ASCE Standard 4-98 Seismic Analysis of Safety – Related Nuclear Structures and Commentary

CONTENTS

PREFACE v

ACKNOWLEDGMENTS vi

Standard

1.0 GENERAL 1

1.1 INTRODUCTION 1

1.1.1 Purpose 1

1.1.2 Scope 1

1.1.2.1 Types of Structures Covered by This Standard 1

1.1.2.2 Foundation Material Stability 1

1.1.3 General Requirements 1

1.1.3.1 Use of Analysis Results 1

1.1.3.2 Alternative Methodologies 1

1.2 DEFINITIONS 1

1.3 NOTATION 2

2.0 SEISMIC INPUT 4

2.1 SEISMIC GROUND MOTIONS 4

2.1.1 General Requirements 4

2.2 RESPONSE SPECTRA 5

2.2.1 General Requirements 5

2.2.2 Site-Specific Horizontal Response Spectra 5

2.2.3 Site-Independent Horizontal Response Spectra 5

2.2.4 Vertical Response Spectra 6

2.3 TIME HISTORIES 6

2.4 POWER SPECTRAL DENSITY FUNCTIONS 8

2.4.1 PSD Computed from Time Histories 8

2.5 ADDITIONAL REQUIREMENTS FOR STRUCTURES SENSITIVE TO LONG PERIOD MOTIONS 8

2.5.1 Spectral Shape 9

2.5.2 Time Histories 9

3.0 ANALYSIS 9

3.1 MODELING OF STRUCTURES 9

3.1.1 General Requirements 9

3.1.1.1 Models for Horizontal and Vertical Motions 9

3.1.1.2 Multistep and One-Step Methods of Seismic Response Analysis 9

3.1.1.2.1 Models for multistep analysis 10

3.1.1.2.2 Models for one-step analysis 10

3.1.1.3 Discretization Considerations 10

3.1.1.3.1 Selection of finite element type 10

3.1.1.3.2 Selection of mesh size 10

3.1.1.3.3 Reduction of dynamic degrees of freedom 10

3.1.2 Structural Material Properties 10

3.1.2.1 Modulus of Elasticity and Poisson’s Ratio 10

3.1.2.1.1 Concrete 10

3.1.2.1.2 Steel 10

3.1.2.1.3 Aluminum 10

3.1.2.2 Damping 10

SEISMIC ANALYSIS OF SAFETY-RELATED NUCLEAR STRUCTURES

3.1.3 Modeling of Stiffness 11

3.1.3.1 Stiffness of Reinforced Concrete Elements 11

3.1.4 Modeling of Mass 11

3.1.4.1 Discretization of Mass 11

3.1.4.2 Determination of Modal Mass 11

3.1.5 Modeling of Damping 12

3.1.5.1 Damping Properties of Structures 12

3.1.5.1.1 Proportional damping (Rayleigh damping) 12

3.1.5.2 Composite Damping 12

3.1.5.2.1 Substructures with Known Damping Ratios 13

3.1.5.2.2 Substructures with Proportional Damping 13

3.1.5.3 Composite Modal Damping 13

3.1.5.4 Alternate Composite Modal Damping 13

3.1.6 Modeling of Hydrodynamic Effects 13

3.1.6.1 General Requirements 13

3.1.6.2 Dynamic Analysis Formulation for Submerged Structures 13

3.1.6.3 Building Model Hydrodynamic Mass Effects 14

3.1.7 Dynamic Coupling Criteria 15

3.1.7.1 General Requirements 15

3.1.7.2 Single-Point Attachment 15

3.1.7.3 Multipoint Attachment and Static Constraint 15

3.1.8 Requirements for Modeling Specific Structures 15

3.1.8.1 General Requirements 15

3.1.8.1.1 Structures with rigid floors 15

3.1.8.1.2 Structures with flexible floors 16

3.1.8.1.3 Requirements for lumped-mass stick models 16

3.1.8.2 Requirements for Frame Structures 17

3.1.8.3 Requirements for Shear-Wall Structures 17

3.1.8.4 Requirements for Plate and Shell Structures 17

3.1.8.5 Requirements for Adjacent Structures 18

3.2 ANALYSIS OF STRUCTURES 18

3.2.1 General Requirements 18

3.2.2 Time History Method 18

3.2.2.1 General Requirements 18

3.2.2.2 Linear Methods 18

3.2.2.2.1 Modal superposition 19

3.2.2.2.2 Direct integration 19

3.2.2.3 Nonlinear Methods 19

3.2.3 Response Spectrum Method 20

3.2.3.1 Linear Methods 20

3.2.3.2 Nonlinear Methods 20

3.2.4 Complex Frequency Response Method 20

3.2.4.1 General Requirements 20

3.2.4.2 Response Time History 20

3.2.4.3 Methods to Compute Transfer Functions 21

3.2.5 Equivalent-Static Method 21

3.2.5.1 General Requirements 21

3.2.5.2 Cantilever Models with Uniform Mass Distribution 21

3.2.5.3 Other Simple Structures 21

3.2.6 Multiply-Supported Systems 22

3.2.6.1 General Requirements 22

3.2.6.2 Time History Method 22

3.2.6.3 Response Spectrum Method 22

3.2.7 Combination of Modal and Component Responses 22

3.2.7.1 Response Spectrum Analysis 22

3.2.7.1.1 General modal combination rule 22

3.2.7.1.2 Combination of spatial components 23

3.2.7.1.3 Multiple response parameters 23

3.2.7.2 Combination of Spatial Components for Time History Analysis 24

3.3 SOIL-STRUCTURE INTERACTION MODELING AND ANALYSIS 24

3.3.1 General Requirements 24

3.3.1.1 Fixed-Base Analysis 24

3.3.1.2 Spatial Variations of Free-Field Motion 25

3.3.1.3 Three-Dimensional Effects 25

3.3.1.4 Nonlinear Behavior of Soil 25

3.3.1.5 Structure-to-Structure Interaction 25

3.3.1.6 Effect of Mat and Lateral Wall Flexibility 25

3.3.1.7 Uncertainties in SSI Analysis 25

3.3.1.8 Model of Structure 26

3.3.1.9 Embedment Effects 26

3.3.1.10 Wave Incoherence 26

3.3.2 Subsurface Material Properties 26

3.3.2.1 General Requirements 26

3.3.2.2 Shear Modulus 26

3.3.2.3 Material (Hysteretic) Damping Ratio 26

3.3.2.4 Poisson’s Ratio 26

3.3.3 Direct Method 26

3.3.3.1 Seismic Input for Model Boundaries 27

3.3.3.2 Lower Boundary 27

3.3.3.3 Selection of Lateral Boundaries 27

3.3.3.4 Soil Element Size 28

3.3.3.5 Time Step and Frequency Increment 28

3.3.4 Impedance Method 28

3.3.4.1 Determination of Input Motion 28

3.3.4.2 Determination of Foundation Impedance Functions 29

3.3.4.2.1 Equivalent foundation dimensions 29

3.3.4.2.2 Uniform soil sites 29

3.3.4.2.3 Layered soil sites 29

3.3.4.2.4 Embedded foundations 29

3.3.4.3 Analysis of Coupled Soil-Structural System 30

3.4 INPUT FOR SUBSYSTEM SEISMIC ANALYSIS 30

3.4.1 General Requirements 30

3.4.1.1 Types of Seismic Input for Subsystem Analysis 30

3.4.1.2 Direction and Locations for In-Structure Response Spectra or Time Histories 31

3.4.1.3 Subsystem Input Away from Reference Location 31

3.4.1.4 In-Structure Displacements and Rotations 31

3.4.2 In-Structure Response Spectra 31

3.4.2.1 Methods for Generation of In-Structure Response Spectra 31

3.4.2.1.1 Time history method 31

3.4.2.1.2 Direct spectra-to-spectra methods 32

3.4.2.2 Frequency Interval for Generation of In-Structure Response Spectra 32

3.4.2.3 Treatment of Uncertainties in Generating In-Structure Response Spectra 32

SEISMIC ANALYSIS OF SAFETY-RELATED NUCLEAR STRUCTURES

3.4.2.4 Interpolation of In-Structure Response Spectra for Intermediate Damping 32

3.4.3 In-Structure Time History Motions 33

3.4.3.1 Methods for Generation of In-Structure Time History Motions 33

3.4.3.2 Equivalent Broadening and Lowering of In-Structure Time History Motions 33

3.4.3.3 Time Interval and Data Precision Requirements for In-Structure Time History Motions 33

3.4.4 Structural Model or Characteristics for Coupled Subsystem Analysis 33

3.4.4.1 Supporting Soil-Structure Model 33

3.4.4.2 Base Excitation 33

3.5 SPECIAL STRUCTURES 33

3.5.1 General Requirements 33

3.5.2 Buried Pipes and Conduits 34

3.5.2.1 Straight Sections Remote from Anchor Points, Sharp Bends, or Intersections 34

3.5.2.1.1 Maximum axial strain ignoring friction 34

3.5.2.1.2 Maximum axial strain considering friction 34

3.5.2.1.3 Maximum curvature 34

3.5.2.1.4 Maximum joint displacement and rotation in segmented structures 35

3.5.2.2 Forces on Bends, Intersections, and Anchor Points 35

3.5.2.3 Anchor Point Movement 35

3.5.3 Earth-Retaining Walls 35

3.5.3.1 General Requirements 35

3.5.3.2 Elastic Solution 35

3.5.3.3 Active Solution 35

3.5.4 Above-Ground Vertical Tanks 35

3.5.4.1 General Requirements 35

3.5.4.2 Horizontal Impulsive Mode 36

3.5.4.2.1 Effective weight of fluid-Impulsive mode 36

3.5.4.2.2 Spectral acceleration-Impulsive mode 36

3.5.4.2.3 Overturning moment at base of tank-Impulsive mode 37

3.5.4.2.4 Hydrodynamic pressure on tank shell-Impulsive mode 37

3.5.4.3 Horizontal Sloshing (Convective Mode) 37

3.5.4.3.1 Effective weight of fluid-Sloshing mode 37

3.5.4.3.2 Spectral acceleration-Sloshing mode 37

3.5.4.3.3 Overturning moment at base of tank-Sloshing mode 37

3.5.4.3.4 Hydrodynamic pressure on tank shell-Sloshing mode 37

3.5.4.3.5 Fluid slosh height-Fundamental sloshing mode 37

3.5.4.4 Vertical Fluid Response Mode 38

3.5.4.4.1 Hydrodynamic pressure on tank shell-Vertical mode 38

3.5.4.5 Other Considerations 38

3.5.4.5.1 Overturning moment and longitudinal compressive force 38

3.5.4.5.2 Hoop tension in tank shell 38

3.5.4.5.3 Freeboard requirements 38

3.5.4.5.4 Special provision for full tanks 38

3.5.4.5.5 Attached piping 38

3.5.4.5.6 Tank foundation 38

3.5.5 Raceways 38

3.5.5.1 General Requirements 38

3.5.5.2 Damping 38

3.5.6 Seismic-Isolated Structures 39

3.5.6.1 General Requirements 39

3.5.6.2 Specification of Seismic Input Motion 39

3.5.6.3 Modeling of Structures 39

3.5.6.4 Response Spectrum Analysis 40

3.5.6.5 Time History Analysis 40

Nonmandatory Appendix

A1.0 NONMANDATORY APPENDIX A: EVALUATIONS BEYOND THE DESIGN BASIS 41

A1.1 INTRODUCTION 41

A2.1 HISTORY OF SPRA AND SMA 41

A3.1 PURPOSE AND OVERVIEW OF SEISMIC PROBABILISTIC RISK ASSESSMENT 42

A4.1 PURPOSE AND OVERVIEW OF SEISMIC MARGIN ASSESSMENT METHODOLOGY 44

A5.1 COMPARISON OF SEISMIC EVALUATION METHODOLOGIES 47

A6.1 COMPARISON OF SPRA TO STANDARD 47

A7.1 COMPARISON OF SMA TO STANDARD 51

A8.1 REFERENCES 53

Commentary

C2.0 SEISMIC INPUT 55

C2.1 SEISMIC GROUND MOTIONS 55

C2.1.1 General Requirements 55

C2.2 RESPONSE SPECTRA 55

C2.2.1 General Requirements 55

C2.2.2 Site-Specific Horizontal Response Spectra 56

C2.2.3 Site-Independent Horizontal Response Spectra 56

C2.2.4 Vertical Response Spectra 56

C2.3 TIME HISTORIES 57

C2.3.1 General Requirements 57

C2.4 POWER SPECTRAL DENSITY FUNCTIONS 59

C2.5 ADDITIONAL REQUIREMENTS FOR STRUCTURES SENSITIVE TO LONG-PERIOD MOTIONS 59

C2.5.1 Spectral Shape 59

C2.5.2 Time Histories 60

C3.0 ANALYSIS 61

C3.1 MODELING OF STRUCTURES 61

C3.1.1 General Requirements 61

C3.1.1.1 Models for Horizontal and Vertical Motions 61

C3.1.1.2 Multistep and One-Step Methods of Seismic Response Analysis 61

C3.1.1.3 Discretization Considerations 62

C3.1.1.3.2 Selection of mesh size 62

C3.1.1.3.3 Reduction of dynamic degrees of freedom 62

C3.1.2 Structural Material Properties 62

C3.1.2.1 Concrete 62

C3.1.2.2 Damping 62

C3.1.3 Modeling of Stiffness 62

C3.1.3.1 Stiffness of Reinforced Concrete Elements 62

C3.1.4 Modeling of Mass 63

C3.1.4.1 Discretization of Mass 63

C3.1.4.2 Determination of Nodal Mass 64

SEISMIC ANALYSIS OF SAFETY-RELATED NUCLEAR STRUCTURES

C3.1.5 Modeling of Damping 64

C3.1.5.1 Damping Properties of Structures 64

C3.1.5.1.1 Proportional damping (Rayleigh damping) 64

C3.1.5.2 Composite Damping 64

C3.1.5.2.1 Substructures with known damping ratios 64

C3.1.5.2.2 Substructures with proportional damping 64

C3.1.5.3 Composite Modal Damping 64

C3.1.5.4 Alternate Composite Modal Damping 64

C3.1.6 Modeling of Hydrodynamic Effects 64

C3.1.6.1 General Requirements 64

C3.1.6.2 Dynamic Analysis Formulation for Submerged Structures 64

C3.1.6.3 Building Model Hydrodynamic Mass Effects 66

C3.1.7 Dynamic Coupling Criteria 67

C3.1.7.2 Single Point Attachment 67

C3.1.7.3 Multipoint Attachment and Static Constraint 67

C3.1.8 Requirements for Modeling Specific Structures 67

C3.1.8.1.3 Requirements for lumped-mass stick models 67

C3.1.8.3 Requirements for Shear-Wall Structures 68

C3.1.8.4 Requirements for Plate and Shell Structures 68

C3.2 ANALYSIS OF STRUCTURES 70

C3.2.2 Time History Method 70

C3.2.2.1 General Requirements 70

C3.2.2.2.1 Modal superposition method 70

C3.2.2.2.2 Direct integration 71

C3.2.2.3 Nonlinear Methods 71

C3.2.3 Response Spectrum Method 72

C3.2.3.1 Linear Methods 72

C3.2.3.2 Nonlinear Methods 73

C3.2.4 Complex Frequency Response Meethod 73

C3.2.4.1 General Requirements 73

C3.2.4.2 Response Time History 74

C3.2.4.3 Methods to Compute Transfer Functions 74

C3.2.5 Equivalent-Static Method 74

C3.2.5.1 General Requirements 74

C3.2.5.3 Other Simple Structures 75

C3.2.6 Multiply-Supported Systems 75

C3.2.6.1 General Requirements 75

C3.2.6.2 Time History Method 75

C3.2.6.3 Response Spectrum Methods 75

C3.2.6.3.1 Envelope spectrum method 75

C3.2.6.3.2 Multiple-spectrum method 76

C3.2.6.3.3 Combination of inertial and seismic anchor displacement effects 76

C3.2.7 Combination of Modal and Component Responses 76

C3.2.7.1 Response Spectrum Analysis 76

C3.2.7.1.1 General modal combination rule 76

C3.2.7.1.2 Combination of components 77

C3.2.7.1.3 Multiple response parameters 77

C3.3 SOIL-STRUCTURE INTERACTION MODELING AND ANALYSIS 83

C3.3.1 General Requirements 83

C3.3.1.1 Fixed-Base Analysis 84

C3.3.1.2 Spatial Variations of Free-Field Motion 84

C3.3.1.3 Three-Dimensional Effects 85

C3.3.1.4 Nonlinear Behavior of Soil 85

C3.3.1.5 Structure-to-Structure Interaction 85

C3.3.1.6 Effect of Mat and Lateral Wall Flexibility 86

C3.3.1.7 Uncertainties in SSI Analysis 86

C3.3.1.8 Model of Structure 86

C3.3.1.9 Embedment Effects 87

C3.3.1.10 Wave Incoherence 87

C3.3.2 Subsurface Material Properties 87

C3.3.2.1 General Requirements 87

C3.3.2.2 Shear Modulus 88

C3.3.2.3 Damping Ratio 88

C3.3.2.4 Poisson’s Ratio 88

C3.3.3 Direct Method 89

C3.3.3.1 Seismic Input for Model Boundaries 89

C3.3.3.3 Selection of Lateral Boundaries 90

C3.3.3.4 Soil Element Size 90

C3.3.3.5 Time Step and Frequency Increment 91

C3.3.4 Impedance Method 91

C3.3.4.1 Determination of Input Motion 91

C3.3.4.2 Determination of Foundation Impedance Functions 92

C3.3.4.2.1 Equivalent foundation dimensions 92

C3.3.4.2.2 Uniform soil sites 92

C3.3.4.2.3 Layered soil sites 92

C3.3.4.2.4 Embedded foundations 92

C3.4 INPUT FOR SUBSYSTEM SEISMIC ANALYSIS 95

C3.4.1 General Requirements 95

C3.4.1.1 Types of Seismic Input to Subsystem Analysis 95

C3.4.1.2 Direction and Locations for In-Structure Response Spectra or Time Histories 95

C3.4.1.3 Subsystem Input Away from Reference Location 95

C3.4.2 In-Structure Response Spectra 96

C3.4.2.1.2 Direct spectra-to-spectra methods 96

C3.4.2.2 Frequency Interval for Generation of In-Structure Response Spectra 96

C3.4.2.3 Broadening and Lowering of Raw In-Structure Response Spectra 97

C3.4.2.4 Interpolation of In-Structure Response Spectra for Intermediate Damping 98

C3.4.3 In-Structure Time History Motions 98

C3.4.3.1 Methods for Generation of In-Structure Time History Motions 98

C3.4.3.2 Equivalent Broadening and Lowering of In-Structure Time History Motions 100

C3.4.3.3 Time Interval and Data Precision Requirements for In-Structure Time History Motions 101

C3.4.4 Structural Model or Characteristics for Coupled Subsystem Analysis 101

C3.4.4.1 Supporting Structure Model 101

C3.5 SPECIAL STRUCTURES 103

C3.5.2 Buried Pipes and Conduits 103

C3.5.2.1 Straight Sections Remote from Anchor Points, Sharp Bends, or Intersections 103

C3.5.3 Earth-Retaining Structures 104

C3.5.3.1 General Requirements 104

C3.5.3.2 Elastic Solution 104

SEISMIC ANALYSIS OF SAFETY-RELATED NUCLEAR STRUCTURES

C3.5.3.3 Active Solution 105

C3.5.4 Above-Ground Vertical Tanks 105

C3.5.4.2 Horizontal Impulsive Mode 105

C3.5.4.2.1 Effective weight of fluid-Impulsive mode 105

C3.5.4.2.2 Spectral acceleration-Impulsive mode 106

C3.5.4.2.3 Overturning moment at base of tank-Impulsive mode 107

C3.5.4.2.4 Hydrodynamic pressure on tank shell-Impulsive mode 107

C3.5.4.3 Horizontal Sloshing (Conective) Mode 107

C3.5.4.3.1 Effective weight of fluid-Sloshing mode 107

C3.5.4.3.2 Spectral acceleration-Sloshing mode 107

C3.5.4.3.3 Overturning moment at base of tank-Sloshing mode 107

C3.5.4.3.4 Hydrodynamic pressure on tank shell-Sloshing mode 107

C3.5.4.3.5 Fluid slosh height-Fundamental sloshing mode 108

C3.5.4.4 Vertical Fluid Response Mode 108

C3.5.4.4.1 Hydrodynamic pressure on tank shell-Vertical mode 108

C3.5.4.5 Other Considerations 108

C3.5.4.5.1 Overturning moment and longitudinal compressive force 108

C3.5.5 Raceways 108

C3.5.5.1 General Requirements 108

C3.5.5.2 Damping 109

C3.5.6 Seismic Isolated Structures 110

C3.5.6.1 General Requirements 110

C3.5.6.3 Modeling of Structures 111

C3.5.6.4 Response Spectrum Analysis 111

C3.5.6.5 Time History Analysis 111

Index 115