Aging, Shaking, and Cracking of Infrastructures

Mechanics is where it all starts. Rooted in mathematics, it provides a solid underpinning for subsequent engineering solutions. Rather than providing a classical introductory “Mechanics of Materials” approach, we have opted for the more concise and powerful continuum mechanics based one. Far from exhaustive, this chapter limits itself to the fundamental concepts.As the title indicates, we focus on solid mechanics characterized by vectorial fields. A subsequent chapter will address scalar field problems in mechanics (such as the heat equation).

Plasticity is probably the most commonly studied failure mechanism. Its usage in metals is wide-spread; however, it has its limitations in capturing concrete failure (especially in tension). Failure modes, causes of plastic failures, and implications on computational plasticity will be addressed.

Ultimately and at different scales, fracture is the leading cause of material failures. As continuum mechanics by its very essence can not capture fracture, a different branch of mechanics addresses this complex failure mode.Hence, this chapter will be devoted to the fundamentals of theoretical fracture mechanics. Coverage will be substantially more expansive than the previous chapter on plasticity as it is, to some extent, more complex to tackle fracture of both brittle and quasi-brittle (such as concrete) materials. Both linear and nonlinear fracture mechanics will be addressed.

Creep is a quintessential form of concrete aging. It has been the subject of countless studies, and indeed in many cases it is a phenomenon that must be properly accounted for. Though it should never be discounted, its importance may be minimized by other aging mechanisms (such as ASR).This chapter will provide a basic coverage that should assist engineers in their investigation.

Seismology is the scientific study of earthquakes and the propagation of elastic waves through the earth. A seismologist is a scientist who does research in seismology. A field that uses geology to infer information regarding past earthquakes is paleoseismology. On the other hand, the seismicity refers to the geographic and historical distribution of earthquakes.Earthquake design of a structure always depends on degree of regional seismic activity. Many seismological factors directly influence the work of a structural engineer such as: (1) distribution of earthquake sources affecting the construction site, (2) fault mechanisms of various sources, (3) seismic activity of various sources in terms of recurrence of magnitudes, (4) ground motion intensity level, and (5) attenuation of the ground motion signal with distance. This chapter is an introduction to the fundamental characteristics of the engineering seismology.

Dynamics is a sine qua non for seismic investigation of structures. Rather than reviewing its fundamentals, this chapter will focus on the computational aspects as implemented in finite element analysis codes.

This chapter aims to provide the fundamentals of probability and statistics. This is an essential topic, and most of the advanced topics and majority of the applied examples are rooted in probabilistic-based simulations. First the differences between discrete and continuous random variables are explained. Next, the properties of several widely-used distributional models are discussed. Finally, the concept of multivariate distributions and joint probability functions is presented.

In many respects, concrete is a far more complex material to model in the inelastic range than steel. Only relatively recently has the research community embraced fracture mechanics as a model to capture its cracking. Given the importance of the topic, a separate chapter is hence devoted to this form of fracture. It is composed of two parts: macro and micro cracks.In the former, emphasiz will be on Hillerborg’s model that is by now universally accepted for the fracture of cementitious material. Then the important phenomenon of strain localization and accompanying size effect laws will be addressed.In the second part of the chapter, the impact of micro-cracks in concrete will be addressed.

There are two major forms of environmentally induced concrete deterioration: the first is caused by the ingress of chloride (in marine environments or whenever salt based de-icing is used) and the other by carbonation from the atmosphere. Although per se these ingress will not deteriorate the concrete, they will eventually cause internal rebar corrosion. Given sufficient time, the corrosion will lead to cracking, splitting of the concrete, exposure of the rebars, and formation of what is commonly referred as “pot-holes.”Each of the above-mentioned phenomena will be separately covered in this chapter.

Alkali aggregate reaction (AAR), also known as alkali silica reaction (ASR), is a major form of concrete deterioration for older structures. AAR will eventually weaken the concrete, induce cracking, and can jeopardize the integrity of dams and nuclear structures to the point of having them decommissioned.This chapter will solely address a theoretical model for AAR developed by the first author and one that proved to be popular enough to have been implemented in numerous finite element codes.

A key factor in finite element analysis is often neglected: modeling. As this chapter implies, this is both an art and a science whose exercise can impact results.It will first cast the analysis within the general framework of an investigation and identify the associated tasks. More details are addressed subsequently in terms of key considerations to be accounted for.

Two important aspects of the finite element method are summarized in this chapter. Starting with the derivation of the principle of virtual work (displacement), a general expression for the element stiffness matrix is derived. In the second part, details of the formulation of the most commonly used element (isoparametric) are presented.Though understanding of this chapter is not critical for the practitioner, it does nevertheless hint to practical issues that they may be confronted with (such as element distortion, nodal equivalent loads, stress recovery, or convergence) as the practicing engineer.

Safety assessment of structures can not be purely code based and certainly not based on linear elastic analyses. Hence, this chapter will cover key aspects of non-linear finite element analysis.

Whereas Chaps. 3 and 8 addressed the theoretical underpinning of classical (linear and nonlinear) fracture mechanics and concrete fracture mechanics, this chapter will cover modeling of cracks. It is broken into four parts: (a) linear elastic fracture mechanics (use of singular elements to determine the stress intensity factors); (b) nonlinear fracture mechanics (J integral); (c) smeared crack model; and finally (d) cohesive crack model for concrete. The last two sections are based on models developed by J. Červenka.

This chapter addresses the interaction between the structure and its foundation. It begins with a seldom covered problem: rocking of the structure on the foundation and possible “lift-off” that would act as stress reliever. Different techniques to model this problem are outlined. Then, deconvolution, the technique to apply a proper seismic excitation at the base of a model foundation as opposed to the accelerations recorded at the surface, is presented. It will be followed by the derivation of the wave equation which is essential to understanding the most commonly used soil structure interaction (SSI) model: the one by Lysmer. Then, the roles of both SSI and adjoining free field are discussed in a model developed by the first author along with a battery of simple validation problems highlighting the benefits of simple or complex SSI are presented. Finally, the chapter concludes with techniques to properly mesh a structure where the SSI is addressed.

Fluid-structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. FSI is an interdisciplinary research field with several applications in structural engineering, e.g., interaction of reservoir water, dam, and the surrounding canyon, or dynamic interaction of wind with high-rise towers.The focus of FSI in this book will be on dam engineering application in static and dynamic conditions.

Whereas the boundary conditions for vector field problems are straightforward, this is not the case for thermal (diffusion) problems. Those are particularly important in the thermal analysis of concrete dams, and the proper investigation of chloride diffusion.Hence, they are addressed separately in this chapter.

Uncertainty quantification (UQ) is “the science of quantitative characterization and reduction of uncertainties in both computational and real world applications.” It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. This chapter discusses the fundamental concepts in UQ of structural systems, including different terminologies of risk-based assessment and failure probability.

In general, the methods in structural analysis and design can be classified into two main groups: (1) deterministic simulations and (2) probabilistic simulations. In the case that the finite element method (FEM), used for discretization of the medium, is combined with statistics and reliability methods, the so-called probabilistic finite element method (PFEM) is developed and can be applied to both linear and non-linear systems.Uncertainty can be propagated in both the finite element and applied load. Different sampling techniques based on crude MCS or more efficient techniques can be used. This chapter discusses three elements: (1) Mathematical review on sampling techniques, (2) Propagation of uncertainty in the response spectrum method (loading) and proposing the “random response spectrum method” (RRSM), and (3) Propagation of uncertainty directly in finite element and discussion on random finite element method (RFEM).

A metamodel, or surrogate model, is a model of a model. Metamodeling refers to a process of generating such metamodels which is based on analysis, construction and development of the frames, rules, constraints, models and theories applicable and useful for modeling a predefined class of problems. On the other hand, machine learning is an application of artificial intelligence that provides systems the ability to automatically learn and improve from experience without being explicitly programmed. This chapter provides a review on different design of experiment techniques, as well as various machine learning algorithms.

Over the past years there have been two concomitant developments: (1) performance based earthquake engineering (PBEE) which is a proposed new paradigm for the seismic safety investigation of a building and (2) potential failure mode analysis (PFMA) which is a generally accepted methodology to assess dam safety. Though similar, and written by different communities, much can be gained through an attempt to bring together those two paradigms. Figure 21.1 highlights the similarities between the two approaches in general. Each one will be discussed later in detail.

Ground motion is the movement of the earth’s surface from earthquakes or explosions. The earthquake ground motion is produced by waves that are generated by a sudden slip on a fault and travel through the earth and along its surface. Typical the ground motion records, such as acceleration time histories, contain a tremendous amount of information. For engineering purposes, the three main characteristics of ground motions are: (1) amplitude, (2) frequency content, (3) duration.

This section explains the fundamentals of seismic hazard analysis as part of earthquake engineering. According to Elnashai and Di Sarno (Fundamentals of earthquake engineering: from source to fragility. Wiley, London, 2015), Earthquake Engineering is a branch of engineering concerned with the estimation of earthquake consequences and the mitigation of these consequences. It is an interdisciplinary subject involving seismologists, structural and geotechnical engineers, architects, urban planners, information technologists, and social scientists.

Structural analyses are an important part of safety assessment. In this chapter, the concept of a “capacity function” is explained in the context of existing structural analysis techniques. Loading due to seismic, hydrologic, and aging hazard are studied from a probabilistic point of view. Single, multiple, and combined capacity functions are derived. Moreover, the summarized capacity functions and their confidence intervals are presented.

Fragility functions are resulted Fragility Function from a structural assessment of the system (in the case of analytical form). In simple language, the fragility can be defined as “the quality of being easily broken or damaged” Porter (A Beginner’s guide to fragility, vulnerability, and risk. Springer, Berlin, 2015). The seismic fragility functions are first introduced by Kennedy et al. (Nucl Eng Des 59:315–338, 1980) as a probabilistic relationship between frequency of component failure in a nuclear power plant and peak ground acceleration. Fragility functions are not specific to earthquake events and can be developed for any “stressor” (i.e., flood, hurricane, wind).

The performance of the infrastructures subjected to internal or external loading should be a property quantified to be used in the context of performance based engineering. Quantification of the potential damage due to earthquakes has the utmost importance. Seismic damage indices (DI) are widely used for this purpose. Having a comprehensive list of DIs, one may derive any type of fragility function. The objective of this chapter is to propose a series of mass and reinforced concrete structure-related damage indices and the corresponding damage states.

Identification, description, and evaluation of site-specific potential failure modes (PFMs) are the most important steps towards a risk analysis. Potential failure mode analysis (PFMA) is a standard and state-of-the-practice technique in dam engineering and forms the basis for risk evaluations and event tree development. Figure 27.1 illustrates the key steps of a PFMA. It should be noted that it is purely Potential Failure Mode Analysis qualitative. This chapter presents both the qualitative and quantitative failure metrics for a variety of concrete dams.

This chapter is, in fact, a summary of the Federal Energy Regulatory Commission (FERC) Risk-Informed Decision Making Risk Informed Decision Making Guidelines to identify, analyze, assess, and manage the risks in dams. The concept of risk and its differences with other similar topics (e.g. hazard, vulnerability, fragility) are already discussed in Sect. 18.3.3 .

Six examples of deterministic nonlinear analyses of dams are presented in this chapter. The first is a potential failure mode analysis that relies on nonlinear joint elements to capture potential sliding. The next two examples are nonlinear AAR analyses of an arch gravity dam and a hollow buttress dam. The next two report the seismic safety evaluation analysis of dams, and the last example addresses the impact of SSI modeling on a dam.

This chapter will present two classes of advanced analysis of dams. In the first one, thirteen case studies based on probabilistic concepts are presented. They are followed by four additional ones based on machine learning. Uncertainties considered are material properties, dam geometry and ground motion record-to-record variability.

This is the first of four chapters dedicated to the analysis of nuclear structures, or Containment Enclosure Building (CEB) more precisely. It constitutes an attempt to contextualize the complex, and seldom fully addressed, problematic of the safety of nuclear reactor enclosure buildings.This chapter will begin with some general remarks associated with seismic analysis of nuclear structures. Then, a broad review of the literature related (primarily but not exclusively) to the probabilistic risk assessment of nuclear structures is presented. Finally, the third section will revisit the summary report of (what the authors consider) a landmark report by Sandia. This report (Hessheimer and Dameron, NUREG/CR-6906 SAND2006-2274P: containment integrity research at Sandia National Laboratories; an overview, 2006) contains many recommendation for the nonlinear finite element analysis (many of which have not “‘aged”) that could be invaluable for the modern analyst.

Aging Management Programs (AMP) are unique to the nuclear industry and are designed to ensure the continuous safety of nuclear power plant as they age.Whereas this chapter will focus on the needs of AMP, implementation details will be omitted and simply referenced.Though AMP have been developed for the nuclear industry, they can certainly inspire similar programs for other ageing infrastructures such as dams.

This chapter focuses on reported (finite element) studies/investigation in four NPP that have received much attention lately: Gentilly 2, Ikata, and Crystal River. The first two are the only ones reported to have suffered from ASR, and the last has notoriously delaminated following detensioning for steam generator replacement.Each case is treated separately (and not all with the same level of details) in a section itself composed of two parts. First attempt is made to summarize findings on the basis of open literature, and then the authors provide a critical review. In writing the second part (review), the authors have exercised the same “zeal” that they would have used by a University researcher reviewing a manuscript being considered for publication. Undoubtedly, in many cases reviews by industry or some governmental agencies tend to be less strict. We do not necessarily agree with this presupposition if the consequence of an accident can be too severe.Again, the authors acknowledge that in some cases they may be limited in either their description of the facts or in their assessment. This is simply due to a lack of full documentation, and they do apologize for possible mis-representations.It should be noted that, given the sensitivity of the subject (specially in the last case study), all information are exclusively extracted from publicly available documents.

Whereas in the previous chapter we have detailed, and commented on, reported analyses of NPP by others, this one will provide an alternative numerical solution to these case studies using methods covered in this book.

Though the title of this book implies exclusive focus on concrete dams and nuclear structures, coverage (most of it) applies also to other types. By way of example, this chapter will use two distinct illustrative examples: (a) a massively reinforced concrete supporting structure and (b) a landmark bridge.Each one of those two examples will provide a different set of methods wrapped around the central issue of ASR.

In this chapter, we examine a particularly complex case-study, one that brings together multiple issues separately addressed in this book and is thus a fitting last chapter.More specifically. we examine the response by a single nuclear reactor’s private owner and the governmental regulator to aging and cracking issues due to ASR. The reactor, Seabrook Station Unit 1 in New Hampshire, owned and operated by NextEra NextEra@NextEra Energy Seabrook LLC, is the first and only United States reactor where ASR has been discovered. ASR affects significant safety structures at Seabrook, including the containment enclosure building (CEB) which surrounds the reactor containment and protects against radiation releases from the reactor core. Because the adequacy of NextEra’s program for detection and monitoring of ASR at Seabrook was subject to an investigation and licensing process by the regulator, the U.S. Nuclear Regulatory Commission (NRC), the response to ASR at Seabrook is relatively Nuclear power plant (NPP) Seabrook well-documented.As previously discussed, ASR is a highly complex problem that poses significant challenges in any attempt to assess it. In the case of a nuclear reactor, the stakes are particularly high, given the increase in seismic vulnerability that may be induced by ASR. In the case of Seabrook, both the private licensee and the government regulator pursued a code-based engineering heuristic approach. While that approach is standard and often acceptable for addressing nuclear reactor engineering problems, it is not sufficiently sophisticated to account for the complexities of ASR. From the authors’ (Though this chapter will make multiple references to the “authors”, it was entirely written by the first author of the book: V. Saouma.) point of view, the most critical concerns are the licensee’s inability to detect internal potential delamination, and the reduced shear capacity of the CEB in resisting seismic excitation. This is a serious deficiency, given the importance of the CEB in protecting public health and safety against the inadvertent release of radioactivity during an earthquake.