, the inertial force of water was again taken into account as well as 500 psf cohesion between the rock and the concrete. The worst case providing the greatest cumulative displacement is the second case. This case was analyzed for peak horizontal ground accelerations of 0.35g and 0.75g. 8.2 RESULTS The maximum displacement occurred in horizontal ground acceleration of 0.75g eration. The displacement was 0. 5 feet. the second case, with a peak combined with vertical accel- It should be noted that the inertial force of the water is not usually considered in such a dynamic analysis and resulted in slight decreases in critical acceleration for all sections. There was no movement for the construction case earthquake of O.lg and essentially no movement for the design basis earthquake of 0.3Sg, with its worst displacement being about 1/100 of a foot with no cohesion assumed. It is concluded that the movement of the spillway under earthquake loading will be small and considering the keyed and fixed-edge plate configuration will likely be zero even in the MCE case. The amount of intact rock-concrete area needed to force critical wedge accelerations of at least 0.75g and 0.35g was also calculated. The required amounts were 2.4% and 0.3% of the surface area respectively in the worst case based on a rock shear strength of 1500 psi. As intact shear-capable rock is expected to be in excess of 75% under all sections, 3777R/205R/LS 8-2 the resultant stability is expected to be far in excess of that needed to prevent movement. Similarly, with no intact rock, but using a contact shear strength of 160 psi, the percent bonded area to prevent movement during the MCE and DBE would be 22 and 2.5 percent, repsectively. The sununary of MCE load displacements for Case 2 is presented 1n Table 8-1. Seismic displacement plots for the four ogee sections, and two non-overflow sections for the MCE case are presented in Figures 28-33. TABLE 8-1 SARMA RESULTS Case 2: 0 = 450, no cohesion, Zangar's water force Critical Max Gnd Displacement Base El. Section Acceleration Acceleration (ft) 1160 Ogee 0.231 0.75g 0.51 1150 Ogee 0.282 0.75g 0.32 1130 Ogee 0.258 0.75g 0.38 1124 Ogee 0.263 0.75g 0.37 1160 Non-overflow 0.443 0.75g 0.06 1124 Non-Overflow 0.334 0.75g 0.20 3777R/205R/LS 8-3 9.0 CONCLUSIONS 9.1 CRITICAL CASES Static loading Case I requires the addition of reinforcing steel on the upstream face near the ogee crest to prevent cracking due to the ice loads. All other static loading conditions, including the Usual Condition without ice loads considered, meet the stability criteria without cracking. The dynamic analyses for the seismic loading conditions indicate that the structure is stable under the Extreme Loading Conditions. The finite element analyses indicate that the concrete stresses due to the Extreme Loading Conditions are within acceptable limits. The Sarma analyses indicate that the potential spillway deformation is not extreme under the earthquake condition even assuming no cohesion or intact rock at the spillway base. Consequently, the spillway stability is considered to be acceptable under the seismic loading for the given Maximum Credible Earthquake and all lesser events. 9.2 SUMMARY OF STABILITY CONDITIONS The calculated stresses and factors of safety for the bases of the analyzed structures are summarized on Figures 34-36. The maximum calculated tensile stress is 87 psi and the maximum calculated compressive stress is 166 psi, well within allowable stresses as specified in Table 4-1. The minimum calculated shear-friction factor of safety for Cases I, II, or IV is 5.2, also with a margin of safety to minimum requirements. The maximum calculated MCE permanent mass displacement, assuming a hypothetical continuous and cohesionless failure plane, is small enough (6 inches) that it would not result in breaching of the spillway. With the anticipated rock conditions and specified foundation surface preparation, the MCE is expected to result in no measurable permanent base displacement. Consequently, the spillway is considered stable under all given loading conditions. 377R/205R/LS 9-1 10.0 BIBLIOGRAPHY 1. Design of Gravity Dams, United States Department of the Interior, Bureau of Reclamation, 1976. 2. Woodward-Clyde Consultants, "Report on the Bradley Lake Hydroelectric Project, Design Earthquake Study," submitted to Alaska District, Corps of Engineers, Nov. 10, 1981. 3. Woodward-Clyde Consultants, "Seismicity Study, Bradley Lake Hydroelectric Project," submitted to Alaska District, Corps of Engineers, March 28, 1980. 4. Stability Criteria of Existing Concrete Gravity Dams, FERC Guideline, dated Nov. 7, 1985. 5. STARDYNE program, by R. Rosen, Mechanical Research Inc., 9841 Airport Boulevard, Los Angeles, CA. 6. Design of Small Dams, United States Department of the Interior, Bureau of Reclamation, (1977). 7. Water pressure on Dams During Earthquakes, by H.M. Westergaard, Transactions American Society of Civil Engineers, Vol. 98, pg. 418, 1933. 8. Finite Element Methods in Analysis and Design of Dams, International Commission on Large Dams (ICOLD), Bulletin 30, January 1978. 9. Seismic Amplification Response by Modal Analysis, "SARMA," SWEC Program GT-055 Version 01, Level 00, September 1986. 10. Effects of Earthquake on Dams and Embankments, Newmark, N. M., Fifth Rankine Lecture in Geotechnique Vol. XV No. 2, Institution of Civil Engineers, 1965. 3777R/205R/LS 10-1 11. Engineering Guidelines for the Evaluation of Hydropower Projects, FERC 0119-1, Federal Energy Regulatory Commission, Office of Hydropower Licensing , July 1987. 12. Stone & Webster Engineering Corp., "1987 Geotechnical Exploration Program, Bradley Lake Hydroelectric Project", February 1988 13. Stone & Webster Engineering Corp. , "Geotechnical Interpretive Report, Bradley Lake Hydroelectric Project", Addendum No. 1, March 1, 1988. 3777R/20SR/LS 10-2 ~ KACHEMAK BAY MUD FLAT ~~ ~ EG3 _-tfF l/ ELEVATIONS SHOWN ARE BASED ON PROJECT LAYO,UT PROJECT DATUM. MEAN SEA LEVEL DATUM • PROJECT DATUM PLUS 4.02 FT. MAP t' ~'-,.,__) ( s ~~£ . ,_ ' .:'..::': '"" -FIGURE 1 s=~=r---= ::::: . ...----------.. r----loeo ' \ \ \ \ \ \ ~wg.x ROCK , \ I I \ \ I I \I\\\ ,,,, '', '~'~'->-''"'' '~" '\ ,-..,_ --:::: .... ,, ... _'.: .... ,', ,~, ,,,, ,,, '\ ,\\ \ ' \ \ \ \ \ \ ,,,\1 1\\ \ ,,, i\ \ \ 51 I \I \ \ '11, \ II I ·~ \ • I! t\ ;-,\ \I loll .\ 'l?tl ,, ' 1 II ' i ACCESS ROAD7 I / /~ASTE DISPOSAL AREA B . LL 1100.0'MAX ~-?;-0.0 00 0 ( WASTE DISPOSAL AREA ~h I!L 1090.0' MAX/ ( ...... ' l I \ \ \ ',',,, ,, ' ' \ ~ \ I I \ \ \ \ 'b I \ I \ r, I \1 ,.,... I I ', / --- ' ' MAXIMUM NORMAL I 1 OPERATING WATER • C3~1 1 ~RF.OCE EL 1\80 O' I 1 I I \ \ \ t WASTE DISI'OSAL}-l I ~ AREA F 1 1 EL 10900' MAX , / \~ ~ / I \ / / \ I I I I I 1 I \ I \ I \ \ \ I I I I ,.-.,06 \ : \ I I I $,_, \ ', \ \ I ........ ,.,,:, .... ·,, '~ '... '' ' ' '', ... , '':..',',, '-. ',, ', ', ', ',, ",,'' '-.., ', ',,'-, ''o ' .... , ', ', ', '', ~o .... ',,', ', ', 't> ', '',, "'-,', ' ... _: .... ~.... .............. -- ' ' -h', ', ......... ,,~, ........ ', " .... ... ' .... ' .... '-s_\~~~~~~-:__ ~ ------- SYMBOLS KEY G SURIIEY MONUMENT • SEISMOGRAPH INSTALLATION @ WCRK POINT troo----_ GENERAL ARRANGEMENT MAIN DAM AREA FIGURE 2 ~ /,/ct>" _.. ..-/ , / / I ~" -/~~ / / -./ / I I I I I /{-/ / " f// I / /-/ I -/ / \\\ }/// ,.\' // ----/ / I I / I I/" / / // / " ~~'"--1 I(// ,/ ,...-;_---:::_~,... / _.... / //I//\./ / /..-,.-- "-\"i-.\~:::::_-....~1/!/ /P' /~,...,..-~---//:,..-"'..-_.///I l( I I \ \ '{~\~\:-'...--/; // (;' / ,...",t ,..._.... # 1 f I , ! I _; \ ';.~ ~~'---/ / / / 1 1 I g 1 / .... ~" I I 1 ) y I /-- \ \ I J I \ 'b~\\"-,..,..,..( ( -~/ \ 1 / I I 1 I ;l\.1 1 \ '~~~-) \ \ r\ ,/r~YMOf'U.£~\ \ I / _../ I I ' \. \ ' -I J ' / ' I I I P~,...BBB\ J I ' I HANOR LOCA liON OF ROCK I CONCRETE INTERFACE WILL VARY WITH ROCK TOPOGRAPHY 1 I I \ \ \ I 0 0 "' ! l \ I IJ.1 I I I 11 Ill /1 )/It! /t/!1 ,../If// J MONUMENT I ~ \ \ \ \ \ l -t.L "Jq.>~v [ ~ , , \ \ \ INTERMEDlAT~ '-... '-\ I t"\ \ TRAINING WALL----~ '-\ \ I \ \ ~I W£S T TRAiNING "' \ I rt! ~ WALL ' " [;..~tL Tr11NING \ \ ' "l I ' \\ \ \ . " II \\ , I \\\\ \ '\ J J (\ \ \ ~'-",, , __ -.. "', "-, \\," "-, ....... , \ ' '' -----"'"' "" ,_ --1 -/ / J J I \ '-'-'--...... -...._ '\ "\ -....... "'-----, / /:/ // J \\ ........... -------\''"' ---//// / I '-... --....... ""----::-' \ ' \ ' __.-·-///,/' "/ (\"' -"' --...-.. ' ,,___ .,.-_ ,/,.- !"_., / " --....... ------' " "1170·----::.;://,:;: / / \ \ ""' ( '----, "'-~, -........ , ',-,,So'\ ", --.:::::::::: __ .......... ~~ //;:/':/if \ \\'\\ \ r----.. '~"'"-"'-'----""' --....--:::._,_,":.__,~60 -=----/////I !1 II;! l \ ' "-' ""''--...._, -....._ ' -------...-// I 111/11 1 \ 1 ' -...._ -----"" ', --/ / / _ __,nr;::;"i J I l !TOR "" "---=:--...., -,....._ --.,,~_ ',._:--_ _:::---I;! 1/ :/1/ .::-1/ I jl; I 1/1 I I I I / ' ' '--..._, -----/1/1 I I " " '--.... --'// o/ I f I I ""' '--~''<'o -----·-/ /_/ "' / I / .,..-, ---'...._ // /,· / I / / --.... --I/ 1-" / , / / I ------, ----r:;%: I / jl NON-OVER!" LOW f'IX£0 LOlNtF.. E.l.._ll~ ... ILAlteN' >ER SHAf EL 114 113.4-90' ~ EAST TRAINING WALL / 1-/ // / PLAN-SPILLWAY ---no--------- / / ---- 1()!)•_,.... OVERFLOW 52(.6t4 .,,,..------__ ,_ ____ , / ~/\DRAINAGE GALLERY INTERMEDIATE TRAINING WALL GALLERY ACCESS & DOOR [L_1190,00:_ UIS CREST ",;• 2.62' Yc' 1.00' Rl ' 5.66' R2:: 1.72 1 UPSTREAM FACE X FLOW '( !SPILLWAY 1BASELINE I Yc DIS CURVE COORDINAl]S X I y PC 1 14.~4' 9.~4' PI I 19.04' 1$.00' PT 1 26. 11 ' 15.00' PC 2 35.4 1' 35.62' PI 2 42.92' 45.00' PT 2 !>4.93' 45.00• DIS CREST COORDINATES X 0 t.oo· 2.00' l.oo• 4.00' ~.oo· s.oo• '~00' a.oo• 9.00' 10.00' 11,00' 12.oo~ 13.00' 14.00' 1!1.07' y 0 0.07' 0.24' 0.52' o.aa• 1.3Jf 1.66' 2,4 7' J, 161 3.93' 4.76' 5. 70t 6.69' 7.76' 6.90' 10.19'TANGENT CURVE INTERSECT ,---------CURvE EQUATION OVERFLOW SECTION GEOMETRY NTS ~SPILLWAY BASELINE LON :: 7-t,-t--· 16 ·.o• ---1 HIGH PT EL ll!il:C 00' ~LOPE I !;L tt95.QII' f!,OWh _!;:l__ill!5_,QQ! FILL CONCRETE EL VA?::fivk;w:«; 1 f \ I 14-IUPU fll NON-OVERFLOW SECTION GEOMETRY NTS V•0.0678X 1.8<1 6 Et.D OF SPILLWAY A PRClN (CAST AGAINST ROCK! 0 10 40FEET ------:-1 ELEVATION-LOOKING UPSTREAM SCALE A: 1•• 20' GENERAL ARRANGEMENT SPILLWAY FIGURE 3 REF WOODWARD-CLYDE CONSULT REPORT' "DESIGN EARTHQUAKE STUD{ NOV 10,1981 ~2 25 l-~--~T··-1 Vl 1.881 ~ [ ~FOR HYBRID rARTHOUAKt +-~-+~ ro RESPONSE SPECTRUM z 0 ~ 1 50 0:::. w _j w u 1.13 u <( ~~~ 1 l BRADLEY LAKE HYDROELECTRIC PROJECT MEAN RESPONSE SPECTRUM FOR MCE (NEARBY SHALLOW CRUSTAL FAULT} r t I _j <( 0.75 0:::. MEAN RESPONSE SPECTRUM FOR DBE 1-w 0.. 0.38 (}) 000 0.00 0.25 -- 050 075 100 25 150 1 PERIOD (SEC) 2 00 2 25 PROJECT RESPONSE SPECTRA 2 50 2 ~-------------------------------------------------FIGURE 4 00 MODIFIED ACCELEROGRAM 0£1TAINED FROM THE FOLLOWING TWO ACCELEROGIIAMS KERN COUNTY EARTHQUAKE 7-21-52 IIA004 TAFT LINCOLN SCHOOL TUNNEl, COMP S69E SCALE FACTOR = 3.50 FRIULI. ITALY EARTHQUAKE 9·15 · 7ti AND 1·3-16!) ITALY SAN ROCCO, COMP EW SCALE FACTOR = 3.18 0.75r------------------------------------------------------------------------------------------------, 0.50 ,... Cl ....., z 0 0.25 i= c( a: w ..J ~ 0.00 0 c( a z ::l -0.25 0 a: (!) -0.50 0.00 SEC TO 2.32 SEC OF MODIFIED • 0.00 SEC TO 2.32 SEC 'OF KERN CO. 2.34 SEC T0·4.30 SEC OF MODIFIED • 2.14 SEC TO 4.10 SEC OF FRIULI 4.32 SEC TO 55.14 SEC OF MODIFIED • 3.58 SEC TO 54.40 SEC OF KERN CO. THIS PLOT LIMITED TO FIRST 48.0 SECONDS OF THE MODIFIED.ACCELEROGRAM -0.75L-----~-------L------~----~~----~-------L------~------L-----~------~------~----~ 0.00 4.00 8.00 12.00 16.00 20.00 24.00 26.00 32.00 36.00 40.00 44.00 46.00 TIME (sec) HYBRID ACCELERGRAM FIGURE 5-------~ NEGLECT 1. oo" CREST CREST EL 1180 10.19' ---EL 1165 NEGLECT APRON AT EL 1150 a 1160 4~0 11 RAD ALLERY G_DRAINS \. ~~---N----------\ 51.7' ' \ \. \. SPILLWAY SECTION NEGLECT UPLIFT ON APRON STATIC SPILLWAY. MODEL ASSUMED GEOMETRY NEGLECT APRON EL 1135 EL 1130 EL 1124 ...._--------------FIGURE 6 CASE I-NORMAL RESERVOIR RESULTANT PRESSURES INCLUDING UPLIFT (psi) \7 WS EL 1180 EL 1175 fs = 3.4ksi EL 1170 F5 = 1.4ksi EL 1165 3.6 psi TENSION EL 1160 1.1 psi TENSION EL 1150 3.2 psi EL 1140 I!Spsi 16 psi NOTE: GALLERY SLAB ISOLATED FROM STRUCTURE SO WILL NOT PROVIDE RESISTANCE. SLAB DEBONDED FROM ROCK SO ACTUAL UPUFT WILL BE NEGLIBILE (TYP). STATIC ANALYSIS BASE EL 1124 ..__---------------FIGURE 7 __ __, CASE II-PMF RESULTANT PRESSURES INCLUDING UPLIFT (psi) \] WS EL 1191 EL 1180 0.3 psi EL 1170 0.9pai EL 1160 I. 4 psi EL 1150 3.4 psi EL 1140 15 psi EL 1135 II psi I } CREST I STATIC ANALYSIS BASE EL 1124 ......_---------------FIGURE 8 CASE Til-CONSTRUCTION ( 0.1 g HORIZ) RESULTANT PRESSURES (psi) CREST EL 1180 EL 1170 9.6 psi EL 1160 18.5 psi EL 1150 27.1 psi EL 1140 4!5 psi EL 1135 48psi GROUND ACCELERATION STATIC ANALYSIS BASE EL 1124 ..._---------------FIGURE 9 EL 1140 EL 1180 ...... I l r.......... 11 I'... .I 1 l ~ __ ___.,.:..:CO:..:..:N:.;.;CR.;.;;;;ETE 1 A ...... ,.,. / ~ ROCK I J T / 't-,_,r--it--~-\__.;tt-~~...-.,._..,.....::E..!:::..L ..!..!.11!:.::63~ EL 1160 l f ] .I I~ 20' 39. 45' I 20' ..... FINITE ELEMENT MODEL BASE EL 1160 ~I ........ --------------FIGURE I 0 EL 1141 EL 1120 30' - EL 1180 J 1 1 ]] If J 7":. / EL II 57 42.25 1 - FINITE ELEMENT MODEL BASEEL1150 30' '----------------FIGURE II EL 1068 I~ --=..E L::......:..:...ll .:::..::80:.___, r,._, 56' J ""'\ 1 L'.... .. ,. 79 1 FINITE ELEMENT MODEL BASE EL 1124 56' .. J ....._--------------FIGURE 12 CASE ill-EARTHQUAKE (0.75g HORIZ +0.50g VERT) MAX VERTICAL TENSILE STRESSES W/0 UPLIFT (PSI) +45.4 -17.5 +TENSION -COMPRESSION -22.2 -7.8 -t2.1 -23. 8 -10. 8 -3. I +I. 4 EL 1160 FINITE ELEMENT ANALYSIS BASE EL 1160 ...._-------------FIGURE 13 CASE ill-EARTHQUAKE ( 0.75 g HOR IZ + 0. 50g VERT) MAX VERTICAL COMPRESSIVE STRESSES W/0 UPLIFT CPS!) -36.8 -16.6 -6.6 -:52.3 -44.4 -22.2 -17.! +TENSION -COMPRESSION ~---._~~E~L~tt~so~---------_.---------~----~--~--~ FINITE ELEMENT ANALYSIS BASE EL 1160 ---------------FIGURE 14 -14.0 CASEY -EARTHQUAKE ( 0.75g HOR I Z + 0.50g VERT) MAX VERTICAL TENSILE STRESSES (PSI) CREST EL 1180 +TENSION -COMPRESSION +0.8 -3.4 +5.8 -16.5 -4.9 +1.2 +3.9 EL 1160 FINITE ELEMENT ANALYSIS BASE EL 1160 ...._-------------FIGURE 15 CASEY -EARTHQUAKE (0.75g HORIZ +0.50g VERT) MAX VERTICAL COMPRESSIVE STRESSES (PSI) -29.5 -48.4 CREST EL 1180 +TENSION -COMPRESSION -II. 8 -12.2 -37.1 -16.3 -13.0 -10.1 EL 1160 FINITE ELEMENT ANALYSIS BASE EL 1160 ..._-------------FIGURE 16 CASElli -EARTHQUAKE {0.75g HORIZ + 0.50g VERT) MAX VERTICAL TENSILE STRESSES W/0 UPLIFT (PSI) CREST EL 1180 + TENSION -COMPRESSION 1"17.8 +17.3 -1.8 -5.1 -0.3 -6.8 -3.9 -0.3 -6.6 -7.4 -2.2 -6.0 -5.0 -10.2 -7.9 -5.9 -11.6 -10.3 -+6.3 -9.8 -12. B -12.3 EL 1150 FINITE ELEMENT ANALYSIS BASE EL 1150 +2. 3 -t-1.0 -4.5 -+6.0 -6.6 -I. I -9.3 ...__--------------FIGURE 17 CASElli -EARTHQUAKE (0.75g HORIZ + 0.50g VERT) MAX VERTICAL COMPRESSIVE STRESSES W/0 UPLIFT (PSI) -59.0 -77.9 CREST EL 1180 + TENSION -COMPRESSION -10.2 -11.7 -13.5 -13.0 -15.7 -15.8 -25.4 -16.6 -21.4 -22.8 -20.9 -25.2 -22.1 -66.1 -34.6 -29.2 -25.7 EL 1150 FINITE ELEMENT ANALYSIS BASE EL 1150 -9.8 -20.9 -14.9 -38.6 -21.4 -21.9 -25.3 -31.1 ------------~--------------FIGURE IS CASEY -EARTHQUAKE {0.75g HORIZ + 0.50g VERT) MAX VERTICAL TENSILE STRESSES (PSI) CREST EL. 1180 + TENSION -COMPRESSION +0.2 +_9.1 +0.2 -2.4 -0.4 -:3. B -3.2 -1.7 -5.0 -7.9 -4.3 -9.4 -7.4 -1.5 -10.2 -II. 2 -9.6 EL. 1150 FINITE ELEMENT ANALYSIS BASE EL 1150 +2.9 -2.0 +14.1 -3.5 +2.9 -5.8 +5.5 ---------------FIGURE 19 -63.1 -84.3 CASEY -EARTHQUAKE (0.75g HORIZ + 0.50g VERT) MAX VERTICAL COMPRESSIVE STRESSES . (PSI) CREST EL 118 0 -2.4 + TENSION -COMPRESSION -8.2 -6.5 -13.0 .-8.6 -15.8 -13.0 -30.4 -16.1 -20.4 -20.5 -17.3 -37.0 -23.0 -19.2 -35.0 -27.6 -23.0 EL 1150 FINITE ELEMENT ANALYSIS BASE EL 1150 -15.8 -7.9 -12.4 -30.5 -18.3 -17.9 -21.8 -25.9 ~-------------FIGURE 20 CASE ill -EARTHQUAKE (0.75g HORIZ + 0.50g VERT) MAX VERTICAL TENSILE STRESSES W/0 UPLIFT . (PSI) -0.2 + TENSION -COMPRESSION + 3.9 +0.2 t5.8 -7.5 +13.6 +7.1 -10.3 +2.9 +3.8 -11.8 -6.0 +9.7 -12.5 +1.6 +23.0 -17.0 -5.9 +8.2 +21.1 -14.4 -2.1.1 -13.1 -1.6 +8.7 FINITE ELEMENT ANALYSIS BASE EL 1124 +17.2. +9.5 .__-------------FIGURE 21 EL 1124 CASE ill -EARTHQUAKE (0.75g HORJZ + 0.50g VERT) MAX VERTICAL COMPRESSIVE STRESSES W/0 UPLIFT (PSI) CREST EL II 8 0 J. -5.6 ~-14.8 f-, •• -15.4 -2~ + TENSION -26.B~ -COMPRESSION . -40.1 -23.9 1-49.2 -735-t -57.7 -32.0 -24.1 -49.4 ~ tra -69.0 -39.3 -27.1 -43.3 -68.1 ~ I -77.6 -41.6 -33.4 -40.4 -54.7 -120.1__......~ hl5.6 --- /-126 1 ~t&~J_--46-.2-l.---4-0._7 .l---55-.o-l---7-0 ._6--l,.-i-l_l._a --r-_ 1 _,.2 . 5 ~35., ~,.., -53-3 -45.6 -54.9 -··. 2 - 6 3. • _ 3... _, o. 0 / 1---,5-5-. 1-~-1---s 5--.~~ -5-5-e6-.. ooj--6.;-3.-5+---6-0.-2 +---50-.7-+--5-7.-5+---s-o-. o-+-_-6-4.-r -+---4-B-.3--f......_-~ L----L---v~ \/'--~t-...1.----L--.L....----L----1-----~,.;..--...L..-----EL 1124 FINITE ELEMENT ANALYSIS BASE EL 1124 ~--------------~----------FIGURE22 CASEY. -EARTHQUAKE (0.75g HORIZ +0.50g VERT) MAX VERTICAL TENSILE STRESSES (PSI) +1.6 + TENSION -COMPRESSION +3. 6 +5.9 FINITE ELEMENT ANALYSIS BASE EL 1124 ~--------------------------FIGURE23 CASE --sL -EARTHQUAKE (0.75g HORIZ ·+ 0.50g VERT) MAX VERTICAL COMPRESSIVE STRESSES (PSI) -13.6 + TENSION -COMPRESSION -48.6 -24.2 -21.1 -32.9 -20.2 -41.7 -74.9 -40.5 -24.4 -37.5 -37.5 -48.8 -61.3 -52.6 -42.2 49.2 -58.3 -55.6 -60.4 -47.1 -52.0 -57.8 -56.6 -42. 9 FINITE ELEMENT ANALYSIS BASE EL 1124 ....... -------------FIGURE 24 CREST EL I I 80 CENTER OF GRAVITY ACTUAL OGEE--------~~ ASSUMED MODEL OF EQUAL MASS AND CENTER OF GRAVITY. GEOMETRY EL 1160 BASE EL 1160 CREST EL II 80.0 ACTUAL OGEE~-,' GEOMETRY ;r' ASSUMED MODEL I 38.8' ~ BASE EL 1150 SARMA ANALYSIS MODEL OGEE SECTIONS SHEET I EL 1150.0 '------------------FIGURE 25 CREST EL 1180.0 ACTUAL OGEE--ASSUMED MODEL GEOMETRY CREST EL 1180 ACTUAL OGEE~, GEOMETRY ;' I 19.1 1 61.8 1 BASE EL 1130 .---ASSUMED MODEL 69.01 BASE EL 1124 SARMA ANALYSIS MODEL OGEE SECTIONS SHEET 2 EL 1130 ..._--------------FIGURE 26 ASSUMED~ MODEL ""' EL 1195.0 ACTUAL~r--NONOVERFLOW : GEOMETRY I I 35.5' ACTUAL~ NON OVERFLOW GEOMETRY ,-EL 1195.0 BASE EL 1160 LEFT ABUTMENT 1 I ' ' \ CENTER OF ', GRAVITY 29.3' BASE EL 1124 RIGHT ABUTMENT ASSUMED MODEL OF EQUAL MASS AND CENTER OF GRAVITY EL 1145.0 EL1124.0 SARMA ANALYSIS MODEL NON-OVERFLOW SECTIONS EL 1168.0 EL 1160.0 ~-----------------------------+IGURE 27 TIME HISTORY OF WEDGE MOTIONS o.oo 5-00 10.00 !5.00 20.00 25.00 30.00 35.00 40.00 45.00 so.oo 55.00 60.00 0 UJ~ do -----------------------------------------------~ UJo zo o,; ~INIIliUI ...... 1- a: a::: a w.,.. _J • wo ul u a: 0 (0 ";'-INDICRT!S ERATHVUAK[• HYD~ID ACC~LfKDORAn • K(ftN CO. TAfT '"9[1 4 fMIULI ITALY SAN MOCCO lfWl INDICATES CftiTICAl ACCELERATION, 0.231 0'5 0 1-w w. wo I.J_ UJO .... 1-• zo w l:: w CLo UJ 0 INDICATES WEDGE 016PLACfftfHTS 4 RCC!L!RRTIOIIS. SARMA ANALYSIS MCE CASE W/0 BASE EL 1160-OGEE FOUNDATION COHESION DRTR ARE CDfffiCifNT$ Of 0--2151 fOIIITS •!" • 0.020 5£CONOS .oo 45.00 so.oo ss.oo 0 .... 0 0 0 0 0 .... 0 I 0 CD 0 I 0 <D 0 0 .... 0 0 N 0 FIGURE 28 TIME-HISTORY OF WEDGE MOTIONS o.oo 5.00 55.00 60.00 0 (/)~ do C> ([) 0 ------------------------------------~-----------------------------------------------~ 0 ... 0 lliflNIIIP qp,A M~liV' 1-\&uY\L::/i'I.A,# \f'W.'WV•'vui_..·.M.,•~ 1 ~ 0 -------------------------U< 0 ... I INOICATU fARTHQUAM£1 HYBRID IICCfl!ROOIIRn 1 kfRH CO. TAFT 1519!1 ' FUUU ITALY IAN ROCCO IfNI DATA RRf COffr!CifNU Of G--Z157 tOINT& •T • 0.020 5fCOIIDS 1-0 ("} W• wo lL (1)0 ~---~ z.o w :c w u a:o .....J": (LC> (f) ...... 0 ----IHOICATU CRITICAl ACCflfftATION. Q.t82 11'8 IHOICRTU WfDOf OISrUC!"fHU ' ACCflURTIONI. r--- J 0 I") 0 0 N 0 0 C> 0 0 0 C> . . 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 ° TIME SECONDS SARMA ANALYSIS: BASE EL 1150-0GEE MCE CASE W/0 FOUNDATION COHESION FIGURE 29 o.oo D w"' . . s.oo TIME-HISTORY OF WEDGE MOTIONS ----------------------------------------------------------- .oo D ... D D --·-~-~-~------------ --------- ------------------------~ 0 D a:> '7---INOICATU fiiUHGURKfl HYIKIO ACtflfROOilA" 1 KfU CO. TAH IU&fl ~ fRIUll ITALY 8AN ROCCO IfNI ----INOICATU UHICRL ACCfLUAIION. o.t51 0'6 D f-to w· wo lL.. U)D ._": zo w :c w u a:D _j~ CL.D U) D INDICRTU NfDO£ oUrLACfnfNT5 ~ RCCflf~IITION&. r- DATA Allf COfff!CifNU Of 0--2151 rOINT5 •T • 0.020 UCONO& ... D to D 0 ... D D N D Dj D D D . . ~.oo s.oo to.oo ts.oo 2o.oo 25.oo 3o.oo 35.oo 4o.oo 4s.oo so.oo ss.oo Go.oo o TIME -SECONDS SARMA ANALYSIS: BASE EL 1130-0GEE MCE CASE W/0 FOUNDATION COHESION FIGURE 30 ' TIME-HISTORY OF WEDGE MOTIONS o.oo 5.00 10.00 15.00 20.00 25.00 30.00 35.00 0 rn"" ~c;; 1-0 ..., W• wo lJ.._ (f)o ~--~ zo w :I: w u a:o ...J": Q...o (f) ,_, Cl IHOICATr& rAUifQUIIKrr I!YUIO Rtt£LODOftA" 1 KCI!H to. TAfT ISU£1 < F!IULI ITALY SAN I!OCCD lfWl IHDICATU CKITICAL IICC£LEI!ATIIIH. 0.261 0'6 --lNDICATU W£01)[ lll&tLIICE"[HI& < lltt[LEIIIHIONS • ANALYSIS: BASE EL 1124-0GEE SARMA MCE CASE W/0 FOUNDATION COHESION 40.00 45.00 u c - -~ -u, DATA Ill!£ CIICFFICIEHTS 0~ 0--t751 ,OINIS •I = 0.020 5CCOHD6 C) ... 0 I 0 C) 0 I~ C) ., 0 0 N C) C) C) FIGURE 31 TIME-HISTORY OF WEDGE MOTIONS 0 .oo 5 .oo 0 U)"" -------------------------------------------------------------------------------------~ j~ d~ U)o zo 0~ >---< 1-- a: 0:::: wo _J~ wo ~I 1------a----------~------------------------------------------------------------------------------------------------U, U: 0 IX> --INOICIIT[S ~llftiHOUIIKfl HYIRIO IICCHUOO~~" 1 Kf~N CO. TAfT IU9fl l fUULI ITALY &lllf ~OCCO IfNI DATA liRE CO[ff ICUNTi Of 0 --2151 tO lifT& •T • 0.020 UCIIND5 1--t.P w~ wo IJ... ({) .... ~---~ w u a:N _JD (Lo U) 0 0 0 ---INOICIITU CRltiC~l RCCflfRIITIDH. Q.U, O"f ·--IHOICRTU NfOOf Dl6rLACfHfNT6 l RCCfL£1RT IONS. +-----~~-------.-------.--------.-------.-------.r-------.-------.-------.----~.00 s.oo 10.00 15.00 20-00 25.00 30.00 35.00 40.00 45.00 50.00 TIME SECONDS SARMA ANALYSIS: BASE EL 1160-LEFT ABUTMENT MCE CASE W/0 FOUNDATION COHESION 55.00 0 0 0 0 0 ... t.P 0 0 .... 0 0 N 0 D ~-----------------------------------------------FIGURE 32 o.oo 0 V'Joq d.; V'Ja zo o.; ...... f-a: Ck:o w ... _J • wo u' u cc 0 co 0 5.00 TIME-HISTORY OF WEDGE MOTIONS 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 ~ ------------------------------------------------------------------------------------- ----------------------------------------------------------------------------- I --INDICAJU (llliTHDUAKfl HYBRID ACCflUOIN!Aft 1 MUN tO. TAfT 166$(1 l fUUll ITALY &liN l!OCCO IfNI ----INOICATU UH JCIIL IICCfLURTJON, 0.3U G'& DATil ARE C0[ffJClfNJ6 Of G --t1$1 POINT& •T : 0.0~0 &fCONDI f-(D w":' wo lL.. V'J"" f.--: zo w ::c w u a:"' -lo o__.; If.) ...... Cl --lNOicATU WfOGf DI&PLIICfnfNTI l IICCfLUATJ0118. 0 oq 0 0 0 0 0 oq 0 I 0 co co 0 N 0 <.0 0 0 o a a a . . 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 ° TIME SECONDS SARMA ANALYSIS: BASE EL 1124-RIGHT ABUTMENT MCE CASE W/0 FOUNDATION COHESION ~-----------------------------------------------FIGURE 33 PMF EL 1191' EL 1179' - -5' EST DRAW DOWN WATER SURFACE CREST EL 1180' 64.3' EL 1130' LOADING DIAGRAM NOTES: 1. Stability analysis based on gravity method. Static analysis for Cases 1, 2 and 4. Finite element analysis for Cases 3 and 5. 2. Loads: D ~ Dead weight of structure at 145 lbs/cu. ft. (concrete). EH ~ Horizontal inertial force due to earthquake Ev ~ Vertical inertial force due to earthquake Hw"' Horizontal hydrostatic force Vw= Vertical hydrostatic force I = Ice force at 12 kips/lin ft. HE Hydrodynamic earthquake force LJ = Uplift force Numeral subscript indicates load case 3. Load Cases: Case 1 -Normal A. • Dead weight B. -Hydrostatic forces for normal maximum reservoir level of El 1180' C. Ice D.· Uplift and seepage forces Case 2 -Probable maximum flood (PMF) A. -Dead weight B. -Hydrostatic forces for maximum reservoir level ofEI1190.6' (rounded up to 1191') C. · Uplift and seepage forces Case 3 • Earthquake A.· Dead weight B. -Hydrostatic forces for normal maximum reservoir level of El 1180' C.-Ice D. · Earthquake inertial and hydrodynamic forces for maximum credible earthquake (0.75g horizontal & 0.5g vertical) E. Uplift and seepage forces Case 4 · Construction A.· Dead weight B. · 1) Earthquake inertial forces for operational basis earthquake (0.1 g horizontal) or; 2) Wind Case 5 • Low reservoir level earthquake A. • Dead weight B. -Earthquake inertial forces for maximum credible earthquake (0.75g horizontal & 0.5g vertical) 4. Base pressures for Case 3 and Case 5 determined by two dimensional finite element analysis with earthquake inertia load computed from response spectrum analysis and hydro- dynamic effects approximated by Westergaard added masses. 5. Uplift pressures assume a drain efficiency of 50% at the base. 6. Uplift assumed to act over 100% of base area. 7. Base pressures for uncracked sections calculated without in- cluding uplift as an active external force. Uplift pressures were combined with the resulting base pressures by the superposition method. 8. Allowable stress in PSI: Concrete (3000 PSI) Rock (40KSF = 280 PSI) Tension Compression Compression Case 1 60 1000 140 Case 2 90 1500 185 Case 3 270 3000 250 Case 4 90 1500 185 Case 5 270 3000 250 9. Sliding factor of safety for Cases 1, 2 and 4 is based on shear friction factor of safety formula with 160 PSI coheston and an internal angle of friction of 45 degrees SPILLWAY STABILITY ANALYSIS SUMMARY SHEET I FIGURE 34 CASE I NORMAL CASE 2 PMF BASE PRESSURE DIAGRAMS EL 1124 t t t t t t' .. .. • • t r • • CASE 4 CONSTRUCTION CASE RESULTANT KIPS NUMBER :Ev :EH 1 237 110 2 222 136 4 294 32 BASE EL 1124 BASE PRESSURE ·PSI X W/UPLIFT W/0 UPLIFt FT U/S D/S U/S DIS 135.5 10 32 ~4 ~4 34.8 4 34 33 36 42.9 47 11 47 11 SAFETY FACTOR SLIDING 17.0 13.6 61.0 CRACK LENGTH FEET 0 0 0 STATIC STABILITY RESULTS BASE PRESSURE DIAGRAMS EL 1135 •• t t t t j t_tjt t t j ~· BASE EL 1135 BASE PRESSURE DIAGRAMS EL 1150 DOJ Q[IJ r--[J7 t) BASE EL1150 CASE rESUlTANT, KIPS NUMBER :Ev I 1: H X FT 1 I 76 I 40 19.1 I 1 o I 22 I 23 I 22 2 I 67 I 49 20.0 f 9 I 20 I 26 I 20 __ 4 I 95 10 24.91 37 I 5 I 37 I 5 BASE PRESSURE ·PSI SAFETY CRACK CASE RESULTANT KIPS X W/UPLIFT W/0 UPLIFT FACTOR lENGTH NUMBER :Ev :EH FT U/S D/S U/S D/S SliDING FEET , 126 75 28.9 16 26 35 28 17.2 2 137 94 28.7 11 26 35 29 13.8 0 4 198 21 35.5 48 8 48 8 64.3 0 SAFETY FACTOR SliDING 21.6 17.6 86.6 BASE PRESSURE DIAGRAMS EL 1160 CRACK LENGTH FEET _o_ 0 0 O[J] om orv BASE El1160 BASE PRESSURE ·PSI SAFETY FACTOR SLIDING I. CASE RESUlTANT KIPS X W/UPLIFT W/0 UPLIFT NUMBER LV :EH FT U/S DIS U/S D/S 1 2 4 31 25 12.3 2 18 11 2_0 22 26 14.7 5 13 18 15 45 5 18.3 23 5 23 5 SPILLWAY STABILITY ANALYSIS SUMMARY SHEET 2 23.0 21.0 118 CRACK lENGTH FEET 0 0 L---------------------------------------FIGURE 35 -~ FINITE ELEMENT ANALYSIS RESULTS MAXIMUM STRESSES (PSI) BASE CASE TENSION TENSION SLIDING ELEV NUMBER COMPRESSION W/0 UPLIFT WITH UPLIFT STABILITY-tc 1124 III 155.7 87.3 111.6 Stable v 165.5 77.5 Stable 1150 III 77.9 32.1 45.1 Stable v 86.3 18.3 Stable 1160 III 52.3 45.4 54.1 Stable v 48.8 22.5 Stable *Based on negligible calculated displacements from SARMA analysis. SPILLWAY STABILITY ANALYSIS SUMMARY I SHEET 3 ... ---------------FIGURE 36 _..,