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Overview: Material Issues in Nuclear Reactors Vol. 61, No.7 pp. 35-41

JULY 2009 ISSUE
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FIGURE 1.
Figure 2
The Trojan nuclear power plant in Rainier, Oregon. Shown is the cooling tower and its post-tensioned concrete containment.

 

 

FIGURE 2.
Figure 1a
Figure 1b
The normalized concrete compressive strength data obtained (a) from the literature and (b) by testing nuclear power plant-related concrete samples.

 

 

FIGURE 3.
Figure 3
An example of application of pachometer survey to a general civil engineering floor structure.

 

 

FIGURE 4.
Figure 4
An example of application of structural reliability theory to investigate the impact of degradation.27

 

 

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© 2009 The Minerals, Metals & Materials Society

In this paper, nuclear power plant concrete structures are described and their operating experience noted. Primary considerations related to management of their aging are noted: degradation mechanisms, damage modeling, and material performance; assessment and repair; and applications of structural reliability theory. Several topics are noted where additional research would be of benefit.

INTRODUCTION

In the United States, the Atomic Energy Act and regulations of the United States Nuclear Regulatory Commission (USNRC) limit commercial power reactor licenses to an initial 40-year period, but also permit such licenses to be renewed. Other countries may not have a limit set on the plant operating license period but the utility must obtain a permanent renewal of its operating license subject to numerous and continuous justifications (e.g., periodic safety reevaluations). This 40-year term for reactor licenses was based on economic and antitrust considerations—not on limitations of nuclear technology. Due to this selected period, however, some structures and components may have been engineered on the basis of an expected 40-year service life.

Currently the United States has 104 nuclear power plant units licensed for commercial operation that provide about 20% of the electricity supply. The first of these units is nearing the end of its initial operating license period. In order to help assure an adequate energy supply, the USNRC has established a timely license renewal process and clear requirements that are needed to ensure safe plant operation for an extended plant life. These requirements are codified in Parts 51 and 54 of Title 10, “Energy,” of the Code of Federal Regulations (CFR) and provide for a renewal of an operating license for an additional 20 years. In order to ensure the safe operation of nuclear power plants, it is essential that the effects of age-related degradation of plant structures, as well as systems and components, be assessed and managed during both the current operating license period as well as subsequent license renewal periods.

HOW WOULD YOU...

…describe the overall significance of this paper?
This paper provides a description of nuclear power plant concrete structures, their operating experience, potential degradation mechanisms, approaches for assuring their continued performance, and areas where additional research would be beneficial.

…describe this work to a materials science and engineering professional with no experience in your technical specialty?
This paper describes large concrete structures that provide safety functions in nuclear power plants, their performance, potential factors that could infl uence their continued reliable performance, methods for estimating future performance, and desired research to provide added assurance of continued reliable and safe service.

…describe this work to a layperson?
Concrete structures in nuclear power plants are described, a review of their operational experience provided, potential environmental effects that could potentially impact their performance provided, and methods described that can identify and mitigate any environmental effects that could impact continued reliable and safe performance of the concrete structures.

CONCRETE STRUCTURES AND OPERATING EXPERIENCE

Concrete Structures
All commercial nuclear power plants in the United States contain concrete structures whose performance and function are necessary for protection of the safety of plant operating personnel and the general public, as well as the environment. The basic laws that regulate the design (and construction) of nuclear power plants are contained in Title 10 of the CFR, which is clarified by documents such as Regulatory Guides, U.S. Nuclear Regulatory Commission NUREG reports, and Standard Review Plans.

A myriad of concrete-based structures are contained as part of a lightwater reactor (LWR) plant to provide foundation, support, shielding, and containment functions. Typical safety-related concrete structures contained in LWR plants may be grouped into four general categories: primary containments, containment internal structures, secondary containments/reactor buildings, and other structures. Only information related to primary containment structures for pressurized-water (PWR) and boiling-water reactor (BWR) plants is summarized here. (Information on other concrete structures is provided elsewhere.1)

Of the PWR plants that have been licensed for commercial operation in the United States, approximately 80% use either reinforced or prestressed concrete primary containments. The concrete containments are of three different functional designs: subatmospheric (reinforced concrete), ice condenser (reinforced concrete), and large/dry (reinforced and prestressed concrete). The primary differences between these containment designs relate to volume requirements, provisions for accident loadings/pressures, and containment internal structures layout. The PWR containment structure generally consists of a concrete basemat foundation, vertical cylindrical walls, and dome. Leak tightness of a containment is provided by a steel liner attached to the containment inside surfaces. Exposed surfaces of the carbon steel liner are typically painted to protect against corrosion and to facilitate decontamination should it be required. Depending on the functional design (e.g., large dry or ice condenser), the concrete containments can be on the order of 40 m to 50 m in diameter and 60 m to 70 m high, with wall and dome thicknesses from 0.9 m to 1.4 m, and base slab thicknesses from 2.7 m to 4.1 m. Figure 1 presents the Trojan nuclear plant cooling tower and post-tensioned concrete containment prior to decommissioning and demolition. Pressurized-water reactor plants that utilize a metallic primary containment (large dry and ice condenser designs) are usually contained in reinforced concrete “enclosure” or “shield” buildings that, in addition to withstanding environmental effects, provide radiation shielding and particulate collection, and ensure that the free-standing metallic primary containment is protected from the natural environment.

Of the BWR plants in the United States, approximately 30% utilize either reinforced or prestressed concrete primary containments. Boiling-water reactor containments, because of provisions for pressure suppression, typically have “normally dry” sections (dry well) and “flooded” sections (wet well) that are interconnected via piping or vents. Boiling-water reactor plants that utilize steel primary containments have reinforced concrete structures that serve as secondary containments or reactor buildings. These structures generally are safety-related because they provide additional radiation shielding; provide resistance to environmental and operational loadings; and house safetyrelated mechanical equipment, spent fuel, and the primary metal containment. Although these structures may be massive in cross section in order to meet shielding or load-bearing requirements, they generally have smaller elemental thicknesses than primary containments because of reduced exposure under postulated accident loadings.

Operating Experience
In general, the performance of nuclear power plant safety-related concrete structures has been very good. However, there have been a few isolated incidences of degradation that primarily occurred early in life and have been corrected.2 Causes generally were related either to improper material selection or construction/design deficiencies. Examples of some of these problems include low concrete compressive strengths, voids under the post-tensioning tendon bearing plates, cracking of post-tensioning anchor heads, containment dome delaminations, misplaced steel reinforcement, post-tensioning system button-head deficiencies, and water-contaminated corrosion inhibitors.

Several incidences of degradation related to environmental effects have occurred. Examples include corrosion of steel reinforcement in water intake structures, corrosion of post-tensioning tendon wires, leaching of tendon gallery concrete, low prestressing forces, and leakage of corrosion inhibitors from tendon sheaths. Other aging-related problems include cracking and spalling of containment dome concrete due to freezing and thawing, and corrosion of containment liners. As the plants age incidences of degradation are expected to increase, primarily due to environmental effects. Additional information on degradation of U.S. nuclear power plant concrete structures is available,3,4 as well as problem areas experienced with nuclear power plant concrete structures in other countries.5

AGING MANAGEMENT

Guidelines for production of durable concrete are available in national consensus codes and standards (e.g., ACI 318)6 that have been developed over the years through knowledge acquired in testing laboratories and supplemented by field experience. Serviceability of concrete has been incorporated into the codes through strength requirements and limitations on service load conditions in the structure (e.g., allowable crack widths, limitations on mid-span deflections of beams, and maximum service level stresses in prestressed members). Durability has been included in the design through specifications for maximum water-cement ratios, requirements for entrained air, minimum concrete cover over reinforcement, etc. Service-related degradation, however, can affect the performance of nuclear power plant concrete structures. As these plants mature, environmental factors are going to become increasingly important. Demonstration of continued safe and reliable operation of the plants will involve implementation of a program that effectively manages aging to ensure the availability of design safety functions throughout the plant service life.

General guidance on developing an aging management program for concrete containment buildings has been developed.5 Additional information is available through organizations such as The Electric Power Research Institute, The International Union of Laboratories and Experts in Construction Materials, Systems and Structures, and the Nuclear Energy Agency Committee on the Safety of Nuclear Installations under its Integrity of Components and Structures Working Group.

DEGRADATION MECHANISMS, DAMAGE MODELING, AND MATERIAL PERFORMANCE

Degradation Mechanisms
Exposure to the environment (e.g., temperature, moisture, cyclic loadings, etc.) can produce degradation of reinforced concrete structures. The rate of deterioration is dependent on the component’s structural design, materials selection, and quality of construction, curing, and aggressiveness of environmental exposure. Termination of a component’s service life occurs when it no longer can meet its functional and performance requirements.

Primary mechanisms (factors) that, under unfavorable conditions can produce premature deterioration of reinforced concrete structures include those that impact either the concrete or steel reinforcing materials (i.e., mild steel reinforcement or post-tensioning systems). Degradation of the concrete can be caused by adverse performance of either its cement-paste matrix or aggregate materials under chemical or physical attack. In nearly all chemical and physical processes influencing the durability of concrete structures, dominant factors involved include the transport mechanisms within the pores and cracks, and the presence of water. Degradation of mild steel reinforcing materials can occur as a result of corrosion, irradiation, elevated temperature, or fatigue effects, with corrosion being the most likely form of attack. Posttensioning systems are susceptible to the same degradation mechanisms as mild steel reinforcement plus loss of prestressing force, primarily due to tendon relaxation, and concrete creep and shrinkage. Additional information on durability of nuclear power plant reinforced concrete structures is available.7

Damage Modeling
Extensive research and studies have been carried out to determine the durability of concrete under various service conditions, and thus information on the progressive changes in the physical and chemical nature of concrete under such conditions is available.8 Damage models for reinforced concrete in large measure have addressed corrosion of steel reinforcement and new construction. Improved damage models and guidelines for their use are required to predict failure probability of a degraded concrete structure, either at present or at some future point in time. Synergistic effects involving more than one degradation factor and the interaction of loading and environment also need to be investigated in more detail.

Material Performance
Nuclear safety-related concrete structures are composed of several constituents that, in concert, perform multiple functions (e.g., load-carrying capacity, radiation shielding, and leak tightness). Primarily, these constituents include the following material systems: concrete, conventional steel reinforcement, prestressing steel, steel liner plate, and embedment steel. Data on the long-term performance of the reinforced concrete materials is of importance for demonstrating the durability of the nuclear power plant concrete structures and in predicting their performance under the influence of pertinent aging factors and environmental stressors. This information also has application to establishing limits on hostile environmental exposure for these structures and to the development of inspection and maintenance programs that will prolong component service life and improve the probability of the component surviving an extreme event such as a loss-of-coolant accident.

Reviews of research conducted on concrete materials and structures indicate that only limited data are available on the long-term (40 to 80 years) properties of reinforced concrete materials.2 Where concrete properties have been reported for conditions that have been well documented, the results were generally for concretes having ages < 5 years, or for specimens that had been subjected to extreme, nonrepresentative environmental conditions such as seawater exposure or accelerated aging. Relatively few investigations were reported providing results on examinations of structures that had been in service for the time period of interest, 20 to 100 years, and they did not generally provide the “high quality” baseline information (e.g., baseline material characteristics and changes in material properties with time) that is desired for meaningful assessments to indicate how the structures have changed under the influence of aging factors and environmental stressors.

Limited data on the long-term performance of reinforced concrete materials reported in the literature, results from concrete cores removed from nuclear power plants, and specimens cast in conjunction with nuclear power plant facilities have been reported.9 As noted in Figure 2, these results generally show an increase in compressive strength (relative to 28-d reference strength) at a decreasing rate with age, but the data obtained from the literature were for concrete ages ≤ 50 years and the nuclear plant data for ages ≤ 27 years. With the availability of decommissioned nuclear power plants and plant modifications requiring removal of materials, opportunities exist to obtain samples for use in providing an improved understanding of the effects of extended exposure under the conditions found in nuclear power plants. Results could then be input into an operational database to help monitor and benchmark specific plant performance. Examples of areas of interest would be the effects of long-term thermal loadings at moderate temperature levels and effects of irradiation on load-bearing concrete structures operating > 40 years. Additional applications of a concrete material sampling activity would be for assessment of construction quality, development of improved damage models, assessment and validation of non-destructive testing methods, and evaluation of the performance of repair activities.

With respect to ungrouted post-tensioning systems, current examination programs are adequate for determining the condition of the post-tensioning system materials and evaluating the effects of conventional degradation. Isolated incidences of wire failure due to corrosion have occurred. Leakage of tendon sheathing filler has occurred at a few plants, but except for the potential loss of corrosion protection, the problem appears to be primarily aesthetic.10 Tendon forces at most plants are acceptable by a significant margin, but larger than anticipated loss of force has occurred at a few older plants. Although bonded prestressing tendons are less vulnerable to local damage than ungrouted tendons, the grouted tendons can not be visually inspected, mechanically tested, or re-tensioned in the event of larger than anticipated loss of prestress. Improved guidance on inservice inspection of grouted tendons is desired. Other potential research topics related to post-tensioning systems include development of an improved relationship between the end-anchorage force measured by the lift-off test and change in mean force along the tendon length for unbonded tendons.

ASSESSMENT AND REPAIR

Operating experience has demonstrated that periodic inspection, maintenance, and repair are essential elements of an overall program to maintain an acceptable level of reliability for structures over their service life. Assessment and management of aging in nuclear power plant concrete structures requires a more systematic approach than simple reliance on existing code margins of safety.11 What is required is the integration of structural component function, potential degradation mechanisms, and appropriate control programs into a quantitative evaluation procedure. A methodology to demonstrate the reliable and safe performance of these structures should include identification of structures important to public health and safety; identification of environmental stressors, aging mechanisms and their significance, and likely sites for occurrence; a monitoring or in-service-inspection-based methodology that includes criteria for resolution of existing conditions; and a remedial measures program.

Component Selection
The most effective structural condition assessment programs are those that focus on the components most important to safety and at risk due to environmental stressor effects. Aging assessment methodologies have been developed to provide a logical basis for identifying the critical concrete structural elements and degradation factors that can potentially impact the performance of these structures.12,13 An evaluation of the impact on plant risk due to structural aging can also be used in the selection of structural components for evaluation.14 A combination of finiteelement analysis and nondestructive testing methods for evaluation of aging and degradation of concrete containments has also been proposed as a basis for component selection.15

In-service Inspections
In-service inspection programs are conducted to help ensure that the nuclear power plant structures have sufficient structural margins to continue to perform in a reliable and safe manner. A secondary goal is to identify environmental stressors or aging factor effects before they reach sufficient intensity to potentially degrade structural components. Routine observation, general visual inspections, leakage-rate tests, and destructive and nondestructive examinations are techniques available to identify areas of nuclear power plants that have experienced degradation. Determining the existing performance characteristics and extent and causes of any observed distress is accomplished through a structural condition assessment that routinely initiates with a general visual inspection to identify suspect areas followed by application of destructive or nondestructive examinations to quantify the extent and significance of any observed degradation.

More detailed information on guidelines on conduct of surveys of existing civil engineering buildings is available.16 Figure 3 presents an example of a survey to locate and characterize steel reinforcement embedded in a general civil engineering concrete structure. Some general guidance on assessment of nuclear power plant degradation is also available.17 However, nuclear power plant reinforced concrete structures present special challenges for development of acceptance criteria because of their massive size, limited accessibility in certain areas, stochastic nature of past and future loads, randomness in strength, uncertainty in material changes due to aging and possibly degradation, and qualitative nature of many nondestructive evaluation techniques. Improved guidelines and criteria to aid in the interpretation of condition assessment results, including development of probability-based degradation acceptance limits, are desired.

Nondestructive Examinations
Application of nondestructive examination methods to nuclear power plant reinforced concrete structures presents challenges: wall thicknesses can be in excess of one meter; structures often have increased steel reinforcement density with complex detailing; there can be a number of penetrations or cast-in-place items; accessibility may be limited due to the presence of liners or other components, harsh environments, or structures may be located below ground; experience with nondestructive examinations of nuclear power plant concrete structures is somewhat limited; and methods utilized for the nuclear power plant structures are often based on equipment developed for other materials or technologies. Available methods are relatively good at identifying cracking, voids, and delaminations, and indicating the relative quality of concrete. Methods for determining concrete properties, however, are somewhat more qualitative than quantitative because they tend to be indirect in that they often require the development of correlation curves for relating a measured parameter (e.g., ultrasonic velocity or rebound number) to a property (e.g., concrete compressive strength). Identification and description of methods for determining the strength of concrete and evaluation of concrete structures is provided elsewhere.18,19 A practical guide related to nondestructive examination of concrete has been developed that not only identifies and describes the capabilities, limitations, and applications of the various methods that are available, but presents results from a number of examples.20

Noninvasive techniques for characterization, inspection, and monitoring of thick-walled, heavily reinforcedconcrete structures in nuclear power plants to provide additional assurances of their continued structural integrity are desirable (e.g., as-built or current structural features determination, flaw detection and characterization, identification of honeycomb areas and embedded items, and location of voids adjacent to the liner). Methods that can be used to inspect the basemat without the requirement for removal of material and techniques that can detect and assess corrosion are of particular interest. Acoustic (e.g., ultrasonic pulse velocity, spectral analysis of surface waves, impact echo, and acoustic tomography), radar, and radiography appear to have potential for this application, however, additional development is required.

The most commonly used type of foundation for both concrete and steel nuclear power plant containments is a mat foundation, which is a flat, thick slab supporting the containment, its interior structures, and any shield building surrounding the containment. As such, the concrete foundation elements of nuclear power plants are typically either partially or totally inaccessible for inspection. Under conditions such as this the foundation structures are only accessible for inspection after removal of adjacent soil, coatings, waterproof materials, or portions of neighboring components or structures. As a result, indirect methods related to environmental qualification are often utilized to indicate the potential for degradation of the nuclear power plant concrete foundations.21 This is generally done through an evaluation of the surrounding medium (e.g., air, soil, humidity, groundwater, or cooling water).

Remedial Methods
Deterioration of reinforced concrete generally will result in cracking, spalling, or delamination of the cover concrete. Whenever damage is detected, corrective actions are taken to identify and eliminate the source of the problem thereby halting the degradation process. A remedial measures strategy is formulated based on the consequence of damage (e.g., affect of degradation on structural safety), time requirements for implementation (e.g., shutdown requirements, immediate or future safety concern), economic aspects (e.g., partial or complete repair), and residual service life requirements (e.g., influences action taken). Basic guidance on the repair of degraded structures is available.22 Improved guidance, however, is desired relative to assessment of defects (e.g., cracks) as well as information on the performance and effectiveness of subsequent repairs (e.g., durability of repair materials).

APPLICATIONS OF STRUCTURAL RELIABILITY THEORY

If properly designed and constructed, the concrete structures in nuclear power plants generally have substantial safety margins; however, additional investigations to establish available margins of degraded structures are desired. In addition, improved understanding of how age-related degradation may affect dynamic properties (e.g., stiffness, frequency, and dampening), structural response, structural resistance/capacity, failure mode, and location of failure initiation is desired to provide additional assurance that the current licensing basis is maintained under all loading conditions.

Decisions as to whether to invest in maintenance and rehabilitation of structures, systems, and components as a condition for continued service and risk mitigation, and the appropriate level of investment, should consider the nature and level of uncertainties in their current condition and in future demands.23 Recent advances in structural reliability analysis, uncertainty quantification, and probabilistic risk assessment make it possible to perform such evaluations and to devise uniform risk-based criteria by which existing facilities can be evaluated to achieve a desired performance level when subjected to uncertain demands.24 Reliability-based approaches have been applied to the nuclear power plant concrete structures,25 and in evaluation of the prestress level in concrete containments with unbonded tendons.26

Degradation effects can be quantified with fragility curves developed for both undegraded and degraded components. Fragility analysis is a technique for assessing, in probabilistic terms in the presence of uncertainties, the capability of an engineered system to withstand a specified event. Fragility modeling requires a focus on the behavior of the system as a whole and, specifically, on things that can go wrong with the system. The fragility modeling process leads to a median-centered (or likely) estimate of system performance, coupled with an estimate of the variability or uncertainty in performance. The fragility concept has found widespread usage in the nuclear industry, where it has been used in seismic probabilistic safety and/or margin assessments of safety-related plant systems. The fragility modeling procedures applied to degraded concrete members can be used to assess the effects of degradation on plant risk and can lead to the development of probability-based degradation acceptance limits. This approach has been applied to a limited extent to degraded flexural members and shear walls.27 Figure 4 presents an example of use of structural reliability theory to investigate the affect of different assumed degradation states (i.e., combinations of loss of steel reinforcement cross section and concrete cover) on the probability of failure of a propped cantilever beam subjected to uniform loading. Additional work is desired in this area for the purpose of refining and applying the time-dependent reliability methodology for optimizing in-service inspection/maintenance strategies and for developing and evaluating improved quantitative models for predicting future performance (or failure probability) of a degraded concrete structure, either at present or some future point in time.

CONCLUSIONS

In general, the performance of nuclear power plant concrete structures has been very good with the majority of identified problems initiating during construction and corrected at that time; however, aging of concrete structures occurs with the passage of time that can potentially result in degradation if its effects are not controlled. Periodic inspection, maintenance, and repair are key elements in managing the aging of concrete structures. Several areas have been identified where additional research would be of benefit to aging management of nuclear power plant concrete structures: compilation of material property data for long-term performance and trending, evaluation of environmental effects, and assessment and validation of nondestructive evaluation methods; evaluation of long-term effects of elevated temperature and radiation; improved damage models and acceptance criteria for use in assessments of the current as well as estimating the future condition of the structures; non-intrusive methods for inspection of thick-walled, heavily reinforced concrete structures and basemats; data on application and performance (e.g., durability) of repair materials and techniques; utilization of structural reliability theory incorporating uncertainties to address time-dependent changes to structures to assure minimum accepted performance requirements are exceeded and to estimate ongoing component degradation to estimate end-of-life; and application of probabilistic modeling of component performance to provide risk-based criteria to evaluate how aging affects structural capacity.

REFERENCES

1. D.J. Naus, C.B. Oland, and B.R. Ellingwood, Report on Aging of Nuclear Power Plant Reinforced Concrete Structures, NUREG/CR-6424 (Washington, D.C.: U.S. Nuclear Regulatory Commission, March 1996).
2. D.J. Naus, Concrete Component Aging and Its Significance Relative to Life Extension of Nuclear Power Plants, NUREG/CR-4652 (Washington, D.C.: U.S. Nuclear Regulatory Commission, September 1986).
3. H. Ashar and G. Bagchi, Assessment of Inservice Conditions of Safety-Related Nuclear Plant Structures, NUREG-1522 (Washington, D.C.: U.S. Nuclear Regulatory Commission, July 1995).
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5. Assessment and Management of Major Nuclear Power Plant Components Important to Safety: Concrete Containment Buildings, IAEA-TECDOC-1025 (Vienna, Austria: International Atomic Energy Agency, June 1998).
6. Building Code Requirements for Structural Concrete and Commentary, ACI Standard 318-05 (Farmington Hills, MI: American Concrete Institute, November 2005).
7. D.J. Naus, Primer on Durability of Nuclear Power Plant Reinforced Concrete Structures—A Review of Pertinent Factors, NUREG/CR-6927 (Washington, D.C.: U.S. Nuclear Regulatory Commission, February 2007).
8. ACI Committee 365, “Service-Life Prediction,” ACI 365.1R-00 (Farmington Hills, MI: American Concrete Institute, 2000).
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10. D.J. Naus and C.B. Oland, “An Investigation of Tendon Sheathing Filler Migration in Concrete,” NUREG/CR-6598 (Washington, D.C.: U.S. Nuclear Regulatory Commission, March 1998).
11. J.A. Christensen, “NPAR Approach to Controlling Aging in Nuclear Power Plants,” Proceedings of the 17th Water Reactor Safety Information Meeting, Vol. 3, NUREG/CP-0105 (Washington, D.C.: U.S. Nuclear Regulatory Commission, 1990), pp. 509–529.
12. C.J. Hookham, Structural Aging Assessment Methodology for Concrete Structures in Nuclear Power Plants, ORNL/NRC/LTR-90/17 (Oak Ridge, TN: Martin Marietta Energy Systems, Inc., Oak Ridge National Laboratory, March 1991).
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23. B.R. Ellingwood, “Acceptable Risk Bases for Design of Structures,” Progress in Structural Engineering and Materials, 3 (2) (2001), pp. 170–179.
24. Y.K. Wen and B.R. Ellingwood, “The Role of Fragility Assessment in Consequence-Based Engineering,” Earthquake Spectra, EERI 21(3) (2005), pp. 861–877.
25. B.R. Ellingwood and D.J. Naus, “Chapter 6, Aging Nuclear Structures,” Modeling Complex Engineering Structures, ed. R.E. Melchers and R. Hough (Reston, VA: American Society of Civil Engineers, 2007), pp. 137–170.
26. P. Anderson, M. Hansson, and S. Thelandersson, “Reliability-Based Evaluation of the Prestress Level in Concrete Containments with Unbonded Tendons,” Structural Safety, 30 (1) (2008), pp. 78–89.
27. J.I. Braverman et al., “Probability-Based Evaluation of Degraded Reinforced Concrete Components in Nuclear Power Plants,” NUREG/CR-6715 (Washington, D.C.: U.S. Nuclear Regulatory Commission, March 2001).

D.J. Naus, distinguished research staff member, is with the Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6069; nausdj@ornl.gov.