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Seismic Design Bases of the US-APWR Standard Plant MUAP-10001-NP (R4)

Mitsubishi Heavy Industries, LTD.

Seismic Design Bases

of the US-APWR Standard Plant

Non-Proprietary Version

October 2011

©2011 Mitsubishi Heavy Industries, Ltd. All Rights Reserved



Revision History

Revision Page Description

0

All

Original Issue

1 All General revision to update the description of modeling including the reactor coolant loop, including references to MUAP-10006 for results of analyses, and change to model verification methodology. Updated soil profiles 270-200, 270-500, 560-100, 560-200 and 560-500.

2 5-21 to 5-41

Revised figures 5.3.3.3-4 and 5.3.3.3-9 per response to RAI 603-4666, question 03.07.02-10. Revised sections 3.4, 4.2.1 and figure 5.3.3.1-2 per response to RAI 625-4924. Per response to RAI 542, question 03.07.02-35, the PS/B stick model is no longer used. Updated ACS SASSI to version 2.3.0.

3 All Update the report to represent the change in methodology from the lumped mass stick model to the finite element model for the R/B complex structures.

4 Deleted soil profiles 560-200, 560-100; updated soil profiles 270-500, 270-200, 560-500, 900-200, 900-100, 2032-100.

Replaced the Mt. Baldy, CA, recording of the January 14, 1994, Northridge earthquake with the Site 3 recording of the December 23, 1985, Nahanni, Canada, earthquake as the seed motions for the time histories.

Revised Sections 3.2, 4.1, 4.2, 4.2.1, 4.2.2, 4.3.1.2, 4.4.1.2, 5.1, 5.2.2, 5.4.1.

Added Subsections 4.1.1, 4.1.2, and 4.1.3.

Added references 31, 32 and 33 in Section 6.0.

Revised Tables 4.2-1, 4.3.1.2-1, 4.4.1-2, 4.5.3-1, 5.1-1, 5.1-2, 5.1-3, 5.2-1 thru 5.2-14

Deleted Tables 5.2-6, 5.2-7

Revised Figures 4.2-1, 4.3.1.2-1, 5.1-4, 5.1-5, 5.1-6, 5.1-7, 5.2-1 thru 5.2-7, 5.2-9

Divided Figures 5.1-1, 5.1-2, and 5.1-3 each into three



Revision Page Description

sub-figures (5.1-1a, b. and c, etc.).

Deleted Figures 5.2-8, 5.2-10, 5.2-11.

Corrected section numbers of sections 5.4.1 thru 5.4.6

Made other minor editorial changes throughout the document.



©2011

MITSUBISHI HEAVY INDUSTRIES, LTD. All Rights Reserved

This document has been prepared by Mitsubishi Heavy Industries, Ltd. (“MHI”) in connection with the U.S. Nuclear Regulatory Commission’s (“NRC”) licensing review of MHI’s US-APWR nuclear power plant design. No right to disclose, use or copy any of the information in this document, other than by the NRC and its contractors in support of the licensing review of the US-APWR, is authorized without the express written permission of MHI.

This document contains technology information and intellectual property relating to the US-APWR and it is delivered to the NRC on the express condition that it not be disclosed, copied or reproduced in whole or in part, or used for the benefit of anyone other than MHI without the express written permission of MHI, except as set forth in the previous paragraph.

This document is protected by the laws of Japan, U.S. copyright law, international treaties and conventions, and the applicable laws of any country where it is being used.

Mitsubishi Heavy Industries, Ltd. 16-5, Konan 2-chome, Minato-ku

Tokyo 108-8215 Japan


Mitsubishi Heavy Industries, LTD. i

TABLE OF CONTENTS

Table Title Page No.

LIST OF ACRONYMS...............................................................................................................iv

LIST OF FIGURES....................................................................................................................vi

LIST OF TABLES ...................................................................................................................xiv

ABSTRACT..............................................................................................................................xv

1 INTRODUCTION ............................................................................................................. 1-1

2 PURPOSE ....................................................................................................................... 2-1

3 OBJECTIVES .................................................................................................................. 3-1 3.1 CSDRS Compatible Ground Motion Time Histories .............................................. 3-1 3.2 Generic Layered Soil Profiles and Strain Compatible Properties .......................... 3-1 3.3 Dynamic Finite Element Model of R/B Complex.................................................... 3-1 3.4 ACS SASSI Dynamic Finite Element Model of the PS/Bs ..................................... 3-2 3.5 Consideration of Concrete Cracking in Dynamic Analyses ................................... 3-3

4 APPROACH .................................................................................................................... 4-1 4.1 Time Histories........................................................................................................ 4-1

4.1.1 CSDRS Compatible Ground Motion Time Histories ................................. 4-1 4.1.2 Verification of Response Spectra from Time Histories............................. 4-7 4.1.3 Strong Motion Duration of Time Histories ................................................ 4-8

4.2 Development of Soil Profiles and Strain Compatible Properties ........................... 4-8 4.2.1 Selection of Profiles.................................................................................. 4-9 4.2.2 Development of US-APWR CSDRS Strain Compatible Properties........ 4-10

4.3 ACS SASSI Dynamic Finite Element Model of R/B Complex.............................. 4-15 4.3.1 Development of the R/B Complex Dynamic FE Model........................... 4-15

4.3.1.1 Finite Element Modeling......................................................... 4-15 4.3.1.2 Discretization Considerations: Mesh Size.............................. 4-26 4.3.1.3 Modeling of Stiffness and Damping ....................................... 4-27 4.3.1.4 Modeling of Mass ................................................................... 4-28 4.3.1.5 Adjustment of Stiffness and Mass Properties ........................ 4-29 4.3.1.6 Stiffness of Composite Steel-Concrete Beams and Columns 4-31 4.3.1.7 Implementation of Stiffness Reduction in the Dynamic

FE Model................................................................................ 4-33 4.3.1.8 Adjustment of Out-of-Plane Dynamic Properties of

R/B Slabs ............................................................................... 4-34 4.3.1.9 Adjustment of Dynamic Properties of SC Modules ................ 4-37

4.3.2 Validation of Dynamic FE Model ............................................................ 4-37 4.3.3 Conversion of the R/B Complex Dynamic FE Model from ANSYS to ACS SASSI Format ............................................................................ 4-38


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4.4 ACS SASSI Dynamic Finite Element Model of PS/B........................................... 4-40 4.4.1 Development of the PS/B Dynamic FE Model........................................ 4-40

4.4.1.1 Finite Element Modeling......................................................... 4-40 4.4.1.2 Discretization Considerations: Mesh Size.............................. 4-43 4.4.1.3 Modeling of Stiffness and Damping ....................................... 4-44 4.4.1.4 Modeling of Mass ................................................................... 4-45 4.4.1.5 Adjustment of Stiffness and Mass Properties ........................ 4-45 4.4.1.6 Implementation of Stiffness Reduction in the

Dynamic FE Model................................................................. 4-46 4.4.2 Out-of-Plane Dynamic Properties of PS/B Slabs ................................... 4-46 4.4.3 Validation of PS/B Dynamic FE Model ................................................... 4-48 4.4.4 Conversion of the PS/B Dynamic FE Model from ANSYS to ACS SASSI Format ................................................................................ 4-48

4.5 Consideration of Concrete Cracking in Dynamic Analyses ................................. 4-48 4.5.1 Effects of Concrete Cracking on Reinforced Concrete Shear Wall Structures ............................................................................ 4-49 4.5.2 Effects of Concrete Cracking on the CIS................................................ 4-50 4.5.3 Approach to Address Concrete Cracking in Site-Independent SSI Analyses .......................................................................................... 4-51

5 RESULTS AND CONCLUSIONS.................................................................................... 5-1 5.1 CSDRS Compatible Ground Motion Time Histories .............................................. 5-1 5.2 Development of Soil Profiles ............................................................................... 5-15

5.2.1 Site Response Analyses ........................................................................ 5-23 5.2.2 Strain Compatible Properties ................................................................. 5-28

5.3 ACS SASSI FE Model of the R/B Complex ......................................................... 5-77 5.3.1 Development of the R/B Complex Dynamic FE Model........................... 5-77 5.3.2 Reactor Coolant Loop (RCL) Model ....................................................... 5-85

5.3.2.1 Description of RCL Model ...................................................... 5-85 5.3.2.2 Coupling of RCL Model .......................................................... 5-93

5.3.3 Validation of the R/B Complex Dynamic FE Model .............................. 5-101 5.3.3.1 Validation of the R/B-FH/A ................................................... 5-101

5.3.3.1.1 1g Static Analysis ............................................... 5-101 5.3.3.1.2 Modal Analysis ................................................... 5-106 5.3.3.1.3 Modal Superposition Time History Analysis ....... 5-108

5.3.3.2 Validation of the CIS ............................................................ 5-123 5.3.3.2.1 1g Static Analysis ............................................... 5-123 5.3.3.2.2 Modal Superposition Time History Analysis ....... 5-146

5.3.3.3 Validation of the PCCV ........................................................ 5-164 5.3.3.3.1 1g Static Analysis ............................................... 5-164 5.3.3.3.2 Modal Analysis ................................................... 5-166 5.3.3.3.3 Modal Superposition Time History Analysis ....... 5-168

5.3.4 Validation of the Dynamic FE Model Translation into ACS SASSI Format ..................................................................................................5-177 5.3.4.1 Validation of the R/B ............................................................ 5-177 5.3.4.2 Validation of the CIS ............................................................ 5-187 5.3.4.3 Validation of the PCCV ........................................................ 5-201


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5.3.5 Summary of Dynamic Properties of R/B Complex Dynamic FE Model 5-209 5.4 Dynamic FE Model of the PS/B ......................................................................... 5-214

5.4.1 Development of the FE Model of the PS/B........................................... 5-214 5.4.2 Attributes Assigned to the PS/B Dynamic FE Model............................ 5-218 5.4.3 Validation of the PS/B Dynamic FE Model ........................................... 5-218

5.4.3.1 1g Static Analysis................................................................. 5-219 5.4.3.2 Modal Analysis ..................................................................... 5-224 5.4.3.3 Modal Superposition Time History Analysis......................... 5-226

5.4.4 Local Out-of-Plane Vibration of the Slabs ............................................ 5-235 5.4.5 ACS SASSI Validation.......................................................................... 5-238 5.4.6 Results and Conclusion........................................................................ 5-247

6 REFERENCES ................................................................................................................ 6-1

APPENDIX A - DELETED .....................................................................................................A-1

APPENDIX B - EFFECTS OF CONCRETE CRACKING ON THE US-APWR PRE-STRESSED CONCRETE CONTAINMENT VESSEL (PCCV) RESPONSE ..................................................................................................B-1


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LIST OF ACRONYMS

The following list defines the acronyms used in this document.

3-D Three Dimensional

AISC American Institute of Steel Construction

APDL ANSYS Parametric Design Language

ARS Acceleration Response Spectra

ASCE American Society of Civil Engineers

ASME American Society of Mechanical Engineers

ATF Amplification Transfer Function

CEUS Central and Eastern United States

CIS Containment Internal Structure

CSDRS Certified Seismic Design Response Spectra

EPRI Electrical Power Research Institute

EW East-West

FE Finite Element

FH/A Fuel Handling Area

GMPE Ground Motion Prediction Equation

H Horizontal

ISRS In-Structure Response Spectra

HVAC Heating, Ventilating, and Air Conditioning

LMSM Lumped Mass Stick Model

MCP Main Coolant Piping

NRC Nuclear Regulatory Commission

NS North-South

NSSS Nuclear Steam Supply System

OBE Operating-Basis Earthquake

PCCV Pre-stressed Concrete Containment Vessel

PEER Pacific Earthquake Engineering Research

PGA Peak Ground Acceleration

PS/B Power Source Building

RAI Request for Additional Information

R/B Reactor Building

RC Reinforced Concrete

RCL Reactor Coolant Loop


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RCP Reactor Coolant Pump

RG Regulatory Guide

RV Reactor Vessel

RVT Random Vibration Theory

SC Steel-Concrete

SG Steam Generator

SRP Standard Review Plan

SSE Safe-Shutdown Earthquake

SSC Structural System and Component

SSI Soil-Structure Interaction

TF Transfer Function

TR Technical Report

V Vertical

Vs Shear Wave Velocity

WNA Western North America

WUS Western United States

ZPA Zero Period Acceleration


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LIST OF FIGURES

Figure Title Page No.

Figure 4.1.1-1 US-APWR Horizontal CSDRS ................................................................4-4 Figure 4.1.1-2 US-APWR Vertical CSDRS ....................................................................4-5 Figure 4.2-1 Top 500 ft of the Candidate Shear-Wave Velocity Profiles and

Associated )30( mVS Velocities .............................................................4-13 Figure 4.2-2 (TR-102293, Reference 7) Cohesionless Soil Modulus Reduction

and Hysteretic Damping Curves ...........................................................4-14 Figure 4.3.1.1-1 Integrated R/B Complex Dynamic FE Model ........................................4-20 Figure 4.3.1.1-2 Overview of the R/B Detailed FE Model ...............................................4-21 Figure 4.3.1.1-3 Overview of the PCCV Detailed FE Model ...........................................4-22 Figure 4.3.1.1-4 Overview of the CIS Detailed FE Model ...............................................4-23 Figure 4.3.1.1-5 Connection of Shell to Solid Elements..................................................4-24 Figure 4.3.1.1-6 Connection of Beam to Solid Elements ................................................4-25 Figure 4.3.1.1-7 Connection of Beam to Shell Elements ................................................4-25 Figure 4.3.1.4-1 Perpendicular Liquid Masses................................................................4-29 Figure 4.3.1.5-1A FE Models to Calculate Wall Stiffness Reduction Factors –

Model A.................................................................................................4-30 Figure 4.3.1.5-1B FE Models to Calculate Wall Stiffness Reduction Factors –

Model B.................................................................................................4-30 Figure 4.3.1.8-1 Extracted Detailed FE Model of Floor Slabs .........................................4-36 Figure 4.3.1.8-2 Floor Slab Model Boundary Conditions ................................................4-36 Figure 4.4.1.1-1 Overview of the PS/B Detailed FE Model .............................................4-42 Figure 4.4.1.1-2 Overview of the PS/B Dynamic FE Model ............................................4-43 Figure 4.4.2-1 Extracted Detailed FE Model of Floor Slabs .........................................4-47 Figure 4.4.2-2 Floor Slab Model Boundary Conditions ................................................4-47 Figure 5.1-1a Acceleration Time History for Component H1 (270) ...............................5-1 Figure 5.1-1b Velocity Time History for Component H1 (270) ......................................5-2 Figure 5.1-1c Displacement Time History for Component H1 (270) .............................5-2 Figure 5.1-2a Acceleration Time History for Component H2 (360) ...............................5-3 Figure 5.1-2b Velocity Time History for Component H2 (360) ......................................5-3 Figure 5.1-2c Displacement Time History for Component H2 (360) .............................5-4 Figure 5.1-3a Acceleration Time History for Component V (UP) ..................................5-4 Figure 5.1-3b Velocity Time History for Component V (UP)..........................................5-5 Figure 5.1-3c Displacement Time History for Component V (UP) ................................5-5 Figure 5.1-4 5% Damped Response Spectra Plots for Adjusted Nahanni Station

3 Component H1 (270) ...........................................................................5-6 Figure 5.1-5 5% Damped Response Spectra Plots for Adjusted Nahanni, Station

3 Component H2 (360) ...........................................................................5-7 Figure 5.1-6 5% Damped Response Spectra Plots for Adjusted Nahanni, Station

3 Component V (UP)...............................................................................5-7 Figure 5.1-7 Normalized Arias Intensity of Time History Components Showing

5%-75% Duration Component 270 .......................................................5-12 Figure 5.1-8 Normalized Arias Intensity of Time History Components Showing

5%-75% Duration Component 360 .......................................................5-13 Figure 5.1-9 Normalized Arias Intensity of Time History Components Showing

5%-75% Duration Component UP ........................................................5-14 Figure 5.2-1 Final Foundation Level Base-Case Shear- and Compression-Wave

Velocity Profiles (Sheet 1 of 4)..............................................................5-17


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Figure 5.2-1 Final Foundation Level Base-Case Shear- and Compression-Wave Velocity Profiles (Sheet 2 of 4)..............................................................5-18

Figure 5.2-1 Final Foundation Level Base-Case Shear- And Compression-Wave Velocity Profiles (Sheet 3 of 4)..............................................................5-19

Figure 5.2-1 Final Foundation Level Base-Case Shear- And Compression-Wave Velocity Profiles (Sheet 4 of 4)..............................................................5-20

Figure 5.2-2 Poisson Ratios Computed for the Six Soil Profiles(Sheet 1 of 2) .........5-21 Figure 5.2-2 Poisson Ratios Computed for the Six Soil Profiles(Sheet 2 of 2) .........5-22 Figure 5.2-3 Median Spectra (5% damped) Compared to CSDRS Horizontal

Components..........................................................................................5-25 Figure 5.2-4 Median Spectra (5% damped) Compared to CSDRS Vertical

Components..........................................................................................5-26 Figure 5.2-5 Median Spectra (5% damped) Compared to CSDRS Vertical

Components Using RG 1.60 V/H Ratios...............................................5-27 Figure 5.2-6 Strain Compatible Properties Computed for Profile 270, 500 ft

Depth to Bedrock (Sheet 1 of 3) ...........................................................5-55 Figure 5.2-6 Strain Compatible Properties Computed for Profile 270 500 ft

Depth to Bedrock (Sheet 2 of 3) ...........................................................5-56 Figure 5.2-6 Strain Compatible Properties Computed for Profile 270 500 ft Depth to Bedrock (Sheet 3 of 3) .................................................5-57 Figure 5.2-7 Strain Compatible Properties Computed for Profile 270 200 ft



Depth to Bedrock (Sheet 3 of 3) ...........................................................5-60 Figure 5.2-8 Deleted .................................................................................................5-61 Figure 5.2-9 Strain Compatible Properties Computed for Profile 560, 500 ft

Depth to Bedrock (Sheet 1 of 3) ...........................................................5-62 Figure 5.2-9 Strain Compatible Properties Computed for Profile 560, 500 ft

Depth to Bedrock (Sheet 2 of 3) ...........................................................5-63 Figure 5.2-9 Strain Compatible Properties Computed for Profile 560, 500 ft

Depth to Bedrock (Sheet 3 of 3) ...........................................................5-64 Figure 5.2-10 Deleted..................................................................................................5-65 Figure 5.2-11 Deleted..................................................................................................5-66 Figure 5.2-12 Strain Compatible Properties Computed for Profile 900, 200 ft

Depth to Bedrock (Sheet 1 of 3) ...........................................................5-67 Figure 5.2-12 Strain Compatible Properties Computed for Profile 900 200 ft Depth to Bedrock (Sheet 2 of 3) .................................................5-68 Figure 5.2-12 Strain Compatible Properties Computed for Profile 900 200 ft Depth to Bedrock (Sheet 3 of 3) .................................................5-69 Figure 5.2-13 Strain Compatible Properties Computed for Profile 900 100 ft

Depth to Bedrock (Sheet 1 of 3) ...........................................................5-70 Figure 5.2-13 Strain Compatible Properties Computed for Profile 900 100 ft Depth to Bedrock (Sheet 2 of 3) .................................................5-71 Figure 5.2-13 Strain Compatible Properties Computed for Profile 900 100 ft Depth to Bedrock (Sheet 3 of 3) .................................................5-72 Figure 5.2-14 Strain Compatible Properties Computed for Profile 2032 100 ft

Depth to Bedrock (Sheet 1 of 3) ...........................................................5-73 Figure 5.2-14 Strain Compatible Properties Computed for Profile 2032 100 ft Depth to Bedrock (Sheet 2 of 3) .................................................5-74


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Figure 5.2-14 Strain Compatible Properties Computed for Profile 2032 100 ft Depth to Bedrock (Sheet 3 of 3) .................................................5-75 Figure 5.2-15 Shear Column Frequencies of Top Soil Strata (Truncated Profiles).....5-76 Figure 5.3.1-1 Dynamic R/B Model ..............................................................................5-79 Figure 5.3.1-2 Section View of Dynamic R/B Model Looking East...............................5-80 Figure 5.3.1-3 Section View of Dynamic R/B Model Looking South ............................5-81 Figure 5.3.1-4 Dynamic PCCV Model ..........................................................................5-82 Figure 5.3.1-5 Dynamic CIS Model – Solid Elements ..................................................5-83 Figure 5.3.1-6 Dynamic CIS Model – Shell and RCL Elements ...................................5-84 Figure 5.3.2.2-1 US-APWR Reactor Coolant Loop (RCL) ..............................................5-94 Figure 5.3.2.2-2 Lumped Mass Dynamic Model of RCL .................................................5-95 Figure 5.3.2.2-3 Reactor Vessel Support ........................................................................5-96 Figure 5.3.2.2-4 Reactor Vessel Support FE Model Connection ....................................5-97 Figure 5.3.2.2-5 Steam Generator Lower Lateral Support ..............................................5-98 Figure 5.3.2.2-6 Reactor Coolant Pump (RCP) Tie Rod .................................................5-99 Figure 5.3.2.2-7 Steam Generator Supports FE Model Connections............................5-100 Figure 5.3.3.1.1-1 Lateral Displacement Locations on R/B Exterior Walls.......................5-102 Figure 5.3.3.1.1-2 R/B 1g Static Analysis Results – NS Direction (X) at Location C .......5-103 Figure 5.3.3.1.1-3 R/B 1g Static Analysis Results – EW Direction (Y) at Location C.......5-103 Figure 5.3.3.1.1-4 R/B 1g Static Analysis Results – NS Direction (X) at Location H .......5-104 Figure 5.3.3.1.1-5 R/B 1g Static Analysis Results – EW Direction (Y) at Location H.......5-104 Figure 5.3.3.1.2-1 R/B Modal Analysis Results–Cumulative Mass in the NS Direction

(X) .......................................................................................................5-106 Figure 5.3.3.1.2-2 R/B Modal Analysis Results–Cumulative Mass in the EW

Direction (Y) ........................................................................................5-107 Figure 5.3.3.1.2-3 R/B Modal Analysis Results–Cumulative Mass in the Vertical

Direction (Z) ........................................................................................5-107 Figure 5.3.3.1.3-1 R/B NS Direction ARS Results – Location D – Comparison at EL.

76’-5”...................................................................................................5-108 Figure 5.3.3.1.3-2 R/B EW Direction ARS Results – Location D – Comparison at EL

76’-5”...................................................................................................5-109 Figure 5.3.3.1.3-3 R/B Vertical Direction ARS Results – Location D – Comparison at

EL 76’-5” .............................................................................................5-110 Figure 5.3.3.1.3-4 R/B NS Direction ARS Results – Location H – Comparison at EL

131’-6”.................................................................................................5-111 Figure 5.3.3.1.3-5 R/B EW Direction ARS Results – Location H – Comparison at EL

131’-6 ..................................................................................................5-112 Figure 5.3.3.1.3-6 R/B Vertical Direction ARS Results – Location H – Comparison at

EL 131’-6.............................................................................................5-113 Figure 5.3.3.1.3-7 R/B Vertical Direction ARS Results – Comparison at Slab Group

-8SG1 (EL -8’-7”) ................................................................................5-114 Figure 5.3.3.1.3-8 R/B Vertical Direction ARS Results – Comparison at Slab Group

3SG1 (EL. 3’-7”)..................................................................................5-115 Figure 5.3.3.1.3-9 R/B Vertical Direction ARS Results – Comparison Slab Group

25SG1 (EL. 25’-3”)..............................................................................5-116 Figure 5.3.3.1.3-10 R/B Vertical Direction ARS Results – Comparison Slab Group



76SG5 (EL. 76’-5”)..............................................................................5-119


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Figure 5.3.3.1.3-13 R/B Vertical Direction ARS Results – Comparison Slab Group 86SG1 (EL. 86’-4”)..............................................................................5-120

Figure 5.3.3.1.3-14 R/B Vertical Direction ARS Results – Comparison Slab Group 101SG6 (EL. 101’-0”)..........................................................................5-121

Figure 5.3.3.1.3-15 R/B Vertical Direction ARS Results – Comparison Slab Group 115SG7 (EL. 115’-6”)..........................................................................5-122

Figure 5.3.3.2.1-1 CIS 1g Static Analysis Results – NS Direction (X) at North Face of Structure (Uncracked Analysis) ..........................................................5-124

Figure 5.3.3.2.1-2 CIS 1g Static Analysis Results – EW Direction (Y) at North Face of Structure (Uncracked Analyses) .........................................................5-125

Figure 5.3.3.2.1-3 CIS 1g Static Analysis Results – NS Direction (X) at Reactor Vessel (Uncracked Analyses) .............................................................5-126

Figure 5.3.3.2.1-4 CIS 1g Static Analysis Results – EW Direction (Y) at Reactor Vessel (Uncracked Analyses) .............................................................5-127

Figure 5.3.3.2.1-5 CIS 1g Static Analysis Results – NS Direction (X) at Northwest Steam Generator (Uncracked Analyses) ............................................5-128

Figure 5.3.3.2.1-6 CIS 1g Static Analysis Results – EW Direction (Y) at Northwest Steam Generator (Uncracked Analyses) ............................................5-129

Figure 5.3.3.2.1-7 CIS 1g Static Analysis Results – NS Direction (X) at Southeast Reactor Coolant Pump (Uncracked Analyses) ...................................5-130

Figure 5.3.3.2.1-8 CIS 1g Static Analysis Results – EW Direction (Y) at Southeast Reactor Coolant Pump (Uncracked Analyses) ...................................5-131

Figure 5.3.3.2.1-9 CIS 1g Static Analysis Results – NS Direction (X) at North Face of Structure (Cracked Analyses) .............................................................5-132

Figure 5.3.3.2.1-10 CIS 1g Static Analysis Results – EW Direction (Y) at North Face of Structure (Cracked Analyses) .............................................................5-133

Figure 5.3.3.2.1-11 CIS 1g Static Analysis Results – NS Direction (X) at Reactor Vessel (Cracked Analyses).................................................................5-134

Figure 5.3.3.2.1-12 CIS 1g Static Analysis Results – EW Direction (Y) at Reactor Vessel (Cracked Analyses).................................................................5-135

Figure 5.3.3.2.1-13 CIS 1g Static Analysis Results – NS Direction (X) at Northwest Steam Generator (Cracked Analyses) ................................................5-136

Figure 5.3.3.2.1-14 CIS 1g Static Analysis Results – EW Direction (Y) at Northwest Steam Generator (Cracked Analyses) ................................................5-137

Figure 5.3.3.2.1-15 CIS 1g Static Analysis Results – NS Direction (X) at Southeast Reactor Coolant Pump (Cracked Analyses) .......................................5-138

Figure 5.3.3.2.1-16 CIS 1g Static Analysis Results – EW Direction (Y) at Southeast Reactor Coolant Pump (Cracked Analyses) .......................................5-139

Figure 5.3.3.2.2-1 CIS Modal Analysis Results – Cumulative Mass in the NS Direction (X) (Uncracked Analyses) ...................................................................5-140

Figure 5.3.3.2.2-2 CIS Modal Analysis Results – Cumulative Mass in the EW Direction (Y) (Uncracked Analyses)....................................................5-141

Figure 5.3.3.2.2-3 CIS Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z) (Uncracked Analyses) ....................................................5-142

Figure 5.3.3.2.2-4 CIS Modal Analysis Results – Cumulative Mass in the NS Direction (X) (Cracked Analyses).......................................................................5-143

Figure 5.3.3.2.2-5 CIS Modal Analysis Results – Cumulative Mass in the EW Direction (Y) (Cracked Analyses)........................................................5-144

Figure 5.3.3.2.2-6 CIS Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z) (Cracked Analyses)........................................................5-145

Figure 5.3.3.2.3-1 CIS ARS Results – Comparison at Top of Pressurizer, X-direction (Uncracked Analyses).........................................................................5-146


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Figure 5.3.3.2.3-2 CIS ARS Results – Comparison at Top of Pressurizer, Y-direction (Uncracked Analyses).........................................................................5-147

Figure 5.3.3.2.3-3 CIS ARS Results – Comparison at Top of Pressurizer, Z-direction (Uncracked Analyses).........................................................................5-148

Figure 5.3.3.2.3-4 CIS ARS Results – Comparison at Top of West SG Compartment, X-direction (Uncracked Analyses).......................................................5-149

Figure 5.3.3.2.3-5 CIS ARS Results – Comparison at Top of West SG Compartment, Y-direction (Uncracked Analyses).......................................................5-150

Figure 5.3.3.2.3-6 CIS ARS Results – Comparison at Top of West SG Compartment, Z-direction (Uncracked Analyses).......................................................5-151

Figure 5.3.3.2.3-7 CIS ARS Results – Comparison at Top of Reactor Vessel, X-direction (Uncracked Analyses).......................................................5-152

Figure 5.3.3.2.3-8 CIS ARS Results – Comparison at Top of Reactor Vessel, Y-direction (Uncracked Analyses).......................................................5-153

Figure 5.3.3.2.3-9 CIS ARS Results – Comparison at Top of Reactor Vessel, Z-direction (Uncracked Analyses).......................................................5-154

Figure 5.3.3.2.3-10 CIS ARS Results – Comparison at Top of Pressurizer, X-direction (Cracked Analyses).............................................................................5-155

Figure 5.3.3.2.3-11 CIS ARS Results – Comparison at Top of Pressurizer, Y-direction (Cracked Analyses).............................................................................5-156

Figure 5.3.3.2.3-12 CIS ARS Results – Comparison at Top of Pressurizer, Z-direction (Cracked Analyses).............................................................................5-157

Figure 5.3.3.2.3-13 CIS ARS Results – Comparison at Top of West SG Compartment, X-direction (Cracked Analyses) ..........................................................5-158

Figure 5.3.3.2.3-14 CIS ARS Results – Comparison at Top of West SG Compartment, Y-direction (Cracked Analyses) ..........................................................5-159

Figure 5.3.3.2.3-15 CIS ARS Results – Comparison at Top of West SG Compartment, Z-direction (Cracked Analyses)...........................................................5-160

Figure 5.3.3.2.3-16 CIS ARS Results – Comparison at Top of Reactor Vessel, X-direction (Cracked Analyses) ..........................................................5-161

Figure 5.3.3.2.3-17 CIS ARS Results – Comparison at Top of Reactor Vessel, Y-direction (Cracked Analyses) ..........................................................5-162

Figure 5.3.3.2.3-18 CIS ARS Results – Comparison at Top of Reactor Vessel, Z-direction (Cracked Analyses)...........................................................5-163

Figure 5.3.3.3.1-1 PCCV 1g Static Analysis Results – NS Direction (X) at North Face of Structure .........................................................................................5-164

Figure 5.3.3.3.1-2 PCCV 1g Static Analysis Results – EW direction (Y) at North Face of Structure .........................................................................................5-165

Figure 5.3.3.3.2-1 PCCV Modal Analysis Results – Cumulative Mass in the NS Direction (X) ........................................................................................5-166

Figure 5.3.3.3.2-2 PCCV Modal Analysis Results – Cumulative Mass in the EW Direction (Y) ........................................................................................5-167

Figure 5.3.3.3.2-3 PCCV Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z) ........................................................................................5-167

Figure 5.3.3.3.3-1 PCCV ARS Results – Comparison at Elev. 86.25 ft, X-direction ........5-168 Figure 5.3.3.3.3-2 PCCV ARS Results – Comparison at Elev. 86.25 ft, Y-direction ........5-169 Figure 5.3.3.3.3-3 PCCV ARS Results – Comparison at Elev. 86.25 ft, Z-direction ........5-170 Figure 5.3.3.3.3-4 PCCV ARS Results – Comparison at Elev. 145.58 ft, X-direction ......5-171 Figure 5.3.3.3.3-5 PCCV ARS Results – Comparison at Elev. 145.58 ft, Y-direction ......5-172 Figure 5.3.3.3.3-6 PCCV ARS Results – Comparison at Elev. 145.58 ft, Z-direction ......5-173 Figure 5.3.3.3.3-7 PCCV ARS Results – Comparison at Elev. 232 ft, X-direction ...........5-174 Figure 5.3.3.3.3-8 PCCV ARS Results – Comparison at Elev. 232 ft, Y-direction ...........5-175


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Figure 5.3.3.3.3-9 PCCV ARS Results – Comparison at Elev. 232 ft, Z-direction ...........5-176 Figure 5.3.4.1-1 R/B ARS Results – Comparison at Slab Sb40A8 (EL. 3’-7”),

Z-direction...........................................................................................5-177 Figure 5.3.4.1-2 R/B ARS Results – Comparison at Slab S28A12b (EL. 25’-3”),

Z-direction...........................................................................................5-178 Figure 5.3.4.1-3 R/B ARS Results – Comparison at Slab S38A1 (EL. 35’-2”),

Z-direction...........................................................................................5-179 Figure 5.3.4.1-4 R/B ARS Results – Comparison at Slab S46B3 (EL. 48’-6”),

Z-direction...........................................................................................5-180 Figure 5.3.4.1-5 R/B ARS Results – Comparison at Slab S40C8 (EL. 63’-4”),

Z-direction...........................................................................................5-181 Figure 5.3.4.1-6 R/B ARS Results – Comparison at Slab S44C2 (EL. 75’),

Z-direction...........................................................................................5-182 Figure 5.3.4.1-7 R/B ARS Results – Comparison at Slab S20A3 (EL. 86’-4”),

Z-direction...........................................................................................5-183 Figure 5.3.4.1-8 R/B ARS Results – Comparison at Slab S15D2 (EL. 99.75’),

Z-direction...........................................................................................5-184 Figure 5.3.4.1-9 R/B ARS Results – Comparison at Slab S40G1 (EL. 115’-5”),

Z-direction...........................................................................................5-185 Figure 5.3.4.1-10 R/B ARS Results – Comparison at Exterior Wall Location D Roof

Level, X-direction ................................................................................5-186 Figure 5.3.4.1-11 R/B ARS Results – Comparison at Exterior Wall Location B Roof

Level, Y-direction ................................................................................5-187 Figure 5.3.4.2-1 Transfer Function – Base of CIS/PCCV, X-Direction (Uncracked

Analyses) ............................................................................................5-188 Figure 5.3.4.2-2 Transfer Function – Base of CIS/PCCV, Y-Direction (Uncracked

Analyses) ............................................................................................5-189 Figure 5.3.4.2-3 CIS ARS Results – Comparison at Top of Pressurizer

Compartment X-Direction (Uncracked Analyses) ...............................5-190 Figure 5.3.4.2-4 CIS ARS Results – Comparison at Top of West Steam Generator

X-Direction (Uncracked Analyses) ......................................................5-191 Figure 5.3.4.2-5 CIS ARS Results – Comparison at 3rd Floor Y-Direction (Uncracked

Analyses) ............................................................................................5-192 Figure 5.3.4.2-6 CIS ARS Results – Comparison at Top of Reactor Cavity

Z-Direction (Uncracked Analyses) ......................................................5-193 Figure 5.3.4.2-7 CIS ARS Results – Comparison at 2nd Floor Z-Direction

(Uncracked Analyses).........................................................................5-194 Figure 5.3.4.2-8 CIS ARS Results – Comparison at Top of RCP Y-Direction

(Uncracked Analyses).........................................................................5-195 Figure 5.3.4.2-9 CIS ARS Results – Comparison at Top of Pressurizer

Compartment X-Direction (Cracked Analyses) ...................................5-196 Figure 5.3.4.2-10 CIS ARS Results – Comparison at Top of West Steam Generator

Compartment X-Direction (Cracked Analyses) ...................................5-197 Figure 5.3.4.2-11 CIS ARS Results – Comparison at Top of RCP Y-Direction

(Cracked Analyses).............................................................................5-198 Figure 5.3.4.2-12 CIS ARS Results – Comparison at Top of 4th Floor Operational

Y-Direction (Cracked Analyses)..........................................................5-199 Figure 5.3.4.2-13 CIS ARS Results – Comparison at Top of Pressurizer

Compartment Z-Direction (Cracked Analyses) ...................................5-200 Figure 5.3.4.2-14 CIS ARS Results – Comparison at Top of West SG Compartment

Z-Direction (Cracked Analyses) ..........................................................5-201 Figure 5.3.4.3-1 PCCV ARS Results – Comparison at Elev. 86.25 ft, X-direction ........5-202


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Figure 5.3.4.3-2 PCCV ARS Results – Comparison at Elev. 145.58 ft, X-direction ......5-203 Figure 5.3.4.3-3 PCCV ARS Results – Comparison at Elev. 86.25 ft, Z-direction ........5-204 Figure 5.3.4.3-4 PCCV ARS Results – Comparison at Elev. 86.25 ft, Y-direction ........5-205 Figure 5.3.4.3-5 PCCV ARS Results – Comparison at Elev. 232 ft, Y-direction ...........5-206 Figure 5.3.4.3-6 PCCV ARS Results – Comparison at Elev. 145.58 ft, Z-direction ......5-207 Figure 5.3.4.3-7 PCCV ARS Results – Comparison at Elev. 232 ft, Z-direction ...........5-208 Figure 5.3.5-1 Integrated R/B Complex Dynamic FE Model ......................................5-209 Figure 5.3.5-2 Section View of R/B Complex Dynamic FE Model Looking East........5-210 Figure 5.3.5-3 Section View of R/B Complex Dynamic FE Model Looking South......5-211 Figure 5.4.1-1 Overview of PS/B Dynamic FE Model ................................................5-215 Figure 5.4.1-2 PS/B Dynamic FE Model (EL. -26’-4”) ................................................5-215 Figure 5.4.1-3 PS/B Dynamic FE Model (EL. -14’-2”) ................................................5-216 Figure 5.4.1-4 PS/B Dynamic FE Model (EL. -3’-7”) ..................................................5-216 Figure 5.4.1-5 PS/B Dynamic FE Model (EL. 24’-2”) .................................................5-217 Figure 5.4.1-6 PS/B Dynamic FE Model (Roof – EL. 39’-6” and EL. 49’-0”) ..............5-217 Figure 5.4.1-7 PS/B Dynamic FE Model (Beams and Columns)................................5-218 Figure 5.4.3-1 PS/B 1g Static Analysis Results – NS Direction (X) at Northeast

Corner .................................................................................................5-220 Figure 5.4.3-2 PS/B 1g Static Analysis Results – EW Direction (Y) at Northeast

Corner .................................................................................................5-220 Figure 5.4.3-3 PS/B 1g Static Analysis Results – NS Direction (X) at Northwest

Corner .................................................................................................5-221 Figure 5.4.3-4 PS/B 1g Static Analysis Results – EW Direction (Y) at Northwest

Corner .................................................................................................5-221 Figure 5.4.3-5 PS/B 1g Static Analysis Results – NS Direction (X) at Southeast

Corner .................................................................................................5-222 Figure 5.4.3-6 PS/B 1g Static Analysis Results – EW Direction (Y) at Southeast

Corner .................................................................................................5-222 Figure 5.4.3-7 PS/B 1g Static Analysis Results – NS Direction (X) at Southwest

Corner .................................................................................................5-223 Figure 5.4.3-8 PS/B 1g Static Analysis Results – EW Direction (Y) at Southwest

Corner .................................................................................................5-223 Figure 5.4.3-9 PS/B Modal Analysis Results – Cumulative Mass in the NS

Direction (X) ........................................................................................5-224 Figure 5.4.3-10 PS/B Modal Analysis Results – Cumulative Mass in the EW

Direction (Y) ........................................................................................5-225 Figure 5.4.3-11 PS/B Modal Analysis Results – Cumulative Mass in the Vertical

Direction (Z) ........................................................................................5-226 Figure 5.4.3-12 PS/B ARS Results – Comparison at Elev. 3’-7” Interior, X-direction ..5-227 Figure 5.4.3-13 PS/B ARS Results – Comparison at Elev. 3’-7” Interior, Y-direction ..5-228 Figure 5.4.3-14 PS/B ARS Results – Comparison at Elev. 3’-7” Interior, Z-direction...5-229 Figure 5.4.3-15 PS/B ARS Results – Comparison at Elev. 3’-7” Perimeter,

X-direction...........................................................................................5-230 Figure 5.4.3-16 PS/B ARS Results – Comparison at Elev. 3’-7” Perimeter,

Y-direction...........................................................................................5-231 Figure 5.4.3-17 PS/B ARS Results – Comparison at Elev. 3’-7” Perimeter,

Z-direction...........................................................................................5-232 Figure 5.4.3-18 PS/B ARS Results – Comparison at Elev. 39’-6” Interior,

X-direction...........................................................................................5-233 Figure 5.4.3-19 PS/B ARS Results – Comparison at Elev. 39’-6” Interior,

Y-direction...........................................................................................5-234 Figure 5.4.3-20 PS/B ARS Results – Comparison at Elev. 39’-6” Interior, Z-direction.5-235


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Figure 5.4.4-1 Ground Floor (EL. 3’-7”) – Detailed Model - 1st Dominant Frequency...........................................................................................5-236

Figure 5.4.4-2 Ground Floor (EL. 3’-7”) – Dynamic Model - 1st Dominant Frequency...........................................................................................5-236

Figure 5.4.4-3 Ground Floor (EL. 3’-7”) – Detailed Model – 2nd Dominant Frequency...........................................................................................5-237

Figure 5.4.4-4 Ground Floor (EL. 3’-7”) – Dynamic Model – 2nd Dominant Frequency...........................................................................................5-237

Figure 5.4.5-1 PS/B ACS SASSI Results – Transfer Functions NS Direction............5-239 Figure 5.4.5-2 PS/B ACS SASSI Results – Transfer Functions EW Direction...........5-240 Figure 5.4.5-3 PS/B ACS SASSI Results – Transfer Functions Vertical Direction.....5-241 Figure 5.4.5-4 PS/B ACS SASSI Results – ARS Comparison at Elev. 3’-7”

X-direction...........................................................................................5-242 Figure 5.4.5-5 PS/B ACS SASSI Results – ARS Comparison at Elev. 3’-7”

Y-direction...........................................................................................5-243 Figure 5.4.5-6 PS/B ACS SASSI Results – ARS Comparison at Elev. 3’-7”

Z-direction...........................................................................................5-244 Figure 5.4.5-7 PS/B ACS SASSI Results – ARS Comparison at Elev. 39’-6”

X-direction...........................................................................................5-245 Figure 5.4.5-8 PS/B ACS SASSI Results – ARS Comparison at Elev. 39’-6”

Y-direction...........................................................................................5-246 Figure 5.4.5-9 PS/B ACS SASSI Results – ARS Comparison at Elev. 39’-6”

Z-direction...........................................................................................5-247 Figure 5.4.6-1 Section View of Dynamic PS/B Model Looking East ..........................5-248 Figure 5.4.6-2 Section View of Dynamic PS/B Model Looking South ........................5-248


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LIST OF TABLES

Table Title Page No.

Table 4.1-1 Target Control Points for US-APWR CSDRS .........................................4-3 Table 4.2.1-1 Final Profile Categories.........................................................................4-10 Table 4.2-1 Initial Profile Categories........................................................................4-12 Table 4.3.1.1-1 Summary of Element Types..................................................................4-17 Table 4.3.1.1-2 Input Material Properties.......................................................................4-18 Table 4.3.1.1-3 SC Module Stiffness Values .................................................................4-19 Table 4.3.1.2-1 Wave Passage Frequencies for Basemat FE Mesh .............................4-27 Table 4.4.1-1 Summary of Element Types..................................................................4-42 Table 4.4.1-2 Wave Passage Frequencies for Basemat FE Mesh .............................4-44 Table 4.4.1-3 Assigned Stiffness and Damping Properties.........................................4-45 Table 4.5.3-1 Material Properties of Models used for Seismic Response

Analyses ...............................................................................................4-53 Table 5.1-1 Comparison of 5% Damping ARS of Artificial Time History and

CSDRS ...................................................................................................5-9 Table 5.1-2 Spectra Matching Requirements for Converted Time Histories............5-10 Table 5.1-3 Duration of Motion of US-APWR Artificial Time History

Components Computed from Arias Intensity Values ............................5-11 Table 5.2-1 Deleted..................................................................................................5-16 Table 5.2-2 Magnitudes, Distances, and Median Peak Accelerations .....................5-24 Table 5.2-3 Deleted .................................................................................................5-30 Table 5.2-4 Strain Compatible Properties for Profile 270, 200 ft (Sheet 1 of 3).......5-31 Table 5.2-5 Strain Compatible Properties for Profile 270, 500 ft (Sheet 1 of 6).......5-34 Table 5.2-6 Deleted..................................................................................................5-40 Table 5.2-7 Deleted..................................................................................................5-41 Table 5.2-8 Strain Compatible Properties for Profile 560, 500 ft (Sheet 1 of 6).......5-42 Table 5.2-9 Strain Compatible Properties for Profile 900, 100 ft (Sheet 1 of 2).......5-48 Table 5.2-10 Strain Compatible Properties for Profile 900, 200 ft (Sheet 1 of 2).......5-50 Table 5.2-11 Strain Compatible Properties for Profile 2032, 100 ft (Sheet 1 of 2).....5-52 Table 5.2-12 Shear Column Frequencies of Top Soil ................................................5-54 Table 5.3.2.1-1 Lumped Masses of RV Model...............................................................5-86 Table 5.3.2.1-2 Element Properties of RV Stick Model..................................................5-87 Table 5.3.2.1-3 Lumped Masses of SG Model...............................................................5-88 Table 5.3.2.1-4 Element Properties of Steam Generator Stick Model ...........................5-89 Table 5.3.2.1-5 Lumped Mass of Reactor Coolant Pump (RCP) Model ........................5-90 Table 5.3.2.1-6 Element Properties of Reactor Coolant Pump (RCP) Stick Model .......5-91 Table 5.3.2.1-7 Spring Stiffness Values of RV, SG, and RCP.......................................5-92 Table 5.3.2.1-8 Material Properties of RCL Stick Models ..............................................5-92 Table 5.3.3.1.1-1 R/B Floor Mass Comparison...............................................................5-101 Table 5.3.3.1.1-2 R/B Roof Lateral Displacement Comparison ......................................5-105 Table 5.3.5-1 R/B – Mass per Elevation ...................................................................5-212 Table 5.3.5-2 PCCV – Mass per Elevation ...............................................................5-212 Table 5.3.5-3 CIS – Mass per Component................................................................5-213 Table 5.3.5-4 Dominant Frequencies of the R/B Complex Dynamic FE Model ........5-213 Table 5.4.3-1 PS/B Floor Mass Comparison.............................................................5-219 Table 5.4.3-2 PS/B Roof Lateral Displacement Comparison ....................................5-224 Table 5.4.6-1 Dominant Frequencies of the PS/B Dynamic FE Model .....................5-249


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ABSTRACT

The purpose of this Technical Report is to present the seismic design bases of the US-APWR standard plant.

This Report describes:

Establishment of Input Ground Motion Acceleration Time Histories

Development of Generic Layered Soil Profiles

Enhancement and Validation of the ACS SASSI Model of Power Source Building (PS/B)

Development of ACS SASSI Model of Reactor Building (R/B) Complex

Consideration of Concrete Cracking in Dynamic Modeling


Mitsubishi Heavy Industries, LTD. 1-1

1 INTRODUCTION

The design of US-APWR standard plant structures is based on the analyses of the seismic responses of dynamic models, considering the effects of soil-structure interaction (SSI). Consistent with NRC Standard Review Plan (SRP) 3.7.1 (Reference 1), the seismic response analyses incorporates each of the following issues:

development of suitable acceleration time histories, compatible to the US-APWR certified seismic design response spectra (CSDRS) used as input design ground motion in the analyses;

consideration of generic soil profiles that can provide an adequate representation of conditions at candidate sites within the United States;

adequate consideration of the frequency dependence of the SSI;

ability of the models to adequately represent the dynamic properties of the structures, and to address the effects of concrete cracking on the seismic response.

ability of the model to develop design basis ISRS for seismic qualification of the equipment.

This Report documents the development of time histories of the three ground motion components compatible to US-APWR CSDRS. The time histories are synthesized using seed ground motion recordings that are in full compliance with the criteria of Standard Review Plan SRP 3.7.1 (Reference 1), Subsection 3.7.1.II.1B. In addition, the seismic design is to be based on a set of SSI analyses performed using the computer program ACS SASSI (Reference 2) that captures the frequency dependence of the SSI system and addresses the effect of the soil layering and elevation of the ground water table. These SSI analyses consider generic profiles representing layered subgrade properties. The development of the generic layered site profiles consistent with the CSDRS are documented in this Technical Report.

A finite element (FE) structural model for SSI analyses of the bounding power source building (PS/B) configuration is developed and converted into ACS SASSI format. This Report presents the PS/B Dynamic FE structural model and the results of the validation analyses performed to demonstrate its ability to accurately represent the dynamic properties of the PS/B at all important modes of vibration.

An FE model is developed representing the dynamic properties of the Reactor Building (R/B) complex consisting of the pre-stressed concrete containment vessel (PCCV), containment internal structures (CIS), the R/B, and the common foundation basemat. To account for the effects of dynamic coupling of the CIS with the equipment and the piping, the dynamic FE model of the R/B complex also includes a model of the reactor coolant loop (RCL) representing the stiffness and mass inertia properties of the major equipment and piping located in the PCCV. Section 4.3 in this Report presents the methodology used for development of the Dynamic FE model for ACS SASSI analyses of the R/B complex. The results of the validation analyses of the model are described in Section 5.3.

Two different levels of stiffness and damping properties are assigned to the dynamic FE models of the R/B complex and the PS/B in order to capture the possible variations of the material properties of the structural members due to cracking. The first level represents the full



(uncracked concrete) stiffness of the structures corresponding to low stress levels, and the second level represents the reduced stiffness (cracked concrete) of the structures corresponding to high stress levels. The operating-basis earthquake (OBE) damping values are assigned to the models with full (uncracked concrete) stiffness in order to model the lower level of dissipation of energy in the structure when subjected to lower stresses. The safe-shutdown earthquake (SSE) damping values are assigned to the models with reduced (cracked) concrete properties in order to model the higher dissipation of energy in the structure when subjected to high stresses. For each soil case considered, two sets of SSI analyses are performed to obtain the seismic response of the R/B complex and the PS/B corresponding to each of the two bounding levels of stiffness and damping. The responses obtained from the two SSI analyses for the two different stress levels are enveloped in order to address the possible range of effects of concrete cracking on the seismic response of the buildings. This Report further describes how the effects of the concrete cracking are addressed in the dynamic modeling of the R/B complex and the PS/B.

The CSDRS compatible ground motion time histories, the generic layered profiles, and the structural dynamic models described in this report define the input for the SSI analyses of the US-APWR standard plant Seismic Category I Structures. Refer to Technical Report MUAP-10006, “Soil-Structure Interaction Analyses and Results for the US-APWR Standard Plant” (Reference 23), for the results of these SSI analyses. The validations of the dynamic FE models of the R/B complex and the PS/B are performed following the methodology described in Section 4.3.2, Section 4.4.3 and Section 5.3.3 through 5.3.5 of this Technical Report. The validation of the PS/B Dynamic FE structural model is performed following the methodology and results described in Section 5.4.5 of this Technical Report.



2 PURPOSE

The purpose of this Technical Report is to outline the technical approach related to the development of the design bases for the seismic response analyses of the US-APWR R/B complex and PS/Bs. This Report outlines the general methodology used for the development of the structural models of the R/B complex and PS/Bs and the soil profiles used for standard design.

A detailed discussion regarding the following input parameters and modeling issues is also provided to resolve Request for Additional Information (RAI) questions and comments by the NRC including:

1. Establishment of CSDRS compatible acceleration time histories

2. Development of generic layered soil profiles and strain compatible properties

3. Development and validation of the ACS SASSI Dynamic FE model of the R/B complex

4. Development and validation of the ACS SASSI Dynamic FE Model of the PS/B

5. Consideration of Concrete Cracking



3 OBJECTIVES

3.1 CSDRS Compatible Ground Motion Time Histories

In compliance with the requirements of SRP 3.7.1 (Reference 1), Subsection 3.7.1.II.1B, Option 1 Approach 2, the objective is to generate a set of three components of an artificial time history earthquake by adjusting real ground motion recordings from an actual earthquake as the seed. This results in a set of three statistically independent time history components that are compatible with the two horizontal directions and the vertical direction of the US-APWR CSDRS. These adjusted acceleration time histories are used as input ground motion for the SSI analyses described within this Technical Report.

3.2 Generic Layered Soil Profiles and Strain Compatible Properties

The objective of the Generic Layered Soil Profiles and Strain Compatible Properties is to provide a set of input soil properties for the SSI analyses that are compatible with the strains generated by the seismic ground motions whose spectra at ground surface are enveloped by US-APWR CSDRS. A set of generic layered soil profiles are developed to be used as input for the site independent SSI analyses of the US-APWR standard plant. These subgrade properties are developed from a database of both Western United States (WUS) as well as Central and Eastern United States (CEUS) measured velocities. Since the geology is continuous between WUS and CEUS, soil and rock dynamic material properties are similar between the two regions. The representative generic profiles are developed by averaging suites of profiles reflecting similar surficial geology in the two regions. The generic layered profiles, for which strain-compatible properties, shear- and compression-wave velocities and corresponding hysteretic damping values are developed, provide dynamic subgrade properties that capture a wide range of SSI responses expected at candidate sites across the CEUS, including the effects of the frequency dependence of the SSI, the layering of the subgrade, and the elevation of the water table.

3.3 Dynamic Finite Element Model of R/B Complex

The objective of the Dynamic Finite Element Model of R/B Complex is to describe the development and validation of the US-APWR R/B complex 3-D Dynamic FE Model for SSI analyses using ACS SASSI. The US-APWR Reactor Building Complex consists of the R/B and Fuel Handling Area (FH/A), PCCV, and CIS supported on a common reinforced concrete basemat.

The dynamic FE Model of the R/B complex is developed using ANSYS (Reference 11) before being translated to ACS SASSI (Reference 2). The purpose of the ACS SASSI model is to adequately represent the dynamic (stiffness and mass) properties of the R/B Complex structures, and to capture or address the following effects:

Coupling of the structure with the major nuclear steam supply system (NSSS) equipment and piping.

Flexibility of the common basemat foundation.

Variation of stiffness due to concrete cracking.

Local out-of-plane modes of vibration with frequencies up to 50 Hz.



Variations in damping values.

The resulting dynamic FE model is used for the ACS SASSI analyses of the R/B complex structures documented in Technical Report MUAP-10006 (Reference 23) to provide input design parameters that appropriately address the effects of the frequency dependence of the SSI impedance, layering of the subgrade, elevation of the water table and scattering of input ground motion. ACS SASSI uses complex damping formulation to account for the dissipation of the energy due to material damping.

The ACS SASSI dynamic FE model is a 3-D FE model of the R/B-FH/A, PCCV, and CIS structures modeled together on a common basemat. Despite sharing a common basemat, these structures are otherwise independent of each other. With the exception of the RCL, all masses inside the R/B and the PCCV are included in the model by assigning nodal masses or adjusting the density of the supporting slabs/walls areas under the footprint of equipment. A lumped mass stick model of the RCL that represent the dynamic properties of Reactor Vessel (RV), Steam Generators (SG), Reactor Coolant Pumps (RCP) and main coolant piping (MCP) is coupled with the 3-D FE model of CIS. The model is initially developed using the computer program ANSYS before being translated into ACS SASSI format using the built-in file converter in ACS SASSI. The ACS SASSI dynamic FE model initially developed in ANSYS is less detailed than the reference detailed FE model developed in ANSYS for the detailed design. This dynamic FE model captures the essential dynamic properties of the static FE model while reducing the number of dynamic degrees of freedom to facilitate the computation time required for the ACS SASSI analysis.

The ACS SASSI dynamic FE model is validated as follows: First, fixed based static and dynamic analyses are performed on a detailed static FE model of the R/B complex structures. A set of fixed-base static and modal analyses are then performed on the ANSYS dynamic FE model and the results compared to those obtained from the detailed static FE model analyses. This process validates the dynamic properties and accuracy of the ANSYS dynamic FE model before being translated into ACS SASSI. Once translated to ACS SASSI, validation of SSI analyses are performed with the newly translated R/B complex structures dynamic model resting on the surface of a uniform half-space with very high stiffness (hard rock) to simulate fixed base conditions. Transfer functions (TFs) and acceleration response spectra (ARS) are obtained from the ACS SASSI validation analyses at selected nodes and are then compared to the results obtained from the analyses on the detailed static model.

3.4 ACS SASSI Dynamic Finite Element Model of the PS/Bs

The objective of the ACS SASSI Dynamic FE model of the PS/B is to adequately represent the dynamic properties of the building and to capture SSI effects related to the flexibility of the basemat foundation. This dynamic model is used for the ACS SASSI analyses of the PS/B documented in Technical Report MUAP-10006 (Reference 23) to provide input design parameters that appropriately address the effects of the frequency dependence of the SSI impedance, layering of the subgrade, elevation of the water table and scattering of input ground motion. The ACS SASSI analyses use complex damping formulation to account for the dissipation of energy due to material damping.

The ACS SASSI Dynamic FE model is a (3-D) FE model representing the configuration of the west PS/B. It is initially developed using the computer program ANSYS (Reference 11) before being translated into ACS SASSI format using the built-in file converter in ACS SASSI (Reference 2).



The Dynamic FE model is validated as follows: First, static and dynamic analyses are performed on a detailed static FE model of the PS/B to obtain a validation basis. The detailed static FE model is a 3-D model of the structure and is used for structural stress analysis and basic structural design of the building. It is developed using ANSYS but with a finer mesh size (1’ to 4’) and includes more structural details than the Dynamic FE model of PS/B. A set of fixed-base static and modal analyses are then performed on the Dynamic FE model, and the results compared to those obtained from the detailed model analyses to validate the dynamic properties and accuracy of the Dynamic model before being translated into ACS SASSI. Once translated to ACS SASSI, validation SSI analyses are performed with the newly translated PS/B Dynamic model resting on the surface of a uniform half-space with very high stiffness to simulate fixed base conditions. TFs and ARS are obtained from the ACS SASSI validation analyses at selected nodes and are then compared to the results obtained from the ANSYS analyses on the Dynamic model.

3.5 Consideration of Concrete Cracking in Dynamic Analyses

The cracking of concrete affects the dynamic characteristics of the US-APWR structures that are made of reinforced concrete, pre-stressed concrete and steel-concrete (SC) modules, altering their responses when subjected to seismic excitation. An important objective of the dynamic structural models used for SSI analyses of the R/B Complex and PS/B is to appropriately address the variations of the dynamic properties of concrete structures reflecting the different extents and patterns of concrete cracking that can occur under different loading conditions.

Two levels of stiffness and damping properties are developed and assigned to the structural models used for seismic response analyses in order to capture the variations of structural stiffness and damping due to concrete cracking: (1) full (uncracked concrete) stiffness corresponding to low stress levels; and (2) reduced (cracked concrete) stiffness corresponding to high stress levels. In accordance with the associated stress level and recommendations of RG 1.61 (Reference 30) and the industry standards, the lower OBE values for structural damping are assigned in conjunction with the full (uncracked concrete) stiffness properties, and the higher SSE damping values are assigned in conjunction with the reduced (cracked concrete) stiffness properties. In order to ensure that the standard seismic designs of the US-APWR R/B complex and PS/B properly address the effects of the concrete cracking, the envelope of the results obtained from the seismic response analyses of dynamic FE models with full and reduced stiffness are used to develop the seismic design.

Section 4.5 describes the structural modeling approach used to include the variation of stiffness and damping properties due to concrete cracking. Provisions of the current NRC and industry standards are reviewed for consideration of the effects of concrete cracking when modeling the effective stiffness of reinforced concrete members for dynamic analyses. The reduction of stiffness of the reinforced concrete members that crack under the most critical load combination are adjusted based on the provisions and recommendations of the industry standards. Appendices A and B of this Report provide the technical basis for the selection of the stiffness reduction levels for the PCCV and CIS.



4 APPROACH

4.1 Time Histories

4.1.1 CSDRS Compatible Ground Motion Time Histories

One set of three statistically independent components of an artificial time history seismic motion is generated for use as the input seismic motion in the earthquake response analysis of the US-APWR standard plant. The three time history components were generated to represent the ground motion for three mutually orthogonal earthquake component directions. Following the requirements of SRP 3.7.1 (Reference 1), Subsection 3.7.1.II.1B, Option 1 Approach 2, two components (“H1” in the north-south [NS] direction, and “H2” in the east-west [EW] direction) compatible to the horizontal direction target response spectra and one component (“V” in the vertical direction) compatible to the vertical direction target response spectra are generated.

The three orthogonal directions may be alternately referred to within this Technical Report using the following different designations:

H1 (270) = Direction 1 = NS = Plant north-south = Global X-axis (North = +X)

H2 (360) = Direction 2 = EW = Plant east-west = Global Y-axis (West = +Y)

V (UP) = Direction 3 = Vertical = UD = Up-Down = Global Z-axis (Up = +Z)

Approach 2 is implemented with the objective of generating artificial acceleration time histories such that, when converted to response spectra, achieve approximately mean-based fits to the target CSDRS presented in Figures 4.1.1-1 and 4.1.11-2 below. The control points of the CSDRS are shown in Table 4.1-1 for damping of 0.5%, 2%, 5%, 7% and 10%. The control points of the CSDRS are based on a modified RG 1.60 (Reference 15).

The peak ground acceleration (PGA) used for the purpose of the site-independent design of the seismic category I SSCs of the US-APWR standard plant is 0.3 g ground acceleration for the two horizontal directions and the vertical direction.

The CSDRS are derived from RG 1.60 (Reference 15) spectra by scaling the spectra contained in RG 1.60 from 1.0 g to 0.3 g zero period acceleration (ZPA) values, and by modifying the RG 1.60 control points to broaden the spectra in the higher frequency range. The RG 1.60 spectral values are based on deterministic values for western United States earthquakes. However, recent seismic research including recently published attenuation relations indicates that earthquakes in the Central and Eastern United States (CEUS) have more energy content in the higher frequency range than earthquakes in the Western United States (WUS). Thus, the RG 1.60 (Reference 15) spectra control points have been modified by shifting the control points at 9 Hz and 33 Hz to 12 Hz and 50 Hz, respectively, for both the horizontal and the vertical spectra. Therefore, for the US-APWR CSDRS, the horizontal spectra control points are at 0.25, 2.5, 12, and 50 Hz and the vertical response spectra control points are at 0.25, 3.5, 12, and 50 Hz.

Consistent with RG 1.60 (Reference 15), the CSDRS representing the vertical accelerations is obtained by scaling the horizontal ARS by a factor of 2/3 for frequencies less than 0.25 Hz. The scaling factor that varies from 2/3 to 1.0 is applied for the frequency range between 0.25 and 3.5 Hz. The horizontal and vertical acceleration spectra are kept identical above



frequency 3.5 Hz and, consequently, the vertical PGA is taken as the same as the horizontal PGA.

The modified RG 1.60 response spectra used as the target spectra is extended here to 0.1 Hz. The extension maintains the constant displacement below 0.25 Hz, as shown on the tripartite curves of RG 1.60. The average ratio of the ARS calculated from the artificial time histories to the corresponding target CSDRS is kept only slightly greater than one. The spectral acceleration ratio is calculated at each of the 100 frequency points per decade.

The Nahanni, Canada earthquake recorded at Site 3 on December 23, 1985 is used for the seed motions to develop the time histories with ARS matching the CSDRS for the US-APWR. This earthquake has a magnitude of M6.76. The depth of the earthquake is listed at 8 km and the epicentral distance to Site 3 at 22.36 km. The recording instrument is located at ground level. The records were obtained from “The Pacific Earthquake Engineering Research (PEER) Center, University of California at Berkeley” strong motion database (Reference 21).

The components of the recorded time history earthquake were spectrally matched to the target response spectra at the damping of 5%. In order to achieve this goal, the Fourier amplitudes of the seed acceleration time histories were modified to generate three new acceleration time histories. The final duration of these time histories is 20 seconds with a time step of 0.005 seconds. This Fourier amplitude modification process iterates until the response spectra of the new time histories envelop the target response spectra. These acceleration time histories were base line corrected to ensure that the displacements are zero at the end of the input.



Table 4.1-1 Target Control Points for US-APWR CSDRS

Horizontal Control Points Vertical Control Points

Frequency (Hz) Acceleration (g) Frequency (Hz) Acceleration (g)

0.5% Damping 0.5% Damping

A (50) 0.3 A (50) 0.3

B (12) 1.49 B (12) 1.49

C (2.5) 1.79 C (3.5) 1.70

D (0.25) 0.22 D (0.25) 0.15

E (0.1) 0.035 E (0.1) 0.024

2% Damping 2% Damping

A (50) 0.3 A (50) 0.3

B (12) 1.06 B (12) 1.06

C (2.5) 1.28 C (3.5) 1.22

D (0.25) 0.17 D (0.25) 0.12

E (0.1) 0.028 E (0.1) 0.018


A (50) 0.3 A (50) 0.3

B (12) 0.78 B (12) 0.78

C (2.5) 0.94 C (3.5) 0.89

D (0.25) 0.14 D (0.25) 0.094

E (0.1) 0.0226 E (0.1) 0.015


A (50) 0.3 A (50) 0.3

B (12) 0.68 B (12) 0.68

C (2.5) 0.82 C (3.5) 0.78

D (0.25) 0.13 D (0.25) 0.086

E (0.1) 0.021 E (0.1) 0.014


A (50) 0.3 A (50) 0.3

B (12) 0.57 B (12) 0.57

C (2.5) 0.68 C (3.5) 0.65

D (0.25) 0.12 D (0.25) 0.078

E (0.1) 0.019 E (0.1) 0.012 Notes: 1. 0.3 g PGA 2. Based on RG 1.60, Revision 1 amplification factors 3. For Control Point D & E, acceleration is computed as follows:

Acceleration = (2D / 386.4 in/sec2)(FA)(0.3) = 2(frequency) [rad/sec] D = Displacement [in] FA = Amplification Factor from Regulatory Guide 1.60



1.79

1.49

1.28

0.94

0.68

0.57

0.300.035

0.22

0.0280.17

1.06

0.0230.14

0.78

0.0210.13

0.82

0.68

0.30

0.019 0.120.0

0.5

1.0

1.5

2.0

0.1 1 10 100

Frequency (Hz)

Acc

eler

atio

n (

G)

0.5%

10%

7%

5%

2%

Note: spectra for damping 0.5 2, 5, 7, 10%

Horizontal

Figure 4.1.1-1 US-APWR Horizontal CSDRS



1.70

1.49

1.22

0.89

0.65

0.57

0.30

0.150.024

1.06

0.120.018

0.78

0.0940.015

0.68

0.78

0.0860.0140.080.012

0.30

0.0

0.5

1.0

1.5

2.0

0.1 1 10 100

Frequency (Hz)

Acc

eler

atio

n (

G)

0.5%

10%

7%

5%

2%

Note: spectra for damping 0.5 2, 5, 7, 10% Vertical

Figure 4.1.1-2 US-APWR Vertical CSDRS



The computation and SRP 3.7.1 post-processing verification scheme is described below:

1. Select a seed ground motion time series.

2. Run a computer code to calculate and modify the Fourier amplitude of each seed ground motion.

3. Calculate the response spectra of the modified motions and compare them to the target spectra.

4. Modify the Fourier amplitude by the ratio of the response spectra.

5. Repeat steps 3 and 4 as needed to optimize the spectral match of the time series to the target.

6. Baseline correct the final time histories.

7. Perform SRP 3.7.1 verifications

a. Plot time series b. Compute and plot response spectra c. Compute the Arias intensity and duration d. Compute components correlation

8. Review record properties from SRP 3.7.1 post-processing verifications. If the record matches all the criteria, it is considered to be final. If the record does not match one of the criteria, it is discarded.



4.1.2 Verification of Response Spectra from Time Histories

The 5% damped acceleration response spectra of the three modified and base line corrected components of the Nahanni earthquake were calculated at 301 frequencies as recommended in Reference 1, using program SPECTRUM (Reference 31).

The requirements for artificial time histories and enveloping the target spectra are described below (Reference 1):

a. The time history shall have a sufficiently small time increment and sufficiently long duration.

For a 20 second time history the time step should be at least 0.01 second (Nyquist frequency of at least 50 HZ). The time step is 0.005 second with a Nyquist frequency of 100 Hz.

b. Spectral accelerations shall be computed at a minimum of 100 points per frequency decade, uniformly spaced over the log frequency scale from 0.1 Hz to 50 Hz or the Nyquist frequency. The comparison of the response spectrum obtained from the artificial ground motion time history with the target response spectrum shall be made at each frequency computed in the frequency range of interest.

The 5% damped ARS of the times histories were calculated at 301 frequencies between 0.1 Hz and 100 Hz uniformly spaced over the log frequency scale. The target spectra were also calculated at the same frequencies.

c. The computed response spectrum of the accelerogram shall not fall more than 10% below the target response spectrum at any one frequency. To prevent response spectra in large frequency windows from falling below the target response spectrum, the response spectra within a frequency window of no larger than 10% centered on the frequency shall not be allowed to fall below the target response spectrum. This corresponds to response spectra at no more than 9 adjacent frequency points defined in (b) above from falling below that target response spectrum.

These requirements are met as shown in Figures 5.1-4 to 5.1-6.

d. In lieu of the power spectrum density requirement, the computed response spectrum of the artificial ground motion time history shall not exceed the target response spectrum at any frequency by more than 30% in the frequency range of interest. If the response spectrum for the accelerogram exceeds the target response spectrum by more than 30% at any frequency range, the power spectrum density of the accelerogram needs to be computed and shown to not have significant gaps in energy at any frequency over this frequency range.

Figures 5.1-4 to 5.1-6 show that the response spectrum for the modified time histories does not exceed the target response spectrum by more than 30%. Table 5.1-1 shows the maximum, minimum, and average of the ratio of the time history spectrum and the target spectrum for each component. Table 5.1-2 provides a summary demonstrating how the computed spectra satisfy the requirements from SRP 3.7.1.

Thus, the base line corrected time histories meet all the requirements listed above.



4.1.3 Strong Motion Duration of Time Histories

The strong motion duration is defined in Reference 1 as the time required for the Arias Intensity to rise from 5% to 75%.

The Arias Intensity is proportional to the energy, which defined as:

E(t) = a2() d

Where a() is the acceleration time history. Program PSDTH (Reference 32) was used to calculate the energy distribution.

The cumulative energy E(t), as a percentage of the total energy, is plotted in Figure 5.1-7.

According to the definition of the strong motion duration, the strong motion duration tm for each of the modified Nahanni time histories is described below:

Component H1(270): tm = 7.795 seconds (from 2.845 to 10.641 seconds)

Component H2(360): tm = 8.286 seconds (from 2.729 to 11.015 seconds)

Component V(UP): tm = 7.165 seconds (from 3.026 to 10.191 seconds)

The strong motion duration for each component is calculated directly by the computer code PSDTH (Reference 32) using the energy distribution with time. These values can be also calculated from the plots in Figure 5.1-7. Table 5.1-3 also provides a summary of the resulting duration of motion data.

Arias Intensity plots in Figure 5.1-7 show that the distribution of energy with time for the modified time histories is very similar to the original Nahanni earthquake. Thus, the modified earthquake is a good representation of an actual earthquake.

4.2 Development of Soil Profiles and Strain Compatible Properties

A complete suite of soil profiles and depths to basement material (to be subsequently referred to as “baserock”) is considered. The soil profiles are selected from a database of initial small-strain site properties that cover the range of generic site conditions from deep soft soil to firm rock that may exist across the continental US. The initial profile development recognizes that for the softer conditions, the shallow materials would be either removed or improved for appropriate foundation conditions. From the exhaustive suite of candidate sites, a subset of profiles and depths to baserock is selected to serve as input for the site-specific SSI analyses of US-APWR standard plant buildings. The intent of the selected subset of profiles is to provide a wide range of SSI responses at typical candidate sites. The input for the SSI analyses are the strain compatible properties, shear- and compression-wave velocities and corresponding hysteretic damping values that are developed from site response analyses of this subset of profiles and baserock depths. The dynamic soil/rock properties used as input for site-independent SSI analyses are compatible to the strains generated by the seismic ground motions which spectra at ground surface are enveloped by US-APWR CSDRS.

The whole suite of baseline is based on averaging measured profiles with similar velocities at sites located in western North America (WNA), and the CEUS, with judgment.



Measurements of site profiles typically do not extend to the same depths for all profiles averaged within groups of similar surficial geology or velocities. The number of available profiles generally decreases rapidly with depth as noted in "Surface Geology Based Strong Motion Amplification Factors for the San Francisco Bay and Los Angeles Areas" (Reference 6). Therefore, judgment has to be used to extend the generic profiles at the deeper depths.

To make the suite of profiles regionally appropriate for CEUS sites, the baserock conditions are set to that of hard rock, approximately 9,300 ft/s (2.83 km/s, EPRI Technical Report TR-102293 Reference 7). This value is consistent with the hard rock site conditions defined in EPRI TR-1009684 (Reference 8) ground motion prediction equations (GMPEs) that are currently used to characterize the hard rock hazard in CEUS. The generic profiles are classified using a nominal shear-wave velocity SV (30m) representing the average shear-wave

velocity over the top 30 meters. This classification is consistent with current practice for building codes and is a convenient metric with which to distinguish the initial profiles, prior to soil removal or improvement. The initial suite of eight small strain baseline candidate profiles is illustrated in Figure 4.2-1 to depths of 500 feet and ranges in nominal shear wave velocity

SV (30m) from soft soil at 180 m/s to firm rock at 2,032 m/s.

To accommodate the possible range in profiles for CEUS, a suite of profile depths to rock conditions is developed ranging from 25 feet to 2,000 feet. The suite of nine profile depth bins is listed on Table 4.2-1 along with the SV (30m) values for each category. A layer of sedimentary type of rock with gradually increasing stiffness is inserted above the hard basement rock ( SV = 2.83 km/sec, Table 4.2-1) to accommodate the presence of sedimentary rocks (sandstones, shales, claystones) beneath the shallow softer soil profiles with nominal shear-wave velocity of 560m/sec below and nominal top soil thickness of 500 feet and less. The occurrence of sedimentary rock or weathered basement overlying hard basement rock is common across much of the CEUS. The soft rock layers are assumed to exhibit linear behavior under the moderate loading levels of the site response analyses (Section 5.2.1) with the shear- and compression-wave damping fixed at 0.5% (QS,P = 100). For site conditions consisting of shallow soils or soft rock directly overlying hard rock (e.g. VS ≥ 2.83 km/sec) site-specific analyses will be performed. Also, listed on Table 4.2-1 for reference, is the hard rock crustal model, the top layer of which defines the CEUS baserock conditions (EPRI TR-102293 (Reference 7) and TR-1009684 (Reference 8).

4.2.1 Selection of Profiles

A subset of profiles is selected from the wide database of generic profiles for the development of strain compatible properties that include soft and hard soil profiles (nominal shear-wave velocity of 270 m/s and 560 m/s respectively) and soft and firm rock profiles (nominal shear-wave velocity of 900 m/s and 2,032 m/s, respectively). The development of softer soil strain compatible profiles considers additional soil removal if necessary to maintain a minimum (-1σ) strain compatible shear-wave velocity of at least 800 ft/s near the plant grade surface. Two profiles of softer 270 m/s soil are considered with depths of 200 feet and 500 feet above rock foundations consisting of sedimentary or weather rock section overlying Precambrian basement material. The third soil profile that is considered includes 500 feet thick layer of stiff 560 m/s soil over 1000 feet deep strata of sedimentary or weather rock resting on the rock basement. Two soft rock profiles (900 m/s) are considered with depths of 100 feet and 200 feet. The firm rock profile with nominal shear-wave velocity of 2,032 m/s and depth of 100 feet is selected to represent a residual soil (saprolite) over weathered rock and underlain by hard rock. This profile is intended to reflect hard rock foundation depths after removal of the



soft surficial residual soils. The types of selected generic profiles are appropriate for both Eastern and Western US. The final soil profile categories are summarized in Table 4.2.1-1.

The development of generic profiles assumed a water table located at the plant surface elevation by setting the value of compression wave velocity at or above 5,000 ft/s which is the compressional wave velocity of water. The specifies a water table depth of one foot below the plant grade which, for the development of vertical motions, is equivalent to the surface. Due to the absence of fluids over the top one foot, the lower compression-wave velocity has a very minor impact on vertical motions for the softer profiles.

Table 4.2.1-1 Final Profile Categories

Category (initial SV [30m]) Depth to Rock* (ft)

200 270

500

560 500

100 900

200

2,032 100

* For soil and soft rock profiles 270m/sec and 560m/sec, underlying baserock conditions reflect soft rock with a shear-wave velocity of 1 km/sec. For firm rock profiles 900m/sec and 2,032m/sec, underlying baserock conditions reflect hard rock with a shear-wave velocity of 2.83 km/sec (Table 4.2-1).

4.2.2 Development of US-APWR CSDRS Strain Compatible Properties

Thirty realizations are generated for each base profile in order to characterize in a fully probabilistic manner the range and variation in strain compatible properties of the top soil. Thirty realizations provide a very stable estimate of the mean, the statistic of importance as the median spectrum defines the loading level for each soil and rock profile (Figure 5.2-3). For the standard deviation, thirty realizations are sufficient to estimate sigma within twenty percent at the ninety percent confidence level from standard statistical tables and sixty realizations marginally improves the stability to only fifteen percent. To substantially improve the stability to five percent requires over five hundred realizations. Since the interest in the standard deviation is only for the ± sigma strain dependent properties to develop a reasonable range between -1 sigma and +1 sigma properties for SSI analyses, a suite of thirty realizations is considered sufficient. For each realization of dynamic material properties, each base-case profile is randomized in velocity as well as nonlinear dynamic material properties represented by degradation curves defining the stiffness reduction and the damping as functions of strain.



Random vibration theory (RVT) equivalent-linear site response analyses are then performed (refer to EPRI TR-102293 (Reference 7) and NUREG/CR-6728 (Reference 9)) on each random profile for horizontal motions while linear analyses were used for vertical motions (refer to EPRI TR-102293 (Reference 7) and NCEER 97-0010 (Reference 10)). For the horizontal component site response analyses, modulus reduction and hysteretic damping curves from EPRI TR-102293 (Reference 7) are used. The curves are appropriate for generic soils comprised of gravels, sands, and low PI clays (refer to Reference 7) and are shown in Figure 4.2-2. These curves also provide realistic strain compatible properties for the generic rock materials when subjected to low intensity strains generated by ground motions that are consistent with the spectra at the ground surface that are enveloped by US-APWR CSDRS.

The US APWR CSDRS is adopted from the R.G. 1.60 spectral shape which reflects a median plus one-sigma analysis of several earthquakes and a range in site conditions. Because the R.G. 1.60 and the CSDRS were based on a plus one-sigma analysis of earthquakes ranging in magnitude from approximately 5.4 to 7.7, the overall shape is consistent with a median magnitude of approximately M 7.5. For consistency with the spectral shape of the CSDRS, control motions are used as input for the site response analyses that reflect a representative magnitude of M7.5 for CEUS hazard. A point-source model is used to develop control motions (refer to References 7 and 9). Source distances (loading levels) are adjusted such that the median 5% damped response spectrum developed for each profile and depth to baserock approaches, but does not exceed, the CSDRS. For site response analyses, the use of a realistic control motions, reflecting a magnitude consistent with the shape of the CSDRS, results in reasonable levels of cyclic shear strains for each soil/rock column and avoids the condition of overdriving the soil/rock columns if excited by a broad band CSDRS defined input motion. The broad band nature of the CSDRS can be taken to reflect the envelope of motions from a single earthquake and a range in site conditions. With this approach, shear strain levels and associated strain compatible properties reflect realistic loading conditions for CEUS sites and are appropriate for use as input in the site-independent SSI analyses. On the other hand, the use of a broad band CSDRS excitation would result in unrealistically high values for the strain compatible soil damping that will overestimate the dissipation of energy in the SSI system due to soil material damping. The resulting strain compatible properties are developed as median and ±1σ estimates from the analyses of the random profile realizations. It should be noted, because a single CSDRS reflects design motions representing a suite of profiles, its use to characterize input motions for SSI analyses with any single profile results in conservative motions within the structure over a wide frequency range (Figure 5.2-3).



Table 4.2-1 Initial Profile Categories

Categories SV (30m)

190

270

400

560

760

900

1,364

2,032

2830

Depth to Rock (ft) for each Category

25 ± 10

50 ± 20

100 ± 40

200 ± 80

500 ± 200

1,000 ± 400

2,000 ± 800

Hard rock crustal model (References 7 and 9)

Depth (km) Vs (km/s) Vp (km/s) p (cgs)

1 2.83 4.90 2.52

11 3.52 6.10 2.71

28 3.75 6.50 2.78

INFINITE 4.62 8.00 3.35



0

50

100

150

200

250

300

350

400

450

500

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Vs (ft/s)D

epth

(ft

)

190 m/sec

270 m/sec

400 m/sec

560 m/sec

760 m/sec

900 m/sec

1364 m/sec

2032 m/sec

2830 m/sec

Figure 4.2-1 Top 500 ft of the Candidate Shear-Wave Velocity Profiles and Associated )30( mVS Velocities



Figure 4.2-2 (TR-102293, Reference 7) Cohesionless Soil Modulus Reduction and Hysteretic Damping Curves



4.3 ACS SASSI Dynamic Finite Element Model of R/B Complex

An integrated Dynamic FE Model of the R/B Complex is developed and validated using ANSYS (Reference 11) and then translated into ACS SASSI (Reference 2) format in the following steps:

Step 1: Develop the R/B Complex Dynamic FE Model.

ANSYS preprocessor and ANSYS Parametric Design Language (APDL) are used to develop an integrated 3-D FE model that includes the R/B, PCCV, and CIS that is coupled with the lumped mass stick model (LMSM) representing the dynamic properties of the RCL. The numbering of the nodes is adjusted following the guidelines of the ACS SASSI manual in order to optimize the computational effort.

Step 2: Validate the R/B complex dynamic FE Model to ensure that the model adequately captures the dynamic behavior of the structures.

For validation purposes, the dynamic FE model is separated into three parts: R/B-FH/A (including the common basemat); PCCV; and CIS. Static and dynamic analyses using ANSYS solvers are performed on each of the three components of the dynamic FE model by establishing fixed boundary conditions at the base of each structure, respectively. An identical set of fixed base analyses are also performed on the detailed FE models of the R/B, PCCV, and CIS. The results obtained from the dynamic FE models and detailed FE models are compared to demonstrate the ability of the less refined dynamic FE model to adequately capture the dynamic behavior of the corresponding detailed FE models.

Step 3: Translate the Dynamic FE Model into ACS SASSI format and verify the accuracy of the translation.

The translator built into the ACS SASSI code serves as the platform for the translation of the dynamic FE model from ANSYS to ACS SASSI house module format. In order to validate the translation of the model, validation SSI analyses are performed on the ACS SASSI dynamic FE model resting on a very stiff elastic half space. The dynamic properties of the model revealed by the resulting amplification transfer functions (ATF) and 5% damping ARS at selected locations are compared to the fixed base dynamic properties and responses obtained from ANSYS modal and time history analyses to ensure the translation is competed correctly.

4.3.1 Development of the R/B Complex Dynamic FE Model

4.3.1.1 Finite Element Modeling

The R/B complex dynamic FE model consists of beam, shell, solid, and spring elements. The use of finite elements provides an accurate representation of the dynamic properties of the structures and the foundation that enables an accurate modeling of dynamic interaction with the flexible foundation and the surrounding soil. Shell elements are used to model the reinforced concrete shear walls and slabs. Three-dimensional (3-D) beam elements model the



reinforced concrete or steel columns and beams. Solid elements are used to model the basemat foundation and the massive structural members of the CIS. Spring and beam elements are used to model the supports and connection of the RCL lumped-mass-stick model with the CIS FE mesh. The ANSYS finite element types used in the model are compatible with the ACS SASSI built in converter.

The integrated R/B Complex dynamic FE model is presented in Figure 4.3.1.1-1. This model has a total of 18598 nodes, 22390 elements with an average mesh size of 9 ft. Table 4.3.1.1-1 provides the different element types that are used in the R/B complex dynamic FE model. Table 4.3.1.1-2 provides the input material properties.

The development of the model provides that the connection between two different FE types is such that an adequate transfer of forces and/or moments from one structural component to the other is enabled. The nodes of the ACS SASSI solid elements have only three translational degrees of freedom and can therefore not transfer the moments from shell or beam elements. In order to enable the transfer of bending moments from the walls modeled by shell elements to the basemat and CIS massive structural members modeled by solid elements, the shell elements are extended into the solid elements so that the moments can be transferred to at least 2 layers of nodes belonging to the solid elements as shown in Figure 4.3.1.1-5. Shell elements providing the connection have identical stiffness properties as the shells modeling the walls but are assigned a zero mass.

In addition, each node of the ACS SASSI shell elements has five degrees of freedom that enable beam elements to transfer forces and bending moments to shell elements but not torsional or drilling moments. Therefore, massless beam elements are generated on the surface of the shell or solid elements as shown in Figure 4.3.1.1-6 and Figure 4.3.1.1-7 in order to provide adequate transfer of moments from beams in all three rotational degrees of freedom. For beams or columns connecting to slabs or walls in the R/B model, the effect of adding drilling stiffness to the slab and wall shell elements (Allman in-plane rotational stiffness in ANSYS SHELL63 element) is evaluated and the impact on the results is found to be negligible.



Table 4.3.1.1-1 Summary of Element Types



Table 4.3.1.1-2 Input Material Properties

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

Mits

ubis

hi H

eavy

Indu

strie

s, L

TD

.

4-19

Tab

le 4

.3.1

.1-3

S

C M

od

ule

Sti

ffn

ess

Val

ues

(s

ee T

able

7-1

of

MU

AP

-110

18, R

efer

ence

34)



Figure 4.3.1.1-1 Integrated R/B Complex Dynamic FE Model



Figure 4.3.1.1-2 Overview of the R/B Detailed FE Model



Figure 4.3.1.1-3 Overview of the PCCV Detailed FE Model



Figure 4.3.1.1-4 Overview of the CIS Detailed FE Model

(includes the CIS and the RCL Models)



Figure 4.3.1.1-5 Connection of Shell to Solid Elements



Figure 4.3.1.1-6 Connection of Beam to Solid Elements

Figure 4.3.1.1-7 Connection of Beam to Shell Elements



4.3.1.2 Discretization Considerations: Mesh Size

The 3-D FE models have an adequate number of discrete mass degrees of freedom to capture the global and local translational, rocking, and torsional responses of the structures. The element size is selected such that the dynamic response of the structure and the SSI effects will be adequately captured. The mesh size also ensures that the discretized structures with full (uncracked concrete) stiffness properties is able to capture the local responses and responses of significant modes of vibration with frequencies equal to or below 70 Hz.

For wave passage in the structure, in order to transmit shear waves with frequencies up to 70 Hz, the maximum element size shall not be greater than one fifth of the wave length to be transmitted (Reference 11). The maximum structural element size is determined as follows:

Given: Concrete Strength fc’=4,000 psi, Poisson’s Ratio =0.17 and unit weight = 0.15 kcf

The modulus of Elasticity and Shear Modulus of concrete are:

ksf 221846)17.01(2

519120

)1(2

ksf 519120 3605400057'57

c

c

cc

EG

ksifE

The shear velocity of the concrete is:

sec/711915.0

2.32221846ft

gGVs c

c

Wave length of the wave with frequency of 70 Hz:

ft 10270

7119

max

f

VsTVs c

cc

The maximum size of an element determined by wave passage in the structure alone:

ft 205

ft 102

5 c

FEd

Therefore, the mesh size of the model is equal or less than 20 feet in order to be able to transfer shear waves with frequencies of up to 70 Hz.

The capability of the basemat FE model for wave passage from the subgrade to the structure is considered in conjunction with the stiffness properties of the subgrades used in the site-independent SSI analysis; in particular the strain-compatible shear wave velocity (Vs) of the soil layer interacting with the structure. Per the ACS SASSI manual (Reference 2), the elements at the soil-structure interface can transfer seismic shear waves with wavelengths equal to or more than five times the normal mesh size (dFE). Therefore, the maximum frequency for wave passage (fFE_max) from the subgrade to the structure is calculated as follows:



FEFE d

Vsf

5max_

For a selected nominal mesh size at the basemat interface with soil dFE = 9 ft, Table 4.3.1.2-1 provides the wave passage frequencies for the six different generic subgrade conditions.

Table 4.3.1.2-1 Wave Passage Frequencies for Basemat FE Mesh

Soil Vs(1) dFE fFE max Soil Case

(fps) (ft) (Hz)

270-500 1308 29.1

270-200 1232 27.4

560-500 1779 39.5

900-200 3197 71.0

900-100 3368 74.8

2032-100 7126

9

158.8

(1) Vs is taken at the base of the foundation at a depth of 40’

The table shows that for the SSI analyses of harder subgrade profiles, the dynamic FE model of R/B Complex is sufficiently refined to transmit waves with frequencies up to 50 Hz through the soil-foundation interface. The SSI analyses of softer soil profiles for which the wave passage frequencies of dynamic FE model are lower than 50 Hz provide responses that are enveloped in the high frequency range by the responses obtained from analyses of harder soil profiles. Therefore, the SSI analyses of all six generic soil profiles provide adequate envelope responses up to 50 Hz as required by ISG-01.

4.3.1.3 Modeling of Stiffness and Damping

The ACS SASSI house module introduces the stiffness and damping properties of the structure into SSI analysis in the form of a frequency-independent complex stiffness matrix (Refer to the ACS SASSI Theoretical Manual, Reference 2). Complex moduli are used to represent the stiffness and damping properties of the different structural materials which leads to stiffness and damping ratios which can be different for different materials assigned to the finite elements.

While maintaining geometry, mass, and FE meshing, two different levels of stiffness are assigned to the model in order to address the effect of concrete cracking on the seismic response. The responses obtained from the analyses of the models with two different stiffness properties are enveloped to develop the basis for standard seismic design of the US-APWR plant.



4.3.1.4 Modeling of Mass

The equivalent dynamic mass included in the R/B Complex dynamic FE model includes contributions from the structural mass in addition to that of other applicable equipment, dead loads, and live loads to which the structure is subjected.

As a general rule, the structural mass is assigned as density to the finite elements based on the material properties of the components of the structures. The density is then increased to account for equipment, live, snow and other applicable loads. A mass equivalent to 25% of floor design live load and 75% of roof design snow load, as applicable, is included in the model. Each load is applied over a particular area and the density of the elements in that area is increased such that the total increase in dynamic mass matches the applied load magnitude.

Equipment load also includes a 60 psf miscellaneous pipe load is applied on all walls and slabs on the R/B model, with the exception of a few locations where a pipe load of 100 psf is used instead.

The above process is not applicable for the nuclear steam supply system (NSSS) and major piping that constitutes the RCL. The RCL dynamic mass is included directly in the RCL lumped-mass-stick model provided in Reference 28.

In the case of the R/B, the equivalent dynamic mass is applied to the dynamic FE model in two steps. First, a mass density equal to the sum of the structural self-weight and pipe load is calculated and assigned to each of the shell elements modeling the R/B walls and slabs.

Various macros are then developed to apply the remaining loads as either additional mass densities on slab shell elements or concentrated lumped masses on wall and slab key points.

The density and thickness of the elements are further modified to account for stiffness reductions due to openings and cracking, but it is done is such a way as to not change the mass of the elements.

Liquid masses contained in the Spent Fuel Pit, Emergency Feed Water Pits, and Refueling Water Storage Pit are applied as impulsive mass to walls and slabs. The direction of the mass is perpendicular to the surface of the walls or slabs as shown in Figure 4.3.1.4-1. Nodes i and j are the nodes of walls to which the horizontal masses are attached, and node k is the node of slabs to which the vertical mass is attached. The attached directional masses are horizontal masses on nodes i and j, and vertical masses on node k.



Figure 4.3.1.4-1 Perpendicular Liquid Masses

4.3.1.5 Adjustment of Stiffness and Mass Properties

The coarse FE mesh of the Dynamic FE Model does not always permit an accurate modeling of the openings in the walls. The elastic modulus and thickness of shell elements are adjusted to accurately model the reduction of shear stiffness of the wall due to openings.

The density of shell elements is also adjusted to accurately represent the mass of the wall accounting for openings and the adjusted wall thickness.

A set of FE analyses is performed using ANSYS to obtain the stiffness reduction factors needed to adjust the material properties and account for the reduced stiffness of the shear wall openings. The correction factors are obtained by comparing the results from the static analyses of two detailed solid FE models shown in Figures 4.3.1.5-1A and B. Model A represents the actual geometry of the wall with openings, and Model B represents the wall without openings. Unit displacements are applied at the top of each model in both the in-plane and the out-of-plane directions, to generate the reactions at the bottom, which can then be used to calculate the in-plane and out-of-plane wall stiffness. The ratio between the reaction obtained from Model A and Model B is used to determine out-of-plane stiffness reduction factors (m) and the in-plane stiffness reduction factor (n) that are then used to determine the adjusted elastic modulus (Eo), thickness (to), and density (γo) of the wall as described in Section 4.3.1.7.



Figure 4.3.1.5-1A FE Models to Calculate Wall Stiffness Reduction Factors – Model A

Figure 4.3.1.5-1B FE Models to Calculate Wall Stiffness Reduction Factors – Model B



4.3.1.6 Stiffness of Composite Steel-Concrete Beams and Columns

In the FH/A, the crane supporting steel columns and girts are continuously anchored to the exterior concrete walls with headed steel studs. The steel roof beams and girders are also continuously anchored to the concrete roof slabs. The concrete/steel composite moment of inertia is based on the effective width of concrete and the degree of compositeness provided by the studs. The shear force that can be transferred between steel and concrete depends on the capacity of the studs, the yield strength of the steel section and the ultimate compressive strength of the effective concrete.

Based on AISC 360-05 Commentary (Reference 25), 75% of the composite transformed moment of inertia is used in calculating the effective moment of inertia of the composite section (Ieff):

Where: Qn = shear capacity of the studs

Cf = smaller of steel yield force or concrete ultimate compressive force

Ix = moment of inertia of the steel column or beam

Itr = composite transformed moment of inertia, calculated as follows:

Where: tc = slab or wall thickness

td = steel deck thickness, if any

d = depth of the steel member

ybar = centroidal distance of the transformed section, measured from the top of concrete

As = area of the steel member

beff = effective width of concrete, after transforming to steel = be/n

be = effective width of concrete, before transforming to steel

n = modular ratio = Es/Ec

Es = Young’s modulus for steel

Ieff min 0.75 Itr Ix

Qn

CfItr Ix

Itr Ix tc tdd

2

ybar

2As

beff tc3

12 ybar

tc

2

beff tc



Ec = Young’s modulus for concrete

In order to incorporate the composite stiffness of the steel beams and the reinforced concrete slabs the moments of inertia of the beams are increased. This modeling approach provides an accurate representation of the actual out-of-plane bending stiffness of the composite concrete-steel cross-sections which is validated through comparison of responses obtained from the detailed and dynamic models.

In the above, the effective width of concrete (before transformation to steel section) is based on AISC 360-05, Section I3 (excerpt shown below in italics):

I3. FLEXURAL MEMBERS 1. General 1a. Effective Width The effective width of the concrete slab is the sum of the effective widths for each side of the beam centerline, each of which shall not exceed: (1) one-eighth of the beam span, center-to-center of supports; (2) one-half the distance to the centerline of the adjacent beam; or (3) the distance to the edge of the slab.

Above requirements are applicable when the flange of the composite section is in compression. When the flange is in tension, smaller values of be could be used.

The centroidal distance of the transformed section, measured from the top of concrete is calculated as:

In the Dynamic FE Model, shell elements and beams are used to represent the individual members. The locations of the centerlines of the beam and shell elements are coincident so the effective bending stiffness of the section (EI) in the dynamic FE model is the sum of the individual moments of inertia:

Therefore, the moment of inertia of the beam element that results in bending stiffness of the section (EI) that is equivalent to the stiffness of the actual composite section is calculated as follows:

ybar

0.5 beff tc2 As tc td 0.5 d

beff tc As

EItc

3be

12Ec Ix Es

Is Ix Ieff

tc3

beff

12



Where: XS II is a factor used to adjust the bending moment of inertia of the beam

element in the FE model in order to simulate the actual composite stiffness of the reinforced concrete-steel beam cross sections.

4.3.1.7 Implementation of Stiffness Reduction in the Dynamic FE Model

The R/B Complex Dynamic FE Model only uses finite elements with isotropic material properties to represent the stiffness and mass properties of reinforced concrete members. The cracking of the concrete can affect different aspects of the stiffness of the members depending on the cracking pattern developed under different loading conditions. For example, a loads applied on a slab will generate cracks in the concrete that will affect mainly the out-of plane stiffness and will have a small effect on the in-plane stiffness of the slab. Modeling procedures are described for reduction of stiffness properties of beam and shell element in order to simulate different cracking effects.

The stiffness matrix of beam elements is defined by material properties (modulus of elasticity and Poisson’s ratio) and the beam section properties (moment of inertia, shear area, etc). The most convenient way to reduce the stiffness of those reinforced members modeled by beam elements is through assigning reduced section properties while maintaining the same modulus of elasticity and Poisson’s ratio. For example, if the flexural stiffness is required to be reduced, then the bending moment of inertia of the beam is reduced.

Four shell element input parameters including modulus of elasticity (E0), Poisson’s ratio (), shell thickness (t0) and unit weight (0) define the dynamic properties of the modeled reinforced concrete member. The following procedure is used to reduce stiffness of the reinforced concrete member shell elements by adjusting the shell modulus of elasticity to value (Ec), the shell thickness to value (tc) and the shell unit weight to value (c):

Case 1: If the concrete cracking reduces both in-plane and out-of-plane stiffness of the member by 1/n reduction factor, the adjusted properties of shell element are:

Case 2: If the concrete cracking reduces out-of-plane stiffness of the member by 1/n reduction factor and the in-plane stiffness remains the same, the adjusted properties of shell element are:

Ec1

nE0

tc t0

c 0

Ec n E0



Case 3: If the concrete cracking reduces in-plane stiffness of the member by 1/n reduction factor and the out-of-plane stiffness remains the same, the adjusted properties of shell element are:

It is noted that the changes in thickness and modulus of elasticity discussed above affect the in-plane axial stiffness of the shell element, as well as the shear stiffness values. Since the axial stiffness only has a minor impact on the response of slab and shear wall structures to seismic loadings, the changes of axial stiffness are acceptable.

4.3.1.8 Adjustment of Out-of-Plane Dynamic Properties of R/B Slabs

The development of the Dynamic FE Model requires simplifications of the model geometry in order to produce regular FE mesh and to minimize the size of the model to be suitable for time history frequency domain SSI analyses using ACS SASSI. In order to accurately capture the SSI effects, the R/B footprint dimensions represent the actual configuration of the basemat. The Dynamic R/B Model has the shell elements of the exterior walls placed at the perimeter of the building unlike the Detailed R/B Model where the shear walls are modeled at the centerline of the walls. These differences in modeling the building geometry affect the spans of some of the floor slabs in the Dynamic R/B Model and their local out-of-plane response. The stiffness and mass properties of these flexible slabs are adjusted to mimic the actual mass and dynamic properties of the slab.

The dynamic properties of the slabs at each major floor elevations are obtained by isolating each elevation. Figure 4.3.1.8-1 shows an FE model of the R/B floor slabs that are extracted from the Detailed FE Model. Boundary conditions are established as shown in Figure 4.3.1.8-2 at the upper and lower border of the model to restrain horizontal displacements of the walls and accurately mimic the bending stiffness at the wall/slab interfaces. The horizontal and vertical displacements of the wall are also restrained at slab elevation in order to eliminate the effects of the axial stiffness of the walls on the modal analyses results and to disregard the slab horizontal modes as well. Where the slab is supported by columns, the vertical displacement is constrained.

tc1

nt0

c n 0

Ecn

n2

E0

tc n t0

c1

n 0



Modal analysis using ANSYS is performed on the isolated elevations of Detailed FE Model and the dynamic FE model to obtain the dynamic properties. If the frequency of first dominant mode of the slab obtained from the detailed FE Model with full (uncracked concrete) stiffness properties is greater than 70 Hz, the slab is considered rigid. There is no need to adjust the stiffness of the shell elements modeling rigid slabs.

For the flexible slabs with frequencies below 70 Hz, the stiffness is adjusted as needed by tuning the modulus of elasticity of the slab shell elements in the Dynamic FE Model to match the frequency obtained from the Detailed FE model. The matching criterion is the difference in the first dominant frequency of vibration of the slab obtained from the modal analyses of the two FE models is being measured within 5%.



Figure 4.3.1.8-1 Extracted Detailed FE Model of Floor Slabs

Figure 4.3.1.8-2 Floor Slab Model Boundary Conditions



4.3.1.9 Adjustment of Dynamic Properties of SC Modules

Simplifications in the geometry of the otherwise complex structure are introduced in the dynamic CIS model in order to produce a coarser FE mesh and to minimize the size of the model in order to be suitable for SSI analyses using ACS SASSI. Stiffness and mass properties of elements modeling some of the SC walls of the CIS are adjusted in order to calibrate the dynamic response of the simplified dynamic FE model to match the actual response of the CIS as represented in the Detailed FE Model. The adjustments of the unit density and the elastic moduli of the shell elements are introduced to capture the actual distribution of mass and stiffness. The calibration of the model properties is performed based on the results of a 1-g static analysis, and then verified using the results of modal and time history analyses.

4.3.2 Validation of Dynamic FE Model

The development of the R/B Complex Dynamic FE Model is based on a number of adjustments in geometry and load configurations in order to minimize the size of the model and make it suitable for SSI analysis. The validation ensures that these modeling assumptions and simplifications do not affect the ability of the Dynamic FE Model to accurately represent the dynamic response of the R/B complex structures as mandated by SRP Sections 3.7.2.II.1 and 3.7.2.II.3 and by ISG-01, Section 3.1.

In order to reduce the computational effort and speed up the validation, the R/B Complex Dynamic FE Model is divided into three parts: R/B-FH/A (including common basemat), CIS coupled with RCL, and PCCV. A series of fixed-base analyses are performed on the three separated models using ANSYS and the results are compared to the ones obtained from corresponding analyses on the Detailed FE models of the R/B, CIS and PCCV structures. The stiffness and mass attributes that are assigned to the Dynamic FE Model and Detailed FE Models are consistent.

The validation of the R/B and PCCV dynamic FE models is performed on the models with full (uncracked concrete) stiffness. In order to ensure that the model with reduced (cracked concrete) stiffness properties can meet the requirement of ISG-01 Section 3.1 (Reference 26) to accurately capture responses with frequencies up to 50 Hz, the validation of the model with full stiffness properties compares dynamic responses up to frequencies of at least 70 Hz to ensure that validation results performed on models with full (uncracked concrete) stiffness are also applicable for the model with 50% reduce stiffness representing cracked concrete stiffness properties of the structure .

Due to the complexity of the CIS, different stiffness and damping values are assigned to different types of structural components for the two bounding stiffness and damping conditions. As described in Table 4.3.1.1-3, the reduction of stiffness applied to the CIS to account for cracking of the concrete of SC modules, reinforced concrete slabs and massive concrete portions is non-uniform. Therefore, unlike the other US-APWR standard plant Category I structures, two sets of validation analyses are performed for the CIS to ensure the adequacy of the CIS dynamic FE model with full (uncracked concrete) stiffness and reduced (cracked concrete) stiffness.

The FE analysis computer program ANSYS (Reference 11) serves as the platform for three different types of analyses performed to validate the dynamic properties of the R/B Complex



Dynamic FE Model:

1. 1g Static Analysis

2 Modal Analysis

3. Modal Superposition Time History Analysis

4.3.3 Conversion of the R/B Complex Dynamic FE Model from ANSYS to ACS SASSI Format

The translator built into the ACS SASSI code serves as the platform for the translation of the Dynamic FE Model from ANSYS to ACS SASSI house module format. Prior to the translation, the nodes of the model are renumbered according to the guidelines provided in the ACS SASSI manual (Reference 2) in order to minimize the bandwidth of the complex stiffness matrix and thus, reduce the computational effort.

The translation of the model from ANSYS into ACS SASSI format is validated by performing validation SSI analyses of the translated ACS SASSI Dynamic FE Model in which fixed-base conditions are simulated by placing the model on a very stiff elastic half-space. The results of the validation of the SSI analyses for Amplification Transfer Functions (ATFs) and 5% damping Acceleration Response Spectra (ARS) at selected locations are compared with the results of the ANSYS fixed base dynamic analyses. The peaks in the ATF’s indicate that the dominant natural frequencies of the structure are compared to the results of the fixed base modal analyses. The 5% damping ARS results are compared with the corresponding 5% damping ARS results obtained from the ANSYS mode superposition time history analyses using an integration time step of 0.005 sec.

At representative node locations, 5% damping acceleration response spectra (ARS) in the three orthogonal directions are calculated for each of the three directions of the input ground motion. The responses obtained for the three directions of the input ground motion are combined using the square root sum of the squares (SRSS) method as follows:

where:

ARS(m)(n) are the SASSI ARS results for the response in “n” direction due to earthquake in “m” direction,

ARSX, ARSY and ARSZ are the combined ARS of the structural response in NS (x), EW (y), and vertical (z) direction.



The enveloped ARS obtained from the results of the time history analyses of the Dynamic FE Model and the Detailed FE Model are compared to ensure that the Dynamic FE Model provides accurate dynamic responses of the structure.

The following guidelines are used to confirm the accuracy of the translation through comparison of results obtained from the validation of SSI and ANSYS analyses.

The frequency ATF’s peak indicating the first dominant natural frequency of the structure shall be within 5% of the first dominant frequency extracted from the ANSYS modal analyses of the dynamic FE model.

The peaks indicating the subsequent dominant frequencies of the structure shall be within 10% of the results calculated by the ANSYS fixed base modal analyses of the dynamic FE model.

The frequencies where the significant peaks occur in the ARS calculated from the ACS SASSI SSI validation analyses shall be within 10% of those obtained from the ANSYS time history analyses of the dynamic FE model.

The ARS results obtained for the ACS SASSI validation analyses shall be within 10% of those obtained from the time history analyses of the dynamic FE model.

The comparison of the results from the ANSYS fixed base analyses and ACS SASSI validation analyses can indicate larger deviation than those specified in the guidelines above.

The following are some sources of deviations that can be observed in the ARS results obtained from ANSYS modal superposition and ACS SASSI frequency domain time history analyses that are investigated on the case by case basis:

The very stiff subgrade for the SSI model is not infinitely stiff or “rigid" as it is postulated in the ANSYS fixed base analyses. The relative flexibility of the subgrade may produce some minor SSI effects differences in the higher frequency range. These SSI effects are manifested by some small deviations from 1.00 of the acceleration transfer functions calculated for the response at the foundation-stiff subgrade interface.

ACS SASSI uses a mixed mass matrix (average lumped and consistent

masses) to represent the mass of the structure. The mode superposition analyses in ANSYS are performed using either a lumped or consistent mass matrix.

The ANSYS modal superposition time history analysis uses analysis time

integration scheme to solve the decoupled dynamic response equations. ACS SASSI frequency domain solution is based on the convolution of the complex Fourier spectra of the input motion and the complex acceleration transfer functions computed for a limited number of selected frequencies, not at all Fourier points.



ANSYS uses constant value modal damping ratio to account for the dissipation of energy due to structural damping. ACS SASSI uses the complex damping approach in which the dissipation of energy due to structural damping is accounted for in the complex stiffness matrix of the system that is assembled from the complex stiffness matrices of the finite elements. The ACS SASSI analyses allow different structural damping to be used to account for the dissipation of energy in different structural components.

4.4 ACS SASSI Dynamic Finite Element Model of PS/B

Similar to the R/B complex model, the dynamic FE model of the PS/B is first developed using ANSYS (Reference 11) before being translated into the format of ACS SASSI (Reference 2) by using the built-in converter in ACS SASSI. The node numbering is adjusted following the guidelines of the ACS SASSI manual in order to optimize the computational effort.

Static and dynamic analyses using ANSYS solvers are then performed on the Dynamic FE Model by establishing fixed boundary condition at the base of the structure. An identical set of fixed base analyses are also performed on a Detailed FE model of the PS/B to obtain a validation basis. The PS/B Detailed FE Model is also developed using ANSYS (Reference 11) but with a finer average mesh size of one foot to four feet. Figure 4.4.1.1-1 shows the overview of the PS/B detailed FE model. Structural details such as openings in walls and slabs are included in the model, with the exception of a few minor details and openings. Results obtained from the two set of analyses are than compared to demonstrate the ability of the less refined Dynamic FE Model to adequately capture the dynamic behavior of the corresponding Detailed FE Model.

The translator built into the ACS SASSI code serves as the platform for the translation of the Dynamic FE Model from ANSYS to ACS SASSI house module format. In order to validate the translation of the model, validation of the SSI analyses are performed on the ACS SASSI Dynamic FE Model resting on a very stiff elastic half-space. The dynamic properties of the model revealed by the resulting ATFs and 5% damping Acceleration Response Spectra (ARS) at selected locations are compared to the fixed base dynamic properties and responses obtained from the Detailed and Dynamic ANSYS analyses to ensure the translation is completed correctly.

4.4.1 Development of the PS/B Dynamic FE Model

4.4.1.1 Finite Element Modeling

The PS/B Dynamic FE model is generated only for the West PS/B of the US-APWR standard plant. Since the East and West PS/B structures are nearly identical structurally, this model is used to represent both structures for seismic design. The two PS/B structures do have different roof configurations such as openings at the roof level for air inlets and supply and exhaust systems. Theses differences will have some impact on the vertical ISRS at the roof level. However, the openings in both PS/Bs are for penetration of duct only and the interaction between the roof and the duct will be minimal. Therefore, the difference in the ISRS at the roof level will not impact the design and safety of the HVAC systems or the supply and exhaust systems. In addition, an intermediate partial floor spans between column lines 4P and 5P, between column lines AP and CP in the west PS/B only. While this intermediate floor would affect the out-of-plane behavior of the shear walls to which it is connected, it is not anticipated



to have a significant impact on the in-plane behavior. The impact will be addressed in the stress analysis and detailed design of the PS/B structures.

The PS/B Dynamic FE model includes shell elements representing walls and slabs, beam elements representing beams and columns, and solid elements representing the basemat, with a mesh varying in size from four foot to eight foot. The total number of nodes in the model is 3347 nodes and the total number of elements is 3797 elements. To reduce the size of the Dynamic FE model and to permit a coarser mesh size, minor structural details and minor wall/slab openings are not included in the model. The use of finite elements provides an accurate representation of the dynamic properties of the structures and the foundation that enables an accurate modeling of dynamic interaction with the flexible foundation and the surrounding soil. The ANSYS finite element types used in the model are compatible with the ACS SASSI built in converter. Table 4.4.1-1 provides the different element types that are used in the PS/B Dynamic FE Model. Figure 4.4.1.1-2 shows overview of the PS/B Dynamic FE model.

The development of the PS/B dynamic model also allows that the connection between two different FE types is such that an adequate transfer of forces and/or moments from one structural component to the other is enabled. The nodes of the ACS SASSI solid elements have only three translational degrees of freedom and can therefore not transfer the moments from shell or beam elements. In order to enable the transfer of bending moments from the walls modeled by shell elements to the basemat modeled by solid elements, the shell elements are extended into the solid elements so that the moments can be transferred to 2 layers of nodes belonging to the solid elements as shown in Figure 4.3.1.1-5. Shell elements providing the connection have identical stiffness properties as the shells modeling the walls but are assigned a zero mass



Table 4.4.1-1 Summary of Element Types

Figure 4.4.1.1-1 Overview of the PS/B Detailed FE Model



Figure 4.4.1.1-2 Overview of the PS/B Dynamic FE Model

4.4.1.2 Discretization Considerations: Mesh Size

Using the methodology described in Section 4.3.1.2, the element size of the PS/B Dynamic FE Model is selected such that the structural response is not significantly affected by further refinement of the element size. The model mesh size also ensures that the discretized structure with full (uncracked concrete) stiffness properties is able to capture the local responses and responses of significant modes of vibration with frequencies equal to or less than 70 Hz. As mentioned before, this will ensure that the model with reduced stiffness is capable of capture the response of significant modes with frequencies up to 50 Hz.

For consideration of wave passage in the structure only, in order to transmit shear waves with frequencies up to 70 Hz, the maximum element size shall not be greater than one-fifth of the wave length to be transmitted (Reference 11). As determined in Section 4.3.1.2 for a concrete strength of 4,000 psi with a Poisson’s ratio of 0.17 and a unit density of 0.15 kcf, the maximum structural element determined by wave passage of shear wave with frequencies up to 70 Hz in the structure alone is 20 ft. The PS/B maximum element size of the PS/B Dynamic FE model is approximately eight feet and satisfies this requirement.



The capability of the PS/B basemat for wave passage from the subgrade to the structure is considered in conjunction with the stiffness properties of the subgrades used in the site-independent SSI analysis; in particular, the strain-compatible shear wave velocity (Vs) of the soil layer directly interacting with the structure, i.e. the top soil layer for analysis of surface mounted structure. Per Section 4.3.1.2, for a selected average mesh size of six feet at the basemat interface, the maximum wave passage frequencies at the PS/B soil-structure interface are as follows:

Table 4.4.1-2 Wave Passage Frequencies for Basemat FE Mesh

Soil Vs(1) dFE fFE max Soil Case

(fps) (ft) (Hz)

270-500 1308 43.6

270-200 1232 40.1

560-500 1779 59.3

900-200 3197 106.6

900-100 3368 112.3

2032-100 7126

6

237.5

(1) Vs is taken at the base of the foundation at a depth of 40’

Table 4.4.1-2 shows that for the SSI analyses with subgrade profiles of 560 series and harder, the PS/B dynamic FE model is refined enough to transmit waves with frequencies up to 50 Hz through the soil-foundation interface. For the profiles of 270-200 and 270-500, the element size of six feet will allow transmitting wave with frequencies up to 39 to 41 Hz, respectively. It is expected that, in high frequency range, the response of the soil-structure system will be controlled by the harder soils. Therefore, the SSI analyses of all six generic soil profiles provide adequate envelope responses up to 50 Hz as required by ISG-01.

4.4.1.3 Modeling of Stiffness and Damping

As mentioned in Section 4.3.1.3, two different levels of stiffness and damping are assigned to the PS/B model in order to address the effect of concrete cracking on the seismic response. They are presented in Table 4.4.1-3 and can be summarized as follows:

- A full stiffness level representing the case when the stresses in the PS/B reinforced concrete structure are of low intensity such that the concrete remains essentially

uncracked ( ksf 519120 3605400057'57 ksifE cc for f’c = 4,000 psi). An

OBE damping value of 4% is assigned to the PS/B model in this case to account for the lower energy dissipation levels in the structure.

- A reduced stiffness level representing the case when the reinforced concrete structure is subjected to higher stress levels resulting in cracking of concrete and a 50% reduction of its stiffness. An SSE damping value of 7% is assigned to the PS/B model in this case to account for the higher energy dissipation levels in the structure.



The implementation of stiffness reduction in the PS/B Dynamic FE Model follows methodology specified in Section 4.3.1.7 of this report.

Responses obtained from the two sets of analyses are enveloped to develop design SSE loads and In-Structure Response Spectra (ISRS) while the ones obtained from analyses on the model with reduced stiffness are enveloped to develop SSE loads. The results are provided for standard seismic design of the US-APWR plant.

Table 4.4.1-3 Assigned Stiffness and Damping Properties

Model Stiffness Level

Stiffness Damping

4%

7%

Full (Uncracked) Stiffness

Reduced (Cracked) Stiffness

100%

50%

4.4.1.4 Modeling of Mass

The equivalent dynamic mass included in the PS/B Dynamic FE Model includes contributions from the structural mass in addition to that of all applicable permanent equipment, 50 psf floor/wall miscellaneous dead loads representing minor equipment, piping, electrical raceways, etc., 25 percent of floor design live loads, and 25 percent of roof design live load and 75% snow loads, whichever is greater.

As a general rule, the structural mass is assigned as density to the finite elements based on the material properties of the components of the structures. The density is then increased to account for all other applicable loads. Each load is applied over a particular area and the density of the elements in that area is increased such that the total increase in dynamic mass matches the applied load magnitude. Grating floor loads are included as nodal masses in the model.

The density and thickness of the elements are further modified to account for stiffness reductions due to openings and cracking, but it is done is such a way as to not change the mass of the elements.

4.4.1.5 Adjustment of Stiffness and Mass Properties

The elastic modulus and thickness of the PS/B shell elements are adjusted using the method described in Section 4.3.1.5 to accurately model the reduction of shear stiffness of walls due to openings.



4.4.1.6 Implementation of Stiffness Reduction in the Dynamic FE Model

The implementation of the stiffness reduction in the PS/B dynamic FE model is performed as described in Section 4.3.1.6.

4.4.2 Out-of-Plane Dynamic Properties of PS/B Slabs

The development of the Dynamic FE Model requires simplifications of the model geometry in order to produce a regular FE mesh and to minimize the size of the model to be suitable for SSI analyses using ACS SASSI. In order to accurately capture the SSI effects, the PS/B footprint dimensions represent the actual configuration of the basemat. The PS/B Dynamic FE Model has the shell elements of the exterior walls placed at the perimeter of the building, unlike the PS/B Detailed FE Model where the shear walls are modeled at the centerline of the walls. These differences in modeling the structure geometry may affect the spans of some of the floor slabs in the PS/B Dynamic FE Model and their local out-of-plane response. The stiffness and mass properties of these flexible slabs are checked to verify if they mimic the actual mass and dynamic properties of the slab obtained from the Detailed model.

The dynamic properties of the slabs at each major floor elevations are obtained by isolating each elevation. Figure 4.4.2-1 shows a typical FE model of the PS/B isolated floor slabs that are extracted from the Detailed FE Model. Boundary conditions are established as shown in Figure 4.4.2-2 at the upper and lower border of the model to restrain horizontal displacements of the walls and accurately mimic the bending stiffness at the wall/slab interfaces. The horizontal and vertical displacements of the slab are also restrained at slab elevation in order to eliminate the effects of the axial stiffness of the walls on the modal analyses results and to disregard the slab horizontal modes as well. Where the slab is supported by columns, the vertical displacement is constrained.

Modal analysis using ANSYS is performed on the isolated elevations of Detailed FE Model and Dynamic FE model to obtain the dynamic properties. If the frequency of the first dominant mode of the slab obtained from Detailed FE Model with full (uncracked concrete) stiffness properties is greater than 70 Hz, the slab is considered rigid. There is no need to adjust the stiffness of the shell elements modeling rigid slabs.

For the flexible slabs with frequency less than 70 Hz, the stiffness of flexible slabs is adjusted as needed by tuning the modulus of elasticity of the slab shell elements in the Dynamic FE Model to match the frequency obtained from the Detailed FE model. The matching criterion is that the difference in the first dominant frequency of vibration of the slab obtained from the modal analyses of the two FE models is within 5%.



Figure 4.4.2-1 Extracted Detailed FE Model of Floor Slabs

Figure 4.4.2-2 Floor Slab Model Boundary Conditions



4.4.3 Validation of PS/B Dynamic FE Model

The development of the PS/B Dynamic FE Model is based on a number of adjustments in geometry and load configurations in order to minimize the size of the model and make it suitable for SSI analysis. The validation ensures that these modeling assumptions and simplifications do not affect the ability of the Dynamic FE Model to accurately represent the dynamic response of the PS/B structure as mandated by SRP Sections 3.7.2.II.1 and 3.7.2.II.3 (Reference 3) and of ISG-01 Section 3.1 (Reference 26).

A series of fixed-base analyses are performed on both the PS/B Dynamic FE and Detailed FE Models using ANSYS and the results are compared. The stiffness and mass attributes assigned to the PS/B Dynamic FE model with full stiffness and reduced stiffness are consistent. Therefore, the validation of the PS/B Dynamic FE Model is performed with full (uncracked concrete) stiffness. In order to ensure that the model with reduced (cracked concrete) stiffness properties can meet the requirement of ISG-01 Section 3.1 (Reference 26) to accurately capture responses with frequencies up to 50 Hz, the validation of the Dynamic model with full stiffness properties compares dynamic responses up to frequencies of at least 70 Hz.

The three different types of analyses performed to validate the dynamic properties of PS/B Dynamic FE model are the same as those used in the validation of the R/B Complex Dynamic FE Model. They consist of a:

1. 1g Static Analysis

2. Modal Analysis

3. Modal Superposition Time History Analysis

4.4.4 Conversion of the PS/B Dynamic FE Model from ANSYS to ACS SASSI Format

The PS/B dynamic FE model is translated into the ACS SASSI Format and the translation is validated as described in Section 4.3.3. ATF’s at selected locations are checked to compare the resonant frequencies revealed by ANSYS modal analyses and ACS SASSI analyses. 5% damped ARS are also compared. Same acceptance criteria as described in 4.3.3 are applied for PS/B dynamic FE model validation.

4.5 Consideration of Concrete Cracking in Dynamic Analyses

In order to capture the variations of dynamic properties of US-APWR standard plant Category I structures due to concrete cracking, the site-independent SSI analyses consider two levels of stiffness and damping properties:

1) full (uncracked concrete) stiffness and lower operating-basis earthquake (OBE) material damping; and

2) reduced (cracked concrete) stiffness and higher SSE material damping

The bounding case of a full stiffness level represents the case when the stresses in the reinforced concrete, pre-stressed concrete and steel-concrete modular structures are of low intensity such that the concrete remains essentially uncracked. The OBE Damping values are



assigned to the model with full (uncracked) stiffness to account for the lower dissipation of energy in the structures when subjected to low stress levels. A reduced stiffness level considers the case when the structures are subjected to higher stress levels that result in cracking of the concrete. The SSE damping values are assigned to the model with reduced (cracked concrete) stiffness to account for the higher dissipation of energy in the structures when subjected to higher stress levels.

This section describes the approach used to include the effect of the concrete cracking on the stiffness and damping properties in the dynamic structural models of PCCV, CIS, R/B and PS/B. An explanation of the methodology implemented to address the effect of concrete cracking in the development of seismic design basis is also provided together with a matrix of required seismic response analyses required of the R/B Complex and PS/B models with different stiffness and damping levels.

4.5.1 Effects of Concrete Cracking on Reinforced Concrete Shear Wall Structures

In accordance with ASCE 4-98 (Reference 12), Section 3.1.3, and ASCE/SEI 43-05 (Reference 13), Section 3.4.1, traditional reinforced concrete members and elements are to be modeled as either cracked or uncracked sections, depending on their stress level due to the most critical load combinations that include seismic design loads. For the uncracked sections/elements, the stiffness is directly obtained from the concrete linear elastic properties and the section or element geometric dimensions. For the cracked concrete, a reduction to the uncracked concrete stiffness is taken into account. The reduction factors shown in Table 3-1 of ASCE/SEI 43-05 are used in linear elastic analysis to address the effects of concrete cracking on the seismic response of the US-APWR seismic Category I structures.

The design of the reinforced concrete shear wall structures is based on the ultimate capacity of the reinforced concrete sections. Therefore, the design of reinforced concrete members addresses code stress limits corresponding to reduced cracked concrete stiffness properties and higher SSE material damping levels as discussed in Section 1.2 of RG 1.61 (Reference 30). However, there is a possibility that the response of the structure under lower stress levels at certain frequency ranges will be higher than the response corresponding to the higher stress state under cracked conditions. In order to ensure that the structural integrity and functionality of the components and the equipment is not compromised under all possible seismic loading conditions, the development of in-structure response spectra (ISRS) has to also consider the responses of the reinforced concrete structure with full (uncracked concrete) stiffness properties and lower OBE damping levels.

The seismic response analyses of reinforced concrete shear wall type of structures consider two stiffness and damping in order to address the possible variations in the extent of concrete cracking:

1. Full stiffness representing low stress levels corresponding to uncracked concrete properties where the stiffness of the members are represent by gross cross sectional properties.

2. Reduced stiffness representing higher stress levels resulting in cracking of the concrete where the stiffness of the members are reduced in accordance with guidelines provided in Table 3-1 of ASCE/SEI 43-05. The stiffness of the composite members made of reinforced concrete and steel beams, such as the walls and the roof



of Fuel Handling Area (FH/A) are also reduced accordingly to represent 50% reduction in stiffness in the reinforced concrete part of the composite sections.

The structural material damping values used for these two different stress levels are OBE damping of 4% for the full (uncracked concrete) stiffness condition and SSE damping of 7% for the reduced (cracked concrete) stiffness condition.

4.5.2 Effects of Concrete Cracking on the CIS

The US-APWR Containment Internal Structure (CIS) is comprised of different types of structural members including composite steel-concrete (SC) walls, massive reinforced concrete sections, and reinforced concrete slabs that serve different functions such as supporting the NSSS equipment, providing primary or secondary radiological shielding and containment of the refueling water. The members can experience varying levels of stress resulting in different patterns of concrete cracking under the different loading conditions that can exist in the reactor containment. Depending on the reactor operating conditions, the CIS members can be subjected to design seismic loads in combination with normal operating or accidental thermal loads resulting in different levels of stiffness reduction due to concrete cracking. Table 4.3.1.1-3 describes the methodology to address the effect of concrete cracking on CIS dynamic properties and provides for the different CIS members that are classified in six categories, two stiffness levels corresponding to:

1. Normal operating conditions characterized with insignificant reduction of stiffness and concrete cracking; and

2. Accidental conditions characterized with significant reduction of stiffness due to cracking of the concrete under high accidental thermal loads.

Different material damping values are assigned to the different members depending on the level of stresses and corresponding concrete cracking. For the SC walls, OBE damping of 4% is used for normal operating loading conditions, and SSE damping of 5% for accidental loading conditions.

Similar to the CIS, the level of stresses in the PCCV during a seismic design event depend on the reactor containment operating conditions. The design of the PCCV structure is based on the premise that during normal operating conditions the pre-stress concrete cross sections remain in compression. During the normal operating conditions, the earthquake design loads can cause only limited cracking having insignificant effect on the overall stiffness of the PCCV. Accordingly, the dissipation of energy due to material damping of the PCCV structure under normal operating conditions is low. The accident loading conditions include high temperatures and pressure loads in the reactor containment that can generate high stresses in the pre-stressed concrete accompanied with cracking that can result in a reduction of the global stiffness of the PCCV structure and higher dissipation of energy due to the material damping. The stress evaluations provided in Appendix B, indicate that the reduction of the overall stiffness of PCCV structure under seismic design loads in combination with accident loads can be up to 50%.

Two stiffness levels are considered by the seismic response analyses of PCCV:

1. Normal operating conditions corresponding to insignificant concrete cracking and full (uncracked concrete) stiffness of the pre-stressed concrete structure; and



2. Accident conditions when the high thermal and pressure loads generate high stresses that can result in significant cracking of the pre-stressed concrete and a 50% reduction of the stiffness.

The structural material damping values used for these two different stiffness and stress levels are OBE damping of 3% for the full (uncracked concrete) stiffness or normal operating conditions and SSE damping of 5% for the reduced (cracked concrete) stiffness or accidental conditions.

4.5.3 Approach to Address Concrete Cracking in Site-Independent SSI Analyses

In order to address the effect of concrete cracking on the standard seismic design basis of US-APWR reinforced concrete structures, two sets of site-independent SSI analyses of PS/B dynamic FE model are performed using structural models representing two bounding stiffness and damping levels:

1) full (uncracked concrete) stiffness;

2) reduced (cracked concrete) stiffness.

Two sets of analyses are also performed on the dynamic FE model of R/B complex using full (uncracked concrete) stiffness and reduced (cracked concrete) stiffness. The dynamic FE model of the R/B complex with full stiffness represents the levels of concrete cracking of the PCCV and the CIS corresponding to normal operating conditions in the reactor containment. In order provide overall bounding responses of the R/B complex corresponding to lower levels of stresses and structural material damping, the models of the CIS and the PCCV with full stiffness are accompanied with the FE model of the R/B reinforced concrete structure having full (uncracked concrete) stiffness. The R/B complex model with reduced stiffness will provide responses of the CIS and PCCV corresponding to accidental conditions. The PCCV and CIS models with reduced stiffness will be accompanied with model of the R/B complex having reduced (cracked concrete) stiffness in order to obtain overall bounding responses of the R/B complex structures representing higher stress and damping levels. In developing the reduced stiffness models, global stiffness reductions are applied.

The seismic response analyses of the R/B complex and the PS/B provide results that serve as basis for development of SSE loads for design of structural members, maximum displacements for evaluation of gaps between buildings and in-structure response spectra (ISRS) for design of components and equipment. Responses obtained from the models with two different levels of stiffness and damping are enveloped in order to develop ISRS for design of the seismic category I and II equipment and components. The SSE loads used for the PCCV and the CIS design are also developed based on the responses obtained from the analyses of models with two different level of stiffness in order to ensure that the design uses seismic loads enveloping both normal operating and accident loading conditions.

Responses obtained from models with reduced (cracked concrete) stiffness and SSE damping are used to develop SSE loads for the design of shear walls or reinforced concrete structures since this condition corresponds to the ultimate stress conditions. This approach is consistent with Section 1.2 of RG 1.61. The models with reduced (cracked concrete) stiffness properties will also provide the bounding results for maximum seismic displacements relative to the free field, which are used for evaluation of the gaps between buildings.



Table 4.5.3-1 provides the percent of stiffness reduction and damping values used for the different structural components for the site-independent SSI analyses of US-APWR R/B complex and PS/B. Table 4.5.3-1 also describes how the results of the SSI analyses of models with different stiffness are used to develop the basis for standard seismic design of the different US-APWR buildings.



Table 4.5.3-1 Material Properties of Models used for Seismic Response Analyses

Design Basis Stiffness

Level Model

Structural Component

Stiffness DampingSSE Load

ISRS Max. Displ.

SC module (CIS) 100% 4% X X X

Pre-stressed (PCCV)

100% 3% X X X

Reinforced Concrete (R/B)

100% 4% N/C X X

Composite (FH/A) 100% 4% conc. 3% steel

N/C X X

Steel 100% 3% X N/A N/A

RCL 100% 3% N/A X X

R/B Complex

massive concrete 100% 4% X X X

Reinforced Concrete

100% 4% N/C X X

Ful

l (U

ncra

cked

) S

tiffn

ess

PS/B


SC module (CIS)50%

5%See Table 4.3.1.1-3X X X

Pre-stressed (PCCV)

50% 5% X X X

Reinforced Concrete (R/B)

50% 7% X X X

Composite (FH/A)

50% concrete

7% conc. 4% steel

X X X


RCL 100% 3% N/A X X

R/B Complex

Massive concrete

100% 4% X X X

Reinforced Concrete

50% 7% X X X

Red

uced

(C

rack

ed)

Stif

fnes

s

PS/B


Note: N/C - Not Considered; N/A - Not Applicable



5 RESULTS AND CONCLUSIONS

5.1 CSDRS Compatible Ground Motion Time Histories

One set of three statistically independent components of a modified seed recorded time history motion is generated for use as the input seismic motion to the earthquake response analysis of the US-APWR standard plant including the R/B, PCCV, CIS, and PS/Bs. The three individual time history orthogonal direction components represent the CSDRS earthquake ground motion, labeled in this report as two horizontal (“H1” and “H2”) and one vertical (“V”). The artificial time history motion plots for the ground accelerations, velocity, and displacements in three orthogonal directions (“H1,” “H2,” and “V”) are shown in Figures 5.1-1, 5.1-2, and 5.1-3, respectively. The time history motion plots of the ground acceleration, velocity, and displacement are shown together to demonstrate their non-stationary process.

Figure 5.1-1a Acceleration Time History for Component H1 (270)

-0 .40

-0 .30

-0 .20

-0 .10

0.00

0.10

0.20

0.30

0.40

0 5 10 15 20

Tim e (sec)

Acc

eler

atio

n (

g)



Figure 5.1-1b Velocity Time History for Component H1 (270)

Figure 5.1-1c Displacement Time History for Component H1 (270)

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20

Tim e (sec)

Ve

loc

ity

(in

/se

c)

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0 5 10 15 20

Tim e (sec)

Dis

pla

cem

ent

(in

)



Figure 5.1-2a Acceleration Time History for Component H2 (360)

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20

Tim e (sec)

Ve

loc

ity

(in

/se

c)

Figure 5.1-2b Velocity Time History for Component H2 (360)

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 5 10 15 20

Tim e (sec)

Acc

eler

atio

n (

g)



-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0 5 10 15 20

Tim e (sec)

Dis

pla

ce

me

nt

(in

)

Figure 5.1-2c Displacement Time History for Component H2 (360)

-0 .40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 5 10 15 20

Tim e (sec)

Acc

eler

atio

n (

g)

Figure 5.1-3a Acceleration Time History for Component V (UP)



-25

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20

Tim e (sec)

Vel

oci

ty (

in/s

ec)

Figure 5.1-3b Velocity Time History for Component V (UP)

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0 5 10 15 20

Tim e (sec)

Dis

pla

ce

me

nt

(in

)

Figure 5.1-3c Displacement Time History for Component V (UP)



Figures 5.1-4, 5.1-5 and 5.1-6 show the ARS of the US-APWR artificial time histories with 5% damping for the three orthogonal directions H1, H2, and V, respectively. The plots of the CSDRS are superimposed on the figures to illustrate that the ARS converted from the artificial time histories match those of the CSDRS for 5% damping. The CSDRS plots connect the control points shown in Table 4.1-1 and are based on the modified Regulatory Guide (RG) 1.60 (Reference 15) response spectra. The horizontal and vertical modified RG 1.60 response spectra used as the target spectra are extended to a lower frequency of 0.1 Hz. These figures demonstrate that the artificial acceleration time histories do not have significant gaps in the response spectra, and are also not biased high with respect to the target CSDRS to demonstrate uniform energy distribution.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0.1 1 10 100

Frequency (hz)

Acc

eler

atio

n (

g)

Target Spectrum at 5% D am ping

T im e H istory Spectrum at 5% Dam ping

90% of Target

130% of Target

Figure 5.1-4 5% Damped Response Spectra Plots for Adjusted Nahanni Station 3 Component H1 (270)



0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0.1 1 10 100

Frequency (hz)

Acc

eler

atio

n (

g)

Target Spectrum at 5% Dam pingT im e H istory Spectrum at 5% Dam ping90% of Target130% of Target

Figure 5.1-5 5% Damped Response Spectra Plots for Adjusted Nahanni, Station 3 Component H2 (360)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0.1 1 10 100

Frequency (hz)

Acc

eler

atio

n (

g)

Target Spectrum at 5% Dam ping

T im e H istory Spectrum at 5% D am ping

90% o f Target

130% of Target

Figure 5.1-6 5% Damped Response Spectra Plots for Adjusted Nahanni, Station 3 Component V (UP)



The time histories meet all of the requirements and conditions set forth in Section II of NUREG-0800, SRP 3.7.1 (Reference 1) for the generation of a single set of time histories Option 1, Approach 2, as summarized in Table 5.1-1 and described in the following, steps (a) through (d):

(a) The US-APWR artificial time histories have sufficiently small time increments (Δt =0.005 seconds) and a total duration of 20 seconds. The time history data records have a Nyquist frequency of Nf = 1/(2Δt) =100 Hz, and meet the NUREG-0800 SRP 3.7.1 (Reference 1) requirement of a total duration of at least 20 seconds. The time increment of 0.005 seconds is lower than the maximum time increment of 0.01 seconds permitted by SRP 3.7.1. The Nyquist frequency of 100 Hz is considered to be above the range of frequencies important for the design of the US-APWR plant and assures that the seismic analysis capture the responses of SSCs in the high frequency range. This is particularly important for site-specific subgrade conditions where seismic category I structures are founded on a hard rock subgrade.

(b) The 5% damped ARSs of the US-APWR artificial time history components, shown in Figures 5.1-1, 5.1-2, and 5.1-3, are computed at 301 frequency points with a minimum of 100 points per frequency decade, uniformly spaced over the log frequency scale from 0.1 Hz to 50 Hz or the Nyquist frequency. Each ARS obtained from the three artificial ground motion time history components are compared with the target response spectra over the frequency range.

(c) The 5% damped ARSs computed for each of the three US-APWR artificial time history components do not fall more than 10% below the corresponding CSDRS target response spectra at any particular frequency. In addition, within a frequency window no larger than ±10% centered at any frequency data point, none of the three ARSs (H1, H2, and V) falls below their corresponding target CSDRS. Exceeding the requirements of SRP 3.7.1 (Reference 1), is confirmed by assuring that, for each of the spectra derived from the artificial time history components, no more than nine (9) adjacent frequency points fall below the CSDRS target response spectra for frequencies between 0.1 Hz and 100 Hz. This ensures that the response spectra resulting from the artificial time history components do not fall below the corresponding target response spectra in large frequency windows. Table 5.1-1 demonstrates that these requirements are met by showing a comparison of the artificial time history ARS and the CSDRS.

(d) In lieu of the power spectral density requirement of Option 1 Approach 1 in SRP 3.7.1 (Reference 1), Approach 2 specifies that the computed 5% damped response spectra of each artificial ground motion time history component does not exceed its target response spectra at any frequency by more than 30% (a factor of 1.3) in the frequency range of interest. For the US-APWR, the response spectra derived from the artificial time histories are checked to ensure that they do not exceed the corresponding target spectra (CSDRS) by more than 30% at any frequency range measured as described in item (b) above. The results of this check are presented in Table 5.1-2.



Table 5.1-1 Comparison of 5% Damping ARS of Artificial Time History and CSDRS

Frequency Range 0.1 – 1 Hz 1 – 10 Hz 10 – 100 Hz 0.1 – 100 Hz

Tim

e H

isto

ry

No. Freq. Data Points 101 101 101 301

Min. 0.907 0.942 0.967 0.907

Max. 1.055 1.064 1.038 1.064 ARS/CSDRS ratio

Ave. 1.005 1.008 1.014 1.009

Ho

rizo

nta

l

H

1

Max. No. of Data Point Non-Exceedances Within Any One Particular Frequency Window (1)

7 4 2 7

Min. 0.938 0.937 0.985 0.937


Ave. 1.025 1.005 1.015 1.015

Ho

rizo

nta

l

H2


5 5 3 5

Min. 0.949 0.972 0.984 0.949


Ave. 1.009 1.006 1.011 1.009

Ver

tica

l

V


5 3 2 5

(1) Maximum number of frequency data points in any one particular sequence (frequency window) for which the acceleration values of the time histories ARS are below those of the CSDRS.



Table 5.1-2 Spectra Matching Requirements for Converted Time Histories

SRP 3.7.1 Criterion for 5% Critical Damping: H1

(270

) S

SE

x

H2

(360

) S

SE

y

V (

up)

SS

Ez

Average of converted/target acceleration ratios for all frequency points (if > 1.0 o.k.) 1.009 1.015 1.009Rise time duration Arias Intensity 5% 2.845 2.729 3.026 Required for Magnitude 6.5 earthquake(1) (2) 1 1 1Strong motion time duration Arias intensity 75% - 5% 7.795 8.286 7.165 Required for Magnitude 6.5 earthquake(1) (2) 7 7 7Decay time duration Arias intensity 100% - 75% 9.360 8.985 9.809 Required for Magnitude 6.5 earthquake(1) (2) 5 5 5Statistical Independence Correlation coefficient X and Y (if abs value < 0.16 o.k.) -0.0327 -0.0327

Correlation coefficient X and Z (if abs value < 0.16 o.k.) 0.1390 0.139

0

Correlation coefficient Y and Z (if abs value < 0.16 o.k.) 0.11700.117

0SRP 3.7.1 Option 1, Approach 2 Number of points with acceleration ratio > 1.30 (if = 0 o.k.) 0 0 0Number of points with acceleration ratio < 0.90 (if = 0 o.k.) 0 0 0Number of windows wider than 9 points below the target spectra (if = 0 o.k.) 0 0 0

(1) The seed recorded time history earthquake for the US-APWR Standard Plant CSDRS has a Magnitude of 6.5 (References 7 and 21).

(2) See Table 2.3-1 of ASCE 4-98 (Reference 12) for guidance on length of time appropriate for rise, strong motion, and decay

The time histories also meet the requirements set forth in Acceptance Criteria 1B, on page 3.7.1-9 of SRP 3.7.1 (Reference 1) as summarized in Table 5.1-2 and further described below:

Cross Correlation between Components The cross-correlation coefficients between the three components of the artificial time history earthquake are as follows: ρ12 = -0.0327, ρ23 = 0.1170, and ρ31 = 0.1390 where 1, 2, and 3 are the three global directions corresponding to NS, EW, and vertical directions for the US-APWR standard plant. Since the absolute values of the cross-correlation coefficients of the US-APWR artificial time histories are less than 0.16, as listed above, in accordance with NUREG/CR-6728 (Reference 9), the time histories are considered statistically independent of each other.



Duration of Motion The set of three statistically independent components of the artificial time history earthquake which are developed for design of the US-APWR seismic Category I buildings are characterized by the strong duration of motion times, listed in Table 5.1-2 and total duration of motion time of 20 seconds. The strong motion duration time is defined as the time required for the Arias Intensity to rise from 5% to 75%, and is required to meet a minimum of 6 seconds, in accordance with SRP 3.7.1 (Reference 1). The duration of motion of the US-APWR artificial time histories with respect to time achieved from 5% to 75% Arias intensities example provided in Table 5.1-3 shows the subtraction of Arias Intensity values to determine the duration. This is similarly computed for rise and decay times listed in Table 5.1-2. The guidance of ASCE 4-98 (Reference 12) for minimum duration, rise, and decay times for a Magnitude 6.5 earthquake is also met.

Table 5.1-3 Duration of Motion of US-APWR Artificial Time History Components Computed from Arias Intensity Values

Arias Intensity

Time for 5% (seconds)

Time for 75% (seconds)

Arias Duration

75%Ia - 5%Ia (seconds)

ASCE 4-98 (1) Arias

Min. Duration (seconds)

H1 2.845 10.640 7.795 7

H2 2.729 11.015 8.286 7

V 3.026 10.191 7.165 7

(1) ASCE 4-98 guidance for a 6.5 Magnitude Earthquake

The uniformity of the growth of this Arias Intensity is shown in Figure 5.1-7 for each of the three components of the artificial time history earthquake. The total duration of motion equals the minimum acceptance criterion of 20 seconds, as required by SRP 3.7.1, SRP Acceptance Criteria, 1 B Option 1 ii, Approach 2 Part (a).



Arias' Intensity - Recorded and Modified Nahanni Earthquake Component 270

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time (sec)

%

Modified C 270: Strong Motion Duration = 7.795 sec

Recorded C 270: Strong Motion Duration = 6.787 sec

Figure 5.1-7 Normalized Arias Intensity of Time History Components Showing 5%-75% Duration Component 270



Arias' Intensity - Recorded and Modified Nahanni Earthquake Component 360

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time (sec)

%

Modified C 360: Strong Motion Duration = 8.286 sec

Recorded C 360: Strong Motion Duration = 7.260 sec

Figure 5.1-8 Normalized Arias Intensity of Time History Components Showing 5%-75% Duration Component 360



Arias' Intensity - Modified Nahanni Earthquake Component Up

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time (sec)

%

Modified C UP: Strong Motion Duration = 7.165 sec

Recorded C UP: Strong Motion Duration = 6.748 sec

Figure 5.1-9 Normalized Arias Intensity of Time History Components Showing 5%-75% Duration Component UP



5.2 Development of Soil Profiles

Following the approach discussed in Section 4.2.2, strain compatible properties are developed for the SV (30m) profile categories of 270 m/s, 560 m/s, 900 m/s, and 2,032 m/s. The selected shear- and compression-wave profiles are shown in Figure 5.2-1 to their maximum depths with Poisson ratios shown in Figure 5.2-2. To accommodate realistic soil foundation conditions in developing the strain compatible properties, approximately 68 feet of soft soil is removed from the softest profile, SV (30m) = 270 m/s. The soil removal increased the original surficial shear-wave velocity of 520 ft/s (Figure 4.2-1) to 1,247 ft/s at a foundation level, although the profile name of 270 m/s is retained (the SV (30m) for the revised 270m/sec profile has increased to 425m/sec). The remaining three profiles are assumed to reflect appropriate conditions at the plant surface and are left unaltered. Due to their steep velocity gradients (Figure 5.2-1), the depth ranges for soft and firm rock profiles of 900 m/s and 2,032 m/s are restricted to 100 feet and 200 feet for soft rock (900 m/s) and 100 feet for firm rock (2,032 m/s). The final profile categories and depth bins are listed in Table 4.2.1-1.

Since the water table was taken at the foundation level, the minimum compression-wave velocity was set at 5,000 ft/s for the soil profiles. The effects of ground water table fluctuations on the seismic responses of the R/B are evaluated in MUAP-11007 (Reference 33). The related SSI analysis results indicate that the lower water table elevation can slightly lower the peak frequencies and amplify the magnitude of the peak responses. The frequency shifts and the peak response amplifications are small and will not have an impact on the standard seismic design. The uncertainty introduced in the standard design by the effects of ground water fluctuations on the seismic response are small and within the general level of variation present in the seismic response analyses. As such, it is deemed unnecessary to directly address in the standard design the effects that the water table fluctuations can have on the seismic response.

MUAP-11007 analysis results with embedment included show that embedment causes noticeable but not significant seismic response variations. For the five generic soil profiles (270-200, 560-100, 900-100, 900-200, and 2032-100) studied, such variations are covered by the seismic response envelopes derived from the results for the same five generic site profiles considered for the standard design assuming a surface-supported foundation condition. Thus, design-basis ISRS envelopes generated without embedment effects are conservative and need not be modified to account for embedment effects. While the studies contained in MUAP-11007 use different soil profiles than the design basis analyses, they are sufficiently similar so that the conclusions of this report are not compromised by the differences.



Table 5.2-1 Deleted



0

200

400

600

800

1000

1200

1400

1600

1000 2000 3000 4000 5000 6000 7000 8000 9000

Vs (ft/sec)

Dep

th (

ft)

270-200 270-500

560-500 900-100

900-200 2032-100

Figure 5.2-1 Final Foundation Level Base-Case Shear- and Compression-Wave Velocity Profiles (Sheet 1 of 4)

Note: Since the water table was taken at the foundation level, the minimum compressional-wave velocity was set at 5,000 ft/s.



0

50

100

150

200

250

300

350

400

450

500

550

600

1000 2000 3000 4000 5000 6000 7000 8000 9000

Vs (ft/sec)D

epth

(ft

)

270-200 270-500

560-500 900-100

900-200 2032-100

Figure 5.2-1 Final Foundation Level Base-Case Shear- And Compression-Wave

Velocity Profiles (Sheet 2 of 4)

Note: Since the water table was taken at the foundation level, the minimum

compressional-wave velocity was set at 5,000 ft/s.



0

200

400

600

800

1000

1200

1400

1600

4000 6000 8000 10000 12000 14000 16000

Vp (ft/sec)

Dep

th (

ft)

270-200 270-500

560-500 900-100

900-200 2032-100

Figure 5.2-1 Final Foundation Level Base-Case Shear- And Compression-Wave Velocity Profiles (Sheet 3 of 4)

Note: Since the water table was taken at the foundation level, the minimum

compression-wave velocity was set at 5,000 ft/s.



0

50

100

150

200

250

300

350

400

450

500

550

600

4000 6000 8000 10000 12000 14000 16000

Vp (ft/s)

Dep

th (

ft)

270-200 270-500

560-500 900-100

900-200 2032-100

Figure 5.2-1 Final Foundation Level Base-Case Shear- And Compression-Wave Velocity Profiles (Sheet 4 of 4)

Note: Since the water table was taken at the foundation level, the minimum compression-wave velocity was set at 5,000 ft/s.



0

200

400

600

800

1000

1200

1400

1600

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Poisson Ratio (n)

Dep

th (

ft)

270-200

270-500

560-500

900-100

900-200

2032-100

Figure 5.2-2 Poisson Ratios Computed for the Six Soil Profiles (Sheet 1 of 2)



0

100

200

300

400

500

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Poisson Ratio ()D

epth

(ft

)

270-200

270-500

560-500

900-100

900-200

2032-100

Figure 5.2-2 Poisson Ratios Computed for the Six Soil Profiles(Sheet 2 of 2)



5.2.1 Site Response Analyses

The site response analyses are conducted using the equivalent linear RVT approach (Reference 7, Reference 9, and NUREG/CR-6769 (Reference 16)) with the point-source model used to generate both the horizontal and vertical motions (References 7, 9, and 10). Magnitude M7.5 is used as its broad spectral shape is consistent with that of the CSDRS. Distances are adjusted such that the median spectrum computed for each profile approaches, but does not exceed, the horizontal and vertical CSDRS. The distances and median estimates of the horizontal and vertical peak accelerations are listed in Table 5.2-2 and the median spectrum computed for each profile is compared to the CSDRS spectrum in Figure 5.2-3 for horizontal components. Due to the shape of the US-APWR CSDRS, nearly all the profile spectra approach the design spectrum at high frequency (approximately 25 Hz to 50 Hz). This frequency range then becomes the effective control for non exceedance and associated distance adjustment for most of the profiles. The exceptions being reflected by the fundamental low-frequency resonance of the softest (270 m/s and 560m/sec) and deepest (500 feet) profiles.

For the vertical motions, Figure 5.2-4 compares the median spectra computed for the profiles with the vertical component CSDRS. In this case, the vertical motions are modeled assuming incident inclined P-SV wave using a linear analysis (References 7, 9, and 10). Linear analyses for vertical motions with incident inclined P-SV waves has been shown to be appropriate for loading levels up to approximately 0.5g (Reference 7) and consistent with empirical GMPEs from “Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes” (Reference 17). Use of linear analyses is also consistent with observations of spectral shapes for vertical motions at soil sites being independent of loading level (Reference 10). For applications to sites with a water table at or very near the surface, linearity of the constrained modulus is also a realistic assumption as compressional waves control the high-frequencies in vertical motions (Refer to “Properties of Vertical Ground Motions”, Reference 18), where nonlinearity has its largest effect.

As Figure 5.2-4 shows, most of the vertical spectra fall significantly below the vertical CSDRS design spectrum which was based on the RG 1.60 (Reference 15) V/H ratio. This trend is consistent with vertical spectra recorded at both soil and rock sites in WNA and is a result of the large source distances (Reference 9) (e.g. > 50 km, Table 5.2-2). Empirical (Refer to Reference 19) as well as simulated (References 9 and 10) V/H ratios decrease with increasing distance in both WNA and CEUS and are less than one at distances exceeding 50 km.

Using the RG 1.60 (Reference 15) V/H ratios, which are conservatively independent of distance, the vertical motions are considerably elevated as shown in Figure 5.2-5. With the conservative RG 1.60 V/H ratios, there are some minor exceedances near 0.5 Hz and 1.0 Hz for the softest profile (270 m/s) and largest depths to soft rock material (500 feet).



Table 5.2-2 Magnitudes, Distances, and Median Peak Accelerations

Profile M D(km) PGA*H(g) PGA*V(g)

270 – 200 7.5 62.0 0.272 0.125

270 – 500 7.5 62.0 0.227 0.121

560 – 500 7.5 57.0 0.259 0.124

900 – 100 7.5 84.0 0.197 0.074

900 – 200 7.5 87.0 0.192 0.072

2032 - 100 7.5 58.0 0.162 0.075

Δσ = 110 bars

Q(f) = 670 f 0.33

κ = 0.006 sec, hard rock outcrop horizontal component

κ = 0.003 sec, hard rock outcrop vertical component

* Median peak acceleration at profile surface



Figure 5.2-3 Median Spectra (5% damped) Compared to CSDRS Horizontal Components

Note: Magnitude is M 7.5 with median peak accelerations and distances listed in Table 5.2.2: Horizontal components



Figure 5.2-4 Median Spectra (5% damped) Compared to CSDRS Vertical Components

Note: Magnitude is M7.5 with median peak accelerations and distances listed in Table 5.2.2: Vertical components



Figure 5.2-5 Median Spectra (5% damped) Compared to CSDRS Vertical Components Using RG 1.60 V/H Ratios

Note: Magnitude is M7.5 with median peak accelerations and distances listed in Table 5.2.2: Vertical components using RG 1.60 V/H ratios



5.2.2 Strain Compatible Properties

For the six combinations of selected profile categories and depths to hard or soft rock material (Table 4.2.1-1) strain compatible properties are developed reflecting median (best estimate) and ± 1σ (upper and lower range) estimates over the thirty (30) realizations of profiles and G/Gmax and hysteretic damping curves (Section 4.2.2). The strain compatible properties are summarized in Tables 5.2-4 to 5.2-11, with Figures 5.2-6 to 5.2-14 showing the median and ±1σ estimates for the shear- and compression-wave velocities and associated damping.

The following properties are taken from the results of the site response analyses listed in Tables 5.2-4 to 5.2-11 and used as input for site-independent SSI analyses:

Unit weight

Median values of strain compatible shear-wave velocities (Vs)

Median values of strain compatible compression-wave velocities (Vp)

Median values of strain compatible shear-wave damping (Ds)

The site profiles used for the site-specific soil-structure interaction (SSI) analyses use the median values of shear wave damping for both shear and compression-wave damping in order to account in a more realistic manner for the dissipation of energy in the soil under the wave propagation pattern present in the SSI model. Due to the simplified assumption in wave propagation in SSI analyses as vertically propagating compression-waves, strain iterated shear-wave damping is typically assumed for compression-wave damping to avoid unrealistic vertical motions at high-frequencies. Also, seismic SSI analysis is usually performed separately for horizontal and vertical seismic input motions. In these analyses, the horizontal and vertical input motions are assumed caused by different horizontal and vertical seismic wave field excitations even though the seismic input environment is always 3-D consisting of simultaneous 3-component seismic input motions.

Correlation studies of the vertical site response motions recorded in actual earthquakes with the vertical motions predicted from vertical 1-D wave propagation site response analyses have been made (Reference 35). These studies conclude that, using the strain-compatible soil damping values derived from the horizontal site response analyses as the damping values for vertical site response analysis, but limiting their values to no more than 10%, produces reasonably good correlation between the predicted and recorded vertical site response motions. Consistent with this conclusion, the soil damping values used for the horizontal and vertical SSI analyses are the shear-strain-compatible soil damping values derived from the horizontal free-field site response analyses. The horizontal SSI response analyses are performed assuming vertically propagating plane shear (SV or SH) wave-field excitations with the shear-strain-compatible damping values limited to no more than 15%, as required by the SRP. The vertical SSI response analysis is performed assuming vertically propagating plane compression wave-field excitation, the shear-strain-compatible damping values derived from the horizontal site response analyses are used but with their values limited to no more than 10%, as recommended by the correlation studies reported in Reference 35.

The site response analyses use very low values for the material damping of hard baserock in order to model the low dissipation of energy in the deep hard rock strata. In order to improve



the numerical stability of SSI results, the damping of the baserock material when included in the site profile is set to a low nominal value of 0.1%. This modification does not affect the SSI response because unlike in the site response analyses the thickness of the modeled hardrock strata in the SSI site model is with finite thickness so the use of higher damping values realistically projects the actual dissipation of energy in the baserock.

In order to obtain a general description of the range of subgrade properties considered in the site-independent SSI analyses, the shear column frequencies of the selected median soil profiles are calculated as follows:

H

Vsf avesc

4

where: H is the depth of the soil column taken as the nominal depth of the top soil strata, and Vsave is the average shear-wave velocity of the top soil layers calculated as follows using the equivalent arrival time method:

i i

iave

VsdH

Vs

where: di and Vsi are the thickness and shear-wave velocity of each layer of top soil.

Table 5.2-12 summarizes the shear column frequencies for each of the selected profiles. Two values for shear column frequencies are presented for full profile with depth equal the nominal depth of the profile (100 feet, 200 feet or 500 feet) and truncated profile for which the top 40 feet of soil are removed to account for the embedment of the US-APWR standard plant buildings. Figure 5.2-15 shows a bar chart distribution of the shear column frequencies of truncated profiles used as input for the SSI analyses.

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-30

Tab

le 5

.2-3

D

elet

ed

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-31

Tab

le 5

.2-4

S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 2

00 f

t

(Sh

eet

1 o

f 3)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

Med

ian

1 7.

92

0.00

0.

1250

12

11

4969

1.

6356

1.

1972

0.

468

2 7.

91

7.92

0.

1250

12

12

5171

2.

3976

1.

1972

0.

471

3 7.

92

15.8

3 0.

1250

12

09

5133

2.

4909

1.

0045

0.

470

4 7.

91

23.7

5 0.

1250

12

24

5264

2.

7439

1.

0045

0.

471

5 8.

58

31.6

6 0.

1250

11

84

5173

3.

0995

1.

0045

0.

472

6 8.

58

40.2

4 0.

1250

12

32

5379

3.

1960

1.

0045

0.

472

7 8.

58

48.8

2 0.

1250

12

60

5528

3.

2984

1.

0045

0.

472

8 8.

58

57.4

0 0.

1250

12

81

5642

3.

4009

1.

0045

0.

473

9 8.

58

65.9

8 0.

1250

13

11

5779

3.

4500

1.

0045

0.

473

10

8.58

74

.56

0.12

50

1345

59

49

3.46

87

1.00

45

0.47

3 11

9.

38

83.1

4 0.

1250

13

20

5852

2.

7019

0.

7992

0.

473

12

9.37

92

.52

0.12

50

1358

60

18

2.69

59

0.79

92

0.47

3 13

9.

38

101.

89

0.12

50

1373

61

05

2.73

76

0.79

92

0.47

3 14

9.

37

111.

27

0.12

50

1410

62

64

2.73

61

0.79

92

0.47

3 15

9.

38

120.

64

0.12

50

1446

64

23

2.73

16

0.79

92

0.47

3 16

9.

37

130.

02

0.12

50

1493

66

21

2.68

56

0.79

92

0.47

3 17

10

.00

139.

39

0.13

13

1486

65

91

2.68

25

0.79

92

0.47

3 18

10

.00

149.

39

0.13

13

1490

66

14

2.73

73

0.79

92

0.47

3 19

10

.00

159.

39

0.13

13

1508

66

96

2.77

21

0.79

92

0.47

3 20

10

.00

169.

40

0.13

13

1501

66

89

2.83

30

0.79

92

0.47

3 21

10

.00

179.

40

0.13

13

1555

69

03

2.77

68

0.79

92

0.47

3 22

10

.60

189.

39

0.13

13

1538

68

61

2.84

65

0.79

92

0.47

3 23

16

4.1

200.

00

0.13

13

2452

80

43

0.50

00

0.50

00

0.44

9 24

16

4.1

364.

05

0.13

44

3281

89

24

0.50

00

0.50

00

0.42

2 25

16

4.1

528.

1 0.

1400

49

21

1124

0 0.

5000

0.

5000

0.

381

26

164.

1 69

2.2

0.14

38

6562

14

270

0.50

00

0.50

00

0.36

6 27

16

4.1

856.

2 0.

1500

82

03

1542

0 0.

2500

0.

2500

0.

303

28

3281

10

20

0.15

75

9285

16

080

0.00

05

0.00

05

0.25

0

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-32

Tab

le 5

.2-4

(S

hee

t 2

of

3) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 2

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

-1 S

igm

a 1

7.92

0.

00

0.12

50

914

3804

1.

1788

1.

1713

0.

467

2 7.

91

7.92

0.

1250

88

8 39

36

1.59

36

1.17

13

0.46

8 3

7.92

15

.83

0.12

50

876

3899

1.

6751

0.

9829

0.

467

4 7.

91

23.7

5 0.

1250

89

1 40

40

1.94

69

0.98

29

0.46

7 5

8.58

31

.66

0.12

50

885

4089

2.

2086

0.

9829

0.

468

6 8.

58

40.2

4 0.

1250

95

6 42

90

2.34

56

0.98

29

0.46

9 7

8.58

48

.82

0.12

50

1000

44

97

2.42

14

0.98

29

0.46

9 8

8.58

57

.40

0.12

50

1017

46

11

2.44

99

0.98

29

0.46

9 9

8.58

65

.98

0.12

50

1067

47

92

2.42

62

0.98

29

0.47

0 10

8.

58

74.5

6 0.

1250

10

93

4976

2.

4137

0.

9829

0.

470

11

9.38

83

.14

0.12

50

1072

48

90

1.93

39

0.78

36

0.47

0 12

9.

37

92.5

2 0.

1250

11

02

5020

1.

9649

0.

7836

0.

470

13

9.38

10

1.89

0.

1250

11

07

5097

2.

0377

0.

7836

0.

470

14

9.37

11

1.27

0.

1250

11

45

5241

2.

0540

0.

7836

0.

470

15

9.38

12

0.64

0.

1250

11

84

5416

2.

0910

0.

7836

0.

470

16

9.37

13

0.02

0.

1250

12

14

5561

2.

0402

0.

7836

0.

470

17

10.0

0 13

9.39

0.

1313

12

14

5578

2.

1015

0.

7836

0.

470

18

10.0

0 14

9.39

0.

1313

12

73

5789

2.

1190

0.

7836

0.

470

19

10.0

0 15

9.39

0.

1313

12

71

5785

2.

0035

0.

7836

0.

470

20

10.0

0 16

9.40

0.

1313

12

73

5849

2.

0512

0.

7836

0.

470

21

10.0

0 17

9.40

0.

1313

13

15

5964

2.

0463

0.

7836

0.

470

22

10.6

0 18

9.39

0.

1313

12

96

5955

2.

0554

0.

7836

0.

470

23

164.

1 20

0.00

0.

1313

19

09

6265

0.

5000

0.

5000

0.

449

24

164.

1 36

4.05

0.

1344

32

81

8924

0.

5000

0.

5000

0.

422

25

164.

1 52

8.1

0.14

00

4921

11

240

0.50

00

0.50

00

0.38

1 26

16

4.1

692.

2 0.

1438

65

62

1427

0 0.

5000

0.

5000

0.

366

27

164.

1 85

6.2

0.15

00

8203

15

420

0.25

00

0.25

00

0.30

3 28

32

81

1020

0.

1575

92

85

1608

0 0.

0005

0.

0005

0.

250

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-33

Tab

le 5

.2-4

(S

hee

t 3

of

3) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 2

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

+1

Sig

ma

1 7.

92

0.00

0.

1250

16

03

6490

2.

2693

1.

2237

0.

470

2 7.

91

7.92

0.

1250

16

54

6794

3.

6072

1.

2237

0.

474

3 7.

92

15.8

3 0.

1250

16

68

6759

3.

7039

1.

0265

0.

474

4 7.

91

23.7

5 0.

1250

16

83

6859

3.

8673

1.

0265

0.

475

5 8.

58

31.6

6 0.

1250

15

85

6545

4.

3499

1.

0265

0.

476

6 8.

58

40.2

4 0.

1250

15

88

6744

4.

3547

1.

0265

0.

475

7 8.

58

48.8

2 0.

1250

15

90

6795

4.

4932

1.

0265

0.

476

8 8.

58

57.4

0 0.

1250

16

13

6904

4.

7211

1.

0265

0.

476

9 8.

58

65.9

8 0.

1250

16

11

6968

4.

9059

1.

0265

0.

476

10

8.58

74

.56

0.12

50

1656

71

14

4.98

46

1.02

65

0.47

6 11

9.

38

83.1

4 0.

1250

16

25

7002

3.

7750

0.

8150

0.

476

12

9.37

92

.52

0.12

50

1674

72

14

3.69

88

0.81

50

0.47

6 13

9.

38

101.

89

0.12

50

1703

73

12

3.67

79

0.81

50

0.47

6 14

9.

37

111.

27

0.12

50

1736

74

86

3.64

47

0.81

50

0.47

6 15

9.

38

120.

64

0.12

50

1767

76

17

3.56

84

0.81

50

0.47

6 16

9.

37

130.

02

0.12

50

1837

78

83

3.53

52

0.81

50

0.47

6 17

10

.00

139.

39

0.13

13

1818

77

88

3.42

42

0.81

50

0.47

6 18

10

.00

149.

39

0.13

13

1743

75

56

3.53

61

0.81

50

0.47

6 19

10

.00

159.

39

0.13

13

1789

77

50

3.83

57

0.81

50

0.47

6 20

10

.00

169.

40

0.13

13

1771

76

51

3.91

28

0.81

50

0.47

7 21

10

.00

179.

40

0.13

13

1838

79

89

3.76

81

0.81

50

0.47

6 22

10

.60

189.

39

0.13

13

1826

79

05

3.94

21

0.81

50

0.47

7 23

16

4.1

200.

00

0.13

13

3148

10

327

0.50

00

0.50

00

0.44

9 24

16

4.1

364.

05

0.13

44

3281

89

24

0.50

00

0.50

00

0.42

2 25

16

4.1

528.

1 0.

1400

49

21

1124

0 0.

5000

0.

5000

0.

381

26

164.

1 69

2.2

0.14

38

6562

14

270

0.50

00

0.50

00

0.36

6 27

16

4.1

856.

2 0.

1500

82

03

1542

0 0.

2500

0.

2500

0.

303

28

3281

10

20

0.15

75

9285

16

080

0.00

05

0.00

05

0.25

0

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-34

Tab

le 5

.2-5

S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 5

00 f

t (S

hee

t 1

of

6)

T

hick

nes

s T

op-D

ept

h U

nit

Wei

ght

Vs

Vp

Vs

Dam

p.V

p D

amp.

Laye

r [ft

] [ft

] kc

f ft/

sec

ft/se

c %

%

Poi

sson

R

atio

Med

ian

1 7.

92

0.00

0.

1250

11

73

5068

1.

6326

1.

1975

0.

472

2 7.

91

7.92

0.

1250

11

35

5106

2.

4771

1.

1975

0.

474

3 7.

92

15.8

3 0.

1250

12

02

5230

2.

4484

1.

0042

0.

472

4 7.

91

23.7

5 0.

1250

12

52

5492

2.

6407

1.

0042

0.

472

5 8.

58

31.6

6 0.

1250

12

70

5472

2.

8359

1.

0045

0.

471

6 8.

58

40.2

4 0.

1250

13

08

5662

2.

9301

1.

0045

0.

472

7 8.

58

48.8

2 0.

1250

13

39

5809

3.

0151

1.

0045

0.

472

8 8.

58

57.4

0 0.

1250

13

21

5778

3.

2180

1.

0045

0.

472

9 8.

58

65.9

8 0.

1250

13

24

5820

3.

3514

1.

0045

0.

472

10

8.58

74

.56

0.12

50

1330

58

79

3.45

26

1.00

45

0.47

3 11

9.

38

83.1

4 0.

1250

13

84

6084

2.

5318

0.

7992

0.

473

12

9.37

92

.52

0.12

50

1392

61

39

2.60

73

0.79

92

0.47

3 13

9.

38

101.

89

0.12

50

1400

61

99

2.67

46

0.79

92

0.47

3 14

9.

37

111.

27

0.12

50

1409

62

55

2.70

42

0.79

92

0.47

3 15

9.

38

120.

64

0.12

50

1451

64

27

2.69

72

0.79

92

0.47

3 16

9.

37

130.

02

0.12

50

1443

64

14

2.77

38

0.79

92

0.47

3 17

10

.00

139.

39

0.13

13

1461

64

86

2.70

82

0.79

92

0.47

3 18

10

.00

149.

39

0.13

13

1479

65

67

2.73

15

0.79

92

0.47

3 19

10

.00

159.

39

0.13

13

1498

66

51

2.74

21

0.79

92

0.47

3 20

10

.00

169.

40

0.13

13

1514

67

24

2.75

12

0.79

92

0.47

3 21

10

.00

179.

40

0.13

13

1527

67

88

2.76

86

0.79

92

0.47

3 22

10

.00

189.

39

0.13

13

1565

69

57

2.74

46

0.79

92

0.47

3 23

10

.60

199.

39

0.13

13

1592

70

70

2.73

45

0.79

92

0.47

3 24

10

.60

209.

99

0.13

13

1636

70

29

2.42

38

0.70

33

0.47

1 25

11

.50

220.

59

0.13

13

1628

70

13

2.47

37

0.70

33

0.47

1 26

11

.50

232.

09

0.13

13

1628

70

27

2.50

87

0.70

33

0.47

1 27

17

.67

243.

59

0.13

13

1631

70

47

2.54

10

0.70

33

0.47

2 28

17

.67

261.

26

0.13

13

1658

71

70

2.54

27

0.70

33

0.47

2

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-35

Tab

le 5

.2-5

(S

hee

t 2

of

6) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 5

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

Med

ian

(Con

tinue

d)

29

17.6

7 27

8.93

0.

1313

16

47

7142

2.

6022

0.

7033

0.

4717

30

18.2

5 29

6.60

0.

1313

16

61

7209

2.

6359

0.

7033

0.

4718

31

18.2

5 31

4.84

0.

1313

17

24

7469

2.

5816

0.

7033

0.

4717

32

18.2

5 33

3.09

0.

1313

17

09

7421

2.

6492

0.

7033

0.

4718

33

18.2

5 35

1.34

0.

1313

17

21

7482

2.

6695

0.

7033

0.

4719

34

20.0

0 36

9.59

0.

1313

17

98

7772

2.

5837

0.

7033

0.

4716

35

20.0

0 38

9.59

0.

1313

18

08

7820

2.

6013

0.

7033

0.

4717

36

20.0

0 40

9.59

0.

1313

18

39

7956

2.

5878

0.

7033

0.

4716

37

20.0

0 42

9.59

0.

1313

18

43

7983

2.

6178

0.

7033

0.

4717

38

20.0

0 44

9.60

0.

1313

18

10

7869

2.

6963

0.

7033

0.

4719

39

20.0

0 46

9.60

0.

1313

18

17

7908

2.

7143

0.

7033

0.

4720

40

10.4

0 48

9.60

0.

1313

17

76

7768

2.

7968

0.

7033

0.

4722

41

164.

1 50

0.00

0.

1313

23

94

7856

0.

5000

0.

5000

0.

4488

42

164.

1 66

4.05

0.

1344

32

81

8924

0.

5000

0.

5000

0.

4219

43

164.

1 82

8.10

0.

1400

49

21

1124

0 0.

5000

0.

5000

0.

3814

44

164.

1 99

2.15

0.

1438

65

62

1427

0 0.

5000

0.

5000

0.

3659

45

164.

1 11

56

0.15

00

8203

15

420

0.25

00

0.25

00

0.30

2746

32

81

1320

0.

1575

92

85

1608

0 0.

0005

0.

0005

0.

2499

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-36

Tab

le 5

.2-5

(S

hee

t 3

of

6) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 5

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

-1 S

igm

a 1

7.92

0.

00

0.12

50

907

3953

1.

2197

1.

1743

0.

471

2 7.

91

7.92

0.

1250

85

3 39

32

1.84

67

1.17

43

0.47

2 3

7.92

15

.83

0.12

50

879

4021

1.

6539

0.

9838

0.

468

4 7.

91

23.7

5 0.

1250

95

2 43

80

1.90

97

0.98

38

0.46

9 5

8.58

31

.66

0.12

50

1006

45

46

2.10

45

0.98

29

0.46

8 6

8.58

40

.24

0.12

50

1073

48

73

2.09

86

0.98

29

0.46

8 7

8.58

48

.82

0.12

50

1127

50

63

2.19

40

0.98

29

0.46

8 8

8.58

57

.40

0.12

50

1115

50

41

2.45

77

0.98

29

0.46

9 9

8.58

65

.98

0.12

50

1111

50

44

2.43

60

0.98

29

0.46

9 10

8.

58

74.5

6 0.

1250

11

09

5100

2.

5430

0.

9829

0.

469

11

9.38

83

.14

0.12

50

1156

52

16

1.84

74

0.78

36

0.47

0 12

9.

37

92.5

2 0.

1250

11

64

5254

1.

9130

0.

7836

0.

470

13

9.38

10

1.89

0.

1250

11

74

5348

1.

9269

0.

7836

0.

470

14

9.37

11

1.27

0.

1250

11

66

5354

1.

9255

0.

7836

0.

470

15

9.38

12

0.64

0.

1250

12

01

5460

1.

9267

0.

7836

0.

470

16

9.37

13

0.02

0.

1250

12

11

5528

2.

0749

0.

7836

0.

470

17

10.0

0 13

9.39

0.

1313

12

16

5582

2.

0152

0.

7836

0.

470

18

10.0

0 14

9.39

0.

1313

12

36

5652

2.

0447

0.

7836

0.

470

19

10.0

0 15

9.39

0.

1313

12

62

5731

2.

0311

0.

7836

0.

470

20

10.0

0 16

9.40

0.

1313

12

68

5754

2.

0959

0.

7836

0.

470

21

10.0

0 17

9.40

0.

1313

12

66

5761

2.

0751

0.

7836

0.

470

22

10.0

0 18

9.39

0.

1313

13

16

6029

2.

0930

0.

7836

0.

470

23

10.6

0 19

9.39

0.

1313

13

41

6100

2.

0017

0.

7836

0.

470

24

10.6

0 20

9.99

0.

1313

13

94

6086

1.

6607

0.

6859

0.

469

25

11.5

0 22

0.59

0.

1313

13

80

6080

1.

6809

0.

6859

0.

469

26

11.5

0 23

2.09

0.

1313

13

86

6121

1.

7608

0.

6859

0.

469

27

17.6

7 24

3.59

0.

1313

13

90

6134

1.

7547

0.

6859

0.

469

28

17.6

7 26

1.26

0.

1313

13

97

6208

1.

7655

0.

6859

0.

469

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-37

Tab

le 5

.2-5

(S

hee

t 4

of

6) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 5

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

-1 S

igm

a (C

ontin

ued)

29

17

.67

278.

93

0.13

13

1375

61

36

1.82

78

0.68

59

0.46

8830

18

.25

296.

60

0.13

13

1430

63

56

1.90

99

0.68

59

0.46

9031

18

.25

314.

84

0.13

13

1502

67

01

1.89

53

0.68

59

0.46

8832

18

.25

333.

09

0.13

13

1503

67

11

1.93

12

0.68

59

0.46

9033

18

.25

351.

34

0.13

13

1522

68

23

1.95

81

0.68

59

0.46

9034

20

.00

369.

59

0.13

13

1613

70

25

1.90

38

0.68

59

0.46

9235

20

.00

389.

59

0.13

13

1610

70

02

1.88

92

0.68

59

0.46

9336

20

.00

409.

59

0.13

13

1633

71

36

1.84

21

0.68

59

0.46

9237

20

.00

429.

59

0.13

13

1647

72

32

1.87

24

0.68

59

0.46

9238

20

.00

449.

60

0.13

13

1618

71

49

1.95

85

0.68

59

0.46

9339

20

.00

469.

60

0.13

13

1626

71

94

1.99

87

0.68

59

0.46

9340

10

.40

489.

60

0.13

13

1580

71

20

2.02

82

0.68

59

0.46

9341

16

4.1

500.

00

0.13

13

2040

66

92

0.50

00

0.50

00

0.44

8842

16

4.1

664.

05

0.13

44

3281

89

24

0.50

00

0.50

00

0.42

1943

16

4.1

828.

10

0.14

00

4921

11

240

0.50

00

0.50

00

0.38

1444

16

4.1

992.

15

0.14

38

6562

14

270

0.50

00

0.50

00

0.36

5945

16

4.1

1156

0.

1500

82

03

1542

0 0.

2500

0.

2500

0.

3027

46

3281

13

20

0.15

75

9285

16

080

0.00

05

0.00

05

0.24

99

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-38

Tab

le 5

.2-5

(S

hee

t 5

of

6) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 5

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

+1

Sig

ma

1 7.

92

0.00

0.

1250

15

17

6497

2.

1853

1.

2212

0.

473

2 7.

91

7.92

0.

1250

15

10

6630

3.

3226

1.

2212

0.

476

3 7.

92

15.8

3 0.

1250

16

43

6803

3.

6246

1.

0251

0.

475

4 7.

91

23.7

5 0.

1250

16

46

6887

3.

6517

1.

0251

0.

476

5 8.

58

31.6

6 0.

1250

16

02

6587

3.

8215

1.

0265

0.

475

6 8.

58

40.2

4 0.

1250

15

94

6577

4.

0912

1.

0265

0.

475

7 8.

58

48.8

2 0.

1250

15

91

6665

4.

1434

1.

0265

0.

475

8 8.

58

57.4

0 0.

1250

15

65

6623

4.

2137

1.

0265

0.

476

9 8.

58

65.9

8 0.

1250

15

78

6716

4.

6108

1.

0265

0.

476

10

8.58

74

.56

0.12

50

1595

67

78

4.68

74

1.02

65

0.47

6 11

9.

38

83.1

4 0.

1250

16

57

7097

3.

4697

0.

8150

0.

475

12

9.37

92

.52

0.12

50

1665

71

74

3.55

36

0.81

50

0.47

6 13

9.

38

101.

89

0.12

50

1669

71

84

3.71

25

0.81

50

0.47

6 14

9.

37

111.

27

0.12

50

1702

73

09

3.79

78

0.81

50

0.47

6 15

9.

38

120.

64

0.12

50

1752

75

67

3.77

58

0.81

50

0.47

6 16

9.

37

130.

02

0.12

50

1720

74

42

3.70

81

0.81

50

0.47

6 17

10

.00

139.

39

0.13

13

1756

75

37

3.63

95

0.81

50

0.47

6 18

10

.00

149.

39

0.13

13

1769

76

30

3.64

89

0.81

50

0.47

6 19

10

.00

159.

39

0.13

13

1778

77

19

3.70

21

0.81

50

0.47

6 20

10

.00

169.

40

0.13

13

1807

78

57

3.61

14

0.81

50

0.47

6 21

10

.00

179.

40

0.13

13

1841

79

99

3.69

39

0.81

50

0.47

6 22

10

.00

189.

39

0.13

13

1860

80

29

3.59

89

0.81

50

0.47

6 23

10

.60

199.

39

0.13

13

1890

81

94

3.73

54

0.81

50

0.47

6 24

10

.60

209.

99

0.13

13

1921

81

19

3.53

76

0.72

11

0.47

4 25

11

.50

220.

59

0.13

13

1920

80

90

3.64

04

0.72

11

0.47

4 26

11

.50

232.

09

0.13

13

1914

80

67

3.57

43

0.72

11

0.47

4 27

17

.67

243.

59

0.13

13

1913

80

96

3.67

98

0.72

11

0.47

4 28

17

.67

261.

26

0.13

13

1968

82

81

3.66

19

0.72

11

0.47

4

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-39

Tab

le 5

.2-5

(S

hee

t 6

of

6) S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

70, 5

00 f

t

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

-1 S

igm

a (C

ontin

ued)

29

17

.67

278.

93

0.13

13

1972

83

13

3.70

48

0.72

11

0.47

4730

18

.25

296.

60

0.13

13

1930

81

76

3.63

79

0.72

11

0.47

4631

18

.25

314.

84

0.13

13

1980

83

24

3.51

64

0.72

11

0.47

4532

18

.25

333.

09

0.13

13

1942

82

06

3.63

40

0.72

11

0.47

4733

18

.25

351.

34

0.13

13

1947

82

06

3.63

94

0.72

11

0.47

4834

20

.00

369.

59

0.13

13

2005

85

99

3.50

64

0.72

11

0.47

4035

20

.00

389.

59

0.13

13

2030

87

35

3.58

17

0.72

11

0.47

4036

20

.00

409.

59

0.13

13

2072

88

71

3.63

52

0.72

11

0.47

4137

20

.00

429.

59

0.13

13

2061

88

12

3.65

98

0.72

11

0.47

4338

20

.00

449.

60

0.13

13

2025

86

63

3.71

21

0.72

11

0.47

4639

20

.00

469.

60

0.13

13

2031

86

93

3.68

61

0.72

11

0.47

4640

10

.40

489.

60

0.13

13

1997

84

74

3.85

65

0.72

11

0.47

5241

16

4.1

500.

00

0.13

13

2811

92

22

0.50

00

0.50

00

0.44

8842

16

4.1

664.

05

0.13

44

3281

89

24

0.50

00

0.50

00

0.42

1943

16

4.1

828.

10

0.14

00

4921

11

240

0.50

00

0.50

00

0.38

1444

16

4.1

992.

15

0.14

38

6562

14

270

0.50

00

0.50

00

0.36

5945

16

4.1

1156

0.

1500

82

03

1542

0 0.

2500

0.

2500

0.

3027

46

3281

13

20

0.15

75

9285

16

080

0.00

05

0.00

05

0.24

99

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-40

Tab

le 5

.2-6

D

elet

ed

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-41

Tab

le 5

.2-7

D

elet

ed

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-42

Tab

le 5

.2-8

S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 5

60, 5

00 f

t (S

hee

t 1

of

6)

T

hick

nes

s T

op-D

ept

h U

nit

Wei

ght

Vs

Vp

Vs

Dam

p.V

p D

amp.

Laye

r [ft

] [ft

] kc

f ft/

sec

ft/se

c %

%

Poi

sson

R

atio

Med

ian

1 6.

00

0.00

0.

1250

11

06

4791

2.

0672

1.

4005

0.

472

2 6.

50

6.00

0.

1250

13

69

5042

2.

5977

1.

4006

0.

460

3 6.

50

12.5

0 0.

1250

13

28

5147

3.

1927

1.

4006

0.

464

4 11

.00

19.0

0 0.

1250

14

76

5021

2.

4676

1.

1954

0.

452

5 10

.00

30.0

0 0.

1313

17

98

5601

2.

2832

1.

1944

0.

442

6 10

.00

40.0

0 0.

1313

17

79

5653

2.

4900

1.

1946

0.

445

7 18

.00

50.0

0 0.

1313

20

47

5851

2.

0452

1.

0088

0.

430

8 14

.50

68.0

0 0.

1313

21

74

5900

2.

0804

1.

0097

0.

421

9 14

.50

82.5

0 0.

1313

21

61

6103

2.

1957

1.

0091

0.

428

10

20.0

0 97

.00

0.13

13

2182

58

77

2.28

03

1.01

00

0.42

0 11

20

.00

117.

00

0.13

13

2168

60

69

1.78

17

0.79

77

0.42

6 12

22

.67

137.

01

0.13

13

2412

64

25

1.70

06

0.79

74

0.41

8 13

22

.67

159.

67

0.13

13

2401

66

38

1.76

36

0.79

76

0.42

4 14

22

.67

182.

34

0.13

13

2391

68

30

1.82

04

0.79

78

0.43

0 15

21

.00

205.

00

0.13

13

2834

76

62

1.63

52

0.79

76

0.42

1 16

21

.00

226.

00

0.13

13

2826

77

46

1.67

37

0.79

76

0.42

3 17

12

.50

247.

00

0.13

13

2877

76

33

1.48

48

0.70

71

0.41

7 18

12

.50

259.

50

0.13

13

2874

76

19

1.50

08

0.70

71

0.41

7 19

12

.50

272.

00

0.13

13

2871

75

97

1.51

60

0.70

71

0.41

7 20

12

.50

284.

50

0.13

13

2869

75

84

1.53

06

0.70

72

0.41

6 21

12

.50

297.

00

0.13

13

2866

75

68

1.54

44

0.70

72

0.41

6 22

12

.50

309.

50

0.13

13

2864

77

13

1.55

75

0.70

70

0.42

0 23

12

.50

322.

01

0.13

13

2862

77

53

1.57

00

0.70

69

0.42

1 24

12

.50

334.

51

0.13

13

2860

77

40

1.58

20

0.70

69

0.42

1 25

12

.50

347.

01

0.13

13

2857

77

18

1.59

34

0.70

70

0.42

0 26

12

.50

359.

51

0.13

13

2856

76

96

1.60

48

0.70

70

0.42

0 27

12

.50

372.

01

0.13

13

2853

77

03

1.61

59

0.70

70

0.42

0 28

12

.50

384.

51

0.13

13

2852

78

31

1.62

64

0.70

68

0.42

3

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-43

Tab

le 5

.2-8

(S

hee

t 2

of

6)

Str

ain

Co

mp

atib

le P

rop

erti

es f

or

Pro

file

560

, 500

ft

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

Med

ian

(Con

tinue

s)

29

12.5

0 39

7.01

0.

1313

28

50

7869

1.

6368

0.

7067

0.

4243

30

12.5

0 40

9.51

0.

1313

28

48

7847

1.

6466

0.

7068

0.

4240

31

12.5

0 42

2.01

0.

1313

28

46

7825

1.

6561

0.

7068

0.

4236

32

12.5

0 43

4.51

0.

1313

28

45

7804

1.

6654

0.

7068

0.

4232

33

12.5

0 44

7.02

0.

1313

28

43

7782

1.

6743

0.

7068

0.

4228

34

12.5

0 45

9.52

0.

1313

28

42

7896

1.

6830

0.

7067

0.

4254

35

13.1

2 47

2.02

0.

1313

28

40

8011

1.

6916

0.

7065

0.

4279

36

14.8

6 48

5.14

0.

1313

28

39

7988

1.

7001

0.

7065

0.

4275

37

164.

05

500.

00

0.13

44

3303

89

85

0.50

00

0.50

00

0.42

1938

16

4.05

66

4.05

0.

1400

49

21

1124

0 0.

5000

0.

5000

0.

3814

39

164.

05

828.

10

0.14

38

6562

14

270

0.50

00

0.50

00

0.36

5940

16

4.05

99

2.15

0.

1500

82

03

1542

0 0.

2500

0.

2500

0.

3027

41

3281

.0

1156

.20

0.15

75

9285

16

080

0.00

50

0.00

50

0.24

99

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-44

Tab

le 5

.2-8

(S

hee

t 3

of

6)

Str

ain

Co

mp

atib

le P

rop

erti

es f

or

Pro

file

560

, 500

ft

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

-1 S

igm

a 1

6.00

0.

00

0.12

50

843

3709

1.

4737

1.

3690

0.

471

2 6.

50

6.00

0.

1250

96

7 36

98

1.74

87

1.35

50

0.45

6 3

6.50

12

.50

0.12

50

925

3775

2.

1309

1.

3567

0.

460

4 11

.00

19.0

0 0.

1250

11

35

3973

1.

7574

1.

1551

0.

448

5 10

.00

30.0

0 0.

1313

14

25

4577

1.

6637

1.

1475

0.

437

6 10

.00

40.0

0 0.

1313

14

04

4620

1.

7947

1.

1485

0.

439

7 18

.00

50.0

0 0.

1313

17

54

5076

1.

5605

0.

9645

0.

426

8 14

.50

68.0

0 0.

1313

18

56

5131

1.

6262

0.

9604

0.

416

9 14

.50

82.5

0 0.

1313

18

43

5307

1.

7176

0.

9630

0.

423

10

20.0

0 97

.00

0.13

13

1807

49

55

1.72

62

0.95

90

0.41

4 11

20

.00

117.

00

0.13

13

1783

51

17

1.32

93

0.76

29

0.42

0 12

22

.67

137.

01

0.13

13

1984

53

89

1.31

18

0.75

97

0.41

1 13

22

.67

159.

67

0.13

13

1974

55

67

1.36

14

0.76

22

0.41

8 14

22

.67

182.

34

0.13

13

1966

57

29

1.40

58

0.76

44

0.42

4 15

21

.00

205.

00

0.13

13

2592

70

47

1.27

27

0.76

13

0.41

6 16

21

.00

226.

00

0.13

13

2585

71

24

1.30

33

0.76

22

0.41

8 17

12

.50

247.

00

0.13

13

2630

70

21

1.08

38

0.66

65

0.41

3 18

12

.50

259.

50

0.13

13

2627

70

08

1.09

58

0.66

64

0.41

3 19

12

.50

272.

00

0.13

13

2625

69

88

1.10

72

0.66

62

0.41

2 20

12

.50

284.

50

0.13

13

2622

69

76

1.11

81

0.66

60

0.41

2 21

12

.50

297.

00

0.13

13

2620

69

61

1.12

85

0.66

59

0.41

2 22

12

.50

309.

50

0.13

13

2617

70

94

1.13

83

0.66

72

0.41

5 23

12

.50

322.

01

0.13

13

2615

71

31

1.14

77

0.66

75

0.41

7 24

12

.50

334.

51

0.13

13

2613

71

19

1.15

67

0.66

74

0.41

6 25

12

.50

347.

01

0.13

13

2611

70

98

1.16

53

0.66

72

0.41

6 26

12

.50

359.

51

0.13

13

2608

70

78

1.17

36

0.66

70

0.41

5 27

12

.50

372.

01

0.13

13

2606

70

85

1.18

15

0.66

71

0.41

6 28

12

.50

384.

51

0.13

13

2604

72

03

1.18

90

0.66

81

0.41

9

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-45

Tab

le 5

.2-8

(S

hee

t 4

of

6)

Str

ain

Co

mp

atib

le P

rop

erti

es f

or

Pro

file

560

, 500

ft

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

-1 S

igm

a (C

ontin

ues)

29

12

.50

397.

01

0.13

13

2602

72

38

1.19

64

0.66

85

0.41

9730

12

.50

409.

51

0.13

13

2601

72

18

1.20

34

0.66

83

0.41

9331

12

.50

422.

01

0.13

13

2599

71

98

1.21

01

0.66

81

0.41

8832

12

.50

434.

51

0.13

13

2597

71

78

1.21

67

0.66

79

0.41

8333

12

.50

447.

02

0.13

13

2595

71

58

1.22

31

0.66

77

0.41

7834

12

.50

459.

52

0.13

13

2593

72

63

1.22

93

0.66

87

0.42

0635

13

.12

472.

02

0.13

13

2592

73

69

1.23

54

0.66

96

0.42

3336

14

.86

485.

14

0.13

13

2590

73

47

1.24

15

0.66

94

0.42

2837

16

4.05

50

0.00

0.

1344

30

02

8164

0.

5000

0.

5000

0.

4218

38

164.

05

664.

05

0.14

00

4921

11

240

0.50

00

0.50

00

0.38

1439

16

4.05

82

8.10

0.

1438

65

62

1427

0 0.

5000

0.

5000

0.

3659

40

164.

05

992.

15

0.15

00

8203

15

420

0.25

00

0.25

00

0.30

2741

32

81.0

11

56.2

0 0.

1575

92

85

1608

0 0.

0050

0.

0050

0.

2499

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-46

Tab

le 5

.2-8

(S

hee

t 5

of

6)

Str

ain

Co

mp

atib

le P

rop

erti

es f

or

Pro

file

560

, 500

ft

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

+1

Sig

ma

1 6.

00

0.00

0.

1250

14

52

6189

2.

8998

1.

4327

0.

473

2 6.

50

6.00

0.

1250

19

38

6875

3.

8589

1.

4479

0.

464

3 6.

50

12.5

0 0.

1250

19

07

7018

4.

7837

1.

4460

0.

469

4 11

.00

19.0

0 0.

1250

19

20

6346

3.

4648

1.

2371

0.

457

5 10

.00

30.0

0 0.

1313

22

67

6853

3.

1332

1.

2433

0.

447

6 10

.00

40.0

0 0.

1313

22

53

6916

3.

4545

1.

2426

0.

450

7 18

.00

50.0

0 0.

1313

23

90

6743

2.

6803

1.

0551

0.

434

8 14

.50

68.0

0 0.

1313

25

47

6785

2.

6613

1.

0614

0.

427

9 14

.50

82.5

0 0.

1313

25

35

7018

2.

8069

1.

0575

0.

433

10

20.0

0 97

.00

0.13

13

2634

69

70

3.01

24

1.06

38

0.42

6 11

20

.00

117.

00

0.13

13

2637

71

99

2.38

79

0.83

40

0.43

3 12

22

.67

137.

01

0.13

13

2931

76

60

2.20

46

0.83

70

0.42

4 13

22

.67

159.

67

0.13

13

2919

79

13

2.28

47

0.83

47

0.43

1 14

22

.67

182.

34

0.13

13

2908

81

43

2.35

73

0.83

27

0.43

6 15

21

.00

205.

00

0.13

13

3099

83

30

2.10

09

0.83

55

0.42

5 16

21

.00

226.

00

0.13

13

3090

84

21

2.14

92

0.83

48

0.42

8 17

12

.50

247.

00

0.13

13

3147

82

99

2.03

42

0.75

02

0.42

1 18

12

.50

259.

50

0.13

13

3144

82

84

2.05

54

0.75

03

0.42

1 19

12

.50

272.

00

0.13

13

3141

82

60

2.07

57

0.75

06

0.42

1 20

12

.50

284.

50

0.13

13

3139

82

46

2.09

51

0.75

08

0.42

1 21

12

.50

297.

00

0.13

13

3136

82

28

2.11

34

0.75

10

0.42

1 22

12

.50

309.

50

0.13

13

3134

83

86

2.13

10

0.74

91

0.42

4 23

12

.50

322.

01

0.13

13

3132

84

29

2.14

77

0.74

86

0.42

5 24

12

.50

334.

51

0.13

13

3130

84

15

2.16

36

0.74

88

0.42

5 25

12

.50

347.

01

0.13

13

3128

83

91

2.17

88

0.74

91

0.42

5 26

12

.50

359.

51

0.13

13

3126

83

67

2.19

46

0.74

93

0.42

5 27

12

.50

372.

01

0.13

13

3124

83

75

2.21

00

0.74

92

0.42

5 28

12

.50

384.

51

0.13

13

3123

85

14

2.22

49

0.74

76

0.42

8

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-47

Tab

le 5

.2-8

(S

hee

t 6

of

6)

Str

ain

Co

mp

atib

le P

rop

erti

es f

or

Pro

file

560

, 500

ft

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

+1

Sig

ma

(Con

tinue

s)

29

12.5

0 39

7.01

0.

1313

31

21

8556

2.

2393

0.

7472

0.

4290

30

12.5

0 40

9.51

0.

1313

31

19

8532

2.

2530

0.

7475

0.

4287

31

12.5

0 42

2.01

0.

1313

31

18

8508

2.

2665

0.

7477

0.

4284

32

12.5

0 43

4.51

0.

1313

31

16

8484

2.

2794

0.

7480

0.

4281

33

12.5

0 44

7.02

0.

1313

31

15

8461

2.

2920

0.

7482

0.

4278

34

12.5

0 45

9.52

0.

1313

31

14

8585

2.

3041

0.

7468

0.

4303

35

13.1

2 47

2.02

0.

1313

31

12

8710

2.

3164

0.

7455

0.

4326

36

14.8

6 48

5.14

0.

1313

31

11

8685

2.

3281

0.

7458

0.

4323

37

164.

05

500.

00

0.13

44

3636

98

89

0.50

00

0.50

00

0.42

1938

16

4.05

66

4.05

0.

1400

49

21

1124

0 0.

5000

0.

5000

0.

3814

39

164.

05

828.

10

0.14

38

6562

14

270

0.50

00

0.50

00

0.36

5940

16

4.05

99

2.15

0.

1500

82

03

1542

0 0.

2500

0.

2500

0.

3027

41

3281

.0

1156

.20

0.15

75

9285

16

080

0.00

50

0.00

50

0.24

99

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-48

Tab

le 5

.2-9

S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 9

00, 1

00 f

t (S

hee

t 1

of

2)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

Med

ian

1 5.

00

0.00

0.

1250

15

64

4951

1.

5680

1.

4006

0.

445

2 7.

00

5.00

0.

1313

17

37

4741

1.

8670

1.

4002

0.

422

3 8.

00

12.0

0 0.

1313

21

69

5135

1.

9600

1.

3993

0.

391

4 9.

00

20.0

0 0.

1313

23

21

5617

1.

5550

1.

1906

0.

397

5 11

.00

29.0

0 0.

1313

29

72

7556

1.

4417

1.

1919

0.

408

6 13

.00

40.0

0 0.

1344

33

68

8409

1.

3962

1.

1915

0.

404

7 20

.00

53.0

0 0.

1344

40

34

9736

1.

2309

1.

0111

0.

396

8 23

.00

73.0

0 0.

1400

51

16

1170

9 1.

1550

1.

0122

0.

382

9 4.

00

96.0

0 0.

1425

54

31

1187

7 1.

1458

1.

0131

0.

368

10

164.

1 10

0.00

0.

1500

80

02

1504

5 0.

2500

0.

2500

0.

303

11

3281

26

4.05

0.

1575

92

85

1608

0 0.

0050

0.

0050

0.

250

-1 S

igm

a 1

5.00

0.

00

0.12

50

1008

32

26

1.17

56

1.34

52

0.44

4 2

7.00

5.

00

0.13

13

1262

35

08

1.42

39

1.32

51

0.41

9 3

8.00

12

.00

0.13

13

1702

40

92

1.36

26

1.30

05

0.38

5 4

9.00

20

.00

0.13

13

1830

44

69

1.10

13

1.11

94

0.39

3 5

11.0

0 29

.00

0.13

13

2305

58

92

1.12

26

1.12

77

0.40

6 6

13.0

0 40

.00

0.13

44

2488

62

49

1.08

24

1.12

52

0.40

2 7

20.0

0 53

.00

0.13

44

3132

76

22

0.93

36

0.95

37

0.39

4 8

23.0

0 73

.00

0.14

00

4180

95

84

0.89

00

0.94

88

0.38

1 9

25.0

0 96

.00

0.14

25

4472

98

08

0.90

44

0.94

40

0.36

6 10

34

.00

121.

00

0.14

38

5730

12

068

0.71

22

0.74

15

0.35

3 11

45

.00

155.

00

0.14

69

6068

12

365

0.71

27

0.73

74

0.34

0

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-49

Tab

le 5

.2-9

S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 9

00, 1

00 f

t (S

hee

t 2

of

2)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.La

yer

[ft]

[ft]

kcf

ft/se

c ft/

sec

%

%

Poi

sson

R

atio

+1

Sig

ma

1 5.

00

0.00

0.

1250

21

46

6738

2.

0739

1.

4581

0.

446

2 7.

00

5.00

0.

1313

22

16

5993

2.

4758

1.

4796

0.

425

3 8.

00

12.0

0 0.

1313

30

02

7011

2.

6655

1.

5056

0.

396

4 9.

00

20.0

0 0.

1313

31

80

7610

2.

0856

1.

2663

0.

401

5 11

.00

29.0

0 0.

1313

39

40

9917

1.

9805

1.

2597

0.

412

6 13

.00

40.0

0 0.

1344

42

36

1048

1 1.

8768

1.

2617

0.

408

7 20

.00

53.0

0 0.

1344

49

80

1195

6 1.

6236

1.

0719

0.

399

8 23

.00

73.0

0 0.

1400

61

10

1397

5 1.

5127

1.

0797

0.

383

9 4.

00

96.0

0 0.

1425

63

68

1391

6 1.

4837

1.

0873

0.

369

10

164.

1 10

0.00

0.

1500

10

687

2009

1 0.

2500

0.

2500

0.

303

11

3281

26

4.05

0.

1575

92

85

1608

0 0.

0050

0.

0050

0.

250

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-50

Tab

le 5

.2-1

0 S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 9

00, 2

00 f

t (S

hee

t 1

of

2)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.P

oiss

on

Rat

io

Laye

r [ft

] [ft

] kc

f ft/

sec

ft/se

c %

%

Med

ian

1 5.

00

0.00

0.

1250

14

28

4531

1.

6056

1.

4006

0.

445

2 7.

00

5.00

0.

1313

17

36

4749

1.

8777

1.

4002

0.

423

3 8.

00

12.0

0 0.

1313

22

83

5393

1.

8551

1.

3993

0.

391

4 9.

00

20.0

0 0.

1313

23

73

5734

1.

5053

1.

1906

0.

397

5 11

.00

29.0

0 0.

1313

28

54

7257

1.

4543

1.

1919

0.

408

6 13

.00

40.0

0 0.

1344

31

97

7990

1.

4410

1.

1915

0.

405

7 20

.00

53.0

0 0.

1344

39

40

9516

1.

2435

1.

0111

0.

397

8 23

.00

73.0

0 0.

1400

50

39

1153

7 1.

1623

1.

0122

0.

382

9 25

.00

96.0

0 0.

1425

53

28

1166

0 1.

1666

1.

0131

0.

368

10

34.0

0 12

1.00

0.

1438

66

37

1396

9 0.

9079

0.

7957

0.

354

11

45.0

0 15

5.00

0.

1469

68

56

1395

9 0.

9150

0.

7952

0.

341

12

164.

05

200.

00

0.15

00

8197

15

410

0.25

00

0.25

00

0.30

3 13

32

81.0

0 36

4.05

0.

1575

92

85

1608

0 0.

0050

0.

0050

0.

250

-1 S

igm

a 1

5.00

0.

00

0.12

50

1008

32

26

1.17

56

1.34

52

0.44

4 2

7.00

5.

00

0.13

13

1262

35

08

1.42

39

1.32

51

0.41

9 3

8.00

12

.00

0.13

13

1702

40

92

1.36

26

1.30

05

0.38

5 4

9.00

20

.00

0.13

13

1830

44

69

1.10

13

1.11

94

0.39

3 5

11.0

0 29

.00

0.13

13

2305

58

92

1.12

26

1.12

77

0.40

6 6

13.0

0 40

.00

0.13

44

2488

62

49

1.08

24

1.12

52

0.40

2 7

20.0

0 53

.00

0.13

44

3132

76

22

0.93

36

0.95

37

0.39

4 8

23.0

0 73

.00

0.14

00

4180

95

84

0.89

00

0.94

88

0.38

1 9

25.0

0 96

.00

0.14

25

4472

98

08

0.90

44

0.94

40

0.36

6 10

34

.00

121.

00

0.14

38

5730

12

068

0.71

22

0.74

15

0.35

3 11

45

.00

155.

00

0.14

69

6068

12

365

0.71

27

0.73

74

0.34

0 12

16

4.05

20

0.00

0.

1500

72

07

1354

9 0.

2500

0.

2500

0.

303

13

3281

.00

364.

05

0.15

75

9285

16

080

0.00

50

0.00

50

0.25

0

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-51

Tab

le 5

.2-1

0 S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 9

00, 2

00 f

t (S

hee

t 2

of

2)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.P

oiss

on

Rat

io

Laye

r [ft

] [ft

] kc

f ft/

sec

ft/se

c %

%

+1

Sig

ma

1 5.

00

0.00

0.

1250

20

22

6364

2.

1929

1.

4581

0.

446

2 7.

00

5.00

0.

1313

23

88

6431

2.

4762

1.

4796

0.

426

3 8.

00

12.0

0 0.

1313

30

63

7107

2.

5256

1.

5056

0.

396

4 9.

00

20.0

0 0.

1313

30

76

7357

2.

0577

1.

2663

0.

400

5 11

.00

29.0

0 0.

1313

35

35

8938

1.

8841

1.

2597

0.

411

6 13

.00

40.0

0 0.

1344

41

09

1021

8 1.

9185

1.

2617

0.

407

7 20

.00

53.0

0 0.

1344

49

56

1188

2 1.

6563

1.

0719

0.

399

8 23

.00

73.0

0 0.

1400

60

74

1388

7 1.

5180

1.

0797

0.

384

9 25

.00

96.0

0 0.

1425

63

49

1386

0 1.

5047

1.

0873

0.

370

10

34.0

0 12

1.00

0.

1438

76

87

1616

9 1.

1575

0.

8538

0.

355

11

45.0

0 15

5.00

0.

1469

77

46

1575

9 1.

1747

0.

8575

0.

342

12

164.

05

200.

00

0.15

00

9322

17

526

0.25

00

0.25

00

0.30

3 13

32

81.0

0 36

4.05

0.

1575

92

85

1608

0 0.

0050

0.

0050

0.

250

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-52

Tab

le 5

.2-1

1 S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

032,

100

ft

(Sh

eet

1 o

f 2)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.P

oiss

on

Rat

io

Laye

r [ft

] [ft

] kc

f ft/

sec

ft/se

c %

%

Med

ian

1 4.

17

0.00

0.

1400

49

06

9179

3.

2250

3.

1229

0.

300

2 4.

17

4.17

0.

1400

51

47

9549

3.

2250

3.

1208

0.

295

3 8.

33

8.33

0.

1400

53

93

9825

3.

2250

3.

1157

0.

284

4 8.

33

16.6

7 0.

1400

56

09

9964

3.

2250

3.

1082

0.

268

5 8.

33

25.0

0 0.

1400

63

15

1104

4 3.

2250

3.

1033

0.

257

6 6.

66

33.3

4 0.

1400

65

48

1134

3 3.

2250

3.

1002

0.

250

7 10

.01

40.0

0 0.

1400

71

26

1234

3 3.

1580

3.

1008

0.

250

8 16

.67

50.0

0 0.

1400

73

33

1270

1 3.

1580

3.

1008

0.

250

9 16

.67

66.6

7 0.

1400

77

46

1341

7 3.

1580

3.

1008

0.

250

10

16.7

83

.34

0.14

00

8128

14

077

3.15

80

3.10

08

0.25

0 11

32

81

100.

00

0.15

75

8599

16

794

0.00

0001

0.00

0001

0.32

2 -1

Sig

ma

1 4.

17

0.00

0.

1400

36

93

6909

1.

8632

2.

7247

0.

300

2 4.

17

4.17

0.

1400

39

99

7420

1.

8714

2.

7165

0.

295

3 8.

33

8.33

0.

1400

41

59

7578

1.

8975

2.

6973

0.

284

4 8.

33

16.6

7 0.

1400

43

81

7782

1.

9340

2.

6696

0.

268

5 8.

33

25.0

0 0.

1400

50

04

8751

1.

9419

2.

6516

0.

257

6 6.

66

33.3

4 0.

1400

53

25

9223

1.

9556

2.

6406

0.

250

7 10

.01

40.0

0 0.

1400

60

24

1043

5 2.

1982

2.

7293

0.

250

8 16

.67

50.0

0 0.

1400

62

74

1086

7 2.

2031

2.

7293

0.

250

9 16

.67

66.6

7 0.

1400

65

43

1133

3 2.

2121

2.

7293

0.

250

10

16.7

83

.34

0.14

00

7119

12

329

2.21

59

2.72

93

0.25

0 11

32

81

100.

00

0.15

75

6030

11

775

0.00

0001

0.00

0001

0.32

2

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-53

Tab

le 5

.2-1

1 S

trai

n C

om

pat

ible

Pro

per

ties

fo

r P

rofi

le 2

032,

100

ft

(+1

Sig

ma

Co

nti

nu

ed)

(Sh

eet

2 o

f 2)

Thi

ckne

ss

Top

-Dep

th

Uni

t W

eigh

t V

s V

p V

s D

amp.

Vp

Dam

p.P

oiss

on

Rat

io

Laye

r [ft

] [ft

] kc

f ft/

sec

ft/se

c %

%

+1

Sig

ma

1 4.

17

0.00

0.

1400

36

93

6909

1.

8632

2.

7247

0.

300

2 4.

17

4.17

0.

1400

39

99

7420

1.

8714

2.

7165

0.

295

3 8.

33

8.33

0.

1400

41

59

7578

1.

8975

2.

6973

0.

284

4 8.

33

16.6

7 0.

1400

43

81

7782

1.

9340

2.

6696

0.

268

5 8.

33

25.0

0 0.

1400

50

04

8751

1.

9419

2.

6516

0.

257

6 6.

66

33.3

4 0.

1400

53

25

9223

1.

9556

2.

6406

0.

250

7 10

.01

40.0

0 0.

1400

60

24

1043

5 2.

1982

2.

7293

0.

250

8 16

.67

50.0

0 0.

1400

62

74

1086

7 2.

2031

2.

7293

0.

250

9 16

.67

66.6

7 0.

1400

65

43

1133

3 2.

2121

2.

7293

0.

250

10

16.7

83

.34

0.14

00

7119

12

329

2.21

59

2.72

93

0.25

0 11

32

81

100.

00

0.15

75

6030

11

775

0.00

0001

0.00

0001

0.32

2

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

MU

AP

-100

01-N

P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-54

Tab

le 5

.2-1

2

Sh

ear

Co

lum

n F

req

uen

cies

of

To

p S

oil

Ful

l T

runc

ated

Pro

file

Dep

th

(ft)

F

requ

ency

(H

z)

Dep

th

(ft)

F

requ

ency

(Hz)

270-

500

500

0.8

460

0.9

270-

200

200

1.7

160

2.2

560-

500

500

1.2

460

1.4

900-

200

200

5.1

160

8.3

900-

100

100

7.7

60

17.8

2

032-

100

100

16.8

60

28

.1



0

40

80

120

160

200

240

280

320

360

400

440

480

0 500 1000 1500 2000 2500

Vs (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile

Shear Wave Velocity Profile 270-500

Figure 5.2-6 Strain Compatible Properties Computed for Profile 270, 500 ft Depth to Bedrock (Sheet 1 of 3)



0

40

80

120

160

200

240

280

320

360

400

440

480

0 2000 4000 6000 8000 10000

Vp (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile

Compression Wave Velocity Profile 270-500

Figure 5.2-6 Strain Compatible Properties Computed for Profile 270 500 ft Depth to Bedrock (Sheet 2 of 3)



0

40

80

120

160

200

240

280

320

360

400

440

480

0% 2% 4% 6% 8% 10%

Damping

Dep

th (

ft)

Median

16th Percentile

84th Percentile

Shear Wave Damping Profile 270-500




0

40

80

120

160

200

0 500 1000 1500 2000 2500

Vs (ft/sec)D

epth

(ft

)

Median

16th Percentile

84th Percentile


Figure 5.2-7 Strain Compatible Properties Computed for Profile 270

200 ft Depth to Bedrock (Sheet 1 of 3)



0

40

80

120

160

200

0 2000 4000 6000 8000 10000

Vp (ft/sec)D

epth

(ft

)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0% 2% 4% 6% 8% 10%

DampingD

epth

(ft

)

Median

16th Percentile

84th Percentile





Figure 5.2-8 Deleted



0

40

80

120

160

200

240

280

320

360

400

440

480

0 500 1000 1500 2000 2500 3000 3500

Vs (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile


Figure 5.2-9 Strain Compatible Properties Computed for Profile 560, 500 ft Depth to

Bedrock (Sheet 1 of 3)



0

40

80

120

160

200

240

280

320

360

400

440

480

0 2000 4000 6000 8000 10000

Vp (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile






0

40

80

120

160

200

240

280

320

360

400

440

480

0% 1% 2% 3% 4% 5% 6%

Damping

Dep

th (

ft)

Median

16th Percentile

84th Percentile


Figure 5.2-9 Strain Compatible Properties Computed for Profile 560, 500 ft Depth to Bedrock (Sheet 3 of 3)



0

40

80

120

160

200

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Vs (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile






0

40

80

120

160

200

0 5000 10000 15000 20000

Vp (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0% 1% 2% 3% 4% 5%

Damping

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0 2000 4000 6000 8000 10000 12000

Vs (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0 5000 10000 15000 20000

Vp (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0% 1% 2% 3% 4% 5%

Damping

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0 2000 4000 6000 8000 10000

Vs (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0 5000 10000 15000 20000

Vp (ft/sec)

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

40

80

120

160

200

0% 1% 2% 3% 4% 5%

Damping

Dep

th (

ft)

Median

16th Percentile

84th Percentile





0

5

10

15

20

25

30

270-500 560-500 270-200 900-200 900-100 2032-100

Fre

qu

ne

cy

(H

z)

Figure 5.2-15 Shear Column Frequencies of Top Soil Strata (Truncated Profiles)

Soil Profile



5.3 ACS SASSI FE Model of the R/B Complex

5.3.1 Development of the R/B Complex Dynamic FE Model

Built using the ANSYS preprocessor, the R/B Complex Dynamic FE model is an integrated 3-D model of the R/B-FH/A, PCCV and CIS structures resting on top of a common 9’-11” to 38’-2” thick basemat. Typical element size in the basemat and the slabs is approximately 9 ft, while the element size for the walls in the vertical direction is approximately 1.5 times larger (Refer to Section 4.3.1.1 and Table 4.3.1.1-1 for the element type used to simulate the R/B Complex structure). As a result, the total number of nodes in the model is 18,598 and the total number of elements is 22,390. Figure 5.3.1-1 shows an overview of the R/B model, while Figures 5.3.1-2 and 5.3.1-3 reveal the interior structures with section views. Figure 5.3.1-4 through Figure 5.3.1-6 show the PCCV, CIS (including the RCL). Note that the global origin is located at the center of the PCCV and top of the basement with X pointing North, Y pointing West, and Z pointing upward. The element mesh used in the dynamic model is selected to provide sufficient modeling to capture the dynamic properties of the structure. Finer mesh models will be used to evaluate stresses and strains in the structure.

The R/B Complex Dynamic FE Model is developed incrementally using the ANSYS postprocessor n the following seven steps:

Step 1: R/B complex structures geometry is created in a manner that allows control of the model FE mesh.

Step 2: Attributes are assigned and additional mass are applied on each of the structures.

Step 3: Mesh controls are set and the model, excluding the RCL, is meshed.

Step 4: Modifications are implemented as needed to make the model more consistent with the Detailed FE model

Step 5: The nodes are renumbered sequentially in the order of their X, Y, and Z coordinates as recommended by ACS SASSI Manual in order to enhance computational efficiency

Step 6: The lumped mass stick model used for ANSYS analyses of RCL is translated into format that can be translated into ACS SASSI.

Step 7: RCL structure is added to the FE model of R/B complex structures and proper connections are implemented to represent the physical supports attached to the CIS structure

In order to accurately capture the effects of foundation geometry for SSI, the basemat footprint in the Dynamic FE model is extended to the external face of perimeter walls instead of their centerline. For simplicity without compromising accuracy, slab elevations in the Dynamic FE Model are slightly shifted upward or downward such that the middle planes of nearby upper or lower slabs fall into a major common horizontal plane. Also, only large openings in slabs and walls are included in the model. Wall properties are adjusted to account for the presence of small openings not included in the model as described in Section 4.3.1.5.



Special attention is given in the Dynamic FE Model as to how wall and slab shell elements are connected to the basement/mat solid elements. Wall shell elements are extended into the basemat solid elements to ensure a proper transfer of bending moment between them. Likewise, slab shell elements joining the basement walls are extended one element to overlay the basement top surface. These connecting elements are also assigned a zero density not to increase the overall mass of the basemat.

Also for simplicity, only the main steel frame in the Fuel Handling crane support system, including a simplified rail truss girder, is modeled in the Dynamic FE Model. The steel sections are modeled as beam elements within, but unattached to concrete shell elements representing the Fuel Handling exterior walls and slab. As a result, the composite behavior of the crane support system is not really represented in the FE model. To compensate for such a deficiency, all steel sections are assigned an increased moment of inertia in their strong axis to account for their composite behavior. An adjusted moment of inertia is also assigned to the embedded sections of the crane support steel columns between elevation 65’-0” and 76’-5”, encased in 7’-8” by 4’-0” concrete columns.

The thickness of the PCCV is also simplified for ease of modeling. Only the large equipment hatch is modeled and the elements modeling the buttresses on the East and West sides of the structure are not offset with respect to adjacent elements. Also, the personnel airlocks as well as the Main Steam and Feed Water penetrations are not modeled in the Dynamic FE Model. Figure 5.3.1-4 shows the Dynamic PCCV Model.

The mass of the polar crane (crane self-weight supported by the polar crane girder) is modeled into the PCCV shell directly using four lumped Mass21 elements, in a 60/40 split between the corbels located at the 00 and 1800 azimuths. Detailed modeling and analysis of the polar crane will be performed on a site specific basis.

The Dynamic CIS Model contains approximately 3600 elements and 2600 nodes with nominal mesh size of 7.2’ in vertical direction and 9’ in horizontal direction. It consists of a combination of shell, solid and beam elements. The solid elements shown in Figure 5.3.1-5 make up the CIS base which starts at elevation 2’-7” and the reactor support which extends up to elevation 35’-10.87”. The shell elements model the remaining walls and slabs of the structure and begin at the same elevation as the CIS solid elements, but extend to the top of the pressurizer compartment at 138’-7”. The beam elements model the supports for the RCL components, and the columns between the 2nd and 4th floors. Connection details and explanation for the interface between the varying element types are presented in Section 4.3.1.1.

The Dynamic CIS model utilizes numerous simplifications to preclude meshing difficulties. The geometry of some of the CIS components are simplified, and the various small openings throughout the structure are neglected. In order to maintain the dynamic properties of the detailed CIS model the material properties of some of the CIS members are modified.



Figure 5.3.1-1 Dynamic R/B Model



Figure 5.3.1-2 Section View of Dynamic R/B Model Looking East



Figure 5.3.1-3 Section View of Dynamic R/B Model Looking South



Figure 5.3.1-4 Dynamic PCCV Model



Figure 5.3.1-5 Dynamic CIS Model – Solid Elements



Figure 5.3.1-6 Dynamic CIS Model – Shell and RCL Elements



5.3.2 Reactor Coolant Loop (RCL) Model

5.3.2.1 Description of RCL Model

The US-APWR is a four loop nuclear power plant with four safety trains. Each of the four reactor coolant loops that are connected to the Reactor Vessel (RV) includes a Steam Generator (SG), Reactor Coolant Pump (RCP), and the Main Coolant Piping (MCP) system as shown in the schematic sketch in Figure 5.3.2.2-1. The MCP is separated in three legs: (1) a hot leg piping transferring coolant flow from the RV to SG, (2) a crossover leg piping transferring coolant from SG to RCP; and (3) a cold leg piping transferring coolant from the RCP back to the RV.

The model used for dynamic analyses of RCL includes lumped mass stick models representing the dynamic properties of the NSSS components and MCP. Spring elements model the stiffness of the supports of the components and piping. Figure 5.3.2.2-2 presents the lumped mass stick model used for dynamic analyses of RCL. The properties of RCL are provided in Table 5.3.2.1-1 through Table 5.3.2.1-8.

The lumped mass stick model of the RCL and major piping components used for seismic analyses of NSSS are translated into an acceptable ACS SASSI format and then coupled with the Dynamic CIS Model. The translation included changes of ANSYS modeling features such as pipe element types, rigid links and constraint equations in a format that can be supported by the ACS SASSI translator. The pipe elements are replaced by 3-D beam elements with stiffness values equivalent to those of the straight and curved pipe sections. The rigid links and constraint equations are replaced by rigid beams. The validation of the model in Section 5.3.3 demonstrates that these necessary modifications do not affect the overall stiffness of the model and thus the dynamic response of the RCL components.



Table 5.3.2.1-1 Lumped Masses of RV Model

Description Elevation

(ft)

Weight

Symbol

Wx

(kip)

Wy

(kip)

Wz

(kip)

RV09 RV Head CG 49.94 426.6 426.6 397.5

RV08 Upper Core Support Flange 46.79 241.0 241.0 241.0

RV07 Core Ridge of Core Barrel 45.36 672.9 672.9 108.2

RV06 Center of Nozzles 40.39 246.3 246.3 241.8

RV05 Upper Core Plate 35.88 154.3 154.3 149.7

RV04 Division Point 30.51 159.6 159.6 154.3

RV03 Division Point 24.57 165.3 165.3 159.8

RV02 Radial Support Key 18.8 566.4 566.4 82.5

RV01 Bottom Head CG 15.25 113.1 113.1 117.1

RV11 UCI 42.08 0 0 271.8

RV12 LCI 42.08 0 0 1129



Table 5.3.2.1-2 Element Properties of RV Stick Model

Element Nodes Moment of Inertia (ft4)

Start End

Axial Area (ft2)

Shear Area (ft2) Torsion Bending

RV09 RV08 41.26 21.86 2303 1152

RV08 RV07

RV07 RV06

RV06 RV05

69.19 36.66 5720 2859

RV05 RV04

RV04 RV03

RV03 RV02

48.61 25.76 3858 1929

RV02 RV01 25.90 13.72 1357 678.6

Start End Vertical Stiffness (kip/ft)

RV07 RV11 103,080

RV07 RV12 572,280

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

M

UA

P-1

0001

-NP

(R

4)

Mits

ubis

hi H

eavy

Indu

strie

s, L

TD

.

5-

88

Tab

le 5

.3.2

.1-3

L

um

ped

Mas

ses

of

SG

Mo

del

Des

crip

tion

Ele

vatio

n

(ft)

M

ass

Iner

tia

Sym

bols

Wei

ght

(kip

)

Jyy

(kip

-ft2

)

Jxx

(kip

-ft2

)

Jzz

(kip

-ft2

)

S(A

/B/C

/D)

12

Ste

am O

utle

t Noz

zle

113.

76

- -

- -

S(A

/B/C

/D)

11

Upp

er S

hell/

Upp

er H

ead

108.

06

152.

0 4,

526

4,52

6 6,

849

S(A

/B/C

/D)

10

Upp

er S

hell

Sup

port

96

.58

241.

1 8,

711

8,71

1 13

,096

S(A

/B/C

/D)

09

Fee

d W

ater

Noz

zle

90.8

4 -

- -

-

S(A

/B/C

/D)

08

Tra

nsiti

on C

one

Upp

er S

ide

86.8

7 16

3.6

4,98

6 4,

986

7,50

9

S(A

/B/C

/D)

07

Tub

e S

uppo

rt P

late

(#8)

Pt.

80.7

4 51

.57

769.

0 76

9.0

1,47

3

S(A

/B/C

/D)

06

Tra

nsiti

on C

one

Low

er S

ide

79.3

8 -

- -

-

S(A

/B/C

/D)0

5 M

iddl

e S

hell

Sup

port

75

.42

156.

6 2,

790

2,79

0 4,

239

S(A

/B/C

/D)0

4 Lo

wer

She

ll/M

iddl

e S

hell

64.7

2 18

8.5

4,98

4 4,

984

4,54

7

S(A

/B/C

/D)0

3 A

djus

tmen

t Po

int

54.7

1 10

8.4

1,72

5 1,

725

2,56

7

S(A

/B/C

/D)0

2 Le

g P

oint

of I

nte

rsec

tion

49.5

97

.7

1,25

4 1,

254

2,37

0

S(A

/B/C

/D)0

1 Lo

wer

Sup

port

45

.64

101.

5 1,

377

1,37

7 2,

199



Table 5.3.2.1-4 Element Properties of Steam Generator Stick Model

Element Nodes Pipe Cross Section

Start End Outer

Diameter (ft)Thickness

(ft)

S(A/B/C/D)11 S(A/B/C/D)12




16.62 0.36

S(A/B/C/D)07 S(A/B/C/D)08 14.89 0.37

S(A/B/C/D)06 S(A/B/C/D)07 12.74 0.37





12.20 0.29

S(A/B/C/D)01 S(A/B/C/D)02 Rigid



Table 5.3.2.1-5 Lumped Mass of Reactor Coolant Pump (RCP) Model

Symbols Description Elevation

(ft)

Weight

(kip)

P(A/B/C/D)24 Top of RCP 63.21 -

P(A/B/C/D)23 61.04 -

P(A/B/C/D)22 60.78 -

P(A/B/C/D)21 59.13 -

P(A/B/C/D)20 Rotor 58.51 38.58

P(A/B/C/D)19 58.51 -

P(A/B/C/D)18 58.19 -

P(A/B/C/D)17 Upper Bracket 56.84 -

P(A/B/C/D)16 Motor Mass Point 56.35 72.53

P(A/B/C/D)15 55.18

P(A/B/C/D)14 Lower Bracket 53.52 -

P(A/B/C/D)13 52.20 -

P(A/B/C/D)12 51.35 -

P(A/B/C/D)11 50.76 -

P(A/B/C/D)10Motor Stand Upper Side

50.51 -

P(A/B/C/D)09Motor Stand

Opening Upper Side

49.86 -

P(A/B/C/D)08Motor Stand

Opening Lower Side

46.58 -

P(A/B/C/D)07Motor Stand Lower Side

45.09 -

P(A/B/C/D)06Casing Upper

Side 43.78 -

P(A/B/C/D)05Lower Support

Point 42.61 -

P(A/B/C/D)04 Pump Mass Point 41.67 127.43

P(A/B/C/D)03Cold Leg Point of

Intersection 40.39 -

P(A/B/C/D)02 Transition Point 36.11 -

P(A/B/C/D)01Cross Over Leg

Intersection Point35.29 -

Sei

smic

Des

ign

Bas

es o

f the

US

-AP

WR

Sta

ndar

d P

lant

M

UA

P-1

0001

-P (

R4)

M

itsub

ishi

Hea

vy In

dust

ries,

LT

D.

5-91

Tab

le 5

.3.2

.1-6

E

lem

ent

Pro

per

ties

of

Rea

cto

r C

oo

lan

t P

um

p (

RC

P)

Sti

ck M

od

el

Ele

men

t Nod

es

Pip

e S

ectio

n B

eam

Are

a B

eam

Mom

ent o

f Ine

rtia

Sta

rt

End

O

uter

D

iam

. (f

t)

Thi

ck

(ft)

A

xial

(f

t2 )

She

ar

(ft2 )

NS

She

ar

(ft2 )

EW

Izz

(f

t4 ) T

orsi

on

Iyy

(f

t4 )

N

S

Ixx

(f

t4 )

EW

P

(A/B

/C/D

)23

P(A

/B/C

/D)2

46.

509

0.01

5-

- -

- -

- P

(A/B

/C/D

)22

P(A

/B/C

/D)2

36.

916

0.62

5-

- -

- -

- P

(A/B

/C/D

)21

P(A

/B/C

/D)2

25.

955

0.08

2-

- -

- -

- P

(A/B

/C/D

)19

P(A

/B/C

/D)2

1-

- 3.

918

3.91

83.

918

18.2

3911

.343

6.58

3P

(A/B

/C/D

)18

P(A

/B/C

/D)1

9-

- 3.

918

3.91

83.

918

18.2

3911

.343

6.58

3P

(A/B

/C/D

)17

P(A

/B/C

/D)1

86.

562

0.08

2-

- -

- -

- P

(A/B

/C/D

)16

P(A

/B/C

/D)1

7-

- 2.

444

2.44

42.

444

38.3

4921

.205

17.1

49P

(A/B

/C/D

)15

P(A

/B/C

/D)1

6-

- 2.

444

2.44

42.

444

38.3

4921

.205

17.1

49P

(A/B

/C/D

)14

P(A

/B/C

/D)1

5-

- 2.

594

2.59

42.

594

40.6

6823

.057

17.6

12P

(A/B

/C/D

)13

P(A

/B/C

/D)1

46.

562

0.12

5-

- -

- -

- P

(A/B

/C/D

)12

P(A

/B/C

/D)1

3-

- 2.

960

2.96

02.

960

15.3

0711

.507

3.80

0P

(A/B

/C/D

)11

P(A

/B/C

/D)1

2-

- 3.

262

3.26

23.

262

30.5

8915

.292

15.2

92P

(A/B

/C/D

)10

P(A

/B/C

/D)1

17.

559

1.69

3-

- -

- -

- P

(A/B

/C/D

)09

P(A

/B/C

/D)1

07.

038

0.13

1-

- -

- -

- P

(A/B

/C/D

)08

P(A

/B/C

/D)0

9-

- 1.

951

1.65

61.

656

23.2

547.

108

16.1

41P

(A/B

/C/D

)07

P(A

/B/C

/D)0

87.

038

0.13

1-

- -

- -

- P

(A/B

/C/D

)06

P(A

/B/C

/D)0

7-

- 2.

368

2.09

92.

099

19.3

389.

664

9.66

4P

(A/B

/C/D

)C1

P(A

/B/C

/D)C

2P

(A/B

/C/D

)06

P(A

/B/C

/D)C

3P

(A/B

/C/D

)C1

P(A

/B/C

/D)C

2P

(A/B

/C/D

)02

P(A

/B/C

/D)C

3P

(A/B

/C/D

)C1

P(A

/B/C

/D)C

2P

(A/B

/C/D

)C2

P(A

/B/C

/D)C

3P

(A/B

/C/D

)C3

P(A

/B/C

/D)C

1

Rig

id

P(A

/B/C

/D)1

9 P

(A/B

/C/D

)20

- -

4.46

78.

5035

440.

8R

igid

P

(A/B

/C/D

)19

P(A

/B/C

/D)2

0-

- 3.

229

12.1

1044

0.8



Table 5.3.2.1-7 Spring Stiffness Values of RV, SG, and RCP

Support Name Elevation

(ft) Support

Stiffness x 103 (kip/ft)

Krh 1,002 Inlet Nozzle Support Krv 1,086

Krh 1,124 RV

Outlet Nozzle Support

40.39

Krv 1,086

Ku11 40.28

Ku12 39.29

Ku13 40.28

Upper Shell Support

96.58

Ku14 39.29

Km11 40.23

Km12 41.70

Km13 40.23

SG

Intermediate Shell Support

75.42

Km14 41.70

RCP Lower Support 42.61 Kpt 221.9

Table 5.3.2.1-8 Material Properties of RCL Stick Models

Component Material (ASME) Temp.

(°F)

Young's Modulus

(106) (ksf)

Poisson's ratio

RV SA508 Gr3.CI.1 583.8 3.640 0.3 SG SA508 Gr.3.CI.2 534.8 3.676 0.3

Elev. 50.51’ to 63.21’ SA36 120.0 4.209 0.3 Elev. 45.09’ to 50.51’ SA516 Gr.70 140.0 4.193 0.3

Casing Bolt Elev. 43.78’ to 45.09’

SA540 Gr.B24.Cl.4 335.4 3.815 0.3 RCP

Elev. 36.11’ to 43.78’ Rigid

Bracket SA299 368.5 4.016 Support Pipe SA524 Gr.1 SG Leg

Block SA541 Gr.3.Cl.1 120.0 4.209

0.3

Bracket SA299 335.3 4.045 Support Pipe SA524 Gr.1

RCP Leg

Block SA541 Gr.3.Cl.1 120.0 4.209

0.3

Hot Leg SA182 F316LN or

SA336 F316LN 617.0 3.632 0.3

Crossover Leg MCP

Cold Leg SA182 F316LN or

SA336 F316LN 550.6 3.679 0.3

*The material damping value for the RCL model is 3%.



5.3.2.2 Coupling of RCL Model

The system supporting the Reactor Vessel (RV) consists of eight steel support pads which are integrated with the inlet and outlet nozzle forgings. The support pads are placed on brackets, which are supported by a steel structure embedded in the primary shield wall. The supports allow radial thermal growth of RV and reactor coolant system. Figure 5.3.2.2-3 shows the configuration of the RV support. Details of the modeling of the connection of the RV with the dynamic and detailed FE models of the CIS are presented in Figure 5.3.2.2-4.

The SG support system consists of an upper shell support structure, an intermediate shell support structure, and a lower support structure shown in Figure 5.3.2.2-5. The upper and intermediate shell supports are lateral restraints (snubbers) attached to structural steel brackets. The lower support structure provides both vertical and lateral support to the SG and is constructed entirely of structural steel. It consists of four pinned-end columns of the lower support transfer the vertical loads from the SG to CIS structure and lateral supports that transfer lateral loads to the CIS only when they are in contact with the SG. This design solution allows for the thermal expansion of the SG and attached piping but introduces geometric non-linearity in the dynamic system because the springs modeling the lower lateral support are engaged only when they are in compression. Figure 5.3.2.2-6 shows the RCP tie rod support. Figure 5.3.2.2-7 presents modeling of the connections between the lumped mass stick model of SG and Dynamic and Detailed FE models.



Figure 5.3.2.2-1 US-APWR Reactor Coolant Loop (RCL)



Figure 5.3.2.2-2 Lumped Mass Dynamic Model of RCL



Figure 5.3.2.2-3 Reactor Vessel Support



Figure 5.3.2.2-4 Reactor Vessel Support FE Model Connection



Figure 5.3.2.2-5 Steam Generator Lower Lateral Support



Figure 5.3.2.2-6 Reactor Coolant Pump (RCP) Tie Rod



Figure 5.3.2.2-7 Steam Generator Supports FE Model Connections



5.3.3 Validation of the R/B Complex Dynamic FE Model

Validation of the R/B Complex Dynamic FE Model is carried out in accordance with the methodology described in Section 4.3.2. A summary of these results is presented hereafter for each of the three models.

5.3.3.1 Validation of the R/B-FH/A

5.3.3.1.1 1g Static Analysis

Partial static solutions under 1g vertical load are performed using ANSYS to calculate masses of each floor. Table 5.3.3.1.1-1 presents the comparison of the major floor masses for the North and South halves of the R/B obtained from the analyses of the two FE models – the dynamic FE model and the detailed FE model. The mass of each floor section is taken as the mass of the floor plus that of the walls between the current floor and the floor at the immediate lower elevation. The results in Table 5.3.3.1.1-1indicate that the two models have a comparable total mass with a difference of 2.18% for the North half of R/B, 2.27% for the South half of R/B, and 1.55% for the basement/mat. The mass differences for each floor section range from 0.09% to 6.94%.

Table 5.3.3.1.1-1 R/B Floor Mass Comparison

Detailed ModelDynamic

Model Floor (kips*sec2/ft) (kips*sec2/ft)

Difference

Base 9,284 9,140 -1.55%

North Half

2nd Floor 1,445 1,502 3.97% 3rd Floor 1,196 1,208 1.01% 4th Floor 1,309 1,341 2.44% 5th Floor 688 693 0.69%

Roof 384 358 -6.82% Total w/o base 5,022 5,102 1.59%

South Half

2nd Floor 1,078 1,120 3.88% 3rd Floor 1,135 1,154 1.61%

3rd Mezzanine Floor 570 571 0.17% 4th Floor 794 804 1.22% 5th Floor 963 985 2.34%

Roof 666 687 3.07% Total w/o base 5,207 5,321 2.18%

Figure 5.3.3.1.1-4 presents the displacement at the mid span of the wall of FH/A that is a composite wall with significant offset from the centerline of the other walls. This offset and precise modeling of the composite wall section is present in the detailed model. Simplifications were required in the modeling of the FH/A wall in dynamic model which are the cause of some of the displacement inconsistencies. Nevertheless, the effect of this simplification on the response is small as shown by ARS comparisons.



ANSYS static analyses are performed on both the Detailed and Dynamic FE models of the R/B with 1g quasi-static accelerations applied in the horizontal (X and Y) directions and full constraints at the bottom of the common basemat.

Displacement results from the 1g static analyses are used to compare the distributions of mass and horizontal stiffness of the two models. Lateral displacement in the two horizontal directions (X and Y) along the height at various exterior wall locations C and H of both models are plotted in Figures 5.3.3.1.1-1 though Figure 5.3.3.1.1-5. They demonstrate that the Dynamic Model lateral stiffness is comparable to that of the Detailed Model (structure behavior follows the same trend for both models). Table 5.3.3.1.1-2 indicates that the maximum roof level lateral displacement difference between the two models at the various locations varies from 0.07% to 5.14% in the NS (X) direction and from 1.21% to 3.86% in the EW (Y) direction.

Figure 5.3.3.1.1-1 Lateral Displacement Locations on R/B Exterior Walls



Figure 5.3.3.1.1-2 R/B 1g Static Analysis Results – NS Direction (X) at Location C

Horizontal Displacement of RB at South West Corner in E-W Direction

-40

-20

0

20

40

60

80

100

120

140

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Displacement (f t)

Ele

vatio

n (f

t)

Detailed RB Model

Seismic RB Model

Figure 5.3.3.1.1-3 R/B 1g Static Analysis Results – EW Direction (Y) at Location C

Horizontal Displacement of RB at South West Corner in N-S Direction

-40

-20

0

20

40

60

80

100

120

140

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Displacement (ft)

Ele

vatio

n (f

t)

Detailed RB Model

Seismic RB Model



Horizontal Displacement of RB at North Side in N-S Direction

-40

-20

0

20

40

60

80

100

120

140

160

180

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Displacement (ft)

Hei

ght (

ft)

Detailed RB Model

Seismic RB Model

Figure 5.3.3.1.1-4 R/B 1g Static Analysis Results – NS Direction (X) at Location H

Horizontal Displacement of RB at North Side in E-W Direction

-40

-20

0

20

40

60

80

100

120

140

160

180

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Displacement (ft)

Hei

ght

(ft)

Detailed RB Model

Seismic RB Model

Figure 5.3.3.1.1-5 R/B 1g Static Analysis Results – EW Direction (Y) at Location H



Table 5.3.3.1.1-2 R/B Roof Lateral Displacement Comparison

NS Direction EW Direction

Displacement (in) Displacement (in) Locations Detailed Model

Dynamic Model

Difference Detailed Model

Dynamic Model

Difference

A 0.368 0.354 -3.65% 0.363 0.346 -4.72%

B 0.329 0.344 4.37% 0.565 0.537 -4.93%

C 0.413 0.419 1.48% 0.47 0.463 -1.48%

D 0.578 0.547 -5.35% 0.481 0.471 -2.02%

E 0.411 0.398 -3.21% 0.47 0.459 -2.37%

F 0.336 0.335 -0.29% 0.604 0.568 -5.96%

G 0.691 0.663 -4.00% 0.486 0.467 -3.85%

H 0.932 0.886 -4.87% 0.481 0.46 -4.37%



5.3.3.1.2 Modal Analysis

Fixed base modal analyses using ANSYS are performed on both the Detailed and the Dynamic FE Models of the R/B. Plots of Cumulative Mass versus Frequency are shown in Figure 5.3.3.1.2-1 through Figure 5.3.3.1.2-3. The results of the modal analysis indicate that the Dynamic FE model adequately captures the dynamic properties of the Detailed FE model.

Figure 5.3.3.1.2-1 R/B Modal Analysis Results–Cumulative Mass in the NS Direction (X)



Figure 5.3.3.1.2-2 R/B Modal Analysis Results–Cumulative Mass in the EW Direction (Y)

Figure 5.3.3.1.2-3 R/B Modal Analysis Results–Cumulative Mass in the Vertical Direction (Z)



5.3.3.1.3 Modal Superposition Time History Analysis

A dynamic time history response analysis using modal superposition is performed on both R/B models using ANSYS. ARS with 5% damping are generated for each model at various locations. These acceleration response spectra indicate that the Dynamic FE Model captures the structure response to dynamic loads in all directions properly.

Figure 5.3.3.1.3-1 through Figure 5.3.3.1.3-15 show the comparison of Detailed and Dynamic Model ARS for representative locations.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.1 1 10 100Frequency (Hz)

Acc

eler

atio

n (

g)

Detailed FE Model - NS Direction -Exterior Wall Location D Elev. 76'-5"

Dynamic FE Model - NS Direction -Exterior Wall Location D Elev. 76'-5"

Figure 5.3.3.1.3-1 R/B NS Direction ARS Results – Location D – Comparison at EL. 76’-5”



0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


Acc

eler

atio

n (

g)

Detailed FE Model - EW Direction -Exterior Wall Location D Elev. 76'-5"

Dynamic FE Model - EW Direction -Exterior Wall Location D Elev. 76'-5"

Figure 5.3.3.1.3-2 R/B EW Direction ARS Results – Location D – Comparison at EL 76’-5”



0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Acc

eler

atio

n (

g)

Detailed FE Model - Vertical Direction -Exterior Wall Location D Elev. 76'-5"

Dynamic FE Model - Vertical Direction -Exterior Wall Location D Elev. 76'-5"

Figure 5.3.3.1.3-3 R/B Vertical Direction ARS Results – Location D – Comparison at EL 76’-5”



0

0.5

1

1.5

2

2.5

3

3.54

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

10.5

11

11.512

12.5

13

13.5

14

14.5

15

15.5


Acc

eler

atio

n (

g)

Detailed FE Model - NS Direction -Exterior Wall Location H Elev. 131'-6"

Dynamic FE Model - NS Direction -Exterior Wall Location H Elev. 131'-6"

Figure 5.3.3.1.3-4 R/B NS Direction ARS Results – Location H – Comparison at EL 131’-6”



0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5


Acc

eler

atio

n (

g)

Detailed FE Model - EW Direction -Exterior Wall Location H Elev. 131'-6"

Dynamic FE Model - EW Direction -Exterior Wall Location H Elev. 131'-6"

Figure 5.3.3.1.3-5 R/B EW Direction ARS Results – Location H – Comparison at EL 131’-6



0

0.5

1

1.5

2

2.5

3

3.5


Acc

eler

atio

n (

g)

Detailed FE Model - Vertical Direction -Exterior Wall Location H Elev. 131'-6"

Dynamic FE Model - Vertical Direction -Exterior Wall Location H Elev. 131'-6"

Figure 5.3.3.1.3-6 R/B Vertical Direction ARS Results – Location H – Comparison at EL 131’-6



0

0.5

1

1.5

2


Acc

eler

atio

n (

g)

Detailed FE Model - Vertical Direction -EL-8'-7'' - Slab Group -8SG1

Dynamic FE Model - Vertical Direction -EL-8'-7'' - Slab Group -8SG1

Figure 5.3.3.1.3-7 R/B Vertical Direction ARS Results – Comparison at Slab Group -8SG1 (EL -8’-7”)



0

0.5

1

1.5

2

2.5

0.1 1 10 100

Frequency (Hz)

Ac

ce

lera

tio

n (

g)

Detailed FE Model - Vertical Direction -EL3'-7'' - Slab Group 3SG1

Dynamic FE Model - Vertical Direction -EL3'-7- Slab Group 3SG1

Figure 5.3.3.1.3-8 R/B Vertical Direction ARS Results – Comparison at Slab Group 3SG1 (EL. 3’-7”)



0

0.5

1

1.5

2

2.5

3

3.5

4

0.1 1 10 100

Frequency (Hz)

Acc

eler

atio

n (

g)


Dynamic FE Model - Vertical Direction -EL25'-3'' - Slab Group 25SG1

Figure 5.3.3.1.3-9 R/B Vertical Direction ARS Results – Comparison Slab Group 25SG1 (EL. 25’-3”)



0

0.5

1

1.5

2

2.5

3

3.5


Ac

ce

lera

tio

n (

g)


Dynamic FE Model - Vertical Direction -EL50'-2'' -Slab Group 50SG5




0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5


Acc

eler

atio

n (

g)






0

0.5

1

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Detailed FE Model - Vertical Direction -EL86'-4'' - Slab Group 86SG1Dynamic FE Model - Vertical Direction -EL86'-4'' - Slab Group 86SG1




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5.3.3.2 Validation of the CIS

Due to the complexity of the CIS, different stiffness and damping values are assigned to different types of structural components for the two bounding stiffness and damping conditions as described in Table 4.3.1.1-3. Hence, a non-uniform reduction of stiffness is applied for the different types of components in order to account for cracking of the concrete in SC modules, reinforced concrete slabs and massive concrete portions of the CIS. Therefore, unlike the other US-APWR standard plant Category I structures, two sets of validation analyses are performed for the CIS to ensure the adequacy of the CIS dynamic FE model with full (uncracked concrete) stiffness and reduced (cracked concrete) stiffness.


A 1g static analysis in the vertical (Z) direction with full constraints at the bottom of the Containment Internal Structure is performed on both the uncracked (full stiffness) and cracked (reduced stiffness) versions of the detailed and dynamic CIS models to verify their overall static weight. For the uncracked model analyses, the total weight of the dynamic model is found to be 100,930 kips while the total weight of the detailed model is found to be 101,290 kips. This represents a difference of 0.35% between the total weights of the uncracked models. For the cracked model analyses, the total weight of the dynamic model is found to be 100,930 kips while the total weight of the detailed model is found to be 101,560 kips. This represents a difference of 0.62% between the total weights of the cracked models.

A 1g static analysis in the horizontal (X and Y) directions with full constraints at the bottom of the CIS is also performed on both the uncracked and cracked versions of the dynamic and detailed models. The displacement results from the static analyses are used to compare the structure stiffness of each model in the lateral directions. The displacement distributions at several locations along the height of the uncracked CIS models are plotted in Figure 5.3.3.2.1-1 through Figure 5.3.3.2.1-8 below and indicate that distribution of mass and stiffness of the dynamic FE model with full stiffness is comparable to that of the detailed FE model. The displacement distributions at several locations along the height of the cracked CIS models are plotted in Figure 5.3.3.2.1-9 through Figure 5.3.3.2.1-16 below and indicate that distribution of mass and stiffness of the dynamic FE model with reduced stiffness is comparable to that of the detailed FE model.



Horizontal Displacements at North of CIS in NS Direction

-40

-20

0

20

40

60

80

100

120

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Displacement (ft)

Ele

va

tio

n (

ft)

Detailed Model Dynamic Model

Figure 5.3.3.2.1-1 CIS 1g Static Analysis Results – NS Direction (X) at North Face of Structure (Uncracked Analysis)



Horizontal Displacements at North of CIS in EW Direction

-40

-20

0

20

40

60

80

100

120

0.00E+00 2.00E-03 4.00E-03 6.00E-03 8.00E-03 1.00E-02 1.20E-02

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-2 CIS 1g Static Analysis Results – EW Direction (Y) at North Face of Structure (Uncracked Analyses)



Horizontal Displacements at Reactor in NS Direction

0

20

40

60

0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-3 CIS 1g Static Analysis Results – NS Direction (X) at Reactor Vessel (Uncracked Analyses)

Note: the reactor is supported at the 40 ft. elevation, thus the deflection curves slope downward.



Horizontal Displacements at Reactor in EW Direction

0

20

40

60

0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012

Displacement (ft)

Ele

vati

on

(ft

)


Figure 5.3.3.2.1-4 CIS 1g Static Analysis Results – EW Direction (Y) at Reactor Vessel (Uncracked Analyses)




Horizontal Displacements at NW SG in NS Direction

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140

160

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-5 CIS 1g Static Analysis Results – NS Direction (X) at Northwest Steam Generator (Uncracked Analyses)



Horizontal Displacements at NW SG in EW Direction

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-20

0

20

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100

120

140

160

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-6 CIS 1g Static Analysis Results – EW Direction (Y) at Northwest Steam Generator (Uncracked Analyses)



Horizontal Displacements at SE RCP in NS Direction

-40

-20

0

20

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60

80

100

120

0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-7 CIS 1g Static Analysis Results – NS Direction (X) at Southeast Reactor Coolant Pump (Uncracked Analyses)



Horizontal Displacements at SE RCP in EW Direction

-40

-20

0

20

40

60

80

100

120

0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-8 CIS 1g Static Analysis Results – EW Direction (Y) at Southeast Reactor Coolant Pump (Uncracked Analyses)



Horizontal Displacements at North of CIS in NS Direction

-40

-20

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-9 CIS 1g Static Analysis Results – NS Direction (X) at North Face of Structure (Cracked Analyses)



Horizontal Displacements at North of CIS in EW Direction

-40

-20

0

20

40

60

80

100

120

0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-10 CIS 1g Static Analysis Results – EW Direction (Y) at North Face of Structure (Cracked Analyses)



Horizontal Displacements at Reactor in NS Direction

0

20

40

60

0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-11 CIS 1g Static Analysis Results – NS Direction (X) at Reactor Vessel (Cracked Analyses)




Horizontal Displacements at Reactor in EW Direction

0

20

40

60

0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012

Displacement (ft)

Ele

vati

on

(ft

)


Figure 5.3.3.2.1-12 CIS 1g Static Analysis Results – EW Direction (Y) at Reactor Vessel (Cracked Analyses)




Horizontal Displacements at NW SG in NS Direction

-40

-20

0

20

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60

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100

120

140

160

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-13 CIS 1g Static Analysis Results – NS Direction (X) at Northwest Steam Generator (Cracked Analyses)




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-20

0

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100

120

140

160

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-14 CIS 1g Static Analysis Results – EW Direction (Y) at Northwest Steam Generator (Cracked Analyses)



Horizontal Displacements at SE RCP in NS Direction

-40

-20

0

20

40

60

80

100

120

0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-15 CIS 1g Static Analysis Results – NS Direction (X) at Southeast Reactor Coolant Pump (Cracked Analyses)




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160

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Displacement (ft)

Ele

vat

ion

(ft

)


Figure 5.3.3.2.1-16 CIS 1g Static Analysis Results – EW Direction (Y) at Southeast Reactor Coolant Pump (Cracked Analyses)



Modal Analysis

A modal analysis using ANSYS is performed on both the uncracked and cracked versions of the detailed and dynamic FE models. Plots of Cumulative Mass versus Frequency for the uncracked CIS models are shown in Figure 5.3.3.2.2-1 through Figure 5.3.3.2.2-3 below. Plots of the Cumulative mass versus Frequency for the cracked CIS models are shown in Figure 5.3.3.2.2-4 through Figure 5.3.3.2.2-6 below. The results of the modal analyses indicate that the Dynamic FE models adequately capture the dynamic properties of the Detailed FE models.

Figure 5.3.3.2.2-1 CIS Modal Analysis Results – Cumulative Mass in the NS Direction (X) (Uncracked Analyses)



Figure 5.3.3.2.2-2 CIS Modal Analysis Results – Cumulative Mass in the EW Direction (Y) (Uncracked Analyses)



Mass Participation Vertical Response

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90 100

Freq. (Hz)

Co

m. M

ass

.

Detailed

Dynamic

Figure 5.3.3.2.2-3 CIS Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z) (Uncracked Analyses)



Figure 5.3.3.2.2-4 CIS Modal Analysis Results – Cumulative Mass in the NS Direction (X) (Cracked Analyses)



Figure 5.3.3.2.2-5 CIS Modal Analysis Results – Cumulative Mass in the EW Direction (Y) (Cracked Analyses)



Figure 5.3.3.2.2-6 CIS Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z) (Cracked Analyses)




A dynamic time history analysis using modal superposition is performed on both the cracked and uncracked versions of the detailed and dynamic CIS models using ANSYS. Acceleration Response Spectra (ARS) with 5 % damping are generated for each model at various locations. Figure 5.3.3.2.3-1 through Figure 5.3.3.2.3-9 show the comparison of detailed and dynamic model ARS for representative locations within the uncracked models. Figure 5.3.3.2.3-10 through Figure 5.3.3.2.3-18 show the comparison of detailed and dynamic model ARS for representative locations within the cracked models. The comparison of the acceleration response spectra for both the cracked and uncracked models indicates that the dynamic CIS models capture the structure response to dynamic loads in all directions properly.

Figure 5.3.3.2.3-1 CIS ARS Results – Comparison at Top of Pressurizer, X-direction (Uncracked Analyses)



Figure 5.3.3.2.3-2 CIS ARS Results – Comparison at Top of Pressurizer, Y-direction (Uncracked Analyses)



Figure 5.3.3.2.3-3 CIS ARS Results – Comparison at Top of Pressurizer, Z-direction (Uncracked Analyses)



Figure 5.3.3.2.3-4 CIS ARS Results – Comparison at Top of West SG Compartment, X-direction (Uncracked Analyses)



Figure 5.3.3.2.3-5 CIS ARS Results – Comparison at Top of West SG Compartment, Y-direction (Uncracked Analyses)



Figure 5.3.3.2.3-6 CIS ARS Results – Comparison at Top of West SG Compartment, Z-direction (Uncracked Analyses)



Figure 5.3.3.2.3-7 CIS ARS Results – Comparison at Top of Reactor Vessel, X-direction (Uncracked Analyses)



Figure 5.3.3.2.3-8 CIS ARS Results – Comparison at Top of Reactor Vessel, Y-direction (Uncracked Analyses)



Figure 5.3.3.2.3-9 CIS ARS Results – Comparison at Top of Reactor Vessel, Z-direction (Uncracked Analyses)



Figure 5.3.3.2.3-10 CIS ARS Results – Comparison at Top of Pressurizer, X-direction (Cracked Analyses)



Figure 5.3.3.2.3-11 CIS ARS Results – Comparison at Top of Pressurizer, Y-direction (Cracked Analyses)



Figure 5.3.3.2.3-12 CIS ARS Results – Comparison at Top of Pressurizer, Z-direction (Cracked Analyses)



Figure 5.3.3.2.3-13 CIS ARS Results – Comparison at Top of West SG Compartment, X-direction (Cracked Analyses)



Figure 5.3.3.2.3-14 CIS ARS Results – Comparison at Top of West SG Compartment, Y-direction (Cracked Analyses)



Figure 5.3.3.2.3-15 CIS ARS Results – Comparison at Top of West SG Compartment, Z-direction (Cracked Analyses)



Figure 5.3.3.2.3-16 CIS ARS Results – Comparison at Top of Reactor Vessel, X-direction (Cracked Analyses)



Figure 5.3.3.2.3-17 CIS ARS Results – Comparison at Top of Reactor Vessel, Y-direction (Cracked Analyses)



Figure 5.3.3.2.3-18 CIS ARS Results – Comparison at Top of Reactor Vessel, Z-direction (Cracked Analyses)



5.3.3.3 Validation of the PCCV


A 1g static analysis in the vertical (Z) direction with full constraints at the bottom of the Containment structure is performed on both PCCV models to verify their overall static weight. The total weight of the Dynamic PCCV model is 78,732 kips while the total weight of the Detailed PCCV Model is 76,979 kips. This represents a difference of 2.23% between the total weights of both models.

Static analyses with 1g quasi acceleration loads applied in both horizontal (X and Y) directions with full constraints at the bottom of the containment structure are also performed on both models of PCCV. The displacement results from both static analyses are used to compare the distribution of mass and lateral stiffness of the two models. The displacement distributions along the height of the Containment Vessel are plotted for the North face of the structure in Figure 5.3.3.3.1-1and Figure 5.3.3.3.1-2 below, and indicate that the Dynamic PCCV Model stiffness is comparable to that of the Detailed Model (structure behavior follows the same trend for both models).

Figure 5.3.3.3.1-1 PCCV 1g Static Analysis Results – NS Direction (X) at North Face of Structure



Horizontal Displacements of PCCV at North Side in E-W Direction

0

50

100

150

200

250

0.000 0.010 0.020 0.030 0.040 0.050 0.060

Displacement (ft)

Ele

va

tio

n (

ft)

Detailed PCCV Model

Dynamic PCCV Model

Figure 5.3.3.3.1-2 PCCV 1g Static Analysis Results – EW direction (Y) at North Face of Structure



5.3.3.3.2 Modal Analysis

Fixed base modal analyses using ANSYS are performed on both the Detailed FE Model and the Dynamic FE Model of PCCV. Plots of Cumulative Mass versus Frequency are shown in Figure 5.3.3.3.2-1 through Figure 5.3.3.3.2-3 below and provide the comparison of the modal analyses results. The results of the modal analysis indicate that the Dynamic FE model adequately captures the dynamic properties of the Detailed FE model.

Figure 5.3.3.3.2-1 PCCV Modal Analysis Results – Cumulative Mass in the NS Direction (X)



Figure 5.3.3.3.2-2 PCCV Modal Analysis Results – Cumulative Mass in the EW Direction (Y)

Figure 5.3.3.3.2-3 PCCV Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z)




Fixed base dynamic time history analyses using modal superposition are performed on both Dynamic and Detailed FE models of PCCV using ANSYS. ARS with 5% damping are generated for each model at various locations. These acceleration response spectra indicate that the Dynamic PCCV Model properly capture the structure response to dynamic loads in all directions.

Figure 5.3.3.3.3-1 through Figure 5.3.3.3.3-9 show the comparison of Detailed and Dynamic Model acceleration response spectra for representative locations grouped by elevation.

Figure 5.3.3.3.3-1 PCCV ARS Results – Comparison at Elev. 86.25 ft, X-direction



Figure 5.3.3.3.3-2 PCCV ARS Results – Comparison at Elev. 86.25 ft, Y-direction



Figure 5.3.3.3.3-3 PCCV ARS Results – Comparison at Elev. 86.25 ft, Z-direction



Figure 5.3.3.3.3-4 PCCV ARS Results – Comparison at Elev. 145.58 ft, X-direction

Note: The coordinates of Nodes are different between Dynamic and Detail model.



Figure 5.3.3.3.3-5 PCCV ARS Results – Comparison at Elev. 145.58 ft, Y-direction



Figure 5.3.3.3.3-6 PCCV ARS Results – Comparison at Elev. 145.58 ft, Z-direction



Figure 5.3.3.3.3-7 PCCV ARS Results – Comparison at Elev. 232 ft, X-direction



Figure 5.3.3.3.3-8 PCCV ARS Results – Comparison at Elev. 232 ft, Y-direction



Figure 5.3.3.3.3-9 PCCV ARS Results – Comparison at Elev. 232 ft, Z-direction



5.3.4 Validation of the Dynamic FE Model Translation into ACS SASSI Format

5.3.4.1 Validation of the R/B

Acceleration Response Spectra (ARS) with 5% damping are developed for the Reactor Building in ACS SASSI for hard rock soil conditions to verify proper model translation. The ACS SASSI generated ARS at various structure locations are then compared to the ANSYS fixed base analysis and are presented in Figure 5.3.4.1-1 through Figure 5.3.4.1-11. The comparison of the acceleration response spectra indicates that ACS SASSI model captures the structure response to dynamic loads in all directions properly, thus justifying proper translation. Please note that this analysis was performed for the uncracked R/B model only since the cracked model consists of a uniform reduction of stiffness (50% reduction of Young’s Modulus) and did not warrant any further justification.

Figure 5.3.4.1-1 R/B ARS Results – Comparison at Slab Sb40A8 (EL. 3’-7”), Z-direction



Figure 5.3.4.1-2 R/B ARS Results – Comparison at Slab S28A12b (EL. 25’-3”), Z-direction



Figure 5.3.4.1-3 R/B ARS Results – Comparison at Slab S38A1 (EL. 35’-2”), Z-direction



Figure 5.3.4.1-4 R/B ARS Results – Comparison at Slab S46B3 (EL. 48’-6”), Z-direction



Figure 5.3.4.1-5 R/B ARS Results – Comparison at Slab S40C8 (EL. 63’-4”), Z-direction



Figure 5.3.4.1-6 R/B ARS Results – Comparison at Slab S44C2 (EL. 75’), Z-direction



Figure 5.3.4.1-7 R/B ARS Results – Comparison at Slab S20A3 (EL. 86’-4”), Z-direction



Figure 5.3.4.1-8 R/B ARS Results – Comparison at Slab S15D2 (EL. 99.75’), Z-direction



Figure 5.3.4.1-9 R/B ARS Results – Comparison at Slab S40G1 (EL. 115’-5”), Z-direction



Figure 5.3.4.1-10 R/B ARS Results – Comparison at Exterior Wall Location D Roof Level, X-direction



Figure 5.3.4.1-11 R/B ARS Results – Comparison at Exterior Wall Location B Roof Level, Y-direction

5.3.4.2 Validation of the CIS

Acceleration Response Spectra with 5% damping are developed for the CIS in ACS SASSI for hard rock soil conditions for both the uncracked and crack models to verify proper model translation. The ACS SASSI generated ARS at various structure locations are then compared to the ANSYS fixed base ARS and are presented in Figure 5.3.4.2-3 through Figure 5.3.4.2-8 for the uncracked model and Figure 5.3.4.2-9 through 5.3.4.2-14 for the cracked model. The comparison of the ARS indicates that ACS SASSI model captures the structure response to dynamic loads in all directions properly, thus justifying proper translation. Please note that the ARS produced by ACS SASSI demonstrate higher peak responses due to the additional amplification from slight variations in the models used for analysis (variations present in both cracked and uncracked models). The fixed base analysis for the ANSYS model considers fixed boundary conditions at the base of the CIS structure. The SSI validation analysis with hard rock soil conditions considers the entire R/B complex with fixed base boundary conditions at the bottom of the basemat. As discussed in Section 4.3.3, this difference in support elevation creates amplifications at the base of the CIS as presented in the transfer functions provided in Figure 5.3.4.2-1 and Figure 5.3.4.2-2.



Figure 5.3.4.2-1 Transfer Function – Base of CIS/PCCV, X-Direction (Uncracked Analyses)



Figure 5.3.4.2-2 Transfer Function – Base of CIS/PCCV, Y-Direction (Uncracked Analyses)



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ele

rati

on

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Detailed Model Envelope at Elev. 138.58 ft Top of Pressurizer X-X Dynamic Model Envelope at Elev. 138.58 ft Top of Pressurizer X-X

Figure 5.3.4.2-3 CIS ARS Results – Comparison at Top of Pressurizer Compartment X-Direction (Uncracked Analyses)



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ce

lera

tio

n (

g)

Detailed Model Node 43524 Elev. 112 ft Top of W St Gen Comp X-X

Dynamic Model Node 2575 Elev. 112 ft Top of W St Gen Comp X-X

Figure 5.3.4.2-4 CIS ARS Results – Comparison at Top of West Steam Generator X-Direction (Uncracked Analyses)



0

0.2

0.4

0.6

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1

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1.8

2


Acc

ele

rati

on

(g

)

Detailed Model Envelope at Elev. 49.5 ft 3rd Floor Y-Y Dynamic Model Envelope at Elev. 49.5 ft 3rd Floor Y-Y

Figure 5.3.4.2-5 CIS ARS Results – Comparison at 3rd Floor Y-Direction (Uncracked Analyses)



0

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1

1.2


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 35.906 ft Top of Reactor Cav Z-Z Dynamic Model Envelope at Elev. 35.906 ft Top of Reactor Cav Z-Z

Figure 5.3.4.2-6 CIS ARS Results – Comparison at Top of Reactor Cavity Z-Direction (Uncracked Analyses)



0

0.2

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0.6

0.8

1

1.2


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 23.583 ft 2nd Floor Z-Z Dynamic Model Envelope at Elev. 23.6 ft 2nd Floor Z-Z

Figure 5.3.4.2-7 CIS ARS Results – Comparison at 2nd Floor Z-Direction (Uncracked Analyses)



0

1

2

3

4

5

6

7

8


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 63.209 ft Top of RCP Y-Y Dynamic Model Envelope at Elev. 63.209 ft Top of RCP Y-Y

Figure 5.3.4.2-8 CIS ARS Results – Comparison at Top of RCP Y-Direction (Uncracked Analyses)



0

2

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10

12

14

16


Acc

ele

rati

on

(g

)

Detailed Model Envelope at Elev. 138.58 ft Top of Pressurizer X-X Dynamic Model Envelope at Elev. 138.58 ft Top of Pressurizer X-X

Figure 5.3.4.2-9 CIS ARS Results – Comparison at Top of Pressurizer Compartment X-Direction (Cracked Analyses)



0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.10 1.00 10.00 100.00Frequency (Hz)

Ac

ce

lera

tio

n (

g)

Detailed Model Node 43524 Elev. 112 ft Top of W St Gen Comp X-X

Dynamic Model Node 2575 Elev. 112 ft Top of W St Gen Comp X-X

Figure 5.3.4.2-10 CIS ARS Results – Comparison at Top of West Steam Generator Compartment X-Direction (Cracked Analyses)



0

1

2

3

4

5

6

7

8

9


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 63.209 ft Top of RCP Y-Y Dynamic Model Envelope at Elev. 63.209 ft Top of RCP Y-Y

Figure 5.3.4.2-11 CIS ARS Results – Comparison at Top of RCP Y-Direction (Cracked Analyses)



0

0.5

1

1.5

2

2.5

3

3.5


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 75.417 ft 4th Floor Y-Y Dynamic Model Envelope at Elev. 75.4 ft 4th Floor Y-Y

Figure 5.3.4.2-12 CIS ARS Results – Comparison at Top of 4th Floor Operational Y-Direction (Cracked Analyses)



0

1

2

3

4

5

6

7


Acc

ele

rati

on

(g

)

Detailed Model Envelope at Elev. 138.58 ft Top of Pressurizer Z-Z Dynamic Model Envelope at Elev. 138.58 ft Top of Pressurizer Z-Z

Figure 5.3.4.2-13 CIS ARS Results – Comparison at Top of Pressurizer Compartment Z-Direction (Cracked Analyses)



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.10 1.00 10.00 100.00Frequency (Hz)

Ac

ce

lera

tio

n (

g)

Detailed Model Node 43524 Elev. 112 ft Top of W St Gen Comp Z-Z

Dynamic Model Node 2575 Elev. 112 ft Top of W St Gen Comp Z-Z

Figure 5.3.4.2-14 CIS ARS Results – Comparison at Top of West SG Compartment Z-Direction (Cracked Analyses)

5.3.4.3 Validation of the PCCV

Acceleration Response Spectra with 5% damping are developed for the PCCV in ACS SASSI for hard rock soil conditions to verify proper model translation. The ACS SASSI generated ARS at various structure locations are then compared to the ANSYS fixed base ARS and are presented in Figure 5.3.4.3-1 through Figure 5.3.4.3-7. The comparison of the ARS indicates that ACS SASSI model captures the structure response to dynamic loads in all directions properly, thus justifying proper translation. Please note that the ARS produced by ACS SASSI demonstrate higher peak responses due to the additional amplification from slight variations in the models used for analysis. The fixed base analysis for the ANSYS model considers fixed boundary conditions at the base of the PCCV structure. The ACS SASSI analysis with hard rock soil conditions considers the entire R/B complex with fixed base boundary conditions at the bottom of the basemat. As discussed in Section 4.3.3, this difference in support elevation creates amplifications at the base of the PCCV as presented in the transfer functions provided in Figure 5.3.4.2-1 and Figure 5.3.4.2-2. This analysis was performed for the uncracked PCCV model only since the cracked model consists of a uniform reduction of stiffness (50% reduction of Young’s modulus) and does not warrant any further justification.



Figure 5.3.4.3-1 PCCV ARS Results – Comparison at Elev. 86.25 ft, X-direction



Figure 5.3.4.3-2 PCCV ARS Results – Comparison at Elev. 145.58 ft, X-direction



Figure 5.3.4.3-3 PCCV ARS Results – Comparison at Elev. 86.25 ft, Z-direction



Figure 5.3.4.3-4 PCCV ARS Results – Comparison at Elev. 86.25 ft, Y-direction



Figure 5.3.4.3-5 PCCV ARS Results – Comparison at Elev. 232 ft, Y-direction



0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 145 ft Z-Z Dynamic Model Envelope at Elev. 145.58 ft Z-Z

Figure 5.3.4.3-6 PCCV ARS Results – Comparison at Elev. 145.58 ft, Z-direction



0

1

2

3

4

5

6

7

8

9


Ac

ce

lera

tio

n (

g)

Detailed Model Envelope at Elev. 230.08 ft Z-Z Dynamic Model Envelope at Elev. 232 ft Z-Z

Figure 5.3.4.3-7 PCCV ARS Results – Comparison at Elev. 232 ft, Z-direction



5.3.5 Summary of Dynamic Properties of R/B Complex Dynamic FE Model

The entire R/B Complex, including the R/B-FH/A, CIS, and PCCV, is represented by the integrated 3-D Dynamic FE Model. The complex is approximately 309 feet in the North-South direction and 213 feet in the East-West direction, resulting in a total footprint area of 65,820 ft2. The model weighs 806,810 kips in total, with an average contact pressure under the foundation of approximately 12.3 ksf

Validation of the Dynamic FE Model is carried out in accordance with the methodology described in Section 4.3 to ensure that the integrated 3-D Dynamic FE Model truly represents the dynamic properties of the R/B Complex structures. Validation procedures and results are summarized in Section 5.3. Figure 5.3.5-1 shows an overview of the integrated 3-D Dynamic FE Model while Figure 5.3.5-2 and Figure 5.3.5-3 reveal the interior structures with section views.

The fixed base dynamic properties of the integrated 3-D Dynamic FE model are presented hereafter. Tables 5.3.5-1 through 5.3.5-3 present the mass per elevation and/or component for each of the three Complex Structures (R/B, CIS and PCCV). Table 5.3.5-4 presents their first three dominant frequencies.

Figure 5.3.5-1 Integrated R/B Complex Dynamic FE Model



Figure 5.3.5-2 Section View of R/B Complex Dynamic FE Model Looking East



Figure 5.3.5-3 Section View of R/B Complex Dynamic FE Model Looking South



Table 5.3.5-1 R/B – Mass per Elevation

Basement - Solid Element excluded El. -26'-4" - El. 3'-7" 2483Solid Element in Basement El. -26'-4" - El. 3'-7" 6657

2nd Floor El. 3'-7" - El. 25'-3" 25963rd Floor El. 25'-3" - El. 50'-2" 29174th Floor El. 50'-2" - El. 76'-5" 21775th Floor El. 76'-5" - El. 101'-0" 1666

Roof excluding FHA El. 101'-0" & up 467FHA El. 76'-5" - El. 154'-6" 586

19549Total Mass

ComponentDynamic Model Elevation

(ft)Mass

(K-s2/ft)

Table 5.3.5-2 PCCV – Mass per Elevation

1 230'-10" 232 322 225'-8" 225 723 202'-4" 198 3114 173'-9" 176 2665 146'-3" 146.2 3886 116'-2" 113.38 2197 92'-10" 99.812 1528 77'-1" 86.25 2269 68'-11" 68.215 16410 50'-10" 50.16 20411 25'-11" 32.146 26012 2'-7" 2.583 153

2447Total Mass

Mass (K-s2/ft)Mass #

Elevation (ft)

Dynamic Model Z coord. (ft)



Table 5.3.5-3 CIS – Mass per Component

Mass (K-s2/ft) Component

Dynamic Model Elevation (ft)

Isolated Pressurizer El. 75'-5" - El. 138'-7" 111 Isolated Steam Generators El. 75'-5" - El. 112'-0" 242

Isolated Reactor Cavity El. 23'-7" - El. 75'-5" 469 Top Slab El. 75'-5" 132

Intermediate Slab El. 49'-6" 77 Bottom Slab El. 23'-7" 180

Water --- 168

Total Mass (*) 1378 (*) Total mass does not include the mass of the walls and solid elements below El. 75'-5"

Table 5.3.5-4 Dominant Frequencies of the R/B Complex Dynamic FE Model

Mode Frequency Mode Frequency Mode Frequency

1 4.47 1 4.47 13 12.442 4.50 2 4.50 14 12.6316 12.93 14 12.63 16 12.93

1 6.03 2 6.71 36 14.325 8.16 3 7.57 115 21.5128 12.37 22 11.55 116 21.60

1 4.57 2 5.16 20 11.503 5.42 4 5.67 22 11.885 6.38 12 8.92 25 12.55

PCCV

CIS

R/B

X Direction Y Direction Z Direction



5.4 Dynamic FE Model of the PS/B

5.4.1 Development of the FE Model of the PS/B

The east and west PS/Bs provide two emergency power sources. The plan dimension of each PS/B is 114’-10” x 69’-4”. Each PS/B is a reinforced concrete structure consisting of vertical shear/bearing walls and horizontal slabs with one floor level under ground and the main floor level above ground.

The west PS/B borders the R/B, A/B, and T/B, while the east PS/B borders the R/B and the T/B. Each PS/B rests on its own basemat. The geometry of the west PS/B is slightly more complicated in that it includes an additional floor slab and walls to create a tray space above elevation 24’-2”. This additional feature, and the fact that the west PS/B borders the A/B as well as the R/B and T/B, makes the west PS/B the worst case configuration. The PS/B analytical models are therefore based on the west PS/B.

Built using the ANSYS preprocessor before being translated into ACS SASSI, the PS/B Dynamic FE model is a 3-D model of the west PS/B resting on top of a 9’-11” thick basemat. It includes shell elements representing walls and slabs, beam elements representing beams and columns, and solid elements representing the basemat. Typically, element sizes in the model range from 4’ to 8’. As a result, the total number of nodes in the model is 3,347 and the total number of elements is 3,797. Figures 5.4.1-1 through 5.4.1-7 show an overview of the PS/B model and reveal its interior structure with various section views. Note that the global origin is located at the center of the PS/B structure at Elevation 0’-0” with X pointing South, Y pointing East, and Z pointing upward.

For transferring the model into ACS SASSI for SSI analyses, all nodes are renumbered sequentially in the order of their X, Y, and Z coordinates to enhance computational efficiency while the necessary 3rd orientation node is added to all beam elements.

For SSI purposes, the basemat footprint in the Dynamic FE model is extended to the external face of perimeter walls instead of their centerline.

For simplicity without compromising accuracy, some of the slab elevations in the Dynamic FE Model are slightly shifted upward or downward such that the middle planes of these slabs fall into a common horizontal plane. Also, only large openings in slabs and walls are included in the model. Wall properties are adjusted to account for the presence of small openings not included in the model as described in Section 4.4.1.5.

Special attention is also given in the Dynamic FE Model as to how wall and slab shell elements are connected to the basement/mat solid elements. Wall shell elements are extended into the basemat solid elements to ensure a proper transfer of bending moment between them. These connecting elements are also assigned a zero density not to increase the overall mass of the basemat.



Figure 5.4.1-1 Overview of PS/B Dynamic FE Model

Figure 5.4.1-2 PS/B Dynamic FE Model (EL. -26’-4”)



Figure 5.4.1-5 PS/B Dynamic FE Model (EL. 24’-2”)

Figure 5.4.1-6 PS/B Dynamic FE Model (Roof – EL. 39’-6” and EL. 49’-0”)



Figure 5.4.1-7 PS/B Dynamic FE Model (Beams and Columns) (elements shown are beam elements but are displayed by ANSYS as brick type shapes)

5.4.2 Attributes Assigned to the PS/B Dynamic FE Model

The material, sectional properties and dynamic mass attributed to the Dynamic FE model are calculated as per the methodology described in Section 4.4 and its subsections. The attributes of the model include:

Adjusted material and sectional properties for PS/B walls with and without openings to include applicable additional dynamic masses.

Adjusted material and sectional properties for PS/B slabs to include applicable additional dynamic masses.

Material and sectional properties for PS/B beams and columns.

5.4.3 Validation of the PS/B Dynamic FE Model

Validation of the PS/B Dynamic FE Model is carried out in accordance with the methodology described in Section 4.4.3. A summary of these results is presented hereafter.

It is noted that the Detailed PS/B Model utilizes uncracked concrete material properties. Therefore, for comparison and validation purposes, uncracked concrete material properties are also assigned to the Dynamic PS/B Model.



Partial solutions are performed using ANSYS to calculate masses of each floor. The mass of each floor section is taken as the mass of the floor plus that of the walls between the current floor and the floor at the immediate lower elevation. Results in Table 5.4.3-1 indicate that the total mass of the two models are comparable with a difference of 3.74%. The mass differences for each floor section are also acceptable, ranging from 0.44% to 5.92%.

Table 5.4.3-1 PS/B Floor Mass Comparison


Floor Bottom Elev. (ft)

Top Elev. (ft)

Weight (kips)

Bottom Elev.

Top Elev.

Weight (kips)

Difference

B1F Elev. -26'-4" -36.25 -26.33 12,515 -36.25 -26.33 13,303 5.92% B1MF Elev.

-14'-2" -26.33 -5.67 6,996 -26.33 -5.33 7,323 4.46%

1F Elev. 3'-7" -5.67 12.68 9,014 -5.33 12.58 9,153 1.51% Elev. 24'-2" 12.68 33.21 4,253 12.58 32.29 4,234 -0.44%

Roof Elev. 39'-6" 33.21 38.88 3,976 32.29 38.88 4358 8.78% Roof Elev. 49'-0" 38.88 48.38 3,144 38.88 48.38 3489 9.89%

Total -- -- 39,898 -- -- 41,830 4.62%

5.4.3.1 1g Static Analysis

1g static analysis in the horizontal (X and Y) directions with full constraints at the bottom of the common basemat are performed on both the Detailed and Dynamic FE models of the PS/B.

Displacement results from the 1g static analyses are used to compare the structure stiffness of the two models in the horizontal directions. Lateral displacements in the two horizontal directions (X and Y) along the height of the four corners of both models are plotted in Figures 5.4.3-1 though 5.4.3-8. They all demonstrate that the Dynamic Model lateral stiffness is comparable to that of the Detailed Model (structure behavior follows the same trend for both models) in both directions (X and Y). Table 5.4.3-2 indicates that the maximum roof level lateral displacement difference between the two models varies from 1.22% to 7.94% in the NS (X) direction and from 0.11% to 1.35% in the EW (Y) direction.



Figure 5.4.3-1 PS/B 1g Static Analysis Results – NS Direction (X) at Northeast Corner

Figure 5.4.3-2 PS/B 1g Static Analysis Results – EW Direction (Y) at Northeast Corner



Figure 5.4.3-3 PS/B 1g Static Analysis Results – NS Direction (X) at Northwest Corner

Figure 5.4.3-4 PS/B 1g Static Analysis Results – EW Direction (Y) at Northwest Corner



Figure 5.4.3-5 PS/B 1g Static Analysis Results – NS Direction (X) at Southeast Corner

Figure 5.4.3-6 PS/B 1g Static Analysis Results – EW Direction (Y) at Southeast Corner



Figure 5.4.3-7 PS/B 1g Static Analysis Results – NS Direction (X) at Southwest Corner

Figure 5.4.3-8 PS/B 1g Static Analysis Results – EW Direction (Y) at Southwest Corner



Table 5.4.3-2 PS/B Roof Lateral Displacement Comparison

Detailed Model

Dynamic Model

Detailed Model

Dynamic Model

Northeast 0.0160 0.0155 3.18% 0.0103 0.0103 0.11%Northwest 0.0132 0.0122 7.94% 0.0096 0.0095 -1.23%Southeast 0.0147 0.0142 3.79% 0.0097 0.0098 1.35%Southwest 0.0154 0.0152 1.22% 0.0114 0.0114 -0.27%

Locations

NS Direction EW Direction

Displacement (in)Difference

Displacement (in)Difference

5.4.3.2 Modal Analysis

A modal analysis using ANSYS is performed on both the Detailed and the Dynamic FE Models of the PS/B. Plots of Cumulative Mass versus Frequency are shown in Figure 5.4.3-9 through Figure 5.4.3-11. The results of the modal analysis indicate that the Dynamic FE model captures the dynamic properties of the Detailed FE model adequately.

Figure 5.4.3-9 PS/B Modal Analysis Results – Cumulative Mass in the NS Direction (X)



Figure 5.4.3-10 PS/B Modal Analysis Results – Cumulative Mass in the EW Direction (Y)



Figure 5.4.3-11 PS/B Modal Analysis Results – Cumulative Mass in the Vertical Direction (Z)

5.4.3.3 Modal Superposition Time History Analysis

A dynamic time-history response analysis using modal superposition is performed on both PS/B models using ANSYS. Acceleration response spectra (ARS) with 5% damping are generated for each model at various locations. These acceleration response spectra indicate that the Dynamic FE Model captures the structure response to dynamic loads in all directions properly. Figure 5.4.3-12 through Figure 5.4.3-20 show the comparison of Detailed and Dynamic FE Model ARS for representative locations. Generally, results of ARS from both modes are comparable and negligible deviations are observed. Figure 5.4.3-14 shows marginal difference between two models for the Z direction response due to Z direction excitations. The difference is contributed to the factors that the compared locations are not exactly same locations for the two models and the geometry (span) of the slabs in the two models are slightly different. The impact of this difference on the ISRS of the floor is expected to be minimal because the ISRS will be obtained from enveloping and broadening the SSI analysis results from the model with two level of stiffness.



Figure 5.4.3-12 PS/B ARS Results – Comparison at Elev. 3’-7” Interior, X-direction



Figure 5.4.3-13 PS/B ARS Results – Comparison at Elev. 3’-7” Interior, Y-direction



Figure 5.4.3-14 PS/B ARS Results – Comparison at Elev. 3’-7” Interior, Z-direction



Figure 5.4.3-15 PS/B ARS Results – Comparison at Elev. 3’-7” Perimeter, X-direction



Figure 5.4.3-16 PS/B ARS Results – Comparison at Elev. 3’-7” Perimeter, Y-direction



Figure 5.4.3-17 PS/B ARS Results – Comparison at Elev. 3’-7” Perimeter, Z-direction



Figure 5.4.3-18 PS/B ARS Results – Comparison at Elev. 39’-6” Interior, X-direction



Figure 5.4.3-19 PS/B ARS Results – Comparison at Elev. 39’-6” Interior, Y-direction



Figure 5.4.3-20 PS/B ARS Results – Comparison at Elev. 39’-6” Interior, Z-direction

5.4.4 Local Out-of-Plane Vibration of the Slabs

As discussed in Section 4.4.2, the dynamic properties, i.e., mass and stiffness (modulus of elasticity), of the flexible slabs with frequency below 70 Hz are checked by performing a series of modal analyses using ANSYS on isolated sub-models at each elevation. The first 3 dominant frequencies of each slab from the original models are obtained and the frequencies compared. The frequencies of all major slabs were found to match those of the Detailed FE model. The results from these analyses are presented hereafter.

Figure 5.4.4-1 to Figure 5.4.4-4 are a sample of the plots obtained from the modal analysis performed on the isolated elevations of the Detailed and Dynamic FE model using ANSYS.



Figure 5.4.4-1 Ground Floor (EL. 3’-7”) – Detailed Model - 1st Dominant Frequency

Figure 5.4.4-2 Ground Floor (EL. 3’-7”) – Dynamic Model - 1st Dominant Frequency



Figure 5.4.4-3 Ground Floor (EL. 3’-7”) – Detailed Model – 2nd Dominant Frequency

Figure 5.4.4-4 Ground Floor (EL. 3’-7”) – Dynamic Model – 2nd Dominant Frequency



5.4.5 ACS SASSI Validation

After the Dynamic FE Model is validated against the Detailed FE Model, it is translated into ACS SASSI (Reference 2) using the built in file converter. To confirm that the translation is accurate and correct, an analysis is run with the PS/B model sitting on hard rock to simulate a fixed base condition. Transfer functions from this analysis are compared with the modal analysis results of the Dynamic FE Model to ensure that the mass and stiffness properties are accurate. Response spectra produced are also compared with the ARS from the Dynamic FE Model to ensure that the structural response is accurate as well. Figures 5.4.5-1 through 5.4.5-3 show the transfer function plots. These plots indicate that the ACS SASSI model accurately captures the dynamic properties of the PS/B when compared against the validated Dynamic FE Model. Figures 5.4.5-4 through 5.4.5-9 present the ACS SASSI response spectra compared to the Dynamic FE Model ARS for selected group of nodes. The ARS curves in the plots are the envelope of ARS of the corresponding group of nodes. In the plots, label with “ACS SASSI” indicates the curves are the results of SSI analysis performed on the model sitting on a very stiff half space while label with “Dynamic Model” indicates the curves are obtained from ANSYS modal superposition time history analysis performed on the model with fixed base boundary condition. The comparison shows that the ACS SASSI model accurately represents the structural response of the validated Dynamic FE Model. Differences are observed from the figures for the analysis results using two different codes. They are acceptable based on acceptance criteria and justifications discussed in Section 4.3.3 of this report.



Figure 5.4.5-1 PS/B ACS SASSI Results – Transfer Functions NS Direction



Figure 5.4.5-2 PS/B ACS SASSI Results – Transfer Functions EW Direction



Figure 5.4.5-3 PS/B ACS SASSI Results – Transfer Functions Vertical Direction



Figure 5.4.5-4 PS/B ACS SASSI Results – ARS Comparison at Elev. 3’-7” X-direction



Figure 5.4.5-5 PS/B ACS SASSI Results – ARS Comparison at Elev. 3’-7” Y-direction



Figure 5.4.5-6 PS/B ACS SASSI Results – ARS Comparison at Elev. 3’-7” Z-direction



Figure 5.4.5-7 PS/B ACS SASSI Results – ARS Comparison at Elev. 39’-6” X-direction



Figure 5.4.5-8 PS/B ACS SASSI Results – ARS Comparison at Elev. 39’-6” Y-direction



Figure 5.4.5-9 PS/B ACS SASSI Results – ARS Comparison at Elev. 39’-6” Z-direction

5.4.6 Results and Conclusion

Figures 5.4.6-1, 5.4.6-2 and 5.4.6-3 present the Dynamic FE model developed for the SSI analysis of the US-APWR East and West Power Source Buildings. Developed using ANSYS preprocessor before being translated into ACS SASSI, this model is generated only for the West PS/B but it represents both buildings since both are nearly identical structurally. The overall dimensions of the model are 69’-4” in the N-S direction by 114’-10” in the EW direction, resulting in a total footprint area of 7,962 ft2. The model weighs 41,845 kips in total, with an average contact pressure under the foundation of approximately 5.3 ksf.

Based on the results of the validation analyses summarized in this report, it can be concluded that the Dynamic FE model of the PS/B truly represents the dynamic properties of the two PS/B structures. Table 5.4.6-1 presents the dominant frequencies of the PS/B Dynamic FE model with full stiffness, while Figures 5.4.6-1 to 5.4.6-2 show additional section views of the model. A structure overview and other sectional views of the model are presented in figures 5.4.1-1 through 5.4.1-7.



Figure 5.4.6-1 Section View of Dynamic PS/B Model Looking East

Figure 5.4.6-2 Section View of Dynamic PS/B Model Looking South



Table 5.4.6-1 Dominant Frequencies of the PS/B Dynamic FE Model

NS Direction (X) EW Direction (Y) Vertical Direction (Z)

Mode Frequency (Hz) Mode Frequency (Hz) Mode Frequency (Hz)

1 7.8 2 9.4 9 17.4

13 18.7 11 18.1 10 17.7

15 19.9 19 21.4 12 18.5

26 23.5 20 21.9 48 31.5



6 REFERENCES

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2. ACS SASSI: Version 2.3.0 Including Option A, “An Advanced computational Software for 3-D Dynamic Analysis Including Soil-Structure Interaction,” User Manuals Revision 3.0, Ghiocel Predictive Technologies, Inc., December 30, 2010.

3. Seismic System Analysis, NUREG-0800 Section 3.7.2, Revision 3, U.S. Nuclear Regulatory Commission, Washington, DC, March 2007.

4. Non-Stationary Spectral Matching, Seismological Research Letters #63, Page 30, Abrahamson, N. A., 1992.

5. Generation of Synthetic Time Histories Compatible with Multi-Damping Design Response Spectra, 9th SMiRT, pages 105-110, Lilhan, K, and W.S. Tseng, 1987.

6. Surface Geology Based Strong Motion Amplification Factors for the San Francisco Bay and Los Angeles Areas, A PEARL report to PG&E/CEC/Caltrans, Award No. SA2120-59652. Silva, W. J.S. Li, B. Darragh, and N. Gregor, 1999.

7. Guidelines for Determining Design Basis Ground Motions, Volumes 1-5, TR-102293, Electric Power Research Institute, Palo Alto, CA, 1993.

Vol.1: Methodology and Guidelines for Estimating Earthquake Ground Motion in Eastern North America

Vol. 2: Appendices for Ground Motion Estimation

Vol. 3: Appendices for Field Investigations

Vol. 4: Appendices for Laboratory Investigations

Vol. 5: Quantification of Seismic Source Effects

8. CEUS Ground Motion Project, Final Report, Technical Report TR-1009684, Electric Power Research Institute, Palo Alto, CA, 2004.

9. Technical Basis for Revision of Regulatory Guidance on Design Ground Motions: Hazard- and Risk-Consistent Ground Motions Spectra Guidelines, NUREG/CR-6728, Prepared for Division of Engineering Technology, Washington, DC., 2001.

10. Characteristics of Vertical Strong Ground Motions for Applications to Engineering Design, NCEER-97-0010, Proceedings of the FHWA/NCEER Workshop on the National Representation of Seismic Ground Motion for New and Existing Highway Facilities, I.M. Friedland, M.S Power and R. L. Mayes eds., Silva, W.J., 1997.

11. ANSYS, Advanced Analysis Techniques Guide, Release 11.0, ANSYS, Inc., 2007.

12. Seismic Analysis of Safety-Related Nuclear Structures and Commentary, ASCE 4-98, American Society of Civil Engineers, 1998.

13. Seismic Design Criteria for Structures, Systems, and Components in Nuclear Facilities, ASCE/SEI 43-05, American Society of Civil Engineers, 2005.



14. Code Requirements for Nuclear Safety Related Concrete Structures, ACI 349-01, American Concrete Institute, 2001.

15. Design Response Spectra for Seismic Design of Nuclear Power Plants, RG 1.60, Revision 1, U. S. Nuclear Regulatory Commission, December 1973.

16. Technical Basis for Revision of Regulatory Guidance on Design Ground Motions: Development of Hazard- and Risk-Consistent Seismic Spectra for Two Sites, NUREG/CR-6769, U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, Washington, DC 20555-0001, 2002.

17. Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes, Seismological Research Letter, 68(1), pages 94-127, Abrahamson, N.A. and Silva, W.J., 1997.

18. Properties of vertical ground motions, Bulletin of the Seismological Society of America, 92(2), pages 3152-3164, Beresnev, I.A, Nightengale, A.M. Silva, W.J., 2002.

19. Updated Near-Source Ground-Motion (Attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra, Bulletin of the Seismic Society of America, 93(1), pages 314-331, Campbell, K. W. and Y. Bozorgnia, 2003.

20. SPECTRA 2650, User's Manual, URS Washington Division, Version 3.0.

21. PEER NGA Strong Motion Database, Pacific Earthquake Engineering Research Center, http://peer.berkeley.edu/nga/, University of California, Berkeley, CA, 2006.

22. Earthquake Engineering Criteria for Nuclear Power Plants, Energy. Title 10, Code of Federal Regulations, Part 50, Appendix S, U.S. Nuclear Regulatory Commission, Washington, DC.

23. Soil-Structure Interaction Analyses and Results for the US-APWR Standard Plant, MUAP-10006, Revision 2, Mitsubishi Heavy Industries, Ltd., October, 2011.

24. Assessment of Seismic Hazard at 34 U.S. Nuclear Plant Sites, TR-1016736, Electric Power Research Institute, Palo Alto, CA, 2008.

25. Specification for Structural Steel Buildings, AISC 360-05, American Institute of Steel Construction, Inc., Chicago, IL 2005.

26. Interim Staff Guidance on Seismic Issues Associated with High Frequency Ground Motion in Design Certification and Combined License Applications, DC/COL-ISG-1, Nuclear Regulatory Commission, May 2008.

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29. US-APWR Standard Design, Load Distribution, Power Source Building, N0-EHB0021, Revision 4, Mitsubishi Heavy Industries, Ltd., September 2009.

30. Damping Values for Seismic Design of Nuclear Power Plants, RG 1.61, Revision 1, U. S. Nuclear Regulatory Commission, March 2007.

31. APA Consulting Computer Code SPECTRUM, Version 2.0

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33. Results of Evaluation Using LMSM for R/B Complex, MUAP-11007, Revision 1, Mitsubishi Heavy Industries, Ltd., October 2011.

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35. Mok, Chin Man, Chang, C.-Y., and Lagapsi, Dante E., “Site Response Analyses of Vertical Excitation”, Proceedings of the Third Specialty Conference on Geotechnical Earthquake Engineering and Soil Dynamics, Seattle, Washington, Geotechnical Special Publication No. 75, ASCE, August 3 – 6, 1998.

36. Nahanni, Canada earthquake-December 23, 1985. 37. Dynamic FE Model Development of R/B Complex, URS Calculation

REB-13-05-113-003, June 9, 2011, URS Corporation.

38. Dynamic Model Development and Validation of PS/B, URS Calculation PSB-13-05-113-001, June 17, 2011, URS Corporation.


Mitsubishi Heavy Industries, LTD. A-1

APPENDIX A - DELETED


Mitsubishi Heavy Industries, LTD. B-1

APPENDIX B - EFFECTS OF CONCRETE CRACKING ON THE US-APWR PRE-STRESSED CONCRETE CONTAINMENT VESSEL (PCCV) RESPONSE



Effects of Concrete Cracking on the US-APWR Pre-stressed Concrete Containment Vessel (PCCV) Seismic Response

The design evaluation of the PCCV structure was done considering both Service and Factored load conditions in accordance with ASME Section III (Reference B4), Division 2 load combinations. Cracked concrete conditions were evaluated using section design results for locations from the top of the base mat to the dome apex based on the initial PCCV dynamic response that assumed only uncracked concrete material properties. The cracked conditions were evaluated for two load conditions; 1) Primary loads only, and 2) Primary plus Secondary (thermal), for the various ASME load combinations. Based upon the analyses, tension induced concrete cracking would be expected to occur in the area near the basemat and at the transition area between the dome and the cylindrical shell for primary load combinations that include pressure and pressure plus seismic loads. For the load combinations that include primary plus secondary thermal conditions, the design evaluation found varying degrees of concrete cracking would be expected to occur in generally all areas from the base mat to the dome apex.

It is recognized that in addition to a redistribution of forces, concrete cracking may affect the stiffness of the PCCV structure and ultimately affecting the seismic structural response. Given the PCCV structure is predicted to crack under primary load conditions excluding thermal, it is reasonable to use a reduced stiffness in the evaluation of the PCCV seismic response. In absence of industry guidance specific to post tensioned containment structures, the recommended reduced stiffness values consistent with industry standards for RC (reinforced concrete) structures will be used and are considered conservative for the PCCV post tensioned concrete structure. The effects of concrete cracking will be addressed in the further evaluation of the dynamic response for the PCCV consistent with CC-3320 of the ASME code (Reference B4) and within the guidance of NUREG-0800 (Reference B6). This is done using an upper bound and lower bound dynamic analysis that is used to develop an enveloping structural response in each orthogonal direction for further use in PCCV seismic design.

Each PCCV seismic response analysis will use the same analytical model changing only the stiffness and damping levels. The upper bound analysis will use full stiffness properties representing the uncracked PCCV as follows:

Flexural Rigidity: 1.0EcIg

Shear Rigidity: 1.0GcAw

Axial Rigidity: 1.0EcAg

For the upper bound case the load combination stress levels are taken to be less than 80% of the applicable code stress limits, thereby an operating basis earthquake (OBE) damping value of 3% critical damping will be used.

The lower bound analysis will use reduced stiffness properties representing the cracked concrete PCCV as follows:

Flexural Rigidity: 0.5EcIg

Shear Rigidity: 0.5GcAw



Axial Rigidity: 0.5EcAg

For the lower bound condition the load combination stress levels are taken to be at least 80% of code stress limits, thereby a safe shutdown earthquake (SSE) damping value of 5% critical damping will be used.

Nomenclature: Ec = Concrete compressive modulus = 57,000(f`c)½

Ig = Gross moment of inertia

Gc = Concrete shear modulus = 0.4Ec

Aw = Web (shear) area

Ag = Gross area of concrete section

REFERENCES:

B1. FEMA 356 “Prestandard and Commentary for the Seismic Rehabilitation of Buildings” prepared by American Society of Civil Engineers (ASCE) for Federal Emergency Management Agency, Washington D.C., November 2000.

B2. ASCE Standard 4-98, “Seismic Analysis of Safety-Related Nuclear Structures and Commentary”, American Society of Civil Engineers.

B3. ASCE/SEI Standard 43-05, “Seismic Design Criteria for Structures, Systems and Components in Nuclear Facilities”, American Society of Civil Engineers and Structural Engineering Institute.

B4. ASME B&PVC, “ ASME Boiler and Pressure Vessel Code, Section III Division 2, 2001 through 2003 Winter Addenda, American Society of Mechanical Engineers, New York, N.Y.

B5. NUREG/CR-6926, “Evaluation of the Seismic Design Criteria in ASCE/SEI Standard 43-05 for Application to Nuclear Power Plants”, U.S. Nuclear Regulatory Commission, March 2007.

B6. NUREG-0800 “Standard Review Plan”, Office of Nuclear Reactor Regulation, U.S. Nuclear Regulatory Commission, Washington D.C.

B7. ICONE-7405 “Seismic Proving Test of a Prestressed Concrete Containment Vessel Shaking Test and Analytical Results”, Y. Sasaki, S. Tsurumaki, K. Satoh, H. Fuyama, T. Kitani, H. Eto, K. Tsuda, K. Takiguchi, H. Akiyama, April 1999.

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