Effects of Degradation 

on the Severe Accident 

Consequences for a PWR 

Plant with a Reinforced 

Concrete Containment 

Vessel

Office of Nuclear Regulatory Research

NUREG/CR-7149

SAND2009-6323P
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infringe privately owned rights.
Effects of Degradation 

on the Severe Accident 

Consequences for a PWR

Plant with a Reinforced 

Concrete Containment 

Vessel

Manuscript Completed: July 2010

Date Published: June 2013

Prepared by:

J. P. Petti, D. A. Kalinich, J. Jun, K.C. Wagner 

Sandia National Laboratories

Operated by Sandia Corporation for the 

U.S. Department of Energy

Albuquerque, New Mexico 87185

Prepared for

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

Jose Pires, NRC Project Manager

NRC Job Code N6371

Office of Nuclear Regulatory Research

NUREG/CR-7149

SAND2009-6323P

iii

ABSTRACT

Various forms of degradation have been observed in the containment vessels of a number of operating 

nuclear power plants in the United States. Examples of degradation include corrosion of the steel shell or 

liner, corrosion of reinforcing bars and prestressing tendons, loss of prestressing, and corrosion of 

bellows. The containment serves as the ultimate barrier against the release of radioactive material into the 

environment. Because of this role, compromising the containment could increase the risk of a large 

release in the unlikely event of an accident. Previous work in this area has assessed the effects that 

degradation has on the pressure retaining capacity of the containment vessel through structural analysis 

that account for degradation. These analyses have provided useful information about the effects of the 

degradation on the structural capacity of the containment in both deterministic and probabilistic fashions. 

However, the appropriate metric to use in assessing containment degradation effects during a severe 

accident was determined to require additional study. The previous work with probabilistic descriptions of 

the containment capacity were obtained from the results of the structural analysis models, and used as 

input for the risk models (Probabilistic Risk Assessment analyses). The risk was formulated in terms of 

the large early release frequency (LERF). The relative LERF values were computed for various 

postulated cases of degradation. In that study, an instance of degradation was treated as a change in the 

plant’s licensing basis and assessed with U.S. NRC Regulatory Guide 1.174, “An Approach for Using 

Probabilistic Risk Assessment in Risk-Informed Decisions on Plant-Specific Changes to the Licensing 

Basis.” The Regulatory Guide provides the limits of the acceptable increases in LERF due to changes in 

the plant. Many of the cases of postulated degradation were those consisting of local corrosion in the 

liner or shell that produce leaks that do not contribute significantly to LERF, and in some cases, cause no 

change in LERF. Early releases due to small leaks were found to contribute to the small early release 

frequency (SERF). Since Regulatory Guide 1.174 does not provide guidance on the limits of SERF, 

additional deterministic analyses were performed in this study to assess the effects of degradation on the 

consequences using metrics other than LERF. This study was performed using the Sandia codes 

MELCOR and MACCS. These codes were used to simulate two different accident scenarios (long- and 

short-term station black-outs) and compute the resulting consequences for a PWR plant with a reinforced 

concrete containment. The structural analyses used in the previous probabilistic study were used to 

develop the containment behavior models for the accident simulations. Several different postulated cases 

of liner corrosion were considered to enable a comparison of the consequences.

v

FOREWORD

This is the latest report of a multiple year study to obtain insights on the degree of degradation a 

containment can have and still be left in service without repair and without significant impact on risk. 

The goal was to enhance understanding of containment safety margins for degraded conditions. The 

study examined effects of degradation in containments using deterministic and risk-informed methods. 

Initially, the study evaluated the effects of degradation on several types of containments with respect to 

the guidelines given in Regulatory Guide 1.174, “An Approach for Using Probabilistic Risk Assessment 

in Risk-Informed Decisions on Plant-Specific Changes to the Licensing Basis.” It integrated fragility 

curves, developed for non-degraded and postulated degraded conditions using structural analysis, with 

pre-existing probabilistic risk assessment models used in NUREG-1150, “Severe Accident Risks: An 

Assessment for Five U.S. Nuclear Power Plants.” A conclusion from the first part of the study was that 

several cases of postulated degradation involving corrosion of the liner or shell showed small increases, 

no increases or even decreases in Large Early Release Frequency (LERF). This is because the postulated 

corrosion degradation leads to containment failure by leakage, with an increase in Small Early Release 

Frequency (SERF), rather than rupture. 

Following that conclusion, NRC examined the effects of liner degradation using metrics other than LERF. 

Additional deterministic analyses were performed and documented here to assess the effects of liner 

degradation on consequences using metrics other than LERF. The report documents a method that 

integrates containment fragility functions for non-degraded and postulated degraded conditions with 

accident progression analyses and offsite consequence assessments made with the Sandia National 

Laboratories-developed codes MELCOR and MACCS. 

The method reported is valuable to inform case-by-case examination of containment degradation effects. 

The methods and results in this report and in reports for the earlier and preliminary phases of this study 

(NUREG/CR-6920, “Risk-Informed Assessment of Degraded Containment Vessels,” and NUREG/CR6706, “Capacity of Concrete and Concrete Containment Vessels with Corrosion Damage”) are valuable to 

inform regulatory decisions that relate to the performance of a containment structure in a degraded 

condition such as: license renewal reviews and inspection, monitoring and repair of potentially degraded 

containments. They are also valuable to support other studies or research programs by informing them of 

the relative risk significance of potential degradation processes, and to support updating of guidance that 

relates to the performance of degraded or non-degraded containments for beyond design basis severe 

accidents.

Michael J. Case, Director

Division of Engineering

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

vii

TABLE OF CONTENTS

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

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

TABLE OF CONTENTS .........................................................................................................................vii

LIST OF FIGURES ................................................................................................................................... ix

LIST OF TABLES...................................................................................................................................... x

ACKNOWLEDGEMENTS ...................................................................................................................... xi

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

2. CONTAINMENT PERFORMANCE CHARACTERIZATION ................................................... 5

2.1 Containment Modeling................................................................................................................ 5

2.1.1 Performance Characterization for a Reinforced Concrete Containment................................6

2.1.1.1 Steel Liner Leak Criterion for Corroded Regions..........................................................6

2.1.1.2 Penetration Leak Criterion .............................................................................................8

2.1.1.3 Concrete Containment Rupture Criterion.......................................................................9

2.1.1.4 Catastrophic Rupture Criterion.....................................................................................10

3. DETERMINISTIC CONSEQUENCE ANALYSIS PROCEDURES .......................................... 11

3.1 MELCOR .................................................................................................................................. 11

3.2 MACCS ..................................................................................................................................... 12

4. PROBABILISTIC RISK ASSESSMENT PROCEDURES TO ASSESS CONTAINMENT 

DEGRADATION.............................................................................................................................. 15

4.1 Guidelines for Assessing Containment Degradation Using Probabilistic Risk Assessments.... 15

4.2 Procedure for Risk-Informed Containment Analysis................................................................ 16

5. SEVERE ACCIDENT CONSEQUENCE ANALYSES OF PWR PLANT WITH 

REINFORCED CONCRETE CONTAINMENT.......................................................................... 19

5.1 Structural Model of Reinforced Concrete Containment............................................................ 20

5.1.1 Axisymmetric Global Model................................................................................................20

5.1.2 Local Detail and Corrosion Modeling..................................................................................21

5.1.3 Structural Analysis with Best Estimate Properties...............................................................23

5.1.4 Fragility Curve Development for PRA Analyses.................................................................27

5.1.5 Leak Area Curve Development for Deterministic Accident Analyses................................36

5.2 MELCOR and MACCS Deterministic Accident Analysis........................................................ 41
viii

5.2.1 MELCOR Model for a 3-Loop PWR with a Reinforced Concrete Subatmospheric 

Containment.........................................................................................................................41

5.2.2 Description of MELCOR Model Modifications for Degraded Containment Analysis........42

5.2.3 Description of Degraded Containment MELCOR Calculations..........................................45

5.2.4 MACCS2 Analyses..............................................................................................................53

5.2.5 MACCS2 Generic Input Parameters....................................................................................53

5.2.6 MACCS2 Site Specific Input Parameters............................................................................54

5.2.7 MACCS2 Station Blackout Severe Accident Analysis Results...........................................55

5.3 PRA Analysis ............................................................................................................................ 65

6. SUMMARY & CONCLUSIONS .................................................................................................... 69

7. REFERENCES ................................................................................................................................. 71
ix

LIST OF FIGURES

Figure 2.1: Strain Magnification Factors for Typical Discontinuities in Reinforced Concrete 

Containments (approximation of the curves from Tang et al., 1995).................................8

Figure 4.1: Acceptance Guidelines for Large Early Release Frequency.............................................16

Figure 5.1: Postulated Corrosion in Liner of RC Containment (Spencer et al., 2006)........................19

Figure 5.2: Axisymmetric Finite Element Model of RC Containment (Spencer et al., 2006)............21

Figure 5.3: Finite Element Mesh of Corrosion at Midheight ..............................................................22

Figure 5.4: Finite Element Mesh of Corrosion in Wall Near Basemat ...............................................23

Figure 5.5: Failure Potential at Corrosion and Discontinuity Locations (Leaks)................................26

Figure 5.6: Failure Potential at Corrosion and Discontinuity Locations (Ruptures)...........................26

Figure 5.7: Fragility Curves for Leak at Discontinuity Locations ......................................................30

Figure 5.8: Fragility Curves for Leak at Corroded Locations.............................................................30

Figure 5.9: Fragility Curves for Rupture and Catastrophic Rupture ...................................................31

Figure 5.10: Cumulative Probability of Failure Curves for Original and Degraded RC Containment .31

Figure 5.11: Conditional Probability of Failure for Original Containment (No Corrosion) .................32

Figure 5.12: Conditional Probability of Failure for 50% Corrosion at Basemat...................................33

Figure 5.13: Conditional Probability of Failure for 65% Corrosion at Basemat...................................33

Figure 5.14: Conditional Probability of Failure for 50% Corrosion at Midheight................................34

Figure 5.15: Conditional Probability of Failure for 65% Corrosion at Midheight................................34

Figure 5.16: Conditional Probability of Failure for 10 Regions of 50% Corrosion at Basemat ...........35

Figure 5.17: Conditional Probability of Failure for 10 Regions of 50% Corrosion at Midheight ........35

Figure 5.18: Conditional Probability of Failure for 10 Regions of 65% Corrosion at Midheight ........36

Figure 5.19: Total Crack Area vs. Pressure for Best Estimate Cases (Nominal)..................................38

Figure 5.20: Total Crack Area vs. Pressure Detailed View for Best Estimate Cases (Nominal)..........38

Figure 5.21: Total Crack Area vs. Pressure for Lower Bound Cases....................................................39

Figure 5.22: Total Crack Area vs. Pressure Detailed View for Lower Bound Cases............................39

Figure 5.23: Total Crack Area vs. Pressure for Upper Bound Cases....................................................40

Figure 5.24: Total Crack Area vs. Pressure Detailed View for Upper Bound Cases............................40

Figure 5.25: Containment Nodalization ................................................................................................44

Figure 5.26: Containment Pressure – STSBO, Nominal Cases (see Table 5.3 for case descriptions)..50

Figure 5.27: Containment Pressure – LTSBO, Nominal Cases (see Table 5.3 for case descriptions)..50

Figure 5.28: Containment Pressure – STSBO, Lower Bound Cases (see Table 5.3 for case 

descriptions)......................................................................................................................51

Figure 5.29: Containment Pressure – LTSBO, Lower Bound Cases (see Table 5.3 for case 

descriptions)............................................................................................................ 51

Figure 5.30: Containment Pressure – STSBO, Upper Bound Cases (see Table 5.3 for case 

descriptions)......................................................................................................................52

Figure 5.31: Containment Pressure – LTSBO, Upper Bound Cases (see Table 5.3 for case 

descriptions)......................................................................................................................52

Figure 5.32: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Total Cesium Release 

to the Environment for STSBO Cases..............................................................................60

Figure 5.33: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Total Cesium Release 

to the Environment for LTSBO Cases..............................................................................60

Figure 5.34: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Peak Containment 

Pressure for STSBO Cases................................................................................................61

Figure 5.35: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Peak Containment 

Pressure for LTSBO Cases...............................................................................................61

Figure 5.36: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Maximum 

Containment Leakage Area for STSBO Cases.................................................................62
x

Figure 5.37: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Maximum 

Containment Leakage Area for LTSBO Cases.................................................................62

Figure 5.38: Individual Latent Cancer Facility Risk (10 Miles) as a Function of the Pressure at which 

Containment Failure Initiates for STSBO Cases..............................................................63

Figure 5.39: Individual Latent Cancer Facility Risk (10 Miles) as a Function of the Pressure at which 

Containment Failure Initiates for STSBO Cases..............................................................63

Figure 5.40: Containment Pressure for STSBO Cases UB1 and UB3 ..................................................64

Figure 5.41: Containment Failure Area for STSBO Cases UB1 and UB3............................................64

LIST OF TABLES

Table 5.1: Summary of Locations and Failure Pressures...................................................................25

Table 5.2: Random Input Parameters.................................................................................................29

Table 5.3: Corrosion Condition .........................................................................................................37

Table 5.4: STSBO Accident Progression Sequence of Events..........................................................47

Table 5.5: LTSBO Accident Progression Sequence of Events..........................................................49

Table 5.6: Aerosol Deposition Velocity.............................................................................................53

Table 5.7: Cohort Population Fractions.............................................................................................55

Table 5.8: STSBO Health Effects......................................................................................................56

Table 5.9: LTSBO Health Effects......................................................................................................57

Table 5.10: STSBO Health Effects (single weather trial)....................................................................58

Table 5.11: LTSBO Health Effects (single weather trial)....................................................................58

Table 5.12: Core Damage Frequency (yr-1

) .........................................................................................65

Table 5.13: Large Early Release Frequency (yr-1

)...............................................................................65

Table 5.14: Probability of Large Early Containment Failure Conditional on Core Damage...............66

Table 5.15: Change in the Large Early Release Frequency (yr-1

) due to Degradation ........................66

Table 5.16: Small Early Release Frequency (yr-1

) and the Change in SERF.......................................67

Table 5.17: Total Early Release Frequency (yr-1

) and the Change in TERF .......................................67
xi

ACKNOWLEDGEMENTS

The project team acknowledges the guidance and support from the NRC project managers over the life of 

the program, Jose Pires and Herman L. Graves III, Office of Research, U.S. Nuclear Regulatory 

Commission. 

Special thanks are extended to everyone involved for their support and contribution to this project. The 

project team would also like to thank Sandia colleagues, Michael F. Hessheimer, Randall O. Gauntt, and 

Nathan E. Bixler, as well as former Sandia colleague Jason V. Zuffranieri

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 DEAC04-94AL85000.

1

1. INTRODUCTION

Various forms of degradation have been observed in the containment vessels of a number of 

operating nuclear power plants in the United States. Examples of degradation include corrosion 

of the steel shell or liner, corrosion of reinforcing bars and prestressing tendons, loss of 

prestressing, and corrosion of bellows. The containment serves as the final barrier between the 

reactor vessel and related components and the environment. Because of this critical role, 

compromising the containment could increase the risk of a release of radionuclides to the 

surrounding environment in the unlikely event of a severe accident. 

A series of previous studies have investigated the ability of degraded containments to resist 

leakage under overpressurization. Cherry and Smith (2001) investigated how corrosion in the 

steel shell or liner influences the predicted failure pressures of steel, reinforced concrete, and 

prestressed concrete containments. Specific effects related to the loss of prestressing force on the 

pressure capacity of prestressed concrete containment vessels were studied by Smith (2001). 

These studies found, in general, that the pressure capacities of containments were in excess of the 

design pressures, even with the presence of significant degradation. These computed failure 

pressures are critical in assessing the effects during a severe accident since those conditions can 

produce pressures far exceeding the design pressure. This general conclusion is supported by 

testing performed at Sandia National Laboratories over the past 25 years (Hessheimer, 2003). 

These tests proved to be of significant importance in assessing the behavior of different types of 

containment vessels and when performing analytical studies.

Even though the previous analytical studies provided valuable information on the pressure 

capacity of degraded containments, they did not study how degradation may affect the risk of a 

radioactive release. The initial step in the coupling of deterministic structural analyses of 

degraded containments within a risk framework was introduced by Ellingwood and Cherry 

(1999). They developed fragility curves for a steel containment with corrosion damage under 

overpressurization by performing multiple analyses with statistical variation in the material 

properties and other uncertainties. This method was used to compare the effects of degradation in 

a probabilistic setting.

Building on the work by Ellingwood and Cherry (1999), Spencer et al. (2006) integrated 

structural analysis results and their fragility curves with pre-existing probabilistic risk assessment 

(PRA) models to gain a risk-informed perspective on the issue of containment degradation. The

PRA models used were originally developed for NUREG-1150, “Severe Accident Risks: An 

Assessment for Five U.S. Nuclear Power Plants,” and NUREG/CR-4551 (Volume 1), 

“Evaluation of Severe Accident Risks: Methodology for the Containment, Source Term, 

Consequence and Risk Integration Analysis.” The coupled structural-risk approach was applied 

to case studies of containment degradation at four “typical” U.S. nuclear power plants explored in 

NUREG-1150. This methodology enabled not only the determination of the risk, in terms of the 

large early release frequency (LERF), but also the changes in LERF due to postulated cases of 

degradation. The limits of the acceptable increases in LERF are provided in Regulatory Guide 

1.174 (U.S. NRC, 2001) for changes in the plant’s license basis. Here, the increase in LERF due 

to an instance of degradation was treated as such a change.

Typical degradation in the form of local corrosion in the liner or shell made up the majority of the 

postulated cases of degradation considered by Spencer et al. (2006). However, local corrosion in 
2

the liner of a typical reinforced or prestressed concrete containment was shown to only produce a 

noticeable effect on the pressure at which a leak would initiate, and not the pressure at which 

larger rupture or catastrophic rupture failures would occur. Due to the binning process used in 

the NUREG-1150 PRA models, degradation cases that only affect the leak pressure do not 

contribute to LERF. In some cases, LERF was shown to decrease due to earlier leaks caused by 

local corrosion. This was due to these earlier small leak failures in the PRA analysis being

binned into the small early release frequency (SERF) instead of LERF. In the NUREG-1150 

PRA models, leaks were defined as breaches that would not lead to depressurization in less than 2 

hours. Therefore, outcomes in the PRA analysis leading to a leak failure of the containment were 

therefore included in SERF not LERF. Regulatory Guide 1.174 provides guidance for limits on 

changes in LERF and not on the limits for SERF. There is currently no appropriate guidance for

assessing the risk significance of degradation in containment structures that cause only increases 

in SERF. Since LERF and SERF are only surrogates for the release consequences, the current 

study includes deterministic source term and consequence analyses to assess the effects of 

degradation on the consequences using metrics other than LERF.

The consequence analyses performed in this study employ two codes developed at Sandia 

National Laboratories, MELCOR and MACCS. MELCOR 1.8.6 (Gauntt et al., 2005) is a fully 

integrated, engineering-level computer code that models the progression of severe accidents in 

light water reactor nuclear power plants. MELCOR is being developed at Sandia National 

Laboratories for the U.S. Nuclear Regulatory Commission as a second-generation plant risk 

assessment tool and the successor to the Source Term Code Package. A broad spectrum of severe 

accident phenomena in both boiling and pressurized water reactors is treated in MELCOR in a

unified framework. These include thermal-hydraulic response in the reactor coolant system, 

reactor cavity, containment, and confinement buildings; core heat-up, degradation, and relocation; 

core-concrete attack; hydrogen production, transport, and combustion; fission product release and 

transport behavior. Current uses of MELCOR include estimation of severe accident source terms 

and their sensitivities and uncertainties in a variety of applications. The MACCS code (Chanin, 

1990) was developed for the U.S. Nuclear Regulatory Commission (NRC) to evaluate offsite 

consequences of hypothetical severe accidents at nuclear power plants (NPPs) based on 

calculated or assumed fission product releases. The code is designed to take input directly from 

the fission product releases calculated by MELCOR. MACCS also incorporates geographic, 

demographic, and meteorological data for a given plant, as well as assumptions concerning 

biological uptake. The output results can be expressed in terms of both health consequences and 

economical impacts. However, the present study only considers the health consequences in terms 

of dose, as well as prompt and latent cancer fatalities at different distances and times. As stated 

previously, these estimates are based on the MELCOR prediction for release and other 

representative assumptions for the local geography and meteorological conditions.

Since the analyses performed in MELCOR and specifically for the MACCS calculations are plant 

specific, an actual plant and accident scenario were chosen for this exploratory study. This was 

similar to the actual plants used in the NUREG-1150 study and the previous work on degradation 

effects by Spencer et al. (2006). Here, we examined a station blackout accident scenario at the 

Surry Power Station. Surry is a PWR plant with a subatmospheric reinforced concrete 

containment. The long- and short-term station blackout accident scenarios were selected since 

they produce the high internal pressures necessary to initiate cracks in the steel liner and outer 

concrete containment wall. In addition, the station blackout scenarios have been identified by 

NRC Standardized Probabilistic Analysis Risk (SPAR) models as being potentially important risk 

contributors. The station blackout scenarios are also commonly identified as important 

contributors in PRAs due to their common failure mode nature as well as the fact that both the 

containment and reactor safety systems are affected. 
3

The degradation postulated for this containment was restricted to local corrosion in the steel liner 

near the wall-basemat junction and at the mid-height of the containment. The structural analyses 

of the reinforced concrete containment at Surry which incorporate the effects of these postulated 

cases of degradation were completed during the previous study by Spencer et al. (2006). Those 

results were used in this work to develop crack open area vs. internal pressure distributions for 

each of the postulated corrosion cases. These area vs. pressure curves are then introduced into the 

containment representation within the MELCOR analyses. The resulting source term output for 

each case of degradation are used as input for the MACCS code to determine the health 

consequences. The changes in consequences due to differences in corrosion location and extent 

are compared to the analyses of the containment without degradation. Using the Spencer study, 

three sets of analyses were performed: best estimate, lower bound, and upper bound. These 

bounding calculations are based on the crack area vs. pressure response space as determined in 

the structural analyses performed in the Spencer study. Even though the structural models, 

MELCOR, and MACCS models were used for the Surry Power Station, the cases of degradation 

assumed in this study are, as stated previously, hypothetical in nature, and do not reflect the 

actual conditions at Surry or at any other existing nuclear power plant. This study was conducted 

solely to demonstrate an analysis methodology and to examine the sensitivity of the consequences 

to varying cases of degradation. 

In addition to the new deterministic source term and consequence analyses, this study includes 

∆LERF results for several new cases of degradation. These new cases of degradation are 

modified versions of the cases examined in the previous study by Spencer et al. (2006). These 

cases are based on the same cases of degradation used previously, but include multiple instances 

of each simultaneously. The single cases of corrosion examined previously, were local in nature, 

extending only over several square inches. Since corrosion at an actual plant may be much more 

widespread, additional analyses which include more extensive degradation are also included in 

this study. The goal of these new PRA analyses, along with the deterministic MELCOR and 

MACCS analyses, is to further the state of knowledge regarding the appropriate metrics for 

assessing degradation in existing containment vessels. This can also provide valuable insights

into the performance of the containment under beyond-design-basis loading events. An improved 

understanding of the significance and influence of the various factors that contribute to the risk

and consequences may lead to important changes in the decision-making process when 

determining how to address these evolving safety issues at aging nuclear power plants. 

5

2. CONTAINMENT PERFORMANCE 

CHARACTERIZATION

In order to perform a severe accident simulation, a representation of the containment performance 

under internal pressurization must be developed. When studying the pressure capacity of 

containment vessels, it is important to have an understanding of how these structures behave 

under this loading. The most critical, and difficult, task is to choose and then measure the 

performance criterion of a containment structure using the results of a structural analysis. 

One of the potential measurements of a containment vessel undergoing pressurization is the leak 

rate at a given pressure. In addition, a given containment will also have a limiting pressure where

the structure either catastrophically ruptures, or at a minimum, the containment contains sufficient 

leak paths to no longer be capable of remaining pressurized. These structural capacity limit 

pressures are also a critical performance characteristic, however, they are often of lesser 

importance since they are usually larger than the pressure at which the containment first begins to 

leak. The study by Spencer et al. (2006) showed that this was especially true for reinforced and 

prestressed concrete containment vessels. 

In the PRA analyses performed for NUREG-1150, the containment performance was 

characterized by three categories of failures: “Leak”, “Rupture”, and “Catastrophic Rupture”. 

Even though the leak rate for an actual containment vessel is a continuous function of the internal 

pressure, NUREG-1150 uses distinct categories for computational convenience in the binning 

process. A leak is defined as “... an opening that would arrest a gradual containment pressure 

buildup but would not result in containment depressurization within 2 h.” “... A rupture is an 

opening that would result in rapid (<2 h) containment depressurization.” A catastrophic rupture 

“... would eliminate major portions of the containment structures”. These definitions are used in 

NUREG-1150 and in the previous study by Spencer et al. (2006) to estimate specific sizes of 

holes corresponding to the threshold leak rates for leak, rupture, and catastrophic rupture. 

In the NUREG-1150 and the previous study by Spencer et al. (2006) the pressures indicating the 

onset of leak, rupture, and catastrophic rupture are cast in terms of fragility curves, or 

probabilistic representations of the failure pressure. In order to construct fragility curves from 

deterministic structural analyses, a series of analyses were required which included variations in 

the material and modeling uncertainties. For the current study, the same procedures used in the 

previous work by Spencer et al. (2006) are employed to compute the fragility curves for the PRA 

analyses in this study. However, several cases with more extensive degradation are examined in 

addition to those explored by Spencer et al. (2006). In addition, the source term and consequence 

analyses performed here with MELCOR and MACCS make use of the same structural analyses as 

those used for the PRA analyses. The MELCOR and MACCS analyses do not use fragility 

curves as input, but employ the leak area (total crack area) as a function of the internal pressure

for a specific case. This section describes the general procedures used to model the containment 

capacity and compute the failure pressures and leak area vs. pressure distributions.

2.1 Containment Modeling

This study uses the analysis results from structural models developed under the previous study by 

Spencer et al. (2006). These models examined two concrete and two steel containments in order 

to estimate the pressures at which the various performance limits are met. The previous study 
6

focused on specific performance limits (“leak”, “rupture”, and “catastrophic rupture”) required 

for input into the PRA models. Here, these performance limits are used in the additional PRA 

analyses performed in this study. In addition, the leak area, or crack open area, as a continuous 

function of pressure is also of interest for input into the MELCOR analyses.

Leaks in the containment boundary are caused by tears in containment liners and shells and

initiate in regions of stress concentration (e.g. welds, local geometric details, or corrosion). These 

stress concentrations are generally several orders of magnitude smaller than the outer dimensions 

of the containment structure. Therefore, the structural modeling approach taken by Spencer et al. 

(2006), and adopted here, is to employ global finite element models of the containment structure 

to compute displacements and strains near the regions of anticipated stress concentrations. These 

displacements and strains are used as boundary conditions for detailed finite element models of 

local details or degraded regions. 

The finite element models used for the structural analyses were completed with the ABAQUS 

(HKS, 2002) general-purpose nonlinear finite element analysis program. 

The general procedures used to determine the containment performance for a reinforced concrete 

containment are summarized here. These procedures are the same as used by Spencer et al. 

(2006) with the relevant portions extended here for use in the deterministic MELCOR and 

MACCS analyses. 

2.1.1 Performance Characterization for a Reinforced Concrete Containment 

2.1.1.1 Steel Liner Leak Criterion for Corroded Regions

When examining the failure of the steel liner of the concrete containment considered in this study, 

it is assumed that the “leak” criterion is met when a tear initiates. At internal pressures below the 

level at which a tear first initiates, testing shows that there will probably exist a small amount of 

leakage, but it is assumed to be below the level of the “leak” threshold as defined in the PRA 

analyses and is assumed to not be consequence significant for the MELCOR and MACCS 

analyses.

Difficulties lie in determining where the first tear(s) is likely to occur due to the large number of 

local details that can potentially produce stress concentrations. In this regard, engineering 

judgment was used to select details and regions that exhibit the potential for the manifestation of 

high stress concentrations at lower pressures. Since actual containments contain a complex series 

of penetrations, welds, and other details, it is more than possible that some critical details have 

not been included in these computations. In addition, failures are likely to occur at local details 

not appearing on structural drawings (e.g. poor welds). The sampling of details and modeling 

methods considered in this study are assumed to be sufficient to provide a reasonable balance 

between the actual structural behavior and the practical matter of modeling that behavior. 

Tears in the liner are predicted to initiate when the effective plastic strain, p,eff ε , from the finite 

element analysis reaches a limiting value. The baseline limiting value of p,eff ε is the plastic 

strain found from a uniaxial tension test, denoted as fail ε . Various conditions may be present that 

can cause a tear to initiate when p,eff ε is less than fail ε . Spencer et al. (2006) adopted a modified 

version of the approach by Cherry and Smith (2001) to account for these effects. Equation 2.1 

illustrates the adjustment procedure used to modify the effective plastic strains from the analysis 
7

to account for the multiaxial stress state, the effect of corrosion on the failure strain, and the 

model sophistication, or gauge length:

p m c c u g FEM u p eff f f f f f , ε ε = − − (2.1)

The factors in this equation are defined as follows,

• mf accounts for the effects of multiaxial stress state, 

• c f accounts for the presence of corrosion, 

• c u f − accounts for the uncertainty in cf , 

• gf is a gauge length factor,

• FEM u f − denotes a finite element modeling uncertainty factor, 

• p ε denotes the factored plastic strain, and

• fail ε denotes the uniaxial tensile strength.

The factored plastic strain, p ε accounts for all of these effects. Failure occurs when p ε is greater 

than fail ε . 

The multiaxial stress state factor, denoted as mf was developed by Hancock and Mackenzie 

(1976): 

vm

e

fm σ σ σ )/ 2σ 1 2 3 ( 1.648

1.0

− + + = , (2.2)

where σ i are the principal stresses and σ vm is the von Mises stress. 

Experiments by Cherry and Smith (2001) found that a corroded steel plate could reasonably be

modeled by reducing the thickness of the plate uniformly. However, the failure strain in the 

corroded areas only reached approximately 50% of the no corrosion failure strain value. This is 

due to unevenness and pits present on the corroded surface producing local stress and strain 

concentrations. Therefore, corroded shell or liner regions are modeled with uniform thinning in 

addition to the application of a corrosion factor, cf equal to 2.0. In the PRA analyses the 

uncertainty of this effect is accounted for with the factor, c u f − , which is introduced as a random 

parameter which is statistically varied when developing the fragility curves. The value of c u f −

follows a lognormal distribution with 1.0 as the median and 0.2 as the β factor. In all other 

areas of the model, cf and c u f − are set equal to 1.0. For the containment representations used in 

the best estimate MELCOR/MACCS analyses, c u f − is set equal to 1.0, and to the same values 

used in the Spencer study for the upper/lower bound analyses.

Additional adjustments are included to account for the analysis sophistication, or gauge length,

with the factor, gf . This factor reflects the observation that strains tend to localize in areas of 

minor imperfections in the material. These localized strains can be much higher than the strains 

in the rest of the material a short distance from the localization area. The value assumed for this 

factor was based on work be Tang et al. (1995) who employed a gauge length factor of 4.0 in the 

derivation of strain magnification factors used to represent typical details in reinforced and 
8

prestressed concrete containments. In addition, FEM u f − reflects the uncertainty in the finite 

element model and the local strains computed with the meshes developed, boundary conditions, 

as well as other assumptions. Here, we use a lognormal distribution with 1.0 as the median and 

0.30 and 0.35 as the β factors for 3D models and shell models, respectively, to represent 

FEM u f − . Again, the best estimate value used for the MELCOR/MACCS containment 

representation is set to 1.0, and to the same values used in the Spencer study for the upper/lower 

bound analyses.

2.1.1.2 Penetration Leak Criterion

In reinforced concrete containments, a “leak” is assumed to initiate when tearing occurs in the 

steel liner. Here, the results of analytical models and experiments on typical discontinuities have 

been applied as reported in a study reported by Tang et al. (1995) and Castro et al. (1993). In 

these investigations, strain magnification factors were developed to approximate the effects of 

discontinuities typical of those found in the liners of reinforced and prestressed concrete 

containments.

The four locations identified as being susceptible to early tearing reside at large steam 

penetrations, at the junction of the wall and the basemat, at personnel or equipment hatches, and 

at the springline. Detailed finite element models, and in some cases, experimental models, were 

developed in the work by Tang et al (1995) and Castro et al. (1993) to determine the extent of the 

strain concentrations at those locations. These studies produced a series of strain magnification 

factors that enable the computation of the plastic strain in a discontinuity region using the global 

strain calculated with a simple axisymmetric model of the containment. Figure 2.1 illustrates the 

magnification factors for the four discontinuities as functions of the normalized global strain. 

The normalized global strain is defined as the appropriate global strain quantity from the 

axisymmetric analysis divided by the yield strain of the liner material.

Figure 2.1: Strain Magnification Factors for Typical Discontinuities in Reinforced 

Concrete Containments (approximation of the curves from Tang et al., 1995)
9

As with the adjustment factors presented in the previous section for local analyses, these strain 

magnification factors adjust the global strain, g ε , for multiaxial stress state, gauge length, and 

geometry effects. 

The magnification factor, M, is determined using the appropriate curve in Figure 2.1. The 

magnified global strain, or the factored plastic strain, p ε , is then simply computed as:

p FEM u g ε M f ε = −

(2.3)

where FEM u f − denotes a finite element modeling uncertainty factor. Tearing failure is predicted 

to occur when the factored plastic strain, p ε , at the specific discontinuity location within an 

axisymmetric model at a given pressure exceeds fail ε . In this study, corrosion was not assumed 

to exist at any of the typical discontinuities. Therefore, Eq. (2.3) does not include any adjustment 

for corrosion effects. For the MELCOR/MACCS analyses, FEM u f − is equal to 1.0 for the best 

estimate analyses and to the same values used in the Spencer study for the upper/lower bound 

analyses.

2.1.1.3 Concrete Containment Rupture Criterion

In the NUREG-1150 PRA analyses, the hole size in the steel liner required to meet the rupture

criterion is estimated between 0.028 m2 (0.3 ft2

) and 0.093 m2 (1.0 ft2). Here we define rupture 

using the more conservative value of 0.028 m2 (0.3 ft2

). For the MELCOR/MACCS analyses, the 

distribution of the crack area vs. pressure as a continuous function is required. The analyses 

performed in the study by Spencer et al. (2006) did not explicitly model the actual crack (leak) 

initiation and growth, but used the tearing criterion summarized above. Therefore, an 

approximate method developed by Dameron et al. (1995) was employed to estimate the hole size. 

Given a location and orientation (meridional or hoop) of an assumed crack within a model, a 

crack width is calculated by 

w s g = ε (2.4)

where g ε denotes the global strain and s equals the span or spacing between anchorages or stud 

layers perpendicular to the liner crack. The area of the opening can be estimated by multiplying 

the crack width by an assumed crack length, a.

A = w a (2.5)

The length of the crack can be estimated as the region of uniform peak strains or stresses, the size 

of local features, or the spacing of anchorages of studs in the direction of the crack. Equation 2.5

leads to an approximate estimate of the opening area since, among other factors, the opening is 

assumed square. Alternate estimates of the crack area can be constructed, but Equation 2.5 is 

assumed sufficient due to the large number of approximations employed here. 

Since Equation 2.5 estimates the area for only one crack, the total open area at a given pressure is 

computed by

( ....) Atotal = frupt−u A1δ 1n1 + A2δ 2 n2 + (2.6)

where the subscripts 1 and 2 are associated with different locations within the model where 

cracks are assumed to have a possibility of initiating.

• Ai denotes the crack area for one crack at location i, 
10

• δ i equals 1 if the leakage criterion has been obtained at location i and equals 0 if leakage

has not initiated, 

• i n denotes the number of cracks assumed to exist and initiate at location i, and 

• rupt u f − accounts for the uncertainty in the total area. 

The variable, δ i , enforces the requirement that a leak must initiate prior to a specific location 

contributing to the total open area. The crack number variable, ni , enables the inclusion of the 

effects of multiple cracks initiating near the same location. Based on Equation 2.6, the total crack 

area is computed as a function of the internal pressure. For the PRA applications, a rupture is 

defined at the pressure when the total area, Atotal , equals or exceeds 0.028 m2 (0.3 ft2

). The 

MELCOR/MACCS analyses use the total area as a continuous function of internal pressure. 

Since the best estimate MELCOR/MACCS analyses use the median values for all properties, the 

area uncertainty, rupt u f − , is set to 1.0. For the lower/upper bound analysis, the same uncertainties 

used in the Spencer study are employed. 

2.1.1.4 Catastrophic Rupture Criterion

A simple method is used to estimate the onset of catastrophic rupture for use in the PRA analyses. 

By assuming a cylinder with contributions only from the rebar and liner, the pressure to cause 

catastrophic rupture is computed with 















 = + − −

− − R

t

R s

A

P f liner ult liner

rebar

rebar ult rebar

cat rupt cat u

σ σ (0.9)

(2.7)

where 

• σ rebar−ult and σ liner−ult , denote the ultimate strength for the rebar and liner, 

• Arebar is the area of the rebar,

• rebar s denotes the spacing of the rebar, 

• liner t is the thickness of the liner, 

• R equals the radius of the containment, and 

• cat u f − accounts for the uncertainty in the catastrophic rupture pressure. 

In addition, Equation 2.7 includes a reduction factor of 0.9. This factor reflects overestimation of 

the simple method observed in the analysis and testing of a 1:4-scale prestressed containment. 

The 1:4-scale prestressed containment tested at Sandia National Laboratories (Hessheimer et al., 

2003) failed at 1.42 MPa, while the simple ultimate strength estimated failure at 1.54 MPa 

(Dameron et al., 2000). The ratio of 1.42 MPa to 1.54 MPa is reduced slightly to 0.9. 
11

3. DETERMINISTIC CONSEQUENCE ANALYSIS

PROCEDURES

The consequence analyses performed in this study employ two codes developed at Sandia 

National Laboratories, MELCOR and MACCS, with descriptions below. 

3.1 MELCOR

MELCOR 1.8.6 (Gauntt, et al., 2005) is a fully integrated, engineering-level computer code that 

models the progression of severe accidents in light water reactor nuclear power plants. MELCOR 

is being developed at Sandia National Laboratories for the U.S. Nuclear Regulatory Commission 

as a second-generation plant risk assessment tool and the successor to the Source Term Code 

Package. A broad spectrum of severe accident phenomena in both boiling and pressurized water 

reactors is treated in MELCOR in a unified framework. These include:

• Thermal-hydraulic response of the primary reactor coolant system, the reactor cavity, the 

containment, and the confinement buildings

• Core uncovering (loss of coolant), fuel heatup, cladding oxidation, fuel degradation (loss 

of rod geometry), and core material melting and relocation

• Heatup of reactor vessel lower head from relocated fuel materials and the thermal and 

mechanical loading and failure of the vessel lower head, and transfer of core materials to 

the reactor vessel cavity

• Core-concrete attack and ensuing aerosol generation

• In-vessel and ex-vessel hydrogen production, transport, and combustion

• Fission product release (aerosol and vapor), transport, and deposition

• Behavior of radioactive aerosols in the reactor containment building, including scrubbing 

in water pools, and aerosol mechanics in the containment atmosphere such as particle 

agglomeration and gravitational settling

• Impact of engineered safety features on thermal-hydraulic and radionuclide behavior

• The various code packages have been written using a carefully designed modular 

structure with well-defined interfaces between them. This allows the exchange of 

complete and consistent information among them so that all phenomena are explicitly 

coupled at every step. The structure also facilitates maintenance and upgrading of the 

code. 

Initially, the MELCOR code was envisioned as being predominantly parametric with respect to 

modeling complicated physical processes (in the interest of quick code execution time and a 

general lack of understanding of reactor accident physics). However, over the years as 

phenomenological uncertainties have been reduced and user expectations and demands from 

MELCOR have increased, the models implemented into MELCOR have become increasingly 

best estimate in nature. The increased speed (and decreased cost) of modern computers (including 

PCs) has eased many of the perceived constraints on MELCOR code development. Today, most 

MELCOR models are mechanistic, with capabilities approaching those of the most detailed codes 

of a few years ago. The use of models that are strictly parametric is limited, in general, to areas of 

high phenomenological uncertainty where there is no consensus concerning an acceptable 

mechanistic approach.

Current uses of MELCOR often include uncertainty analyses and sensitivity studies. To facilitate 

these uses, many of the mechanistic models have been coded with optional adjustable parameters. 
12

This does not affect the mechanistic nature of the modeling, but it does allow the analyst to easily 

address questions of how particular modeling parameters affect the course of a calculated 

transient. Parameters of this type, as well as such numerical parameters as convergence criteria 

and iteration limits, are coded in MELCOR as sensitivity coefficients, which may be modified 

through optional code input.

MELCOR modeling is general and flexible, making use of a "control volume" approach in 

describing the plant system. No specific nodalization of a system is forced on the user, which 

allows a choice of the degree of detail appropriate to the task at hand. Reactor-specific geometry 

is imposed only in modeling the reactor core. Even here, one basic model suffices for 

representing either a boiling water reactor (BWR) or a pressurized water reactor (PWR) core, and 

a wide range of levels of modeling detail is possible. For example, MELCOR has been 

successfully used to model East European reactor designs such as the Russian VVER, and 

RMBK-reactor classes. Current uses of MELCOR include estimation of severe accident source 

terms and their sensitivities and uncertainties in a variety of applications. The MELCOR Users 

Guide (Gauntt et al., 2005) provides extensive descriptions of the codes capabilities. 

3.2 MACCS

The MACCS2 code (Chanin et al., 1990) was developed for the U.S. Nuclear Regulatory 

Commission (NRC) to evaluate offsite consequences of hypothetical severe accidents at nuclear 

power plants (NPPs) based on calculated or assumed fission product releases. The code is 

designed to take input directly from the fission product releases calculated by MELCOR. 

MACCS2 models the radioactive materials being released as being dispersed in the atmosphere 

while being transported by the prevailing wind. The specification of the release characteristics, 

often referred to as “source term”, consists of Gaussian plumes (Systems Applications, 1982). 

Downwind population would be exposed to radiation, and land, buildings, and crops would be 

exposed to radioactive materials deposited from the plume. MACCS2 estimates the range and 

probability of the health effects induced by the radiation exposures and of the economic costs and 

losses that would result from the contamination of land, buildings, and crops. This section further 

describes a general calculation procedure of MACCS2. More detailed information on MACCS2 

can also be found in the code manual for MACCS2 (Channin et al., 1990).

MACCS2 calculations are divided into modules and phases. This division is based on the 

sequence of societal response that would follow the occurrence of an accident. These phases are 

defined by the Environmental Protection Agency (EPA) in its Protective Action Guides, and 

referred to as the emergency, intermediate, and long-term phases (EPA, 1991). In addition, there 

are three distinctive modules within the MACCS2 calculation frame, and each module prepares 

for or performs calculations related to those three phases. 

The first module, ATMOS, performs calculations related to atmospheric transport, dispersion and 

deposition, and the radioactive decay that occurs prior to release and while in atmosphere. 

Calculations in this module involve assessment of pre-accident inventories of radionuclides, 

transport and dispersion of radioactive material to offsite through development of a plume in the 

wake of plant buildings, and the subsequent downwind transport using a straight line Gaussian 

plume model. The results from the ATMOS module are then stored for use by other modules. 

The second module, EARLY, performs calculations pertaining to the emergency phase which 

include user specified emergency response scenarios such as evacuation, sheltering, and 

relocation. Direct exposure pathways, dosimetry, and any mitigative actions and health effects 

during the emergency phase are evaluated in the EARLY module. 
13

The third module, CRONC, models the events that occur following the emergency phase. The 

individual health effects that results from direct exposure to contaminated ground and from 

inhalation of resuspended materials, as well as indirect health effects caused by the consumption 

of contaminated food and water are calculated by the CRONC module. Additionally, CRONC 

simulates the economic consequences, such as the cost of the long-term protective actions or the 

cost of the emergency response actions that were modeled in the EARLY module. 

In this study, the following input data were made available to perform the consequence analysis 

using MACCS2. Further discussions on the development of specific input parameters and 

assumptions used in the analysis are provided in Section 5.2.

• The radioactive nuclide inventory important for the consequence analysis at accident 

initiation. 

• The atmospheric source term resulting from the accident including time and duration of 

release.

• Meteorological characteristics of the site region such as wind speed, atmospheric 

stability, and rainfall readings.

• The population distribution about the reactor site. 

• Emergency response assumptions (evacuation time and average moving speed, 

effectiveness and occurrence of sheltering, criteria and timing for post-accident relocation 

of people, decontamination criteria and effectiveness, temporary interdiction criteria for 

land and buildings, and disposal criteria for contaminated crops).

• Land usage (habitable land fractions and farm land fractions) and economic data (crops 

worth, land, and buildings) for the region about the site. 

In general, MACCS2 generates results for all possible combinations of a representative set of 

weather sequences and a representative set of exposed downwind population distributions, since 

consequences vary with source term magnitude, weather, and population density (Breeding et al., 

1992). Hence, in MACCS2, results are reported in terms of statistical distributions of 

consequence measures such as doses, health effects, or costs. It should be noted, however, that the 

focus of this study is placed on relative health consequence results produced from different levels 

of containment degradation, not economic consequences. 

15

4. PROBABILISTIC RISK ASSESSMENT PROCEDURES

TO ASSESS CONTAINMENT DEGRADATION

The following section provides a summary of the PRA procedures used in the previous study by 

Spencer et al. (2006) to assess containment degradation. These same procedures have been 

adopted for the current study in examining several additional cases.

4.1 Guidelines for Assessing Containment Degradation Using

Probabilistic Risk Assessments

The United States Nuclear Regulatory Commission (NRC) has recognized (NRC, 1995) the value 

of PRA techniques for nuclear applications in part due to improved safety and better allocation of 

limited resources, and has encouraged expanded use of PRA in regulatory decisions. Regulatory 

Guide 1.174 (USNRC, 2001) outlines the NRC’s guidelines for using PRA methods when 

making changes to a nuclear power plant’s licensing basis. Here, cases of degradation are treated 

as changes to the plant’s licensing basis.

The five principles to guide a risk-informed licensing basis change as outlined in Regulatory 

Guide 1.174 are:

• “The proposed change meets the current regulations unless it is explicitly related to a 

requested exemption or rule change, i.e., a “specific exemption” under 10 CFR 50.12 or a 

“petition for rulemaking” under 10 CFR 2.802.”

• “The proposed change is consistent with the defense-in-depth philosophy.”

• “The proposed change maintains sufficient safety margins.”

• “When proposed changes result in an increase in core damage frequency (CDF) or risk, 

the increases should be small and consistent with the intent of the Commission’s Safety 

Goal Policy Statement. “ (NRC, 1986)

• “The impact of the proposed change should be monitored using performance 

measurement strategies.”

The fourth principle states that if a change results in an increase in risk, the increase in risk must 

be small and fall within certain acceptance guidelines. Regulatory Guide 1.174 designated both

core damage frequency and large early release frequency (LERF) as criteria for assessing the

proposed change. Since this study is only examining degradation in the containment vessel, only 

changes in LERF will be examined here. 

Figure 4.1 illustrates the acceptance criteria for a proposed licensing basis change in terms of 

LERF. The change in LERF is plotted versus the baseline metric and includes three regions. 

Region I defines the conditions where the increase in the risk due to a proposed change is deemed 

too high to be acceptable, and the change is not permitted. For Region II, the risk increase is 

smaller than Region I, and the change is permitted but requires additional monitoring. In Region 

III, the change is permitted since the increase in the risk is defined as very small. In addition, the 

risk increases that fall in Region III are deemed so small enough that the value of the baseline risk 

metric does not need to be computed. 
16

The application of Regulatory Guide 1.174 requires that the licensees clearly define the proposed 

change(s) and conduct sufficient analyses to demonstrate that the acceptance guidelines are met.

The licensee must also present a methodology for implementing and monitoring the proposed 

change. 

Since containment degradation reduces the pressure containing capacity of the structure, it is 

possible that determining the change in risk (e.g. LERF) may provide a means of assessing that 

degradation. In the study by Spencer et al. (2006), the guidelines of Regulatory Guide 1.174 were

applied to assess the risk associated with various types of postulated degradation of containment 

vessels and bellows. The degradation was considered to be a temporary change in the plant’s 

licensing basis using a coupled structural-PRA analysis and Regulatory Guide 1.174.

4.2 Procedure for Risk-Informed Containment Analysis

As applied in the study by Spencer et al. (2006) and in this study, the structural fragility under 

internal pressurization serves as the interface between the structural analyses and PRA models 

created for NUREG-1150. Since structural analyses are deterministic in nature, a probabilistic 

distribution of the structural capacity is required. This probabilistic distribution, or fragility 

curve, is the cumulative probability of failure for the containment under internal pressure. The 

criterion used to assess the potential structural failures was described in Section 2. In order to 

expand these deterministic, point values, a modified version of the methodology used by 

Ellingwood and Cherry (1999) was employed by Spencer et al. (2006). This method included 

uncertainty in the structural capacity using both the inherent randomness in the components that 

make up the structure and the uncertainty in the analyst’s ability to characterize the behavior of 

the structure. These are often referred to as aleatory uncertainty and epistemic uncertainty, 

respectively.

Figure 4.1: Acceptance Guidelines for Large Early Release Frequency
17

The study by Spencer et al. (2006) includes a rigorous method to determine the structural 

fragility. This included estimating or determining the probability distributions associated with the 

individual components within the structure. Since the number of random variables required to 

perform a full Monte Carlo simulation is not reasonable for a complex containment structure, a 

Latin Hypercube Simulation (LHS) technique (McKay et al, 1979) was used to reduce the 

number of samples required. LHS analyses do not generate purely random variables for each 

sample; however, the stratum for each variable is randomly selected. The use of the LHS 

technique reduces considerably the number of structural analyses required to construct a 

structural fragility curve. Spencer et al. (2006) used the DAKOTA (Eldred et al, 2002) 

uncertainty analysis software to generate the LHS samples for the structural analyses.

In addition to the overall fragility curve, the NUREG-1150 PRA models also require the

conditional probabilities of failure. The overall fragility describes the cumulative probability of 

failure as a function of the internal pressure, where failure is defined as any of leak, rupture, or 

catastrophic rupture. The conditional probability of failure describes the probability of each 

different type of failure and/or mode, given that there is a failure. Since the effects that different

modes of failure have on the accident progression are critical, these differences must be 

accounted for during the compilation of the fragility curves. 

For the given containment, thirty sets of random parameters were produced using the LHS 

procedure and used as input into the analytical models of the containment. Locations of potential

failure are modeled using a combination of global and local finite element models. The failure 

criteria used to determine the pressure at which failure occurs at a specific location within the 

containment were described in Section 2. 

A fragility curve at each location of potential failure is compiled using rank probabilities. For 

each of the 30 analyses, the failure pressures at a given location are ranked with each assigned a 

probability. The lowest pressure analysis is assigned the lowest failure probability equal to (1-

0.5)/n, where n is 30 here. The next highest pressure is assigned a probability of (2-0.5)/n, or (i0.5)/n for i=1,2...30. Fitted lognormal distributions are used to extrapolate the failure pressures 

to probabilities in the tail regions. 

The fragility curves for all of the failures are combined into one cumulative probability of failure 

curve using de Morgan’s rule (Ang and Tang, 1975). The probability of occurrence of any one of 

a number of statistically independent events En can be computed as

( ... ) 1 (1 ( ))(1 ( ))...(1 ( )) P E1 ∪ E2 ∪ ∪ En = − − P E1 − P E2 − P En . (4.1)

Failure in containments typically occurs at stress concentrations around penetrations, and the 

various penetrations in a containment can reasonably be assumed to be statistically independent. 

The penetrations modeled are just a sample of what may be a large number of very similar 

penetrations. The overall fragility is the cumulative distribution of the probability of a failure of 

any size. In addition, a larger size of failure at a location can only occur after the smallest size of 

failure (e.g. leak) at that location can occur; therefore, the distribution function for the smallest 

failure mode at every location is used in this calculation.

The conditional probabilities of failure of the three sizes (leak, rupture, and catastrophic rupture) 

are then computed. A leak is a breach that is smaller than the rupture size. A rupture is bigger 

than the leak size, but smaller than the catastrophic rupture size. The NUREG report by Spencer 

et al. (2006) describes the method used to compute the conditional probabilities. Using their 

method, the probability of each type of failure is given at a given pressure, given that a failure has 

occurred.
18

These cumulative and conditional failure probabilities are used as input into the PRA models 

developed in NUREG-1150 and described in detail in NUREG/CR-4551. In general, no detailed 

analyses were performed in that study to determine the containment performance/capacity. 

Instead, experts provided their estimates of failure pressure distributions using a number of 

methods including hand-calculations and experience. In addition, the original NUREG-1150 

study did not investigate the effects of degradation in the containments. Since the purpose of the 

PRA analysis performed by Spencer et al. (2006) was to determine the change in LERF due to 

degradation, the PRA analyses are performed with the containment in its original and degraded 

states. Since containment degradation does not impact the core damage frequency, that portion of 

the original NUREG-1150 study is unchanged. The NUREG by Spencer et al. (2006) includes a 

short description of the PRA methodology and accident progression analyses. In the current 

study, we employ the same approach as Spencer et al. (2006), but examine additional cases of 

degradation.

While the study by Spencer et al. (2006) was successful in demonstrating a methodology to 

determine the change in LERF due to containment degradation, several cases of degradation 

proved to not affect LERF. In some cases, degradation even caused decreases in LERF. This 

could lead to the misleading conclusion that degradation may be beneficial from a risk standpoint. 

This is obviously not acceptable and shows that changes in LERF may not be the appropriate 

criteria to be applied in assessing containment degradation. Spencer et al. (2006) included the 

small early release frequency (SERF), as well as LERF. In the degradation cases that showed no 

change or decreases in LERF, SERF typically increased. Unfortunately, Regulatory Guide 1.174 

does not provide guidance on acceptable changes in SERF. 

Due to the results of the study by Spencer et al. (2006), the current work will examine additional 

cases of degradation to those considered previously. These additional cases will focus on 

including degradation extending over a larger area of the containment shell or liner. The previous 

analyses might have shown that LERF was relatively insensitive to degradation due to the regions 

of degradation being too small. These small regions of degradation, while causing earlier leaks, 

did little to affect the larger rupture and catastrophic rupture pressures. The binning process used 

in NUREG-1150 placed only these larger failures into LERF and the smaller leak failures into 

SERF. The more extensive degradation considered here is intended to produce larger effects on 

the rupture type failures, and consequently, LERF.
19

5. SEVERE ACCIDENT CONSEQUENCE ANALYSES OF 

PWR PLANT WITH REINFORCED CONCRETE

CONTAINMENT

As examined by Spencer et al. (2006), a reinforced concrete (RC) containment for a pressurized 

water reactor (PWR) nuclear power plant was analyzed here to explore the effects of degradation

during a severe accident. Corrosion in the steel liner wall was assumed near the wall-basemat 

juncture and at the mid-height of the containment as shown in Figure 5.1.

These locations were employed in this study and by Spencer et al. (2006) since these regions 

reside in areas of high liner strains and because water could accumulate in these regions. 

However, the study by Spencer et al. (2006) only explored analyses which included one small 

region of corrosion in the liner for each case. Here, we extended this work by assuming multiple 

locations of corrosion for a number of cases. These additional analyses were included to provide 

an understanding of the sensitivity of the risk and consequences to the extent of corrosion. The 

effects of the degradation on LERF are included in this study as well as deterministic analyses 

Figure 5.1: Postulated Corrosion in Liner of RC Containment (Spencer et al., 2006)
20

using MELCOR and MACCS. The structural analysis results from the study by Spencer et al. 

(2006) were used and modified in some cases for the present study. 

Although the dimensions and properties of the Surry containment vessel were used to construct 

the structural model and site specifics data in the MACCS model, a number of assumptions have 

been made here including the hypothetical corrosion assumed for this study. Therefore, these 

analyses are not representative of actual conditions observed at that plant, or any other existing

plant. This study was conducted to demonstrate an analysis methodology and to explore the 

potential effects that corrosion can have on risk and consequences. 

5.1 Structural Model of Reinforced Concrete Containment

The experimental study by Horschel (1992) of a pressurization test of a 1:6 scale RC containment 

vessel with a steel liner showed that failures occur generally by tearing in the liner at geometric 

discontinuities. These tears then provide a leak path for material through the containment wall. 

Therefore, Spencer et al. (2006) assumed that a tear in the linear produced a failure of the 

containment. In addition, these tears would occur at penetrations or regions of corrosion. The 

modeling procedure used by Spencer is similar to that used by Cherry and Smith (2000). Cherry 

and Smith developed an axisymmetric model of the RC containment and determined the global 

strains in the liner. These global strains defined the boundary conditions for local models that 

include thinned areas caused by corrosion. A strain criterion was used in both studies to compute 

when tearing initiated. However, Spencer et al. (2006) include distinctions between leak, rupture, 

and catastrophic rupture to use in the PRA analyses, where Cherry and Smith only considered 

leak in their failure estimates. Here, we use the structural analysis results from the study by 

Spencer et al. for use in additional PRA analyses and in the MELCOR/MACCS analyses.

5.1.1 Axisymmetric Global Model

The axisymmetric finite element mesh of the containment shown in Figure 5.2(a) was used in the 

study by Spencer et al. (2006). The reinforced concrete containment is approximately 1.37 m (4.5 

feet) thick with a 9.53 mm (0.375 inch) thick steel liner. The concrete is modeled using the 

ANACAP-U (ANATECH, 1997) constitutive model, which is linked with the ABAQUS (HKS, 

2002) finite element program. Reinforcing bars are modeled by embedding them within the 

concrete elements. The liner is modeled with axisymmetric shell elements directly attached to the 

concrete elements on the inside face of the containment. Nonlinear spring elements are used to 

represent the interface conditions between the containment and the soil. These springs exhibit 

high elastic stiffness in compression with no strength in tension.

For the analyses by Spencer et al. (2006), the containment model was subjected to a 

monotonically increasing internal pressure loading with an increasing temperature. The 

temperature load is increased as the pressure loading increases. The initial temperature of the 

liner was set at 21o Celsius (70o Fahrenheit) and increases to a peak temperature of 176o Celsius 

(349o Fahrenheit) at a pressure of 1.38 MPa (200 psi). 

Figure 5.2(b) shows the deformed shape (magnified by 10) of the axisymmetric model for a 

typical case near the end of the analysis. 
21

5.1.2 Local Detail and Corrosion Modeling

In Section 2.1.1.2, the strain magnification factors are described for use when approximating the

strain concentrations in the liner at discontinuities. Section 2.1.1.1 provides the method used 

when assessing the detailed 2-D finite element models used to model regions of hypothetical 

corrosion. Two locations of liner corrosion were studied by Spencer et al. (2006), one at the midheight of the containment and the other in the containment wall just above the junction with the 

basemat. Corrosion was assumed to have thinned the original liner at two different levels, 50% 

and 65% for each location. These are the percentages of material that is no longer in its near 

original condition. A thin layer of severely reduced strength corroded steel constituents would be 

attached, but is ignored using this uniform thinning method. Corrosion was assumed to have 

occurred over an in-plane region 8 cm (3 in) wide and 13 cm (5 in) high for the mid-height case 

as shown in Figure 5.3. The outer boundaries of the mesh cover a 91 cm (36 in) wide square 

region. Figure 5.4 shows the finite element mesh used in the basemat region of the containment. 

The corroded region is approximately 25 cm (10 in) wide and 18 cm (7 in) high. At the 

boundaries of the mesh, the average length of an element edge is 25 mm (1 in), while in the 

corroded area, the mesh is refined considerably and the average element length is approximately 

8 mm (0.3 in). In both of these cases, a single layer of elements surround the corroded region to 

provide a gradual transition from the corrosion zone to the undamaged liner. In that layer of 

elements, the corrosion is assumed to penetrate 25% and 32.5% of the wall thickness for the 50% 

and 65% corrosion cases, respectively. Nonlinear spring elements are used to approximate the 

behavior of the shear studs that attach the liner to the concrete wall. The stud locations are 

 (a) Original Mesh (b) Deformed at 1.05 MPa (152 psi)

 (magnified 10x)

Figure 5.2: Axisymmetric Finite Element Model of RC Containment (Spencer et al., 2006)
22

illustrated in the finite element meshes, and are typical of details that would be seen in an actual 

RC containment. 

The size and shape of the corroded regions employed here are hypothetical in nature and not 

based on any specific corrosion data at any existing plant. They were developed in order to 

provide a large enough area of corrosion to manifest a sufficient stress/strain concentration where 

a crack would initiate. Actual corrosion in plants will vary widely in shape, extent, and level. 

This study’s goal is to demonstrate a methodology and not to assess any specific plant. If specific 

plant corrosion data is available, a site specific analysis should be performed.

The results from the local models were post-processed to determine the point at which tearing 

occurs. For a tear to initiate, the effective plastic strains are multiplied by factors to account for 

the effects of the multiaxial stress state, corrosion, gauge length, and modeling uncertainty, as 

described in Section 2.1.1.1. 

Figure 5.3: Finite Element Mesh of Corrosion at Midheight
23

5.1.3 Structural Analysis with Best Estimate Properties

The focus of the structural analysis performed by Spencer et al. (2006) was to develop fragility 

curves for use as the interface with the NUREG-1150 PRA models. Their study also included a 

description of the baseline analysis results that used the median values of the input parameters. 

This baseline analysis was used here for input into the MELCOR accident analysis model, and 

therefore, is summarized below.

Six potential liner failure modes are considered: failure at the four locations of geometric 

discontinuities for which magnification factors are used (see Section 2.1.1.2), failure at a 

corroded region at the wall midheight, and failure at a corroded region on the wall near the 

basemat. To investigate the potential for failure (leak) at all of these locations, the global 

axisymmetric model is analyzed, and results are extracted for use as displacement boundary 

conditions for the two local corrosion models. The two local corrosion models are run with 50% 

and 65% corrosion and post-processed to find the most critical value of p ε at every loading step

using the leak criterion (see Section 2.1.1.1). A separate post-processing tool is applied to the 

results of the axisymmetric model to apply appropriate magnification factors to find p ε for the 

four selected discontinuity locations at every loading increment. The uniaxial plastic failure 

strain, fail ε , was assumed to be 25% for these analyses. The gauge length factor was assumed to 

be 4.0 for the local corrosion models in this baseline analysis. 

Figure 5.5 shows the plot of the ratio of p ε to fail ε (0.25) for the 6 failure modes as a function of 

internal pressure for the baseline analysis. A horizontal line has been drawn at 1.0 to show the 

failure criterion. It is evident that the failure condition is met first at the corroded area at the 

midheight, and that the corroded area near the basemat appears to be the least critical location. 

Of the geometric discontinuities, the steam penetration is the most critical. From this analysis, it 

appears that a containment without any degradation would fail at 0.896 MPa (129.9 psi) at the 

steam penetration. If the postulated corrosion were present at the mid-height, it would fail at that 

Figure 5.4: Finite Element Mesh of Corrosion in Wall Near Basemat
24

location at an internal pressure of 0.829 MPa (120.3 psi) and 0.812 MPa (117.8 psi) for 50% and 

65% corrosion, respectively. Leak near the corroded basemat does not occur until 0.947 MPa 

(137.4 psi) and 0.939 MPa (136.2 psi) for 50% and 65% corrosion, respectively. Leakage occurs

at the steam penetration prior to leak in the corroded basemat location. Table 5.1 summarizes the 

leak pressures for each location. 

Figure 5.6 and Table 5.1 also include failure curves and pressures for five rupture cases examined 

by Spencer et al. (2006): the original containment with no corrosion, 50% corrosion at the 

basemat, 65% corrosion at the basemat, 50% corrosion at the midheight, and 65% corrosion at the 

midheight. In addition, Table 5.1 includes three new cases not explicitly examined under the 

previous study by Spencer et al. (2006). These cases assume that 10 regions of local corrosion 

exist in the containment. The three new cases are 10 regions of 50% corrosion at the basemat, 10 

regions of 50% corrosion at the mid-height, and 10 regions of 65% corrosion at the mid-height. It 

is assumed that for each of these cases, the local corrosion regions do not interact. Therefore, the 

contribution of the corroded area to the total crack area is 10 times the amount that is used in the 

original, or single, corrosion region cases. The procedure in Section 2.1.1.3 is used to compute 

the ratio of the total rupture area, Atotal , to the rupture area limit of 0.028 m2 (0.3 ft2

), as a 

function of pressure. The four features, steam penetration, wall-basemat junction, hatch, and 

springline, are assumed to contain four cracks ( ni ) each after the leak criterion has been reached. 

The choice of four cracks at each location is based on the upper limit of the number of tears 

observed in the 1:6 scale reinforced concrete containment testing at Sandia National Laboratories 

(Horschel, 1992). The number of cracks at each location could have been introduced as a random 

variable for the PRA fragility analysis, but due to the severely approximate nature of the rupture 

estimate employed here, a random variable with a large uncertainty is imposed on the total 

rupture area. One crack is assumed at the basemat and midheight locations for cases considering 

corrosion. For each of the 10 regions of corrosion cases, 10 cracks are assumed.

For the two single basemat corroded cases, leak does initiate prior to the overall rupture failure. 

This has only a negligible effect on the total rupture area, since only one crack is assumed to 

initiate at the corroded location. Therefore, the rupture curves for the original case with no 

corrosion and the two basemat corrosion cases essentially share the same curve. A small increase 

in the rupture area is caused by a single region of corrosion at the midheight. Since the global 

strains do not differ between the 50% and 65% corrosion cases, the rupture curves are nearly 

identical. Obviously, the assumption of more than one corroded location for each case causes an

increase in the rupture area and lowers the rupture pressure. This is especially true for corrosion 

at the midheight, where leak initiates at the corroded location well before initiation at the steam 

penetration. The effects of multiple basemat corroded locations are minimal since leak at the 

corroded basemat initiates just prior to the current rupture thresholds. Variation in the total area 

assumed to cause rupture (0.028 m2 or 0.3 ft2

) will also affect the rupture pressure. As mentioned 

previously, a large uncertainty is imposed on the total rupture area to account for the approximate 

nature of the rupture criterion when computing the fragility curves in the next section. Finally, 

Figure 5.6 and Table 5.1 include the simple estimate for catastrophic rupture described in Section 

2.1.1.4.

The next section describes the procedures used for developing the fragility curves used in the 

PRA analyses. For the deterministic MELCOR/MACCS analyses, three sets of analyses were 

performed. These include a best estimate (or nominal case), and lower and upper bound sets of 

analyses. The best estimate cases use the structural analysis results described in this section, 

where the lower and upper bound analyses use the structural analysis results from the analyses 
25

described in the next section on fragility curve development. Section 5.1.5 then provides the area 

vs. pressure curves for each set of analyses as they were extracted from the structural analyses.

Table 5.1: Summary of Locations and Failure Pressures

Location Failure Pressure

MPa (psig)

Leak Steam Penetration 0.896

(129.9)

Leak Wall-Basemat Junction 0.988

(143.3)

Leak Hatch 0.935

(135.6)

Leak Springline 0.992

(143.9)

Leak Base 50% Corrosion 0.947

(137.4)

Leak Base 65% Corrosion 0.939

(136.2)

Leak Midheight 50% Corrosion 0.829

(120.3)

Leak Midheight 65% Corrosion 0.812

(117.8)

Rupture No Corrosion 0.983

(142.6)

Rupture Base 50% Corrosion 0.983

(142.6)

Rupture Base 65% Corrosion 0.983

(142.6)

Rupture Midheight 50% Corrosion 0.976

(141.6)

Rupture Midheight 65% Corrosion 0.976

(141.6)

Catastrophic Rupture 1.195

(173.3)

Rupture Base 50% Corrosion 10x 0.975

(141.5)

Rupture Midheight 50% Corrosion 10x 0.920

(133.5)

Rupture Midheight 65% Corrosion 10x 0.920

(133.5)
26

Figure 5.5: Failure Potential at Corrosion and Discontinuity Locations (Leaks)

Figure 5.6: Failure Potential at Corrosion and Discontinuity Locations (Ruptures)

0.0

0.5

1.0

1.5

2.0

0 25 50 75 100 125 150 175 200

pressure [psig]

Failure Function (1.0=failure) 

Leak Steam Penetration

Leak Wall-Basemat Junction

Leak Hatch

Leak Springline

Leak Base 50% Corrosion

Leak Base 65% Corrosion

Leak Midheight 50% Corrosion

Leak Midheight 65% Corrosion

Design Pressure

0.0

0.5

1.0

1.5

2.0

0 25 50 75 100 125 150 175 200

pressure [psig]

Failure Function (1.0=failure) 

Rupture No Corrosion

Rupture Base 50% Corrosion

Rupture Base 65% Corrosion

Rupture Midheight 50% Corrosion

Rupture Midheight 65% Corrosion

Rupture Base 50% Corrosion 10x

Rupture Midheight 50% Corrosion 10x

Rupture Midheight 65% Corrosion 10x

Catastrophic Rupture

Design Pressure

Catastrophic Rupture
27

5.1.4 Fragility Curve Development for PRA Analyses

The principal goal of the study by Spencer et al. (2006) was to integrate structural analyses of 

degraded containments with risk analysis models to understand the significance of the 

degradation from a risk-informed perspective. Fragility curves of containments under 

pressurization with and without degradation serve as the interface between the structural and risk 

analyses. As explained in Section 4.2, Latin Hypercube Sampling was used to generate sets of 

random variables to be used as input to the structural finite element analyses. In the Spencer 

study, 19 input parameters were selected as random variables, and 30 samples of those parameters 

were developed for analysis.

Of the 19 input parameters, 14 describe the inherent randomness, or aleatory uncertainty, in the 

basic properties of concrete, reinforcing bars, and liner steel. The remaining 5 parameters 

describe epistemic uncertainty, or uncertainty in the ability to characterize the failure pressure. 

Several of the random input parameters are correlated with others. For concrete, the tensile 

strength, t f ' , and modulus of elasticity, Ec , are correlated with the cylinder compressive 

strength, c f ' . Likewise, there is correlation between the yield strength and ultimate strength of 

steel. 

Whenever possible, statistical test data was used as the basis for the probability distributions in 

this study. When such data was unavailable, engineering judgment was used to provide 

reasonable estimates of uncertainty. A thorough statistical analysis of concrete strength was 

performed by Mirza et. al. (1979). Based on recommendations from that analysis, the elastic 

modulus of concrete is computed as:

c c E c 60400 f ' = 1

(5.2)

where 1 c is a random variable with a median of 1.0 and a coefficient of variation of 0.077. 

Likewise, t f ' is computed as:

t c f ' c 8.3 f ' = 2

(5.3)

where 2 c has a median of 1.0 and a coefficient of variation of 0.196. Units of psi are used in 

both of these equations. Under average control conditions, Mirza et al. (1979) suggest that a

coefficient of variation (COV) of 0.15 can be assumed for c f ' .

The RC containment investigated in this study has reinforcing bars of both Grade 40 and Grade 

50 steel. Unfortunately, less information was available on the correlation between yield strength 

and ultimate strength, and between the elastic modulus and strength for steel. The elastic 

modulus, Es , is assumed to be independent of the yield strength, y f , and the ultimate strength, 

uf . Correlation is induced between y f and uf in a manner similar to that for concrete:

y u f s r f = 1 (5.4)

where 1 s is a random variable with a median of 1.0. The variable r is the ratio of the yield stress 

to the ultimate stress, and differs depending on the type of steel. For Grade 40 reinforcement, a 

value of 0.6 was assumed for r . For Grade 50 reinforcing, this value was set at 0.62, and for the 

liner steel, a value of 0.535 was used.

Five separate variables are used to describe the epistemic uncertainty. Variable describes the 

uncertainty inherent in predicting the global strains, the local strains from the 2-D submodels with 
28

corrosion, the strain magnification in the presence of corrosion, the calculation of the rupture 

area, and the simple estimate for catastrophic rupture. 

Each of these variables has a median value of 1.0. A COV of 0.3 was assumed for the global 

strain prediction variable, FEM u f − . This agrees well with the scatter in the analytical predictions 

submitted by several analysts for the behavior of the 1:6 scale RC containment test conducted at 

Sandia National Laboratories (Clauss, 1987). The magnification factors for the liner 

discontinuities are simply multiplied by this uncertainty factor in Equation 2.3.

The COV of the local model uncertainty factor, FEM u f − , was set to 0.35 because it was felt that 

there is more uncertainty in the local models than in the global models. For the local detailed 

models, Equation 2.1 is used to compute the magnified strains. Since the local models contain 

corrosion, the corrosion factor, c f , equals 2 and is multiplied by an uncertainty factor, c u f − , with 

a COV of 0.20.

The final two epistemic factors account for the uncertainty in the rupture area, rupt u f − , and 

catastrophic rupture pressure, cat u f − . Since the calculation of the rupture area in Equation 2.6

contains several approximations, a large COV is employed, equal to 0.40. The simple method 

used here to compute the catastrophic rupture pressure (Equation 2.7) should provide a reasonable 

estimate, enabling the use of a low COV of 0.10. This uncertainty is in addition to the variation 

in the ultimate strengths random variables used in Equation 2.7. Since different criteria are used 

for the rupture and catastrophic rupture failures, there is no correlation between their uncertainty 

factors. 

Table 5.2 shows all of the random input parameters. This table shows the median values of the 

parameters, a measure of the variation assumed for the parameter, and the type of distribution. 

For variables with normal distributions, the COV is used as the measure of variation, while β is 

used for variables represented with a lognormal distribution.

A total of 30 sets of these input parameters were generated based on analyses using the specified 

distribution functions. Once the analyses were run, the 30 leak pressures were used to develop 

fragility curves for each of the four locations of linear discontinuity. Figure 5.7 shows the 

fragility curves based on the sorted analyses values and associated lognormal curve fits. The 

fragility curves represent the leak pressures for the four discontinuity locations. Figure 5.8 shows 

the fragility curves for leaks at the two corroded locations, basemat and midheight, at the two 

levels of corrosion, 50% and 65%. These plots indicate that increasing the level of corrosion 

from 50% to 65% of the liner thickness has only a minimal effect. Due to the shape of the 

distributions, the lognormal curve fits for each of the corroded cases require one curve fit for high 

probabilities and one curve fit for low probabilities.
29

Table 5.2: Random Input Parameters

Property Median COV/β Distribution

Concrete

Compressive Strength ( c f ' ) 27.3 MPa 

(3.956 ksi)

0.15 Lognormal

Elastic Modulus factor ( 1 c ) 1.0 0.077 Normal

Tensile Strength factor ( 2 c ) 1.0 0.196 Normal

Grade 40 Reinforcing Steel

Ultimate Strength ( uf ) 508.3 MPa

(73.72 ksi)

0.09 Lognormal

Yield Strength Factor ( 1s ) 1.0 0.07 Normal

Elastic Modulus ( Es ) 200 Gpa

(29000 ksi)

0.06 Normal

Grade 50 Reinforcing Steel

Ultimate Strength ( uf ) 590.5 MPa

(85.65 ksi)

0.09 Lognormal

Yield Strength Factor ( 1s ) 1.0 0.07 Normal

Elastic Modulus ( Es ) 200 Gpa

(29000 ksi)

0.06 Normal

Liner Steel

Ultimate Strength ( uf ) 577.1 MPa

(83.70 ksi)

0.09 Lognormal

Yield Strength Factor ( 1s ) 1.0 0.07 Normal

Elastic Modulus ( Es ) 200 GPa

(29000 ksi)

0.06 Normal

Uniaxial Failure Strain ( fail ε ) 0.25 0.12 Normal

Corrosion Depth Uncertainty 1.0 0.10 Normal

Epistemic Uncertainty

Axisymmetric Model Strain Factor 

Uncertainty ( FEM u f − )

1.0 0.30 Lognormal

Submodel Model Strain Factor Uncertainty 

( FEM u f − )

1.0 0.35 Lognormal

Corrosion Factor Uncertainty ( c u f − ) 1.0 0.20 Lognormal

Leak Area for Rupture Uncertainty 1.0 0.40 Lognormal

Catastrophic Rupture Uncertainty 1.0 0.10 Lognormal
30

As discussed previously, the rupture threshold is assumed to be reached when the total crack 

opening caused by initiated leaks exceeds 0.028 m2 (0.3 ft2

). Figure 5.9 shows the rupture 

fragility curves for the eight cases examined in this study. The crack opening near the midheight 

corroded locations are large enough to cause a decrease in rupture pressure. Since the global 

strains are employed to estimate the rupture pressure, the single location 50% and 65% midheight 

corroded cases are the same. The 10 regions of corrosion cases at the midheight show a 

noticeable decrease in the rupture fragility, with the 65% decreasing slightly more than the 50% 

case. The basemat cases with a single corrosion location do not vary from the no corrosion case, 

while the 10 region case is only slightly decreased from the single corrosion cases. Figure 5.9

also illustrates the fragility curve for catastrophic rupture. Since the criteria for catastrophic 

Figure 5.7: Fragility Curves for Leak at Discontinuity Locations

Figure 5.8: Fragility Curves for Leak at Corroded Locations

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Probability of Failure

Leak - Steam Penetration

Leak - Wall-Basemat Junction

Leak - Hatch

Leak - Springline

Design Pressure

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Probability of Failure

Leak - Base 50% Corrosion

Leak - Base 65% Corrosion

Leak - Midheight 50% Corrosion

Leak - Midheight 65% Corrosion

Design Pressure
31

rupture is not affected by the corrosion in the liner, the catastrophic rupture fragility remains the 

same for all eight cases.

Figure 5.10 shows the cumulative probability of failure (leak) curves obtained in the Spencer

study for the containment with corrosion degradation at the midheight and at the basemat, along 

with the fragility of the containment in its original condition. As would be expected from the 

baseline analysis, the drop in capacity due to corrosion at the mid-height is much greater than that 

due to corrosion at the basemat. The introduction of multiple regions of corrosion does not affect

the cumulative probability of failure since it is assumed that when one corroded locations tears, 

all 10 regions tear simultaneously. 

Figure 5.9: Fragility Curves for Rupture and Catastrophic Rupture

Figure 5.10: Cumulative Probability of Failure Curves for Original and Degraded RC 

Containment

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Probability of Failure

Rupture - No Corrosion

Rupture - Base 50% Corrosion

Rupture - Base 65% Corrosion

Rupture - Midheight 50% Corrosion

Rupture - Midheight 65% Corrosion

Catastrophic Rupture

Rupture - Base 50% Corrosion 10x

Rupture - Midheight 50% Corrosion 10x

Rupture - Midheight 65% Corrosion 10x

Design Pressure

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Cumulative Probability of Failure

Original - No Corrosion

Base 50% Corrosion

Base 65% Corrosion

Midheight 50% Corrosion

Midheight 65% Corrosion

Base 50% Corrosion 10x

Midheight 50% Corrosion 10x

Midheight 65% Corrosion 10x

Design Pressure
32

The conditional probability of failure curves were computed for each of the eight cases and 

shown in Figure 5.11 through Figure 5.18. Since the rupture and catastrophic curves are 

relatively constant throughout the original five cases examined by Spencer et al. (2006), the 

conditional probability distributions are extremely similar. At low pressures (P < 0.65 MPa), the 

probability of leak is equal to 1 with the rupture and catastrophic rupture probabilities at 0. 

Increases in pressure cause the rupture and eventually the catastrophic rupture conditional 

probabilities to increase. The leak probability decreases quickly as the rupture probabilities 

increase. The rupture curve peaks at approximately 1.1 MPa. At this point, both the leak and 

rupture curves decrease gradually to probabilities of 0 and the catastrophic curve increase to a 

probability of 1 at approximately 1.7 MPa. For the 10 regions of basemat corrosion cases, the 

change in the conditional probabilities is similar to those for the original cases. However, the 

cases of multiple corrosion at the midheight do cause a noticeable increase in the rupture 

probabilities at lower pressures. The slight “wave” in the leak and rupture curves in Figure 5.17

and Figure 5.18 reflect the sensitivity to the curve fits used at the low pressure (P < 0.75 MPa) for 

the leak and rupture fragility curves in Figure 5.8 and Figure 5.9. This is especially true for those 

two cases where the 10 regions of midheight corrosion dominate the rupture areas at low 

pressures.

The fragility and conditional failure curves presented in this section are used as input in the PRA 

analyses. Those results are shown in Section 5.3. As mentioned in the previous section, the 

deterministic MELCOR/MACCS analyses were performed using three sets of data. The best 

estimate (or nominal case) uses the data from the previous section. The lower and upper bound 

sets of analyses use the structural analysis results from this section. The next section provides the 

area vs. pressure curves for each set of analyses as they were extracted from the structural 

analyses.

Figure 5.11: Conditional Probability of Failure for Original Containment (No Corrosion)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure
33

Figure 5.12: Conditional Probability of Failure for 50% Corrosion at Basemat

Figure 5.13: Conditional Probability of Failure for 65% Corrosion at Basemat

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure
34

Figure 5.14: Conditional Probability of Failure for 50% Corrosion at Midheight

Figure 5.15: Conditional Probability of Failure for 65% Corrosion at Midheight

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure
35

Figure 5.16: Conditional Probability of Failure for 10 Regions of 50% Corrosion at Basemat

Figure 5.17: Conditional Probability of Failure for 10 Regions of 50% Corrosion at 

Midheight

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure
36

5.1.5 Leak Area Curve Development for Deterministic Accident Analyses

As mentioned in the previous two sections, the MELCOR analyses require the area vs. pressure 

curves for the containment behavior as input. These curves were developed from the structural 

analyses for five different cases: no corrosion, 50% corrosion at the midheight, 65% corrosion at 

the midheight, 10 locations of 50% corrosion at the midheight, and 10 locations of 65% corrosion 

at the midheight. The basemat corrosion cases were initially examined as well, but they were not 

included since their area vs. pressure curves did not vary from the no corrosion case until well 

past the point where the MELCOR analyses showed peak pressures. This is not a general 

conclusion regarding basemat corrosion vs. other locations. The exact location, extent, level, and 

plant specific geometry all affect the severity of a given corrosion site and should be examined 

individually. In addition, curves were developed for each case for the best estimate structural 

analyses described in Section 5.1.3, and lower and upper bound structural analyses originally 

performed for the PRA analyses which are outlined in Section 5.1.4. The procedure in Section 

2.1.1.3 was used to compute the ratio of the total rupture area, Atotal , as a function of the 

pressure. This function was originally determined not just for the best estimate case, but also for 

each of the 30 analyses used in the fragility curve computations in the previous section. The best 

estimate total area versus pressure curves for each of the cases examined are shown in Figure 

5.19 and Figure 5.20. Figure 5.20 illustrates the detailed view of the curves in the region of area 

and pressure that are obtained in the MELCOR analyses. For the lower and upper bound 

analyses, the area vs. pressure curves were developed by bounding the area vs. pressure curves 

for the 30 analyses used in the fragility analysis. The 30 curves for a given corrosion case were 

plotted together and lowest and highest (upper) most curves were drawn as to bound that space. 

Therefore, “lower bound” refers to the lower bound of the pressure for the 30 area vs. pressure 

curves. The “upper bound” therefore refers to the upper bound of the pressure for the 30 area vs. 

pressure curves. The lower bound curves are shown in Figure 5.21 and Figure 5.22. The upper 

Figure 5.18: Conditional Probability of Failure for 10 Regions of 65% Corrosion at 

Midheight

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Conditional Probability of Failure

Leak

Rupture

Catastrophic Rupture

Design Pressure
37

bound curves are shown in Figure 5.23 and Figure 5.24. The cases and labeling used for the 

MELCOR and MACCS analyses are summarized in Table 5.3. It is important to identify the 

lower and upper bound identifiers with the lower and upper leak pressures and not lower and 

upper bound for consequences. This is critical since the lower bound cases lead to earlier leaks at 

lower pressures which can lead to higher consequences. The opposite is therefore true for the 

upper bound cases leaking at higher pressures and possibly leading to lower consequences. The 

next section on the MELCOR and MACCS analyses describe the consequence results in detail.

Table 5.3: Corrosion Condition

Condition Label

no corrosion

lower bound

nominal

upper bound

LB1

N1

UB1

1 location, 50% midheight corrosion

lower bound

nominal

upper bound

LB2

N2

UB2

1 location, 65% midheight corrosion

lower bound

nominal

upper bound

LB3

N3

UB3

10 locations, 50% midheight corrosion

lower bound

nominal

upper bound

LB4

N4

UB4

10 locations, 65% midheight corrosion

lower bound

nominal

upper bound

LB5

N5

UB5
38

Figure 5.19: Total Crack Area vs. Pressure for Best Estimate Cases (Nominal)

Figure 5.20: Total Crack Area vs. Pressure Detailed View for Best Estimate Cases (Nominal) 

0.0

25.0

50.0

75.0

100.0

125.0

150.0

0 25 50 75 100 125 150 175 200

pressure [psig]

total crack area [in2] 

N1 - No Corrosion

N2 - Midheight 50% Corrosion

N3 - Midheight 65% Corrosion

N4 - Midheight 50% Corrosion 10x

N5 - Midheight 65% Corrosion 10x

0.0

1.0

2.0

3.0

4.0

5.0

110.0 112.5 115.0 117.5 120.0 122.5 125.0 127.5 130.0 132.5 135.0

pressure [psig]

total crack area [in2] 

N1 - No Corrosion

N2 - Midheight 50% Corrosion

N3 - Midheight 65% Corrosion

N4 - Midheight 50% Corrosion 10x

N5 - Midheight 65% Corrosion 10x
39

Figure 5.21: Total Crack Area vs. Pressure for Lower Bound Cases

Figure 5.22: Total Crack Area vs. Pressure Detailed View for Lower Bound Cases 

0.0

25.0

50.0

75.0

100.0

125.0

150.0

0 25 50 75 100 125 150 175 200

pressure [psig]

total crack area [in2] 

L1 - No Corrosion

L2 - Midheight 50% Corrosion

L3 - Midheight 65% Corrosion

L4 - Midheight 50% Corrosion 10x

L5 - Midheight 65% Corrosion 10x

0.0

1.0

2.0

3.0

4.0

5.0

95.0 97.5 100.0 102.5 105.0 107.5 110.0 112.5 115.0 117.5 120.0

pressure [psig]

total crack area [in2] 

L1 - No Corrosion

L2 - Midheight 50% Corrosion

L3 - Midheight 65% Corrosion

L4 - Midheight 50% Corrosion 10x

L5 - Midheight 65% Corrosion 10x
40

Figure 5.23: Total Crack Area vs. Pressure for Upper Bound Cases

Figure 5.24: Total Crack Area vs. Pressure Detailed View for Upper Bound Cases 

0.0

25.0

50.0

75.0

100.0

125.0

150.0

0 25 50 75 100 125 150 175 200

pressure [psig]

total crack area [in2] 

U1 - No Corrosion

U2 - Midheight 50% Corrosion

U3 - Midheight 65% Corrosion

U4 - Midheight 50% Corrosion 10x

U5 - Midheight 65% Corrosion 10x

0.0

1.0

2.0

3.0

4.0

5.0

135.0 137.5 140.0 142.5 145.0 147.5 150.0 152.5 155.0 157.5 160.0

pressure [psig]

total crack area [in2] 

U1 - No Corrosion

U2 - Midheight 50% Corrosion

U3 - Midheight 65% Corrosion

U4 - Midheight 50% Corrosion 10x

U5 - Midheight 65% Corrosion 10x
41

5.2 MELCOR and MACCS Deterministic Accident Analysis

5.2.1 MELCOR Model for a 3-Loop PWR with a Reinforced Concrete 

Subatmospheric Containment

A model of the Surry Power Station units has been developed by Sandia National Laboratories

using MELCOR (Gauntt, et al., 2005, U.S.NRC, 2010). The model was originally generated for 

code assessment applications at Idaho National Engineering Laboratories (INEL) in 1988 (Dobbe,

1988). This model has been updated by Sandia National Laboratories (1990 to present) for the 

purpose of testing new models, advancing the state-of-the-art in modeling of PWR accident 

progression, and providing support to decision-makers at the U.S. Nuclear Regulatory 

Commission (NRC) for analyses of various issues that may affect operational safety. Significant 

changes have been made during the last ten years in the approach to modeling core behavior and 

core melt progression, as well as the nodalization and treatment of coolant flow within the RCS 

and reactor vessel. Assessment reports have been prepared to discuss this model evolution as part 

of the MELCOR code development program (Gauntt, et al. 2005).

Recent significant enhancements to the MELCOR model have been made to take advantage of 

MELCOR 1.8.6 modeling capabilities. The updates concern two key areas. The first area is an 

upgrade to MELCOR Version 1.8.6 vessel and core modeling. These enhancements include:

• a hemispherical lower head model that replaces the flat bottom-cylindrical lower head model,

• new models for the core former and shroud structures that are fully integrated into the 

material degradation modeling, including separate modeling of debris in the bypass region 

between the core barrel and the core shroud,

• models for simulating the formation of molten pools both in the lower plenum and the upper 

core, crust formation, convection in molten pools, stratification of molten pools into metallic 

and oxide layers, and partitioning of radionuclides between stratified molten pools,

• a reflood quench model that separately tracks the component quench front, quench 

temperature, and unquenched temperatures,

• a control rod silver aerosol release model, and 

• an application of the CORSOR-Booth release model for modern high-burn-up fuel.

The second area focused on the addition of user-specified models to represent a wide spectrum of 

plant design features and safety systems to broaden the capabilities of MELCOR to a wider range 

of severe accident sequences. These enhancements included:

• update of the containment leakage model,

• update of core degradation modeling practices,

• modeling of individual primary and secondary relief valves with failure logic for rated and 

degraded conditions,

• update of the containment flooding characteristics,

• heat loss from the reactor to the containment,

• separate motor and turbine-driven auxiliary feedwater models with control logic for plant 

automatic and operator cooldown responses,

• new turbine-driven auxiliary feedwater models for steam flow, flooding failure, and 

performance degradation at low pressure,

• nitrogen discharge model for accumulators, 

• update of the fission product inventory, the axial and radial peaking factors, and an extensive 

fission product tracking control system, and
42

• improvements to the natural circulation in the hot leg and steam generator and the potential 

for creep rupture.

5.2.2 Description of MELCOR Model Modifications for Degraded 

Containment Analysis

In the MELCOR model, containment failure is simulated with a flow path1 whose area is a 

function of the containment pressure. Figure 5.25 shows the nodalization of the containment with 

the location of the containment failure flow path.

A MELCOR flow path is defined by the following parameters:

Orientation: Based on the geometry of the problem the containment failure flow path was 

modeled as a horizontal, rather than a vertical, flow path.

Opening Height: The location of the containment failure is between control volume 5 (CV5) and 

the Environment (CV999). Since the source term release only consists of vapors and gases, as 

long as the containment failure flow path connects the Basemat CV to the Environment CV, the 

specific opening height location is not important (all of the leaks we consider are combined in 

CV5, so a detailed breakdown of the different leak paths will not affect the source term). As such, 

a height half-way between the top of the basemat and the bottom of the upper dome was selected 

(16.85 m, 55.28 ft). 

Open Area: The open area is set equal to the maximum open area for the area vs. pressure 

relationship of interest. As the pressure increases, the open area from the area vs. pressure curves 

is used. At the point that the pressure decreases, the open area in the MELCOR analyses remains 

at the maximum value reached. This is a slightly conservative assumption, since there will be 

some crack closure. However, the crack region will now be irreversibly damaged and would not 

follow back along the original curve. In the absence of more sophisticated techniques, the area is 

assumed to remain at its maximum value as the pressure drops.

Length: The flow path length was assumed to be the thickness of the containment wall (4.5 ft). 

While the cracks may actually have a longer length, this minimum value was chosen as a 

conservative lower bound in the sense that a shorter length corresponds to a higher flow rate, and 

hence more source term release from the flow path.

Fraction of Flow Path Open: The fraction of flow path that is open is derived from the area vs. 

pressure relationship of interest by dividing the area by the maximum open area.

Forward and Reverse Loss Coefficients: The code default values of 1.0 were used.

Forward and Reverse Choked Flow Coefficients (i.e., k): The code default values of 1.0 were 

used.

 1 A flow path is a MELCOR model element that connects two control volumes (CVs) (in this particular 

case, the containment CV to the environment CV) and allows material flow (e.g., liquid, vapor, gas, source 

term aerosol) between the CVs.
43

Hydraulic Diameter: The hydraulic diameter was computed assuming a set of 12 identical cracks. 

Each crack has a rectangular geometry. The in-plane length of each crack is assumed to be 2 ft. 

Although the number or cracks and lengths varied in the computation of the area vs. pressure 

curves from the structural analyses, the numbers were held constant in the MELCOR analysis

when computing the hydraulic diameter.

The hydraulic diameter is defined as

P

A Dh = 4 (5.5)

where 

Dh - hydraulic diameter

A - flow path area

P - flow path perimeter

MELCOR requires that a constant value be specified for the hydraulic diameter. Therefore, the 

actual temporal change in hydraulic diameter as the crack opens cannot be modeled. As a 

conservatism, the hydraulic diameter was calculated based on the maximum open area. Hence 

given the assumption of a rectangular crack geometry and “N” cracks, the perimeter of the 

containment failure flow path is equal to 

P = 2N(h + w) (5.6)

Nh

A

w = (5.7)

where

N - number of cracks

h - crack height

w - crack width

This treatment yields the maximum possible hydraulic diameter, which maximizes the flow rate, 

and hence source term release from the flow path. In addition, it should be noted that the 

hydraulic diameter is not a function of the crack length (e.g. containment wall thickness). It is 

only a function of the crack open area and the perimeter of the crack opening.

Surface Roughness: A surface roughness (0.3 mm) similar to a lower-bound value for concrete 

pipes was assumed. This value was chosen as a conservative lower bound in the sense that a 

lower surface roughness corresponds to a higher flow rate, and hence a higher source term release 

from the flow path.

It should be noted that for the majority of the time that leakage occurs, the flow through the leak 

path will be choked. In this flow regime k, Dh, W, P, and surface roughness are not relevant. 

However, regardless of the flow regime (i.e., choked or non-choked) MELCOR requires that 

these parameters be specified. Moreover, the parameters are relevant during the time that the flow 

through the leak path is non-choked.
44

For this analysis, the containment failure flow path in the original model was replaced with a set 

of 15 flow paths (see Table 5.3), each of which simulates one of the postulated containment 

failure area versus containment pressure response curves (see Figure 5.19 through Figure 5.24). 

Control logic was added to the model which allows the containment failure flow paths to be either 

“active” or “inactive”. The fraction open area for an active flow path is set equal to that derived 

from its failure area versus containment pressure response curve. The fraction open area for an 

inactive flow path is equal to zero – hence no flow occurs through an inactive flow path. When 

the model was run, only one of 15 containment failure flow paths would be set to “active”, with 

the remaining 14 set to “inactive”. 

Figure 5.25: Containment Nodalization

Environment

CV 999

CV41

CV's

20,30,

40

CV55

CV50

0.56 m

7.21 m

25.83 m

32.84 m

CV42

CV5 CV5

CV10

Pressurizer

Steam Generator

PRT

16.85 m

Approx. Grade = 12.13 m

MELCOR Ref.

Elevations

CV800

LHSI

Safeguards

Area

Reactor

Vessel

Cont. Spray Cont. Spray

Aux. Bldg. Model

Note: Cable vault, electrical

vault, pipe tunnel, aux. feed.

area, and auxiliary building

currently modeled as separate

CV’s. Detailed model for

fission product transport

shown in additional model.

CV810-818

Auxiliary Building

Flow path from the 

containment to the 

environment
45

5.2.3 Description of Degraded Containment MELCOR Calculations

For the purposes of quantifying variances in consequences of liner degradation, two unmitigated 

station blackout (SBO) sequences were selected; the unmitigated short-term station blackout 

(STSBO) and the unmitigated long-term station blackout (LTSBO). The SBO sequences do not 

credit any successful mitigative actions, such as those developed in the severe accident 

management guidelines (SAMGs) and mitigation measures codified in 10 CFR 50.54(hh). The

unmitigated SBO severe accident sequences produce an over-pressurization failure challenge to 

the containment, which allows quantification of the source term as a function of liner degradation 

parameters. The range of liner degradations are not best-estimate representations of the reference 

plant (i.e., Surry) but rather parameters to evaluate regulatory issues related to liner degradation. 

The resulting distributions of results are evaluated to identify trends as a function of degradation 

type and magnitude as well as identify threshold conditions that lead to a significantly different 

result. 

The short-term station blackout is initiated by a large earthquake (0.5–1.0 peak ground 

acceleration - pga). The seismic event results in a loss-of onsite power (LOOP) and failure of 

onsite emergency alternating current (AC) power resulting in a station blackout (SBO) event 

where neither onsite nor offsite AC power are recoverable. All systems dependent on AC power 

are unavailable, including the containment engineering safety systems (e.g., the containment 

spray and fan coolers). The seismic event also causes a loss of direct current (DC) power, which 

makes the turbine-driven auxiliary feedwater (TDAFW) system unavailable. The reactor coolant 

system (RCS) and containment are undamaged and the containment is isolated. No 

instrumentation is available. Following the loss of the seal cooling flow, the reactor coolant 

pump (RCP) seals will nominally leak at 21 gpm (i.e., at normal operating pressure and 

temperature). The RCP seals fail later in the accident when the RCP seal region heats to saturated 

conditions. All emergency core cooling system (ECCS) equipment is inoperable primarily due to 

electrical and physical system damage due to the seismic event. However, the accumulators are 

available when the RCS depressurizes.

The LTSBO is initiated by a moderately large earthquake (0.3–0.5 pga). The seismic event 

results in LOOP and failure of onsite emergency AC power resulting in a station blackout event 

where neither onsite nor offsite AC power are recoverable. Unlike the unmitigated STSBO 

described above, the turbine-driven auxiliary feedwater (TDAFW) system is available initially. 

In the long term, the loss of the TDAFW may occur due to battery depletion and loss of DC 

power for sensing and control. The TDAFW is also only available until the emergency 

condensate storage tank empties. The station batteries provide instrumentation until they exhaust

at 8 hr. The secondary power-operated relief valves (PORVs) are initially available for a manual 

100o

F/hr system cooldown. The secondary PORVs are assumed to close following battery 

failure. No other systems are available. 

Although the LTSBO is not successfully mitigated by emergency procedures and equipment 

codified in 10 CFR 50.54(hh), it is assumed that two operator actions are successful. The 

operator is (a) initially successful to maintain normal water levels in the steam generators (SG) 

using TDAFW and (b) performs a controlled depressurization of the steam generators to 

approximately 120 psi to achieve an RCS cooldown of 100o

F per hour by manually opening the 

SG PORVs.

At the start of the accident progression in the unmitigated STSBO sequence, the reactor 

successfully scrams in response to the loss of power. The main steam line isolation and 
46

containment isolation valves close in response due to the loss of power. The reactor coolant and 

main feedwater pumps also trip to the loss of power. Once the main steam lines close, the normal 

mechanism of heat removal from the primary system is unavailable. Consequently, both the 

primary and secondary system pressures rise. The secondary system quickly pressurizes to the 

safety relief valve opening pressure, which results in the safety relief valves to open and then 

subsequently close when the closing pressure criterion is achieved. The relief flow through the 

SG safety relief valves is the principal primary system energy removal mechanism in the 

first hour. The water inventory in the steam generators was completely boiled away by 

1 hr 16 min. Although the steam generator relief valves continue to cycle and release steam, the 

associated heat removal is inadequate and the primary system sharply increases to the pressurizer 

safety relief valve opening pressure. The safety valves on the pressurizer begin opening and 

closing to remove excess energy. However, the pressurizer relief valve flow causes a steady 

decrease in the primary system coolant inventory. The fuel starts to uncover at 2 hr 19 min. (See 

Table 5.4 for a summary of timings in the unmitigated STSBO).

Following the uncovery of the fuel, an in-vessel natural circulation flow develops between the hot 

fuel in the core and the cooler structures in the upper plenum. Hot gases from inside the vessel 

also flow along the top the hot leg and into the steam generator. The large masses of the hot leg 

nozzle, hot leg piping, and the steam generator tubes absorb the heat from the gases exiting the 

vessel. The cooler gases leaving the steam generator return to the vessel along the bottom of the 

hot leg. Due to its close proximity to the hot gases exiting in the vessel, the hot leg nozzle at the 

carbon steel interface region to the stainless steel piping was predicted to fail by creep rupture at 

3 hr 45 min.

Upon creep failure of the hot leg nozzle, a large hole opened that rapidly depressurized the RCS 

(i.e., like a large break loss-of-coolant accident). The RCS depressurization permitted a complete 

accumulator injection at low-pressure. Following the accumulator injection, the decay heat from 

the fuel boiled away the injected water. By 4.3 hr, a large debris bed had formed in the center of 

the core. The debris continued to expand until 5.8 hr when all the fuel had collapsed and was 

resting on the core plate. The hot debris failed the core support plate and fell onto the lower core 

support plate, which failed at 6.6 hr. Following the lower core support plate failure, the debris 

bed relocated onto the lower head. The small amount of remaining water in the lower head was 

quickly boiled away. The hot debris quickly heated the lower head and it failed at 7 hr 16 min 

due to the creep rupture failure criterion (i.e., primarily due the thermal stress component due to 

the low differential pressure).

Nearly all the hot debris relocated from the vessel by 7.5 hr into the reactor cavity in the 

containment under the reactor vessel. The hot debris boiled away the water in the reactor cavity 

and started to ablate the concrete. The ex-vessel core-concrete interactions (CCI) continued for 

the remainder of the sequence, which generated non-condensable gases. In addition, the hot 

gases exiting the reactor cavity and the radioactive heating from airborne and settled fission 

products steadily evaporated the water on the containment floor outside the reactor cavity from 

7.3 hr to 44 hr. The resultant non-condensable gas and steam generation pressurized the 

containment. At 25.5 hr, the containment failed due to liner tearing near the containment 

equipment hatch at mid-height in the cylindrical region of the containment (in the original 

MELCOR model, the location and timing varies slightly for each of the degradation cases). The 

containment continues to pressurize until the leakage flow balanced the steam and 

non-condensable gas generation. By 44 hr, all the water on the floor has evaporated. The 

containment depressurized thereafter due to only a smaller gas loading from the non-condensable 

gas generation. The containment failure locations were all placed at locations that would not lead 
47

to releases into surrounding buildings (e.g., not adjacent to the auxiliary or safeguards buildings). 

Consequently, all released fission products are released directly to the environment.

The fission product releases from the fuel started following the first thermo-mechanical failures 

of the fuel cladding in the hottest rods at 2 hr 57 min, or about 38 min after the uncovery of the 

top of the fuel rods. The in-vessel fission product release phase continued through vessel failure 

at 7.3 hr. Approximately 97% and 98% of the iodine and cesium, respectively, were released 

from the fuel prior to vessel failure while the remaining amount was released ex-vessel. At the

time of the hot leg failure, approximately 40% of these volatile radionuclides had been released. 

The resultant blowdown of the vessel immediately discharged the airborne fission products to the 

containment. Within the first day, most of the airborne fission products in the containment settled 

on surfaces. This was significant because the containment failure occurred at 25 hr 32 min. 

Consequently, there was little airborne mass that could be released to the environment. Again, 

these times are those taken from the original MELCOR accident scenario. This study uses 

different containment capacity models, and therefore, the time for increased containment leakage 

and subsequent events in the accident progression will vary slightly for each of the degradation 

cases.

Table 5.4: STSBO Accident Progression Sequence of Events

Event Description Time

hh Initiating event

 

00:00:00

MSIVs close

R t ti

 

00:00:00

First SG SRV opening 00:03:00

SG dryout 01:16:00

Pressurizer SRV opens 01:27:00

Pressurizer relief tank rupture disk opens 01:46:00

Start of fuel heatup 02:19:00

RCP seal failures 02:45:00

First fission product gap releases 02:57:00

Creep rupture failure of the A loop hot leg nozzle 03:45:00

Accumulators start discharging 03:45:00

Accumulators are empty 03:45:00

Vessel lower head failure by creep rupture 07:16:00

Debris discharge to reactor cavity 07:16:00

Cavity dryout 07:27:00

Containment at design pressure (0.31 MPa, 45 psig) 11:00:00

Start of increased leakage of containment (P/Pdesign = 2.18) 25:32:00

Containment pressure increase slows 32:00:00

Containment pressure stops decreasing 44:14:00

End of calculation 4 days
48

The response of the unmitigated LTSBO is similar to the unmitigated STSBO. (See Table 5.5 for 

a summary of timings in the unmitigated LTSBO). However, the key events in the LTSBO are 

delayed due the operation of the LTSBO and the two successful operator actions. The TDAFW 

initiates at full flow but is subsequently controlled by the operator after 15 min to maintain level. 

The TDAFW restores the steam generator liquid levels by about 30 min and is throttled 

thereafter. After the closure of the main steam isolation valves, the secondary system quickly 

pressurizes to the safety relief valve opening pressure, which causes the safety relief valves to 

open and then subsequently close when the closing pressure criterion is achieve. The relief flow 

through the SG SRVs is the principle primary system energy removal mechanism in the first 

90 min. At 90 min, the operator starts a controlled (~100o

F/hr) cooldown of the primary system 

by venting the steam generator PORVs. As the secondary pressure decreases, the saturation 

temperature of the water in boiler section of the steam generator also decreases, which cools the 

primary system fluid. At about 3.5 hr, the steam generators reached 0.93 MPa (120 psig), where 

the secondary system pressure was stabilized. No operator actions were credited to replenish the 

emergency condensate storage tank inventory (e.g., the source of water for the TDAFW) and it 

drains by 5 hr 8 min. Subsequently, the steam generator level starts to decrease and is empty by 

12 hr 18 min.

At 8 hr, the station batteries were estimated to fail. At the same time, the steam generator relief 

valves closed and were no longer actively controlled. In response to the steam generator valve 

closure, both the primary and secondary systems rapidly pressurized. Once the steam generators 

boiled dry, the primary system pressurized to the pressurizer safety relief valve opening set point 

and began to relieve steam and water. The top of the fuel was uncovered by 14.3 hr and the core 

heatups began. 

Similar to the STSBO (see above), natural circulation flows developed between the hot fuel in the 

core and the cooler structures in the upper plenum, hot leg, and the steam generator. The hot leg 

nozzle at the carbon steel interface region to the stainless steel piping was first predicted to fail by 

creep rupture at 17 hr 6 min. The remainder of the sequence of events were similar to the STSBO 

but delayed in timing as summarized in Table 5.5. The containment failed at 45.5 hr, due to liner 

tearing near the containment equipment hatch at mid-height in the cylindrical region of the 

containment (for the original MELCOR containment model). 

The fission product releases from the fuel started following the first thermo-mechanical failures 

of the fuel cladding in the hottest rods at 16 hr 4 min, or about 1 hr 40 min after the uncovery of 

the top of the fuel rods. Approximately 99% of the iodine and cesium were released from the fuel 

prior to vessel failure while the remaining amount was released ex-vessel. The majority of the 

radionuclides released in-vessel went to the containment. Within 36 hr, most of the airborne 

fission products in the containment settled on surfaces. This was significant because the 

containment failure occurred at 45 hr 32 min. Consequently, there was little airborne mass that 

would be released to the environment. As with the STSBO, these times are for the original 

MELCOR models for containment capacity. The models developed in this study cause a slightly 

different timing for the events in the accident progression.
49

Table 5.5: LTSBO Accident Progression Sequence of Events

Event Description Time

hh Initiating event

 

00:00:00

MSIVs close

R t ti

 

00:00:00

TD-AFW auto initiates at full flow 00:00:30

Operators control TD-AFW to maintain level 00:15:00

Operators initiate controlled cooldown of secondary at ~100oF/hr 01:30:00

Vessel water level drains into upper plenum 01:57:00

Initial minimum vessel water level 02:30:00

Accumulators begin injecting 02:25:00

SG cooldown stopped at 120 psig to maintain TDAFW flow 03:35:00

First SG SRV opening 00:03:00

Emergency CST empty 05:08:00

dc Batteries Exhausted 08:00:00

S/G PORVs reclose 08:00:00

Pressurizer SRV opens 13:06:00

PRT failure 13:40:00

Start of fuel heatup 14:16:00

RCP seal failures (calculated) 14:46:00

First fission product gap releases 16:04:00

Creep rupture failure of the C loop hot leg nozzle 17:06:00

Accumulator empty 17:06:00

Vessel lower head failure by creep rupture 21:08:00

Debris discharge to reactor cavity 21:08:00

Cavity dryout 21:16:00

Containment at design pressure (0.31 MPa, 45 psig) 28:00:00

Start of increased leakage of containment (P/Pdesign = 2.18) 45:32:00

Calculation terminated 4 days

The 15 corrosion conditions were evaluated for both the STSBO and LTSBO scenarios (see Table 

5.3). Figure 5.26 through Figure 5.31 show the containment pressure as a function of time for 

each corrosion case and for the best estimate and lower/upper bounds. The release constituents 

are also computed in MELCOR for each of these cases to be used as input in the MACCS 

analyses described in the next section.

For a number of cases in Figure 5.26 through Figure 5.31, the pressure curves rise above or drop 

below other curves. This is due to the complex interaction between the pressure vs. area curve 

and the timing of the accident scenario being examined.
50

Figure 5.26: Containment Pressure – STSBO, Nominal Cases (see Table 5.3 for case 

descriptions)

Figure 5.27: Containment Pressure – LTSBO, Nominal Cases (see Table 5.3 for case 

descriptions)

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 12 24 36 48 60 72 84 96

pressure [psig]

time [hr]

STSBO

N1

N2

N3

N4

N5

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 12 24 36 48 60 72 84 96

pressure [psig]

time [hr]

LTSBO

N1

N2

N3

N4

N5
51

Figure 5.28: Containment Pressure – STSBO, Lower Bound Cases (see Table 5.3 for case 

descriptions)

Figure 5.29: Containment Pressure – LTSBO, Lower Bound Cases (see Table 5.3 for case 

descriptions)

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 12 24 36 48 60 72 84 96

pressure [psig]

time [hr]

STSBO

LB1

LB2

LB3

LB4

LB5

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 12 24 36 48 60 72 84 96

pressure [psig]

time [hr]

LTSBO

LB1

LB2

LB3

LB4

LB5
52

Figure 5.30: Containment Pressure – STSBO, Upper Bound Cases (see Table 5.3 for case 

descriptions)

Figure 5.31: Containment Pressure – LTSBO, Upper Bound Cases (see Table 5.3 for case 

descriptions)

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 12 24 36 48 60 72 84 96

pressure [psig]

time [hr]

STSBO

UB1

UB2

UB3

UB4

UB5

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 12 24 36 48 60 72 84 96

pressure [psig]

time [hr]

LTSBO

UB1

UB2

UB3

UB4

UB5
53

5.2.4 MACCS2 Analyses 

The offsite consequence analysis was performed using MACCS2 for each of the source terms

generated by MELCOR. The MACCS2 input model employs site specific emergency response 

scenarios for severe accidents that are characterized with the timing of actions taken by onsite and 

offsite response organizations to protect the general public by evacuation and sheltering. These 

emergency response scenarios were developed in order to achieve a greater degree of realism than 

previous consequence analyses performed by MACCS2. The following subsections summarize 

the development of those emergency response scenarios as well as generic and site specific input 

parameters used in this study.

5.2.5 MACCS2 Generic Input Parameters

Generic input parameters are neither site nor accident scenario specific. These include dose 

factors which are used to relate the dose to each organ to the concentration of each of the 

isotopes, specification of spatial grid elements to specify radial distances from the plant at which 

the results are to be reported, decontamination parameters, and some parameters concerning 

deposition and dispersion of released materials.

Many of these generic input parameters used in this study are identical to those used in the 

NUREG-1150 study. Sample Problem A, which is documented in the MACCS2 User’s manual 

(Channin et al., 1990), corresponds to one of the NUREG-1150 calculations that were performed 

for Surry. For brevity, only the parameters that differ from those used in Sample Problem A are 

discussed here. While spatial grid elements are set identical to the one used in the NUREG-1150 

study for Surry plant, dose factors are updated based on Federal Guidance Report (No.13) by the 

US Environmental Protections Agency (EPA, 1999).

Calculations performed for the NUREG-1150 study simplistically considered a single aerosol bin 

with a deposition velocity of 1 cm/s. Currently, MELCOR calculates aerosol size distributions 

using a 10-bin representation. Here, MELCOR size-distribution data are used to better quantify 

aerosol deposition rates. Table 5.6 shows wet and dry deposition velocities applied in this study

(U.S.NRC, 2010). 

Table 5.6: Aerosol Deposition Velocity 

# Bin Dry and Wet Deposition Velocity (m/s)

1 8.58E-04

2 7.88E-04

3 1.03E-03

4 1.74E-03

5 3.40E-03

6 6.96E-03

7 1.34E-02

8 2.20E-02

9 2.73E-02

10 2.73E-02
54

5.2.6 MACCS2 Site Specific Input Parameters

The site specific parameters typically involve source term (also accident specific), physical 

dimensions of the plant building complex, and meteorological and demographic data specific to 

the plant region. 

The source term generated by MELCOR was evaluated using MELMACCS (McFadden et al., 

2005), a tool developed by Sandia to generate MACCS2 input from MELCOR calculations. 

MELMACCS reads a MELCOR output file containing initial and released mass of radioactive 

materials. MELMACCS requires a number of user specified inputs such as fission product classes 

to be analyzed, assumed burnup used to calculate the fission product inventory, and the initial 

plume dimensions. 

The analysis includes the standard set of fission product classes (i.e., Xe, Cs, Ba, I, Te, Ru, Mo, 

Ce, and La), and the initial radionuclide inventory was calculated by MELMACCS with an 

assumed burnup of 49 Mwd/kg at mid cycle. When specifying plume segments, releases were 

broken up into two-hour plume segments. For any non-significant release, such as those with less 

than 1 percent of the release fractions, they are broken up into longer time intervals. 

Other site specific input parameters relate to the dimensions of the building from which the 

release occurs. These are the 1) the building height, 2) the initial value of cross-wind dispersion 

(σy), and 3) the initial value of vertical dispersion (σz). The building height used in this study is 50 

m. Even though MELCOR uses a lower release height (16.85 m), the MACCS analyses use a 

conservative release height at the top of the containment dome (50 m). The initial values for σy 

and σz used here are 9.302 and 23.26, respectively. These values are the initial plume standard 

deviations for the plume dimensions based on the building dimensions.

The meteorological data involve one year of hourly windspeed, atmospheric stability, and rainfall 

readings recorded at the site. The population data is constructed from the year 2000 census data, 

then scaled by a factor of 1.0533 to adjust for growth between the years 2000 and 2005. Details 

on the meteorological and population data surrounding the site are discussed in Bixler et al. 

(2003).

Finally, the analyses include more realistic emergency response scenarios accounting for site 

specific evacuation time estimates as described in NUREG-1935 (U.S.NRC, 2010) . These 

scenarios resulted from an assessment of the variation in emergency response for the site within 

the emergency planning zone (EPZ; within 16.1 km, or 10 miles, of the plant) and also included 

evacuation and sheltering of population groups beyond the EPZ to a distance of 32.2 km (20 

miles) from the site. Each emergency scenario involves a population subgroup, referred to as a 

cohort, that moves differently from other population groups to account for members of the public 

who evacuate early, those who evacuate late, those who do not evacuate, or those who decide to 

evacuate from areas not under an evacuation order (defined as shadow evacuation). Six cohorts 

were established as described below.

Cohort 1: 0 to 10 mile Schools. This cohort includes school populations within the EPZ.

Cohort 2: 0 to 10 Special Needs and 0 to 10 Tail. This group includes two distinct population 

subgroups that were combined because of the small population fraction of each individual group. 

The Special Needs population includes residents of hospitals, nursing homes, assisted living 

communities and prisons. The Tail is defined as the last 10% of the public to evacuate. The 0 to 

10 Special Needs and 0 to 10 Tail groups were combined because they mobilize in a similar 
55

manner and would both exit the area last. The Special Needs cohort is assumed to have a greater 

shielding factor during the sheltering phase prior to evacuating due to the expectation that they 

would likely be indoors within a facility more protective than an average home. 

Cohort 3: 0 to 10 Public and 10 to 20 Shadow. This cohort includes the public residing within 

the EPZ and the shadow evacuation from the 10 to 20 mile area beyond the EPZ. The Shadow 

population from 10 to 20 miles is assumed to begin movement at the same time as the 0 to 10 

Public. 

Cohort 4: 10 to 20 Public. This cohort was established to assess sheltering of residents beyond 

the EPZ and to support sensitivity analyses. Cohort 4 is the largest population group, and 

consists of the public in the region from 10 to 20 miles beyond the EPZ. 

Cohort 5: 10 to 20 Special Needs, 10 to 20 Tail. This cohort was also established to assess 

sheltering of this population group and to support sensitivity analyses and is the last population 

group to begin to evacuate. 

Cohort 6: Non-evacuating public. This cohort group represents the portion of the public who 

refuse to evacuate, assumed for this project as 0.5% of the total population. 

Each cohort was then assigned with population fractions within 20 miles (32.2 km) (though some 

cohorts only include populations from 0 to 10 miles or 10 to 20 miles) as described in the 

following table.

Table 5.7: Cohort Population Fractions

Cohort Description Population Fraction

1 0 to 10 mile schools 0.061

2 0 to 10 special needs and 0 to 10 tail 0.021

3 0 to 10 public and 10 to 20 shadow 0.369

4 10 to 20 public 0.467

5 10 to 20 special needs and 10 to 20 tail 0.077

6 0 to 20 non-evacuating public 0.005

As mentioned previously, emergency response scenarios are characterized by the timing of 

actions taken by onsite and offsite response organizations to protect the general public by 

evacuation and sheltering. This is represented in evacuation time estimates (ETE). ETE were 

developed based on the Surry ETE report and are further described in NUREG-1935 (U.S.NRC, 

2010) 

The spatial movement of cohorts is then simulated using WinMACCS (McFadden et al, 2007) 

which allows for the movement by grid element while accounting for the speed and direction of 

the evacuating cohorts. The roadway network was also modeled in order to simulate evacuations 

and traffic movement. Detailed discussions on the development of the roadway network is also 

provided in NUREG-1935 (U.S.NRC, 2010)

5.2.7 MACCS2 Station Blackout Severe Accident Analysis Results

The following section presents MACCS2 consequence results for postulated Surry Station 

Blackout Accident scenarios. While MACCS2 consequence model calculates a large number of 

different consequence measures including economic consequence measures, only the results of 

the latent cancer fatality risk (within a 10 miles, or 16.1 km, radius from the plant) is used. This
56

consequence measure is defined as the mean probability of dying from cancer due to the accident 

for an individual within 10 miles, or 16.1 km, of the plant (Breeding et al. 1990). Additionally, in 

order to assess the significance of the increase in health effects compared to the NRC Quantative 

Health Objectives (QHOs), CDF values for both STSBO and LTSBO are multiplied by the 

results. The corresponding CDF values for STSBO and LTSBO sequences in NUREG-1150 are 

5.4E-06 and 2.2E-05, respectively. 

It should be noted that the results presented here are strictly based on linear-no-threshold 

hypothesis (LNTH), where an assumption is made that the relationship between exposure to 

ionizing radiation and human cancer risk is linear. Since the focus of this study is placed on 

relative health consequence outcomes resulting from different levels of containment degradation, 

no other dose truncation is considered for low dose rates. Additionally, the selection of LNTH 

assumption over the dose truncation does not represent the view of authors on how one should 

treat the health effects for low dose rates. The LNTH model is simply chosen for shorter 

calculation times and simplicity in setting up the problem and easier comparison of the results 

between different runs. 

A total of 15 different corrosion conditions (see Table 5.3) were evaluated for both STSBO and 

LTSBO scenarios at 96 hours. Results are presented in Table 5.8 and Table 5.9. Using the site 

meteorological data, MACCS2 generated output in terms of probability distributions of the 

consequence estimates resulting from the statistical variability in the seasonal and meteorological 

conditions during the accident. Values reported here represent arithmetic averages over the 

annual weather data used in the analysis. 

Table 5.8: STSBO Health Effects 

Corrosion Level

(see Table 5.3 for 

case descriptions)

Individual Lat. 

Can. Fat. Risk, 

10 mi (16.1 km)

STSBO

CDF Multiplied

N1 3.90E-04 2.11E-09

N2 4.36E-04 2.35E-09

N3 4.40E-04 2.38E-09

N4 4.80E-04 2.59E-09

N5 5.02E-04 2.71E-09

LB1 4.79E-04 2.59E-09

LB2 4.87E-04 2.63E-09

LB3 4.77E-04 2.58E-09

LB4 4.88E-04 2.64E-09

LB5 5.04E-04 2.72E-09

UB1 2.11E-04 1.14E-09

UB2 2.11E-04 1.14E-09

UB3 2.00E-04 1.08E-09

UB4 2.99E-04 1.61E-09

UB5 3.19E-04 1.72E-09
57

Table 5.9: LTSBO Health Effects 

Corrosion Level

(see Table 5.3 for 

case descriptions)

Individual Lat. 

Can. Fat. Risk, 

10 mi (16.1 km)

LTSBO 

CDF Multiplied

N1 7.64E-05 1.68E-09

N2 7.90E-05 1.74E-09

N3 8.00E-05 1.76E-09

N4 9.43E-05 2.07E-09

N5 8.90E-05 1.96E-09

LB1 1.06E-04 2.33E-09

LB2 1.07E-04 2.35E-09

LB3 1.08E-04 2.38E-09

LB4 1.26E-04 2.77E-09

LB5 1.53E-04 3.37E-09

UB1 3.92E-05 8.62E-10

UB2 3.86E-05 8.49E-10

UB3 3.71E-05 8.16E-10

UB4 4.54E-05 9.99E-10

UB5 4.82E-05 1.06E-09

While the results produced with the site specific meteorological data addressed uncertainty in the 

weather, it was difficult to draw conclusions from this set of results due to abnormalities observed 

in some cases. For example, there were no apparent differences in the arithmetic average results 

between cases UB1 and UB2 for STSBO although it was expected to be somewhat different 

based on the levels of corrosion applied in those cases. However, further examination of the 

results showed that differences were only found in some quartiles. Because of this, it was decided 

to re-run the cases using only a single weather trial so that the results produced could be 

compared in a more deterministic fashion. 

Results obtained using a single weather trial are presented in Table 5.10 and Table 5.11. Note that 

the single weather trial cases yield consequence results on the same order as the averaged

consequence results over all of the weather cases. However, the single weather trial case risks are 

given that that weather trial occurs. The specific weather trial used assumed a 2 m/s wind speed 

and a Class F stability. In the averaged weather results, the wind speed varies from case to case 

between different intervals from 0 to 1 m/s, to 7 m/s and greater. The stability classes vary from 

A to F to determine the plume meander factor (“A” is very unstable, “F” is moderately stable).
58

Table 5.10: STSBO Health Effects (single weather trial)

Corrosion Level

(see Table 5.3 for 

case descriptions)

Individual Lat. 

Can. Fat. Risk, 

10 mi (16.1 km)

STSBO

CDF Multiplied

N1 1.55E-04 8.37E-10

N2 1.92E-04 1.04E-09

N3 1.92E-04 1.04E-09

N4 2.64E-04 1.43E-09

N5 2.50E-04 1.35E-09

LB1 2.14E-04 1.16E-09

LB2 2.34E-04 1.26E-09

LB3 2.16E-04 1.17E-09

LB4 2.28E-04 1.23E-09

LB5 2.59E-04 1.40E-09

UB1 1.47E-04 7.94E-10

UB2 1.48E-04 7.99E-10

UB3 1.41E-04 7.61E-10

UB4 1.92E-04 1.04E-09

UB5 2.11E-04 1.14E-09

Table 5.11: LTSBO Health Effects (single weather trial)

Corrosion Level

(see Table 5.3 for 

case descriptions)

Individual Lat. 

Can. Fat. Risk, 

10 mi (16.1 km)

LTSBO 

CDF Multiplied

N1 5.74E-05 1.26E-09

N2 5.93E-05 1.30E-09

N3 5.93E-05 1.30E-09

N4 7.01E-05 1.54E-09

N5 6.62E-05 1.46E-09

LB1 7.84E-05 1.72E-09

LB2 8.04E-05 1.77E-09

LB3 8.03E-05 1.77E-09

LB4 9.38E-05 2.06E-09

LB5 1.10E-04 2.42E-09

UB1 3.09E-05 6.80E-10

UB2 3.09E-05 6.80E-10

UB3 2.98E-05 6.56E-10

UB4 3.58E-05 7.88E-10

UB5 3.75E-05 8.25E-10
59

Given the NRC QHO of 2x10-6 fatalities per year for latent cancer fatalities (NRC, 1989), the 

results obtained here do not indicate a risk significance in the increases observed between 

different levels of corrosion. In some cases, no changes were seen in the consequence results of 

different levels of degradation. In one case, a decrease in health consequence was observed with 

more severe degradation. Because of this, no direct conclusion was drawn with regards to the 

NRC QHOs, other than to the extent that the increase in health consequences is not significant 

compared to the QHOs for the cases examined. 

It was anticipated that the latent cancer risks as well as other health consequences would be 

proportional to the extent of the corrosion. The logic behind this being that more corrosion would 

yield larger containment failure areas, result in higher source term releases to the environment, 

and hence higher consequences. Four parameters were evaluated with respect to consequences for 

the single weather trial in Table 5.10 and Table 5.11 (specifically with respect to the 10-mile, or 

16.1 km, individual latent cancer fatality risk) to determine the validity of this supposition.

• total mass of Cesium released to the environment2 (Figure 5.32 and Figure 5.33)

• peak containment pressure (Figure 5.34 and Figure 5.35)

• maximum leak area (Figure 5.36 and Figure 5.37)

• initial pressure at which containment failure occurs (Figure 5.38 and Figure 5.39)

Inspection of the results finds the following general trends:

• the consequence is proportional to the source term release to the environment

• the more corrosion area in most, but not all, cases resulted in higher consequences

• higher maximum containment failure area in most, but not all, cases resulted in higher 

consequences

• lower initial containment failure pressure in most, but not all, cases resulted in higher 

consequences

A detailed examination of cases UB1 and UB3 is made to ascertain the causes for case UB3, 

while having added a corrosion area (leaks at a lower pressure), not having a higher consequence 

in comparison to case UB1. Examination of the containment pressure (Figure 5.40) and 

containment failure area (Figure 5.41) for cases UB1 and UB3 finds that for case UB3, the initial 

containment failure occurs earlier (~35.5 hr vs. ~38.6 hr) than for case UB1. The early venting of 

the containment that occurs as a result causes case UB3 to have a lower containment pressure

post-failure in comparison to case UB1. This in turn causes the failure area (crack area) for case 

UB3 to be lower than that for UB1 (once failure occurs in UB1). The combination of a smaller 

failure area and lower containment pressure in case UB3 compared to case UB1 results in less 

source term being released to the environment (as confirmed by comparing the two cases in 

Figure 5.32) and hence a lower consequence. This comparison illustrates that issues other than 

the extent of corrosion (in this particular case the initiation time of the failure) impact the 

consequence results.

 2 An evaluation of the MACCS2 results found that the Cesium mass released to the environment was the 

dominant contributor to the risk results.
60

Figure 5.32: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Total Cesium 

Release to the Environment for STSBO Cases

Figure 5.33: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Total Cesium 

Release to the Environment for LTSBO Cases

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

total Cesium release to the environment [kg]

STSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

0.00 0.05 0.10 0.15 0.20 0.25

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

total Cesium release to the environment [kg]

LTSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5
61

Figure 5.34: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Peak 

Containment Pressure for STSBO Cases

Figure 5.35: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Peak 

Containment Pressure for LTSBO Cases

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

100.0 110.0 120.0 130.0 140.0 150.0 160.0

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

peak pressure [psig]

STSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

100.0 110.0 120.0 130.0 140.0 150.0 160.0

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

peak pressure [psig]

LTSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5
62

Figure 5.36: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Maximum 

Containment Leakage Area for STSBO Cases

Figure 5.37: Individual Latent Cancer Facility Risk (10 Miles) as a Function of Maximum 

Containment Leakage Area for LTSBO Cases

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

maximum leak area [in2]

STSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

maximum leak area [in2]

LTSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5
63

Figure 5.38: Individual Latent Cancer Facility Risk (10 Miles) as a Function of the Pressure at 

which Containment Failure Initiates for STSBO Cases

Figure 5.39: Individual Latent Cancer Facility Risk (10 Miles) as a Function of the Pressure at 

which Containment Failure Initiates for STSBO Cases

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

100.0 110.0 120.0 130.0 140.0 150.0 160.0

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

initial leak pressure [psig]

STSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

100.0 110.0 120.0 130.0 140.0 150.0 160.0

Individual Latent Cancer Fatality Risk, 10 mi (16.1 km) [-]

initial leak pressure [psig]

LTSBO

LB1

LB2

LB3

LB4

LB5

N1

N2

N3

N4

N5

UB1

UB2

UB3

UB4

UB5
64

Figure 5.40: Containment Pressure for STSBO Cases UB1 and UB3

Figure 5.41: Containment Failure Area for STSBO Cases UB1 and UB3

140.0

142.0

144.0

146.0

148.0

150.0

152.0

154.0

156.0

158.0

160.0

34 35 36 37 38 39 40 41 42

pressure [psig]

time [hr]

UB1

UB3

0.0

0.5

1.0

1.5

2.0

2.5

34 35 36 37 38 39 40 41 42

contaiment failure area [in2]

time [hr]

UB1

UB3
65

5.3 PRA Analysis

The PRA analyses performed in the study by Spencer et al. (2006) are reported here but with the 

addition of three cases: 10 locations of 50% corrosion at the basemat, 10 locations of 50% 

corrosion at the midheight, and 10 locations of 65% corrosion at the midheight. The procedures 

outlined in Section 4.2 were used to develop the fragility curves and conditional probability of 

failure curves illustrated in Section 5.1.4. These curves were used in the NUREG-1150 PRA 

models to determine the effects of these three new cases. The basemat corrosion cases were 

included in the PRA analysis since some differences from the no corrosion case result. This was 

not the case in the MELCOR/MACCS analyses, and therefore, none of the basemat corrosion 

cases were including in those results. The reason for this lies in the fact that the 

MELCOR/MACCS analyses are deterministic, so for the cases examined, there was no noticeable 

difference in the computed leak areas for the basemat cases. However, when considering all 30 

of the analyses used to develop the fragility and conditional probability of failure curves, a small 

difference was seen between the no corrosion case and the basemat corrosion cases.

Table 5.12 shows the CDF values from NUREG-1150. Because the containment response does 

not affect the CDF for this plant, the results are the same for all of the cases studied. These CDF 

values are the total for all accident scenarios considered in NUREG-1150.

Table 5.12: Core Damage Frequency (yr-1

)

Case Mean 5% 50% 95%

All 4.1E-5 6.8E-6 2.3E-5 1.3E-4

Table 5.13 shows the LERF results, and Table 5.14 shows the probability of large early 

containment failure conditional on core damage. LERF is the product of the CDF and the 

probability of large early containment failure conditional on core damage. In Table 5.13 and

Table 5.14, the “Un-damaged (NUREG-1150 Reference)” LERF values are also included. These 

values were those computed in the original NUREG-1150 study. That study used expert 

elicitations to develop the containment fragility curves. The current study employs the finite 

element modeling methods described in this report. As would be expected, there is a slight 

difference between the two LERF values. In addition, the Mean, 5%, 50%, and 95% values are

reported in these tables. This variation is due solely to the uncertainties introduced in the original 

NUREG-1150 PRA study. 

Table 5.13: Large Early Release Frequency (yr-1

)

Case Mean 5% 50% 95%

Un-damaged (NUREG-1150 Reference) 1.10E-7 0 3.61E-10 1.54E-6

No Corrosion (Current Study) 1.00E-7 0 1.65E-10 1.12E-6

50% Corrosion near basemat 1.00E-7 0 1.65E-10 1.12E-6

50% Corrosion at midheight 1.00E-7 0 1.65E-10 1.12E-6

65% Corrosion near basemat 1.00E-7 0 1.65E-10 1.12E-6

65% Corrosion at midheight 1.00E-7 0 1.65E-10 1.12E-6

10 Regions 50% Corrosion near basemat 1.00E-7 0 1.65E-10 1.12E-6

10 Regions 50% Corrosion at midheight 1.34E-7 0 2.03E-10 1.55E-6

10 Regions 65% Corrosion at midheight 1.44E-7 0 2.03E-10 1.70E-6
66

Table 5.14: Probability of Large Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (NUREG-1150 Reference) 0.0027 0 1.57E-5 0.019

No Corrosion (Current Study) 0.0024 0 7.19E-6 0.0086

50% Corrosion near basemat 0.0024 0 7.19E-6 0.0086

50% Corrosion at midheight 0.0024 0 7.19E-6 0.0086

65% Corrosion near basemat 0.0024 0 7.19E-6 0.0086

65% Corrosion at midheight 0.0024 0 7.19E-6 0.0086

10 Regions 50% Corrosion near basemat 0.0024 0 7.19E-6 0.0086

10 Regions 50% Corrosion at midheight 0.0033 0 8.84E-6 0.0119

10 Regions 65% Corrosion at midheight 0.0035 0 8.84E-6 0.0130

Table 5.15: Change in the Large Early Release Frequency (yr-1

) due to Degradation

Case Mean 5% 50% 95%

50% Corrosion near basemat 0 0 0 0

50% Corrosion at midheight 0 0 0 0

65% Corrosion near basemat 0 0 0 0

65% Corrosion at midheight 0 0 0 0

10 Regions 50% Corrosion near basemat 0 0 0 0

10 Regions 50% Corrosion at midheight 3.34E-8 0 3.81E-11 4.27E-7

10 Regions 65% Corrosion at midheight 4.33E-8 0 3.81E-11 5.74E-7

The key risk criteria for acceptance of a proposed plant change in Regulatory Guide 1.174 

(USNRC, 2001) are the baseline values of CDF and LERF, and the changes in those values due to 

the proposed modification, denoted as ∆CDF and ∆LERF. The acceptance criteria must be met 

for both the pairs of ∆CDF and CDF and of ∆LERF and LERF. Because CDF is assumed to be 

unaffected by the containment properties in this particular plant, ∆CDF is 0. 

For mean LERF values, there is no change in LERF relative to the undamaged containment in the 

case where corrosion exists near the basemat. In addition, the single cases of corrosion at the 

midheight also do not cause any increase in LERF. However, the two cases with 10 regions of 

corrosion at the midheight did cause a measurable increase in LERF as shown in Table 5.15. 

These increases in LERF are small and still fall into Region III for the LERF acceptance criteria

in Figure 4.1. Therefore, the corrosion cases investigated in this study would be permissible 

modifications from a risk standpoint by Regulatory Guide 1.174. However, the addition of the 

new cases with more widespread degradation might show a greater effect.

Even so, the results presented above can potentially be somewhat misleading. One would 

intuitively expect that at least a small increase in the risk measure would be observed in the cases 

with any level of containment degradation. As expected, these increases were manifested in at 

least some of the deterministic MELCOR/MACCS analyses. This lack of increase in the risk 

measures for the PRA analyses presented in Table 5.13 and Table 5.14 can be traced to the 

definition of LERF used in the process of binning the risk analysis results. LERF is, by 

definition, the frequency of large, early containment failures resulting from accidents stemming 

from a certain set of initiating events. The question of whether the failure is large is determined 

by the mode of failure, which is computed based on the combination of the overall fragility curve 
67

and the conditional probabilities of leak, rupture, and catastrophic rupture. Failure occurrences 

are grouped into LERF only if the containment fails in a rupture or catastrophic rupture mode.

As examined in the Spencer study, the Small Early Release Frequency (SERF) and the Total 

Early Release Frequency (TERF) were also computed. TERF is defined as the sum of LERF and 

SERF. The PRA analyses bin the leak failures into SERF which is useful in examining what 

information is left out when analyzing the LERF data alone. Table 5.16 and Table 5.17

summarize the SERF and TERF mean values for each of the cases examined as well as the 

change in each of the degraded cases from the no corrosion case. Due to the liner corrosion 

examined in this study leading to leak failures, the change in SERF from the no corrosion case is 

more pronounced than for LERF. For the cases where ∆LERF equal 0, ∆SERF and ∆TERF will 

be equal. Most interesting is that the largest increase in SERF is for the 65% Corrosion at 

midheight case. However, the TERF for the 65% Corrosion at the midheight and the same case 

with 10 regions of corrosion are the same. This shows that the failures for the single corrosion 

case were all under the rupture limit (e.g. leaks) and were all binned into SERF. The case with 10 

regions of corrosion had failures split between leak and rupture causing increases in both SERF 

and LERF. As discussed in the Spencer study, there is no regulatory guidance or limits on 

smaller leak failures binned into SERF. The MELCOR/MACCS analyses showed that these 

small earlier leaks do potentially cause an increase in consequences.

Table 5.16: Small Early Release Frequency (yr-1

) and the Change in SERF

Case Mean SERF ∆SERF

No Corrosion 4.36E-8 N/A

50% Corrosion near basemat 4.62E-8 2.58E-9

50% Corrosion at midheight 1.14E-7 7.01E-8

65% Corrosion near basemat 4.62E-8 2.58E-9

65% Corrosion at midheight 1.45E-7 1.02E-7

10 Regions 50% Corrosion near basemat 4.62E-8 2.58E-9

10 Regions 50% Corrosion at midheight 8.08E-8 3.73E-8

10 Regions 65% Corrosion at midheight 1.02E-7 5.83E-8

Table 5.17: Total Early Release Frequency (yr-1

) and the Change in TERF

Case Mean TERF ∆TERF

No Corrosion 1.44E-7 N/A

50% Corrosion near basemat 1.46E-7 2.58E-9

50% Corrosion at midheight 2.14E-7 7.01E-8

65% Corrosion near basemat 1.46E-7 2.58E-9

65% Corrosion at midheight 2.45E-7 1.02E-7

10 Regions 50% Corrosion near basemat 1.46E-7 2.58E-9

10 Regions 50% Corrosion at midheight 2.14E-8 7.06E-8

10 Regions 65% Corrosion at midheight 2.45E-7 1.02E-7

The example plant examined here serves as a good case study which indicates that one should be 

very cautious about simply applying the ΔLERF criterion to evaluate the significance of 

containment degradation. It is important to closely examine how degradation can increase the 

likelihood of one failure mode while decreasing the likelihood of another, and evaluate the 

consequences of these different modes. It cannot be stressed enough that the cases of degradation 
68

examined here are extremely limited in scope. There are currently no means of predicting 

degradation prior to its discovery. Since the location and specific nature of any degradation could 

dramatically affect the containment capacity and risk, a detailed analysis of that scenario would 

be required. There are also a number of assumptions that would require additional consideration 

when performing a site specific analysis. The specific results reported in this study should not be 

applied to making specific regulatory decisions on existing plants.
69

6. SUMMARY & CONCLUSIONS

This study has examined the effects of local liner degradation on the consequences during a 

severe accident for a reinforced concrete containment vessel at a PWR plant. Two different 

methods were used to compute the consequences: a series of PRA analyses to compute LERF, 

and deterministic analyses to compute direct health consequences. The PRA analysis method was 

developed in the study by Spencer et al. (2006). In that work, a series of structural analyses were 

conducted to develop fragility curves for the failure probability distributions for various cases of 

degradation. The Spencer study examined four different containments, but the current study only 

includes the reinforced concrete containment. The results of that study showed that local liner 

corrosion contributed mainly to the small early release frequency due to the binning process used 

in the PRA modeling. The goal of that work was to show if LERF could be used as a metric with 

Regulatory Guide 1.174 to assess containment degradation. The Spencer study showed that this 

may work when applied to cases of degradation that affect the rupture pressures (e.g. LERF 

contributors), but may miss potential consequences due to early, small leaks. The goal of the 

current study was to explore alternate metrics beyond LERF. In order to examine other metrics, a 

series of deterministic analyses were performed. These analyses were conducted using the 

Sandia-developed MELCOR and MACCS codes to perform the accident progression simulations 

and the resulting consequence calculations. Both the long- and short-term station black-out 

(LTSBO and STSBO) accident scenarios were examined. Each scenario was examined for 5 

different containment conditions: no corrosion, one small patch of 50% corrosion at the 

midheight, one small patch of 65% corrosion at the midheight, ten small patches of 50% 

corrosion at the midheight, and ten small patches of 65% corrosion at the midheight. The cases 

of near-basemat corrosion studied for the PRA analyses performed for the Spencer study were 

determined to not vary from the no corrosion case due to other failures dominating, and therefore, 

were not examined. For each accident scenario and corrosion condition, analyses were performed 

using best estimate crack area vs. pressure curves computed from the structural analysis results 

created during the Spencer study. In addition, upper and lower bound area vs. pressure curves 

were also used as input for additional MELCOR/MACCS analyses. These upper and lower 

bound cases were computed by enveloping the area vs. pressure curve for a given corrosion case 

using 30 different analyses of each given degradation case. These 30 cases were used to develop 

the fragility curves for the PRA analysis and account for uncertainties in the crack area vs. 

pressure response. A number of response metrics were examined as a function of the 

consequences determined in MACCS for the different corrosion cases. These include:

• total mass of Cesium released to the environment (Figure 5.32 and Figure 5.33)

• peak containment pressure (Figure 5.34 and Figure 5.35)

• maximum leak area (Figure 5.36 and Figure 5.37)

• initial pressure at which containment failure occurs (Figure 5.38 and Figure 5.39)

As summarized in the MACCS results section, inspection of the results finds the following 

general trends:

• consequence is proportional to the source term release to the environment

• more corrosion area in most, but not all, cases resulted in higher consequences

• higher maximum containment failure area in most, but not all, cases resulted in higher 

consequences
70

• lower initial containment failure pressure in most, but not all, cases resulted in higher 

consequences

These are mostly general trends since cases were observed where the timing of the containment 

leakage affected the consequences. Higher levels of liner corrosion and the extent of that 

corrosion led to leakage at lower pressures and to a larger amount of crack area at lower 

pressures. Though in some cases, small amounts of corrosion were shown to act as a vent. This

lowered the internal pressure of the containment vessel prior to the inventory of radionuclides 

fully developing. Therefore, when more consequence significant material was generated within 

the containment, the pressure could be lower than in a case with no corrosion, or less corrosion, 

pushing less material out to the environment. 

The PRA computations performed in the Spencer study were also reexamined with the addition of 

cases where more extensive corrosion exists. It was found that while the small local corrosions 

were not large enough to cause a change in LERF, more extensive corrosion did affect the rupture 

pressures and LERF did increase for some cases. However, the PRA method of examining only 

LERF for assessment in Regulatory Guide 1.174 does miss the smaller early releases as 

demonstrated when examining SERF and in the MELCOR/MACCS analyses. 

The example plant examined here serves as a good case study indicating that one should be very 

cautious about simply applying a LERF criterion or assuming a general trend exists in more 

deterministic severe accident simulations when evaluating the significance of containment 

degradation. It is important to closely examine how degradation can change the consequence 

response of the containment on a case-by-case basis. Due to the more detailed information and 

fidelity in the different responses, the deterministic accident scenarios may be more useful when 

examining a specific case of degradation. It cannot be stressed enough that the cases of 

degradation examined here are extremely limited in scope and should not be used to generalize 

results. In addition, the cases of corrosion examined here are postulated and the results in this 

report should not be used to assess actual cases of corrosion. The patches of corrosion were very 

small and assumed to have reduced the liner thickness by 50% or 65%. Recent interest has 

focused on initial through liner corrosion in concrete containments. In these cases, a hole has 

reduced the liner thickness by 100% over some area. The tensile limit of the concrete will be 

reached at very low pressures within the containment leading to leak paths through the hole in the 

liner and cracked concrete. Here, the timing of the accident becomes critical in the resulting 

consequences. The earlier leaks in the containment would not allow the pressure to increase as 

much as a non-degraded liner. Therefore, the amount of high consequence material created later 

in the accident will not be ejected to the environment at the same rate. However, the total time of 

release to the environment will increase. There is no way to develop a general conclusion as to 

the effects of initial through holes or cracks just as there is no method to generalize any case of 

degradation. Most power plants in the U.S. are unique, which requires a case by case 

examination of the containment structural response and the examination of plausible site specific

accident scenarios. There are also a number of assumptions that would require additional 

consideration when performing a site specific analysis. In addition, there are other accident 

scenarios that would require assessment for a site specific case. These include events with rapid 

pressurization (e.g., hydrogen burn) among others. Therefore, the specific results reported in this 

study should in no way be applied to making specific regulatory decisions on specific plants.
71

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NUREG/CR-7149 Effects of Degradation on the Severe Accident Consequences for a

PWR Plant with a Reinforced Concrete Containment Vessel