NUREG/CR-6906

 SAND2006-2274P 

Containment Integrity Research at

Sandia National Laboratories

An Overview 

Sandia National Laboratories

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
 

 

 

 NUREG/CR-6906

 SAND2006-2274P

Containment Integrity Research at

Sandia National Laboratories

An Overview

Manuscript Completed: March 2006

Date Published: July 2006

Prepared by

M. F. Hessheimer1

R. A. Dameron2

1 Sandia National Laboratories 

P.O. Box 5800

Albuquerque, NM 87185

2 David Evans and Associates, Inc.

9635 Granite Ridge Drive

Suite 300

San Diego, CA 92123

A. Sheikh, Program Manager

Prepared for

Division of Fuel, Engineering & Radiological Research

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Job Code Y6757
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ABSTRACT 

For nearly thirty years, significant research has been performed at Sandia National Laboratories to 

improve the understanding of the response of nuclear power plant steel and concrete containment 

structures and their capacity to withstand accidents beyond their design basis and other extreme 

loads. This work has consisted of experimental programs and analytical studies to investigate the 

response and capacity of containment structures and components for a wide variety of loading 

conditions with a primary emphasis on internal overpressurization. This report summarizes the 

work that has been performed and the results of these efforts, and identifies common themes that 

have emerged. The most detailed information provided is of the research conducted at Sandia 

National Laboratories, sponsored by the Nuclear Regulatory Commission. But effort is made to 

also highlight work conducted by other research organizations throughout the world to put the 

Sandia/NRC research into context and to attempt to summarize the current practice for evaluating 

containments subjected to accident loads. 
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CONTENTS 

ABSTRACT ................................................................................................................................... iii 

FOREWORD....................................................................................................................................v 

EXECUTIVE SUMMARY............................................................................................................xv

ACKNOWLEDGEMENTS ..........................................................................................................xix 

ACRONYMS ................................................................................................................................xxi 

1 INTRODUCTION.......................................................................................................1

1.1 Objectives................................................................................................................... 1

1.2 Scope .......................................................................................................................... 1

1.3 Report Organization ................................................................................................... 2

2 BACKGROUND.........................................................................................................3

2.1 Historical Background on U.S. Containment Design and Performance 

Criteria........................................................................................................................ 3

2.2 Containment Design Practice ..................................................................................... 6

2.2.1 Containment Types......................................................................................................6

2.2.2 Containment Design ..................................................................................................22

2.2.3 Containment Response to Severe Accidents .............................................................25

2.3 Background of Containment Testing at Sandia........................................................ 35

3 CONTAINMENT MODEL TESTS..........................................................................37

3.1 Containment Model Testing for ‘Beyond-Design Basis’ Loading........................... 37

3.2 Modeling Considerations.......................................................................................... 40

3.2.1 Scaling .......................................................................................................................41

3.2.2 Failure........................................................................................................................42

3.3 Steel Containment Model Tests................................................................................ 44

3.3.1 NRC 1:32-scale steel models.....................................................................................44

3.3.2 NRC 1:8-scale steel containment model....................................................................47

3.3.3 NUPEC/NRC 1:10/1:4-scale steel containment vessel model ..................................52

3.3.4 Other Steel Model Tests ............................................................................................59

3.3.5 Conclusions of Steel Model Tests .............................................................................59

3.4 Reinforced Concrete Containment Model Tests....................................................... 61

3.4.1 NRC 1:6-scale reinforced concrete model.................................................................62

3.4.2 Separate Effects Tests for Reinforced Concrete Model ............................................66

3.4.3 CTL/EPRI Tests ........................................................................................................68

3.5 Prestressed Concrete Containment Models .............................................................. 74
viii 

3.5.1 NUPEC/NRC Prestressed Concrete Containment Vessel (PCCV) Model 

Test ............................................................................................................................74

3.5.1.1 Pressure Tests ........................................................................................................... 78

3.5.1.2 Analysis .................................................................................................................... 88

3.5.2 1:10-scale prestressed concrete model (Sizewell-B) .................................................99

3.5.3 Other Prestressed Concrete Containment Model Tests ...........................................103

3.5.3.1 1:12-scale prestressed concrete model (India) [59] ................................................ 103

3.5.3.2 1:10-scale prestressed concrete model (Poland) [60] ............................................. 103

3.5.3.3 1:14-scale prestressed concrete CANDU model (Canada) [61, 62, 63, 64] ........... 103

3.5.3.4 Large-scale prestressed concrete model (EPR, France/Germany, Civaux) ............ 104

3.6 Component (Penetration) Tests .............................................................................. 104

3.6.1 Compression Seals & Gaskets [83, 84] ...................................................................104

3.6.2 Electrical Penetration Assemblies [85]....................................................................104

3.6.3 Personnel Airlocks [86, 87].....................................................................................105

3.6.4 Inflatable Seals [88].................................................................................................106

3.6.5 Equipment Hatch, Drywell Head [89, 90]...............................................................106

3.6.6 Bellows [93, 94] ......................................................................................................106

3.7 Related Containment Research Activities .............................................................. 108

3.7.1 Containment Performance Goals.............................................................................108

3.7.2 Degraded Containment Capacity Analyses .............................................................109

3.7.3 Risk-Informed Assessment of Degraded Containment Capacity ............................110

3.7.4 Seismic Capacity Tests and Analyses .....................................................................112

3.7.5 Impact Tests and Analyses ......................................................................................112

3.7.5.1 Turbine Missile Tests ............................................................................................. 113

3.7.5.2 Full-Scale Aircraft Impact Test at SNL.................................................................. 113

3.7.5.3 Full Scale Engine Tests .......................................................................................... 114

3.7.5.4 ‘Water-Slug’ Tests.................................................................................................. 114

3.7.6 Leakage Tests ..........................................................................................................114

4 ASSESSMENT OF CONTAINMENT PRESSURE CAPACITY..........................117

4.1 Insights from Containment Testing ........................................................................ 117

4.2 Insights from Containment Analysis ...................................................................... 119

4.3 Analysis Goals........................................................................................................ 120

4.3.1 Global Response Prediction.....................................................................................120

4.3.2 Local Response Prediction ......................................................................................121

4.3.3 Failure Prediction ....................................................................................................122
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4.4 Analytical Research Findings................................................................................. 123

4.4.1 Steel Containment Analysis.....................................................................................123

4.4.1.1 Material Modeling .................................................................................................. 123

4.4.1.2 Geometric Nonlinearities........................................................................................ 124

4.4.1.3 Element Formulation .............................................................................................. 124

4.4.2 Concrete Containment Analysis ..............................................................................124

4.4.2.1 Material Modeling .................................................................................................. 124

4.4.2.2 Geometric Nonlinearities and Other Issues ............................................................ 125

4.4.3 Comparison of Analyses Methods Used for Predicting Model Behavior with 

US Containment Design Practice ............................................................................125

4.4.4 Temperature Effects ................................................................................................126

4.5 Recommendations for Prototype Containment Capacity Estimates....................... 133

4.5.1 Current Practice .......................................................................................................133

4.5.2 Recommendations for Design and Performance .....................................................136

4.5.3 Recommendations for Containment Capacity Analysis ..........................................137

4.5.3.1 Steel Containments................................................................................................. 137

4.5.3.2 Concrete Containments........................................................................................... 137

4.6 Conclusions from Containment Model Tests ......................................................... 140

4.7 Issues for Future Consideration.............................................................................. 141

4.7.1 Leakage....................................................................................................................141

4.7.2 Other Considerations ...............................................................................................142

5 REFERENCES ........................................................................................................145

 APPENDIX - Containment Capacity Analysis Guidelines.................................... A-1 
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FIGURES 

Figure 1 Typical PWR Large Dry Containment with Prestressed Containment (e.g. 

Palisades)...................................................................................................................11

Figure 2 Large Dry Steel Containment with Reinforced Concrete Shield Building 

(e.g. Davis-Besse)......................................................................................................12

Figure 3 Typical PWR Subatmospheric Reinforced Concrete Containment 

(e.g. Diablo Canyon) .................................................................................................13

Figure 4 Typical PWR Ice Condenser Steel Containment with Concrete Shield 

Building (e.g. Sequoyah)...........................................................................................14

Figure 5 Typical BWR Mark I Concrete Containment with Steel Torus.................................15

Figure 6 Typical BWR Mark II Containment [1] ....................................................................16

Figure 7 BWR Mark II Concrete Containment (LaSalle Units 1 & 2) ....................................17

Figure 8 BWR Mark II Steel Containment with Concrete Shield Building (Columbia, 

previously WNP-2)....................................................................................................18

Figure 9 BWR Mark II Reinforced Concrete Containment (Limerick 1 & 2).........................19

Figure 10 Typical BWR Mark III Containment.........................................................................20

Figure 11 Typical BWR Mark III Containment.........................................................................21

Figure 12 Typical Containment Volume and Design Pressure for US plants [1] ......................24

Figure 13 Containment Failure Pressures for NUREG-1150 Plants [7] ....................................28

Figure 14 IPE Fragility Curves for Large Dry Prestressed Concrete Containments .................30

Figure 15 IPE Fragility Curves for Large Dry Reinforced Concrete Containments..................31

Figure 16 IPE Fragility Curves for Large Dry Steel Containments...........................................31

Figure 17 IPE Fragility Curves for Ice Condenser Containments .............................................32

Figure 18 IPE Fragility Curves for Sub-Atmospheric Reinforced Concrete 

Containments.............................................................................................................32

Figure 19 IPE Fragility Curves for BWR Mark I ......................................................................33

Figure 20 IPE Fragility Curves for BWR Mark II .....................................................................33

Figure 21 IPE Fragility Curves for BWR Mark III....................................................................34

Figure 22 Timeline for Containment Integrity Research at SNL...............................................38

Figure 23 1:32-Scale Steel Containment Vessel Models...........................................................46

Figure 24 SC-1 and SC-3 Tests .................................................................................................46

Figure 25 1:8-Scale Steel Containment Model Layout..............................................................47

Figure 26 1:8-Scale Steel Containment Model ..........................................................................48

Figure 27 Results of 1:8-Scale Steel Containment Vessel Model Test.............................49 & 50

Figure 28 Comparison of Predicted and Measured Hoop Strains in the 1:8-Scale Steel 

Containment Vessel Model. [25]...............................................................................51
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Figure 29 Pretest Analysis vs. As-built Configuration of Stiffeners at 1:8-Scale Steel 

Model Equipment Hatch............................................................................................51

Figure 30 1:10-Scale Steel Containment Model Summary........................................................54

Figure 31 Posttest View of Tears at E/H, 1:10-Scale Steel Containment Model.......................55

Figure 32 Posttest Interior View of the 1:10-Scale Steel Model ...............................................55

Figure 33 Tear at Horizontal Stiffener ‘Rat-Hole’, 1:10-Scale Steel Containment 

Model.........................................................................................................................56

Figure 34 Displacement contours (x10) @ 4.5 MPa..................................................................57

Figure 35 Cross-section through large tear at equipment hatch.................................................57

Figure 36 Comparison of Pretest Predictions of Hoop Strain with Test Results .......................59

Figure 37 Cross-section of the 1:6-Scale Reinforced Concrete Containment Vessel 

Model.........................................................................................................................62

Figure 38 1:6-Scale Reinforced Concrete Containment Model Construction ...........................63

Figure 39 Major Liner Tear in 1:6-Scale Reinforced Concrete Model......................................64

Figure 40 Developed Elevation of the 1:6 Scale RC Model Cylinder showing Liner 

Tear Locations...........................................................................................................64

Figure 41 Posttest Analysis of 1:6-Scale RC Model Liner at 1.0 MPa (145 psig) ...................66

Figure 42 Separate Effects Test Liner Specimens .....................................................................67

Figure 43 Containment Wall Panel Specimen Test Strategy for EPRI/CTL Tests [51] ............69

Figure 44 Typical R/C, P/C Containment Geometries used in EPRI Global Analyses 

[51] ............................................................................................................................70

Figure 45 Liner Vertical Strains Measured (and Analyzed) in EPRI/CTL Specimen 

2.5, Wall-Skirt Juncture of a Typical P/C Containment............................................70

Figure 46 Liner Plate Details for EPRI/CTL Specimen 2.4.......................................................71

Figure 47 Liner Plate Details for EPRI/CTL Specimen 2.2, Which Studied Leak Rates 

Through an Advancing Liner Crack Tip ...................................................................72

Figure 48 Idealization of Flow of Pressurized Gas Through a Liner Tear [56].........................73

Figure 49 Ohi Nuclear Power Station, Ohi-cho, Fukui, Japan...................................................75

Figure 50 PCCV Model Elevation and Cross-Section...............................................................76

Figure 51 PCCV Model Construction........................................................................................77

Figure 52 Completed PCCV Model...........................................................................................77

Figure 53 PCCV Pressurization Plan Sequence (not to scale)...................................................78

Figure 54 Limit State Test Pressure and Average Temperature ................................................79

Figure 55 Internal Acoustic Sensor Signals @ the Equipment Hatch .......................................80

Figure 56 LST - Estimated Leak Rates (2.5-3.1 Pd) ..................................................................80

Figure 57 LST Estimated Terminal Leak Rates.........................................................................81

Figure 58 LST - Deformation @ Az. 135o and 324o (Z and L)..................................................82
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Figure 59 Post-LST Liner Tears ................................................................................................82

Figure 60 Tear #7 at Equipment Hatch......................................................................................83

Figure 61 Tear #12 at Equipment Hatch....................................................................................83

Figure 62 SFMT: Rupture of the PCCV Model.........................................................................85

Figure 63 PCCV Model after the Structural Failure Mode Test................................................85

Figure 64 SFMT – Radial Displacement at Az. 135o, El. 6200 .................................................86

Figure 65 SFMT Wire Break Events vs. Pressure vs. Displacement.........................................87

Figure 66 SFMT - Deformation @ Az. 135o (Z) .......................................................................87

Figure 67 SFMT - Deformation @ Az. 324o (L) .......................................................................88

Figure 68 Axisymmetric Model of 1:4-scale PCCV..................................................................89

Figure 69 Local Model of Equipment Hatch .............................................................................89

Figure 70 Three-Dimensional Cylinder Mid-Height Model (#DCM) .......................................90

Figure 71 Radial Displacement at Cylinder Wall Mid-height (SOL 6) .....................................92

Figure 72 Posttest Analysis of SFMT at Rupture (~1.38MPa).................................................94

Figure 73 Case 1 Saturated Steam Pseudo-Time History ..........................................................98

Figure 74 Case 2 Station Black-Out Time History ....................................................................98

Figure 75 Schematic of 1:10 Scale Sizewell Model ................................................................101

Figure 76 Section View of Posttest Condition of the 1:10-Scale Model .................................101

Figure 77 Hoop Tendon Gage Data Near Cylinder Mid-height ..............................................102

Figure 78 Comparison of Pretest Analyses vs. Experiment Results for 1:10 Scale P/C 

Model.......................................................................................................................102

Figure 79 Typical applications of inflatable seals in personnel airlock doors [82] .................105

Figure 80 Inflatable Seal Schematic and Typical Designs [82]...............................................106

Figure 81 Typical application of process piping bellows [82].................................................107

Figure 82 Bellow Test..............................................................................................................107

Figure 83 Acceptance Guidelines for Large Early Release Frequency ...................................111

Figure 84 Leak Fragility for Surry Containment with Liner Corrosion...................................111

Figure 85 Turbine Missile Test Sequence................................................................................113

Figure 86 Full-Scale Aircraft Impact Test Sequence...............................................................113

Figure 87 ‘Water Slug’ Test Sequence ....................................................................................114

Figure 88 ISP 48 Phase 3, Case 1 Loading and Temperature..................................................128

Figure 89 ISP 48 Phase 3, Case 2 Loading and Temperature..................................................128

Figure 90 Axisymmetric Model Thermal Boundary Conditions .............................................129

Figure 91 Concrete Compression Strength Ratio vs. Temperature..........................................132

Figure 92 Steel Yield Strength and Modulus Ratio vs. Temperature ......................................132
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Figure 93 Combined Probability of Liner Tear by PLPM Software for the Reinforced 

Concrete Containment Example..............................................................................135

Figure 94 Probability of either Leakage, Rupture, or Catastrophic Rupture Occurring 

given that failure has occurred for Reinforced Concrete Containment ...................135

Figure 95 Idealization of Reinforced Concrete Containment Behavior...................................139

Figure 96 Idealization of Prestressed Concrete Containment Behavior ..................................139

Figure A-1 Examples of Steel Containment Models [97]......................................................... A-8

Figure A-2 Typical Axisymmetric Model and Temperature Boundary Conditions ............... A-22
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TABLES 

Table 1 Number of U.S. Containments by Type ..................................................................... 7

Table 2 PWR Containment Construction Types ..................................................................... 8

Table 3 BWR Containment Construction Types ..................................................................... 9

Table 4 Containment Strength Under Static Pressure[7]....................................................... 29

Table 5 Replica Modeling Law to Satisfy Pi Terms.............................................................. 42

Table 6 Summary of Results of Experiments for Steel Containment Models....................... 45

Table 7 Pretest Failure Predictions for 1:10-Scale Steel Containment Model ...................... 58

Table 8 Summary of Results of Experiments for Reinforced Concrete Containment 

Models and Liner Tearing and Leakage ................................................................... 61

Table 9 Summary of Results of Experiments for Prestressed Concrete Containment 

Models ...................................................................................................................... 74

Table 10 Summary of PCCV RR Pretest Results.................................................................... 93

Table 11 Summary of ISP 48 Results...................................................................................... 99

Table 12 Release Paths in LWR Containments..................................................................... 122

Table A-1 Summary of Analytical Model Types Used for Containment Studies ................... A-6
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EXECUTIVE SUMMARY 

Research into the integrity of containment structures or vessels for nuclear power plants has been 

conducted around the world in those countries where nuclear energy is produced and provides, or 

is expected to provide, a significant portion of the domestic energy supply. While the 

contributions of each of these efforts to the understanding of the role of containment in ensuring 

the safe operation on nuclear power plants is important, the most comprehensive experimental 

effort has been conducted at Sandia National Laboratories, primarily under the sponsorship of the 

US Nuclear Regulatory Commission (NRC). This report describes the background and context 

for the more than 25 years of NRC-sponsored Containment Integrity Research at Sandia National 

Laboratories and summarizes the major results of the experimental efforts and the observations 

and insights gained from the analytical efforts. 

Beginning in the 1950’s, the US Atomic Energy Commission and its successor, the NRC, 

established the safety requirements for US nuclear power reactors. The safety strategy that 

emerged became know as ‘defense in depth’. The elements of ‘defense in depth’ included 

accident prevention, redundancy of safety systems, containment, accident management and 

remote siting/emergency planning (sheltering and evacuation). Along with defining the rules 

which governed design, construction and operation and licensing and regulating the plants, the 

NRC engaged in an extensive research program to investigate safety issues associated with highly 

unlikely events, such as the complete rupture of the pressure vessel, which were not considered in 

the design of the plants. While research into the performance of the containment to resist these 

‘beyond-design-basis’ loads had already been initiated, the accident in 1979 at Unit 2 of the Three 

Mile Island nuclear power plant in Pennsylvania, gave new impetus to this research. 

All of the 103 operating nuclear power plants in the United States are light-water reactors, either 

pressurized water reactors (69) or boiling water reactors (34). Each of these plants includes either 

a steel or steel-lined, reinforced concrete containment as the final barrier against the release of 

radio-nuclides to the environment. The reinforced concrete containments use either conventional 

or prestressed/posttensioned reinforcing. The containments are designed to accommodate the 

pressures associated with a loss of coolant accident by either having large volumes, as in the large 

dry and subatmospheric containments, or by utilizing a pressure suppression system to reduce the 

volume, as in the ice-condenser or the Mark-I, -II, or –III boiling water reactors which include a 

suppression pool filled with water. 

A 1980 study conducted for the NRC by Sandia concluded that the scant empirical data on the 

ultimate capacity of containment structures were not adequate to ensure that predictions based on 

analysis were accurate or reliable. Based on this conclusion, an ambitious program to conduct 

tests of models of containment structures to failure and determine the suitability of existing 

analytical methods to predict failure was undertaken. 

A series of increasingly large and complex tests of scale models of containment structures and 

components were conducted at Sandia National Laboratories between 1983 and 2001. In 

conjunction with these experiments, an exhaustive analytical effort was conducted to predict the 

behavior of the models during the tests and to understand and simulate the actual behavior after 

the tests. The Sandia models, which were all subjected to static overpressurization at ambient 

temperature, consisted of 

• Four 1:32-scale models of steel containment structures typical of a large dry or icecondenser PWR containment 

o Two simple cylindrical shells with a hemispherical dome 
xvi 

o One of similar geometry with hoop stiffeners 

o One of similar geometry with simulated penetrations 

• A 1:8-scale model of a free-standing steel containment typical of ice-condenser PWR 

containments 

• A mixed scale model of the steel containment of an improved BWR Mark II 

o The overall geometric scale was 1:10, the shell thickness scale was 1:4 to 

facilitate fabrication and to allow the use of prototypical materials 

o This model was constructed by the Nuclear Power Engineering Corporation 

(NUPEC) of Japan and tested by Sandia National Laboratories as part of a 

Cooperative Containment Research Program between NUPEC and the NRC. 

• A nominal 1:6-scale model of a reinforced concrete PWR containment 

• A 1:4-scale model of a large, dry PWR prestressed concrete containment 

o This model was also constructed by NUPEC and tested by Sandia National 

Laboratories as part of the Cooperative Containment Research Program. 

For most of these tests, various international nuclear research agencies, including regulatory 

bodies, designers, operators, universities and consultants, were invited to participate in test 

planning, pretest prediction and posttest analysis. Over 25 different agencies agreed to participate 

in the various tests. Their efforts complimented the analyses performed by Sandia and it’s 

subcontractors and supported the objectives of the program to demonstrate and improve the 

ability to predict containment performance up to and including failure. 

In addition to these tests of models of the containment structure, Sandia also tested full-scale and 

scale models of electrical penetration assemblies, personnel air locks, equipment hatches, drywell 

heads, penetration bellows and penetration seals and gaskets. 

Some general conclusions on predicting containment behavior can be made from this series of 

containment vessel model tests: 

• Although establishing a generic margin of safety was not the purpose of the SNL 

program, the steel models have pressure capacities of 4-6 times, of the design pressure 

and the reinforced concrete models have pressure capacities of 2.5 to 3.5 times the design 

pressure. 

• Global, free-field strains on the order of 2-3% for steel, 1.5 to 2% for reinforced concrete 

and 0.5 to 1.0% for prestressed concrete can be achieved before failure or rupture. 

• Model (and presumably prototype) capacities are limited by high strains arising at local 

discontinuities which are present in both the model and the prototype. 

• In the absence of a ‘backup’ structure, steel containment structure model capacities tend 

to be limited by gross structural failure or ‘rupture’. Due to the inherent structural 

redundancy of the liner and concrete system, steel lined concrete containments appear to 

be limited by functional failure (leakage). While the behavior that leads to tearing of the 

steel vessel or the steel liner is similar, i.e. local exceedence of the ductility limits of the 
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steel at geometric discontinuities, the subsequent response of the vessels differs due to the 

presence of the surrounding structure. 

• It seems reasonable to assume that with the added complexity of the actual containments, 

there is a higher probability that these local strain risers are present in, and possibly more 

severe than in any of the models tested. As a result, the capacities of the model, can, at 

best, be interpreted as an upper bound on capacity of prototypical containments. 

• Analytical methods currently used are adequate to predict global response into the 

inelastic regime. One caveat on this statement is the discrepancy between predictions and 

observations of global yielding. Further investigation is required to understand the nature 

of this discrepancy (e.g. residual stresses, etc.) and its significance for calculation of 

prototypical containment capacities. 

• Predictions of local failure mechanisms are highly dependent on the experience of the 

analyst, on the availability of accurate as-built information (geometry and material 

properties) at discontinuities, and on fabrication processes. Even if this information is 

available (not typical for actual containments) the prediction, a priori, of local failures is 

at best an uncertain proposition. The large scale model tests have, however, educated and 

sensitized the community to the types of details which may be critical in limiting 

containment capacities, and, hopefully, have improved the reliability of the predictions. 

• These conclusions are predicated on failure of the containment structure. Any evaluation 

of the capacity of an actual containment must be based on the entire system, including 

mechanical and electrical penetrations and other potential leak paths. 
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ACKNOWLEDGEMENTS 

It is impossible to identify all of the individuals who participated in the work described in this 

report and contributed to the current understanding of containment integrity, however we would 

like to acknowledge their efforts and dedication, albeit anonymously. 

Some individuals, however, deserve special mention. Dr. James F. Costello, US NRC (retired) 

and Dr. Walter A. von Riesemann, Sandia National Laboratories (retired) provided the inspiration 

and were the guiding force behind the majority of the efforts described in this report. Similarly, 

Dr. Yusef R. Rashid, ANATECH, was instrumental in the development and application of many 

of the analytical tools and methods described in this report. 

It should also be noted that at the inception of this program, a Peer Review Panel, consisting of 

representatives from industry, academia, other research laboratories and private consultants, was 

organized. This panel, the specific make-up of which varied over the course of the program, 

actively participated in reviewing the research plans and results and provided guidance to the 

NRC and Sandia on the direction of the program. The author’s are especially indebted to Mr. 

Thomas J. Ahl, CBI (retired), private consultant; Mr. Bryan A. Erler, Sargent and Lundy, Engr’s 

(retired), private consultant; Mr. Lyle Gerdes, ABB Combustion (retired); Mr. Theodore E. 

Johnson, Bechtel (retired), private consultant; Dr. Richard S. Orr, Westinghouse Electric 

Corporation; Mr. Bert Pfeiffer, Bechtel (retired); Professor Mete A. Sozen, Purdue University; 

Dr. John D. Stevenson, Stevenson & Associates; Dr. H. T. Tang, Electric Power Research 

Institute; Mr. Harold Townsend, General Electric (retired); Dr. Joseph Ucciferro, Day & 

Zimmerman; and Professor Richard N. White, Cornell University (emeritus). 

The authors are, to a large extent, gratefully standing on their shoulders. 

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin 

Company, for the United States Department of Energy’s National Nuclear Security 

Administration under Contract DE-AC04-94AL85000. 
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ACRONYMS 

3DCM Three-dimensional Cylinder Mid-height model 

A/L (Personnel) Air Lock 

ACI American Concrete Institute 

ACRS Advisory Committee on Reactor Safeguards 

AEC Atomic Energy Commission 

AECL Atomic Energy of Canada Limited 

ALWR Advanced Light Water Reactor 

ANL Argonne National Laboratory, US 

ANPA Agenzie Nazionale per la Protezione dell' Ambiente, Italy 

ASCE American Society of Civil Engineers 

ASME American Society of Mechanical Engineers 

ASTM American Society for Testing and Materials 

B&PV Boiler and Pressure Vessel (Code) 

BARC Bhabha Atomic Research Center, India 

BE British Energy 

BWR boiling water reactor 

CANDU Canadian Heavy Water Reactor 

CBI Chicago Bridge and Iron 

CCFP conditional containment failure probability 

CEA Commissariat a l’Énergie Atomique, France 

CEGB Central Electric Generating Board, UK 

CFF containment failure frequency 

CFR Code of Federal Regulations 

CS contact structure 

CSNI Committee on Safety of Nuclear Installations (OECD/NEA) 

CTL Construction Technologies Laboratory 

DAS data acquisition system 

DBA design-basis accident 

DEA David Evans and Associates 

DOD Department of Defense 

E/H Equipment Hatch 

EDF Électricité de France 

EGP Energoprojekt Praha, UJV Rez. Div. 
xxii 

EPDM ethylene propylene 

EPR European (or Evolutionary) Pressurized Reactor 

EPRI Electric Power Research Institute, US 

ESF engineered safety features 

FORTUM Fortum Nuclear Services, Ltd. 

FSAR Final Safety Analysis Report 

GD/EB General Dynamics/Electric Boat Division, US 

GRS Gesellschaft für Anlagen und Reaktorsicherheit mbH 

HAZ heat affected zone 

HSE Health and Safety Executive, U.K. 

HTGR High Temperature Gas Reactor 

IBRAE Nuclear Safety Institute, Russia 

ICONE International Conference on Nuclear Engineering 

ILRT Integrated Leak Rate Test 

INEL Idaho National Engineering Laboratory 

INER Institute of Nuclear Energy Research, Republic of China 

IPE Individual Plant Examinations 

IPSN Institut de Protection et de Sûreté Nucléaire, France 

IRSN Institut de Radioprotection et de Sûreté Nucléaire 

ISP International Standard Problem 

JAERI Japan Atomic Energy Research Institute 

JAPC Japan Atomic Power Company, Japan 

JPRG Japan PCCV Research Group 

KINS Korea Institute of Nuclear Safety, Korea 

KOPEC Korea Power Engineering Company, Korea 

LERF Large Early Release Frequency 

LST limit state test 

LOCA loss-of-coolant accident 

LVDT linearly variable displacement transducer 

LWR light water reactor 

METI Ministry of Economics, Trade and Industry, Japan 

MIT Massachusetts Institute of Technology 

MPA Materialprüfungsanstalt Universität Stuttgart, Universität Stuttgart, Germay 

NASA National Aeronautics and Space Administration 

NEA Nuclear Energy Agency (OECD) 
xxiii 

NII/HSE Nuclear Installations Inspectorate/Health & Safety Executive 

NPP nuclear power plant 

NRC Nuclear Regulatory Commission 

NSSS nuclear steam supply system 

NUPEC Nuclear Power Engineering Corporations, Japan 

OBE operating basis earthquake 

OECD Organization for Economic Cooperation and Development 

P/C prestressed concrete 

PCCV prestressed concrete containment vessel 

Pd design pressure 

PLPM Probabilistic Leakage Prediction Methodology 

PORV pressure operated relief valve 

PRA probabilistic risk assessment 

PRIN Principia Ingenieros Consultores, S.A., Spain 

PWR pressurized water reactor 

R/C reinforced concrete 

RCCV reinforced concrete containment vessel 

RINSC Russia International Nuclear Safety Center, Russia 

RPV reactor pressure vessel 

SAR Safety Analysis Report 

SCANSCOT Scanscot Technology, Sweden 

SCV steel containment vessel 

SFMT structural failure mode test 

SIT structural integrity test 

SMiRT Structural Mechanics in Reactor Technology (Conference) 

SNL Sandia National Laboratories 

SOL standard output location 

SRP Standard Review Plan 

SSE safe shutdown earthquake 

TMI-2 Three Mile Island, Unit 2 

UKAEA United Kingdom Atomic Energy Agency 
xxiv 

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1 

1 INTRODUCTION 

1.1 Objectives 

The objectives of this report are 

• to describe the background and context for the more than 25 years of NRC-sponsored 

Containment Integrity Research at Sandia National Laboratories. The support, 

partnership and participation of a large variety of domestic and international 

organizations, notably the Nuclear Power Engineering Program of Japan will also be 

described; 

• to provide a knowledge base and reference list, documenting SNL’s containment integrity 

research, 

• to summarize of the major results of the experimental efforts performed at Sandia 

National Laboratories and the observations and insights gained from the analytical 

efforts, both internal and the international Round Robin exercises; 

• to document ‘lessons learned’ from the containment model testing and analyses, provide 

insights on the current level of understanding of containment overpressure behavior and 

the ‘state of the practice’ for containment beyond design basis loads evaluation; 

• to provide recommendations for containment design to improve reliability and 

performance to beyond-design basis loads; 

• to recommend principles and procedures for analysis of containment structures to 

beyond-design basis loads and criteria for interpreting analytical results with regard to 

functional or structural behavior; 

• to provide more realistic, physics-based approach to modeling containment behavior in 

PRA models and in risk-informed decision making, 

• to provide an assessment of the level of success of the analytical methods in 

predicting/simulating containment model response and failure modes, 

• to discuss criteria for functional and structural failure, 

• to recommend methods for prediction of containment capacity, including insights on 

model error and model uncertainty for PRAs and risk-informed regulations, 

• and to identify future work that may support the safety and licensing review of the next 

generation of U.S. containments. 

1.2 Scope 

Research into the integrity of containment structures or vessels for nuclear power plants has been 

conducted around the world in those countries where nuclear energy is produced and provides, or 

is expected to provide, a significant portion of the domestic energy supply. While the 

contributions of each of these efforts to the understanding of the role of containment in ensuring 

the safe operation on nuclear power plants is important, the most comprehensive experimental 

effort has been conducted at Sandia National Laboratories, primarily under the sponsorship of the 
2 

US NRC. The scope of this report focuses primarily on the work conducted at SNL. While it 

would be a very useful exercise, it is beyond the scope of this report to provide a complete and 

comprehensive summary of work conducted elsewhere, although some relevant summaries and 

references have been included. 

Also, while the experiments and analyses summarized in this report have broad relevance to 

safety-related issues for nuclear power plants throughout the world, the insights and lessons 

learned are focused primarily on the current fleet of US light water reactors and advanced light 

water reactors which might be constructed in the future. Some of these insights and lessons 

learned may also have applicability to future generations of LWR and non-LWR plants. 

However, the designs of these plants may have significantly different demands, and significantly 

different approaches to meeting those demands, for containment systems. 

1.3 Report Organization 

This report summarizes the major accomplishments and insights obtained over 25 years of 

primarily NRC-sponsored research on the integrity of nuclear power plant containment structures 

and their capacity to resist loads beyond those for which they were designed. Chapter 2 describes 

the evolution of containment design in the context of the US commercial nuclear power industry. 

Chapter 2 also describes the typical design of the six major containment types used in the US, the 

statutory design requirements and the role of containment in severe accident, probabilistic risk 

assessment and risk-informed regulation. 

Chapter 3 summarizes the major experimental and analytical programs conducted at Sandia 

National Laboratories along with the results and conclusion from each program. Relevant 

programs conducted elsewhere are also briefly summarized. 

Chapter 4 synthesizes the experimental and analytical results, and attempts to summarize the 

major insights and lessons learned from all the experiments, identify issues which are unresolved 

or which were not addressed and suggest future work needed to resolve these items, and 

document the implications for on-going regulation of existing plants and licensing of future 

plants. 

In addition to providing detailed references for the information summarized in this report, 

Chapter 5 provides a fairly extensive bibliography of the relevant literature on containment 

integrity issues. 
3 

2 BACKGROUND 

2.1 Historical Background on U.S. Containment Design and Performance 

Criteria1

Following World War II, peaceful uses of nuclear energy included plans to construct commercial 

reactors for electric power generation. The Atomic Energy Act of 1946 established the Atomic 

Energy Commission (AEC) and provided the statutory basis for the development of commercial 

nuclear power plants in the US. In the first few years after the war, several low power (<50MWt) 

test reactors were constructed. These reactors followed the practice established during the 

Manhattan Project of siting them on remote government reservations. WASH-3 [2] defined this 

siting practice. The rule of thumb for the residence exclusion distance, R, was given as 

R (miles) = 0.0 1 [P (kWt)]1⁄2

For a 3000 MWt plant (P=3,000.000 kWt), this would result in an exclusion distance of 17.3 m 

(27.8 km). 

An early exception to this siting approach and the first use of containment in the US was the 

Submarine Intermediate Reactor Mark A at the Knolls Atomic Power Laboratory which was only 

19 miles from Schenectady, NY. The entire reactor was enclosed in a gas-tight steel sphere, or 

containment (although this term was not applied to this structure), designed to withstand “a 

disruptive core explosion” and to contain radionuclides that might be released in a reactor 

accident. 

Early commercial nuclear power plants in the US were based on naval nuclear power submarines. 

Since submarine bases were major ports with generally large population centers, remote siting 

criteria could not be applied to submarines. The Navy therefore relied on rigorous accident 

prevention strategies along with the containment capability provided by the hull (although this 

did not protect the crew). Prevention and safety-system strategies developed for submarine 

reactors evolved in the 1950s and 1960s for application to commercial nuclear reactors. 

The safety strategy that emerged became know as ‘defense in depth’. The elements of ‘defense in 

depth’ included accident prevention, redundancy of safety systems, containment, accident 

management and remote siting/emergency planning (sheltering and evacuation). While this 

describes the layers of the defense-in-depth strategy, it does not specify, with regard to 

containment for example, how strong the containment should be or what containment leakage rate 

should be limited to. 

The first civilian nuclear power plant, the Shippingport Atomic Power Station was a pressurized 

water reactor owned by the Duquesne Light Company and designed and operated by 

Westinghouse. The Shippingport plant was located about 20 miles from Pittsburgh, PA and did 

not meet the siting criteria, hence a containment building was provided. In 1955 and 1956 the 

AEC received applications for three large commercial power reactors: Dresden 1, about 35 miles 

from Chicago, IL; Indian Point 1, 24 miles north of New York City; and the Enrico Fermi plant, 

25 miles south of Detroit, MI. Containments were proposed for all three reactors. 

 

1

 Background information extracted from Reference [1] 
4 

The advent of containment was a decisive step in moving large power reactors closer to populated 

electrical load centers. Containment provided a barrier to the release of radionuclides that was 

desirable for public safety and public acceptance of nuclear power. All commercial nuclear 

power plants approved for construction in the US have containments. 

The earliest rules for containment were given in the Reactor Site Criteria, 10 CFR 100 published 

in 1962. 10 CFR 100 introduced the concepts of a maximum credible accident, subsequently 

referred to as the design-basis accident (DBA) or design basis loss-of-coolant accident (LOCA), 

and the expected leak rate from the containment. Containments were designed to withstand the 

peak pressure associated with the reactor coolant system blowdown and remain intact, limiting 

the release of radionuclides to the environment at a specified design leak rate. They were not 

designed to withstand the loads associated with gross rupture of the vessel. 

The industry response to the 10 CFR 100 criteria was to take credit for engineered safety features 

(ESFs) such as suppression pools, containment sprays, containment heat removal systems and aircleaning systems. San Onofre, Connecticut Yankee, Oyster Creek, Nine Mile Point and Dresden 

2 were approved for construction based on the use of ESFs. In 1962, an application was 

submitted for the two-unit Ravenswood plant, which included double containments for the 

Westinghouse nuclear steam supply system (NSSS), to be located, essentially in the heart of New 

York City. Calculations by the AEC staff indicated that, even while taking credit for the ESFs, 

the containment leak rate would have to be limited to 10-4 cfm in order to meet the siting 

guidelines. Consolidated Edison subsequently withdrew its application in 1963. 

In 1966, two issues called into question the assumption of containment as an independent barrier: 

reactor pressure vessel integrity and the ‘China syndrome’. Containments were not designed to 

withstand a gross rupture of the reactor pressure vessel since this was not considered to be a 

credible event. Further research and actual failures which occurred during pressure testing of 

steam generators led the Advisory Committee on Reactor Safeguards (ACRS) to express concerns 

regarding this assumption and require improved design and inspection methods for reactor 

pressure vessels. In 1974 the ACRS concluded that the possibility of a RPV failure was less than 

10-6 per vessel year. Studies also suggested that a loss of coolant could lead to the molten core 

breaching the lower head of the Reactor Pressure Vessel (RPV), penetrating the concrete 

containment basemat and coming into contact with the earth. This scenario was euphemistically 

referred to as the ‘China Syndrome’. As a result, emphasis shifted from containment to 

prevention and, until the TMI-2 accident in 1979, the focus was on demonstrating emergency 

core cooling, not on what to do if core cooling failed. 

The Reactor Safety Study was initiated in response to a congressional request for a 

comprehensive assessment of reactor safety. WASH-1250, “The Reactor Safety Study of Nuclear 

Power Reactors (Light Water-Cooled) and Related Facilities”[3] discussed the conservatisms 

applied on the design of nuclear power plants, but did not address the likelihood or potential 

consequences of beyond-design-basis accidents. Beyond-design-basis accidents include those 

initiated by reactor pressure vessel rupture, by seismic events greater than the Safe Shutdown 

earthquake (SSE) and those involving multiple system failures. A subset of beyond-design-basis 

accidents that could lead to substantial core damage are called severe (or Class 9) accidents. 

In response to the questions raised by WASH-1250, a major probabilistic study was initiated in 

1972. Also known as the Rasmussen report after the study director, Professor Norman 

Rasmussen of MIT, this study used a methodology pioneered by the DOD and NASA, called 

probabilistic risk assessment (PRA) to predict the effects of component failures on large, complex 

systems. One of the tasks “...was to determine the thresholds and modes of failure of reactor 

buildings (containments)...when subjected to internal pressures and temperatures greater than the 
5 

design values” for two prototypical plants. Some computer analyses plus hand calculation 

solutions were used, but no experimental work was carried out. The results were issued as 

WASH-1400 (NUREG-75/014) [4]. The study concluded that, while the risks of a core melt 

accident were small, they were more likely than previously thought, approximately 5x10-5 per 

reactor year. The study also suggested that different containment types may differ in their 

capability to withstand core melt accidents. 

At 4:00 AM on March 28, 1979, the most severe accident in US nuclear history began when a 

resin blockage in the condensate system caused the condensate and condensate booster pumps to 

trip. The sequence of events and actions which eventually led to damage and partial melting of 

the core of the Three Mile Island-2 plant, an 880 MWe PWR, detailed in various documents and 

reports, are summarized in Reference 1. During the course of the accident, the containment 

building was subjected to a peak pressure spike (recorded by one sensor as 28 psig) when 

hydrogen, released when a pressure operated relief valve (PORV) was opened, ignited and burned 

with oxygen in the reactor building atmosphere. The accident at Three Mile Island 2 put to rest 

the notion that severe nuclear power accidents were not credible. It also led to significant 

changes in the NRC and the industry and increased emphasis on the importance of containment 

survival during severe accidents. 

Following the TMI-2 investigations and after several years of deliberation, the NRC established 

both qualitative and quantitative safety goals in August 1986.2

 The quantitative safety goals 

established are: 

“Individual members of the public should be provided a level of protection from the 

consequences of nuclear power operations such that individuals bear no significant 

additional risk to life and health.” 

“Societal risks to life and health from nuclear power plant operation should be 

comparable or less than the risks of generating electricity by viable competing 

technologies and should not be a significant addition to other societal risk.” 

The corresponding quantitative safety goals are: 

“The risk to an average individual in the vicinity of a nuclear power plant of prompt 

fatalities that might result from reactor accidents should not exceed one-tenth of one 

percent of the sum of prompt fatality risks resulting from other accidents to which 

members of the U.S. population are generally exposed. 

“The risk to the population near a nuclear power plant of cancer fatalities that might 

result from nuclear power plant operation should not exceed one tenth of one percent of 

the sum of cancer fatality risks resulting from all other causes.”

Also following TMI-2, NRC research was redirected to focus on severe accidents. The NRC 

issued a policy statement on severe accidents in 19853

. Recognizing the plant specific nature of 

severe accident vulnerabilities, the NRC issued a generic letter in 1988 [5] requiring each nuclear 

power plant operating or under construction to perform a systematic Individual Plant Examination 

(IPE) [6]. The results of the research efforts were integrated into a major PRA for five reference 

 

2

 Federal Register, Vol. 51, No. 149, 1986 

3

 Federal Register, Vol. 50, 32,138, August 8, 1985 
6 

plants in 1990, known as NUREG-1150 [7], which essentially replaced the earlier Reactor Safety 

Study. Both of these efforts attempted to show that containments have the capacity to withstand 

many of the beyond-design basis challenges including severe accidents. 

Prior to the TMI-2 accident, the NRC had initiated work at Sandia National Laboratories and 

elsewhere to study containment systems. This effort gained new impetus following the accident 

The first Sandia study [8], described in more detail in Section 2.3 concluded that the few 

experiments on containment integrity had been either of too small a scale or lacked sufficient 

details of actual plants to be of reliable use for understanding containment response to beyonddesign-basis accidents. Based on this study, the program, which is the subject of this report, was 

formulated to investigate containment systems subjected to beyond-design-basis loads. This 

program’s objective has been the validation of methods used to predict the performance of light 

water reactor (LWR) containment systems when subjected to loads beyond those specified in the 

design codes and not to determine the pressure carrying capacity of actual containments by 

testing scale models. 

2.2 Containment Design Practice 

2.2.1 Containment Types 

Before discussing the Containment Integrity Research program, it is worth a brief review of 

containment designs for the current fleet of US nuclear power reactors. As of 2006, there were 

103 US commercial light-water nuclear reactors (LWR) with operating licenses at 64 sites in 31 

states, 69 pressurized water reactors (PWR) and 34 boiling water reactors (BWR). There are six 

basic containment types in the fleet. Four of these designs primarily use the passive pressure 

suppression concept, and two rely primarily on large, strong volumes. All of these containments 

are constructed of either steel or concrete with a steel liner for leak tightness. BWR designs, 

which have evolved from the Mark I to the Mark III design, all use a pressure suppression pool. 

A few Westinghouse PWRs have ice-condenser (pressure suppression) containments, but most 

PWRs have large dry containments or a subatmospheric variation of the large dry containment. 

Table 1 summarizes the number of containments for each of the six basic types. Tables 2 and 3 

further characterize these containments by construction type. Even within these subcategories, 

further differences exist in terms of liner and liner anchorage details, reinforcing and, prestressing 

details, etc. It is safe to say that no two containments, even so-called twin units, are identical. 

Around the world, a larger variety of primary systems are used for nuclear power generation. In 

addition to light-water systems, a number of plants use gas, heavy water or, in a few, liquid metal, 

as the primary coolant. Most of these plants use some type of containment or confinement 

structure in a variety of configurations. Most are made of steel or reinforced concrete in a variety 

of shapes ranging from steel spheres to double wall reinforced or prestressed concrete, unlined or 

with steel or epoxy liners. It is beyond the scope of this report to investigate the full range of 

containment types in the world-wide fleet, however, a more thorough review of these designs 

may prove useful for any new plant construction in the US. 
7 

Table 1 Number of U.S. Containments by Type 

Containment Type Number

PWR Large Dry 53 

PWR Subatmospheric 7 

 PWR Ice Condenser 9 

Total PWRs 69 

BWR Mark I 22 

BWR Mark II 8 

BWR Mark III 4 

Total BWRs 34 

US Total 103 

A database of US containments prepared by Sandia provides more extensive information about 

each containment in the fleet [9]. A brief description of each of the six basic US containment 

types follows. 

Large Dry PWR 

A large dry containment (Figures 1 and 2) is designed to contain the blow-down mass and energy 

from a large break LOCA, assuming any single active failure in the containment heat removal 

systems. These systems may include containment sprays and/or fan coolers, depending on the 

particular design. Large dry containments can be of either concrete or steel construction. All US 

concrete containments have steel liners to assure leak tightness. (Some non-US concrete 

containments are unlined or include non-metallic liners.) Large dry (and all other) containments 

have a large, thick basemat that provides seismic capability, supports the structures, and, while 

not designed for this, may serve to contain molten material during a severe accident. 

Subatmospheric PWR 

Subatmospheric containments (Figure 3) are very similar to large dry containments. The major 

difference is that the containment is maintained at a negative pressure (~ 5 psi or 35 kPa) with 

respect to the outside atmosphere. This negative pressure means that leakage during normal 

operation is into the containment rather than to the atmosphere. Further, this negative pressure 

provides some additional margin for response to design basis accidents, and therefore the design 

pressure and/or volume can be reduced accordingly. Keeping the containment at a 

subatmospheric pressure also means that any significant containment leaks will be readily 

detected, when maintaining the negative pressure becomes more difficult. 

Ice Condenser PWR 

Ice condenser containments (Figure 4) are constructed of either concrete or steel. Ice condenser 

containments are the only PWR containments that rely primarily on passive pressure suppression. 

The containment consists of an upper and a lower compartment connected through an ice bed. In 

the event of a design basis LOCA, steam flows from the break, into the lower compartment, and 

up into the ice beds where most of the steam is condensed. Return air fans maintain a forced 

circulation from the upper to lower compartments, enhancing flow through the ice beds. One-
8 

way doors are present at the entrance and exit of the ice bed region. These doors open upon slight 

pressure from the lower compartment, but close if air flow occurs in the reverse direction. 

Table 2 PWR Containment Construction Types 

Kewaunee

Prarie Island 1

Prarie Island 2

Davis-Besse

St. Lucie 1

St. Lucie 2

Waterford 3

Comanche Peak 1

Comanche Peak 2

Diablo Canyon 1

Diablo Canyon 2

Indian Point 2

Indian Point 3

Salem 1

Salem 2

Shearon Harris 1

Reinforced Concrete

Cylinder with

Steel Liner and

Secondary Containment

Seabrook 1

Ginna

HB Robinson

Diagonal

Posttensioned Concrete

Cylinder with

Steel Liner

Fort Calhoun

3-D

Posttensioned Concrete

Cylinder with

Steel Liner

and Secondary Containment

Millstone 2

Beaver Valley 1

Beaver Valley 2

North Anna 1

North Anna 2

Surry 1

Surry 2

Reinforced Concrete

Cylinder

with Steel Liner

Millstone 3

Sequoyah 1

Sequoyah 2

Watts Bar 1

Catawba 1

Catawba 2

McGuire 1

McGuire 2

DC Cook 1

DC Cook 2

Arkansas 1

Arkansas 2

Oconee 1

Oconee 2

Oconee 3

Crystal River 3

Three Mile Island 1

Calvert Cliffs 1

Calvert Cliffs 2

Palisades

Palo Verde 1

Palo Verde 2

Palo Verde 3

San Onofre 2

San Onofre 3

Braidwood 1

Braidwood 2

Byron 1

Byron 2

Callaway

Farley 1

Farley 2

Point Beach 1

Point Beach 2

South Texas 1

South Texas 2

Summer

Turkey Point 3

Turkey Point 4

Vogtle 1

Vogtle 2

Wolf Creek

1-D Vertical

Posttensioned Concrete

Cylinder with

Steel Liner

3-D

Posttensioned Concrete

Cylinder with

Steel Liner

Posttensioned Concrete

Cylinder with

Steel Liner

Large Dry

Primary Containment

Steel Cylinder

with Reinforced

Concrete Shield Building

Steel Cylinder

Reinforced Concrete

Cylinder with

Reinforced Concrete Steel Liner

Cylinder with

Steel Liner

Reinforced Concrete

Cylinder

with Steel Liner

Ice Condenser

Primary Containment

Reinforced Concrete

Cylinder

Subatmospheric with Steel Liner

Primary Containment

Steel Cylinder

with Reinforced

Concrete Shield Building
9 

Table 3 BWR Containment Construction Types 

Nine Mile Point 1

Oyster Creek

Dresden 2

Dresden 3

Monticello

Pilgrim 1

Quad Cities 1

Quad Cities 2

Browns Ferry 1

Browns Ferry 2

Browns Ferry 3

Cooper

Duane Arnold

Fermi 2

Fitzpatrick

Hatch 1

Hatch 2

Hope Creek 1

Peach Bottom 2

Peach Bottom 3

Mark II

Steel Drywell

&

Wetwell

Columbia

Perry 1

Riverbend 1

Brunswick 1

Brunswick 2

Limerick 1

Limerick 2

Susquehanna 1

Susquehanna 2

Nine Mile Point 2

Clinton 1

Grand Gulf 1

LaSalle 1

LaSalle 2

Mark I

Steel

Drywell

&

Wetwell

Mark III

Reinforced

Concrete Drywell

Steel Wetwell

Free Standing Steel 

Primary Containment

Mark I

Reinforced Concrete

Drywell & Wetwell

Mark III

Reinforced Concrete

Drywell & Wetwell

Reinforced Concrete

Primary Containment

with Steel Liner

Post-tensioned Concrete

Primary Containment

with Steel Liner

Mark II

Reinforced Concrete 

Drywell

Posttensioned Wetwell

Mark II

Reinforced Concrete

Drywell & Wetwell
10 

The ice beds are more than adequate to limit the peak pressure from a design-basis LOCA. 

However, in a long-term accident, the ice will eventually melt and containment heat removal will 

be required. Thus, containment sprays are provided in the upper compartment of the 

containment. Water from the sprays drains through sump drain lines, down into the lower 

compartment sump, where it can be recirculated for long term heat removal. 

BWR Mark I 

The Mark I is a pressure suppression containment (Figure 5), which allows the containment to be 

smaller in volume. The containment is divided into the drywell containing the reactor vessel and 

the wetwell (torus) containing the suppression pool. The containments are constructed of either 

concrete or steel. The water in the suppression pool acts as an energy absorbing medium in the 

event of an accident. If a LOCA occurs, steam flows from the drywell through a set of vent lines 

and downcomers into the suppression pool, where the steam is condensed. Steam can also be 

released from the reactor vessel through the safety relief valves and associated piping directly into 

the suppression pool. In the event that the pressure in the wetwell exceeds the pressure in the 

drywell, vacuum breakers are provided that equalize the pressure. Mark I containments are 

equipped with lines connected to the wetwell that can be used to vent the containment if the 

pressure becomes too high. 

BWR Mark II 

Mark II containments (Figures 6 through 9) are similar in concept to Mark I containments. The 

suppression pool design is simplified, and the entire containment structure is more unified. 

Instead of the complicated torus design included in the Mark I containment, the suppression pool 

simply sits in the wetwell region below the drywell. Containment heat removal systems (sprays 

and suppression pool cooling) are the same as for the Mark I containments. Containment venting 

can also be performed in a similar fashion to the Mark I containments. 

BWR Mark III 

The Mark III design (Figures 10 and 11) is an intermediate-sized containment, much like the ice 

condenser containment. Mark III containments can be freestanding steel or steel-lined concrete. 

These containments have a drywell that functions much as the older designs, but have a larger 

surrounding containment that includes the wetwell. In the Mark III design, the suppression pool 

is located in an annular region outside the drywell. If the pressure in the outer containment 

exceeds the pressure in the drywell, then vacuum breakers open to equalize the pressure. Longterm containment heat removal can be accomplished with suppression pool cooling or by 

containment sprays (with appropriate circulation of the water through heat exchangers) in the 

outer containment. An important asset of the Mark III design is construction of the outer 

containment around the drywell, effectively providing a double layer of protection. If 

containment failure were to occur, in many cases the outer containment would fail first, leaving 

the drywell and suppression pool intact. Any subsequent fission product releases would still be 

scrubbed as they passed through the suppression pool, greatly reducing the source term. Thus, the 

only accidents (other than bypass sequences) likely to produce large source terms must involve 

failure of the outer containment plus either loss of the suppression pool or failure of the drywell. 
11 

Containment

sprays

Polar crane

Steam generators

Reactor vessel

Reactor cavity

In-core 

instrument 

tunnel

Containment

sprays

Polar crane

Steam generators

Reactor vessel

Reactor cavity

Containment

sprays

Polar crane

Steam generators

Reactor vessel

Reactor cavity

In-core 

instrument 

tunnel

Figure 1 Typical PWR Large Dry Containment with Prestressed Containment (e.g. 

Palisades) 
12 

Figure 2 Large Dry Steel Containment with Reinforced Concrete Shield Building 

(e.g. Davis-Besse) 
13 

Figure 3 Typical PWR Subatmospheric Reinforced Concrete Containment 

(e.g. Diablo Canyon) 
14 

Figure 4 Typical PWR Ice Condenser Steel Containment with Concrete Shield Building (e.g. Sequo
15 

EL.92'-6"

EL.110'-0"

EL.134'-6"

EL.165'-0"

195'-0"

EL.234'-0"

EL.265'-4"

EL.290'-0"

EL.84'

GRADE

LEVEL

Drywell

Wetwell

(Torus)

Reactor Bldg

EL.92'-6"

EL.110'-0"

EL.134'-6"

EL.165'-0"

195'-0"

EL.234'-0"

EL.265'-4"

EL.290'-0"

EL.84'

GRADE

LEVEL

Drywell

Wetwell

(Torus)

Reactor Bldg

Figure 5 Typical BWR Mark I Concrete Containment with Steel Torus 
16 

Figure 6 Typical BWR Mark II Containment [1] 
17 

Figure 7 BWR Mark II Concrete Containment (LaSalle Units 1 & 2) 
18 

Figure 8 BWR Mark II Steel Containment with Concrete Shield Building (Columbia, 

previously WNP-2) 
19 

Figure 9 BWR Mark II Reinforced Concrete Containment (Limerick 1 & 2) 
20 

Reactor Drywell

Upper pool

Supression pool

Weir wall

Horizontal vents

Reactor 

shield wall

Containment

Containment sprays

Hydrogen igniter

Reactor Drywell

Upper pool

Supression pool

Weir wall

Horizontal vents

Reactor 

shield wall

Containment

Containment sprays

Hydrogen igniter

Figure 10 Typical BWR Mark III Containment 

Freestanding Steel with Concrete Shield Building 

(Perry, Riverbend) 
21 

Figure 11 Typical BWR Mark III Containment 

Reinforced Concrete with Steel Liner 

(Clinton, Grand Gulf) 
22 

2.2.2 Containment Design 

The containment is often thought to consist of only the structural concrete and/or steel shell 

surrounding the nuclear steam supply system. In reality the containment not only includes the 

structural shell and basemat, but also all of the penetrations (fixed and operable) and any other 

component which completes the pressure boundary. Any evaluation of containment integrity 

must also include an evaluation of these penetrations. The containment system is primarily 

designed to: 

1. Contain any radioactive material that may be released from the primary system in case of 

an accident. 

2. Protect the nuclear system from weather and other external threats such as missiles 

produced by earthquakes, tornadoes, wind, and in some cases aircraft impact. 

3. Act as a supporting structure for operational equipment, e.g. cranes. 

Until 1965, there were no written criteria for design and review of all commercial power reactor 

licenses was on a case-by-case basis. In 1965, the AEC issued the first draft of the General 

Design Criteria, Appendix A of 10 CFR 50. (10 CFR Part 50 specifies the regulations 

promulgated by the Nuclear Regulatory Commission pursuant to the Atomic Energy Act of 1954 

to provide for the licensing of production and utilization facilities.) The final version of 

Appendix A, published in 1971, did not require the containment to be designed to withstand a full 

core meltdown (as the original draft had). The first five criteria define overall requirements for 

quality assurance and protection against natural phenomena, fire, environmental and dynamic 

effects (including loss of coolant accidents), and sharing of systems, structures and components. 

Criterion 1, Quality standards and records, requires, in part, that 

“Structures, systems, and components important to safety shall be designed, fabricated, 

erected, and tested to quality standards commensurate with the importance of the safety 

functions to be performed. Where generally recognized codes and standards are used, 

they shall be identified and evaluated to determine their applicability, adequacy, and 

sufficiency and shall be supplemented or modified as necessary to assure a quality 

product in keeping with the required safety function.” 

Criterion 16, Containment Design states: 

“Reactor containment and associated systems shall be provided to establish an 

essentially leak-tight barrier against the uncontrolled release of radioactivity to the 

environment and to assure that the containment design conditions important to safety are 

not exceeded for as long as postulated accident conditions require.” 

Criteria 50 through 57 give specific requirements for reactor containment. These criteria address 

the containment design basis, testing and inspection requirements and containment isolation 

requirements. 

10 CFR 50.55a, Codes and Standards, specifies that structures, systems and components of 

boiling and pressurized, water-cooled nuclear power reactors must be designed, fabricated, 

erected, constructed, tested, and inspected according to the requirements of the ASME Boiler and 

Pressure Vessel (B&PV) Code [10] as amended by NRC Regulatory Guide 1.84, Design and 

Fabrication and Materials Code Case Acceptability, ASME Section III. The ASME publishes a 

new edition of the B&PV Code, which includes Section III for nuclear power, every 3 years, and 
23 

new addenda every year. The latest editions and addenda of Section III that have been approved 

for use by the NRC are referenced in 10 CFR 50.55a(b). The ASME also publishes Code Cases 

quarterly. Code Cases provide alternatives developed and approved by ASME or explain the 

intent of existing Code requirements. Reg. Guide 1.84 identifies the Code Cases that have been 

determined by the NRC to be acceptable alternatives to applicable parts of Section III. 

Division 1, Subsection NE of Section III “establishes rules for material, design, fabrication, 

examination, inspection, testing and preparation or reports for metal containment vessels” or 

Class MC Components. Regulatory Guide 1.57 specifies the ‘Design Limits and Loading 

Combinations for Metal Primary Reactor Containment System Components’. 

Division 2 (comprised of Subsection CC) of Section III “establishes rules for material, design, 

fabrication, construction, examination, testing, marking, stamping, and preparation or reports for 

prestressed and reinforced containments”. The containments covered by Subsection CC include 

the “structural concrete pressure resisting shells and shell components, shell metallic liners and 

the penetrations liners extending the containment liner through the surrounding shell concrete”. 

Subsection CC applies for containments having a design pressure greater than 5 psi (35 kPa). For 

“parts and appurtenances of concrete containments not backed by structural concrete for load 

carrying purposes, the rules of Division 1 apply”. 

Section III, Division 2 was prepared and is maintained by the Joint ACI-ASME Technical 

Committee on Concrete Components for Nuclear Service under the sponsorship of the American 

Concrete Institute and the American Society of Mechanical Engineers. Basis documents prepared 

independently by ACI and ASME committees were merged in 1972 and published as a proposed 

standard for Concrete Reactor Vessels and Containments which became Section III, Division 2 in 

1973. This standard is also designated as ACI 359, Concrete Components for Nuclear Reactors. 

Provisions for concrete reactor vessels, which comprised Subsection CB of Division 2, were 

removed from the B&PV Code in 1990. 

ASCE Manual No. 58 [11] and Klamerus, et. al., [12] provide comprehensive summaries and 

comparison of the design practices for both steel and reinforced concrete containments. Without 

repeating these summaries, a few significant observations are worth noting. Historically, design 

practices for steel containments (Division 1) were developed solely by ASME which treats them 

as pressure vessels and specifies allowable stresses for the prescribed loads. Design practices for 

concrete containments (Division 2), which were developed primarily by ACI and ASME, treats 

them as a structure. This approach combines the ACI practice of applying Load Factors (ranging 

from 1.0 to 1.5 per Table CC-3230-1) to the design loads in consideration of their importance to 

safety, while retaining the concept of allowable stresses used by ASME. This difference in 

approach, leads to some inherent differences in design margin between steel and concrete 

containments, depending on the mode of failure. 

Application reviews for commercial power reactor construction and operating licenses are based 

on the preliminary and final safety analysis reports prepared by the licensees. Regulatory Guide 

1.70, “Standard Format and Content of Safety Analysis Reports for Nuclear Power Plants” 

specifies the requirements for these safety analysis reports (SARs). NUREG-0800, “Standard 

Review Plan (SRP) for the Review of Safety Analysis Reports for Nuclear Power Plants” 

describes the criteria used by the NRC to review the SARs. Chapter 3.8.1 of the SRP specifies 

the extent of compliance with Subsection CC-3000 of Section III, Division 2 for concrete 

containments. Chapter 3.8.2 specifies the extent of compliance with Subsection NE of Section 

III, Division 1 and with Regulatory Guide 1.57 for steel containments. The applicants are also 

required to identify the potential accident initiating events in Chapter 15 of the SAR. The designbasis accident (DBA) is the postulated set of failure events that the plant is designed and built to 
24 

withstand without exceeding the offsite exposure criteria (10 CFR 100). The containment is 

designed to have a very low leakage rate when subjected to the maximum internal pressure 

predicted for the DBA. Typical containment volumes and design pressures for the six types of 

US containments are shown in Figure 12. 

0 10 20 30 40 50 60 70 80 90 100 110

BWR Mark I

BWR Mark II

PWR Ice Condenser

BWR Mark III

PWR Sub-Atmospheric

PWR Large Dry

Containment design pressure (psig)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Containment net free volume (x106

 ft3)

Pressure

Volume

Design pressure =58 psig

Design pressure =50 psig

Design pressure =20 psig

Design pressure = 15 psig

Design pressure = 52 psig

Design pressure = 53 psig

0.6%

0.6%

0.3%

0.5%

0.24%

0.21%

Figure 12 Typical Containment Volume and Design Pressure for US plants [1] 

Containment leakage rates are determined in the SAR and Technical Specifications. Figure 12 

also shows the typical maximum leakage rates for each type of containment. Leakage rates are 

typically described in terms of a percentage of the total containment atmosphere mass or weight 

leaked over a 24 hour day. Criteria for testing containment leakage are set forth in 10 CFR 50, 

Appendix J. This appendix became effective in 1973. Its purpose is to implement, in part, 10 

CFR 50, Appendix A, General Design Criteria 16 which mandates “an essentially leak-tight 

barrier against the uncontrolled release of radioactivity to the environment ...” for postulated 

accidents. 

The design loads and their combinations as well as the response limits are specified in NRC Reg. 

Guide 1.57 (for steel containments), the ASME B&PV Code Section III, Div. 2 and the SRP. 

There are other types of loads that must be considered in the design. These loads include: 

1. temperature transients and gradients 

2. safe shutdown earthquake loads 

3. internal and external missiles 

4. mechanical loads from pipe rupture 

will be used in 

lieu of 

validation
25 

5. external pressures 

6. winds and tornadoes. 

Severe accidents are not part of the design bases, due to their perceived low probability of 

occurrence, and pressure relief valves on the containment are not required (although Mark I and 

Mark II BWR containments include vents, as noted). 

2.2.3 Containment Response to Severe Accidents 

As noted in Section 1.1.1, the most exhaustive study of the risks of severe accidents to date is the 

benchmark study, NUREG-1150 [7]. NUREG-1150, hereafter referred to as the Risk Study, was 

a detailed assessment of the risks of severe accidents at five plants: 

• Zion, a large dry PWR 

• Surry, a subatmospheric PWR 

• Sequoyah, and ice condenser PWR 

• Peach Bottom, a Mark I BWR and 

• Grand Gulf, a Mark III BWR 

An analysis of LaSalle, a Mark II BWR was performed in a separate study [13]. 

These plants were selected as representative examples of the US fleet. A variety of internal 

(equipment failure, operator error) and external (earthquakes) initiating events were investigated 

to estimate the frequency of severe accidents. Plant performance models, which took into 

account containment response and other mitigating features, were coupled with probabilistic risk 

assessment (PRA) to determine accident consequences in terms of health effects and property 

damage. 

Since the containment building constitutes the ultimate barrier between the in-plant environment 

and the outside atmosphere, its performance during a severe accident has a substantial impact on 

the severe accident risk characteristics of the plant. Uncertainty regarding the capability of a 

containment is, therefore, an important contributor to the uncertainty in risk. In risk models, 

determining containment performance involves assessing the probability that the containment 

would ‘fail’ under a range of severe accident conditions. 

Containment failure probability is largely dependent on the individual containment design and the 

particular phenomena or load that challenges the integrity of the containment. Particular severe 

accident challenges to the containment include: 

1. overpressure 

2. dynamic pressure (shock waves) 

3. internal missiles 

4. external missiles 
26 

5. melt-through 

6. bypass 

While the last four challenges were recognized, the Risk Study focused on the response of the 

containment to overpressurization and the corresponding thermal loads. Some of the severe 

accident pressure loads can be quite rapid from a thermo-physical perspective (e.g. deflagrations, 

detonations, etc.) however, the rate of loading for most scenarios is essentially static from a 

structural perspective. (In addition to these severe accident challenges, other external threats 

from acts of terrorism or war can both challenge containment integrity as well as initiating core 

damage sequences.) 

No precise definition of containment failure was given, however, it generally implied a loss of 

containment function (i.e. excess leakage) and not necessarily gross structural failure. For risk 

purposes, the containment was considered to have failed to perform its function when the leak 

rate of radionuclides to the environment is substantial (~10% mass/day). Thus, failure could 

occur as the result of a structural failure of the containment, tearing of the containment liner, or a 

high rate of a leakage through a penetration. Containment bypass was not considered 

containment failure in the risk study and the approach to characterizing failure sizes was 

subjective and based on a consideration of public health consequences. 

In addition to the likelihood of failure, other critical factors in the characterization of containment 

performance in NUREG-1150 included: 

• Failure size: The larger the hole in the containment, the more rapid the escape of radioactive 

material in the containment atmosphere to the outside environment. This reduces the time 

available for radioactive material to deposit within the containment building and also reduces 

the opportunity for effective offsite emergency response. 

Three possible failure sizes were distinguished in the risk study: leak, rupture, and 

catastrophic rupture. Working quantitative definitions of each failure size were based on 

thermal-hydraulic evaluations of containment depressurization times. 

o A leak was defined as a containment breach that would arrest a gradual pressure buildup 

but would not result in containment depressurization in less than 2 hours. (The 2 hour 

‘threshold’ was likely based on consideration of minimum evacuation times.) The typical 

leak size was evaluated for all plants to be on the order of 0.1 ft2

. (This estimate of leak 

size was subsequently revised to 0.3 ft2

 to 0.5 ft2) 

o A rupture was defined as a containment breach that would arrest a gradual pressure 

buildup and would depressurize the containment within 2 hours. For all plants, a rupture 

was evaluated to correspond to a hole size in excess of approximately 1.0 ft2

. 

o A catastrophic rupture was defined as the loss of a substantial portion of the containment 

boundary. 

• Location of failure: The retention of radioactive material by a breached containment building 

may be highly dependent upon the location of failure relative to containment systems 

designed to mitigate accident conditions. For example, in an ice condenser containment, 

failure of the containment in the lower compartment permits radioactive material to bypass 

the ice compartments while escaping to the outside environment. In contrast, containment 

failure in the upper compartment, provided the ice condenser is not degraded, requires that 
27 

radioactive material pass through the ice compartments before escaping to the outside. In the 

latter case, retention of material by the ice would substantially reduce the radioactive release. 

• Rate of loading: The rate of loading may be important in determining the failure mode and 

the ultimate severity of the failure. 

• Time of failure: If the containment function does fail, the timing of failure can be very 

important. The longer the containment remains intact relative to the time of core melting and 

radionuclide release from the reactor coolant system, the more time is available to remove 

radioactive material from the containment atmosphere by engineered safety features or 

natural deposition processes. 

In evaluating the performance of a containment in NUREG-1150, it was convenient to consider 

no failure, late failure, bypass, and early failure of containment as separate categories 

characterizing different degrees of severity. For those plants in which intentional venting was an 

option, this was also represented as a separate category. 

With this somewhat subjective definition of failure, a panel of experts from universities, industry 

and the national laboratories was assembled to provide estimates of containment structural 

performance subjected to predicted severe accident loads. The experts provided distributions that 

defined the probability of failure as a function of pressure and of the mode and location of failure. 

Previous structural evaluations of varying degree of sophistication for each plant (or a similar 

plant), supplemented by calculations performed by individual experts, were used in the elicitation 

process which provided the basis for quantification of containment failure probabilities for each 

plant. 

The results of the expert estimates of the range of containment failure pressure are summarized in 

Appendix C.8 of NUREG-1150. Figure 13 shows the range of failure pressures. Table 4 adds a 

description of the dominant failure location. The detailed results of the expert elicitation are 

documented in a separate report [14]. The basis for the expert panel’s estimates of the range of 

failure pressures for each plant is summarized below: 

Zion: Prestressed concrete w/ steel liner, 1-2% strain in hoop tendons, shear at the 

wall base junction, both resulting in leakage although the possibility of rupture 

or catastrophic rupture were possible at the upper range of pressures 

Surry: Yielding of hoop rebar and tearing of steel liner resulting in leakage near the 

springline; possible leakage at penetrations; little consensus; catastrophic 

rupture at upper pressure, unlikely. 

Sequoyah: Free-standing steel; membrane failure in upper compartment at 2-10% strain 

resulting in rupture or catastrophic rupture; ovalization of equipment hatch 

resulting in leakage. 

Peach Bottom: Steel Mark I; material failure in the drywell or wetwell, no specific criteria 

defined but strains in the range of 1% to 5% were proposed in the detailed 

report, resulting in leak and possibly catastrophic rupture; effects of high 

temperatures on material properties considered. 

Grand Gulf: Reinforced Concrete with steel liner; Drywell design pressure 30 psi, Wetwell 

15 psi; range of failure pressures was from approximately twice the design 

pressure to pressure resulting in ultimate hoop strength of the wetwell 
28 

0

20

40

60

80

100

120

140

160

180

200

Failure Pressure (psig)

ZION

X

X

X

X

X

X

SURRY SEQUOYAH PEACH BOTTOM GRAND GULF

X

95th percentile

50th percentile

5th percentile

Design internal

pressure

High temp.

cases

Drywell

YY

(a)

(b)

(c)

(a) Drywell temperature = 800°F 

(b) Drywell temperature = 1200°F 

(c) Drywell pressure capacity = pressure differential across wall 

Figure 13 Containment Failure Pressures for NUREG-1150 Plants [7] 

One of the documented review comments on the estimates of containment failure pressures 

stated: 

“Experimental data on the ultimate potential strength of containment buildings and their 

failure modes are lacking. This lack of data renders questionable the methods used in 

draft NUREG-1150 for assigning probabilities and locations of failure.” 

The author’s response included the following acknowledgement: 

“The present data on the potential strength of containment structures under severe 

accident loadings and the potential modes of failure are limited..” 

It should be noted that the Risk Study was conducted at the same time NRC-sponsored and other 

research into containment integrity and other severe accident processes were in progress. Some 

of the estimates of containment capacity were informed by some of the early results of this 

research, however, the bulk of the results of this research was not available and no comprehensive 

effort to integrate this research into the risk models have subsequently been made. The broad 

range of failure pressures shown in Figure 8 and Table 4 are not surprising given that it resulted 

from elicitation of panelists who had no agreed upon methodology for containment overpressure 

response assessment and no real consensus on the definition of failure. It should also be noted 
29 

that there has been criticism, by the utility side of the industry, of the failure sizes and 

consequence definitions. Some have argued that the very existence of a rupture or catastrophic 

rupture definition presupposes that such rupture sizes are possible, and counter that they are not 

possible for concrete containments due to the hypothesis of leak-before-break. These topics are 

discussed in more detail in later chapters, but are mentioned here for historical perspective. 

Table 4 Containment Strength Under Static Pressure[7] 

Plant Containment Free 

Volume 

(Millions of Cubic 

Feet) 

Design 

Internal 

Pressure 

(psig) 

Failure 

Pressure 

Range (a) 

(psig) 

Sizes/Locations 

Dominant Failure 

Zion 2.6 47 108-180 Leak/rupture in cylinder wall 

or basemat/wall intersection 

Surry 1.8 45 95-150 Leak/rupture near dome/wall 

intersection 

Sequoyah 1.2 11 40-95 Gross rupture of the containment or rupture 

 in the lower compartment 

Peach 

Bottom 

0.16 (drywell) 

0.12 (wetwell) 

56 120-174 Leak at drywell head or leak/rupture 

of wetwell 

 high temp 

case: 

75-150 

(b) Leak at drywell head or in wetwell above 

suppression pool 

 high temp 

case: 

6-67 

(c) Leak at drywell head or rupture of 

the drywell wall 

Grand 

Gulf 

0.27 (drywell) 

1.4 (wetwell) 

15 38-72 Leak/rupture near dome/wall intersection 

 Drywell: 30 50-120 (d) 

(a) 5th-95th percentile range 

(b) Drywell temperature at 800oF 

(c) Drywell temperature at 1200oF 

(d) Drywell/wetwell pressure differential in psi 

As noted previously, alongside NUREG-1150, the licensees were required to perform ‘Individual 

Plant Evaluations’ or IPEs [6]. The results of these IPEs included estimates of containment 

fragility, i.e. the cumulative containment failure probability for a given pressure. The fragilities 

reported by the licensees for each operating (and several closed) plants are summarized in the 

previously referenced Containment Data Base [9]. A cursory review of the containment 

overpressure fragility curves suggests considerable variation in: the definitions of failure used by 

the licensees; the failure modes and corresponding criteria considered; the methods used to 

calculate the response; and the methods used to incorporate uncertainty. The fragility curves 

summarized in the Containment Data Base represent the cumulative probability of containment 

failure as a function of overpressure, where failure is primarily characterized as either leak or 

rupture, although the application of these terms is not as rigorous as the definition in NUREG1150. 

It is beyond the scope of this report to perform a comprehensive review and comparison of the 

plant IPEs (and by extension the plant PRAs), however, the current (2005) emphasis on riskinformed regulation suggests that such a review could be an invaluable asset in ensuring a level of 

quality and consistency which is currently lacking. Furthermore, lessons learned from the 

experimental efforts described in Chapter 2, could be incorporated into improved estimates of 

containment fragility resulting in higher quality PRAs and risk-informed decision making. 

With these caveats in mind, it is nevertheless worthwhile summarizing the containment fragility 

estimates for the current fleet of plants. Figures 14 through 21 show the normalized overpressure 
30 

fragility curves (where available) for the current fleet of US plants, grouped by reactor and 

containment type. These figures illustrate the large variation in overpressure fragility, even 

among similar containment types. This variation reflects further differences in containment 

design, even within each category, but also reflects the different approaches to estimating 

containment overpressure capacities and fragility. 

IPE Fragility Curves for Large Dry Prestressed Containments

Byron 2

Braidwood 2

Fort Calhoun

HB Robinson

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Normalized Pressure (P/Pdesign)

Failure Probability

Arkansas 1

Arkansas 2

Braidwood 1

Braidwood 2

Byron 1

Byron 2

Callaway

Calvert Cliffs 1&2

Crystal River 3

Farley 1&2

Fort Calhoun

Ginna

Milstone 2

Oconee 1,2&3

Palisades

Palo Verde1,2&3

Point Beach 1&2

HB Robinson

San Onofre 2&3

South Texas 1&2

Summer

TMI-1

Turkey Point 3&4

Vogtle 1&2

Wolf Creek

Figure 14 IPE Fragility Curves for Large Dry Prestressed Concrete Containments 
31 

IPE Fragility Curves for Large Dry Reinforced Concrete Containments

Comanche Peak 1&2

Shearon Harris 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Normalized Pressure (P/Pdesign)

Failure Probability

Comanche Peak 1&2

Diablo Canyon 1&3

Haddam Neck

Indian Point 2

Indian Point 3

Maine Yankee

Salem 1&2

Seabrook 1

Shearon Harris 1

Figure 15 IPE Fragility Curves for Large Dry Reinforced Concrete Containments 

IPE Fragility Curves for Large Dry Steel Containments

Davis-Besse

Kewaunee

Prarie Island 1&2

St. Lucie 1&2

Waterford 3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Normalized Pressure (P/Pdesign)

Failure Probability

Davis-Besse

Kewaunee

Prarie Island 1&2

St. Lucie 1&2

Waterford 3

Figure 16 IPE Fragility Curves for Large Dry Steel Containments 
32 

IPE Fragility Curves for Ice Condenser Reinforced Concrete and Steel Containments

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Normalized Pressure (P/Pdesign)

Failure Probability

Cook

McGuire

Catawba

Sequoyah

Watts Bar

Figure 17 IPE Fragility Curves for Ice Condenser Containments 

IPE Fragility Curves for Sub-Atmospheric Reinforced Concrete Containments

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Normalized Pressure (P/Pdesign)

Failure Probability

Beaver V.

Milstone 3

North An.

Surry

Figure 18 IPE Fragility Curves for Sub-Atmospheric Reinforced Concrete 

Containments 
33 

IPE Fragility Curves for BWR Mark I Containments

Nine Mile

Point 1 Cooper

Browns Ferry

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Normalized Pressure (P/Pdesign)

Failure Probability

Nine Mile Point 1

Oyster Creek

Dresden 2

Dresden 3

Monticello

Pilgrim 1

Quad Cities 1

Quad Cities 2

Browns Ferry 1

Browns Ferry 2

Browns Ferry 3

Cooper

Duane Arnold

Fermi 2

Fitzpatrick

Hatch 1

Hatch 2

Hope Creek 1

Peach Bottom 2

Peach Bottom 3

Brunswick 1

Brunswick 2

Figure 19 IPE Fragility Curves for BWR Mark I 

IPE Fragility Curves for BWR Mark III Containments

Nine Mile Point 2

LaSalle 1 & 2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Normalized Pressure (P/Pdesign)

Failure Probability

Nine Mile Point 2

LaSalle 1

LaSalle 2

Figure 20 IPE Fragility Curves for BWR Mark II 
34 

IPE Fragility Curves for BWR Mark III Containments

Perry 1

Clinton 1

Grand Gulf 1

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

Normalized Pressure (P/Pdesign)

Failure Probability

Perry 1

Riverbend 1

Clinton 1

Grand Gulf 1

Figure 21 IPE Fragility Curves for BWR Mark III 

Containment Performance Parameters in Risk Analysis. 

A comprehensive summary and definition of the various containment performance parameters 

used in risk analysis, e.g. containment failure probability, cumulative containment failure 

probability or fragility, containment failure frequency, conditional containment failure 

probability,... would be extremely useful. A review of the literature, i.e. a number of reports that 

either define or use these parameters suggests that the definitions and usage are not always 

consistent or rigorously applied or interpreted. It is beyond the scope of this current effort to 

identify or resolve all these uncertainties, but a formal presentation of the subject would be 

invaluable to the structural and risk communities. 

Both NUREG-1150 and the IPEs included estimates of containment failure in terms of the 

conditional containment failure probability (CCFP) and the containment failure frequency 

(CFF). These estimates were based on expert opinion and simplified analyses. The conditional 

containment failure probability is the probability of containment failure given an accident. The 

containment failure frequency is the frequency per reactor year of accidents involving 

containment failure. These quantities are defined as: 

i

n

i

i C

CDF

S CCFP = ∑ ⋅ =1

i

n

i

CFF = ∑Si ⋅C =1

where CCFP is the conditional containment failure probability, 
35 

 CFF is the containment failure frequency, 

 CDF is the total core damage frequency, 

 Si is the frequency of accident sequence i, 

 Ci is the conditional probability of containment failure given accident sequence i, and 

 n is the total number of accident sequences. 

Because Si and Ci depend on the particular accident sequences (which vary considerably among 

the plants), both CCFP and CFF can be significantly different for two plants with identical 

containments. 

2.3 Background of Containment Testing at Sandia 

Given the importance of the containment as one of the cornerstones of the NRC ‘defense-indepth’ strategy coupled with the lack of data and analysis tools to characterize containment 

performance to ‘beyond design basis’ loads, the NRC commissioned Sandia to perform a 

‘background’ study, completed in 1981, to “develop a methodology for reliably predicting the 

ultimate capacity of steel and concrete containment structures under loadings caused by accidents 

and severe environments” [8]. This study included a review of US containment types, a brief 

summary containment design practices and a review of previous tests of scale models of 

containment structures and actual containments. At the time of this study, a total of 181 

commercial nuclear power reactors were either operating, under construction or proposed, 

although twenty-one of the proposed plants were either delayed or cancelled. Some of these 

previous tests are described in Chapter 3. 

This review concluded that the ‘large amplitude, nonlinear response of steel containments (had) 

not been investigated experimentally. The pressure tests of concrete containments indicate(d) 

that the models behave(d), in a gross sense, as predicted”. The concrete tests indicated, however, 

the importance of the behavior of the liner and penetrations which were not accurately 

represented in the models. The tests of actual containments were limited to small overpressures 

and provided little information on large deformation non-linear response. 

Based on this review, an ambitious program was proposed to conduct tests of models of 

containment structures to failure and determine the suitability of existing analytical methods to 

predict failure by comparison with the test results. The tests envisioned included static and 

dynamic internal pressurization and seismic loading. The survey of operating and future US 

plants showed a large variety of containment types, however, hybrid steel, reinforced and 

prestressed concrete containments encompassed 75%, so the proposed program focused on these 

types. Because the scope of this report is, primarily, the end result of the program proposed in 

1980, the principles laid out at that time for this program bear repeating: 

“Because it is impractical to test full-size containment structures, scale models will be used. 

Several requirements are necessary to achieve credible results. Each of the items below is an 

integral part of this program. 

• A sound theoretical basis for the model design, the test loading, and interpretation of test 

data must be established. 

• The model scale must be chosen such that the characteristics to be determined in the test 

are accurately represented in the model. 
36 

• The scale model must be fabricated with sufficient care to insure that failure mechanisms, 

not present in the prototype, are not introduced into the model. 

• The test methods must be such that failure modes are not introduced or eliminated in the 

structure as a result of test procedures or test facilities. 

• Instrumentation of sufficient accuracy and sensitivity to record all phenomena of interest 

must be employed. 

• Adequate analytical support must be incorporated into all phases of the experimental 

plan. 

• Repeatability of experimental results must be demonstrated. 

Because the ultimate capacity and modes of failure of steel or concrete containments cannot 

be predicted with confidence using existing computer codes, an analytical task that parallels 

the experimental effort will be undertaken. Qualification of existing codes will be attempted; 

modifications of existing codes and development of new codes may be required. The end 

results of this program will be: 

• Bench-mark data from scale-model tests of selected classes of containments. 

• A set of qualified computer programs that can be used to determine the ultimate capacity 

of containment structures.” 

The summary of the experimental and analytical program described in the following sections of 

this report will describe the extent to which these principles were followed and define the success 

of the program in meeting the original objectives. 

It should also be noted that at the inception of this program, a Peer Review Panel, consisting of 

representatives from industry, academia, other research laboratories and private consultants, was 

organized. This panel, the specific make-up of which varied over the course of the program, 

actively participated in reviewing the research plans and results and provided guidance to the 

NRC and Sandia on the direction of the program. 
37 

Many modelers or code developers 

speak of ‘validating’ their codes or 

models by comparing them with 

experimental data. In practice, most 

models, particularly those for complex 

structures and/or loading conditions, are 

compared to very limited empirical data. 

While the availability of a fairly 

extensive suite of experimental data may 

increase our confidence in the predictive 

capabilities of our analysis, in most 

cases, the rigor implied by the term 

validation is not present. Unfortunately, 

this is especially true when analysts 

report on “validation” analyses which 

are conducted post-test and with data inhand. Conducting “blind” predictions 

provides stronger evidence for 

“validation.” Nevertheless, for purposes 

of this report, the term ‘benchmarking’ 

3 CONTAINMENT MODEL TESTS 

3.1 Containment Model Testing for ‘Beyond-Design Basis’ Loading 

The background study [8] summarized in Section 1.1.3 identified three types of loading to be 

considered in the proposed experimental program: 

• Static internal pressure 

• Dynamic internal pressure 

• Seismic loading 

While the background study did not explicitly identify temperature loads, the accident sequences 

resulting in either static or dynamic pressure loading of the containment always result in elevated 

temperatures inside the containment. As the program evolved, the focus of the experimental 

work was limited to the response of containments to severe accident loading, i.e. those accidents 

which could lead to substantial core damage. Due to the higher costs and complexity, 

containment capacity to seismic loads was addressed by analysis [15] and no experiments were 

proposed at SNL for seismic loading, although some opportunities to participate in tests 

conducted elsewhere were exploited (see Section 3.7.4). 

Severe accidents in the context of containment evaluation can be defined as follows: accidents 

which cause pressurization and/or temperatures within the containment which exceed the design 

basis pressure and temperature. In the context of this program, such accidents refer to the quasistatic generation of steam that results from partial core melt contacting water within the 

containment. When this occurs, and with the volume of the containment essentially fixed, the 

generation of pressure is assumed to be large enough to eventually breach the containment 

boundary, resulting in leakage in excess of design 

specification for the plant. In the authors’ view, most 

of the containment research community agrees with 

this basic definition, however, accident definitions 

begin to diverge when trying to define the 

pressurization rate because this introduces the 

controversial concept of an equilibrium leakage rate. 

The general principles for the experimental and 

analytical program conducted at SNL, stated in the 

background study were listed in Section 1.1.3. The 

resulting test program carried out by SNL over 

twenty-plus years, roughly 1980 through 2003, was 

aimed primarily at benchmarking analysis methods, 

not at proof-testing. 

The program was an integrated one of testing models 

of containment structures and components (both 

scaled and full-size specimens) coupled with detailed 

pretest and posttest analyses. Figure 22 shows a 

timeline of the major containment integrity programs 

along with other milestone events. 
38 

1950 WASH-3: Exclusion vs. Confinement 

1957 Shippingport Nuclear Power Plant 

1971 10 CFR 50, Appendix A: General Design Criteria 

1973 WASH-1250: Reactor Safety Study (definition of Severe Accidents) 

1973 ASME B&PV Code, Section III, Div. 2 (ACI-359) (concrete containment 

design rules) 

1975 WASH-1400: Rasmussen Report (estimates of containment capacity 

1979 Three Mile Island, Unit 2 Accident 

 1981 SNL Background Study on Containment Capacity 

1982 NRC-sponsored Containment Integrity Program at SNL 

 1982 1:32-Scale Steel Model Tests 

 1984 1:8-Scale Steel Model Test 

1986 NRC Qualitative Safety Goals 

1986 Individual Plant Examination Guidance 

 1987 1:6-Scale Reinforced Concrete Model Test 

 ~1988 SNL and EPRI/CTL Separate Effects Tests 

 ~1988 Personnel Airlock Test 

 1988 F4 Phantom Jet Impact Test 

 ~1989 Electrical Penetration Tests 

1989 Sizewell-B 1:10-Scale Model Test 

1990 NUREG-1150: Risk Study (probabilistic risk assessment, PRA) 

1991 NUPEC-NRC Cooperative Containment Research Program at SNL 

 1994 Containment Bellows Tests 

 1996 1:10/1:4-Scale Steel Model Test 

1996 Watts Bar 1 (latest US commercial nuclear power plant) 

 2000 1:4-Scale Prestressed Concrete Model Limit State Test 

2000 NUPEC 1:10-Scale Seismic Capacity Tests 

 2001 1:4-Scale Prestressed Concrete Model Structural Failure Test 

 2005 OECD/NEA/CSNI ISP #48 on Containment Capacity 

 2006 Containment Integrity at SNL Summary 

Figure 22 Timeline for Containment Integrity Research at SNL 

In line with the test program principles, the scale of the models were selected such that some 

representative features of prototypical containments could be included in the models, and the 

response mechanisms would simulate the response of the prototypes (more about scaling later). 
39 

The analytical efforts focused on evaluating and improving the tools and techniques used in the 

evaluation of actual containments by applying them to the test models. Additionally, important 

insights, and a general feel for the state of the industry, were gained through the organization and 

compilation of round-robin pretest and posttest prediction exercises for three of the largest model 

tests. 

For the severe accident response tests, it was necessary to decide whether both thermal and 

pressure loads would be applied to the model, either separately or simultaneously, what the 

pressurization medium should be, and whether the transient characteristics of these loads should 

be considered. Programmatically, the decisions to perform static, pneumatic overpressurization 

tests at ambient temperature were dictated by risk, cost and experimental considerations and 

previous experience. 

The choice of pneumatic versus hydrostatic pressurization was dictated primarily by the goals 

of the test program. If ultimate capacity was the primary objective, the tests could have been 

conducted using water as the pressurization medium (as was done for a number of the tests 

conducted elsewhere). The minor perturbations in the pressure distribution due to gravity are not 

significant at ultimate load and can be accounted for by the analysis. Hydrostatic testing is 

preferable from a safety viewpoint due to the incompressibility of the pressurization medium; 

however, it raises operational problems and requires protection of sensitive electronics and wiring 

from the water under high pressure. The containment atmosphere during a severe accident 

consists of a combination of air, steam, and other by-products of the accident, including hydrogen 

and particulates (aerosols). The primary program interest is in observing and measuring the 

structural response of the containment to pressure loads and identifying failure modes. 

Containment failure (see 3.2.2) includes both functional failure, i.e. leakage, and structural 

failure, i.e. rupture of the pressure resisting elements. There is not a rigorous distinction between 

functional and structural failure, and it is conceivable that they might occur simultaneously. 

Conventional wisdom holds, however, that local, limited failure (e.g. seal failure or liner tearing) 

and leakage will occur prior to, and at pressures below those required to cause catastrophic 

structural failure. As a result, detection of leakage which is indicative of a tear in the steel liner 

or failure of a penetration seal, is a higher priority than measurement of actual leak rates for real 

containment atmospheres as a function of pressure. The choice of a pressurization medium, then 

is dictated more by safety and operational considerations and reproduction of the actual 

containment atmosphere under severe accident conditions is not practical. Pneumatic testing, 

while inherently more dangerous, present risks that can be managed cost effectively and does not 

require any unusual measures to protect the instrumentation. 

All tests conducted as part of the Sandia program, except one, were conducted using dry nitrogen. 

Nitrogen gas was chosen as the primary pressurization medium for the model tests primarily for 

operational considerations. Nitrogen gas has the advantage of being dry, which benefits the 

performance of the instrumentation, and it allows simpler and more accurate calculation to detect 

a small leak. Fairly large quantities of nitrogen could be delivered at a remote test site in liquid 

form with a limited amount of fixed equipment. This decision dictated that careful planning and 

additional safety precautions were incorporated into the test programs due to the large stored 

energy and potentially violent nature of a catastrophic failure. 

For the final test of the 1:4-Scale Prestressed Concrete Containment Vessel (PCCV), the 

Structural Failure Mode Test, the vessel was filled 95% with water, and the top 5% volume filled 

with nitrogen, in order to leverage the nitrogen supply system to achieve higher overall 

pressurization rate. This is discussed in more detail later (see 3.5.1). 
40 

The effects of severe accident temperature loads on the structural response of the containment 

building are primarily limited to (1) the effects of elevated temperatures on the mechanical 

properties of the materials and (2) the mechanical loads resulting from differential or constrained 

thermal expansion. The effects of temperature on the material properties can be determined from 

standard material tests methods. Thermal effects could be incorporated into the evaluation of the 

prototypical containment vessels without adding the complexity and cost (in terms of generating 

the thermal environment and protecting the instrumentation) to the PCCV model test. The added 

complexity and cost of simulating the thermal environments to reproduce these local effects was 

judged not to be justified for these experiments. It was further concluded that, since there is no 

unique pressure-temperature relationship for severe accidents, the effects of temperature could be 

addressed using analytical methods which had been benchmarked against the pressure tests [16]. 

Therefore, the decision was made to conduct these model tests at ambient temperature. 

Regarding the stresses imposed by differential thermal expansion, there are only a few locations 

in a steel and/or concrete containment building where these effects are significant, notably at the 

junction of the containment wall and the basemat or, in the case of the steel lined concrete 

containments,, the differential thermal expansion between the steel liner and the concrete shell 

under non-steady state thermal conditions. One further area, not represented in the containment 

model tests, is the differential expansion between the containment itself and adjacent structures 

and components, e.g. the shield building, and pipes which penetrate the containment boundary. 

Polar cranes, supported on the containment wall in some plants, are another example where 

differential expansion could result in damage to the containment or other internal components, in 

the event the crane fell from its supports. 

In terms of the transient aspect, as noted previously, the pressure and temperature loads resulting 

from a severe accident can be quite rapid from a thermo-physical perspective (e.g. deflagrations, 

detonations, etc.), however the typical rates of loading (on the order of tens of seconds to 

minutes) are essentially static from a structural perspective. As a result, the dynamic aspects can 

be ignored and the tests can be conducted in a pseudo-static manner in the test program with no 

significant change in the response of the containment. 

3.2 Modeling Considerations 

The testing program that was developed and evolved at Sandia included the three major 

construction types used in current US containments: free-standing steel containments, steel lined 

reinforced concrete containments and steel lined prestressed concrete containments. For each 

type of containment model, the same guiding principles were used in the development of the 

model design, namely that the models would incorporate representative features of the prototypes, 

would not knowingly preclude a potential failure mode and would not incorporate details which 

were unique to the model and not representative of the prototype. While these principles are easy 

to articulate, their realization in practice is not always simple or straightforward. The scales of 

the models were chosen to reflect these principles and typically, as a result, the more complex the 

features were to be incorporated into the model, the larger the scale. As analytical research 

programs were planned and carried out in conjunction with the testing, an additional goal of the 

experiments became to determine if any unanticipated structural behaviors would occur. 

The Background Study [8] recognized that an important element of an experimental program is 

repetition of experiments to prove reproducibility of results: 

“It cannot be overemphasized that reproducibility of results must be demonstrated before 

conclusions can be drawn. For each individual experiment, a sound statistical treatment 

of all measured data (both control and response) is required prior to considering the 
41 

experiment complete. The results of this complete experiment must then be demonstrated 

as reproducible by repetition; i.e., the experiment must be conducted again in as nearly 

the same manner as possible, limited only by the experimenter's ability and random 

factors. 

Random factors will always be present. They may be associated with model fabrication, 

load application, response measurement, material variability, or other variables. The 

variations between experiments will produce a scatter in the results of seemingly 

identical experiments. Therefore, the results are reproducible if the measured response 

in all attempts fall within an acceptable scatter band. Careful error analysis is necessary 

to determine an acceptable scatter band. In complicated experiments with multiple 

responses it is possible that only some responses will be reproducible.” 

Unfortunately, cost and schedule constraints usually prevent repetition of model tests, especially 

for the type of large-scale, detailed models of complex structures which are the subject of this 

report. Nevertheless, the principle of reproducibility of results is still important and should be an 

important consideration in interpreting and applying the results of the tests. 

3.2.1 Scaling 

In all cases, with some minor exceptions, straight geometric or replica scaling was utilized in the 

design of the models. This is possible since for most severe accident pressure loading, the rate of 

pressurization is slow enough that the model responds essentially statically and dynamic effects 

are not significant. The background study included a fairly thorough review of the scaling laws 

considered for the test program and a brief review of the scaling issues is warranted at this point 

in the summary. 

Considering all parameters relating to geometry, material properties, loading conditions, the 

Buckingham Pi Theorem was used to generate a list of non-dimensional pi terms. For a model 

and prototype system to be equivalent, only the pi terms (and not each individual parameter) have 

to be identical in both systems. This principle introduces the concept of scale factor for the 

various parameters in the problem. Inspection of the pi terms yields the scale factors for the 

various parameters of interest, shown in Table 5. 

A replica model is built with the same materials in corresponding model and prototype locations, 

but is smaller by a geometric scale factor λ. In a replica model, all material properties such as 

density ρ, strength σ, and strain rate coefficient Ki are the same as in the prototype. However, not 

all phenomena are scaled without distortion in a replica model. Three problem areas are 

identified in the table. We can’t easily scale gravity, short of constructing models on the moon, 

and if we use the same materials in the model and the prototype, strain-rate dependent properties 

and viscous damping cannot be modified. For static loading, the latter parameters, and others 

which are time-dependent, are not critical and do not affect the results. Since gravity affects the 

dead load stresses, our inability to scale gravity could be important if dead loads are a significant 

portion of the total load on the model. Typically, severe accident loadings dominate the response 

of the structures and the differences in response to gravity loading between the model and 

prototype are not typically significant, but should not be ignored. 
42 

Table 5 Replica Modeling Law to Satisfy Pi Terms 

Parameter Symbol Factor 

Lengths, displacements L, x, X λ 

Angles θi 1.0 

Times, duration t, T, To λ

Velocities v, V 1.0 

Accelerations a, A 1/λ

Stresses σ 1.0 

Densities ρ, ρ o 1.0 

Strains ε 1.0 

Pressures P, p(t), Po 1.0 

Frequencies ω 1/λ

Forces F λ2

Number of reinforcing bars Ni 1.0 

Leakage rate m& λ2

Acceleration of gravity g 1/λ

Strain-rate coefficient Ki λ

Equivalent viscous damping βi λ2

The background study did not address scaling of thermal response since the model tests proposed 

were conducted at ambient temperature. If future tests or analysis of models include temperature 

loading, the scale factors for thermal response should be investigated. For example, the scale 

factor for thermal conductivity will not be 1.0 and the through-wall gradients will be different for 

the model and the prototype. 

It is also important to note that the scale factor for leak rate is λ2

. Leak rates measured from 

model tests should include consideration of this scale factor when compared to allowable values. 

In general, all features of a prototype containment cannot be represented in a scale model. 

Specific feature such as welds, fasteners (bolts, rebar couplers, tendon anchors, etc.), tolerances in 

fabrication and construction and other details can only be represented approximately. Each of 

these features of the prototype must be evaluated to determine its impact on the response and 

whether its inclusion in the model is necessary. For any realistic model test, compromises, often 

based only on engineering judgment, are inevitable regarding the fidelity of modeling small 

details in the structure. Often these compromises result in the elimination of failure modes from 

the model. The results of model tests should always be interpreted with an understanding of these 

compromises. 

3.2.2 Failure 

For pretest and post-test evaluations of the test models, especially the concrete ones, failure 

predictions have been made based on criteria developed during the early (1980s) phase of the 

containment research, and refined by large scale tests and supporting analysis. There has been a 

lack of consistency in the literature over what is meant by ‘failure’ of containments. For the 

Containment Integrity program at SNL, two working definitions of ‘failure’ have been used. 

‘Functional failure’ has been taken to denote a loss of containment function, i.e. a leak rate in 

excess of the specified minimum leak rate of the containment, usually associated with a loss of 
43 

liner integrity of loss of penetration sealing. Functional failure typically occurs when global 

deformations and strains exceed the elastic limit and/or local strains exceed the material strain 

limits. Functional failure can include the concepts of ‘leak’ and ‘rupture’ used in NUREG-1150. 

‘Structural failure’ denotes the limit of resistance to the applied load and is characterized by large 

global deformations and extensive material failure. Structural failure includes the concept of 

‘catastrophic rupture’ in NUREG-1150. For the work described in this report, the term “failure” 

is taken to mean the occurrence of such large deformations (strains) of the liner or of a 

containment structural element, that a breach of the containment pressure boundary is predicted. 

Functional failure criteria have been difficult to define due to a lack of correlation between 

functional performance parameters (i.e. leak rate) and structural performance parameters (e.g. 

stress, deformation, strain) which can be measured in an experiment or calculated by analysis (see 

2.7.6). Surrogate structural failure criteria have been used in lieu of functional criteria. These 

surrogate criteria have been based on engineering judgment and experimental results. One of the 

objectives of the Containment Integrity program at SNL is to provide further insights and, 

hopefully, improved recommendations for these surrogate criteria. 

Current practice for predicting local failure for steel and steel-lined concrete containments for 

pressure-only loading is based on either the explicit prediction of liner strains high enough to 

exceed the material strain limits, including consideration of tri-axial strain fields, e.g. the Davis 

Triaxiality Factor [17], if the finite element mesh is refined enough, or assumes the existence of 

high strains near a liner discontinuity. Typically, the liner discontinuity is not explicitly modeled 

or not modeled with a highly refined mesh and strain concentration factors, based on experiment 

or detailed analysis, are applied to the computed strains. Cherry and Smith [18] provided a 

comprehensive summary of failure criteria for steel containment analysis. Dameron [19] 

summarized a range of strain concentration factors for typical details in steel liners of concrete 

containments. The use of strain concentration factors has been shown to be successful for 

predicting the behavior and failure of large scale models, and there is evidence that for steel and 

steel-lined concrete vessels with quasi-static pressurization, tearing will occur when the strain 

fields in the vicinity of a discontinuity, i.e. the so-called ‘near-field’ or ‘driving’ strains, are on 

the order of 1 to 2%. Obviously, the use of strain concentration factors in lieu of detailed local 

analysis is dependent on the specific details used in the construction, however, this is not as 

serious a deficiency as it might appear given the difficulties in defining and modeling the as-built 

configuration accurately. This suggests that valid surrogate criteria may be developed for both 

local and global (or near-field) strains. 

While the approach for defining surrogate failure criteria for steel or steel-lined concrete 

containments may be similar, the response upon reaching failure may be dramatically different. 

For a steel containment, the onset of tearing usually denotes an instability and failure progresses 

nearly instantaneously to catastrophic rupture. For conventionally reinforced or prestressed 

concrete containments, the onset of liner tearing can lead to either leakage and gradual 

depressurization or catastrophic rupture. Arguments regarding the validity of the concept of 

‘leak-before-break’, which find their origin in the design of piping systems, for containment 

systems are discussed in subsequent sections. 

One mode of failure not explicitly considered in the Containment Integrity program is the 

potential for large displacement of the containment structure relative to adjacent structures and 

piping which could result in loss of containment or by-pass. Since the model tests did not include 

these external structures and did not simulate the thermal loading which can lead to large 

deformations, this failure mode was not represented in the experiments. Nevertheless, this mode 

could be critical and should be considered in any complete evaluation of containment integrity. 
44 

On a practical note, functional failure criteria are not particularly useful for conducting tests to 

determine the structural capacity of a containment vessel model, especially when the objectives 

are 1) to generate large inelastic response modes for comparison with analytical predictions, 

which may be well beyond the levels required to cause functional failure, and 2) to gain some 

insight into design margins, i.e. the functional and structural capacity beyond the specified design 

load conditions. The pressurization system is typically designed to allow the model to be 

pressurized to levels significantly above those expected to cause local strains in the model to 

exceed the ultimate strain limits of the materials. In some cases, the tests were terminated when 

the model and the pressurization system were incapable of maintaining or increasing the model 

pressure-due to excessive leakage or gross rupture. The maximum pressure achieved prior to the 

termination of the tests should not be confused with the failure pressure, since failure is defined in 

terms of some acceptance criteria, not the operational inability to maintain pressure in the model. 

3.3 Steel Containment Model Tests 

A series of scale models of steel containment vessels, of increasing size and complexity were 

tested at Sandia between 1982 and 1996. Table 6 summarizes the details of the models and the 

results of the tests. Each series of tests are described in the subsequent sections. Details are 

provided in the references cited in the table. 

3.3.1 NRC 1:32-scale steel models 

The first tests conducted at SNL, in 1983, were on four simplified 1:32-scale models of a 

cylindrical steel shell with a hemi-spherical head. The models are illustrated in Figures 23 and 

24. The containments are typical of a large dry or ice-condenser PWR containment. Two models 

(SC-0 and SC-1) had no penetrations or stiffeners, one (SC-2) had ten ring stiffeners brazed to the 

cylinder wall, one (SC-3) had a mock-up of three penetrations (an equipment hatch and two 

personnel locks) with no gaskets or seals, i.e. the penetrations were welded shut. Details of the 

tests and supporting analyses are described Horschel in [20] and [21]. 

The results of these small scale tests demonstrated the value of conducting scale model tests of 

containments, both for comparison with analytical predictions and for gaining insight into 

response and failure modes. In general, the results indicated that simple shells, without 

significant perturbations such as stiffeners and penetrations could withstand pressures causing 

large strains up to the uniaxial tensile strain limits. The failures initiated near the mid-heights of 

the cylinders The presence of even ‘minor’ perturbations or discontinuities resulted in a 

significant reduction of free field strains with some reduction in the pressure capacity. Pretest 

analyses gave good comparisons with the global response and the observed failure pressures. The 

calculated failure pressures of SC-0 and SC-1 was 0.91 MPa with failure occurring at mid-height; 

for SC-2 the calculated pressure was 0.95 MPa with failure of the stiffener rings; failure of SC-3 

was predicted to occur at 0.84 MPa at the sleeve of the equipment hatch (E/H). 

One interesting result of these tests was that the calculated initial yield was below the observed 

yield. At the time this was dismissed as being due to the initial stresses in forming the shells 

(they were cold-rolled) and the Bauschinger effect. Since the calculations beyond the initial yield 

joined the experimental results it was not considered a significant effect and this discrepancy was 

dismissed, however, as shown in the next two sections, this appears to be typical of all the steel 

containment models tested. 
45 

Table 6 Summary of Results of Experiments for Steel Containment Models 

Test Scale Shape R/t Pressure 

Ratio 

(Pd/Pmax) 

Global 

Strain at 

Failure 

Material Remarks 

SNL SCO 

(12/2/82, 

12/12/82) 

1:32 Cylinder w/ 

hemispherical 

dome 

450 

(R=549, 

t=1.22) 

0.93* 20% AISI 1008 Catastrophic 

rupture and 

fragmentation 

initiating at 

vertical weld 

seam. [20, 21] 

SNL SC1 

(4/20-21/83) 

1:32 Cylinder w/ 

hemispherical 

dome 

500 

(R=546, 

t=1.09) 

0.76* 6% AISI 1008 Tearing and 

leakage next to 

vertical weld 

seam.[ 20, 21] 

SNL SC2 

(7/21/83) 

1:32 Cylinder w/ hoop 

stiffeners and 

hemispherical 

dome 

478 (R=546, 

t=1.17) 

0.93* 2.7% AISI 1008 Leakage and 

tears at cylinderdome interface; 

repaired. 

(8/11/83) 0.97* 2.5% Retest; 

catastrophic 

rupture and 

fragmentation. 

[20, 21] 

SNL SC3 

(11/30/83) 

1:32 Cylinder w/ 

penetrations and 

hemispherical 

dome 

478 

(R=546, 

t=1.17) 

0.83* 14.5% AISI 1008 Catastrophic 

rupture initiating 

at E/H. [20, 21] 

SNL 1:8 

(11/15-

17/84) 

1:8 Cylinder w/ 

stiffening rings, 

penetrations and 

hemispherical 

dome 

448 

(R=2134, 

t=4.76) 

4.9 

⎛1.34⎞ 

⎝0.27⎠

3% SA516, 

Gr. 70 

Catastrophic 

rupture and 

fragmentation 

initiation at 

stiffener near 

E/H. [22, 23, 24, 

25] 

NUPEC/ 

SNL 

SCV 

(12/11/96) 

1:10 

geom./ 

1:4 

thick. 

Improved BWR 

Mark II w/ 

contact structure 

135-161 

(R=2027-

2900, 

t=7.5-9.0) 

6.0 

⎛ 4.7 ⎞ 

⎝0.78⎠

2.0% SPV490, 

SGV 480 

Tearing and 

leakage at 

vertical seam 

weld and at E/H 

insert plate weld. 

[26, 27, 28, 29, 

30, 31, 32] 

*Design pressure not specified, maximum pressure (MPa) given. 
46 

46.2”

65.8”

CLEAN SHELL RING STIFFENED 

SHELL

SHELL WITH 

PENETRATIONS

WALL 

THICKNESS 

= 0.048”

SC-0 

SC-1 SC-2 SC-3

46.2”

65.8”

CLEAN SHELL RING STIFFENED 

SHELL

SHELL WITH 

PENETRATIONS

WALL 

THICKNESS 

= 0.048”

SC-0 

SC-1 SC-2 SC-3

Figure 23 1:32-Scale Steel Containment Vessel Models 

SC-1 SC-1

SC-3

Figure 24 SC-1 and SC-3 Tests 
47 

3.3.2 NRC 1:8-scale steel containment model 

A 1:8-scale model of a free-standing steel containment, which represented some features typical 

of large dry or ice-condenser PWR containments or a Mark III BWR containment, was the next 

model tested in the series of tests sponsored by the NRC at Sandia. The model is illustrated in 

Figure 25 and a picture of the model prior to testing is shown in Figure 26. The model was 

designed and built according to the ASME B&PV code with a design pressure of 40 psig (.27 

MPa). The model included 11 penetrations typical of the prototypical plants including functional 

representations of the equipment hatch and personnel airlocks. The cylindrical shell was stiffened 

by external stiffeners with prototypical fabrication details. Details of the model design are 

provided in [22]. Pretest analysis indicated failure would occur due to ovalization of the E/H and 

leakage past the seals [23]. 

Figure 25 1:8-Scale Steel Containment Model Layout 
48 

Figure 26 1:8-Scale Steel Containment Model 

After a series of low pressure tests, the model was tested to failure in late 1984. Pretest analyses 

predicted failure would occur by ovalization of the equipment hatch sleeve resulting in a failure 

of the seals and leakage. Before the expected leakage could occur at the hatch, a tear, 

subsequently discovered as initiating at a stiffener detail adjacent to the E/H, resulted in 

catastrophic rupture and fragmentation of the vessel. The results of the test are illustrated in the 

composite Figure 27. The figure shows the predicted and measured response of the model. The 

posttest picture of the test site shows that fragments of the vessel were thrown over 1500 ft by the 

violent release of stored energy in the compressed gas. Video of the test was too slow to capture 

the failure of the vessel, but a wisp of ‘steam’, associated with escape of the nitrogen gas, was 

reported as being seen in the vicinity of the E/H immediately prior to vessel rupture. 
49 

(a) Model with View of EH1 and Cracked Stiffener at 190 psig 

(b) Aerial View of Site after Rupture 

Figure 27 Results of 1:8-Scale Steel Containment Vessel Model Test 
50 

(c) Ovalization Increased Rapidly after Cylinder Membrane Yielding Occurred 

(d) Summary of Performance 

Figure 27 (cont’d) Results of 1:8-Scale Steel Containment Vessel Model Test 

Results of the test were reported by Koenig [24]. Global behavior compared favorably with the 

predicted response, however, as with the 1:32-scale models, the analysis over-predicted the 

pressure at which generalized yielding of the shell occurred. Figure 28 compares the predicted 

and measured free-field hoop strain at the mid-height of the cylinder wall. (The curve denoted 

‘CP’ refers to the hoop strain measured in the vicinity of a constrained penetration.) Again this 

discrepancy was dismissed as post-yield response approached the predicted behavior. 
51 

Figure 28 Comparison of Predicted and Measured Hoop Strains in the 1:8-Scale Steel 

Containment Vessel Model. [25] 

Posttest analyses confirmed that a high strain concentration at the eccentric intersection of 

stiffeners around the E/H (Figure 29) was responsible for the tear and subsequent rupture by 

exceeding the ductile limits of the material. While demonstrating the large excess capacity of the 

model above the design specification (almost 5 times the design pressure), the test also 

highlighted the significance of local details in defining the limits of the prototypical containment 

structure [26]. 

Two circular samples (1.8 mm uniform thickness, 890 mm diameter) of the actual steel used in 

the construction of the model were tested by Kernforschungszentrum Karlsruhe, Germany, in a 

special test fixture that applied oil pressure to one side of the sample, to obtain biaxial stressstrain relationships. Similar tests were conducted on a typical German containment steel: two 

tests of uniform thickness samples (2 mm thick by 860 mm diameter) and two tests with a 

circular reinforcement (3.4 mm thick by 132 mm diameter) at the center [27]. Both unreinforced 

samples failed at 4.3 MPa while the reinforced samples failed at 2.8 and 3.2 MPa, illustrating the 

dramatic effects of a discontinuity on the capacity.

Figure 29 Pretest Analysis vs. As-built Configuration of Stiffeners at 1:8-Scale Steel 

Model Equipment Hatch 

Experiment 

Analysis 
52 

3.3.3 NUPEC/NRC 1:10/1:4-scale steel containment vessel model 

The final steel containment vessel model tested at SNL under the joint sponsorship of the Nuclear 

Power Engineering Corporation (NUPEC) of Japan and the US NRC was a mixed scale model 

representative of the containment of an improved BWR Mark II in Japan. The model geometry 

was scaled 1:10 from the prototype while the shell thickness was scaled 1:4 to facilitate 

fabrication and to allow the use of prototypical materials. The configuration of the model is 

illustrated in Figure 30. The portion of the model above the material change interface, which is 

slightly below the equipment hatch centerline, was fabricated of SGV480, a mild steel, while the 

lower portion of the model and the reinforcement plate around the penetration were fabricated 

from high strength SPV490 steel. The conical shape of this structure and the re-entrant curvature 

at the top head are unique containment design features not tested in previous models. While not 

identical, this ‘knuckle’ is also present in Mark I designs. This model included a representation 

of the top head and the equipment hatch, although these were non-functional (i.e. welded shut) 

and not a credible leak path. Separate tests of functional drywell and equipment hatches have 

been conducted in Japan [28, 29]. The design pressure of the prototype containment is 0.31 MPa, 

whereas the scaled design pressure for this mixed scale model is 0.78 MPa. A separate steel 

contact structure surrounded the steel containment model during the test. This contact structure 

was incorporated into the test to represent the confining effect of the concrete shield building 

surrounding the containment during accident conditions. 

The model was fabricated in Japan and shipped to Sandia National Laboratories, Albuquerque, 

NM, USA for instrumentation and testing. After the model was delivered to Sandia, a 38 mm 

thick steel (ASTM SA516 Grade 70) contact structure (CS) was installed over the SCV model 

prior to testing to represent some features of the reactor shield building in the actual plant. A 

nominal gap of 18 mm was maintained between the SCV model and the CS. Instrumentation of 

the model consisted of more than 800 channels of strain gages, displacement transducers, 

temperature and pressure sensors, and an acoustic emission device, in addition to video 

monitoring. 

Luk [30] described the design, fabrications and testing of this model. The high pressure test of 

the model was conducted on December 11-12, 1996, at Sandia National Laboratories. After 

approximately 16.5 hours of continuous, monotonic pressurization using nitrogen gas, testing was 

terminated at a pressure 4.66 MPa or approximately six times the design pressure when a large 

tear (190 mm) developed adjacent the E/H insert plate weld seam with the main body of the 

vessel (Figures 31 and 32). Rapid venting of the model was observed and the pressurization 

system, operating at capacity (37 scm/m, standard cubic meters per minute), was unable to 

maintain pressure in the model. 

Posttest visual inspection of the interior of the model revealed a large tear, approximately 190 

mm long, adjacent to the weld at the edge of the equipment hatch reinforcement plate (Fig. 25). 

The tear appears to have initiated at a point roughly 30 mm below the material change interface 

(around 8 o’clock when viewed from the inside) in the high strength SPV490 steel shell, and 

propagated in both directions along the weld seam before it stopped. Interestingly, while the right 

side of the equipment hatch did not tear, significant necking was observed at a location symmetric 

with the tear (Fig. 32). 

In addition, a small meridional tear, approximately 85 mm long, was found in a vertical weld (at 

an azimuth of 201°) underneath a semi-circular weld relief opening at the middle stiffening ring 

(Fig. 33). Some evidence suggests that this small tear might have occurred first but did not grow, 

and the pressurization system was able to compensate for any leakage through this tear. This tear 
53 

also had a counterpart at a similar, diametrically opposed detail. While no tear developed at this 

location, necking in the weld was observed. 

After this initial inspection of the interior of the model, the contact structure was removed to 

allow inspection of the exterior of the model. In addition to the observations noted above, visual 

inspection revealed evidence of the pattern of contact between the model and the CS in the form 

of crushed instrumentation lead wires and transfer of mill markings from the interior of the CS. 

In addition, concentrated crack patterns in the paint indicated that global strains in the higher 

strength SPV490 shell were concentrated at the vertical weld seams while the uniformly 

distributed cracks in the SGV480 shell indicate that the hoop strains were fairly uniform. 

More than 97% of the instruments survived the high pressure test. The failed gages, which 

consisted primarily of those on the exterior of the model, were damaged when the model made 

contact with the CS. The raw strain data were corrected to compensate for temperature variations 

and cross-axis strains, and the displacement data were corrected to account for any movement of 

the center support column to which the displacement transducers were anchored. The complete 

data record is included in the SCV Test Report [30]. A brief summary of the test data follows. 

Local Response Adjacent To The Equipment Hatch: An extensive array of single element, strip 

and rosette strain gages was installed around the equipment hatch to characterize the local strain 

distribution. Figure 32 shows the locations of a few critical strain gages around the equipment 

hatch viewed from inside the model. A strip gage (STG-I-EQH-16), adjacent to the upper end of 

the tear, registered a maximum strain of 4.2%, and the two rosette gages (RSG-I-EQH-12 and -8) 

above it recorded maximum strains of 3.7% and 2.8%, respectively. The rosette gage (RSG-IEQH-22) slightly below the lower end of the tear recorded a maximum strain of 1.3%. However, 

the highest strain reading of 8.7% was recorded by a strip gage (STG-I-EQH-37) at 3 o’clock, just 

above the material change interface. 

Global Response: The global response of the SCV model was monitored using free-field strain 

gages and an array of internal displacement transducers that measured the strains and 

displacements at several elevations along four cardinal azimuths (0 ̊, 90 ̊, 180 ̊, and 270 ̊). 

Maximum free-field hoop strains ranging from 1.7 to 2.0% were measured at 4.5 MPa at the 

upper conical shell section. Hoop strains calculated from the displacement measurements (∆r/r) 

were consistent with the strain gage measurements at these locations. 
 54 

5201.8

1450 500 829.4 695.5 419 664.7 387.4 255.8 2900 2026.9 965

50

9

9

8.5

7.5

8

6

6

Note: All d

72

SGV 4

SPV 

5201.8

1450 500 829.4 695.5 419 664.7 387.4 255.8 2900 2026.9 965

50

9

9

8.5

7.5

8

6

6

Note: All d

72

SGV 4

SPV 

Figure 30 1:10-Scale Steel Containment Model Summary 

Japanese Improved BWR Mark II supplied by NUPEC Scale: 1:10 on geometry; 1:4 on thickness Diameter: 2900 mm (9.5’) Overall Height: 5900 mm (19.5’) Internal Volume: 21 m3 (740 ft3) Weight: 13,000 kg (28,634 lb) Design Pressure:  Pda=0.31 MPa (45 psig)-actual  Pds=0.78 MPa (112.5 psig)-scaled Materials:  SGV480 (Fy= 265 MPa, 38 ksi) ~ SA-516 Grade 70;  SPV490 (Fy= 490 MPa,71ksi) ~ SA-537 Class 2 Contact Structure Weight - 9 metric tons (20,000 lbs) Material: SA-516-70 (Fy =38 ksi) Nominal thickness = 38.1 mm (1.5 in.) Low Pressure Test: 1.50 Pds =1.17 MPa (169 psig) High Pressure Test Date: Dec. 9 - 13, 1996 Instrumentation: SCV External: 113 Strain Gages, 6 Displacement Transducers SCV Internal: 151 Strain Gages, 57 Displacement Transducers CS: 15 Strain Gages, 10 Gap LVDT’s, 59 Contact Probes Failure Pressure~Mode: 

6 Pds: 4.7 MPa (676 psig)~tearing and leakage in HAZ of SPV 490 adjacent to E/H insert plate. 
 55 

Figure 31 Posttest View of Tears at E/H, 1:10-Scale Steel Containment Model 

(inside view)

STG-I-EQH-37a

(2680

) STG-I-EQH-16b

(92.50

)

RSG-I-EQH-12

(66.50

)

Material

Change

Interface

Tear (~190mm long)

Thickened

Insert Plate

Note: All dimensions in mm

STG: strip strain gage

RSG: rosette strain gage

Equipment

Hatch 135

146

159

149

146

RSG-I-EQH-8

(440

)

157

200

00

900

1800

2700

(122.50)

(91.50

)

(990) 143 (2600

)

(2460

)

Thinned Area

(~85mm long)

RSG-I-EQH-22

(1350

)

156

(2610)

Figure 32 Posttest Interior View of the 1:10-Scale Steel Model 
 56 

Figure 33 Tear at Horizontal Stiffener ‘Rat-Hole’, 1:10-Scale Steel Containment Model 

Figure 34 shows the spatial variation of displacements at the cardinal azimuths at 4.5 MPa. It 

should be noted that the displacement pattern is fairly axisymmetric with the exception of 90 ̊, the 

azimuth where the equipment hatch is located, where the displacements in the lower conical shell 

section, below the material change interface, are much larger than at the free-field azimuths (0 ̊, 

180 ̊, and 270 ̊). This is of particular interest because this area was actually displaced inward 

during fabrication of the SCV model and this is the area where the large tear occurred. 

In addition to the posttest visual inspection described above, a detailed metallographic evaluation 

of the SCV model was conducted to characterize the local failure mechanisms and provide some 

insight into both the global and local response of the model. This detailed evaluation and analysis 

is described in Reference 33. Briefly, sections were removed from the model surrounding the 

tears and areas of necking or other obvious structural distress. Fractographic inspection of the 

failure surfaces indicated that the tearing mechanism was ductile and did not display any evidence 

of flaws or other defects that might have acted to initiate failure. It was therefore concluded that 

the model failure resulted from strains exceeding the material strength, and it is possible to 

characterize failure based on the material properties of the steel. 

After this inspection, smaller sections were removed from the model and polished cross-sections 

normal to the model surface were examined using a scanning electron microscope to characterize 

the grain structure. Hardness tests were also performed on these polished specimens to look for 

variations in material properties. A section through the major tear surrounding the equipment 

hatch is shown in Fig. 35. The results of these inspections revealed changes in the grain structure 

of the SPV490 material in the heat affected zone (HAZ) surrounding the reinforcement plate weld 
 57 

and a significant reduction in the hardness of the HAZ and adjacent parent material. Using wellestablished relationships between hardness and tensile strength, these results indicate a significant 

reduction in tensile strength along with a corresponding, though less well-defined, reduction in the 

yield strength of the material. These results indicate that one possible explanation for the strain 

patterns observed around the equipment hatch and in the weld seams of the SPV490 shell may be 

due to this localized microstructural alteration and reduced hardness and strength in the HAZ of 

the SPV490 alloy plate. 

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

1600.00

0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00

Elevation (mm)

Radius (mm)

Undeformed

0°

90°

180°

270°

LST

E/H

MST

UST

Figure 34 Displacement contours (x10) @ 4.5 MPa 

Figure 35 Cross-section through large tear at equipment hatch 

Pretest predictions of failure pressures, summarized in Table 7, ranged from 5 to 15 times the 

design pressure with failure modes ranging from ductile material failure to buckling of the top 

head. These predictions were the result of separate blind analyses performed by a variety of 

international agencies which were provided with identical design, fabrication and material 

property data prior to the test [31, 32]. While the lowest predicted failure pressures compared 

Lower Stiffener 

Equipment Hatch 

Middle Stiffener 
 58 

favorably with the test results, the mechanisms which these predictions were based on were not 

the apparent cause of the failure. Furthermore, the mechanism giving rise to the small tear was 

not recognized prior to the test. 

Table 7 Pretest Failure Predictions for 1:10-Scale Steel Containment Model 

Organization* Failure Pressure 

(MPa) 

Failure Location Failure Mode 

Test (4.5) 

4.7 

(“Rat-hole”) 

E/H Insert Plate 

Material Failure 

ANL 4.9-5.5 Knuckle Material Failure 

ANPA 10.9 Drywell Head Buckling 

BARC 11.5-12.0 Drywell Head Material Failure or Buckling

GD/EB 4.7 Thinned Liner @ E/H Material Failure 

JAERI >4 Drywell Head Buckling 

NUPEC 4 – 7.3 

7.3 – 11.8 

Thinned Liner @ E/H

Knuckle 

Material Failure 

SNL 4.5 Thinned Liner @ E/H Material Failure 

 *See Acronyms for Organizations 

As with the previous tests, this test demonstrated the large margin in the capacity of the model 

above the design pressure. Also, as with the previous tests, the importance of details at 

discontinuities in defining the limits of the vessel capacity was also demonstrated. The exact 

nature of the local strains and/or stresses which resulted in the tears developing was the subject of 

extensive posttest investigation and analysis. Furthermore, the contact structure, by arresting or 

preventing uncontrolled deformation, had some effect on the response of the vessel. 

While post-yield response and failure predictions were heavily influenced by modeling of the 

contact behavior, predictions of global yielding and post-yield behavior prior to contact were very 

consistent among the participating analysts. It is interesting to note however, that, as in the 

previous tests, the pressures at which global yielding was predicted were higher than observed 

during the test. Figure 36 compares predictions of global hoop strain at the mid-height of the 

vessel with test results. Predictions which based on uniaxial tensile test results of material 

coupons over-predicted the onset of global yielding by 30 to 50%, whereas those analyses that 

used (somewhat arbitrarily) a reduced yield strength (e.g. BARC) matched the test results more 

closely. Furthermore, post-yield predictions and measured response did not converge as in the 

previous tests. While this discrepancy is much more disturbing than in previous tests, there has 

been some speculation that it may have be due to the combined effect of residual stresses and the 

fact that the mixed scale resulted in smaller diameter to thickness ratios than the previous tests or 

than is typical of the prototype. These results, when taken with similar behavior observed in 

previous tests, suggest that some factor or factors are not being considered in the analysis. It also 

suggests that standard material tests using small scale specimens, which are essentially quality 

assurance tests, may not be adequate for defining material constitutive models for larger scale 

structures. This issue will be discussed further in Chapter 3. 
 59 

Hoop Strain @ UCS, El. 2536

Used nominal gap = 18 mm

Used nominal gap = 18 mm.

Used nominal gap = 18 mm

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

Pressure (MPa)

HCP-I-UCS-36 (270°)

RSG-O-UCS-15a

RSG-I-UCS-16c

Analysis @ 270°

Sandia (μ=0.2)

Bhabha/Abaqus (μ=0.75)

NUPEC (μ=0.2)

Electric Boat (μ=0.4)

Used Fy=386 MPa for 

SGV480.

Used Fy=405 MPa for 

SGV480.

Used test data for 

SGV480, 

Fy=420 MPa 

μ is the assumed coefficient of friction between the SCV and Contact Structure 

Figure 36 Comparison of Pretest Predictions of Hoop Strain with Test Results 

3.3.4 Other Steel Model Tests 

Except for the steel containment model tests conducted at SNL, other tests reported in the 

literature to investigate the capacity of steel containments have focused uniaxial or multi-axial 

material tests or component tests. 

NUPEC conducted a series of small-scale cylindrical pressure vessel tests in support of the 1:10-

scale SCV test program. Several tests and investigations were conducted in Germany to 

investigate the behavior of spherical steel PWR containments to overpressure and hydrogen 

detonation [37, 38, 39, 40]. 

3.3.5 Conclusions of Steel Model Tests 

With regard to the program objectives, the conclusions overpressurization tests of the steel 

containment models include the following: 

• The tests provided experimental data for checking the capabilities of analytical methods 

well into the inelastic range of the models. 

• In the absence of any other factors (local thinning or the presence of a shield building to 

restrain deformation) all of the steel models failed catastrophically. 

BARC (μ=0.75)

Hoop 

Strain 
 60 

• The onset of global yielding for all of the models occurred at lower pressures, on the 

order of 10% to 30% lower, than predicted by analyses using material models based on 

uniaxial tensile test results. While this has been attributed to fabrication effects (e.g. coldworking or welding) or strain-rate effects, no conclusive explanation has been provided. 

• Following the onset of yielding, deformation and strains grew rapidly with only a small 

increase in pressure. 

• Failure was initiated at strain concentrations caused by penetrations or stiffeners. 

o The 1:32-scale models without stiffeners or penetrations were able to utilize the 

full membrane capacity of the model. The hoop strain at the cylinder mid-height 

for SC0 was estimated to be on the order of 20% prior to failure. 

o Global hoop strains for the models with stiffeners and penetrations were 

significantly lower at failure than the simple models. With the exception of SC3, 

the global hoop strains in the 1:32-scale models were between 2.5% to 3%. The 

maximum global hoop strain was 3% in the 1:8-scale model and 2% in the 

1:10/1:4-scale steel model. 

• The ratio of ultimate pressure to design pressure was 4.5 for the 1:8-scale model and over 

6 for the 1:10/1:4-scale steel model. Design pressures were not specified for the 1:32-

scale models. 

• The analytical methods used for predicting the global behavior of the model were 

generally adequate with the exceptions noted. The post-yield response was generally less 

accurate. 

• Pretest predictions for the locations and modes of failure were usually incorrect. As noted 

by Clauss [25]: 

“An analyst using finite element methods must be able to anticipate the various locations 

and types of response that can be encountered in shells in order to design a mesh that can 

be used to accurately calculate the containment response. Localized behavior can have 

important consequences on the overall containment behavior, as demonstrated by the 

outcome of the scale model test(s). In particular, any area where there is a potential 

breakdown of the membrane load carrying action of the structure should be carefully 

analyzed.” 

In most cases, the analysts did not ‘anticipate’ the correct type or location of the shell 

discontinuities prior to the test, however, posttest analyses were generally able to 

reproduce the observed failure mode. 

• No general rules regarding material rupture or failure criteria resulted from the tests. 

Posttest analyses suggest that analyses of local discontinuities using highly refined finite 

element meshes can yield strain on the order of (or in excess) of the material strain limits 

from uniaxial tensile tests. These results are heavily dependent on the accuracy of the 

model (including ‘as-built’ effects), the level of refinement and the experience of the 

analyst. 
 61 

3.4 Reinforced Concrete Containment Model Tests 

Table 8 summarizes the results of tests of scaled reinforced concrete containment models and 

local specimens used to investigate liner tearing and leakage. A description of the tests follows. 

Details are provided in the references cited in the table. 

Tests of reinforced concrete containment models or models of portions of containments have been 

conducted elsewhere, although there have been no other large-scale model tests comparable to the 

test conducted at SNL. 

Danisch [41] reported on the plans for conducting pressure tests on a reinforced concrete 

containment mock-up in Walldorf, Germany. These tests were focused on investigating the 

performance of a composite liner for the European Pressurized Reactor (EPR). Very little has 

been reported in the literature on the results of these tests. 

Two, nominally, 1:17-scale models were tested hydrostatically in Japan [42, 43]. A rubber 

bladder was inserted into the models to prevent leakage and the models were tested at room 

temperature and with a gradient of approximately 45oC across the wall. The results were nearly 

identical with the models failing at a little more than twice the design pressure. 

Table 8 Summary of Results of Experiments for Reinforced Concrete Containment 

Models and Liner Tearing and Leakage 

Test Scale Shape R/t Pressure 

Ratio 

(Pd/Pmax) 

Global 

Strain at 

Failure 

Liner 

Material 

Remarks 

SNL RCCV 1:6 PWR: cylindrical 

concrete shell w/ 

steel liner and 

hemispherical 

dome and 

penetrations 

13.5 

(R=3353 

t=248) 

3.2 

⎛ 1.0 ⎞ 

⎝0.32⎠

1.7% SA414 Gr .D, 

SA516 Gr. 60 

Tearing and 

leakage at 

penetration insert 

plate. [44, 45, 46, 

47, 48] 

CTL Spec. 

2.5 

Full prestressed 

concrete wallbase juncture 

- 2.6* 1.6% Steel Several tears at 

wall-skirt 

juncture [51] 

CTL Spec. 

2.4 

Full prestressed 

concrete wall 

with penetration 

- 2.4* 2.2% Steel Large tear at 

penetration 

[51,52] 

CTL Spec. 

3.2 

Full Reinforced wall 

with penetration 

- 2.9* 2.7% Steel Severe liner 

necking next to 

anchorage [51, 

52] 

CTL Spec. 

2.2 

Full prestressed 

concrete wall 

with initial liner 

flaw 

- - - Steel Ductile extension 

of Pre-existing 

flaw [51, 52] 

CTL Spec. 

3.3 

Full Reinforced - - 1.6% Steel Strain 

concentration 

measured near 

penetration 

(4.3% strain) [51, 

52] 

*best estimate based on global strains since models were not pressure vessels. 
 62 

3.4.1 NRC 1:6-scale reinforced concrete model 

A model of a reinforced concrete containment building, designed and constructed by United 

Engineers, was tested by Sandia Laboratories in July 1987. It represented a nominal 1:6-scale 

model of a reinforced concrete PWR containment and was designed according to the ASME code 

for a design pressure of 0.32 MPa (46 psig). The model, shown in cross-section in Figure 37, 

consisted of a reinforced concrete shell with steel liner and included functional models of 

equipment hatches, an airlock and smaller penetrations. Eight layers of primary reinforcing were 

included in the cylinder wall and the steel liner was anchored to the concrete using headed studs, 

as in similar prototype containments. Over 1200 channels of instrumentation were installed in the 

model, the majority consisting of strain gages and displacement transducers. Details of the model 

construction and instrumentation were described by Horschel [44] and are shown in Figure 38. 

Figure 37 Cross-section of the 1:6-Scale Reinforced Concrete Containment Vessel 

Model 
 63 

After a series of low pressure tests, including a Structural Integrity Test and an Integrated Leak 

Rate Test, the model was tested pneumatically to failure in July 1987. A series of independent 

pretest calculations predicted failure by various mechanisms including hatch leakage, liner tearing 

and base shear failures at pressures ranging from 0.90 to 1.31 MPa. [45] 

The model was slowly pressurized using nitrogen gas and after 32 hours the test was concluded 

due to excessive leakage. At 0.96 MPa (140 psig) the leak rate was estimated to be approximately 

10 scfm. The leak rate grew to 50 scfm at 0.98 MPa (143 psig) and to over 5000% mass/day or 

4000 scfm at 1.0 MPa (145 psig). At this point the pressurization system could not compensate 

for the leakage of gas through the liner tear and cracked concrete and the test was terminated. The 

major source of leakage was a 22 inch long tear in the liner plate at a row of studs adjacent to a 

thickened insert plate assembly, shown in Figure 39. After the test, further inspection revealed a 

number of smaller (1/8 to 1⁄2 inch long) liner tears and incipient tears in highly distressed areas as 

shown in Figure 40. All of these tears were adjacent to liner anchor studs near penetrations [46]. 

Figure 38 1:6-Scale Reinforced Concrete Containment Model Construction 
 64 

Figure 39 Major Liner Tear in 1:6-Scale Reinforced Concrete Model 

Locations (Arrows with Solid Lines Had Measurable Leakage; Arrows with 

Dashed Lines Showed ‘Distress,’ but Leakage Could not be Confirmed) 

Figure 40 Developed Elevation of the 1:6 Scale RC Model Cylinder showing Liner Tear 

Locations 
 65 

Horschel [46] summarized the major results of the overpressure test: 

• No new cracks developed during the high pressure test but cracks in the concrete which had 

developed during low pressure testing became much wider, up to 1/8 inch. 

• Overall response was not perfectly axisymmetric. Maximum radial displacement were on the 

order of 1-1/2 to 2 inches (ΔR/R ~ 1 to 1.5%). Free-Field hoop strains measured in the liner 

and reinforcing at the mid-height of the cylinder were on the order of 1.5 to 2%. 

• The peak strains measured in the liner was 8%. 

• One of the equipment hatch sleeves was deformed into an oval shape. The change in 

diameter was on the order of 1.5% in the horizontal direction and minus 1.5% in the vertical 

direction, comparable to the overall hoop strain. 

• A perceptible dishing of the basemat was observed with an average uplift of 3/8-inch at the 

outer edge. 

It should be noted that as a result of tearing of the liner and leakage, the limits on the nonlinear 

structural response and the ultimate structural capacity, i.e. catastrophic rupture, were not 

challenged. While some consideration was given to ‘sealing’ and re-pressurizing the model, this 

was not done and efforts focused on understanding the local liner and penetration behavior. It 

was generally conceded that catastrophic failure could not occur and the structural capacity limits 

were well above the limits on the liner and penetrations. 

Posttest analysis confirmed the presence of large strain concentrations at the locations shown in 

Figure 40 which are very similar to details used in prototypical plant construction. Figure 41 

shows the results of an analysis of the strains in the liner at the location of the major tear. This 

analysis suggests maximum strains were near the material strain limits at the time of failure. 

Pretest predictions of global response compared favorably to the test results, however, as with the 

previous steel containment model tests, the mechanism which defined the limit state of the model 

was not recognized prior to the test by many of the analysts. Some analysts presented a list of 

candidate liner tearing locations and associated leakage pressure range and, in this way, were able 

to reasonably predict the test failure pressures and locations. These predictions, however, still 

relied substantially on judgment in addition to the analytical tools involved [48]. Following the 

post-test examination, it was postulated that the many small tearing locations may have occurred 

within a narrow pressure range (which was predicted by analysis), but that the tear near the 

rectangular insert plate dominated because this tear had a propensity to lengthen along a constant 

elevated strain field. Thus with only slight increase in pressure, this tear and the associated leak 

size grew large while other tears did not. While the conditions that gave rise to tearing of the liner 

were recognized, it was, and still is, the case that the ability to model the behavior of the liner 

after the tear initiated and predict the subsequent leakage rate is beyond our current analytical 

capabilities. 
 66 

Liner

Insert Plate

Stud

Figure 41 Posttest Analysis of 1:6-Scale RC Model Liner at 1.0 MPa (145 psig) 

Following the test and posttest analyses, Von Rieseman [49] summarized the ‘state of knowledge’ 

on the behavior of steel liners. His key observations included: 

• Prior to the test, while “the possibility of local liner failure was recognized as a major 

uncertainty”, little effort was invested into understanding the behavior of the liner. There was 

“a false sense of security” that the anchor studs would fail before the liner tore. Also, while 

the presence of strain concentrations at the penetrations were recognized, the belief was that 

the high ductility of the liner material would be adequate to prevent tearing. 

• The strength of the cylinder wall-basemat intersection was underestimated. Pretest analyses 

over-predicted the deformations in this area and as a result predicted this as the most likely 

location for liner tearing to occur [50]. 

3.4.2 Separate Effects Tests for Reinforced Concrete Model 

In the years following the 1:6 Scale RCCV model test, SNL conducted analytical [53] and 

experimental [54, 55] investigation of the strain concentrations and mechanisms leading up to and 

causing liner tear. The analytical work consisted of local models “driven” by boundary conditions 

taken from global analysis models. Similar studies were undertaken by EPRI [51] (see 3.4.3). 

The experimental work at SNL consisted of uniaxial tests of a series of specimens that simulated 

certain features of the 1:6-scale model liner. These specimens were instrumented with strain 
 67 

gages and photo-elastic coatings. One series of six tests, shown in Figure 42(a) were conducted 

by applying a varying preload to the liner and then applying a separate load to the concrete block 

to shear the stud anchors. These tests showed that at low preloads, the studs failed while at higher 

preloads the liner failed. 

 

 (a) (b) 

Figure 42 Separate Effects Test Liner Specimens 

A second series of tests were conducted in an attempt to reproduce the liner tearing mechanism 

observed in the 1:6-scale R/C containment model. The test specimen, shown in Figure 42(b), 

included the liner and insert plate with the anchor studs, reinforcing and concrete to represent a 

section through the wall. While the liner tore in the same relative location, these tests did not 

replicate the behavior observed in the 1:6-scale model. The elongation required to tear the liner 

was much higher, attributed to the lack of lateral restraint. 

The primary value of these tests was to demonstrate that the liner failure mechanism observed in 

the 1:6-scale R/C model test was not an artifact of the model and to provide insights into the 

sources/mechanisms giving rise to strain concentrations in the liner, including: 

1. thickness change 

2. liner-to-concrete anchor geometry 

3. strain magnification across a concrete crack, either in-plane with the liner, or in shear if the 

crack is a “dislocation” associated with a local “hard spot” in the concrete wall due to a 

reinforced penetration or thickened wall segment. 

Each of these strain concentrations can act independently or can compound each other if they are 

coincident. The thickness change concentration also tends to be exacerbated by presence of a 

weld, which does not yield at the same stress as the base metal and so adds to the strain 

concentration in the base metal. Though this work added to the understanding of causes of liner 

tears, these results have never been implemented into a prediction methodology as part of the 

SNL research. 
 68 

3.4.3 CTL/EPRI Tests 

As part of a 6-year EPRI sponsored concrete containment research program, a variety of 

containment panel tests (models of typical containment wall sections) were performed at full scale 

at Construction Technology Laboratories in Skokie Illinois [51]. These experiments further 

demonstrated that strong liner strain concentrations exist near penetrations and other 

discontinuities. These tests, when combined with the results of the Sandia full model test, provide 

some evidence the existence of liner strain concentrations and a liner tearing, ‘leak before break’ 

failure mode for concrete containments. 

All together, nine specimens were designed, constructed and tested, starting with simple, unlined 

R/C wall panel elements, and then including steel lined R/C test units that included complex 

details liner connection and penetration details found in typical R/C and P/C containments in the 

U.S. Figure 43 shows a schematic depicting the test specimen planning strategy, i.e., to choose 

small portions of containment walls and load these panels with the biaxial conditions they might 

experience in a containment subjected to overpressure. This biaxial loading consisted of direct 

loading applied to individual rebars and applied to liner edges, and also some out-of-plane loading 

for specimens with discontinuities. The loading was planned by using axisymmetric analysis of 

the typical R/C and P/C containments shown in Figure 44. Some details of the more important 

tests are shown in Figures 45 through 47. The overall failure mode and equivalent failure 

pressure information for Specimens 2.2, 2.4, 2.5, 3.2, and 3.3 were summarized in Table 8. These 

specimens all focused on the existence and causes of liner strain concentrations and liner tearing, 

and all tended to support the hypothesis of ‘leak before break’ failure mode for concrete 

containments. 

These tests, combined with the results of the Sandia 1:6-scale model test (global deformation 

results and local liner strain results near penetrations) and Sizewell B 1:10-scale model test 

(global deformation results) (see 3.5.2) were used to form the basis of a liner tearing and leakage 

prediction methodology that was used for the containment portions of a number of Individual 

Plant Examinations in the early 1990s. Though the database of liner tearing geometries and 

measured strains at failure is not exhaustive, the methodology does represent the first attempt at 

developing a systematic approach to containment leakage prediction. The basic approach, which 

is described in more detail in Analysis Methods sections of Chapter 3, introduces global strain as 

a ‘driving strain’ to which are applied strain concentration factors to produce a local strain that 

can then be compared directly to a liner failure criteria. The research also represented one of the 

first attempts to quantify pressurized gas leakage through cracks, and quantify the associated 

growth in leak rate with the growth of tear size in the liner. These early steps toward a leak 

prediction methodology are described in [56]. An illustration of the basic assumptions for leakage 

through liner tears in concrete containments is shown in Figure 48. The phenomena illustrated 

here were studied with the leak rate measurements performed on EPRI/CTL Specimen 2.2. Some 

developmental, but extensive, work quantifying the flow of pressurized gas through cracked 

concrete has been reported in Canada by Rizkalla, et al [57]. 
 69 

Figure 43 Containment Wall Panel Specimen Test Strategy for EPRI/CTL Tests [51] 
 70 

Figure 44 Typical R/C, P/C Containment Geometries used in EPRI Global Analyses 

[51] 

(best available figure) 

Figure 45 Liner Vertical Strains Measured (and Analyzed) in EPRI/CTL Specimen 2.5, 

Wall-Skirt Juncture of a Typical P/C Containment 
 71 

Figure 46 Liner Plate Details for EPRI/CTL Specimen 2.4 
 72 

Figure 47 Liner Plate Details for EPRI/CTL Specimen 2.2, Which Studied Leak Rates 

Through an Advancing Liner Crack Tip 
 73 

Figure 48 Idealization of Flow of Pressurized Gas Through a Liner Tear [56] 
 74 

3.5 Prestressed Concrete Containment Models 

A number of scale model tests of prestressed concrete reactor pressure vessel and containment 

vessel models have been conducted. Table 9 is a list of the major tests and includes a brief 

comparison of the results. References to ongoing or recent tests are also included even though the 

results of these tests may not be available. This section will focus on the 1:4-scale prestressed 

containment vessel model tested by SNL for then US NRC and NUPEC and analyses conducted 

in support of the 1:10-scale model of the Sizewell B prestressed concrete containment tested in 

the UK. A brief description of the other tests concludes this section. 

Table 9 Summary of Results of Experiments for Prestressed Concrete Containment 

Models 

Test Scale Shape R/t Pressure 

Ratio 

Global 

Strain at 

Failure 

Liner Material Remarks 

Pressure Vessel Tests 

Fort St. Vrain 

G.A. Model 

1, USA 

1:4.5 Cylinder 5 3.5,2.5 0.22% Steel [58] Liner tear / 

leakage occurred. 

Wylfa Vessel, 

U.K. 

1:12 Sphere 5 See remark 0.1% Rubber 2.7 pressure ratio 

reached with no 

leakage [58] 

Oldburry 

Vessel, U.K. 

1:8 Cylinder 3 0.4% Steel [58] Liner tear / 

leakage occurred 

" 1:12 Sphere 5 2 - 3 0.4% Rubber 

" 1:8 Cylinder 3.5 2 - 3 - Steel Shear-type failure 

artificially induced 

[58] 

1000 MWe 

HTGR G.A. 

Model 2, 

USA 

1:4 Cylinder 2.4 2 0.06% Steel Liner tear / leakage 

occurred 

Containment Model Tests 

Indian Model 1:12 (CANDU) 20 1.9 - 1mm steel liner Liner tearing and 

leakage esp. around 

penetration [59] 

Polish Model 1:10 (CANDU) 20 1.9 - 1mm steel liner Liner tearing and 

leakage esp. around 

penetration [60] 

Canadian 

Model 

1:14 Gentilly-2: 4-

buttress w/ ring 

buttress 

12.6 8.6 - none 

(hydrostatic) 

Vertical and hoop 

tendon rupture. [61, 

62, 63, 64] 

Sizewell-B 

(CEGB) 

1:10 Sizewell-B 8.6 2.4 - Rubber bladder 

(hydrostatic) 

Basemat bending 

failure [65-70] 

EPR Model 

(Civaux Test) 

? Cylinder, inner 

containment 

6.7 0.65 * - unlined and 

partial composite 

liner 

[71] 

0.39* -- SGV 410 LST: Liner 

tear/leakage 

NUPEC/NRC 

PCCV 

(SNL) 

1:4 Large, dry PWR: 2-

buttress cylinder w/ 

hemispherical 

dome 

16.5 

3.6 1.4% SFMT: Tendon 

rupture and 

through-wall 

rupture [72-76] 

*Design pressure (MPa). 

3.5.1 NUPEC/NRC Prestressed Concrete Containment Vessel (PCCV) Model Test 

As part of a Cooperative Containment Research Program that was co-sponsored and jointly 

funded by the Nuclear Power Engineering Corporation (NUPEC) of Japan and the U.S. Nuclear 

Regulatory Commission (NRC), Office of Nuclear Regulatory Research, Sandia National 
 75 

Laboratories (SNL) conducted of a 1:4-scale model of a large, dry PWR prestressed concrete 

containment vessel. The PCCV model was a 1:4-scale model of the prestressed concrete 

containment vessel (PCCV) of an actual nuclear power plant in Japan, Ohi-3 (Figure 49). Ohi-3 

is an 1127 MWe Pressurized Water Reactor (PWR) unit, one of four units comprising the Ohi 

Nuclear Power station located in Fukui Prefecture, owned and operated by Kansai Electric Power 

Company. 

Figure 49 Ohi Nuclear Power Station, Ohi-cho, Fukui, Japan 

The design pressure, Pd, for the model and the prototype is 0.39 MPa. The features and scale of 

the PCCV model were chosen so that the response of the model would mimic the global behavior 

of the prototype and local details, particularly those around penetrations, would be represented. 

The model includes a steel liner anchored to the concrete shell by semi-continuous structural 

shapes (T’s). Conventional reinforcing ratios match the prototype and prestressing tendons match 

1-to-1 with the prototype. The un-bonded prestressing system consists of three, seven-wire 

strands per hairpin tendon, anchored in the basemat and identical, 360 ̊ hoop tendons anchored in 

opposing vertical buttresses. The overall geometry and dimensions of the PCCV model are 

shown in Figure 50. Figure 51 shows the sequence of the model construction from erection of the 

liner, to installation of the prestressing tendon ducts to placement of the concrete wall and dome. 

Figure 52 shows the completed model. Details of the design, including the design drawings, and 

construction are reported in the PCCV test report [72] 

Model construction commenced at the Containment Technology Test Facility at Sandia National 

Laboratories on January 3, 1997. Concurrent with the construction of the model, Sandia installed 

nearly 1500 transducers to monitor the strain, displacement, forces, temperatures and pressures in 

the model. These transducers were monitored by a data acquisition system (DAS) which provided 

for near-continuous scanning of all transducers while providing real time display of any sensor 

channel. In addition to this suite of instrumentation, an independent acoustic monitoring system 

and internal and external video and still cameras were used to record the response of the model 

during pressure testing. 
 76 

Construction and instrumentation of the PCCV model was completed on June 25, 2000. Prior to 

the completion of construction, tensioning of the model prestressing tendons commenced March 

8, 2000 after the majority of the model transducers had been installed and certified. Initial model 

response was recorded on March 3 and monitored continuously through the prestressing 

operations and pressure testing. 

Prestressing levels for the model tendons were selected so that the net anchor forces (considering 

all losses due to anchor seating, elastic deformation, creep, shrinkage and relaxation) at the time 

of the Limit State Test matched those expected in the prototype after 40 years of service. One 

further adjustment was made by increasing the vertical tendon stress level to account for the 

additional gravity load in the prototype, which is lost in the geometric scaling. Eight instrumented 

tendons and load cells at the ends of 1/6th of the model tendons were monitored continuously 

during prestressing. Unfortunately over half of the strain gages installed on the tendons were 

damaged during prestressing operations, nevertheless, enough survived to provide useful data on 

the tendon response during prestressing and pressurization tests. Since all model sensors were 

scanned during and after prestressing, the overall response of the model to prestressing forces as 

well as ambient thermal response and time dependent effects was also recorded. 

32.5 cm

27.5 cm

22.5 cm (8 7/8”)

1.6 mm liner

45° 15°

(12.8")

537 cm (17'-7 5/8")

1075 cm (35'-3 1/4")

(1140 cm) (37'-4 7/8")

(10 13/

16")

565 cm (18'-6 7/16")

1640 cm (53'-9 5/8

1075 cm(35'-3 

")

1/4")

350 cm (11'-4 3/4")

720 cm (23'-7 7/16")

18 hoop tendons 90 hoop tendons

90 meridional hairpin tendons 

(45 E/W, 45 N/S)

0°

62°

90°

180°

270°

324°

CL Equipment 

Hatch

CL Personnel 

Airlock

Buttress

537.5cm

CL Main Steam 

& Feedwater 

Penetrations

Buttress

Figure 50 PCCV Model Elevation and Cross-Section 
 77 

Figure 51 PCCV Model Construction 

Figure 52 Completed PCCV Model 
 78 

3.5.1.1 Pressure Tests 

The final test sequence for the PCCV model is shown in Figure 53. Pressure testing of the model 

consisted of a series of static overpressurization tests of increasing magnitude, beginning with the 

System Functionality Test (SFT) to 0.5Pd (0.2 MPa) on July 18-20, 2000. This test was 

conducted to confirm the operation of all test and data acquisition systems, verify that the model 

was leak tight and calibrate the leak detection/measurement system. It also provided some 

preliminary response data on the model. The next tests were a combined Structural Integrity and 

Integrated Leak Rate Test (SIT/ILRT). The PCCV model was pressurized to 1.125Pd (0.44 MPa) 

on September 12, 2000 and after holding pressure for approximately 1 hour, the model was 

depressurized to 0.9 Pd (0.36 MPa)and held at this pressure for 24 hours. During this period a 

leak rate of less than 0.1% mass/day was calculated, essentially demonstrating that the model was 

leak-tight. While holding at the ILRT Pressure, a limited amount of crack mapping was 

performed. Cracks widths were not measured. 

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Time (hours)

Pressure (Pd)

SFT 0.5 Pd

SIT 1.125 Pd ILRT 0.9 Pd

LIMIT STATE TEST, 5.3Pd Max

Figure 53 PCCV Pressurization Plan Sequence (not to scale) 

Limit State Test 

The Limit State Test (LST) was designed to fulfill the primary objectives of the PCCV test 

program, i.e. to investigate the response of representative models of nuclear containment 

structures to pressure loading beyond the design basis accident and to compare analytical 

predictions to measured behavior. The LST was conducted after the SIT and ILRT were 

completed and the data from these tests evaluated. The PCCV model was depressurized between 

the SIT/ILRT and the LST. The LST began at 10:00 AM, Tuesday, September, 26, 2000 and 

continued, without depressurization, until the test was terminated just before 5:00 PM on 

Wednesday, September 27. The LST pressure and temperature time histories are shown in Figure 

54. The model was pressurized in increments of approximately 0.2Pd to 1.5 Pd (0.08 to 0.6 MPa) 

when a leak check was conducted yielding a leak rate of 0.48% mass/day. Pressurization of the 
 79 

model continued, in increments of approximately 0.1Pd, to 2.0Pd (0.78 MPa) when a second leak 

check resulted in a calculated leak rate of 0.003%, i.e. essentially zero. Pressurization of the 

model resumed in increments of 0.1Pd to 2.5Pd (0.98 MPa). At 2.4Pd (0.94 MPa) the acoustic 

system operator reported hearing a change in the acoustic output which might indicate that 

“something had happened”. Plots of the output of the four internal acoustic sensors surrounding 

the E/H at 2.3, 2.4 and 2.5 Pd are shown in Figure 55. The model was isolated for a third leak 

check and after approximately 1-1/2 hours, a fairly stable leak rate of 1.63% mass per day was 

calculated, indicating that the model was leaking, most likely from a tear in the liner in the 

vicinity of the equipment hatch. The average hoop strain at 2.5Pd, coinciding with the onset of 

liner tearing and leakage was 0.18%. 

1.30

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

9/26/2000 8:00

9/26/2000 12:009/26/2000 16:00

9/26/2000 20:00

9/27/2000 0:009/27/2000 4:009/27/2000 8:00

9/27/2000 12:009/27/2000 16:00

9/27/2000 20:00

9/28/2000 0:009/28/2000 4:009/28/2000 8:00

9/28/2000 12:009/28/2000 16:00

9/28/2000 20:00

9/29/2000 0:009/29/2000 4:009/29/2000 8:00

Time (day/hour)

Gage Pressure (MPa)

12.00

14.00

16.00

18.00

20.00

22.00

24.00

26.00

28.00

30.00

32.00

Temperature (c)

Pressure Average Temperature

Figure 54 Limit State Test Pressure and Average Temperature 
 80 

Figure 55 Internal Acoustic Sensor Signals @ the Equipment Hatch 

After concluding that the model had functionally failed between 2.4 and 2.5 Pd, the next goal was 

to continue to pressurize the model as high as possible to collect data on the inelastic response of 

the structure and to observe, if possible, a structural failure mode. Pressurization continued in 

increments of 0.05 Pd. The pressure was increased to slightly over 3.3 Pd before the leak rate 

exceeded the capacity of the pressurization system and the test was terminated. Estimated leak 

rates during the final pressurization and depressurization phases are shown in Figures 56 and 57. 

0.0%

50.0%

100.0%

150.0%

200.0%

250.0%

300.0%

350.0%

10:00

11:00

12:0013:0014:0015:0016:00

Time (hour)

Leak Rate (% mass/day)

Total Time Point-to-Point

2.5 Pd

2.55 Pd 

2.6 2.65

2.7 2.75 2.8

2.85 2.90

2.95

3.0

3.1 Pd

Figure 56 LST - Estimated Leak Rates (2.5-3.1 Pd) 

@ 2.3 Pd

@ 2.4 Pd

@ 2.5 Pd
 81 

56.7%

391.1%

585.4%

27.3%

851.83%

0.0%

100.0%

200.0%

300.0%

400.0%

500.0%

600.0%

700.0%

800.0%

900.0%

9/27/2000 12:009/27/2000 16:00

9/27/2000 20:00

9/28/2000 0:009/28/2000 4:009/28/2000 8:00

9/28/2000 12:009/28/2000 16:00

9/28/2000 20:00

9/29/2000 0:009/29/2000 4:009/29/2000 8:00

Time (day/hour)

Leak Rate (% mass/day)

Total Time Point-Point

Leak Rate @ 170 psig

Terminal Leak Rate @ 180 psig

Figure 57 LST Estimated Terminal Leak Rates 

Figure 58 shows the displacement profiles (exaggerated by a factor of 100) at Azimuths 135o, 

representing the axisymmetric response, and 324o, at the centerline of the equipment hatch. The 

profiles are based on interior measurements of the model surface prior to prestressing (3/3/00, 

11:47am) and at multiples of the design pressure 0Pd, 1.0Pd (0.389 MPa), 2.0Pd (0.776 MPa), 

2.5Pd (0.978 MPa), 3.0Pd (1.162 MPa) and 3.3Pd (1.295 MPa). The profile at 324o illustrates the 

buckling of the liner which occurred at Elev. 9200 due to prestressing. This bulge in the liner 

disappeared when the model was initially pressurized and did not affect the capacity of the liner. 

At maximum pressure local liner strains approached 6.5% and global hoop strains (computed 

from the radial displacement) at the mid-height of the cylinder averaged 0.4%. 

While large local liner strains were measured and the liner was torn in several locations (see 

Figure 59), the remainder of the structure appeared to have suffered very little damage with the 

exception of more extensive concrete cracking at some locations. Figures 60 and 61 show two of 

the large tears near the equipment hatch, along with photographs of the liner anchor details at 

these locations taking during construction of the model. There was no indication of tendon or 

rebar failure and the data showed that no tendon strains exceed the elastic limit while only a few 

dozen rebar strain gages showed strains in excess of 1%. 
 82 

0.0

2000.0

4000.0

6000.0

8000.0

10000.0

12000.0

14000.0

16000.0

18000.0

0.00

2000.004000.006000.008000.00

10000.00

Radius (mm)

Elevarion (mm)

3/3/00

11:47

0.000

0.389

0.776

0.978

1.162

1.295

Pressure

(MPa)

0.0

2000.0

4000.0

6000.0

8000.0

10000.0

12000.0

14000.0

16000.0

18000.0

0.0

2000.04000.06000.08000.0

10000.0

Radius (mm)

Elevarion (mm)

3/3/00

11:47

0.000

0.389

0.776

0.978

1.162

1.295

Pressure

(MPa)

 (135o) (324o) 

Figure 58 LST - Deformation @ Az. 135o and 324o (Z and L) 

0° 62° 90° 180° 270°

A/L M/S, F/W E/H

1

2

3

4

5

6

7

8

9

10

11

12

13

A DE B C F G H I J KL A

16125

15716

14551

12807

10750

9230

7730

6200

4680

2630

1430

250

0

Tendon Gallery

-1175

-2000

-3500

Z

Buttress Free-Field Buttress

30° 60° 120° 135° 150° 210° 240° 300° 324 ° 330° 360°

Elev ation 

(mm)

Azimuth

#14

#8

#1

#9

#2

#16

#10

#3

#4

#5 #6

#11

#15

#13

#12

#7

#17 #18

Figure 59 Post-LST Liner Tears 

#12 (Fig. 61)

#7 (Fig. 60)

x100 x100
 83 

Image reversed for comparison

Figure 60 Tear #7 at Equipment Hatch 

Image reversed for comparison

Figure 61 Tear #12 at Equipment Hatch 

Structural Failure Mode Test 

Almost immediately after the completion of the LST, it was recognized that while the PCCV 

model had demonstrated its capacity to resist pressures well above the design pressure and 

confirmed, arguably, liner tearing and leaking as the functional failure mode, the test objectives 

were not fully met with respect to observing large inelastic deformations, for comparison with 

analyses, and witnessing the structural failure mode of the PCCV model. NUPEC and NRC 

approved a concept proposed by SNL to seal the interior surface of the liner with an elastomeric 

membrane, fill the model with water to 1.5m (5 ft.) from the dome apex, approximately 97% of 

Weld 

‘Rat-hole’ 
 84 

the interior, and re-pressurize the remaining gas pocket with nitrogen until the model failed or 

pressure could not be maintained. 

The Structural Failure Mode Test (SFMT) began shortly after 10:00 AM on Wednesday, 

November 14, 2001. The model was continuously pressurized at a rate of approximately 0.035 

MPa/min (5 psi/min). All active sensors (approximately 500) were continuously scanned at 

intervals of approximately 30 seconds and video cameras were continuously recording the 

response of the model. As the pressure was increased, evidence of leakage was visible by 

increasing wetting of the concrete surface. At 10:38 AM, the effective pressure in the model 

equaled the peak pressure achieved during the LST, 3.3 Pd. At approximately 10:39 AM, the 

acoustic system recorded a very high noise level event which was interpreted as the breaking of a 

tendon wire. At this point in the test, events occurred very quickly. Shortly after detecting the 

wire break, a small spray of water was observed at approximately 0o azimuth and additional 

tendon wire breaks were detected by the acoustic system with increasing frequency. The rate of 

pressurization was decreasing and the nitrogen flow rate was increased to maintain the 

pressurization rate. Pressurization of the model continued until a second spray of water was 

observed and then, suddenly, at 10:46:12, at an effective pressure of 3.63 Pd (1.42 MPa or 206.4 

psig) the PCCV model ruptured violently at ~6o azimuth near the mid-height of the cylinder. Four 

external video cameras recorded the rupture of the model and the moment of rupture is captured 

in Figure 62. The condition of the model after the SFMT, viewed from 0o, is shown in Figure 63. 

The radial displacement of the model at Az. 135o, Elevation 6200 during the LST and SFMT is 

illustrated in Figure 64. (The SFMT response was ‘offset’ in this figure by adding the residual 

displacement at the end of the LST to facilitate comparison.) This figure demonstrates that the 

hoop stiffness during the SFMT is essentially identical to the post-cracking stiffness during and 

after the LST. It also shows that the SFMT displacement is nearly identical to the LST 

displacement at the maximum LST pressure, suggesting that, if the LST could have been 

continued, the response would have been almost the same as that measured during the SFMT. It 

thereby confirms the assumption that, again with the exception of the liner and cracking of the 

concrete, the model was essentially undamaged by the LST. 
 85 

 (a) 0o Azimuth (b) 90o Azimuth 

 (a) 180o Azimuth (b) 270o Azimuth 

Figure 62 SFMT: Rupture of the PCCV Model 

Figure 63 PCCV Model after the Structural Failure Mode Test 
 86 

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

0.000.390.79

1.18

1.57

Pressure (MPa)

Displacement (mm)

LST

SFMT

Figure 64 SFMT – Radial Displacement at Az. 135o, El. 6200 

The acoustic monitoring system used during the LST was also employed for the SFMT minus the 

interior sensors which were removed to allow the elastomeric liner to be installed. Since the 

SFMT was not focused on detecting liner tearing/leaks, this was not a significant compromise. 

The focus of the acoustic system during the SFMT was to detect tendon wire breaks and any other 

events which might indicate structural damage. Fifty seven wire break or probable wire break 

events were identified between 10:39:47 and rupture of the model at 10:46:12. Figure 65 plots the 

time history of all the wire break events along with the effective pressure time history and radial 

displacement time history. It is readily apparent that the frequency and magnitude of the wire 

break events increases just prior to rupture. 

The displacement profiles at Azimuths 135o and 324o during the SFMT are shown in Figures 66 

and 67. Since the displacement transducers used during the LST were removed and replaced by 

water-proof transducers for the SFMT, the initial profile was taken as that prior to prestressing. In 

Figures 66(a) and 67(a), the displacement profiles are plotted for the hydrostatic pressure (0.18 

MPa) and multiples of the design pressure, approximately 1.0Pd (0.389 MPa), 2.0Pd (0.776 MPa), 

2.5Pd (0.978 MPa), 3.0Pd (1.162 MPa), 3.5Pd (1.295 MPa) and the peak pressure of 3.63Pd (1.42 

MPa). The maximum average hoop strain at the peak pressure of 3.63 Pd was 1.02%. The 

profiles are expanded between 3.0Pd and 3.63Pd in Figures 66(b) and 67(b). These figures also 

show that after reaching the peak pressure, the model continued to expand significantly, even 

though the pressure decreased to 3.57Pd (1.40 MPa) yielding a maximum hoop strain of 1.65% 

just prior to rupture. 
 87 

0.0

50.0

100.0

150.0

200.0

250.0

11/14/01 10:39:0011/14/01 10:40:00

11/14/01 10:41:00

11/14/01 10:42:0011/14/01 10:43:0011/14/01 10:44:0011/14/01 10:45:0011/14/01 10:46:0011/14/01 10:47:00

Time

Pressure (psig)

0

20

40

60

80

100

120

140

160

180

200

220

240

Displacement (mm) or Acoustic Energy (dB)

Effective Pressure (DAS) Effective Pressure (Supply) Wire Break Events Radial Displacement @L6

Figure 65 SFMT Wire Break Events vs. Pressure vs. Displacement 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0.00

2000.004000.006000.008000.00

10000.0012000.00

Radius (mm)

Elevation (mm)

11/06/01

8:50:13

H2O

1.00

1.99

2.54

3.02

3.50

3.63

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0.00

2000.004000.006000.008000.00

10000.0012000.0014000.00

Radius (mm)

Elevation (mm)

11/06/01

8:50:13

0.18

3.02

3.50

3.56

3.61

3.63

3.57

 (a) 0Pd to3.63Pd (b) 3.0Pd to3.63Pd

Figure 66 SFMT - Deformation @ Az. 135o (Z) 

x100 x100
 88 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0

2000400060008000

1000012000

Radius (mm)

Elevation (mm)

11/06/01

8:50:13

H2O

1.00

1.99

2.54

3.02

3.50

3.63

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0

2000400060008000

10000120001400016000

Radius (mm)

Elevation (mm)

11/06/01

8:50:13

H2O

3.02

3.50

3.56

3.61

3.63

3.57

 (a) 0Pd to3.63Pd (b) 3.0Pd to3.63Pd

Figure 67 SFMT - Deformation @ Az. 324o (L) 

3.5.1.2 Analysis 

Pretest Analysis 

The principal objectives of the pretest analyses were to (1) validate analytical methods for 

predicting global structural response of a prestressed concrete containment, (2) gain insight into 

potential structural failure modes of a prestressed concrete containment, and (3) support planning 

of test procedures and instrumentation. The pretest prediction analyses were completed many 

months prior to the LST in order to document and publish the predictions prior to the test [73]. 

Because the pretest analysis predictions were needed well in advance, they did not include certain 

as-built features, actual measured prestressing and associated losses, nor creep and temperature 

effects. Prestress values, losses due to friction, anchor set, and concrete creep were approximated 

from the assumptions used in the PCCV model design. 

A list of possible failure modes and failure locations was developed in the preliminary analysis 

phase prior to conducting the analyses. Some of the potential failure modes were specifically 

addressed by the global analysis while others were addressed by local models. Preliminary 

analyses suggested that liner failure at the mid-height of the cylinder near a penetration and a 

shear/bending failure at the base of the cylinder wall had significant probability of occurring. The 

basic ‘workhorse’ of the Pretest analysis was an axisymmetric model (Figure 68). The model 

represents the 135o azimuth which was assumed to be typical of a "free-field" azimuth, away from 

buttresses or penetrations. Local models were developed for: the Equipment Hatch region (Figure 

69), the Personnel Airlock region, and the Main Steam Penetration region. A detailed 3D model 

of the entire cylinder mid-height region (3DCM) was also developed to investigate tendon 

behavior in the cylinder and 3D effects that drive the local strain concentrations near the 

penetrations (Figure 70). The ABAQUS [77] general purpose finite element program along with 

the ANACAP-U [78] concrete and steel constitutive modeling program were used for all analysis. 

x100 x100
 89 

Figure 68 Axisymmetric Model of 1:4-scale PCCV 

Figure 69 Local Model of Equipment Hatch 
 90 

Figure 70 Three-Dimensional Cylinder Mid-Height Model (#DCM) 

The results of the Pretest analyses include the following 

• The model deforms radially out more at 4.68 m (cylinder mid-height) than at 8.96 m, 

which is the same trend as in the axisymmetric model. 

• The largest hoop expansion occurs at the Equipment Hatch, and the "free-field 

displacement" (displacement at 0o and 180o) are slightly less and are approximately equal 

to each other. 

• At pressures greater than 3.0Pd the radial displacements at 135o (and elsewhere) become 

somewhat larger in the 3DCM model than in the axisymmetric analysis, while below 

3.0Pd, the axisymmetric analysis agrees well with the 135o azimuth of the 3DCM model. 

• There is significant local circumferential bending adjacent to each buttress. 

• There are significant strain concentrations at terminations or step-downs in rebar patterns. 

• There are significant strain concentrations near hatches and near the edges of wall 

embossments. 

• Using a strain-based failure criteria which considers the triaxiality of stress and a 

reduction in ductility in the vicinity of a weld, the liner failure strain was 0.16. The 

failure pressure at which a local analysis computed effective plastic strain that reached the 

failure strain, was 3.2Pd or 1.3MPa. The location for this liner-tearing failure was near 

the Equipment Hatch (E/H), adjacent to a vertical liner anchor that terminated near the 

liner insert plate transition. 
 91 

• The 3DCM model with its detailed tendon representation, predicted rupture of hoop 

tendons closest to the E/H at a model pressure of about 3.5Pd. However, this mode was 

predicted to be precluded by the liner tearing and leakage failure mode. 

Pretest Round-Robin Analysis 

Prior to pressure testing the scale models, a number of regulatory and research organizations were 

invited to participate in a pretest Round Robin analysis to perform predictive modeling of the 

response of scale models to overpressurization. Seventeen organizations responded and agreed to 

participate in the pretest PCCV Round Robin analysis activities: 

AECL Atomic Energy of Canada Limited Canada 

ANL Argonne National Laboratory U.S. 

CEA Commissariat a l’Énergie Atomique France 

EDF Électricité de France France 

Glasgow University of Glasgow U.K. 

HSE Health and Safety Executive U.K. 

IBRAE Nuclear Safety Institute Russia 

INER Institute of Nuclear Energy Research Republic of China 

IPSN Institut de Protection et de Sûreté Nucléaire France 

JAERI Japan Atomic Energy Research Institute Japan 

JAPC The Japan Atomic Power Company Japan 

KINS Korea Institute of Nuclear Safety Korea 

KOPEC Korea Power Engineering Company Korea 

NUPEC Nuclear Power Engineering Corporation Japan 

PRIN Principia Ingenieros Consultores, S.A. Spain 

RINSC Russia International Nuclear Safety Center Russia 

SNL Sandia National Laboratories/ANATECH U.S. 

The purpose of the Round Robin effort was to provide a forum for researchers in this area, and the 

industry in general, to apply current (state-of-the-art) analysis methodologies to predicting the 

response and capacity of the PCCV model. Each participant was supplied with the same basic 

information, including the design drawings of the PCCV model and the material properties of the 

structural components. Each participant used his own chosen analytical methods and performed 

independent analyses. Participants were asked to submit response histories at 55 Standard Output 

Locations along with predicting the most likely failure mode and pressure. Luk [74] compiled the 

results along with the individual participant reports and these were discussed in a pretest 

workshop in October, 1999. 

Figure 71 shows the predicted radial displacement at the mid-height of the cylinder wall where the 

maximum response is expected. Table 10 summarizes these estimates and predictions of the 

pressure for various milestones (onset of cracking, yielding, etc.) leading up to failure. 

Comparing the results of the various analyses, the following observations can be made: 

• Predictions of elastic response were, for the most part, very consistent up to the onset of 

global yielding (hoop) which appears to occur around 2.5 Pd or about 1.0 MPa. Predictions of 

response diverge significantly beyond this point with responses varying by a factor of three to 

five or more at a given pressure. 

• There are considerable differences in the predictions of some local strains, such as those close 

to a penetration, after global yielding has occurred. 
 92 

• Nevertheless, the predicted capacity of the model is fairly consistently bounded at 4 to 5 Pd. 

For failure predictions based on material failure of the steel components (liner, rebar or 

tendons), the average predicted pressure at failure is 3.6 Pd or 1.46 MPa. 

• Approximately half the participants predicted failure based on structural failure, i.e., rupture 

of rebar or tendons, while approximately half the participants predicted functional failure 

from excessive leakage through a tear in the liner and/or cracks in the concrete. No one 

predicted a shear failure or leakage through the penetrations. 

-20

0

20

40

60

80

100

120

140

160

180

200

0.00 0.39 0.79 1.18 1.57 1.97

Pressure, MPa (divisions are multiples of Pd)

Displacement, mm

AECL ANL CEA EDF

Glasgow HSE IBRAE-2d IBRAE-3d

INER JAERI JAPC KINS

KOPEC NUPEC PRINCIPIA RINSC

SNL/ANATECH

Figure 71 Radial Displacement at Cylinder Wall Mid-height (SOL 6) 
 93 

Table 10 Summary of PCCV RR Pretest Results 

Participant* Pressure (MPa) Failure Mode 

ANL 1.51-1.62 local liner tear/hoop tendon failure @ El. 6.4 m 

AECL 0.94-1.24 complete cracking/axisymmetric yield 

CEA 1.60-1.70 numerically unstable 

EDF 1.95 

INER 0.81 

JAERI — buckling @ dome or local fracture by bending in cylinder

JAPC 1.45-1.55 hoop tendon/rebar/liner rupture @ El. 7 m 

KINS 1.25-1.44 tendon rupture 

KOPEC 1.30-1.51 tendon rupture (@3.55% strain) 

HSE/NNC 1.98 liner tear w/ extensive concrete cracking @ buttress 

NUPEC 1.49-1.57 tendon rupture 

IBRAE 1.26 tendon rupture 

Principia 1.30 tendon yielding 

RINSC 1.50 hoop failure of vessel 

ANATECH/SNL 1.25 liner tearing (16%) @ Equipment Hatch 

 1.40 tendon rupture 

Limit State Test 0.98 1.5% mass/day leak through liner tear @ E/H 

 1.30 limit of pressurization capacity 

Structural Failure Test 1.42 hoop tendon rupture 

Posttest Analysis 

The post-test analysis represents the third phase of a comprehensive PCCV analysis effort. The 

principal objectives of the post-test analyses were: (1) to provide insights to improve the 

analytical methods for predicting the structural response and failure modes of a prestressed 

concrete containment, and (2) to evaluate by analysis any phenomena or failure mode observed 

during the test that had not been explicitly predicted by analysis. Comparisons between measured 

behavior and predicted behavior of the liner, concrete, rebar, and tendons, a variety of failure 

modes and locations were investigated. Pretest and post-LST analysis results were also compared 

to the SFMT data and additional analyses, to provide some insight into the mechanisms leading to 

the structural failure. 

Extensive additional studies were also performed for the posttest 3DCM analysis. A modeling 

assumption, found to be at significant variance with observed test behavior, was the representation 

of friction in the tendon modeling. 

Posttest analyses were also performed for the penetration sub-models. Liner strains measured in 

the vicinity of the E/H penetration collar were much lower than predicted by pretest analysis. 

Since the predicted high strain locations were fundamental to the failure predictions, significant 

effort was spent reanalyzing the E/H model after the test. Posttest analysis showed that by 

preventing relative slip between liner and concrete, the overall behavior of the system (concrete 
 94 

strains, tendon strains, liner strains away from the hatch) remained the same, but the elevated 

strains close to the collar (the thicker insert plate surrounding the penetration sleeve) were 

eliminated. The results of a detailed liner ‘rat-hole’ (see Figure 61) analysis show that the 

elevated strain associated with this detail, and similar details, is enough to exceed the liner tearing 

strain criteria. Considering both the effects of a discrete crack and elevated local strains at the rathole, a liner tear could have been predicted to occur as early as 2.8 Pd. 

Posttest analysis of the SFMT showed that good simulation of the PCCV global behavior through 

and including tendon rupture is possible with a 3D shell model as shown in Figure 72. The main 

limitations of the shell model were a lack of local liner strain concentration prediction and a lack 

of accuracy in the predictions of local wall-base-juncture behavior. However, accuracy in global 

behavior prediction did not seem to be lost when a bonded tendon assumption was used. The 

SFMT model provided additional insight as to how the structural failure likely developed. The 

additional hoop reinforcing surrounding the Equipment Hatch penetration (an increase of 

approximately 50% over the reinforcing in the free-field) is terminated near the 6o azimuth of the 

cylinder wall. At 3.49 Pd (1.36 MPa), the wall and tendon hoop strains at Azimuth 0o to 6o 

(Figure 72) are approximately 4%, higher than all other azimuths. Assuming a maximum tendon 

strain of 4%, the first hoop tendon rupture occurs at this pressure. The analysis subsequently 

shows neighboring tendons rupturing and deformations spreading quickly along this azimuth. By 

3.65 Pd (1.42 MPa), the analysis shows rupture to have spread over a vertical distance of 

approximately 6 m. This is consistent with the behavior observed during the test. 

Figure 72 Posttest Analysis of SFMT at Rupture (~1.38MPa) 

The PCCV test showed that the response quantity driving the limit state of the vessel is radial 

expansion of the cylinder. This response must be predicted correctly in order to reliably predict 

vessel capacity and, at least approximately, the local response mechanisms (local liner strains, 

penetration ovalization, etc.) that are driven by the cylinder expansion. This, and other steel-lined 

concrete vessel tests, show that many competing strain concentrations occur around the midheight of the cylinder. Although it is difficult to predict which local liner detail will tear first, and 

although some particular response quantities, like basemat uplift, were not predicted exactly by 

the pretest analysis of the PCCV model, the average radial expansion or hoop strain of the 

4% 

Hoop 

Strain 
 95 

cylinder was predicted very accurately by the axisymmetric analysis. The axisymmetric analysis 

also predicted the cylinder wall-base flexure and shear response, another critical response mode, 

accurately. Even though the hoop stiffness/strength of most containments is not uniform along 

the circumference, these results suggest that a minimum requirement for containment 

overpressure evaluation should certainly be a robust axisymmetric analysis. A ‘robust’ 

analysis consists of an accurate representation of the structural elements and material properties in 

a numerically-stable nonlinear finite element solution. Analytical robustness is quality of a 

solution which exhibits a degree of insensitivity to numerical solution strategy and control 

parameters, i.e. the solution is primarily dependent on the structure def 

The lessons learned which may be most instructive are those related to tendon friction behavior. 

As a result of this project, the best calculation methods recommended for tendon friction 

modeling are, in descending order of preference, 1) an advanced contact friction surface between 

the tendons and the concrete, 2) pre-set friction ties applied in one direction during prestressing 

and then added in the other direction during pressurization and, 3) if neither of these methods are 

practical within the scope of the calculation, it is best to start with an “average” stress level (using 

a friction loss design formula), but assume uniform stress distribution in the tendons throughout 

pressurization, i.e., an unbonded tendon assumption, and finally 4) same as 3, but using a bonded 

tendon assumption. It should be recognized for method 4, however, that this can lead to a 

premature prediction of tendon rupture, because the tendon strain increments during 

pressurization will match the hoop strain increments of the vessel wall one-to-one, and this was 

not observed to be the case during the PCCV LST. 

The relevance of this work to full size U.S. Containments is highly significant. All of the analysis 

methods tried, calibrated, and validated are applicable to full-scale structures. The posttest work 

also provides a reasonably simple liner-only mesh approach for predicting local strains near weld 

seams, and the test itself underscores the need for continuous back-up bars on all liner seam welds 

as required in the ASME code. 

OECD/NEA/CSNI International Standard Problem #48 on Containment Capacity 

While no formal posttest Round Robin analysis was conducted as part of the NUPEC/NRC 

Cooperative Containment Program, an informal meeting of the participants was held at SNL 

following the LST. This forum included a comprehensive discussion of the results of the LST and 

a critical review of the pretest analyses. While the results of this meeting were never formally 

documented, many of the participants presented the results of their posttest analyses in a variety 

of technical forums including the SMiRT and ICONE conferences. These discussions also 

contributed to the technical impetus for conducting the SFMT due to a general consensus that the 

data from the LST was inadequate to benchmark analyses for large inelastic deformations. 

One question which remained following the PCCV test was how temperature loading might have 

affected the results of the test. In an attempt to answer, or at the least shed some light on, this 

question, a proposal was made to the Committee on the Safety of Nuclear Installations (CSNI) of 

the Nuclear Energy Agency (NEA), Organization for Economic Cooperation and Development 

(OECD), to sponsor an international standard problem (ISP) to investigate the role of temperature 

on Containment Capacity. The proposal was accepted and at the planning meeting for held in 

Stockholm in November, 2002. Two questions were posed which summarize the objectives of the 

ISP: 

• With addition of temperature, would the onset of leakage occur later in the pressure 

history and, possibly, closer to the burst pressure? 
 96 

• How would including the effect(s) of accident temperatures change the prediction of 

failure location and failure mode? 

Eleven organizations (or teams), including several participants in the Pretest Round Robin 

analysis, participated in the ISP: 

BE/HSE/NNC British Energy 

Nuclear Installations Inspectorate/Health & Safety Executive 

NNC Ltd. 

UK 

EDF Électricité de France France 

EGP Energoprojekt Praha, UJV Rez. Div. Czech Rep. 

FORTUM Fortum Nuclear Services Ltd. Finland 

GRS Gesellschaft für Anlagen und Reaktorsicherheit mbH Germany 

IRSN/CEA Institut de Radioprotection et de Sûreté Nucléaire 

Commissariat a l’Energie Atomique 

France 

JPRG Japan PCCV Research Group Japan 

KAERI Korea Atomic Energy Research Institute Korea 

KOPEC Korea Power Engineering Company Korea 

NRC/SNL/DEA US Nuclear Regulatory Commission 

Sandia National Laboratories 

David Evans and Associates 

US 

SCANSCOT Scanscot Technology Sweden 

The ISP consisted of four phases: 

• Phase 1: Data Collection and Identification 

• Phase 2: Calculation of the Limit State Test (LST), i.e. static pressure loading 

• Phase 3: Calculation of response to both Thermal and Mechanical Loadings 

• Phase 4: Reporting Workshop 

The results of the ISP were reported in [79]. Following the Phase 2 calculations which comprised 

a posttest analysis of the LST, two cases of combined thermal and pressure analysis were 

considered: 

• Case 1: Saturated Steam Conditions (mandatory for all Phase 3 participants) (Figure 73) 

o Monotonically increasing static pressure and temperature (saturated steam). 

• Case 2: Station Blackout Scenario (Figure 74) 

o A representative severe-accident scenario for a four-loop PWR including vessel failure 

and hydrogen detonation 

The results of the ISP are summarized in Table 11. While there was no clear consensus regarding 

the effect of temperature on the failure mode and pressure, some observations could be made. 
 97 

With addition of temperature, would the onset of leakage occur later in the pressure history 

and, possibly, closer to the burst pressure? 

• Results predict failure at both lower and higher pressure when temperature is considered. 

• The margin between leak and rupture does not appear to change significantly 

• Change in ‘failure’ pressures are generally small (<10%). 

• Consideration of ‘realistic’ severe accident scenario (Case 2) yields lower ‘failure’ 

pressure than saturated steam conditions. 

• Effects of material degradation are significant for ‘realistic’ severe accident scenarios. 

How would including the effect(s) of accident temperatures change the prediction of failure 

location and failure mode? 

• While leak or rupture pressures are not significantly changed, displacements are 

significantly greater, especially when considering material property degradation. 

o Case 1: Vertical displacements increase 

o Case 2: Radial displacements increase 

• Failure at penetrations appear more likely, and may control, under combined pressure and 

temperature loading. 
 98 

0.00

50.00

100.00

150.00

200.00

250.00

0.00 10.00 20.00 30.00 40.00 50.00

Time (m)

Temperature (C)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Pressure (MPa)

Temperature Pressure

Figure 73 Case 1 Saturated Steam Pseudo-Time History 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90

time [hr]

Pressure [MPa]

Calculated Simplified

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90

time [hr]

Temperature [C]

Calculated Simplified Hydrogen Burn/Detonation

RPV Failure

Dryout of lower compartment

Reactor Coolant Pump trip

Hot Leg Nozzle failure

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90

time [hr]

Pressure [MPa]

Calculated Simplified

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 90

time [hr]

Temperature [C]

Calculated Simplified Hydrogen Burn/Detonation

RPV Failure

Dryout of lower compartment

Reactor Coolant Pump trip

Hot Leg Nozzle failure

Figure 74 Case 2 Station Black-Out Time History 
 99 

Table 11 Summary of ISP 48 Results 

Pressure Only

Pressure (MPa) 

 Liner 

Tearing 

Pressure 

@ Failure

Hoop 

Strain

Radial

Disp. 

Criteria 

LST 0.98 0.17% Liner tear, 1% leak 

SFMT 1.42 1.4% Tendon rupture 

BE/HSE/NNS 1.10 1.40 0.12% 39 mm Liner tearing 

Fortum 1.30 1.60 12mm 

JPRG Failure does not occur 

NRC/SNL/DEA 1.33 1.33 0.74% 40mm Liner tearing 

Scanscot 1.3 1.38 2.1% 91mm Tendon rupture 

Pressure plus Temperature

Pressure (MPa) 

 Liner 

Tearing

Pressure 

@ Failure

Hoop 

Strain

Radial

Disp. 

Criteria 

BE/HSE/NNS 1.25 1.40 

1.50 

0.18% 39 mm Liner tearing 

Tendon rupture 

EGP 1.15 1.25 0.3% 16mm 

Fortum 1.40 1.69 17mm Tendon rupture 

GRS (Case 1) 

 (Case 2) 

1.40 1.40 

>1.30 

1.5% 

0.4% 

85mm 

23mm 

Liner tearing 

JPRG Failure does not occur 

KOPEC (Case 1) 

 (Case 2) 

1.20 

0.41 

– 114mm Tendon rupture 

NRC/SNL/DEA 1.28 1.28 1.11% 60mm Multiple liner tears 

Scanscot (Case 1) 

 (Case 2) 

1.3 

1.33 

1.45 

>1.33 

3% 

0.75% 

134mm 

54mm 

Tendon rupture 

3.5.2 1:10-scale prestressed concrete model (Sizewell-B) 

In July, 1989 a test was conducted for a 1:10-scale model of a prestressed concrete containment 

vessel by the Central Electricity Generating Board (CEGB) in the United Kingdom. This model 

of the Sizewell-B NPP containment structure utilized seven-wire strands in plastic sheaths to 

represent the vertical hairpin and hoop tendons. The vertical tendons were anchored below the 

basemat, and the 240 ̊ hoop tendons were anchored in two of the three vertical buttresses. The 

model was unlined (although a bladder was inserted in the model to prevent leakage) and included 

an equipment hatch penetration. Instrumentation included rebar, tendon and concrete strain 

measurements, and measure of displacements and tendon anchor forces. The model was tested 

hydrostatically. The NRC, through an agreement with the United Kingdom Atomic Energy 
 100 

Authority (UKAEA), participated in the test program with SNL and ANATECH providing 

technical support to the NRC [80, 81]. 

As with other model tests with international participation, the principal objectives were to use 

blind pretest analyses to critically evaluate analytical methods for predicting global structural 

response, and gain insight into potential structural failure modes of a PCCV. The geometry of the 

model is shown in Figure 75. The model was tested with four loading cycles to 1.15 x design 

pressure, followed by one ultimate pressure test. Design pressure of the model was 0.345 MPa 

(50 psig). The model behavior was observed to be primarily elastic during the low pressure tests, 

except that the basemat uplift response was somewhat larger at the end of the fourth low pressure 

test than after the first, indicating the occurrence of inelastic damage to the basemat or wall-base 

region, or both. During the high pressure test, a maximum pressure of 0.834 MPa (121 psig) was 

reached at the model base (2.4 x design pressure). Failure occurred when excessive bending of the 

basemat slab led to rounding of the underside of the basemat, model tilting and potential 

instability, spalling of basemat under-surface concrete, and termination of the test. Upon post test 

inspection, model failure was postulated to have been associated with the basemat spallation and 

the resulting loss of bond in basemat bottom reinforcement as illustrated in the sketch of Figure 

76. Another interesting result was the observation that the tendons, constructed with wire strand 

sheathed in plastic coating (not conventional post-tensioning that is free to slide in metal ducts) 

showed evidence of significant friction, and by parametric analysis, this was shown to influence 

model behavior. Evidence of this is shown in Figure 77 in which the tendon strain measurements 

on hoop tendons indicate higher strains, the further a gage is located from the tendon anchorage. 

A tendon behaving in frictionless fashion would not exhibit these strain gradients. 

The maximum radial displacement (not including tilting of the model) was 13.5 mm, but basemat 

uplift exceeded 30 mm. So only a small amount of rebar and tendon yielding occurred in the 

cylinder, while extensive inelastic behavior occurred in the basemat. 

Pretest analysis consisted primarily of axisymmetric analysis, but two different parametric 

assumptions were used for the tendons—a bonded tendon assumption and an unbonded 

(frictionless) tendon assumption. While the cylinder expansion predictions were not significantly 

influenced by the vertical tendon friction assumption (and showed good agreement with test 

measurements), the analysis results with the bonded tendon assumption compared better with the 

basemat bending and uplift response than the results with frictionless tendons. A sampling of 

pretest analysis results versus experiment are shown in Figure 78. So as with other experiments, 

axisymmetric modeling resulted in satisfactory prediction of containment cylinder global 

response, the modeling was unsatisfactory for predicting local and 3D effects such as rebar debonding, very localized concrete spallation, and behavior near penetrations. 
 101 

(best figure available) 

Figure 75 Schematic of 1:10 Scale Sizewell Model 

(best figure available) 

Figure 76 Section View of Posttest Condition of the 1:10-Scale Model 
 102 

(best figure available) 

Figure 77 Hoop Tendon Gage Data Near Cylinder Mid-height 

(best figure available) 

Figure 78 Comparison of Pretest Analyses vs. Experiment Results for 1:10 Scale P/C 

Model 
 103 

3.5.3 Other Prestressed Concrete Containment Model Tests 

A number of large concrete pressure vessels were tested to failure in the late 1960’s and 1970’s as 

part of research to proof-test concrete reactor vessels used in high temperature gas-cooled 

reactors. While these tests were not of containments and so involved larger wall thicknesses and 

higher pressures than are seen in containments, this body of research helped shape more modern 

evaluation methods used today on containments. Some of these vessels, particularly those with 

steel liners exhibited liner tearing and leakage failures, while a few of the tests ended in major 

through-wall shear failures of either the cylinder wall or the top head. 

3.5.3.1 1:12-scale prestressed concrete model (India) [59] 

A 1:12 scale model was constructed in India using micro-concrete and annealed wire to represent 

the reinforcing and prestressing wire for the tendons. The inside of the model was coated with a 

type of vinyl paint similar to that used in the prototype. The model included six non-functional 

penetrations. The model leaked at a pressure of 0.13 MPa (19.5 psig), lower than the design 

pressure of 0.17 MPa (25 psig), due to excessive cracking. 

3.5.3.2 1:10-scale prestressed concrete model (Poland) [60] 

A test of a 1:10-scale model of a prestressed containment vessel was conducted in Poland in the 

late 1970s. The prestressing tendons consisted of two, unbonded, 6 mm wires anchored in six 

buttresses for the hoop tendons and a ring buttress at the springline for the dome and hoop 

tendons. The model also included a steel liner and representation of an equipment hatch and 

airlock. The model was tested using air to 80% of the design pressure followed by dynamic 

testing to determine frequencies and mode shapes and finally a hydrostatic test to failure. 

Instrumentation consisted of liner, rebar and concrete strains, displacements and tendon anchor 

loads. 

During the final pressure test, large radial cracks developed around the equipment hatch 

penetration, ultimately leading to liner tearing and leakage. Pretest predictions based on the 

capacity of the reinforcing and tendons slightly overestimated the capacity of model and did not 

anticipate the cracking patterns and ultimate response modes. 

3.5.3.3 1:14-scale prestressed concrete CANDU model (Canada) [61, 62, 63, 64] 

A 1:14-scale model of a prestressed containment vessel was tested in Canada in the 1970s. Wall 

thicknesses were scaled at approximately 1:8 to accommodate reinforcing. The prestressing 

consisted of grouted, seven wire strands with the hoop tendons anchored in four vertical buttresses 

and the vertical and dome tendons anchored in the ring girder. The model was unlined (although 

a plastic liner was used to prevent leakage after cracking of the concrete) and included an access 

hatch penetration. Instrumentation consisted of rebar, tendon and concrete strains, displacements 

and crack widths. Testing to failure was performed using water as the pressurization medium. 

Failure occurred when the plastic liner ruptured and leaked following a progressive sequence of 

structural events beginning with cracking and bearing failures at the buttresses, large deflections 

and cracking in the cylinder, tendon rupture and, finally spalling and ejection of the concrete. The 

authors concluded that the pretest predictions of response compared favorably with the test results 

with the exception of under-predicting the deflections. 
 104 

3.5.3.4 Large-scale prestressed concrete model (EPR, France/Germany, Civaux) 

A large-scale model of the inner containment for the European Pressurized Reactor was 

constructed and tested in late 1997 at Civaux, France. The model consisted of a horizontal section 

of the cylindrical containment section including conventional reinforcing and prestressing steel 

capped by stiff slabs. Portions of the model were unlined, while other portions included an 

innovative composite liner. After a series of leak tests with air and steam at LOCA conditions, 

the model was tested to failure hydrostatically. Unfortunately, the results of the test have not been 

published. 

3.6 Component (Penetration) Tests 

In reporting on the results of the 1:8-scale steel containment vessel model test, Clauss [25] made 

the following observation: 

“The level of analysis that will be required to provide these answers will depend largely 

on the results of investigations into the leakage characteristics of containment 

penetrations that are now in progress. If these studies identify penetrations or seal 

geometries that are likely to leak prior to the onset of membrane yielding, the structural 

analyses of containments to be used for consequence analyses can be relatively simple. 

However, preliminary indications are that leakage from penetrations will not occur below 

the membrane yield pressure. If this is the case, predictions for leakage and rupture 

would require structural analyses to be carried out to pressures greater than the 

membrane yield pressure, and the analyses would therefore be similar in complexity to 

those conducted for the 1:8-scale steel model.” 

As noted previously, the containment system consists of several elements. In addition to the 

primary structure, these include various components such as the mechanical (hatches, piping) and 

electrical (instrumentation and controls) penetrations. For US containments there are a large 

variety of designs [91, 92] and not all can be tested. Since the variety of penetration designs 

could not be incorporated into the model tests, a series of tests of a variety of penetrations types 

were conducted to determine their leakage characteristics under severe accident conditions. Parks 

and Clauss summarized the research on penetration performance [82]. 

3.6.1 Compression Seals & Gaskets [83, 84] 

Compression seals and gaskets are used in many operable penetrations such as equipment hatches, 

personnel air locks and drywell heads. Aged and un-aged gaskets of ethylene propylene (EPDM), 

silicone and neoprene were tested at SNL [83] and the Idaho National Engineering Laboratory 

(INEL). The gaskets were tested up to pressures of (0.98 to 1.10 MPa (143 to 160 psig) and 

temperatures up to 370oC (700oF). The test indicated that failure, i.e. leakage, was independent of 

aging and that the silicone seals failed at lower temperatures in steam than in air or nitrogen, 

while EPDM was not affected by the pressurization medium. 

3.6.2 Electrical Penetration Assemblies [85] 

Electrical penetration assemblies are used to provide a leak-tight feed-through into the 

containment building for power, control and instrumentation cables. Electrical penetrations, in 

addition to serving as a closure, in most cases will have to function ‘electrically’ during a severe 

accident and this function must also be evaluated. Three different commercial penetration designs 

were tested at SNL at pressures of 0.51 to 1.07 MPa (75 to 155 psia) and temperature from 180 

to370°C (360oF to 700oF) for up to 10 days. None of the penetrations assemblies tested failed. 
 105 

The authors of the test report, however, cautioned against assuming that all electrical penetration 

assemblies would perform identically to the three tested. 

3.6.3 Personnel Airlocks [86, 87] 

A full size personnel airlock (Figure 79), originally fabricated for the cancelled Callaway Unit 2, 

was tested by CBI Research Corporation under contract to SNL. [86, 87]. Double EPDM gaskets 

provided the seal between each door and the bulkhead. The airlock was designed for an external 

pressure of 0.41 MPa (60 psig) and a maximum temperature of 170oC (340oF). It was tested to a 

pressure of 2.07 MPa (300 psig) and a temperature of 204oC (400oF) without failure. The inner 

door leaked when subjected to a pressure of 0.07 MPa (10 psig) at oC (650oF), although the outer 

door did not leak. Again, the authors of the test report cautioned against extrapolating the results 

of this test to all airlocks, since designs can vary significantly. 

Figure 79 Typical applications of inflatable seals in personnel airlock doors [82] 
 106 

3.6.4 Inflatable Seals [88] 

A series of test of un-aged and aged EPDM inflatable seals were conducted at SNL. Inflatable 

seals are used to seal personnel airlock and escape lock doors at approximately 10% of US PWR 

or Mark III BWR containments (Figure 80). In operation the seals are maintained at a constant 

internal pressure of 0.34 to 0.69 MPa (50 to 100 psig). (It should be noted that inflatable seals 

will leak at containment pressures greater than the seal pressure.) The tests were conducted to 

determine the combination of temperature and pressure which would result in significant leakage 

past the seals. The tests showed that, regardless of seal design, aging or operating pressure, the 

seals did not leak until the containment pressure exceeded the normal operating seal pressure. 

There was evidence of breakdown in the seal material at temperatures above 176oC (350oF). 

Figure 80 Inflatable Seal Schematic and Typical Designs [82] 

3.6.5 Equipment Hatch, Drywell Head [89, 90] 

A series of tests were conducted on the pressure unseating equipment hatch included in the 1:6-

scale reinforced concrete containment model (see 2.4.1). An analytical method was proposed to 

predict the pressure at which significant leakage would first occur and the subsequent rate of 

leakage for pressures and temperatures beyond this level. The tests showed that the leak initiation 

pressure could be predicted reasonably well by the analytical model; however the subsequent leak 

rate could not be predicted with confidence. Also, since only the hatch was pressurized, the effect 

of global structural deformation, i.e. ovalization of the hatch sleeve, was not represented in the 

tests or the analyses. 

For pressure unseating equipment hatches [89] and for BWR drywell heads [90], analytical 

techniques depend on knowledge of the force of the connecting or tie-down bolts. In most cases 

this is not known and must be estimated. Even knowing the torque used to tighten the bolt is not 

in itself adequate in calculating the force in the connection. 

The increase in the horizontal diameter of an equipment hatch may be approximated [45], and this 

will provide some insight into whether there may be leakage past the seals. Note that in the 1:8-

scale steel test [24] considerable ovalization occurred in the test. 

3.6.6 Bellows [93, 94] 

Bellows are employed at most process piping penetrations in steel containments (Figure 81) to 

minimize the loads imposed by the pipe on the steel shell. Bellows are also used at the fuel 

transfer tube penetration in all concrete containments. 
 107 

Figure 81 Typical application of process piping bellows [82] 

Two series of bellows pressurization tests were conducted at SNL: 

• Thirteen ‘like new’ bellows were tested under various combinations of internal pressure 

and temperature, axial and lateral loading. Two specimens were single-ply bellows and 

11 were double-ply bellows. 

• Six bellows (One single ply, 5 two-ply) were corroded by exposure to magnesium 

chloride to produce transgranular stress corrosion cracking before testing. 

Figure 82 shows an un-corroded specimen before and after testing. 

Figure 82 Bellow Test 
 108 

The containment bellows tests concluded that: 

• “Like-new” specimens withstood the full range of compression (i.e. full metal-to-metal 

contact) or elongation before leakage occurred. 

• Corroded specimens: 

o When only one ply of a two ply bellow was corroded, the bellows were capable of 

resisting extreme loading conditions similar to the bellows in a ‘like-new” condition. 

o Three corroded bellows were leak tight before loading. They withstood severe 

deformations before developing leaks. 

o The corroded bellows that were not leak-tight before loading exhibited an increasing leak 

rate during loading. The leak rate depended heavily on the corroded condition of the 

bellows. 

3.7 Related Containment Research Activities 

3.7.1 Containment Performance Goals 

In 1990, the NRC staff proposed a safety policy goal for Advanced Light Water Reactors 

(ALWRs) that required a conditional containment failure probability of 0.1 (10%) or less for 

severe accident conditions.4

 In lieu of performing a full probabilistic assessment of the loads and 

containment behavior, the staff proposed an alternative, deterministic acceptance criteria for steel 

containments: 

“The containment should maintain its role as a reliable leak tight barrier by ensuring 

that containment stresses do not exceed ASME Service in Level C limits ....” 

The NRC tasked SNL with evaluating this alternative criteria and, since Service Level C limits 

only apply to steel containments, to investigate if similar criteria could be defined for reinforced 

and prestressed concrete containments. A panel of four experts in containment design was 

enlisted to advise the NRC and SNL in defining the scope of this program and reviewing the 

results. Klamerus, et. al. [12] reported on the results of this program. 

The approach chosen to investigate these questions consisted of designing six simplified surrogate 

containments to ASME code requirements and investigating their performance to severe accident 

loading conditions. The surrogate containments investigated were: 

• One reinforced concrete containment 

• One prestressed concrete containment 

• Four steel containments 

o Cylinder with hemispherical dome and torispherical base, SA-537 Cl. 2 

o Cylinder with hemispherical dome and torispherical base, SA-516 Gr. 70 

 

4

 SECY-90-016 
 109 

o Sphere, SA-537 Cl. 2 

o Sphere, SA-516 Gr. 70 

The same volume and design pressure, 45 psig, was used for each of the surrogate containments. 

The resulting designs were then each analyzed to determine the failure pressure under thermal 

loading conditions of 400oF and 600oF. The failure criteria used in these analyses was 2% global 

hoop strain for the reinforced concrete and steel containments and 1% global hoop strain for the 

prestressed containment. 

It should be noted here that these were relatively simplistic ‘models’ and criteria and did not take 

into account the effect of local strain concentrations and penetration details. Failure criteria were 

not explicit in terms of the mode of failure, but suggested ‘incipient leakage’ and did not attempt 

to differentiate between leak and catastrophic rupture. The study also did not have the advantages 

of the insights gained in the subsequent containment model tests. Nevertheless, the results 

provide some insights on containment performance criteria, and it might be valuable to revisit 

these questions with the benefit of the subsequent research. 

The primary ‘conclusions’ or insights gained from this study include the following: 

• Current ASME design practices and requirements for concrete containment are based on 

yield criteria. Similarly, although steel containment designs are usually governed by 

some fraction of the ultimate allowable stress [ Smc ≅ 1.1( Su/4) ], the ASME Level C 

allowable are, in fact, based on (code specified) yield. As a result, the concrete design 

requirements specified in Section III, Division 2 and the alternative Safety Goal criteria 

based on the Level C allowable for steel containment have some equivalence. The margin 

to yield computed for both the concrete and steel surrogate containment were 

approximately equal, roughly 1.7 times the design pressure. This suggested that concrete 

code requirements posses a similar level of margin to yield as that provided by the 

alternative Level C allowable criteria currently in place for steel containments. 

• A similar evaluation of failure pressures also suggested a level of equivalence between 

the Service Level C requirements for steel containments and the requirements for Section 

III, Division 2 for concrete containments. 

• When severe accident conditions (in this case based on an ongoing NRC study on Direct 

Containment Heating) were convolved with the containment failure probabilities (based 

on assumed variations on median failure pressures and Monte Carlo simulation), the 

resulting CCFPs were less than 0.02 (2%). Alternately, the severe accident pressure of 

twice the design pressure was required for the CCFP to exceed the safety goal of 10%. A 

CCFP of 50% corresponded to a pressure load of 3Pd. 

These results suggest that alternative criteria based on ASME code design requirements satisfy the 

Commission’s safety policy goal. This conclusion, however, should be confirmed by more 

rigorous analysis and utilize the results of the latest containment experimental research results. 

3.7.2 Degraded Containment Capacity Analyses 

Since corrosion damage in the containment has been found in over one-third of the current US 

fleet of operating nuclear power plants, and it is expected that incidences of corrosion damage 

will increase as the fleet ages, the NRC tasked SNL to investigate how corrosion degrades the 

capacity of the containment to resist design and severe accident pressures. Along with 

experimental work on the effect of corrosion on the tensile behavior of steel coupons, Cherry and 
 110 

Smith [18] performed detailed finite element analyses of containments, in this case the plants 

studied in NUREG-1150, with corrosion damage representative of observed conditions. They 

considered the following situations: 

• Steel Ice Condenser (Sequoyah) 

o Local thinning of steel shell at wall-basemat junction, upper floor and ice basket. 

• Steel Mark I (Peach Bottom) 

o Local thinning of the steel shell at the knuckle, sand pocket and torus. 

• Large, Dry Reinforced Concrete Containment (Surry) 

o Local thinning of the steel liner at the wall basemat junction, mid-height of the 

cylinder wall and at the equipment hatch. 

• Large, Dry Prestressed Concrete Containment (Zion) 

o Local thinning of the steel liner at the wall basemat junction, mid-height of the 

cylinder wall and at the equipment hatch. 

o Corrosion of prestressing and loss of prestressing simulated [95]. 

In all cases of corrosion of the steel shell or liner, corrosion was modeled as local thinning of the 

liner with no additional factors (e.g. local material degradation, local cracks, etc.) considered. 

This assumption was made as a result of the tensile tests on the corroded steel coupons which 

showed that corrosion could essentially be represented as a loss of cross-section. 

The results of the steel liner and shell analyses showed that if corrosion damage occurs in a highly 

stressed region of the structure, the pressure capacity of the structure would be reduced. On the 

other hand, corrosion in non-highly stressed areas, assuming it did not penetrate the entire 

thickness, was found to not have any significant effect on the capacity of the containment. 

As noted previously, Cherry and Smith [18] included a fairly detailed discussion of failure criteria 

for steel shells and liners. While Cherry and Smith addressed this problem deterministically, a 

companion study conducted by Ellingwood and Cherry [96] considered it from a probabilistic 

perspective. 

Smith [95] investigated the effects of corrosion damage on prestressing tendons and loss of 

effective prestress by performing finite element analyses of the containment without damage and 

with varying levels of damage to the tendons. He concluded that the loss of vertical prestress had 

no effect on containment capacity. (This result is consistent with the behavior of the 1:4-scale 

PCCV model test.) He further concluded that loss of hoop prestress had little effect on the 

ultimate capacity of the containment as long as the strength of the tendons was not degraded. It is 

not clear how this hypothetical condition would manifest itself. Only loss of the hoop tendons 

themselves had any effect on the ultimate capacity and this was proportional to the number of 

tendons lost, especially if the losses occurred in the highly stressed regions near the mid-height of 

the cylinder. 

3.7.3 Risk-Informed Assessment of Degraded Containment Capacity 

Sandia is completing a study, to be published as a NUREG/CR, to assess containment degradation 

from a risk-informed perspective. Reg. Guide 1.174 [98] describes a risk-based approach for 
 111 

evaluating changes in a plant’s licensing basis, which could include damage or degradation of the 

containment boundary. Spencer and Petti have built on the previous analytical work by Cherry 

and Smith by investigating the risk-significance of hypothetical occurrences of corrosion in the 

steel shell and liner the NUREG-1150 plants in terms of Large Early Release Frequency (LERF). 

LERF is used in Reg. Guide 1.174 as a quantitative surrogate risk metric for the Quantitative 

Health Objective specified in the Commissions Safety Policy Goal Statement. Small increases in 

LERF (Region II and III in Figure 83) are not considered risk significant. 

Region I

Region II

Region III

LERF

6 10− 5 10−

7 10− ΔLERF

6 10−

Region I

Region II

Region III

LERF

6 10− 5 10−

7 10− ΔLERF

6 10−

Figure 83 Acceptance Guidelines for Large Early Release Frequency 

Finite element models were used, along with Latin Hypercube sampling of up to 30 model 

parameters, to generate fragility curves for various containment pressure failure modes. Figure 84 

shows an example of the original and degraded (due to liner corrosion) fragility curves for the 

Surry containment. 

Figure 84 Leak Fragility for Surry Containment with Liner Corrosion 
 112 

The degraded fragility curves for all failure modes are combined and conditional cumulative 

failure probability curves for leak, rupture and catastrophic rupture were used in revised Level 1 

PRA analyses to determine the effect on LERF. 

The analyses resulted in both a positive and negative change in LERF (ΔLERF), however, these 

analyses were not intended to be used to determine the risk-significance, with subsequent 

implications for inspection and/or repair, for actual occurrences of corrosion or damage in real 

containments. Rather, the study provides an approach and demonstrates how risk-informed 

decision making might be applied to real occurrences. The study also suggests that alternate risk 

metrics might be more appropriate for making decisions regarding individual systems, structures 

or components. 

3.7.4 Seismic Capacity Tests and Analyses 

During the first 15 years of the SNL containment research program, no special consideration or 

research was applied to the seismic behavior or performance of containments. Seismic 

reinforcement that is added to containments was included in scale model designs, but the 

objectives of the tests did not include seismic behavior. The first large scale investigations for 

seismic behavior of containments were performed starting in the late 1980s in Japan. These were 

carried out by NUPEC, using the large-scale shaking table at the Tadotsu Engineering Laboratory. 

These tests were sponsored by the Ministry of Economy, Trade and Industry (METI) of Japan, but 

the NRC and SNL had a participatory role, particularly in conducting pre- and post-test analysis 

[99]. These analyses were conducted by SNL with analytical support by ANATECH Corp. [100, 

101]. Tests of both an RCCV and a PCCV (1:10 scale) were performed, and the project was 

completed in March, 2000. An interesting aspect of the tests was that many different earthquake 

records and magnitudes were applied to the same model specimen, starting with small ground 

motions and building up to larger motions, which eventually failed the structures. So the effects 

of accumulating damage to the structures became an important part of the observed and analyzed 

behavior. Ultimately, this caused both advantages and disadvantages to the process of 

interpreting the shake table testing and analysis results, because while the tests qualitatively 

demonstrated significant changes in structure dynamic behavior with the accumulation of damage, 

these effects were difficult to quantify or analytically simulate because to introduce them required 

analysis of each and every shake table record in cumulative fashion. As with any large scale 

shake table test, there were also difficulties with delivering the intended ground motion signature, 

when the stiffness and mass of the shake table apparatus and test specimen both have significant 

influence on the motion that actually occurs at the shake table-specimen interface. 

The Tadotsu experiments served dual goals set by the project sponsors, namely, those of proof 

testing, and those of benchmarking for improving analytical methods. Although there may be 

lack of agreement as to how comprehensively these goals were met, the tests did succeed in 

calling attention to the importance of the amount and the dynamic character of seismic energy 

delivered to a containment structure, and the role that concrete containment cracking plays in 

containment dynamic response. These issues are largely ignored in containment seismic design, 

and perhaps need to be considered in future design practice. 

3.7.5 Impact Tests and Analyses 

In addition to the programs described in this report which address the capacity of nuclear power 

plant containment structures to resist beyond-design basis loads resulting from severe accidents 

and seismic events, SNL has performed a number of experimental and analytical programs to 

investigate the response of structures (not necessarily containments) to impact loads which may 

result from failures of equipment such as turbines, tornado-generated missiles and aircraft. It is 
 113 

beyond the scope of this report to describe these programs in detail; however, a brief description 

of the major programs, with references for further details, is included for completeness. 

3.7.5.1 Turbine Missile Tests 

A series of tests were conducted for the Electric Power Research Institute (EPRI) at SNL’s rocket 

sled track to accelerate full-scale quarter segments of turbine rotor disk into concrete containment 

wall targets and turbine casings [102, 103]. 

(best available figure) 

Figure 85 Turbine Missile Test Sequence 

3.7.5.2 Full-Scale Aircraft Impact Test at SNL 

A full-scale F4 Phantom jet was accelerated to 210 m/s (496 mph) to impact a ballistic pendulum, 

comprised of a 3.6 m (12 ft) thick reinforced concrete block on air bearings. This test was 

conducted for the Kobori Research Complex, Tokyo, Japan. The purpose of the test was to 

measure the impulse of the aircraft impacting a rigid mass. The results of the test have been used 

to benchmark analytical models for aircraft loading time histories [104]. 

Figure 86 Full-Scale Aircraft Impact Test Sequence 
 114 

3.7.5.3 Full Scale Engine Tests 

Full-scale jet engine tests were conducted at SNL to observe the penetration and damage response 

of concrete wall panels of varying thickness, reinforcing and with and without steel liners. These 

tests were also conducted at Sandia’s rocket sled track for the Kobori Research Complex. [105, 

106]. 

3.7.5.4 ‘Water-Slug’ Tests 

The previous tests investigated the behavior of rigid missiles impacting flexible or ‘soft’ targets 

and flexible missiles impacting rigid targets. In order to understand the full spectrum of loading 

conditions, SNL conducted a series of impact tests for soft missiles on flexible targets. In these 

tests, a thin aluminum cylinder was filled with water, referred to as the ‘water slug’, and 

accelerated to impact a reinforced concrete panel. Tests were conducted varying the ‘water slug’ 

size and impact velocity. The results of these tests and the analyses conducted to simulate the 

tests were published in a limited distribution report. 

Figure 87 ‘Water Slug’ Test Sequence 

3.7.6 Leakage Tests 

As described in Chapter 2, containment performance criteria are qualitatively and quantitatively 

described in terms of a leakage rate. However, experimental models and analyses typically 

measure containment response to pressure loading in terms of stress, strain or displacement. Two 

primary containment leakage modes have been identified: by-pass leakage through penetrations, 

typically at the seals, and tearing or rupture of the steel shell or liner. Experimental and analytical 

investigations of penetration leakage were discussed in Section 3.6. Experimental results of steel 

containments suggest that, in most cases, material failure in the steel shell progresses rapidly from 

leakage to rupture. In the case of concrete containments, however, the transition between large 

local material strains to material failure, manifested as a tear or hole, coupled with cracking in the 

concrete and fluid mechanics of the gas flow through the tear and the cracked concrete is 

currently beyond ability to model. This problem can be de-coupled into the problem of predicting 

the progression of material failure in the steel and the problem of gas flow through cracked 
 115 

concrete. Castro [56] proposed a model for predicting the size of tears in a steel liner (see Section 

3.4.3), however, this model has yet to be benchmarked against test data. Various researchers have 

investigated the fluid mechanics problem experimentally and have proposed analytical models to 

simulate the observed behavior. 

Salmon, Cuesta, and Pardoen [108] provide a good summary of relevant research on leakage 

through cracked concrete that may be applicable to containments; however, this research, to date, 

has not been implemented directly into SNL containment research. 

The flow rate of air through concrete depends upon the air permeability, the thickness of the 

concrete, and the pressure gradient applied. The flow rate appears to be inversely proportional to 

the slab thickness and directly proportional to the pressure difference across the slab. A literature 

review covering the past 30 years examined published works on air permeability measurements in 

concrete. Most of the works reviewed dealt with gas flow and permeability measurements in 

undamaged concrete. But there is work that deals with gas flow through cracks, and some of this 

may be applicable to concrete containments. 

Rizkalla et al. [57] proposed a mathematical expression for the rate of pressurized air flow 

through idealized cracks. In their work, Rizkalla et al. simulated the membrane stresses in a 

concrete containment structure subjected to large internal pressures by tensioning the longitudinal 

reinforcement which protrude along the ends of the test specimen. Steady-state differential air 

pressures were created by controlling the pressurized air to the upstream chamber of the 

specimen, while maintaining the downstream pressure at atmospheric pressure. Rizkalla refined 

the proposed equation for flow rate by using the experimental data obtained from several concrete 

specimens subjected to uniform tensile stresses. Although these data are valuable, it is doubtful 

whether they are applicable to seismic induced shear cracks, or out-of-plane bending cracks. 

Mayrhofer et al. [109] investigated the airflow through cracked reinforced concrete. This effort 

was aimed at determining the gas impermeability of shelter roof slabs loaded to their maximum 

carrying capacity with uniform pressure. The out-of plane pressure load causes the slabs to bend. 

Gas impermeability for the slabs was defined by the ability to maintain a minimum overpressure 

of 0.5 to 1.0 millibar. Square slabs with length dimensions of 114 cm (45 in) and 300 cm (118 in), 

0.14% and 0.3% reinforcement by area, and a thickness of 17.8 cm (7 in) were used in the 

experiments. The slabs were pressure loaded statically in monotonically increasing load steps. 

Airflow was measured upon completely unloading the structure after each load step. Data 

presented included static load-deformation curves, crack patterns, and airflow-overpressure 

curves. A mathematical expression to correlate slab deflection with gas permeability was 

described in detail. A correlation between deformation and permeability was possible because the 

loading and resulting crack patterns in all slabs were similar. 

Suzuki et al investigated the gas leakage rate through cracks in both reinforced and unreinforced 

concrete [110]. Sensitivity studies on the leakage rate due to the kind of fine aggregate and the 

size of the course aggregate were performed. Suzuki’s test were limited to concrete crack widths 

less than 0.5 mm , and differential pressures less than 250 kPa (36.2 psi). Although limited in 

samples for reinforced concrete, Suzuki’s recommended flow equations based on his empirical 

data may be used as a benchmark. 

Okamoto and others performed an experiment on a three-dimensional one-tenth-scale specimen 

based on a part of a prototype boiling-water reactor nuclear power plant [111]. The study was 

conducted to measure the air-leakage as a function of lateral load, or shear cracks. The specimen 

was subjected to nine static load cycles up to and beyond the specimen design bases. Leakage rate 

data were obtained at both the peak, and upon removal of the load at each cycle. 
 116 

Greiner and Ramm [112] performed a series of experiments on both reinforced concrete and 

unreinforced concrete in an effort to derive an equation for the leak rates of air as a function of 

crack width and overpressure. Their efforts were limited to the following parameter ranges: 

1. crack width, 0.20 mm to 1.30 mm (0.008 in to 0.05 in) 

2. overpressure at the beginning of the crack, 0.10 MPa to 0.80 MPa; (14.5 psi to 116 psi) 

3. fine aggregate particle size, # 8 (2.36 mm) , #16 (1.18mm) and #32 (0.6mm). 

They concluded that for unreinforced concrete, their proposed flow equations were good for the 

experimentally proven ranges, while for reinforced concrete, their predicted flow equations were 

conservative (i.e., measured flows were less than those predicted). 

Dameron, et al [113] evaluated leak test results that were available in the open literature, and 

suggested a methodology for calculation of leak rates in lined concrete containment vessels. As 

part of their research, Dameron, et al were required to estimate the flow rate through the concrete 

containment vessel. They used the method developed by Rizkalla in calculating the measured leak 

rates, and found good agreement between the measured values and the calculated values for 

micro-concrete. 

Riva, et al [114] performed a single experiment on a reinforced concrete slab subjected to 

differential pressure and uniaxial tension. In their experiment, they compared the measured leak 

rates with those calculated using the leak formulae available in the literature. Riva concluded 

that, among the formulations considered: 

1. the leak rate prediction formula given by Rizkalla et al. provides the best fit to his 

experimental data, 

2. the leak rate prediction formula given by Greiner and Ramm [112] would be more 

suitable for higher differential pressures, 0.1MPa (14.5 psi); 

3. the Poiseuille equation generally overestimates the leak rate, and 

4. the expressions by Suzuki et al. [110] obtained the best results for the smallest pressure 

gradient (0.01 MPa) (14.5 psi). 

In summary, the literature review indicates that there are very little data on the permeability of 

cracked reinforced concrete or on earthquake damaged reinforced concrete. Data that are available 

include that published on gas permeability in undamaged concrete, that published by various 

researches on concrete subjected to uniaxial tension, and that of Farrar and Girrens on the single 

shear wall tested to below its design capacity. The experimental data available on cracked 

concrete were directly applicable for reinforced concrete containments that are subjected to high 

internal pressure loads. 
 117 

4 ASSESSMENT OF CONTAINMENT PRESSURE CAPACITY 

No assessment of containment pressure capacity can be formulated without definition of what 

constitutes containment failure. And there still remains a lack of consensus on the definitions of 

failure modes, so it is appropriate to begin this chapter by summarizing the definitions from the 

authors’ perspective. These definitions are generally supported by the observed behavior. For the 

Sandia program, failure of the models has been defined in terms of functional failure, that is, the 

inability of the containment to meet its primary functional objective of maintaining a pressure 

boundary to prevent the release of radioactive materials to the environment or ‘leakage’. This 

may coincide with the common understanding of failure as gross structural failure or ‘bursting’, 

i.e. the limit state of the primary load resisting system. In many cases however, functional failure 

may occur well below the loading limits of the structure. Alternately, the difference between 

‘leakage’ and ‘bursting’ has been described as the difference between local loss of function at a 

discrete location and loss of structural integrity. Experience has shown that steel containments 

may exhibit ‘bursting’ or gross structural failure while reinforced concrete containments with 

steel liners would exhibit ‘leakage’ or local functional failure. The data on failure of prestressed 

concrete containments is inadequate to draw unequivocal conclusions regarding failure although 

‘leakage’ appears to be the most likely limit state. 

This difference between functional and structural failure has led some researchers to include 

features in the model to allow loading beyond the functional limits of the model, e.g. the inclusion 

of resilient bladders to prevent leakage of the pressurization medium, usually water. One problem 

with including these model artifacts is that they may tend to mask real functional failure modes 

which could occur in prototypical plants. Since the objective of Sandia’s program has been to 

investigate representative behavior of actual containments, the decision was made not to ‘mask’ 

the functional failure modes and to rely on the primary containment function as the definition of 

failure. 

The following sections briefly describe the research conducted at Sandia and elsewhere for each 

of the main containment types, as well as the components, with an emphasis on the results as they 

pertain to assessment of containment pressure capacity. 

4.1 Insights from Containment Testing 

As previously described, the Sandia containment test program was geared toward conducting 

experiments to gain insight on, and “benchmark,” analytical methods for calculating containment 

response and capacity. None of the tests were “proof tests.” Nevertheless, the implications and 

insights on containment overpressure behavior provided directly by the tests should not be 

completely discounted. The design of each of the large scale containment tests (especially the 

1:6-scale RCCV, mixed scale SCV, and 1:4-scale PCV) was performed using, then current, 

containment design codes and procedures, and the test structures were designed as pressure 

vessels. They were not designed simply by geometric scaling. This means that it is probably 

reasonable to draw some general conclusions from trends observed from these tests. These 

conclusions would include, for example, the following. 

• Scale Effects: The results of the tests clearly demonstrate the necessity of conducting 

model tests at a scale large enough to: 

a. utilize materials which exhibit the characteristics of the materials used in the 

prototype, 
 118 

b. allow the design details and construction methods used in the prototype to be 

represented in the model, and 

c. avoid non-representative details and as-built conditions to be present in the 

model. 

• Material Properties: As a corollary to the previous point, it is worth making a few 

observations regarding the data from tests used to define the properties of the construction 

materials. Typically, the properties are obtained from standardized tests of small or 

representative samples of the materials used in the construction of the model. These test 

methods have, as their primary purpose, the function of assuring that the materials used in 

the construction meet a minimum quality standard. Experience has shown that if these 

minimum standards are met, the structure will meet the design requirements. This is 

subtly, but significantly, different from characterizing the in-situ properties of a 

structure’s constitutive elements. 

Nevertheless, these standardized test results are usually all that is available, and most 

engineers would be happy to have actual material data rather than minimum specified 

properties. The difficulty arises when the properties of these sample tests are used to 

develop mathematical material models for use in analysis, especially when these material 

models include inelastic behavior and failure conditions, to predict the response of 

structures well beyond their design limits. 

The 1:4-scale PCCV model tests clearly demonstrated that the tendons failed shortly after 

the cylinder wall and measured tendon strains were approximately 1%, much less than the 

4 to 7% strain obtained from laboratory tests of tendon specimens. Similarly, the 

measured (and calculated) liner strains at the pressure level when the liner tore were well 

below the ultimate strain of the liner coupons, even when considering local strain 

concentrations. 

This raises the question, then, of whether current standard material test methods are being 

used to perform a function for which they were not originally intended and if they are 

adequate for the task. If not, can alternate test methods be devised which might provide a 

better basis for constitutive models? (Another way of looking at this is to consider that 

there have been significant advances in the computational methods used to simulate 

structural response. However, there has been no comparable advance in measurement 

and characterization of the material models on which these computational methods 

depend.) 

A second question related to the material properties is what type and amount of data is 

considered adequate for calculating the response of actual containments? A fairly 

extensive suite of material tests were typically conducted in conjunction with the model 

tests, and actual properties were used in all cases. It is not clear that this level of 

information would be available for all containments. If it is not, the quality of the 

capacity predictions may be reduced with a corresponding increase in uncertainty. 

• Loading: The reasons for conducting static, pneumatic over-pressurization tests at 

ambient temperature were discussed in Section 2.1. While the tests were successful in 

obtaining data on the response to pressurization and, secondarily, to prestressing, the 

application and interpretation of these results should recognize the fact that the test load is 

not a faithful representation of the complex loading environment which will exist during a 

severe accident. The effects of temperature, the temporal relationship between pressure 
 119 

and temperature, the composition of the internal atmosphere and the rate of loading may 

all have an effect on the response and failure modes and the sequence of these events 

should be considered in any evaluation of containment capacity. 

Other containment model tests attempted to consider some or all of these aspects of 

severe accident loads. Future efforts should consider evaluating the effects of these other 

loads on the response of the prototype, and the results of these efforts may indicate the 

need for additional testing which includes these loads. 

• Failure Criteria: Nevertheless, the test did provide some insight into issues which 

should be considered in establishing failure criteria for actual containments. 

First, the primary functional failure criteria defined in terms of a maximum leak rate, 

cannot be applied directly to conventional mechanistic models of containment structures, 

which output response in terms of displacement, strain, force, stress, etc. As a result 

design philosophies have focused on limiting these response variables to ensure that no 

leakage occurs. Further study of the relationship between leakage and structural response 

may provide some insights which could be applied to regulations and design requirements 

based on functional criteria. 

Secondly, predictions of containment capacity have often been based on the structural 

capacity of the components used in the construction. For example, using the ultimate 

strength or elongation of samples of the prestressing tendons, liner, rebar, etc. as the limit 

criteria. The model tests have demonstrated, as noted in the discussion on material 

properties, that the strain levels measured at failure can be much less than the limiting 

values obtained from standard tests of sample specimens. The test results should provide 

some guidance to the development of appropriate failure criteria to be used in future 

capacity calculations. 

• Leak Rate Measurements: SITs/ILRTs conducted in accordance with the specified 

procedures, demonstrated the difficulty of measuring leak rates with the accuracy 

required to guarantee that they do not exceed the specified limits. Even with the 

relatively simple, controlled structure represented by the PCCV model, and the extensive 

suite of instruments available during testing, it was not possible to accurately measure 

leak rates on the order of 0.1% mass/day. An apparent leak rate of 0.5% mass/day at 

1.5Pd during the LST was due to thermal expansion of the model in response to ambient 

temperature changes and direct heating of the model. In light of these results, a review of 

leak rate measurement methods and the leak rate test criteria should be considered. 

4.2 Insights from Containment Analysis 

In reporting on the results of the 1:8-scale steel containment vessel model test, Clauss [25] made 

the following observation: 

“The analysis of a nuclear containment subject to loads arising during a severe accident 

can be divided into two distinct steps. The first step consists of solving for the strains and 

displacements at different pressure (and temperature) levels. Implicit in this first step is 

an analyst's ability to identify which sections of the containment are critical and the 

amount of detail that must be included in an analytical model to obtain accurate results. 

The next step consists of inferring structural performance (by evaluating criteria for 

leakage and rupture) from the predicted strains and displacements in the model, as well 

as other parameters, such as thermal and radiation aging of seals, and aerosols.”
 120 

While the SNL containment test series provide insight into the behavior and capacity of actual 

containments, it should always be kept in mind that actual containments are much more complex 

than even the most detailed model tested. Conclusions about the capacity of actual containments 

can only be made from a reasoned evaluation of the test data and the results of detailed analysis of 

the actual containments using experimentally validated methods. Full size or large-scale 

component tests were planned to complement, and increase the understanding of, the capacity of 

the containment boundary, especially where complex geometries challenge the ability to perform 

reliable numerical simulations (e.g. bellows, electrical penetrations) or to verify these predictions. 

The results of this research, both experimental and analytical, have been and probably will 

continue to be used to characterize the behavior of actual containment structures. This behavior 

can then be used in risk analyses. The step from predicting deformation response to performing a 

risk analysis is not necessarily straightforward. Depending on the risk analysis model, the 

containment performance may have to be input as a leakage or as a function of the loads, or a 

probability function. If the risk analyses indicate that the containment is dominating the risk, then 

it is also possible to go back to the containment analyses and "sharpen the pencil," to improve the 

results. One must realize that, for example, performing a full 3-D non-linear analysis of the 

containment system including all of the details of the as-built containment system is expensive, 

and not necessarily required. But suffice it to say that there still is work required in using the 

results of the containment analyses. Examples of how one might go about utilizing deterministic 

response analyses results in a probabilistic risk assessment have been developed in EPRI 

sponsored research of the late 1980’s. A summary of this methodology is provided in Section 4.5 

which discusses current practice, and ‘what we know versus what we don’t know.’ 

One of the key difficulties of a probabilistic framework is, again, the lack of extensive data on the 

size of leaks that develop after liner tears or other form of rupture occurs in the containment. 

Some data is available, and this was used to the extent possible in the EPRI probabilistic leak 

prediction approach, but most of the containment research, both experimental and analytical, has 

been focused on prediction of the first liner tear or rupture. Another difficulty with developing a 

probabilistic framework occurs when the analyses indicate a weak feature of the containment 

system. That item may become a candidate for retrofit, thus dramatically changing the 

containments risk characteristics. Also, analysis results can be used to write improved code 

requirements and to enhance new designs, which could significantly influence risk assessment. 

4.3 Analysis Goals 

Since one of the main objectives of containment integrity research programs has been the 

validation of analytical methods, most of this research has had a significant analysis component. 

These efforts can be grouped into the categories: global containment response, local response near 

stiffness discontinuities, and the prediction of failure and its consequences. 

4.3.1 Global Response Prediction 

Global response prediction can be further subdivided into containment types, namely steel versus 

concrete containments, because of the significantly different requirements for the corresponding 

analytical tools. 

Global response analyses of steel containments have been conducted by researchers throughout 

the world [21] in conjunction with tests of steel containments and pressure vessels. Basic 

methods of analysis have been in place for as much as three decades, i.e. since the development of 

reliable shell element formulations and steel plasticity models in finite element programs. 

However, steel containment analysis research has provided extensive lessons learned as to how to 
 121 

apply these tools to containments. A detailed summary of these insights and lessons is provided 

in [46, 53]. Issues that analysts continue to find challenging are the accurate prediction of onset 

of yield, made complicated by the three dimensionality of the stress state, and the prediction of 

pressure versus deformation in the final stages of loading, i.e., on the “descending branch” of the 

load versus deformation response curve. 

Tools for modeling steel and concrete containments have a more recent history due to the lack in 

the early 1980's of a generally accepted concrete finite element program. The Three Mile Island 

accident highlighted the need for capability to analyze concrete containments for beyond design 

basis pressure loads. This need triggered analytical research in the US and elsewhere to develop 

and improve concrete analysis software. One such research program which started in 1983 and 

ran for 7 years was the EPRI-sponsored containment research program. This effort had an 

experimental program and an analytical one and was aimed at developing not only a usable tool, 

but also an experimentally verified one. The analysis tool evolving from this work was 

ABAQUS-EPGEN [115], a general purpose F.E. program with special-purpose concrete and rebar 

sub-elements, and ANACAP-U, a user-supplied concrete constitutive modeling module. 

ANACAP-U is based on the smeared-crack approach to concrete modeling. The ability of the 

software to predict global containment response was tested and verified with pre-test analysis 

exercises performed on the Sandia 1:6 scale reinforced concrete containment model pressure 

tested to failure in 1987 [44, 46], the CEGB's 1:10 scale prestressed concrete containment model 

pressure tested to failure in 1991 in the United Kingdom [65], and on the Sandia 1:4 Scale 

Prestressed Concrete Containment model pressure tested to failure [72] in 1999/2001. Similar 

constitutive model development efforts were conducted and have successfully predicted global 

containment model test response for the following software tools: DIANA, ADINA, CASTEM, 

NEPTUNE, NFAP, PAFEC, BOSOR5 and ANSYS. Prediction of global, free-field containment 

response has, therefore, been reasonably well established as long as analyses are performed with 

validated tools and by sufficiently experienced analysts. 

4.3.2 Local Response Prediction 

Prediction of the response near stiffness discontinuities and the local deformation states of 

containment components such as the liner, rebar, or prestressing tendons is more difficult and has 

less widespread experimental verification. The first large scale tests of local concrete 

containment details were those of the EPRI program in which wall panel tests of different 

geometries and different discontinuities (penetrations and other details) were stressed biaxially as 

they would be in a containment subjected to overpressure. Local discontinuities have also been 

tested in other component test programs and by detailed instrumentation of these details within 

various global containment tests. Prediction of strain concentrations near these details in steel 

containments is made more difficult by the presence of welds (and heat affected zones), residual 

stresses associated with rolling and fabrication, and incomplete knowledge of actual plastic 

behavior of materials, particularly under three dimensional states of stress. Local response 

prediction in concrete containments involves all of these difficulties (all of these are present in the 

liner alone) and others stemming from liner/concrete/rebar interactions, and difficulties in 

modeling the shearing response of concrete [50]. Nevertheless significant advances in local and 

component modeling have been made by various researchers and a few of these are examined 

later in this chapter. Accurate representation of the local response is now generally accepted to be 

reasonably good provided analysts have sufficient time and resources to devote to the modeling 

effort, a proviso not often satisfied in the design of new facilities. 
 122 

4.3.3 Failure Prediction 

This last analytical research area is, perhaps, the least mature, and in some ways the most 

debatable in the containment research community. It is immature because it involves the 

combination of the most refined analytical techniques and constitutive modeling, the latest 

information on failure criteria, and often reliance on engineering judgment. The last of these is 

difficult to codify or otherwise disseminate to the containment analysis community. 

The failure criteria define a threshold environment which is the pressure and temperature at which 

leakage or rupture is imminent. In a LWR containment building, there are a number of potential 

failure mechanisms, or release paths. The release paths we have considered are described in 

Table 12. Separate structural calculations may have to be made for each release path, each with 

its own unique modeling requirements. 

One of the reasons for the immaturity of the failure prediction part of containment analysis is the 

difficulty with measuring and even defining failure. Experiments on complete containments 

provide a wealth of global and local response information that is available for analytical 

correlation and validation, but these tests only fail in one, or at most a few, locations. Further, it 

is nearly impossible to precisely gage an exact fracture location so knowledge of the strains that 

exist just before fracture remains limited and therefore controversial. 

Table 12 Release Paths in LWR Containments 

Rupture of Containment wall or shell 

Leakage past Sealing Surfaces (Operable Penetrations) 

o Pressure Seating Equipment Hatches 

o Pressure Unseating Hatches (Drywell Heads, Equipment 

Hatches) 

o Personnel Air Locks 

Leakage past Purge and Vent Valves 

Leakage from Electrical Penetration Assemblies 

Leakage due to Failure of a Bellows (Expansion Joint) 

Also adding to the debate in this area is the disagreement amongst analysts, especially for 

concrete containments, and practitioners over "just how good is good enough". For example, 

prediction of the failure pressure of the 1:6 scale reinforced concrete was made within a relatively 

narrow band, but the prediction of the location consisted of a relatively long list of potential "hot 

spots"[45]. Once global hoop strains of between 1% and 2% are reached, most researchers and 

analysts are reasonably certain that containments will fail, and some say that this knowledge may 

be complete enough. Others, however, argue that failure locations and failure sequence have 

highly varying consequences on risk, on potential release of radionuclide’s, and on mitigation 

measures; therefore, reducing these uncertainties justifies the furtherance of containment analysis 

research. 
 123 

For steel containments, the failure criteria, and the implementation of it by way of analysis is a 

little more straightforward and universally accepted. The rupture criterion for steel shells is 

tensile instability. For steel containments, tensile instability will generally occur when the strain 

is near the material’s ultimate strain. Thus, rupture will occur if, at any point on the pressure 

boundary, the equivalent strain exceeds the material’s ultimate strain (the strain at maximum load 

for a uniaxial tensile test). If the strain is due primarily to bending, somewhat higher strain may 

be allowable (to account for crack growth through the thickness). 

Through-wall cracks in a steel containment resulting from quasi-static internal pressurization will 

grow in a stable fashion or a short period of time until a critical length is reached, at which point 

rupture occurs. The stored energy in a containment at the rupture pressure is so great that venting 

through the growing crack does not cause a significant drop in pressure before the critical crack 

length is reached. Consequently, the stresses at the crack tip are not relieved and the crack cannot 

be arrested. It is concluded that a through-wall crack that would cause a venting of the 

containment precluding rupture is extremely unlikely. Therefore, the rupture criterion represents 

any shell failure. 

4.4 Analytical Research Findings 

The authors have concluded from the analytical research that the only approach to reliably predict 

the nonlinear response, especially for the complex geometry of containments, is with nonlinear 

finite element analysis. There is a restricted class of general purpose computer codes that has the 

features needed to represent the mechanics of large strain and large deformation typical of 

containment response. Based on comparisons of calculated response with experimental data, 

features of analysis that are needed to obtain reliable results are listed below. 

4.4.1 Steel Containment Analysis 

The experimental results and nonlinear analyses of scale models has demonstrated that the postyield behavior cannot be extrapolated from linear analyses. Linear analyses cannot account for 

the effects of load redistribution, plastic flow, or the shape of the stress-strain curve for steel. For 

instance, at the base of a cylinder where radial displacement is constrained, an elastic stress 

concentration associated with bending is observed. The stress at the base is nearly twice that at 

mid-height while the response is still elastic. Yielding occurs near the base of the cylinder well 

below the general yield pressure, but the stress and strain do not increase appreciably until general 

yield occurs. Then, as the pressure is increased beyond general yield, the strains at mid-height 

increase more rapidly than those at the base. In the scale model tests, rupture was always 

associated with high strains near the cylinder mid-height. Failures have been unrelated to the 

stress concentration at the base of the cylinder. 

4.4.1.1 Material Modeling 

The stress-strain relationship for each type of steel should be represented by a multi-linear curve 

up to at least the ultimate strain. Minimum specified properties are not normally representative of 

the actual materials; properties may vary as a function of heat (i.e., production run) and thickness. 

The specified properties for the material also give little indication of the shape of the stress-strain 

curve. Variations of properties within a particular heat are negligible. However, the temperature 

dependence of the yield strength, tensile strength, and work hardening slopes of steels can have an 

important effect on performance, and should be represented in the material model. 

Material properties should be determined from uniaxial tensile tests on the actual fabrication 

materials if at all possible. However, using the uniaxial yield stress has been found to over-
 124 

predict the pressure at first yield. Such uncertainties in predictions are still being studied, but one 

potential reason for this is the residual stresses of fabrication. Of course, these factors introduce 

uncertainty into the predictions for structural performance. One of the best ways to reduce 

uncertainties is to “test” analyst decision-making by analyzing one of the existing steel 

containment tests prior to starting analytical study of an actual containment. Lessons learned 

through this process are likely to greatly improve the reliability of the response prediction. 

Prediction of failure of steel plate material should be based on strain measurements in coupon 

tests and on consideration of the triaxiality of the stress state. A failure criteria that includes 

triaxial stress considerations proposed in [17] has been used in much of the containment analysis 

research described herein. 

4.4.1.2 Geometric Nonlinearities 

Second-order and large-rotation terms need to be included in the strain-displacement relations. 

The stiffness matrix should be updated to reflect the changes in geometry, including thinning of 

the wall. Distributed forces should be formed on the basis of current geometry (i.e., loads from 

pressure should remain normal to the surface. 

4.4.1.3 Element Formulation 

Thin shell elements appear to work well for steel containment analysis. Elements should be 

benchmarked against known solutions before being used for the first time in a predictive analysis. 

The effects of elevated temperature were not incorporated into the scale model structural tests, 

and therefore, the analytical methods are not benchmarked for elevated temperature. 

Nevertheless, the authors feel that the effects of elevated temperature can be handled by most 

general-purpose finite element codes. See for example [77]. The main difficulty is in 

determining the actual temperature profiles in the shell and the penetrations. 

4.4.2 Concrete Containment Analysis 

Reliably predicting the threshold environment for leakage or failure of a concrete containment 

requires accurately calculating the post-yield response. Nonlinear 3D calculations for the 

structural response are also necessary for local stiffness discontinuities and penetrations if liner 

tearing and leakage is to be accurately predicted. Methods for performing such analyses will 

almost certainly require the use of sub-models of local regions rather than a 2D or 3D analysis of 

the entire containment. Local sub-models can be loaded via specified boundary displacements 

generated from coarser global analyses. These boundary conditions need to include the effects of 

the interaction of the penetration or discontinuity with the free-field structure. For example, 

penetration regions have been observed to displace smaller radial distances than the free-field, 

causing out-of-plane relative motion between the penetration and the free-field [46, 47]. 

For equipment hatches and drywell heads, the structural response parameters used in the seal 

leakage criterion developed in [82] characterizes approaches applicable to calculating the 

response. However, to predict leakage from many types of penetrations, the nonlinear response of 

the supporting wall must be known. 

4.4.2.1 Material Modeling 

Pertinent details for modeling steel materials were discussed previously under "Steel Containment 

Analysis". These factors must also be included in reinforced and prestressed concrete 
 125 

containment analyses for modeling the liner. In particular, the strain hardening of liner steels in 

the yield plateau requires careful verification of the strains in the nonlinear response range. 

Concrete constitutive models should include tensile cracking (normally treated as occurring in the 

principal stress directions at the integration points). Alternatively, the concrete can be treated as a 

no-tension material in analyses aimed at predicting global response. Some method for simulating 

post-cracking shear retention should also be included. Shear retention is particularly important at 

the wall base, and numerical solutions in this region are found to be sensitive to the shear 

retention algorithm used. Description of these methods, and a reasonable assessment of the 

current “state of the practice” in concrete modeling is available from the report on Round-Robin 

pretest analyses of the 1:4 Scale PCCV Model [74]. 

While most of the concrete elements in a computational grid will probably experience no 

compressive stress at high pressures, a few elements at the outer wall base and along the top of the 

basemat will experience compression, sometimes large enough to exceed fc’. Thus, it is important 

to properly model concrete crushing. An elastic/perfectly plastic stress-strain curve has shown 

reasonable results in most cases, but inclusion of strain-softening is preferred for completeness. 

(Although, the associated plasticity algorithm is more complex.) As complex behavior is to be 

expected at the wall base, it is important that the concrete compressive yield algorithm properly 

treat the effective stress and strain calculation. Compressive yield is more likely to be reached by 

the combination of vertical compressive stress and shear stress rather than any one component 

stress reaching fc’. This condition is essential for predicting potential wall-base shear failure. 

4.4.2.2 Geometric Nonlinearities and Other Issues 

Contrary to the recommendations for steel containment analysis, it has been found that the second 

order and large rotation terms need not be included in the strain-displacement relations for 

concrete containment analyses. The stiffness matrix need not be updated to reflect the changes in 

geometry or thinning of the wall, as it is in steel shells. This recommendation carries with it some 

practical advantages, especially for modeling such complexities as prestressing tendons. 

Restricting the solution to small-displacement theory provides some options as to approximate 

formulations for friction and other effects. The effects of elevated temperature discussed 

previously are also relevant to concrete containments, and these are described later in this chapter. 

4.4.3 Comparison of Analyses Methods Used for Predicting Model Behavior with US 

Containment Design Practice 

Design practices for US containment designs were discussed in Section 2.2.2. The authors are not 

aware of any standard for analysis of containment for design loads or for response to beyond 

design basis loads. A comprehensive survey of the FSARs and IPEs, would be required to 

‘establish’ or characterize current practice, however this is beyond the scope of the current effort. 

Presumably most designs utilize conventional linear elastic analysis methods, either simplified, 

closed-form analytic solutions or elastic finite element analysis methods. The liner plate is not 

considered a structural element for design. 

It was not until the 1980s that containment failure analyses were conducted for overpressure 

conditions. Because of the highly nonlinear behavior of concrete containment structures, the 

analytical requirements for failure analysis differ significantly from those for design analysis. The 

absence of containment failure analysis from general practice has been due mainly to the 

demanding analytical requirements involved. It was not until the Three Mile Island (TMI) 

accident, which created the need for better understanding of containment overpressure behavior, 

that such investigations were undertaken. 
 126 

4.4.4 Temperature Effects 

The subject of temperature remains largely an untested issue with regard to global containment 

behavior. This is due to the experimental difficulties involved with scale modeling of elevated 

temperatures. Conclusions about global behavior must be taken primarily from analytical studies. 

Experiments have, however, been conducted for local structural details and penetrations by both 

SNL in the NRC research and CTL in the EPRI research. Results of the analytical and 

experimental studies are summarized below. 

Studies of temperature effects in the EPRI research included a test of a prestressed containment 

specimen (specimen 2.6 in the CTL test series 10), a reinforced containment specimen (specimen 

2.7), and analyses of these specimens. Typical prestressed and reinforced geometries have also 

been investigated by analysis for combined pressure and global temperature up to 204 ̊C (400 ̊F), 

plus the addition of a local temperature spike simulating a local hydrogen burn. 

The specimen tests and analyses were aimed at inducing thermal buckling in the liner. The results 

of that work showed that temperatures in the ranges predicted to occur (by NUREG-1150, for 

example, 177 ̊ to 204 ̊C (350 ̊ to 400 ̊F)) have only a small effect on the ultimate pressure 

capacity of both reinforced and prestressed containment structures because the cracked concrete 

carries no tension regardless of temperature. Also, temperatures in this range have only a minor 

effect on typical rebar properties. 

The increase in temperature changes the liner stress-strain behavior in the low pressure range, but 

the end results near failure are essentially the same as in the pressure only cases. The addition of 

local temperature spikes to the temperature history cause small local liner-concrete separation (a 

precursor to liner buckling) in prestressed containments. However, this is not so in reinforced 

containments. The tendency for liner buckling in prestressed containments is viable only for 

temperatures about 204 ̊C (400 ̊F) and pressures at or below design pressures; this may not be a 

plausible combination, thus effectively eliminating liner buckling as a realistic concern. 

The liner buckling findings were suggested by the experiments mentioned above. In both 

prestressed and reinforced containments subjected to elevated temperature, the liner experiences 

compressive yield at low pressures, but eventually develop tension at higher pressures regardless 

of added temperature. Similar conclusions have been reached by other researchers, such as 

Wesley et al., at NTS/Structural Mechanics Associates. It was concluded for reinforced concrete 

containments that temperature effects are primarily limited to steel material properties. 

If temperatures were developed in the range of 370 ̊ to 427 ̊C (700 ̊ to 800 ̊F) and existed long 

enough to heat up the embedded rebar or tendons, ultimate pressure capacities would be 

dramatically reduced because of degradation of the modulus and yield strength of the steel 

elements. With regard to liner tearing and leakage, the effect of temperature can delay tearing 

until slightly higher pressures, but at temperatures of 204 ̊C (400 ̊F) and below, it is generally 

believed that the effect is not enough to change the characteristic of leakage before catastrophic 

burst for gradual pressurization. Once liner yield is reached during pressurization, the global 

structure strain would need to be approximately 0.2% larger with a 204 ̊C (400 ̊F) temperature to 

cause the same global liner strain that would occur without temperature. The effect of 

temperature on leakage pressure predictions is easily handled by incorporating temperature 

distribution into a global containment analysis such as that recommended herein. 

As described earlier, until recently, the NRC/SNL containment research program did not focus 

heavily on the application of temperature as a severe accident loading condition for the 

containment structures. (Testing of seals, gaskets, electrical penetration assemblies, personnel 
 127 

airlocks and equipment hatch models were conducted at temperatures associated with severe 

accidents.) But as an off-shoot of the 1:4 Scale PCCV test work and post-test analysis, NRC/SNL 

participated in the International Standard Problem (ISP 48) on containment integrity and 

providing assistance to NEA/CNSI in distributing data and interpretations from the PCCV model 

test to participants in an analysis exercise [79]. The main focus of the workshop was to take first 

steps toward addressing fundamental questions about temperature effects on PCCVs that were not 

addressed in previous research programs, namely: 

a. With the addition of temperature, would the onset of leakage occur later in the pressure 

history and, possibly, closer to the burst pressure? 

b. How would including the effect(s) of accident temperatures change the prediction of 

failure location and failure mode? 

Two thermal analysis cases (Figures 88 and 89) were selected as representative challenges to 

typical containments: 

• Case (1) a Saturated Steam Condition, basically, adding a temperature to each pressure 

step from the original PCCV pressure analysis, and 

• Case (2) an accident safety case, essentially a Station Blackout scenario, with a hydrogen 

burn at about 4-1/2 hours into the event. 

The thermal-mechanical analysis was approached in two steps: 1) add temperature to the 

mechanical solution without consideration of material property degradation due to temperature, 

and 2) temperature and material property degradation. Analysis results were presented for these 

cases individually to gain better understanding of the behavior differences and the causes of 

failure, when temperature is introduced. The primary tool for the ISP Exercise was axisymmetric 

modeling, so while the temperature behavior discussions emphasize global behavior, the effects of 

temperature on local behavior were also examined. 
 128 

ISP 48 Phase 3, Case 1, Loading

0.00

50.00

100.00

150.00

200.00

250.00

0.00 10.00 20.00 30.00 40.00 50.00

Time (m)

Temperature (C)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Pressure (MPa)

Temperature Pressure

Figure 88 ISP 48 Phase 3, Case 1 Loading and Temperature 

ISP 48 Phase 3, Case 2, Loading

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.00 600.00 1200.00 1800.00 2400.00 3000.00 3600.00

Time (m)

Temperature (C)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

Pressure (MPa)

Temperature Pressure

Figure 89 ISP 48 Phase 3, Case 2 Loading and Temperature 
 129 

The following procedures and assumptions are recommended for thermal analysis of concrete 

containments. 

1. Perform a Heat Transfer analysis. (In some programs like ABAQUS, this means all elements 

relevant for thermal analysis need to be changed to diffusive heat transfer element types which 

only have temperature degrees of freedom.) 

Thermal boundary conditions are imposed at the outer surface of the cylinder and dome wall 

consisting of “free convection with air. The heat transfer coefficient, h, varies with temperature 

according to the following relationship: 

1/ 3 h = 0.00382(ΔT) lbf/in-s-oF (T in oF) for a full scale containment analysis, 

The boundary condition on the basemat foundation consists of heat conduction with soil with a 

sink temperature. An example of a heat transfer coefficient developed for the horizontal surface 

of the foundation in contact with soil is: 

5 5.76 10− h = x lbf/in-s-oF for a full scale containment. 

For Temperature Case 2, a steady state heat transfer analysis step would precede a dynamic heat 

transfer analysis with the time history temperature input. The steady state heat transfer step is 

used to bring the model up to an ambient/operating temperature of 25o

C. Figure 90 shows the 

location of the prescribed thermal boundary conditions for the axisymmetric model of the PCCV. 

Axisymmetric Model CL

Nodal 

Temperature BC

(Time History Input)

Free Convection BC

(Air, T=25) f,

o

∞

Conduction BC

(Soil or Concrete, T=25) s,

Figure 90 Axisymmetric Model Thermal Boundary Conditions 
 130 

A literature review was conducted to develop reasonable concrete thermal properties, and for 

degradation of concrete and steel material properties. References [116] through [123] proved 

useful in support of this study. Though there are scores of publications on these subjects, the 

references cited are considered to be a reasonably representative sample of the general literature. 

A summary of conclusions that were found relevant to concrete containments is as follows. 

Density 

Use the average density of the concrete. For the PCCV at the time of construction was 

reported as 2186 kgf/m3

 for the nominal 300 kgf/cm3 (used in the basemat) and 2176 

kgf/m3

 for the nominal 450 kgf/cm3 (used in the tendon gallery, wall and dome). Using a 

nominal 2% by volume of reinforcing steel and other embedments, a nominal value of 

2290 kgf/m3

 was used for the PCCV thermal analysis. 

Specific Heat 

Specific Heat of ordinary concrete at normal temperatures can vary from: 0.50 to 1.13 

kJ −1 −1 kg K . A value of 0.879 kJ −1 −1 kg K was used in the analysis of the PCCV 

model. 

Generally it is assumed that changes in aggregate, mix, and age do not have a significant 

effect on this, but moisture content does have a significant effect. Reducing moisture 

content from 25 to 12.5% by volume can reduce overall specific heat by 25%; the authors 

have assumed moisture content in the containment wall will be relatively low. At high 

temperatures, specific heat can go up considerably, approximately doubling from 150oC 

to 500oC; however, the authors assumed a constant value of specific heat since the very 

high temperature is of relatively short duration. 

Thermal Conductivity 

Assuming igneous amorphous aggregate leads to the following: 

Thermal conductivity 1 1 1.0 1.6 − − = − Wm C (1.4 Wm-1 C-1 was used in the analysis.) 

This is not significantly variable with temperature, but tends to decrease by ~10% to 30% 

between 20oC and 200oC. 

Thermal Spalling of Concrete 

Thermally induced spalling may occur in either quiescent or violent fashion, and the 

probability increases at higher heating rates. A primary cause of this is moisture content; 

the greater the moisture the greater the spalling potential. High steel reinforcement ratios 

can also increase spalling potential. 

Strength 

Significant reductions in strength occur when T>300oC, and at 690oC, strength can be 

assumed to reduce by about 80%. On reaching this conclusion, it is noted there is a lot of 

scatter in experimental results, owing to different test conditions and to the composition 

of various concretes and aggregates. But for conventional aggregates, the following 

observations have been made: 

• between 80 and 90oC reductions range from 10 to 35% 
 131 

• between 90 and 200oC, compressive strength ranges from continuing decrease to even 

slight increase. 

• from 200oC and higher, there is continuous decrease. 

• rich mixes show greater reduction in strength 

• different water-cement ratios have little effect 

• there is also a significant time of exposure factor 

• there is some specimen shape and size effect. Small specimens lose more strength 

than large ones. 

• Poisson’s ratio also drops from about 0.2 to 0.1 at 400oC 

• tensile strength decreases showed similar trends as the compressive strength 

decreases 

• modulus of elasticity reductions also showed similar trends as strength losses, but 

overall reductions are less. Tends to follow the square-root relationship commonly 

used. 

The choice of generic properties to use for analysis has been based on an approximate 

“median” of literature data; a smooth curve for strength degradation versus temperature 

was estimated below and plotted in Figure 91. 

Concrete Strength Ratio, 1.8 S exp (T / 632) Rc

− = where T is in degrees C. 

Further, in lieu of more precise data, it appears reasonable to continue to base the 

modulus on the standard ACI formula: E = 57,000 fc′ (English Units) such that a 

Modulus Reduction Ratio can be defined as: 

2

1

( Rc) M R = S

It should be noted that the peak strain at which the concrete compressive strength limit is 

reached also shifts with increasing temperature. While at 25C, this strain is 

approximately 0.002, it can reach two to three times this value at high temperatures. 

Temperature variation of steel is also important for the highest temperatures. This 

variation has been idealized based on curves provided in the literature: 

Steel Yield Strength Ratio, 1.9 = exp (( − 340)/ 300) − S Rs T where T is in degrees C. 

S Rs = 1.0,T ≤ 340C

For steel, the Young’s Modulus follows the yield strength one-to-one, rather than the 

square-root relationship found in concrete. The steel yield strength reduction is shown in 

Figure 92. 
 132 

Figure 91 Concrete Compression Strength Ratio vs. Temperature 

Figure 92 Steel Yield Strength and Modulus Ratio vs. Temperature 
 133 

4.5 Recommendations for Prototype Containment Capacity Estimates 

4.5.1 Current Practice 

Standard Review Plan Sections 3.8.1.II.4.j provides general guidance for determining ultimate 

capacity of concrete containment. It requires that a licensee submit a report to the NRC providing 

details of the analysis, failure design criteria, and behavior of the liner under postulated 

conditions. ASME Section III, Division 2 does not provide any guidance for determining ultimate 

capacity of containment. IPEs of different plants use differing criteria for determining the 

ultimate capacity and probability. Neither the SRP nor ASME Code provide specific guidelines 

for determining containment ultimate capacity. 

For concrete containments, a few of the plants’ IPEs followed a methodology developed by EPRI 

and ANATECH in the late 1980s, early 1990s, which provided a framework not only for making 

deterministic failure prediction analysis, but also extended these results to a PRA framework, 

compatible with NUREG-1150. These procedures, covered in detail in [98], are summarized here 

in an attempt to identify ‘what we do know and don’t know’ about containment failure/leakage 

prediction. 

A deterministic leakage prediction criterion was postulated based on the fundamental assumption 

for concrete containments that quasi-static pressurization would lead to a leakage rate that is in 

equilibrium with the gradual pressurization rate. But this criterion does not provide information 

on the effect of rapid pressurization on failure sequences and the evolution of failure modes, or 

the conditional probability of the catastrophic burst (ultimate) failure mode. All of these scenarios 

were presented in NUREG 1150 along with NRC’s direction to plant owners that they needed to 

be considered in the IPEs. 

An EPRI deterministic leakage prediction methodology provides guidelines for global 

axisymmetric analysis, and local strain concentration factors near stiffness discontinuities such as 

thickened liners, penetrations, and liner anchorages. It was developed using detailed local 

analyses and the body of experimental research described in Chapter 2. Along with predicting 

where liner tears would occur, a formula was adopted for quantifying liner tear size (leak area) 

[56, 57] as shown in Figure 48. So these guidelines estimate where liner rupture can occur and at 

what pressure levels. This implies that rapid pressurization could trigger more than one failure 

location with the possibility of exceeding (at elevated pressures) the definition of leakage, defined 

to be a leakage path with a depressurization time of two hours or greater (NUREG 1150). (For 

depressurization within two hours, the containment is defined to experience either rupture or burst 

failure.) Within the context of NUREG 1150 for severe accident risk evaluation, a containment 

failure criterion is meaningful only in a probabilistic sense. 

Extending the methodology to PRA, the process of predicting failure locations was separated into 

two parts: 1) identifying and quantifying the probabilities associated with locations with large 

peak strains, and 2) determining relative probabilities between leak size categories defined by 

assigning specific leak areas to individual liner tears. 

The EPRI Probabilistic Leakage Prediction Methodology (PLPM) developed assigned 

randomness and uncertainty ranges to the ability to predict global liner strain, strain concentration 

factors, and liner strain failure criteria. Applying these, and assuming lognormal distribution of 

the parameters, determined the probability of failure at given locations. Then these probabilities 

from all locations were combined and this determines the probability of a total leak area 

exceeding a particular size as defined in NUREG 1150. Three leak area cutoffs are designated: a 

slow leak characterized by a flow area less than 0.1 ft2

 (subsequently revised to 0.3 to 0.5 ft2), a 
 134 

moderate rupture of flow area greater than 1 ft2

, and a catastrophic rupture characterized by a flow 

area of 10 ft2

. The probabilities of liner tears at possible locations are combined to determine the 

total size of flow areas, within a probabilistic framework. For example, an equipment hatch may 

have four possible tear initiation points (at locations symmetric around the penetration). If the 

area of a single tear is 0.09 ft2

, then one tear would create a flow area defined as a leak. However, 

if several of these tears and tears at other penetrations (or ‘hot spots’) occurred, the flow area 

would reach more than 1 ft2

, which is a rupture. Clearly, the probability that at least one tear will 

occur is higher than that of many tears occurring, and algorithms for calculating probabilities of 

multiple tears were developed based on standard probability theory. 

In the EPRI work, the liner tearing and leakage prediction methods were demonstrated by 

application to two large dry concrete containments, chosen to be typical of a prestressed and a 

reinforced concrete US containment. (These examples are shown in Figure 44 earlier in this 

report.) These predictions and the log normally distributed variations on these predictions are 

then combined and ‘binned’ as conditional probabilities that a leakage, rupture, or catastrophic 

rupture occurs, given that a leak of any size has already occurred. At low pressures, small leakage 

is the dominant mode and so has a conditional probability of nearly 1.0. At high pressures, only 

reachable by rapid pressurization which may leapfrog the leakage mode, rupture conditional 

probability eventually surpasses leakage. This should not be confused with probability of failure; 

this is entirely separate as shown in Figure 93. This is simply the probability of the first liner 

tearing occurring. One way of visualizing the relationship between failure probability and the 

conditional leakage/rupture calculation is by plotting, as shown in Figure 94. The plot represents 

the probability of a leakage, rupture, or catastrophic rupture mode, given non-occurrence of the 

other modes. In the physical sense, the non-occurrence of modes other than small ‘leakage’ are 

attributed to rapid pressurization. 

To apply NUREG 1150, some simplifying assumptions are made: 1) any pressurization scenario 

must be categorized as either gradual or rapid pressurization. More research would be required to 

characterize these, but for simplicity in the IPEs, it was postulated that general pressurization after 

vessel breach is slow, but steam explosion or hydrogen detonations are rapid; 2) for slow 

pressurizations, all event tree sequences end in leakage – for all other pressurizations, the 

conditional probabilities of leak, rupture, or catastrophic rupture are used. 
 135 

Figure 93 Combined Probability of Liner Tear by PLPM Software for the Reinforced 

Concrete Containment Example 

Figure 94 Probability of either Leakage, Rupture, or Catastrophic Rupture Occurring 

given that failure has occurred for Reinforced Concrete Containment 

In reviewing this methodology now 15 years after it was developed, it is clear that some liberal 

doses of engineering judgment were required to develop the PRA assessments using the limited 

data available, and the work heavily relies on the concept of equilibrium leakage, which may not 
 136 

yet have consensus within the industry. Nevertheless, the methodology does provide a framework 

for PRA for containments that allows implementation of sophisticated, deterministic containment 

response analysis, and so in the author’s opinion is an advancement over containment failure 

prediction based solely on expert elicitation and hand calculation. What is needed to increase the 

reliability of the method is significantly more data quantifying the development and growth of 

liner-tear/leak-areas after initial liner tear occurs, and how the size of these tears relate to total 

leakage in the containment. A peer review of the procedure and an expert elicitation of the 

lognormal distribution parameters would also seem appropriate. Neither the SRP nor the ASME 

Code provide specific guidelines for determining containment ultimate capacity. 

4.5.2 Recommendations for Design and Performance 

With the inception of the idea of equilibrium leakage, especially for concrete containments, most 

groups have focused on the prediction of the onset of liner tearing as the “failure performance” 

criteria for containments. They have accomplished this by improving and refining advanced 

structural analysis techniques, and computing very localized liner strains with greater and greater 

precision. However, to our knowledge, these studies have not included fracture mechanics 

refinements to estimate crack size and trajectory. These exclusions are due to the complexity of 

the liner-concrete-anchorage interaction. 

As described in an earlier discussion, the fundamental gap in knowledge for estimating release 

risks during loss of coolant accidents is in estimating leak areas and leakage rates. In order to 

interface with regulatory requirements, leak areas and leakage rates must eventually be addressed. 

Some preliminary work has been conducted in this area by different groups. But the subject of 

estimating leak rates through liner tears and cracked concrete is particularly complex. 

Nevertheless, based on existing work in this area, some fundamental conclusions can be drawn 

regarding leakage through cracks in concrete containments. In most cases, if liner tearing occurs 

in a region experiencing far-field rebar yield, leakage rates can be assumed to be governed by the 

liner tear aperture itself. This will not be greatly affected by any obstruction to the leak path posed 

by the concrete. Such a conclusion is supported by experiments performed. At the University of 

Alberta, EPRI leak rate experiments, and leak rate measurements taken form the SNL 1:6-scale 

model. 

To illustrate this further, for a concrete containment undergoing global hoop strain of 0.5% at the 

barrel mid-height (still well within its ultimate barrel capacity) and using a concrete cracking 

strain of 100x10-6, the sum of all the primary crack widths around the circumference of the barrel 

of 45.7 m (150-ft) diameter containment is. 71cm (28 in). At 1.3% strain, as was the case when 

the 1:6-scale containment liner tears occurred, the sum of concrete crack widths in a full-scale 

containment is. 1.8 m (72 in). Once the liner tears at far field strains of this magnitude, it is clear 

that the leak paths through the concrete will be quite large and the obstruction to flow through the 

concrete will be negligible in comparison to the throttling of flow through a small liner aperture. 

With the EPRI approach described earlier, approximate leak area and leak rate prediction rules 

have been established based on the Canadian tests, an EPRI test, and the 1:6-scale containment 

measurements. 

Areas where further work is needed to link the Containment Capacity research to design practice 

include: 

• Liner welding rules and anchorage details and their role in containment performance 
 137 

• Containment performance in terms of leak rate in a format useful for PRA work that can 

be used for IPE and system analysis. 

4.5.3 Recommendations for Containment Capacity Analysis 

Detailed guidelines for developing finite element models of steel and concrete containments are 

provided in the Appendix, but a general discussion of recommendations for containment capacity 

analysis is provided here. 

The analyst should be focused on making a best estimate prediction. Consistent with the 

supposition that leakage is not likely prior to the onset of general yielding, some methods can be 

eliminated as candidates for predicting containment performance. For instance, a failure criterion 

often used in the past is based on rupture occurring at general yield of 1% strain. Simple 

axisymmetric models, either finite element or closed form formulations, could be used in 

conjunction with such a failure criteria. But such simplifications may tend to underestimate the 

rupture pressure and provide conservative predictions of maximum pressure capacity. 

4.5.3.1 Steel Containments 

In order to evaluate shell rupture, at least two structural models, one including an equipment hatch 

or a personnel airlock and one modeling the general shell behavior is necessary. It has been 

learned that it is important to include details of any local breakdown in the membrane action of 

the shell or stiffeners. In the 1:8 scale steel model, for example, the strength of the stiffeners was 

reduced by an eccentricity in the stiffener pattern around the equipment hatches, which caused 

primary bending in the stiffener. As a result, when the stiffener failed, the load was transferred 

into the shell, and the shell failed at a lower pressure than expected. When the analytical program 

is considered, the analyst needs to identify eccentricities and other small details that affect the 

capacity and the failure mechanism of in-service steel containments. 

Ensuring that the model has been properly discretized depends largely on the analyst’s ability to 

anticipate the type of behavior (i.e., membrane action, bending, shear, etc.) that will occur in any 

given location. In this respect, a thorough understanding of the differences in element 

formulations is needed. For example, bending occurs at discontinuities such as intersections 

between penetrations and pipes and the containment shell. It occurs where there are changes in 

the shell geometry and thickness. 

The analyst must exercise considerable engineering judgment in constructing the model and 

discretizing a finite element mesh. The element choices must be assessed by verifying that the 

solutions do not violate fundamental mechanics (for example, force equilibrium), and perhaps 

even with sensitivity studies with element size and order as the parameters. 

Predictions for leakage from pressure seating equipment hatches can be based in part on the same 

three-dimensional model of the shell and equipment hatch used in the analysis for rupture. In 

order to accurately predict ovalization of the sleeve, the stiffener pattern around an equipment 

hatch must be modeled explicitly. 

4.5.3.2 Concrete Containments 

Calculations show that substantial hoop cracking can occur in a reinforced concrete containment 

between 70% and 90% of the design pressure, depending on the percentage of steel. Therefore, a 

reinforced containment, unlike a prestressed containment, will experience extensive cracking 

before the design pressure is reached. When a reinforced containment cracks, the main 
 138 

reinforcement is stressed only to approximately 30% of its yield, whereas tendon reinforcement in 

a prestressed containment is at 80% or 90% of yield when the concrete cracks. 

This, combined with the fact that conventional rebar has greater ductility than prestressing 

tendons, gives reinforced containments an after-cracking pressure capability range that is 

significantly larger than in prestressed containments. This implies that leakage before catastrophic 

rupture is more likely to occur in a reinforced containment than in a prestressed containment. 

On the other hand, some typical details of prestressed containment designs include stronger liner 

anchorages and more severe stiffness discontinuities than in reinforced containment designs, as 

evidenced by the EPRI-sponsored Construction Technology Laboratories (CTL) specimen test 

series. Therefore, with the site specific nature of containment designs, it is not possible to 

generalize what pressures cause leakage in prestressed containments as compared to reinforced 

containments. The relative behavior of the two containment types can be summarized by Figures 

95 and 96 that show the stress-strain behavior of the primary load carrying elements for reinforced 

and prestressed concrete containments, respectively. 

The liner and rebar behavior is basically the same in both cases except that, in the prestressed 

case, the liner and rebar stresses remain compressive until approximately 1.4 times the design 

pressure (shown as 1.4 DP on Figure 96). The significance of the figures lie in the relative 

positions of the liner yield range versus the yield range of the primary load carrying components 

and the ultimate strain capacity of the materials. The S-shaped curves shown represent the general 

shape and relative location of the expected probability of leakage and probability of catastrophic 

rupture curves. 

After liner yielding, the probability of leakage becomes significant due to liner strain 

concentrations. It should be noted that it is not until much larger global strain (and pressure) that 

the probability of catastrophic rupture becomes significant. And in conjunction with this, if the 

failure pressure is approached from below in quasi-static fashion, the range of pressure needed for 

catastrophic rupture might never be reached. 

There are two major issues involved in developing the finite element models for concrete 

containments: determining what geometric detail of a containment need to be represented and 

establishing proper mesh discretization. Here again, the models need to be consistent with the 

failure criteria and the analytical methods that are adopted. 

In a global analysis (such as a global axisymmetric or 3D analysis) it is not necessary, nor is it 

recommended, to predict liner strain concentrations across cracks or at liner embedment 

discontinuities. These strain concentrations are predicted with special local techniques rather than 

in a global model. In the main wall and dome regions, use of 8-node elements with quadratic 

displacements along element sides allows relatively large element spacing. For cracking analyses, 

higher order elements with lower order integration (i.e., 8-node quadrilaterals with 2x2 

integration) are preferred because of their superior numerical behavior under cracking conditions. 

Finer element integration typically leads to poorer convergence characteristics because of the 

significant increase in unique cracking states that can occur in any given element. 
 139 

Figure 95 Idealization of Reinforced Concrete Containment Behavior 

Figure 96 Idealization of Prestressed Concrete Containment Behavior 
 140 

The modeling of rebars in a finite element code varies widely from code to code. Displacement 

compatibilities between the rebars and the concrete require that the rebars be represented by the 

same displacement shape functions as the continuum element in which they reside. This is not 

generally observed in all computer codes. Another difficulty is the translation of rebar drawings to 

computer code input. For 2D axisymmetric grids, rebar modeling is relatively straightforward. 

However, for 3D continuum analysis, the rebar arrangements are very complex. As such, it is 

virtually impossible to develop computer input without preprocessing software. 

The present state of the art of modeling and analysis of concrete structures consists of finite 

element computer codes in which: (a) plain concrete and steel reinforcement are modeled as two 

materials joined together as structural elements; (b) plain concrete material models account for 

compressive plasticity and tensile cracking (smeared over the element) with post-cracking tension 

stiffening and shear retention capabilities; or (c) reinforcement is treated as simple tensioncompression members fully bonded to the concrete. 

Accurate predictions of the threshold environment for leakage or failure of a concrete containment 

requires accurate calculation of post-yield response. Nonlinear 3D calculations for the structural 

response are also necessary for local stiffness discontinuities and penetrations if liner tearing and 

leakage is to be accurately predicted. Methods for performing such analyses will almost certainly 

require the use of sub-models of local regions rather than 3D analysis of entire containments. 

Local sub-models can be driven by boundary conditions generated from coarse global analyses. 

These boundary conditions need to include the effects of the interaction of the penetration, or 

discontinuity with the free field structure. For example, penetration regions have been observed to 

move less radially outward than the free field, causing out-of-plane relative motion between the 

penetration and the free field. 

Other more detailed guidelines may be found in the Appendix. 

4.6 Conclusions from Containment Model Tests 

Some general conclusions on predicting containment behavior can be made from the series of 

containment vessel model tests that were described in Chapter 2: 

• Although establishing a generic margin of safety was not the purpose of the SNL 

program, the steel models have pressure capacities on the order of 4-6 times the design 

pressure [46]. The reinforced concrete models have pressure capacities significantly 

larger than the design pressure. The margin to failure, on the order of 2.5 to 3.5 times the 

design pressure, is lower than in the steel containments. 

• Global, free-field strains on the order of 2-3% for steel and 1.5 to 2% for reinforced and 

0.5 to 1.0% for prestressed concrete can be achieved before failure or rupture. 

• Model (and presumably prototype) capacities are limited by high strains arising at local 

discontinuities which are present in both the model and the prototype. 

• In the absence of a ‘backup’ structure, steel containment model capacities tend to be 

limited by gross structural failure or ‘rupture’. (The 1:10-scale NUPEC steel model 

developed a tear and leaked after the model had apparently made contact with the 

surrounding shell.) Due to the inherent structural redundancy of the liner and concrete 

system, steel lined concrete containments appear to be limited by functional failure 

(leakage). While the behavior that leads to tearing of the steel vessel or the steel liner is 

similar, i.e. local exceedence of the ductility limits of the steel at geometric 
 141 

discontinuities, the subsequent response of the vessels differs due to the presence of the 

surrounding structure. It should be noted, however, that many tests conducted on 

concrete pressure vessels have, typically, used hydrostatic pressurization. (Often this 

decision is made because of the likelihood of a liner tearing/leakage failure mode when 

using a steel liner). Hydrostatic testing significantly decreases the probability of a 

catastrophic rupture of the pressure vessel because sudden local expansions of a portion 

of the vessel results in a rapid drop in driving pressure. 

• It seems reasonable to assume that with the added complexity of the actual containments, 

there is a higher probability that these local strain risers are present in, and possibly more 

severe than in any of the models tested. As a result, the capacities of the model, can, at 

best, be interpreted as an upper bound on capacity of prototypical containments. 

• Analytical methods currently used are adequate to predict global response into the 

inelastic regime. One caveat on this statement is the discrepancy between predictions and 

observations of global yielding. Further investigation is required to understand the nature 

of this discrepancy (e.g. residual stresses, etc.) and its significance for calculation of 

prototypical containment capacities. 

• Prediction of local failure mechanisms are highly dependent on the experience of the 

analyst, on the availability of accurate as-built information (geometry and material 

properties) at discontinuities, and on fabrication processes. Even if this information is 

available (not typical for actual containments) the prediction, a priori, of local failures is 

at best an uncertain proposition. The large scale model tests have, however, educated and 

sensitized the community to the types of details which may be critical in limiting 

containment capacities, and, hopefully, have improved the reliability of the predictions. 

• These conclusions are predicated on failure of the containment structure. Any evaluation 

of the capacity of an actual containment must be based on the entire system, including 

mechanical and electrical penetrations and other potential leak paths. 

4.7 Issues for Future Consideration 

4.7.1 Leakage 

A great deal has been learned about containment behavior and containment analysis methods in 

the last two decades of containment research, but questions still remain. One of the most 

important behavior questions is that it is not known with certainty whether a leakage failure will 

reach an equilibrium state or if it will lead to a catastrophic failure. The arguments for each 

follow below. 

Equilibrium Leakage: For steel containments, testing has shown that equilibrium leakage 

will probably not occur unless the expanding vessel has a structural redundancy such as a 

"contact structure" as in the recent US NRC/Sandia SCV test. The equilibrium leakage 

concept for concrete containments first introduced in WASH-1400 [2] and related work 

has been covered in numerous reports over the last decade. With this in mind, a quasistatic pressurization failure scenario for concrete containments is as follows. As a 

concrete containment building (either reinforced or prestressed) begins to expand in 

response to quasi-static pressurization, liner strain concentrations occur at local stiffness 

discontinuities. The strain concentrations can be strong or weak depending on the type of 

discontinuity and the type of liner to concrete anchorage system. The strength of the 

discontinuity affects the level of global strain needed to tear the liner. These global 
 142 

strains have been found (from testing and analysis) to arrange from 0.2% (just above 

yield) to about 2%. With regards to the weakest discontinuities, 2% global strain is still 

well within the ultimate capabilities of the concrete containment reinforcement; thus, a 

liner tear is deemed to be almost certain to occur. Once the strain concentration causes a 

tear to initiate, the tear will not grow beyond the size required to maintain equilibrium 

between pressure increase and leakage. This is because: (a) the structure's residual 

stiffness at initial rupture is sufficiently large to restrain the liner from rapid expansion, 

and (b) the liner tearing is a stable fracture process due to the highly redundant crack 

arrest mechanism offered by the concrete backing. This leads to the conclusion that liner 

crack growth beyond the equilibrium leak area requires further pressure rise. 

No Equilibrium Leakage: The high pressure expulsion of molten material from the 

reactor vessel, the deflagration of combustible gases, and the rapid generation of steam 

through the interaction of molten fuel with water in the containment are phenomena that 

could lead to pressure rises in the containment over a period of a fraction of a second. 

While this pressure rise time is still effectively quasi-static, there is some concern that the 

rapid rise time would not allow large enough tears to develop. This would lead to a more 

severe failure of the liner. While the general consensus supports giving a high probability 

to the occurrence of leakage, for certain pressurization rates, more severe failure modes 

involving higher pressures may also be reached. 

4.7.2 Other Considerations 

Many aspects of containment integrity have still not been addressed in the various containment 

integrity research programs. Some of these topics are listed below: 

• The behavior of the containment under elevated temperature and pressure loads has not 

been thoroughly investigated. Most of the containment tests have ignored the effects of 

temperature on the material properties and thermal induced stresses associated with 

elevated temperatures. 

• The effect of aerosols within the containment atmosphere during an accident has not been 

investigated. Aerosols may plug holes in the containment that may lead to a higher 

pressure capability, but have the potential to change the mode of failure from a possible 

benign mode to a burst mode. This applies to unlined concrete containments and lined 

containments when the liner has failed. 

• Seismic loadings coupled with severe accident loads have not been investigated in any 

detail. 

• Liner-anchorage-concrete interaction is significant in determining how liners tear in 

concrete containments. These phenomena are still not fully understood. 

o Under what conditions will stud or other anchorage shear failure occur rather than 

liner tearing? 

o How is the failure mode of the liner-anchorage system affected by scaling? For 

example, it could be affected by the ratio of liner thickness to stud diameter and 

by membrane loading of the liner (before the development of high stud shear 

forces). 

o To what extent is the magnitude of liner strain concentrations affected by friction 

and bond between the concrete and liner? An example of this could be by 
 143 

differential radial motion at a major concrete crack, or by stud or anchorage 

spacing. 

o How is the magnitude of liner strain concentrations and the resulting tear length 

and trajectory affected by the size and shape of insert plates? What is the best 

way to extend the current analysis techniques to predict tear areas? 

Investigation and validation of methods for evaluating other potential failure modes is still 

needed. Shear failure is particularly difficult to evaluate; there is no generally recognized, reliable 

method of determining shear capacity of a reinforced concrete section under simultaneous 

application of tensile load and bending moment. Failure of large rebars where they are bent 

around penetrations, as occurred in an EPRI test [47], are also of some concern. The effects of 

cold working on the available ductility to these bars should be studied further. Rates of 

pressurization and effects of temperature must be considered in more detail. At high rates of 

pressurization, there is a possibility that sequential failure modes could occur; that is, for very 

high rates of pressurization, liner tearing may not arrest the pressure buildup within the 

containment, and another failure mode could occur at slightly higher pressure. This is the basic 

reason for emphasizing the development and validation of analysis methods. A reliable 

evaluation of containment performance must be based on careful, detailed analysis of the specific 

containment geometry and loading of interest. 
 144 

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This page intentionally blank 
 A-1 

Appendix – Containment Capacity Analysis Guidelines 

A.1 Introduction 

This Appendix provides guidelines which analysts may use in performing analysis to determine 

the capacity of containment structures to withstand loads beyond their design basis. These 

guidelines address only overpressurization in combination with elevated temperature, i.e. the 

scenarios associated with severe accidents. These guidelines come directly out of experience and 

lessons learned from the Sandia containment research program, both direct experience from 

Sandia (and contractor) analysis, and the shared experience of international participants in roundrobin analyses. 

In general, containment structural analysts need to develop a model that represents the geometry, 

structural details and material properties which are ‘important’ to the response regime being 

analyzed and to the goals of the analysis. With continuing advances in computational power, the 

trend (and temptation of analysts) may be to model containments with more elements, more 

detail, and more comprehensiveness than ever before. But there remain real limits on what the 

state-of-the-art in material models can simulate and, generally, very real limits on the 

experimental data which is needed for interpreting and verifying the quality of complex model 

representations. 

“Everything should be made as simple as possible, but no simpler!”- Albert Einstein 

Though cliché, this is still probably the best philosophy, but also the biggest challenge, for 

containment analysis. Any analysis effort should include at least the following four steps: 

1. Planning and identifying the goals of the analysis; 

2. Developing model(s); 

3. Calculating the response; 

4. Interpreting and checking the results. 

This Appendix is structured around these four key steps. And although the topics presented here 

are discussed separately, these overall tasks must also be well integrated. Failure criteria must be 

consistent with the geometric details in the model(s) and the physical phenomena (i.e., plasticity, 

large deformations, etc.) accounted for in the calculations. Failure criteria have been proposed, 

and calculation methods are described here, as well as the geometric details that should be 

considered to be consistent with the proposed criteria. It also must be decided how predictions 

for containment performance will be used, because this strongly influences choices of methods 

and modeling details. 

A.2 Analysis Goals and Planning 

The first step in choosing an analysis method is to ask how the results will be used, i.e. what 

question the analysis will answer or what decisions will be made based on the results. For most 

containment capacity analyses, the results will be used to answer questions regarding safety 

margins and may be used in Level 2 PRA analyses and risk-informed licensing decisions. 

The answer to this question affects selection of the tools and methods, which are important 

features of the work. For example, analysis of containments for the specified design loads can 
 A-2 

usually be done with elastic or mildly nonlinear analysis since the code-specified design limits on 

stresses are usually constrain the response to the elastic regime. But predictions of containment 

response to severe accidents or ultimate capacity typically require capabilities for simulation far 

into the nonlinear range of response. Both the load limits, in terms of pressure and temperature, 

and the modes of response or failure are important for severe accident risk assessments and 

emergency preparedness planning. For example, in the event of a severe accident, the 

consequences of an early containment failure typically are greater than those of a late failure and 

the consequences of rupture are worse than those of leakage. Since the elastic analysis methods 

used in design are well understood (note the near uniformity the Round Robin predictions of 

response in the elastic regime[32, 34, 42, 45, 74, 79]) and have been benchmarked against the 

experiments, this appendix will focus on methods of analysis for severe accident loading and 

capacity/failure mode predictions. It should also be noted that the level of confidence in analyses 

of the non-linear response or capacity of the containment is less, or conversely the uncertainty is 

greater, than design or elastic response analyses. 

Analysis planning and goals should be established as follows. 

a. Identify the loads to be applied. 

• Typically, severe accident containment loads consist of both transient pressure and 

thermal loading. 

• In some cases, the pressure transient may be considered independent of the thermal 

load because the peak pressure may not occur simultaneously with significant 

thermal loading. (See Section A.5.3 for guidelines regarding what constitutes 

“significant.”) 

• The transient nature of the pressure and thermal loading is usually ignored since the 

duration of the loading is usually longer than the period of the structure. As a result, 

static analysis methods are usually adequate. 

• While these simplifications are usually valid, the analyst should review their validity 

in planning the analysis approach. 

b. Conduct an initial “failure/vulnerability review”. 

• Identify potential failure locations and modes and the types of models needed to 

simulate them. 

• It is helpful to discriminate between functional failure modes, i.e. loss of containment 

integrity or leakage, which is generally progressive and structural failure modes 

which can occur rapidly. The primary value of discriminating between these modes 

of failure is in determining the risk significance of any given mode. Usually, this is 

beyond the scope of the structural analysis, but is important to the interpretation and 

application of the analysis results. 

• Failure modes and thresholds of ‘engineered components’ such as penetration 

assemblies, may rely on some level of analysis, but are typically determined by 

testing. This appendix focuses on recommendations for the analysis of the structure 

that comprises the primary containment boundary. 
 A-3 

c. Define the engineering significance of the failure prediction. For example, is the goal to 

determine the margin of safety between the design pressure and the pressure at which a 

loss of containment integrity occurs. 

d. Determine if the focus the analysis is on making a best estimate prediction or on a 

‘conservative’ lower bound estimate. Typically, containment analyses have been 

deterministic due to the complexity of performing detailed non-linear structural analyses. 

Estimates of uncertainty or probability of failure have been based on engineering 

judgment or multiple simplified analyses which are usually restricted to considering 

model parameter uncertainty. 

This last item has consequences on choices of material properties (i.e., using actual properties, 

when available, rather than design-spec properties, etc.), and choices on modeling parameters, 

such as friction, foundation spring stiffness, etc. 

It is crucial to not underestimate the importance of planning the analysis. The obvious, but often 

overlooked, fact is that only those features of the structure or modes of response/failure that are 

included in the model will be represented in the results. Experience has shown that the critical 

response or failure modes of the real structure are often not considered important or overlooked 

and not included in the model. As a result, analysis planning should also make use of judgment 

and experience on containment behavior. 

For example for a prestressed concrete containment, since it appears likely that measurable 

leakage will not occur prior to the onset of general yielding; simplified methods can be used to 

predict containment performance. A failure criterion based on an average hoop strain of 1 to 2 % 

appears reasonable based on the (limited) experimental data. Simple axisymmetric models, either 

finite element or closed form formulations, could be used in conjunction with such a failure 

criteria. While this method may tend to underestimate the rupture pressure, yet, it could be 

acceptable if it can be demonstrated that significant leakage occurs (past penetration seals, 

bellows, or isolation valves, for example) at a lower pressure. If leakage does not occur before 

general yielding, a method based on a simple model and failure criteria like that described above 

is not adequate. This is due to it not allowing for the possibility of leakage which can occur at a 

local tear, and preclude the occurrence of rupture. 

A.3 Simulation Code Selection 

Containment capacity analyses require the use of a robust, general-purpose finite element code. 

There are a large number of code that meet the basic requirements and the selection of a 

particular code often depends on features that make the development of the model, the definition 

of the material constitutive models and the analysis of the results more efficient and convenient 

for the analyst. 

It is not appropriate to recommend or endorse any particular finite element code in this report, 

however, the required or desirable features should include the following: 

• Solution algorithm appropriate for simulating nonlinear response 

• Suitable element library (including rebar for concrete containments) 

• Appropriate material models that work for all needed element types (either resident in the 

program, or having an interface for user-supplied models) 

• Capability to apply prestress (for a PCCV) 
 A-4 

• Numerically robust Contact Simulation (only for some specific modeling procedures) 

• Track record of performance for this class of problems 

More specific requirements on element types and material modeling are provided later in this 

Appendix. The last item, “track record of performance,” is included to stress the need to test 

finite element programs for new applications (at least new to the user). Sometimes, while a 

program may have theoretically sound published capabilities, in practice, it may prove difficult to 

advance solutions far into the nonlinear response range. 

A.4 Model Development 

A.4.1 Geometric Considerations 

One of the primary modeling decisions to be made is to determine the scope or extent of the 

simulation model and which elements of the real structure can be ignored or simplified without 

affecting the analysis goals. Decisions made in this step are a continuation of the model planning 

and goal setting, particularly the “failure/vulnerability review.” The geometric considerations 

which enter into this step include: 

a. Global versus Local models 

• Probably the most fundamental decision to be made is whether to construct a detailed 

global model which incorporates all of the relevant features of structure or a 

simplified global model which captures the global behavior combined with submodels to capture the local behavior. With ongoing increases in computing 

capacities and simulation codes that can take advantage of these capacities, there may 

be (is) a tendency or temptation to construct the most detailed, three-dimensional 

model possible. If these modeling capabilities are used judiciously this can provide a 

very accurate simulation, however, the potential complexities can often mask the 

underlying mechanisms and can also introduce model artifacts. 

• This decision is tightly coupled with the choice of a global or local failure criterion. 

It should be obvious that all failures initiate at the local level, but experience has 

shown it is much more difficult to identify and simulate local response, which is 

often driven or influenced by as-built conditions, than the global response of the 

structure. 

b. What structure “idealizations” can be made without loss of achieving analysis goals? 

• Typically small penetrations can reasonably be ignored in terms of their effect on 

overall containment response. 

• Typically basemat irregularities, such as reactor cavities or access tunnels for control 

mechanisms, can be ignored. 

• Typically, the gravity effects of containment internal structures and adjacent external 

structures can be ignored due to the high stiffness of the basemat. 

These last two simplifications should be carefully reviewed if a relatively flexible 

basemat is encountered. 
 A-5 

c. What symmetries in the structure can be exploited? If existing symmetries can be 

exploited, a finer mesh can usually be used than would be possible in a full, 3D model. 

• Bi-symmetric about one plane or Quarter-symmetry about two orthogonal planes? 

• Wedge or Sector symmetry, i.e. can a ‘slice’ or repeating sector (e.g. 30o) of the 

structure represent the response of the entire structure 

• Axisymmetric? A majority of the containment structures currently in use or proposed 

can be fairly represented by an axisymmetric model. This makes sense since a 

uniform shell is more efficient in resisting internal pressure than an irregular 

structure. The axi-symmetry of the containment is usually compromised, however, 

by constructability and operational considerations. Nevertheless, idealizing the 

structure as axisymmetric is usually possible and reasonable. Sources of nonaxisymmetric behavior include 

o Major openings (usually the Equipment Hatch and Personnel Airlocks) 

o Hoop tendon buttresses 

o Dome tendon layout (part of which is often rectilinear) 

o Basemat rebar layout (part of which is often rectilinear) 

It should be noted that apparent geometric symmetries can often mask underlying 

asymmetries in the structure, such as changes in stiffness associated with variations 

in reinforcing in concrete containments or local thickening or stiffeners in steel 

structures. 

d. Interaction with adjacent structures or components. 

• Is there a shield structure or other adjacent structure that could restrict containment 

“growth”? 

• Can the pipe penetrations and equipment supports accommodate differential 

movement (both radial and vertical)? 

As discussed in section A.4.1, there are two major issues involved in developing the finite 

element models: determining what geometric detail of a containment need to be represented and 

establishing proper mesh discretization. As part of the last two decades of Sandia containment 

research, many containments have been analyzed, and for the Sandia large scale model tests, 

many analyses were conducted by round-robin participants. In most cases, to complete a 

thorough set of predictions of behavior to overpressure, several different model types are 

developed and analyzed for each containment. These modeling decisions made for the Sandia 

Containment model tests are summarized in Table A-1. 
 A-6 

Table A-1 Summary of Analytical Model Types Used for Containment Studies 

Test Scale Shape R/t Press. 

Ratio 

Global Models Local 

Models 

Remarks 

SNL SCO 

(12/2/82, 

12/12/82) 

1:32 Cylinder w/ 

hemispherical 

dome 

450 

(R=549, 

t=1.22) 

0.93* Axisymm. 

SNL SC1 

(4/20-

21/83) 

1:32 Cylinder w/ 

hemispherical 

dome 

500 

(R=546, 

t=1.09) 

0.76* Axisymm. 

SNL SC2 

(7/21/83) 

1:32 Cylinder w/ hoop 

stiffeners and 

hemispherical 

dome 

478 (R=546, 

t=1.17) 

0.93* Axisymm. 

(8/11/83) 0.97* Axisymm. 

SNL SC3 

(11/30/83) 

1:32 Cylinder w/ 

penetrations and 

hemispherical 

dome 

478 

(R=546, 

t=1.17) 

0.83* Axisymm. 

SNL 1:8 

(11/15-

17/84) 

1:8 Cylinder w/ 

stiffening rings, 

penetrations and 

hemispherical 

dome 

448 

(R=2134, 

t=4.76) 

4.9 3D Sector 3D of Local 

Stiffener 

Detail 

NUPEC 

SCV 

(12/11/96) 

1:10 

geom./ 1:4 

thick. 

Improved BWR 

Mark II w/ 

contact structure 

135-161 

(R=2027-

2900, 

t=7.5-9.0) 

6.0 3D Sector 3D E/H 

SNL 

RCCV 

1:6 PWR: cylindrical 

concrete shell w/ 

steel liner and 

hemispherical 

dome 

13.5 

(R=3353 

t=248) 

3.2 Axisymm.; 3D 

coarse global 

(half symmetry) 

2D Wallbase 

juncture; 

3D E/H; 3D 

P/A 

PRETEST 

SNL 

RCCV 

1:6 “ “ “ 13.5 

(R=3353 

t=248) 

3.2 Axisymm. 3D of small 

penetration 

group 

POST-TEST 

Sizewell-B 1:10 Sizewell-B 8.6 2.4 Axisymm.; 3D 

coarse global 

(half symmetry) 

 

NUPEC 

PCCV 

NUPEC 

PCCV 

1:4 Large, dry PWR: 

2-buttress 

cylinder w/ 

hemispherical 

dome 

16.5 3.2 Axisymm.; 

3DCM 

3D E/H; 3D 

P/A; 

3D M/S 

Pen. 

PRETEST 

NUPEC 

PCCV 

NUPEC 

PCCV 

1:4 “ “ “ 16.5 3.6 Axisymm.; 

3DCM; 

3D-Shell 

3D E/H; 3D 

M/S; 3D 

tendon ring 

slice; liner 

rat-hole 

POSTTEST/SFMT 

*Design pressure not specified, maximum pressure (MPa) given.

The model types used include: axisymmetric, 3D global, 3D sector, 2D local, and 3D local 

models of various details. As evidenced from this work and the round-robin participant 

submittals, the minimum analytical assessment of containments is achieved with an axisymmetric 

model. (Some analysts choose to use a 3D sector model if the program used does not have a full 

suite of axisymmetric element types, but the analyses, and the results obtained are essentially 

equivalent.) Some argue that a 3D model is also needed to capture the non-axisymmetric features 

of containment response. Setting this minimum standard depends on how the results are to be 

used. 
 A-7 

A.4.1.1 Special Considerations for Steel Containments 

The overall geometry of steel containments ranges from relatively complex (e.g. BWR Mark I) to 

relatively simple (e.g. the free standing steel cylinder for a large, dry PWR). The modeling of the 

basic shell geometry is relatively straight forward. The primary considerations for modeling steel 

containments are the representation of transition regions (changes in basic geometry such as at the 

wall-base junction, the springline or knuckle regions or changes in shell thickness) that may give 

rise to bending stresses and discontinuities such as penetrations, supports and stiffeners. Some 

representative models are shown in Figure A-1. 

One fundamental question in developing the model of a steel containment is whether shell or 

solid elements will be used to represent the structure. Typically, shell elements are adequate for 

representing thin-shell steel structures. Certain discontinuities in the structure, however, such as 

local eccentricities or where other sharp gradients in strain occur, may require the use of solid 

elements. Usually, solid elements are only used where perceived to be necessary since there is a 

penalty, in terms of degrees of freedom, to be paid to achieve the resolution required. Thermal 

loading considerations may also dictate whether shell or solid elements are required. Shell 

elements do not have the capability of simulating steep thermal gradients through thick sections. 

Normally, the through thickness gradient is a less significant effect than the average increase in 

material temperature. 

The test programs illustrated the importance of including accurate representation of the details 

that may result in local breakdown in the membrane action of the shell or stiffeners. For 

example, in the 1:8-scale steel model, an eccentricity in the stiffener pattern around the equipment 

hatch was responsible for introducing primary bending into the stiffener. As a result, when the 

stiffener failed, the load was transferred into the shell, and the shell failed at a lower pressure than 

expected. Similarly, the ‘rat-hole’ detail in the hoop stiffener in the 1:10-scale NUPEC model 

resulted in a local strain concentration which resulted in a tear. The analyst needs to be sensitive 

to the presence of details that may introduce local strain concentrations and decide if these 

features are significant enough to include in the analysis. 

These features may be included in a single model, but more commonly a simplified 

representation of the structure is used to analyze the general shell behavior and sub-models are 

used to investigate local discontinuities. Each approach has advantages and disadvantages. A 

detailed, comprehensive model may require some level of simplification to manage the model 

size while the boundary conditions for sub-models may reduce the accuracy of the model if not 

applied properly. 

Typically, it is not practical to include highly localized details, such as local weld geometry (and 

associated variations in material properties for the weld metal and heat affected zones), even in 

sub-models, although tests have shown that failure may initiate at these locations. Similarly, 

since most steel containment structures are not stress relieved after cold work (rolling or forging), 

there may be considerable residual stresses which are not represented in the finite element 

models. These effects are usually addressed in the interpretation and evaluation of the analysis 

results and in the selection of failure criteria. 
 A-8 

intersection of steel shell and concrete basemat

Figure A-1 Examples of Steel Containment Models [97] 

Predictions for leakage from operable penetrations such as pressure seating equipment hatches 

can be based in part on the same three-dimensional model of the shell and equipment hatch used 

in the analysis for structural response. The results of these analyses are typically used in analytic 

solutions of bolt and/or seal behavior or compared to empirical results. In order to accurately 

predict ovalization of the sleeve, the stiffener pattern around an equipment hatch must be 

modeled explicitly. The technique of “smearing” local stiffening details is limited application to 

analyses of global behavior and cannot be used to obtain accurate predictions of leakage from 

ovalization of pressure seating equipment hatches. 

Cherry and Smith [18] and Petti and Spencer [97] provided additional consideration for modeling 

of steel containments subjected to corrosion damage. Their recommendations on failure criteria 

should be applied judiciously, however, since the purpose of the analyses were to demonstrate 

how analyses could be used to estimate the effects of damage and were not benchmarked against 

actual test data. 
 A-9 

A.4.1.2 Special Considerations for Concrete Containments 

The composite nature of reinforced concrete structures requires considerations beyond those for 

steel containments when developing the model geometry. In addition to representing the visible 

dimensions of the structure, the model must also be capable of accurately reflecting the embedded 

features of structure, primarily the pattern of reinforcing. Prestressed (or posttensioned) 

reinforcing adds further complexities if accurate modeling of variations in loading and anchorage 

details are considered to be important. Since all operating US plant with concrete containments 

include a steel liner, the anchorage and stiffening details of the liner are also important. These 

geometric considerations are closely coupled with selection of element type and constitutive 

material models. For example, finite element codes offer the capability of modeling the 

reinforcing as ‘smeared’ with the concrete, embedded in the concrete element or modeled 

discretely as separate elements. Fortunately, the experimental evidence suggests that many of 

these details ado not have a significant effect on the limit states of the containment. 

Unfortunately, because of the large variety of details used in construction of even geometrically 

similar containments, it is not always obvious which of these details can safely be ignored. 

Because the details associated with the component materials can be quite complex, most analysts 

are required to choose which details they will include, simplify or ignore, depending on the 

postulated modes of response and or failure. Predicting loss of containment function in concrete 

containments generally requires that leakage be predicted, or at least not overlooked as the 

pressure-temperature demand increases.. The experiments suggest that generalized liner yielding 

is a necessary condition for liner tearing to occur if there are no construction or material defects. 

Once generalized yielding occurs, the initiation of tearing in the liner is dependent on the strain 

concentrations associated with local details. Recognizing when liner tearing occurs, however, 

may be problematic because the criteria for liner material failure are dependent, in part on the 

element size. 

The experiments also suggest that cracking of the concrete may be a precondition for liner tearing 

and especially large, i.e. wide, cracks may initiate tearing in the liner by concentrating the strain. 

At high pressures, cracking-induced liner-anchorage-concrete interaction is similar in both 

reinforced and prestressed containment structures even though it is initiated earlier in reinforced 

structures. As the concrete cracks, the liner begins to deform plastically, generally earlier in 

reinforced containments than in prestressed containments. A comparison of event sequences in 

reinforced concrete versus prestressed concrete containments was illustrated in Figures 88 and 89. 

While the experiments are not, conclusive on this matter, they suggest that some attention be paid 

to these mechanisms. 

It should be noted that, again based on the experiments, the leak rate does not appear to depend 

on whether the concrete is uncracked or cracked. Apparently, even relatively intact concrete 

contains enough shrinkage cracks or other leak paths that the flow of gas is not significantly 

impeded. This appears to be true whether the concrete is posttensioned or not. The conclusion 

from this discussion is that simulation of discrete cracks is probably not important for steel lined 

concrete containments. The significance of generalized cracking for containment analysis is 

primarily the loss of stiffness, which affects the global strains which lead to tearing of the liner or 

rupture. 

This is not true for unlined concrete containments used outside the US, notably in France. For 

these containments, the prediction of concrete cracking and the character of these cracks are 

essential for simulating containment performance. This may also become important for future US 

nuclear power plants if unlined concrete containments or ‘confinement’ structures are proposed. 
 A-10 

Liner tearing, under quasi-static pressurization, will probably manifest itself as leakage, if there is 

residual structural strength in rebar and tendons. If significant tearing and leakage of the liner 

does not occur, as the pressure and global strains increase, perhaps rapidly, the probability of 

catastrophic rupture becomes more significant. 

A.4.1.3 Element Types for Concrete Containments 

a. Concrete is typically modeled with continuum elements. In 2D planar or axisymmetry, 

8-node (quadratic edge) continuum elements, but reasonable accuracy can also be 

obtained with a finer mesh using 4-node (linear edge) continuum elements. In 3D, 20-

node (quadratic edge) or 8-node ‘brick’ elements are recommended. 

b. In concrete elements which crack at the finite element integration points, it is best to 

select elements with reduced integration, as long as appropriate care is taken as to meshsize and to control of numerical issues such as ‘hour-glass.’ (These issues are beyond the 

scope of this guidelines appendix, but are usually well covered by the theory manuals of 

finite element programs.) The reason for this is improved convergence characteristics 

once cracking begin to develop. 

c. An axisymmetric liner should be modeled with two-node or three-node shell elements 

(whatever is compatible with the adjoining concrete elements), and beam elements can be 

used for representing liner angle anchors or stiffeners. In most models except for those 

studying very localized effects of liner/concrete interaction, the liner is considered to be 

fully bonded to the concrete. In 3D models, the liner should be modeled with 3D shell 

elements. (It should be noted that for the original designs, the liner was generally ignored 

in analysis.) 

d. smeared rebar sub-elements should be used to model reinforcement. Such elements 

assume strain compatibility between rebar and concrete. 

e. Smeared rebar sub-elements can be used to model tendons for global axisymmetric 

analysis of a P/C containment. (In an axisymmetric analysis, strain compatibility of hoop 

tendons is automatic, but with meridional tendons, the analyst has a choice of modeling 

tendons as ordinary rebar, or as separate truss elements external to the grid and attached 

to the grid with linkage elements. (Extensive study of axisymmetric analysis for the 1:4 

PCCV did not show good ‘return on invested labor’ (in terms of improved accuracy) for 

modeling vertical tendons with explicit elements that could slide relative to the concrete. 

A different conclusion was reached, however, for 3D local models targeting 

circumferential variations related to hoop tendon behavior; such analytical goals require 

special treatment of prestressing tendons with separate elements tied to the concrete, but 

also allowed to slip and have different hoop strain than the neighboring concrete.) 

A.4.1.4 Mesh Size 

Properly discretizing the model depends on the analyst’s ability to anticipate the type of behavior 

(i.e., membrane action, bending, shear, etc.) that will occur in any given location. In this respect, 

a background in plate and shell behavior is needed, as well as an understanding of the differences 

in element formulations. For example, bending occurs at discontinuities such as intersections 

between penetrations and pipes and the containment shell. It occurs where there are changes in 

the shell geometry and thickness. The elastic bending response of a shell typically has the form 

of an exponentially decaying sinusoid. The maximum size of the elements in areas characterized 

by bending can be estimated if the characteristic wavelength of the elastic response, which 
 A-11 

depends on the radius and thickness of a shell, and the element shape functions are known. For 

instance, to represent the bending response of a shell with a characteristic wavelength, at least 

four or five linear elements are needed per wavelength. 

The analyst must exercise judgment in constructing the model and discretizing the mesh. The 

element choices must be assessed by verifying that the solutions do not violate fundamental 

mechanics (for example, force equilibrium), and perhaps even with sensitivity studies with 

element size and element ‘order’ as the sensitivity parameters. The best advice to an analyst with 

little experience in modeling containments, is to conduct a modeling exercise using one of the 

Sandia test models most similar to the structure of interest, and validate decisions on element 

types and sizes by comparison of results to the published test data. Then once validated, the 

analyst can proceed to the real structure and make similar meshing decisions with confidence. 

In addition to these general guidelines, the following specific guidelines apply to containment 

analysis. 

a. Grid refinement at the wall-base juncture is mandatory to capture the large shear and 

moment gradients that occur at the base of the wall. At a region of high bending moment, 

it is important to calculate the strain in the various rebar layers correctly by explicit 

modeling of the discrete layers, rather than smearing properties for the entire wall 

section. 

b. In most cases, relatively coarse, idealized modeling of basemats is adequate. More 

detailed modeling of the basemat has been found to be important only in some 

circumstances, namely, if there were any possibility of potential failures at the wall-base 

juncture. Basemat discretization is generally not important in predicting the response of 

the barrel and the dome. Accuracy is required in predicting basemat liftoff that can occur 

at high pressures and control the global behavior, as in the case of the Sizewell-B 1:10-

scale model. Local basemat details, such as sumps, cutouts, and keyholes, are generally 

ignored in global analyses, particularly because they have not been included in the test 

models, and this appears to be reasonable, even for evaluating a full scale prototype. 

c. For axisymmetric analyses, a regularly spaced grid is recommended over to the symmetry 

line to adequately calculate the bending moment in the basemat, which is a maximum at 

the axis of symmetry. This bending moment causes the possibility of yielding the 

basemat bottom bars that, in the cases of the 1:10-scale containment and the 1:6-scale 

containment, led to basemat liftoff (more so in the 1:10-scale containment). But in most 

actual reinforced or prestressed containments, leakage is likely to occur before yielding 

of the basemat bottom bars in bending. 

A.4.2 Boundary Conditions 

For global axisymmetric analysis, the boundary conditions are straightforward - constraint of 

displacement ur at the symmetry axis (R=0), and constraint of uz along the underside of the 

basemat (i.e., if foundation springs are modeled, uz=0 on the ground side of the springs). For 3D 

global analysis, the boundary conditions are similarly intuitive, with vertical displacement 

constraint under the basemat, and horizontal displacement constraint applied at the center of the 

basemat. 

For sector models representing a vertical slice of the structure, the boundary conditions are 

similar to axisymmetric analysis, but with the caveat that care must be taken to assign 
 A-12 

displacement constraint along the “slice edges” which are truly perpendicular to the slice plane, 

i.e., free radial expansion must be allowed. 

For all other forms of sub-models, the derivation and application of boundary conditions can be 

very complex, and in past work has often required the development of boundary condition input 

processors/subroutines. The 3D local models of the 1:6 Scale RCCV, 1:4 Scale PCCV, and 

mixed scale SCV, were all “driven” by combinations of pressure applied to the liner or steel shell, 

and boundary condition “displacement histories” applied at the nodes along the boundaries of the 

model. These displacement histories are nodally unique displacements in three coordinates, 

which change with pressure, and they are derived or extracted from another analysis that provides 

global behavior simulation. The challenges to analysts for these models include: 

a. Ensuring that boundaries are cut far enough away from the local area of interest in the 

analysis that the behavior at the boundary is not influenced by the behavior of the local 

component 

b. Ensuring that the 3D local simulation of the containment wall is compatible with the 

global one – if not, a local stress/strain concentration can occur near the boundary when 

the displacement boundary conditions are applied. 

c. Ensuring (for example with a 3D R-θ slice model) that rigid body displacements are 

adequately constrained, without over-constraining the sub-model. 

For more details on how these challenges were addressed in past analytical studies, the reader is 

directed to the analysis reports for the 1:6 Scale RCCV, 1:4 Scale PCCV, and mixed scale SCV. 

A.4.3 Material Properties 

The materials of construction of the containment structure are usually provided in the engineering 

design drawings or construction specifications. Depending on the stage of design, construction or 

operation, the analyst may only have access to preliminary material specifications, properties of 

sample materials, properties of specimens of the actual materials taken during construction or, 

possibly properties of materials which may have been degraded during the operating life of the 

plant. The analyst must decide which set of properties to use in the analysis. In the case where 

not actual material data exists, the analyst’s options are limited, but even here, information from 

previous construction experience, e.g. results of tests on similar materials for previous projects, 

may be used to modify the nominal properties of the specified materials. When test data is 

available, it is usually desirable to use this information, however, the analyst should be familiar 

with the scope of material testing and whether it is statistically significant. 

When performing probabilistic assessments, the range in material properties from actual or 

representative test data can be used, with some judgment, to estimate the range of uncertainty, 

either directly or by defining the parameter variation when multiple analyses are performed, e.g. 

Monte Carlo or Latin-Hypercube Sampling. 

A.4.3.1 Special Considerations for Steel Containments 

a. The basic material properties, yield strength, ultimate strength, and maximum elongation, 

should be determined from standard uniaxial tensile tests on the actual materials of 

construction, if possible. Again, an adequate number of specimens should be tested in 

order to have a statistically representative sample. Also, for plate material, specimens 

should be taken both parallel and perpendicular to the rolling direction. While properties 
 A-13 

may vary as a function of heat (i.e., production run) and thickness, variations of 

properties within a particular heat are probably negligible. 

b. The experiments have shown, however, that direct application of uniaxial tests of small 

gage length specimens tends to over predict these properties. This may be due to the fact 

that these materials are typically subjected to stresses and strains in the fabrication 

process (cold rolling, weld-induced stresses) which are typically not considered in the 

analysis. It has also, appears, although this is not conclusive, that there may be a size 

effect that tends to decrease the apparent properties of full-scale structures. Regardless of 

the reason, it appears prudent to apply a reduction factor on the order of 10 to 20% to 

both the yield and tensile strength. 

c. While certain failure mechanisms may require additional material tests to model 

correctly, e.g. fracture toughness, fatigue strength, the basic properties discussed above 

are generally adequate for most containment analyses. When measuring these properties, 

it is desirable to obtain the full engineering stress-strain relationship, rather than just the 

basic values, to characterize the post-yield material response. Depending on the finite 

element code, the stress-strain relationship can be input directly or approximated. For 

non-linear analysis, the engineering stress-strain is usually converted to true stress-true 

strain. 

d. Since steel containments are constructed by welding, the behavior of the welds is 

important. The experiments have shown that most, if not all pressure-induced failures in 

steel containment structures (excluding penetration leakage) occur at or near the welds, 

usually in the heat-affected zone (HAZ) of the parent material. This may be due to local 

changes in the properties of the parent material, weld induced stresses or both. While this 

is not normally done for actual containments, it is helpful to test welded specimens, 

preferably at the same thickness as the materials used in the construction. If this is not 

possible, posttest inspection of the steel models suggests that estimates of changes in 

material properties can be obtained from surface hardness tests. 

e. Since severe accidents impose both thermal and pressure loads on steel containments, it is 

desirable to know the dependence of the yield strength, post-yield response (i.e. 

hardening), tensile strength and maximum elongation on temperature. Again, these 

properties are not normally measured during construction, however, reasonable estimates 

can be made based on published studies. Since all of the Sandia experiments were 

conducted at ambient temperature, the data from these tests do not provide any insights 

regarding response of steel containments at elevated temperatures. For many severe 

accident scenarios, the estimated temperatures are not high enough or of long enough 

duration, to have a significant effect on the material properties. In these cases, the 

primary effect of temperature loading is stresses induced due to constraint of thermal 

expansion. 

A.4.3.2 Special Considerations for Concrete Containments 

a. Again, due to the composite nature of reinforced concrete, the material issues are 

considerably more complex, and subject of variation, than for steel containments. 

b. First the concrete itself provides special challenges since it is a brittle material which 

responds differently in tension and compression. Material testing for concrete 

construction is primarily for quality control purposes and not to define properties for 

analysis. While methods have been developed for direct or indirect measurement of 
 A-14 

tensile properties, most material models are based on a fundamental parameter, the 

unconfined compressive strength, fc’. The other necessary material parameters are 

typically derived from fc’ based on large amounts of empirical data. It is far more 

difficult to obtain uniaxial tensile properties than it is for compression. For containment 

capacity analyses, however, the tensile and shear properties of concrete both are usually 

much more important than the compressive properties. Shear strength is usually 

addressed as diagonal tension in concrete models using solid elements, however, care 

should be exercised in evaluating shear behavior in models using shell elements. 

While the concrete containment models tested by Sandia utilized more exhaustive testing, 

including measurement of tensile and compressive stress-strain behavior, it appears that 

defining tensile strength, elastic modulus, etc. based on fc’ is generally adequate, although 

again it appears to overestimate these properties. If more extensive testing is conducted, 

it is important that a statistically significant number of specimens are tested. 

In the absence of detailed tensile stress-strain data, the following values are 

recommended: 

4 ' c f (fc’ in psi ) as the tensile stress at first cracking, and 

0.0001 for tensile strain at first cracking 

Though there are some observable differences in Young’s Modulus in compression 

versus tension, it has been found adequate to use Young’s Modulus in compression for 

both compression and tension 

The post-cracking stress-strain curve is known as ‘tension-stiffening,’ and this is 

discussed further in Section A.4.3, Constitutive Modeling. 

Poisson’s Ratio is typically not measured and a conventional value of 0.2 can be 

assumed. 

c. Considerations for the material properties of the liner and embedments are similar to 

those discussed for steel containments. Since the liner does not typically contribute 

significantly to the overall pressure capacity of concrete containments and is relatively 

thin compared to steel containment walls, the reduction factor does not apply. 

d. Tensile properties of reinforcing bars and prestressing tendons or strands, if measured, 

should include the full stress-strain curve obtained for full size specimens of each bar 

type and size used in construction. 

For normal reinforcing, larger bars typically exhibit lower strength properties and 

elongation than small bars even though the material is nominally identical. Tensile 

properties obtained from machined specimens of rebar typically over predict the tensile 

strength and should be used with caution or a reduction factor. 

Tensile properties of prestressed reinforcing determined for quality control usually test the 

individual wires or strands rather than full tendons. The experiments suggest that the 

tensile properties of the tendon system, including anchor hardware are weaker and less 

stiff than would be expected from the strand test data. Since it is not always feasible to 

test the tendon systems to failure, a reduction factor (5 to 10%) should be applied on 

stiffness and strength of the individual wire or strand data. On stiffness, this reduction is 
 A-15 

associated with “strand wrap angle” effects. On strength, this reduction would be 

associated with failures in the anchorage systems. It should be noted, however, that it is 

possible, but not 100% certain, for tendon systems to achieve their full strength as implied 

from a strand test. 

A.4.4 Constitutive Modeling 

After selecting or defining a set of material properties, the next choice is the selection of an 

appropriate constitutive model. For linear-elastic analysis, this choice is straight forward, but for 

non-linear, quasi-static or dynamic analysis, this is more difficult and requires experienced 

judgment. This is further complicated by the fact that constitutive models are often dependent on 

the code and solution strategy used. It is not possible to specify a particular constitutive model 

that is applicable in all cases, but the considerations given below may help guide the analysis of 

containment structures. 

A.4.4.1 Special Considerations for Steel Containments 

Pertinent details for modeling steel materials are discussed in Chapter 3, "Steel Containment 

Analysis" of the report. These factors must also be included in reinforced and prestressed 

concrete containment analyses for modeling the liner. In particular, the strain hardening of liner 

steels in the yield plateau requires careful verification of the strains in the nonlinear response 

range. In general, with the caveats previously noted, standard J-2 plasticity models have been 

shown reliable for containment steel material response prediction. There generally is no need for 

special characterization of cyclic response for severe accident loading analysis, so this simplifies 

the selection of “hardening” options, e.g., choosing isotropic versus kinematic hardening, and 

obviates the need for including the Bauschinger Effect. 

A.4.4.2 Special Considerations for Concrete Containments 

a. Concrete constitutive models should include tensile cracking (normally treated as 

occurring in the principal stress directions at the integration points). Alternatively, the 

concrete can be treated as a no-tension material in analyses aimed at predicting global 

response. 

b. There is a wide range of opinion within the industry as to the proper simulation of the 

concrete post-cracking stress-strain curve. From the many years of analysis during the 

Sandia containment research program it has been concluded that while it is the most 

theoretically robust to implement an experimentally-verified tension stiffening curve, it is 

not absolutely necessary to achieve reasonable failure predictions for containments. 

What is more important is to caution against using overly “strong” tension-stiffening 

curves, which is often tempting to analysts, because their use can significantly improve 

convergence characteristics. For failure prediction, it is better (and conservative!) to 

assign little or no tension stiffening to post-cracked concrete than to assign too much. 

c. Some method for simulating post-cracking shear retention should also be included. Shear 

retention is particularly important at the wall base junction, and numerical solutions in 

this region are found to be sensitive to the shear retention algorithm used. Description of 

these methods, and a reasonable assessment of the current “state of the practice” in 

concrete modeling are available in the report on the Round-Robin Pretest Analyses of the 

1:4 Scale PCCV Model [74]. 
 A-16 

d. While most of the concrete elements in a computational grid will probably experience no 

compressive stress at high pressures, a few elements at the outer wall base and along the 

top of the basemat will experience compression, sometimes large enough to exceed the 

concrete compressive strength, fc’. Thus, it is important to properly model concrete 

crushing. An elastic/perfectly plastic stress-strain curve has shown reasonable results in 

most cases, but inclusion of strain-softening is preferred for completeness. (Although, 

the associated plasticity algorithm is more complex.) As complex behavior is to be 

expected at the wall base, it is important that the concrete compressive yield algorithm 

properly treat the effective stress and strain calculation. Compressive yield is more likely 

to be reached by the combination of vertical compressive stress and shear stress rather 

than any one component stress reaching fc’. This condition is essential for predicting 

potential wall-base shear failure. 

e. Geometric Nonlinearities. Though not a constitutive modeling issue, it is still a 

nonlinearity. Contrary to the recommendations for steel containment analysis in which 

geometric nonlinearity formulation is required to predict failure, it has been found that 

second order and large rotation terms need not be included in the strain-displacement 

relations for concrete containment analyses. The stiffness matrix need not be updated to 

reflect the changes in geometry or thinning of the wall, as it is in steel shells. This 

recommendation carries with it some practical advantages, especially for modeling such 

complexities as prestressing tendons. Restricting the solution to small-displacement 

theory provides some options as to approximate formulations for friction and other 

effects. 

The constitutive modeling aspects of simulating temperature property degradation were described 

in Chapter 3. Most finite element programs handle the mechanical analysis of thermal expansion 

well, and it is generally adequate to assign a linear thermal expansion coefficient. But the 

analyses of coupled pressure and temperature accident scenarios become exceedingly more 

complex when temperatures reach high enough to cause significant material property degradation. 

These thresholds are approximately 150°C (300°F) for concrete and 427°C (800°F) for steels; 

these are the temperatures at which material strengths degrade by about 10%.%. And degradation 

curves become much steeper beyond these temperatures. 

A.4.5 Boundary Conditions 

For global axisymmetric analysis, the boundary conditions are straightforward - constraint of 

displacement ur at the symmetry axis (R=0), and constraint of uz along the underside of the 

basemat (i.e., if foundation springs are modeled, uz=0 on the ground side of the springs). For 3D 

global analysis, the boundary conditions are similarly intuitive, with vertical displacement 

constraint under the basemat, and horizontal displacement constraint applied at the center of the 

basemat. 

For sector models representing a vertical slice of the structure, the boundary conditions are 

similar to axisymmetric analysis, but with the caveat that care must be taken to assign 

displacement constraint along the “slice edges” which are truly perpendicular to the slice plane, 

i.e., free radial expansion must be allowed. 

For all other forms of sub-models, the derivation and application of boundary conditions can be 

very complex, and in past work has often required the development of boundary condition input 

processors/subroutines. The 3D local models of the 1:6-Scale RCCV, 1:4-Scale PCCV, and 

mixed scale SCV, were all “driven” by combinations of pressure applied to the liner or steel shell, 

and boundary condition “displacement histories” applied at the nodes along the boundaries of the 
 A-17 

model. These displacement histories are unique displacements at each node in three coordinates, 

which change with pressure, and they are derived or extracted from another analysis that provides 

global behavior simulation. The challenges to analysts for these models include: 

d. Ensuring that boundaries are cut far enough away from the local area of interest in the 

analysis that the behavior at the boundary is not influenced by the behavior of the local 

component 

e. Ensuring that the 3D local simulation of the containment wall is compatible with the 

global one – if not, a local stress/strain concentration can occur near the boundary when 

the displacement boundary conditions are applied. 

f. Ensuring (for example with a 3D R-θ slice model) that rigid body displacements are 

adequately constrained, without over-constraining the sub-model. 

For more details on how these challenges were addressed in past analytical studies, the reader is 

directed to the analysis reports for the 1:6-Scale RCCV, 1:4-Scale PCCV, and mixed scale SCV. 

A.4.6 Loading 

Consideration of loadings parallels the above discussion on boundary conditions, but has some 

unique challenges, particularly for prestressed concrete containments. 

For global and local models, loading application should follow basic principles; dead loads are 

applied using body forces (therefore proper assignment of mass densities to elements should be 

made), and pressure loads are applied perpendicular to the surface of the liner or steel shell. For 

the containment scale models that were tested hydrostatically, it was appropriate to add linearly 

varying hydrostatic force to the dead loading. 

For prestressed concrete containments, an essential part of the pre-loading of the structure is the 

application of prestress, and in the past research program, this has been addressed and studied 

with varying levels of detail. The following discussion addresses most aspects of prestress 

loading that should be considered. 

Prestressing losses should be estimated to accurately represent the actual stresses that will exist in 

the containment. In general, the philosophy used should be 

a. calculate best estimate “in service” values based on the nominal design values and 

modified for creep or any other in situ conditions; 

b. apply tendon stresses according to best estimate values, and allow the model to 

equilibrate to final tendon stresses that are reasonably close to these best estimate values, 

including anchor slip. 

In axisymmetric analysis, there is no opportunity to simulate the progression of friction along the 

tendon path in the hoop tendons, but this phenomenon can be included in the meridional tendons. 

Standard prestressing losses, from Reference [16], along with a brief explanation of the basis for 

their consideration are listed below: 

(1) Elastic Shortening – occurs simply due to equilibrium-seeking displacement within the 

finite element analysis. 

(2) Steel Relaxation – normally considered by the containment designers in calculating the 

"nominal in-service" values. 
 A-18 

(3) Shrinkage of Concrete – normally considered in combination with creep, and also, 

normally considered by designers in calculating “in-service” values. 

(4) Creep of Concrete – studied in detail for the PCCV, but for design, should probably be 

addressed using standard design formulae. The combination of creep and shrinkage 

comprises a significant prestress loss over time, often reaching 5%-10% of overall 

prestressing. 

(5) Anchorage Slip – can be considered explicitly in local model analysis; but not directly 

relevant for axisymmetric analysis. For conventionally anchored tendons, anchor slip in 

the range of 4-6mm is typical. The amount of actual stress loss resulting from this is tied 

to the angular friction assumption. 

(6) Angular Friction (and wobble friction) - Considered explicitly in local analysis of hoop 

tendons, and in global axisymmetric analysis of meridional tendons in dome. Also 

considered in calculating the average hoop tendon stress to be assigned in global 

axisymmetric analysis. (Also see below.) 

(7) Others: Temperature - Not considered, but it should be noted that for a thermal analysis, 

if tendons become significantly heated, significant loss of prestress can occur simply due 

to αΔT expansion and the associated stress relaxation. 

With post-tensioning, the amount and distribution of elastic shortening depends on the order of 

post-tensioning. In general, it should be assumed that the tendons are jacked in a sequence 

appropriate to reacting the total desired lock-off force. In ABAQUS, an option called 

"PRESTRESS HOLD" allows an initial post-tensioning equilibrium step that holds the tendon 

stresses at a preset value while the structure iterates to equilibrium and thus maintains a constant 

stress regardless of elastic shortening. However, in some past versions of the program, various 

program errors were encountered using this option, so in general an iterative procedure is 

recommended for arriving at the appropriate tendon stresses after the prestressing step. This can 

generally be achieved within two or three attempts, by applying larger than target prestress, 

reaching equilibrium in the containment, noting the final prestress, then adjusting and applying 

the prestress load step again. 

Angular Friction, Wobble friction and friction in straight portions of meridional tendons in the 

barrel below the springline can generally be neglected. From standard prestressed concrete texts, 

the angular friction should be included in the curved tendon portions with the formula: 

T2 = T1e

-(μα)

where α is the angle between T1 and T2, and μ is the coefficient of static angular friction. T1 is 

the tendon force next to a jack before friction losses, and T2 is the tendon force at some angle α

away from T1. In the 1:4 Scale PCCV, the angular friction coefficient was observed (by ancillary 

testing) to be 0.21, but for a full-scale prototype, a coefficient of 0.15 is probably more 

appropriate. 

Example 

Meridional Tendons: 

α = 90° = 1.57 Radians, μ = 0.21 from specifications 

T1 = T2e

-1.57 x 0.21 = T2 (1.0817) 
 A-19 

T2 = 92.4% T1

this is the percentage loss from the springline up to the dome apex. 

A.5 Solution Strategy 

Solution strategy for containment analysis of severe accident conditions and quasi-static loadings 

has consisted mostly of implicit-based, incremental loading, with equilibrium iteration. A few of 

the Round Robin analysis submittals for the three large scale model tests have utilized explicitbased calculations (using some form of numerical damping to suppress dynamic response to 

quasi-static loading), but the norm has been implicit. The equilibrium iteration schemes vary, but 

for ABAQUS, a standard “Full-Newton” method is typically employed. The stiffness is reformed 

at each new load increment, but not at each successive equilibrium iteration. Equilibrium 

iterations modify the residual force vector, one iteration to the next. The choice of increment step 

size is sometimes left to an automatic “time stepping” algorithm (based on convergence), and 

sometimes pre-set by the user. This is discussed in more detail below. 

It is also typical to apply initial loads (like dead loads and prestress) first, reach equilibrium, and 

then apply the accident loads. For combined pressure and temperature loads this creates a unique 

set of challenges as described in more detail below. 

A.5.1 Special Considerations for Steel Containments 

Steel containment analysis tends to have far less difficulties for convergence than concrete 

containment analysis, but in the pressure range near failure, steel containments have their own 

unique challenge. Since it is possible for steel containments (as demonstrated by scale model 

tests) to be loaded to the point of actual thinning (‘necking’) of the shell, the primary stress 

carrying element of the structure, normal force-incremented solutions (and the structure itself) 

can become very unstable. A special loading algorithm (found in ABAQUS, and possibly in 

other programs) which has worked well in the past is the RIKS method, which computes and 

applies deformation-based selections of load increments. When successfully applied, this has 

allowed solutions to reach maximum pressure and continue to track somewhat past peak pressure 

(while wall-thinning is occurring) with reasonable accuracy. The method is, however, an 

advanced user option, should be used with caution, and tested prior to use. 

A.5.2 Special Considerations for Concrete Containments 

Experience (and calculations) shows that substantial hoop cracking can occur in a reinforced 

concrete containment between 70% and 90% of the design pressure, depending on the percentage 

of steel. Therefore, a reinforced containment, unlike a prestressed containment, will experience 

extensive cracking before the design pressure is reached. So unlike steel containments, very 

significant nonlinearities and difficult convergence issues tend to crop up relatively early in 

concrete containment analysis. Over the years, and for the analyses in support of the Sandia large 

scale model testing, good structure simulation success was achieved using ANACAP-U 

(developed by Rashid, et al, at ANATECH) concrete material modeling in conjunction with 

ABAQUS, and using a convergence algorithm/philosophy known in ABAQUS nomenclature as 

“DIRECT=NOSTOP.” With this approach, the user can select load incrementation ‘directly’, and 

the solution can proceed under less stringent convergence criteria than would be normally be 

used. Long a subject of debate amongst concrete analysis researchers, a well-known difficulty of 

smeared-cracking analysis (where multi-directional cracks can form at the element integration 

points) is the fundamental lack of convergence of internal element forces relative to the element’s 

possible cracking states. With experience, test validation, and judgment, it has been found that a 
 A-20 

lack of internal element force convergence is not necessarily a good measure of the quality of 

solution, and in fact, the philosophy of ignoring internal element force convergence (but still 

enforcing global external force convergence and displacement convergence) has led to many 

good pretest predictions of containment large scale tests for many years. But it should also be 

noted that other programs, concrete models, and solution/convergence philosophies have also 

been used with reasonable success. The key remains to test and validate a program and a 

modeling/solution-strategy approach before attempting an in-depth containment analysis. 

A few comments comparing reinforced and prestressed concrete containment solution strategies 

are also in order. When a reinforced containment cracks, the main reinforcement is stressed only 

to approximately 30% of its yield, whereas tendon reinforcement in a prestressed containment is 

at 80% or 90% of yield when the concrete cracks. This, combined with the fact that conventional 

rebar has greater ductility than prestressing tendons, gives reinforced containments an aftercracking pressure capability range that is significantly larger than in prestressed containments. 

This implies that leakage before catastrophic rupture may be more likely to occur in a reinforced 

containment than in a prestressed containment. It also makes solution incrementation more 

critical and difficult early in the pressure history for RCCVs versus later in the pressure history 

for PCCVs. On the other hand, once tendon yield is reached in PCCVs, structure response can 

grow very quickly with small increments of additional pressure, so at this stage PCCV solution 

convergence can become even more challenging. 

A.5.3 Thermal Analysis 

The subject of temperature remains largely an untested issue with regard to global containment 

behavior. This is due to the experimental difficulties involved with modeling elevated 

temperatures. Conclusions about global behavior must be taken primarily from analytical studies. 

In early work in the 1980s, and then in post-test work for the 1:4 Scale PCCV, typical prestressed 

and reinforced geometries have been investigated by analysis for combined pressure and global 

temperature up to 400 ̊F (204 ̊C), plus the addition of a local temperature spike simulating a local 

hydrogen burn. The results of that work showed that temperatures in the ranges predicted to 

occur (by NUREG-1150, for example, 350 ̊ to 400 ̊F (177 ̊ to 204 ̊C)) have only a small effect on 

the ultimate pressure capacity of both reinforced and prestressed containment structures because 

the cracked concrete carries no tension regardless of temperature. Also, temperatures in this 

range have only a minor effect on typical rebar (or steel containment shell) properties. 

But if temperatures were developed in the range of 700 ̊ to 800 ̊F (370 ̊ to 427 ̊C) and existed 

long enough to heat up the embedded rebar or tendons, ultimate pressure capacities could be 

dramatically reduced because of degradation of the modulus and yield strength of the steel 

elements. 

As performed for the 1:4 Scale PCCV for an International Standard Problem (ISP-48) exercise, 

the thermal-mechanical analysis of a containment can be approached in two steps: 1) add 

temperature to the mechanical solution without consideration of material property degradation 

due to temperature, and 2) perform analysis including temperature and material property 

degradation. Analysis results were presented in ISP-48 for these cases individually to gain better 

understanding of the behavior differences and the causes of failure, when temperature is 

introduced. The primary tool for the ISP Exercise was axisymmetric modeling (and ABAQUS). 

The steps are as follows. 
 A-21 

Step ‘1’

Perform a Heat Transfer analysis. (In some programs like ABAQUS, this means all elements 

relevant for thermal analysis need to be changed to diffusive heat transfer element types which 

only have temperature degrees of freedom.) Thermal boundary conditions are imposed at the 

outer surface of the cylinder and dome wall consisting of “free convection with air. The heat 

transfer coefficient, h, varies with temperature according to the following relationship: 

1/ 3 h = 0.00382(ΔT ) lbf/in-s-oF (T in oF) for a full scale containment analysis [79], 

The boundary condition on the basemat foundation consists of heat conduction with soil with a 

sink temperature (Tfo). An example of a heat transfer coefficient developed for the horizontal 

surface of the foundation in contact with soil is: 

5 5.76 10− h = • lbf/in-s-oF for a full scale containment [79] 

For a proposed accident temperature scenario, a steady state heat transfer analysis step would 

precede a dynamic heat transfer analysis with the time history temperature input. The steady state 

heat transfer step is used to bring the model up to an ambient/operating temperature of 25oC. 

Figure A-2 shows the location of the prescribed boundary conditions for the axisymmetric model 

of the PCCV. 

Step “1” provides a heat transfer solution, either steady state, or transient versus time, and thus 

provides unique temperatures (either single-valued or versus time) at all the nodes in the model. 

Literature reviews were conducted to develop reasonable concrete thermal properties, and for 

degradation of concrete and steel material properties, and these were provided in Chapter 3. 

Step ‘2’

Conduct the semi-coupled heat transfer and pressure mechanical solution analysis. Here the 

solution is advanced step by step by incrementally applying all the nodal point temperatures 

(which cause αΔT deformations) and applying the pressure loads. The material property 

degradation can either be tied directly to the constitutive modeling of the materials, or as a more 

approximate approach, introduced manually to zones of elements particularly influenced by 

temperature. Such an approach is called semi-coupled because the mechanical solution is 

influenced by the temperature, but not vice-versa. 
 A-22 

Axisymmetric Model CL

Nodal 

Temperature BC

(Time History Input)

Free Convection BC

(Air, T=25) f,

o

∞

Conduction BC

(Soil or Concrete, T=25) s,

Figure A-2 Typical Axisymmetric Model and Temperature Boundary Conditions 

A.6 Interpretation and Evaluation of Results 

A.6.1 Basic Model Checks 

Conducting basic quality and “sanity” checks are essential to completing a containment analytical 

study. And although many such checks are part of the ‘skills of the trade’ learned through 

experience, for containment global analysis, at a minimum, the analyst should conduct basic hand 

calculation of approximate event milestones (in terms of pressure) for the radial expansion of the 

containment cylinder. The calculations are not overly complex, and a detailed example of such a 

calculations (conducted for the 1:4 Scale PCCV) is provided in Section A.6.3, “Example 

Verification Analysis”. 

A.6.2 Failure Criteria and Interpreting Analytic Solution 

The importance of defining failure criteria to the implementation of finite element results cannot 

be overstated. Is it a performance-based criteria that requires prediction of actual release of 

containment contents, or is it a criteria which predicts the onset of a material failure. Until very 

recently, nearly all containment analysis in the Sandia research program has invoked the latter. 

And the criteria that is widely used is the multiaxial stress ductility limit for steel plate material 
 A-23 

(either the shell of a steel containment or the liner of a concrete containment) defined by 

Manjoine [xx]. This criteria, which uses the ‘Davis Triaxiality Factor,’ is provided in Chapter 3. 

Some performance-based criteria concepts are introduced at the end of the report. 

But even with the ductility-based criteria (which predicts failure when steel strains are in the 

range of 15%-25%), engineering judgment is needed to interpret finite element analysis results. It 

is only with the very finest of meshes and detailed modeling approaches that such high strains can 

be reliably predicted, and even with very fine meshes, some measure of mesh-size sensitivity will 

always be present near structural discontinuities. This means that for most analysis, judgment 

will be required to extrapolate from global model predicted strains of 1%-2% to high strains 

likely to exist near structural discontinuities. And though a comprehensive database of strain 

concentration factors is still lacking, there is substantial evidence (found in test and analysis 

reports cited herein) to support such engineering judgment and failure prediction based on global 

analysis. 

Investigation and validation of methods for evaluating other potential failure modes is still 

needed. Shear failure is particularly difficult to evaluate; there is no generally recognized method 

of determining shear capacity of a reinforced concrete section under simultaneous application of 

tensile load and bending moment. Failure of large rebars where they are bent around 

penetrations, as occurred in an EPRI test [47], are also of some concern. The effects of cold 

working on the available ductility to these bars should be studied further. Rates of pressurization 

and effects of temperature must be considered in more detail. At high rates of pressurization, 

there is a possibility that sequential failure modes could occur; that is, for very high rates of 

pressurization, liner tearing may not arrest the pressure buildup within the containment, and 

another failure mode could occur at slightly higher pressure. This is the basic reason for 

emphasizing the development and validation of analysis methods. A reliable evaluation of 

containment performance must be based on careful, detailed analysis of the specific containment 

geometry and loading of interest. 

A.6.3 Example Verification Analysis 

1:4-Scale Prestressed Concrete Containment Vessel Model

As with any nonlinear analysis of a complex structure, the first step is to identify and categorize 

structural components and to compute the approximate response behavior to use for guidance in 

establishing the load stepping strategy for nonlinear finite element analysis. A summary of the 

major milestones predicted by hand calculation was developed and is described in this subsection. 

The following definitions refer to the formulae in this subsection. 

ρ = reinforcement ratio 

ρhoop rebar = ρhr = Area of hoop reinforcement/gross concrete area 

ρliner = Area of liner/gross concrete area 

ρhoop tendons = ρht

tliner = thickness of liner = 0.16cm 

teq = equivalent concrete thickness or transformed section thickness (concrete section area 

with steel portion transformed by ratio of Young's Moduli) 

t'eq = teq including rebar and tendons 
 A-24 

tc = thickness of concrete wall = 32.5cm 

σo(concr) = compressive concrete stress after prestressing 

R = Inside radius of cylinder = 538cm 

Erebar, Ec, Eliner = Young's Moduli of rebar, concrete, and liner, respectively 

εcr = Concrete cracking strain = 80x10-6

εry = rebar yield strain 

σbarult = rebar ultimate strength 

σtendonult = tendon ultimate strength 

(stress at 4.77% strain was used in this analysis as an upper bound; the PCCV test 

suggests ultimate tendon strains of 1 to 2% might be more realistic.) 

Pressure at Which Cylinder Stress Overcomes Prestress, Po

Since there are three 16mm hoop bars and five 13mm bars every 45cm (measured 

vertically) 

ρhoop rebar x cm x cm

cm x cm = = 3 2 01 5 1 33 +

32 5 45

2 2

0 00865 . .

. .

ρliner

t

cm

liner = == 32 5

0 16

32 5 0 00492 . .. .

( liner ) c

c

liner

hr c

rebar

eq t

E

E

E

E t = 1+ ρ + ρ

 tc

33

200(0.00492 (0.00865) 33200 1 ⎟

⎠

⎞ ⎜

⎝

⎛ = + +

t cm eq = 35 2.

There are four hoop tendons of area 3.39cm2

 in every 45cm wall segment. 

ρhoop tendons x cm

x = = 4 3 39

32 5 45

2

0 00927 .

. .

ρtotal = 0.00865 + 0.00492 + 0.00927 = 0.0228 

In compression under tendon action, 

σo(concr) = -ρtendon σitendon = -0.00927x 953 MPa 

(Avg. prestress in hoop tendons including assumed losses) 

σo = -8.83 MPa 

pressure to overcome prestress, Po is 
 A-25 

P MPa o

t

R

o eq == = −σ −8 83 35 3)

538 0 580 . (. . 

Cylinder Hoop Cracking Pressure, Phc

Total equivalent t including tendons = t'eq

( ) 0.0228 32.5 37.0cm 33

200 1

t

E

E

t' 1 total c

c

steel

eq

⎟ = ⎠

⎞ ⎜

⎝

⎛ +

⎟ = ⎠

⎞ ⎜

⎝

⎛ = + ρ

P P hc

t E

R o eq c cr x xx = += +

′ − ε 37 0 33 000 80 10

538

6

0 580 . (, ) .

Phc = 0.762 MPa 

Pressure at Rebar Yield, Pry

Assuming the tendons have not yielded, the hoop stiffness after cracking is 

approximately that of elastic rebar, liner and tendons acting alone. Therefore, 

( )

( ) 0.00228

200,000

Pr 455 = = = − = s

y

tota c s

y o

ry

t E E

P R

l

σ

ρ

ε

Solving, 

Pry = +

0 00228 0 0228 32 5 200 000

538 0 580 . (. ) .( , ) .

Pry = 1.21 MPa 

Ultimate Barrel Failure Based on Ultimate Strengths of Steel Components, Pult

 

Pult = σbar ult ρhr t c

R + σtendon ult ρht t cR + σliner ult ρliner t cR

( ) ( )

( )

1.54MPa 4.0Pd

498 0.00492 ]/ 538

Pult 32.5[658 0.00865 1876 0.00927

= =

+

= +